"Arts, Faculty of"@en . "Geography, Department of"@en . "DSpace"@en . "UBCV"@en . "Yap, David Hamilton"@en . "2011-03-10T21:06:03Z"@en . "1973"@en . "Doctor of Philosophy - PhD"@en . "University of British Columbia"@en . "A yaw sphere-thermometer assembly (YST), to measure sensible heat flux density by the eddy correlation method, was built following the design of Tanner and Thurtell (1970). Wind tunnel experiments indicate that the sphere constant should be 1.57, which is significantly less than the previously\r\nused theoretical value of 2.25. The effects of tilt indicate that heat fluxes may be in error by 5 per cent per degree of tilt in unstable, and up to 11 per cent per degree in stable conditions. A modified thermometer assembly was found necessary to provide durability. Field comparisons of the heat fluxes measured by the yaw sphere-thermometer system and a Bowen ratio apparatus produced satisfactory agreement.\r\n\r\nDirect measurements of sensible heat fluxes over a grass surface at Ladner, B.C. indicate a diurnal course very similar to that of the net radiation. In general, half-hour averaging periods showed no phase lag between sensible\r\nheat and net radiation. Field comparison of two YST systems gave good and consistent agreement. At a height of 2 m above ground and a horizontal crosswind separation of 1.5 m, less than 5 per cent variability was noted in the heat flux measurements from the two systems. For a 19 m horizontal separation, the variability was found to be less than 20 per cent. It is shown that the parameter (a), advanced by Priestley and Taylor (1972), can be a useful climatic indicator.\r\nThe applicability of the eddy correlation technique to the measurement of sensible heat transfer between the atmosphere and the urban interface is demonstrated\r\nfor a limited area of the city of Vancouver, B.C. Despite the enormous complexities of the turbulent heat exchange processes, the urban sensible heat flux pattern, obtained directly at heights of 1.2, 2, 4 and 20 m above roof-top level, largely reflected time and magnitude changes in the net radiation field, during the daytime. Nocturnal urban sensible heat fluxes, near roof-top level, were found to be directed away from the active surface. This is the reverse of the normal rural case. Within the local roof-top boundary layer, the sensible heat flux was found to be approximately constant with height and space (20% variation) during the daytime. At night, the existence of flux divergence and hence, non-constancy of the heat flