UBC Theses and Dissertations

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UBC Theses and Dissertations

Synoptic estimates of air sea fluxes Marsden, Richard Frank 1980

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SYNOPTIC ESTIMATES OF AIE SEA FLUXES by BJCHARD FRANK MARSDEN B.Sc, Royal Mi l i t a r y College Of Canada, 1972 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF EOCTOE OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES "* ' (Department of Physics) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1980 C)Richard Frank Marsden, 1980 In presenting th is thes is in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho la r ly purposes may be granted by the Head of my Department or by h is representat ives . It is understood that copying or pub l ica t ion of th is thes is for f inanc ia l gain sha l l not be allowed without my wri t ten permission. The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 6 i i AESTRACT S y n o p t i c and c l i m a t o l o g i c a l dynamic s t u d i e s g e n e r a l l y r e l y cn b u l k aerodynamic f l u x f o r m u l a e t o d e s c r i b e a i r - s e a heat and momentum exchange on s y n o p t i c and c l i m a t o l o g i c a l s c a l e s . B a r o m e t r i c p r e s s u r e maps (which i n v o l v e an i n t r i n s i c t e m p o r a l a v e r a g i n g o f the wind) and wind r o s e s p r o v i d e two s o u r c e s o f s p a t i a l and t e m p o r a l wind i n f o r m a t i o n f o r f l u x c a l c u l a t i o n s . S e v e r a l i n v e s t i g a t o r s have shown t h a t , due t o t h e n o n - l i n e a r dependence o f the b u l k aerodynamic f o r m u l a e on the winds, t i m e -averaged e s t i m a t e s o f the f l u x e s based on v e c t o r averaged winds s y s t e m a t i c a l l y u n d e r e s t i m a t e t h e a c t u a l t i m e - a v e r a g e d f l u x e s . U s i n g 10 t o 2 1 years o f t h r e e - h o u r l y sampled sea s u r f a c e m e t e o r o l o g i c a l o b s e r v a t i o n s from 9 w e a t h e r s t a t i o n s i n the No r t h A t l a n t i c Ocean and 2 w e a t h e r s t a t i o n s i n t h e North P a c i f i c Ocean, the t h r e e - h o u r l y s t r e s s e s , l a t e n t heat f l u x e s and s e n s i b l e h e a t f l u x e s were c a l c u l a t e d . The sampled data and t h e c a l c u l a t e d f l u x e s were then averaged o v e r p e r i o d s v a r y i n g up t o 28 days. The e s t i m a t e s of the averaged f l u x e s based on the v e c t o r averaged winds were then compared t o t h e d i r e c t l y averaged v a l u e s . A s i m p l e a n a l y s i s r e v e a l e d t h a t an upper bound f o r the d i f f e r e n c e i n the two s t r e s s c a l c u l a t i o n s was d i r e c t l y p r o p o r t i o n a l t o the sum o f the x and y component wind v a r i a n c e s l o s t t h r o u g h t h e a v e r a g i n g p r o c e s s ( i n agreement w i t h F o f o n o f f , 1960) and i n v e r s e l y p r o p o r t i o n a l t o the square o f the v e c t o r averaged wind speed. Ihe wind averaged and d i r e c t l y averaged f l u x e s t i m a t e s were grouped a c c o r d i n g t o the B e a u f o r t wind speed i i i c a t e g o r y and the p e r i o d over which t h e v a r i a t e s were averaged. .A m u l t i v a r i a t e r e g r e s s i o n was then performed t o o p t i m i z e a t r a n s f o r m a t i o n frcm the wind averaged t o t h e d i r e c t l y averaged c a s e . For a l l f l u x e s , t h e t r a n s f o r m a t i o n d r a m a t i c a l l y improved the wind averaged e s t i m a t e s o f the c l i m a t o l o g i c a l means and v a r i a n c e s of t h e d i r e c t l y averaged f l u x e s . The r e s i d u a l e r r o r between the two e s t i m a t e s was d e c r e a s e d up t o a f a c t o r of 5 over the u n c o r r e c t e d case and the c o r r e l a t i o n c o e f f i c i e n t s showed a moderate i n c r e a s e . The r e g r e s s i o n c o e f f i c i e n t s showed s i m i l a r v a l u e s f o r a l l temperate l a t i t u d e s t a t i o n s . Based on c o n s i s t e n c i e s observed i n the wind speed and a v e r a g i n g p e r i o d dependencies o f the m u l t i v a r i a t e c o e f f i c i e n t s , an e m p i r i c a l f o r m u l a was found which i n t e r p o l a t e d the wind speed and a v e r a g i n g dependence and d u p l i c a t e d t h e m u l t i v a r i a t e r e g r e s s i o n r e s u l t s . The d a t a from t h e t e n temperate l a t i t u d e s t a t i o n s were grouped and a s i n g l e f o r m u l a found which o n l y m o d e rately i n c r e a s e d the e r r o r s between the wind-averaged and d i r e c t l y averaged e s t i m a t e s . The g e o g r a p h i c a l l y averaged f o r m u l a was not a p p l i c a b l e a t S t a t i o n N, l o c a t e d a t the n o r t h e r n e x t r e m i t y o f the North P a c i f i c Trade Wind- r e g i o n . A n a l y s i s c f the 28 day wind-averaged f l u x s p e c t r a l e s t i m a t e s showed t h a t t hey u n d e r e s t i m a t e d the 28 day d i r e c t l y averaged f l u x s p e c t r a l e s t i m a t e s . A p p l i c a t i o n o f the s p e c i f i c s h i p e m p i r i c a l f o r m u l a g r e a t l y improved agreement between the two s p e c t r a l d e n s i t i e s and reduced t h e r e s i d u a l s e r i e s power d e n s i t y a t a l l f r e q u e n c i e s . High l a t e n t heat f l u x e r r o r s a t S t a t i o n N, c o u l d be reduced by a p p l i c a t i o n of a s e a s o n a l i v c o r r e c t i o n . The d a t a were a l s o grouped i n t o monthly wind r o s e c o n f i g u r a t i o n s and the wind r o s e monthly f l u x e s t i m a t e s were compared t o the d i r e c t l y c a l c u l a t e d l o n g - t e r m monthly mean f l u x e s . In a l l c a s e s , the wind r o s e f l u x e s compared f a v o u r a b l y w i t h the d i r e c t l y c a l c u l a t e d f l u x e s . V TABLE OF CONTENTS ABSTRACT , .. , i i TABLE OF CONTENTS v LIST OF TABLES v i i LIST OF FIGURES v i i i LIST OF SYMEOLS x i i ACKNOWLEDGEMENTS xiv CHAPTER I Introduction ................................... 1 CHAPTER II Data Preparation 10 2.1 Data Origin ...................................... 10 2.2 Data V e r i f i c a t i o n .... 10 2.3 Density Calculations ............................. 16 2.4 Assumptions 18 2.5 Analysis And Definitions ......................... 23 CHAPTER III Momentum Fluxes 29 3.1 Vector Averaged 3H And VA Stress 29 3.2 Previous Studies 38 3.3 Individual Ratios ................................ 43 3.4 Multiple Regression Analysis 54 3.5 Variance Underestimation 58 3.6 Wind Dependent Correction Factors ................. 61 3.7 Accuracy Of Transformations ...................... 64 CHAPTER IV Heat Fluxes * , 69 4.1 Three-hourly Heat Fluxes 69 4.2 Uncorrected Test Results 73 4.3 Heat Regression _ 78 4.4 Wind Dependent Corrections Factors ............... 81 v i 4.5 Beaufort Grouped Test Results 83 CHAPTER V Empirical Formula And Temporal Variations 88 5.1 Intrcducticn 88 5.2 Empirical Formula 89 5.3 Ship Parameter Estimates 97 5.4 Geographical Averaged Results ....................107 5.5 I n t r i n s i c Temporal Variations ......113 CHAPTER VI Wind Rose Measurements .129 6.1 Introduction 129 6.2 Analysis ......................................... 130 6. 3 Results 136 Stress Magnitude Errors ......................... 137 Stress Direction Errors .140 Heat Fluxes 142 CHAPTER VII Summary And Conclusions 146 BIBLIOGRAPHY 152 APPENDIX A 155 APPENDIX B 162 APPENDIX C 169 APPENDIX D 187 APPENDIX E 19 4 APPENDIX F • , 198 APPENDIX G . 216 APPENDIX H 219 APPENDIX I 222 APPENDIX J 231 LIST OF TABLES TABLE I TABLE I I TABLE I I I TABLE IV TABLE V TABLE VI TABLE V I I TABLE V I I I TABLE I X TABLE X TABLE XI TABLE X I I TABLE X I I I TABLE XIV D e t a i l s of the s t a t i o n l o c a t i o n s and number of y e a r s o f c o l l e c t e d d a t a . ..................... 12 Out-of-range l i n - i t s f o r the i n i t i a l s t a g e o f data p r o c e s s i n g . ................................ . 13 T o t a l number of m i s s i n g , o u t - o f - r a n g e , and erroneous (spiked) d a t a p o i n t s per time s e r i e s and w e a t h e r s t a t i o n . 16 Years of e l i m i n a t e d data f o r each w e a t h e r s t a t i o n 17 The x and y component 3H s t r e s s means and s t a n d a r d d e v i a t i o n s f o r a l l s h i p s and y e a r s examined. ...................................... 33 Symbols used i n t h e f i g u r e s t h r o u g h o u t the t e x t 36 The s t r e s s v a r i a n c e s f o r both drag c o e f f i c i e n t s as a f u n c t i o n of a v e r a g i n g p e r i o d . 37 The S (L) r e a d i n g s f o r a l l years of data a t W e a t h e r s t a t i o n A u s i n g t h e c o n s t a n t drag c o e f f i c i e n t . 43 B e a u f o r t wind speed i n t e r v a l s 46 The mean and s t a n d a r d d e v i a t i o n s of t h e x and y component wind v e l o c i t i e s , t h e a i r - s e a t e m p e r a t u r e d i f f e r e n c e s , the a i r - s e a h u m i d i t y d i f f e r e n c e s , and t h e l a t e n t and s e n s i b l e heat f l u x e s . 7 2 The a b s o l u t e l a t e n t and s e n s i b l e heat f l u x v a r i a n c e s as a f u n c t i o n of a v e r a g i n g p e r i o d . .,. 74 The g e o g r a p h i c a l average s h i p s ' r e g r e s s i o n c o e f f i c i e n t s . i ^/for t h e form 7£ =1+ ^ ( U 2 + V 2 ) ' L X .. 109 The summer and w i n t e r f o r m u l a c o e f f i c i e n t s r e g u i r e d a t S t a t i o n N f o r t h e heat f l u x e s a t L=28. 0 days. 122 Ceding f c r the wind r o s e l e v e l s c a l c u l a t e d i n Chapter VI 136 LIST OF FIGURES v i i i F i g u r e 1. The n e t t r a n s p o r t i n t h e Greenland and Norwegian Seas f o r F e b r u a r y , 1965. .. 6 F i g u r e 2. L o c a t i o n s of the 11 w e a t h e r s t a t i o n s i n v o l v e d i n t h e s t u d y . 11 F i g u r e 3.. Ihe dew p o i n t temperature a t t h r e e l e v e l s o f p r o c e s s i n g . .................................... 14 F i g u r e 4. X and Y components o f t h e 3H s t r e s s a t W e a t h e r s t a t i o n C as a f u n c t i o n o f y e a r and month. ... ., 31 F i g u r e 5. . The 3H s t r e s s as a f u n c t i o n of month a t S t a t i o n C i n d i c a t i n g s t a n d a r d d e v i a t i o n s o f the monthly means.......................... 32 F i g u r e 6. 3H v e r s u s VA s t r e s s a t S t a t i o n A, L=28.0 days. 34 F i g u r e 7. Example of the co m p o s i t e t e s t f u n c t i o n s f o r a l l s h i p s , x component, c o n s t a n t drag c o e f f i c i e n t w i t h no c o r r e c t i o n a p p l i e d . ........ 35 F i g u r e 8. Ihe r a t i o of the wind s t r e s s magnitude computed from wind d a t a t h a t a r e v e c t o r averaged over a p e r i o d , T, t o t h e d i r e c t l y c a l c u l a t e d wind s t r e s s . ..40 F i g u r e 9. S (L) and A (L) as f u n c t i o n s of a v e r a g i n g p e r i o d f o r Weatherships A and C. ............... 42 F i g u r e 10. Histogram o f B j ( . 25) a t W e a t h e r s t a t i o n C u s i n g the c o n s t a n t drag c o e f f i c i e n t . ........... 47 F i g u r e 11. Histogram of Bj(.25) a t W e a t h e r s t a t i o n C u s i n g the c o n s t a n t drag c o e f f i c i e n t .48 F i g u r e 12.. R (L) f o r a l l s h i p s a t r e p r e s e n t a t i v e a v e r a g i n g p e r i o d s and wind speeds u s i n g t h e c o n s t a n t drag c o e f f i c i e n t . 51 F i g u r e 13. G e o g r a p h i c a l l y averaged v a l u e s o f R (L) f o r the c o n s t a n t drag c o e f f i c i e n t f o r a l l a v e r a g i n g p e r i o d s and wind speeds.. .54 F i g u r e 14. B (L) f o r r e p r e s e n t a t i v e a v e r a g i n g p e r i o d s and wind speeds f o r a l l s h i p s u s i n g t h e c o n s t a n t drag c o e f f i c i e n t . 55 F i g u r e 15. S y s t e m a t i c v a r i a n c e u n d e r e s t i m a t i o n f o r a l l s h i p s u s i n g i n i t i a l e s t i m a t e s of 59 F i g u r e 16. The r e l a t i v e e r r o r i n d u c e d i n the r e s i d u a l by a p p l i c a t i o n of a c o r r e c t i o n f a c t o r t o r e a d j u s t f o r the s y s t e m a t i c b i a s i n the d i f f e r e n c e v a r i a n c e s . .......................... 62 F i g u r e 17. C o r r e c t i o n f a c t o r s ' / ^ ^ f o r t h e c o n s t a n t drag c o e f f i c i e n t . 63 F i g u r e 18. The t e s t f u n c t i o n s o b t a i n e d when the s h i p s ' i n d i v i d u a l v a l u e s were used. ............... 65 F i g u r e 19. Improvement i n t h e t e s t v a l u e s over t h e raw t e s t r e s u l t s a f t e r a p p l i c a t i o n of the i n d i v i d u a l s h i p s ' c o r r e c t i o n . .................. 66 F i g u r e 20. The y e a r - t o - y e a r and monthly v a r i a t i o n s of the mean heat f l u x e s . . . . . . . . . . . . . . . . . . . . . . . . 7 0 F i g u r e 21. The t e s t q u a n t i t i e s w i t h no c o r r e c t i o n a p p l i e d t o the VA heat f l u x e s . ................... 75 F i g u r e 22. The s e n s i b l e and l a t e n t 3H v e r s u s VA heat f l u x e s at S t a t i o n C, L=28.0 days. .79 F i g u r e 23. S h i p s ' 1/$^^ v a l u e s f o r the heat f l u x e s . .82 F i g u r e 24. Test v a l u e s w i t h t h e i n d i v i d u a l s h i p s ' ^ *--e a p p l i e d t c t h e heat f l u x e s . . 84 F i g u r e 25. Test v a l u e improvements over the u n c o r r e c t e d case. 85 F i g u r e 26. The £</».* -1 v a l u e s as a f u n c t i o n of wind speed. ...90 F i g u r e 27. The£<*e_-1 v a l u e s as a f u n c t i o n of a v e r a g i n g p e r i o d . ........................................ 92 F i g u r e 28. D i f f e r e n c e s between t h e H fe-e and e m p i r i c a l f o r m u l a r e s i d u a l v a r i a n c e s w i t h no c o r r e c t i o n a p p l i e d f o r the DV t i a s . ....................... 98 F i g u r e 29. The d i f f e r e n c e means u s i n g the e m p i r i c a l f o r m u l a . 103 F i g u r e 30. The d i f f e r e n c e v a r i a n c e s u s i n g the e m p i r i c a l f o r m u l a . , 104 F i g u r e 31. The r e s i d u a l v a r i a n c e s u s i n g t h e e m p i r i c a l f o r m u l a . .........................106 F i g u r e 32. The c o r r e l a t i o n c o e f f i c i e n t s w i t h t h e s h i p s ' e m p i r i c a l f o r m u l a a p p l i e d . ........ .......107 F i g u r e 33. . The d i f f e r e n c e means u s i n g the g e o g r a p h i c a l l y averaged e m p i r i c a l f o r m u l a . ...................... 110 X F i g u r e 34. The d i f f e r e n c e v a r i a n c e s u s i n g t h e g e o g r a p h i c a l l y a v e r a g e d e m p i r i c a l f o r m u l a . ....... 11 1 F i g u r e 35. The r e s i d u a l v a r i a n c e s u s i n g t h e g e o g r a p h i c a l l y a v e r a g e d e m p i r i c a l f o r m u l a . . 112 F i g u r e 36. The c o r r e l a t i o n c o e f f i c i e n t s u s i n g t h e g e o g r a p h i c a l l y a v e r a g e d e m p i r i c a l f o r m u l a . .....114 F i g u r e 37. The s p e c t r a o f t h e u n c o r r e c t e d VA, r e s i d u a l and 3H h e a t f l u x t i m e s e r i e s a t S t a t i o n C and N f o r L=28.0 d a y s . . .....118 F i g u r e 38. Ihe s p e c t r a o f the c o r r e c t e d h e a t f l u x f o r t h e 3H, VA and r e s i d u a l s e r i e s a t S t a t i o n s C and N. ...... 119 F i g u r e 39. The c o r r e c t e d r e s i d u a l s e r i e s a t S t a t i o n s N and C f o r t h e l a t e n t h e a t f l u x , L=28.0 d a y s . ...123 F i g u r e 40. Ihe h e a t f l u x s p e c t r a u s i n g t h e s e a s o n a l l y a d j u s t e d c o r r e c t i o n s a t S t a t i o n N, L=28.0 days 124 F i g u r e . 4 1 . . The X and Y component s t r e s s s p e c t r a , l i n e a r d r a g c o e f f i c i e n t , f o r t h e u n c o r r e c t e d and c o r r e c t e d VA s e r i e s a t S t a t i o n D, L=28.0 d a y s . .125 F i g u r e 42. The l i n e a r d r a g c o e f f i c i e n t s p e c t r a a t S t a t i o n D, L=28.0 d a y s , c o r r e c t e d w i t h t h e g e o g r a p h i c a l l y a v e r a g e d f o r m u l a . . . . . . . . . . . . . . . . .127 F i g u r e 43. The s t r e s s s p e c t r a a t S t a t i o n N c o r r e c t e d w i t h t h e S t a t i o n N e m p i r i c a l f o r m u l a , L=28.0 d a y s , l i n e a r d r a g c o e f f i c i e n t . . . . . . . . . . . . . . . . . . 127 F i g u r e 44. C o n s t r u c t i o n o f t h e p i e c e w i s e l i n e a r d i s t r i b u t i o n f o r t h e d i r e c t i o n i n t e r p o l a t i o n . ..132 F i g u r e 45. The magnitude mean e r r o r s and e r r o r s t a n d a r d d e v i a t i o n s between t h e a c t u a l s t r e s s and wind r o s e s t r e s s as a f u n c t i o n o f s h i p and month. ...138 F i g u r e 46. Ihe d i r e c t i o n mean e r r o r s and e r r o r s t a n d a r d d e v i a t i o n s between t h e a c t u a l s t r e s s and wind r o s e s t r e s s as f u n c t i o n c f s h i p and month. ....... 141 Figure 47. The mean e r r o r s and e r r o r s t a n d a r d d e v i a t i o n s between t h e a c t u a l s e n s i b l e h e a t f l u x e s and th e wind r o s e s e n s i b l e h e a t f l u x e s as a f u n c t i o n o f s h i p and month. ....................143 F i g u r e 48. The mean e r r o r s and e r r o r s t a n d a r d d e v i a t i o n s between t h e a c t u a l l a t e n t h e a t f l u x e s and t h e x i wind r o s e l a t e n t h e a t f l u x e s as a f u n c t i o n o f s h i p and month. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 x i i TABLE OF SYMBOLS C o n s t a n t s Cd Cg C t Cp Drag c o e f f i c i e n t D a l t o n number S t a n t o n number S p e c i f i c h e a t o f a i r a t c o n s t a n t p r e s s u r e L a t e n t h e a t o f e v a p o r a t i o n C o n s t a n t - 1. 5x 10 ~ 3 l i n e a r (see E q u a t i o n 2. 5) 1.5x10 -3 1.5x10-3 1.0x10 3 j kg-i o c - i 2.46x106 J k g - l G e n e r a l Symbols A (L) s h i f t i n d i r e c t i o n between t h e c l i m a t o l o g i c a l t h r e e -h o u r l y a v e r a g e d s t r e s s and t h e c l i m a t o l o g i c a l v e c t o r a v e r a g e d s t r e s s . B j ( L ) s h i f t i n d i r e c t i o n between t h e j e s t i m a t e o f t h e v e c t o r a v e r a g e d s t r e s s magnitude and the j e s t i m a t e o f t h e t h r e e - h o u r l y a v e r a g e d s t r e s s m a g n i t u d e . B (L) c l i m a t o l c g i c a l t i m e a v e r a g e o f E j ( L ) DM d i f f e r e n c e means DV d i f f e r e n c e v a r i a n c e s Hs s e n s i b l e h e a t f l u x HI l a t e n t h e a t f l u x L a v e r a g i n g p e r i o d (days) q' f l u c t u a t i n g a b s o l u t e a i r h u m i d i t y (Jcg/m 3) q mean a b s o l u t e a i r h u m i d i t y (kg/m 3) Rj (L) r a t i o o f t h e j e s t i m a t e o f t h e v e c t o r a v e r a g e d s t r e s s magnitude and t h e j e s t i m a t e o f t h e t h r e e -h o u r l y a v e r a g e d s t r e s s m a g n i t u d e . R(L) c l i m a t o g i c a l a v e r a g e o f R j ( L ) RV r e s i d u a l v a r i a n c e S(L) r a t i o o f c l i m a t o l o g i c a l v e c t o r a v e r a g e d s t r e s s tcagnitude and c l i m a t o l c g i c a l t h r e e - h o u r l y a v e r a g e d s t r e s s I a v e r a g e s t r e s s m agnitude (dPa) t» f l u c t u a t i n g a i r t e m p e r a t u r e (°C) u x component o f wind v e l o c i t y (m/sec) v y component o f wind v e l o c i t y (m/sec) u' f l u c t u a t i n g m i c r o s c a l e downstream wind v e l o c i t y (m/sec) V v e c t o r a v e r a g e d wind s p e e d (m/sec) VA v e c t o r a v e r a g e d w' f l u c t u a t i n g m i c r o s c a l e v e r t i c a l wind v e l o c i t y (m/sec) X t h r e e - h o u r l y a v e r a g e d f l u x X' v e c t o r a v e r a g e d f l u x 3H t h r e e - h o u r l y a v e r a g e d f l u x * x i i i G reek Symbols AQ a i r s e a h u m i d i t y d i f f e r e n c e (kg/m 3) A T a i r sea t e m p e r a t u r e d i f f e r e n c e ( C ° ) 1 e m p i r i c a l f o r m u l a used t o t r a n s f o r m a v e c t o r a v e r a g e d q u a n t i t y t o a t h r e e - h o u r l y a v e r a g e d g u a n t i t y g e o g r a p h i c a l l y a v e r a g e d form o f ^ B e a u f o r t c a t e g o r y / a v e r a g i n g p e r i o d g r o u p e d r e g r e s s i o n c o n s t a n t u s e d t o t r a n s f o r m t h e V& f l u x t o r e s e m b l e a 3H f l u x g e o g r a p h i c a l a v e r a g e o f p a i r d e n s i t y (kg/m 3) S u p e r s c r i p t s v e c t o r a v e r a g e d q u a n t i t y t i m e a v e r a g e S u b s c r i p t s i member o f t h e t h r e e - h o u r l y sampled and c o n s t r u c t e d t i m e s e r i e s j member o f t h e s e t o f v a r i a t e s a v e r a g e d o v e r L d a y s k k + h E e a u f c r t c a t e g o r y 1 l + h a v e r a g i n g p e r i o d x x d i r e c t i o n ( e a s t ) y y d i r e c t i o n ( n o r t h ) x i v ACKNOWLEDGEMENT I s h o u l d l i k e to t h a n k t h e p e r s o n s i n v o l v e d i n t h e c o m p l e t i o n o f t h i s p r o j e c t . T h e s e few l i n e s c a n n o t a d e q u a t e l y e x p r e s s my g r a t i t u d e t o my s u p e r v i s o r , Dr. S. Pond, w i t h o u t whose k n o w l e d g e , e n c o u r a g e m e n t and a s s i s t a n c e , t h i s work c o u l d n o t have been c o m p l e t e d . The N o r t h A t l a n t i c w e a t h e r s h i p d a t a was s u p p l i e d by Dr. B. P c l l a r d o f t h e I n s t i t u t e o f O c e a n o g r a p h i c S c i e n c e s , Wormley and t h e S t a t i o n N d a t a was o b t a i n e d from Dr. C. D o r i a n , San D i e g o S t a t e U n i v e r s i t y . Mr. . B. Walker p e r f o r m e d t h e i n i t i a l s t r u c t u r i n g c f t h e computer t a p e s . D r . W. L a r g e o f f e r e d many p r a c t i c a l s u g g e s t i o n s i n p r o c e s s i n g t h e l a r g e amounts o f d a t a i n v o l v e d . The p r o j e c t was s u p p o r t e d by t h e U n i t e d S t a t e s O f f i c e o f N a v a l R e s e a r c h ( C o n t r a c t N00014-76-C-0446 under P r o j e c t 083-207) and by t h e N a t u r a l S c i e n c e and E n g i n e e r i n g B e s e a r c h C o u n c i l o f Canada ( G r a n t A8301). I p e r s o n a l l y r e c e i v e d a p o s t g r a d u a t e s c h o l a r s h i p f r o m NSEEC. 1 CHAPTER I INTRODUCTION The s p a t i a l and t e m p o r a l s c a l e s of t h e t u r b u l e n t e n v i r o n m e n t f o r a i r - s e a c o u p l e d s y s t e m s may v a r y o v e r s i g n i f i c a n t o r d e r s o f magnitude. F o r example, t r e n d s i n t h e l o n g - t e r r a h e a t i n g and c o o l i n g o f t h e E a r t h ' s s u r f a c e o f c o n s e q u e n c e t o Man may r e q u i r e . m a n y d e c a d e s t o d e t e r m i n e w h i l e t u r b u l e n t d i f f u s i o n o f momentum w i t h i n t h e s e a must be measured i n f r a c t i o n s o f a s e c o n d . F i e d l e r and P a n o f s k y ( 1 9 7 0 ) have s u g g e s t e d s e v e r a l o v e r l a p p i n g t e m p o r a l (and s p a t i a l ) s c a l e r a n g e s t o a i d i n t h e d e s c r i p t i o n o f t i m e - d e p e n d e n t m e t e o r o l o g i c a l phenomena. The f i r s t i s t h e m i c r o s c a l e r a n g i n g from l e s s t h an a s e c o n d t o a b o u t one. h o u r . The m e s o s c a l e r a n g e s from s e v e r a l m i n u t e s t o s e v e r a l d a y s , t h e s y n o p t i c s c a l e s s t a r t a t a b o u t one d a y and e x t e n d to s e v e r a l weeks. The s e a s o n a l and c l i m a t i c s c a l e s a r e l o n g e r t h a n th e s y n o p t i c s c a l e s . Wind s t r e s s and s e n s i b l e and l a t e n t h e a t f l u x e s c a n be d e s c r i b e d as t h e v e r t i c a l t r a n s f e r o f h o r i z o n t a l momentum, t e m p e r a t u r e , and h u m i d i t y f r o m t h e a i r t o t h e s e a . M i c r o s c a l e e x p e r i m e n t a l t e c h n i q u e s a r e r e q u i r e d t o measure them. Among t h e t e c h n i q u e s d e v e l o p e d a r e t h e e d d y - c o r r e l a t i o n , p r o f i l e and d i s s i p a t i o n methods. A d e t a i l e d d i s c u s s i o n o f them may be f o u n d i n t h e . t u r b u l e n c e l i t e r a t u r e . B r i e f l y , however, t h e v e r t i c a l and downstream wind components and t e m p e r a t u r e and h u m i d i t y f l u c t u a t i o n s a r e sampled a t a h i g h r a t e ( u s u a l l y s e v e r a l H e r t z ) f o r p e r i o d s up t o one h o u r . The t r a n s p o r t f l u x e s a r e d e t e r m i n e d t h r o u g h c o r r e l a t i o n o f t h e v e r t i c a l v e l o c i t y f l u c t u a t i o n s w i t h 2 the downstream wind component, t e m p e r a t u r e and h u m i d i t y f l u c t u a t i o n s as shown below: 1 1.1(a) Hs p CP w t ' I ' 1.1(b) He. = E w'cr" 1. 1 (c) where ~T i s t h e m i c r o s c a l e wind s t r e s s , f> i s t h e a i r d e n s i t y , Hs i s t h e s e n s i b l e h e a t f l u x , HI i s t h e l a t e n t h e a t f l u x , w' i s t h e v e r t i c a l v e l o c i t y , u' i s t h e downstream v e l o c i t y f l u c t u a t i o n , t ' i s t h e a b s o l u t e a i r t e m p e r a t u r e f l u c t u a t i o n , g' i s t h e a b s o l u t e h u a i d i t y f l u c t u a t i o n , E i s t h e l a t e n t h e a t o f v a p o r i z a t i o n ( 2 . 4 6 x 1 0 6 J kg -») , Cp i s t h e s p e c i f i c h e a t o f a i r a t c o n s t a n t p r e s s u r e ( 1 . 0 x 1 0 3 J k g - 1 °C-») and t h e o v e r b a r r e p r e s e n t s t h e ensemble a v e r a g e where a l l u n i t s a r e assumed t o be S . I . N o r m a l l y e r g o d i c i t y i s i n v o k e d and i n p r a c t i c e a t i m e a v e r a g e i s a c t u a l l y u s e d . E g u a t i o n s 1.1 a r e e x a c t . The r a p i d s a m p l i n g r e q u i r e d , however, (about 10 H e r t z i n t h e a t m o s phere) g e n e r a t e s t o o much d a t a f o r l o n g t i m e s c a l e s t u d i e s . M e a s u r i n g t h e v e r t i c a l f l u c t u a t i o n i n p a r t i c u l a r and t h e r a p i d i t y o f measurements i n g e n e r a l n e c e s s i t a t e s u s i n g h i g h l y s o p h i s t i c a t e d e q u i p m e n t t h a t i s g e n e r a l l y beyond t h e s c o p e o f t h e . s y n o p t i c s c a l e i n v e s t i g a t o r . , The m i c r o s c a l e f l u x e s can be r e l a t e d t o t h e a v e r a g e o f m e s o s c a l e measurements o f one h o u r (or l e s s ) o f s a m p l i n g 3 d u r a t i o n t h r o u g h t h e b u l k p a r a m e t e r i z a t i o n s g i v e n by (eg. R o l l , 1965) : T- P Cd l 1.2(a) o r i n components: ^ s p C^Ct V AT where, T i s t h e wind s t r e s s m a g n i t u d e , Tx and Ty a r e t h e x and y components o f t h e wind s t r e s s , V t h e m e s o s c a l e v e c t o r - a v e r a g e d wind s p e e d , u and v a r e t h e x and y components o f t h e m e s o s c a l e a v e r a g e d wind v e l o c i t y , A T i s t h e a v e r a g e a i r - s e a t e m p e r a t u r e d i f f e r e n c e , A Q i s t h e a v e r a g e a i r - s e a a b s o l u t e h u m i d i t y d i f f e r e n c e . Cd, C t and Cg a r e n o n d i m e n s i o n a l t r a n s f e r c o e f f i c i e n t s commonly known as t h e d r a g c o e f f i c i e n t , and S t a n t o n and D a l t o n numbers r e s p e c t i v e l y . They r e l a t e t h e m e s o s c a l e mean v a r i a b l e s o f E g u a t i o n 1.2 t o t h e m i c r o s c a l e f l u c t u a t i o n s o f E g u a t i o n 1.1. E x c e p t f o r s p e c i f i c t u r b u l e n c e s t u d i e s , h o u r l y wind measurements a r e seldom a v a i l a b l e . Many c a l c u l a t i o n s o f t r a n s p o r t f l u x e s a r e d e r i v e d f r o m q u a n t i t i e s t h a t a r e e f f e c t i v e l y a v e r a g e d o v e r p e r i o d s much l o n g e r t h a n one day. . I f we l e t o v e r b a r s d e n o t e a t i m e a v e r a g e t h e n an e s t i m a t e o f t h e 1. 2 (b) 1. 2 (c) 1. 2 (d) 4 a v e r a g e x component s t r e s s i s : I 1 . 3 where t h e r e a r e I o b s e r v a t i o n s and t h e s u b s c r i p t i d e n o t e s t h e s e t o f wind components, a i r d e n s i t i e s and d r a g c o e f f i c i e n t o b s e r v a t i o n s . An e s t i m a t e o f t h e x component o f s t r e s s b a s e d on t h e component a v e r a g e d winds i s g i v e n by: i t i s e v i d e n t t h a t E g u a t i o n 1.3 and 1.4 a r e not i d e n t i c a l . By s i m i l a r a rguments t h e a v e r a g e d h e a t f l u x e s c a l c u l a t e d from E g u a t i o n s 1.2(c) and (d) w i l l d i f f e r from the e s t i m a t e s o f t h e a v e r a g e d heat f l u x e s b a s e d on t h e p r o d u c t o f t h e a v e r a g e d c o n s t i t u e n t v a r i a b l e s . M a l k u s ( 1 9 6 2 ) examined 59 t h r e e - h o u r l y sampled wind o b s e r v a t i o n s f r c m t h e C a r i b b e a n Sea and f o u n d t h a t t h e f l u x e s ( i n c l u d i n g momentum, l a t e n t h e a t , and s e n s i b l e h e a t ) c a l c u l a t e d from th e a v e r a g e d c o n s t i t u e n t s ( E g u a t i o n 1.4) u n d e r e s t i m a t e d t h e d i r e c t l y a v e r a g e d f l u x e s ( E q u a t i o n 1.3) by o n l y 7.0%. S i m i l a r c a l c u l a t i o n s f o r t h e s t r e s s e s , p e r f o r m e d on t h r e e - h o u r l y s a m p l e d winds a t W e a t h e r s t a t i o n C r e v e a l e d t h a t t h e a v e r a g e d c o n s t i t u e n t v a r i a b l e s p r e d i c t e d a s t r e s s m agnitude o f o n l y 35% o f t h e d i r e c t l y c a l c u l a t e d v a l u e . She a t t r i b u t e d t h e d i f f e r e n c e s i n r e d u c t i o n t o t h e s t e a d i n e s s o f t h e T rade Winds where the l o n g -t e r m c l i m a t o l o g i c a l a v e r a g e s a r e i n d i c a t i v e of t h e s h o r t - t e r m y 1 . 4 5 m e s o s c a l e and s y n o p t i c s c a l e c o n d i t i o n s . Over m i d d l e l a t i t u d e o c e a n s , t h e winds a r e much more v a r i a b l e , b e i n g d o m i n a t e d by f o u r to s e v e n day c y c l o n i c s t o r m s , and t h e l o n g - t e r m wind a v e r a g e s do n o t a d e q u a t e l y i n d i c a t e s h o r t e r p e r i o d a c t i v i t y . The wind s t r e s s i n p u t f o r many o c e a n o g r a p h i c c a l c u l a t i o n s i s d e r i v e d f r o m e s t i m a t e s o f t h e g e o s t r o p h i c s u r f a c e winds c a l c u l a t e d f r o m a v e r a g e d b a r o m e t r i c p r e s s u r e maps. These maps a r e c o n s t r u c t e d t h r o u g h l a r g e s p a t i a l s c a l e s a m p l e s t a k e n s e v e r a l t i m e s d a i l y then t e m p o r a l l y a v e r a g e d o v e r p e r i o d s o f up t o a month c r more. F o f o n o f f ( 1960) i n c a l c u l a t i n g o c e a n i c t r a n s p o r t s i n t h e N o r t h P a c i f i c Ocean b a s e d on g e o s t r o p h i c w i n d s d e r i v e d from monthly p r e s s u r e maps s u g g e s t s t h a t t h e d i f f e r e n c e between t h e m o n t n l y s t r e s s and t h e s t r e s s c a l c u l a t e d from a v e r a g e d p r e s s u r e s i s p r o p o r t i o n a l t o t h e v a r i a n c e o f t h e p r e s s u r e g r a d i e n t . The v a r i a n c e c f t h e p r e s s u r e g r a d i e n t i s e q u i v a l e n t t o the sum o f t h e u and v wind component v a r i a n c e s o v e r t h e p e r i o d i n which t h e p r e s s u r e was a v e r a g e d . A a g a a r d {1S70) p r o v i d e d a p a r t i c u l a r l y s t r i k i n g example o f the e f f e c t o f u s i n g monthly a v e r a g e d p r e s s u r e maps i n c a l c u l a t i n g t r a n s p o r t s i n the Norwegian and G r e e n l a n d S e a s . S t a r t i n g w i t h s i x - h o u r l y a v e r a g e d p r e s s u r e maps, he c a l c u l a t e d tne s i x - h o u r l y S v e r d r u p t r a n s p o r t s f o l l o w i n g F o f o n o f f ( 1960). The s i x - h o u r l y t r a n s p o r t s were t h e n a v e r a g e d o v e r F e b r u a r y 1965 t o a r r i v e a t a m o n t h l y a v e r a g e t r a n s p o r t which a p p e a r s i n F i g u r e 1 ( a ) . He t h e n a v e r a g e d t h e b a r o m e t r i c p r e s s u r e s o v e r t h e same p e r i o d and r e c a l c u l a t e d a p r e s s u r e a v e r a g e d e s t i m a t e o f t h e t o t a l t r a n s p o r t f o r F e b r u a r y 1965. T h i s r e s u l t a p p e a r s i n fa • f i g u r e 1 (a) F i g u r e 1 (b) F i g u r e 1. The n e t t r a n s p o r t i n t h e G r e e n l a n d and N o r wegian Seas f o r F e b r u a r y , 1965 b a s e d on s i x - h o u r l y b a r o m e t r i c p r e s s u r e maps. F i g u r e 1 (a) shows the month a v e r a g e o f t h e s i x - h o u r l y t r a n s p o r t s and F i g u r e 1(b) shows the t r a n s p o r t s b a s e d on the month a v e r a g e o f s i x - h o u r l y b a r o m e t r i c p r e s s u r e s . T r a n s p o r t u n i t s a r e 1 0 6 m3 s e c - 1 . (from A a g a a r d , 1970) F i g u r e 1 ( b ) . I t i s q u i t e e v i d e n t t h a t i n r e g i o n s of l a r g e a v e r a g e t r a n s p o r t , t h e mean p r e s s u r e a p p r o a c h u n d e r e s t i m a t e s t h e mean " t r a n s p o r t a p p r o a c h by a f a c t o r o f f o u r t o f i v e . W i l l e b r a n d ( 1 978) used t w e l v e - h o u r l y a v e r a g e d p r e s s u r e maps to c a l c u l a t e s p a t i a l and t e m p o r a l wind s t r e s s s p e c t r a on t h e N o r t h A t l a n t i c and N o r t h P a c i f i c O c e a n s . A l t h o u g h t h e o v e r a l l s p e c t r a l s h a p e s may be q u a l i t a t i v e l y c o r r e c t , t h e s t r e s s power d e n s i t y e s t i m a t e s a r e p r o b a b l y low. Many o c e a n o g r a p h i c phenomena s u c h as t h e r e v e r s a l o f t h e c u r r e n t r e g i m e i n t h e I n d i a n Ocean, t h e o n s e t of E l Nino i n t h e P a c i f i c Ocean, t h e r e v e r s a l o f t h e C a l i f o r n i a and D a v i d s o n c u r r e n t s o f f t h e Western U n i t e d S t a t e s , and t h e o n s e t o f c o a s t a l u p w e l l i n g have been l i n k e d w i t h t h e t e m p o r a l d ependence o f t h e wind s t r e s s f o r c i n g . A p o i n t o f c o n t e n t i o n i s w h e t h e r t h e l a r g e s c a l e ( c f t h e o r d e r o f 100 km) wind f i e l d and c o n s e q u e n t l y 7 Sverdrup t r a n s p o r t s ( c u r l of the wind s t r e s s ) a r e i m p o r t a n t or whether l o c a l wind s t r e s s e s (about 30 km) and Ekman t r a n s p o r t s are c o n t r o l l i n g mechanisms. In the case o f E l N i n o , i t has been demonstrated t h a t the t o t a l o c e a n i c s t r e s s i s i m p o r t a n t (see Mcc r e a r y , 1976 and H u r l b u r t , e t . a l . 1976) w h i l e t h e l o c a l Ekman t r a n s p o r t s a re i m p o r t a n t f o r c o a s t a l u p w e l l i n g ( M i e n , 1980). For c o a s t a l phenomena the l o c a l w i n d s , sampled a t about h o u r l y i n t e r v a l s , can be r e a d i l y o b t a i n e d from c o a s t a l s t a t i o n s . Open ocean wind f i e l d data are much more d i f f i c u l t t o o b t a i n ( O ' B r i e n , 197 1) and g e o s t r o p h i c wind c a l c u l a t i o n s from Daromexric p r e s s u r e maps at p r e s e n t a r e t h e o n l y v i a b l e s o u r c e o f wind i n f o r m a t i o n c o v e r i n g l o n g t i m e and l a r g e s p a t i a l s c a l e s . I n the f u t u r e s a t e l l i t e s c a t t e r c m e t r y may p r e s e n t an a l t e r n a t i v e source of wind i n f o r m a t i o n but a t p r e s e n t t h e s e measurements are s t i l l i n t h e i r i n f a n c y . I t i s o n l y r e c e n t l y t h a t time-dependent m e t e o r o l o g i c a l c o n d i t i o n s have been used t o d r i v e s i m u l a t i o n models of t h e f l o w i n l a r g e o c e a n i c b a s i n s . Among o t h e r s , a r e c e n t attempt i n t h i s v e i n has been the work of Huang(1978 and 1979) i n m o d e l l i n g c l i m a t o l o g i c a l and s e a s o n a l v a r i a t i o n s of t h e North P a c i f i c Ocean. Two s t a g e s o f h i s model have been p r e s e n t e d . F i r s t , the model was spun up t c g u a s i - s t e a d y s t a t e u s i n g an i n i t i a l s e t of da t a based on c l i m a t o l o g i c a l l y averaged (over 20 years) s t r e s s , l a t e n t heat f l u x and s e n s i b l e heat f l u x . The s t r e s s f i e l d resemnied t h a t c f Hellerman (1967). In t h e next s t a g e , a second s e t of d a t a was used based on monthly e s t i m a t e s of the t h r e e f l u x e s at each g r i d p c i n t from monthly averaged v a l u e s o f a i r te m p e r a t u r e , vapour p r e s s u r e and z o n a l and m e r i d i o n a l winds. A 8 g u a s i - d e t e r m i n i s t i c a n n u a l c y c l e was t h e n c a l c u l a t e d a t ea c h g r i d p o i n t by f i t t i n g t h e f i r s t t h r e e h a r m o n i c s of the a n n u a l c y c l e t o t h e s e c o n d d a t a s e t and a c c e p t i n g t h e c l i m a t o l o g i c a l i n f o r m a t i o n c f t h e f i r s t d a t a s e t f o r t h e c o n s t a n t t e rm. I x i s e v i d e n t t h a t h i s t e c h n i q u e s h o u l d l e a d t o t h e e r r o r s o u t l i n e d by Aaga a r d (1970) shown i n F i g u r e 1. Some o f t h e i n h e r e n t a v e r a g i n g e r r o r s i n Huang's model have been compensated by u s i n g a d r a g c o e f f i c i e n t o f 2 . 5 x l 0 - 3 which i s a p p r o x i m a t e l y d o u b l e t h e more r e c e n t e s t i m a t e s (eg. L a r g e 1979, S m i t h and Banke 1974). Inus an o b j e c t i v e o f t h i s t h e s i s i s t o g u a n t i f y on t h e m e s o s c a l e and s y n o p t i c s c a l e , t h e r e d u c t i o n s i n a i r sea f l u x e s o c c u r r i n g when e s t i m a t e s a r e made u s i n g a v e r a q e d wind and t e m p e r a t u r e d a t a . F i s s e l (1975) made an i n i t i a l a t t e m p t a t q u a n t i f y i n g t h e d i s c r e p a n c y u s i n g a s a d a t a base t e n y e a r s o f m e t e o r o l o g i c a l o b s e r v a t i o n s a t W e a t h e r s t a t i o n P. He foun d t h a t t h e s t r e s s c a l c u l a t e d t h r o u g h E q u a t i o n 1.4 c o n s i s t e n t l y u n d e r e s t i m a t e d t h a t c a l c u l a t e d t h r o u g h E q u a t i o n 1.3 and t h a t t h e r e d u c t i o n s were q u i t e r e g u l a r f o r a v e r a g i n g p e r i o d s up t o two y e a r s . The p r e s e n t s t u d y examines a d a t a base of m e t e o r o l o g i c a l o b s e r v a t i o n s s a m p l e d a t t h r e e - h o u r l y i n t e r v a l s f r o m n i n e w e a t h e r s t a t i o n s on t h e A t l a n t i c Ocean and two w e a t h e r s t a t i o n s on the P a c i f i c Ocean t o d e t e r m i n e t h e e x t e n t o f t h e d i s c r e p a n c i e s r e f e r r e d t o above and any g e n e r a l i t i e s which may be p r o j e c t e d from t h e r e s u l t s . N o r m a l l y c l i m a t o l c g i c a l wind s t r e s s i n f o r m a t i o n i s b a s e d on a wind r o s e a n a l y s i s a s o u t l i n e d by H e l l e r m a n (1965). Here i r r e g u l a r l y sampled wind measurements a r e s o r t e d i n t o d i s c r e t e 9 wind s p e e d and d i r e c t i o n c a t e g o r i e s . The p r o b a b i l i t y d i s t r i b u t i o n o f t h e wind components can be c a l c u l a t e d and used t o o b t a i n e s t i m a t e s o f t h e monthly o r a n n u a l wind s t r e s s . C a l c u l a t i o n s o f t h i s s o r t have been used p a r t i c u l a r l y f o r t h e s t e a d y s t a t e momentum f l u x i n p u t s o f l a r g e - s c a l e o c e a n c i r c u l a t i o n n u m e r i c a l models. The d a t a b a s e o f the e l e v e n w e a t h e r s h i p s ' m e t e o r o l o g i c a l o b s e r v a t i o n s c o u l d be r e a d i l y s o r t e d i n t o v a r i o u s c h o i c e s o f wind r o s e c o n f i g u r a t i o n s . The "wind r o s e " f l u x e s were t h e n compared to the a c t u a l i n d i v i d u a l l y d e t e r m i n e d f l u x e s ( u s i n g E q u a t i o n 1.3) t o i n v e s t i g a t e t h e e r r o r i n d u c e d by i n t r i n s i c wind r o s e a v e r a g i n g o f t h e winds and t h u s e r r o r s i n t h e e s t i m a t e s o f t h e c l i m a t o l o g i c a l wind s t r e s s f i e l d s . 10 CHIP.HE I I DATA PEEPAEATION 2. 1 D a t a O r i g i n Tne d a t a b a s e f o r t h e s t u d y o r i g i n a t e d f r o m m e t e o r o l o g i c a l o b s e r v a t i o n s a t Ocean W e a t n e r s t a t i o n s A l p h a , B r a v o , C h a r l i e , D e l t a , E c h o , I n d i a , J u l i e t , K i l o , Mike, November and Papa which w i l l n e n c e f c r t h be r e f e r r e d t o by t h e c a p i t a l l e t t e r o n l y o f t h e s t a t i o n (eg. W e a t h e r s t a t i o n E ) . Ihe q u a n t i t i e s r e c o r d e d a t e a c h s t a t i o n were wind s p e e d and d i r e c t i o n , b a r o m e t r i c p r e s s u r e , wet and d r y b u l b t e m p e r a t u r e s and s e a s u r f a c e t e m p e r a t u r e which were sampl e d a t t h r e e - h o u r l y i n t e r v a l s . Maps o f t h e w e a t h e r s h i p l o c a t i o n s a p p e a r i n F i g u r e 2. D a t a f r o m S t a t i o n s A t h r o u g h M were t r a n s f e r r e d f r o m IBM punch c a r d s t o s e v e n - t r a c k m a g n e t i c t a p e a t t h e U n i v e r s i t y o f Southampton, E n g l a n d w h i l e S t a t i o n N d a t a were t r a n s f e r r e d to s e v e n t r a c k m a g n e t i c t a p e a t Oregon S t a t e U n i v e r s i t y . The wet and d r y b u l b t e m p e r a t u r e s were c o n v e r t e d t o a dew p o i n t t e m p e r a t u r e cn t h e s e t a p e s . The S t a t i o n P d a t a were e n t i r e l y p r o c e s s e d a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a and d e t a i l s o f t h e e d i t i n g c a n be f o u n d i n Hertzman, e t . a l . ( 1 9 7 4 ) . A resume o f t h e number of y e a r s of d a t a , c o u n t r y r e s p o n s i b l e f o r c o l l e c t i o n , and l a t i t u d e and l o n g i t u d e o f t h e s t a t i o n s c a n be f o u n d i n T a b l e I . F u r t h e r d e t a i l s o f d a t a c o l l e c t i o n t e c h n i q u e s can be f o u n d by a d d r e s s i n g i n q u i r i e s t o t h e n a t i o n a l w e a t h e r b u r e a u s e r v i c e s o f t h e r e s p o n s i b l e c o u n t r i e s . 2.2 D a t a V e r i f i c a t i o n I n o r d e r f o r t a p e s from t h e U n i v e r s i t y o f Southampton and 11 F i g u r e 2(a) North A t l a n t i c S t a t i o n s . Figure 2(t) North P a c i f i c S t a t i o n s . F i g u r e 2. L o c a t i o n s of the 11 w e a t h e r s t a t i o n s i n v o l v e d i n the study. 12 1ABLE I D e t a i l s o f t h e s t a t i o n s l o c a t i o n s and number o f y e a r s o f d a t a t h a t were c o l l e c t e d . The s t a r t d a t e i s 1 J a n u a r y o f t h e s t a r t y e a r and t h e end d a t e i s 31 December o f t h e end y e a r . STATION| COUNTRY | LATITUDE I LONGITUDE | START | END RESPONSIBLE| i DATE | DATE A j N e t h e r l a n d s | -U.S. | 6 1 - 6 3 o N 1 3 1 - 3 5 ow | 1 9 4 9 | 1 9 6 5 B I Canada | -U.S. | 5 5 . 5 - 5 7 . 5 O N I 4 9 . 5 - 5 2 . 5 o w | 1 9 4 9 | 1967 C | U.S. | 5 1 . 5 - 5 3 . 5 O N | 3 4 - 3 7 ow | 1 9 4 9 | 1 9 6 7 D | U.S. | 4 3 - 4 5 °N J 4 0 - 4 2 OW | 1 9 4 9 | 1 9 6 7 £ 1 U. S. | 3 4 - 3 6 o N | 4 7 - 4 9 o W | 1 9 4 9 | 1 9 6 7 I | U.K. | 5 9 - 6 1 ON 1 1 8 - 2 1 o W | 1 9 4 9 | 1 9 6 4 J | N e t h e r l a n d s 1 - U.S. | 5 2 . 3 - 5 4 . 3 O N I 1 7 . 8 - 2 0 . 8 O N | 1 9 4 9 | 1 9 6 5 K 1 N e t h e r l a n d s | - F r a n c e | 44-46 °N | 1 5 - 1 7 o w | 1 9 4 9 I 1 96 1 M | Norway | 6 5 - 6 7 JO-4 °E j 1 9 4 9 I 1 9 6 3 N j U.S. | 2 8 . 5 - 3 1 .5 o N | 1 3 8 - 1 4 2 ow | 1 9 4 9 | 1 9 6 9 P 1 Canada j 4 8 . 5 - 5 1 . 5 O N | 1 4 2 . 6 - 1 4 7 . 6 o w | 1 9 5 8 | 1 9 6 7 Oregon S t a t e U n i v e r s i t y t o be c o m p a t i b l e w i t h t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a computer s y s t e m s , t h e o r i g i n a l d a t a t a p e s had t c be r e f o r m a t t e d from s e v e n t o n i n e t r a c k s . S i m u l t a n e o u s l y , m i s s i n g d a t a were i d e n t i f i e d and f l a g g e d by r e p l a c i n g t h e m i s s i n g v a l u e s w i t h -999.9. The r e c o n s t r u c t e d t i m e s e r i e s were t h e n compared, p o i n t - b y - p o i n t , t o extreme v a l u e s as o u t l i n e d i n T a b l e I I . Any d a t a which had v a l u e s o u t s i d e t h e s e r a n g e s were c o n s i d e r e d t o be i n e r r o r and t h e s e were a l s o e l i m i n a t e d from c a l c u l a t i o n s by f l a g g i n g them w i t h -999.9. An example o f t h e dew p o i n t t e m p e r a t u r e t i m e s e r i e s f o r W e a t h e r s t a t i o n A a t t h i s l e v e l o f p r o c e s s i n g i s shown i n F i g u r e 3 ( a ) . At t h i s s t a g e , t h e u and v wind v e l o c i t y component time s e r i e s were p r o d u c e d from the wind d i r e c t i o n and speed c h o o s i n g t h e p o s i t i v e x and y d i r e c t i o n s as e a s t and n o r t h r e s p e c t i v e l y . 13 O u t - o f - r a n g e l i m i t s f o r t h e i n i t i a l s t a g e o f d a t a p r o c e s s i n g , QUANTITY Wind D i r e c t i o n Wind Speed B a r o m e t r i c P r e s s u r e A i r Tem p e r a t u r e Dew P o i n t T e m p e r a t u r e Sea S u r f a c e T e m p e r a t u r e UNITS 0 from N m/sec m i l l i b a r s °C. °C. ° c . LOWER LIMIT -180 0 900 -20 -20 -10 UPPER LIMIT 180 70 1060 40 40 40 B e c a u s e t h e d a t a a n a l y s i s r e q u i r e d a c o n t i n u o u s t h r e e -h o u r l y t i m e s e r i e s , t h e f l a g g e d d a t a o f a l l c h a n n e l s were r e p l a c e d by a v a l u e which was l i n e a r l y i n t e r p o l a t e d between t h e n e a r e s t p r e c e d i n g good p o i n t and t h e n e x t a n t e c e d i n g good p o i n t . The wind u and v components were i n t e r p o l a t e d and t h e s p e e d and d i r e c t i o n t h e n c a l c u l a t e d from t h e components. F i g u r e 3(b) shows t h e i n t e r p o l a t e d t i m e s e r i e s r e c o n s t r u c t e d from F i g u r e 3 ( a ) . T h e r e were two main t y p e s o f e r r o r s p r e s e n t . The c l a c k e n e d a r e a s o f F i g u r e 3(a) c o r r e s p o n d t o e v e r y s e c o n d o r t h i r d measurement b e i n g e i t h e r m i s s i n g o r o u t - o f - r a n g e . When t n e s e v a l u e s a r e r e p l a c e d , t h e c o r r e s p o n d i n g s e c t i o n s i n F i g u r e 3(b) a r e v i r t u a l l y i n d i s t i n g u i s h a b l e f r o m t h e r e m a i n d e r o f t h e ti m e s e r i e s . The arrow i n F i g u r e 3(a) i n d i c a t e s where d a t a a r e m i s s i n g f o r s e v e n d a y s c o r r e s p o n d i n g to i n s t r u m e n t m a l f u n c t i o n o r t h e s h i p b e i n g o f f s t a t i o n . As can be s e e n i n F i g u r e 3 ( b ) , 14 f i g u r e 3 ( a ) . M i s s i n g and o u t - o f - r a n g e f l a g g e d d a t a . S o . U J ™ U J o 0.0 40 .0 80 .0 120.0 T I M E I N D A Y S 160.0 200 .0 f i g u r e 3 ( b ) . Same as a r r o w s i n d i c a t e s p i k e s . above w i t h bad d a t a i n t e r p o l a t e d . The U J O r o o 40 .0 80 .0 120 0 T I M E I N D A Y S i 160 .0 200 .0 f i g u r e 3 ( c ) . Same as above w i t h t h e s p i k e s i d e n t i f i e d and i n t e r p o l a t e d . f i g u r e 3 . The dew p c i n t t e m p e r a t u r e a t t h r e e l e v e l s o f p r o c e s s i n g f o r S t a t i o n A from J a n 1 1951 t o J u l y 2 0 , 1951. 15 the l i n e a r i n t e r p o l a t i o n r e s u l t s i n a f l a t t e n e d r e g i o n where t h e v a r i a n c e has t e e n m a r k e d l y r e d u c e d . The a r r o w s i n F i g u r e 3(b) i l l u s t r a t e examples of " s p i k e s " o r r e g i o n s where t h e d a t a a r e d i s c o n t i n u o u s and o b v i o u s l y e r r o n e o u s even t h o u g h w i t h i n t h e l i m i t s o f T a b l e I I . I n t h e mere p r o m i n a n t c a s e , t h e dew t e m p e r a t u r e r i s e s f r o m -4.8<>C to 36.1°C and t a c k t o -3.9°C i n t w e l v e h o u r s . C o n s e q u e n t l y a l l t h e d a t a were v i s u a l l y m o n i t o r e d on t h e UBC D e p a r t m e n t o f O c e a n o g r a p h y PDP - 12 c o m p u t e r . O b v i o u s s p i k e s were i d e n t i f i e d and the p o i n t s r e p l a c e d by i n t e r p o l a t e d v a l u e s . at t h i s s t a g e an e i g h t b i t f l a g r e c o r d e d each d a t a p o i n t which had been i n t e r p o l a t e d . T a b l e I I I g i v e s t h e t o t a l number o f m i s s i n g , e r r o n e o u s , and o u t - o f - r a n g e d a t a p o i n t s f o r e a c h o f t h e measured q u a n t i t i e s . The S t a t i o n P i n f o r m a t i o n was e x t r a c t e d from F i s s e l ( 1 9 7 5 ) . With t h e e x c e p t i o n of W e a t h e r s t a t i o n I, t h e dew p o i n t t e m p e r a t u r e d i s p l a y s the l a r g e s t number o f i n t e r p o l a t e d p o i n t s . T h i s i s r e p r e s e n t a t i v e o f a l a r g e number o f m i s s i n g r e a d i n g s r a t h e r t h a n s p i k e s . W e a t h e r s h i p A, f o r example, has dew p o i n t measurements f o r e v e r y s e c o n d r e a d i n g o n l y f o r t h e p e r i o d 1952 t o 1954. S i m i l a r s i t u a t i o n s e x i s t f o r t h e e t h e r w e a t h e r s h i p s . A n a l y s e s a t t e m p t e d i n t h e s t u d y r e g u i r e d y e a r l y b l o c k s o f d a t a t h a t c l o s e l y a p p r o x i m a t e d t h e a c t u a l t i m e s s e r i e s . The r e g u l a r l y n i s s i n g ( t h a t i s , e v e r y s e c o n d o r t h i r d p o i n t ) d a t a p r e s e n t e d l i t t l e p r o b l e m b e c a u s e major f e a t u r e s s u c h as t h e d i u r n a l c y c l e r e m a i n e d i n t a c t . L a r g e b l o c k s o f m i s s i n g d a t a s e v e r e l y d i s t o r t e d t h e time s e r i e s t o t h e e x t e n t t h a t i t was f e l t t h a t t h e y c o u l d i n f l u e n c e t h e f i n a l r e s u l t s . F o r any 16 1 1 B L E I I I T o t a l number o f m i s s i n g , c u t - o f - r a n g e , and e r r o n e o u s (spiJced) d a t a p o i n t s p e r t i m e s e r i e s and w e a t h e r s t a t i o n . The t o t a l column s i g n i f i e s t h e t o t a l number o f s a m p l e s t a k e n ( i e . t h e number o f days s t u d i e d t i m e s 8) . TIME SERIES —I 1 1TOTAL| I I I I SHIP -1 WIND BARO-METER AIR TEMP. DEW TEMP. SEA TEMP. | +-A | 49 11| 46 1 81 4620| 8668 j 5659)49672J E | 2043| 2029| 2061 17730| 6341|55512| C | 1702| 1692| 1 708 | 17654| 3102|55512| D | 1567| 1532| 1523| 17851| 5955|555121 E 1 1677| 1678| 1642| 17683| 592 11555 1 2| I | 2466| 2395| 2377| 2405| 2577|46752| J | 3703| 3837 1 3669| 43251 3636) 49672| K | 1704| 1591 | 1619| 4767| 4758|37984| M | 2778| 2780| 2938| 4605| 2879|43824| N | 1432| 1278| 1 2981 178141 5754|64280| P 1 235| 238( 23 11 2 33 | 244| 292 16 1 v a r i a t e which c o n t a i n e d more t h a n 125 c o n s e c u t i v e m i s s i n g d a t a p o i n t s i n any g i v e n mcnth, the e n t i r e y e a r o f d a t a f o r t h a t v a r i a b l e was r e j e c t e d . T a b l e IV shows t h e y e a r s o f r e j e c t e d d a t a f o r e a c h s h i p . 2.3 D e n s i t y C a l c u l a t i o n s Page F-S c f the Handbook o f P h y s i c s and C h e m i s t r y (59th e d i t i o n ) g i v e s an e m p i r i c a l f o r m u l a f o r t h e d e n s i t y o f m o i s t a i r as: p = 1. 2929 (273. 13/la) (P-0. 3783e/760) 2. 1 where p i s t h e a i r d e n s i t y i n kg/m 3, Ta i s t h e d r y a i r t e m p e r a t u r e i n °K, P i s t h e b a r o m e t r i c p r e s s u r e i n mmHg, and e 17 TABLE IV The y e a r ( s ) o f e l i m i n a t e d d a t a f o r each w e a t h e r s t a t i o n . SHIP J STEESS HEAI FLUXES j A | 1950 1950 B | - | 5 2 , 5 3 c I - | 1 9 5 3 D I - | 5 2 , 5 3 E 1 - j 5 2 , 5 3 I | 1952 | 1 9 5 2 J 1 1952 | 5 2 , 5 7 K 1 1953 j 4 9 , 5 0 , 5 1 5 3 , 5 4 H | 1949 | 1 9 4 9 N | - | 5 2 , 5 3 j? I — I -i s t h e v a p o u r p r e s s u r e of t h e m o i s t u r e i n mmHg. Hertzman e t . a l . (1974) g i v e a f o r m u l a t o c a l c u l a t e t h e a b s o l u t e h u m i d i t y b a s e d on v a l u e s i n t h e CEC Handbook o f P h y s i c s and C h e m i s t r y ( 5 1 s t e d i t i o n ) : g=6. 4038x108 exp (-51C7.4/Td) 2. 2 wnere g i s t h e a b s o l u t e h u m i d i t y i n gm/m3 and Td i s t h e dew p o i n t t e m p e r a t u r e i n °K. By t h e i d e a l gas law: e/Ta=qE 2. 3 where E i s t h e i d e a l gas c o n s t a n t = 8 . 0 1 4 3 J m o l - 1 (°K) - 1 and Ta i s t h e a i r t e m p e r a t u r e i n °K. The q u a n t i t i e s r e c o r d e d a r e t h e b a r o m e t r i c p r e s s u r e i n m i l l i b a r s and t h e a i r and d e w - p o i n t t e m p e r a t u r e s i n d e g r e e s C e l s i u s . Making a p p r o p r i a t e u n i t 18 c o n v e r s i o n s , and s u b s t i t u t i n g E q u a t i o n 2.3 i n 2.2 g i v e s : e=2. 2158x106 x ( T a ) x exp (- 5 10 7. 4/Td) 2.4 A f t e r o b t a i n i n g t h e v a p o u r p r e s s u r e E q u a t i o n 2.4 was s u b s t i t u t e d i n E q u a t i o n 2. 1 t o g i v e t h e a i r d e n s i t y . 2.4 A s s u m p t i o n s The most s e n s i t i v e p a r a m e t e r s i n t h e b u l k a e r o d y n a m i c f l u x f o r m u l a e o f E q u a t i o n s 1.2 a r e t h e t r a n s f e r c o e f f i c i e n t s . F o r example, th e f o r m of the d r a g c o e f f i c i e n t has u ndergone c o n s i d e r a b l e d e b a t e . E s t i m a t e s v a r y f r c m a c o n s t a n t v a l u e (Pond e t a l . 197 1 ) , t o a s t e p f u n c t i o n o f wind s p e e d (Hossby and Montgomery 1935), t c a l i n e a r f u n c t i o n o f wind s p e e d (Smith and Banke, 19.75). T r a d i t i o n a l l y m e s c s c a l e and s y n o p t i c s c a l e dynamic s t u d i e s have employed t h e c o n s t a n t f o r m . R e c e n t e s t i m a t e s (eg. L a r g e , 1979) a t wind s p e e d s g r e a t e r t h a n 15 m/sec have i n d i c a t e d t h a t t h e l i n e a r form may be a p p r o p r i a t e . C o n s e q u e n t l y f o r t h i s s t u d y two d r a g c o e f f i c i e n t f o r m u l a t i o n s were used a c o n s t a n t form o f 1. 5x10 ~ 3 ( a f t e r Pond, 1971) and a l i n e a r form (from L a r g e , 1979) : Cd = 1.14x10-3 0< V < 10 m/sec 2.5 Cd = (0. 49 + 0.065V) x10 -3 V > 10 m/sec where V i s the wind v e l o c i t y a v e r a g e d o v e r one h o u r . The S t a n t o n and D a l t o n numbers a r e l e s s w e l l u n d e r s t o o d t h a n t h e d r a g c o e f f i c i e n t . L a r g e l i s t s i n s t r u m e n t c o n t a m i n a t i o n 19 from s e a s p r a y as a major impediment i n t h e i r measurement. Thus a v a l u e o f 1.5x10- 3 a f t e r Pond e t a l . ( 1974) was t a k e n . N o r m a l l y t h e t r a n s f e r c o e f f i c i e n t s a r e assumed t o be c a l c u l a t e d a t a r e f e r e n c e l e v e l o f 10m and u nder c o n d i t i o n s o f n e u t r a l s t a b i l i t y . N e i t h e r of t h e s e c o n d i t i o n s i s met by most of th e d a t a used i n t h i s s t u d y . The anemometer l e v e l , f o r example, a t S t a t i o n P i s a t 22m. Over most of t h e N o r t h e r n t e m p e r a t e o c e a n s t h e s e a i s g e n e r a l l y warmer t h a n t h e a i r and t h e s e a s u r f a c e s a t u r a t i o n i s g e n e r a l l y g r e a t e r t h a n t h e a b s o l u t e h u m i d i t y o f the s u r r o u n d i n g a i r i n d i c a t i n g t h a t g e n e r a l l y u n s t a b l e c o n d i t i o n s e x i s t . L a r g e ( 1 979) and T u r n e r (1973) g i v e t h e c o r r e c t i o n s r e q u i r e d to t h e t r a n s f e r c o e f f i c i e n t s t o a c c o u n t f o r n o n - n o r m a l c o n d i t i o n s . C o r r e c t i o n s a p p l i e d i n t u r b u l e n c e s t u d i e s r e q u i r e the c a l c u l a t i o n o f a f l u x R i c h a r d s o n number i n v o l v i n g t h e c o r r e l a t i o n c f t h e v e r t i c a l v e l o c i t y f l u c t u a t i o n s w i t h t h e a i r t e m p e r a t u r e f l u c t u a t i o n s and t h e a i r a b s o l u t e h u m i d i t y f l u c t u a t i o n s a t m i c r o s c a l e s a m p l i n g r a t e s . A b u l k s t a b i l i t y p a r a m e t e r c o u l d be e s t i m a t e d from t h e d a t a . L a r g e (1979) i n d i c a t e s t h a t c e r t a i n o c e a n i c c o n d i t i o n s ( e g . an a i r - s e a t e m p e r a t u r e d i f f e r e n c e o f 5.0 °C and a wind s p e e d c f 10.0 m/sec) c o u l d i n d u c e a b o u t a 105? e r r o r i n t h e t r a n s f e r c o e f f i c i e n t s due to s t a b i l i t y . A v e r a g i n g t h e f l u x e s would l e a d t o much s m a l l e r e r r o r s and b e c a u s e the s t u d y w i l l be c o n c e r n e d w i t h r a t i o s o f f l u x e s , s u c h e r r o r s w i l l f u r t h e r c a n c e l . F u r t h e r m o r e , t h e r e l a t i o n s h i p between t h e s t a b i l i t y and t h e f l u x r a t i o s a t S t a t i o n A f o r 1949 was i n v e s t i g a t e d and no c o r r e l a t i o n was e v i d e n t . Thus s t a b i l i t y c o n s i d e r a t i o n s a r e l e f t a s m i n o r e r r o r s 20 i n t h e d a t a . N o n - s t a n d a r d h e i g h t i s not. c o r r e c t e d b e c a u s e i t would i n v o l v e a d i r e c t m u l t i p l i c a t i o n f a c t o r t o t h e s t r e s s e s ( f i s s e i e t a l . 1977). S i n c e t h i s s t u d y w i l l be c o n c e r n e d w i t h r a t i o s o f s t r e s s , t h e h e i g h t c o r r e c t i o n s c a n c e l . (Indeed any c o n s t a n t f o r m u l a t i o n o f the t r a n s f e r c o e f f i c i e n t s c a n c e l s ) . Thus i t i s assumed t h a t t h e t r a n s f e r c o e f f i c i e n t s d e f i n e d i n E q u a t i o n s 1.3 and 1.4 a r e a t 10m r e f e r e n c e h e i g h t and a t n e u t r a l s t a b i l i t y . I n o r d e r t o c a l c u l a t e t h e l a t e n t h e a t f l u x i t was n e c e s s a r y to f i n d t h e s e a s u r f a c e s a t u r a t i o n and a b s o l u t e a i r h u m i d i t y d i f f e r e n c e . The a b s o l u t e a i r h u m i d i t y i s g i v e n by E q u a t i o n 2.2. The s e a s a t u r a t i o n was assumed t o be a t t h e s e a s u r f a c e t e m p e r a t u r e . Ts was used i n p l a c e o f Td t o c a l c u l a t e t h e s e a s u r f a c e h u m i d i t y . T h i s v a l u e was t h e n m u l t i p l i e d by 0.98 t o a c c o u n t f o r t h e d e p r e s s i o n o f t h e s a t u r a t i o n p o i n t due t o t h e p r e s e n c e o f s a l t . T h r o u g h o u t t h e t h e s i s , t h e a i r - s e a h u m i d i t y d i f f e r e n c e s and not t h e c o n s t i t u e n t s e a s u r f a c e and dew p o i n t t e m p e r a t u r e s were a v e r a g e d . F o r u s u a l c l i m a t i c c a l c u l a t i o n s , however, a v e r a g e d h u m i d i t y d i f f e r e n c e s a r e seldom a v a i l a b l e . R a t h e r , t h e n o r m a l i n f o r m a t i o n i s t h e a v e r a g e d c o n s t i t u e n t v a r i a b l e s . C o n s e q u e n t l y a s y s t e m a t i c e r r o r i s i n d u c e d i n most c a l c u l a t i o n s . I f we c o n s i d e r a s i n g l e e s t i m a t e o f q t o be based upon a mean t e m p e r a t u r e f and a d e v i a t i o n from t h e mean T* t h e n (see E q u a t i o n 2 . 2 ) : q=Clexp (C2/ (T+T *) ) 21 Assuming t h a t t h e mean t e m p e r a t u r e i s much g r e a t e r t h a n t h e f l u c t u a t i o n , t h e e x p o n e n t i a l c a n t h e n be r e - e x p r e s s e d as ; A t y p i c a l r a t i o o f Y*~z/fz f o r t h e dew p o i n t t e m p e r a t u r e s was f o u n d to be 1.2x10-*. A l l o w i n g a f l u c t u a t i o n o f 5 s t a n d a r d d e v i a t i o n s and a v a l u e o f C2/T = -18.0 ( i e . T-273 °K) , t h e t e r m s above i n t h e e x p o n e n t i a l a r e c o r r e c t t o 0 ( 1 0 - 2 ) . E x p a n d i n g E g u a t i o n 2.7 i n a T a y l o r s e r i e s and k e e p i n g a l l terms o f O(>10~ 2) g i v e s : whicn oecomes: 2. 7 2. 8 A v e r a g i n g b o t h s i d e s o f E q u a t i o n 2.8 and r e c o g n i z i n g t h a t C l e x p ( C 2 / f ) i s t h e a b s o l u t e h u m i d i t y d e t e r m i n e d from t h e a v e r a g e t e m p e r a t u r e (g (T) ) the n : 22 I -If C-L z 2.9 6 T- _ 1 + -U / C ^ I f t h e d i s t r i b u t i o n i s r e a s o n a b l y G a u s s i a n then: a. -n odd =0.0 r . T R * = 3x ("T~r2) 2 The t e r m s i n T ' * / l * a r e a l l 0(<10-3) and E g u a t i o n 2.9 r e d u c e s t o : 2. 10 T a k i n g (C2/T) = -18.0 and T ^ / T 2 = 1.2x10-* (a t y p i c a l v a l u e ) we see t h a t : q = q (T) (1+0.02) S i n c e t h e maximum a v e r a g i n g p e r i o d i s 28 d a y s , an upper l i m i t on the s y s t e m a t i c e r r o r i n d u c e d i n a v e r a g i n g t h e h u m i d i t i e s o v e r a v e r a g i n g t h e dew p o i n t t e m p e r a t u r e s i s a p p r o x i m a t e l y 2.0%. F u r t h e r m o r e , t h e T , 2 / T 2 r a t i o f o r t h e s e a s u r f a c e t e m p e r a t u r e s was a b o u t one h a l f t h a t o f t h e dew p o i n t t e m p e r a t u r e s . T h i s g i v e s a s y s t e m a t i c s e a s u r f a c e h u m i d i t y b i a s o f a b o u t 1.0$. S i n c e t h e two b i a s e s a r e s u b t r a c t e d i n t h e l a t e n t h e a t f l u x , t h i s g i v e s a n e g a t i v e s y s t e m a t i c a i r - s e a h u m i d i t y d i f f e r e n c e b i a s o f o n l y LOSE. T h i s was c o n s i d e r e d n e g l i g i b l e i n c o m p a r i s o n w i t h t h e p r o b a b l e s a m p l i n g e r r o r s i n t h e d a t a . 23 2.5 A n a l y s i s And D e f i n i t i o n s B e c a u s e each s h i p c o n t a i n e d a v a r y i n g number o f y e a r s c f d a t a , t h e y were r e c o n s t r u c t e d i n t o y e a r l y b l o c k s o f 29 12 o b s e r v a t i o n s e a c h . The 2912 f i g u r e was c h o s e n b e c a u s e i t was e v e n l y d i v i s i b l e by m u l t i p l e s c f 2, 4, and 13 a l l o w i n g s e m i -a n n u a l and l u n a r m o n t h l y d i v i s i o n s o f t h e y e a r . The e i g h t (or 16 f o r a l e a p year) o b s e r v a t i o n s a t t h e end o f e a c h y e a r were o m i t t e d from c a l c u l a t i o n s . T h i s i s u n l i k e l y t o s i g n i f i c a n t l y i n f l u e n c e t h e f i n a l r e s u l t s . From t h e raw t h r e e - h o u r l y d a t a s e t , t h e t h r e e - h o u r l y d e n s i t i e s , a b s o l u t e h u m i d i t i e s , s t r e s s e s and h e a t f l u x e s were c a l c u l a t e d . The sampled and c a l c u l a t e d v a r i a t e s were then a v e r a g e d i n s e t s c f 2, 4, 8, 16, 32, 56, 112, and 224 r e a d i n g s , c o r r e s p o n d i n g t o a v e r a g i n g e v e r 0.25, 0.5, 1.0, 2.0, 4.0, 7.0, 14.0, and 28.0 d a y s . Thus f o r a one y e a r s a m p l e , the s e t o f v a r i a t e s a v e r a g e d e v e r 224 t h r e e - h o u r l y r e a d i n g s c o n t a i n s 29 12/224=13 members. The l e n g t h o f t i m e o v e r w h i c h t h e t h r e e -n o u r l y d a t a s e t was a v e r a g e d w i l l be r e f e r r e d t o as t h e a v e r a g i n g p e r i o d , w i l l be d e n o t e d t y t h e c a p i t a l l e t t e r L, and w i l l be e x p r e s s e d i n d a y s . Thus a v e r a g i n g 224 t h r e e - h o u r l y measurements y i e l d s an a v e r a g i n g p e r i o d o f L=28.0 d a y s . The f l u x e s were t h e n r e c a l c u l a t e d u s i n g t h e a v e r a g e d c o n s t i t u e n t d a t a . The winds and f l u x e s c a l c u l a t e d i n t h i s manner w i l l r e f e r r e d t o as t h e v e c t o r a v e r a g e d o r VA winds and f l u x e s . The VA f l u x e s were t h e n compared t o t h e d i r e c t l y a v e r a g e d f l u x e s f r o m the o r i g i n a l t h r e e - h o u r l y t i m e s e r i e s . The d i r e c t l y a v e r a g e d f l u x e s w i l l be r e f e r r e d t o a s t h e t h r e e - h o u r l y a v e r a g e d o r 3H f l u x e s . 24 An example u s i n g the s t r e s s components s h o u l d c l a r i f y t h e s e d e f i n i t i o n s . D e f i n i n g the p o s i t i v e x and y d i r e c t i o n s a s e a s t and n o r t h r e s p e c t i v e l y , t h e 3H s t r e s s v e c t o r components a v e r a g e d o v e r L days a r e : 2. 11 where I=L days x 8 measurements/day, u L and vL" a r e t h e c o n s t i t u e n t wind components from t h e raw t h r e e - h o u r l y s e r i e s , jDc a r e t h e t h r e e - h o u r l y a i r d e n s i t i e s , Cd i a r e t h e t h r e e h o u r l y d r a g c o e f f i c i e n t s , and Tx^ and Ty^ a r e t h e 3H x and y s t r e s s c o mponents. The VA wind v e c t o r s o v e r t h e same a v e r a g i n g p e r i o d are; (UJ , v : ) = ( j _ 2 » I H^i ) 2 ' 1 2 where uj and v^' a r e t h e VA wind components a v e r a g e d o v e r L days. A VA s t r e s s c a n t h e n be c a l c u l a t e d from t h e VA winds by : •Iv • * . r , . i •>• . , \ V v t r . . j 2 . 13 i s t h e d e n s i t y a v e r a g e d o v e r L d a y s , Cd^' i s t h e d r a g c o e f f i c i e n t b a s e d on t h e VA wind and Tx^- and Tyj a r e t h e VA s t r e s s component e s t i m a t e s . T h r o u g h o u t t h e t e x t , t h e s u b s c r i p t i w i l l r e f e r t o a member o f t h e raw t h r e e - h o u r l y d a t a s e t and t h e s u b s c r i p t j w i l l r e f e r to a member o f t h e d a t a s e t o b t a i n e d from a v e r a g i n g t h e t h r e e -2 5 h o u r l y s e t i n L day g r o u p s . The 3H f l u x e s w i l l a p p e a r w i t h o u t p r i m e s and t h e VA f l u x e s w i l l a p p e a r w i t h p r i m e s . The a n a l y s i s o f t h e d i f f e r e n c e s between t h e VA and 3H f l u x e s r e q u i r e s t h r e e d i s t i n c t s t e p s . F i r s t , t h e raw VA and 3H v a r i a t e s must be e v a l u a t e d s t a t i s t i c a l l y t o d e t e r m i n e t h e i n h e r e n t d i f f e r e n c e s between t h e two e s t i m a t e s . Next, s i n c e t h e 3H v a r i a t e i s t h e more a c c u r a t e f l u x e s t i m a t e , t r a n s f o r m a t i o n s must ne f c u n d f o r the VA v a r i a t e so t h a t i t more c l o s e l y a p p r o x i m a t e s t h e 3H v a r i a t e . Once a s u i t a b l e t r a n s f o r m a t i o n h a s been f o u n d , i t must be a p p l i e d t o t h e VA v a r i a t e and t h e s t a t i s t i c s r e - e v a l u a t e d . Thus, t h e a n a l y s i s i n v o l v e s two d i s t i n c t c a l c u l a t i o n s — c o m p u t i n g t h e s t a t i s t i c a l r e l a t i o n s h i p between t h e VA and 3H v a r i a t e s and c o m p u t i n g the t r a n s f o r m a t i o n i t s e l f . L e t X j and X ' j be members o f t h e 3H and VA f l u x v a r i a t e s r e s p e c t i v e l y f o r an a v e r a g i n g p e r i o d L. The X ' j may o r may n o t i n c l u d e t h e t r a n s f o r m a t i o n s t e p and Xj and X ' j d e f i n e g e n e r a l l y t h e x c r y components o f s t r e s s o r t h e l a t e n t o r s e n s i b l e h e a t f l u x e s . The l o n g - t e r m means (T,XT) ar e d e f i n e d a s : wnere J i s t h e t o t a l number o f a v e r a g i n g s a v a i l a b l e i n t h e r e c o r d f o r a g i v e n a v e r a g i n g p e r i o d L. S i m i l a r l y t h e l o n g term 2 . 1 4 v a r i a n c e s , and <?~t a r e d e f i n e d a s : 2 . 1 5 26 The r e l a t i o n s h i p between d e f i n e d i n t e r m s o f f o u r c o l l e c t i v e l y be c a l l e d t h e e f f e c t i v e n e s s o f d e t e r m i n i n g by: Ax - \ Y - Sc\ t h e 3H and VA v a r i a t e s i s t h e n s t a t i s t i c a l q u a n t i t i e s w h i c h w i l l t e s t f u n c t i o n s . F i r s t , t h e th e l o n g t e r m mean f l u x i s d e f i n e d 2. 16 T h i s w i l l be r e f e r r e d t o as t h e d i f f e r e n c e mean (or DM). A measure o f t h e c o n s e r v a t i o n o f t h e t o t a l v a r i a n c e , i n t h e t r a n s f o r m a t i o n , i s g i v e n by: 2.17 and w i l l be r e f e r r e d t o as the d i f f e r e n c e v a r i a n c e (DV). The e f f e c t i v e n e s s o f t h e t r a n s f o r m a t i o n on a p c i n t - b y - p o i n t b a s i s i s g i v e n by t h e r e s i d u a l v a r i a n c e ( E V ) , d e f i n e d a s : 3"* 2. 18 F i n a l l y , t h e c o r r e l a t i o n c o e f f i c i e n t d e t e r m i n e s t h e s t a t i s t i c a l d e pendence o f one v a r i a t e on t h e o t h e r and i s d e f i n e d by: 27 Assuming t h a t t h e a t m o s p h e r e has a c l i m a t o l o g i c a l s t e a d y s t a t e , t h e DMs i n d i c a t e whether t h e c l i m a t o l o g i c a l mean o f t h e VA v a r i a t e a p p r o a c h e s t h a t o f t h e 3H v a r i a t e . F o r s p e c t r a l s t u d i e s s u c h as W i l l e t r a n d ( 1 9 7 8 ) b o t h t h e t o t a l v a r i a n c e and t h e f r e q u e n c y - b y - f r e q u e n c y power s p e c t r a l d e n s i t i e s f o r t h e two v a r i a t e s s h o u l d match. The f o r m e r c o n d i t i o n i s d e t e r m i n e d by tne DVs; t h e l a t t e r c o n d i t i o n w i l l be i n v e s t i g a t e d i n C h a p t e r V. Ihe fiVs d e t e r m i n e t h e r e l a t i o n s h i p between t h e VA and 3H v a r i a t e s on a p c i n t - b y - p c i n t b a s i s ( i e . On t h e t i m e s c a l e s o f the a v e r a g i n g p e r i o d i t s e l f ) . F i n a l l y , t h e c o r r e l a t i o n c o e r f i c i e n t s d e t e r m i n e s t a t i s t i c a l l y t h e a b i l i t y o f one v a r i a t e t o i n f e r t h e o t h e r . I t i s q u i t e c o n c e i v a b l e , f o r e x a m p l e , to f i n d a s c a l e f a c t o r which w i l l e f f e c t i v e l y r e d u c e t h e DMs, DVs, and Ms, w h i l e l e a v i n g t h e c o r r e l a t i o n c o e f f i c i e n t s unchanged. In e DVs, EVs and c o r r e l a t i o n c o e f f i c i e n t s have been n o r m a l i z e d by t h e 3tf v a r i a n c e f o r e a s e o f i n t e r - c o m p a r i s o n between s h i p s . T h i s e f f e c t i v e l y removes t h e h e i g h t c o r r e c t i o n ( d i s c u s s e d i n S e c t i o n 2.4) from t h e s t a t i s t i c s s i n c e i t would a p p e a r t o t h e same power i n t h e n u m e r a t o r and d e n o m i n a t o r i n a l l t h r e e c a s e s . The DMs have n o t been n o r m a l i z e d b e c a u s e an a p p r o p r i a t e n o r m a l i z i n g f a c t o r would be t h e mean 3H f l u x v a l u e . At c e r t a i n l o c a t i o n s , however, i t a p p r o a c h e d 0 dPa f o r t h e s t r e s s ( D e c i P a s c a l s a r e used f o r u n i t s and a r e n u m e r i c a l l y e q u i v a l e n t t c dynes/cm 2) and 0 Watts/m 2 f o r t h e h e a t f l u x e s . 28 Tne a b s o l u t e v a l u e i s used i n t h e DM c a l c u l a t i o n b e c a u s e we a r e c o n c e r n e d t h a t t h e c l i m a t o l o g i c a l 3H v a l u e be e s t i m a t e d i r r e s p e c t i v e o f s i g n . R e c e n t i n f o r m a t i o n ( L a r g e , p e r s o n a l c o m m u n i c a t i o n , 1980) i n d i c a t e s t h a t t h e S t a n t o n and D a l t o n numbers used i n t h i s s t u d y (1.5x10" 3) a r e a b o u t 20.0% h i g h , f u r t h e r m o r e , t h e n c n - s t a n d a r d h e i g h t and t h e s t a b i l i t y a s s u m p t i o n s o u t l i n e d i n S e c t i o n 2.4 may i n d u c e a f u r t h e r 20.0% e r r o r i n t h e d a t a . Thus, when a DM or a mean 3H f l u x i s q u o t e d , the v a l u e s g i v e n may be b i a s e d h i g h . A d i s c u s s i o n o f t h e VA t r a n s f o r m a t i o n p r o c e d u r e s f o r m s an i n t e g r a l p a r t c f t h e t e x t and w i l l be d i s c u s s e d i n more d e t a i l l a t e r . In a l l c a s e s , however, t h e t e s t f u n c t i o n s d e f i n e d i n E q u a t i o n s 2.16 t o 2.19 w i l l be used t o e v a l u a t e t h e e f f e c t i v e n e s s o f the t r a n s f o r m a t i o n s . 29 CHAPTER I I I MOMENTUM FLUXES The p r o c e s s e d d a t a base o u t l i n e d i n C h a p t e r I I was a n a l y s e d to d e t e r m i n e t h e e x t e n t o f t h e e x p e c t e d u n d e r e s t i m a t i o n o f s t r e s s when u s i n g w i nds a v e r a g e d o v e r t i m e s l o n g e r t h a n one h o u r . The r e d u c t i o n s a r e s t u d i e d b o t h f o r c a l c u l a t i o n s o f c l i m a t o l o g i c a l v a l u e s c f l o n g term n e t s t r e s s e s , (based on wind d a t a a v e r a g e d o v e r a month o r more) and f o r c a l c u l a t i n g a c t u a l t i m e h i s t o r y v a l u e s f o r which d a t a might be a v e r a g e d t o a b o u t one month. C l i m a t o l c g i c a l s t r e s s e s a r e used as an i n p u t i n n u m e r i c a l models a t t e m p t i n g t o c a l c u l a t e t h e s t e a d y s t a t e o c e a n i c c i r c u l a t i o n . The t e m p o r a l v a r i a t i o n s a r e r e g u i r e d f o r s u c h s t u d i e s as t h a t by W i l l e b r a n d ( 1 9 7 8 ) f o r c a l c u l a t i o n s o f t h e s t r e s s s p e c t r a u s i n g v e c t o r a v e r a g e d winds d e r i v e d from p r e s s u r e maps o r f o r models a t t e m p t i n g t o examine t h e e f f e c t s o f t i m e -d e p e n d e n t wind s t r e s s f o r c i n g . The b u l k a e r o d y n a m i c f o r m u l a e f o r the c a l c u l a t i o n o f t h e s t r e s s e s a r e g i v e n i n E q u a t i o n s 1.2(a) and ( b ) . 3.1 The V e c t o r A v e r a g e d 3H And VA S t r e s s The 3H s t r e s s p r o v i d e s an e s t i m a t e o f t h e ' t r u e ' s t r e s s and w i l l be examined f i r s t . The a n n u a l c y c l e , i n t e r m s o f m o n t h l y 3H means and s t a n d a r d d e v i a t i o n s w i l l be examined u s i n g 224 p o i n t s p e r mcnth g i v i n q 13 l u n a r months p e r y e a r . Due t o t h e enormous amount o f d a t a a n a l y s e d , n o t a l l o f t h e r e s u l t s c a n be p r e s e n t e d i n t h i s t h e s i s . A l l s h i p s e x h i b i t e d a w i n t e r maximum and summer minimum b o t h i n t h e a v e r a g e s t r e s s and i n the s t r e s s v a r i a b i l i t y o f which W e a t h e r s t a t i o n C i s an 30 e x a m p l e . T h i s p a t t e r n i s i n d i c a t i v e o f a w i n t e r s t o r m s e a s o n t y p i c a l o f t h e n o r t h e r n t e m p e r a t e l a t i t u d e s . A p l o t o f t h e s t r e s s components f o r w e a t h e r s t a t i o n C a p p e a r s i n F i g u r e s 4(a) t h r o u g h ( d ) . The e r r o r b a r s a r e + 1 s t a n d a r d d e v i a t i o n a b o u t t h e mean. I t i s r e a d i l y a p p a r e n t t h a t the s t a n d a r d d e v i a t i o n s may be as much as one o r d e r of m a g n i t u d e l a r g e r t h a n t h e mean s t r e s s v a l u e (and t h u s t h e v a r i a n c e t o mean s q u a r e s r a t i o c f o r d e r 100) i n e i t h e r component f o r any g i v e n y e a r . Over t h e whole r e c o r d , t h e x component mean v a l u e i s p o s i t i v e w i t h an o v e r a l l a v e r a g e v a l u e o f a b o u t 1.0 dPa (wh i c h i s n u m e r i c a l l y e q u i v a l e n t t o 1.0 dynes cm- 2) w h i l e t h e y component a v e r a g e v a l u e i s about 0.20 dPa and t h e x component s t a n d a r d d e v i a t i o n i s ab o u t 1.25 t i m e s g r e a t e r t h a n t h e y component s t a n d a r d d e v i a t i o n . Ihe maximum d i f f e r e n c e i n s t a n d a r d d e v i a t i o n between y e a r s a p p e a r s i n t h e x component between 1952 and 1959 where t h e r a t i o i s a b o u t 2. F i g u r e s 4(c) and (d) d e m o n s t r a t e t h e a n n u a l c y c l e i n v a r i a b i l i t y ; t h e r a t i o o f s t a n d a r d d e v i a t i o n s between month 1 ( J a n u a r y ) and month 7 ( J u l y ) i s a b o u t 3. The s t a n d a r d d e v i a t i o n o f t h e monthly means was a l s o c a l c u l a t e d and a p p e a r s i n F i g u r e 5 t o show t h e i n t e r - a n n u a l v a r i a b i l i t y o f t h e monthly s t r e s s mean. The a n n u a l c y c l e o f t h e mean s t r e s s i s e v i d e n t p a r t i c u l a r l y i n t h e x component which v a r i e s from a b c u t 1.5 dPa i n t h e w i n t e r t o ab o u t 0.5 dPa i n t h e summer. An a n n u a l c y c l e i n t h e mean y s t r e s s i s n o t e v i d e n t . A c o m p a r i s o n between t h e s t a n d a r d d e v i a t i o n s o f F i g u r e s 5 and 4(c) and (d) i n d i c a t e s t h a t t h e y have been r e d u c e d by a f a c t o r o f two t o t h r e e , n o t t h e f a c t o r o f 15 one might e x p e c t i f t h e 224 31 WEATHERSHIP C WEATHERSHIP C TflUX CONSTANT TAUX LINEAR 56.0 60 0 TERR 64.0 tn CTir.' TAUy CONSTANT T A U y LINEAR 48.0 52.0 56.0 60 0 TERR F i g u r e 4(a) F i g u r e 4 (b) WEATHERSHIP C cr TAUX CONSTANT TAUX LINEAR 2 3 4 5 6 7 MONTH 9 10 11 12 13 WEATHERSHIP C T A U y CONSTANT TAUy LINEAR 2 3 4 5 6 7 MONTH 9 10 11 12 13 F i g u r e 4 ( c) F i g u r e 4 (d) F i g u r e 4. X and Y components o f t h e 3H s t r e s s a t W e a t h e r s t a t i o n C as a f u n c t i o n o f y e a r and month. The s c l i d l i n e shows ± 1 s t a n d a r d d e v i a t i o n u s i n g the c o n s t a n t d r a g c o e f f i c i e n t and t h e dashed l i n e ± 1 s t a n d a r d d e v i a t i o n u s i n g t h e l i n e a r d r a g c o e f f i c i e n t . Means a r e i n d i c a t e d oy h o r i z o n t a l b a r s . r h r e e - h o u r l y v a l u e s on which e a c h m o n t h l y mean i s b a s e d were s t a t i s t i c a l l y i n d e p e n d e n t . The r e s u l t s u g g e s t s t h a t measurements a b o u t 3 t c 7 days a p a r t a r e i n d e p e n d e n t whicn i s 32 W E R T H E R S H I P C TflUX CONSTANT IflUX. LINEAR i Ii Ii 2 3 4 5 6 7 MONTH 9 10 11 12 13 F i g u r e 5 (a) WERTHERSHIP C TAU Y CONSTANT TRU Y LINEAR 1 ° CCfM " (_> CO cr Q_ " l_l UJo 1 2 3 4 5 6 7 MONTH 9 10 11 12 13 F i g u r e 5 (b) F i g u r e 5. The 3H s t r e s s as a f u n c t i o n c f month a t S t a t i o n C. The s o l i d l i n e i s ± 1 s t a n d a r d d e v i a t i o n o f t h e m o n t h l y means u s i n g t h e c o n s t a n t d r a g c o e f f i c i e n t and t h e d a s h e d l i n e + 1 s t a n d a r d d e v i a t i o n o f t h e m o n t h l y means u s i n g t h e l i n e a r d r a g c o e f f i c i e n t . The means a r e i n d i c a t e d by t h e h o r i z o n t a l b a r s . s i m i l a r t o t h e t i m e s c a l e s o f s t o r m s i n t h e m i d - l a t i t u d e s . T a b l e V g i v e s t h e a v e r a g e s and s t a n d a r d d e v i a t i o n s o f t h e e n t i r e r e c o r d f o r a l l t h e s t a t i o n s e x a m i n e d . Note t h a t S t a t i o n 33 The x and y components o f d e v i a t i o n s f o r a l l s h i p s and 3H s t r e s s means and s t a n d a r d y e a r s e x a m i n e d . The s t a n d a r d d e v i a t i o n = (Tk2-fT^2)i/2 where k d e n o t e s t h e x o r y component. A l l measurements a r e i n dPa. i j SHIP j. A B C D E I J K M N P CONSTANT ER AG COEFFICIENT TX I | LINEAR DEAG COEFFICIENT + + +  Tx I r x | l y I (Ty — J Ty -4- +-3.21| -3.38|-3. 551 3.39| 1.81| 3. 22| 2. 96| 2.43|-2.30| .80C|-2.69| I .074 .438 . 902 1.0 1 .478 .497 .925 . 6 14 . 338 -.311 . 805 2. 47 | 2. 5 6 | 2. 62 | 2. 43 | 1. 48 | 2. 56 j 2. 33 J 1. 98 J 1. 93 | .845 |-1.99| I -. 035 -.298 . 161 . 2C4 . 199 . 544 .492 •. 045 .065 •. 126 . 330 2. 35 2. 36 2. 17 2. 24 1. 50 2.25 2.07 1.81 2.21 . 847 1.71 . 128 .473 1.06 1. 18 .510 .575 1.03 . 673 .394 .238 . 9 10 ,029 .375 , 1 56 .197 .170 ,591 .5 13 .038 ,058 .09 1 ,304 2. 97 3.02 2. 82 2.88 1.72 2.84 2. 51 1.81 2. 70 . 825 2. 19 N v a l u e s o f t h e s t a n d a r d d e v i a t i o n a r e 1/3 t o 1/2 of t h o s e o f the o t h e r w e a t h e r s h i p s (or the v a r i a n c e i s 1/9 t o 1/4 o f t h e o t h e r s ) . I n F i g u r e 6, the 3H s t r e s s components a r e p l o t t e d v e r s u s the VA s t r e s s components f o r t h e c o n s t a n t d r a g c o e f f i c i e n t and L=28.0 d a y s f o r S t a t i o n A. Ihe d i a g o n a l s o l i d l i n e i n d i c a t e s t h e e q u i v a l e n c e l i n e between t h e 3H and VA s t r e s s . R a t h e r t h a n s c a t t e r i n g a r o u n d t h i s l i n e , t h e a b s o l u t e v a l u e o f t h e VA s t r e s s i s c o n s i s t e n t l y l e s s t h a n t h a t o f t h e 3H s t r e s s a l t h o u g h t h e y a r e f a i r l y w e l l c o r r e l a t e d . F i g u r e 7, shows e s t i m a t e s o f t h e f o u r t e s t f u n c t i o n s d e f i n e d i n E g u a t i o n s 2.16 - 2.19 f o r t h e x component, c o n s t a n t d r a g c o e f f i c i e n t when no c o r r e c t i o n t o t h e VA s t r e s s h a s been 34 X COMPONENT Y COMPONENT -2.0 2.0 6.0 10.0 -2.0 2.0 6.0 10.0 VR STRESS IN DPfl Vfl STRESS IN DPR F i g u r e 6. 3H v e r s u s VA s t r e s s f o r t h e c o n s t a n t d r a g c o e f f i c i e n t a t S t a t i o n A, L=28.0 days w i t h no c o r r e c t i o n s a p p l i e d . a p p l i e d . Ihe a c t u a l v a l u e s f o r b o t h components and d r a g c o e f f i c i e n t s a r e g i v e n i n A p p e n d i x B . Symbols t h a t w i l l be used i n t h e f i g u r e s t h r o u g h o u t the t e x t t o i n d i c a t e s h i p a r e g i v e n i n T a b l e V I . In F i g u r e 7 ( a ) , the d i f f e r e n c e means a r e s m a l l f o r s h o r t a v e r a g i n g p e r i o d s i n d i c a t i n g t h a t t h e VA s t r e s s c l o s e l y a p p r o x i m a t e s t h e l o n g term 3H mean. As t h e a v e r a g i n g p e r i o d i n c r e a s e s , t h e VA e s t i m a t e s become i n c r e a s i n g l y i n a c c u r a t e and the e r r o r s a p p e a r t o i n c r e a s e a p p r o x i m a t e l y e x p o n e n t i a l l y w i t h a v e r a g i n g p e r i o d . There i s a d i s t i n c t o r d e r i n g i n t h e DMs by s h i p t h r o u g h a l l a v e r a g i n g p e r i o d s . A c o m p a r i s o n o f A p p e n d i x B and T a b l e V i n d i c a t e s t h a t t h e o r d e r i n g may be d e p e n d e n t upon t h e mean 3H s t r e s s component v a l u e a v e r a g e d o v e r t h e e n t i r e 35 X COMPONENT CO CO z . UJ UJ CJ UJ a 0.1 1.0 10.0 AVERAGING PERIOD IN DAYS 100.0 CJ a z o ' - i cr. cr UJ cj\r UJ U_ -u_ X COMPONENT 0 1 ioo innn AVERRGING PERIOD IN DAYS f i g u r e 7(a) DMs i n dPa. F i g u r e 7(b) L J ^ C L i — i cr CE H _lr\j Q CO . UJ cr 0.1 X COMPONENT 1.0 10.0 AVERRGING PERIOD IN DAYS 100.0 UJ i—'CO C_jcn • — 1 0 • u_ CJ cr C J ° X COMPONENT 0.1 1.0 10.0 100 0 AVERAGING PERIOD IN DAYS F i g u r e 7(c) F i g u r e 7 (d) F i g u r e 7. Example of t h e c o m p o s i t e t e s t f u n c t i o n s f o r a l l s h i p s , x component, c o n s t a n t d r a g c o e f f i c i e n t w i t h no c o r r e c t i o n a p p l i e d . r e c o r d . Those s h i p s w i t h l a r g e r i n i t i a l 3H v a l u e s a p p e a r t o nave l a r g e d i f f e r e n c e mean s t r e s s e s . The d i f f e r e n c e v a r i a n c e s a p p ear i n F i g u r e 7 ( D ) . F o r 36 TABLE VI Symbols used i n t h e f i g u r e s t h r o u g h o u t t h e t e x t . r T 1 i SHIP|SYMBOL | f . — + -I a 1 a 1 B j 0 1 c | 1 D 1 + 1 E | 1 I 1 1 J 1 1 K | i M | z 1 N | Y 1 P 1 I i I Note: When i t i s i n d i c a t e d t h a t S t a t i o n N i s e x c l u d e d f r o m t h e f i g u r e , S t a t i o n F i s i n d i c a t e d by Y r e f e r e n c e , t h e 3H s t r e s s v a r i a n c e s f o r a l l a v e r a g i n g p e r i o d s a p p e a r i n T a b l e V I I . A g a i n t h e VA v a r i a n c e c l o s e l y a p p r o x i m a t e s the 3ti v a r i a n c e f o r s m a l l a v e r a g i n g p e r i o d s . By L=1.0 d a y s , however, t h e VA v a r i a n c e u n d e r e s t i m a t e s t h e 3H v a r i a n c e by a b o u t 20/4. At L=28 d a y s , t h e v a r i a n c e r e d u c t i o n i s 60 t o 80%. The s h i p - t o - s h i p DVs a r e more t i g h t l y g r o u p e d t h a n t h e d i f f e r e n c e means. The r e l a t i v e p o s i t i o n o f each s h i p a p p e a r s t o s h i f t as the a v e r a g i n g p e r i o d i n c r e a s e s . The r e s i d u a l v a r i a n c e s a p pear i n F i g u r e 7 ( c ) . At L=0.25 d a y s , t h e r e s i d u a l s a r e l e s s t h a n 1.0% o f t h e t o t a l 3H v a r i a n c e . By L=4.Q d a y s t h i s r i s e s t o a mean o f a b o u t 10% and by 28 days t h e v a l u e i s between 20 and 40% o f t h e t o t a l 3H v a r i a n c e . O v e r a l l , t h e c o r r e l a t i o n c o e f f i c i e n t s shown i n F i g u r e 7(d) a r e q u i t e h i g h . At L=0.25 d a y s , a l l v a l u e s a r e g r e a t e r t h a n 0.99 w n i l e a t L=28.0 days a l l v a l u e s l i e between 0.93 and 0.97. A l t h o u g h o n l y t h e x component, c o n s t a n t d r a g c o e f f i c i e n t a p p e a r s h e r e , t h e r a n g e of v a l u e s f o r t h e y component c o n s t a n t 37 TABLE V I I The s t r e s s v a r i a n c e s f c r b o t h d r a g c o e f f i c i e n t s a s a f u n c t i o n o f a v e r a g i n g p e r i o d . The columns r e f e r t o t h e a v e r a g i n g l e n g t h i n da y s and t h e v a r i a n c e s a r e i n (dPa) 2 . X COMPONENT CONSTANT D.C. 7.0 j +-1.725| 1.975J 2.093| 1.859 | 0. 886 | 2.244| 1.990 | 1. 54 8 j 1.133j 0.33 1 | 1.318) SHIP | 0.25 j 0.50 | 1.0 | 2.0 | 4.0 | -+-14.0 H-j 28. 0 A i 5.535| 5.000| a. 169| 3. 160| B I 6. 388 | 5.829| 4. 924 | 3. 759| C j 6. 4 58 | 5. 825| 4. 843| 3. 685| D J 5. 53 11 4. 973j 4. 0941 3. 135| E J 2. 203 | 2.0301 1. 779| 1. 440 | I | 5. 849 | 5.347) 4. 626j 3. 739| J i 4. 9 19j 4. 514 | 3. 9 1S| 3. 195| K | 3. 556| 3.3 17 | 2. 972J 2. 533| M | 3. 200 | 2.9221 2. 515J 2. 0101 N j 0. 706 j 0.658| 0. 598| 0. 513( P I 4.579| 4.093| 349| 2. 508| 2.288| 2.703| 2.6481 2.34 9 J 1. 144| 2.8891 2.487| 2.044| 1.495 | 0. 406 | 1.788J 1. 165 1 .325 1.446 1.324 0. 662 1.4 94 1. 309 0. 948 0.704 0. 220 0.870 0.705 0. 902 1.0 18 0. 862 0. 50 1 0.907 0.914 0. 585 0.447 0. 144 0. 525 S H I P ! 0.25 | + 0. 50 1 4.692 + 4. 806 3. 726 3.835 1. 838 4. 109 3. 442 2. 50 1 3. 632 0. 649 4.998 Y COMPONENT CONSTANT B.C. + + + 4. 1.0 | 2.0 | 4.0 | 7.0 1 14. 0 -+ I 28.0 A B C D E I J K M N P 5.084 5. 278 4. 24 1 4.462 2. 054 4. 503 3. 843 2. 821 3. 932 0.710 5. 5S7 4. 4, 3. 2. 1. 3. 2. 2. 3. 0. 4. 084| 021J 000 | 964 i 4981 5291 8571 0411 157J 570J 103| 3. 260 2. 925 2. 150 1. 999 1. 086 2. 788 2. 172 1. 575 2. 546 0. 465 3. 057 2.44 1 1.900 1.425 1. 196 0. 684 2.065 1.572 1. 162 1. 837 0. 340 2. 141 1.801 1. 359 1.032 0.771 0. 472 1.582 1. 156 0. 850 1.385 0.261 1.575 1. 174 0.824 0.644 0.468 0. 285 1.010 0.730 0.545 0.826 0. 180 1 .002 0. 772 0. 474 0. 406 0. 266 0. 159 0.664 0.477 0. 304 0. 494 0.121 0.661 S H I p | 0.25 | 0.50 | A j 7. 7621 6.84 1 B 1 9. 090| 8. 132 C | 10- 001 8. 858 D | 9. 106| 8.0 10 E | 2. 704| 2.440 I | 7. 896| 7.078 J 1 6.571| 5.912 K j 4. 4291 4. 036 M J 3. 676| 3.305 N 1 0. 536| 0.491 £ 1 6.128| 5.372 COMPONENT 0 | 2. 0 LINEAB D + 4 I 4.0 | 2.871 3.478 3. 647 3. 427 1. 257 3. 575 2.986 2. 254 1.579 0.285 2. 1 50 ,C. i 7.0 | 4 2. 1 17 2. 517 2.856 2. 715 0. 960 2. 775 2.378 1.679 1. 193 0.232 1.53 8 -4 I 28.0 1. 14.0 -4- -4-5. 6. 7. 6. 2. 5. 4. "3 ~» . 2. 0. 4. 514 684 206 346 077 973 993 530 773 439 23 1 4. 039 4. 982 5. 283 4. 708 1. 625 4. 708 3. 949 2.891 2. 165 0. 369 3. 089 1 .424 1.648 1. 958 1.966 0.715 1.816 1 .547 1 .025 0. 739 0. 150 1.012 0. 862 1. 102 1.381 1. 304 0.538 1.110 1.077 0. 625 0. 475 0.097 0. 6 15 -4- Y COMPONENT LINEAR D.C. + . 50 i I SHIP | 0.25 | 0. .0 A | 6. 768 | 6. 138| 5. 220| 4.048| 2.9611 B | 7. 183 | 6. 4 22| 5.239| 3. 7 16| 2. 349| C I 5.880| 5. 039| 3.9101 2. 75 3 | 1. 785 J D | 6.093| 5. 074| 3.754| 2.4821 1.462| E | 2. 20 1| 1. 93 11 1.5 14| 1. 075| 0.661| I J 5.848] 5. 221 | 4. 346J 3. 35 11 2.415| J | 4.667| 4. 074 j 3. 293| 2. 44 21 1.7281 K 1 3. 344| 2. 889| 2.253| 1.691) 1.211| M j 4. 449| 4. 0 17| 3.394| 2.671| 1.8681 N j 0.568| 0. £ 10 | 0.442J 0. 353| 0.253| P 1 8.383| 7. 310J 5.8311 4. 208| 2.835| +-I 4-1671 662 | 273| 936) 4511 830| 262 | 871 J 418| 1921 075 | 14.0 -+ -I I 28.0 | "+ i 0.931| 0. 557 | 0.495| 0.327j 0. 149 J 0.748 1 0.506J 0. 309 | 0.478 | 0.088) 0.870| 1 z . 1. 1. 0. 0. 1. 1. 0. 1. 0. 2. 1.4 16 0. 985 0.779 0.572 0.267 1 .148 0.785 0.557 0. 816 0. 13 1 1.313 d r a g c o e f f i c i e n t a r e s i m i l a r t o t h o s e q u o t e d above w i t h d i f f e r e n c e s o c c u r r i n g o n l y i n t h e d e t a i l o f t h e s c a t t e r . The d i f f e r e n c e means, d i f f e r e n c e v a r i a n c e s and r e s i d u a l v a r i a n c e s a r e g r e a t e r f o r a l l s h i p s and a v e r a g i n g p e r i o d s u s i n g t h e l i n e a r d r a g c o e f f i c i e n t t h a n when u s i n g t h e c o n s t a n t d r a g c o e f f i c i e n t w h i l e t h e c o r r e l a t i o n c o e f f i c i e n t s a r e c o n s i s t e n t l y s m a l l e r . 3.2 P r e v i o u s S t u d i e s E i s s e l (1975) a n a l y s e d 10 y e a r s o f d a t a f r o m S t a t i o n P. He d i v i d e d h i s d a t a i n t o f i v e t w o - y e a r b l o c k s o f 5832 d a t a p o i n t s e a c h and q u a n t i f i e d t h e r e d u c t i o n i n t e r m s o f two f u n c t i o n s which 1 d e f i n e as : 39 A ( L V /Wf^i^y A r c - f e i x ^ ^ wnere T'x and 1'y a r e t h e x and y component VA e s t i m a t e s o f t h e two-year mean s t r e s s e s f o r an a v e r a g i n g p e r i o d o f L d a y s and Tx and Ty a r e t h e t w o - y e a r mean 3H s t r e s s components. One S(L) and A (L) v a l u e was c a l c u l a t e d f o r e a c h 5832 p o i n t b l o c k , and t h e sample means and s t a n d a r d d e v i a t i o n s were c a l c u l a t e d o v e r t h e f i v e b l o c k s . The F i s s e l r e s u l t s a p p e a r i n F i g u r e 8. ( F i s s e l u s e d t h e l i n e a r Cd f o rm c f Deacon and Webb(1S62) r a t h e r t h a n t h e one used h e r e ) . The 95% c o n f i d e n c e z o n e s ( e q u a l t o ± 2 s t a n d a r d d e v i a t i o n s o f t h e two-year means) were t y p i c a l l y of t h e o r d e r 0.1 t i m e s t h e mean v a l u e c f S(L) and 2° f o r A ( L ) . S (L) d e t e r m i n e s t h e r a t i o o f t h e c l i m a t o l o g i c a l a v e r a g e VA s t r e s s m a g n i t u d e t o t h e a v e r a g e 3H s t r e s s m a g n i t u d e and A (L) d e t e r m i n e s t h e a v e r a g e d i f f e r e n c e between t h e 3H and VA s t r e s s d i r e c t i o n s . E x a c t l o n g - t e r m mean 3H s t r e s s f r o m VA s t r e s s e s w i t h i n the t w o - y e a r a v e r a g i n g b l o c k s h o u l d r e s u l t from t h e a p p l i c a t i o n o f S(L) and A(L) t o t h e VA s t r e s s e s . The t e s t f u n c t i o n s were c a l c u l a t e d by a p p l y i n g S(L) and A(L) t o t h e d a t a and t h e DMs were s u b s t a n t i a l l y i m p r o v e d b u t t h e o t h e r t e s t q u a n t i t i e s r e m a i n e d n e a r l y i d e n t i c a l t o t h o s e i n F i g u r e 7 where no c o r r e c t i o n was a p p l i e d . T n i s t e c h n i q u e was a t t e m p t e d on t h e N o r t h A t l a n t i c s h i p d a t a . In the p r e s e n t s t u d y , i t was f o u n d t h a t o n e - y e a r l y b l o c k s o f 2912 d a t a p o i n t s s i m p l i f i e d t h e a n a l y s i s when u s i n g d a t a o f a v a r y i n g number o f y e a r s . F o r most w e a t h e r s t a t i o n s , t h e S t a t i o n P r e s u l t s were w e l l r e p l i c a t e d as shown i n F i g u r e s 9 (a) and (b) 40 f i g u r e 8. The r a t i o c f t h e wind s t r e s s magnitude computed from wind d a t a t h a t a r e v e c t o r a v e r a g e d o v e r a p e r i o d , T t o t h e d i r e c t l y c a l c u l a t e d wind s t r e s s . The l o w e r p l o t r e p r e s e n t s t h e d i f f e r e n c e between t h e d i r e c t i o n o f t h e d i r e c t l y c a l c u l a t e d wind s t r e s s and t h e d i r e c t i o n of the wind s t r e s s computed from the v e c t o r a v e r a g e d d a t a . The v e r t i c a l e r r o r b a r s r e p r e s e n t a p p r o x i m a t e 95% c o n f i d e n c e i n t e r v a l s o f t h e mean. (From F i s s e l ( 1 9 7 5 ) ) 41 f o r S t a t i o n C. The S(L) v a l u e s a t W e a t h e r s t a t i o n A ( F i g u r e s 9 (c) and ( d ) ) , however, d i f f e r m a r k e d l y f r o m t h e o t h e r s h i p s . Whereas S t a t i o n s P and C, S (L) v a l u e s a r e c o n s i s t e n t l y l e s s t h a n 1.0, S t a t i o n A h a s s e v e r a l v a l u e s s i g n i f i c a n t l y g r e a t e r t h a n 1.0. The s t a n d a r d d e v i a t i o n s f o r a v e r a g i n g p e r i o d s from 0.5 t o 26.0 d a y s a r e as much as 100 t i m e s l a r g e r a t A t h a n C and a r e l a r g e compared t o t h e mean S(L) v a l u e s . S t a t i o n A has d i r e c t i o n s h i f t s (A(L)) o f up t o 30° f o r a v e r a g i n g p e r i o d s g r e a t e r t h a n 14 day s . F c r a l a r g e v a l u e t o a r i s e i n S ( L ) , t h e d e n o m i n a t o r o f E g u a t i o n 3. 1 may t e n d t o 0 w h i l e t h e n u m e r a t o r r e m a i n s f i n i t e . One would e x p e c t h i g h v a l u e s o f S(L) t o o c c u r f o r low v a l u e s o f t n e a v e r a g e 3H s t r e s s m a g n i t u d e . The y e a r l y v a l u e s o f S(L) a t S t a t i o n A a r e l i s t e d i n T a o l e V I I I a l o n g w i t h t h e y e a r l y a v e r a g e d 3ri s t r e s s m a g n i t u d e s . From T a b l e V I I I i t i s c l e a r t h a t g e n e r a l l y low y e a r l y a v e r a g e d s t r e s s v a l u e s l e a d t o S(L)>1 ( a l s o t r u e f o r t h e l i n e a r d r a g c o e f f i c i e n t ) . T h i s i s n o t , however, a s u f f i c i e n t c o n d i t i o n . The 1955 s t r e s s m a g n i t u d e i s 0.3 dPa w h i l e S (0.25) = 1. 0005; i n 1952 t h e s t r e s s i s 0.1C7 dPa b u t S(0.25)<1.0. The h i g h e s t s t r e s s v a l u e f o r which S(L) i s g r e a t e r t h a n 1.0 i s a t W e a t h e r s t a t i o n B i n 1965 where t h e s t r e s s was 0.372 dPa. I n g e n e r a l , however, s m a l l v e c t o r a v e r a g e d 3H s t r e s s m a g n i t u d e s l e a d t o l a r g e v a l u e s of S ( L ) . F u r t h e r m o r e t h e l o w e r t h e 3d s t r e s s , t h e more a v e r a g i n g p e r i o d s a r e a f f e c t e d . A l l v a l u e s o f S(L) g r e a t e r t h a n 2.0 have v e c t o r a v e r a g e d 3H s t r e s s m a g n i t u d e s l e s s t h a n 0.05 dPa. 42 WEATHERSHIP C WEATHERSHIP C i ~i—i 11 1 1 M I— i—i 1111111—i—| 11 i im— i—i 1111HI 10"' 3 5 10° 3 5 10' 3 5 10' 3 5 10S AVERAGING PERIOD IN DAYS UJ •-Q LD cc,, io-' I I I 1 I " "I ' I ' I " " I ' I ' I'"' 3 5 10° 3 5 10' 3 5 10' 3 5 10 AVERAGING PERIOD IN DAYS F i g u r e 9(a) S (L) F i g u r e 9 (b) A (L) WEATHERSHIP A WEATHERSHIP fl cr^ ~i I ' I <ni| i I i I "HI 1 I > | H I I | 1—| i 11ni| IO- 3 5 10" 3 5 10' 3 5 10' 3 5 10' AVERAGING PERIOD IN DAYS L U o . Cc ^ U J U _ o L L - O . O U J ° - J o ' | l | 11 ll| 1—| I | ""I 1' | I | I 1111 1—| I ] 11 ll| IO" 3 5 10" 3 5 10' 3 5 10' 3 5 AVERAGING PERIOD IN DAYS 10' F i g u r e 9 ( c ) S (L) F i g u r e 9(d) A (L) F i g u r e 9. S (L) and A (L) ( i n Degrees) as f u n c t i o n s of a v e r a g i n g p e r i o d f o r W e a t h e r s h i p s A and C. The mean f o r t h e c o n s t a n t d r a g c o e f f i c i e n t i s i n d i c a t e d by * with ± 1 s t a n d a r d d e v i a t i o n of the y e a r l y means by t h e narrow h o r i z o n t a l l i n e s . The mean f o r t h e l i n e a r d r a g c o e f f i c i e n t i s i n d i c a t e d by X and ± 1 s t a n d a r d d e v i a t i o n c f t h e y e a r l y means by t h e wide h o r i z o n t a l l i n e s . 43 TABLE V I I I The S(L) r e a d i n g s f o r a l l y e a r s o f d a t a a t W e a t h e r s t a t i o n A u s i n g t h e c o n s t a n t d r a g c o e f f i c i e n t . The 3H v e c t o r a v e r a g e d s t r e s s magnitude i s i n dPa. | AVERAGING PERIOD I N DAYS YEAR l s T R E S S | 0 . 2 5 | . 5 | 1 . 0 | 2 . 0 j 4 . 0 | 7 . 0 | 1 4 . 0 | 2 8 . 0 j. 1949 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 196 1 1962 1963 1964 1965 + + 0 . 48 0 . 39 0 . 11 0 . 5 1 0 . 36 0 . 30 0 . 6 7 0 . 0 1 0 . 12 0 . 27 0 . 4 7 0 . 0 8 0 . 12 0 . 21 0 . 33 0 . 4 7 0 . 0 . 0 . 1. 0 . 1 . 0 . 1 . 1 . 0 . 1. 0 . 0 . 1 . 0 . 1 . WEATHERSTATION A — + — 96 96 98 00 99 00 99 28 06 98 00 96 97 00 98 00 0 . 9 2 0 . 9 5 0 . 9 8 0 . 9 5 0 . 9 5 0 . 9 8 0 . 93 2 . 12 1 . C7 0 . 8 9 0 . 9 9 0 . 8 6 0 . 8 4 0 . 9 9 0 . 9 4 0 . 9 5 0 . 8 4 0 . 8 9 0 . 7 2 0 . 8 8 0 . 8 8 0 . 9 6 0 . 8 7 3 . 3 0 1 . 0 9 0 . 7 8 0 . 9 7 0 . 7 9 0 . 7 8 1 . 0 3 0 . 8 8 0 . 9 2 0 . 0 . 0 . 0 . 0 . 0 . 0 . 6 . 0 . 0 . 0 . 0 . 0 . 0 . 0 . 0 . 74 80 77 77 85 84 8C 46 £6 57 S1 73 59 S7 74 80 .55 59 , 57 57 ,7C 70 , 7C 67 .77 53 ,86 04 ,33 , 92 71 72 0 . 0 . 0 . 0 . 0 . 0 . 0 . 1 0 . 0 . 0 . 0 . 1. 0 . 0 . 0 . 0 . 61 68 28 49 50 68 59 98 60 53 71 54 32 79 62 65 0. 0, 0. 0, 0, 0. 0, 9. 0. 0, 0. 1. 0. 0. 0. 0. 52 i 53 16 47 43 27 52 261 54 60 50 I 68 3 3 j 56 51 51 0 . 4 1 0 . 4 7 0 . 17 0 . 4 1 0 . 351 0. 20 0 .4 1 8. 51 0 . 27| 0 . 76 | 0 .43] 0 . 8 8 | 0 . 24| 0 . 4 3 | 0 . 33i 0 . 4 1 3 . 3 I n d i v i d u a l R a t i o s In a t t e m p t i n g t o g u a n t i f y the r e d u c t i o n i n s t r e s s due to v e c t o r a v e r a g i n g t h e wind, the f u n c t i o n s S ( L) and A(L) have s e v e r a l d i s a d v a n t a g e s . F i r s t , i n r e g i o n s o f s m a l l a v e r a g e s t r e s s , t h e f u n c t i o n s may assume r a d i c a l l y d i f f e r e n t v a l u e s from cne y e a r t o t h e n e x t , i n d i c a t i n g t h a t t h e y may n o t be g e n e r a l l y a p p l i c a b l e t o y e a r s o t h e r t h a n t h o s e o v e r which t h e i n i t i a l a v e r a g i n g was dene. Second, t h e S ( I ) and A(L) f u n c t i o n s do n o t i m p r o v e t h e RVs and c o r r e l a t i o n c o e f f i c i e n t s . F o r c a l c u l a t i o n s o f a c t u a l t i m e v a r i a t i o n s i t i s n e c e s s a r y t o e s t i m a t e t h e a c c u r a c y o f t h e i n d i v i d u a l s t r e s s v a l u e s . C o n s e q u e n t l y two f u n c t i o n s R j ( L ) and B j (L) were d e f i n e d a s : 44 1 (J*fr + CT 3.3 T - 1 wnere T'x^- and T ' y a r e t h e s e t s o f VA x and y component s t r e s s e s t i m a t e s and Tx^- and Tyj . a r e t h e s e t s o f 3H x and y component s t r e s s e s t i m a t e s f o r an a v e r a g i n g p e r i o d o f L d a y s f o l l o w i n g t h e n o t a t i o n g i v e n i n S e c t i o n 2.5. The E j ( L ) f o r any g i v e n a v e r a g i n g p e r i o d c a n be examined m a t h e m a t i c a l l y t o g a i n some i n s i g h t i n t o i t s e x p e c t e d b e h a v i o u r . E q u a t i o n 3.3 f o r t h e c o n s t a n t d r a g c o e f f i c i e n t c a n be r e w r i t t e n a s : R I(L .V — 4  w i t h t h e a p p r o x i m a t i o n t h a t the a i r d e n s i t y and t h e d r a g c o e f f i c i e n t a r e c o n s t a n t . A p p l y i n g t h e S c h w a r t z i n e q u a l i t y (see P r e i f f e r , 1965, pp. 223) t o t h e d e n o m i n a t o r and r e a r r a n g i n g t e r m s , a l o w e r bound f o r t h e f u n c t i o n can be e s t a b l i s h e d : 1 Where: and CTs^ ' a r e t h e x and y wind v e l o c i t y component v a r i a n c e s i n a v e r a g i n g p e r i o d j . Thus t h e l o w e r bound f o r any p a r t i c u l a r a v e r a g i n g p e r i o d i n c r e a s e s f o r h i g h e r v e c t o r a v e r a g e d mean winds and l c w e r v a r i a n c e s . 45 E j (L) has no upper bound. I f one t a k e s t h e s e t u =v =( 3,4,-5 } and s u b s t i t u t e s i n t o E q u a t i o n 3.5, t h e n t h e n u m e r a t o r i s f i n i t e and t h e d e n o m i n a t o r i s 0.0, o r S j ( L ) = co. The p r o b a b i l i t y o f s u c h an o c c u r r e n c e i s r e m o t e . Whenever t h e 3H s t r e s s a v e r a g e d e x a c t l y to 0.0, l e a d i n g t o R j ( L ) = o o , t h e p a r t i c u l a r a v e r a g i n g v a l u e s were e l i m i n a t e d f r o m c a l c u l a t i o n s . A f t e r i m p o s i n g t h i s c r i t e r i o n , i n o v e r 750,000 c a s e s ( a l l s h i p s , a v e r a g i n g p e r i o d s and d r a g c o e f f i c i e n t s ) e x a m i n e d , n o t one i n s t a n c e o f Rj (L) g r e a t e r t h a n 1.0 a p p e a r e d . F u r t h e r m o r e , i n a l l c a s e s where t h e 3H s t r e s s was 0, t h e mean VA s t r e s s was a l s o 0. The smoothed wind d a t a as e n c o u n t e r e d i n s u r f a c e p r e s s u r e maps, h i d e s t h e i n t e r n a l v a r i a n c e t h r o u g h t h e a v e r a g i n g p r o c e s s , nut t h e s g u a r e o f t h e v e c t o r a v e r a g e d wind i s n o t o n l y r e a d i l y c a l c u l a b l e but e s s e n t i a l i n d e t e r m i n i n g t h e j v a l u e o f VA f l u x e s . A l t h o u g h t h e v a l u e o f any s i n g l e R j (L) and t h e l o w e r bcund may net c o i n c i d e , an a v e r a g e v a l u e (R (L)) may be wind speed d e p e n d e n t . C o n s e q u e n t l y t h e e f f e c t o f g r o u p i n g 3 j ( L ) v a l u e a c c o r d i n g t o the v e c t o r a v e r a g e d wind speed was i n v e s t i g a t e d . Rj (L) and Bj (L) were s o r t e d i n t o t w e n t y e q u a l l y s p a c e d d i v i s i o n s a c c c r d i n q t c v a l u e . F o r e a c h R j ( L ) and B j (L) r e a d i n g t h e v e c t o r a v e r a g e d wind speed (u.s + v 2 ) 1 / 2 was d e t e r m i n e d and ' 0 tne f u n c t i o n s were f u r t h e r s o r t e d i n t o t h i r t e e n d i v i s i o n s a c c o r d i n g t o t h e B e a u f c r t number o f t h e j ^ n v a l u e o f t h e v e c t o r a v e r a g e d wind s p e e d . The B e a u f o r t wind s p e e d s a c c o r d i n g t o t h e Ma r i n e C l i m a t i c A t l a s , U.S. O f f i c e o f N a v a l O p e r a t i o n s a r e g i v e n i n T a b l e IX. 46 BEAUFORT WIND SPEED INTERVALS EEAUFORT # SPEED INTERVAL m/sec MEAN VALUE m/sec —I 1 | 0.0-0.4 I 0.2 2 I 0.4-1.6 I 1.0 3 I 1.6-3.4 I 2.5 4 I 3.4-5.5 I 4.45 5 | 5.5-8.0 I 6.75 6 | 8.0-10.8 I 9.4 7 I 10.8-13.9 | 12.35 8 | 13.9-17.2 I 15.55 9 I 17.2-20.8 | 19.0 10 | 20.8-24.5 j 22.65 1 1 I 24. 5-28.5 I 26.5 12 J 28. 5-33.5 I 31.0 13 I > 33. 5 1 35. 0 F i g u r e 10 i s the h i s t o g r a m o f E j (L) and F i g u r e 11 t h e h i s t o g r a m f o r B j ( L ) f o r t h e c o n s t a n t and l i n e a r d r a g c o e f f i c i e n t s r e s p e c t i v e l y a t W e a t h e r s t a t i o n C. B e a u f o r t numbers 2 (1.0 m / s e c ) , 6 (9.4 m/sec), and 10 (22. 65 m/sec) f o r an a v e r a g i n g p e r i o d o f L=0.25 days were s e l e c t e d a s b e i n g r e p r e s e n t a t i v e . The s t a n d a r d d e v i a t i o n was c a l c u l a t e d f r o m a l l the v a l u e s o f E j ( L ) and B j ( L ) i n e a c h wind s p e e d - a v e r a g i n g p e r i o d c a t e g o r y and w i l l be r e f e r r e d t o as t h e sample s t a n d a r d d e v i a t i o n and i t s s q u a r e w i l l be r e f e r r e d t o a s t h e sample v a r i a n c e . As s e e n i n F i g u r e 10 a t 1.0 m/sec, Rj (L) has a d i s t i n c t mode between 0.45 and 0.50 w i t h an a v e r a g e v a l u e o f 0.530. The r e s t o f t h e d i s t r i b u t i o n i s n e a r l y f l a t . At 9.40 m/sec t h e d i s t r i b u t i o n o f R j ( L ) becomes m a r k e d l y skewed t o w a r d s 1.0. The s t a n d a r d d e v i a t i o n has a l s o s i g n i f i c a n t l y d e c r e a s e d . At 22.65 m/sec, t h e skewness becomes even more p r o n o u n c e d t o 1.0 w i t h 93$ 47 8 § in t-£ r» fe 8 Q K O I J z £ « cn O'OOI — 1 1— O'Si — i 1 1— O'OS 0 5 2 NI w a y g o i S I H oo 8 £ 2 in >-II <c tn — i - > °- v B fa 8 o K O £ i 5 i tn CD tn • fc 9 13 B in o K O I 1 8 | z ^ in s I O'OOI T 1 r~ o-st J.N33d3d O'OOI T O'Si O'OS O'SZ !N33d3d NI Wbd3QlSIH O'O O'OS O'SZ NI MbHDQlSIH f i g u r e 10. H i s t o g r a m c f B(0.25) a t W e a t h e r s t a t i o n C u s i n g t h e c o n s t a n t d r a g c o e f f i c i e n t . 48 — I 1 1 1 r— O'Si _ O'OS D'SZ iN3oa3d NI w o a a o i s i H F i g u r e 11. H i s t o g r a m c f B(0.25) c o n s t a n t d r a g c o e f f i c i e n t . a t W e a t h e r s t a t i o n C u s i n g t h e 49 o f the d i s t r i b u t i o n i n t h e 0.9 5 t o 1.0 s l o t . B e c a u s e o f t h e i n c r e a s i n g c o n c e n t r a t i o n of v a l u e s t o t h e n i g h end o f t h e d i s t r i b u t i o n , t h e s t a n d a r d d e v i a t i o n c o n t i n u e s t o d e c r e a s e w i t h a v e r a g i n g s p e e d . The t r e n d t o h i g h e r fiTT) v a l u e s and l o w e r s t a n d a r d d e v i a t i o n s f o r i n c r e a s i n g wind s p e e d i s g e n e r a l l y t r u e f o r a l l a v e r a g i n g p e r i o d s . B j (L) has a d i s t i n c t l y s p i k e d d i s t r i b u t i o n a t low wind s p e e d s . The h i s t o g r a m f o r 1.0 m/sec has €4% o f t h e t o t a l number o f 383 p o i n t s i n the 0 t o 1.0° d i r e c t i o n s h i f t s l o t . T h e r e a r e , however, an a d d i t i o n a l 59 p o i n t s f r o m - 1 0 ° t o - 1 8 0 ° and an a d d i t i o n a l 68 p o i n t s f r c m 10° t o 180° a c c o u n t i n g f o r t h e l a r g e 18.021° s t a n d a r d d e v i a t i o n . As the wind s p e e d i n c r e a s e s t o 9.40 m/sec, t h e mean r e m a i n s v e r y c l o s e t o 0 . 0 ° . The number o f e x t e r i o r p o i n t s d e c r e a s e s c a u s i n g t h e sample s t a n d a r d d e v i a t i o n t o d e c r e a s e so t h a t a t 22.65 m/sec t h e d i s t r i b u t i o n a p p e a r s a p p r o x i m a t e l y G a u s s i a n . The j o i n t h i s t o g r a m f o r B j ( L ) and B j (L) was c a l c u l a t e d f o r a l l s n i p s . The a r i t h m e t i c means, E(L) and B ( L ) , were t h e n c a l c u l a t e d f o r e a c h B e a u f o r t c a t e g o r y and a v e r a g i n g p e r i o d . Thus e a c h s h i p was a s s i g n e d E ( L ) and B(L) v a l u e s t h a t were f u n c t i o n s c f w i n d s p e e d and a v e r a g i n g p e r i o d . Ine mean E(L) v a l u e s f o r a l l t h e s h i p s a p p e a r i n F i g u r e 12 w h i l e t h e means E (L) v a l u e s appear i n F i g u r e 14. Two s t a n d a r d d e v i a t i o n s a r e a l s o shown. P a r t i c u l a r l y f o r l a r g e r VA wind s p e e d s and l o n g e r a v e r a g i n g p e r i o d s , B(L) and B (L) may be c a l c u l a t e d f r c m d i f f e r i n g numbers o f measurements. F i r s t , w e i g h t s p r o p o r t i o n a l t c t h e number o f e s t i m a t e s w i t h i n each B e a u f o r t - a v e r a g i n g p e r i o d c a t e g o r y were a p p l i e d t o t h e s h i p 50 means v a l u e s c f E (L) and B (L) t o a r r i v e at an e s t i m a t e o f the s t a n d a r d d e v i a t i o n s of the g e o g r a p h i c means. T h i s i s the s t a n d a r d d e v i a t i o n of the means shown i n the f i g u r e s and i t i s i n d i c a t e d by t h e dashed l i n e s . Next s i m i l a r w e i g h t s were a p p l i e d t o the sample v a r i a n c e s to a r r i v e at an average sample v a r i a n c e . T h i s i n d i c a t i v e of the average sample v a r i a b i l i t y acout any s i n g l e E(L) e s t i m a t e and i s i n d i c a t e d by the s o l i d l i n e i n F i g u r e s 12 and 14. F i n a l l y , i t w i l l be shown t h a t S t a t i o n N d i f f e r s markedly from o t h e r l o c a t i o n s and i t s v a l u e s are e x c l u d e d e n t i r e l y frcm s t a n d a r d d e v i a t i o n e s t i m a t e s . F i g u r e 12(a) shows E(0.25) (the 0.25 i n d i c a t e s L=0. 25 days) as a f u n c t i o n of wind speed. The v a l u e of E (0.25) approaches 0 f c r very s m a l l wind speeds. For l a r g e r v e c t o r averaged winds E(0.25) r a p i d l y i n c r e a s e s . at 7 m/sec E(0.25) i s 0.90. As t h e wind speed i n c r e a s e s , the v a l u e s approach 1.0. Both the s t a n d a r d d e v i a t i o n s of t h e sample and the s t a n d a r d d e v i a t i o n s of the s n i p s * means have maxima at low wind speeds and then decrease g r a d u a l l y as the wind speed i n c r e a s e s . For a l l wind speeds, t h e average e r r o r i n the sample i s much l a r g e r than the e r r o r i n t h e means i n d i c a t i n g t h a t t h e v a l u e cf R(0.25) may be independent of g e o g r a p h i c a l l o c a t i o n . The r e s u l t s can be e x p l a i n e d i n terms of E g u a t i o n 3.6. An a v e r a g i n g p e r i o d of 0.25 days c o n t a i n s o n l y twc t h r e e - h o u r l y measurements. Lower v e c t o r averaged winds r e s u l t from s i m u l t a n e o u s c a n c e l l a t i o n of the x and y wind components. Thus tne v a r i a n c e s w i l l be much g r e a t e r than t h e means of the components r e s u l t i n g i n a l o w e r bound t h a t approaches 0. For h i g h e r wind speeds one e x p e c t s a s t r o n g s t e a d y wind t o blow f o r 51 RVERflGING PERIOD*0.25 DATS | I • " • B RVERRGING PER10D=4.00 DOTS 0.0 3 . 5 7.0 " I - 1 1 1 1 10 5 14 0 17.5 21.0 24 5 WINOSPEEO IN M/SEC 26.0 31.5 35.0 10.5 14.0 17.5 21 .0 24 ! WINDSPEED IN M/SEC F i g u r e 12 (a) F i g u r e 12(b) WINDSPEED =6.7S M/SEC 5HVERfiGING 2 PERI0u 6 i eN DAYS 2 2 " F i g u r e 12(c) F i g u r e 12. P l o t s c f B(L) f o r r e p r e s e n t a t i v e a v e r a g i n g p e r i o d s and wind s p e e d s of a l l s h i p s u s i n g t h e c o n s t a n t d r a g c o e f f i c i e n t . Y d e n o t e s W e a t h e r s t a t i o n N. The s o l i d l i n e i s a w e i g h t e d mean sample s t a n d a r d d e v i a t i o n and t h e da s h e d l i n e i s the s t a n d a r d d e v i a t i o n o f t h e s h i p s ' means. S i n c e N d i f f e r s from t h e o t h e r s h i p s , i t s v a l u e s were n o t i n c l u d e d i n t h e c a l c u l a t i o n c f t h e s t a n d a r d d e v i a t i o n s . 52 a r e l a t i v e l y l o n g l e n g t h of t i m e i n which c a s e t h e v a r i a n c e o f t h e two components i s s m a l l compared t o t h e v e c t o r a v e r a g e d wind and t h e l o w e r hound i n E g u a t i o n 3.6 a p p r o a c h e s 1. 6(4) a p p r o a c h e s 0 as t h e wind s p e e d goes t o C m/sec. The v a l u e of B (4) i n c r e a s e s w i t h wind s p e e d . The s c a t t e r i n measurements f o r b o t h t h e mean and sample v a l u e s i s l a r g e r t h a n f o r R ( 0 . 2 5 ) . At t h e l a r g e s t wind s p e e d , the s c a t t e r i n t h e means a p p e a r s t o be mere s i g n i f i c a n t t h a n t h e s c a t t e r i n t h e i n d i v i d u a l e s t i m a t e s . The f o u r v a l u e s a t 2 1 m/sec, however, c o m p r i s e l e s s t h a n 1% o f t h e t o t a l number c f p c i n t s measured and t h i s v a l u e c a n n o t be c o n s i d e r e d s t a t i s t i c a l l y r e l i a b l e . From 0 t o 14 m/sec, W e a t i i e r s h i p N has s y s t e m a t i c a l l y h i g h e r v a l u e s t h a n t h e o t h e r s . F i g u r e 12(c) e x h i b i t s f u r t h e r e v i d e n c e o f t h e h i g h e r v a l u e s o f R(L) f o r W e a t h e r s h i p N. H e r e , R(L) f o r v a r y i n g a v e r a g i n g p e r i o d s i s p l o t t e d f o r a c o n s t a n t wind s p e e d o f 6.75 m/sec. The S t a t i o n N R (L) v a l u e s a r e more t h a n two s t a n d a r d d e v i a t i o n s o f t h e mean l a r g e r t h a n any e t h e r s h i p i n d i c a t i n g t h a t i t s v a l u e s a r e s i g n i f i c a n t l y l a r g e r t h a n t h e e t h e r s t a t i o n s . The s c a t t e r i n t h e i n d i v i d u a l measurements r e a c h e s a maximum f o r an a v e r a g i n g p e r i o d o f two days and t h e n d e c r e a s e s s l o w l y w i t h i n c r e a s i n g a v e r a g i n g p e r i o d . The s c a t t e r i n the s h i p s ' means i n c r e a s e s r a p i d l y t o two d a y s and t h e n m a i n t a i n s a r e l a t i v e l y c o n s t a n t v a l u e . The anomaly i n R (L) a t S t a t i o n N i s c o n s i s t e n t b o t h w i t h E q u a t i o n 3.6 and t h e f i n d i n g s o f o t h e r r e s e a r c h e r s . Walkus(1962) n o t e s t h a t S t a t i o n N i s a t t h e n o r t h e r n e x t r e m i t y or the N o r t h e r n P a c i f i c T r a d e Wind r e g i o n c h a r a c t e r i z e d i n b o t h d i r e c t i o n and m a g n i t u d e by moderate and s t e a d y w i n d s . T h i s i s 53 c o n f i r m e d i n T a b l e V where t h e t o t a l 3H v a r i a n c e i s a b o u t 1/10 t i m e s t h a t o f t h e more n o r t h e r l y s t a t i o n s . Thus E q u a t i o n 3.6 p r e d i c t s t h a t one s h o u l d g e t s y s t e m a t i c a l l y l a r g e r v a l u e s o f R j (L) and hence R ( l ) . T h i s i s c o n f i r m e d by Malleus where s u b s t a n t i a l l y s m a l l e r d i s c r e p a n c i e s between t h e 3H and VA s t r e s s o v e r a s i n g l e m o n t h l y a v e r a g i n g were f o u n d i n the C a r i b b e a n Sea a t 190 N , 66° W t h a n were f o u n d a t S t a t i o n C. Thus t h e c o r r e c t i o n s r e q u i r e d f c r t h e t r o p i c s and s u b t r o p i c s may r>e much l e s s t h a n t h e s e r e q u i r e d f o r t e m p e r a t e l a t i t u d e s . F i g u r e 13 shews t h e g e o g r a p h i c ( i e . a v e r a g e o f a l l t h e s t a t i o n s ) a v e r a g e v a l u e s o f R(L) f o r t h e c o n s t a n t d r a g c o e f f i c i e n t , e x c l u d i n g N, as a f u n c t i o n o f wind s p e e d . The w e i g h t i n g o u t l i n e d above was employed i n t h e c a l c u l a t i o n o f t h e s e g e o g r a p h i c a l l y a v e r a g e d v a l u e s . A l l t h e c u r v e s a p p e a r t o be r e g u l a r w i t h t h e e x c e p t i o n o f t h e h i g h e s t wind s p e e d s . T h i s may be a r e s u l t o f t h e r e b e i n g t o o few a v e r a g i n g s a t the h i g h e r wind s p e e d s t o y i e l d a r e p r e s e n t a t i v e v a l u e o f R ( L ) . Ihe s c a t t e r and b e h a v i o u r o f E(L) as a f u n c t i o n o f a v e r a g i n g p e r i o d a r e i n d i c a t e d i n F i g u r e 14. T h e r e i s a h i g h d e g r e e o f s c a t t e r a t a wind speed o f 0.2 m/sec f o r b o t h t h e sample and between s h i p s . T h e r e does not a p p e a r t o be a s y s t e m a t i c d i f f e r e n c e between s h i p s . A t 6.75 m/sec, t h e sample s t a n d a r d d e v i a t i o n i s r e d u c e d f r o m 35c to a b o u t 15° and t h e v a r i a b i l i t y between s h i p s i s n e a r l y z e r o . F i g u r e 14(c) c l e a r l y i n d i c a t e s t h a t n o n - z e r o v a l u e s o f E(L) o c c u r o n l y f o r low wind s p e e d s . F o r winds g r e a t e r t h a n a b o u t 3 m/sec, B(L) a v e r a g e s t o e x a c t l y z e r o . I t i s net c l e a r whether t h e l a r g e v a l u e s o f B(L) f o r low wind s p e e d s a r e s t a t i s t i c a l l y s i g n i f i c a n t s i n c e t h e low 54 o l I I 1 I ~1 I 1 ~1 1 I 0.0 3.5 7.0 10.5 14.0 17.5 21.0 24.5 28.0 31.5 35.0 WINDSPEED IN M/SEC F i g u r e 13. G e o g r a p h i c a l l y a v e r a g e d S (L) v a l u e s f o r a l l wind s p e e d s and a v e r a g i n g p e r i o d s . The numbers i n d i c a t e l i n e s o f . e q u a l a v e r a g i n g p e r i o d s ( i n d a y s ) . S t a t i o n N has been e x c l u d e d f r o m t h e a v e r a g i n g . wind s p e e d s a c c o u n t f o r o n l y a v e r y s m a l l p e r c e n t a g e o f t h e t o t a l number o f wind measurements made. 3.4 M u l t i p l e R e g r e s s i o n A n a l y s i s From t h e p r e v i o u s d i s c u s s i o n i t i s e v i d e n t t h a t t h e r e d u c t i o n i n s t r e s s due t o v e c t o r a v e r a g i n g o f winds v a r i e s w i t h t h e a v e r a g i n g p e r i o d and t h e measured VA winds.. F o r wind s p e e d s g r e a t e r t h a n 3.0 m/sec the a v e r a g e s h i f t i n d i r e c t i o n i s 06 i n d i c a t i n g t h a t , on a v e r a g e , t h e r e may n o t be s i g n i f i c a n t d i f f e r e n c e s between t h e t r a n s f o r m a t i o n s r e q u i r e d f o r t h e x and y components. T h i s i m p l i e s t h a t a s i n g l e t r a n s f o r m a t i o n b a s e d on 55 i * WINDSPEEO =0.20 H/SEC WINDSPEED =6.73 H/SEC 5.6 11.2 16.6 22.4 AVERAGING PERIOD !N DATS —I a.o cn —™B a • — I i — i 1 i 1 1 r~ 5 6 11 2 16.8 22.4 AVERAGING PERIOD IN DATS F i g u r e 14(a) F i g u r e 14 (b) (WERRG1NG PERI00=4.00 CATS -So 1 — i — i i — i — i — i — 7.0 14.0 21 0 28.0 WINDSPEED IN M/SEC F i g u r e 14 (c) F i g u r e 14. P l c t s c f B (L) f o r r e p r e s e n t a t i v e a v e r a g i n g p e r i o d s and wind s p e e d s f o r a l l s h i p s u s i n g t h e c o n s t a n t d r a g c o e f f i c i e n t . The s o l i d l i n e d e n o t e s t h e a v e r a g e s t a n d a r d d e v i a t i o n o f t h e sample and t h e dashed l i n e i s one s t a n d a r d d e v i a t i o n o f t h e s h i p s ' mean v a l u e s . 56 t h e s t r e s s m agnitude i s f e a s i b l e . A s i n g l e s e t o f c o r r e c t i o n f a c t o r s e q u a l l y a p p l i c a b l e t o b o t h components r e d u c e s t h e r e q u i r e d p a r a m e t e r s by a f a c t o r o f 2 . The o b j e c t o f any t r a n s f o r m a t i o n i s t o r e d u c e t h e d i f f e r e n c e s means, d i f f e r e n c e v a r i a n c e s , and r e s i d u a l v a r i a n c e s t o p r e d i c t a c c u r a t e l y t h e l o n g - t e r m and p o i n t - b y - p o i n t 3H s t r e s s from t h e VA s t r e s s . S p e c i f i c a l l y , i f t h e p o i n t - b y - p o i n t 3H s t r e s s (as q u a n t i f i e d by t h e r e s i d u a l v a r i a n c e ) can be a c c u r a t e l y d e t e r m i n e d t h e n t h e d i f f e r e n c e v a r i a n c e s and means s h o u l d a l s o be r e d u c e d . The r e s i d u a l v a r i a n c e c a n be o p t i m a l l y r e d u c e d by a l e a s t s q u a r e s f i t . To t h i s end t h e 3H and VA s t r e s s m a g n i t u d e s were c a l c u l a t e d and s o r t e d a c c o r d i n g t o t h e B e a u f o r t i n t e r v a l as p r e v i o u s l y o u t l i n e d . F o r e a c h a v e r a g i n g p e r i o d , t h e f o l l o w i n g q u a n t i t y : was m i n i m i z e d by c) 3. 8 g i v i n g : « . 1- 3.9 where T t e j and T « K ^ a r e t h e 3H and VA s t r e s s m a g n i t u d e s , S«T i s the s t r e s s m a g n i t u d e r e s i d u a l v a r i a n c e f o r t h e 1 a v e r a g i n g p e r i o d , 1^<L i s a m u l t i p l i c a t i v e f a c t o r which m i n i m i z e s t h e 57 r e s i d u a l s i n B e a u f o r t c a t e g o r y k and t h e l l f a ' a v e r a g i n g p e r i o d , N i s t h e t o t a l number o f a v e r a g i n g s a v a i l a b l e i n t h e r e c o r d and J i ? . i s t h e number o f a v e r a g i n g s w i t h i n B e a u f o r t c a t e g o r y k. £fe^  i s t h e s l o p e o f a s t r e s s m agnitude r e g r e s s i o n l i n e p a s s i n g t h r o u g h t h e o r i g i n . T h i s i s n o t a bad a s s u m p t i o n i n l i g h t c f F i g u r e 6, where t h e s c a t t e r o f t h e x and y s t r e s s components beccmes c o n s t r i c t e d a t t h e o r i g i n . Appendix A g i v e s an o u t l i n e o f seme o f t h e r e l a t i o n s h i p s between t h e d i f f e r e n c e v a r i a n c e s , r e s i d u a l v a r i a n c e s , and c o r r e l a t i o n c o e f f i c i e n t s f o r t h e r e g r e s s i o n a n a l y s i s . N o t i c e t h a t E g u a t i o n 3.7 u n l i k e E q u a t i o n 2.18 e x c l u d e s the mean t e r m s . They were e x c l u d e d b e c a u s e as d e m o n s t r a t e d i n F i g u r e 4 and T a b l e V, t h e s t r e s s component f l u c t u a t i o n s d o m i n a t e the mean. Ap p e n d i x A.1 i n c l u d e s t h e i n f l u e n c e o f t h e l i n e a r t e r m on the r e s i d u a l s . T h i s f o r m o f t h e r e g r e s s i o n w i l l be a p p l i e d p r e s e n t l y t o t h e h e a t f l u x e s . In f a c t a r e g r e s s i o n o f t h e t y p e o u t l i n e d i n Appendix A. 1, i n c l u d i n g t h e mean s t r e s s m agnitude was t r i e d on t h e s t r e s s m a g n i t u d e s . Up t c B e a u f c r t i n t e r v a l 3, seme o f t h e £«t«. v a l u e s were f o u n d t o be n e g a t i v e i n c o n t r a d i c t i o n w i t h E q u a t i o n 3.3. F u r t h e r m o r e , t h e component r e s i d u a l v a r i a n c e s were s i g n i f i c a n t l y l a r g e r t h a n when t h e means were e x c l u d e d . An e s t i m a t e o f 95% c o n f i d e n c e zone o f t h e s l o p e was made by: t«. , . o 2 5 A £fc<L = ' c CJV-Z) TL T v ^ -where tfe rox5" i s t h e S t u d e n t t s t a t i s t i c w i t h J -1 d e g r e e s o f f r e e d o m a t a 0.95 l e v e l o f s i g n i f i c a n c e . T h i s i s n o t a p r e c i s e 3. 10 58 e s t i m a t e o f t h e e r r o r b e c a u s e as shown i n t h e p r e v i o u s s e c t i o n , t h e d i s t r i b u t i o n c f E j ( L ) i s h i g h l y skewed a r o u n d t h e mean f o r most a v e r a g i n g p e r i o d s and wind s p e e d s and c o n s e q u e n t l y t h e s t a t i s t i c s a r e n o t G a u s s i a n . 3.5 V a r i a n c e U n d e r e s t i m a t i o n The v a l u e s were c a l c u l a t e d f o r e a c h s h i p and t h e f o u r t e s t f u n c t i o n s o u t l i n e d i n S e c t i o n 2.6 were t h e n f o u n d by a p p l y i n g t o t h e VA s t r e s s components. The d i f f e r e n c e v a r i a n c e s u s i n g t h e c o n s t a n t d r a g c o e f f i c i e n t a r e shown i n F i g u r e 15. V a l u e s f o r a l l s h i p s , components and d r a g c o e f f i c i e n t s a r e g r e a t l y r e d u c e d f r o m t h e v a l u e s shown i n F i g u r e 7. A l l v a l u e s a r e p o s i t i v e d e f i n i t e which i m p l i e s t h a t t h e l o n g t e r m 3H v a r i a n c e i s s y s t e m a t i c a l l y l a r g e r t h a n t h e l o n g term c o r r e c t e d VA v a r i a n c e . A l t h o u g h o n l y the c o n s t a n t d r a g c o e f f i c i e n t r e s u l t s a r e shown, e v e r y c a s e examined showed a p o s i t i v e d i f f e r e n c e v a r i a n c e . T h i s i s an a r t i f a c t o f t h e r e g r e s s i o n a n a l y s i s . A p p e n d i x A. 1 shows t h a t when t h e o p t i m a l i s a p p l i e d , t h e d i f f e r e n c e v a r i a n c e and t h e r e s i d u a l v a r i a n c e s must be i d e n t i c a l . Note t h a t even t h o u g h Appendix A.1 a p p l i e s t o i n c l u d i n g t h e l o n g - t e r m d i f f e r e n c e means i n t h e c a l c u l a t i o n o f .^fe,e_ r i d e n t i c a l r e s u l t s can be o b t a i n e d by s e t t i n g t h e DMs t o 0. S i n c e the r e s i d u a l v a r i a n c e must be p o s i t i v e d e f i n i t e , so i s t h e d i f f e r e n c e v a r i a n c e . F o r t h i s r e s u l t t o be e x a c t l y a p p l i c a b l e i n t h e s t r e s s components, t h e x and y components must be r e g r e s s e d i n d e p e n d e n t l y and a s e p a r a t e s e t o f t r a n s f o r m a t i o n s f o u n d f o r e a c h component. Here t h e s t r e s s m a g n i t u d e was r e g r e s s e d and 59 on 5 -I X COMPONENT a J * . .1 1.0 10.0 AVERAGING PERIOD IN DATS 100. ol co z: . cr° cn cr -I Ujco CJ° . LU L i -0.1 Y COMPONENT I 1 -I—I—5-I ' J | 8 8 S ° 4 ' 1.0 10.0 AVERAGING PERIOD IN OATS 100.0 F i g u r e 15. S y s t e m a t i c v a r i a n c e u n d e r e s t i m a t i o n f o r a l l s h i p s , c o n s t a n t d r a g c o e f f i c i e n t u s i n g t h e i n i t i a l e s t i m a t e s o f S t a t i o n N i s r e p r e s e n t e d by v( a p p l i e d i d e n t i c a l l y t o each component. Thus t h e a p p l i e d t r a n s f o r m a t i o n may d i f f e r from t h e o p t i m a l component t r a n s f o r m a t i o n . The f a c t t h a t t h e DV c o r r e c t i o n s i n t h i s s e c t i o n a r e p o s i t i v e d e f i n i t e i n d i c a t e s t h a t t h e c a l c u l a t e d Zfe.e b a s e d on t h e s t r e s s m a g n i t u d e s a p p r o x i m a t e s t h e o p t i m a l component c o r r e c t i o n s r e a s o n a b l y w e l l . F i n a l l y , t h i s s u g g e s t s t h a t a t r a d e - c f f c c c u r s i n which one can e i t h e r r e d u c e t h e RVs t o a minimum v a l u e and a c c e p t a s y s t e m a t i c e r r o r i n t h e l o n g -term v a r i a n c e o r m i n i m i z e t h e DVs and a c c e p t an i n c r e a s e i n t h e r e s i d u a l s . I f t h e d i f f e r e n c e v a r i a n c e s f o r each component were i d e n t i c a l t h e n t h i s b i a s c o u l d be made e x a c t l y 0 by m u l t i p l y i n g ^Vtt-by e i t h e r °* /(£*' o r ^ CPy_» where ( i f * , <f\y ) and ( (jV , <Ty ) a r e t h e component 3H and VA s t a n d a r d 60 d e v i a t i o n s w i t h t h e t r a n s f o r m a t i o n a p p l i e d t o t h e VA v a r i a t e . T h i s i s n o t e x a c t l y t h e c a s e . C o n s e q u e n t l y a new cE ^ t e r m was f o u n d uy : £ \ % \ ^ > 3. 1 1 Tne jlt-t> has been m u l t i p l i e d by the mean c o r r e c t i o n r e q u i r e d f o r b o t h t h e x and y VA s t r e s s components. The DVs f o r the c o r r e c t e d t r a n s f o r m a t i o n a p p e a r i n A p p e n d i x D, and t h e s p e c i f i c c o n s t a n t d r a g c o e f f i c i e n t r e s u l t s w i l l be shown l a t e r . The v a r i a n c e d i f f e r e n c e s a r e now r a n d o m l y s c a t t e r e d p o s i t i v e and n e g a t i v e . A p p e n d i x D shows t h a t f o r a l l s h i p s , c omponents, d r a g c o e f f i c i e n t s and a v e r a g i n g p e r i o d s , a p o s i t i v e d i f f e r e n c e v a r i a n c e i n t h e x component i m p l i e s t h a t t h e y component DV i s , w i t h i n s e v e r a l t e n t h s o f a p e r c e n t , t h e e x a c t n e g a t i v e . S i n c e t h e o b j e c t i v e has been t o m i n i m i z e t h e RV, t h e c o r r e c t i o n a p p l i e d t o £ t o remove the s y s t e m a t i c b i a s from t h e v a r i a n c e d i f f e r e n c e s p e r t u r b s t h e r e s i d u a l v a r i a n c e so t h a t i t i s no l o n g e r a minimum. Ihe amount c f t h i s p e r t u r b a t i o n c a n be c a l c u l a t e d under two d i f f e r e n t s e t s o f a s s u m p t i o n s a s o u t l i n e d i n A p p e n d i c e s A.2 and A. 3. I f we d e f i n e : C H 6 ^ ^^all^n 3.12 and assume t h a t vTV/ffV* ^ / ^ V , t h e n i t i s d e m o n s t r a t e d i n A p p e ndix A.3 t h a t : 61 3 . 1 3 where O«-T 1 S t h e BV a f t e r ( 1 + £ ) has been a p p l i e d . The r e l a t i v e i n c r e a s e i n the EV c a n be d e t e r m i n e d i n t e r m s o f t h e a p p l i e d c o r r e c t i o n and t h e c o r r e l a t i o n c o e f f i c i e n t . F i g u r e 16 shows t h i s f u n c t i o n f o r t h e r a n g e s o f € a n d ^ r a s s o c i a t e d w i t h t h i s p r o b l e m . E x c l u d i n g S t a t i o n N, F i g u r e 15 i n d i c a t e s t h a t t h e l a r g e s t DV v a l u e s a r e a b o u t 0.C8 which g i v e s a t y p i c a l v a l u e o f 0.04 f o r t=. . A lew e s t i m a t e o f t h e c o r r e l a t i o n c o e f f i c i e n t i s 0.95. When E g u a t i o n 3.13 i s t h e n e v a l u a t e d , t h e r e l a t i v e i n c r e a s e i n BV i s 2.435. a l l o w i n g f o r a r e s i d u a l v a r i a n c e as h i g h a s 50??, t h e a b s o l u t e change i n EV i s a b o u t 1%. (The i n i t i a l r e s i d u a l v a r i a n c e s a r e , i n f a c t , s i g n i f i c a n t l y l e s s t h a n 10%). The a c t u a l change i n EV was c a l c u l a t e d and i n a l l c a s e s was s u b s t a n t i a l l y l e s s t h a n 1.0%. H e n c e f o r t h , t h e p r i m e s w i l l be d r o p p e d and i t w i l l be u n d e r s t o o d t h a t £ * t i n c l u d e s t h e DV c o r r e c t i o n . . 3.6 Wind Dependent C o r r e c t i o n F a c t o r s The c o r r e c t i o n f a c t o r s £tz.e f o r a l l s h i p s , a v e r a g i n g p e r i o d s and wind s p e e d s a r e g i v e n i n A p p e n d i x C - P a r t I . The c o r r e s p o n d i n g e r r o r e s t i m a t e s o f t h e 95% c o n f i d e n c e i n t e r v a l s on t h e s e v a l u e s as e s t i m a t e d by t h e S t u d e n t ' t * t e s t a r e g i v e n i n A p p e n d i x C - P a r t I I . F i g u r e 17 shows t h e i n v e r s e o f c o r r e c t i o n f a c t o r s ( I Iticit) a s f u n c t i o n s o f wind s p e e d and a v e r a g i n g p e r i o d . The i n v e r s e i s p l o t t e d f o r e a s e of c o m p a r i s o n w i t h F i g u r e 12. A l s o , t h e i n v e r s e r a t i o i s bounded between 0 and 1.0.. S i n c e jE t e € i n c r e a s e s as t h e wind speed a p p r o a c h e s 0 m/sec, the i n v e r s e 62 F i g u r e 16. The r e l a t i v e e r r o r i n d u c e d i n t h e r e s i d u a l v a r i a n c e s by a p p l i c a t i o n o f a c o r r e c t i o n f a c t o r 0 + 6 ) t o r e a d j u s t f o r t h e s y s t e m a t i c b i a s i n t h e d i f f e r e n c e v a r i a n c e s . r a t i o i s more c o n v e n i e n t f o r p l o t t i n g . I n a l l r e s p e c t s , t h e r e g r e s s e d c o r r e c t i o n f a c t o r s a r e q u a l i t a t i v e l y s i m i l a r t o t h e a v e r a g e r a t i o o f s t r e s s e s (R(L) d e f i n e d b e f o r e ) . The mean s h i p v a l u e s a r e n e a r l y i d e n t i c a l . The d i s p a r i t y o f S t a t i o n N a t L=4.0 d a y s and 6.75 m/sec p l o t s i s a l s o e v i d e n t . The g e o g r a p h i c s t a n d a r d d e v i a t i o n s a r e s i m i l a r i n shape and m a g n i t u d e . F i n a l l y an e x a m i n a t i o n o f Appendix C P a r t I I r e v e a l s t h a t t h e e r r o r i n t h e s l o p e i s l a r g e r t h a n t h e s c a t t e r between s h i p s and has t h e l a r g e s t v a l u e s f o r low wind s p e e d s . . 63 AVERAGING PERIOD= 0 .25 DAYS HVERHG1MG PERIOD= 4.00 DAYS 0.0 14.0 28 0 0.0 14.0 28.0 W I N D S P E E D I N M / S E C W I N D S P E E D I N M / S E C WIND SPEED =6.75 M/SEC I—o ' C J CL LU CXL O (_) Y Y T 1 0.0 12.0 AVERAGING PERIOD 24.0 I N DAYS F i g u r e 17. C o r r e c t i o n f a c t o r s ^ f o r t h e c o n s t a n t d r a g c o e f f i c i e n t . S t a t i o n N i s X . The s o l i d l i n e i s ± 1 s t a n d a r d d e v i a t i o n o f t h e g e o g r a p h i c a l l y a v e r a g e d mean v a l u e . 64 3.7 A c c u r a c y Of T r a n s f o r m a t i o n s The d i f f e r e n c e means, d i f f e r e n c e v a r i a n c e s , r e s i d u a l v a r i a n c e s and c o r r e l a t i o n c o e f f i c i e n t s were d e t e r m i n e d by a p p l y i n g and t h e r e s u l t s a p p e a r i n A p p e n d i x D. T h e s e q u a n t i t i e s w i l l be examined i n l i g h t o f t h e i r a c t u a l v a l u e s and the a r i t h m e t i c d i f f e r e n c e between t h e u n i m p r o v e d v a l u e s o f A p p e n d i x 6 and t h e i m p r o v e d v a l u e s c f Appendix D. As an example, t h e d i f f e r e n c e means f o r t h e x component, c o n s t a n t d r a g c o e f f i c i e n t a p p e a r i n F i g u r e 18(a),. A c o m p a r i s o n w i t h F i g u r e 7 i l l u s t r a t e s s e v e r a l i n t e r e s t i n g f e a t u r e s . F i r s t , t h e d i f f e r e n c e means have been r e d u c e d by a f a c t o r of a b o u t 10. S e c o n d , t h e r e a p p e a r s t o be an i n v e r s e r e l a t i o n i n t h e amount o f r e d u c t i o n a c h i e v e d . I n F i g u r e 7 S t a t i o n s A and N, w i t h no c o r r e c t i o n a p p l i e d , have t h e s m a l l e s t d i f f e r e n c e means. In F i g u r e 18, a f t e r a p p l i c a t i o n o f £ie£ , t h e y now have t h e l a r g e s t d i f f e r e n c e mean v a l u e s . C o n v e r s e l y , S t a t i o n s C and D h a v e t h e h i g h e s t d i f f e r e n c e means with no c o r r e c t i o n , b u t a r e l e s s t h a n 0.02 dFa f o r a l l a v e r a g i n g p e r i o d s a f t e r c o r r e c t i o n . The i m p r o v e m e n t s a p p e a r i n F i g u r e 19(a) f o r t h e x component, c o n s t a n t d r a g c o e f f i c i e n t . In a l l c a s e s t h e r e was some improvement. An i n s p e c t i o n o f A p p e n d i c e s B and D i n d i c a t e s t h a t t h e most d r a m a t i c i m p r o v e m e n t s o c c u r where t h e u n c o r r e c t e d v a l u e s were i n i t i a l l y l a r g e — i n p a r t i c u l a r f o r l o n g e r a v e r a g i n g p e r i o d s and t h e l i n e a r d r a g c o e f f i c i e n t . The d i f f e r e n c e v a r i a n c e v a l u e s a r e now r a n d o m l y s c a t t e r e d and bounded between about ± 6% u s i n g t h e c o n s t a n t d r a g c o e f f i c i e n t and a b o u t ± 10% u s i n g t h e l i n e a r d r a g c o e f f i c i e n t — a g a i n a 10 f o l d improvement o v e r t h e u n c o r r e c t e d v a l u e s . The 65 X COMPONENT cog C E ° LU LU a o o 0.1 1.0 10.0 AVERAGING PERIOD IN DAYS 100.0 CO K g 2 : . cr° cr cr . > C\l UJo <->o. 2 : I LU cr 0.1 X COMPONENT 1.0 10.0 AVERAGING PERIOD IN DAYS 100 .0 F i g u r e 18 <a) F i g u r e 18(b) Lug CX I — I cr J > _ l ° C E o ' ZD Q t 1 CO ' LU cr 0.1 X COMPONENT f I I 1.0 10.0 AVERAGING PERIOD IN DAYS 100.0 CO '—'cn , LU O CJ O o " LU CTm crcn <-> 0.1 X COMPONENT Y 1.0 10.0 100 0 AVERAGING PERIOD IN DAYS F i g u r e 18 (c) F i g u r e 18(d) F i g u r e 18. The t e s t f u n c t i o n s o b t a i n e d when t h e s h i p s 1 i n d i v i d u a l v a l u e s were u s e d . The example i s f o r t h e x component c o n s t a n t d r a g c o e f f i c i e n t . S t a t i o n N i s X 6 6 X COMPONENT CO C O c r 0 LU 2: LU <_) Cu-LU U _ U _ Q 0.1 1.0 10.0 AVERAGING PERIOD IN DAYS 100 .0 CO LU C->co e r r CE C J " 2 c LU Cr: 0 0 0 .1 X COMPONENT 1.0 10.0 AVERAGING PERIOD I.N DAYS 100.0 F i g u r e 19 (a) F i g u r e 19(b) co LU<j CJ •• Cr: . cr. > C E o " ZD Q co • LU cr o 0.1 X COMPONENT 1.0 10.0 . AVERAGING PERIOD IN DAYS 100.0 CO O CJ CM Z ° O o ' c r LU cr C J 0 X COMPONENT 1.0 10.0 AVERAGING PERIOD IN DAYS 100.0 F i g u r e 19 (c) F i g u r e 19(d) F i g u r e 19. Improvement i n t h e t e s t v a l u e s o v e r t h e raw t e s t r e s u l t s a f t e r a p p l i c a t i o n o f t h e i n d i v i d u a l s h i p s 1 £«.e c o r r e c t i o n f a c t o r f o r the x component c o n s t a n t d r a g c o e f f i c i e n t . 67 most a c c u r a t e v a l u e s c c c u r , n o t u n e x p e c t e d l y , f o r t h e l o w e r a v e r a g i n g p e r i o d s . The d i f f e r e n c e s between F i g u r e s 18 and 7 f o r e a c h a v e r a g i n g p e r i o d a p p e a r i n F i g u r e 1 9 ( b ) . A g a i n a l l c h a n g e s a r e p o s i t i v e , i n d i c a t i n g t h a t t h e c o r r e c t i o n s h a v e i m p r o v e d t h e l o n g - t e r m v a r i a n c e . I n d e e d f o r L=28 days t h e r e a r e i m p r o v e m e n t s up t o 85% i n t h e 3H v a r i a n c e . F i g u r e 18(c) shows t h e f i n a l c a l c u l a t e d r e s i d u a l v a r i a n c e s f o r the x component c o n s t a n t d r a g c o e f f i c i e n t . . Note t h a t t h e EV a x i s s c a l e has been i n c r e a s e d by a f a c t o r o f 5.0 from F i g u r e 7 ( c ) . W i t h t h e e x c e p t i o n c f S t a t i o n N a l l v a l u e s a r e l e s s t h e n 6%. F i g u r e 19 (c) i n d i c a t e s t h e i m p r o v e m e n t s a c h i e v e d . F o r low a v e r a g i n g p e r i o d s , the d i f f e r e n c e s a r e q u i t e s m a l l . By L=4 d a y s , however, an improvement o f a b o u t 5% has been a c h i e v e d . T h e s e i m p r o v e m e n t s i n c r e a s e t o L=28 days where i m p r o v e m e n t s o f the o r d e r of 20% f o r t h e c o n s t a n t d r a g c o e f f i c i e n t s and 30% f o r t h e t h e l i n e a r d r a g c o e f f i c i e n t s v a l u e s a r e common. F i g u r e 18(d) shows the f i n a l c o r r e l a t i o n c o e f f i c i e n t s . B e c a u s e t h e raw c o r r e l a t i o n c o e f f i c i e n t s a r e a l l q u i t e h i g h (>0.90), the b r o a d f e a t u r e s o f 19(d) a r e n o t s i g n i f i c a n t l y d i f f e r e n t from t h e raw v a l u e s . The h i g h i n i t i a l c o r r e l a t i o n s a c c o u n t f o r t h e l a r g e r e d u c t i o n s i n t h e r e s i d u a l v a r i a n c e s t h a t c a n be a c h i e v e d w i t h c n l y a l i n e a r r e g r e s s i o n . F i g u r e 1 9 ( d ) , however, d e m o n s t r a t e s t h e i m p r o v e m e n t s a c h i e v e d o v e r t h e raw c o r r e l a t i o n c o e f f i c i e n t s . I n a l l c a s e s t h e i m p r o v e m e n t s a r e s m a l l f o r low a v e r a g i n g p e r i o d s and r i s e t o v a l u e s o f up t o 0.05 a t L=28 d a y s . An e x a m i n a t i o n o f A p p e n d i x E r e v e a l s t h a t a t L=2 d a y s t h e r e a r e no v a l u e s l e s s t h a n 0.99 . S i n c e t h e c o r r e l a t i o n c o e f f i c i e n t i s bounded by 1.0, t h e r e i s l i t t l e room f o r 68 improvement a t t h e low a v e r a g i n g p e r i o d s . F o r a v e r a g i n g p e r i o d s o f g r e a t e r t h a n 1.0 d a y s , t h e VA e s t i m a t e s o f t h e l o n g - t e r m v a r i a n c e s as q u a n t i f i e d by t h e DV and t h e p c i n t - b y - p c i n t v a r i a n c e as q u a n t i f i e d by t h e EV c a n be s u b s t a n t i a l l y i m p r o v e d t h r o u g h a p p l i c a t i o n o f t h e c o r r e c t i o n s g i v e n i n A p p endix C. I n r e g i o n s where t h e u n i mproved e s t i m a t e s o f the c l i m a t o l o g i c a l VA f l u x e s d i f f e r e d g r e a t l y f r o m t h e 2H f l u x e s (as q u a n t i f i e d by t h e DMs), d r a m a t i c i m p r o v e m e n t s r e s u l t e d w i t h a p p l i c a t i o n o f t h e ^<?f f a c t o r . The major s t r e n g t h o f t h e m u l t i v a r i a t e r e g r e s s i o n i s t o i n c r e a s e t h e c o r r e l a t i o n c o e f f i c i e n t s p a r t i c u l a r l y a t l o n g e r a v e r a g i n g p e r i o d s . I f a s i m i l a r r e g r e s s i o n had been p e r f o r m e d i r r e s p e c t i v e o f wind speed g r o u p i n g no i m p r o v e m e n t s would have r e s u l t e d b e c a u s e t h e c o r r e l a t i o n c o e f f i c i e n t i s i n d e p e n d e n t o f an o v e r a l l s c a l e change. 69 CHAPTER IV HEAT FLUXES T h i s c h a p t e r d e s c r i b e s t h e e f f e c t s o f a v e r a g i n g w i nds, t e m p e r a t u r e s , and a b s o l u t e h u m i d i t i e s on t h e s e n s i b l e and l a t e n t h e a t f l u x e s . The s e n s i b l e h e a t f l u x i s a measure o f t h e h e a t t r a n s f e r r e d by c o n v e c t i o n i n t o o r o u t o f t h e s e a s u r f a c e w h i l e the l a t e n t h e a t f l u x i s a measure o f t h e heat l o s t o r g a i n e d by t h e e v a p o r a t i o n o r c o n d e n s a t i o n . The b u l k a e r o d y n a m i c f o r m u l a e f o r t h e i r c a l c u l a t i o n a r e g i v e n i n E g u a t i o n s 1.2(c) and ( d ) . 4.1 T h r e e - h o u r l y Heat F l u x e s S i m i l a r t o t h e 3H momentum f l u x e s , t h e 3H h e a t f l u x e s had summer minima and w i n t e r maxima a v e r a g e v a l u e s o f which s t a t i o n C was c h o s e n as an example. P l o t s f c r S t a t i o n C o f t h e y e a r l y and m o n t h l y l a t e n t and s e n s i b l e 3H h e a t f l u x e s w i t h e r r o r b a r s i n d i c a t i n g ± 1 sample s t a n d a r d d e v i a t i o n a p p e a r i n F i g u r e s 20 (a) and ( b ) . . S i m i l a r g r a p h s w i t h ± 1 s t a n d a r d d e v i a t i o n o f t h e m o n t h l y means a p p e a r i n F i g u r e s 20(c) and (d) r e s p e c t i v e l y . I n t h i s s e c t i o n , t h e s e n s i b l e h e a t r e s u l t s w i l l be q u o t e d i n p a r e n t h e s e s f o l l o w i n g t h e l a t e n t h e a t r e s u l t s . The e x t r e m e v a l u e s i n t h e means a r e much g r e a t e r between months t h a n between y e a r s . Between months t h e maximum v a l u e s a r e 80.8 (34.7) W a t t s / m 2 i n D e c e m b e r ( J a n u a r y ) and t h e minimum v a l u e s a r e 12.4 (-7.4) Watts/m 2 i n J u l y ( J u l y ) . The minus s i g n i n d i c a t e s a net t r a n s p o r t o f h e a t f r o m t h e a i r t o t h e s e a . T h i s may be due t o a d v e c t i o n o f warm c o n t i n e n t a l a i r i n t h e summer to t h e m i d - A t l a n t i c . Between y e a r s t h e 70 WEATHERSHIP C WEATHERSHIP C SENSIBLE HEAT LATENT HEAT 52.0 " i r 56.0 60.0 YEAR 64.0 66.0 d 0 UJ X SENSIBLE HEAT LATENT HEAT J F M A M J J A S O N Q MONTH f i g u r e 20 (a) F i g u r e 20 (b) WEATHERSHIP C WEATHERSHIP C 48.0 SENSIBLE HEAT LATENT HEAT 56.0 YEAR 64.0 68.0 000 5<o UJ SENSIBLE HEAT LATENT HEAT J F M A M J J MONTH A S 0 N D F i g u r e 20 (c) F i g u r e 20„ The y e a r - t o - y e a r and h e a t f l u x e s a t S t a t i o n C. The s t a n d a r d d e v i a t i o n i n F i g u r e s d e v i a t i o n o f the monthly means i n F i g u r e 20 (d) m o n t h l y v a r i a t i o n s o f t h e mean e r r o r b a r s a r e ± 1 sample 20(a) and (b) and ± 1 s t a n d a r d F i g u r e s 20(c) and ( d ) . 71 l a t e n t ( s e n s i b l e ) h e a t f l u x e s have maxima i n 1959(1957) o f 67.9(19.9) Watts/m 2 and minima i n 1949(1949) o f 34.5(2.3) Watts/m 2 . I t i s c l e a r f r o m F i g u r e 20 t h a t t h e s t a n d a r d d e v i a t i o n s i n the y e a r l y h e a t v a l u e s a r e f a i r l y c o n s t a n t . The maximum y e a r l y s t a n d a r d d e v i a t i o n s f o r the l a t e n t ( s e n s i b l e ) h e a t f l u x e s a r e 90.3 (69. 8) Watts/m* f o r 1957 (1957) w h i l e t h e minimum v a l u e s a r e 62.2 (34.4) Watts/m 2 i n 1956 (1950). The s t a n d a r d d e v i a t i o n s o f t h e m o n t h l y means f o r b o t h h e a t f l u x e s a r e a p p r o x i m a t e l y one-h a l f o f t h e t o t a l s t a n d a r d d e v i a t i o n s b a s e d on a l l t h e t h r e e -h o u r l y f l u x r e a d i n g s i n d i c a t i n g t h a t a b o u t o n e - g u a r t e r o f t h e t o t a l v a r i a n c e may be i n p e r i o d s o f g r e a t e r t h a n one month. F i g u r e s 20 (b) and (d) show t h e d i f f e r e n c e i n s t a n d a r d d e v i a t i o n between t h e summer and w i n t e r months. The December h e a t f l u x s t a n d a r d d e v i a t i o n i s 91.1(69.5) Watts/m 2 w h i l e t h e J u l y v a l u e s a r e 38.3(19.0) Watts/m 2. The s t a n d a r d d e v i a t i o n s of the m o n t h l y means v a r y from 34.0(26.8) Watts/m 2 i n December t o 12.8(6.3) Watts/m 2 i n J u l y i n d i c a t i n g t h a t t h e a n n u a l c y c l e i s p r e s e n t i n t h e means and t h e v a r i a n c e s . The t o t a l s h i p s ' means and s t a n d a r d d e v i a t i o n s o f t h e v e l o c i t y components, a i r - s e a t e m p e r a t u r e , a i r - s e a a b s o l u t e h u m i d i t y d i f f e r e n c e , l a t e n t h e a t and s e n s i b l e f l u x e s a p p e a r i n T a o l e X. The mean h e a t f l u x e s a r e a l l o f t h e same o r d e r as t h e s t a n d a r d d e v i a t i o n s . O c e a n c g r a p h i c a l l y , t h e d a t a may be d i v i d e d i n t o f o u r main r e g i m e s . S t a t i o n s A, B , C, and M a r e i n S u b - A r c t i c r e g i o n s . They a r e c h a r a c t e r i z e d by s e a s u r f a c e t e m p e r a t u r e s o f a b o u t 1° C and c o l d e r a i r t e m p e r a t u r e s . As one p r o c e e d s s o u t h t h e a i r 72 The mean and s t a n d a r d d e v i a t i o n s o f t h e x and y component wind v e l o c i t i e s , t h e a i r - s e a t e m p e r a t u r e d i f f e r e n c e s , t h e a i r - s e a h u m i d i t y d i f f e r e n c e s and t h e l a t e n t and s e n s i b l e h e a t f l u x e s . The f i r s t l i n e f o r e a c h s h i p i s t h e mean v a l u e and t h e s e c o n d l i n e i s s t a n d a r d d e v i a t i o n . SHIP A 1 1 m/sec I -0. 1 I 7.8 m/sec 0.0 8.0 1 A T 1 o c | 1.6 I 2.2 g/m 3 1.7 1.3 I v4s I W/m2 i 34.4 I 60.5 W/m2 62.8 65. 3 B I -0.8 I 7.8 ! 1.7 8.3 1.8 2.9 1. 5 1.2 I 41.4 | 79.6 ! 58. 9 64. 5 C | 0.7 | 7.3 I 3.1 8.2 i 0.5 2. 0 i 1. 4 1. 5 | 12.0 | 51.3 ! 54. 1 74. 5 | D I L I | 7.6 ! 3.9 7.6 i 2. 1 3. 1 ! 3.6 2. S I 45.9 | 85.4 ! 140. 1 , 150.7 E I 1.3 I 6.3 j 2.0 6.1 0. 9 1.7 ! 4.4 2.7 | 14.0 1 34.7 ! 124.7 116.2 | I I 2.0 1 7.5 ! 1.6 8.3 i 1.6 1.8 ! 2. 0 1. 3 I 32.9 i 49.9 j 78. 1 | 6 9.8 | J I 2.0 1 7.3 ! 3.4 7.7 ! 1.0 1.5 i 1.9 1. 5 I 20.3 { 38.8 I 73.7 , 72.8 | K | -0. 2 I 6.8 j 2. 1 7.3 ! 0. 3 1.7 ! 2. 2 1.9 j 5.3 | 32.6 j 71.8 | 80.6 | M | 0.3 I 7.6 i 1.0 6.9 i 1.9 2. 1 i 2. 0 1. 3 I 34.9 I 50.0 ! 69. 1 | 5 9.7 I N I -0.8 I a. 6 i -2. 5 4.7 i 1.2 1.2 ! 4. 8 1. 9 I 14.4 | 19.5 ! 110.1 | 75.0 | P I u.o I 7.6 ! 1.4 7.5 ! 0.3 1.2 ! 1. 1 1. 2 I 5. 8 I 31.1 ! 42. 4 | 57.5 | t e m p e r a t u r e i n c r e a s e s , d e c r e a s i n g t h e a i r - s e a t e m p e r a t u r e d i f f e r e n c e . S t a t i o n D l i e s a t t h e t r a n s i t i o n r e g i o n between t h e G u l f S tream and N o r t h A t l a n t i c D r i f t . Here t h e water i s r e l a t i v e l y 73 warm (about 5-10°C) a c c o u n t i n g f o r l a r g e a i r - s e a t e m p e r a t u r e d i f f e r e n c e s . The a d v e c t i o n o f l a r g e h o r i z o n t a l s e a s u r f a c e t e m p e r a t u r e g r a d i e n t s and i n v a s i o n s o f c o n t i n e n t a l a i r a c c o u n t f o r l a r g e s t a n d a r d d e v i a t i o n s i n t h e h e a t f l u x e s . S t a t i o n s E and N l i e i n t h e m i d d l e o f t h e l a r g e A t l a n t i c and P a c i f i c s u b - t r o p i c g y r e s . They a r e c h a r a c t e r i z e d by m o d e rate a i r - s e a t e m p e r a t u r e d i f f e r e n c e s and by d r y p r e v a i l i n g winds t h u s a c c o u n t i n g f o r moderate s e n s i b l e h e a t s and l a r g e l a t e n t h e a t f l u x v a l u e s . S t a t i o n N i s t h e T r a d e Wind r e g i o n , where s t e a d y summer winds a c c o u n t f o r t h e s m a l l h e a t f l u x s t a n d a r d d e v i a t i o n s i n c o m p a r i s o n t o S t a t i o n E . S t a t i o n s I , J , and K l i e on t h e e a s t e r n b o undary o f t h e A t l a n t i c Ocean. P r o c e e d i n g s o u t h , t h e a i r t e m p e r a t u r e becomes warmer more g u i c k l y t h a n the c o r r e s p o n d i n g i n c r e a s e i n s e a s u r f a c e t e m p e r a t u r e a c c o u n t i n g f o r l o w e r s e n s i b l e h e a t f l u x e s . The t h r e e s t a t i o n s show s i m i l a r a i r - s e a h u m i d i t y d i f f e r e n c e s and m o d e rate l a t e n t h e a t f l u x v a l u e s . 4.2 U n c o r r e c t e d T e s t R e s u l t s The d i f f e r e n c e means, d i f f e r e n c e v a r i a n c e s , r e s i d u a l v a r i a n c e s and c o r r e l a t i o n c o e f f i c i e n t s as d e f i n e d i n E g u a t i o n s 2.16-2.19 were c a l c u l a t e d w i t h no c o r r e c t i o n f a c t o r s a p p l i e d . The r e s u l t s a p p e a r i n F i g u r e s 21(a) t h r o u g h (h) w h i l e t h e raw v a l u e s a r e i n A p p e n d i x E. T a b l e XI c o n t a i n s t h e 3H h e a t f l u x v a r i a n c e a t e ach a v e r a g i n g p e r i o d so t h e d i f f e r e n c e v a r i a n c e s and r e s i d u a l v a r i a n c e s c a n be c o n v e r t e d t o a b s o l u t e q u a n t i t i e s . As i n t h e wind s t r e s s c a s e , t h e h e a t f l u x d i f f e r e n c e means (DMs) a p p e a r t o be d e p e n d e n t upon t h e a v e r a g e 3H h e a t f l u x v a l u e 74 TABLE XI The a b s o l u t e l a t e n t and s e n s i b l e h e a t f l u x v a r i a n c e s as a f u n c t i o n o f a v e r a g i n g p e r i o d . The columns r e f e r t o t h e a v e r a g i n g p e r i o d i n days and t h e v a r i a n c e s a r e i n ( W a t t s / m 2 ) 2 X i Q 3 . j. + + SHIP| 0.25 | +-VARIANCES 0.50 | 1. - SENSIBLE 0 | 2.0 | HEAT FLUX 4.0 | 7.0 | 14.0 } 28. 0 A B C D E I J K M N P 3. 5 11 6. 154 2.4S6 6.947 1. 133 2.374 1.423 1.001 2. 398 0. 34 1 0. 896 3. 303 5. 900 2. 3 14 6.512 1.057 2.219 1. 3 16 0. 941 2. 266 0.302 0. 806 2. 2. 5. 0. 1. 1. 0. 2. 0. 0. 982 461 020 725 92 1 998 160 860 058 275 708 2. 508 4.870 1. 626 4.646 0. 759 1. 687 0. 968 0. 764 1. 775 0. 236 0. 577 2.0 35 4. 142 1. 263 3.679 0. 573 1.383 0.747 0. 672 1. 453 0. 192 0.448 1.669 3.684 1.045 3.084 0. 451 1. 133 0.602 0. 589 1.200 0. 162 0.345 1.331 3.077 0.797 2.479 0. 326 0.867 0.412 0.510 0.900 0. 124 0.240 0.994| 2. 530| 0.566| 1.892 0. 245| 0. 670 0. 325 0.442| 0.70 6| 0. 08 1 0. 18(1 VARIANCES - LATENT HEAT FLUX •+ + (-| 2. 0 | 4.C I +-14.0 | 1 28. 0 1 1. 064| 1.518| 1. 23 3 | 6. 17 1 3.295| 1. 029 | 0. 8 36 j 1.668j 0. 884| 0. 8701 0. 750 SHIP1 0.25 J 0.50 | 1.0 I 7.0 A B C D E I J K M N P 4. 078 4. 0 17 5.326 21.51 12. 79 4.600 5.0 10 6. 155 3. 374 5.084 3. 1 15 3.785 3.795 4. 951 20. 15 12. 01 4. 205 4.582 5.753 3. 122 4. 701 2. 853 3.343 3.443 4. 330 17. 70 10.74 3.655 3.966 5. 165 2.747 4. 2 13 2.509 2. 75 1 2. 989 3. 495 14.71 9. 036 2. 933 3.112 4. 351 2. 297 3. 542 2. 034 2. 2. 11 7. 2. 2. 3. 1. 2 • 1. 179 484 663 . 67 008 318 242 500 838 732 580 1. 2, 2. 9. « 1. 1. 2. 1. 2. 1. 812| 161 | 154 | 680 | 693 j 879 | 732 | 84 7 J 50 2 | 157| 253 J I 1.426 1.812 1.639 7.830 4.237 1.373 1. 132 2.091 1. 133 1.481 0.957 and w i t h m i n e r e x c e p t i o n s , i n c r e a s e a p p r o x i m a t e l y e x p o n e n t i a l l y w i t h a v e r a g i n g p e r i o d . A c o m p a r i s o n o f T a b l e X and A p p e n d i x E i n d i c a t e s t h a t t h e s i z e s o f t h e d i f f e r e n c e means a r e w e l l c o r r e l a t e d w i t h t h e a v e r a g e 3H h e a t f l u x . . At L=28.0 d a y s , t h e s e n s i b l e h e a t f l u x e s f a l l i n t o two d i s t i n c t g r o u p s -- S t a t i o n s A, B, D, I , and M w i t h a v e r a g e DMs g r e a t e r t h a n 18 Watts/m 2 and 0.1 SENSIBLE HEAT FLUX 1.0 10.0 AVERAGING PERIOD IN DATS 100.0 C X 0 0 L U C J or? L U o o ' LATENT HEAT FLUX .1 1.0 10.0 100.0 AVERAGING PERIOD IN DATS F i g u r e 2 1 ( a ) DMs i n Watts/m 2 F i g u r e 2 1 ( b ) DMs i n W a t t s / m 2 SENSIBLE HEAT FLUX .1 1.0 10.0 100.0 AVERAGING PERIOD IN DATS CO L U <->LO z . cr° » « or c r . > L U C J " L U O i L U o . i 0.1 LATENT HEAT FLUX 1.0 10.0 AVERAGING PERIOD IN DAYS 100.0 F i g u r e 2 1 (c) F i g u r e 2 1 (d) SENSIBLE HERT FLUX 0.1 1.0 10.0 fiVERRGING PERIOD IN DRYS 100.0 tn LUo, CJ . ^-o CT ^ d o ' D CO LU c r LATENT HERT FLUX .1 1.0 10.0 • RVERRGING PERIOD IN DRYS 100 .0 F i g u r e 21 (e) F i g u r e 2 1 ( f ) S^ ENSJ BLE HERT FLUX i « 8 F i g 1 1.0 10.0 RVERRGING PERIOD IN DRYS ure 21 (g) 100.0 CO i— -z. o L J zT. Oo" •—i I— cr _ i • LU cr crm <-> o.l l^ flTENT HERT FLUX 1.0 10.0 RVERRGING PERIOD JN DRYS F i g u r e 21 (h) .100.0 F i g u r e the VA 21. The t e s t g u a n t i t i e s w i t h no c o r r e c t i o n a p p l i e d h e a t f l u x e s . 77 S t a t i o n s C,D, E, J , N, and P h a v i n g BMs l e s s t h a n 10 Watts/m 2. The l a t e n t h e a t f l u x e s have t h r e e d i s t i n c t g r o u p s . S t a t i o n s D and E have u n c o r r e c t e d DMs g r e a t e r t h a n 60 Watts/m 2. a t L=28.0 da y s , S t a t i o n s A, B, C, I , J , K, M and N have DMs i n t h e r a n g e o f 20 t o 60 Watts/m 2; S t a t i o n P has d i s t i n c t l y s m a l l e r DMs a t l e s s t h a n 20.0 Watts/m 2. The same g r o u p i n g s o c c u r i n t h e 3H mean f l u x v a l u e s shown i n T a b l e X i n d i c a t i n g t h a t t h e l a r g e r c l i m a t o l o g i c a l e r r o r s o c c u r i n r e g i o n s w i t h t h e h i g h e r i n i t i a l mean f l u x . The d i f f e r e n c e v a r i a n c e s (DVs) f o r a l l s h i p s e x c l u d i n g S t a t i o n N d i f f e r c n l y s l i g h t l y . B o t h h e a t f l u x e s show i n c r e a s e s f r o m n e a r 0 a t L=0.25 d a y s t o mean maximum v a l u e s o f a b o u t 0.55 t o 0.65 a t 1=28.0 d a y s . S t a t i o n N has m a r k e d l y l o w e r DVs from L=1.0 t o L=14.0 d a y s ' i n t h e s e n s i b l e h e a t f l u x . F o r t h e l a t e n t h e a t f l u x . S t a t i o n s N's v a l u e s a r e n e a r l y 0.0 Watts/m 2 up t o L=4.0 d a y s and t h e n go n e g a t i v e — i n c o n t r a s t t o a l l t h e o t h e r s h i p s . . A l l s h i p s have s i m i l a r r e s i d u a l v a r i a n c e s (EVs) up t o L=4 d a y s . The s e n s i b l e h e a t f l u x e s t h e n s p l i t i n t o two d i s t i n c t g r o u p s . . The f i r s t i n c l u d e s S t a t i o n s A, E , I , M, and N h a v i n g BV v a l u e s o f g r e a t e r t h a n 40.0% at 1=28.0 d a y s . The o t h e r s have EVs l e s s t h a n 30.0%. T h e . l a t e n t h e a t f l u x EVs a r e g e n e r a l l y l a r g e r ( e x c e p t a t S t a t i o n E) t h a n f o r t h e s e n s i b l e h e a t f l u x e s . The a v e r a g e v a l u e a t L=28.0 days i s abo u t 35%. Dp t o L=7.0 d a y s , t h e S t a t i o n N v a l u e s a r e i n d i s t i n g u i s h a b l e ( a l t h o u g h b i a s e d h i g h ) from t h e o t h e r v a l u e s . At 1=14.0 d a y s , however, t h e S t a t i o n N v a l u e s a r e much g r e a t e r t h a n t h e o t h e r s h i p s . I n d e e d , a t L= 28.0 d a y s t h e S t a t i o n N RV i s g r e a t e r t h a n 100.0% 78 which i s n o t shown i n F i g u r e 21. The c o r r e l a t i o n c o e f f i c i e n t s f o r t h e h e a t f l u x e s a r e l o w e r t h a n f o r t h e momentum f l u x e s . T h o s e f o r t h e l a t e n t h e a t f l u x a r e l o w e r t h a n f o r t h e s e n s i b l e h e a t f l u x . At L=28.0 days S t a t i o n N has t h e l o w e s t c o r r e l a t i o n c o e f f i c i e n t o f 0.438 (not shown) f o r t h e l a t e n t h e a t f l u x and 0.736 f o r t h e s e n s i b l e h e a t f l u x . A f t e r L=14.0 d a y s , t h e s e n s i b l e h e a t f l u x c o r r e l a t i o n c o e f f i c i e n t s d i v i d e i n t o t h e same two g r o u p s a s f o r t h e BV v a l u e s -- S t a t i o n s A, E, I , M, and N w i t h v a l u e s l e s s t h a n 0.835 (at L=28.0 days) and the r e s t h a v i n g c o r r e l a t i o n c o e f f i c i e n t s g r e a t e r t h a n 0.900. 4 • 3 Heat R e g r e s s i o n F i g u r e 22 shows an example o f t h e 3H h e a t f l u x p l o t t e d a g a i n s t t h e VA h e a t f l u x f o r S t a t i o n A, L=28 d a y s . S i m i l a r t o the s t r e s s c a s e , shown i n F i g u r e 6, t h e s c a t t e r i n c r e a s e s f o r extreme p o s i t i v e and n e g a t i v e v a l u e s . As t h e VA f l u x a p p r o a c h e s 0.0 W a t t s / m 2 , t h e s c a t t e r becomes more, c o n s t r i c t e d . N o t e , however, t h a t t h e r e i s a b i a s t o w a r d s p o s i t i v e h e a t f l u x e s . . Two i m p o r t a n t d i f f e r e n c e s e x i s t between t h e h e a t f l u x r e g r e s s i o n and t h e momentum f l u x r e g r e s s i o n . F i r s t , t h e a n a l y s i s o f t h e raw 3H v a l u e s r e v e a l e d t h a t t h e l a t e n t and s e n s i b l e h e a t f l u x e s a r e s t a t i s t i c a l l y q u i t e d i s t i n c t q u a n t i t i e s . C o n s e q u e n t l y t h e r e g r e s s i o n was p e r f o r m e d s e p a r a t e l y on each f l u x . T hus, no a t t e m p t was made t o assume t h a t t h e f l u x e s might be s i m i l a r and t h u s p r o d u c e a s i n g l e t r a n s f o r m a t i o n a p p l i c a b l e t o b o t h . S e c o n d , as shown i n T a b l e X, the means a r e o f t h e same magnitude as t h e s t a n d a r d d e v i a t i o n s . 79 SENSIBLE HEAT FLUX LATENT HERT FLUX -40.0 ' 4 0 . 0 120.0 200 -40.0 40.0 120 0 -Vfl HERT FLUX IN WRTTS/MXX2 VR HERT FLUX IN WRTTS/MXX2 F i g u r e 22. The s e n s i b l e and l a t e n t 3H v e r s u s VA h e a t f l u x e s a t S t a t i o n C, L=28.0 d a y s . C o n s e q u e n t l y t h e f o l l o w i n g q u a n t i t y : |3 J"i». was m i n i m i z e d as o u t l i n e d i n A p p e n d i x A.1 where X and X 1 a r e t h e 3fl and VA v a r i a t e s f c r e i t h e r t h e l a t e n t o r s e n s i b l e h e a t f l u x e s . T h i s g i v e s : where a l l v a r i a t e s a r e d e f i n e d i n S e c t i o n 2.5. T h i s i s a m a t r i x 80 e q u a t i o n o f t h e form x= t> + A x where x and b a r e v e c t o r s w i t h components c o r r e s p o n d i n g t o 13 B e a u f o r t c a t e g o r i e s and _A i s a 13x13 m a t r i x . The s o l u t i o n was o b t a i n e d by G a u s s i a n e l i m i n a t i o n f o l l o w e d by i t e r a t i v e i mprovement u n t i l a r e l a t i v e e r r o r o f l e s s t h a n .001 was f o u n d . A p p e n d i x A. 1 shows t h a t t h e DVs were e x a c t l y e q u a l t o t h e fiVs and t h e s y s t e m a t i c p o s i t i v e DV b i a s a g a i n e x i s t s . T h i s f a c t p r o v i d e d a c o n v e n i e n t c h e c k t o e n s u r e t h a t t h e computer programmes were r u n n i n g c o r r e c t l y . The s y s t e m a t i c b i a s was e l i m i n a t e d by : STy *»-where ^-4* i s t h e 3H s t a n d a r d d e v i a t i o n , T i t ' i s t h e VA s t a n d a r d d e v i a t i o n w i t h ^ t e a p p l i e d and ^ r e p r e s e n t s e i t h e r t h e l a t e n t o r s e n s i b l e h e a t . An a t t e m p t was made t o c o r r e c t £b_e on a B e a u f o r t c a t e g o r y b a s i s ( i e . = ) . However, i n many <Syw_ c a s e s t h e r e g u i r e d i t e r a t i o n s f a i l e d t o c o n v e r g e . A p p e n d i x A.3 shows t h a t when r e a d j u s t i n g f r o m t h e minimum EV v a l u e , t h e c o r r e c t i o n g i v e n i n E q u a t i o n 4.4 i n d u c e s a f u r t h e r e r r o r i n EV g i v e n by: Thus f o r c o r r e l a t i o n c o e f f i c i e n t s o f 0.9 o r g r e a t e r , t h e i n d u c e d 81 e r r o r i s l e s s t h a n 1.0%. A g a i n , the p r i m e s w i l l be d r o p p e d and i t w i l l be u n d e r s t o o d t h a t i n c l u d e s t h e DV c o r r e c t i o n . 4.4 Wind Dependent C o r r e c t i o n F a c t o r s The $ w « f o r t h e h e a t f l u x e s were c a l c u l a t e d and a p p e a r i n A p p e n d i x F - P a r t I. F i g u r e 25 shows t h e I / £ fa*values as f u n c t i o n s o f wind s p e e d and a v e r a g i n g p e r i o d . I n g e n e r a l , the i n v e r s e h e a t c o r r e c t i o n s l|£n^ f o l l o w a s i m i l a r p a t t e r n t o t h e s t r e s s v a l u e s . F o r low wind s p e e d s a p p r o a c h e s 0.0 (lh.eapproaches oo ) As t h e wind s p e e d i n c r e a s e s , I ( £ a p p r o a c h e s 1.0 f o r a l l a v e r a g i n g p e r i o d s . I n g e n e r a l A p p e n d i x F i n d i c a t e s t h a t t h e c o r r e c t i o n s r e q u i r e d f o r t h e s e n s i b l e h e a t f l u x e s a r e l a r g e r t h a n t h o s e r e q u i r e d f o r t h e l a t e n t h e a t f l u x e s . F u r t h e r m o r e , a c o m p a r i s o n w i t h A p p e n d i x C i n d i c a t e s t h a t t h e s t r e s s c o r r e c t i o n s a r e l a r g e r t h a n b o t h t h e h e a t c o r r e c t i o n s . An e s t i m a t e c f t h e e r r o r i n £ t « was o b t a i n e d by e m p l o y i n g t h e S t u d e n t ' t ' t e s t as o u t l i n e d i n E q u a t i o n 3.10. The r e s u l t s a p p e a r i n A p p e n d i x F - P a r t I I . These r e s u l t s s h o u l d be viewed somewhat s k e p t i c a l l y as no a t t e m p t was made t o a s s u r e t h a t t h e s c a t t e r a b o u t t h e r e g r e s s i o n was G a u s s i a n . S i m i l a r p a t t e r n s t o t h e s t r e s s e r r c r s , however, a r e e x h i b i t e d i n t h e h e a t f l u x e r r o r s . F o r t h e l o w e s t wind speed c a t e g o r i e s , t h e 95% c o n f i d e n c e zone i s l a r g e compared t o t h e ^t^-e v a l u e s . By B e a u f o r t i n t e r v a l 3 (1.6 - 3.4 m/sec 2) e r r o r s i n t h e c a l c u l a t i o n s a r e r e d u c e d t o l e s s t h a n 10% o f t h e c a l c u l a t e d v a l u e f o r a l l a v e r a g i n g p e r i o d s . I n g e n e r a l , t h e e r r o r s 82 SENSIBLE 4 AVERAGING LENGTH s 8 B B • • B 19 0.25 DRYS • § § x 1 1 1 1 1 0.0 14.0 28.9 " WIND SPEED IN PI/SEC X CC o I— C J ex C J LU CCO LATENT RVERRGING LENGTH =0.25 Qfi/S Y M 6 B B B B B 1 I I I I 0.0 14.0 28.0 WIND SPEED IN M/SEC RVERRGING LENGTH = 4.00 DRYS RVERRGING LENGTH = 4.00 DRYS • x CC o CC C J ' UJ CC CCa> + 0.0 WIND 14.0 SPEED IN 28.0 M/SEC C J i r 0.0 14.0 WIND SPEED 28.0 IN M/SEC UINDSPEED = 6.75 M/SEC 1 co o or o h~ C J cr O C J " LU cr. cro '1X I 1 I I I 0.0 12.0 24.0 AVERAGING PERIOD IN DAYS cr o C J cr C J ' LU CC c r o WINDSPEED =6.75 M/SEC ^ 1 1 1 1 ! 0.0 12.0 24.0 AVERAGING PERIOD IN DAYS F i g u r e 23. S h i p s ' 1/$^ v a l u e s f o r t h e h e a t f l u x e s . The l i n e a t t h e bottom i n d i c a t e s ± one s t a n d a r d d e v i a t i o n of t h e means e x c l u d i n g S t a t i o n N. S t a t i o n N i s y ' S t a t i o n K i s % .. 83 i n c r e a s e as t h e a v e r a g i n g p e r i o d i n c r e a s e s . The cEvi« h e a t c o r r e c t i o n s f o r a l l s h i p s a r e f a i r l y t i g h t l y g r o u p e d . S t a t i o n N shows s i g n i f i c a n t l y l a r g e r 1.0/ ( s m a l l e r ) v a l u e s a t a v e r a g i n g p e r i o d s g r e a t e r t h a n 0.5 d a y s . S t a t i o n K a l s o shows s i g n i f i c a n t l y l a r g e r 1.0/1"^ v a l u e s f o r t h e s e n s i b l e h e a t f l u x — l y i n g between t h e S t a t i o n N v a l u e s and t h e main s h i p g r o u p i n g . kxi i n s p e c t i o n c f t h e s e n s i b l e h e a t raw s t a t i s t i c s i n T a b l e X does n o t r e v e a l a n y t h i n g e i t h e r t o d i s t i n g u i s h S t a t i o n K f r o m t h e o t h e r s h i p s c r t o show any c o n s i s t e n c i e s w i t h S t a t i o n N t o a c c o u n t f o r t h e d i f f e r e n c e . I n the l a t e n t h e a t f l u x e s , t h e S t a t i o n K v a l u e s a r e b i a s e d t o w a r d s h i g h v a l u e s i n t h e 1.0/f t t < p l o t s but c a n be c o n s i d e r e d w i t h i n t h e g e n e r a l s h i p s ' g e o g r a p h i c g r o u p i n g and a r e f a r below t h o s e o f S t a t i o n N. 4.5 B e a u f o r t G r o u p e d T e s t R e s u l t s The t h r e e t e s t q u a n t i t i e s were c a l c u l a t e d f o r t h e £"(e^ v a l u e s g i v e n i n A p p e n d i x F. The r e s u l t s a p p e a r i n A p p e n d i x G and a r e shewn i n F i g u r e . 2 4 . The a r i t h m e t i c d i f f e r e n c e s between F i g u r e s 24 and 21 a r e shown i n F i g u r e 25. The d i f f e r e n c e v a r i a n c e s a r e n o t c o n s i d e r e d i n t h i s s e c t i o n b e c a u s e t h e c o r r e c t i o n f o r t h e s y s t e m a t i c b i a s f o r c e d a l l v a l u e s t o e x a c t l y 0.0. . The d i f f e r e n c e means h a v e i m p r o v e d m a r k e d l y a f t e r t h e a p p l i c a t i o n o f £fe.e.« A c o m p a r i s o n o f F i g u r e s 24 and 21 i n d i c a t e s t h a t b o t h t h e l a t e n t and s e n s i b l e h e a t f l u x DMs have been i m p r o v e d by a f a c t o r c f 5.0. C l i m a t o l o g i c a l e r r o r s a r e now l e s s t h a n 3.5 Watts/m 2 f o r t h e s e n s i b l e h e a t f l u x and 17.7 Watts/m 2 co^. z o . LU LU CJ o 0.1 S E N S I B L E H E R T F L U X 2 1 . 0 1 0 . 0 AVERAGING PERIOD IN DATS 100 .0 c o ^ z ° -Q-CD LU LU CJ or^ • LU • o o L A T E N T H E A T F L U X , i » 4 X * v i ! 0 • 10.0 100.0 AVERAGING PERIOD IN DAYS F i g ure 24 (a) Watts/m 2 DMs i n F i g u r e 24(b) Watts/m 2 co LUM-<_> _| z ° tx t—» c r J > do' Q CO LU or 0.1 S E N S I B L E H E A T F L U X 1.0 10.0 A V E R A G I N G P E R I O D I N D A Y S 100 .0 CO mv <->•-) z ° cr •—1 or cx CCo' ZD CO 1 LU or 0.1 L A T E N T H E A T F L U X 1.0 10.0 100.0 A V E R A G I N G P E R I O D I N D A Y S F i g u r e 24 (c) F i g u r e 24 (d) co LU 1—'CM , LU O CJ Oo c r 1 LU o r o r o o 0 CJ 0 S E N S I B L E H E A T F L U X 1 1 0 10.0 A V E R A G I N G P E R I O D I N D A Y S CO I— LU —,° Li_ U _ LU . O CJ Oo LU o r o r o 100.0 CJ o.l L A T E N T H E A T F L U X ! • ; 1 0 10.0 100.0 A V E R A G I N G P E R I O D I N D A Y S F i g u r e 24 (e) F i g u r e 24(f) F i g u r e 24* l e s t v a l u e s w i t h i n d i v i d u a l s h i p s ' fe the heat f l u x e s . \ue_ a p p l i e d S E N S I B L E H E A T F L U X L A T E N T H E A T F L U X 85 o.i 1.0 10 .0 A V E R A G I N G P E R I O D I N D A T S 100 .0 tn°. Z c o _ | C E -LL) LU CJ LU . OCco " 0.1 1.0 10.0 A V E R A G I N G P E R I O D I N D A T S 100.0 F i g u r e o.i 25(a)- DMs i n Watts/m 2 S E N S I B L E H E A T F L U X j ! t : i l l * 8 1.0 10,0 100.0 A V E R A G I N G P E R I O D I N D A T S F i g u r e 25 (c) co LUo> CJ - J , cn CE CEo' ZD Q CO LU cn o o * F i g u r e 25(b) DMs i n Watts/m 2 L A T E N T H E A T F L U X 0.1 1.0 10.0 100.0 A V E R A G I N G P E R I O D J N D A T S F i g u r e 25 (d) co i — £ -J o CJ CD O o ' I— OC cn or co o S E N S I B L E H E A T F L U X CJ°0.1 i I 1.0 10.0 A V E R A G I N G P E R I O D I N D A Y S F i g u r e 25 (e) co i — z. zi«> So-J u_ y -1 o CJ co ^ m O o ' CE I -LU cn or co 100.0 CJ o . i L A T E N T H E A T F L U X % 1 b X *. * I z 1 .0 10.0 A V E R A G I N G P E R I O D I N D A Y S F i g u r e 2 5 ( f ) 100.0 F i g u r e 25. T e s t v a l u e improvements o v e r F i g u r e 21, t h e u n c o r r e c t e d c a s e . 86 f o r t h e l a t e n t h e a t f l u x . I g n o r i n g S t a t i o n s E and N f o r t h e l a t e n t h e a t f l u x , t h e DM e r r o r s a r e t h e n a l l l e s s t h a n 10.0 Watts/m 2. The improvements shown i n F i g u r e 25 and a r e v i r t u a l l y a r e p l i c a t i o n o f F i g u r e 21 i n d i c a t i n g t h a t t h e g r e a t e r t h e i n i t i a l DM e r r o r , t h e g r e a t e r t h e improvements t h a t c a n be o b t a i n e d . The r e s i d u a l v a r i a n c e e r r o r s a r e somewhat l e s s e n c o u r a g i n g f o r l o n g e r a v e r a g i n g p e r i o d s . . S t a t i o n N i n p a r t i c u l a r , has e x t r e m e l y h i g h (up t c 0.23 f o r t h e s e n s i b l e h e a t and 0.83 f o r th e l a t e n t h e a t f l u x ) BVs a t L=14.0 and L=28.0 d a y s . . I f one c o n s i d e r s 1 095 t o be an a c c e p t a b l e n o i s e l e v e l t h e n an a p p r e c i a b l e number o f s h i p s l i e above t h i s l e v e l a t L=14.0 days f o r t h e s e n s i b l e h e a t f l u x and a t L = 4.0 days f o r t h e l a t e n t h e a t f l u x . The a p p l i c a t i o n o f ^te£ has m a r k e d l y i m p r o v e d t h e f i n a l r e s i d u a l v a r i a n c e s o v e r t h e i n i t i a l raw v a l u e s . . The BVs a t l o n g a v e r a g i n g p e r i o d s a r e now a b o u t o n e - h a l f t h e u n c o r r e c t e d v a l u e s . F i g u r e 25 i n d i c a t e s t h a t i m provements o f 0.25 f o r the s e n s i b l e h e a t f l u x and 0.15 f o r t h e l a t e n t h e a t f l u x a t L=28.0 d a y s a r e t y p i c a l . The a p p l i c a t i o n o f \ has i m p r o v e d t h e c o r r e l a t i o n c o e f f i c i e n t s . The s e n s i b l e h e a t f l u x c o r r e l a t i o n s , w i t h t h e e x c e p t i o n o f S t a t i o n N, L=28.0 d a y s , a r e a l l a bove 0.90. The l a t e n t h e a t f l u x c o r r e l a t i o n s a r e above 0.90 up t o L=4.0 days a f t e r which seme s t a t i o n s f a l l o f f , f o r example, t o v a l u e s as low as o f 0.583 a t S t a t i o n N and 0.750 a t S t a t i o n E (bo t h n o t shewn) f o r L=28.0 d a y s . A c c o r d i n g t o E q u a t i o n 4.8, t h i s p a r t l y e x p l a i n s t h e l a r g e BVs a t S t a t i o n s N and E. I f t h e DVs were n o t c o r r e c t e d , t h e BVs would be r e d u c e d by 17.4% and 6.25% 87 r e s p e c t i v e l y . The improvements shewn i n F i g u r e 25 have s i m i l a r r a n g e s f o r t o t h t h e l a t e n t and s e n s i b l e h e a t f l u x e s . T h e r e i s a t e n d e n c y f o r t h e s t a t i o n s w i t h t h e l o w e r i n i t i a l c o r r e l a t i o n c o e f f i c i e n t s t o shew t h e most improvement. F o r e x a m p l e , i n F i g u r e 21, t h e s e n s i b l e h e a t f l u x raw c o r r e l a t i o n s a t S t a t i o n s A, E, I , M and B a r e d i s t i n c t l y g r o u p e d l o w e r t h a n t h e o t h e r s . F i g u r e 25 shows t h e s e same s t a t i o n s g r o u ped w i t h t h e most i m p r o v e m e n t . 88 CHAPIEB V EMPIRICAL FORMULA AND TEMPORAL VARIATIONS -5.1 I n t r o d u c t i o n I n t h e p r e v i o u s two c h a p t e r s i t has been e s t a b l i s h e d t h a t s y s t e m a t i c r e d u c t i o n s c c c u r i n t h e 3H momentum and h e a t f l u x e s when e s t i m a t e d t h r o u g h VA p a r a m e t e r s . I n C h a p t e r I I I i t was shown t h a t t h e 1 / £ b 4 o p t i m a l l y r e g r e s s e d s t r e s s r e d u c t i o n s were q u a l i t a t i v e l y s i m i l a r t c the s e t o f a v e r a g e d c o r r e c t i o n s R ( L ) . W ith t h e e x c e p t i o n o f S t a t i o n K, s e n s i b l e h e a t f l u x , i t was n o t e d t h a t t h e 1/£nt o p t i m a l c o r r e c t i o n s f o r t h e h e a t f l u x e s were s i m i l a r t c t h e c o r r e s p o n d i n g c o r r e c t i o n s f o u n d i n t h e s t r e s s . R j (L) o f E q u a t i o n 3 . 1 4 can be r e w r i t t e n a s : u s i n g n o t a t i o n p r e v i o u s l y d e f i n e d . As s t a t e d p r e v i o u s l y t h e v a r i a n c e i n f o r m a t i o n i s l o s t t o t h e a v e r a g i n g p r o c e s s , however, t h e VA wind s p e e d s , (Uj 2+Vj 2) V 2, a r e r e q u i r e d f o r t h e e s t i m a t e s o f a l l t h e VA f l u x e s . . G i v e n t h e s e a r g u m e n t s , an e x p e c t e d wind speed dependence o f f o r a l l f l u x e s i s : " l + * ^ * * f > 5.2 where °^ and (*> a r e c o n s t a n t s t o be d e t e r m i n e d . . The t e m p o r a l a s p e c t s o f t h e r e d u c t i o n s have a l s o n o t been i n v e s t i g a t e d . These may m a n i f e s t t h e m s e l v e s i n two ways. F i r s t , t h e r e may be c o n s i s t e n t v a r i a t i o n s between a v e r a g i n g p e r i o d s which w i l l be c a l l e d f u n c t i o n a l t e m p o r a l v a r i a t i o n s . 89 E s t a b l i s h i n g c o n s i s t e n c i e s i n t h e s e v a r i a t i o n s would a i d g r e a t l y i n i n t e r e c l a t i n g t h e r e d u c t i o n s t o a v e r a g i n g p e r i o d s n o t s p e c i f i c a l l y i n v e s t i g a t e d . S e c o n d , t h e ^h.t t r a n s f o r m a t i o n s may be i n f l u e n c e d by t i m e s c a l e s g r e a t e r t h a n t h e a v e r a g i n g p e r i o d . F o r example, t h e c o r r e c t i o n s r e g u i r e d i n December may be m a r k e d l y d i f f e r e n t from t h o s e r e q u i r e d i n J u l y . These w i l l be c a l l e d i n t r i n s i c t e m p o r a l v a r i a t i o n s . F i n a l l y , i t was shown i n C h a p t e r s I I I and IV t h a t t h e o p t i m a l c o r r e c t i o n s £fce. (with t h e e x c e p t i o n o f S t a t i o n N f o r a l l f l u x e s , and S t a t i o n K f o r t h e s e n s i b l e h e a t f l u x ) dc n o t d i f f e r m a r k e d l y from one s h i p l o c a t i o n t o t h e n e x t . I f a f o r m u l a which i s a p p l i c a b l e a t most s h i p l o c a t i o n s c a n be f o u n d , t h e n t h e e a s e of a p p l y i n g t h e t r a n f c r m a t i o n s would be g r e a t l y e n h a n c e d . 5.2 E m p i r i c a l F o r m u l a To v e r i f y t h e arguments o f t h e p r e v i o u s s e c t i o n , t h e £t?«. v a l u e s o f a p p e n d i x C f o r t h e s t r e s s e s and c f a p p e n d i x F f o r t h e h e a t f l u x e s f o r each s h i p were w e i g h t e d and a v e r a g e d ( e x c l u d i n g S t a t i o n N) a c c o r d i n g t o t h e method o u t l i n e d i n S e c t i o n 3.3 t o a r r i v e a t a g e o g r a p h i c a l l y a v e r a g e d e s t i m a t e ZI^A. o f t h e c o r r e c t i o n s . The r e s u l t s a p p e a r a t t h e ends o f A p p e n d i c e s C and F - P a r t s I . ( £ti«. - 1 ) w a s i n i t i a l l y p l o t t e d v e r s u s (u,2 + v.2) */2 on a l o g s c a l e and t h e r e s u l t s f o r a l l f l u x e s a p p e a r i n F i g u r e 26. The h o r i z o n t a l l i n e i n d i c a t e s where a c o r r e c t i o n of 10% o r g r e a t e r i s r e g u i r e d . I n a l l c a s e s the c u r v e s a r e q u i t e l i n e a r i n t h e r a n g e 0.5 t o 20 m/sec e x c e p t i n t h e l i n e a r d r a g c o e f f i c i e n t c a s e where a d i s c o n t i n u i t y i n t h e s l o p e o c c u r s a t 10 m/sec. T h i s i s 90 CONSTANT DRAG COEFFICIENT LINEAR DRAG COEFFICIENT 280 Days 10-~1 | I | I I I 11 I | I | I I 111 I |—I | II l l | 3 5 10°, 3 5 10' 3 5 10 2 WIND SPEED IN M / S E C X c X • 4 CD • -200 Days • 0 2 5 Days I | I | I I l l | 1 1 I | I I l l | 1 1 I | I I l l | 10"' 3 5 10° ' 3 5 10' 3 5 10 2 WIND S P E E D IN M / S E C SENSIBLE HEAT FLUX LATENT. HEAT FLUX A CD • g — 2 8 Days CD I • Q A+> U R AATTA Q25 Days- • • , I 1 I 1 I I I 111 I | I | I I 111 1 1 I | I I I Ij lO" 1 3 5 10° 3 5 10' 3 5 10 2 WIND S P E E D IN M / S E C •o • + A + A CD • - 2 8 Days A • A + m m A + A 0.25 Days- • 2~1 I 1 I i ' i'l ' J i | m i ] 1 | i | 10"' 3 5 10° 3 5 10' 3 5 10 2 WIND S P E E D IN M / S E C F i g u r e 26. The -1 v a l u e s a s a f u n c t i o n o f wind speed. A l l p o i n t s above t h e h c r i z c n t a l l i n e r e q u i r e g r e a t e r t h a n 10% c o r r e c t i o n . The i n s e t numbers i n d i c a t e a v e r a g i n g p e r i o d i n d a y s . the wind s p e e d a t w h i c h t h e d r a g c o e f f i c i e n t c h a n g e s form (see E g u a t i o n 2.5). F o r wind s p e e d s g r e a t e r t h a n 20 m/sec, t h e p o i n t s become s c a t t e r e d . T h i s may be due t o t h e r e b e i n g 9 1 s u b s t a n t i a l l y f e w e r a v e r a g i n g s i n t h i s r e g i m e . The s l o p e s f o r a l l c u r v e s a p p e a r t o be s i m i l a r f o r a l l a v e r a g i n g p e r i o d s . Note t h a t t y p i c a l wind s p e e d s o f 1-10 m/sec a t L = 2 8 . 0 d a y s y i e l d c o r r e c t i o n s o f a b o u t 1 t o 8 which a r e o f t h e c o r r e c t o r d e r t o imp r o v e t h e t r a n s p o r t c a l c u l a t i o n s by A a g a a r d shown i n F i g u r e 1 ( b ) . The i n d i v i d u a l s h i p s ' p l o t s o f ( ? n « . - 1 ) v e r s u s (u-2 +• v-.2) V 2 were examined and were a l l q u a l i t a t i v e l y s i m i l a r t o t h e g e o g r a p h i c a l l y a v e r a q e d c a s e . N e x t , ( £ f c e - 1 ) was p l o t t e d v e r s u s a v e r a g i n g p e r i o d (L) on a l o g s c a l e t c d e t e r m i n e any f u n c t i o n a l t e m p o r a l v a r i a t i o n s w hich a p p e a r i n F i g u r e 2 7 . A g a i n a l l f l u x e s show s i m i l a r p a t t e r n s . A l l p o i n t s above t h e h o r i z o n t a l l i n e r e q u i r e a t l e a s t 10SS c o r r e c t i o n . B e a u f o r t i n t e r v a l 1 (0 .2 m/sec) i s more s c a t t e r e d t h a n t h e o t h e r s . T h i s e x t e n d s t o B e a u f o r t i n t e r v a l 2 ( 1 . 0 m/sec) on t h e i n d i v i d u a l s h i p s ( £ i e < . - 1 ) v e r s u s L p l o t s . . T h i s i s n o t s u r p r i s i n g s i n c e t h e e x t r e m i t i e s i n wind s p e e d c o n t a i n t h e f e w e s t number o f p c i n t s and t h e l o w e s t wind s p e e d s have t h e l a r g e s t i n h e r e n t e r r o r s o f A p p e n d i c e s C and F - P a r t s I I . . At L = 2 . 0 d a y s , t h e r e p r e s e n t s B e a u f o r t c a t e g o r y 12 ( 2 6 . 0 m/sec) and a p p e a r s d i s t i n c t f r o m t h e p a t t e r n o f t h e r e s t o f t h e p o i n t s . T h i s p o i n t was d e t e r m i n e d from o n l y f o u r o u t o f a p p r o x i m a t e l y one m i l l i o n t o t a l p o s s i b l e a v e r a g i n g s and c a n n o t be c o n s i d e r e d s t a t i s t i c a l l y v a l i d . A l l e t h e r c u r v e s appear t o i n c r e a s e s y s t e m a t i c a l l y . . From L = 0 . 2 5 t o L = 2 . 0 days (which I c a l l R e g i o n I) t h e s l o p e s a r e s t e e p e r t h a n f r c m L = 4 . 0 t c L = 2 8 . 0 days (which I c a l l R e g i o n I I ) . The v e r t i c a l l i n e a t L=3 . 0 d a y s d e m a r c a t e s t h e two r e g i o n s . W i t h i n e a c h r e g i o n the s l o p e s do n o t a p p e a r t o change I 92 CONSTANT ORflG COEFFICIENT m a 0.2 o 1.0 3 5 10' 3 5 IO7 A V E R A G I N G P E R I O D ! " I N D A Y S LINEAR DRAG COEFFICIENT a CD CD CD Q2 REGION T • O CD O 10 IO"' 3 5 10" 3 5 10' 3 5 10' A V E R A G I N G P E R I O D I N D A Y S SENSIBLE HERT FLUX LATENT HEAT FLUX I 11111 i | i | 1111| 3 5 10° 3 5 10' 3 5 102 A V E R A G I N G P E R I O D I N D A Y S IO"1 3 5 10" 3 5 10' 3 5 10J . A V E R A G I N G P E R I O D I N D A Y S F i g u r e 27. The £fee-1 v a l u e s as a f u n c t i o n o f a v e r a g i n g p e r i o d . The v e r t i c a l l i n e d e m a r c a t e s t h e d i v i s i o n between R e g i o n s I and I I and a l l p c i n t s above t h e h o r i z o n t a l l i n e r e q u i r e g r e a t e r t h a n 10% c o r r e c t i o n . The i n s e t numbers i n d i c a t e wind s p e e d i n m/sec. d r a m a t i c a l l y f r o m one B e a u f o r t c a t e g o r y t o t h e n e x t . F i g u r e 26 i n d i c a t e s a power law b e h a v i o u r o f (£r**-1) w i t h wind s p e e d which a p p e a r s t o be i n d e p e n d e n t o f a v e r a g i n g p e r i o d 9 3 and F i g u r e 27 i n d i c a t e s a power law b e h a v i o u r o f (^»e-1) w i t h a v e r a g i n g p e r i o d which a p p e a r s t o be i n d e p e n d e n t o f wind s p e e d . I t i s assumed a p r i o r i t h a t t h e c o r r e c t i o n ^ i s o f t h e f o r m : v 4/2. K where (u 2+v- 2)*/ 2 i s t h e v e c t o r a v e r a g e d wind s p e e d and L i s t h e a v e r a g i n g p e r i o d i n d a y s . The assumed form of t h e X<3H) v a r i a t e and X' (VA) r e s i d u a l i s : 5. 4 where t h e c v e r b a r i n d i c a t e s a v e r a g i n g o v e r a l l B e a u f o r t c a t e g o r i e s and a v e r a g i n g p e r i o d s which can be r e w r i t t e n a s : which i m m e d i a t e l y l e a d s t c : Note t h a t we new r e g r e s s t h e assumed form d i r e c t l y t o t h e d a t a . T h i s i s a n o n - l i n e a r r e g r e s s i o n o f t h e f o r m : o-;T£. ( r - ? ^ ; ^ ^ ) 1 ^ ' ) ' 5 . 6 where Y = X - X' , Xj = <*> , ft , t f o r i= 1 f 2, 3 and 94 f ( Xi; (u-j 2*^ 2) V2»L) = ^ ( U j 2 + v j 2 ) ^ / 2 L * • I f w e flave an i n i t i a l g u e s s f ( XL 0 ), E g u a t i c n 5.6 can be e x p a n d e d i n a T a y l o r s e r i e s to f i r s t o r d e r as f o l l o w s : The q u a n t i t y [ c a n t h e n be m i n i m i z e d g i v i n g : 5.8 t h i s i s a m a t r i x e g u a t i o n o f t h e f o r m : A 5. 9 where. A,-;-- ^\ ^1 * 1 x ^ .Ki - A \," 95 By e v a l u a t i n g e x p l i c i t l y t h e d e r i v a t i v e s i n E q u a t i o n 5.8, t h e can t h e n be i t e r a t e d u n t i l i s s m a l l compared t o . I t e r a t i o n was h a l t e d when \A^ I X i o l <- ° • ° ° i . , Note t h a t XX' and X' 2 a r e the c r o s s p r o d u c t s and s q u a r e s o f t h e i n d i v i d u a l v a r i a t e s and n o t t h e s q u a r e s o f t h e a v e r a g e w i t h i n e a c h B e a u f o r t c a t e g o r y . F u r t h e r m o r e , t h e d i f f e r e n c e means have been removed f r c m the r e g r e s s i o n r e s i d u a l s . I t w i l l be d e m o n s t r a t e d t h a t t h i s has l i t t l e i n f l u e n c e on the f i n a l r e s u l t . S i n c e F i g u r e 27 i n d i c a t e d a d e f i n i t e b r e a k i n t h e s l o p e a t L=3 d a y s , t h e r e g r e s s i o n was p e r f o r m e d p i e c e w i s e w i t h a s e p a r a t e s e t o f c o n s t a n t s f o r t h e two r e g i o n s . A r e g r e s s i o n o f t h i s t y p e g r e a t l y r e d u c e s th e r e q u i r e d number o f c o n s t a n t s t o be s t o r e d ; c o n s e q u e n t l y a s e p a r a t e r e g r e s s i o n was p e r f o r m e d on t h e x and y s t r e s s components. Thus t h e number o f p a r a m e t e r s were r e d u c e d f r o m 104 per s h i p t c 12 f o r t h e s t r e s s e s and 6 f o r each o f t h e h e a t f l u x e s . To be r i g o r o u s , t h e r e g r e s s i o n s h o u l d be p e r f o r m e d d i r e c t l y a g a i n s t t h e VA and 3H e s t i m a t e s from e a c h i n d i v i d u a l a v e r a g i n g . T h i s would e n t a i l c a l c u l a t i o n s i n v o l v i n g a s many as 50,000 p o i n t s per s h i p and f l u x r e p e a t e d o v e r s e v e r a l i t e r a t i o n s . The c o m puter c o s t s would be e x c e s s i v e i n s t o r a g e and p r o c e s s i n g t i m e . The B e a u f o r t - a v e r a g i n g p e r i o d g r o u p i n g s o f t h e sums, sums of s q u a r e s and s ums.cf c r o s s p r o d u c t s o f t h e 3H and VA v a r i a t e s were s t o r e d d u r i n g t h e c a l c u l a t i o n s . By a p p r o p r i a t e l y w e i g h t i n g t h e s e s t o r e d s t a t i s t i c s , an a p p r o x i m a t i o n f o r t h e ^ , ^ and % c c u l d be a c h i e v e d r e q u i r i n g e f f e c t i v e l y o n l y 13x8=104 p o i n t s per s h i p and f l u x . A w e i g h t i n g m a t r i x was c r e a t e d i n o r d e r n o t t o b i a s t h e 96 p a r a m e t e r e s t i m a t e s . F i r s t , e a c h B e a u f o r t c a t e g o r y c o n t a i n e d u n e q u a l numbers o f p o i n t s . The f i r s t o r d e r w e i g h t t h e n was d i r e c t l y p r o p o r t i o n a l t o the number o f 3H/VA a v e r a g i n g s w i t h i n e a c h B e a u f o r t c a t e g o r y . By t h e n a t u r e o f t h e a v e r a g i n g o f t h e 3H and VA v a r i a t e s , t h e l o n g e r a v e r a g i n g p e r i o d s had f e w e r e s t i m a t e s o f t h e r e d u c t i o n which would t e n d b i a s t h e t e m p o r a l power ( t ) i n f a v o u r o f t h e s h o r t e r a v e r a g i n g p e r i o d s . However, we wish an u n b i a s e d e s t i m a t e o v e r a l l a v e r a g i n g p e r i o d s . C o n s e g u e n t l y , t h e number, o f e s t i m a t e s w i t h i n e a c h B e a u f o r t c a t e g o r y and a v e r a g i n g p e r i o d was expanded t o t h e t o t a l number o f raw t h r e e - h o u r l y s a m p l e s t h a t went i n t o t h e c a l c u l a t i o n s o f t h e s t a t i s t i c s o f e a c h c a t e g o r y . Thus, i f B e a u f o r t i n t e r v a l 8 a t L=1.0 d a y s c o n t a i n e d 4 3H/VA e s t i m a t e s , s i n c e t h e r e were 8 r e a d i n g s p e r day, t h e 4 r e a d i n g s were expanded t o 32. T h i s t y p e o f r e g r e s s i o n m i n i m i z e s t h e t o t a l r e s i d u a l s w i t h i n e a c h r e g i o n . T h a t i s , e a c h a v e r a g i n g p e r i o d i s no l o n g e r c o n s i d e r e d as a s i n g l e b l o c k o f d a t a b ut t h e t o t a l r e s i d u a l s f r o m L=0. 25 t o L = 2.0 days ( B e g i o n I) and from L= 4.0 t o L=28.0 (B e g i o n I I ) a r e now m i n i m i z e d . I t w i l l be shown t h a t t h e r e g r e s s i o n p e r f o r m e d i n t h i s manner d i d n o t s i g n i f i c a n t l y i n c r e a s e t h e r e s i d u a l s when compared w i t h a d i r e c t r e g r e s s i o n . The f i r s t g u e s s ( \ L o ) was made by p e r f o r m i n g a l i n e a r r e g r e s s i o n i n l o g s p a c e . A t s e v e r a l l o c a t i o n s , t h e i t e r a t i o n f a i l e d t o c o n v e r g e w i t h t h i s v a l u e . F o r t u n a t e l y , i t was e s t a b l i s h e d t h a t most s h i p s c o n v e r g e d t o v a l u e s o f ^> =-1.0 and =1.0 i n B e g i o n I and V =0.25 i n R e g i o n I I . C o n s e q u e n t l y t h e s e v a l u e s as w e l l as an a r b i t r a r y <^ =2.0 were used as 97 i n i t i a l g u e s s e s . Not o n l y d i d a l l s h i p s c o n v e r g e , b u t i n c a s e s where t h e i t e r a t i o n had p r e v i o u s l y s u c c e e d e d , t h e c o n v e r g e n c e went t o t h e same v a l u e s i n f e w e r r e c u r s i o n s . T h i s i n d i c a t e s t h a t a l i n e a r r e g r e s s i o n i n l o g s p a c e may n o t p r o d u c e s u i t a b l e e s t i m a t e s o f t h e c o e f f i c i e n t s . 5.3 ShijJ P a r a m e t e r E s t i m a t e s I n l i g h t o f t h e d r a m a t i c i m p r o v e m e n t s i n t e s t r e s u l t s a c h i e v e d by t h e ^ ^ j * c a l c u l a t i o n s , t h e y p r o v i d e d an a c c e p t a b l e means o f c o m p a r i s o n t o d e t e r m i n e t h e e f f e c t i v e n e s s o f t h e 7^ t e c h n i q u e . I f t h e r e s u l t s compare f a v o u r a b l y w i t h t h e c ^ t e € r e s u l t s , t h e n th e e m p i r i c a l f o r m u l a would be an e f f e c t i v e r e p l a c e m e n t . I n t h i s s e c t i o n , t h e r e s i d u a l v a r i a n c e s were c a l c u l a t e d by a p p l y i n g t h e r e g r e s s i o n c o e f f i c i e n t s a g a i n s t t h e s t o r e d B e a u f o r t n u m b e r - a v e r a g i n g p e r i o d s t a t i s t i c s o u t l i n e d above and t h e e m p i r i c a l f o r m u l a was n o t a l l o w e d t o i n t e r p o l a t e wind s p e e d . F i g u r e 28 shows the TJ' RV e s t i m a t e minus t h e 2Ve RV e s t i m a t e i n p e r c e n t . F o r t h e s t r e s s e s , n e a r l y a l l r e s u l t s a r e w i t h i n 1.5% o f t h e v a l u e s f o r a l l a v e r a g i n g p e r i o d s . The o n l y e x c e p t i o n i s S t a t i o n D, 1=7.0 d a y s , l i n e a r d r a g c o e f f i c i e n t , x component where t h e d i f f e r e n c e was 2.3% (not shown). . S t a t i o n N was a l s o w i t h i n 1.5% o f t h e £ K J C r e s i d u a l s . Many s t a t i o n s showed an improvement ( i e . n e g a t i v e r e s i d u a l v a r i a n c e s i n F i g u r e 28) i n t h e s t r e s s e s . T h i s o c c u r r e d b e c a u s e h e r e a s e p a r a t e r e g r e s s i o n was p e r f o r m e d on t h e components. The h e a t f l u x RVs ( F i g u r e s 28(e) and ( f ) ) were g e n e r a l l y w i t h i n 4.0% o f t h e &v.t fiVs f o r a l l a v e r a g i n g p e r i o d s . The 98 X COMPONENT 1.0 1 0 . 0 AVERAGING PERIOD IN DAYS 100 .0 Y COMPONENT -i $-AVERAGING PERI0D° IN DAYS 1 0 0 ' ° F i g co u _ i 0 CJ • -J CC cr CXo ' ZD o co • LU u r e 28(a) C o n s t a n t D. C, X COMPONENT o J L 1.0 1 0 . 0 AVERAGING PERIOD IN DAYS 1 0 0 . 0 F i g u r e 28(b) C o n s t a n t D . C Y COMPONENT CO L U 0 CJ • -J cr J CXo ' ID O I 1 co -| LU I 0.1 1.0 1 0 . 0 100 0 AVERAGING PERIOD IN DAYS F i g u r e 28(c) L i n e a r D.C. F i g u r e 28(d) L i n e a r D.C. co L U 0 CE I 1 CC cr CEfM" ZD Q CO -| LU CC o 0.1 S E N S I B L E HERT FLUX 1.0 1 0 . 0 AVERAGING PERIOD IN DAYS 1 0 0 . 0 CO L U 0 CJ • _J CC tx > ! _ J ° CXtNJ ' ZD • Q t—( CO • LU CC o o " LATENT HEAT FLUX i i I , i 0 1 1.0 10 0 : AVERAGING P€RI0D IN DAYS 100 .0 F i g u r e 28(e) F i g u r e 2 8 ( f ) F i g u r e 28. D i f f e r e n c e s between t h e and H: r e s i d u a l v a r i a n c e s w i t h no c o r r e c t i o n a p p l i e d f o r t h e DV b i a s . The v a l u e s a r e i n p e r c e n t . D.C. d e n o t e s d r a g c o e f f i c i e n t . 99 e x c e p t i o n s were S t a t i o n N (not shown) where t h e r e s u l t s i n B e g i o n I I were g e n e r a l l y p oor and S t a t i o n J , L=28.0 d a y s , l a t e n t h e a t f l u x where t h e r e g r e s s i o n i n d u c e d a f u r t h e r e r r o r o f a b o u t 10.0% ( a l s o n o t shown). Note, however, up t o L=14.0 d a y s t h e d i f f e r e n c e s were a l l w i t h i n 1. 5% o f t h e ^v-t v a l u e s . As a f u r t h e r i n d i c a t i o n o f t h e a c c u r a c y o f t h e t e c h n i q u e , a l l f l u x e s (momentum and heat) showed a p o s i t i v e b i a s i n t h e d i f f e r e n c e v a r i a n c e s (not shown). A l t h o u g h t h e y were n o t i d e n t i c a l t o t h e r e s i d u a l v a r i a n c e s , t h e y were c l o s e enough t o i n d i c a t e t h a t a DV/BV s t a t i s t i c a l b i a s i n g was o c c u r r i n g . C o n s e q u e n t l y , oC c f E q u a t i o n 5.3 was a d j u s t e d by a m u l t i p l i c a t i v e f a c t o r t o r e d u c e t h e d i f f e r e n c e v a r i a n c e s . A g a i n c o n s i d e r i n g t h e 3H v a r i a t e t o be X and t h e VA v a r i a t e t o be X', t h e c o n d i t i o n f o r 0 d i f f e r e n c e v a r i a n c e f o r each a v e r a g i n g p e r i o d i s : C^AO-^= E%_ i ^ i i ^ ^ -'"y [ E ^ i L ^ i i i ^ o 5. 10 where t h e summation i s o v e r 13 B e a u f o r t i n t e r v a l s , V i s the minimum a p p r o x i m a t i o n o u t l i n e d i n E q u a t i o n 5.6, i s a m u l t i p l i c a t i v e c o r r e c t i o n f a c t o r f o r c i n g t h e d i f f e r e n c e v a r i a n c e t c 0 f o r e a c h a v e r a g i n g p e r i o d , and X • n t = Z» X &.e^' • T h i s 5. 11 100 where ^ x 4 - \ ^ V € a r e t n e r a w 3H and VA v a r i a n c e s w i t h no c o r r e c t i o n a p p l i e d . - T h i s i s t h e n a q u a d r a t i c i n jj^ . The c o r r e c t r o o t was c h o s e n by c o m p a r i s o n w i t h t h e u n c o r r e c t e d d i f f e r e n c e mean v a l u e . The c o r r e c t i o n s f o r e a c h a v e r a g i n g p e r i o d w i t h i n e a c h r e g i o n were t h e n a v e r a g e d t o d e t e r m i n e a mean r e g i o n a l c o r r e c t i o n . A f t e r t h i s c o r r e c t i o n was a p p l i e d , t h e c o n s t a n t s o{ , , and V c f E g u a t i o n 5.3 were c a l c u l a t e d and t h e r e s u l t s a p p e a r i n A p p e n d i x H. The /3 t e r m f o r t h e l i n e a r d r a g c o e f f i c i e n t ~ 0.9), c o n s t a n t d r a g c o e f f i c i e n t s - 1 . 3 ) , and h e a t f l u x e s (-1.2 t o -1.4) t e n d t o d e c r e a s e i n t h i s o r d e r , f o r most s h i p s . The t e m p o r a l power ( ^ c o e f f i c i e n t ) i s r e g u l a r f o r a l l s h i p s e x c l u d i n g S t a t i o n N. In B e g i o n I , i t v a r i e s f r o m a low o f 0.860 to a h i g h o f 1.04 i n d i c a t i n g t h a t t h e c o r r e c t i o n s r e q u i r e d i n t h i s r e g i o n v a r y a p p r o x i m a t e l y l i n e a r l y w i t h a v e r a g i n g p e r i o d . I n B e g i o n I I the c o e f f i c i e n t s v a r y from 0.166 t o 0. 359 w i t h most l y i n g between 0.20 and 0.30. F u r t h e r m o r e t h e t e m p o r a l power i s i n d e p e n d e n t o f t y p e o f f l u x . Thus t h e d i s c o n t i n u i t y i n the t i m e dependence i s q u i t e d i s t i n c t between two and f o u r days which a p p e a r s t o c o r r e s p o n d t o a d i s c o n t i n u i t y o b s e r v e d i n t h e s l o p e c f t h e s t r e s s components s p e c t r a n o t e d by W i l l e b r a n d (1S78) . The f o u r t e s t f u n c t i o n s were t h e n c a l c u l a t e d . C a l c u l a t i o n o f t h e <£>h.e v a l u e s r e q u i r e d s t o r i n g t h e sums, sums of s q u a r e s , and sums o f t h e c r o s s p r o d u c t s o f t h e 3H and VA v a r i a t e s w i t h i n e a c h B e a u f o r t c a t e g o r y . These s t o r e d v a l u e s s e r v e d a s t h e raw s t a t i s t i c s from which t h e f o u r t e s t f u n c t i o n s were c a l c u l a t e d . The e m p i r i c a l f o r m u l a a l l o w e d i n t e r p o l a t i o n o f t h e VA wind s p e e d 101 c o r r e c t i o n w i t h i n e a c h B e a u f o r t c a t e g o r y . When the e m p i r i c a l f o r m u l a was a p p l i e d t c e a c h VA e s t i m a t e i n d i v i d u a l l y , c e r t a i n s h i p s shewed a d r a m a t i c d e c r e a s e i n r e s i d u a l v a r i a n c e . F o r example, S t a t i o n N l a t e n t h e a t f l u x , had a RV o f 82.0% f o r L=28 d a y s . When t h e e m p i r i c a l f o r m u l a i n t e r p o l a t e d t h e v e l o c i t i e s , t h e RV was o n l y 58.9%. I n t h e s e n s i b l e h e a t f l u x , t h e change was from 23.3% to 12.6%. At L=28.0 d a y s , 78% o f t h e d a t a i s g r o u p e d i n B e a u f o r t c a t e g o r i e s 3 and 4. C o n s e q u e n t l y the i n t e r p o l a t i o n o f t h e c o r r e c t i o n w i t h i n t h e two q r o u p s was i m p o r t a n t . A t l o c a t i o n s where t h e d a t a were more e v e n l y d i s t r i b u t e d among B e a u f o r t c a t e g o r i e s (eg. S t a t i o n C) , t h e improvement by d i r e c t a p p l i c a t i o n o f 1^ was l e s s t h a n 1.0%. T h i s i m m e d i a t e l y s u g g e s t s t h a t t h e e m p i r i c a l f o r m u l a r e g r e s s i o n c o e f f i c i e n t s s h o u l d a l s o be c a l c u l a t e d d i r e c t l y a g a i n s t t h e d a t a r a t h e r t h a n a g a i n s t t h e B e a u f o r t g r o u p e d s t a t i s t i c s . S i n c e t h e r e g r e s s i o n i n v o l v e d s e v e r a l i t e r a t i o n s o f l a r g e amounts o f d a t a t h e o n l y f e a s i b l e method was t o r e g r e s s t h e d a t a i n R e g i o n I I o n l y . T h i s was done f o r s e v e r a l s h i p s i n c l u d i n g S t a t i o n N, l a t e n t h e a t f l u x and i n no c a s e were t h e r e s i d u a l s i m p r o v e d more t h a n (1.0%. I n some c a s e s t h e d i f f e r e n c e v a r i a n c e s i n c r e a s e d t o v a l u e s o f about 30.0%. S i n c e t h e r e g r e s s i o n a g a i n s t t h e d a t a r e q u i r e d s e v e r a l i t e r a t i o n s o v e r l a r g e amounts o f i n f o r m a t i o n p r o v i n g e x t r e m e l y c o s t l y i n computer t i m e and was o f d u b i o u s v a l u e , t h i s avenue was n o t p u r s u e d . The f o u r t e s t f u n c t i o n s were t h e n c a l c u l a t e d by a p p l y i n g ^ t o e a c h VA f l u x and s t r e s s e s t i m a t e . The c o m p l e t e r e s u l t s a p p e a r i n Appendix I w h i l e t h e x component l i n e a r d r a g 102 c o e f f i c i e n t and t h e h e a t f l u x e s a p p e a r i n F i g u r e s 29 t o 32. The d i f f e r e n c e means a p p e a r i n F i g u r e 29. E x c e p t f o r S t a t i o n A, a l l DMs a r e below 0.08 dPa f o r t h e l i n e a r d r a g c o e f f i c i e n t . A c o m p a r i s o n o f A p p e n d i x I w i t h A p p e n d i x D ( B.^_t r e s u l t s ) i n d i c a t e s t h a t t h e v a l u e s f o u n d by t h e e m p i r i c a l f o r m u l a , a l t h o u g h n o t i d e n t i c a l t o t h e DMs, b o t h show s i m i l a r r a n g e s o f v a l u e s . The h e a t f l u x DMs a r e g e n e r a l l y 1.0-2.0 Watts/m 2 l a r g e r w i t h t h e e m p i r i c a l f o r m u l a t h a n w i t h t h e d i r e c t l y a p p l i e d <s«.e t e c h n i q u e . The s e n s i b l e h e a t f l u x DMs, w i t h t h e e x c e p t i o n o f S t a t i o n I , L=28.0 d a y s , a r e a l l l e s s t h a n 2.5 Watts/m 2 w h i l e t h e l a t e n t h e a t f l u x e s a r e m o s t l y below 10 W atts/m 2. S t a t i o n E i n R e g i o n I I i s a n o t a b l e e x c e p t i o n where the DMs a r e as l a r g e as 20 Watts/m 2. A c c o r d i n g t o T a b l e X, S t a t i o n E a l s o has t h e s e c o n d l a r g e s t mean l a t e n t 3H h e a t f l u x a t 124.7 W a t ts/m 2. The d i f f e r e n c e v a r i a n c e s a p p e a r i n F i g u r e 30. S i n c e t h e DVs a t a l l a v e r a g i n g p e r i o d s c o u l d n o t be s e t s i m u l t a n e o u s l y t o 0, t h e y a r e a l l l a r g e r t h a n t h o s e t h a t a p p e a r i n A p p e n d i x D f o r t h e s t r e s s e s ( t h e h e a t f l u x DVs a r e i n d e n t i c a l l y 0 ) . Up t o L=2.0 d a y s t h e DV s t r e s s e r r o r f o r a l l components i s bounded by ± 5.0%. T h i s i n c r e a s e s t o ± 10.0% f o r t h e m a j o r i t y o f s h i p s by L=28.0 d a y s . An e x c e p t i o n i s S t a t i o n D L=28.0 d a y s which w i l l be i n v e s t i g a t e d l a t e r . Up t o L=7.0 days (with t h e e x c e p t i o n o f S t a t i o n N ) , t h e DV h e a t f l u x e r r o r s a r e a l l bounded between ± 10.0%. From L=14.0 to L=28.0 d a y s , p a r t i c u l a r l y i n t h e l a t e n t h e a t f l u x , t h e DV e r r o r s become g u i t e l a r g e — up t o 30.7% a t S t a t i o n M. . These a r e , however, a l l s u b s t a n t i a l l y l o w e r t h a n t h e 60-80% e r r o r i n t h e u n c o r r e c t e d t e s t s o u t l i n e d i n F i g u r e s 7 and SENSIBLE HEAT FLUX 103 LATENT HEAT FLUX C 0 0 z . cx°° LU LU u L U ° LU Li_ C J o o 0.1 -J t-° 2 « 8 • * I ft 4 ' ' 1 . 0 1 0 . 0 AVERAGING PERIOD IN DATS Q-CNJ LU (_) 1 0 0 . 0 or-' LU Lt_ Q o o ' * i f 8 , « 0 . 1 1 . 0 1 0 . 0 1 0 0 0 AVERAGING PERIOD IN DATS F i g u r e 29 (a) F i g u r e 29(b) LU L U ° QTo ' a 0 . 1 X COMPONENT J — J L 1.0 10 .0 100.0 AVERAGING PERIOD IN DATS F i g u r e 29(c) L i n e a r D.C. F i g u r e 29. The d i f f e r e n c e means u s i n g the e m p i r i c a l f o r m u l a . The heat f l u x DMs are i n Watts/m 2 w h i l e the s t r e s s DMs a r e i n dPa. D.C. denotes drag c o e f f i c i e n t . 21. The DV e r r o r i n t h e s t r e s s e s and s e n s i b l e heat f l u x e s appears t o o s c i l l a t e . G e n e r a l l y the f i r s t and l a s t p o i n t s i n each r e g i o n ( i e . L=.25, 2.0, 4.0, and 28.0 days) are b i a s e d lower than t h e middle p o i n t s . T h i s i n d i c a t e s t h a t t h e adjustment t o the c o n s t a n t ( ) term a l o n e of E q u a t i o n 5. 12 may ( SENSIBLE HERT FLUX 104 LATENT HEAT FLUX CO L U „ C_)° z a 2 T . O ex 0 0 ts 1—1 cr + 6 • • . cr V > » o • C J 2 z, 1 U J cr 1 i 1 L L J u_ O o 0.1 ' 1.0 10.0 AVERAGING PERIOD IN DRYS 100.0 0.1 1.0 10.0 RVERRGING PERIOD IN DAYS 100 .0 F i g u r e 30 (a) F i g u r e 30 (b) X COMPONENT CO LU C J C cr-cr cr a i 1 L U O Z. ! LU cr LU C M . 1.0 10.0 AVERAGING PERIOD IN DAYS 100 .0 F i g u r e 30(c) L i n e a r D.C. F i g u r e 30. The d i f f e r e n c e v a r i a n c e s u s i n g t h e e m p i r i c a l f o r m u l a . ftll v a l u e s a r e i n p e r c e n t . D . C . . d e n o t e s d r a g c o e f f i c e n t . n o t be a p p r o p r i a t e and ' t h a t an a d j u s t m e n t o f a l l t h r e e c o e f f i c i e n t s may be n e c e s s a r y t o f o r c e a l l t h e DVs t o z e r o . T h i s was n o t a t t e m p t e d i n l i g h t o f t h e i r r e d u c t i o n s o v e r t h e u n c o r r e c t e d DVs. The r e s i d u a l v a r i a n c e s a p p e a r i n F i g u r e 31. F o r n e a r l y 105 e v e r y s h i p , a v e r a g i n g p e r i o d , and f l u x , t h e d i r e c t l y a p p l i e d e m p i r i c a l f o r m u l a r e g i s t e r s an improvement o v e r t h e Sfce S V s . I n t h e s t r e s s c a s e , t h e improvements a r e m a r g i n a l -- b e i n g l i m i t e d t o a b o u t 1.0%. B o t h o f t h e h e a t f l u x e s , however, show marked i m p r o v e m e n t s . At L=28.0 d a y s , t h e r e a r e many i n s t a n c e s where the e m p i r i c a l f o r m u l a r e s i d u a l s a r e a b o u t o n e - h a l f c f t h e v a l u e s . T h i s i s q u i t e r e m a r k a b l e when one c o n s i d e r s t h a t t h e f o r m u l a p r e d i c t s b o t h t h e t e m p o r a l and v e l o c i t y d e p e n d e n t c o r r e c t i o n s . G e n e r a l l y , t h e l i n e a r d r a g c o e f f i c i e n t s EVs i n c r e a s e w i t h a v e r a g i n g p e r i o d i n B e g i o n I w h i l e t h e . s c a t t e r o f v a l u e s i s a f a i r l y c o n s t a n t i n B e g i o n I I . The x component BVs a r e between 6.0 - 12.0% i n B e g i o n I I w h i l e t h e y component v a l u e s l i e between 8.0 - 17.0%. The c o r r e s p o n d i n g c o n s t a n t d r a g c o e f f i c i e n t v a l u e s a r e about o n e - h a l f o f t h e l i n e a r d r a g c o e f f i c i e n t v a l u e s . The s e n s i b l e h e a t f l u x e s g e n e r a l l y f o l l o w t h e p a t t e r n o f t h e s t r e s s and, w i t h t h e e x c e p t i o n o f S t a t i o n N a r e l e s s t h a n 8.0%» . The l a t e n t h e a t f l u x e s a r e somewhat l e s s a c c u r a t e w i t h a l l s t a t i o n s e x c e p t N, E, and M b e i n g l e s s t h a n 18.0%. A g a i n a marked r e d u c t i o n f r c m t h e u n c o r r e c t e d v a l u e s h a s o c c u r r e d . The c o r r e l a t i o n c o e f f i c i e n t s a p p e a r i n F i g u r e 32. T h o s e p o i n t s h a v i n g low EVs have h i g h c o r r e l a t i o n c o e f f i c i e n t s and v i c e - v e r s a . F o r t h e s t r e s s e s t h e c o r r e l a t i o n s a r e m a r g i n a l l y l a r g e r ( i e . b e t t e r ) t h a n t h e c o r r e l a t i o n s , h a v i n g i m p r o v e m e n t s c f s e v e r a l p a r t s p e r t h o u s a n d . More s u b s t a n t i a l i m p r o v e m e n t s a r e shown i n t h e h e a t f l u x e s where i m p r o v e m e n t s o f 0.05 t o 0.1 a r e common. SENSIBLE *€AT FLUX LRTENT HEAT FLUX 106 Y L U P C J o . CE cn . CE CE2-J ZD CD CO 1 LU cn o s * J £ 1 ! 2 | .1 1 1.0 10.0 100.0 •• AVERAGING PERIOD IN DAYS CO, U o . cn CE T^CD -CCr\j CD CO " LU cn CD CD ' 0.1 1.0 10.0 AVERAGING PERIOD IN DAYS 100 .0 F i g u r e 31(a) F i g u r e 31 (b) X COMPONENT L U ° CJco . cn cr CCco ' ZD CD 1 1 co • LU cn CD 0 . 1 9 8 1.0 10 .0 100.0 AVERAGING PERIOD IN DAYS F i g u r e 31. a p p l i e d , c o e f f i c i e n t . F i g u r e 31(c) L i n e a r D.C. The r e s i d u a l v a r i a n c e s w i t h t h e e m p i r i c a l f o r m u l a A l l v a l u e s a r e i n p e r c e n t . D.C. d e n o t e s d r a g Even t h o u g h t h e mean was n o t i n c l u d e d i n t h e n o n - l i n e a r r e g r e s s i o n , a l l f o u r t e s t f u n c t i o n s c l o s e l y p r o x i m a t e t h e t e s t r e s u l t s f o r t h e h e a t f l u x e s where t h e mean was i n c l u d e d . The e m p i r i c a l f o r m u l a o f f e r s s u b s t a n t i a l improvement o v e r t h e u n c o r r e c t e d t e s t r e s u l t s . 107 co 'CO C_) •-, _ , o LU . O CJ L U or Qrcn O LJ°0.1 SENSIBLE HERT FLUX LRTENT HERT F L U X 1.0 10.0 RVERRGING PERIOD IN DRYS 100.0 CO o C J O o _ I— cx or Qrcn O o ~ <-> 0 I 8 § z 5 1.0 10.0 RVERRG1NG PERIOD IN DRYS 100.0 F i g u r e 32 (a) F i g u r e 32(b) X COMPONENT CO i — -LU cn , C J —I LU O C J O o " cr _j • LU or orcn O o ' <-> 0.1 1.0 10.0 100.0 AVERAGING PERIOD IN DAYS F i g u r e 32(c) L i n e a r D.C. F i g u r e 32. The c o r r e l a t i o n c o e f f i c i e n t s w i t h t h e s h i p s 1 e m p i r i c a l f o r m u l a a p p l i e d . D.C. d e n o t e s d r a g c o e f f i c i e n t . 5.4 G e o g r a p h i c a l A v e r ag e d R e s u l t s The sums, sums o f s q u a r e s , and t h e sums of t h e c r o s s p r o d u c t s o f t h e VA and 3H v a r i a t e s were s a v e d f r o m th e i n i t i a l %> c a l c u l a t i o n s and were t h e n added ( e x c l u d i n g S t a t i o n N) t o c r e a t e a s e t c f t o t a l s t a t i s t i c s f o r a l l t h e s h i p s . The non-l i n e a r r e g r e s s i o n ( E q u a t i o n 5.9) was t h e n a p p l i e d t o a c h i e v e an 106 e s t i m a t e o f g e o g r a p h i c a l l y a v e r a g e d r e g r e s s i o n c o e f f i c i e n t s ( 7^ ) and hence a s i n g l e s e t o f f o r m u l a e a p p l i c a b l e t o most s h i p l o c a t i o n s . The r e s u l t s a p p e a r on t h e aVG row o f a p p e n d i x H and i n T a b l e X I I . The g e o g r a p h i c a l l y a v e r a g e d e m p i r i c a l f o r m u l a ( ^ ) was t h e n used t o d e t e r m i n e t h e f o u r t e s t f u n c t i o n s a t e a c h l o c a t i o n . The c o m p l e t e r e s u l t s f o r a l l s h i p s i n c l u d i n g S t a t i o n N and K, a p p e a r i n a p p e n d i x J . a g a i n o n l y t h e x component l i n e a r d r a g c o e f f i c i e n t and t h e h e a t f l u x e s w i l l be p r e s e n t e d . The d i f f e r e n c e means a r e shown i n F i g u r e 33. I n g e n e r a l t h e r a n g e o f v a l u e s i s s i m i l a r t o t h o s e o f t h e ^ r e s u l t s w i t h most v a l u e s b e i n g l e s s t h a n 0.1 dPa f o r t h e s t r e s s , and 5.0 and 12.0 Watts/m 2 f c r t h e s e n s i b l e and l a t e n t h e a t f l u x e s . . The i n a p p l i c a b i l i t y o f ~)\ a t S t a t i o n N i s r e a d i l y e v i d e n t i n t h e a b n o r m a l l y l a r g e DM v a l u e s f o r a l l t h r e e f l u x e s (see a p p e n d i x The d i f f e r e n c e v a r i a n c e s a p p e a r i n F i g u r e 34 e x c l u d i n g S t a t i o n N f o r a l l f l u x e s and S t a t i o n K f o r t h e s e n s i b l e h e a t f l u x . F o r a l l f l u x e s , t h e DV v a l u e s have a r a n g e a p p r o x i m a t e l y t w i c e t h a t o f t h e DVs. The o s c i l l a t i n g b e h a v i o u r i s no l o n g e r e v i d e n t . I n t h e s t r e s s c a s e , t h e DVs a r e d i s p e r s e d f a i r l y r e g u l a r l y a r o u n d 0.0%. The h e a t f l u x e s , however, have a p o s i t i v e b i a s . S t a t i o n K was n o t removed from a v e r a g i n g i n t h e s e n s i b l e h e a t f l u x e s . The e f f e c t o f t h e g e o g r a p h i c a l f o r m u l a on S t a t i o n K i s r e f l e c t e d i n i t s a b n o r m a l l y low DV v a l u e s i n t h e s e n s i b l e h e a t f l u x (see a p p e n d i x J) -- i n d i c a t i n g t h a t t h e g e o g r a p h i c a l a v e r a g e d f o r m u l a o v e r e s t i m a t e d t h e 3H flux,. , T h e r e a r e two p o s s i b l e c a u s e s f o r t h e p o s i t i v e DV b i a s . The 109 TABLE X I I The g e o g r a p h i c a l l y a v e r a g e d s h i p s ' r e g r e s s i o n c o e f f i c i e n t s f o r t h e f o r m y{ = H <*(u2 + v z p i * . The C d e n o t e s t h e c o n s t a n t d r a g c o e f f i c i e n t , t h e L d e n o t e s t h e l i n e a r d r a g c o e f f i c i e n t , t h e X d e n o t e s t h e x component, t h e Y d e n o t e s t h e y component, t h e H d e n o t e s t h e h e a t f l u x e s , t h e S d e n o t e s t h e s e n s i b l e h e a t f l u x and t h e L d e n o t e s t h e l a t e n t h e a t f l u x . I T T" |SHIP |TYPE | I I I BEGION I .25 - 2.0 DAYS REGION I I 4.0 - 28.0 DAYS -+ I | 4.237 J 4. 639 |3.276 |3.754 |3.S46 | 2. 33 5 I I-| AVG I I IC IC IL |L IH IH i 6 i Y 6 Y I 1-1.150 |0.261 |-1.183 |0.231 1-0.795 |0.310 I-0.853 |0.275 1-1.244 |0.244 |-1. 108 |0.263 X |3.337 1-1. 322 | 0. 920 Y 13.437 1-1.336 |0.901 X | 2. 325 | -0. 910 J 0.967 Y |2.322 1-0.910 |0.940 S |2.874 1-1.469 |0.984 L | 1.365 1-1 .25 1 | 1.021 g e o g r a p h i c a l a v e r a g e , ~v{ , may g e n e r a l l y r e d u c e t h e r e s i d u a l s s u f f i c i e n t l y so t h e DV v a l u e s b e g i n t o a p p r o a c h t h e BV v a l u e s ; o r t h e e f f e c t o f i n c l u d i n g S t a t i o n K i s t o weight t h e s t a t i s t i c s so t h e c a l c u l a t e d r e g r e s s i o n c o e f f i c i e n t s s l i g h t l y u n d e r -e s t i m a t e t h e r e q u i r e d c o r r e c t i o n s . . S i n c e t h e p o s i t i v e b i a s i s a l s o f e l t i n t h e l a t e n t h e a t f l u x .where S t a t i o n K d i d n o t d i f f e r r a d i c a l l y from t h e o t h e r l o c a t i o n s , t h e f o r m e r i s t h e p r o b a b l e c a u s e o f t h e b i a s . The r e s i d u a l v a r i a n c e s a p p e a r i n F i g u r e 35. The g e o g r a p h i c a l l y a v e r a g e d v a l u e s a r e , w i t h t h e e x c e p t i o n of S t a t i o n N, r e m a r k a b l y s i m i l a r t o t h e i n d i v i d u a l s h i p e m p i r i c a l f o r m u l a EV v a l u e s . F o r t h e s t r e s s e s and t h e s e n s i b l e , h e a t f l u x e s , t h e EVs a t a l l a v e r a q i n g p e r i o d s a r e w i t h i n 1.0% o f t h o s e l i s t e d i n Appendices.'D and G. S t a t i o n K s e n s i b l e h e a t f l u x v a l u e s show a 5.0% i n c r e a s e i n t h e r e s i d u a l s a t L=28 days o v e r t h e i n d i v i d u a l l y c a l c u l a t e d v a l u e s . As n o t e d i n C h a p t e r IV SENSIBLE HERT FLUX 1 10 LRTENT HERT FLUX C 0 0 z . CD LU 2: LU CJ L U ° LU o 0.1 1.0 10.0 AVERAGING PERIOD IN DAYS 100.0 Q-CNJ LU LU CJ L U 0 LU O o o ' 0.1 -3—t-1.0 10.0 AVERAGING PERIOD IN DAYS 100.0 F i g u r e 33 (a) F i g u r e 33(b) •X COMPONENT cnS Z . LU LU CJ ^ c o U J ° C t o ' LU Li-ft m 0.1 1.0 10.0 AVERAGING PERIOD IN DRYS 100.0 F i g u r e 33(c) L i n e a r DC F i g u r e 33. The d i f f e r e n c e means u s i n g t h e g e o g r a p h i c a l l y a v e r a g e d e m p i r i c a l f o r m u l a . The h e a t f l u x DMs a r e i n Watts/m 2 w h i l e t h e s t r e s s DMs a r e i n dPa. DC d e n o t e s d r a g c o e f f i c i e n t . The S t a t i o n N v a l u e s a r e o m i t t e d . , t h e S t a t i o n K v a l u e s d i f f e r q u i t e m a r k e d l y f r o m t h e o t h e r s h i p s ' v a l u e s . The 8.0% r e s i d u a l l i s t e d i n A p p e n d i x J i s n o t , however, m a r k e d l y l a r g e r t h a n t h o s e c a l c u l a t e d f o r t h e o t h e r s h i p s . I n s e v e r a l i n s t a n c e s , t h e g e o g r a p h i c a l l y a v e r a g e d EVs show 111 t o cr cr UJo CJcn. Z I LU cr LU r~iin SENSIBLE HERT FLUX l.o io o inn n AVERAGING PERIOD IN DAYS CO o ° Z o . a " i—i cr cr > o Lu' • C J 2 cr in . LATENT HERT FLUX 1.0 10 0 AVERAGING PERIOD IN DAYS 100 .0 F i g u r e 34 (a) F i g u r e 34 (b) c o C J ° . Q-rsj c r cr . UJo C J m LU cr LU T i — f -X COMPONENT 0 1 1.0 10 0 AVERAGING PERIOD IN DAYS 100 .0 F i g u r e 34(c) L i n e a r DC F i g u r e 34. The d i f f e r e n c e v a r i a n c e s u s i n g t h e g e o g r a p h i c a l l y a v e r a g e d e m p i r i c a l f o r m u l a . A l l v a l u e s a r e i n p e r c e n t . DC d e n o t e s d r a g c o e f f i c i e n t . S t a t i o n N i s e x c l u d e d i n a l l f l u x e s and S t a t i o n K i s e x c l u d e d from t h e s e n s i b l e h e a t f l u x . an i m provement o v e r t h e i n d i v i d u a l s h i p EVs. F o r example, a t S t a t i o n D L=4.0 d a y s , t h e g e o g r a p h i c a l l y a v e r a g e d l a t e n t h e a t f l u x EV i s 12.2% w h i l e t h e i n d i v i d u a l EV i s 13.3%. A c o m p a r i s o n between t h e r e s p e c t i v e d i f f e r e n c e v a r i a n c e s i n d i c a t e s a r i s e t o 13.8% from -7.0%. Thus t h e g e o g r a p h i c e m p i r i c a l f o r m u l a h a s S E N S I B L E HERT FLUX LATENT HERT FLUX co L U ° O o . GC CX cr2-CD CO LU or 1.0 10.0 A V E R A G I N G P E R I O D I N D A Y S 100 .0 CO, cn CX cxS-4 X) a co LU or 1.0 10.0 A V E R A G I N G P E R 100 I N D A Y S 100.0 F i g u r e 35 (a) F i g u r e 35 (b) X C O M P O N E N T CO L U ° C_)CD . CX cn cx CXco ' ZD CD CO • LU cn. 1 0 10 0 100 0 A V E R A G I N G ^ E R J O D I N D A Y S F i g u r e 35(c) L i n e a r DC F i g u r e 35. The r e s i d u a l v a r i a n c e s u s i n g t h e g e o g r a p h i c a l l y a v e r a g e d e m p i r i c a l f o r m u l a . A l l v a l u e s a r e i n p e r c e n t . S t a t i o n N i s e x c l u d e d . DC d e n o t e s d r a g c o e f f i c i e n t . . . more c l o s e l y a p p r o a c h e d t h e l e a s t s g u a r e s e s t i m a t e o f t h e S t a t i o n D p a r a m e t e r s and n e g a t e d t h e DV b i a s c o r r e c t i o n . The l a t e n t h e a t f l u x g e o g r a p h i c >( r e s i d u a l s a r e s u b s t a n t i a l l y l a r g e r i n s e v e r a l i n s t a n c e s t h a n t h e i n d i v i d u a l l y c a l c u l a t e d v a l u e s . F o r example, a t S t a t i o n I , t h e g e o g r a p h i c 113 r e s i d u a l s a t L=28.0 days a r e 27.6% where t h e i n d i v i d u a l f o r m u l a , ^ , g i v e s 18.0%. I n a l l o t h e r c a s e s , t h e g e o g r a p h i c r e s i d u a l s a r e w i t h i n 5.0% o f t h e i n d i v i d u a l l y c a l c u l a t e d v a l u e s . I h e c o r r e l a t i o n c o e f f i c i e n t s a p p e a r i n F i g u r e 36. I n a l l c a s e s , t h e g e o g r a p h i c a l l y a v e r a g e d c o r r e l a t i o n s a r e a b o u t 0.02 l e s s t h a n the >| v a l u e s . I h e g e o g r a p h i c a l l y a v e r a g e d e m p i r i c a l f o r m u l a a p p r o a c h , w i t h two e x c e p t i o n s , a p p e a r s t o y i e l d n e a r l y i d e n t i c a l r e s u l t s to the i n d i v i d u a l s h i p s e m p i r i c a l f o r m u l a . T h i s a p p r o a c h i s n o t v i a b l e f o r any o f t h e f l u x e s a t S t a t i o n N and may n o t be t h e b e s t e s t i m a t e f o r t h e S t a t i o n K s e n s i b l e h e a t f l u x c o r r e c t i o n . F o r S t a t i o n D, p a r t i c u l a r l y a t l o n g e r ave-raging p e r i o d s , t h e g e o g r a p h i c a l e m p i r i c a l f o r m u l a shows EV improvement o v e r t h e i n d i v i d u a l s h i p s e m p i r i c a l f o r m u l a b e c a u s e no a t t e m p t i s made t o remove the DV b i a s . T h i s i s a l s o r e f l e c t e d i n t h e g e n e r a l p o s i t i v e DV b i a s i n d i c a t i n g t h a t t h e g e o g r a p h i c a l a v e r a g e may n o t p r e d i c t t h e l o n g - t e r m 3H v a r i a n c e q u i t e a s a c c u r a t e l y a s t h e i n d i v i d u a l s h i p s ' e m p i r i c a l f o r m u l a ( ) . 5.5 I n t r i n s i c T e m p o r a l V a r i a t i o n s The l a t e n t h e a t f l u x c o r r e c t i o n s a t S t a t i o n N a r e c h a r a c t e r i z e d by markedly l a r g e r r e s i d u a l s and l o w e r c o r r e l a t i o n c o e f f i c i e n t s f o r a v e r a g i n g p e r i o d s i n B e g i o n I I . When t h e e m p i r i c a l f o r m u l a , , i s a p p l i e d , a t L=28.0 d a y s , t h e r e s i d u a l s a r e as h i g h as 58.9% o f t h e 3H v a r i a n c e . a l t h o u g h t h e s e n s i b l e h e a t f l u x r e s i d u a l s a r e l a r g e r a t S t a t i o n N t h e y a r e l e s s p r o n o u n c e d t h a n f o r t h e l a t e n t h e a t f l u x . The r e q u i r e d t r a n s f o r m a t i o n s may be i n h e r e n t l y non-114 SENSIBLE HEAT FLUX t o 'CD , L u Li_ L U O O O o ' cr Qico o 0 -<~> 0 I • ! 1.0 10.0 AVERAGING PERIOD IN DAYS 100 .0 CO 1 co , LL_ LU O C J co •^.co O o • CX CC Ct co <-> 0.1 LATENT HEAT FLUX 1.0 10.0 AVERAGING PERIOD IN DAYS 100 .0 F i g u r e 36 (a) F i g u r e 36 (b) X COMPONENT CO i— LU co '—CO O • , , o U_ LL. LU O o O o ' CX _ J L U CC o r co O o " o . l 1.0 10 0 100 0 AVERAGING PERIOD IN DAYS F i g u r e 36(c) L i n e a r DC F i g u r e 36. The c o r r e l a t i o n c o e f f i c i e n t s u s i n g t h e g e o g r a p h i c a l l y a v e r a g e d e m p i r i c a l f o r m u l a . DC d e n o t e s d r a g c o e f f i c i e n t . s t a t i o n a r y . I t has been assumed t h a t t h e w i n t e r c o r r e c t i o n s , f o r e x a m p l e , a r e i d e n t i c a l to t h e summer c o r r e c t i o n s . Dorman (1974) h a s d e m o n s t r a t e d t h a t a t S t a t i o n N t h e r e a r e l a r g e amounts o f e n e r g y a t the a n n u a l c y c l e s f o r t h e winds, wind components, s e a s u r f a c e t e m p e r a t u r e s , a i r t e m p e r a t u r e s and dew 115 p o i n t t e m p e r a t u r e s . E x c e p t f o r s e a s u r f a c e t e m p e r a t u r e s , t h e c h a r a c t e r of a l l component v a r i a t e s c h a n g e s m a r k e d l y from w i n t e r t o summer. Dorman a l s o showed t h a t t h e w i n t e r c l o c k w i s e wind component power i s more t h a n f o u r t i m e s t h a t o f t h e summer power. . Some o f t h e s c a t t e r t h a t i s e v i d e n t between the 3H and VA v a r i a t e s may be due t o s e a s o n a l c h a n g es i n t h e r e g u i r e d c o r r e c t i o n s . One method t o d e t e r m i n e whether the a n n u a l c y c l e p l a y s a d o m i n a n t r o l e i n t h e r e q u i r e d c o r r e c t i o n s i s t o examine t h e 3H and VA and r e s i d u a l (3H - VA) s p e c t r a . I f a s i g n i f i c a n t peak i n the r e s i d u a l s p e c t r a o c c u r s , t h e n a s e a s o n a l l y d e p e n d e n t c o r r e c t i o n may be n e c e s s a r y . To t h i s end S t a t i o n C was s e l e c t e d a s a c o n t r o l b e c a u s e i t e x h i b i t s p a r t i c u l a r l y s t a b l e h e a t f l u x r e s i d u a l s a t L=28.0 d a y s — 7.6% f o r t h e l a t e n t h e a t f l u x and 3.8% f o r t h e s e n s i b l e h e a t f l u x as compared t o 58.9% and 12.6% r e s p e c t i v e l y a t S t a t i o n N a f t e r t h e s h i p s e m p i r i c a l f o r m u l a , T| , was a p p l i e d . The d a t a a t b o t h s h i p s were a v e r a g e d , and t h e l u n a r m o n t h l y 3H, VA and r e s i d u a l s t r e s s e s were c a l c u l a t e d . The t h r e e t i m e s e r i e s were t h e n b r o k e n i n t o 9 ,two-year b l o c k s a t S t a t i o n C and 10 t w o - y e a r b l o c k s a t S t a t i o n N. E a c h b l o c k o f d a t a was d e t r e n d e d and a c o s i n e t a p e r was a p p l i e d ( f o l l o w i n g Bendat and P i e r s c l (197 1)) t o 10.0% o f t h e d a t a a t each end c f t h e b l o c k s t o r e d u c e r i n g i n g from t h e c o n v o l u t i o n i n f r e q u e n c y space o f t h e box window i n h e r e n t i n t h e d a t a . The s p e c t r a l c h a r a c t e r i s t i c s o f t h e box window and t h e c o s i n e t a p e r c a n be s e e n i n B endat and P i e r s o l ( 1 9 7 1 ) pp. 324-325. The c o s i n e t a p e r a l s o t e n d s t o r e d u c e t h e power o f t h e i n p u t s i g n a l . C o n s e q u e n t l y t h e v a r i a n c e was c a l c u l a t e d b e f o r e 116 and a f t e r t h e t a p e r and a l l t h e o u t p u t s p e c t r a m u l t i p l i e d by t h e a p p r o p r i a t e c o r r e c t i o n a t each f r e g u e n c y . The t w e n t y - s i x p c i n t s w i t h i n each b l o c k were the n f a s t f o u r i e r t r a n s f o r m e d by t h e UBC FOURT programme and t h e s q u a r e o f the m a g n i t u d e o f e a c h f o u r i e r s i n e / c o s i n e p a i r was c a l c u l a t e d . The s p e c t r a l d e n s i t y e s t i m a t e s f o r a l l b l o c k s were added and t h e mean power d e n s i t y e s t i m a t e was f o u n d . The e r r o r i n t h e mean s p e c t r a l d e n s i t y e s t i m a t e s f o l l o w s a X - d i s t r i b u t i o n w i t h 2N d e g r e e s o f f r e e d o m ( J e n k i n s and W a t t s , 1972) where N i s t h e number o f b l o c k s . The 95% c o n f i d e n c e zone i s d e t e r m i n e d f r c m : where ^ i s t h e number o f d e g r e e s o f freedom (2N) jX^^.ou' and ~)Cro, ©.11 ^  a r e t h e "](_ s t a t i s t i c s a t 0.025 and 0. 975 p r o b a b i l i t i e s and ~9 d e g r e e s o f f r e e d o m , s 2 i s t h e s p e c t r a l d e n s i t y e s t i m a t e and T 2" i s t h e a c t u a l unknown s p e c t r a l d e n s i t y . E q u a t i o n 5. 12 i s c o r r e c t assuming t h a t t h e i n p u t s e r i e s i s G a u s s i a n and t h a t the s p e c t r a l e s t i m a t e s between b l o c k s a r e i n d e p e n d e n t . D e t e r m i n i s t i c s i g n a l s , n o n - s t a t i o n a r i t y , and n o n - n o r m a l i t y o f t h e i n p u t s e r i e s r e d u c e t h e a c t u a l d e g r e e s o f f r e e d o m c a u s i n g an i n c r e a s e i n t h e c o n f i d e n c e z o n e s . S o p h i s t i c a t e d t e c h n i q u e s have been d e v e l o p e d t o c a l c u l a t e t h e e f f e c t i v e d e g r e e s of f r e e d o m . These w i l l n o t be i m p l e m e n t e d b e c a u s e t h e aim i s t o d e t e r m i n e o n l y i f o u t s t a n d i n g peaks e x i s t i n t h e d a t a . C o n s e q u e n t l y i t w i l l be assumed t h a t 2N i s a l s o t h e e f f e c t i v e d e g r e e s of f r e e d o m and t h e f a c t o r (-y*^  j&onJ w i l l c e q u o t e d . . F o r two d e g r e e s 1 17 o f f r e e d o m ( i e . one i n d e p e n d e n t s p e c t r a l e s t i m a t e ) , t h i s f a c t o r i s a p p r o x i m a t e l y (.25,4.0). The s p e c t r a of t h e u n c o r r e c t e d l a t e n t and s e n s i b l e h e a t f l u x e s a t S t a t i o n s C and N a p p e a r i n F i g u r e 37. . I n a l l c a s e s , the a n n u a l c y c l e i n t h e 3H f l u x i s e v i d e n t . . At S t a t i o n C, t h e VA power i s a l w a y s l e s s t h a n t h e 3H power and i f one c o n s i d e r s the 3H p eaks t o a be a f a c t o r o f 4.0 above t h e 3H n o i s e l e v e l , t h e y a r e s i g n i f i c a n t t c l e s s t h a n 2.0 d e g r e e s o f f r e e d o m . At S t a t i o n N, however, t h e VA power d e n s i t i e s o f t e n e x c e e d the 3H v a l u e s i n t h e l a t e n t h e a t f l u x , c o n s i s t e n t w i t h t h e n e g a t i v e u n c o r r e c t e d DV v a l u e s shown i n F i g u r e 21. I n t h e s e n s i b l e h e a t f l u x , t h e VA a n n u a l c y c l e i s w e l l w i t h i n t h e VA n o i s e l e v e l w h i l e t h e 3H a n n u a l c y c l e i s w e l l above the 3H n o i s e l e v e l . F u r t h e r m o r e , the r e s i d u a l s e r i e s power d e n s i t y f o r b o t h f l u x e s a t t h e a n n u a l c y c l e i s much g r e a t e r t h a n t h e r e s i d u a l n o i s e l e v e l . I n f a c t , t h e a n n u a l c y c l e f r e q u e n c y band f o r t h e l a t e n t h e a t f l u x a c c o u n t s f o r 42% o f t h e t o t a l power o f t h e r e s i d u a l s . The p r o c e s s e s b e h i n d t h i s power may a l s o i n f l u e n c e the s e m i - a n n u a l c y c l e c a u s i n g s l i g h t l y l a r g e r power d e n s i t i e s a t t h i s f r e g u e n c y . s p e c t r a f o r t h e h e a t f l u x e s r e c a l c u l a t e d . The r e s u l t s a p p e a r i n F i g u r e 38. At S t a t i o n C, s e n s i b l e h e a t f l u x , t h e VA s e r i e s c l o s e l y matches t h e 3H s e r i e s a t a l l f r e q u e n c i e s . At 0.5 c y c l e s / y e a r t h e VA s e r i e s s l i g h t l y u n d e r p r e d i c t s t h e 3H s e r i e s w h i l e a t 3.5 c y c l e s / y e a r , i t s l i g h t l y o v e r p r e d i c t s t h e 3H s e r i e s . The o v e r and u nder p r e d i c t i o n s c o u n t e r - b a l a n c e a c c o u n t i n g f o r t h e low The i n d i v i d u a l e m p i r i c a l f o r m u l a was a p p l i e d and t h e 1 18 STATION c SENSIBLE HERT FLUX H 3 * 4 4 — I 1 1 1 1—~ 2.0 4.3 . 6.0 FREQUENCY IN ]/YEARS F i g u r e 37 (a) STATION C L^ATENT HEAT FLUX CT. 3 I I I I I 2.0 4.0 6 0 FREOUENCr JM J/YEARS 8.0 F i g u r e 37 (b) STATION N SENSIBLE HEAT FLUX STATION N LATENT HEAT FLUX CC X x X + + X ^ $ *j  ' $ + X X * * » 0.0 20 4.0 G,.0 FREQUENCY IN ]/ YEARS 8.3 x • X 0.0 2.0 4.0 6.0 FREQUENCY IN ]/TEARS F i g u r e 37 (c) F i g u r e 37 (d) F i g u r e 37. The s p e c t r a c f t h e u n c o r r e c t e d VA, r e s i d u a l , and 3H h e a t f l u x t i m e s e r i e s at S t a t i o n s C and N. The VA s e r i e s i s i n d i c a t e d by + , t h e 3H s e r i e s by x and t h e r e s i d u a l s e r i e s by <t> . The 95% c o n f i d e n c e l i m i t s a r e (.57,2.19) f o r S t a t i o n C and (.59,2. 08) f o r S t a t i o n N. 1 1 9 STATION C SENSIBLE HER! FLUX * 1 c r -* « » + * * * * K ^ A ft, l*\ ^  ,*t T "' T "' '!' • — I 1 0.0 2.0 4.0 6.0 B.O F R E Q U E N C Y I N 1 / Y E R R S F i g u r e 38(a) STATION C LRTENT HERT FLUX CMo X • co x * & *> i i 1 r i 1 0.0 2.0 4.0 6.0 8.0 F R E Q U E N C Y I N 1 / Y E A R S F i g u r e 38 (b) STAIION N SENSIBLE NEST FLUX STATION N LATENT HEAT FLUX 5-°. — o . Ul or. cr . * x * )£ * + X X » e ° « e « o 2.0 4.0 6 0 F R E Q U E N C Y I N 1 / Y E A R S l 8.0 ¥ x » 2.0 4.0 6.0 F R E Q U E N C Y I N 1 / Y E A R S 8.0 F i g u r e 38 (c) F i g u r e 38 (a) F i g u r e 38. The s p e c t r a o f t h e c o r r e c t e d h e a t f l u x f o r t h e 3H, VA and r e s i d u a l s e r i e s a t S t a t i o n s C and N. The V& s e r i e s i s i n d i c a t e d by +, t h e 3H s e r i e s by x, and t h e r e s i d u a l s e r i e s by <> . The c o n f i d e n c e l i m i t s a r e (.57,2.19) a t S t a t i o n C and (.59,2. 08) a t S t a t i o n N. 120 0.5% DV l e v e l shown i n a p p e n d i x I . The r e s i d u a l s e r i e s power i s q u i t e n e g l i g i b l e a t a l l f r e q u e n c i e s compared t o t h e 3H s e r i e s . The l a t e n t h e a t f l u x VA s e r i e s a l s o c l o s e l y a p p r o x i m a t e s t h e 3H s e r i e s f o r a l l b u t the a n n u a l c y c l e . The 350 ( W a t t / m 2 ) 2 y e a r s d i f f e r e n c e a t t h i s f r e q u e n c y a c c o u n t s f o r a l a r g e p o r t i o n o f t h e 3.0% d i f f e r e n c e v a r i a n c e . The r e s i d u a l s e r i e s shows a s l i g h t i n c r e a s e a t t h e a n n u a l c y c l e b u t i t c a n n o t be c l a s s i f i e d as s i g n i f i c a n t . T hus, even t h o u g h t h e r e i s s u b s t a n t i a l power i n the 3H and VA v a r i a t e s a t t h e a n n u a l c y c l e t h e r e i s no i n d i c a t i o n o f a s u b s t a n t i a l peak i n t h e r e s i d u a l s e r i e s . At S t a t i o n N.# t h e s e n s i b l e h e a t f l u x r e s u l t s a p p r o x i m a t e the 3H r e s u l t s r e a s o n a b l y w e l l a t a l l f r e q u e n c i e s e x c e p t t h e a n n u a l c y c l e where t h e VA r e s u l t s u n d e r e s t i m a t e t h e 3H r e s u l t s . At 8 o t h e r h a r m o n i c s , t h e VA s e r i e s s l i g h t l y o v e r e s t i m a t e s the 3H s e r i e s . In a t t e m p t i n g t o r e d u c e t h e DV e r r o r t o 0.0, t h e v a r i a n c e d i f f e r e n c e a t t h e a n n u a l c y c l e may have been i n c r e a s e d t o t h e d e t r i m e n t o f t h e o t h e r f r e q u e n c i e s . The r e s i d u a l s e r i e s shows a s l i g h t r i s e a t t h e a n n u a l c y c l e b u t i s p r o b a b l y n o t s i g n i f i c a n t i n c o m p a r i s o n t o t h e e r r o r a t t h e o t h e r f r e q u e n c i e s . I n t h e l a t e n t h e a t f l u x a t S t a t i o n N, t h e va s e r i e s u n d e r e s t i m a t e s t h e 3H s p e c t r a l d e n s i t i e s a t most f r e q u e n c i e s , at t h e a n n u a l c y c l e , t h e r e s i d u a l power d e n s i t y i s more t h a n 4 t i m e s t h a t a t any o t h e r f r e q u e n c y . Thus s e a s o n a l c o r r e c t i o n s may be r e q u i r e d a t S t a t i o n N i n t h e l a t e n t h e a t f l u x and t h i s may i n p a r t a c c o u n t f o r i t s l a r g e r r e s i d u a l v a r i a n c e s . The r e s i d u a l power d e n s i t y i s a p p r o x i m a t e l y e q u a l t o t h e sum o f t h e VA and 3H powers. I t i s d e m o n s t r a t e d i n A p p e n d i x A.4 t h a t t h i s can o c c u r when a t h e r e i s a 90° phase s h i f t between the 3H and 121 VA v a r i a t e s . The t i m e s e r i e s o f t h e r e s i d u a l l a t e n t h e a t f l u x a t S t a t i o n N w i t h 7| a p p l i e d i s shown i n F i g u r e 3 9 ( a ) . The a n n u a l c y c l e i s e v i d e n t . I n c o n t r a s t , the S t a t i o n C r e s i d u a l s a r e i n F i g u r e 3 9 ( b ) . As s u g g e s t e d i n t h e s p e c t r a , t h e r e a r e no d o m i n a n t s i g n a l s . An i n s p e c t i o n of t h e d a t a a t S t a t i o n N, L=28.0 d a y s , l a t e n t h e a t f l u x r e v e a l e d t h a t g r o u p i n g months 1-5 and 11-13 i n c l u s i v e r e f l e c t e d a p o s i t i v e b i a s i n t h e r e s i d u a l s w h i l e months 6-10 i n c l u s i v e r e f l e c t e d a n e g a t i v e b i a s i n t h e r e s i d u a l s . The d a t a were t h e n a r r a n g e d i n t h e s e g r o u p s and a w i n t e r and summer e m p i r i c a l f c r m u l a c a l c u l a t e d f o r L=28.0 d a y s . The r e s u l t s a p p e a r i n T a b l e X I I I . The summer ^> v a l u e s o f a b o u t -1.8 a r e s u b s t a n t i a l l y l o w e r (more n e g a t i v e ) t h a n any o t h e r v a l u e s . The l a t e n t h e a t r e s i d u a l s were c a l c u l a t e d u s i n g t h e s e v a l u e s and were r e d u c e d t o 3 1.95? and t h e s e n s i b l e h e a t r e s i d u a l s were r e d u c e d t o 8.08. The s p e c t r a f o r t h e s e a s o n a l l y c o r r e c t e d f l u x e s a t S t a t i o n N a p p e a r i n F i g u r e 40. The 3H and VA s e r i e s VA s e r i e s now match more c l o s e l y a t t h e a n n u a l c y c l e . A c o m p a r i s o n w i t h F i g u r e 38 r e v e a l s t h a t a s l i g h t r e d u c t i o n i n t h e power o f t h e r e s i d u a l s a t 2.0 c y c l e s / y e a r and a s l i g h t r e o r d e r i n g of t h e r e l a t i v e p o s i t i o n s o f t h e VA and 3H s p e c t r a l d e n s i t i e s has o c c u r r e d a t most f r e q u e n c i e s . The s p e c t r a l d e n s i t y o f t h e r e s i d u a l s e r i e s a t t h e a n n u a l c y c l e i s w e l l w i t h i n t h e s c a t t e r o f t h e o t h e r f r e q u e n c i e s . The pcwer o f t h e r e s i d u a l s a t a l l f r e q u e n c i e s o t h e r t h a n t n e a n n u a l c y c l e h as r e m a i n e d , however, v i r t u a l l y unchanged. 122 TABLE X I I I The summer and w i n t e r f o r m u l a c o e f f i c i e n t s r e g u i r e d a t S t a t i o n N f o r t h e h e a t f l u x e s a t L=28.0 d a y s . I T " : T ' "1 J TYPE 1 WINTER I SOMMER I i__ __ __i 1 «_ (3_ "i I S e n s i b l e l 5.337 | -1.368 | 4.399 | -1.730 | | L a t e n t | 4.9S7 | -1.373 | 3.878 | -1.824 | I J 1 L 1. 1 S t a t i o n D has t h e l a r g e s t r e s i d u a l s f o r t h e y component, l i n e a r d r a g c o e f f i c i e n t and t h e s e c o n d l a r g e s t r e s i d u a l s f o r t h e c x component l i n e a r d r a g c o e f f i c i e n t . C o n s e g u e n t l y , the s p e c t r a a t t h i s s t a t i o n were examined a t L=28.0 d a y s . . F i g u r e s 4 1(a) and (b) a r e t h e x and y c c m c c h e n t s p e c t r a c a l c u l a t e d from t h e u n c o r r e c t e d t i m e s e r i e s . The x component 3H and r e s i d u a l s p e c t r a b o t h show d i s t i n c t i n c r e a s e s i n s p e c t r a l d e n s i t y a t t h e a n n u a l c y c l e w h i l e t h e y component i s q u i t e w h i t e . I n b o t h components the r e s i d u a l s p e c t r a a r e l a r g e r a t a l l f r e q u e n c i e s t h a n t h e VA s p e c t r a i n d i c a t i n g t h a t t h e e r r o r i s g r e a t e r t h a n the a c t u a l VA e s t i m a t e o f t h e power.: T h i s i n d i c a t e s t h a t s e v e r e e r r o r s may a r i s e i f g e o s t r o p h i c winds f r o m b a r o m e t r i c p r e s s u r e maps a v e r a g e d o v e r p e r i o d s o f g r e a t e r t h a n p e r h a p s f o u r d a y s a r e used t o c a l c u l a t e s t r e s s s p e c t r a . One e x p e c t s much s m a l l e r e r r o r s i n t h e s p e c t r a c a l c u l a t e d by W i l l e b r a n d (1978) s i n c e t h e e r r o r s f o r t h e 28 day a v e r a g i n g p e r i o d shown h e r e i s much l a r g e r t h a n t h o s e f o r t h e 12 h o u r l y a v e r a g i n g p e r i o d upon w h i c h he b a s e d h i s s t u d y . F i g u r e s 41(c) and (d) show t h e VA and 3H s p e c t r a w i t h ^ a p p l i e d t o t h e VA s e r i e s . . In t h e x component t h e r e i s a d e f i n i t e mis-match between the 3H and VA s p e c t r a a t t h e a n n u a l 123 CM X X 2Io 0.0 4.0 8.0 12.0 16.0 20.0' TIME IN YEARS F i g u r e 39 (a) S t a t i o n N F i g u r e 39 (b) S t a t i o n C F i g u r e 39. The c o r r e c t e d r e s i d u a l s e r i e s a t S t a t i o n s N and C f o r t h e l a t e n t h e a t f l u x , L=28.0 d a y s . O N Hd O H- H-tl lO ID H C C CD H H O (1) ro r+ H-O « r O fc> o tn • Qi f+ t-3 cn ro ci-CD cr n- CD H- PJ O c+ a Hi « c X II rn tOTS oo ro • O. O f+ h P> ^ C m tn ts cn c+ t r ro CO CD OJ cn o ts 0> H K! PJ PJ S in f+ CD Ch o O . CM O CO . X ( N o X O J J CN X X. CDC3 cr STRTION N-LRTENT HERT F L U X c 1-1 ro O ft) +-vft X - 3 H *-R£S!DUR CONFIDENCEC0.53.Z.08) + X <!> X ¥ + * + X <!> ® ® X o < ! > # ¥ < ! > '<!> 0 . 0 T T T" 2.0 4.0 6.0 F R E Q U E N C Y IN 1 / Y E A R S 8 . 0 STATION N SENSIBLE HERT F L U X X * X £ x * f * X + V -3H *-RESIPURL C0NFIDEHCFtO.59.2.O8j + X * + * X I I I I I 1 0 . 0 2 . 0 4.0 6 0 F R E Q U E N C Y I N ] / T E A R S 125 sinn ON o * COMPONENT STATION D r COMPONENT CN X X CXo' LU X $ o.o x x x * 0 <•, • « *^-+ + + ± FREQUENCY*™ 1/YERRS e.o X X CEo LU X » ® X X X « 0.0 © X ® « X X « » X X X 20 4.0 6 0 FREQUENCY IN 1/YERRS e.o F i g u r e 41(a) U n c o r r e c t e d F i g u r e 4 1(b) U n c o r r e c t e d STATION 0 X COMPONENT STATION D r COMPONENT CN X^. o . X CEo' UJ 0.0 x x • x » o c 0 CN CE CL a . X ccT CEo' * * X JS..0 4.0 6.0 FREQUENCY IN 1/YERRS e.o v ¥ x + * $ * ¥ x 0.0 2.0 4.0 6.0 FREQUENCY IN 1/YERRS 8.0 F i g u r e 4 1 ( c ) C o r r e c t e d F i g u r e 4 1(d) C o r r e c t e d F i g u r e 4 1. The x and y component power s p e c t r a , l i n e a r d r a g c o e f f i c i e n t , f o r t h e u n c o r r e c t e d and c o r r e c t e d VA s e r i e s a t S t a t i o n D, L = 28.0 d a y s . The c o n f i d e n c e b a r s a r e (.57,2.19) 126 c y c l e w h i l e t h e r e s i d u a l s p e c t r u m shows a s l i g h t peak. A t a l l o t h e r f r e q u e n c i e s , however, t h e 3H and VA s p e c t r a match q u i t e w e l l . A f t e r c o r r e c t i o n , t h e y component 3H and VA match f a i r l y w e l l a t a l l f r e q u e n c i e s w h i l e t h e r e s i d u a l s e r i e s i s much l o w e r i n power. . S i n c e t h e y component power s c a l e i s 1/2 o f t h e x component power s c a l e , t h e v a r i a n c e o f t h e r e s i d u a l s of t h e y s c a l e a r e somewhat l e s s t h a n 1/2 o f t h o s e o f t h e x component. T a b l e V i n d i c a t e s , however, t h a t t h e a c t u a l 3H v a r i a n c e i n t h e y component a t S t a t i o n D i s o n l y 1/10 o f t h a t i n t h e x component. Thus t h e g e n e r a l l y l a r g e r r e l a t i v e r e s i d u a l v a r i a n c e s shown i n the y component f o r t h e l i n e a r d r a g c o e f f i c i e n t may be p a r t i a l l y a t t r i b u t e d t o d i v i d i n g by t h e s m a l l e r 3H v a r i a n c e . The g e o g r a p h i c a l e m p i r i c a l f o r m u l a , 7[ , was a p p l i e d t o the l i n e a r d r a g c o e f f i c i e n t s t r e s s a t S t a t i o n D and t h e r e s u l t i n g s p e c t r a a p p e a r i n F i g u r e 42. The r e s i d u a l s p e c t r a a r e v i r t u a l l y i d e n t i c a l t o t h o s e o b t a i n e d when t h e i n d i v i d u a l c o r r e c t i o n , , was a p p l i e d . The VA s p e c t r a , however, s y s t e m a t i c a l l y u n d e r e s t i m a t e s t h e 3H s e r i e s s p e c t r a l d e n s i t i e s a t a l l f r e q u e n c i e s . T h i s i s c o n s i s t e n t w i t h t h e i n c r e a s e d d i f f e r e n c e v a r i a n c e s i n d u c e d by a p p l i c a t i o n o f t h e g e o g r a p h i c a l e m p i r i c a l f o r m u l a . The S t a t i o n N r e s i d u a l s e r i e s , l a t e n t f l u x shows a l a r g e amount o f power a t t h e a n n u a l c y c l e which c a n be r e d u c e d by a p p l y i n g a s e m i - a n n u a l c o r r e c t i o n . T h i s s u g g e s t s t h a t a t i m e d e p e n d e n t c o r r e c t i o n may be r e g u i r e d f o r t h e s t r e s s e s a t S t a t i o n N. • The i n d i v i d u a l S t a t i o n N s t r e s s c o r r e c t i o n s f o r t h e l i n e a r d r a g c o e f f i c i e n t were a p p l i e d and t h e r e s u l t s a r e shown i n F i g u r e 4 3. Note t h a t t h e s c a l e on t h e y a x i s ( s p e c t r a l power t 127 STATION D X OPPONENT STATION D T COMPONENT CM e x x + +  ft ft ft X X • + ft ft ft x * a ft ft C\J UJ T" 0.0 2.0 4.0 6 0 FREQUENCY IN I/TEARS B.O ft ft ft ft "T + + X * X X * * ft 0 ft ft ° " 20 ' 4 0 ' e~o FREQUENCY IN ]/TEARS B.O F i g u r e 42. The l i n e a r d r a g c o e f f i c i e n t s p e c t r a a t S t a t i o n D 1=28.0 d a y s , c o r r e c t e d w i t h t h e g e o g r a p h i c a l l y a v e r a g e d f o r m u l a . The 95% c o n f i d e n c e l i m i t s a r e (.57,2.19). STATION N X COMPONENT STATION N T COMPONENT *CD X , ,c c r a . a <Xo' X CO«o UJ 2.0 4.0 6.0 FREQUENCY IN I/YEARS » (*> ft X X * * + ft tj> 6 -£—& $ T 30 4.0 6 0 FREQUENCY IN I/YEARS 8.0 F i g u r e 43. The s t r e s s s p e c t r a a t s t a t i o n N c o r r e c t e d w i t h t h e S t a t i o n N e m p i r i c a l f o r m u l a , L=28.0 d a y s , l i n e a r d r a g c o e f f i c i e n t . The 95% c o n f i d e n c e l i m i t s a r e (. 59, 2.08) 128 d e n s i t y ) h a s been i n c r e a s e d by an o r d e r o f magnitude o v e r t h a t f o r S t a t i o n D c o n s i s t e n t w i t h t h e l o w e r v a r i a n c e s r e p o r t e d i n T a b l e V. T h e r e i s a s l i g h t mis-match o f power between t h e 3H and VA s e r i e s as w e l l as a s l i g h t r i s e i n t h e y component s t r e s s power d e n s i t i e s a t t h e a n n u a l c y c l e . The i n c r e a s e i n t h e r e s i d u a l power i s n o t s i g n i f i c a n t . C o n s e q u e n t l y a m o n thly o r s e a s o n a l dependence i n t h e c o r r e c t i o n s may n o t be r e q u i r e d f o r t h e s t r e s s e s . 129 CHAPTEB VI WIND BOSE MEASUREMENTS 6.1 I n t r o d u c t i o n Over much o f t h e W o r l d s ' s o c e a n s , t h e o n l y s o u r c e o f c l i m a t i c i n f o r m a t i o n i s from weather l o g s o f s h i p s o f o p p o r t u n i t y . The O f f i c e o f t h e C h i e f o f N a v a l O p e r a t i o n s , US Navy has c o m p i l e d and smoothed, i n t h e f o r m a t o f wind r o s e s , t h e m e t e o r o l o g i c a l o b s e r v a t i o n s o f w e a t h e r s t a t i o n s and s h i p s - o f -o p p o r t u n i t y f o r each o f t h e t w e l v e months o f t h e y e a r as w e l l as a c o n g l o m e r a t e wind r o s e b a s e d on a l l t h e a v a i l a b l e d a t a . The wind r o s e i s c o n s t r u c t e d by s o r t i n g t h e d a t a i n t o e i g h t d i r e c t i o n s and f o u r B e a u f o r t c a t e g o r i e s . They a r e t h e n p r e s e n t e d as t h e r e l a t i v e f r e q u e n c y c f wind e v e n t s w i t h i n t h e f o u r d i r e c t i c n / E e a u f c r t g r o u p s and as t h e r e l a t i v e f r e q u e n c y w i t h i n n i n e B e a u f o r t c l a s s e s i r r e s p e c t i v e o f d i r e c t i o n . F u r t h e r d e t a i l s c a n be f o u n d f r c m t h e M a r i n e C l i m a t i c A t l a s (MCA). . H e l l e r m a n (1965 and 1967) has us e d wind r o s e s t o e s t i m a t e w o r l d c l i m a t i c wind s t r e s s p a t t e r n s . U s i n g a d i s c r e t e and a c o n t i n u o u s s t r e s s c a l c u l a t i o n t e c h n i q u e and t h r e e d i f f e r e n t d r a q c o e f f i c i e n t s t c compute . s t r e s s v a l u e s , he e s t i m a t e d t h e wind s t r e s s c u r l and c a l c u l a t e d d i f f e r e n t v a l u e s o f t h e wind d r i v e n w e s t e r n b o u n d a r y c u r r e n t . He c o n c l u d e d t h a t t h e s e l e c t i o n o f d r a g c o e f f i c i e n t had a much l a r g e r i n f l u e n c e on t h e magnitude o f the w e s t e r n boundary c u r r e n t t h a n e r r o r s a r i s i n g f r o m t h e t y p e o f c a l c u l a t i o n o f s t r e s s from wind r o s e s . The w e a t h e r s t a t i o n d a t a o f f e r e d an o p p o r t u n i t y t o i n v e s t i g a t e I n d e t a i l t h e i n a c c u r a c i e s a r i s i n g i n c a l c u l a t i o n o f wind s t r e s s f r c m wind r o s e s . 130 6.2 A n a l y s i s l o f a c i l i t a t e d i s c u s s i o n , t h e n o m e n c l a t u r e o f H e l l e r m a n (1965) w i l l be u s e d . The v a r i a b l e fit^ w i l l r e f e r t o t h e r e l a t i v e f r e g u e n c y o f wind e v e n t s i n B e a u f o r t c a t e g o r y i and d i r e c t i o n j w h i l e F i w i l l r e f e r t o t h e r e l a t i v e f r e g u e n c y o f wind e v e n t s i n B e a u f o r t c a t e g o r y i i r r e s p e c t i v e o f d i r e c t i o n . Note t h a t H e l l e r m a n l a b e l l e d h i s B e a u f o r t c a t e g o r i e s from i = 0 - 11 where t h e p r e s e n t s t u d y w i l l use i n t e r v a l s i = 1 12. B e a u f o r t c a t e g o r y 13 (> 33.5 m/sec) w i l l be a r b i t r a r i l y i n c o r p o r a t e d i n t o c l a s s 12. The o r i g i n a l wind d i r e c t i o n was d i g i t i z e d i n 10° i n c r e m e n t s g i v i n g 36 d i r e c t i o n s . The M a r i n e C l i m a t i c A t l a s was f o r m a t t e d i n t o 8 d i r e c t i o n s . B e c a u s e e i g h t i s n o t a f a c t o r o f 36, t h e i n t e r v a l s between t h e twc wind r o s e s do n o t c o i n c i d e and a b i a s o c c u r s i n t h e c o n s t r u c t i o n s o f t h e 8 d i r e c t i o n wind r o s e as o u t l i n e d by L e a and H e l v e y (1971) . To compensate f c r t h i s b i a s , a l i n e a r l y p i e c e w i s e c o n t i n u o u s 36 d i r e c t i o n d i s t r i b u t i o n f o r each B e a u f o r t c a t e g o r y was c o n s t r u c t e d . H e l l e r m a n used a s i m i l a r t e c h n i q u e t o i n t e r p o l a t e wind s p e e d s ; .we a d a p t e d t h e t e c h n i q u e t o i n t e r p o l a t e d i r e c t i o n a l d i s t r i b u t i o n s . F o r e a c h o f t h e . 36 d i r e c t i o n i n t e r v a l s , f ^ was assumed to be c e n t r e d on t h e j d i r e c t i o n (eg. 5 . 0 ° ) . The r e l a t i v e f r e q u e n c y was d i v i d e d by the w i d t h o f t h e d i r e c t i o n c a t e g o r y ( i n t h i s c a s e 10<>) t o a r r i v e a t a t o t a l f r e q u e n c y d e n s i t y f o r e a c h d i r e c t i o n / E e a u f o r t c a t e g o r y . The f r e g u e n c y d e n s i t i e s a t t h e ends o f e a c h c a t e g o r y (f \ : ) were d e t e r m i n e d by i n t e r p o l a t i o n between a d j a c e n t c e n t r e p o i n t s as shown i n F i g u r e 44. The c e n t r e p o i n t s were t h e n r e a d j u s t e d t o 1 3 1 c o n s e r v e t i e t o t a l f r e q u e n c y d e n s i t y i n t h e i n t e r v a l a c c o r d i n g t o : ^ o ' * 2 Ssj + * - 4 kt 6 . 1 where f ' ^ i s t h e f r e q u e n c y d e n s i t y a t t h e l o w e r end o f t h e j d i r e c t i o n , f j ^ ( i s t h e f r e q u e n c y d e n s i t y a t t h e uppe r end o f t h e c a t e g o r y , f ^ i s t h e r e a d j u s t e d c e n t r e p o i n t , f : ^ i s t h e o r i g i n a l c e n t r e p o i n t f r e g u e n c y d e n s i t y . I n t h e c a s e t h a t f L (j =0.0 the n c. c f ' O , ^ and f\^\ were s e t = 0.0. . I f f : v ^ < 0.0 f was s e t = 0 . 0 and f ' c ^ and f ' i.,j + i were d e t e r m i n e d by: 6 . 2 The p r e c e d i n g c e n t r e p o i n t f was then a g a i n a d j u s t e d to c o n s e r v e t h e c o n t i n u i t y and f r e g u e n c y o f t h e d i s t r i b u t i o n . The a r e a under t h e c u r v e was e q u a l t o t h e f r e q u e n c y o f o c c u r r e n c e o f t h e wind w i t h i n each d i r e c t i o n i n t e r v a l . The t o t a l 3 6 0 O was t h e n d i v i d e d i n t o b l o c k s o f 45° w i t h t h e f i r s t i n t e r v a l c e n t r e d on 0.0° and t h e a r e a w i t h i n e a c h b l o c k was c a l c u l a t e d t o d e t e r m i n e t h e e i g h t d i r e c t i o n f r e q u e n c y f u n c t i o n . The MCft f o r m a t wind r o s e g r o u p s t h e B e a u f o r t i n t e r v a l s as f o l l o w s . : f 3 . t ' J ; f f . t / J ! f 7 . V » J ; f f t = f°,,.o,u,l2, ' J : j=1,8 and: 132 F i g u r e 44. C o n s t r u c t i o n o f t h e p i e c e w i s e l i n e a r d i s t r i b u t i o n f o r t h e d i r e c t i o n i n t e r p o l a t i o n . The M o d i f i e d S c r i p p s p r o c e d u r e (MSc) i n v o l v e s e x p a n s i o n o f t h e o f t h e f L ( ^ c a t e g o r i e s t h r o u g h p r o p o r t i o n a l i t y a s s u m p t i o n s from t h e f o u r s p e e d / d i r e c t i o n g r o u p i n g s t o 1 2 . The s t r e s s i s t h e n c a l c u l a t e d by: H e l l e r m a n expands t h e g a l e f o r c e wind c a t e g o r i e s o n l y f o l l o w i n g t h e MSc p r o c e d u r e s and t h e n a p p l i e s t h e f r e g u e n c y d e n s i t y c o n s e r v a t i o n t e c h n i g u e s t o c a l c u l a t e t h e s t r e s s a s : 133 u 8 .L S i n 6-a 6.4 I g n o r i n g t h e i n t r i n s i c e r r o r o f t h e t r a n s f e r c o e f f i c i e n t s and a c c e p t i n g t h o s e used i n t h e p r e v i o u s c h a p t e r s , t h r e e i m m e d i a t e s o u r c e s o f e r r o r can be i d e n t i f i e d a s f o l l o w s : a. e r r o r s i n t h e d i r e c t i o n a l c o n s t r u c t i o n o f t h e wind r o s e ; b. e r r o r s i n wind magnitude g r o u p i n g ; and c. d i f f e r e n c e s i n c a l c u l a t i o n t e c h n i q u e s . Assuming t h a t t h e 36 d i r e c t i o n wind c o m p r i s e s t h e i n i t i a l d a t a s e t , t h e r e d u c t i o n t o 8 d i r e c t i o n s i n d u c e s e r r o r s t o t h e s t r e s s c a l c u l a t i o n s i n twc ways. F i r s t , s i n c e t h e l i n e a r p i e c e w i s e c o n t i n u o u s d i s t r i b u t i o n i s an a p p r o x i m a t i o n o f t h e a c t u a l c o n t i n u o u s d i s t r i b u t i o n , the assumed o v e r l a p c a l c u l a t i o n s may n o t be a c c u r a t e . S econd, t h e r e d u c t i o n f r o m 36 t o 8 d i r e c t i o n s r e f l e c t s a r e d u c t i o n i n t h e number o f d e g r e e s o f fre e d o m o f t h e d i s t r i b u t i o n (and h e n c e t h e t o t a l i n f o r m a t i o n a v a i l a b l e a bout t h e s t a t i s t i c a l s t r u c t u r e o f t h e system) by a f a c t o r g r e a t e r t h a n f o u r . A wind s p e e d a v e r a g i n g i s i n h e r e n t i n t h e r e d u c t i o n c f number o f d i r e c t i o n s and s h o u l d r e s u l t i n a d e c r e a s e i n a c c u r a c y c f the-Stress c a l c u l a t i o n s . E r r o r s due t o wind s p e e d s m o o t h i n g a r i s e i n a s i m i l a r manner t o t h e e r r o r s due t c d i r e c t i o n s m o o t h i n g . The o r i g i n a l d a t a f o r S t a t i o n s A t h r o u g h N a r e d i g i t i z e d t o 1.0 k n o t (0.515 m / s e c ) . The i n i t i a l g r o u p i n g t o 12 B e a u f o r t i n t e r v a l s m a r k e d l y r e d u c e s t h e number o f d e g r e e s o f fr e e d o m o f t h e d i s t r i b u t i o n and i n d u c e s t h e v e c t o r a v e r a g i n g o f t h e wind. The MCA f o r m a t i n c r e a s e s t h e wind s m o o t h i n g by a f u r t h e r r e d u c t i o n i n g r o u p i n g 134 f r o m 12 B e a u f o r t c a t e g o r i e s p e r d i r e c t i o n t o f o u r . The M o d i f i e d S c r i p p s t e c h n i q u e a t t e m p t s t o overcome t h i s r e d u c t i o n by e x p a n s i o n c f t h e MCA f o r m a t t o 12 B e a u f o r t c a t e g o r i e s whereas H e l l e r m a n e x p a n d s t h r o u g h i n t e r p o l a t i o n o f t h e g i v e n f r e q u e n c y d e n s i t i e s . . The M o d i f i e d S c r i p p s c a l c u l a t i o n i s e s s e n t i a l l y a d i s c r e t e c a l c u l a t i o n i n which i t i s assumed t h a t t h e f r e q u e n c y d e n s i t i e s w i t h i n e a c h B e a u f o r t c a t e g o r y s h o u l d have l i t t l e e f f e c t on t h e f i n a l f l u x r e s u l t s . The H e l l e r m a n t e c h n i q u e assumes t h a t t h e f r e q u e n c y d e n s i t i e s a r e c o n t i n u o u s and t h a t an a t t e m p t t o i n t e r p o l a t e t h e v a r i a t i o n s w i t h i n e ach B e a u f o r t c a t e g o r y may be more e f f e c t i v e . A d i s c r e t e and c o n t i n u o u s f l u x c a l c u l a t i o n t e c h n i q u e c a n be a p p l i e d w i t h f a c i l i t y a t a l l l e v e l s o f wind r o s e c o n s t r u c t i o n . The t o t a l d a t a sample was d i v i d e d i n t o a c t u a l m o n t h l y g r o u p i n g s and t h e s t r e s s e s and h e a t f l u x e s were d i r e c t l y c a l c u l a t e d . To s i m u l a t e i r r e g u l a r s a m p l i n g s by s h i p s - o f -o p p o r t u n i t y , any 3H r e a d i n g which c o n t a i n e d e r r o n e o u s d a t a f o r any v a r i a b l e was r e j e c t e d from c a l c u l a t i o n s . . Wind r o s e s were t h e n c o n s t r u c t e d i n t h r e e s t a g e s i n c l u d i n g monthly and t o t a l wind g r o u p i n g s . The 36 d i r e c t i o n , 12 B e a u f o r t i n t e r v a l was i n i t i a l l y c o n s t r u c t e d . The s t r e s s was t h e n c a l c u l a t e d by t h e d i s c r e t e and c o n t i n u o u s methods t o d e t e r m i n e t h e l o s s i n a c c u r a c y from wind speed s m o o t h i n g a l o n e . An 8 d i r e c t i o n , 12 B e a u f o r t i n t e r v a l wind r o s e was t h e n c o n s t r u c t e d from t h e p r e v i o u s wind r o s e and t h e s t r e s s c a l c u l a t e d by b o t h t e c h n i q u e s to i n d i c a t e t h e l o s s i n a c c u r a c y due t o d i r e c t i o n s m o o t h i n g , f i n a l l y a MCA t y p e wind r o s e o f 8 d i r e c t i o n s and 4 B e a u f o r t 135 i n t e r v a l s was c o n s t r u c t e d and t h e s t r e s s c a l c u l a t e d by t h e H e l l e r m a n c o n t i n u o u s t e c h n i q u e and t h e M o d i f i e d S c r i p p s p r o c e d u r e t o d e t e r m i n e t h e l o s s of a c c u r a c y due t o f u r t h e r wind speed s m o o t h i n g and t h e a c c u r a c y one c a n e x p e c t f r o m M a r i n e C l i m a t i c A t l a s wind r o s e s . In o r d e r t c f a c i l i t a t e i d e n t i f i c a t i o n , t h e t y p e o f c a l c u l a t i o n w i l l be i d e n t i f i e d by t h e number o f d i r e c t i o n s and number o f B e a u f o r t i n t e r v a l s o f t h e wind r o s e and t h e t y p e o f f l u x c a l c u l a t i o n . Ihe t y p e o f f l u x c a l c u l a t i o n w i l l be a b b r e v i a t e d as : (1) D - d i s c r e t e , (2) C - c o n t i n u o u s (3) MSc m o d i f i e d S c r i p p s . Thus t h e 36-12-D s t r e s s w i l l be t h e s t r e s s c a l c u l a t e d f r c m t h e 36 d i r e c t i o n 12 B e a u f o r t i n t e r v a l wind r o s e by t h e d i s c r e t e t e c h n i q u e . The d i s c r e t e t e c h n i q u e a p p l i e s E q u a t i o n 6.3 d i r e c t l y . The MSc method i n v o l v e s t h e e x p a n s i o n o f t h e f o u r B e a u f o r t c a t e g o r i e s t o 12, t h e n t h e . a p p l i c a t i o n o f E q u a t i o n 6.5. The a b b r e v i a t i o n s and s y m b o l s t o be used i n t h e s t a g e s o f c a l c u l a t i o n o f t h e wind r o s e s a p p e a r i n T a b l e XIV. The s t r e s s d i f f e r e n c e s were q u a n t i f i e d by d e t e r m i n i n q t h e a b s o l u t e d i f f e r e n c e s i n s t r e s s m a g n i t u d e and d i r e c t i o n between the wind r o s e s t r e s s and t h e 3H s t r e s s . The h e a t f l u x e s were d e t e r m i n e d by c a l c u l a t i n g t h e m o n t h l y a v e r a g e a i r - s e a t e m p e r a t u r e and h u m i d i t y d i f f e r e n c e s d i r e c t l y . The wind r o s e s were used t o c a l c u l a t e t h e m o nthly a v e r a g e d wind s p e e d s . The wind r o s e h e a t f l u x was t h e n t h e p r o d u c t o f t h e wind r o s e wind s p e e d and t h e monthly a v e r a g e t e m p e r a t u r e o r h u m i d i t y d i f f e r e n c e . The d i f f e r e n c e between t h e d i r e c t l y d e t e r m i n e d and wind r o s e h e a t f l u x e s t h e n q u a n t i f i e d t h e i n a c c u r a c i e s . The d i f f e r e n c e s were d e t e r m i n e d f o r each monthly gr o u p and 136 TABLE XIV C o d i n g f o r t h e wind r o s e l e v e l s c a l c u l a t e d i n C h a p t e r V I . DIRECTIONS SPEEDS ICALCOLATICN |ABBREVIATION | TECHNIQUE | SYMBOL — I 36 36 8 8 8 8 12 12 12 12 MCA MCA | C o n t i n u o u s | D i s c r e t e I c o n t i n u o u s | D i s c r e t e | C o n t i n u o u s I | MSC I 136-12-C I 36-12-D |8-12-C |8-12-D | MCA I c o n t i n u o u s |MCA MSC i X A f o r the c o m p o s i t e r e c o r d wind r o s e f o r e a c h s h i p . The m o n t h l y d i f f e r e n c e s were t h e n a v e r a g e d i n two manners. F i r s t , t h e a n n u a l c y c l e f o r e a c h s h i p was a v e r a g e d and t h e s t a n d a r d d e v i a t i o n s o f t h e monthly d i s c r e p a n c i e s d e t e r m i n e d . F o r example, t h e d i s c r e p a n c i e s from J a n u a r y t h r o u g h December f o r S t a t i o n A were a v e r a g e d t c d e t e r m i n e a t y p i c a l e r r o r f o r S t a t i o n A. T h i s a v e r a g i n g w i l l be r e f e r r e d t o as t h e s h i p a v e r a g e e r r o r and t h e c o r r e s p o n d i n g s t a n d a r d d e v i a t i o n , t h e s h i p e r r o r s t a n d a r d d e v i a t i o n . The s e c o n d a v e r a g i n g was p e r f o r m e d between s h i p s f o r e a c h month. F o r example, t h e J a n u a r y e r r o r s o n l y f o r a l l s h i p s were summed, a v e r a g e d and t h e s t a n d a r d d e v i a t i o n s d e t e r m i n e d . T h i s t e c h n i q u e s h o u l d i n d i c a t e i f t h e e r r o r s a r e i n d u c e d by t h e a n n u a l c y c l e and w i l l be r e f e r r e d t o as t h e monthly a v e r a g e and monthly e r r o r s t a n d a r d d e v i a t i o n . 6.3 R e s u l t s The s t r e s s and h e a t f l u x components were c a l c u l a t e d t h r o u g h t h e s i x s t a g e s p r e v i o u s l y o u t l i n e d . I n a l l c a s e s t h e e r r o r s i n v o l v e d were g e n e r a l l y much s m a l l e r t h a n t h e d i f f e r e n c e mean e r r o r s d i s c u s s e d i n C h a p t e r s I I I , I V , and V. I n most c a s e s t h e 137 error i n stress magnitudes were less than ± 0.05 dPa; the errors i n d i r e c t i o n were generally l e s s than 5.0° ; and the heat flux errors were generally bounded between ± 5 . 0 Watts/m2. Stress Magnitude Errors Figures 45 (a) and (b) contain the ship mean and error standard deviations for the constant drag c o e f f i c i e n t respectively. Figures 45 (c) and (d) contain the monthly mean and error standard deviations respectively for the l i n e a r drag c o e f f i c i e n t . In a l l cases the 36-12-D calc u l a t i o n i s biased s l i g h t l y negatively at about 0.01 dPa i n d i c a t i n g that t h i s technique consistently overestimates the actual stress.. This i s accompanied by a standard deviation of s i m i l a r order of magnitude suggesting that the bias i s s t a t i s t i c a l l y s i g n i f i c a n t . Tt i s doubtful, however, that errors of t h i s magnitude contribute greatly to induce errors in oceanic c i r c u l a t i o n c a l c u l a t i o n s . In both the ship and monthly means, the 36-12-C cal c u l a t i o n s are v i r t u a l l y 0.0 dPa. The error standard deviations are roughly equivalent to the 36-12-D technique. The 8-12-C has a mean error of about 0.02 dPa larger than the 8-12-D calculations with nearly i d e n t i c a l error standard deviations. Furthermore, both cases show a consistent reduction of 0.01 - 0.02 dPa from the respective 36 d i r e c t i o n c a l c u l a t i o n . Thus an e f f e c t cf reduction of direction degrees of freedom i s to induce a s l i g h t underestimation of the stress. It i s i n t e r e s t i n g that t h i s induced underestimation in the discrete 138 C D „ -MEflNS or 0 L U <=>m o X CO o C J fl B C 0 E I J K M N P SHIP c=u-L U L U U _ L L »—i o C D ^ : CO ^ - c o C_) STflNDRRD DEVIATIONS A B C D E I J K M N P S H I P °-o-| F i g u r e 45 (a) C o n s t a n t DC MEANS • L U C J in L U ° or LU LU-LL S'n O o ' c o ? ' CX cn ex. i i J I * ? ? CD Q * x X 8 x J F M A M J J A S O N D T MONTH F i g u r e 45 (b) C o n s t a n t DC STANDARD DEVIATIONS C X ^ L U • L U ° or L U • 'in O o CD CX or i CL" F M A M J J A MONTH S 0 N D T F i g u r e 45(c) L i n e a r DC F i g u r e 45(d) L i n e a r DC F i g u r e 45. The magnitude mean e r r c r s and e r r o r s t a n d a r d d e v i a t i o n s between the a c t u a l s t r e s s and wind r o s e s t r e s s as a f u n c t i o n o f s h i p and month. The T i s t h e c o m p o s i t e wind r o s e b a s e d on a l l t h e d a t a . DC d e n o t e s d r a g c o e f f i c i e n t . 139 c a l c u l a t i o n r e - a d j u s t s a s y s t e m a t i c o v e r e s t i m a t i o n f o r 36 d i r e c t i o n s t o an o v e r - a l l mean o f n e a r l y 0.0 dPa i n t h e 8 d i r e c t i o n c a s e . I n t h e c o n t i n u o u s c a l c u l a t i o n , t h e means a r e c o n s i s t e n t l y u n d e r e s t i m a t e d by a b o u t 0.02 - 0.03 dPa. The MCA c o n t i n u o u s and d i s c r e t e c a l c u l a t i o n s l e a d t o c u r i o u s r e s u l t s . The c o n t i n u o u s c a l c u l a t i o n mean e r r o r s ( w i t h s e v e r a l e x c e p t i o n s ) , a p p e a r t o u n d e r e s t i m a t e t h e t o t a l s t r e s s t o a b o u t t h e same d e g r e e as t h e 8-12-C t e c h n i q u e . . The MCA MSc mean v a l u e s a r e , however, l o w e r than t h e 8-12-D t e c h n i q u e . . I n d e e d , d u r i n g t h e summer months the MCA MSc t e c h n i q u e o v e r e s t i m a t e s t h e " a c t u a l " s t r e s s t o an even g r e a t e r d e g r e e t h a n th e 36-12-D t e c h n i q u e . The s t a n d a r d d e v i a t i o n s f o r t h e d i s c r e t e and c o n t i n u o u s c a l c u l a t i o n s a r e n e a r l y i d e n t i c a l and d i s p l a y d i s t i n c t i n c r e a s e s (up t c 0.1 dPa) i n t h e w i n t e r . The MCA f o r m a t does n o t r e s o l v e t h e g a l e f o r c e winds i n t o d i r e c t i o n c a t e g o r i e s . To a c h i e v e t h i s , H e l l e r m a n d i v i d e s 1/6 o f t h e t o t a l g a l e f o r c e winds i n t o B e a u f o r t c a t e g o r i e s 11 and 12 i r r e s p e c t i v e o f s e a s o n and l o c a t i o n . S i n c e t h e s t r e s s i s c a l c u l a t e d as t h e s q u a r e o f t h e wind s p e e d (a c u b i c i n t h e l i n e a r c a s e ) , even s m a l l g a l e f o r c e wind f r e q u e n c y d e n s i t i e s c a n make d i s p r o p o r t i o n a t e l y l a r g e c o n t r i b u t i o n s t o t h e t o t a l s t r e s s . T hus, i f t h e a c t u a l r a t i o o f B e a u f o r t c a t e g o r i e s 11 and 12 i s s u b s t a n t i a l l y l e s s t h a n 1/6 t h e n a f i c t i t i o u s l y h i g h s t r e s s w i l l r e s u l t . F c r e x ample, a t S t a t i o n J where t h e d i s c r e t e c a l c u l a t i o n y i e l d s a p a r t i c u l a r l y h i g h v a l u e i n J a n u a r y , t h e g a l e f o r c e winds a c c o u n t f o r 18.0 % o f t h e d i s t r i b u t i o n . The r a t i o o f B e a u f o r t c a t e g o r i e s 11 and 12 t o t h e t o t a l g a l e f o r c e winds i s o n l y 11.3% and n o t 16.7%. F u r t h e r m o r e , i n June and 140 J u l y t h e r e a r e no r e c o r d e d v a l u e s i n B e a u f o r t c a t e g o r i e s 11 and 12. A l l e r r o r s c a l c u l a t e d by a l l t h e t e c h n i q u e s a r e v e r y s m a l l . The r e d u c t i o n i n d i r e c t i o n a l d e g r e e s o f f r e e d o m l e a d s to a s l i g h t i n c r e a s e i n t h e u n d e r e s t i m a t i o n o f the " t r u e " s t r e s s . The d i s c r e t e c a l c u l a t i o n c o n s i s t e n t l y y i e l d s l a r g e r s t r e s s m a gnitude e s t i m a t e s t h a n t h e c o n t i n u o u s c a l c u l a t i o n f o r e q u i v a l e n t d e g r e e s o f freedom. I n a c c u r a c i e s a s s o c i a t e d w i t h t h e MCA t e c h n i q u e s may be due t o i n a d e q u a t e i n t e r p o l a t i o n o f t h e g a l e f o r c e winds. S t r e s s D i r e c t i o n E r r o r s The s h i p l i n e a r a n g l e d i f f e r e n c e means and s t a n d a r d d e v i a t i o n s a p p e a r i n F i g u r e s 46 (a) and (b) r e s p e c t i v e l y w h i l e t h e m o n t h l y c o n s t a n t a n g l e d i f f e r e n c e means a p p e a r i n F i g u r e s 46 (c) and ( d ) . The mean a n g l e d i f f e r e n c e s a r e a l l l e s s t h a n 5 . 0 ° . The s t a n d a r d d e v i a t i o n s , w i t h t h e e x c e p t i o n o f S t a t i o n s D and K, l i n e a r d r a g c o e f f i c i e n t , a r e a l s o l e s s t h a n 5 . 0 ° . The means f o r the c o n s t a n t d r a g c o e f f i c i e n t as a f u n c t i o n o f month a r e b i a s e d p o s i t i v e l y w h i l e t h e l i n e a r d r a g c o e f f i c i e n t b i a s e s a p p e a r l e s s e v i d e n t . The mean e r r o r s a p pear t o be dependent upon d e g r e e s o f freedom and n o t upon d i s c r e t e o r c o n t i n u o u s c a l c u l a t i o n t e c h n i q u e s . The 36-12-C, 36-12-D, 8-12-C, and 8-12-D t e c h n i q u e s a r e v i r t u a l l y i d e n t i c a l i n b o t h means and s t a n d a r d d e v i a t i o n s . The two MCA c a l c u l a t i o n s a r e a l s o v e r y c l o s e i n t h e i r mean v a l u e s a l t h o u g h t h e p a r a l l e l i s much l e s s e v i d e n t i n t h e 141 C D Z . cr U J u_ L L O o C D ^ cr cr -| &>. Z i n M E A N S fl B C D E I J K S H I P M N P CD L U C J r L l J " " 5 cr L U O o CD1? CC cr -| S T A N D A R D D E V I A T I O N S 4 x A B C D E I J K M N P S H I P F i g u r e 46 (a) L i n e a r DC F i g u r e 46 (b) L i n e a r DC ^ o L U • L U C J L U • . Q^LO L U U_ U_ I 1 O M E A N S C D C T I — ° C O L O C J o J F M A M J J A S O N D T M O N T H L U L U o L U • . cr COin 0 7 ' o S T A N D A R D D E V I A T I O N S <!> J F M A M J J A S O N D T M O N T H F i g u r e 46(c) C o n s t a n t EC F i g u r e 46(d) C o n s t a n t DC F i g u r e 46. The d i r e c t i o n mean e r r o r s and e r r o r s t a n d a r d d e v i a t i o n s between the a c t u a l s t r e s s and wind r o s e s t r e s s as a f u n c t i o n o f s h i p and month. The T i s t h e c o m p o s i t e wind r o s e b a s e d on a l l t h e d a t a . DC d e n o t e s d r a g c o e f f i c i e n t . 142 s t a n d a r d d e v i a t i o n s . Where t h e two MCA' s t a n d a r d d e v i a t i o n s d i v e r g e , t h e c o n t i n u o u s c a l c u l a t i o n shows more f l u c t u a t i o n s . . Heat F l u x e s The e r r o r s i n t h e s e n s i b l e h e a t f l u x e s a p p e a r i n F i g u r e 47. E r r o r s a r e v e r y s m a l l — t h e means a r e g e n e r a l l y bounded by ± 2.0 Watts/m 2. W i t h i n e a c h s h i p o r month c a t e g o r y t h e s t a n d a r d d e v i a t i o n s f o r a l l c a l c u l a t i o n s t e c h n i q u e s a r e v i r t u a l l y i d e n t i c a l . Ihe r e d u c t i o n f r c m 36 t c 8 d i r e c t i o n s a p p e a r s t o have a n e g l i g i b l e e f f e c t on t h e mean e r r o r f o r e i t h e r t h e d i s c r e t e o r c o n t i n u o u s c a l c u l a t i o n s . T h e r e i s , however, a s l i g h t p o s i t i v e b i a s (or u n d e r e s t i m a t i o n ) i n t h e mean e r r o r f o r the 36-12-C, 36-12-D, 8-12-C, and 8-12-D c a l c u l a t i o n s . Wind speed g r o u p i n g a c c o r d i n g t o t h e MCA f o r m a t i n d u c e s a s m a l l mean e r r o r . The c o n t i n u o u s MCA c a l c u l a t i o n c o n s i s t e n t l y u n d e r e s t i m a t e s t h e s e n s i b l e h e a t f l u x i n c o m p a r i s o n t o t h e o t h e r c a l c u l a t i o n s w h i l e the MCA MSc c a l c u l a t i o n s y i e l d a c o n s i s t e n t o v e r e s t i m a t i c n i n r e l a t i o n to t h e o t h e r t e c h n i q u e s . The e f f e c t o f t h i s s l i g h t o v e r e s t i m a t i o n i s t h a t t h e MCA MSc c a l c u l a t i o n on the a v e r a g e has z e r o b i a s i n t h e means f o r b o t h t h e s h i p and monthly a v e r a g e c a l c u l a t i o n s . The l a t e n t h e a t f l u x r e s u l t s a p p e a r i n F i g u r e 48. Many o f the o b s e r v a t i o n s o f t h e s e n s i b l e h e a t f l u x a r e a l s o a p p l i c a b l e t o t h e l a t e n t h e a t f l u x . There i s l i t t l e d i f f e r e n c e i n t h e means between any c a l c u l a t i o n f o r t h e d i r e c t i o n r e d u c t i o n and the m a j o r d i s c r e p a n c i e s o c c u r f o r t h e MCA f o r m a t . The c o n t i n u o u s MCA c a l c u l a t i o n a g a i n u n d e r e s t i m a t e s t h e l a t e n t h e a t f l u x i n r e l a t i o n t c t h e o t h e r t e c h n i q u e s w h i l e t h e MCA MSc rvj1-: X C D _ X MEANS co • I— I— C X o O m _| co L U L D C O I A B C D' E I J K M N P SHIP 1 43 X t D " X CO ' I— I— d ° ca -I CO z o ' • J C D . CO i STANDARD DEVIATIONS A' B C D' E I J K M N SHIP F i g u r e 47(a) r\j° X CO I— I— c e o CO -ZL<=> CO I % o & 4> i MEANS 8 • i * • J F M A M' J J A S 0' N ' D' T' MONTH F i g u r e 47 (b) X C D X co • I— I— C E O LU I I 1 CO '•Jco. CO 1 STANDARD DEVIATIONS J F M A ' M ' J ' J ' R ' MONTH S 0 N 0 T F i g u r e 47(c) F i g u r e 47(d) F i g u r e 47. The mean e r r o r s and e r r o r s t a n d a r d d e v i a t i o n s between t h e a c t u a l s e n s i b l e h e a t f l u x e s and wind r o s e s e n s i b l e h e a t f l u x e s as a f u n c t i o n o f s h i p and month.. The T r e f e r s t o the c o n g l o m e r a t e wind r o s e . 144 X — X M E A N S co i — I—o U J 1 x O' o ^ * ^ 4, ® ^ ffl * © 4 A ' UJo A B C D E I J K M N P SHIP o (Mm. x ~ X CO t— I—CD S T R N D R R D D E V I A T I O N S CEin . UJ 1 X UJo t m A B C D E I J K M N f SHIP F i g u r e 48(a) F i g u r e 48(b) o X " X CO I— i — o CTuV M E A N S Xm. LU ' X UJo * * * * * * * 4-* 4- • * 4-J F M . R M J J A S O N D M O N T H X — X CO I— I—o Xm' X m . UJ 1 X UJo S T A N D A R D D E V I A T I O N S 4> 4- 4-J F ' M A M J ' J ' A S O N D ' T M O N T H F i g u r e 48(c) F i g u r e 48(d) F i g u r e 48. The mea.n e r r o r s and e r r o r s t a n d a r d d e v i a t i o n s between t h e a c t u a l l a t e n t h e a t f l u x e s and t h e wind r o s e l a t e n t h e a t f l u x e s as a f u n c t i o n o f s h i p and month.- The T r e f e r s t o the c o n g l o m e r a t e wind r o s e . 1 45 c a l c u l a t i o n a g a i n o v e r e s t i m a t e s t h e l a t e n t h e a t f l u x . . The s t a n d a r d d e v i a t i o n s f o r a l l t e c h n i q u e s a r e v i r t u a l l y i d e n t i c a l . The mean l a t e n t h e a t e r r o r s a r e l a r g e l y bounded by ± 5 H a t t s / m 2 w i t h a g e n e r a l n e g a t i v e b i a s f o r f o r a l l t e c h n i q u e s i n b o t h t h e month and s h i p mean e r r o r s . The e f f e c t o f t h e . n e g a t i v e b i a s i s t h a t t h e MC& c o n t i n u o u s c a l c u l a t i o n now p r o v i d e s on a v e r a g e , t h e most a c c u r a t e e s t i m a t e s o f t h e l a t e n t h e a t f l u x . 1 46 CHAPTER V I I SUMMAM AND CONCLUSIONS Time s e r i e s o f v a r y i n g l e n g t h s from n i n e w e a t h e r s h i p s i n the N o r t h A t l a n t i c Ocean and from two w e a t h e r s h i p s on t h e N o r t h P a c i f i c Ocean were examined. The d a t a c o n s i s t e d o f t h r e e - h o u r l y r e a d i n g s o f wind component v e l o c i t i e s , b a r o m e t r i c p r e s s u r e , a i r t e m p e r a t u r e , dew p o i n t t e m p e r a t u r e , and s e a s u r f a c e t e m p e r a t u r e from which were c a l c u l a t e d t h r e e - h o u r l y a i r d e n s i t i e s , a i r - s e a t e m p e r a t u r e d i f f e r e n c e s , a i r - s e a h u m i d i t y d i f f e r e n c e s , x and y component wind s t r e s s e s ( u s i n g b o t h c o n s t a n t and l i n e a r d r a g c o e f f i c i e n t s ) , s e n s i b l e and l a t e n t h e a t f l u x e s . The c a l c u l a t e d g u a n t i t i e s and t h e wind component v e l o c i t i e s were a v e r a g e d o v e r v a r y i n g p e r i o d s . The f l u x e s were t h e n r e c a l c u l a t e d u s i n g t h e a p p r o p r i a t e a v e r a g e d c o n s t i t u e n t v a r i a t e s t o a r r i v e a t a v e c t o r a v e r a g e d (VA) e s t i m a t e . The VA f l u x e s t i m a t e s were t h e n compared t o t h e d i r e c t l y a v e r a g e d ( c a l l e d 3H) f l u x e s . A s y s t e m a t i c under p r e d i c t i o n o f t h e 3H a i r - s e a f l u x e s o c c u r s when t h e y a r e e s t i m a t e d t h r o u g h VA p a r a m e t e r s . The r e q u i r e d t r a n s f o r m a t i o n s t o c o r r e c t f o r t h e s e l o s s e s a r e s i m i l a r f o r a l l f l u x e s and a r e d e p e n d e n t upcn t h e V& wind s p e e d and upon a v e r a g i n g p e r i o d . ( C h a p t e r s I I I and IV) F o u r t e s t f u n c t i o n s : t h e d i f f e r e n c e means, d i f f e r e n c e v a r i a n c e s , r e s i d u a l v a r i a n c e s , and c o r r e l a t i o n c o e f f i c i e n t s were d e f i n e d i n E g u a t i o n s 2.16 - 2.19 t o q u a n t i f y t h e d i f f e r e n c e s between t h e VA and 3H f l u x e s . I n a l l c a s e s t h e d i f f e r e n c e means, d i f f e r e n c e v a r i a n c e s , and r e s i d u a l v a r i a n c e s i n c r e a s e d r o u g h l y e x p o n e n t i a l l y w i t h a v e r a g i n g p e r i o d w h i l e t h e c o r r e l a t i o n c o e f f i c i e n t s showed a s i m i l a r d e c r e a s e . The 147 r e s i d u a l v a r i a n c e measured the p o i n t - b y - p o i n t d i f f e r e n c e s and had maximum u n c o r r e c t e d v a l u e s a t 1=28.0 days o f 30.0-40.0% f o r the c o n s t a n t d r a g c o e f f i c i e n t , 40.0-50.0% f o r t h e l i n e a r d r a g c o e f f i c i e n t , 25.0-45.0% f o r t h e s e n s i b l e h e a t f l u x and 40.0%+ f o r t h e l a t e n t h e a t f l u x . ( S e c t i o n s 3.1 and 4.2) A s i m p l e a n a l y s i s e s t a b l i s h e d a l o w e r bound o f t h e p o i n t -b y - p o i n t magnitude r e d u c t i o n s i n t h e c o n s t a n t d r a g c o e f f i c i e n t s t r e s s , K j ( L ) . They were p r o p o r t i o n a l t o t h e v a r i a n c e o f t h e wind s p e e d l o s t t h r o u g h a v e r a g i n g , and i n v e r s e l y p r o p o r t i o n a l t o the c a l c u l a t e d v e c t o r a v e r a g e d wind s p e e d s g u a r e d . A l t h o u g h n o t e x a c t , t h e s i m p l e model a i d e d i n e x p l a i n i n g many d i s t r i b u t i o n a l f e a t u r e s o f t h e 3H-VA d i s c r e p a n c i e s . The f a c t t h a t t h e p o i n t -b y - p o i n t d i r e c t i o n d i f f e r e n c e s , B j ( L ) , a v e r a g e d t o 0.0° f o r moderate wind s p e e d s i n d i c a t e d t h a t a s i n g l e t r a n s f o r m a t i o n would s u f f i c e f o r b o t h t h e x and y s t r e s s e s . ( S e c t i o n 3.3) The most p r e c i s e method o f c o r r e c t i n g f o r t h e 3H-VA d i s c r e p a n c i e s was t o l i n e a r l y r e g r e s s t h e two v a r i a t e s on a B e a u f o r t c a t e g o r y / a v e r a g i n g p e r i o d b a s i s a r r i v i n g a t a t r a n s f o r m a t i c n . Marked i m p r o v e m e n t s were f o u n d i n a l l f o u r t e s t q u a n t i t i e s . The r e s i d u a l s i n c r e a s e d e x p o n e n t i a l l y t o 3.0 d a y s and t h e n r e m a i n e d f a i r l y c o n s t a n t from 3.0 t o 28.0 d a y s . A t L=28.0 d a y s , t h e c o n s t a n t d r a g c o e f f i c i e n t r e s i d u a l s were r e d u c e d t o 5.0-8.0%, t h e l i n e a r d r a g c o e f f i c i e n t r e s i d u a l s were r e d u c e d t o 10.0-15.0%, t h e s e n s i b l e h e a t f l u x r e s i d u a l s were r e d u c e d t o 5.0-10.0% and t h e l a t e n t h e a t f l u x r e s i d u a l s were r e d u c e d t o 10.0-40.0+%.. S i g n i f i c a n t (>10.0%) t r a n s f o r m a t i o n s were r e g u i r e d f o r a l l wind speed c a t e g o r i e s f o r a v e r a g i n g p e r i o d s g r e a t e r t h a n 0.5 days. ( S e c t i o n s 3.7 and 4.5) 148 Due t o m a t h e m a t i c a l a s p e c t s o f t h e r e g r e s s i o n , i t was f o u n d t h a t a p o s i t i v e b i a s i n t h e d i f f e r e n c e v a r i a n c e s , e x a c t l y e g u a l to t h e r e s i d u a l v a r i a n c e s was i n d u c e d . B e c a u s e c o r r e l a t i o n s were g e n e r a l l y h i g h between t h e 3H and VA v a r i a t e s , t h i s b i a s c o u l d be c o r r e c t e d w i t h o u t m a r k e d l y i n c r e a s i n g t h e r e s i d u a l s . ( S e c t i o n s 3.5 and 4.3) P l o t s o f i n d i c a t e d t h a t t h e t r a n s f o r m a t i o n s may be q u i t e r e g u l a r e v e r v a r y i n g a v e r a g i n g p e r i o d s and v a r y i n g wind s p e e d s f o r a l l f l u x e s . A n o n - l i n e a r r e g r e s s i o n o f t h e form y[ = 1 + U ( u 2 + v2) was p e r f o r m e d and an a n a l y s i s o f t h e t e s t q u a n t i t i e s r e v e a l e d t h a t a p p l i c a t i o n o f t h i s f o r m u l a t o t h e VA f l u x e s p r o d u c e d i d e n t i c a l r e s u l t s t o t h e t e s t r e s u l t s . The b e s t method o f a p p l i c a t i o n o f t h e f o r m u l a was t o a l l o w i t t o c o r r e c t e ach VA e s t i m a t e on a p o i n t - b y - p o i n t b a s i s . ( S e c t i o n The s i m i l a r i t y o f t h e r e s u l t s f o r a l l f l u x e s i n d i c a t e d t h a t t h e v e c t o r a v e r a g i n g c f t h e wind i n g e n e r a l , and t h e l o s s o f wind v a r i a n c e i n f o r m a t i o n i n p a r t i c u l a r , d e t e r m i n e d the e x t e n t o f t h e r e d u c t i o n f o r a l l f l u x e s . T h i s was c o n f i r m e d a t S t a t i o n N where a 10 f c l d r e d u c t i o n i n wind speed v a r i a n c e a c c o u n t e d f o r m a r k e d l y r e d u c e d t r a n s f o r m a t i o n s r e g u i r e d f o r b o t h d r a g c o e f f i c i e n t c a l c u l a t i o n s , and f o r b o t h h e a t f l u x e s . The d i s c r e p a n c y a t S t a t i o n K, s e n s i b l e h e a t f l u x , r e m a i n s an enigma. ( S e c t i o n s 3.1, 3.4, and 4.4) I t was shown by d i r e c t o b s e r v a t i o n t h a t a l l s h i p s e x c l u d i n g S t a t i o n N f o r a l l f l u x e s and S t a t i o n K f o r t h e s e n s i b l e h e a t f l u x r e g u i r e d s i m i l a r t r a n s f o r m a t i o n s . The d i r e c t l y c a l c u l a t e d d i f f e r e n c e means, r e s i d u a l v a r i a n c e s , and c o r r e l a t i o n 5.2) 149 c o e f f i c i e n t s were i n s e n s i t i v e t o a g e o g r a p h i c g r o u p i n g o f t r a n s f o r m a t i o n s . . The d i f f e r e n c e v a r i a n c e s , i n some i n s t a n c e s , r o s e s u b s t a n t i a l l y ( S e c t i o n 5.4). T h i s was c o n f i r m e d i n t h e s p e c t r a a t S t a t i o n D where a g e o g r a p h i c a l l y a v e r a g e d c o r r e c t i o n was a p p l i e d . ( S e c t i o n 5.5) An a n a l y s i s of t h e h e a t f l u x s p e c t r a a t S t a t i o n s C and N d e m o n s t r a t e d some of the i n t e r n a l p r o p e r t i e s o f t h e t r a n s f o r m a t i o n s . A l a r g e a n n u a l c y c l e i n both t h e l a t e n t and s e n s i b l e 3H h e a t f l u x e s d i d not n e c e s s i t a t e a s e a s o n a l t r a n s f o r m a t i c n a t S t a t i o n C where t h e r e s i d u a l v a r i a n c e s were l o w e s t . An a n a l y s i s o f t h e r e s i d u a l s p e c t r a a t S t a t i o n N, e x a c t l y where t h e h e a t f l u x r e s i d u a l s were h i g h e s t , r e v e a l e d t h a t a s e a s o n a l t r a n s f o r m a t i o n c c u l d m a r k e d l y i m p r o v e t h e r e s i d u a l v a r i a n c e . T h u s , t h e g r o s s f o r m o f t h e t r a n s f o r m a t i o n may be d i c t a t e d by t h e v e c t o r a v e r a g i n g o f the wind; d e v i a t i o n s f r o m t h e b r o a d t r a n s f o r m a t i o n s may be de p e n d e n t upon t h e c o r r e l a t i o n o f t h e a n n u a l a i r - s e a t e m p e r a t u r e o r h u m i d i t y d i f f e r e n c e s w i t h t h e a n n u a l w i n d s . O t h e r a r e a s o f h i g h r e s i d u a l s (eg. S t a t i o n E, l a t e n t heat f l u x ) may a l s o r e q u i r e a s e a s o n a l l y dependent t r a n s f o r m a t i o n . ( S e c t i o n 5.5) An a n a l y s i s o f t h e u n c o r r e c t e d s t r e s s component s p e c t r a showed a c o n s i s t e n t u n d e r e s t i m a t i o n o f t h e 3H s p e c t r a by t h e VA s p e c t r a a t a l l f r e q u e n c i e s . Even t h o u g h S t a t i o n D showed t h e h i g h e s t r e s i d u a l s a f t e r t r a n s f o r m a t i o n , t h e r e was no e v i d e n c e t h a t a s e a s o n a l t r a n s f o r m a t i o n i m p r o v e d t h e s i t u a t i o n . ( S e c t i o n 5.5) Any one o f t h e t h r e e t r a n s f o r m a t i o n s ( y[ , ) w i l l g r e a t l y a i d c a l c u l a t i o n s based on a i r - s e a f l u x e s c a l c u l a t e d from 150 a v e r a g e d c o n s t i t u e n t d a t a . The ^.fce t r a n s f o r m a t i o n s f o r t h e c o n s t a n t d r a g c o e f f i c i e n t a r e i n t h e c o r r e c t r a n g e t o a i d i n i m p r o v i n g t h e p r e s s u r e a v e r a g e d t r a n s p o r t s o f F i g u r e 1(b) to more c l o s e l y r e s e m b l e th e a v e r a g e d t r a n s p o r t s c f F i g u r e 1 ( a ) . C o n s e q u e n t l y a p p l i c a t i o n o f t h e t r a n s f o r m a t i o n may y i e l d more a c c u r a t e r e s u l t s f r c m n u m e r i c a l models w h i l e u s i n g more r e a l i s t i c a i r - s e a t r a n s f e r c o e f f i c i e n t s . F u r t h e r m o r e , t h e t e c h n i q u e o f f e r s the p o s s i b i l i t y o f n u m e r i c a l l y d e p i c t i n g t h e t i m e h i s t o r y d e v e l o p m e n t o f s p e c i f i c wind f o r c e d o c e a n i c e v e n t s . G i v e n t h e s i m i l a r i t y i n t h e t e s t f u n c t i o n r e s u l t s between * ' a n d X ' t ^ i e t w o e m p i r i c a l f o r m u l a e s h o u l d ease i m p l e m e n t a t i o n o f t h e t r a n s f o r m a t i o n s w i t h l i t t l e l o s s i n a c c u r a c y . The i mprovements i n t h e s p e c t r a a r e v e r y c l e a r . From a s i t u a t i o n a t L=28.0 d a y s where t h e u n c o r r e c t e d t i m e s e r i e s y i e l d e d l a r g e d i s c r e p a n c i e s between t h e VA and 3H s p e c t r a and a r e s i d u a l s p e c t r u m which was as l a r g e o r l a r g e r t h a n t h e VA e s t i m a t e d s p e c t r u m , t h e >^ t r a n s f o r m a t i o n p r o d u c e d a match between t h e two e s t i m a t e s on a f r e g u e n c y - b y - f r e g u e n c y b a s i s and p r o d u c e d s u b s t a n t i a l r e d u c t i o n s i n t h e r e s i d u a l power d e n s i t y . ( S e c t i o n 5.5) S e v e r a l f a c e t s , p a r t i c u l a r l y i n a p p l y i n g t r a n s f o r m a t i o n s to b a r o m e t r i c p r e s s u r e c a l c u l a t i o n s , r e q u i r e f u r t h e r i n v e s t i g a t i o n . F i r s t , t h e b a r o m e t r i c p r e s s u r e maps have an i n h e r e n t s p a t i a l a v e r a g i n g which c o u l d n o t be s i m u l a t e d i n t h i s s t u d y . . S i m i l a r c a l c u l a t i o n s a t t h e e l e v e n w e a t h e r s h i p l o c a t i o n s b a s e d on g e o s t r o p h i c wind d a t a (such as d e v e l o p e d by W i l l e b r a n d , 1 9 7 8 ) c o u l d c o n f i r m whether s i m i l a r t r a n s f o r m a t i o n s f o r g e o s t r o p h i c 151 wind a r e r e q u i r e d . A p p l i c a t i o n o f t h e t r a n s f o r m a t i o n s t o t r a n s p o r t c a l c u l a t i o n s s i m i l a r t o t h o s e o f A a g a a r d (1970) c o u l d add f u r t h e r c c n f i r m a t i c n . Second, t h e s u b - t r o p i c s , t r o p i c s , and monsoon r e g i o n s (where a s t r o n g l y d e t e r m i n i s t i c a n n u a l s i g n a l i s i n h e r e n t i n t h e winds) have n o t been i n v e s t i g a t e d . I f c o n f i r m a t i o n o f t h e t e c h n i q u e c o u l d be g a i n e d f r o m r e p l i c a t i o n on g e o s t r o p h i c w i n d s , t h e n i t may be p o s s i b l e t o e x t r a p o l a t e t r a n s f o r m a t i o n s t c o t h e r r e g i o n s o f t h e wor l d u s i n g t h e s e d a t a . The wind r o s e e r r o r s were i n v e s t i g a t e d a t a l l l e v e l s o f c o n s t r u c t i o n . I n a l l c a s e s , t h e a v e r a g e e r r o r s were e q u a l t o o r l e s s t h a n t h e c o r r e c t e d d i f f e r e n c e mean e r r o r s f o r t h e e q u i v a l e n t L=28.0 days o f t h e v e c t o r a v e r a g e d winds. S l i g h t o v e r p r e d i c t i c n c o u l d be d e t e c t e d i n t h e d i s c r e t e v e r s u s t h e c o n t i n u o u s c a l c u l a t i o n . Ihe r e d u c t i o n from 36 t o 8 d i r e c t i o n s i n d u c e d a s l i g h t u n d e r e s t i m a t i o n i n t h e 3H s t r e s s . E r r o r s i n the MCA (Marine C l i m a t i c A t l a s ) c a l c u l a t i o n were p r o b a b l y a f f e c t e d by t h e a l l o c a t i o n o f t h e g a l e f o r c e winds and i n h e r e n t c o r r e l a t i o n between t h e winds and t h e a i r - s e a t e m p e r a t u r e and h u m i d i t y d i f f e r e n c e s . ( C h a p t e r VI) 152 BIBLIOGRAPHY A a g a a r d , K. (1S70) W i n d - d r i v e n t r a n s p o r t s i n t h e G r e e n l a n d and Norwegian Seas. Deep Sea Res., J7 ( 2 ) , pp. 281-291 A l l e n , J . S. (1980) M o d e l s o f w i n d - d r i v e n c u r r e n t s on t h e c o n t i n e n t a l s h e l f . . Ann. . Rev. 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The t u r b u l e n t f l u x e s o f momentum and s e n s i b l e h e a t e v e r t h e open s e a d u r i n g moderate t o s t r o n g winds. . PhD T h e s i s , Department o f O c e a n o g r a p h y , U n i v e r s i t y o f B r i t i s h C o l u m b i a . 180pp. L e a , D. . A., and H e l v e y (1971). D i r e c t i o n a l b i a s i n wind r o s e s due t o mixed compass f o r m a t s . J . . A p p l . Met., J_0 (5) ,pp. 1037- 1039. M a l k u s , J . S., (1962). L a r g e - s c a l e i n t e r a c t i o n s . In The Sea V o l . . I e d . by M. H i l l , I n t e r s c i e n c e P u b l i s h e r s , New Y o r k , pp. 88-294. M c C r e a r y , J . P. (1976). E a s t e r n t r o p i c a l o c e a n r e s p o n s e t o c h a n g i n g wind s y s t e m s : w i t h a p p l i c a t i o n t o E l N i n o , J . Phy s . O c e a n o g r . 6, pp. 646-664. O ' B r i e n J . J . (1971). A two d i m e n s i o n a l model o f t h e wind-d r i v e n N o r t h P a c i f i c , I n v e s t . 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P a p e r s i n p h y s i c a l o c e a n o g r a p h y and m e t e o r o l o g y . M a s s a c h u s e t t s I n s t i t u t e o f T e c h n o l o g y and Woods H o l e O c e a n o g r a p h i c I n s t i t u t i o n . 3 (3) , 101 pp. S m i t h , S. D. and E. G. B a n k ( 1 S 7 5 ) . V a r i a t i o n o f t h e s e a s u r f a c e d r a g c o e f f i c i e n t w i t h wind s p e e d . , Q u a r t . J . R. Met. Soc. (1S75) , J 0 J , pp. 665-673 154 T u r n e r , J . S. ( 1973). Buoyancy E f f e c t s i n F l u i d s . C a m b r i d g e U n i v e r s i t y Press,: C a m b r i d g e , U n i t e d Kingdom. . 368 pp. . W i l l e b r a n d , J . ( 1 9 7 8 ) . T e m p o r a l and s p a t i a l s c a l e s o f t h e wind f i e l d o v e r t h e N o r t h P a c i f i c and N o r t h A t l a n t i c . J . P h y s . O c e a n o g r . , 8 ( 6 ) , pp. 1080-1094. 155 A p p e n d i x A Development o f some m a t h e m a t i c a l a s p e c t s of t h e m u l t i p l e r e g r e s s i o n a n a l y s i s . A. 1 E q u i v a l e n c e Of S And A *~ L e t X be t h e 3H v a r i a t e and X' be t h e VA v a r i a t e and k be t h e B e a u f o r t i n t e r v a l (from 1 t o 1 3 ) . The o b j e c t i s t h e n t o m i n i m i z e the r e s i d u a l v a r i a n c e d e f i n e d a s : L v-h=i i - i L * J u^--tr-' N 1. 1A where N i s t h e t o t a l number o f p o i n t s i n t h e . a v e r a g i n g l e n g t h and J i s t h e number o f v a l u e s i n B e a u f o r t c a t e g o r y k« S e t t i n g ^ - O f o r each k: ~) - O 1.2A R e d e f i n e : X* Z *±\ A;; 156 Thus : 1 - 3 A e x p a n d i n g A X i n f u l l g i v e s : [3 J*. T h i s e q u a t i o n was s o l v e d by G a u s s i a n e l i m i n a t i o n w i t h i t e r a t i v e improvement. E x p a n d i n g e q u a t i o n 1 . 1 a g i v e s : \3> S u b s t i t u t i n g 1.3A g i v e s : 1. 4a 1. 5a S i m i l a r l y t h e d i f f e r e n c e v a r i a n c e i s : ^ | ^ ^ ^ - ( i | ^ ( ^ > T i j l < 6 1 A g a i n s u b s t i t u t i n g 1 . 3 a g i v e s : 157 Or: 1. 7A T h i s i s e x a c t l y e q u a l t o 1.5ft o r S . = r x V x « The a p p r o x i m a t i o n f o r the wind s t r e s s was t h a t a l l l i n e a r terms (means) are s m a l l compared t o t h e q u a d r a t i c and c r o s s terms i n which c a s e : <Tv W - ^ A fox - r X^ 1.8A A. 2 The E f f e c t Of The Change In &ta.t On ( T x C j c L e t X and X« be the 3H and WVA v a r i a t e s , and6+^ V—= Ti = £.e ,(T>iSiK-e i s the r e s i d u a l v a r i a n c e b e f o r e a p p l i c a t i o n of C»*-£^ and c T ce> i s the r e s i d u a l v a r i a n c e a f t e r a p p l i c a t i o n of ^•&s) . Then: CrJ" £*t - CTy 4- ( \-<r^CU( - ( ( + - £ ) V ; Tv' 2. 2A Where i s t h e a v e r a g i n g o p e r a t o r . Which reduces t o : 2. 3A 1 58 2. 4A Where B ^ i s t h e c o r r e l a t i o n c o e f f i c i e n t = (.Y^1 - Y fc^/Vx <f* i S i n c e Bv i s i n v a r i a n t under a s c a l e c hange and (_ i+- fe)cr;, - Q-jf ; s u b t r a c t i n g 2.3A from 2.4A g i v e s E q u a t i o n 2.3A c a n be r e w r i t t e n i s t e r m s o f 2. 5A 2. 6A S u b s t i t u t i n q 2.6A i n t o 2.5A q i v e s <r" C C - O » 1 1 < s «- & . s *y D i v i d i n g by (fx g i v e s : 2.7A s u b s t i t u t i n g 2.5A i n t o 2.7A g i v e s : 2. 8A 159 T h i s r e s u l t i s i n d e p e n d e n t o f whether C J ^ i s a t t h e minimum o r n o t and t h u s may ne p o s i t i v e o r n e g a t i v e . A. 3 The E f f e c t Of The Change I n E ^ On When 'cS K€ I s M i n i m i z e d . C o n s i d e r i n g t h e primed v a r i a t e s t o be u n c o r r e c t e d and t h e un p r i m e d v a r i a t e s t o be t h e v a r i a b l e s c o r r e c t e d f o r t h e DV b i a s , t h e n a c c o r d i n g t o S e c t i o n A .2: < ACT! = <r*- T * At t h e minimum: 1 which r e d u c e s t o Now: 3 . 1A 3.24 160 3. 3ft S u b s t i t u t i n g E g u a t i o n 3.1ft g i v e s : ft.4 P r o o f T h a t A S h i f t Of ' k i I s I n d u c e d Between The VA And 3H V a r i a t e s At S t a t i o n I f we l e t t h e s p e c t r a l components o f t h e VA s e r i e s a t any c y c l e be (a ,+ib, ) , and t h e 3H s e r i e s be ( a t + i b ^ ) . S i n c e t h e f o u r i e r t r a n s f o r m o f t h e r e s i d u a l s i s a l i n e a r o p e r a t i o n , t h e power a t t h e r e s i d u a l s i s : i f we c o n s i d e r t h a t t h e VA v a r i a t e must be s t r e t c h e d and r o t a t e d t c match t h e 2fl v a r i a t e t h e n 4. 1A 4.2A where: a. m i s t h e s t r e t c h ; and w i s t h e a n g l e f r c m t h e VA t c t h e 3H s p e c t r a l p a i r s . E x p a n d i n g ^ and m a t c h i n g r e a l and i m a g i n a r y p a r t s g i v e s : a . 3a 161 S q u a r i n g b o t h s i d e s o f E q u a t i o n 4. 3A g i v e s t h e i d e n t i t y S u b s t i t u t i n g E g u a t i o n s 4. 2A and 4. 3A i n t o 4.4A g i v e s V 4. 5A From F i g u r e 5-12, t h e r e s i d u a l power a t t h e a n n u a l c y c l e i s a p p r o x i m a t e l y e g u a l t o t h e sum o f t h e pcwer o f t h e 3H and VA s e r i e s , o r : ( a . - c x t f - i - Gov-b.y--4. 6A U s i n g 4.4A g i v e s : N e i t h e r m nor t h e VA power d e n s i t y e g u a l s 0.0 t h u s = + o r , a 900 phase s h i f t has been i n d u c e d between t h e 3H and VA s e r i e s a t t h e a n n u a l c y c l e . . 162 A ppendix B D i f f e r e n c e means i n dPa, d i f f e r e n c e v a r i a n c e s , r e s i d u a l v a r i a n c e s , and c o r r e l a t i o n c o e f f i c i e n t s f o r t h e u n c o r r e c t e d VA s t r e s s . The f i r s t row g i v e s t h e a v e r a g i n g l e n g t h i n d a y s . 1- 4- ^ _ -+- -+- . _ _ — -+- — -4- X j SHIPj 0.25 | 0. 50 1 1.0 I 2. 0 1 4.0 I 7.0 I 14.0 28. 0 j. 4- + -+- -+- -+- -4- + 1 A j .002 | .008 | . 022 | .044 1 .067 | .070 I . 069 .068 i B 1 .0 10 | .022 | .051 | .098 1 . 145 | . 175 I .220 . 247 1 c j .022 | .058 | . 127 | .233 1 .329 | .391 | .458 .511 1 D | .034 | .079 | . 162 .275 1 .371 | .437 I .516 . 587 i E | .015 | .034 | .066 | .112 1 . 151 . 182 I .227 . 26 1 I I 1 .012 | .027 | . 056 | .098 1 . 135 | .159 I .202 .234 1 J 1 .020 | .049 j . 101 . 175 1 .248 | .296 I . 383 . 449 i K | .018 | .043 | .083 | . 128 1 . 164 | .204 | . 257 .3 13 1 M | .007 J .017 | .038 | .065 1 .090 | .118 I . 153 . 172 1 N j .007 I .0 1 1 | .013 | .0 17 1 .035 | . 058 I . 085 .113 1 P J .014 i .034 1 .065 .098 1 i . 127 I .136 • . 152 . 177 J. X- L _ j — — _ I — — — ^  _ j — -L DIFFERENCE MEANS - CONSTANT D.C. X COMPONENT V + SHIPJ V 4 A B C D E . I J K M N P DIFFERENCE 0.25 | 0.50 .002 .004 .012 .0 15 .007 .015 .0 14 .002 .00 1 .004 .026 .007 .008 .029 .036 .015 .035 ,034 .006 .005 .005 .062 MEANS -- 4 j 1.0 -4 | .009 I .023 I .04 2 I .056 I .023 | .063 | . 068 | . 008 | .007 | .006 I . 126 j MEANS -CONSTANT 4 4 I 2. 0 | 4 4 .009 .054 .048 .073 .039 .093 .093 .006 .008 .009 .225 D.C. 4.0 .007 .094 . 052 .077 .050 . 133 . 127 . 002 .000 .017 .33 1 Y COMPONENT -4 4 4-| 7.0 | 14.0 | -4 4 4-.012 .125 .052 .089 .066 .170 . 161 .015 .006 .022 . 398 . 007 . 157 . 063 . 100 . 086 .210 . 199 .032 . 026 .033 . 501 H 28. 0 1 .0 16 .183 .068 . 109 . 105 .249 .224 .021 .0 28 .044 .578 —I I H DIFFERENCE LINEAR D . C . X COMPONENT SHIP| 0.25 | 0. 50 I 1.0 I 2. 0 I 4.0 1 7.0 I 14.0 I 28.0 A i .005 | .017 I . 043 | .082 | . 115 | .117 | .113 | .113 B | .016 | .033 I . 075 | .139 . 195 | . 225 | . 266 j .289 c i .040 | . 101 I .212 j .370 | . 495 | .561 | . 627 j .674 D | .057 | . 133 I .265 j .420 | .538 | .609 j .686 j .753 E j .023 | .052 I .098 | . 156 | .20 1 j . 233 | . 274 | .302 I | .022 | .049 I .098 . 160 | .212 | .241 | . 286 | .3 17 J | .035 | .082 I . 162 j .270 | . 363 | .417 .508 | .565 K J .030 | .069 I . 127 j .187 j .232 . 278 | .330 | . 377 M | .012 | .030 I . 062 | .100 | .134 | . 163 | . 195 | .210 N J .006 | .009 I .009 | .0 12 | .027 | .044 | . 065 | .086 £ I .024 | .056 I . 100 I .14 1 I . 167 I . 171 . 181 | .201 164 j. + SHIP | 4 A B C D E I J K M N P DIFFEEENCE 0.25 | 0.50 I I MEANS -I 1.0 + 1 .020 04 8 066 07 9 C28 101 10 1 LINEAB D.C. Y COMPONENT | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 .+ L + 4 + 1 ,004 ,0 10 ,02 1 .024 ,009 ,025 ,023 ,004 ,003 ,003 .043 I .013 .019 .047 .056 .020 .059 .054 .011 .0 10 .004 . 104 I I .012 | .014 | .004 | . 206 | .024 | .026 | .027 | .007 .00 1 | .103 .164 .200 .233 1 .256 | .064 | .065 .062 . 072 | .076 I .092 | .086 .093 . 102 . 109 I .042 .047 . 059 .075 | .089 I . 145 | . 197 .235 . 274 . 309 1 .132 | . 168 . 201 . 236 j . 258 | .010 .003 .013 . 026 .017 I .0 18 | .013 | .022 .04 3 | .045 1 .007 .014 . 019 .028 .036 1 -349 | . 484 | .560 .660 .723 J DIFFEEENCE VARIANCES - CONSTANT D. C. X COMPONENT | -+- -+ -4- 1 SHIP | 0. 25 I 0. 50 I 1.0 1 2. 0 | 4.0 1 7.0 1 14.0 i 28.0 | A j .04 1 | . 103 I . 201 | .347 | .487 | .5 85 I .710 | .810 | B i .042 | .099 I . 197 | .335 | . 507 | .624 1 . 725 | .8 11 | C i .042 | . 100 1 . 190 | .336 | . 486 | . 549 1 . 640 | .719 | D ) .04 5 | . 103 1 . 209 | .341 | .465 | .539 I .6 26 | .740 | E i .044 | .098 1 . 182 | .313 | .444 | . 552 1 . 64 1 ,694 | I | .037 | .090 1 . 173 | .299 | .440 | . 524 1 . 648 | .749 | J j .035 | .082 1 . 158 | .270 | .390 | .4 77 1 .595 | .666 | K J .040 | .09 1 1 . 17 1 j .258 | . 369 | .490 j .634 | . 726 | M J .038 j .093 1 . 186 | .320 | .464 | .587 1 .703 | .781 | N | .049 | .096 1 . 160 | .240 | .355 | . 426 j . 520 | .602 | P | .048 • .115 1 • . 234 .366 | .489 1 .6 07 1 .710 .781 | 1 ! . L L 1 DIFFEEENCE VARIANCES - CONSTANT D. C. Y COMPONENT SHIP| 0.25 | 0.50 | 1.0 j 2.0 | 4.0 I 7.0 \ + 1 | 14.0 | 28.0 f — + 1 A I .038 .095 | • 187 | .325 | .465 . 595 .714 | .80 1 B , .043 . 106 * 215 .375 | .540 .634 1 .725 | . 809 C i .058 . 137 | • 255 .405 .561 . 652 | . 728 | .793 D .060 . 142 | • 255 | .399 | . 574 .659 . 743 | . 827 E i .05 1 . 110 • 214 . 339 | .4 86 | .596 .728 | .8 12 I i .045 .106 | • 197 .321 .461 . 561 . 64 8 j .703 J | .043 j . 102 | • 197 | .317 | .456 . 570 . 654 | .715 K I .047 | . 107 | • 207 .323 | .450 .589 .705 | .806 M i .037 | .090 | • 177 | .293 | .445 | . 539 | .697 | .785 N i .053 . 105 j • 172 .285 .406 .522 .629 j .711 P I .04 1 | .09 8 | • 194 .331 | .468 . 520 . 628 I .691 I L 165 DIFFERENCE VARIANCES - LINEAR D.C. X COMPONENT SHIP | 0. 25 I 0. 50 I 1.0 J 2.0 | 4.0 I 7.0 1 14. 0 I 28.0 +-A I .070 | .174 | .321 | .513 | .660 | .746 | . 84 7 | .908 8 J .073 | . 165 | .311 .480 | .690 . 787 | . 860 | .910 c I .072 | . 168 | . 301 | .513 | .687 | .741 | .818 | .876 D j .08 1 | .183 | . 358 | .535 | .667 j .727 | . 809 j .894 E | .077 | . 163 | .297 j .470 | .617 | .717 . 796 .833 I | .067 j . 156 | . 283 | .457 | .617 | .700 | .802 | .876 J | .063 | . 143 | .266 | .421 | .571 | . 660 | .777 .830 K | .072 | . 162 | .295 | .411 | . 548 | . 667 .78 1 | .850 M J .064 | . 155 | . 294 .465 | . 626 .736 | .830 | .876 N 1 .077 . 150 | .239 | .334 | .457 | .522 | .595 .659 P 1 .089 1 . 198 I . 376 I .546 | .674 i .779 J .850 | .89 1 DIFFERENCE VARIANCES - LINEAR D.C. Y COMPONENT i SHIP _ i i 0.25 | 0.50 | 1.0 | 2. 0 | 4.0 | 7.0 I 14.0 | 28.0 I r J A | .064 | . 157 | . _____ ___,_|_. . 296 | _ | _ .480'| .633 | .762 | .849 | .899 1 6 j .073 | . 175 | . 338 | .536 | . 707 | .785 | .852 | .906 1 c j .106 | . 233 | . 396 j .582 | . 738 | .807 I .858 | . 897 i D | . 107 | .239 | . 40 1 | . 566 | . 749 | .808 I .859 j .916 1 E j .094 | . 189 | .334 | .489 | .641 | .740 | .830 | .884 1 I 1 .080 | . 186 | . 323 | .483 | .641 | . 736 I .802 | .839 i J 1 .078 j .180 | .323 | . 476 | .641 | .741 | .803 | .843 1 K | . 083 | .188 | .338 | .490 | .618 J .750 | .826 | .890 1 M j .062 | .15 1 | . 281 | .438 1 . 606 | .692 1 -819 | .870 1 N | .084 | . 160 | . 250 | .387 | .516 | .623 | .706 | .770 1 P i .075 | . 168 | .318 | .515 ( . 670 | .723 1 -819 | .856 RESIDUAL VARIANCE -+ 4 - 4 — SHIP. 0.25 | 0.50 | 1.0 CONSTANT D.C. 4 4 + . X COMPONENT 7.0 I 14.0 I A j .003 5 , .003 C I .004 D .004 E J .003 I .003 J .003 K i .003 M | .003 N i .003 P I .004 .0 10 .0 10 .0 11 .0 13 .009 .008 .008 .008 .008 .007 .012 . 030 .029 . 030 . 037 .023 . 022 . 021 .019 . 024 .016 . 037 I 2.0 .072 .072 .070 .076 .058 .050 .046 .038 .059 .037 .077 I 4-0 I 4. . 132 I .138 I . 125 I .121 | . 105 | .096 | .082 I .069 | .109 | .077 | .125 I .187 .206 . 154 . 160 . 156 . 135 .117 .116 . 172 . 1 10 .187 . 27 1 .283 .213 .205 .205 .213 . 178 .208 .256 . 164 . 257 28.0 . 36 7 . 360 . 267 . 287 . 246 . 300 .227 . 283 .349 .220 . 320 166 EESIDUAL VARIANCE -• CONSTANT D.C. Y COMPONENT -+- -+- -+ H-- h SHIP! 0. 25 1 0. 50 1 1.0 1 2. 0 1 4.0 1 7.0 J 14.0 | 28. 0 A | .002 | .008 | .025 [ .062 | .119 1 . 185 | . 276 | .366 B 1 .003 | .0 10 . 032 | .086 j . 166 1 .224 . 294 | . 380 C I .005 .016 | .045 | .097 | . 167 1 .220 | .286 { . 346 D | .007 | .020 | .049 | .101 | . 186 1 . 243 .312 | .393 E | .004 .012 | .033 | .071 . 141 1 .196 | . 286 | .378 I | .004 | .0 11 | .026 | .0 59 | . 108 I . 157 | .225 | . 287 J | .003 | .0 10 | . 029 | .062 | . 108 1 . 166 | . 220 | .270 K | .004 | .011 | . 030 | .057 | .103 1 .166 . 256 | . 370 M | .002 j .007 | .022 | .051 | . 104 1 . 148 | .255 | . 345 N | .004 | .010 . 020 | .050 | .095 1 . 148 | .218 | .286 P J .004 .01 1 • . 03 1 1 .074 1 . 125 1 i . 146 1 . 203 | .257 1 H I H H I H RESIDUAL VARIANCE • LINEAR D.C. I 2. 0 | 4.0 X COMPONENT -+ 4 +-| 7.0 | 14.0 | -+— + +-SHIP| 0.25 j 0.50 | 1.0 28. 0 A | .007 .024 | . 069 .158 . 262 .335 .433 | .529 B .008 .023 | . 068 .149 | . 272 . 365 . 449 | . 528 C .008 | .024 | . 067 .158 | . 269 | .307 . 39 1 .466 D .009 .031 .095 .183 . 264 . . 317 .383 .496 E .008 .022 | .054 | .127 | .200 | . 274 | . 344 .385 I ; .007 | .021 | . 053 , 1 1 4 | .198 | .2 56 | .360 . 464 J .006 | .020 1 .049 .106 . 178 .230 .331 | .392 K , .006 | .020 | .052 .090 | . 153 . 224 .337 | . 422 M , .006 .019 | . 054 .120 | .203 .292 . 396 .476 N I .007 .015 | .032 | .064 | .120 | .159 | .211 | . 267 P i .011 .033 | .094 .175 .256 . 345 | .425 | .489 RESIDUAL VARIANCE - LINEAfi D.C.. Y COMPONENT I j 28.0 1 .5 19 .539 . 504 . 56 1 .493 .436 . 4 15 .510 . 462 . 349 .449 A B C D E I J K M N P .005 .007 .0 14 .017 .011 .009 .009 .009 .005 .009 .0 10 0. 50 I 1.0 1 2. 0 | 4.0 I 7.0 j 14.0 .020 . -J- — — — — I .057 r +-1 -132 | . 232 | .336 ] .437 .024 | . C73 1 .179 | .310 | .382 i .457 .042 | . 106 I .209 | .324 | .384 I .451 .051 | .117 I .211 | . 349 I .412 I .478 .029 | .077 1 .141 | . 251 | .321 | .411 .028 I . C6 3 ] .130 | .218 j .295 I .376 .027 j .070 | .133 | . 223 | .305 | .365 .028 | .076 1 .134 | .204 I .301 | .392 .0 17 I .052 I .107 | . 197 | . 256 | .383 .0 19 I .038 I .084 1 . 147 | .211 | . 282 .027 I .074 | .168 | . 263 | .295 I .384 167 f- 4- -4- -4- -4- -4- -4- -4-|SHIPj 0. 25 1 0. 50 1 1.0 I 2.0 | 4.0 I 7.0 I 14.0 I 28.0 I A | .999 1 .996 | .990 | .978 .964 | . 953 | .946 | .945 I B j .999 i .996 | .990 | .977 | .965 | . 954 | . 946 I .953 I c J .998 1 .996 | . 989 .978 . 968 j .966 | . 956 | .957 i D j .998 1 .995 | . 986 | .975 | . 967 I .958 | .956 j .954 I E j .939 1 .997 I .992 | .982 | . 973 | .965 I . 963 1 .959 1 I 1 .999 i .997 j . 992 | .986 . 978 | . 972 | . 960 I .949 i J 1 .999 1 .997 | .993 | .985 | .978 | .972 j . 964 | .957 1 K i .999 1 .997 | .994 | .989 | . 984 j .976 | . 957 | .947 1 M | .999 1 .997 | ..992 .983 | .975 j .965 | . 955 | .930 1 N 1 .999 1 .997 I .995 | . 988 | . 976 | .966 | . 949 j .933 i P i .998 1 1 .995 ] . S88 j .978 | .570 J .962 .959 ] .960 CORRELATION COEFFICIENT - CONSTANT B.C. X COMPONENT SHIP! 4 A B C D E I J K M N P CORRELATION 0.25 | 0.50 COEFFICIENT -I 1.0 | 2.0 4 4 .992 . 989 . 585 . 982 . 988 . 992 .990 . 990 .993 .993 .588 CONSTANT -4 4-I 4.0 | D.C. 7.0 Y COMPONENT I 14,0 •4 .944 .936 . 94 6 . 933 . 944 . 95 0 . 958 . 957 .952 .946 . 958 4 I 28.0 4 J .933 .929 .946 . 937 .934 .927 . 950 .935 .937 .933 . 946 . 999 .999 .998 .997 .998 . 998 .995 .998 .999 .998 . 998 .997 .996 .994 .992 .996 .996 .956 .996 .997 .996 . 996 .982 .973 .971 . 967 .978 .983 .981 .984 .985 .985 . 975 968 554 S60 950 957 974 973 576 574 972 965 . 958 .944 .956 .941 .950 .967 . 964 .971 .967 .962 .962 CORRELATION SHIP| 0.25 COEFFICIENT -•4 4 I 1.0 | 2.0 •4-LINEAR D. -4 4-I 4.0 | C. . 7.0 X COMPONENT 4 1 I 28.0 4 1 .929 . 938 .933 .935 . 956 .939 .943 . 94 1 .920 .9 20 .941 | 0.50 .991 .99 1 .991 .988 .992 .992 .992 .993 .993 .995 .988 I 14.0 4 . 920 . 923 . 927 . 924 . 953 . 942 .944 . 943 .939 . 938 . 936 A B C D E I J K M N P .997 . 9.9 7 .997 .996 .997 .997 .997 .997 .997 .997 .995 .977 . 576 .976 . S65 . 983 .983 . 583 .984 . 983 .99 1 . 969 .952 .950 .952 .940 .96 4 .969 .968 .977 .967 .981 .949 .925 .933 .933 .5 26 . 956 .558 .955 .966 .557 .966 .9 37 .912 .919 . 935 .915 . 948 . 953 .952 .961 .945 . 954 .932 L X .X .X .J 168 C O R R E L A T I O N C O E F F I C I E N T - L I N E A R D . C . Y COMPONENT | S H I P . 0. 25 1 0. 50 I 1.0 1 2. 0 1 4 . 0 1 7 . 0 | 1 4 . 0 I 2 8 . 0 | A | . 9 9 8 | . 9 9 3 | . 982 | . 9 6 2 | . 937 | . 924 | . 9 1 9 | . 9 16 | 8 J . 9 9 7 | . 99 1 j . S76 . 9 4 3 | . S08 . 8 9 9 | . 8 9 9 j . 9 0 5 | C I . 9 9 4 | . 9 8 5 | . 9 6 3 | . 935 | . 9 1 7 j . 9 2 1 | . 9 1 7 | . 9 3 1 | D j . 9 9 3 | . 9 8 0 | . S58 | . 9 2 8 | . 901 | . 8 9 0 | . 883 | . 90 1 | E | . 9 9 5 | . 9 8 9 | . 974 . 9 5 8 | . 924 | . 921 | . 921 . 9 1 5 | I . . 996 | . 990 | . 981 | . 9 6 5 . 9 5 2 | . 943 | . 924 | . 903 | J | . 9 9 6 J . 9 9 0 | . 9 7 6 | . 9 6 1 | . 948 | . 937 J . 938 | . 9 3 7 | K | . 9 9 6 | . 990 j . S75 | . 9 6 3 . 9 5 3 . 9 4 9 j . 9 3 7 j . 9 0 4 | M 1 . 9 9 8 | . 9 9 4 | . 983 | . 9 7 0 | . 9 5 4 | . 948 | . 938 j . 925 | N | . 9 9 6 | . 9 9 3 j . 989 | . 9 7 6 | . £61 . 9 4 9 | . 9 3 3 | . 9 1 8 | P 1 . 9 9 5 . 9 9 0 I . S74 1 . 946 1 . 9 2 9 • . 933 | . 937 I . 9 1 6 | j _1 169 Appendix C - P a r t I The Z-xia v a l u e s f o r the s t r e s s e s a f t e r c o r r e c t i o n f o r t h e s y s t e m a t i c b i a s i n t h e v a r i a n c e d i f f e r e n c e s . 0.0 i n d i c a t e s no d a t a . i (. 4 SPEED 1 j. + 0 . 4 1.6 3 . 4 5 . 5 8 . 0 1 0 . 8 1 3 . 9 1 7 . 2 2 0 . 8 2 4 . 5 2 8 . 5 3 3 . 5 3 5 . 0 4-0 . 2 5 | +-0 . 50 | -+-STATION - A CONSTANT 1.0 | 2. 0 | 4 . 0 | 4-2.9 3 9. 3 8 3 . 05 2 . 0 2 1. 56 1. 36 1. 23 1. 17 1. 1 1 1. 1 1 0 . 0 0 . 0 0 . 0 D.C. — 4 7 . 0 | 4 4 5 . 1 1 2 0 . 5 8 4 . 13 2 . 6 5 2 . 0 0 1. 54 1 . 4 3 1. 17 U 0 6 0 . 0 0 . 0 0 . 0 0 . 0 4 1 4 . 0 | 4 1 8 1 . 5 1 7 . 5 3 4 . 6 3 2 . 9 6 2 . 0 7 1 . 6 9 1 . 4 8 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 2 8 . 0 4 . 8 2 2 . 3 3 1. 3 1 1. 13 1. 06 1 . 0 4 1 . 0 3 1. 0 2 1. 0 1 1 . 0 2 1. 01 1. 0 1 1 . 0 0 7. 56 4 . 2 8 1 . 7 0 1. 31 1. 16 1. 10 1 . 0 7 1 . 0 5 1. 0 4 1 . 0 3 1 . 0 3 1 . 0 3 0 . 0 9 . 3 8 8 . 17 2 . 4 2 1 . 6 0 1 . 3 3 1.2 1 1. 13 1 . 1 0 1 . 0 9 1 . 0 6 1 . 0 5 0 . 0 0 . 0 0 . 0 1 4 . 3 5 3 . 8 3 2 . 4 6 1 . 7 7 1 .51 1. 32 1. 2 1 1 . 1 3 1 . 0 8 0 . 0 0 . 0 0 . 0 1 4 . 8 1 18 . 6 2| 5 . 0 5 3 . 12 2 . 26 1. 8 3 1. 46 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 SPEED| 0 . 25 1 0 . 50 I * +- -+ I 0 . 4 . 7. 3 0 | 9 . 73 | i 1 . 6 | 2 . 7 8 | 4 . 8 5 | 1 3 . 4 | 1.3 1 | 1 . 6 7 | 1 5 . 5 | 1. 14 | 1. 30 | 1 8 . 0 . 1 . 0 7 1. 18 | J 1 0 . 8 | 1 . 0 5 | 1. 1 1 | 1 1 3 . 9 J 1. 0 3 | 1. 07 j 1 1 7 . 2 | 1 . 0 2 | 1 . 0 6 | j 2 0 . 8 | 1. 0 2 | 1. 04 | | 2 4 . 5 1 1. 0 2 1. 0 3 | | 2 8 . 5 | 1. 0 1 | 1 . 0 3 | I 3 3 . 5 | 1. 01 j 1 . 0 2 | | 3 5 . 0 | 1, 00 I 0 . 0 STATION - B CONSTANT -4 4 4 . D.C. 7 . 0 { 4 9 7 . 29 1 6 . 3 9 4 . 3 5 2 . 7 8 2 . 0 2 1 . 6 8 1.41 1 . 2 8 1. 1 1 0 . 0 0 . 0 0 . 0 0 . 0 4 1 4 . 0 | 4 7 8 . 98 1 5 . 6 2 4 . 5 8 2 . 9 7 2 . 2 1 1 . 7 4 1 . 4 2 1 . 2 3 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 1 2 8 . 0 1 6 9 . 30 1 4 . 8 2 | 4 . 8 5 3 . 22 2 . 19 1. 85 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 1.0 J 4 4 6 . 0 6 9 . 8 3 2.33 1 . 6 7 1 . 3 6 1 . 2 3 1. 15 1. 1 1 1 . 0 8 1 . 0 7 1 .04 1 . 0 2 0 . 0 2 . 0 | 4 . 0 | 3 4 . 7 6 + * 1 3 . 8 7 3 . 32 2. 15 1 . 6 3 1 . 4 0 1. 28 1. 17 1. 1 1 1. 08 1. 06 1. 04 0 . 0 1 0 6 . 7 (19.86 4 . 0 1 2 . 4 9 1 . 9 0 1. 56 1 . 3 6 1. 24 1. 17 0 . 0 0 . 0 0 . 0 0 . 0 t- +-SPEED I I- +-0 . 4 I 1 . 6 | 3.4 I 5. 5J 8.0| 10.8| 13.91 17. 21 20.81 24. 51 28.51 33. 51 35.0| I 4. 0 . 2 5 I 4. 0 . 5 0 I STATION -1.0 | 2 . C CONSTANT D. C. L 4 4 - — 4 -0 | 4 . 0 I 7 . 0 j 1 4 . 0 J 2 8 . 0 1 2 . 66 3 . 28 1. 36 1. 17 1. 0 9 1. 0 5 1. 04 1 . 0 3 1. 0 2 1. 0 2 1. 0 2 1. 0 2 1.0 1 I 1 4 . 6 5 1 3 C . 8 9 1 2 7 . 3 4 | 5 6 . 6 5 1 2 8 0 . 2 | 6 5 . 84 | I 5 . 4 9 | 8 . 0 9 | 1 5 . 3 5 1 1 7 . 6 6 1 1 7 . 0 0 | 2 6 . 8 5 | 1 1 . 7 9 I 2 . 4 9 | 3. 12 | J . 6 8 | 3 . 9 8 | 4 . 4 0 I I 1 . 3 6 | 1 . 7 2 1 2. 12 | 2 . 3 5 | 2 . 5 2 | 2 . 7 8 | 1 1. 19 | 1 . 3 9 | 1 .61 I 1 .81 | 1 . 9 5 I 2 . 0 5 | | 1 . 1 2 | 1 .24 | 1 . 3 7 | 1. 52 J 1 .62 | 1 . 7 2 J 1 1 . 0 8 | 1 . 1 6 | 1. 26 | 1 . 4 0 | 1 . 4 3 I 1 . 4 9 | I 1 . 0 6 | 1. 12 | 1 . 2 3 | 1 .29 | 1 . 3 5 | 1 . 4 2 1 1 1 . 0 5 | 1 . 1 0 | 1. 14 | 1. 18 | 1 . 2 3 | 0 . 0 1 I 1 . 0 4 | 1 . 0 7 1 1 . 1 3 | 0 . 0 | 0 . 0 | 0 . 0 | | 1 . 0 4 | 1 . 0 6 | 0 . 0 1 0 . 0 | 0 . 0 I 0 . 0 | I 1 . 0 4 | 1 . 0 5 1 0 . 0 1 0 . 0 | 0 . 0 I 0 . 0 1 I 1 . 0 2 | 0 . 0 | 0 . 0 1 0 . 0 | 0 . 0 i 0 . 0 1 274.^9 2 1 . 4 8 | 4 . 72 2. 8 3 2 . 16 1. 87 1. 6 5 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 171 i 1 j. + . SPEEDj !- +-0.41 1 . 6 | 3 . 4 | 5 . 5 | 8 . 0 | 1 0 . 8 | 13. 9J 1 7 . 2 | 2 0 . 8 | 2 4 . 5 | 2 8 . 51 3 3 . 5 | 3 5 . 0 j 0. 25 { 1 4 . 3 3 3. 00 1. 38 1. 18 1.08 1. 05 1.04 1. 03 1. 02 1 .02 1.02 1 .02 1.03 STATION -1.0 | 2. D CONSTANT + 4-0 | 4 . 0 | — + -D.C. 7 .0 | + -14 .0 | —I 0 . 5 0 | 2 8 . 0 I 9 . 7 4 | 38 . 77 | 7 5 . 11| 173. 1 | 9 1 . 5 6 | 5 5 5 . 1 | J 6 . 4 0 | 8 .66 | 13.431 1 8 . 1 3 | 1 9 . 6 8 | 2 2 . 8 7 | I 1*81 | 2 . 5 0 | 3 . 4 6 | 3 . 7 7 | 3 . 9 7 | 4 . 2 2 | I 1 .36 1.72 | 2 . 0 5 | 2 . 3 8 | 2 . 4 8 | 2 . 7 0 | I 1.20 | 1.37 | 1. 58 | 1.81 | 1.93 | 2 . 0 8 | i 1 .13 i 1.23 | 1 .40 | 1 .53 | 1.68 | 1 .78 | I 1.09 | 1. 18 | 1 .28 | 1.42 | 1.49 | 1 .65 | | 1 .07 1. 13 | 1. 21 | 1.31 | 1.31 | 1 .41 | I 1-05 | 1.11 | 1. 12 | 1. 15 | 1. 17 | 1 .28 | I 1 .04 1.05 J 1. 12 | 1. 16 | 0 . 0 | 0 . 0 | I 1*04 | 1.06 | 1.28 | 0 . 0 | 0 . 0 | 0 . 0 | I 1 .03 i 1.20 | 0. 0 1 0 . 0 | 0 . 0 | 0 . 0 | I 1.06 j 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 3 2 5 . 8 1 6 . 4 0 4. 31 2. 80 2. 36 2 . 02 1. 64 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 i r +-SPEED 1 I- +-0 . 4 | 1 . 6 | 3 .4 | 5 . 5 | 8 . 0 j 1 0 . 8 | 1 3 . 9 j 1 7 . 2 | 2 0 . 8 | 24 . 51 28 .51 [33.51 35.01 1 — — 4 0. 25 | 8. 03 1.98 1. 18 1. 10 1 .05 1.04 1. 03 1. 02 1. 02 1. 02 1.0 1 1. 07 1 .0 1 — + 0. 50 J + 6. 20 3 . 9 0 1. 39 1. 20 1. 11 1.08 1.06 1.05 1.04 1.03 1. 02 1.20 1. 0 1 STATION - E CONSTANT -4 4 4. D.C. 7 . 0 J 4. 5 1 . 9 6 13 .58 3 . 16 2 .04 1.73 1 .47 1 .36 1. 18 0 .0 0 .0 0 . 0 0 . 0 0 . 0 4 1 4 . 0 | 3 0 . 7 6 15 .86 3 . 4 6 2 . 2 6 1.84 1.62 1 .37 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 1.0 I 2 . 0 10. 29 4 . 5 9 1 .75 1.37 1.2 1 1. 16 1 .12 1.09 1.06 1.08 0 .0 1 .05 0 .0 1 5 . 5 2 8. 34 2 .4 2 1.63 1. 37 1. 25 1. 20 1. 13 1. 14 1. 05 0 . 0 0. 0 0. 0 4 . 0 I 4 7 . 59 12. 14 2 .90 1 .93 1.54 1.38 1.28 1.22 1. 15 0 . 0 0 . 0 0 . 0 0 . 0 2 8 . 0 1 2 8 . 10 12. 45 3 . 34 2. 57 2. 07 1. 64 1. 50 0 . 0 0. 0 0 . 0 0 . 0 0. 0 0 . 0 J * +-SPEEDl f-0 . 4| 1.6 3 . 4 ( 5 . 5 , 8 . 0 10 .8 13. 9| 17 .2 2 0 . 8 2 4 . 5 2 8 . 5 | 3 3. 5 i 3 5 . 0 4. 0 . 2 5 I 0 . 50 | STATION 1.0 I 4 -12. 18 10. 9 2 2 . 5 0 1.58 1.3 1 1.20 1.12 1.09 1.07 1.07 1.05 0 . 0 0 .0 - I CONSTANT 2 . 0 | 4 . 0 j -+-D.C. 7 i 0 I 4 0 . 0 16 .61 3 . 76 2 . 50 1. 85 1.53 1.36 1.2,8 1. 28 0 . 0 0 .0 0 . 0 0 . 0 4 1 4 . 0 | 4 0 . 0 1 9 . 6 3 4 . 3 0 2 . 7 7 1.99 1 .64 1.43 1 .32 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 1 28. 0 j 0. 0 22 . 0 2 4. 51 2 . 96 2. 08 1. 61 1. 62 0 . 0 0. 0' 0 . 0 0 . 0 0 . 0 0 . 0 6. 2 9 2 . 22 1.48 1. 15 1. 06 1. 05 1.03 1 .02 1. 02 1 .02 1.02 1. 0 1 1. 00 24 . 89 3. 6 1 1.82 1 .33 1. 15 1. 11 1.07 1 .05 1. 04 1. 04 1. 04 1. 04 0. 0 174 . 5 1 2 . 0 4 2. 9 1 1.9 3 1. 52 1. 31 1. 2 1 1. 15 1. 14 1. 08 1. 07 0 . 0 0. 0 4 9 . 4 6 15 .23 3 . 52 2. 27 1.71 1 .45 1.29 1. 23 1. 14 1 .18 0 . 0 0 . 0 0 . 0 I L 172 I 4-SPEED| I- +-0.4 1.6 3.4 5. 5| 8.0 10. 8 13. 9| 17..2-20.8 24. 5| 28.5] 33. 5' 35.0 4-0. 25 j 4-0.50 | STATION -1.0 | 2. 4 -J CONSTANT L 4 -0 | 4.0 | D.C. 7.0 | 4 -14.0 | 28.0 1 69.29 i 6. 94 4. 12 2. 7 1 1.99 1. 65 1. 46 0.0 0. 0 0. 0 0. 0 0.0 0. 0 5.68 2. 19 1. 39 1. 14 1.05 1. 04 1.0 2 1. 02 1. 02 1. 02 1.01 1. 0 1 1.0 2 7.79 4.89 1. 76 1.30 1. 14 1. 09 1.06 1.04 1.04 1. 03 1. 04 1.0 1 0.0 11. 42 5.20 2.30 1.54 1.2 9 1.18 1. 12 1.09 1.07 1.07 1.03 0.0 0.0 59 16 2. 0. 0. .90 . 74 90 87 47 28 19 14 12 07 02 0 0 53. 66 19.87 3. 39 2. 20 1. 60 1.40 1.28 1. 2 1 1. 15 1.03 0. 0 0.0 0.0 0. 0 19.98 3.62 2.39 1.78 1. 49 1.34 1.29 1.10 0.0 0.0 0.0 0.0 0.0 20. 25 4. 22 2.53 1.87 1.60 1.39 0.0 0.0 0.0 0.0 0.0 0.0 —1 I K +-SPEED| j. 4 -0.4| 1.6| 3.4 5.5 | 8.0 10.8 13.9, 17.2 20.8| 24. 5j 28. 5, 33. 51 35.0 4 25 | 0, STATION - K CONSTANT D.C. . 50 | 1.0 | 2.0 | 4.0 | 7.0 | +-14.0 | 28.0 26 43 27 1 1 05 03 02 02 02 02 02 02 04 8. 3« 0. 51 20 45 22 12 08 06 05 04 03 06' 03 0 1 1. 57 5.50 1.83 1.4 1 1.22 1. 15 1. 1 1 1.08 1.08 1.12 1.04 0.0 0.0 70. 47 8. 96 2. 37 1. 65 1.35 1. 22 1. 19 1. 13 1. 12 1. 14 0. 0 0. 0 0.0 2. 89 .83 .87 .93 .51 .34 . 26 . 18 . 13 .0 .0 . 0 .0 1 14. 9 10.20 3. 20 2. 16 1.68 1.45 1. 36 1.24 0.0 0.0 0.0 0.0 0.0 6 12.0 16. 15 3.59 2.44 1.9 1 1.60 1. 39 0.0 0.0 0.0 0.0 0.0 0.0 94. 15 17.90 3. 86 2. 72 2. 0 1 1.69 0. 0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 STATION - M CONSTANT j. 4 SPEED | 0. |. +  0.41 2. 1.6. 3.4 | 5.5| 8.01 10.81 13.9| 17.21 20.8| 24. 51 28.51 33. 51 35.0| I 25 j 0. D.C. 7.0 | 4 74.38 15.96 3.55 2.30 1.80 1.48 1.33 1. 12 1.22 0.0 0.0 0.0 0.0 14.0 j 4 4 6. 18 18.08 4. 1 1 2.57 1.98 1.53 1.5 0 0.0 0.0 0.0 0.0 0.0 0.0 50 I 1.0 | 2.0 65 82 30 12 05 03 02 02 0 1 0 1 0 1 0 1 02 6. 3. 0. 05 73 64 26 13 08 05 04 03 03 04 06 0 10. 02 6.67 2. 10 1.49 1.27 1. 17 1.10 1.08 1.06 1.07 1.03 0.0 0.0 42.93 9. 66 2.72 1. 8 1 1.46 1. 27 1. 18 1. 12 1. 12 1. 15 0. 0 0. 0 0. 0 4.0 | 54.42 14.2 1 3.33 2. 10 1.64 1.38 1. 26 1. 18 1.27 0.0 0.0 0.0 0.0 28. 0 47. 1 71 13. 69 4. 28 2.95 2. 0 5 1. 60 1.49 0. 0 0. 0 0. 0 0.0 0. 0 0. 0 173 1 STATION - N CONSTANT D.C. SPEED J 0. 25 1 0 . 50 I 1.0 1 2. 0 I 4 . 0 I 7 .0 1 14 .0 | 2 8 . 0 1- +- -4- •4- -4- •4- •4- 4-1 0 , 4 f 5 . 24 1 5 . 6 6 | 9 . 5 5 | 2 0 . 0 5 | 21 .981 3 1 . 3 6 J 4 6 . 0 7 | 8 1 . 3 1 1 1.6 1 2 . 0 2 1 3 .08 | 4 . 15 | 6 . 15 I 7 .58 I 8 .90 | 1 5 . 6 9 | 12 . 95 1 3 . 4 | 1. 18 1 1 .35 | 1.57 | 1. 95 I 2. 49 I 2 . 86 I 2 . 9 0 1 3. 28 1 5.51 1. 08 I 1. 14 I 1 .23 j 1. 40 I 1. 59 I 1.73 | 1.87 J 1 .92 1 8 . 0 | 1.04 1 1. 07 | 1.12 1 1. 20 I 1. 29 1 1.36 I 1.44 1 1. 49 1 10.81 1 . 0 3 1 1. 05 | 1.09 | 1. 14 I 1 .20 j 1.28 | 1.27 J 1. 22 1 13.91 1. 02 1 1. 05 | 1.09 | 1. 13 I 1. 20 1 1. 10 | 0 . 0 | 0 . 0 1 1 7 . 2 | 1. 02 1 1.04 | 1.07 1. 13 I 1. 19 1 0 . 0 0 . 0 | 0 . 0 120.81 1. 02 1 1.03 | 1.05 | 1. 07 I 0 . 0 1 0 . 0 0 . 0 1 0. 0 124.51 1. 0 1 1 1 .02 | 0 .0 1 0. 0 I 0 . 0 j 0 . 0 | 0 . 0 | 0 . 0 I 28.51 0. 0 1 0 . 0 | 0 . 0 | 0. 0 I 0 . 0 1 0 . 0 0 . 0 1 0 . 0 133.51 0. 0 I 0 . 0 | 0 .0 | 0. 0 I 0 . 0 j 0 . 0 | 0 . 0 | 0 . 0 135 .0 ] 0 . 0 0. 0 • 0 .0 1 0. 0 I 0 . 0 1 0 . 0 1 0 . 0 1 0 . 0 1 STATION - P CONSTANT D.C. SPEED) 0. 25 1 0. 50 I 1.0 1 2. 0 I 4 . 0 1 7 .0 1 1 4 . 0 | 2 8 . 0 J — — 4 - 4- 4-1 0 .4 | 1 0 . 7 1 | 4 . 53 | 45.241 2 0 . 22 I 16 .5 4 | 9 . 9 0 | 0 . 0 j 0 . 0 1 1.61 2. 49 1 3 . 80 7 . 3 9 1 9. 60 I 2 4 . 3 9 | 23 . 14 I 3 3 . 491 0. 0 1 3 . 4 ] 1. 29 1 1 .76 | 2.21 j 3. 01 I 3 .51 j 4 .01 j 4 . 0 7 J 4 . 0 6 1 5 .51 1. 13 1 1. 3 1 I 1.6 1 j 1. 97 I 2. 27 1 2 . 54 | 2 . 5 8 I 2. 78 J 3 . 0 | 1. 07 I 1. 18 | 1.34 1 1. 60 I 1.78 1 1.84 | 2 . 0 4 | 2 . 22 1 1 0 . 8 | 1.05 1 1. 12 I 1.23 1 1.36 I 1.48 1 1.58 | 1.67 J 1. 82 | 1 3 . 9 | 1 .03 I 1.08 | 1. 16 1 1. 25 I 1. 35 I 1 .40 | 1.57 | 1 .44 | | 1 7 . 2 1 1. 02 I 1.06 | 1.11 1 1. 19 I 1 .26 1 1.30 0 . 0 | 0 . 0 120.81 1. 02 j 1. 05 | 1.09 1 1. 14 I 1. 16 1 0 . 0 | 0 . 0 | 0 . 0 1 24 . 51 1. 02 I 1. 03 1.07 I 1. 13 I 0 . 0 1 0 . 0 | 0 . 0 | 0 . 0 . 128.51 1.0 1 1 1.04 | 1.06 I 0 . 0 I 0 . 0 1 0 . 0 | 0 „ 0 i 0 . 0 | 1 3 3 . 5 | 1. 0 1 1 1. 02 | 0 .0 I 0. 0 I 0 . 0 j 0 . 0 I 0 . 0 | 0 . 0 1 3 5 . 0 | 1 .02 1 1. 02 • 0 .0 0 . 0 I 0 . 0 < 0 . 0 0 . 0 | 0 . 0 j. L - „ L 1 STATION - A LINEAR D. c . SPEED| 0. 25 1 0. 50 I 1.0 1 2. 0 I 4 . 0 1 7 .0 1 1 4 . 0 1 2 8 . 0 1 0 .4 ( 4 . 83 I 7 . 5 9 | 9 . 4 7 I 5 0 . 75 | 0 . 0 | 5 8 . 3 4 | 1 8 3 . 8 | 15. 62 1 1 .61 2 . 3 3 | 4 . 3 3 | 10. 6 3 | 13.301 2 1. 22 1 2 3 . 0 6 | 2 6 . 2 4 | 2 9 . 2 9 1 3 . 4 | 1 .32 1 1.73 | 2 . 6 9 1 3 . 55 4 .81 | 5. 21 | 6 . 4 0 | 7. 01 | 1 5 .51 1. 14 1 1. 35 | 1.73 1 2. 36 | 3 . 1 4 | 3.51 | 4 . 0 4 J 4 . 25 | 1 8 . 0 | 1 .07 1 1.20 | 1.46 I 1. 86 | 2. 27 1 2 . 7 4 2 . 9 0 1 3. 31 1 10.81 1. 08 I 1. 18 I 1.41 1 1 .72 | 2 . 0 7 1 2. 12 | 2 . 4 3 | 2 . 7 7 1 1 3 . 9 | 1.06 I 1. 14 | 1.26 I 1. 49 | 1.71 | 1. 96 | 2 . 0 6 1 1.99 | 1 1 7 . 2 | 1.04 j 1. 11 | 1.21 | 1. 38 | 1.47 | 1.37 | 0 . 0 J 0 . 0 | | 20.81 1. 03 1 1.09 I 1. 19 I 1. 24 I 1. 28 | 1. 13 | 0 . 0 | 0 .0 | 1 24 .51 1. 03 I 1 .07 | 1.13 | 1. 24 | 1. 19 0 .0 | 0 . 0 J 0 . 0 | I 2 8 . 5 | 1. 02 1 1.05 | 1. 12 1 0. 0 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | I 33 .51 1. 02 1 1.0 8 j 0 . 0 1 0 . 0 | 0 . 0 | 0 . 0 j 0 . 0 | 0 . 0 i 135.01 1.0 1 j 0 . 0 | 0 .0 j 0. 0 I 0 . 0 • 0 . 0 1 0 . 0 | 0 . 0 | I L 74 I f +-SPEEDI I +-0.4 1.6 3.4 5.5, 8.0, 10. 8| 13. 9 17. 2i 20.8 24. 5| 28. 5 i 33. 5j 35.0, 4 0. 25 J + 7. 31 2. 78 1. 32 1. 15 1.09 1.09 1.06 1. 05 1. 04 1. 04 1. 03 1. 02 1.00 + 0. 50 | 9.78 5.29 1. 72 1. 33 1. 24 1.21 1. 15 1. 12 1.09 1.07 1. 07 1.05 0.0 STATION 1.0 | +-57. 34 1 1.65 2.58 1.85 1.51 1.44 1. 32 1.23 1. 18 1. 16 1.09 1.05 0.0 - B LINEAR D. 2.0 | 4.0 | 37.94 17. 1 1 4. 10 2. 59 2. 0 0 1. 82 1.60 1. 38 1. 24 1. 20 1. 13 1.09 0. 0 182. C 29. 73 5. 17 3. 19 2.53 2. 18 1.79 1. 52 1. 38 0.0 0.0 0.0 0.0 C. 4 7.0 j 4 1 46, 5 25.06 5.82 3.78 2.78 2.44 1. 91 1. 63 1.23 0.0 0.0 0.0 0.0 4 14.0 | 4 1 12.7 25. 11 6.29 4.08 3. 13 2. 58 1.95 1.49 0.0 0.0 0.0 0.0 0.0 4 28. 0 ^ 139.4| 22. 2 3 | 6.64 4. 58 3. 12 2.78 0.0 0.0 0. 0 0.0 0. 0 0. 0 0. 0 J . — 4 -SPEED| I- 4-0.4 1.6 3. 4 | 5. 5 8.0 10.8, 13. 9| 17.2, 20. 8, 24.5 i 28. 51 33. 5 i 135. 0 4 0. 25 | 4 12.71 3. 36 1.39 1. 18 1. 1 1 1. 10 1.07 1.06 1.05 1.04 1. 04 1. 04 1. 03 4 0. 50 | 4 14. 79 5.80 1.87 1.42 1.26 1. 24 1. 17 1. 14 1. 12 1. 09 1.09 1. 09 1. 04 STATION - C LINEAR D. 1.0 | 2. 0 j 4.0 | 35.98 9.64 2.83 1.92 1.57 1.47 1.35 1.27 1.22 1. 16 1. 13 1. 12 0.0 28. 3 1 21.07 3. 72 2. 56 1.98 1.75 1. 58 1.51 1. 3 1 1. 30 0. 0 0. 0 0. 0 9 1.02 28. 05 4. 56 2.93 2. 36 2. 11 1. 92 1.67 1.4 1 0.0 0.0 0.0 0.0 C. 7.0 | 4 443. 7 25.22 4.96 3. 22 2.66 2.34 1. 96 1.79 1. 53 C O 0.0 0.0 0.0 4 14.0 | 4 88. 52 48.62 5.76 3.72 2. 84 2.58 2. 1 1 2.00 0.0 0.0 0.0 0.0 0.0 -I 28. 0 4 384.9| 40.70| 6. 32 3.78 3. 1 1 2. 88 2. 53 0.0 0. 0 0. 0 0. 0 0. 0 0. 0 j. J - . I I- 4-SPEED j L + . 0. 4 1. 6 3.4 5. 5 8.0 10.8 13.9 17. 2 20.8 24. 5 28.5 33. 5 35.0 4 0. 25 | 19. 36 3. 0 4 1.4 1 1. 20 1. 1 1 1. 10 1.08 1. 06 1.05 1. 04 1.03 1. 04 1. 05 4 0. 50 i 4 9. 84 7. 42 1. 94 1.42 1.28 1. 24 1. 19 1. 15 1. 12 1. 10 1. 10 1.08 1. 13 STATION 1.0 4-40.49 9.74 2.87 1.97 1.57 1.45 1.39 1.29 1.24 1. 13 1. 14 1.49 0.0 - D LINEAR D. -4 4-C. 7.0 | 4 137.4 29.75 4.99 3. 15 2.61 2. 46 2. 11 1. 68 1. 38 0.0 C O 0.0 0.0 4 14.0 | 4 1034. 38. 98 5.44 3. 59 2.89 2.73 2.50 1.89 1.64 0.0 0.0 0.0 0.0 , H 28. 0 457.0| 31. 79| 5. 66 3. 74 3.48 3. 30 2. 45 0. 0 0.0 0. 0 0. 0 0. 0 0.0 I 2.0 | 88. 10 16. 64 4. 34 2. 45 1. 93 1.83 1. 63 1. 47 1. 28 1. 27 1. 82 0. 0 0. 0 4.0 | 4 362. 7 25. 1 1 4.66 2. 97 2.37 2. 13 1.95 1. 69 1.32 1.35 0. 0 0.0 0. 0 175 I L 4. SPEED J +• 0.4 1.6 3.4 5.5 8. 0 10.8 13.9 17.2 20.8 24. 5 28. 5 33.5 35.0 STATION - E LINEAR D.C. 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | +-14.0 | 1 28.0 1 43. 631 16.46 i 3. 81 3. 19 2. 79 2. 27 2. 10 0. 0 0.0 0.0 0.0 0. 0 0. 0 8. 05 1. 98 1. 19 1. 10 1.05 1.07 1.05 1.05 1. 03 1.03 1. 03 1. 14 1.02 6. 4. 22 17 42 2 2 13 14 12 10 09 06 05 43 03 10. 40 5.0 1 1.81 1.43 1.28 1.30 1.25 1.18 1. 14 1.18 0. 0 1. 22 0.0 20. 20 10. S7 2. 67 1.77 1. 52 1.4 9 1.43 1. 28 1. 31 1. 12 0. 0 0. 0 0. 0 80.28 16. 07 3.27 2.20 1.81 1.73 1. 59 1.49 1. 32 0.0 0.0 0.0 0.0 61.55 18.03 3. 65 2.33 2. 15 1.94 1.78 1.41 0.0 0.0 0.0 0.0 0.0 33.35 20.22 4. 10 2.70 2.33 2.26 1.82 0. 0 0.0 0.0 0.0 0.0 0.0 —I 1 r + — SPEED i 0. j. 4 4 +• 25 | 0.50 | 4 + STATION 1.0 | 4_ 12.31 13. 09 2.75 1.69 1.44 1.38 1.26 1.19 1. 16 1. 17 1. 11 0.0 0.0 - I LINEAR D 2.0 | 4.0 | L . — 4 76.01 C. 7.0 0. 0 30.98 4.66 3. 16 2.38 2.07 1.77 1. 62 1.62 0.0 0.0 0.0 0.0 I 4 14.0 | 0.0 3 0, 83 5.60 3. 67 2.66 2.33 1.93 1.67 0.0 0.0 0.0 0.0 0.0 0.4 1.6 3.4 5. 5 8.0 10. 8 13. 9 17.2 20.8 24. 5 28. 5 33. 5 35.0 6. 2. 30 22 49 16 08 09 05 04 03 04 04 02 0 1 3 2. 38 3.63 1. 89 1.37 1. 19 1.20 1. 13 1. 10 1.08 1. 08 1. 08 1. 08 0. 0 227.8 15.37 3. 29 2. 19 1. 78 1. 62 1.43 1.33 1. 3 1 1. 19 1. 16 0. 0 0. 0 20.41 4. 18 2. 74 2.13 1.91 1.63 1. 50 1.31 1. 42 0.0 0.0 0.0 28. 0 1 0. 0 36.96| 5.78 4. 07 2. 86 2. 29 2. 38 0. 0 0.0 0.0 0.0 0. 0 0.0 STATION - J LINEAR D.C. 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | SPEED| r- -r 0.4 1.6 3.4 5.5 8.0 10.8 13. 9 17.2 20.8 24.5 28. 5 33.5 35.0 1 28. 0 1 102. 2| 16. 7 91 5. 20 3.45 2. 67 2. 36 2.0 2 0.0 0.0 0. 0 0.0 0.0 • 0. 0 5.69 2. 21 1.40 1. 15 1. 06 1.08 1. 05 1.04 1.03 1. 03 1. 02 1.03 1. 04 8.36 5. 26 1.8 1 1. 33 1. 18 1. 18 1. 13 1.09 1. 08 1. 08 1.08 1. 03 0. 0 1 1 5. 2. 0. 0. . 55 32 45 64 40 34 25 18 15 17 07 0 0 84.0 1 20. 26 3. 26 2. 12 1.7 1 1. 55 1. 4 1 1. 30 1. 27 1. 16 1. 04 0. 0 0. 0 95.85 26.00 3.93 2.66 1. 92 1.81 1. 61 1. 46 1. 33 1.08 0.0 0.0 0.0 0. 0 28.94 4.36 2. 94 2. 29 1.97 1. 73 1.64 1. 22 0.0 0.0 0.0 0.0 0.0 28. 06 5.55 3.21 2. 43 2. 24 1.87 0.0 0.0 0.0 0.0 0.0 0.0 I 1 I I 176 r 1 1 S T A T I O N - K L I N E AE D.C. | r 4 4 4 4 4 4 4 4 ^ S P E E D | 0. 25 1 0. 50 | 1.0 | 2.0 | 4.0 J 7.0 j 14.0 | 28.0 | I- 4 4 4 4 4 4 4 4 ^ | 0.41 5.27 | 8.55 | 11.70| 137.9 J €4. 29 | 231. 5| 635. 91 142. 0| I 1.6J 1.44 | 3.21 | 6.41 | 9.62 | 9.80 J 12.69 J 22. 40| 29. 4 91 | 3.4 | 1.28 | 1.46 | 1.90 | 2.56 | 3.19 | 3.69 | 4.34 | 4.69 | | 5.51 1.12 | 1.24 | 1.47 | 1.80 | 2.19 | 2.53 | 3.02 | 3.49 j j 8.0| 1.06 | 1.14 j 1.30 | 1.50 | 1.75 | 2.08 | 2.47 J 2.70 | I 10. B | 1.06 | 1.15 | 1.29 | 1.44 | 1.67 | 1.91 | 2.20 | 2.40 | |13.9| 1.05 | 1.12 1 1.23 | 1.40 | 1.56 | 1.77 ( 1.84 | 0.0 | |17.2j 1.04 | 1.10 | 1.18 | 1.29 | 1.40 | 1.55 | 0.0 | 0.0 | 120.81 1.04 | 1.09 | 1.17 | 1.27 | 1.28 | 0.0 | 0.0 | 0.0 | 124. 51 1. 04 | 1.07 | 1.26 | 1.31 | 0.0 | 0.0 | 0.0 | 0.0 | j 2 6 . 5 | 1.04 j 1.12 | 1.05 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 j 133. 51 1. 03 | 1.08 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 j 0.0 | |35.0| 1.07 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 j 0.0 | 0.0 | f. L J 1 1 L L 1 j i S T A T I O N - M L I N E A R D.C. | S P E E D | 0.25 | 0.50 | 1.0 | 2.0 j 4.0 j 7.0 | 14.0 1 28.0 | j. 4 4 + + + + + 4 A | 0.41 2. 66 1 6.07 J 10. 10 | 45. 0 11 93. 2 1| 82.491 85. 761 73.0 21 1 1.6| 1.82 I 3.74 | 7.64 | 12.301 18. 89| 21.491 26.331 18.431 | 3.4 | 1.30 | 1.66 | 2.20 | 3.00 | 3.95 | 4.12 | 4. 98 ) 5. 29 | | 5.51 1.13 I 1.28 | 1.56 | 2.0 1 | 2.42 I 2.74 | 3. 20 1 3. 82 | | 8.0| 1.06 | 1.16 | 1.36 | 1.66 | 1.97 | 2.25 | 2.61 | 2.75 | 110.8| 1.06 | 1.14 | 1.31 | 1.51 I 1.73 I 1.97 J 2.04 | 2.08 | 113.91 1.04 | 1.11 | 1.21 | 1.37 | 1.54 j 1.71 | 2.14 | 2.10 | 117.2| 1.03 | 1.08 | 1.16 | 1.25 | 1.38 | 1.25 | 0.0 | 0.0 | |20.8| 1.03 | 1.07 | 1.14 J 1.24 | 1.57 | 1.48 | 0.0 | 0.0 | | 24.51 1. 02 1 1.06 | 1.16 | 1.30 \ 0.0 J 0.0 | 0.0 J 0.0 I J 28.5 J 1.02 J 1.09 J 1.07 | 0.0 | 0.0 J 0.0 | 0.0 | 0.0 | J 33.5 i 1.02 1 1.12 | 0.0 I 0.0 | 0.0 | 0.0 | 0.0 1 0.0 | 135.0| 1.03 1 0.0 | 0.0 1 0.0 1 0.0 | 0.0 | 0.0 | 0.0 | J I I I I 1 1 I I I J. 1 , 1 J J J L 1 J | 1 S T A T I O N - N L I N E A R D.C. | S P E E D J 0.25 | 0.50 \ 1.0 | 2.0 | 4.0 I 7.0 \ 14.0 | 28.0 | I 0.4 I 5.25 j 5.68 | 9.61 I 21. 391 22. 54 J 36.381 54.02| 117. 81 1 1.61 2.02 | 3.09 | 4.19 | 6.72 | 8.33 | 9.41 1 20. 25| 14. 5 41 | 3.4 J 1.18 l 1.35 | 1.59 | 2.01 | 2.63 1 3.11 | 3.16 | 3.63 | 1 5.51 1.08 | 1.15 | 1.25 1 1. 45 | 1.69 1 1. 87 | 2.03 | 2.11 | | 8.0| 1.04 | 1.08 | 1.15 | 1.25 | 1.38 | 1.48 J 1.58 | 1.64 | 110. 81 1. 05 1 1. 09 | 1.15 1 1.24 | 1.33 | 1.49 | 1.48 1 1. 32 | 113.91 1.04 | 1.09 | 1.16 I 1.24 I 1.40 | 1.18 | 0.0 J 0.0 | (17.21 1.04 | 1.08 J 1.13 | 1.24 | 1.41 J 0.0 | 0.0 | 0.0 | 120.8J 1.03 | 1.07 I 1.10 J 1.14 | 0.0 | 0.0 | 0.0 | 0.0 | 124. 5i 1.03 | 1.05 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 j j 28. 5 i 0.0 1 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 I 133.51 0.0 1 0.0 | 0.0 1 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 135.0| 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 ( 0.0 | 0.0 | L 1- 4-SPEED| f +-0.4 1.6 3.4 5, 5 | 8.0 10.8, 13. Sj 17.2, 20.8 24. 51 28. 5 i 33. 5, 35.0 0. 25 | 10. 74 2. 50 1.31 1. 14 1. 09 1. 10 1.07 1.05 1. 04 1.04 1.03 1. 03 1.04 STATION — P LINEAR D 0.50 | 1.0 | 2.0 J 4.0 | 48. 14| 20. 79J 17.04 8.64 | 11.13| 11.57 2.44 | 3.62 | 4.26 1.77 | 2.34 | 2.81 1.50 | 1.97 | 2.31 1.46 | 1.74 | 1.98 1.34 | 1. 54 | 1.77 1.24 J 1.42 | 1.58 1.20 | 1.32 | 1.36 1.16 | 1.31 | 0.0 1.15 | 0.0 | 0.0 0.0 I 0. 0 | 0.0 0.0 I 0. 0 1 0 . 0 .C. 7.0 | + 14.01 42.75 5.22 3. 30 2.42 2.23 1.89 1.67 0.0 0.0 0.0 0.0 0.0 + 14.0 | + 0.0 63.84 5. 1 1 3.35 2.81 2.38 2.3 1 0.0 0.0 0.0 0.0 0.0 0.0 1 28. 0 1 0. 0 0. 0 5. .17 3.79 3. 16 2. 74 1. 97 0. 0 0.0 0. 0 0. 0 0. 0 0. 0 4. 56 3.82 1. 87 1. 36 1. 24 1. 24 1.17 1. 12 1. 10 1. 07 1.10 1. 05 1. 04 —I y-—+-SPEED| H +-0. 4 | 1.6 3.4 5. 5, 8.0] 10.8 13.9| 17. 2 20.8 24. 5 28. 5 i 33. 5j 35.0 0. 25 1 6.84 2. 28 1. 31 1. 13 1. 07 1.04 1.03 1.02 1. 02 1.02 1.01 1. 02 1.02 AVERAGE 0. 50 | — 4 -9. 77 4.34 1. 65 1.29 1. 16 1. 10 1.07 1.05 1. 04 1.04 1.04 1. 03 1. 03 VALUE 1.0 | + 19.68 7.32 2.21 1.56 1.3 1 1.20 1. 14 1.10 1.08 1.07 1.05 1.08 0.0 - CONSTANT D.C. +• 4.0 | 7.0 | 14.0 | 28.0 | * * mm, m~ —, .j. . 71.48| 84.77| 147.81 _ | j 75.72| 15.73| 16.43| 18.75J 17.03| 3.48 | 3.78 | 4. 16 | 4. 32 | 2.24 | 2.42 | 2.66 | 2.86 | 1.71 | 1.87 | 2.01 | 2. 15 | 1.46 | 1. 56 | 1.66 | 1.78 | 1.32 | 1.39 | 1.46 I 1, 58 | 1.24 | 1.28 | 1.37 | 0.0 | 1. 15 | 1.19 | 1.28 | 0.0 | 1. 12 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 J 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 J 0,0 | 0.0 | 2. 0 41 1 1 2. 0. . 17 . 40 92 92 52 33 23 17 13 1 1 1 1 04 0 1 I 1 28.0 1 120. 0 27.85 5. 58 3. 80 3. 0 2 2.65 2. 31 0.0 0. 0 0.0 0. 0 0. 0 0.0 r 4-SPEEDJ r 4-0.4, 1.6, 3. 4 5.5, 8.0, 10.8 13. 9 ( 17. 2| 20. 8, 24.5 28. 5 33. 5 i 35.0 4 0. 25 | 4 7. 14 2. 29 1. 32 1. 15 1.08 1. 08 1. 06 1.05 1. 04 1. 04 1. 03 1. 03 1.03 AVERAGE VALUE - LINEAR D.C. 0. 50 | 1.0 j 2.0 { 10.691 21. 45} 56. 3 8 + 4.59 I 8.57 I 14.58 1.70 I 2.42 I 3.41 1. 33 1 1.70 | 2.22 1.20 I 1.44 I 1. 79 1.19 | 1.39 | 1.66 1.15 I 1.2 9 | 1. 50 1. 1 1 | 1.22 | 1. 37 1.09 I 1.19 I 1.28 1.08 | 1.16 | 1.25 1.08 I 1.12 I 1.29 1.08 | 1.20 | 1.09 1.08 I 0.0 I 0.0 j.. L 4.0 | 7.0 | 12 5. 8 | 1 26. 7 | 22.79J 24.62| 4.21 | 4.68 | 2.74 | 3.05 J 2. 16 | 2.46 | 1.95 | 2. 16 | 1.71 | 1.86 | 1.53 | 1.62 | 1.34 | 1.42 | 1.26 | 0.0 | 0.0 | 0.0 1 0.0 | 0.0 1 0.0 | 0.0 I 4 14.0 | 2 1 6 . 6 + 28.56 5.36 3.47 2.7 2 2.40 2.04 1.81 1.64 0. 0 0.0 0.0 0.0 I L I Appendix C - P a r t I I E r r o r s o f c a l c u l a t e d fcy t h e S t u d e n t »t' t e s t . 179 I STATION - A CONSTANT D.C. SPEED| 0. 25 1 0. 50 1 1.0 1 2. 0 1 4.0 1 7.0 I 14.0 I 28.0 I 0,41 0. 74 1 3. 54 | 8.26 | 25.75| 0.0 | 0.0 0.0 | 0. 0 I 1.61 0. 30 1 0.67 1 3.20 J 6.7 6 5. 95 | 8.40 | 7. 24 | 5. 11 1 3.41 0. 02 1 0.05 1 0. 12 | 0. 17 | 0. 25 | 0.23 I 0.29 | 0. 33 1 5.51 0.01 1 0.02 | 0.04 0. 06 0.09 1 0. 11 | 0.13 0. 14 1 8.0) 0. 00 1 0.0 1 | 0.02 | 0. 03 | 0.05 | 0.06 | 0. 10 | 0. 18 ] 10.8| 0. 00 1 0.0 1 | 0.01 1 0. 02 | 0. 04 | 0.05 | 0. 1 1 | 0. 20 1 13. 9 | 0. 00 1 0.00 1 0.0 1 | 0. 02 | 0.03 | 0.06 I 0. 10 | 0. 0 I 17. 21 0. 00 1 0.00 | 0.01 | 0. 02 j 0.04 j 0. 07 I 0.0 0.0 1 20.81 0. 00 1 0.00 | 0.01 | 0. 02 | 0.09 | 0.0 | 0.0 | 0. 0 1 24.51 0.00 1 0. 0 1 | 0.02 | 0. 05 | 0.0 1 0.0 | 0.0 j 0. 0 1 28.51 0. 00 1 0. 0 1 | 0.03 | 0. 0 J 0.0 0.0 ] 0.0 0. 0 4 33.51 0. 0 1 1 0. 03 ] 0.0 1 0. 0 | 0. 0 | 0.0 | 0.0 | 0. 0 135.0j 0. 0 1 0.0 1 0.0 1 0. 0 1 0.0 i 0.0 I 0.0 1 0. 0 u_ 1 STATION - B CONSTANT D.C. H I H —I SPEEDl 0. J- + 0.4 1.6 3.4| 5. 5| 8 . 0, 10.8 13. 9| 17. 2i 20.8 24. 5 | 28.5, 33. 5 i 35.0, 25 j 0.50 | 1.0 | 2.0 | 4.0 I 7 . 0 | 1 4 . 0 I -+ +- + 320 . 7| 3 3 9 . 1 5 . 5 3 | 6 . 3 8 0 .24 | 0 i 2 5 0 .11 1 0 . 1 3 0 . 0 6 J 0 . 0 7 0 . 0 4 | 0 . 0 7 0 .06 J 0 . 1 0 0 . 0 8 | 0 . 0 0 . 0 | 0 . 0 0 . 0 J 0 . 0 0 . 0 | 0 . 0 0 . 0 1 0 . 0 0 . 0 I 0 . 0 28.0 1 69.30| 5. 71 0. 30 0. 15 0.09 0. 13 0. 0 0. 0 0.0 0. 0 0. 0 0.0 0.0 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 10 4 1 02 0 1 00 00 00 00 00 00 00 00 0 10. 35 1. 52 0.05 0.02 0.0 1 0.0 1 0. 00 0.00 0. 00 0. 00 0. 01 0.0 1 0.0 34. 55 2.74 0. 10 0.04 0.02 0.0 1 0.0 1 0.0 1 0.01 0.0 1 0.03 0.0 0.0 30 3. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. .98 62 19 06 03 02 02 02 02 04 0 0 0 160. 2 6. 36 0.24 0.08 0. 05 0.03 0.03 0.03 0. 16 0.0 0.0 0.0 0. 0 » • - — + SPEED| I- 4 0.4 1.6 3.4 5.5 8.0 10. 8 13. 9 17.2 20. 8 24. 5 28. 5 33.5 35.0 4-0.25 | 0. 50 | 4 10.34 1.26 0.06 0.02 0.01 0. 01 0.00 0.00 0.00 0.01 0.01 0.02 0.0 STATION -1.0 | 2. 4 39. 4 1 2.43 0. 13 0.04 0.02 0.01 0.0 1 0.01 0.0 1 0.01 0.03 0.07 0.0 C CONSTANT (- 4 0 | 4.0 | 87. 83 9.85 0. 24 0.08 0.04 0. 03 0.04 0. 04 0. 17 0.0 0.0 0.0 0.0 D.C. 7.0 | 4 14.0 | 4 0.0 23.70 0.30 0. 11 0.07 0.08 0.07 0.0 0.0 0.0 0.0 0.0 0.0 28.0 — I 3. 36 0. 56 0. 03 0.0 1 0. 0 1 0. 00 0.00 0. 0 0 0. 00 0. 00 0. 00 0. 0 1 0. 0 1 51 4. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. . 84 66 17 07 03 02 02 03 03 04 0 0 0 0.0 5, 10 0. 20 0. 10 0.05 0.04 0.05 0.08 0.0 0.0 0.0 0.0 0.0 0. 0 5.61 0. 39 0. 13 0. 10 0. 12 0. 19 0. 0 0. 0 0.0 0. 0 0.0 0.0 I L .J I- +-SPEED| h +-0.4 1 . 6 i 3.4 5. 5 i 8.0 (10 . 8 | 13-9 i 17. 2 20.8, 24. 5 j 28. 5, 33. 5 i 35.0 -r-0. 25 | STATION - J 1.0 J 2.0 CONSTANT -+ +-I 4.0 | D.C. 7.0 | +-14.0 | —I » I —I 0.50 | 28.0 6. 27 0.45 0. 03 0.0 1 0.0 1 0.00 0. 00 0.00 0. 00 0. 00 0. 0 0 0. 0 1 0. 03 2. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 60 97 07 02 0 1 01 00 00 01 01 0 1 02 0 40. 84 2.93 0. 13 0.05 0.02 0.0 1 0.01 0.0 1 0.01 0.0 1 0.03 0.0 0.0 0.0 4. 1 1 0. 19 0. 06 0. 03 0. 02 0. 02 0. 02 0. 03 0. 04 0.0 0. 0 0. 0 521. 7 8.97 0. 19 0.08 0.04 0.03 0.04 0.04 0.09 0.0 0. 0 0.0 0. 0 699.3 6.93 0.23 0.09 0.05 0.05 0.06 0. 10 0.21 0.0 0.0 0.0 0.0 0.0 14.6 1 0.30 0. 1 1 0. 06 0.07 0. 17 0. 22 0.0 0.0 0.0 0.0 0.0 STATION - E CONSTANT D.C, x + + — + + + + -0.25 J 0.50 J 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | I * SPEED| L X. 0.4 1.6 3.4, 5. 5j 8.0 10.8, 13.9, 17.2, 20. 8 | 24.5| 28. 5 | 33. 51 35. 0 0. 92 0. 15 0. 0 1 0.0 1 0. 00 0.00 0.00 0.00 0. 00 0.00 0.0 1 0. 16 0. 0 1.35 0. 76 0.03 0.01 0.0 1 0. 00 0.00 0.00 0.0 1 0.0 1 0.0 1 0.0 0.0 4. 13 1.02 0.05 0.02 0.0 1 0.0 1 0.0 1 0.0 1 0.0 1 0.05 0.0 0.0 0.0 54.51 2. 70 0. 12 0. 04 0. 02 0. 02 0. 02 0. 02 0. 05 0. 0 0. 0 0. 0 0. 0 60.6 1 3.77 0. 14 0. 06 0.03 0. 03 0. 03 0.06 0.0 0.0 0.0 0.0 0.0 38. 19 3.14 0. 19 0.07 0.05 0.04 0.05 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4. 13 0.20 0.09 0.07 0.05 0.28 0.0 0.0 0.0 0.0 0.0 0.0 Y J-I r + — SPEED | 0. L +  X. 0.50 | STATION -1.0 I 2. I CONSTANT h +-0 | 4.0 | D. C. 7.0 | +-14.0 | 25 J 0.4 1.6 3.4 5. 5| 8.0 10.8 13.9, 17.2I 20. 8 24. 5] 28.5, 33. 5 j 35. 0, 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 08 3 1 04 0 1 00 00 00 00 00 00 00 00 0 16.85 0. 57 0.07 0.02 0.01 0.0 1 0. 00 0.00 0.00 0.0 1 0. 02 0.05 0.0 21. 30 4.03 0. 15 0.04 0.02 0.0 1 0.0 1 0.0 1 0.01 0.02 0.02 0.0 0.0 0. 3. 0. 0. 0, 0. 0. 0. 0. 0. 0. 0. 0. 0 87 19 06 03 02 01 0 1 03 03 0 0 0 12 2. 1 9. 63 0.28 0.09 0.04 0.02 0.02 0.03 0. 11 0.0 0.0 0.0 0.0 0,0 14.99 0.32 0. 10 0.05 0. 04 0.04 0.06 1.18 0.0 0,0 0.0 0.0 0.0 8. 15 0.34 0. 16 0.07 0.06 0.07 0.0 0.0 0.0 0.0 0.0 0.0 L X X 1 I J. 4 — SPEED | 0. j. - f — STATION - J CONSTANT D.C. 25 I 0.50 | 1.0 | 2.0 | 4.0 | 7.0 __| | j | 14.0 | 28.0 ~r + 1 0.4| 1. 72 7.95 | 9.23 I 15 3. 31 0.0 0.0 0. 0 0. 0 1.6 | 0. 28 1.67 1.61 1 9.44 1 8.59 9.87 6. 68 192.9 3.41 0. 03 0.06 | 0. 1 1 0. 18 | 0.29 0. 27 0. 38 0. 42 5.5J 0.0 1 I 0.02 0. 04 0.07 | 0.09 0. 10 I o. 11 0. 13 8.01 0.00 0.01 j 0.02 0. 03 1 0.03 0.05 0. 05 0.08 10. 81 0. 00 0.01 | 0.01 0. 01 1 0.02 0.03 0. 04 0. 07 13. 91 0.00 0.00 | 0.01 0.01 | 0.02 0.03 0. 05 0.0 17.21 0.00 0. 00 0.01 I 0.0 1 j 0.03 0.05 I o. 0 0. 0 20. 8 | 0. 00 0.00 i 0.0 1 0. 02 | 0. 12 0.0 0. 0 0. 0 24. 5| 0. 00 0.01 | 0.02 I 0.07 | 0.0 0.0 0. 0 0.0 28. 5 1 0. 00 0.02 | 0.03 0. 0 | 0.0 0.0 0. 0 I 0.0 33.5| 0.00 0.02 i 0.0 0. 0 | 0. 0 0.0 I o. 0 0. 0 35.01 0.0 | 0.0 | 0.0 0. 0 I 0.0 | 0.0 | 0. 0 0. 0 r ± I Y 4 SPEED| j. 4 0.4 1.6 3.4 5.5 8.0 10. 8 13. 9 17.2 20.8 24. 5 28. 5 33.5 35.0 i 0. STATION - K CONSTANT 50 1 1.0 j 2. 0 1 4.0 | 255. 4 4. 08 0. 14 0. 05 0. 02 0. 02 0. 02 0. 02 0. 05 0. 93 0. 0 0. 0 0. 0 D.C. 7.0 | 14.0 | 28.0 0.0 18. 14j 0.30 0. 13 0.07 0.07 0. 14 0.0 0.0 0.0 0.0 0.0 0.0 0. 25 1. 17 0. 21 0. 03 0. 0 1 0.00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 0 1 0, 02 0.0 2. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 58 48 04 02 0 1 0 1 00 00 0 1 0 1 04 0 0 7.03 2.77 0.08 0.03 0.02 0.0 1 0.0 1 0.0 1 0.01 0.06 0.0 0.0 0.0 0.0 2. 36 0. 20 0.07 0.04 0.03 0.03 0.04 0. 34 0.0 0. 0 0.0 0.0 0.0 4. 72 0.22 0.09 0.05 0.04 0.04 0.09 0.0 0.0 0.0 0.0 0.0 STATION - M CONSTANT \ + SPEED | 0. j. 4-0.4 1.6 3.4] 5.5. 8.0 10. 8| 13. 9 | 17. 2 20.8 24.5! 28. 5 j I 33.5, 35.0 25 | 0, D.C. 7.0 | 4-14.0 | 50 1 4 53 53 05 02 b i 00 00 00 00 00 04 0 0 1.0 I 2.0 4 58.07 3. 53 0. 15 0. 06 0.03 0. 02 0. 0 1 0.02 0. 03 0. 0 0. 0 0. 0 0.0 I 4.0 | + 4 85.08 5.06 0. 23 0. 07 0.04 0.03 0.03 0.04 0 . 6 0.0 0.0 0.0 0.0 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 26 14 02 0 1 00 00 00 00 00 00 00 01 0 1. 0. 0. 0, 0. 0. 0. 0. 0, 0. 0. 0. 0. 3.52 2.28 0.09 0.03 0.02 0.0 1 0.0 1 0.01 0.0 1 0.04 0.0 0.0 0.0 0.0 4.81 0.21 0.09 0.05 0.04 0.05 0.28 0.0 0.0 0.0 0.0 0.0 0.0 8. 23 0.26 0. 14 0.08 0.07 0.0 0.0 0.0 0.0 0.0 0.0 0.0 I L. 182 1 STATION - N CONST ANT B.C. SPEED| 0. 25 1 0. 50 I 1.0 1 2. 0 1 4.0 1 7.0 | 14.0 I 28.0 I 1 0.41 0. 50 1 1. 02 I 4.19 | 16.011 27.9 3 | 52.521 9.62 | 0.0 | 1 1.61 0. 1 1 1 0. 24 I 0.4 1 | 1.31 1. 79 1 1. 65 | 4. 52 | 4.38 | 1 3.4| 0. 0 1 1 0. 02 I 0.0 3 | 0.06 | 0.09 | 0.11 J 0. 13 | 0. 17 | 1 5.51 0. 00 1 0.00 I 0.0 1 | 0. 02 | 0.03 1 0.04 | 0.06 I 0.08 | 1 8.0| 0.00 1 0.00 I 0.00 | 0.01 | 0.02 1 0.03 | 0.04 | 0.06 1 1 10.81 0. 00 1 0. 00 I 0.00 1 0. 0 1 | 0.02 j 0.03 I 0.09 | 0.0 | 1 13.9| 0.00 1 0.00 I 0.0 1 | 0. 02 | 0.05 | 0.0 | 0.0 j 0.0 | |17.2| 0. 00 1 0.0 1 I 0.0 1 1 0. 04 | 0. 0 | 0.0 | 0.0 | 0.0 | 120.8| 0. 00 1 0.01 I 0.02 | 0. 0 | 0. 0 | 0.0 | 0.0 | 0.0 | 124-5| 0. 0 1 1 0.0 I 0.0 | 0. 0 | 0.0 | 0.0 | 0.0 | 0.0 | | 28.51 0. 0 1 0. 0 I 0.0 | 0. 0 | 0.0 | 0,0 | 0.0 | 0.0 | 133.5| 0. 0 1 0.0 I 0.0 | 0. 0 | 0.0 | 0.0 | 0.0 | 0.0 | 135.0J 0. 0 j 0. 0 ! 0.0 j 0. 0 J 0.0 0.0 i 0.0 J 0.0 J I— I- + S P E E D 1 I- + 0.4 1.6 3.4 5.5 8.0 10.8 13.9 17.2 20.8 24. 5 28. 5 33.5 35.0 .4 + I 0.50 | S.TATION - P 1.0 1 2.0 101.51 0. 0 4.70 | 5.60 0.16 | 0.25 0.06 | 0.09 0.02 1 0.04 0.01 1 0.02 0.01 | 0.02 0.01 | 0.03 0.01 | 0.04 0.03 | 0. 15 0.05 | 0.0 0.0 | 0.0 0.0 | 0.0 CONSTANT 4 — 4 1 4.0 | + 4 0.0 18.20 0.35 0. 10 0.06 0. 03 0.03 0. 06 0. 38 0.0 0.0 0. 0 0. 0 D.C, . 7.0 | 4 763. 1 13.97 0.42 0. 15 0.06 0.04 0.05 0. 15 0.0 0.0 0.0 0.0 0.0 4-14.0 1 0. 25 28.0 1 0.0 0. 0 0. 56 0. 16 0. 08 0. 16 0.0 0.0 0.0 0.0 0. 0 0. 0 0.0 1 1. 74 0. 27 0. 04 0.0 1 0. 0 1 0. 00 0.00 0.00 0. 00 0. 00 0. 0 1 0.0 1 0.03 1.00 0. 56 0.09 0. 03 0.01 0. 01 0. 00 0.00 0.0 1 0.0 1 0.02 0.02 0. 0 0.0 330. 1 0.45 0. 15 0.08 0.07 0. 10 0.0 0.0 0.0 0.0 0.0 0.0 r 4 SPEED j I- + 0.4 1.6 3.4 5. 5 8.0 10.8 13. 9 17.2 20.8 24. 5 28. 5 33. 5 35.0 4-0.25 | STATION - A LINEAR D.C. • — 4 4 + 4 4 -50 I 1.0 J 2.0 j 4.0 | 7.0 | +-14.0 | -4 -28.0 1 0.0 12. 3 1 0.65 0. 28 0. 40 0. 45 0.0 0.0 0. 0 0. 0 0.0 0.0 0. 0 0. 74 0. 30 0. 03 0. 0 1 0.01 0. 00 0.00 0. 0 0 0.00 0. 00 0. 00 0. 0 1 0.0 3. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 54 70 06 03 0 1 0 1 0 1 0 1 0 1 0 1 01 08 0 8.26 7.37 0. 19 0.06 0.03 0.03 0.02 0.02 0.02 0.04 0.08 0.0 0.0 36. 75 12.95 0. 28 0. 1 1 0. 06 0. 05 0. 04 0. 04 0. 04 0. 09 0.0 0. 0 0. 0 0.0 1 1. 51 0.43 0. 19 0.09 0.09 0.07 0.09 0. 18 0.0 0.0 0.0 0.0 0.0 18.66 0.41 0. 22 0. 14 0. 12 0, 13 0. 15 0.0 0.0 0.0 0.0 0.0 0.0 12.85 0.55 0. 27 0.21 0.25 0.23 0.0 0.0 0.0 0.0 0. 0 0.0 i x. .j 183 STATION 1.0 | - 3 LINEAR D 4 4 2.0 | 4.0 | .C. 7.0 J 4 -14. 0 | t -f-SPEED| I- 4 0.4 1.6 3.4 5.5 6.0 10.8 13. 9 17. 2 20. 8 24. a 28. 5 33.5 35.0 4 0. 25 | 4 0. 50 | 28.0 1. 10 0.4 1 0. 03 0. 0 1 0.0 1 0.0 1 0.00 0. 00 0. 00 0.00 0. 0 1 0. 0 1 0. 0 10. 35 2. 22 0.06 0. 02 0.0 1 0.01 0.0 1 0.0 1 0. 0 1 0.01 0.02 0. 03 0.0 40. 96 4.05 0. 16 0.07 0.03 0.02 0.02 0.02 0.02 0.03 0.06 0.0 0.0 39. 60 5. 58 0. 34 0. 11 0. 06 0. 05 0. 04 0. 04 0. 03 0. 10 0. 0 0. 0 0. 0 272. 7 12.23 0. 46 0. 15 0.09 0.08 0.08 0.07 0. 36 0. 0 0.0 0. 0 0.0 568. 7 11.34 0. 46 0.22 0. 12 0. 10 0. 15 0. 19 0.0 0.0 0.0 0.0 0.0 622.3 1 1.79 0.50 0.25 0. 15 0. 16 0.27 0.0 0.0 0.0 0.0 0.0 0.0 148. 7 11. 22 0. 59 0. 33 0. 18 0. 28 0.0 0. 0 0. 0 0. 0 0. 0 0.0 0.0 —I i STATION - C LINEAR D.C. 4 4 4 4-1.0 | 2.0 | 4,0 | 7.0 | 4-14.0 | 4-I- 4 SPEED J f 4 | 0.4 | 1.6 J 3.4 | 5.5 | 8.0 i 10.8 | 13.9 | 17. 2 | 20.8 1 24. 5 | 26.5 ( 33. 5 |35.0 1 j. x. I j. 4 SPEED| I- 4 0.4 1.6 3.4 5.5 8.0 10.8 13. 9 17.2 20. 8 24.5 28.5 33.5 35.0 4 0.25 | 4 0.50 J 28.0 3. 36 0.66 0. 05 0.02 0.0 1 0.00 0.00 0. 00 0. 00 0. 0 1 0.0 1 0. 02 0. 02 10. 34 1. 52 0.09 0.03 0.02 0. 0 1 0.0 1 0.0 1 0. 0 1 0.0 1 0.02 0.04 0. 0 5 2. 2 6 4.84 0.23 0.07 0.03 0.02 0.02 0.02 0.03 0.03 0.05 0. 17 0.0 54.7C 8. 34 0. 29 0. 12 0.06 0. 04 0.04 0. 06 0. 06 0.0 9 0. 0 0. 0 0. 0 168. 7 22. 11 0.42 0. 14 0.08 0.07 0.C9 0.09 0. 39 0.0 0.0 0, 0 0. 0 0.0 8. 59 0.33 0. 19 0. 12 0.09 0. 12 0. 19 0.0 0.0 0.0 0.0 0.0 0.0 73.55 0.62 0. 23 0.15 0. 19 0. 17 0.0 0.0 0.0 0.0 0.0 0.0 0.0 13.0 1 0. 73 0. 25 0.21 0. 30 0. 5 3 0.0 0. 0 0. 0 0. 0 0.0 0. 0 STATION - D 4-0.50 | LINEAR D -4 4 I 4.0 | ,C. 7.0 -4-I -4-4 0.25 | 1.0 -4-2.0 14.0 | 28.0 4 12. H 1 0. 53 0. 04 0. 02 0. 0 1 0. 0 1 0. 00 0.00 0. 00 0.0 1 0. 0 1 0.0 2 0.07 2.60 3. 16 0. 12 0. 03 0.02 0.0 1 0. 0 1 0.0 1 0. 0 1 0. 02 0.02 0. 04 0.0 45. 54 0.16 0.23 0.05 0.04 0.02 0.03 0.02 0.03 0.02 0.06 0.0 0.0 0.0 6.67 0.34 0. 11 0. 06 0. 05 0. 05 0. 05 0. 08 0. 09 0. 0 0. 0 0.0 1281. 17. 83 0.33 0. 14 0.09 0.07 0. 10 0. 10 0. 18 0.0 0.0 0.0 0.0 1534. 12.57 0. 39 0. 17 0. 11 C. 11 0. 16 0.23 0.44 0.0 0.0 C O 0.0 0.0 30.32 0. 53 0.23 0. 14 0.18 0. 42 0.56 0.0 0.0 0.0 0.0 0.0 0. 0 0.0 0. 63 0. 25 0. 23 0. 31 0. 0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 j STATION - E LINEAR D. C. L 4- -+- -+- •+- -4-SPEEDI 0. 25 1 0. 50 1 1.0 1 2. 0 1 4 . 0 1 7 . 0 1 1 4 . 0 I 2 8 . 0 | 1 0 .4 | 0 . 9 2 \ 1. 35 1 4. 13 | 105.S | 1 2 3 . 2 | 4 7 . 7 6 | 0 . 0 | 4 8 . 1 3 | 1 K 6 J 0 . 15 1 0 . 9 9 | 1.73 | 4. .9 4 | 7. 18 I 4 . 72 1 6 . 4 0 | 4. 79 | J 3 . 4 | 0 . 0 1 1 0 . 04 J 0 . 0 7 0. 17 | 0 . 19 I 0 . 2 8 1 0 .32 | 0 . 3 0 J 1 5 . 5 | 0 . 0 1 1 0 . 0 2 0 . 0 3 | 0. 06 | 0 . 0 9 1 0 . 10 1 0 . 16 0 . 22 | 1 8 . 0 | 0 . 0 0 1 0 . 0 1 | 0 . 0 2 | 0. 0 3 | 0 .06 1 0 . 10 1 0 . 12 | 0 . 2 2 | | 1 0 . 8 | 0 . 00 1 0 . 0 1 ] 0 . 0 2 1 0. 03 0 . 0 7 1 0 . 0 9 1 0 . 13 | 0. 23 J J 1 3 . 9 | 0 . 0 0 1 0 . 0 1 | 0 . 0 2 1 0. 04 | 0 . 0 7 1 0. 12 1 0 . 6 1 | 0 . 0 J 1 17-21 0. 00 1 0 . 0 1 | 0 .02 ] 0. 06 | 0 . 15 1 0 . 0 1 0 . 0 0 . 0 | I 2 0 . 8 | 0 . 00 1 0 . 02 | 0 . 0 3 | 0. 13 | 0 . 0 1 0 .0 1 0 . 0 | 0 . 0 | | 2 4 . 5 | 0 . 0 1 1 0 . 0 1 1 0 . 12 j 0 . 0 j 0 . 0 1 0 .0 1 0 . 0 0 . 0 | | 2 8 . 5 | 0 . 0 1 1 0 . 0 3 | 0 . 0 | 0. 0 0 . 0 1 0 . 0 1 0 . 0 | 0 . 0 | 1 3 3 . 5 | 0 . 34 1 0 . 0 | 0 . 0 1 0. 0 | 0 . 0 1 0 . 0 j 0 . 0 j 0 . 0 | 1 3 5 . 0 | 0 . 0 1 0 . 0 1 0 .0 0. 0 1 0 . 0 1 0 . 0 1 0 . 0 1 0 . 0 | f L- L . I. . . . _ i - L mm. mm. mm. — — _ 1 1 STATION - I LINEAR D.C. f •+- +- +- •+-— 1 SPEED| 0. 25 J 0. 50 1 1.0 1 2 . 0 1 4 .0 1 7 . 0 1 14 .0 1 2 8 . 0 | j. -f- -+- +- 1 1 0.41 1. 08 1 2 7 . 5 11 2 1. 3 0 | 0 .0 | 22 1. 21 0. 0 1 0 . 0 | 0 . 0 1 1 1 . 6 | 0 . 3 1 1 0 . 57 | 6 . 7 9 | 6 .01 | 1 5 . 2 6 | 3 0 . 1 7 j 1 5 . 7 9 | 2 1 . 2 61 I 3 . 41 0. 04 1 0 . 10 | 0 . 2 3 0. 28 0 . 47 | 0 .55 1 0 . 59 | 0 . 6 7 | 1 5 . 5 J 0. 02 1 0. 03 | 0.06 | 0. 10 | 0. 15 | 0. 19 1 0 .31 | 0. 35 | 1 8 . 0 | 0. 0 1 1 0 .0 1 | 0 . 0 3 | 0. 05 | 0 . 0 8 | 0 . 0 9 1 0 . 13 j 0 .21 | 1 10.81 0. 0 1 1 0 . 0 1 1 0 . 0 2 | 0. 04 | 0. 05 | 0.08 1 0 . 13 | 0. 18 1 1 1 3 . 9 | 0 . 00 1 0 .01 | 0 . 0 2 1 0 . 03 0 . 05 | 0 . 0 9 1 0 . 17 | 1. 9 1 J 1 17. 21 0. 00 1 0 . 0 1 | 0 .01 | 0. 03 | 0 .08 0 . 15 j o,.o 0 . 0 | 1 2 0 . 3 | 0 . 00 1 0.01 | 0 .02 | 0. 06 | 0 . 22 | 3 .00 1 0 . 0 | 0 . 0 | J 24 .51 0. 0 1 1 0. 0 1 0 . 0 4 1 0. 06 | 0 . 0 | 0 . 0 1 0 . 0 | 0 . 0 | 1 28.51 0. 0 1 1 0 . 0 3 | 0 . 0 5 | 0. 0 | 0 . 0 1 0 . 0 j 0 . 0 j 0 . 0 1 | 33 .51 0. 0 1 1 0. 10 | 0 .0 | 0. 0 | 0 . 0 | 0 . 0 1 0 . 0 | 0 . 0 1 135.01 0 . 0 1 0 . 0 0 . 0 0. 0 1 0. 0 1 0 . 0 i 0 . 0 1 0 . 0 1 1 STATION - J LINEAR D. c. h +- +- +- +- 1 SPEED 1 0 . 25 1 0. 50 1 1.0 1 2. 0 1 4 . 0 1 7 .0 1 1 4 . 0 1 2 8 . 0 | 1 0 .4 | 1 .72 1 1 2 . 3 7 | 9 . 2 3 | 23 1.6 | 0 . 0 | 0 . 0 1 0 . 0 | 0 . 0 | 1 1 .6J 0. 29 1 2 . 53 | 1.75 1 1 2 . 6 5 | 13. 69 | 14.73 1 9 . 52 | 5 2 4 . 8 | 1 3 .41 0 . 0 3 1 0 . 08 0 . 15 | 0. 27 J 0 .44 | 0.44 1 0 . 7 8 | 0 . 8 2 | 1 5.51 0 . 02 1 0 . 0 3 | 0 .06 | 0. 10 | 0. 16 | 0 . 17 1 0 . 2 2 | 0. 23 1 | 8 . 0 | 0 . 0 0 1 0 . 0 1 | 0 . 0 3 0. 05 0 . 0 6 | 0 . 10 1 0.11 j 0 . 15 | 1 10.81 0 . 00 1 0 .01 | 0 .02 | 0. 03 | 0 . 0 5 | 0 . 0 6 1 0 . 10 0. 16 | 1 13.91 0 . 0 0 1 0 . 0 1 | 0 .01 1 0. 03 | 0 . 05 | 0 .06 1 0 . 12 | 0 . 0 | | 17.21 0 . 0 0 1 0 .01 | 0 .0 1 | 0 . 0 3 | 0. 07 | 0. 11 1 0 . 0 0 . 0 | J 2 0 . 8 i 0 . 00 1 0 .01 1 0 .02 0. 04 J 0 . 26 | 0 . 0 1 0 . 0 | 0 . 0 | | 2 4 . 5 | 0 . 0 1 1 0 .01 | 0 .04 | 0. 15 | 0 . 0 | 0 . 0 1 0 . 0 | 0 . 0 | 1 2 8 . 5 J 0 . 0 1 1 0 . 0 3 | 0 . 0 5 1 0. 0 | 0 . 0 J 0 . 0 j 0 . 0 j 0 . 0 | | 3 3 . 5 | 0. 0 1 1 0 . 0 3 | 0 .0 1 0. 0 | 0 . 0 | 0 . 0 1 0 . 0 | 0 . 0 | 1 3 5 . 0 | 0 . 0 1 0. 0 j 0 .0 1 0. 0 1 0 . 0 1 0 . 0 1 0 . 0 1 0 . 0 | L X 185 i I j. + SPEED | j. + 0.4 1.6 3. 4 5.5 8.0 10. 8 13. 9 17.2 20. 8 24. 5 28. 5 33.5 35.0 STATION - K LINEAR D.C. 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | _ + -f -j- + — - 4 +-28.0 1 0.0 23.73 0. 57 0. 31 0. 27 0. 21 0. 0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 1. 17 0. 21 0.03 0.0 1 0.00 0. 00 0. 00 0.00 0. 00 0. 0 1 0. 02 0. 04 0. 0 2. 58 0.48 0.04 0. 02 0.0 1 0. 01 0.0 1 0. 0 1 0.0 1 0.02 0.08 0.0 0.0 1 7.03 589.8| 0.0 | 0.0 0.0 | 1 3.75 5. 13 | 4. 54 9.70 35.601 | 0.10 0- 19 | 0.28 0.34 0.48 | | 0.04 0.08 | 0. 12- 0. 16 | 0.23 | I 0.03 0.04 J 0.07 0. 10 0. 14 | I 0.02 0. 04 | 0. 06 0.08 0.15 | | 0.02 | 0. 04 | 0.06 0. 10 | 0.34 | I 0.02 0. 03 | 0. 10 0.21 0.0 | | 0.03 0. 12 | 0.61 | 0.0 0.0 | 1 0.13 1 1.85 | 0.0 0.0 0.0 | I 0.0 | 0.0 | 0.0 j 0.0 0.0 I | 0.0 0. 0 | 0.0 0.0 0.0 | I 0.0 0. 0 | 0.0 0.0 0.0 | i ^ 4 SPEEDj * 4 0.4 1.6 3.4 5.5 8.0 10. 8 13. 9 17.2 20.8 24. 5 28.5 33. 5 35.0 0. 25 0. 26 0. 14 0. 0 3 0. 02 0.0 1 0. 00 0. 00 0. 00 0. 00 0. 0 1 0. 0 1 0.02 0.0 4 — I o. + — 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. STATION - M LINEAR D. C. 50 53 53 06 02 0 1 0 1 0 1 0 1 01 0 1 08 0 0 | 1.0 | 2.0 | 4.0 | 7.0 + 3. 52 3. 19 0. 11 0.05 0.03 0.02 0.01 0.0 1 0.03 0. 10 0.0 0.0 0.0 | 14.0 j 28.0 .4 + j 65. 8 51 1£6.3| 0.0 I 0.0 ( 0. 0 6. 13 | 9.07 | 7. 85 14.12| 7. 97 0.22 | 0.41 | 0.33 | 0.42 | 0.40 0.09 | 0. 12 | 0. 15 0.25 | 0. 36 0.05 | 0.07 | 0.10 | 0.16 | 0. 26 0.03 | 0.06 | 0.09 0.14 | 0. 84 0. 03 | 0.06 | 0. 11 0.0 | 0.0 0.03 | 0.09 | 0. 62 0.0 | 0. 0 0.06 | 0.0 | 0.0 0.0 | 0. 0 0. 0 | 0.0 | 0.0 0.0 | 0. 0 0.0 | 0.0 | 0.0 0.0 | 0. 0 0.0 | 0.0 | 0.0 0.0 1 0. 0 0. 0 | 0.0 | 0.0 10.0 J 0. 0 — I i f 4 — SPEED| 0. — ~ f +• 25 | 0.50 | STATION - N LINEAR D.C. 1.0 | 2.0 J 4.0 | 7.0 14.0 | 28. o" 1 -4- -4-1 0.4| 0. 50 1.02 4. 19 20.81| 29. 29| 87. 24 | 13. 13| I 1.6 | 0. 1 1 I 0. 24 0.42 1.72 | 2.37 | 1.82 | 6.64 1 1 3.41 0. 01 0.02 | 0.04 0.08 | 0. 10 | 0. 13 1 0. 16 | 1 5.5| 0. 00 0.0 1 | 0.0 1 | 0.03 | 0.05 J 0.06 1 0.08 | j 8.01 0.00 0.00 J 0.0 1 0.0 1 | 0.03 1 0.04 | 0.06 | I 10.8| 0. 00 | 0.00 0.01 | 0.02 | 0.03 | 0.06 | 0. 18 | | 13.9| 0. 00 0.0 1 | 0.02 0. 04 | 0. 10 | 0.0 | 0.0 | 1 17.2| 0. 0 1 0.0 1 | 0.02 | 0.07 | 0.0 | 0.0 | 0.0 | |20.8| 0. 0-1 0.02 | 0.05 0.0 | 0.0 1 0.0 | 0.0 I 124.5J 0.03 i 0.0 | 0.0 1 0.0 | 0.0 | 0.0 1 0.0 | 1 28.5( 0. 0 0.0 | 0.0 0.0 | 0.0 | 0.0 | 0.0 | | 33.5| 0. 0 • 0.0 0.0 1 0. 0 | 0.0 | 0.0 i 0.0 | |35.0| 0.0 0.0 | 0.0 0.0 | 0.0 | 0.0 | 0.0 J 0. 0 5. 16 0. 21 0. 11 0. 10 0. 0 0.0 0.0 0.0 0. 0 0. 0 0.0 0.0 186 r ' 1 i STATION - E LINEAR D.C. I SPEEDI 0.25 | 0.50 | 1.0 | 2.0 | 4. 0 | 7.0 | 14.0 | 28.0 | 1 0.41 1.74 I 1.00 | 133.4| 0.0 | 0.0 | 1629. | 0.0 | 0.0 | 1 1.6| 0.27 | 0.56 I 6.92 J 8.67 | 40.44| 35.961 700. 1J 0.0 | I 3.4| 0.06 I 0.13 | 0.25 | 0.44 | 0.60 | 0.78 | 0.79 | 0.90 | J 5.51 0.02 J 0.04 I 0.11 I 0. 16 I 0. 19 1 0.28 1 0.28 | 0.32 | 1 8.01 0.01 I 0.02 | 0.04 | 0.09 | 0.12 | 0.12 | 0.16 | 0.18 | | 10. SI 0.0 1 1 0.02 I 0.03 I 0.05 | 0.08 | 0.10 | 0.16 | 0.37 1 113.91 0.00 I 0.01 | 0.03 | 0.04 | 0.07 | 0.11 | 0.26 | 0.0 I I 17.2! 0.00 J 0.01 1 0.02 | 0.07 1 0.14 | 0.35 | 0.0 1 0.0 | 120.81 0.01 1 0.01 | 0.03 | 0.10 | 0.85 1 0.0 | 0.0 | 0.0 1 124.51 0.01 I 0.01 I 0.06 | 0.37 | 0.0 1 0.0 | 0.0 1 0.0 1 128.51 0.01 | 0.05 I 0.10 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | i 33.51 0. 02 | 0.04 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | J 35.0 i 0.06 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 I I I I 1 1 I L L r 1 1 187 Ap p e n d i x D D i f f e r e n c e means, d i f f e r e n c e v a r i a n c e s , r e s i d u a l v a r i a n c e s , and c o r r e l a t i o n c o e f f i c i e n t s f o r t h e f i n a l v a l u e s o f t h e t r a n s f o r m a t i o n a f t e r t h e s y s t e m a t i c e r r o r i n t h e v a r i a n c e d i f f e r e n c e has been removed. Ihe u n i t s o f t h e d i f f e r e n c e means a r e d e c i p a s c a l s w h i l e the d i f f e r e n c e v a r i a n c e s a r e i n p e r c e n t . The r e s i d u a l v a r i a n c e s and c o r r e l a t i o n c o e f f i c i e n t s a r e d i m e n s i c n l e s s . DIFFERENCE MEANS - CONSTANT D.C. X i COMPONENT SHIPI 0. 25 - - f -1 j 0. 50 I I 1.0 "T~ I 2. 0 • i — 1 i 4.0 •T-1 7.0 i 1 14.0 1 28. 0 (._ A | .003 •T - .009 .023 .044 •+-1 .065 . 061 • T .069 .066 B J .003 | .0 10 | .017 .024 1 .031 | .037 | .042 j .034 C 1 .005 | .008 | .001 | .0 15 1 .016 | .023 | . 031 | .030 D j .00 1 | .002 | . 006 | .015 1 .003 | .006 . 005 J .021 E | .002 | .006 J .012 | .020 1 .016 .008 | .015 | .0 16 I i .00 1 .000 | .004 | .010 1 .006 | .001 | . 008 j .003 J | .00 1 | .002 j .001 J .008 1 .003 | .014 .004 J .013 K | .004 | .010 | .021 J .030 1 .021 | .011 | . 009 | .000 M | .002 | .005 | .C14 | .022 1 .024 | . 030 | .04 3 | .035 N j .005 | .0 12 .026 | .047 1 .06 1 | .065 | . 067 | .060 P i .002 1 .006 I .010 i .004 1 .C05 • .018 . 029 .018 [ i DIFFERENCE MEANS - CONSTANT D.C. Y COMPONENT SHIP | 0. 25 ! 0. 50 1 1.0 1 2. 0 1 4.0 1 7.0 1 14. 0 1 28. 0 A | .002 1 .008 | .013 .013 | .017 | .0 16 | . 0 13 | .0 13 B 1 .00 1 1 .006 | . 004 | .007 J .022 | .031 | . 036 | . 043 c 1 .005 j .012 j .008 J .0 10 | .032 j .041 | . 044 | .048 D | .005 j .014 | .01 1 | .004 | .027 | .035 1 .04 1 | .0 50 E J .00 1 1 .002 | .011 | .020 | .037 | .042 .044 | . 043 I | .001 .002 | .002 | .014 | .026 | . 032 | . 037 | .042 J | .002 1 .004 | .009 | .007 | .0 17 | .022 | .027 | .031 K | .005 j .0 11 | .017 | .020 .020 | .013 | .000 | .0 14 M J .000 j .002 | .00 2 | .002 | .006 | .006 .004 | .008 N 1 .001 1 .004 | .009 j .0 16 | . 021 i .026 | .021 | .021 P 1 .006 1 .016 . 028 1 .03 1 1 .028 1 .0 33 • .008 • .0 19 i DIFFERENCE MEANS - LINEAR D.C. X COMPONENT SHIPI 0.25 1 0. 50 1 1.0 1 2. 0 1 4.0 1 7.0 1 14. 0 1 28.0 A j .003 1 .013 | .037 | .076 | . 110 | . 105 | . 113 | .111 B J .006 j .02 1 | .036 .051 .071 | . 085 j . 089 | .078 C 1 .013 1 .022 | .015 | .006 | .00 1 | .014 | . 024 .0 17 D | .007 j .015 | . C08 | .002 | .030 | .040 | . 045 | .070 E | .002 j .007 | .012 | .021 .0 15 | .002 | .007 | .011 I | .001 1 .001 .006 j .0 15 .009 | .001 j .008 | .005 J | .003 j .008 | .009 | .001 | - C 11 | .040 | .025 .003 K | .005 1 .013 | .026 | .037 | .025 | . 009 .005 | .001 M | .003 1 .007 | .018 .029 | .033 | .040 j .054 | . 047 N j .006 1 .014 .029 .053 | .069 | . 078 | . 078 | .074 P 1 .005 j .012 j .018 .007 ] .010 j .035 . 054 ] .049 L. 1 89 DIFFERENCE MEANS -SHIP) 0.25 | 0.50 | 1.0 4 4 4 LINEAR D.C. : | 2.0 | 4.0 COMPONENT - + 4 4. I 7.0 | 14.0 | 28.0 "* 4. .0 26 .063 .081 .087 .065 .078 .066 .020 .007 .025 .072 A j .004 | .015 j .026 .031 | .037 | .032 | . 028 | B | .004 .013 | .013 .004 .027 | .041 | . C53 1 C ; .0 1 1 | .024 j . 020 | .012 | .045 .064 .071 | D , .0 11 | .025 | .020 .008 | .048 | .063 | .071 J E ! .00 1 .001 | . 012 .026 .054 . 063 | . 066 J I .002 j .003 | . 005 | .028 | . 049 .059 . 072 | J .002 | .006 | .010 . 0 1 8 1 .042 .0 52 | . 064 | K .007 .017 | .024 .027 .025 .013 .000 J M i .00 1 .004 | .004 | .00 1 .0 13 .0 12 .008 | N .002 .006 .011 .018 . 025 | .029 | .025 ( P .0 15 .034 .06 1 .075 | .070 | . 082 .048 | DIFFERENCE VARIANCES SHIP | 0.25 | 0.50 | 1.0 | - CONSTANT D.C. X COMPONENT 2.0 | 4.0 | 7.0 | 14.0 | A | 0.22 | 0. 54 | 1.02 | 1.45 | 1.62 | 0.35 | 0.47 | B 0.04 | -0. 10 | -0. 38 | -0.7 21 0.09 | 1.69 | 2.09 | C , -0.58 J -1.29| -1.72| -1. 3 1| - 1.49| -2.71| -0. 39 I D -0.44| -1.00| -0. 4 11 0.69 | -0.77| -0.26| - 0 . 051 E j -0. 10| 0.00 1 -0.75| 0.32 J 0.70 | 1.32 | 0.24 | I -0.32| -0.65| -0. 85J -0.30| 0. 23 | -0.74 | 3.38 | J -0.26| -0. 63| - 1. 14| -0.981 -1.43| -2.65| - 0 . 39( K -0.26 i -0.62| - 1. 52| -2.84| -3.04| -3.52| -0.73| M 0.05 | 0. 20 | 0.44 | 1. 51 | 1.76 | 3.55 | 2.02 1 N -0.20 | -0.51 | -0.67| -2. 77| -2.67| -5.66 | -6.73| P 0. 09 | 0. 13 | 0.54 | -0.69| -2.8SI 0.33 | 0.73 1 28. 0 4 - 1 . 25 1. 89 -1.33 -1.17 -2. 87 4. 91 0. 17 -0.74 4. 81 -4. 82 1. 78 DIFFERENCE VARIANCES - CONSTANT D.C. Y COMPONENT 4 4 4 4 — + 4 4 4-SHIPJ 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 J - 4 - -4-28.0 1 1. 23 -1.95 1. 30 1. 15 2. 75 - 5 . 30 -0. 17 0. 73 -5. 18 4. 49 -1.83 A B C D E I J K M N P -0. 22 -0. 04 0.58 0. 43 0. 10 0. 32 0. 26 0. 26 -0. 05 0. 20 -0. 09 -0. 54 0. 10 1. 26 0.99 -0. 00 0. 65 0.63 0. 6 1 -0. 20 0. 50 -0. 13 -1.04 0.38 1.68 0.4 1 0.74 0.84 1.12 1.49 -0. 44 0.66 -0. 54 -1 0. 1. -0 -0 0. 0. 2. - 1 2. 0. .48 71 28 .69 .32 30 96 72 . 55 66 69 - 1.65 -0. 09 1. 46 0.76 -0.71 -0. 22 1.40 2. 91 - 1. 80 2.57 2.77 -0.35 -1.73 2. 60 0.26 -1.35 0.73 2. 55 3.34 -3.75 5.21 -0.33 -0. 47 - 2. 15 0.38 0.05 - 0 . 24 -3.57 0.39 0.72 -2.08 6. 12 -0. 74 1 90 r ^ I DIFFEEENCE VARIANCES - LINEAR D.C. X COMPONENT | h 4 4 4 4 + + 4 + i |SHIP| 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | j. + + + — 4 4 + + + -_ I A i 0.44 j 1.21 I 2.05 | 2.92 | 3.37 | 1.00 | 0.61 | -0.77 J I B 1 0.09 | -0.24| -0.77| -1.63| 0.73 | 2.80 J 2.87 J 3.85 | 1 C | -1.54| -3.10| - 3. 621 -2. 231 -2. 17| -3.79 | -0.42| 0.22 | J D | -1.051 -2. 161 -0. 871 2. 12 J -0.32| 0.71 | 0.46 | -0.46| I E | -0.161 0.37 | -1.18J 1.33 | 1.42 1 2.31 | 0.41 J -2.22| I I 1 -0.66| -1.531 -2.10| -0.87| 0.23 | -1.51 | 4.81 I 9.49 j I J I -0.^8| -1.49| -2.29| -1.35| -1.851 -4.16J 0.83 I 2.87 J I K | -0.47J -1.30| -2.53| -5.41| -4. 78) -6.631 -2. 40| -2.15| 1 M j 0.12 J 0.37 | 0.86 | 2. 32 ( 2. 83 j 5.80 | 3.98 | 7.40 | 1 N | -0. 401 -0. 701 -0. 69| -4.27| -4.01| -8.98| -10.7| -9.02| I P 1 0.41 J 0.78 I 1.56 J -0.94| - 5 . 2 £ | 0.71 | 0.51 J -0.6 51 f- L J . L 1 J . — L i _| | DIFFEEENCE VARIANCES - LINEAR D.C. Y COMPONENT ! j. 4 4 4 4 4 4 4 4 H 1SHIP) 0. 25 1 0. 50 | 1.0 | 2.0 I 4.0 J 7.0 | 14.0 | 28.0 | I A I -0.45| -1.23| -2.11| -3.06| -3. 55^ - 1 . 0 l | -0.62! 0.76 \ J B 1 -0.09| 0.24 I 0.76 1 1. 59 | -C.74| -2.93| - 3 . 001 -4.09| I C J 1.50 I 2.96 i 3.43 | 2.16 | 2.10 | 3.58 | 0.42 | -0. 2 21 1 D I 1.04 I 2. 09 1 0.85 j -2. 19| 0.31 | -0.72| -0.46( 0. 45 1 I E 1 0.16 | -0.38| 1.16 | -1.361 - 1-45. -2.391 -0.421 2. 14 | 1 I 1 0.65 I 1.49 | 2.04 | 0.86 | -0.23J 1.48 J -5- 19 j -11.1| 1 J I 0. 58 1 1.46 J 2.22 | 1. 32 1 1. 80 | 3.91 | -0.84| -3.00 J 1 K I 0.47 I 1.28 | 2.43 J 5.0 1 | 4.46 | 6.03 I 2.32 I 2.08 | | M j -0.121 -0.37| -0. 871 -2.40| -2.95| -6.351 - 4. 231 -8. 321 1 N 1 0. 40 1 0. 70 J 0.69 1 4.01 | 3.79 J 7.91 I 9.23 | 7.94 | | P J -0.41J -0.78| -1.59| 0.93 | 4. 87 1 -0.721 -0.52| 0.65 | I I J I , 1 J L L 1 -J, 1 RESIDUAL VARIANCES - CONSTANT D.C. X COMPONENT | 1SHIP1 0.25 J 0.50 I 1.0 I 2.0 | 4.0 1 7.0 | 14.0 | 28.0 I I A J .002 | .007 | .017 | .031 | . 043 | .047 ] .049 | .042 | | B | .002 | .007 | .017 I .032 | . 042 | .046 | . 039 | .035 | I C I .003 J .008 I .019 | .034 | .047 | .045 | . 052 | .053 | 1 D 1 .003 I .010 J .024 | .040 | .C47 | .051 | .051 | .059 | ] E | .003 | .006 | .014 I .029 | .037 | .043 | . 039 | .037 | 1 I I .002 1 .006 1 .013 1 .022 | . 028 1 . 032 j . 038 | .044 | 1 J I .002 I .006 I .013 | .023 | . C31 | .035 | .044 I . 047 | | K | .002 1 .006 I .012 | .018 | .025 | .032 | .043 1 .056 | 1 M 1 .002 I .006 I .013 | .024 | .031 | . 037 1 .046 1 .049 | I N I .003 1 .004 1 .009 1 .0 1 9 | .032 | .041 | . 053 | . 067 | 1 f 1 .003 1 .008 1 . 021 | .035 | .C42 J .045 | .050 | .035 | I J „J L L. J J L L 1 r 1 J RESIDUAL VARIANCES - CONSTANT D.C. Y COMPONENT | f + + + + + 4 + + H |SHIP| 0.25 J 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | |. 4 4 4 4 . 4 4 + 1 I A J .002 | .006 | .014 1 .027 | .040 | .047 | .051 | .039 | | B | .002 | .007 | .018 | .038 j . 057 | .059 | .055 | .060 | I C J .004 | .011 | .026 | .044 | . 054 | .051 | .053 | .053 | I D | .006 | .014 | .031 | .050 | . 072 | .079 | .078 | .083 | I E | .004 | .008 | .021 | .036 | .065 | .070 J .070 | .079 | j I i .003 | .008 | .014 | .025 | .032 | .037 | . 043 | .054 | | J J .003 | .008 | .018 | .028 | . 036 | .043 J . 039 | .042 | | K | .003 | .008 | .018 | .027 | . 035 | .039 | .057 | .073 | | M | . 002 | .005 | .012 | .022 | . 033 | .036 | . 048 | .047 | J N J .003 | .006 | .011 | .025 | .039 | . 045 | . 064 | .070 | | P | .003 | .008 | . 020 | .040 | .051 | .052 | . 060 | .070 | y J L 1 1—- i L . i i j | RESIDUAL VARIANCES - LINEAR D.C..X COMPONENT | j. 4 + 4 4 4 4 4 + _ _ j ISHIPJ 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | I A J .006 | .017 | .041 | .079 J . 107 | .110 | .107 | .090~j I B | .006 | .016 | . 042 | .076 | .103 | .107 | .089 | .078 | | C | .007 | .018 | . 044 | .086 | .117 | .109 | .121 | .117 | | , D J .008 | .024 | .062 | .101 | .119 | .116 | .104 | .104 | J E | .006 | .014 J .032 | .065 | .078 | . 082 | . 075 | .061 | I I J .006 | .015 | .032 | .053 | .066 | .073 | .081 | .089 | | J j .005 | .015 | . 032 | .056 | .074 | .077 J .093 | .093 | | K | .005 | .014 j . 031 ( .046 | .061 | . 069 | . 084 | . 095 | | M | .005 | .013 | .031 | .056 | .070 | .078 | .092 | .087 | | N | .005 | .009 | .018 | .035 | .057 | .072 | . 082 | .095 | I P | .009 | .023 | .057 | .091 | .105 | .108 | .108 | .084 | |- I L — . . 1 1 I JL 4. I _| j RESIDUAL VARIANCES - LINEAR D.C. Y COMPONENT | |SHIP| 0.25 | 0.50 i 1.0 | 2.0 j 4.0 | 7.0 | 14.0 t 28.0*1 1 A | .004 | .014 | .034 | .064 } . 096 | .109 | .112 | .084~| i B | .006 | .017 | .043 | .089 | .134 { .134 | .123 J .127 | I C | .011 | .029 | . 066 | . 1 1 1 1 .141 | .124 J .128 | .115 | | D i .014 1 .038 | .078 | .125 | .171 | .180 | .174 | .178 | | E | .009 | .019 | .050 | .079 | .136 | .141 | .132 | .139 | | I 1 .008 | .020 | .035 | .060 | .077 | .087 | .096 | .120 | | J | .007 | .019 | .044 | .067 | .087 | .097 | .086 | .086 | I K i .007 | .019 | .04 8 | .069 | .082 | .092 | .113 | .147 | I M | .004 | .011 | .031 | .053 | .074 | .077 | .093 | .089 | i N | .007 | .013 | .022 | .044 | .067 | .076 j .100 | .106 | I P | .009 J .019 | .049 | .098 | .120 j .113 | .116 | .135 | I 1 1 1 1 1 L I - X. I h — - + SHIPJ ^ + A B C D E I J K M N P COEEELATION 0. 25 | 0. 50 .999 I .997 COEFFICIENTS -I 1.0 1 2.0 • CONSTANT D.C. I 4.0 1 7.0 . X COMPONENT | 14.0 | 28.0 .999 .999 .997 .996 .998 | .995 .999 | .997 .999 | .997 .999 | .997 .999 | .997 .999 | .997 .999 | .998 .998 | .996 I . 992 .992 .991 . S88 .993 .994 . 994 .994 .993 .996 . 990 .984 .984 .983 .980 .986 .989 .988 .991 .988 .991 .983 . 578 . S79 .977 .976 .981 .586 . S85 .588 . 984 .984 . 579 , 977 .977 .978 . 975 . 979 . 984 .983 . 985 .981 .980 .578 . 976 . 980 .974 . 974 .980 . 981 , 978 . 978 . 977 . 975 , 97 5 .979 .982 .974 .971 . 982 .978 .976 . 972 .975 . 968 .982 1- i SHIP | j. 4, A B C D E I J K M N P CORRELATION 0.25 | 0.50 COEFFICIENTS -+ + | 1.0 | 2.0 CONSTANT D.C. I 4.0 | 7.0 Y COMPONENT .4 (- 1 | 14.0 | 28.0 .4 4 1 .999 .999 .998 .997 .998 .998 .9.9 9 .998 .999 .998 .998 .997 .997 .994 .993 .996 .996 .996 .996 .998 .997 .996 . 993 . 99 1 ,987 .985 .990 .993 . 99 1 .991 .994 .994 .990 .987 .981 .978 . 975 .982 . 988 .986 .986 .989 .988 .980 .980 .572 . 573 . 964 .967 .984 . 982 .982 .984 .580 . 974 . 977 .971 . 974 . 961 .965 .981 . 979 .980 . 982 .977 . 974 . 975 . 973 . 973 . 96 1 .965 . 979 . 98 1 . 97 2 . 976 .968 . 970 . 980 .9 70 .973 . 958 .960 .974 .979 .963 .977 .965 .965 CORRELATION SHIP. 0.25 | 0.50 COEFFICIENTS | 1.0 | 2. 0 _L L X_ -L 4 - LINEAR D.C. X COMPONENT J 4.0 | 7.0 | 14.0 | 28.0 .4 4 4 j A B C D E I J K M N P .997 .997 .997 .996 . 997 .997 .998 .997 .997 .997 .995 .992 .992 .99 1 .988 .993 .993 .993 .993 .994 .995 .989 . 579 . 579 . 978 . 969 .984 .984 . 984 . 985 . S84 .991 .571 .960 .962 . 958 .949 .967 . 973 .972 .978 .972 .983 .955 ,946 548 942 ,941 961 967 , 563 970 565 972 ,949 .945 . 946 . 94 7 .942 . 958 .964 .962 . 967 .960 . 966 . 946 946 955 940 94 8 962 959 953 959 953 962 946 .955 . 960 .942 .948 . 970 .954 .953 .953 ,9 55 .956 .958 i . x •J. ,j CORRELATION COEFFICIENTS - LINEAR D.C. Y COMPONENT | SHIPj 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | A j .998 . 993 .983 .968 | .953 | . 946 • 944 | .958 5 i .997 .992 | .979 j .955 .933 .934 • 94 0 .938 C .994 .985 | . 96 7 | .944 | .929 | .937 • 936 | . 943 D | .993 .981 | .96 1 .938 .9 14 . 911 • 913 .911 E i .996 .990 | . £75 .961 .9 32 , .931 • 934 .930 I , .996 . 990 | .982 | .970 | .962 .956 • 953 . 944 J , . 996 | .990 | . S78 . 966 , 9 56 | . 951 • 957 | .958 K .996 . 990 | . £76 .965 . £58 . 953 *> 943 | .926 M i . 998 | .994 | . 985 | .974 | .964 i . 963 • 955 | .958 N , .996 . 993 , 989 | .978 | . £66 .961 948 .946 P J .996 | .990 | .976 | .951 | . 939 | . 944 | • 942 .932 194 Appendix E Tiie raw d i f f e r e n c e means, d i f f e r e n c e v a r i a n c e s , r e s i d u a l v a r i a n c e s , and c o r r e l a t i o n c o e f f i c i e n t s f o r t h e h e a t f l u x e s w i t h no c o r r e c t i o n a p p l i e d . The d i f f e r e n c e means a r e i n Watts/m 2 w h i l e t h e e t h e r t e s t p a r a m e t e r s a r e d i m e n s i o n l e s s . 195 DIFFERENCE MEANS - SENSIBLE HEAT FLUX SHIP J 0. 25 I i 0. 50 1 1 1.0 I i 2. 0 1 • 4.0 i i 7.0 I i 14.0 I 28.0 A 0.8 1. 9 4. 1 7. 5 11.1 T 14.3 18. 1 — ! 21. 7 B | 0. 8 ( 1.9 | 4. 1 | 7.8 | 12.0 | 15.3 | 1 9.6 | 23. 2 C | 0. 2 | 0. 5 | 1.2 | 2. 5 | 3. 5 | 4.3 | 5.2 | 6. 1 C | 1. 1 2. 5 | 5.5 | 10. 4 15. 1 | 18.4 | 21.6 | 24. 3 | E | 0.4 | 0.8 | 1.5 | 3.0 | 4.8 | 6. 1 | 7. 1 | 8.0 I j 0.8 | 1.8 | 3.5 | 6. 0 | 8.9 | 11. 5 | 15.3 | 18.8 J j 0.4 | 1. 0 | 1.9 | 3. 3 | 4.8 J 6.0 | 8.0 | 9. 4 K j 0. 1 | 0. 3 | 0.4 | 0. 8 | 1. 1 | 1.8 J 2.8 | 3. 6 M j 0. 7 | 1.7 | 3.5 | 6.3 | 10. 2 | 13.4 | 18.0 | 22. 1 M | 0. 3 | 0.6 | 1.0 | 1. 8 | 3.0 | 3. 9 | 5.3 | 6. 6 £ 0. 1 1 0. 2 1 0.4 1 0.7 1.0 • 1.4 • 1.9 I 2. 2 ! DIFFERENCE MEANS - LATENT HEAI FLUX SHIPI 0. 25 1 0. 50 1 1.0 1 2.0 1 4.0 1 7.0 1 14.0 I 28.0 A | 1. 3 | 3. 2 | 6.8 | 12. 7 | 19.5 | 25.2 | 32. 3 | 39. 3 B j 1. 2 | 2. 8 | 6.0 | 11.6 | 18. 0 | 23.0 | 28.9 | 33. 7 C | 1. 2 | 2. 8 | 5.9 | 11.3 | 16.5 | 20.3 | 24.8 28.7 D j 3.4 j 7. 9 | 16. 8 | 31.2 | 45. 8 | 55.9 6 5. 9 | 74. 4 E j 2.7 j 5. 9 | 11. 9 | 23. 1 | 37. 1 | 48.2 | 58.8 | 68.5 I | 1. 6 | 3.7 | 7.6 j 13.7 | 20.4 | 26.7 | 35.5 | 43.6 J | 1. 2 3. 1 | 6.3 | 11.5 | 17. 1 | 22.0 29. 2 | 34. 3 K 1. 2 2. 8 | 5.5 j 10. 3 | 15.6 22.6 | 33. 2 | 42.0 M | 1.2 | 3.0 6.4 | 12. 2 19.7 | 26.5 | 35.3 | 43.0 N j 2. 1 | 4. 1 | 7.2 | 12.8 | 2 1.3 | 28.3 | 38.4 | 46.4 P i 0. 7 1 1.7 1 3.7 1 7. 1 1 10. 6 • 13.6 16. 9 I 19.3 ! DIFFERENCE VARIANCES - SENSIBLE HEAT FLUX SHIPI 0. 25 1 0. 50 1 1.0 1 2.0 i 4.0 1 7.0 1 14.0 I 28.0 A | .025 j .059 | . 129 | .267 i .401 | . 536 | .652 | .774 B j .024 I .059 | .118 | .222 i . 368 . 449 | . 574 | . 707 C j .037 1 .084 . 175 | . 3 14 i . 433 | .501 | . 594 | . 703 D j .028 | .065 | . 146 | .282 i .411 | .487 .549 | .658 E j .034 .073 . 162 .296 i . 164 | . 574 | . 664 | .729 I | .026 | .064 . 124 | • 222 i . 384 | .465 | .602 | .7 11 J j .024 | .06C | . 123 | .217 i .330 | .418 . 524 | .589 K | .029 .068 | . 141 | .240 i . 344 | . 448 | . 608 | .675 M | .025 j .057 | . 121 | .2 18 i .371 | .472 | .620 | .761 N j .029 I .055 | .088 | . 1 56 i . 2 50 | .307 | . 439 | . 567 P 1 .026 1 .070 . 154 1 .276 • . 392 . 475 • .613 .683 ) 1 ! 1 196 i DIFFERENCE VARIANCES - LATENT HEAT FLUX — — — — . j . — SriXi? | 0. 25 +-1 0. 50 1 1.0 "T 1 1 2. 0 ~ r -I i 4.0 I I 7.0 1 i 14.0 1 » —_ _ _ -—• mm 28. 0 A | .0 16 | .039 + -.088 . 1 97 +- .314 . 436 T . 558 . 688 6 j .019 | .044 j . 093 | .184 j .216 | . 393 J .508 j .627 C i .027 | .059 | . 127 | .244 | .36 1 . 430 I . 505 | . 560 D | .020 | .046 | . 108 | . 231 | . 355 1 . 425 | .492 | .600 E J .018 .039 | .096 | .195 | .331 | .424 . 502 | .539 I J .0 13 | .034 | .072 | . 148 j .270 I .312 | . 414 | .502 J | .0 1 4 j .033 | . 076 | .152 | . 224 1 .268 | .322 | . 388 K j .020 j .045 | . C95 | .168 j . 249 | .348 .561 .644 M J .0 15 | .034 | .075 | . 140 j . 276 1 .347 | . 479 | .637 N J .007 | .009 | .008 | .012 | .008 | -.049| -.070| -. 239 P 1 .017 1 .046 1 .099 .20 5 .312 1 .365 I . 489 1 . 573 _ _ _ _ _ _ L_ RESIDUAL VARIANCES - SENSIBLE HEAT FLUX SHIP | 0. 25 1 0. 50 1 1.0 1 2. 0 4.0 1 7.0 1 14.0 1 28. 0 A 1 .004 | .0 10 | .032 | .075 | . 130 | .215 | . 299 1 .432 B | .003 .008 | .023 | .057 | . 102 I . 135 | .20 1 | . 282 C I .005 | .013 | .033 | .069 .113 I . 145 | . 197 | . 267 D J .004 | .012 J . 036 | .079 | .124 | .162 | . 197 | . 262 E | .005 | .011 | .032 j .083 . 165 | .230 | .315 | .415 I 1 .005 | .012 | .031 j .07 1 | . 12 1 1 . 185 | . 308 | .425 J i .004 j .012 | . 027 | .054 | .C86 I .126 | . 192 . 249 K | .003 j .008 | .019 | .04 1 | .078 I .111 | .215 | . 27 1 M i .004 | .0 12 J . 030 | .067 | . 140 | .185 .323 | .457 N | .006 | .0 13 | .024 | .057 | . 1 17 I . 154 | . 271 | . 464 P . .003 1 .0 10 1 .029 1 .060 .096 • .129 .208 1 . 232 J ! RESIDUAL VARIANCES - LATENT HEAT FLUX Si i I P | 0. 25 1 0. 50 1 1.0 1 2. 0 i 4.0 1 7.0 1 14.0 1 28. 0 A { .005 j .014 j . 046 | .108 i . 187 .289 | . 382 I .498 B 1 .004 | .0 12 | . 037 | .087 i .145 | .180 | . 245 | . 295 C I .005 | .015 | .041 j .087 i . 135 j . 175 | .224 | . 273 D j .006 j .018 . 051 | .111 i . 169 I .213 | . 264 | .333 E J .006 | .014 | . 043 | .124 i . 243 | .347 | . 449 | .573 1 J .006 | .017 | . C47 | .107 i . 180 .255 | .408 | .552 J | .004 | .0 13 .035 | .08 1 j . 134 | . 185 | . 292 | .385 K | .004 j .010 | .025 | .062 i . 115 I .188 | . 347 | . 473 M | .005 I .016 . 044 . 102 i .215 I .278 | . 437 | . 555 N j .006 | .012 | .031 | .093 i .229 I .332 | .661 | 1. 16 P 1 .003 1 .010 1 .03 1 .073 1 . 116 j . 150 1 . 203 ] .210 197 1 I i CORRELATION COEFFICIENTS - SENSI r r~ i SHIP J • j 0. 25 T 1 _i 0.50 | 1.0 I 2. 0 | 4.0 I 7.0 1 r 1 A j .998 T .995 | . 585 | .968 | _ ____________ I .949 I .917 i 8 | . 999 | .996 | .990 I .976 I . 963 | . 954 1 C j .998 | .994 | . 987 I .976 | . 965 I .959 1 D 1 .998 j .994 | .983 | .967 i .954 | .943 1 E 1 .997 | .995 | . 987 I .966 I .936 | .916 1 I i .998 | .994 | . 986 I .968 1 c e i 1 . —/ J | .923 1 J I .998 | .995 | . 988 J .97 7 | .567 j .954 1 K i .999 | .996 | .993 | .986 I . 574 I .970 J M | .998 | . 994 | . 986 I -970 | .939 i .924 I N 1 .997 | .994 | . 989 I .972 | .943 | .924 1 P 1 .999 J .995 | . S88 | .978 | .570 | .963 .889 . 938 .948 . 934 . 880 .86 4 . 930 . 940 , 85 8 . 86 1 . 948 .835 . 933 .945 .923 . 822 .803 .906 . 924 .801 .736 .964 !• +• SHIPJ 0.25 j. +- ' CORRELATION | 0.50 | 1.0 A | .998 | .993 | .977 | .946 | B i .998 .994 .982 .957 | C i .997 .993 .980 j .960 | D .997 .991 j . 975 | .946 | E , .997 | .993 | . 979 .937 | I i .997 | .992 . 576 .945 | J .998 .994 | .983 | .959 | K i .9 98 .995 . 588 . 970 | M . 998 .992 | . 578 | . 948 | N .997 .994 .984 .953 | P .998 .995 .985 .965 | COEFFICIENTS -I 2. 0 | 4.0 .905 .931 . 541 .919 .872 .507 .532 .544 .887 . 885 . 547 LATENT 4 7.0 J 4 . 849 .916 .924 . 898 .810 .864 . 904 .907 .851 .838 .932 HEAT FLUX 14.0 | 28.0 .797 . 889 . 904 .872 . 744 .770 . 84 1 .824 . 751 .681 .915 . 7 29 .883 .880 .843 .654 .671 .784 .740 .67 1 .483 .93 1 198 Append ix F P a r t I - The i n d i v i d u a l l y c a l c u l a t e d C n * v a l u e s f o r t h e h e a t f l u x e s . 0.0 i n d i c a t e s no d a t a . 199 f +• S P E E D | j. +. 0. 4 | 1 . 6 | 3 -4 | 5 . 5 | 8 . 0 | 1 0 . 8 | 1 3 . 9 | 17. 21 20 . 6 | 2 4 . 5 | 2 8 . 5 | 3 3 . 5 | 3 5 . 0 J +• 0 . 2 5 | STATION 0. 50 | A - S E N S I B L E -4 4 I 2 . 0 | HEAT FLUX 4 . 0 | 7 . 0 | + , 1 4 . 0 | +-1.0 2 8 . 0 6. 6 1 1.88 1. 19 1.08 1.04 1 .03 1.02 1. 0 1 1. 0 1 1 .01 1. 0 1 1. 0 1 1. 0 1 | 6 . 7 2 | 6 . 5 8 | 24 . 10| 0 . 0 | 20 . 29 | 2 9 . 07 | i K r , 1 ^ . — 1 6 . 9 1 9. 90 | 14.501 1 2 . 9 0 | 15 .451 1 1-47 | 2 .21 | 2 . 6 5 | 3 . 2 5 | 3 .82 | 3 . 9 8 | I 1. 2 1 | 1.4 1 1.74 | 2 .0 2 | 2 . 3 8 | 2 . 6 9 | I 1.10 j 1.22 | 1.40 | 1.61 | 1.85 | 1 .98 | | 1 .06 | 1. 13 1.24 | 1 .34 | 1 .42 | 1 .60 | I 1.04 j 1.09 1. 18 | 1.26 | 1.34 | 1 .29 | | 1 .03 1.06 | 1 .12 | 1. 18 | 1 .18 | 0 . 0 | | 1.02 1.06 1. 1 1 I 1. 17 | 1.01 | 0 . 0 | | 1. 02 1.05 | 1. 10 | 1 .09 | 0 . 0 | 0 . 0 | | 1.02 1.03 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | | 1. 01 0 .0 1 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | | 0 . 0 0 .0 0. 0 | 0 . 0 | 0 . 0 | 0 . 0 | 3 2 . 2 6 1 3 . 6 5 4. 29 2 . 6 7 2 . 0 1 1. 61 1. 43 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0. 0 — I I- 4-S P E E D j I- 4-0 .4 | 1 . 6 | 3 .4 | 5 . 5 | 8 . 0 J 10.81 1 3 . 9 | 1 7 . 2 | 20 . 81 24 . 51 2 8 . 5 | 1 3 3 . 5 | 35 .01 1 4' 0 . 2 5 J STATION B -0 . 5 0 1 1.0 4-S E N S I B L E -4 h I 2 . 0 | HEAT FLUX 4 .0 | 7 . 0 13 .02 1 1.49 3. 55 2 .08 1. 59 1.33 1.21 1. 16 1.06 0 .0 0 . 0 0 . 0 0 . 0 4-14 .0 1 - 4 -28 . 0 4. 30 2. 6 5 1. 19 1 .07 1.04 1.02 1 .02 1. 0 1 1. 0 1 1.0 1 1.01 1.01 1 .00 8 . 4 4 2 . 6 7 1 .48 1. 19 1 .09 1.06 1 .03 1.03 1.02 1. 02 1 .03 1.02 0 . 0 7 .80 6 . 1 0 1.98 1.42 1 .20 1.12 1.06 1.05 1 .05 1.05 1.04 1.0 1 0 . 0 18. 54 7. 18 3. 01 1.75 1. 34 1. 23 1. 14 1. 09 1. 07 1.04 1. 06 1.02 0. 0 3 1 . 3 3 12 .52 3 .65 2 .34 1.62 1. 41 1.24 1. 18 1 .07 0 . 0 0 . 0 0 . 0 0 . 0 4 1 . 8 4 1 1. 15 3 . 9 4 2 . 4 2 1 .82 1.51 1. 22 1 .11 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 3 0 . 6 3 10. 2 1 4. 19 2. 6 4 1. 84 1.64 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0. 0 0 . 0 STATION C - S E N S I B L E + i 4-0 . 5 0 | 1.0 I 2 . 0 I HEAT F L U X 1 4 . 0 j 4 2 6 . 05 1 4 . 4 5 3 . 30 2 . 3 4 1 .73 1 .53 1. 30 1. 28 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 I- 4-SPEEDJ r 4 0. 4 J 1 . 6 | 3 . 4 1 5 .51 8 . 0 | 10.61 13.91 17.21 20 . 8 | 24 .51 28. 5 | 33 .51 35 .01 4-0 . 2 5 | 4 . 0 | 7 . 0 | 2 8 . 0 -4-6. 94 1 .96 1. 25 1 .08 1.05 1 .03 1.02 1. 02 1. 0 1 1.0 1 1. 0 1 1. 0 1 1.0 1 9 . 2 6 3. 15 1. 57 1. 25 1. 1 1 1 .07 1.05 1.04 1.03 1. 02 1.02 1.0 1 1.01 27. 16 5 .47 1.89 1.4 1 1 .29 1.14 1.10 1.08 1.06 1.04 1.04 1.05 0 .0 2 1 . 4 1 7 . 6 9 2 .44 1. 61 1.41 1. 25 1. 17 1. 14 1. 13 1. 10 0. 0 0. 0 0 . 0 18 .93 7 . 12 2 . 7 7 1 .S9 1. 53 1. 33 1.27 1 .19 1. 1 1 0 . 0 0 . 0 0 . 0 0 . 0 1 8 .88 10. 14 3 . 2 3 2 . 0 9 1.63 1.41 1.29 1 .19 1.32 0 . 0 0 . 0 0 . 0 0 . 0 226 . 3 1 0 . 5 7 3 . 89 2. 23 1. 79 1.68 1. 40 0 . 0 0 . 0 0 . 0 0. 0 0. 0 0 . 0 200 i ; • • ~i j STATION D - SENSIBLE HEAT FLUX | SPEED! 0.25 | 0.50 j 1.0 J 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | 1 0.41 3.35 | 10.33| 18.60| 21-8 71 32- 071 29.001 6 0- 111 45.0 7) | 1.6| 1.9S | 5.35 | 6.17 I 1 1. 251 9. 32 | 14. 151 12.39 J 15.54) 1 3.41 1.24 | 1.61 | 2.20 | 3.03 | 3.39 | 3.42 1 3.69 1 3.88 1 | 5.51 1.10 | 1.20 | 1.55 1 1. 83 | 2. 1 1 1 2. 29 1 2. 49 | 2.67 1 1 8.0J 1.04 | 1.11 | 1.24 I 1.44 I 1. 64 ( 1 - 74 | 1.78 | 1.94 | |10.81 1.03 | 1.06 | 1.13 | 1.29 | 1.39 | 1.50 | 1.51 | 1.66 | 113.91 1.02 I 1.05 | 1.11 I 1.20 | 1.30 I 1.34 | 1.41 | 1.43 | 117.21 1.02 J 1.03 1 1.07 | 1.15 | 1.20 | 1.21 1 1.28 1 0.0 | 1 20.81 1. 0 1 1 1.03 | 1.06 | 1.08 | 1.14 | 1.12 | 1.17 | 0.0 | | 24. 51 1.01 J 1.02 | 1.04 | 1.09 1 1.14 | 0.0 | 0,0 | 0.0 | |28.5| 1.01 | 1.03 | 1.04 I 1.13 | 0.0 1 0.0 1 0.0 | 0.0 1 133.51 1.01 | 1.02 | 1.11 | 0.0 | 0.0 | 0.0 | 0.0 1 0.0 | |35.0| 1.01 J 1.05 I 0.0 I 0.0 | 0.0 I O.O J 0.0 | 0.0 I | 1 —1 X L ,. I 1 L . I _J 1 STATION E - SENSIBLE HEAT FLOX I SPEED! 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | | 0.41 4.61 | 4.13 | 5.23 | 9.3 1 | 19. 131 19. 401 3 1. 86| 27. 391 | 1.6| 1.61 I 2.58 J 3.47 | 8.29 | 10.231 8.91 | 9.53 J 11.96| 1 3.4J 1.16 | 1.27 | 1.59 | 2.32 | 2.77 | 3.30 | 3.42 | 3.82 | 1 5.51 1.05 | 1.13 | 1.27 | 1.43 | 1.82 | 1.87 | 2.09 | 2.47 | I 8.0 | 1.03 | 1.06 1 1.15 | 1.30 | 1.45 | 1.59 | 1.67 | 1.73 | 110.81 1.03 | 1.05 | 1.11 I 1.19 | 1.31 | 1.38 | 1.43 | 1.52 | J13.91 1.02 | 1.03 | 1.08 1 1. 16 | 1.24 | 1.30 | 1.33 | 1.29 | 117.2| 1.01 J 1.03 | 1.07 | 1.09 | 1.20 | 1.28 | 0.0 | 0.0 | I 20.81 1.01 | 1.03 | 1.07 | 1.16 | 1.17 J 0.0 | 0.0 | 0.0 | 124.51 1.0 1 1 1. 03 | 1.06 | 1.14 I 0.0 | 0.0 | 0.0 | 0.0 | 128. 51 1. 0 1 1 1.02 1 0.0 | 0.0 | 0.0 1 0.0 | 0.0 | 0.0 | 133.51 1. 06 | 1.25 | 1.07 ( 0.0 I 0.0 | 0.0 | 0.0 J 0.0 | 135.01 1.01 | 1.02 J 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | J._ 1 J J I , I J L L , _| 1 STATION I - SENSIBLE HEAT FLUX | SPEED| 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | 1 0.4J 6.84 | 11.56| 4.99 j 19.0 5T 2 8 . 4 3 } 0.0 j 0.0 t 0.0 1 1.61 2.78 I 3.28 | 6. 51 1 6. 75 1 9.96 | 12.901 12. 86| 14.61| I 3.4J 1-31 I 1.61 | 2.25 | 2.96 1 3.27 | 3.90 | 4.11 \ 4.83 | I 5.51 L U 1 1.22 I 1.42 I 1. 79 1 2.09 | 2.37 1 2.75 1 2. 79 | 1 8.01 1-04 | 1.10 | 1.22 I 1.39 | 1.56 | 1.62 1 1.80 1 1.88 | | 10.81 1.03 J 1.07 I 1.13 J 1.20 | 1.34 | 1.42 1 1.51 | 1.46 | 113.9| 1.02 | 1.04 | 1.08 | 1.14 | 1.21 | 1.27 | 1.32 | 1.50 | 117.21 1.01 | 1.03 I 1.06 I 1.10 I 1.25 | 1.22 1 1.33 J 0.0 | 120.81 1.01 | 1.03 J 1.06 | 1.13 1 1.09 | 1.29 J 0.0 | 0.0 ( I 24. 51 1.01 I 1.03 I 1.05 1 1. 06 | 1.21 | 0.0 | 0.0 | 0.0 | 128.51 1. 0 1 1 1.05 | 1.04 J 1.08 | 0.0 | 0.0 | 0.0 | 0.0 1 133.5| 1.01 I 1.02 I 0.0 1 0.0 1 0.0 | 0.0 | 0.0 1 0.0 | J35.01 1.00 J 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 I 0.0 | L X 201 I j. + . SPEED| j. + . 0.4 1.6 3.4 5.5 8.0 10.8 13.9 17.2 20.8 24. 5 | 28- 51 33.5j 35.0 4-0.25 | STATION J -0.50 | 1.0 SENSIBLE •4 4-I 2. 0 | -4-HEAT FLUX 4.0 | 7.0 | 14.0 | 28. 0 5. 0 5 1.48 1. 20 1. 10 1. 04 1. 02 1.0 1 1.0 1 1.0 1 1. 0 1 1.0 1 1.0 1 0. 94 5.68 3. 13 1. 5 1 1. 20 1.09 1.06 1.04 1.03 1.02 1. 03 1.02 1. 00 0. 0 5.7 1 3.70 2.06 1.40 1. 19 1.11 1.08 1.05 1.05 1.05 1.03 0.0 0.0 24. 94 8. 62 2.59 1. 59 1. 35 1. 20 1. 12 1. 1 1 1. 09 1. 07 1.02 0. 0 0. 0 108.0 9.36 3. 25 1.92 1.44 1. 27 1.22 1. 17 1. 13 1.04 0.0 0.0 0.0 0. 0 10.58 3. 24 2.09 1.60 1, 35 1. 26 1.23 1. 10 0.0 0.0 0.0 0.0 0.0 16.31 3.89 2. 17 1.67 1.45 1.3 1 0.0 0.0 0.0 0.0 0.0 0.0 26. 18 22.76 4. 30 2. 42 1. 78 1.51 1. 37 0. 0 0.0 0.0 0. 0 0. 0 0.0 L X . I »- 4-SPEED i I — r - 4 -0. 4 1. 6| 3.4 5. 5| 8-0 | 10.8 13. 9, 17. 2i 20.8 24. 5| 28. 5 i 33. 5 35.0 0. 25 { 4 2. 94 1.49 1. 13 1. 04 1. 02 1.02 1. 01 1. 0 1 1. 0 1 1. 01 1. 0 1 1.00 0.0 STA HON K - SENSIBLE 0.50 | 1.0 | 2.0 | HEAT FLOX 4.0 | 7.0 | 3. 9 4 2. 10 1. 27 1. 12 1. 06 1.04 1. 03 1.03 1. 02 1.02 1.04 1.01 0.0 10. 23 3.59 1.49 1.21 1. 10 1.09 1.07 1.05 1.04 1.11 0.0 0.0 0.0 4. 57 4. 66 1.70 1.40 i i . 19 1. 12 1. 14 1. 08 1. 10 1. 15 0. 0 0. 0 0.0 20. 15 7.29 2.62 1.49 1.32 1. 16 1. 16 1. 13 1.18 0.0 0. 0 0.0 0. 0 24.91 4. 10 2. 87 1.77 1.35 1.24 1. 19 1. 10 0.0 0.0 0.0 0.0 0.0 4 14.0 | 4 1 187. 1 1.02 3.01 1.77 1.46 1.36 1.22 0.0 0.0 0.0 0.0 0.0 0.0 1 28. 0 - H 6. 54 10. 39 3. 78 1. 83 1. 44 1. 35 0.0 0. 0 0. 0 0. 0 0.0 0. 0 0. 0 I r 4-SPEEDJ J- 4-0.4 1.6 3.4, 5. 5 i 8.0 10.8 13.9 17.2 20.8 24.51 28.5, 33.5 35.0 STATION M -25 | 0.50 | 1.0 17 38 12 07 03 02 0 1 0 1 0 1 0 1 01 00 02 2. 50 2.79 1.37 1. 17 1.07 1.05 1.03 1.03 1.02 1.02 1.01 1. 03 0.0 4. 12 5.08 1.82 1.30 1.18 1. 10 1.07 1.05 1.05 1.05 1.04 0.0 0.0 SENSIBLE 4 4 I 2.0 | 4 4 9. 7 1 6. 86 2. 28 1. 50 1. 32 1. 19 1. 10 1. 09 1. 10 1. 09 0. 0 0. 0 0. 0 HEAT FLOX 4.0 | 7.0 | 18.8 1 11.68 3. 21 1. 83 1.45 1.31 1. 19 1. 15 1.03 0.0 0.0 0.0 0.0 19.02 11.55 3.05 2.07 1.60 1.35 1.23 1. 16 1. 12 0.0 0.0 0.0 0.0 4 14.0 | .. + 27. 65 13.33 3.79 2.37 1.81 1. 34 1.22 0.0 0.0 0.0 0.0 0.0 0.0 -I 28. 0 1 23.90 12.44 3. 95 2. 58 1.91 1. 38 1. 50 0.0 0.0 0. 0 0.0 0. 0 0. 0 20 2 r 1 -1 1 1 STATION N - S E N S I B L E HEAT FLOX I S P E E D | 0 . 2 5 | 0 . 5 0 | 1 . 0 | 2 . 0 | 4 . 0 | 7 . 0 | 1 4 . 0 | 2 8 . 0 | I- + — — + — — — 4 — — - + + + + — +- i j 0 . 4 | 5 . 0 9 | 2 . 2 3 | 4 . 7 6 | 1 0 . 3 41 1 0 . 69 J 2 0 . 2 . 9 | 1 5 . 8 4 1 3 2 . 64 J | 1 . 6 J 1 . 4 7 | 2 . 0 1 | 2 . 7 6 | 3 . 9 2 | 5 . 9 8 j 5 . 2 2 | 7 . 6 8 | 9 . 3 6 | | 3 . 4 J 1 . 0 7 | 1 . 2 0 | 1 . 3 3 | 1 . 6 8 | 2 . 0 3 | 2 . 2 5 | 2 . 4 0 | 3 . 13 | J 5 . 5 | 1 . 0 4 | 1 . 0 7 | 1 . 1 3 j 1 . 2 1 | 1 . 4 1 I 1 . 4 6 | 1 . 5 8 | 1 . 8 3 | | 8 . 0 j 1 . 0 2 | 1 . 0 4 | 1 . 0 7 | 1 . 1 2 | 1 . 1 9 | 1 . 2 3 | 1 . 2 7 | 1 . 3 4 | 1 1 0 . 8 1 1 . 0 1 | 1 . 0 3 j 1 . 0 4 | 1 . 0 9 | 1 . 1 2 | 1 . 1 3 | 1 . 1 4 | 1 . 3 6 | | 1 3 . 9 | 1 . 0 1 | 1 . 0 2 | 1 . 0 5 | 1 . 0 6 | 1 . 0 8 | 1 , 0 5 | 0 . 0 J 0 . 0 | | 1 7 . 21 1 . 0 1 | 1 . 0 3 | 1 . 0 4 | 1 . 0 6 1 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | | 2 0 . 8 | 1 . 0 1 | 1 . 0 2 | 1 . 0 9 I 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 12 4 . 5 J 1 . 0 0 | 1 . 0 2 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | | 2 8 . 5 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 j 0 . 0 | 0 . 0 | | 3 3 . 5 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 1 3 5 . O i 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 1 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | J. L J. L 1 1 , L . L . I ^ 1 STATION P - S E N S I B L E HEAT FLUX I S P E E D ! 0 . 2 5 | 0 . 5 0 1 1 . 0 | 2 . 0 { 4 . 0 | 7 . 0 | 1 4 . 0 | 2 8 . 0 | | 0 . 4 t 6 . 3 8 | 2 . 4 5 | 7 . 1 3 | 3 5 . S7| 2 0.6s| 3 1 . 3 21 0 . 0 t 0 . 0 | 1 1 . 6 | 1 . 4 8 | 1 . 9 1 I 4 . 3 6 | 9 . 5 6 | 9 . 9 3 I 9 . 3 4 | 1 3 . 9 4 J 0 . 0 | I 3 . 4 1 1 . 1 4 I 1 . 4 7 1 1 . 7 5 | 2 . 27 1 2 . 6 6 | 3 . 1 8 1 3 . 3 4 | 3 . 4 9 | 1 5.51 1 . 0 6 I 1 . 1 8 | 1 . 3 9 1 1 . 59 | 1 . 8 8 | 2 . 1 4 | 2 . 2 6 | 2 . 2 8 | | 8 . 0 | 1 . 0 4 I 1 . 1 0 I 1 . 1 9 | 1 . 4 1 I 1 . 55 1 1 . 56 | 1 . 7 8 | 1 . 8 8 1 1 1 0 . 8 J 1 . 0 2 | 1 . 0 6 | 1 . 1 2 | 1 . 2 2 | 1 . 3 1 J 1 . 3 9 | 1 . 4 9 | 1 . 5 1 | 1 1 3 . 9 1 1 . 0 2 I 1 . 0 4 I 1 . 1 1 I 1 . 1 5 1 1 . 2 3 | 1 . 3 0 | 1 . 3 7 | 1 . 2 0 | 1 1 7 . 2 1 1 . 0 1 | 1 . 0 3 | 1 . 0 7 | 1 . 1 6 I 1 . 1 4 J 1 . 1 4 | 0 . 0 | 0 . 0 | I 2 0 . 81 1 . 0 1 1 1 . 0 3 I 1 . 0 6 I 1 . 0 9 | 1 . 1 3 | 0 . 0 | 0 . 0 | 0 . 0 | 124.51 1 . 0 1 J 1 . 0 2 | 1 . 0 4 | 1 . 0 7 J 0 . 0 I 0 . 0 I 0 . 0 | 0 . 0 | i 2 8 . 51 1 . 0 0 J 1 . 0 2 1 1 . 0 5 1 0 . 0 | 0 . 0 ( 0 . 0 | 0 . 0 | 0 . 0 | 1 3 3 . 5 1 1 . 0 1 I 1 . 0 1 I 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 J 0 . 0 | 0 . 0 | 135. 01 1 . 00 I 1 . 0 3 I 0 . 0 I 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 1 0 . 0 | i I I I I I I I I I J I , L J L I I I L -J I STATION A - LATENT HEAT F I U X | SPEED1 0 . 2 5 I 0 . 5 0 | 1 .0 1 2 . 0 | 4 . 0 1 7 . 0 1 1 4 . 0 1 2 8 . 0 | I 0 . 4 I 4 . 32 1 4 . 64 1 4 . 6 7 | 2 3 . 081 0 . 0 | 1 5 . 9 1 | 2 9 . 241 3 3 . 0 8 | I 1.61 1 . 6 9 | 2 . 0 4 | 4 . 1 1 1 6 . 4 2 | 1 0 . 9 31 1 1 . 5 1 | 1 2 . 4 21 1 0 . 101 1 3 . 4 1 1 - 12 1 1 . 3 4 | 1 . 8 8 I 2 . 4 1 | 2 . 9 0 I 3 . 6 0 | 3 . 8 1 | 3 . 8 9 | I 5 . 51 1 . 0 6 I 1 . 15 I 1 . 3 0 I 1 . 6 3 1 1 . 9 5 | 2 . 2 3 J 2 . 5 5 | 2 . 4 3 | 1 8 . 0 | 1 . 0 3 | 1 . 0 8 | 1 . 1 7 I 1 . 3 4 | 1 . 5 2 | 1.75 j 1 . 8 9 | 1 . 9 4 | 1 1 0 . 81 1. 02 1 1 . 05 1 1 . 10 I 1 . 2 1 I 1 . 3 3 | 1 . 4 1 | 1 , 5 5 j 1 . 5 5 | | 1 3 . 9 | 1 . 0 1 | 1 . 0 3 | 1 . 0 7 I 1 . 1 6 I 1 . 2 4 | 1 . 3 4 | 1 . 3 5 | 1 . 3 6 | | 17 .21 1 . 0 1 I 1 . 0 3 | 1 . 0 6 I 1 . 1 2 I 1 . 1 7 | 1 . 2 1 | 0 . 0 | 0 . 0 | 120.81 1 . 0 1 | 1 . 0 2 | 1 . 0 6 | 1 . 1 0 | 1 . 1 7 1 1 . 0 9 | 0 . 0 | 0.0 | I 2 4 . 51 1 . 0 1 I 1 . 0 2 J 1 . 0 4 I 1 . 0 9 | 1 . 1 0 | 0 . 0 | 0 . 0 1 0 . 0 | 128.51 1 . 0 1 | 1 . 0 1 | 1 . 0 3 I 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 I 0 . 0 I (33.5! 1 . 0 1 i 1 . 0 0 I 0 . 0 I 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 I 0 . 0 ] 1 3 5 . 0 1 1 . 00 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 | 0 . 0 J 0 . 0 J 0 . 0 | 1 x j 203 i I- i-SP£ED| I- +• 0. 4 1.6 3. 4 5. 5 8.0 10.8 13.9 17.2 20.8 24.5 28. 5 I 33. 5 35.0 STATION B - LATENT HEAT FLOX 4 + 4 4 4 0.25 j 0.50 | 1.0 | 2.0 | 4.0 | 7.0 4-14.0 J —I 28. 0 4. 0 5 2. 36 1. 14 1. 05 1.03 1. 02 1. 0 1 1. 0 1 1. 0 1 1. 0 1 1. 0 1 1. 0 1 1.00 8. 10 2.48 1.37 1. 14 1.08 1. 05 1.03 1.03 1. 02 1. 02 1.03 1.02 0.0 11 4. 0. .91 48 82 37 18 1 1 07 05 05 05 02 00 0 11 7. 2. 0. .84 27 54 67 34 21 14 09 08 03 03 0 1 0 12.61 9.23 3.29 1.98 1. 55 1.33 1.21 1. 16 1.07 0. 0 0.0 0.0 0.0 27. 46 10.31 3.32 2. 22 1.60 1.39 1.24 1. 17 1.05 0.0 0.0 0.0 0.0 38. 01 1 1. 51 3.70 2. 33 1.75 1.47 1.20 1.12 0.0 0.0 0.0 0.0 0.0 j. + . SPEED, j. 4. 0.4 J 1.6| 3.4 | 5. 51 8.01 10. 81 13.9| 17.2| 20.81 24. 51 28.51 33. 5( 35.01 4. 0.25 J STATION C - LATENT HEAT FLUX 4 4 L 4 0.50 1 1.0 | 2.0 | 4.0 | 7.0 4 4 4 4 -4-1 4. 14.0 I 6.6 1 1. 96 1. 17 1.07 1.04 1. 02 1.02 1.02 1.01 1.0 1 1.0 1 1. 0 1 1.0 1 4. 97 2.48 1.4 1 1. 18 1. 09 1. 06 1.04 1.03 1.03 1.02 1. 02 1.0 1 1. 02 18 4. 0. .51 59 75 35 21 12 08 07 05 03 03 03 0 18 6. 2. 0. 0. 0. .02 59 36 60 37 23 16 13 09 07 0 0 0 2 1.95 8.00 2.62 1.87 1.53 1.32 1.24 1. 17 1. 12 0.0 0.0 0.0 0. 0 24.50 1 1.03 3.06 2. 1 1 1.63 1.40 1.28 1.20 1.21 0.0 0.0 0.0 0.0 24.96 13. 10 3.39 2. 29 1.75 1.49 1.31 1.25 0.0 0. 0 0.0 0.0 0.0 j. 4. SPEED 1 J- +-0.4 1.6 3.4 5. 51 8.0, 10.8 13.9 17.2, 20.8 24. 5 i 28. 51 33. 5 i 35. 0 STATION D - LATENT HEAT FLUX 4 4 4 4 4 25 I 0.50 I 1.0 | 2.0 | 4.0 | 7.0 I 4-14.0 | 03 84 15 06 03 02 02 0 1 0 1 0 1 0 1 0 1 0 1 7.33 3. 34 1.36 1. 14 1.08 1. 05 1.04 1.03 1.02 1.02 1.02 1. 02 1.04 14. 5: 4.75 1.8 1 1.34 1. 18 1.1 1 1.09 1.07 1.05 1.04 1.04 1. 10 0.0 17.60 7. 37 2. 57 1. 62 1. 36 1. 26 1. 18 1. 14 1. 09 1.08 1. 1 1 0. 0 0.0 25.60 8.43 3. 10 1.95 1. 56 1.38 1. 28 1.21 1. 13 1. 17 0.0 0. 0 0.0 34.81 11. 52 3. 12 2.07 1.68 1.48 1. 32 1.21 1. 12 0.0 0.0 0.0 0. 0 55.75 11.38 3. 45 2. 26 1.76 1.52 1.40 1.29 1. 17 0.0 0.0 0.0 0.0 J 204 STATION 0. 50 | +-2. 41 1.63 1. 12 1.06 1.04 1.03 1.03 1.02 1. 02 1.02 1. 00 1. 17 1.01 E - LATENT HEAT FLOX +. 14.0 | 4 32. 10 8.01 2.74 1.89 1.67 1.50 1.37 0.0 0.0 0.0 0.0 0.0 0.0 -I 28.0 i 21. 24 9. 20 2.50 2. 13 1. 68 1. 54 1. 36 0.0 0. 0 0.0 0. 0 0.0 0. 0 4 -SPEEDi 0.4 | 1.6| 3.4 | 5. 5| 8.0| 10. 8| 13.91 17.21 20.81 24. 51 28. 5 | 33. 5 J 35.01 1 4 0. 25 | 4. 5 2 1.28 1. 07 1.03 1.02 1. 02 1.0 1 1.0 1 1.0 1 1. 0 1 1.0 1 1. 05 1.0 1 1.0 1 2.0 4 .4 4 +-1 4.0 I 7.0 1 . 4 4 4-3.97 2.31 1.31 1.14 1.09 1.08 1.06 1.05 1.05 1.05 0.0 J.07 0.0 6. 11 4. 2 1 1.74 1. 32 1. 22 1. 17 1. 15 1. 10 1. 14 1.09 0.0 0. 0 0. 0 16. 51 7.24 2.24 1. 63 1.40 1.31 1. 26 1.22 1. 19 0.0 0.0 0.0 0.0 18.77 7.98 2.74 1.77 1.57 1.42 1.35 1. 24 0.0 0.0 0.0 0.0 0.0 4-SPEED1 4-0.41 1.61 3.4| 5. 5| 8.01 10.81 13.9| 17.21 20.81 24.5| 28. 51 3 3 . 5 1 3 5 . OJ I 0.25 ] STATION I - LATENT HEAT FLUX 4 4 4 4--0.50 I 1.0 | 2.0 | 4.0 | 7.0 -4-I -4-14.0 j 4 -28. 0 -4-4. 2 1 1.95 1.18 1.07 1.03 1. 02 1.0 1 1.01 1. 0 1 1. 0 1 1. 01 1. 0 1 1. 00 7.69 1.92 1.40 1. 16 1.07 1.05 1.03 1.03 1.02 1.02 1.03 1. 02 0. 0 5.92 4.97 1.87 1.32 1.17 1. 10 1.07 1.06 1.05 1.05 1.04 0.0 0.0 21 6. 2. 0. 0. .42 62 39 63 34 19 14 1 1 13 07 08 0 0 25.30 9.29 2.91 1.90 1. 52 1.32 1. 22 1. 22 1. 12 1.19 0.0 0. 0 0.0 0. 0 11.31 3.21 2.09 1. 58 1.39 1.28 1. 23 1. 28 0.0 0.0 0.0 0.0 0. 0 12.60 3.82 2.47 1. 79 1.53 1 .38 1.37 0.0 0.0 0.0 0.0 0.0 0. 0 12. 18 4. 21 2.64 1. 90 1. 52 1. 53 0.0 0. 0 0.0 0. 0 0.0 0. 0 —I 4. SPEED I 4. 0.4| 1.6 I 3.4 I 5. 51 8.01 10.81 13.9J 17. 21 20.81 24. 5 1 28.51 33. 51 35.01 STATION J - LATENT HEAT FLUX 4 4 4 4 4 0. 25 1 0. 50 J 1.0 I 2.0 I 4.0 | 7.0 -4-I 14.0 | -4-28. 0 •4- -4-4. 50 1.44 1. 12 1. 06 1.02 1. 02 1.0 1 1. 0 1 1. 0 1 1.00 1.0 1 1.0 1 0.9 1 4. 34 2. 16 1. 34 1. 13 1.05 1.04 1. 03 1.02 1.02 1.02 1. 02 1.00 0. 0 4.3 1 3.33 1.68 1.26 1. 14 1.08 1.06 1.05 1.04 1.04 1.03 0.0 0.0 21 7. 2. 0. 0. .99 43 20 47 27 18 12 10 09 05 03 0 0 23. 37 8. 86 2.78 1.73 1. 37 1. 25 1.20 1. 15 1. 13 1.05 0.0 0. 0 0. 0 0. 0 9.45 2.85 1. 88 1. 52 1.31 1.24 1.20 1.11 0.0 0.0 0. 0 0.0 0. 0 14.62 3. 38 1.98 1 .59 1.42 1. 29 0.0 0.0 0. 0 0.0 0.0 0.0 21.05 23. 89 3. 39 2. 20 1.68 1. 50 1. 37 0. 0 0.0 0. 0 0. 0 0. 0 0.0 205 STATION K - LATENT HEAT FLOX J. + _ -+ •+- -+ --I +• SPEEDJ i_ i 0. 25 I t 0. 50 I .x_ 1.0 I i 2. 0 I 4.0 1 1 7.0 1 1—• 1 0.4| 1.42 T 3. 3 1 T 2.73 T 9. 57 _ _ | 14.42 T 25.51 1 1-6| 1. 14 | 1.77 l 3.4 9 | 4. 28 | 9.48 1 6.76 i 3.4< 1.08 | 1. 17 | 1.39 1. 76 | 2. 12 1 2.39 1 5.5| 1.04 | 1.07 | 1. 14 | 1. 31 | 1.44 1 1.73 I 8.0| 1.0 2 | 1.04 I 1.09 1 1. 18 | 1.30 1 1.38 1 10.81 1. 0 1 | 1.04 | 1.08 1 1. 13 I 1.19 1 1. 24 1 13. 9 j 1. 0 1 | 1.03 1.06 | 1. 1 1 I 1. 14 1 1. 24 I 17.2| 1.0 1 | 1. 02 | 1.04 1. 08 | 1. 12 1 1.11 1 20.81 1.0 1 | 1.02 | 1.04 1. 08 | 1. 13 1 0.0 J 24.51 1. 0 1 | 1.02 j 1.04 1 1. 10 I 0.0 1 0.0 |28.5| 1. 00 | 1.02 | 0.0 | 0. 0 I 0.0 J 0.0 133.51 1.00 | 1. 00 | 0.0 0. 0 I 0. 0 1 0.0 135.0| 0. 0 J 0.0 j 0.0 j 0. 0 | 0.0 j 0.0 4. 14,0 J + 106.3 11.07 2. 79 1.8 1 1.56 1.39 1. 20 0.0 0.0 0.0 0.0 0.0 0.0 1 28.0 j 30. 14 8. 52 3. 38 2. 00 1. 62 1.43 0. 0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 f +-SPEED| I- 4-0.4 J 1.61 3.4 | 5.5| 8.01 10.8| 13.9J 17. 2 | 20.8| 24. 5| 28.5| 33.51 35.0| 1 -r 0. 25 | 1. 49 1.31 1. 07 1.04 1.02 1.02 1.0 1 1. 0 1 1. 0 1 1.0 1 1.00 1. 00 1.02 STATION 0. 50 | +-2. 09 2. 18 1. 22 1. 10 1.05 1.04 1. 03 1.02 1.02 1.0 1 1.03 1. 04 0. 0 M -1.0 J 3.08 2.86 1.57 1.21 1.13 1.09 1.06 1.05 1.05 1.05 1.02 0.0 0.0 LATENT + 2. 0 + 7. 42 5.05 2. 00 1.40 1. 25 1. 16 1. 10 1.09 1.09 1. .1 1 0. 0 0. 0 0. 0 HEAT FLUX + 4 4-I 4.0 | 7.0 1 + + x. 16. 75 10. 59 2.73 1.74 1.44 1.30 1. 2 1 1. 17 1. 23 0.0 0.0 0.0 0. 0 19.93 9.80 2. 82 1. 93 1.58 1.36 1.25 1. 17 1.23 0.0 0.0 0.0 0.0 + 14.0 | + 25.70 10.87 3.39 2. 26 1.77 1.38 1.31 0.0 0.0 0.0 0.0 0.0 0.0 28.0 "* 1 22. 43 10. 67 3.52 2. 38 1. 84 1. 42 1.42 0.0 0. 0 0.0 0.0 0. 0 0.0 j. x SPEEDl Y + 0.4 1.6 3.4 5.5 8.0 10.8 13.9 17.2 20.8 24.5 28. 5 33. 5 35.0 3. 0. 0. 0. STATION N - LATENT HEAT FLUX 25 | 0.50 | 1.0 | 2.0 J 4.0 | 7.0 I 14.0 j 7 1 24 03 02 0 1 0 1 0 1 01 0 1 00 0 0 0 1.49 1. 46 1.08 1.03 1.02 1. 0 1 1.02 1.0 1 1.0 1 1. 00 0.0 0. 0 0.0 2.59 1.93 1. 15 1.04 1.02 1.02 1.03 1.02 1.00 0.0 0.0 0.0 0.0 5. 51 2.6 5 1. 35 1. 1 1 1.05 1. 06 1.04 1.05 0. 0 0.0 0. 0 0.0 0. 0 7.68 4.47 1.71 1. 25 1. 12 1. 11 1. 10 0.0 0.0 0.0 0.0 0.0 0.0 13.09 4.04 1.77 1. 23 1. 12 1.10 1.07 0.0 0.0 0.0 . 0 * 6 0.0 0.0 11. 52 5.9 2 1.88 1.29 1. 14 1. 16 0.0 0.0 0.0 0.0 0.0 0.0 0.0 28.0 "* 1 30. 99 6. 06 2. 0 1 1. 22 1. 13 1. 28 0. 0 0. 0 0. 0 0. 0 0. 0 0.0 0.0 i x.. r 1 | STATION P - LATENT HEAT FLUX I SPEED j 0 . 2 5 | 0 . 5 0 | 1.0 | 2 . 0 | 4 . 0 | 7 .0 | 14.0 | 2 8 . 0 | 1 0 . 4 | 7.87 | 1 . 5 8 | 7 . 5 7 | 7.07 | 12.69| 24.60| 0.0 } 0 . 0 ~ | I 1.61 1.74 | 1 . 79 | 2 . 6 9 1 6. 06 | 9.54 | 10 .191 1 2 . 2 1 | 0 . 0 1 | 3.4| 1 . 1 2 1 1 . 33 | 1 . 6 0 | 2.00 | 2.67 | 3 . 0 2 | 3 . 1 5 J 3 . 1 9 1 1 5 .51 1 . 05 | 1.12 | 1 .29 | 1 . 50 | 1 .78 | 2.00 | 2.04 | 2.09 | I 8 .01 1 . 0 3 | 1.07 | 1 .15 1 1 . 34 | 1.46 | 1.51 I 1 . 6 8 | 1.77 | 1 1 0 . 8 J 1. 02 1 1 .05 | 1 . 10 | 1 . 1 7 | 1. 30 1 1.34 1 1. 45 | 1 .51 | 113.91 1-01 I 1 . 03 1 1.07 J 1.14 | 1.21 | 1.26 J 1.36 J 1.23 | J17.2| 1.01 | 1.02 | 1..05 | 1.11 | 1 . 15 | 1.18 | 0.0 | 0.0 1 120.81 1 . 0 1 | 1 . 02 | 1.04 J 1 . 09 | 1 .12 | 0 . 0 | 0 . 0 J 0.0 | I 24. 51 1.01 | 1 .01 | 1.04 | 1 . 05 | 0.0 | 0.0 | 0.0 J 0 . 0 | |28.5 | 1.00 | 1.01 | 1.03 | 0 . 0 | 0.0 | 0.0 J 0.0 | 0.0 | 133.51 1 .01 | 1.02 1 0.0 | 0 . 0 | 0 . 0 | 0.0 | 0.0 | 0 . 0 | 135 .01 1 .Q0 | 1 . 02 | 0 . 0 | 0.0 | 0 . 0 J 0.0 | 0.0 | 0.0 | I I I I i I I I I I j 1 L 1 I II X L I j I AVERAGE VALUE - SENSIBLE HEAT FLUX | SPEED| 0 . 2 5 | 0 . 5 0 | 1 .0 I 2 . 0 | 4.0 | 7.0 | 14.0 | 2 8 . 0 ~ j I 0.41 4 . 8 3 J 6 . 3 9 I 8 . 3 3 | 17. 17| 24 . 19 J 2 3 . 9 4 ^ 3 5 . 7 o | 4 1 .02) 1 1 .61 1.88 | 2 . 9 7 | 5 . 2 0 | 8 . 3 5 | 10.461 11.331 1 2 . 5 9 | 12 .571 I 3 .41 1 . 20 | 1.46 | 1 . 95 1 2 . 6 1 | 3 . 1 2 | 3.43 | 3 . 7 2 | 4 . 0 8 | | 5 . 5 J 1 . 08 | 1.19 I 1 . 39 I 1 . 64 | 1 . 9 7 | 2 . 1 7 | 2 . 4 0 J 2 . 5 3 | | 8 .01 1-04 | 1 .09 1 1.21 | 1. 37 1 1. 54 | 1. 65 1 1.78 | 1 . 85 | 110 .81 1 . 0 2 | 1.06 | 1 . 12 I 1 . 23 | 1.33 1 1 . 40 | 1 . 4 9 | 1 . 5 7 | 1 1 3 . 9 J 1. 02 1 1.04 | 1 .08 | 1 . 1 5 | 1 . 2 4 | 1 .29 | 1.31 | 1 .41 | 117.2| 1 . 01 | 1 .03 | 1 . 06 | 1 . 12 | 1 . 1 9 | 1 . 2 0 | 1 . 2 7 | 0.0 | I 20 .81 1 .01 | 1 . 03 | 1 .06 | 1 . 10 | 1 .12 1 1 . 18 1 1 . 1 7 | 0.0 1 124.51 1.01 | 1.02 | 1 . 0 5 I 1 . 08 | 1.12 | 0 . 0 | 0 . 0 | 0 . 0 | 1 2 8 . 51 1 .01 J 1.03 | 1 .04 | 1 .07 | 0.0 | 0.0 1 0.0 | 0 . 0 | I 3 3 . 5 J 1 -01 | 1 . 0 2 I 1 . 05 | 1 . 0 2 | 0 . 0 | 0.0 | 0.0 I 0 . 0 | 135.01 1.00 1 1 . 03 | 0 . 0 | 0 . 6 | 0 . 0 | 0 . 0 | 0.0 | 0 . 0 | J 1 1 — - — J J L J. , I L_ | I AVERAGE VALUE - LATENT HEAT FLUX | SPEEDI 0 . 25 1 0 . 50 j 1.0 | 2 . 0 1 4 . 0 | 7 .0 | 1 4 . 0 j 2 8 . 0 | j. 4 4 4 4 (- 4 - 4 4 —| 1 0 .41 3. 95 1 4. 40 1 6 . 7 5 | 12 . 5€ | 20 .461 2 3 . 191 4 0 . 27 | 3 0 . 0 0 1 | 1.6| 1 .64 1 2 . 1 3 | 3 . 6 6 | 5 . 9 4 | 8 . 8 9 1 9 . 8 6 1 1 1. 24 | 10.691 J 3 .41 1 .12 | 1. 30 J 1.66 | 2 . 2 0 j 2 . 74 | 3 . 0 6 | 3 . 3 8 | 3 . 5 5 | J 5 .51 1.05 | 1 . 12 1 1.27 | 1. 52 1 1.82 | 2 .01 | 2 . 2 1 | 2 . 3 2 | | 8 .01 1 . 0 3 | 1 .07 | 1 . 15 1 1.31 | 1 .48 | 1 . 5 9 | 1 .73 | 1 .80 I | 1 0 . 8 J 1 . 02 | 1 .04 J 1 . 10 | 1 .20 | 1 .31 | 1 .38 1 1 . 4 7 1 1. 55 | 1 1 3 . 9 | 1 .01 I 1 .03 I 1.07 | 1 . 14 | 1. 22 1 1 . 28 | 1 . 3 2 | 1 . 42 | | 17.21 1.01 | 1 . 03 | 1 . 06 | 1.11 | 1.18 | 1 .19 | 1 .29 | 0 . 0 | 1 2 0 .8| 1 .01 | 1 . 02 | 1 . 05 | 1 . 1 0 | 1 . 1 3 | 1 .17 ( 1 . 1 7 J 0.0 | I 2 4 . 51 1. 0 1 1 1 . 02 | 1 .04 | 1 .07 | 1 .13 | 0 . 0 | 0.0 1 0 . 0 | 1 2 8 . 5 | 1.01 | 1 . 02 | 1.03 | 1 .06 | 0.0 | 0 . 0 | 0 . 0 I 0 . 0 | | 3 3 . 51 1. 0 1 1 1 .02 1 1 .04 J 1 .01 1 0.0 1 0.0 | 0.0 | 0 . 0 | 135.01 1 . 01 | 1 .03 I 0.0 | 0 . 0 | 0 . 0 | 0 .0 I 0.0 | 0 . 0 | L 1 X X 1 1 X 1 L , I 207 P a r t I I The e r x c r e s t i m a t e s o f t h e s l o p e s c a l c u l a t e d by t h e S t u d e n t • t ' t e s t o u t l i n e d i n E g u a t i o n 3.10. I j. 4 SPEEDI I- 4 0.4 1.6 3.4 5. 5 8.0 10. 8 13.9 17.2 20.8 24. 5 28. 5 33. 5 35.0 4 0. 25 | 1. 15 0. 22 0. 02 0. 0 1 0.00 0. 00 0.00 0.00 0. 00 0. 00 0.00 0. 00 0.0 STATION 0.50 | + _ 2.00 0.4 1 0.04 0.02 0.0 1 0.00 0.00 0.00 0. 00 0.00 0.01 0. 06 0. 0 A - SENSIBLE HEAI UO | 2.0 | 4.0 2.04 1.89 0. 11 0.03 0.02 0.0 1 0.0 1 0.01 0.01 0.0 1 0.02 0.0 0.0 24. 7 5 4. 14 0. 18 0. 07 0. 03 0. 02 0. 02 0. 02 0. 03 0. 0 7 0. 0 0.0 0. 0 0.0 4.31 0. 19 0.09 0.06 0.04 0.03 0.05 0. 13 0. 0 0.0 0.0 0.0 FLOX 4 I 7. + — 0. 4. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0 } 14.0 | 28.0 0 71 31 16 10 07 07 12 0 0 0 0 0 0.0 4.72 0.27 0. 18 0. 13 0. 14 0. 10 0.0 0.0 0.0 0.0 0.0 0.0 0. 0 4. 8 3 0.45 0. 28 0. 30 0. 39 0.0 0.0 0. 0 0. 0 0.0 0. 0 0.0 I f 4 SPEEDJ 0. f 4 0,4 1.6 3. 4 5.5 8.0 10.8 13.9 17.2 20.8 24.5 28. 5 33.5 35.0 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. — 4 25 | 4 80 42 02 01 00 00 00 00 00 00 00 00 0 STATION B -0.50 J 1.0 2. 36 0. 44 0.05 0.01 0. 0 1 0.00 0.00 0.0 0 0. 00 0. 00 0.0 1 0.01 0.0 3.74 1.56 0. 10 0.03 0.0 1 0.01 0.0 1 0.01 0.0 1 0.02 0.07 0.0 0.0 SENSIBLE 4 4 I 2.0 | + 4 14. 43 2. 34 0. 23 0. 07 0. 03 0. 02 0. 02 0. 02 0. 02 0. 03 0. 0 0. 0 0. 0 HEAT FLOX 4.0 | 7.0 | 189. 2 3,36 0.27 0.09 0. 05 0.03 0.03 0. 04 0.08 0.0 0.0 0.0 0.0 246. 0 3.95 0.30 0. 14 0.07 0.06 0.06 0. 10 0.0 0.0 0.0 0.0 0.0 4 14.0 1 + 295.4 2.88 0.28 0. 15 0. 1 1 0. 10 0. 1 1 0.0 0.0 0.0 0.0 0.0 0.0 28.0 34.88 5, 31 0. 42 0.30 0. 18 0. 30 0. 0 0. 0 0.0 0. 0 0.0 0. 0 0. 0 1 r + SPEED J j. 4 0.4 1.6 3.4 5. 5 8.0 10.8 13.9 17. 2 20.8 24. 5 28.5 33. 5 35.0 • +• 0.25 | STATION C 0.50 | 1. 4 . - SENSIBLE 4 1--0 | 2. 0 | HEAT FLUX 4.0 | 7.0 | 4-14.0 | — +-28.0 1.80 0.2 1 0.03 0.0 1 0. 00 0. 00 0.00 0.00 0. 00 0.00 0.00 0. 0 1 0.0 1 3. 24 0. 56 0. 05 0.02 0.01 0.0 1 0.00 0.00 0. 00 0.0 1 0.0 1 0.01 0. 0 19 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. .37 10 09 03 02 0 1 01 0 1 01 0 1 01 12 0 50. 36 2. 15 0. 16 0.06 0. 03 0. 02 0. 02 0. 03 0.04 0. 06 0. 0 0. 0 0. 0 2S. 9 1 1.78 0.20 0. 10 0.04 0.03 0.04 0.04 0. 09 0.0 0. 0 0. 0 0.0 0.0 4. 19 0.27 0. 13 0.07 0. 06 0.07 0.09 0.0 0.0 0.0 0.0 0.0 0,0 10.91 0. 24 0. 17 0.09 0. 10 0. 10 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2. 59 0. 58 0. 20 0. 16 0. 26 0. 60 0.0 0.0 0.0 0. 0 0. 0 0.0 i j . -L J L 4_ SPEED| I- +-0.4, 1.6 3.4 5.5 8.0, 10.8 13. 9 i!7.2| 20.8 24. 5 28.5| 33.5, 35.0, H-0.25 | 4 0. 95 0. 26 0. 03 0.0 1 0. 00 0. 00 0. 00 0.00 0. 00 0.00 0.00 0. 0 1 0. 02 STAITON 0. 50 | 4 -3. 92 1. 50 0. 06 0.02 "0.0 1 0. 00 0.00 0. 00 0.00 0.01 0. 0 1 0. 02 0.0 D -1.0 15. 77 1. 58 0.10 0.05 0.02 0.01 0.0 1 0.01 0.0 1 0.01 0.02 0.0 0.0 SENSIBLE 4 + I 2.0 | 4 4 0. 0 4. 05 0.22 0. 07 0. 03 0. 02 0, 02 0. 02 0. 03 0. 05 0. 0 0. 0 0. 0 HEAT FLUX 4.0 | 7.0 | 0.0 14.0 t 28.0 42. 75 2.79 0. 24 0.08 0. 05 0. 04 0.04 0. 04 0. 10 0. 0 0. 0 0.0 0.0 8. 39 0.31 0. 14 0.08 0.07 0.08 0. 13 0.22 0.0 0.0 0.0 0.0 0.0 5.74 0.30 0. 14 0.08 0.08 0. 26 0. 26 0.0 0.0 0.0 0.0 0.0 0. 0 0.0 0. 50 0. 25 0. 19 0. 22 0. 0 0.0 0.0 0.0 0.0 0. 0 0.0 h 4-SPEED| J- 4-0. 4 1. 6; 3.4 5. 5 i 8.0 10. 8| 13.9 17. 2| 20. 8 j 24. 51 28.5, 33.5, 35.0 0.25 | STATION E -0.50 | 1.0 SENSIBLE •4 +-I 2.0 | HEAT FLUX 4.0 | 7.0 | — — + -14.0 | 28.0 31.21 4. 86 0.44 0. 30 0. 22 0. 28 0.0 0. 0 0. 0 0.0 0.0 0.0 0. 0 0. 5 0 0. 13 0. 0 1 0. 0 1 0.00 0. 00 0. 0 0 0. 00 0. 00 0. 00 0. 0 1 0. 15 0. 0 0.90 0.34 0. 02 0.0 1 0. 0 1 0.00 0.00 0.00 0.0 1 0.01 0. 03 0.0 0. 0 1.07 0.64 0.06 0.02 0.0 1 0.0 1 0.01 0.0 1 0.02 0.03 0.0 0.0 0.0 11.51 2. 03 0. 15 0. 04 0. 02 0. 02 0. 02 0. 02 0. 08 0. 0 0. 0 0. 0 0. 0 21.40 2.94 0, 16 0.07 0. 04 0. 04 0. 04 0.07 C O 0.0 0. 0 0.0 0. 0 21.68 2.31 0. 29 0. 10 0.08 0.07 0.09 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.30 0.25 0. 13 0. 10 0.09 0.40 0.0 0.0 0.0 0.0 0.0 0.0 I j. 4 SPEED] 0. !• 4 0.4 1.6 3. 4| 5.5I 8.0 10.8 13.9 17.2, 20-8 i 24.5, 28. 5, 33. 5, 35.0 4. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 4 25 | 4 27 39 03 0 1 00 00 00 00 00 00 00 00 0 STATION I -0.50 | 1.0 3.0 1 0. 74 0.06 0. 02 0.0 1 0.0 1 0.00 0.00 0.00 0. 0 1 0.03 0. 03 0.0 9.95 1.8 1 0. 13 0.04 0.02 0.0 1 0.0 1 0. 01 0.01 0.0 2 0.03 0.0 0.0 SENSIBLE 4 4 I 2.0 | + 4 0. 0 2. 0 4 0. 25 0. 08 0. 03 0. 02 0. 0 2 0. 01 0. 04 0. 04 0. 0 0. 0 0. 0 HEAT FLUX 4.0 | 7.0 { 4 — 4 -4 1. 89 3.89 0. 27 0.09 0.05 0.03 0.02 0.06 0. 13 0.0 0.0 0.0 0.0 0.0 4.95 0.43 0. 17 0.06 0.05 0.05 0. 12 2. 95 0.0 0.0 0.0 0.0 4 14.0 | 4 0.0 4. 28 0.32 0.23 0.08 0.08 0. 10 0.0 0. 0 0.0 0.0 0.0 0.0 28. 0 0. 0 8. 53 0. 69 0. 30 0. 18 0. 17 1. 03 0.0 0. 0 0. 0 0. 0 0.0 0. 0 i .x.. 210 I r 4-SPEED| V 4-0.4 1.6 3.4 5.5| 8.0, 10.8 13.9, 1 7. 2 i 20- 8 | 24. 51 28.5; 33. 51 35.0 + 0.25 | 4 1.92 0. 14 0. 03 Oi 0 1 0.00 0. 00 0.00 0. 00 0. 00 0. 00 0. 00 0. 0 1 0. 0 STATION J -0.50 | 1.0 2.65 0.79 0. 06 0.02 0. 0 1 0.0 1 0. 00 0.00 0.00 0.0 1 0.01 0.04 0. 0 4.84 0.67 0. 12 0.04 0.01 0.0 1 0.01 0.0 1 0.0 1 0.02 0.03 0.0 0.0 SENSIBLE + 4 I 2.0 | 4 4 37. 90 5.07 0. 22 0. 06 0. 03 0. 02 0. 01 0. 02 0. 03 0. 14 0. 0 0. 0 0. 0 HEAT 4.0 0.0 5.41 0.30 0. 10 0. 04 0.02 0.03 0.04 0. 13 0.0 0.0 0.0 0.0 FLOX + I 7. 4 — 0. 6. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0 { 1ft.0 j 28.0 ^ 0 95 38 15 07 05 05 11 0 0 0 0 0 0.0 8.39 0.40 0. 14 0.07 0.07 0. 12 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0. 0 0. 9 3 0. 23 0. 14 0. 14 0. 0 0.0 0. 0 0. 0 0. 0 0. 0 0.0 i L 4 SPEED J 0. L _ 4 STATION K -25 | 0.50 | 1.0 SENSIBLE 4 + . I 2.0 I HEAT FLUX 4.0 | 7.0 J 4-14.0 | 4-28.0 j 0. 0 11.96 0. 97 0. 21 0. 18 0. 53 0. 0 0.0 0. 0 0.0 0.0 0. 0 0.0 0.4 1.6 3. 4, 5. 51 8.0 10. 8 13.9, 17.2, 20. 81 24. 51 28.5j 33.5, 35.0, 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 68 21 03 0 1 00 00 00 00 00 0 1 0 1 02 0 1.55 0.49 0. 04 0.02 0.0 1 0.01 0.00 0. 00 0.0 1 0.0 1 0.08 0.0 0.0 8.37 1.68 0.08 0.02 0.0 1 0.0 1 0.0 1 0.01 0.02 0. 13 0.0 0.0 0.0 7. 93 2. 17 0. 16 0. 06 0. 03 0. 02 0. 02 0. 02 0. 07 0. 0 0. 0 0. 0 0. 0 0. 0 8.46 0.33 0.06 0. 05 0, 02 0. 04 0.06 2. 15 0.0 0.0 0.0 0.0 0.0 1.91 0. 46 0. 14 0.06 0.05 0.09 0. 17 0.0 0.0 0.0 0.0 0.0 0.0 18.62 0.46 0. 14 0. 10 0.14 0. 36 0.0 0.0 0.0 0.0 0.0 0.0 I Ir +-SPEEDJ f 4-0.4 1.6 3.4 5. 51 8.O.1 10.8 13. 9, 17.2 20.8, 24. 5| 28. 5, 33. 5| 35.0, 4 25 I 4 49 , 10 02 0 1 00 00 00 00 00 00 00 0 1 ,0 STATION 0.50 I 4-0.93 0.48 0. 04 0.02 0.0 1 0.00 0.00 0.00 0.00 0.0 1 0. 04 0. 0 0. 0 M -1.0 1.90 1.29 0.08 0.02 0.01 0.0 1 0.01 0.01 0.01 0.02 0.0 0.0 0.0 SENSIBLE 4 4 I 2.0 | 4 h 19.93 2. 30 0. 16 0. 05 0. 03 0. 02 0. 01 0. 02 0. 05 0. 0 0. 0 0.0 0. 0 HEAT FLUX 4.0 | 7.0 | 14.0 I 19.30 3. 83 0. 24 0.07 C. 03 0. 03 0. 03 0.05 0.0 0.0 0.0 0.0 0. 0 0.0 4. 49 0.26 0. 13 0.07 0.05 0. 07 1. 25 0.0 0.0 0.0 0.0 0.0 0.0 5.23 0.32 0. 19 0. 11 0.05 0.0 0.0 0.0 0.0 0.0 0.0 0.0 28.0 4 0. 0 9.03 0.44 0. 35 0. 29 0. 37 0. 0 0.0 0. 0 0.0 0. 0 0. 0 0. 0 1 x. .4. .j 211 STATION N - SENSIBLE HEAT FL 0 X * +- -+- ~ f - , +-SPEED j • i 0. 25 1 1 0.50 I I 1.0 I j 2. 0 1 4.0 I i 7.0 r r 1 0.4J 0. 59 T 0. 52 1.74 T ' 4.70 -+- 10.6 1 20.76 i 1-61 0. 0 8 1 0. 18 ] 0.32 | 0. 89 1 1.09 | 1.47 1 3. 4J 0. 0 1 1 0.02 1 0.03 | 0. 06 1 0.09 | 0. 14 1 5. 5 1 0. 00 1 0.00 1 0.01 ] 0.02 1 0. 03 | 0.05 i 8.0| 0. 00 1 0.00 1 0.00 | 0.01 1 0.0 1 1 0.03 110.8| 0. 00 1 0.00 1 0.00 | 0. 01 1 0.01 j 0.03 1 13.91 0. 00 1 0.00 1 0.0 1 ] 0. 0 1 1 0. 03 | 0.0 1 17.21 0. 00 1 0. 0 1 1 0.01 | 0. 03 1 0. 0 ] 0,0 |20.8l 0. 0 1 1 0.02 1 0.0 | 0. 0 1 0.0 J 0.0 124.5] 0.00 1 0. 0 1 0.0 | 0. 0 1 0.0 J 0.0 | 28.51 0. 0 J 0.0 1 0.0 | 0. 0 1 0. 0 | 0.0 1 33.51 0. 0 J 0.0 1 0.0 | 0. 0 1 0. 0 J 0,0 |35.0] 0. 0 1 0. 0 1 0.0 0. 0 • 0.0 1 0.0 L J - _ 1 1 14.0 | 28.0 15. 71 2. 15 0. 16 0.07 0. 04 0.02 0.0 0.0 0. 0 0.0 0.0 0.0 0.0 0. 0 4. 60 0. 34 0. 13 0. 08 0.0 0.0 0.0 0. 0 0. 0 0. 0 0.0 0. 0 1 t- +— SPEEDI 0. h + 0,4 1.6 3.4 5. 5 8.0 10.8 13.9 17.2 20.8 24.5 28.5 3 3 • !5 35.0 1. 0. 0. 0. 0. 0. 0. 0, 0. 0. 0, 0. 0. 4 25 | 4 40 25 02 0 1 00 00 00 00 00 00 0 1 0 1 06 STATION 0.50 { 4 _ 3.0 1 0.39 0. 07 0.02 0. 01 0.01 0.00 0.00 0.00 0.0 1 0. 0 1 0.03 0. 0 P -1.0 9.21 1.82 0. 13 0.05 0.02 0.0 1 0.01 0.0 1 0.0 1 0.02 0.05 0*0 0.0 SENSIBLE 4 (-I 2.0 | 4 (-0. 0 4. 36 0. 21 0. 09 0. 05 0. 03 0. 02 0. 04 0. 03 0. 15 0. 0 0. 0 0. 0 HEAT 4.0 0.0 6.42 0. 30 0. 12 0.06 0.04 0.04 0. 05 0. 28 0.0 0.0 0. 0 0. 0 FLOX t 7.0 j 14.0 | 28.0 ^ 410.0 11.71 0.49 0. 18 0.08 0.06 0.09 0. 13 0.0 0.0 0.0 0.0 0.0 0.0 57. 81 0.59 0.20 0. 11 0.09 0. 23 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0. 71 0. 28 0. 17 0. 25 0. 0 0.0 0.0 0. 0 0. 0 0. 0 0.0 I j. 4 SPEEDl I- + 0.4 1.6 3.4 5.5 8.0 10.8 13. 9 17.2 20. 8 24.5 28.5 33.5 35.0 4 0.25 | STATION A - LATENT HEAT FLDX 0.50 J 1.0 | 2. 0 I 4.0 | 7,0 | 4 14. 14 2. 76 0. 15 0. 06 0. 03 0. 02 0. 02 0. 01 0. 02 1. 05 0.0 0. 0 0. 0 -h 14.0 | j 28.0 -I 1. 14 1. 76 0. 09 0.03 0. 02 0. 0 1 0. 0 1 0.0 1 0. 0 1 0. 0 1 0. 16 0.43 0.0 2.39 1.56 0.09 0.04 0. 02 0,0 1 0.0 1 0.00 0.0 1 0. 00 0. 28 1. 00 0.0 1 1.32 2.43 0.16 0.07 0.04 0.02 0.02 0.01 0.0 1 0.28 0.67 0.0 0.0 0.0 3. 39 0. 20 0. 10 0.06 0.04 0.03 0. 34 1. 10 0.0 0.0 0.0 0. 0 0.0 2. 10 0. 18 0.09 0.05 0.04 0.04 1.11 0.0 0.0 0.0 0.0 0.0 0.0 3.83 0.21 0. 11 0.09 0.10 0. 12 0.0 0.0 0.0 0.0 0.0 0.0 0. 0 2.26 0. 24 0. 14 0. .13 0. 21 0. 0 0.0 0.0 0.0 0. 0 0. 0 0.0 I L 212 STATION B - LATENT HEAT FLUX |. 4 SPEED | 0. L 4 25 | 0.50 | 1.0 | 2.0 0.4 1.6 3.4 5. 5 8.0 10.8 13. 9 17.2 20.8 24.5 28.5 33. 5 35.0 1. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 9 1 36 10 04 02 0 1 01 00 00 08 16 30 0 2.0 8 1.38 0. 11 0. 04 0. 02 0.01 0.01 0.0 1 0. 00 0. 13 0. 31 0. 64 0.0 16.3 1 2.39 0. 16 0.07 0.03 0.02 0.01 0.0 1 0.01 0.24 3.05 0.0 0.0 13. 49 1. 60 0. 15 0. 06 0. 03 0. 02 0. 01 0. 0 1 0. 02 1. 01 0. 0 0. 0 0. 0 I 4.0 | 4 4 367. 5 2.02 0. 19 0.07 0. 04 0.03 0. 02 0.02 1.19 0.0 0. 0 0.0 0. 0 +• 1- 1 7.0 I 1 14.0 | 28.0 | 125.7 _____ 178.21 ________ __l 8. 11 | 2. 08 | 2.26 | 3. 87 | 0. 17 | 0.22 | 0. 23 | 0. 06 | 0 . 1 0 | 0. 12 | 0.04 | 0.05 | 0.07 | 0.03 | 0.07 | 0. 10 | 0.04 | 1.03 J 0.0 J 0.07 | 0.0 | 0. 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 0.0 | 0.0 | V +• SPEEDJ j. + 0.4 1.6 3.4 5.5 8.0 10.8 13.9 17.2 20. 8 24.5 28. 5 33.5 35.0 4 25 | 4 42 85 07 03 0 1 0 1 0 1 01 00 08 14 27 90 STATION C -0.50 | 1.0 LATENT HEAI FLUX 4 -I 4 4. I 2.0 | 4.0 | 7.0 | .4 -12.02 1. 15 0.07 0. 03 0.02 0.01 0.0 1 0.0 1 0. 0 1 0. 14 0.24 0. 47 0.0 9.64 1.57 0. 14 0.05 0.02 0.02 0.0 1 0.0 1 0.04 0.24 0.52 3.07 0.0 25. 18 1. 87 0. .13 0. 06 0. 03 0. 02 0. 02 0. 02 0. 03 0. 58 0. 0 0. 0 0. 0 60.92 j • 2 3 0. 17 0.07 0.04 0.03 0. 03 0. 04 1. 25 0.0 0.0 0.0 0.0 0.0 2.36 0. 15 0.08 0.04 0.03 0.04 0.06 0.0 0.0 0.0 0.0 0.0 4 14.0 | 4 0.0 6. 26 0.22 0.09 0.05 0.07 0.07 0.0 0.0 0.0 0.0 0.0 0.0 28.0 1 0. 0 1. 19 0. 32 0.09 0. 07 0. 07 0. .15 0. 0 0. 0 0. 0 0. 0 0.0 0.0 t J 1 j. 4 SPEED! r 4 0.4 1.6 3.4 5. 5 8.0 10.8 13.9 17. 2 20. 8 24.5 28.5 33. 5 35.0 4 0.25 I 6.66 1.28 0. 10 0. 04 0. 02 0. 0 1 0. 0 1 0. 0 1 0. 0 1 0. 0 1 0. 15 0. 29 1. 16 STATION D -0.50 I 1.0 7. 24 1. 29 0. 10 0.04 0.02 0. 0 1 0.01 0.0 1 0.0 1 0.0 1 0. 24 0. 67 0.0 14. 8: 3.25 0. 14 0.06 0.03 0.02 0.02 0.0 1 0.01 0.28 0.68 0.0 0.0 LATENT 4 | 2.0 4 0. 0 2. 35 0. 13 0. 05 0. 03 0. 02 0. 02 0. 02 0. 02 0.66 0. 0 0. 0 0. 0 HEAT FLUX .4 4 4-| 4.0 | 7.0 | 4 + 4-103. 3 3.28 0. 17 0.08 0. 04 0.03 0.03 0. 04 0.08 0.0 0.0 0. 0 0.0 0.0 3.06 0.19 0.07 0.04 0.03 0.04 0.09 0. 12 0.0 0.0 0.0 0.0 4 14.0 | 4 0,0 6.62 0.26 0. 1 1 0.06 0.07 0. 11 2. 23 0.0 0.0 0.0 0.0 0.0 28.0 0.0 0. 0 0. 35 0. 10 0.07 0. 07 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 0.0 I L .J 213 I STATION E - LATENT j. 4. -+ +- -4 SPEED| 1 , 1 0. 25 I _ i 0. 50 1 i 1.0 I _L 2. 0 r r I 0.4| 1.91 T 2.84 4 5.32 -+ 8. 90 I 1-6| 0. 90 | 0.67 j 1.25 I 1. 25 1 3.41 0. 05 1 0.04 | 0. 12 I 0. 09 J 5.5| 0.0 2 | 0. 02 J 0.04 | 0. 0 3 1 8.0| 0. 0 1 ] 0.0 1 | 0.02 0. 02 i 10.8 j 0. 0 1 | 0.0 1 | 0.01 | 0. 01 M3. 9| 0.0 1 | 0.0 1 | 0.02 I 0. 0 1 |17.2| 0. 0 1 | 0. 0 1 | 0.02 | 0. 0 1 |20.8] 0. 0 1 | 0.0 1 | 0.26 | 0.65 124.51 0. 17 1 0. 31 | 0.55 i 0. 0 |28.5| 0. 40 | 1. 00 | 0.0 i 0. 0 1 33.51 1. 93 0. 0 0.0 i 0. 0 |35.0| 0.0 0.0 0.0 i 0. 0 I 4.0 | 7.0 J 2 I. 81 1. 73 0. 16 0.06 0.04 0.03 0.03 0.55 0.0 0. 0 0.0 0. 0 0. 0 15.81 0.99 0. 15 0.05 0.04 0.04 0.04 0.0 0.0 0,0 0.0 0.0 0.0 + 14.0 | + 0.0 2.02 0. 23 0. 12 0.06 0.05 0. 15 0.0 0.0 0.0 0.0 0.0 0.0 -j 28.0 1 15. 97 2. 31 0. 23 0. 17 0. 14 0. 17 0. 0 0. 0 0.0 0.0 0. 0 0. 0 0.0 I- 4 SPEED! j. 4 0.4 1.6 3.4 5.5 8.0 10. 8 13. 9 17.2 20.8 24. 5 28.5 33.5 35.0 4 0.25 | 4. 90 1.2 1 0. 12 0. 04 0.0 1 0.0 1 0.0 1 0.0 1 0. 00 0. 02 0. 19 0. 5 1 0.0 STATION 0.50 | - 4 _ 5. 2 5 1.76 0. 11 0. 04 0.02 0.01 0. 0 1 0.0 1 0.00 0.02 0. 39 1. 40 0. 0 I - LATENT 4 . 2. 0 +  0. 0 2. 05 0. 16 0. 06 0. 03 0. 02 0. 01 0. 0 1 0. 04 1. 43 0. 0 0. 0 0. 0 HEAT FLOX •+ 4 4-| 4.0 | 7.0 | •4 4 4-— 4 14.0 | 4 0.0 2.83 0.34 0. 15 0.06 0.04 0.11 0.0 0.0 0.0 0.0 0.0 0.0 1 28. 0 0. 0 1. 92 0. 39 0. 14 0. 09 0. 1 1 0.49 0. 0 0. 0 0.0 0.0 0.0 0. 0 1.0 | 9. 13 2.77 0.22 0.08 0.03 0.02 0.01 0.0 1 0.03 0.29 1.42 0.0 0.0 45. 45 4.98 0. 28 0. 13 0. 05 0.03 0.02 0.04 3. 17 0.0 0.0 0. 0 0. 0 0.0 2.66 0.25 0.09 0.04 0.03 0.03 0.08 15.09 0.0 0,0 0.0 0.0 f 4 SPEED! f 4 0.4 1.6 3.4 5.5 8.0 10.8 13. 9 17*2 20.8 24.5 28.5 33.5 35.0 4 0. 25 | 20. 57 1. 18 0. 12 0.04 0. 0 1 0. 0 1 0. 0 1 0.0 1 0. 0 1 0.00 0. 2 1 0. 5 1 0. 0 STATION 0. 50 1 4 -7.26 1. 45 0. 1 1 0.03 0.01 0. 0 1 0. 0 1 0.0 1 0.01 0. 0 1 0.37 3.0 1 0.0 J - LATENT HEAT FLUX 1.0 | 2.0 I 4.0 6.02 2.97 0. 17 0.07 0.03 0.0 1 0.0 1 0.01 0.0 1 0.33 1.4 1 0.0 0.0 43.47 2* 8 3 0. 14 0. 05 0. 03 0. 01 0. 0 1 0. 0 1 0. 02 1. 87 0. 0 0. 0 0. 0 0.0 6.75 0. 27 0.08 0.04 0.03 0.02 0. 31 1. 51 0.0 0.0 0.0 0.0 -.4. 1 7.0 1 1 14.0 I i 28.0 | j 0.0 •4- 0.0 1 0.0 1 4.66 | 9.00 | 0.0 1 0.22 | 0.35 j 0. 50 1 0.07 | 0. 11 1 0.11 J 0.03 | 0. 06 | 0.08 | 0.02 ! 0.05 | 0.08 | 0.02 I 0.08 1 0.0 | 0.76 I 0.0 | 0.0 | 0.0 1 0.0 | 0.0 | 0.0 I 0.0 | 0.0 | 0.0 1 0.0 1 0.0 | 0.0 | 0.0 | 0.0 I 0.0 j 0.0 0.0 | 214 r : —'• ' n | S T A T I O N K - L A T E N T HEAT E L U X | SPEED I 0.25 J 0.50 ,| 1.0 \ 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | | 0.4| 4.14 | 4.41 I 2 5. 23 J 58. 391 0.0 ] 0.0 | 0.0 | 0.0 ~| i 1.6| 1.34 | 2.02 | 1.30 | 1.54 | 9.30 | 4.19 | 4.96 | 5.71 | I 3.4 | 0.09 | 0.08 | 0.18 j 0.14 { 0.25 j 0.25 J 0.37 | 0.54 | | 5.5J 0.02 | 0.02 \ 0.06 | 0.06 f 0,07 J 0.09 | 0.12 j 0. .17 | | 8.0| 0.01 | 0.01 I 0.02 | 0.02 | 0.04 | 0.05 | 0.08 | 0.19 | I 10.3 J 0.01 | 0.01 ^ 0.01 | 0.02 | 0.03 I 0.03 | 0.08 | 0.38 | | 13.91 0.01 | 0.01 | 0.01 | 0.02 | 0.04 | 0.08 I 1.65 | 0. 0 | |17.2| 0.01 J 0.01 | 0.01 { 0.02 | 0.56 | 1.23 | 0.0 | 0.0 | |20.8| 0.01 | 0.01 | 0.24 | 0.70 | 13. 931 0.0 | 0.0 | 0.0 | 124.5] 0.17-| 0.31 | 0.85 r 0.0 | 0.0 | 0.0 | 0.0 | 0.0 1 |28.5| 0.47 | 1.17 | 0.0 J 0.0 | 0.0 1 0.0 | 0.0 | 0.0 | |33.5l 1.84 J 0.0 | 0.0 1 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 135.01 0.0 j 0.0 1 0.0 | 0.0 | 0.0 | 0.0 1 0.0 1 0.0 | f. 1 J . J 1 1 X A 1 _| 1 S T A T I O N M - L A T E N T HEAT F L U X | I" + + 4 4 -\ + 4 4 1 S P E E D | 0.25 | 0.50 | 1.0 | 2.0 | 4.0 I 7,0 J 14.0 | 28.0 J | 0.4( 2.25 | 3.80 | 8.76 | 17.0 9 } 16.35^ 0.0 j 0.0 | 0.0 ] I 1.61 1.25 I 1.43 | 2.49 I 1.90 | 2.40 | 1.97 | 2.87 | 5.19 | I 3.4J 0.10 1 0.09 I 0.13 | 0.12 | 0.21 | 0.16 | 0.22 | 0.27 | f 5.5| 0.03 I 0.03 J 0.06 | 0.05 | 0.08 1 0.07 1 0, 12 | 0.17 | 1 8.0| 0.01 I 0.01 I 0.03 1 0. 02 1 0.05 f 0.04 J 0.07 j 0.17 | 110.81 0.01 | 0.01 | 0.01 | 0.01 | 0.02 I 0.03 I 0.04 | 0.39 | |13.9| 0.00 I 0.01 1 0.01 I 0. 01 1 0.02 1 0.04 | 0.0 | 0.0 | J17.21 0.00 I 0.00 I 0.01 1 0.01 I 0.46 | 13.77 I 0.0 | 0.0 | ]20.8l 0.00 I 0.01 I 0.01 I 0.04 | 0.0 | 0.0 | 0.0 | 0.0 | |24.5| 0.15 j 0.24 | 0.57 | 0.0 | 0.0 I 0.0 | 0.0 I 0.0 | 128.5 J 0.39 J 1.18 1 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 133.5| 1.00 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 I 0.0 | i 35.0 J 0.0 | 0.0 1 0.0 I 0.0 I 0.0 | 0.0 | 0.0 | 0.0 | I J 1 . — J 1 1 J 1 1 _j J S T A T I O N N - L A T E N T HEAT F L U X | h 4 — -f 4 4- 4 4 - 4 4- 1 S P E E D 1 0.25 I 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | 1 0.41 0.81 | 1.04 I 6.00 | 3.32 I 8.46 I 12.71 j 42.581 0. 0 J I 1.61 0. 43 1 0.30 I 0.49 | 0.57 | 0. 97 1 0.79 1 1.58 | 3.39 | I 3.41 0.03 | 0. 02 1 0.05 | 0.04 | 0.08 1 0.10 | 0.15 | 0.30 I 1 5.51 0.01 I 0.00 I 0.02 I 0.01 1 0.03 | 0.05 | 0.06 | 0.15 | 1 8.01 0.00 J 0.00 I 0.01 I 0.01 | 0.01 | 0.04 1 0.02 1 0. 17 | 110.81 0.00 J 0.00 I 0.00 I 0.01 I 0.01 | 0.05 | 0.12 | 0.0 | |13.9| 0.00 1 0. 00 1 0.01 I 0.02 I 0.55 | 0.0 | 0.0 | 0.0 | |17.2| 0.10 I 0.18 I 0.33 | 0.84 | 0.0 | 0.0 J 0.0 1 0.0 | 120.81 0. 29 ,| 0.60 | 0.0 1 0.0 I 0.0 | 0.0 | 0.0 1 0.0 | 124. 51 1.83 I 0.0 | 0.0 | 0.0 1 0.0 | 0.0 | 0.0 1 0.0 1 128.5J 0.0 I 0.0 I 0.0 1 0.0 | 0.0 1 0.0 | 0.0 1 0.0 | 133.5| 0.0 I 0.0 I 0.0 I 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |35.0| 0.0 I 0.0 I 0.0 1 0.0 I 0.0 1 0.0 | 0.0 J 0.0 I I 1 1 J J I L J _ _ J I 215 \ + — SPEED| 0, r + — STATION P -25 | 0.50 | 1.0 + 23.99 2.69 0.21 0.08 0.03 0.0 2 0.02 0.01 0. 19 0.37 1.41 0.0 0.0 1 0.4 | 3. 55 6. 19 1 1 1.6| 1.68 2.06 1 1 3. 4 | 0. 0 9 0. 1 1 | i 5.5| 0.04 0.04 | 1 8.0] 0. 02 0.02 | 110.8j 0. 0 1 0.01 | |13.9J 0. 0 1 0.01 | | 17.21 0. 0 1 0.01 | |20.8| 0. 0 1 0.0 1 | I24.5| 0. 11 0.19 1 i 28.51 0. 2 1 0.40 | |33.5| 0. 53 1.41 | 135.01 1. 84 0.0 | ATENT HEAT FLOX 2.0 | 4.0 J 7.0 | 0. 0 2.6 2 0. 20 0.08 0. 04 0.02 0. 02 0. 02 0. 38 3.09 0. 0 0. 0 0. 0 0.0 5.57 0. 26 0. 11 0.06 0.04 0.04 0.45 3.26 0.0 0.0 0. 0 r o.o 357. 9 6.34 0.28 0.10 0.05 0.04 0.04 1.31 0.0 0.0 0.0 0.0 0.0 + 14.0 | 0.0 150.7 0.42 0.14 0.08 0.06 0. 15 0.0 0.0 0.0 0.0 0.0 0.0 1 28. 0 j 0. 0 0.0 0. 4 1 0. 10 0.06 0. 12 0. 0 0.0 0. 0 0. 0 0. 0 0. 0 0.0 216 A p p e n d i x G Ihe t e s t v a l u e s f o r t h e c o r r e c t e d c a l c u l a t i o n s f o r t h e h e a t f l u x e s . Ihe d i f f e r e n c e means a r e g i v e n i n Watts/m* and t h e d i f f e r e n c e v a r i a n c e s were f o r c e d t o 0.0 i n a l l c a s e s and a r e n o t shown. 2 i 1 — i j DIFFERENCE MEANS - SENSIBLE HEAT FLUX I ISHJPI 0.25 | 0.50 | 1,0 | 2.0 | 4.0 J 7.0 | 14.0 | 28.0 | f + -f + ^ + + i 4 + 1 I A J 0.03 | 0.06 | 0.37 | 0.78 | 1.01 | 2.28 | 2.49 | 1.12 | | B | 0.05 | 0.01 J 0.02 | 0. 13 | 0.61 | 0.48 | 0.12 | 0.26 | | C | 0.04 | 0.08 | 0.00 | 0.34 | 0.73 | 0.82 | 1.03 | 1.34 | | B J 0.01 | 0.09 | 0.45 | 0.99 | 0.97 | 0.80 | 0.35 | 0.83 | J E | 0.02 | 0.02 | 0.21 | 0.41 | 0.60 | 0.60 | 0.73 | 1.87 | | I 1 0.12 | 0.23 | 0.59 | 1.27 | 2.21 | 2.61 J 3.12 | 2.98 | | J J 0.03 | 0.09 | 0.33 | 0.58 | 0.89 | 1.16 | 1.10 | 1.24 | | K | 0.02 | 0.03 | 0.03 j 0.08 | 0.09 | 0.41 | 1.14 | 1.36 | | M | 0.08 | 0.26 | 0.64 | 0.88 | 2.26 ( 1. 84 | 2.30 | 1.76 | j N | 0.02 | 0.12 | 0.16 | 0.41 I 0.85 l 0.70 | 0.51 | 1.91 | . P | 0.06 | 0.16 | 0.31 | 0.54 | 0.67 | 0.68 | 0.66 | 0.89 | \ DIFFERENCE MEANS - LATENT HEAT FLUX "j j. + 4 + 4 + 4 + - 4 1 1SHIP | 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | | A | 0.00 | 0.00 | 0.49 | 2.16 | 2.29 | 6,75 | 7.19 | 1.12 | | B | 0.03 | 0.03 | 0.24 | 0.72 | 2.31 | 1.54 . 1.23 | 0.26 | | C | 0.12 | 0.23 | 0.45 | 0.79 | 0.74 1 1. 53 | 1.25 | 0.9 1 | | D | 0.48 | 0.79 | 0.23 | 3.76 | 6.95 | 6.75 | 6.76 | 8.61 | j E | 0.39 | 0.98 | 0.33 | 2.97 | 9.73 J 13.8 | 9.89 | 2.02 | | I | 0.05 | 0.22 | 1.12 J 3.15 | 6.31 | 5.83 | 9.96 | 8.5 1 | j J J 0.05 | 0.10 | 0.27 | 1.87 | 2.77 j 3.28 | 2.79 | 2.35 | | K | 0.05 | 0.11 | 0.14 | 0.55 | 0.97 ] 1.07 | 1.52 | 3.92 | J M | 0.07 J 0.08 | 0.35 | 0.57 | 4.82 | 3.47 | 3.65 | 0.24 | | N | 0.86 | 1.64 | 3.12 | 3.27 | 0.02 | 6.25 | 10.4 | 17.7 | j P | 0.04 | 0.14 | 0.41 | 0.92 | 2.11 | 1.91 | 1.76 | 1.43 | J. J 4 . -L 1 L 1 P 1 | RESIDUAL VARIANCES - SENSIBLE HEAT FLUX | ISHIPJ 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 ' J 14.0 | 28.0 j \ A | .003 | .008 | . 022 j .043 j .056 1 -072 | .070 j .099 | I B j .003 | .006 | .017 | .033 | .040 | .035 | . 039 | .042 | | C | .004 | .010 | .021 | .035 | .045 | .042 | . 042 | .048 | J D | .004 | .010 | .026 | .042 1 .051 | .056 | .054 | .062 | | E j .005 j .010 | . 024 | .049 | . 076 | . 089 | .109 | .135 | i I | .004 1 .0 10 J ,021 | .038 | .052 | . 064 | . 085 | .127 | | J . .003 | .010 | .019 | ,032 | .040 | .050 | .064 | .074 | j K | .003 | .007 | .013 | .023 | .034 | .035 | . 043 . .081 | | M | .004 | .010 | .021 | .042 | .066 | . 080 | .119 | .164 | | N | .006 | .011 J . 020 | .042 | .071 | . 086 | .145 | . 233 | i P | .003 | .008 | .021 | .035 | .039 | .038 | .045 | .0 25 | I I , L I , I J I I I _ J L +  SHIPI 0.25 +_ A i .004 6 1 .004 c 1 .005 D | .006 £ | .006 1 | .006 J | .004 K | .004 M | .005 N | .006 P 1 .003 +-SHIPI j 0. 25 r -A | .998 B I .999 c I .998 D | .998 £ | .998 I j .998 J | .998 K | .999 a i .998 N J .997 P I .999 RESIDUAL VARIANCES -| 0.50 | 1.0 | 2.0 | -+ + + h .0 12 .010 .013 .0 17 .013 .015 .0 12 .009 .015 .0 12 .009 .038 .030 .032 . 043 .04 1 .039 . 030 .022 .038 .029 . 026 .079 .062 .057 .078 .111 .076 .060 .049 .084 .086 .056 LATENT 4. 0 | + .122 . 083 .078 .095 . 199 . 116 .093 .084 . 154 . 191 .070 HEAT 7.0 . 165 . 084 . 083 .120 .270 .157 .121 . 122 .197 . 268 .076 FLUX 4 + I 14.0 | +-. + . 201 .095 .092 . 138 .382 .226 . 192 . 198 .317 . 534 .098 1 28. 0 4 ,. 2 54 . 10 2 .099 . 184 . 499 .383 .270 . 3 15 .411 . 834 .0 75 COREELATION | 0.50 J 1.0 .996 | .989 .997 | .992 .995 | .989 .955 | .987 .995 | .588 .995 | .989 .995 | .990 .997 | .994 .995 | .989 .994 | .990 .996 | .989 COEFFICIENTS - SENSIBLE HEAT I 2.0 | 4.0 | 7.0 1 14.0 | | .978 | . 972 | . 964 | .965 | I .984 | . 980 | .983 I .981 | | .982 | . 577 | .979 | .979 | I .979 | . 975 | . 972 1 .973 | I .976 | . 962 | .956 I .946 | | .981 | . 974 | .968. 1 . 958 | | .984 | . 980 | . 975 | .968 | | .988 | . 983 | .982' 1 .979 i I .979 | . 967 | .960 | .940 | 1 .979 | . 964 | .957 I .928 | | .982 | . 980 | . 981 I .977 | FLUX 28.0 1 . 951 .979 .976 .969 .932 .936 . 963 .960 .9 18 .884 . 987 1 _ L CORRELATION COEFFICIENTS • - LATENT HEAT FLUX | 1 IPI 0. 25 T 1 0. 50 | 1.0 I 2.0 | 4.0 _ ____ _____ I 7.0 I 14.0 | 28.0 | L. -+ +- - 4 — . + +- 1 A | .9.9 8 | .994 | . 981 I -961 | .939 | .918 | , 899 j .873 | B I .998 | .995 | . 985 I .969 | .558 I .958 1 .952 | . 949 | C I .997 | .994 | . 984 | .971 | .961 I .959 1 -954 | .951 | D I .997 | .992 | . 578 | .961 | .952 I .940 | .931 | .908 | E | .997 | .993 | . 980 | .945 | .901 | .865 | .809 | . 750 | I | .997 | .993 | .98 1 | .962 | .942 | .922 | .887 | .809 | J | .998 | .994 | . 585 I .970 | .954 I .939 I ,904 | .865 | K | .998 | .995 | . 989 | .975 | .958 | .939 | .90 1 | . 842 | M | .998 J .993 | . 981 I .958 | . S23 I .901 | .842 | .794 | N | . 997 | .994 | . 985 I -957 | . 505 | .866 | .733 | . 583 | P i .999 | .996 | .987 I .972 | . 965 | .962 1 -951 | .962 | 1 , J. J 219 a p p e n d i x H The s h i p s ' r e g r e s s i o n c o e f f i c i e n t s f o r t h e e m p i r i c a l e q u a t i o n o f the form \-|+ * (ttj'+i>y)4'r L < ( • I n e g e o g r a p h i c a l l y a v e r a g e d v a l u e s a p p e a r a t t h e end. The C i n d i c a t e s t h e c o n s t a n t d r a g c o e f f i c i e n t , t h e L i n d i c a t e s t h e l i n e a r d r a g c o e f f i c i e n t , t h e H r e f e r s t o t h e h e a t f l u x w i t h S f o r t h e s e n s i b l e h e a t and L f o r t h e l a t e n t h e a t . I h e X and Y r e f e r t o t h e x and y s t r e s s components r e s p e c t i v e l y . . 220 SHIP TYPE + — -4 J 1 T |C X |4.108 1 c Y |4.190 1 L X 13.081 |L Y | 3.046 1 H S I 3. 227 |H L (2.945 1 c X 14.951 |C Y |4.127 1 L X | 4.259 |L Y I 3.295 IH S |3.997 1 H L |3.164 |C X |4.564 1 c Y | 4. 487 | L X | 3. 222 1 L Y |3.132 IH S i 2. 766 iH L |2.463 |C X | 3. 561 |C Y |4.618 i L X | 2. 895 |L Y | 3. 152 |H S I4.034 IH L |2.639 JC X | 1. 661 |C Y | 2.060 |L X 10.769 |L Y | 1.032 1 H S 12.059 IH L |1.204 |C X |4.413 |C Y | 5.079 1 L X |3. 155 |L Y | 3.592 IH S 14.991 IH L 1 3. 903 REGION I -1. 365 -1.410 -0.982 -1.022 -1.440 -1.433 -1. 423 -1.34 1 - 1. 10 1 -0.S88 -1.589 -1.487 -1.376 -1.318 -0.S75 -0.890 - 1 . 336 -1.35 1 -1.250 -1.334 -0.885 -0.900 -1.484 -1.366 -1.090 -1.172 -0.526 -0.616 - 1 . 327 -1. 145 -1.443 -1.474 -1.04 1 -1.05 4 -1.622 - 1 . 526 REGION I I DAYS | 4. 0 - 2 8 . 0 DAYS J •+- 4 I v i_ oi I i i y ____ | 0 . 9 4 1 —I I 5 . 866 T — 1. 2 12 10. 210 | 0 . 9 5 1 | 5 . 537 | -1 .250 | 0 . 2 6 3 | 0 . 9 8 4 I 5 . 694 j - 0 . 9 4 4 | 0 . 2 5 6 | 0 . 9 9 1 I 5 . 216 j -0 .980 10 .318 | 0 . 9 8 0 |4. 279 j - 1 .204 | 0 . 2 4 3 I 1 .014 I 3 . 967 V" 1. 215 | 0 . 2 5 0 | 0 . 947 }6. 053 1- 1. 189 10 .209 | 0 . 9 7 0 | 5 . 662 1 -1. 162 | 0 . 2 0 3 | 0 . 9 8 0 I 6 . 084 1 - 0. 926 . 0 . 2 4 9 | 1 . 0 2 2 I 5. 430 1 -0 . 8 9 0 10 .248 I 1. 014 |4. 99 1 1 -1. 315 10 .208 | 1 . 0 3 9 | 4* 388 1- 1. 275 JO.214 | 0. 912 | 4. 772 ]- 1. 137 | 0 . 2 3 8 | 0 . 8 8 4 I 5 . 890 J - 1. 168 i 0 . 1 8 9 | 0 . 9 7 2 I 3 . 664 1 -0 . 7 4 5 10 .280 | 0 . 9 3 5 | 5 . 157 1 -0. 8 19 10 .216 | 0 . 9 2 9 | 3 . 358 1 -1. 155 | 0 . 248 | 1 . 003 I 3 . 199 1- 1.171 | 0 . 2 6 8 I 0 . 9 0 8 |4. 030 j - 1. 036 | 0 . 2 4 4 | 0 . 8 6 0 I 6. 302 I - 1. 167 | 0 . 166 | 0 . 9 7 6 | 2 . 758 1 -0. 627 I 0 . 3 0 5 | 0 . 8 9 7 I 5 . 317 j - 0 . 8 0 3 | 0 . 197 | 1 . 0 2 7 I 4. 510 J - 1. 190 | 0 . 2 0 1 | 1 . 0 2 9 I 4 . 068 1- 1. 153 | 0 . 2 0 0 i 0 . 9 1 6 I 2 . 612 J- 1.0 13 | 0 . 2 8 7 | 0. 879 I 3 . c 15 1 -1 .083 | 0 . 2 1 6 | 0 . 9 6 8 I 1- 787 j - 0 . 6 3 2 | 0 . 3 5 9 J 0 . 9 0 7 I 2 . 527 1 - 0. 733 | 0 . 2 8 7 | 0 . 9 9 0 I 3 . 698 1 -1 .226 10 .217 | 1 . 0 2 9 J 3 . 0 4 5 1- 1. 126 | 0 . 2 1 8 I 0 . 924, | 5 . 100 j - 1. 237 | 0 . 2 6 0 | 0 .872 i 5 . 928 1 -1. 291 | 0 . 2 2 5 | 0 . 9 6 6 I 4 . 409 1 - 0. 9 14 | 0 . 2 9 9 | 0 . 9 1 2 | 5 . 140 1- 0. 966 | 0 . 2 6 1 i 0 . 9 0 5 | 5 . 065 1 -1. 355 | 0 . 2 7 8 | 0 . 958 I 4 . 182 J" 1. 296 | 0 . 3 0 0 221 J |C X | 3 . 770 1 - 1 . 4 2 0 1 0 . 9 1 5 1 4 . 44 8 | - 1 . 256 J O . 2 8 0 |C Y | 4 . 5 15 | - 1 . 4 5 8 | 0 . 8 9 5 1 5 . 964 1 - 1 . 3 2 0 | 0 . 2 2 9 |L X | 2 . 426 1 - 0 . 9 7 9 | 0 . 9 5 6 | 2 . 93 1 1 - 0 . 8 13 | 0 . 3 1 9 |L Y 1 3 . 0 1 9 1 - 1 . 0 1 6 | 0 . 9 2 5 1 4 . 77 0 1 - 0 . 9 4 8 1-0. 252 IH S | 3 . 7 5 5 | - 1 . 565 | 0 . 9 4 0 1 4 . 6 8 5 | - 1 . 391 | 0 . 2 7 7 1 H L I 2 . 517 1 - 1 . 4 7 3 | 1 . 0 0 5 1 3 . 879 1 - 1 . 3 4 8 1 0 . 2 9 7 K |C X | 2 . 123 1 - 1 . 2 1 9 J O . 8 6 0 1 2 . 407 1 - 1 . 1 1 4 | 0 . 3 8 8 |C Y J 2 . 242 1 - 1 . 1 9 4 | 0 . 8 5 6 1 2 . 830 | - 1 . 1 0 3 | 0 . 3 4 1 J L X | 1 . 0 1 6 I - 0 . 6 5 7 | 0 . 8 9 1 1 1 - 485 . - 0 . 6 8 5 I 0 . 4 5 8 |L Y | 1 . 0 7 7 I - 0 . 6 2 4 | 0 . 9 0 4 I 1 . 970 I - 0 . 7 09 | 0 . 4 0 2 IH S | 1 . 2 4 8 1 - 1 . 2 3 1 | 0 . 9 2 1 1 3 . 618 1 - 1 . 4 6 8 J 0 . 2 4 6 |H L | 1 . 1 9 9 | - 1 . 2 4 7 1 0 . 9 7 9 1 1 . 807 I - 1. 2 5 3 | 0 . 4 1 9 M |C X | 3 . 8 4 3 1 - 1 . 4 3 7 | 0 . 958 I 3 . 622 1 - 1 . 1 4 6 | 0 . 3 0 2 |C Y | 3 . 837 | - 1 . 4 6 5 | 0 . 9 2 0 I 4 . 4 14 1 - 1 . 2 2 8 | 0 . 2 5 0 |L X | 2 . 4 0 0 I - 0 . 9 8 2 | 0 . 9 9 6 1 2 . 64 4 I - 0 . 8 1 1 | 0 . 3 8 5 IL Y | 2 . 381 | - 1 . C O 9 | 0 . 9 4 3 fl —1 • 439 | - 0 . 912 | 0 . 3 1 5 1 H S | 2 . 5 9 8 | - 1 . 4 5 8 | 0 . 9 6 5 1 3 . 7 1 1 | - 1. 2 6 9 1 0 . 2 7 1 1 H L | 2 . 0 10 1 - 1 . 357 | 1 . 0 1 9 1 2 . 99 8 | - 1 . 2 1 3 | 0 . 3 0 9 N |C X | 2 . 2 1 0 | - 1 . 4 7 4 | 0 . 6 8 2 1 4 . 177 | - 1. 5 5 3 | 0 . 2 3 0 1 c Y | 1 . 943 1 - 1 . 34 1 | 0 . 7 6 4 1 3 . 507 | - 1 . 3 7 8 | 0 . 240 1 L X I 0 . 8 6 0 | - 0 . 8 1 0 | 0 . 6 9 0 1 4 . 305 | - 1 . 3 9 3 1 0 . 2 1 8 1 L Y | 0 . 8 2 7 I - 0 . 7 2 0 | 0 . 7 8 5 1 3 . 217 | - 1. 1 70 I 0 . 2 6 2 1 H S | 1 . 533 1 - 1 . 5 1 6 ! 0 . 8 3 6 1 2 . 082 1 - 1 . 5 2 0 | 0 . 3 2 9 IH 1 | 1 . 9 5 0 | - 1 . 423 | 0 . 8 5 7 1 1 ' 376 1 - 1 . 6 0 3 | 0 . 3 2 7 P 1 c X I 4 . 1 18 1 - 1 . 339 1 0 . 8 8 7 1 5 . 487 1 - 1 . 237 | 0 . 2 5 1 |C Y | 3 . 9 8 9 1 - 1 . 3 3 0 | 0 . 9 0 3 1 4 . 825 | - 1 . 1 5 9 | 0 . 2 4 3 1 L X | 3 . 3 1 5 1 - 0 . 9 6 6 | 0 . 9 3 3 1 4 . 464 1 - 0 . 8 6 3 | 0 . 2 8 0 |L Y 1 3 . 4 9 4 | - 1 . 0 0 6 1 0 . 937 1 3 . 749 1 - 0 . 7 7 3 | 0 . 2 7 9 |H S | 2 . 2 6 5 i - 1 . 3 1 5 | 0 . 998 | 3 . 657 1 - 1 . 2 3 3 J O . 2 6 4 IH L | 1 . 902 1 - 1 . 3 4 5 | 1 . 0 2 0 | 3 . 387 1 - 1 . 2 3 0 | 0 . 2 6 5 AVG |C X | 3 . 3 3 7 J - 1 . 3 2 2 | 0 . 9 2 0 | 4 . 237 | - 1 . 150 | 0 . 2 6 1 |C Y | 3 . 437 1 - 1 . 3 3 6 I 0 . 9 0 1 1 4 . 639 1 - 1 . 183 | 0 . 2 3 1 1 L X | 2 . 325 1 - 0 . 9 1 0 | 0 . 9 6 7 1 3 . 276 1 - 0 . 7 9 5 | 0 . 310 |L Y | 2 . 3 2 2 1 - 0 . 9 1 0 | 0 . 9 4 0 | 3 . 754 | - 0 . 8 5 3 | 0 . 2 7 5 |H S I 2 . 8 7 4 1 - 1 . 4 6 9 | 0 . 9 8 4 1 3 . 94 6 1 - 1 . 2 4 4 I 0 . 2 4 4 IH L | 1. 365 1 - 1 . 2 5 1 | 1 . 0 2 1 1 2 . 3 3 5 | - 1 . 108 | 0 . 2 6 3 222 A p p e n d i x I Ihe f o u r t e s t v a l u e s f o r t h e s t r e s s e s and t h e h e a t f l u x e s when the i n d i v i d u a l s h i p s ' e q u a t i o n 1 + ^ U j 1 * v-£)a,lL.* was a p p l i e d t o e a c h v e l o c i t y i n d i v i d u a l l y . The s t r e s s DMs a r e i n dPa and t h e h e a t f l u x DMs a r e i n Watts/m 2. . 223 r '• 1 J DIFFERENCE MEANS - X COMPONENT CONSTANT D.C. | JSHIPI 0.25 | 0.50 | 1.0 | 2.0 I 4.0 | 7.0 | 14.0 j 28.0 1 | A | 0.003| 0.0091 0.023| 0.045| 0.066J 0.069J O . O 6 9 ! O . O 6 7 I I B I 0. 004J 0. 004| 0.0011 0. 0031 0.0001 0.005J 0.012) 0.006| | C | 0. 002I 0.0 111 0.0361 0. 051J 0.0641 0.078| 0.076J 0. 043| | D I 0.0C5| 0.023| 0.054| 0.060| 0.060| 0.071| 0.068J 0.039| I E I 0.0011 0. 004| 0.007| 0.004| 0.0 141 0.0121 0.0131 0.033| I I i 0.001| 0.003| 0.010| 0.0C8| 0.003| 0.005| 0.013J 0.003| J J J 0. 006) 0.001| 0.0031 0. 0 1 5 | 0 . 0 3 0 | 0.030| 0. 0 171 0. 0 4 11 J K I 0.001| 0. 009| 0.017| 0.0021 0.02 21 0.014| 0.0121 0.020| I M I 0. 0001 0.003| 0.0111 0.012| 0.01 1 | 0.0241. 0.0361 0. 028| I N I 0.014J 0.030| 0.065I 0.1311 0.163J 0. 174 | 0. 1981 0. 233| J P 1 0. 002| 0.012| 0.024| 0. 0 151 0.009| 0.001 1 0. 016) 0.03 1) I DIFFERENCE MEANS - Y COMPONENT CONSTANT D.C. ~ j ISHIPI 0.25 I 0.50 J 1.0 | 2.0 | 4.0 | 7.0 | 14.0 T 28.0 | t 4 4 4- 4 -4 4 4 4 H J A I 0.0031 0.008| 0.0121 0. 01 41 0.0151 0.020| 0.005| 0. 001 ( I B | 0. 002I 0.003| 0.0011 0.012] 0.030| 0.050J 0.065| 0.07 11 I C I 0. 006J 0.016| 0.017| 0. 00 11 0.0 151 0.025| 0.0291 0.042| I D 1 0. 007| 0.0201 0.024| 0.010| 0.00S| 0.013 | 0.0211 0. 036| 1 E 1 0. 005| 0.006| 0.017| 0. 038| 0.055| 0.057| 0.062) 0. 077| I I 1 0.001| 0. 005| 0.005| 0. 0 181 0.0281 0.0171 0.0 161 0. 023| 1 J I 0. 002) 0.004| 0.011| 0. 0181 0.0311 0.024| 0.024J 0.042| 1 K 1 0. 005| 0.0 121 0.0 181 0. 025| 0.026| 0.0151 0.0061 0.022| I M I 0. 0001 0.0021 0.0021 0.0021 0.0151 0-0121 0.003| 0.002J I N 1 0. 005| 0.0 111 0.024| 0. 047| 0.059| 0.065| 0.070| 0. 080) 1 P I 0.006| 0.001| 0.010| 0. 0011 0.0061 0.020| 0.044J 0. 027J J- , L L, X L 1 11 L - X ..J J DIFFERENCE MEANS - X COMPONENT LINEAR D.C. | J. X__ X X X X X X X .J ISHIPI 0.25 I 0.50 J 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | j. x + 4 4 4— 4 4 4 1 1 A 1 0. 003| 0.012| 0.037| 0. 076| 0.114| 0. 1181 0. 1 111 0. 1 121 I B J 0. 0071 0.0111 0.0091 0.0151 0.00S| 0.007| 0.004| 0. 0361 | C | 0.006I 0.014| 0.0511 0. 080| 0.109| 0. 12 51 0. 1 14) 0.065| I D 1 0. 006| 0.0351 0.084| 0. 089| 0.092J 0. 1041 0.092) 0.052) 1 E I 0.0021 0.0041 0.007| 0. 0121 0.02 81 0.029 | 0.032| 0.064| 1 I I 0.001| 0. 0051 0.0 161 0. 0091 0.007| 0.007| 0.0171 0.000| 1 J I 0.011| 0. 0061 0.003| 0.036| 0.055| 0.063 | 0.047| 0.096| 1 K J 0.0001 0.0 121 0.022| 0.0G9| 0.039| 0.028) 0.029| 0.044] ) M I 0. 001) 0.004| 0.013| 0. 0 1 11 0.0 12) 0.030| 0.042| 0.028| I N I 0. 0 181 0. 037| 0.0801 0. 1631 0. 210) 0.2321 0.269) 0. 3 il7 | 1 P I 0. 007) 0.024J 0.041| 0. 032| 0.020| 0.003) 0.032| 0. 0 531 I L 224 Y - 4 4. L_ (. 4 . 4 4- 4- -j ISHIPJ 0.25 | 0. 50 | 1.0 | 2. 0 | 4. 0 I 7.0 J 14 .0 1 28.0 | 1 i & — r _____ ^>_,__J. 0. 0C5| 0.015| 0.025I ._ j 0. 032| 0, ___ | 038| _______ _____ __|_. 0.041 | 0. ________!__ 017| 1 o . o i n 1 B | 0.005| 0.0091 0.003J 0-014| 0. 052J 0.081| 0. 100| 0.103| 1 c j 0. 0 12| 0.030| 0.035| 0. 00 6| 0. 017| 0.035 | 0. 043| 0.061| i D | 0.0 13J 0.035| 0.041| 0. 020| 0. 016| 0.0251 0. 0391 0.0601 1 E | 0.005| 0.0051 0. 0 1 91 0. 048| 0. 077| 0.083| 0. 093| 0.108| | I { 0.002| 0.008| 0.0061 0.032| 0.040| 0.031| 0. 034J 0. 052| 1 J | 0. 003 | 0.006J 0.0 14| 0. 030J 0. 0521 0.0471 0. 053| 0.085| 1 K 1 0.008| 0-0 18| 0.025| 0.034| 0. 034| 0.0181 0. 0071 0.024| I M | 0.0001 0.003| 0.0021 0. 0C5| 0. 021 | 0.016| 0. 005| 0.0031 I N | 0.007J 0.0 15| 0.031| 0. 060| 0. 077| 0.086J 0. 096 1 0.1111 1 P 0.0 13 1 0.0031 0.009J 0. 007J 0. 0 17 | 0.037| 0. 0601 0.0171 DIFFEEENCE MEANS - Y COMPONENT LINEAR D.C. — I DIFFEEENCE VARIANCES SHIPI 0.25 | 0.50 1 1.0 J - X COMPONENT 2.0 | 4.0 | j- 4 -CONSTANT D.C. 7.0 I 14.0 | 1 28.0 4 0. 088 0.032 0. 003 0. 10 3 -. 0 16 0.030 0.007 -.022 0.00 1 -.005 -.006 A 1 -. 0071 0.0 10| 0.0201 -.0 15| -.037| 0.007| 0. 064 | B | -. 004| 0.0081 0.0171 -.026| -.0401 0.038| 0. 057| C J -,006| 0.008 J 0.0 15| -. 0081 -.000| 0.004 J 0. 015| D | -.0C7| 0.0061 0.024| -.0 11| -.0431 -.012 1 0. 019| E 1 -. 004| 0.007| 0.0101 -.0121 -.0231 0.035| 0. 042J I J -. 0 C5 | 0.0081 0.0 151 -.0131 -.0161 0.0091 0. 044 { J 1 -. 0051 0.007| 0.0 14| -. 0 14| -.0091 0.0191 0. 045 | K | -.0051 0.009| 0.0191 -.0261 -.0231 0.017J 0. 059| M I -, 0 05| 0.009| 0.0181 -. 0 18| -.023| 0.038J 0. 0371 N 1 -.006| 0.0071 0.0 14 1 -. 002J 0.008J 0.032| 0. 033| P | -. 0091 0.0081 0.032| 1 -.021| 1 -.0 16| 0.0301 0. 037J h 4 SHIPI 4 A B C D E I J K M N P DIFFEEENCE VARIANCES 0.25 | 0.50 J 1.0 | 0. 009 0.008 0. 0 14 0.017 0.006 0.0 11 0. 010 0.008 0. 009 0.009 0.007 - Y COMPONENT 2.0 | 4.0 | CONSTANT D. C. 7.0 1 14.0 1 1 28.0 1 0.031 0.015 0.023 0. 071 0. 128 -.010 -. 009 -.024 0.029 0. 005 0.002 006 006 008 007 0C5 006 006 007 006 003 008 0.018 0.02 1 0.024 0.021 0.02 1 0.019 0.021 0.023 0.019 0.006 0.020 013 0 17 03 5 , 041 02 1 02 1 024 0 17 ,0 18 005 ,003 -.029 -.0 16 -.009 -.029 -.062 -.003 -.010 -.0 14 -.031 -.004 0.001 0.036 0.033 0.042 0.018 0.007 0.041 0.056 0.051 0.011 0.057 -.009 0.062 0.041 0. 037 0.052 0.089 0. 040 0.050 0.051 0.077 0.064 0.027 L I ' 1 i DIFFERENCE VARIANCES - X COMPONENT LINEAE D.C. | | SHIP | 0.25 | 0.50 | 1.0 | 2.0 | 4 . 0 { 7 .0 { 14.0 | 28.0~| I A | -.012| 0.018| 0.029| - . 0 2 2 } - . 0 4 s t - . O O s j 0 . 0 7 5 } 0 . 078~j I B i -. 007J 0.013| 0.027| -.0491 0501 0.055| 0.061| -,006| | C | -.010| 0.013| 0.015| 0.003| -,009| -.014. 0.018| 0.017] i D ) - . 0 1 1 | 0 . 009| 0.045| -.028| -,070| -.0561 0.004| 0.158| I E I -. 0061 0.008| 0.017| -. 0 141 -. 01 2 | 0.054| 0.048| -. 0 9 91 j I | -.0C8| 0.014| 0.019| -. 028| -. 03 51 -.003| 0.044| 0 . 047| J J I -,007| 0.011J 0.021J -. 029| -. 0391 0 .00 1| 0.077| 0.0 151 1 K I -.0121 0.013| 0.039| -.0441 -. 015 J 0.0321 0.0521 ^.075| 1 M 1 -. 009| 0 . 0 151 0.027| -. 036| -.007| 0.058| 0.034| -. 094| I N 1 -.011| 0 . 0 1 0 | 0.0211 -.010| 0.0361 0.050| 0.011 | -. 0701 I P 1 -.013| 0 . 0 121 0.048| -. 042| -.040] 0.044| 0.046| -. 035| I I I I 1 I I I I I J- J X J J 1 J L I , j 1 DIFFEEENCE VABIANCES - Y COMPONENT LINEAE D.C. | ISHIPI 0.25 I 0.50 I 1.0 | 2.0 | 4 . 0 | 7 . 0 | 14.0 } 28 . 0 | I A 1 -.011| O.014J 0.027| -.018| -.044.1 0 . 0 6 2 } 0 . 0 7 o j - . 0 21~j I B I - . 0 1 0 | 0.013| 0.0321 -, 032| -. 0151 0.042| 0.031| -. 020| 1 C I - , 0 1 0 | 0.024| 0.025| -. 0 6 11 -,020| 0.043| 0.028| 0.002J I D I - . 0 131 0 . 028| 0.0321 - . 0661 -. 0 511 0 . 0 0 2 | 0.028| 0 . 085| | E | -, 006| 0 . 0 101 0.024| -.040| -.052| 0.023| 0.064| 0 . 055| I I I -.011| 0.021| 0.027| -. 047| -. 00 51 0 . 066J 0.041| -.060| I J I -.010| 0.0181 0.032| -,051| -.0161 0.075| 0.049| -.050| I K I -,015| 0.013| 0.038| -. 0 231 0161 0.083| 0.028J -. 0841 I M I - . 0 1 1 | 0.014| 0.029| -.0261 -.014| 0.022| 0.076| -.058| I N 1 '. 004| 0.012| 0.003| -,015| 0.025| 0.0751 0.035| -.0 7 11 I P 1 -. 0 121 0. 007| 0.0291 0. 0101 -.0141 -.0251 0.0621 -.0171 I J I I I I I I I I \ . -I X - . J J 1 - r - X , I.. I J I RESIDUAL VARIANCES - X COMPONENT CONSTANT D.C. | ISHIPI 0.25 I 0.50 I 1.0 | 2.0 J 4.0 | 7.0 | 14.0 | 28.0 | I I | | ___| | j. j. ___x_» j | A J 0. 0 0 2 | 0.0071 0.0 17| 0. 03 11 0.045| 0.047) 0.044| 0. 038| I B I 0. 0031 0.007| 0.017| 0. 032| 0. 0431 0.045| 0.038| 0.031| I C I 0. 0031 0.008| 0.018| 0. 0341 0.045| 0.042| 0.048| 0. 048| I D I 0.004| 0.009| 0.024| 0. 040| 0.048J 0.051| 0.047| 0.0 5 11 1 E I 0. 003| 0.006| 0.014| 0. 029] 0.037| 0.041J 0.038| 0. 0321 | I I 0.002| 0.006| 0.0 131 0. 022) 0.029| 0.030| 0.0351 0. 035J I J I 0. 0021 0.006| 0.013| 0.023| 0.030] 0.033| 0.042| 0. 038| ] K 1 0. 0021 0.0061 0.0121 0. 0 181 0.024| 0.030J 0.039| 0.044| 1 M I 0. 002| 0.006| 0.013] 0. 024| 0.03 1 | 0.035| 0.043| 0. 040| I N I 0.0031 0.0041 0.008] 0.017| 0.025| 0.035| 0.041| 0.0411 I P I 0. 003| 0.008| 0.020| 0. 0341 0.040| 0.043| 0.042| 0.0 351 i 1 1 J J J I L I J I — — — 1 I RESIDUAL VARIANCES - Y COMPONENT CONSTANT D.C. I ISHIPI 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | | A | 0. 0021 0. 005J 0.0141 0. 026| 0.040| 0.046| 0.048| 0. 035| | B | 0. 003| 0.007| 0.017| 0. 037| 0.056| 0. 058J 0.054| 0. 049| | C | 0. 004| 0.0 111 0.025J 0. 044| 0.054| 0.049| 0.049| 0.044| | D | 0. 006| 0.014| 0.030| 0. 050| 0.070| 0.0741 0.074| 0. 075| | E | 0. 004| 0.008| 0.021| O. 036| 0.065| 0. 067| 0.064J 0. 064| | I | 0. 003| 0. 008| 0.014| 0. 024| 0.03 11 0.035| 0.040| 0.042| | J | 0.0031 0. 008| 0.017| 0» 028| 0. 036| 0.041| 0.037| 0.033| | K | 0. 003| 0.008| 0.018| 0. 0271 0.0361 0.040| 0.048| 0. 066| 1 M | 0. 0021 0.0051 0.012| 0. 0221 0.033| 0.034J 0.041| 0.040| | N | 0. 003| 0. 006| 0.011| 0. 024| 0.038| 0.045| 0.052| 0.055| 1 P J 0.0031 0.008| 0.0 191 0. 0 3 91 0. 0501 0.050| 0.0531 0. 067 j 1 RESIDUAL VARIANCES - X COMPONENT LINEAR D.C. ] ISHIPI 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | | A | 0.006| 0.017| 0.041| 0. 082| 0.117| 0.118| 0. 1001 0. 087| 1 B | 0. 0061 0.016| 0.041| 0. 079| 0. 10 71 0. 108J 0.090| 0.079| | C | 0.007| 0.017| 0.0431 0. 0851 0. 1 16| 0. 1071 0.119J 0.118| | D | 0. 008| 0. 0241 0.065| 0.111J 0.133| 0- 138 | 0. 1 151 0. 10 71 1 E 1 0. 006| 0.015| 0.0321 0. 068| 0.079| 0.084| 0.077| 0.064J | I | 0.006| 0.015J 0.0321 0. 054| 0,.065| 0.070| 0.079J 0.085| 1 J 1 0. 005| 0.015| 0.031| 0. 057| 0.077| 0.076J 0.094| 0. 089| | K | 0.005| 0.014| 0.0311 0. 046| 0.061| 0.066| 0.0811 0. 0911 l M J 0. 0051 0.0 13| 0.031| 0. 058| 0.0691 0.078J 0.094| 0. 089| 1 N | 0. 0051 0. 0091 0.018J 0. 034| 0.0531 0.063| 0.065| 0.067| | P | 0. 0091 0.023| 0.0571 0.092| 0- 1051 0. 1091 0.099| 0. 0891 ). L , J J 1 1 L L — J ,~j 1 RESIDUAL VARIANCES - Y COMPONENT LINEAE D.C. I ISHIPI 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | 1 A | 0. 004| 0. 0 141 0.0331 0. 0641 0.0971 0. 111| 0.107| 0.0861 | B | 0. 006| 0.017| 0.042| 0. 093| 0. 1381 0. 136 1 0. 125| 0.116| | C | 0.012| 0.029| 0.066| 0. 117| 0. 1431 0. 1241 0. 1251 0. 111| | D 1 0.015| 0. 0381 0.0781 0. 128 | 0. 17 5 | 0. 179 | 0. 177 | 0. 173 1 | E | 0.010| 0.0211 0.050| 0. 080| 0. 1381 0. 1371 0. 131 ( 0. 124| 1 I | 0. 008| 0. 020| 0.036| 0. 062| 0.076| 0.084| 0. 0 961 0. 10 2 J | J | 0.007J 0.0201 0.044J 0. 070| 0.0 8 91 0.096| 0.0861 0.079| | K | 0. 007| 0.020| 0.0491 0. 072| 0.0851 0.093J 0. 1041 0. 1591 | M | 0.004| 0.011| 0.031| 0. 0531 0.075| 0.075| 0.084| 0. 086| | N 1 0. 007| 0.013| 0.022| 0. 045| 0.068| 0.080| 0.090| 0. 10 11 | P | 0. 009| 0. 0 191 0.048| 0. 0961 0. 1221 0. 1141 0. 1 121 0. 1441 I L L 1 I J J. L , I J CO EBEL ATION SHIP| 0.25 | 0.50 COEFFICIENTS - X I 1.0 | 2-0 | COMPONENT CONSTANT D 4.01 | 7.0 | 14.0 | A B C D E I J K M N P 0. 9S5 0. 9S9 0. 998 0. 998 0. 999 0. 999 0.9 9 9 0. 9 99 0. 999 0.999 0. 998 0.997 0,997 0. 996 0. 995 0. 997 0.997 0.997 0.997 0.997 0. 998 0.996 0.992 0.992 0.991 0.988 0.993 0.994 0.994 0.994 0.993 0.996 0.990 0. 984 0. 984 0. 983 0. 980 0. 986 0. 989 0. 989 0.991 0. 988 0.991 0. 983 0. S78 0.979 0. 978 0.977 0. 982 0.986 0.985 0. 988 0. 985 0.986 0. 980 0, 976 0.977 0. 979 0. 975 0.979 0.985 0. 984 0.985 0. 983 0.982 0. 978 0. 978 0.981 0.976 0. 976 0.981 0. 983 0.979 0.980 0. 978 0.9 79 0.979 .C. j 28. 0 j 0.98 1 0.985) 0. 976| 0. 974 0.984! 0. 982| 0.98 1 0.978, 0.980| 0. 980| 0. 98 2 I COBBEIATION SHIP | 0.25 | 0.50 COEFFICIENTS - Y + + h-1.0 | 2.0 | COMPONENT CONSTANT 4.0 | 7.0 | 14.0 J D. C. 1 28.0 1 0. 982| 0. 975| 0. 9781 0. 962| 0. 968 0. 979| 0. 983| 0. 967| 0.980 0. 972| 0. 9671 A B C D E I J K M N P 0. 999 0. 955 0. 998 0.997 0. 358 0. 958 0.999 0. 958 0. 9 99 0. 998 0. 998 0.997 0.997 0. 994 0. 993 0. 996 0. 996 0.996 0. 996 0.998 0. 997 0. 996 0.993 0.991 0.987 0.985 0.990 0.993 0.991 0.991 0.994 0.994 0.990 0. 987| 0. 98 1| 0. 979| 0.9761 0. 982| 0. 988| 0. 986| 0. 986| 0. 989| 0. 988| 0.9801 0.581 0.972 0.973 0. 965 0.969 0.985 0.982 0. 982 0.984 0.98 1 0.975 0.977 0. 971 0. 975 0.963 0.966 0.983 0.979 0.980 0. 983 0. 977 0. 975 0.976 0. 973 0.975 0.963 0. 968 0. 980 0.981 0.976 0.979 0.973 0.973 COBBELATION SHIP j 0.25 | 0.50 I- + - - - — 4 COEFFICIENTS - X 1.0 | 2.0 | COMPONENT LINEAB D.C 4,0 | 7.0 | 14.0 | A B C D E I J K M N P 0. 997 0. 997 0.997 0. 956 0.997 0.9 97 0. 958 0.9 97 0. 997 0.997 0. 955 0.992 0. 992 0.991 0. 988 0.992 0.993 0. 993 0.993 0.994 0.995 0. 988 0.979 0.979 0.978 0.967 0.984 0.984 0.984 0.984 0.984 0.991 0.971 0. 959 0.962 0. 957 0. 946 0. 966 0. 973 0. 972 0.978 0. 9 72 0. 983 0. 955 0.943 0.948 0.941 0. 936 0. S61 0.966 0. 962 0. 970 0.965 0.973 0. 949 0. 941 0. 945 0.947 0. 933 0.957 0. 965 0. 962 0.967 0. 960 0.968 0. 945 0.949 0. 954 0.940 0. 942 0.961 0.960 0.952 0.959 0.952 0.967 0. 949 28.0 "* H 0. 956 0. 960 0.941 0. 946| 0. 970 | 0. 957 0. 9551 0. 957| 0. 959 0.968, 0. 9 571 I T j CORRELATION COEFFICIENTS - Y COMPONENT LINEAR D.C. | .SHIP. 0.25 | 0.50 | 1.0 J 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | | A | 0. 998| 0 . 993 I 0.983| 0. 9681 0. 953| 0 . 9 4 3 J 0.945| 0. 9581 | B j 0. 997| 0. 992| 0.979| 0. 954| 0. 93 11 0-93 1 1 0. 937| 0. 943| | C | 0. 994| 0. 985| 0.967| 0- 9441 0.929J 0,937| 0.937| 0. 944J j D | 0 . 9931 0.981| 0.9611 0. 939| 0- 9 1 5 | 0- 911 | 0-9101 0. 9 11 | | E | 0. 995| 0.9891 0.975| 0. 96 11 0. 933| 0. 931 | 0.933| 0. 937| 1 I i 0. 996| 0. 990J 0.9821 0.9701 0.962| 0.957| 0.9511 0. 95 11 | J J 0. 996| 0.990| 0.978| 0. 966| 0.956J 0.9511 0.956J 0. 96 21 | K | 0. 996| 0.990| 0.9751 0. 9641 0. 9581 0. 9521 0.948| 0. 925| 1 M 1 0. 998 J 0. 9941 0.984| 0. 974| 0.9631 0.962| 0.957| 0.959| | N J 0. 996| 0. 993| 0.989J 0. 978| 0. 9661 0.9591 0.954J 0. 9 5 21 1 P 1 0. 9961 0. 990| 0.976J 0. 95 21 0.9391 0. 9441 0.9431 0.9 291 (. J JL 1 I 1 L L I J 1 DIFFERENCE MEANS - SENSIBLE HEAT FLUX 1 JSHIPI 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 I 14.0 | 28.0 | 1 A | 0. 235| 0.120| 0.041| 1. 0 131 1.487] 0. 589| 0.324| 1. 28 21 1 B | 0. 1071 0.0 111 0.067| 0. 706| 0.381| 0. 8021 1.7561 1.563| | C I 0.0671 0.046| 0. 1211 0. 3021 0.64 C | 0.924| 1.145| 1.192| | D 1 0.218| 0.157| 0.148| 1. 74 31 0.773| 0.248| 0.348| 0. 19 71 | E 1 0.081| 0.116| 0.265J 0. 7191 0. 747 J 0.4371 0.619J 1.49 71 | I 1 0.3611 0.417| 0.7391 2. 254| 2. 2531 2. 196 | 2.465| 4.619| | J J 0. 1591 0. 106| 0.239| 0. 9581 1.002 ( 0.882| 0.9991 2.007J 1 K J 0 . 0061 0.055| 0.0271 0. 0611 0. 113| 0. 523| 1. 1301 1. 1091 1 M J 0. 302| 0.299| 0.4 711 1. 645) 2.064| 1. 4671 1. 1651 2. 746| 1 N | 0. 1341 0. 2351 0.4 761 C. 9761 0. 5111 0.4691 0 .5891 1. 452| j P | 0. 0 S31 0.130| 0.249J 0. 56 11 0. 7161 0.676| 0 .5701 0. 7 10 | j j 1 J 1 1 x L 1 — . 1 | DIFFERENCE MEANS - LATENT HEAT FLUX | f 4 4 4 4 — (- 4 4 1- 1 1SHIP1 0.25 | 0.50 | 1.0 | 2.0 1 4.0 | 7.0 | 14.0 | 28.0 | 1 A 1 0.628| 0.7311 1.2871 4. 264| 4.6871 3.53 21 3.443| 5. 7621 1 B 1 0.305| 0. 342| 0. 530| 2. 546J 1. 7361 0. 1051 0.572| 0. 79 31 | C | 0. 302| 0.251| 0.221| 1. 566| 0.6761 0.002| 0. 1991 2. 5461 1 D 1 0. 532| 0 . 2601 0. 3471 5. 24 91 9.0771 6.566| 7 .0501 1 0 - 7 0 ) | E J 0. 937| 1.645J 3.537| 8. 837| 19. 16 J 16.61| 17.671 22.881 1 I | 1.132| 1. 634| 3.0471 7.80 11 7. 5581 7.697 | 9.290 | 15. 221 1 J 1 0.481| 0. 397J 0.735| 3. 1401 4. 8061 4 . 5571 5.5 16| 10. 14| 1 K 1 0.314| 0.274| 0.606| 2.0031 1. 3101 0 . 5091 1 .9 17| 3. 3271 | M 1 0.620| 0.7501 1.3451 4. 0861 4.6061 3-4621 3.7061 7.933J 1 N | 3. 272| 5. 9331 1 1 . 3 1 | 2 1 . 5 11 3. 8271 6. 403| 8.7511 6. 8 151 | P | 0. 228| 0.165| 0 .2681 1. 087| 2.444| 2.027J 2. 1501 3. 802| 1 -X X 229 r ' <• 1 J DIFFERENCE VABIANCES - SENSIBLE HEAT FLUX ( 1 SHIP 1 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | I- + + + + 1- + + + I I A | -.004J 0.002| 0.012| 0.016| -.041 | 0.049| 0. 1021 0. 120| 1 B 1 -. 001,1 0.006| 0.007| 0201 -.0301 0.006| 0.0651 0. 103| I C | -.0C5| 0.004J 0.0 191 -.00 11 0.003| 0. 0151 0,0 151 0.005| | D 1 -.0021 0.002| 0.014| -. 004| -.0 101 0.027| 0.0281 0. 064J 1 E | -.0021 0.001J 0.017| -. 0051 -. 0011 0.0581 0.059| 0.004| | I | -.0031 0. 008| 0.0131 -,010| 0.0 12| 0.028| 0.084| 0.045| 1 J 1 -. 004| 0.0C5| 0.015| -.002| -. 00 11 0.037| 0.046| -.041| 1 K | -, 005| 0.004| 0.017| -.0041 0. 001J 0.0371 0.084J -,021| I M 1 -. 0011 0.004| 0.011| -.015| -,023| 0.026J 0. 1041 0.137) 1 N | 0.001| 0.008| 0.002| -. 0121 0.04 11 0.053| 0.0861 0.027| 1 P 1 -. 006| 0.004| 0.020| 0 01 | -,004| 0.009) 0.055| 0.0141 I I I I I I I I I I (. J J 1 — I 1 X L_ I | | DIFFEEENCE VARIANCES - LATENT HEAT FLUX 1 L + x 4 + + + -f 4- H ISHIPI 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | | A J -. 0021 0.0031 0.010| 0. 0 151 - - 0 2 21 0.078] 0.172| 0. 260~1 1 B | 0. 0001 0.004| 0.005| -. 0151 -. 0221 0.019| 0.089| 0.148J | C J -.001| 0.002| 0.009| -.0001 0.00 11 0.033| 0.038| 0.0301 | D | -.Q02| -.000| 0.0091 0.0221 -.013| 0.039| 0.068| 0.1361 | E | -. 002| -.001| 0.012| 0. 0201 0.0221 0. 12 31 0. 1821 0. 203| | I | -. 002| 0.006| 0.012| 0.014| 0.027] 0.049| 0. 1471 0. 2221 | J | -.0021 0. 0011 0.010| 0.017| 0.0061 0.032| 0. 1041 0.113| | K | 002| 0.003| 0.0 101 -.004| 0.0 10| 0.043| 0. 1271 0 1 11 1 M | -, 000| 0.003| 0.0081 -. 0121 0.007| 0.063 ] 0. 1761 0. 307| | N | 0. 003| 0.012| 0.009| 0031 0.095| 0.089| 0. 1631 0. 1361 1 P | -.004| 0. 0021 0.009J 0.017| -.007] -.001| 0.059] 0.0611 | J L J 1 1 L . L I | | RESIDUAL VARIANCES - SENSIBLE HEAT FLUX | ISHIPI 0. 25 1 0. 50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 ] 28.0 | j. + 4, H + h + + + 1 | A ] 0. 003| 0.008| 0.022J 0. 040| 0.0561 0.070| 0.063| 0.053| | B | 0.0031 0.006| 0.016| 0. 0321 0,0391 0.0341 0.031J 0.024| | C | 0. 004] 0.010| 0.021] 0. 034| 0.04 21 0,040| 0.039J 0,0 381 | D | 0. 004| 0.010| 0.0261 0. 039] 0. 0451 0. 047] 0.044| 0. 0 3 71 1 E | 0. 0051 0. 0091 0.023| 0. 046| 0.0691 0.075| 0.076| 0.081| ] I | 0. 004| 0.011| 0.021| 0.038| 0.0441 0.0541 0.0651 0.057J | J | 0. 0031 0.0 101 0.0 191 0. 032| 0.037| 0.045] 0.059| 0. 06 3] ] K | 0. 003] 0.007| 0.0131 0. 023| 0.0311 0.037| 0.037| 0. 0321 1 M | 0. 004| 0.010| 0.021J 0.043) 0.065] 0.069] 0.087| 0. 0701 1 N | 0.0061 0.0 11] 0.0191 0.0421 0. 0721 0.071] 0.094| 0.126| | P | 0.003] 0.008| 0.021J 0. 0351 0.039| 0.036| 0.041| 0. 030| I L 230 L -4- 4. J SHIP| 0.25 | T 1 & — r 0.004| J B | 0. 004| 1 C | 0. 005| 1 D j 0.0061 1 E | 0.006| I I | 0.006| 1 J | 0.004| 1 K 1 0.004| j M | 0. 005| 1 N | 0. 007| 1 P 0.003| |_ 1 1- +-|SHIPI 0. 25 { 1 & | 0. 998| 1 B | 0. 999 | 1 c | 0. 998 | J D | 0. 9S8| 1 E | 0. 998| | I | 0.998| 1 J | 0. 598| i K | 0. 9 99| | M | 0. 9S8| 1 N | 0. 997 | 1 P 1 0.999| j. f -4- + RESIDUAL 0.50 | 1. VARIANCES -0 | 2.0 | 4 4-0. 0 13 0. 0 10 0.0 12 0.0 16 0.0 14 0. 0 16 0. 0 12 0. 009 0. 015 0.0 15 0. 009 0. 0, 0. 0. 0. 0. 0. 0. 0. 0. 0. 038 029 031 042 040 039 030 02 1 038 040 026 0. 077 0. 059 0. 054 0. 071 0. 104 0. 077 0. 060 0. 047 0. 08 1 0. 1 16 0. 053 LATENT 4.0 | 4 0. 1 12 0.077 0.070 0.083 0. 180 0.096 0.079 0.078 0. 142 0. 189 0.067 HEAT 7.0 0. 141 0.074 0.075 0. 094 0. 21 8 0. 114 0. 103 0. 11 1 0. 159 0. 232 0.068 FLUX H 4 | 14.0 | 4 4 0. 148 0.071 0.077 0.098 0. 259 0. 147 0. 139 0. 157 0.215 0.396 0.078 28.0 0. 147 0.060 0.076 0. 095 0. 3 16 0. 180 0. 156 0. 165 0. 204 0. 589 0. 073 CORRELATION. COEFFICIENTS -+ + -I-| 2.0 | 4.0 0. 9 8 0 + 0. 9 84 0.983 0. 980 0.977 0. 981 0. 984 0. 989 0. 979 0.979 0. 983 SENSIBLE 4-7.0 J ., 4 0.964 0.983 0.980 0. 977 0.962 0.973 0. 977 0.981 0. 965 0. 964 0. 982 HEAT 14.0 | 4 0.968 0.984 0.980 0. 978 0.961 0. 967 0. 970 0. 981 0. 956 0.952 0. 979 FLUX 1 28. 0 1 0. 974 0.989 0.98 1 0. 982 0. 960 0.97 1 0. 970 0. 984 0. 965 0.9 36 0. 985 0. 996 0.997 0. 995 0. 995 0.995 0. 955 0.995 0. 9 97 0. 995 0. 994 0. 996 0.989 0.992 0.989 0.987 0.989 0.990 0.991 0.994 0.989 0.390 0.989 0. 973 G.981 0. 979 0.978 0.965 0.5 78 0. 982 0.984 0. 968 0.963 0.981 SHIPI 0.25 1 j. + 4 A | 0.998 B | 0.958 C | 0.957 D | 0.997 E | 0.357 I | 0.9S7 J | 0.998 K | 0.998 M | 0.998 N | 0.997 P J 0.999 CORRELATION COEFFICIENTS -. . . + 1- + + 0.50 | 1.0 | 2.0 | 4.0 | 0.994 0. 955 0.994 0. 992 0.993 0.952 0.994 0. 995 0. 993 0. 993 0. 996 0. 981 0.985 0.384 0.979 0.980 0.980 0.985 0.9 83 0.981 0.980 0.987 0.961 0.971 0.373 0. 964 0. 948 0. 961 0. 970 0. 976 0. 960 0.342 0. 973 0.944 0.962 0.965 0. 95 9 0.909 0.952 0.960 0.96 1 0.929 0. 902 0. 967 LATENT 7.0 | 4 0.928 0. 963 0. 962 0.952 0.885 0. 942 0.948 0. 943 0.919 0. 879 0. 966 HEAT FLUX 14.0 | 28.0 + 1 0. 923 0.964 0.961 0.950 0.862 0.923 0.928 0. 9 18 0.886 0.788 0.960 0.926 0. 971 0. 962 0.952 0. 829 0. 906 0.919 0. 918 0. 894 0. 686 0.96 3 I L .J 231 A p pend ix J The f o u r t e s t v a l u e s f o r t h e s t r e s s e s and t h e h e a t f l u x e s when t h e g e o g r a h i c a l l y a v e r a g e d e g u a t i o n , >f , was a p p l i e d t o t h e v e l o c i t i e s i n d i v i d u a l l y . The s t r e s s DMs a r e i n dPa and t h e h e a t f l u x DMs a r e i n Watts/m 2. r ' * 1 | DIFFEEENCE MEANS - X COMPONENT CONSTANT D.C. | I SHIPI 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | | A | 0. 003 J 0. 009I 0.023| 0. 045J 0.066| 0. 069J 0.069| 0.067| | B | 0. 004| 0. 004| 0.001| 0. 003| 0.000| 0.005| 0-0 121 0.006| | C | 0.002| 0.011| 0.036| 0-0 5 11 0.064| 0.078| 0.076| 0. 043| | D | 0.005| 0.023| 0.054| 0. 060| 0.060| 0-071 | 0-0681 0. 039| j E | 0. 001 | 0.004| O.007| 0.004| 0.014| 0.012 1 0-0 131 0. 033| | I | 0.001| 0. 003| 0.0 101 0.0081 0.00 3 j 0.005| 0.013| 0. 003| J J | 0.006| 0.001| 0.0031 0.015| 0. 030| G.030| 0.017 J 0.041| | K | 0.001| 0.0091 0.0 17| 0.002| 0.022| 0.0141 0.0 121 0.020| | M 1 0. 0001 0.003| 0.0 111 0. 0121 0.01 11 0.024J 0.036| 0.0281 | N | 0.014J 0. 030| 0.065| 0.131| 0. 1631 0. 1741 0. 1981 0. 233| I P | 0.0021 0.0 121 0.024| O.Q15| 0.0091 0.001 | 0.0161 0.0311 J. L X J X 1 J _ L L ^ 1 DIFFEEENCE MEANS - Y COMPONENT CONSTANT D.C. I |SHIP| 0.25 | 0.50 | 1,0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 J 1 A | 0. 003J 0.008| 0.0121 0. 0 141 0.0 15 | 0.020| 0.0051 0. 00 11 | B | 0.002 1 0.003| 0.001| 0. 0121 0.0301 C.050| 0.065| 0.07 11 1 C | 0. 006| 0.0161 0.017| 0. 0011 0.0151 0,025| 0.029| 0.042| | D | 0. 007| 0.020| 0.024J 0. 0 101 0.009| 0. 0 13 | 0. 02 11 0. 036| 1 E | 0.005| 0. 006| 0.017J 0. 0381 0.055| 0.057| 0.062| 0. 077| | I | 0.001| 0.0051 0.0051 0.0181 0.028| 0.0171 0.0(161 0. 023| | J | 0. 002| 0.004| 0.011| 0.018| 0.0 31 | 0.024| 0.0241 0. 042| 1 K 1 0. 005| 0.0 121 0.0181 0. 025| 0.02 61 0.0151 0.006| 0.022| I M | 0.000| 0.002J 0.0021 0.002| 0.0151 0.012| 0.003| 0.002| | N | 0. 0051 0.0 11| 0.0241 0. 047| 0.0591 0.065| O.070| 0.0801 | P | 0. 006| 0.001| 0.0 101 0. 0011 0.006| 0.020| 0.044| 0. 027| |- J X 1 1 1 1 L X | J DIFFEEENCE MEANS - X COMPONENT LINEAE D.C. | + — 4 4 + 4 4 j. _4 — | |SH1P| 0.25 | 0.50 | 1.0 1 2.0 | 4.0 1 7.0 | 14.0 | 28.0 | | A | 0. 0031 0.0121 0.037| 0. 076| C.114| 0.118J 0. 111 | 0. 1121 | B 1 0. 007| 0.011| 0.0091 0. 0 15| 0.009| 0.007| 0.004| 0. 036| 1 C 1 0.0061 0.0141 0.051| 0. 080| 0.109J 0. 1251 0. 1 141 0. 065| | D 1 0.0061 0.035| 0.084| 0. 0891 0.09 21 0. 1041 0.092J 0.052| | E | 0. 002| 0.004| 0.007| 0. 0 121 0.028| 0.0291 0.032| 0. 064| 1 I 1 0. 0011 0. 005| 0.016| 0. 009J 0.007| 0.007| 0.0 171 0.000| | J | 0. 0 111 0.0061 0.0031 0. 036| 0.0551 0.063| 0.047| 0.096| | K J 0. 0001 0.0 121 0.022| 0. 009| 0.0391 0.028| 0.029| 0.044| I M 1 0.0011 0. 004| 0.0 131 0. 0 1 11 0.0121 0.0301 0.042| 0.028| | N 1 0. 0 181 0.0371 0.080| 0. 1631 0. 2 101 0.2321 0. 269| 0. 3171 | P 1 0. 007| 0.024| 0.041| 0. 03 21 0.020J 0.003| 0.032| 0.05 31 I I L X 1 - - J X L I I 233 DIFFEBENCE MIANS - Y •+ + i-COMPONENT 2.0 | 4. LINEAE D.C. 0 | 7.0 | + 4-+ 14.0 | 4 0.0 17 0. 100 0.043 0.039 0. 093 0.034 0.053 0.007 0.005 0.096 0.060 1 28.0 0.0 1 1 0. 103 0.061 0.060 0. 108 0. 052 0. 085 0.024 0. 003 0.111 0.0 17 SHIP| 0.25 | 0.50 | I- + 4 +-B C D E I J K M N P 0.005 0. 005 0.0 12 0.0 13 0. 005 0.002 0. 003 0. 008 0.000 0.007 0. 0 13 0.0 15 0.009 0.030 0.035 0. 005 0. 008 0.006 0.018 0.003 0.0 15 0.003 1.0 | 0.025 0.003 0.035 0.04 1 0. 019 0.006 0.0 14 0.025 0.002 0.031 0.009 0. 032 0. 0 14 0.006 0. 020 0. 048 0. 032 0. 030 0. 034 0. 005 0.060 0. 007 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 038 052 017 016 077 040 052 034 021 077 0 17 0.041 0.081 0.035 0.025 0.083 0. 03 1 0.047 0.018 0.016 0.086 0, 03 7 DIFFEEENCE VABIANCES j. 4 4 4 4 . SHIP] 0.25 I 0.50 I 1.0 ] A I -.004| 0. 0 18 ] 0.038] B i -.001] 0.017| 0.04 1| C ] 0. 002] 0.023| 0.044] D | 0.0061 0.030] 0.069] E ] -. 009] -.003] -.0 14,| I ] -. 0 08| 0.004| 0.0091 J ] -.0 10] -.004] -.008| K I - . 0 1 0 1 -.005| -.015| M ] - « 0 1 6 | -. 008| -.010] N | -, 036| -.067| -.163] P I 0. 0021 0.027| 0.0651 X COMPONENT L 4 0 I 4.0 ] j. 4 03 1| 0.02 7 035| 0.072 052| 0.062 073| 0.068 CONSTANT 7.0 I 14 073 | 020| -. 108 -.029 -.057| -.104 -,114| -.189 -.0591 -.080 -.424| -.599 0. 038| 0.005 0.068 0. 149 0.068 0. 103 -.066 -.002 -.080 -. 140 -.011 -. 685 0.066 0 . 0 . 0 . 0 . 0" 0. D.C. + .0 | 4 1 18 170 079 139 074 042 060 070 001 876 086 28.0 "* 0. 132 0. 145 0. 064 0. 217 -. 152 0. 043 -.103 -. 104 -.015 -1. 19 0. 056 DIFFERENCE VABIANCES - Y COMPONENT CONSTANT D.C. L 4 4 - 1- (-- 4 - ).. (. |SHIP] 0.25 | 0 . 50 | 1.0 | . 2. 0 | 4.0 | 7.0 | 14.0 | r 1 A — r _____4 -.0 10| _ _ , _ _ _ _ _ _ . _ . _ l _ _ , 0.006] 0.0191 _______ _ j 0.006] ____________ _^ _ 0.007] _______! 0.096| ___________ | 0.163| 1 8 | -.0031 0 .0 20] 0.0531 0. 069| 0 . 1 C 7 | 0. 160] 0. 175| 1 c ] 0 . 0 12] 0.049] 0.0891 0. 09 1] 0.120] 0.170| 0.165| 1 D ] 0. 0 13 | 0.053| 0.086| 0. 077| 0. 130 | 0. 169| 0. 188] 1 E | -. 009| -.004| -.0061 -.093] -.1251 -.082| -.049] ] I j -. 003] 0.0 16| 0.0261 -.008| -.011] 0.037| 0.043I 1 J ] -, 008| 0.006] 0.0 15] -.034] -.048| 0.023| 0.021| 1 K j - . 0 07 | 0.004] 0. 007| -.070] -.114| -.033 | 0.0001 | M ] - . 0 18 | -.0 13| -,020| -.088] -. 106| -.063] 0.005] 1 N ] -.031| -,054| -.139| -.34 1] -.481 | -.478] -.578| 1 P -. 000] 0.021] 0.048| 0. 053] 0.058| 0.061 | 0. 1 13| _1 1 28. 0 1 0. 19 1 0. 157 0. 144 0. 185 -.067 0.002 -. 031 -.024 -.038 -.790 0. 109 r — i | DIFFEEENCE VARIANCES - X COMPONENT LINEAR D.C. | |SHIP| 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0~| | A J -,008| 0. 028| 0.054| 0.041| 0. 048| 0. 094| 0 . 1 8 l | 0.198| ] B | -. 0 04| 0.020| 0.049| 0.015| 0.127| 0. 2271 0. 2481 0. 206| | C | -,000| 0.0331 0.056| 0. 0881 0. 145| 0.142| 0. 167 J 0.155| | D | 0.012| 0.055| 0.131] 0.138| 0.138| 0. 1631 0.222] 0. 340| I E ] -. 008] 0.001| -.008| -. 096] -.144| -. 0851 -. 103 J -.261| ] I | -.014] 0.004] 0.002I -.051| -.049] -.014] 0.048| 0. 074| ] J ] -.0181 -.0101 -.021| -.1131 -.161| -.130| -.0601 -. 14 31 I K | -.012] 0.002| -.005| -.181| -. 2831 20 71 -. 135| -.195| | M ] -. 026| -.015| -.0231 -. 1 17| • 1 38 | - . 042 | - . 0 221 -. 083] | N | 0531 -. 104| -.268] -.741] -1.10| -1.34| -1.851 -2. 63| | P | 0.009] 0.051| 0.114] 0.077| 0.048] 0.136| 0.142| 0.067] |- 1 L 1 1 1 L L I | ] DIFFEEENCE VARIANCES - Y COMPONENT LINEAR D.C. I I SHIP | 0.25 | 0.50 | 1.0 ] 2.0 | 4.0 | 7.0 ] 14.0 ] 28.0~| j. 4 4 + 4 H 4 4 4 4. | A | -.021] 0.001] 0.016| -, 009| 0.020| 0.170| 0.248] 0. 257| ] B ] -. 009| 0. 0241 0.074| 0.092] 0.179] 0. 242| 0.2531 0. 235| | C | 0. 026I 0. 090I 0. 1461 0. 160| 0. 237| 0.284] 0. 263| 0. 2211 ] D | 0. 0271 0.095] 0. 1461 0. 126| 0. 248] 0.277] 0.273] 0.281| ] E ] -. 003] 0.0081 0.000] -. 1301 -. 163. -. 112] -.117| 17 41 | I | -.005] 0. 0311 0.0421 -. 018| 0.012] 0.091 | 0.076| -. 0131 ] J ] -.011] 0.015| 0.026| -.061] ^. 0311 0.060] 0.028| -. 082] | K | -. 007] 0.019] 0.030| -.079] -. 1361 -.0061 -.011| -. 0561 ] M j -. 032] -. 026| -.045| -. 1621 -.161| -.114| -. 0321 -. 1391 ] N ] -. 044] -. 085] -.229] -. 567] -. 8261 -.875 | -1.13| - 1. 5 31 ] P | -. 002] 0.027| 0.069| 0.090| 0. 1431 0. 150] 0.240 | 0.194] | J 1 J — J i i _ i i _j | RESIDUAL VARIANCES - X COMEONENT CONSTANT D.C. ] ]SHIP| 0.25 | 0.50 | 1.0 ] 2.0 | 4.0 | 7.0 | 14.0 ] 28.0 ] ] A | 0. 0021 0.007] 0.017| 0. 0311 0. 045] 0.049| 0.04?} 0. 04 0~| | B | 0. 0021 0.007| 0.017| 0.032] 0. 044| 0.051| 0.046] 0.0 351 ] C ] 0.003] 0.008| 0.0 181 0. 0341 0. 045| 0.042| 0.049| 0.048| J D ] 0. 004| 0.0 101 0.025] 0. 040| 0.046] 0.051 | 0.049| 0. 0591 | E | 0. 003| 0.006| 0.014| 0. 0321 0.04 11 0.0421 0.040] 0.038| | I J 0. 002| 0.006| 0.013] 0. 022] 0.029] 0.031 . 0.036| 0. 0361 ] J | 0.002I 0.006| 0.013| 0. 024] 0.034| 0.036] 0.044| 0.043| | K ] 0. 002| 0.006| 0.012| 0. 023| 0.035] 0.036| 0.040] 0.048| ] M | 0. 002] 0.006| 0.0131 0. 025| 0.0331 0.0351 0.043] 0.040] | N | 0. 003| 0. 006| 0.016| 0. 060| 0. 1061 0. 134] 0. 1911 0. 292| ] P ] 0.003| 0. 008| 0.021J 0. 034I 0. 040| 0.045| 0.043I 0. 036| I 1 L L J 1 L L , I I r •* 1 1 RESIDUAL VARIANCES - Y COMPONENT CONSTANT D.C. | ISHIPj 0 . 2 5 | 0 . 5 0 | 1.0 | 2 . 0 | 4 . 0 | 7 .0 | 14 .0 | 2 8 . 0 | | A | 0 . 0 0 2 | 0 . 0 0 5 | 0 . 0 1 4 | 0 . 0 2 6 | 0 . 0 4 0 | 0.0491^0.0551 0 . 0 4 5 | 1 B j 0. 0031 0 . 0 0 7 | 0 .0181 0. 0381 0 . 058 | 0 . 0 6 3 | 0 . 0 6 0 | 0 . 0 5 3 | J C j 0. 0 0 4 | 0 . 0 1 2 | 0 . 0 2 7 J 0 . 0 4 3 | 0 . 0 5 5 | 0 . 0 5 4 | 0 . 0 5 4 | 0 . 0 4 7 | J D | 0. 0 0 6 | 0 .0151 0 . 0 3 1 | 0 . 049 | 0 . 0 7 11 0 . 0 7 7 | 0 . 0 7 8 | 0 . 0 7 8 | | E | 0 . 0 0 4 | 0. 0 0 8 | 0 . 0 2 1 | 0 . 0 4 0 | 0 . 0 6 8 . 0 .0701 0 . 0 6 5 | 0 . 0 6 9 J | I | 0. 0 0 3 | 0 . 0 0 8 | 0 . 0 1 4 | 0. 0 2 4 | 0 . 0 3 2 | 0 . 0 3 6 | 0 .0431 0 . 0 4 7 | | J | 0 . 0 0 3 | 0 . 008 | 0 . 0 1 8 | 0. 0 2 9 | 0 . 0 3 8 | 0 . 0 4 2 | 0 . 0 3 8 | 0. 0 3 5 | j K | 0 .0031 0 . 0 C 8 J 0 . 0 1 9 | 0 . 0 3 0 | 0 . 0 4 0 | 0 . 0 4 1 | 0 . 0 4 8 | 0. 065 | | M I 0 . 0 0 2 . 0 . 0 0 5 | 0 . 0 131 0. 024 | 0 .0371 0 .0361 0 . 0 4 1 | 0 . 0 4 11 | N | 0. 0041 0 . 0 0 7 | 0 . 0 1 7 | 0 . 0 5 5 | 0 . 0 9 4 | 0 . 101 | 0 . 1301 0 . 186 | I P | 0 . 003I 0 .0081 0 . 0 2 0 J 0 . 0 3 9 | 0 . 0 5 0 | 0 . 0 4 9 | 0 . 0 5 4 | 0 . 0 6 6 | f 1 1 J a 1 J L L _ _ | | RESIDUAL VARIANCES - X COMPONENT LINEAR D.C. | |SHIP| 0 . 2 5 | 0 . 5 0 | 1.0 | 2 . 0 | 4 . 0 | 7 .0 | 14 .0 | 2 8 . 0 | | A J 0 . 0061 0 . 0 17) 0 . 0 4 2 | 0 . 08 11 0 . 1 1 6 | 0. 122 | 0 . 1 0 6 | 0 . 0 9 11 | B J 0. 006 | 0 . 0 16 | 0 .0421 0. 079 . 0 . 10 5 | 0 . 1 1 8 | 0 . 1031 0. 085J | C | 0 . 0 0 7 | 0 . 0 1 7 | 0 . 0 4 3 J 0. 0 8 4 | 0 . 1 1 4 | 0 .104 ( 0 . 1 171 0 . 1 1 6 | i D | 0. 0 0 8 | 0 . 0 2 4 | 0 . 0 6 6 | 0 . 1 G 7 | 0 . 122 | 0 . 1281 0 . 113 | 0 . 1241 | E | 0 . 0 0 6 | 0 . 0 151 0 . 0 3 3 | 0. 0741 0 .0891 0 . 0 9 0 | 0 . 0 8 6 | 0 . 0 8 0 | I I 1 0 . 0 0 6 | 0 . 0 15) 0 .0321 0. 0 5 5 | 0 .0711 0 . 0 7 2 | 0 .0801 0 .0841 1 J 1 0 . 0051 0 . 0151 0.0321 0 .0621 0 . 0 8 7 | 0.0851 0 . 1001 0 . 1001 1 K 1 0 . 0 0 5 | 0 . 0 1 4 | 0 . 0 3 2 | 0 . 0581 0 . 0 8 7 | 0 .0831 0 . 0 9 0 | 0 . 10 31 | M | 0. 0 0 5 | 0 . 0 131 0.0321 0. 0631 0 . 0781 0 .0811 0 .0971 0. 0 8 9 | | N | 0 . 0 0 6 | 0 . 0 1 3 | 0 . 0 3 8 | 0 . 1511 0 . 284 | 0 . 3 8 3 | 0 .5981 0. 9761 | P 1 0. 0 0 9 | 0 . 0 2 3 | 0.0581 0 . 0 8 8 | 0 . 1021 0 . 10 91 0 . 1 0 0 | 0 .0861 | L X - X 1 I X _ X I I I RESIDUAL VARIANCES - Y COMPONENT LINEAR D.C. | j. + + 4 4 4 4 4 4 1 |SHIP| 0 . 2 5 | 0 . 5 0 I 1.0 | 2 . 0 | 4 . 0 I 7 . 0 \ 1 4 . 0 | 2 8 . 0 | j. 4 4 4 4 4 4 4 + _ 1 J A l 0 . 005I 0 . 0 1 4 J 0 . 0 3 3 | 0 . 0 6 4 | 0 . 0 9 6 | 0 . 1 141 0 . 1 161 0 . 0 9 7 | 1 B J 0 . 0 0 6 | 0 . 0 1 7 | 0 .0431 0. 09 21 0 . 1381 0 . 143 1 0 . 132 J 0 . 1 1 9 | | C | 0 . 0 1 1 | 0 . 0301 0.0681 0 . 1 111 0 . 1411 0. 131 | 0 . 1291 0 . 1 1 1 | | D | 0 . 0 1 4 | 0 . 039 | 0 . 0 7 9 | 0 . 12 11 0 . 1661 0 . 1751 0 . 1751 0. 1741 1 E 1 0 . 0 1 0 | 0 . 0 2 1 | 0 .0511 0. 0881 0 . 14 91 0 . 1491 0.1441 0. 1451 | I 1 0 . 0 0 8 | 0 . 0 2 0 | 0 . 0 3 6 | 0 . 0611 0 . 0 7 7 | 0 .0851 0 . 0 9 8 | 0 . 1 0 7 | | J | 0. 0 0 7 | 0 . 0 2 0 | 0 . 0 4 4 | 0. 07 11 0 . 0 9 0 | 0 . 0 9 7 | 0 . 0 8 8 | 0 . 0 8 3 | | K 1 0 . 0 0 7 | 0 ,0201 0 . 0 4 9 | 0. 077 J 0 .0941 0.0971 0 . 106| 0 . 1 5 3 | I M | 0 . 005I 0 . 0 1 1 | 0 . 0 3 2 | 0. 0 6 2 | 0 . 0 8 6 | 0 . 0 8 3 | 0 . 0 8 8 | 0 . 0 9 4 | | N | 0 . 008J 0 . 0 1 6 J 0 . 0 3 8 | 0. 124| 0 .2201 0 .251 | 0 . 3461 0. 509 | I P | 0 . 0 0 9 | 0 . 0 2 0 | 0 . 0 4 8 | 0. 0 9 5 | 0.118,1 0 . 1 0 9 | 0 . 1 1 6 | 0 . 13 9 J I J 4 J 1 1 X I I J I —1 I COEEELATION COEFFICIENTS - X COMPONENT CONSTANT D . C . | ,. + 4 + + - + + + 1- 1 ! S H I P | 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | | A | 0.9991 0. 997| 0 .992 | 0.984J 0 .977 | 0. 9751 0 .977 | 0.9811 j B | 0 .9SS | 0.9971 0 .992 | 0. 984| 0. 978| 0.9761 0.9791 0. 984| j C | 0. 9981 0.996I 0 .991 | 0. 98 31 0. 9771 C. 9791 0.975J 0 .976 | | D j 0. 998 | 0. 995 | 0. 988 | 0. 9 8 01 0. 977 | 0. 975 | 0. 976 j 0. 974| | E J 0. 999I 0 .997 | 0 .993 | 0. 9851 0. 982| 0. 980| 0.981 | 0. 985 | 1 I i 0. 999| 0. 997| 0 .994 | 0. 989| 0.9861 0.984J 0.982) 0 .982 | | J | 0. 999| 0. 997| 0 .994 | 0. 9 8 91 O.S85 | 0 .983 | 0 .979 | 0.9811 J K | 0. 9991 0. 997| 0 .994 | 0. 9911 0. 9881 0 .985 | 0. 9811 0. 979| | M | 0. 999| 0 .997 | 0.9931 0. 9881 0. 9851 0. 9831 0.9791 0 .980 | | N | 0. 9991 O.S98 | 0.9951 0. 990| 0. 9861 0. 983) 0. 980| 0 .979 | I P | 0. 998 | 0. 996| 0.9 901 0.983 ( O.S80| 0. 977J 0 .978 | 0. 982| |- 1 1 I L I J . i J | COEEELATION COEFFICIENTS - Y COMPONENT CONSTANT D . C . | ISHIPI 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | t + + + + 1- + 4 H - 1 | A | 0. 9 991 0. 9 971 0 .993| 0. 987| 0 .980 | 0 .976 | 0. 974| 0 .981 | 1 B | 0.9991 0 .997 | 0.9911 0. 9811 0. 971| C .970 | 0.971J 0. 9 7 51 I C 1 0.9981 0 .994 | 0 .987 | 0.978) 0.9731 0 .975| 0. 975| 0 .978 | | D | 0. 997| 0 .993 | 0 .985 | 0. 9 751 0.965) 0 .962 | 0 .962 | 0. 962| | E 1 0. 998| 0. 996| 0. 990| 0.9821 0.96 S | 0 .967 | 0.9681 0. 9671 | I | 0. 998| 0.9961 0.9931 0. 988 J 0 .984 | 0. 982| 0 .978 | 0. 977| | J | 0. 999| 0 .996| 0.9911 0. 986| 0.9821 0i 979| 0.9811 0. 983| | K | 0. 9981 0 .996 | 0.991J 0. 986J 0.9 831 0 .980 | 0 .976 | 0. 968| | M | 0. 9991 0.9981 0 .994 | 0. 989| 0 .984| 0.9831 0. 979| 0. 9801 | N I 0. 9981 0. 9971 0.9941 0. 987) 0.9811 0- 9781 0.974 J 0. 9731 1 P | 0. S 981 0. 996| 0 .990| 0. 980| 0 .975 | 0. 9751 0. 973| 0. 9661 }. J L X 1 J L 1 . L _ J | COEEELATION COEFFICIENTS - X COMPONENT LINEAE D . C . | ISHIPI 0.25 | 0.50 | 1.0 1 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | f -f + + + + + + + H | A | 0 .997 | 0. 992| 0.979) 0.9591 0.94 11 0.937J 0.946| 0.9551 | B | 0. 997| 0 .992 | 0.9 791 0. 960) 0 . 9 4 6 | 0. 941 | 0.9511 0, 959| 1 C | 0. 997| 0 .991 | 0 .978 | 0. 957| 0. 94 11 0 .947 | 0 .940 | 0.941) 1 D | 0. 996| 0.988) 0. 967 | 0. 9 451 0. 937 | 0. 9341 0.944J 0.945) | E | 0. 997| 0 .992 | 0 .984| 0. 966| 0.96 1 | 0. 9581 0. 960| 0.9711 | I | 0 .9S7 | 0. 993 | 0. 984 | 0. 9731 0 .966 | 0. 964 | 0. 959 | 0. 9571 | J | 0. 998 | 0. 9931 0. 984 | 0. 972I 0. 9631 0.962) 0 .952| 0.955) | K | 0. 9971 0 .993 | 0 .984 | 0. 9771 0 .969 | 0. 967 J 0 .960 | 0. 957| | M | 0. 997| 0. 994| 0 .984 | 0. 972| 0.5 6 61 0 .960 | 0.952) 0. 958| | N | 0 .9S7 | 0 .995 | 0.9 90 | 0. 98 11 0. 9 721 0. 9671 0. 964 J 0. 959 J 1 P | 0.9551 0 .988| 0 .971 | 0. 9551 0.9481 0. 944| 0 .949 | 0.9561 L X 237 COEEELATION COEFFICIENTS - Y SHIP | 0.25 j 0.50 | 1.0 1 2.0 j. 4 4 ~ 4 0. 993 0.992 0.985 0. 981 0.989 0. 990 0.990 0.990 0.994 0.993 0.990 28 COMPONENT LINEAB D.C 4.0 | 7.0 | 14.0 | 0.951| 0. 942| 0.943J 0. 0.929) 0. 9281 0.934 | 0. 0.929| 0. 937| 0.937) 0. 0.914| 0.910| 0.910| 0. 0.934| 0.931| 0.9331 0. 0.961| 0.957| 0.950| 0. 0.956) 0. 950| 0.955) 0. 0. 9581 0.9521 0. 947) 0. 0.963| 0. 962| 0.957| 0. 0.9641 0. 9581 0.954) 0. 0. 9391 0.944| 0.943| 0. — H .0 A B C D E I J K M N P 0. 998 0. 997 0. 994 0. 9 53 0. 995 0. 956 0. 9 56 0. 996 0. 598 0.996 0. 956 0.983 0.978 0.966 0.960 0.975 0.982 0.978 0.975 0.985 0.S88 0.976 0. 96 8 0. 953 0. 943 0. 938 0. 960 0. 970 0. 966 0.964 0. 974 0. 97 6 0. 95 1 955 94 1 945 9 1 1 936 947 96 1 926 958 950 928 —1 DIFFEEENCE MEANS - SENSIBLE HEAT 7.0 A B C D E I J K M N P 4- - - + 4 0.25 | 0.50 | 1.0 | 2.0 | 4. 0 I ___ __ __,___^ __ 0.0701 0.204) ________ ______|_ 0.603| _____________ | 0. 275| 0. ____ ___J. 281 | 0. 069| 0.130| 0.408| 0. 229| 0.198| 0.0 17| 0.095| 0.366| 0.6871 0. 739 | 0.068| 0. 499| 1.364) 1. 7521 1. 772 | 0. 125| 0.208| 0.466| 1. 180| 1. 1 80 J 0. 0 12) 0.179| 0.241| 0. 6 16| 1. 245 | 0.088I 0.009| 0.0741 0.720| 1. 3831 0. 0 291 0.024| 0.144 | 0. 322) 0. 531 | 0. 356 | 0.436| 0.8001 2.439) 2. 8841 0.423| 0.9081 1.9861 4. 355) 5. 495J 0. 087 | 0. 118| 0.220| 0. 490| 0. 763| 1.411 1.33 7 1.025 2.694 1.072 0. 531 1. 137 0. 165 2. 156 6.009 0.713 FLUX 4 4 I 14.0 | + — + 2.001 2.240 1. 257 2.562 1. 551 0.383 0.872 0.328 1.553 6.822 0.579 28.0 —-I 1. 392 1. 836 1. 29 1 1. 605 2. 876 0. 086 1. 375 0. 296 2.608 8. 334 0.677 y + 4 SHIPJ 0.25 | J. 4 - + l A I 0. 027J I B I 0.1231 I c | 0.1951 I D I 0. 816| I E J 0. 782| 1 I 1 0. 084 | 1 J 1 0. 190 | 1 K 1 0. 4 17 | 1 M I 0.306| 1 N | 1.8051 1 P 1 0.103| DIFFEEENCE MEANS 0.50 | 1.0 I 2. - LATENT HEAT 0 | 4.0 | 7. 0.643 0. 592 0. 749 2.587 1. 326 0. 698 0. 196 0. 575 0.083 3. 984 0.099 1.592 1.562 1.780 5.764 2.887 1.343 0.425 1.408 0.028 9.403 0.280 1. 2. 2. 8. 7. 0. 0. 4. 1. 21 0. 87 1 300 630 1 11 584 770 655 019 092 . 30 091 2.093 2.818 2.562 8.6 18 •10.05 0.429 2.528 6.961 1.447 30. 13 0, 620 4. 5. 3. 12 7. 2. 0. 3. 1. 31 0. FLUX 4 -0 4 -750 207 992 .29 326 230 960 866 564 .79 383 4 14.0 J 4 7. 173 7.036 4.959 13. 02 8.728 5.462 1. 122 0.661 4.627 33.81 0. 892 4 28.0 1 8. 262 6. 980 4.311 10.20 14. 3 1 6.749 0. 205 1. 604 5. 199 42.42 0. 0 15 I ~ 1 1 I DIFFERENCE VARIANCES - SENSIBLE HEAT FLUX | I- + + + r + + + 1- 1 ISHIPI 0.25 | 0.50 | 1.0 1 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | | A J 0.0021 0.0131 0.034| 0. 064| 0.041| 0,140| 0,206| 0. 241 | | B | 0 021 0. 006| 0.010| 00 11 -.020| 0.010| 0.063| 0. 095| | C | 0. 009I 0. 0261 0.059| 0.067| 0.021| 0.032| 0.028| 0. 005| | D | 0.005 | 0.017| 0.0501 0. 087| 0.080| 0, 1161 0.114J 0.139| | E | -. 002| 0.001| 0.0151 -.021| -.041| '.002| 0381 -. 1661 | I | 0.003| 0.018J 0.029| 0. 023| 0. 028| 0.066| 0. 16 3| 0. 204| | J | ^.002| 0.0081 0.0181 0. 0001 -. 0551 -.011 | 0.016| -. 015 J | K 1 -.012| -.015| -.0331 -. 139| 282 ( -. 2941 -. 2981 -. 497| | M | -.003| 0.001| 0.002| -,041| -. 0 6 2 J -.009 J 0.078| 0.132| | N | -. 020| -.038| -,109| -. 307| -.514| -. 604 | -.7 131 89 21 1 P | -.0021 0.013| 0.038| 0.035| -.015| 0.002| 0.054| 0.024| }. J , 1 J r I I - L L I j | DIFFERENCE VARIANCES - LATENT HEAT FLUX | ISHIPJ 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | j I |._ I ___ _ |__ l_ j ——1 1 A | 0.001| 0.008| 0.0231 0. 060| 0.056| 0. 1651 0.274| 0. 394| 1 B | O.001| 0.008| 0.016| 0. 024| 0.023J 0.060| 0. 1321 0. 1931 | C 1 0.007J 0.018| 0.0431 0. 0751 0.0651 0. 107 | 0. 1321 0. 1411 | D J 0.004| 0.012| 0.0371 0. 09 1J 0.1121 0. 162 | 0. 193 | 0. 26 31 1 E 1 0. 003| 0. 0091 0.032J 0. 0591 0.0781 0. 173 J 0. 230| 0.250| | I | -.001| 0. 005| 0.014| 0.031| 0.043| 0.069| 0. 1761 0. 2811 | J | -.004| -,002| 0.003| 0. 008J -.0401 -. 0171 0.027| 0.080| | K | -, 003| -.0011 -.0021 -.035| —. 1311 -. 0861 0.052| 0.034| | M | -. 000| 0.0021 0.009| -. 0031 0.009| 0.069| 0. 1961 0. 377| | N | -.005| -,010| -.0351 -. 0851 -.2721 -.381| -.4531 -. 6701 | P | -, 003| 0.0051 0.0 15| 0. 034| 0.0161 0.028| 0. 1031 0.1141 J. L 1 4 J -X L 1 L -j | RESIDUAL VARIANCES - SENSIBLE HEAT FLUX | ISHIPI 0.25 | 0.50 | 1.0 | 2.0 | 4.0 | 7.0 | 14.0 | 28.0 | | A | 0.003J 0.008| 0.022! 0. 0411 0.0551 0.074| 0.072! 0.065| | B | 0. 003| 0. 0 06 | 0.0 171 0. 03 11 0.040! 0.037| 0.033 | 0. 0 241 | C 1 0.0041 0.0 101 0.0221 0. 0351 0.04 11 0.039| 0.038| 0. 0391 1 D J 0. 004| 0.010| 0.026| 0.040| 0.0461 0.049| 0.046| 0. 039| | E | 0. 005| 0.010J 0.024| 0. 0491 0.0711 0.076| 0.078| 0. 10 01 | I | 0. 004| 0.010| 0.02 11 0. 037| 0.0471 0.06 1 1 0.082| 0.077| | J | 0.003| 0.010| 0.0 191 0. 0311 0.040| 0.047| 0.059| 0.0481 | K | 0. 003J 0.0071 0.0 15| 0. 035| 0.055| 0.0611 0.063| 0. 0881 | M | 0.004| 0.010| 0.021J 0. 0 461 0.0671 0.0691 0.087| 0.071| J N | 0. 0061 0.014| 0.030| 0. 097| 0.137| 0. 1571 0. 2011 0. 271| 1 P | 0. 003| 0.008| 0.021| 0. 035| 0.0391 0.0361 0.0411 0. 0301 L 1 L J ,J ~—J L _ X I r ~ 1 J RESIDUAL VARIANCES - LATENT HEAT FLUX j I SHIP | 0 . 2 5 | 0 . 5 0 1 1 .0 | 2 . 0 | 4 . 0 | 7.0 | 1 4 . 0 | 28 . 0 | | A | 0.0041 0 . 0 1 2 | 0 . 0 3 8 | 0. 0 7 7 | 0. 1221 0. 1671 0. 190| 0. 204 | | B | 0 . 0 0 4 | 0 . 0 1 0 J 0 . 0 3 0 | 0. 062 | 0 .0881 0 .092 | 0 .0981 0. 0 8 0 | 1 C | 0. 0 0 5 | 0 . 0 1 3 | 0 . 0 3 3 | 0. 056 | 0.0741 0. 0831 0 . 0 8 9 | 0 . 0 9 0 | | D | 0 . 0 0 6 | 0 . 0 1 7 | 0 . 0 4 3 | 0. 0771 0 . 0 9 4 | 0 . 1 10 | 0 . 1 1 9 | 0 . 1 2 3 | i E | 0. 0061 0 . 0 1 4 | 0 . 0 4 0 | 0 . 1 0 3 | 0 . 1 7 6 | 0 . 2 2 1 | 0. 2631 0. 317 | | I i 0 . 0 0 6 | 0 . 0 1 5 | 0 . 0 4 0 | 0. 076 | 0 . 1 1 3 | 0 . 1 4 8 | 0 . 2 2 3 | 0. 276 | j J | 0 . 0 0 4 | 0.012J 0 . 0 3 0 | 0. 0 5 9 | 0 . 0 9 11 0 . 120 ( 0. 1781 0. 1381 | K | 0. 0 0 4 | 0 . 0091 0 .0221 0 . 049 | 0 .0891 0 . 1211 0. 1721 0 . 1821 1 M 1 0 . 0 C 5 I 0 . 0 1 5 | 0 . 0 3 8 | 0. 0 7 9 | 0 . 1511 0. 1751 0 .2521 0 . 2541 1 N 1 0 . 0061 0 . 0121 0 .0331 0. 0 951 0 .2211 0. 301 | 0 . 5 2 7 J 0 . 8 9 4 J | P J 0 .0031 0 . 0 0 9 | 0 . 0 2 6 | 0 . 054 | 0 .06 91 0 . 0 7 5 | 0 . 0 8 7 | 0 . 0 7 5 | J. J I J I I I L L | 1 CORRELATION COEFFICIENTS - SENSIBLE HEAT FLUX | ISHIP1 0 . 2 5 | 0 . 5 0 | 1.0 | 2 . 0 | 4 . 0 | 7 . 0 | 14 .0 1 28 . 0 | | A 1 0. 9981 0. 9961 0.9 891 0 . 9 8 o | 0 . 9 7 2 J 0 . 9 6 3 | 0 . 9 6 7 } 0.97 2^ 1 B 1 0. 9 9 9 | 0 .9971 0.9921 0. 9851 0 . 9 8 0 ) 0 .982 ( 0 . 983 | 0. 9891 1 C I 0 . 9S8 I 0 . 9 9 5 | 0 .9891 0. 9 8 3 | 0. 9791 0 . 9 8 0 | 0. 98 11 0. 9 8 0 | I D I 0. 9 9 8 | 0. 995J 0 .9871 0 .980 ) 0 .9771 0. 976 | 0 . 9 7 8 | 0.98 21 I E I 0. 9 9 7 | 0 . 9 S 5 | 0 . 9 8 8 | 0. 976 | 0. 96 61 0 . 9 6 2 1 0. 9621 0. 9571 1 I 1 0 . 9 S 8 | 0.9951 0.9901 0. 9821 0.976 J 0 . 9 6 9 | 0 . 9 5 9 | 0 . 9 6 3 J 1 J I 0 . 9S8 I 0 .9951 0.9911 0. 9 851 C . 9 8 1 J 0. 976 | 0 . 9 7 0 | 0 . 9 7 6 | I K 1 0. 9 9 9 | 0 . 9 9 6 | 0.993 J 0. 986J 0 .9841 0. 9821 0. 981) 0. 9841 I M I 0. 998 | 0 . 9 S 5 | 0.9891 0. 9 7 8) 0 . S 6 8 | 0.966 | 0 .9561 0. 9651 1 N I 0. 9 9 7 | 0.9941 0 .9871 0. 9661 0. 9661 0 . 966 | 0 .9601 0. 9 5 31 I P I 0 . 999J 0. 9961 0.9891 0. 9821 0 . 9 8 1 J 0.9821 0 . 9 7 9 | 0.9851 1 1 1 I I I I I I I 1 J L 1 — J 1 -J. L ; 1 ^ J CORRELATION COEFFICIENTS - LATENT HEAT FLUX | 1SHIPI 0 . 2 5 J 0 . 5 0 I 1.0 | 2 . 0 | 4 . 0 | 7 . 0 | 14,.0 | 2 8 . 0 | | A | 0 . 9 S 8 | 0 . 994 | 0 . 9811 0. 96 11 0 . 9 3 s | 0 . 9 1 3 J 0 . 9 0 l | 0 . 900 | I B I 0. 9 9 8 | 0 . 9 9 5 | 0 .9851 0 .9691 C.956| 0.9531 0 . 9 5 0 | 0.96 11 I C I 0 . 9 9 7 | 0. 9 9 4 | 0.9841 0. 972 | 0.9631 0. 9581 0.9551 0. 9551 1 D I 0 . 9 S 7 | 0 .9921 0 . 9781 0. 9611 0 . 9521 0 . 9 4 4 | 0 . 9391 0 . 940) I E I 0. 9 9 7 | 0 . 9 9 3 | 0 .9801 0. 9 4 7 | 0 .9091 0 . 8 8 3 | 0.8591 0 .3281 J I I 0 . 9 9 7 | 0 .9931 0.9801 0.9621 0 . 9 4 2 | 0 . 9 2 4 | 0 . 8 8 2 | 0 .8511 I J I 0 . S S 8 I 0 . 9 9 4 | 0 . 9 8 5 | 0 . 9 7 0 | 0 . 9561 0. 9 4 1 | 0.9 10 1 0. 90 3J I K I 0. 998 | 0.9951 0.9 8 9 ,| 0. 976) G. 9601 0. 9431 0.9121 0. 9081 I M I 0 . 998J 0 .9931 0 .981 ) 0. 96 11 0 .9241 0. 910) 0 . 8 6 5 ) 0 . 867) I N 1 0. 9 9 7 | 0. 9 9 4 | 0 .9841 0. 9 5 51 0 . 909) 0 . 8 8 5 ) 0 . 7 9 9 | 0 . 687) 1 P J 0. 9991 0 . 996 | 0 . 9 8 7 | 0 . 9 7 3 | 0. 9651 0 . 9 6 2 | 0 . 9551 0 . 9621 I A 

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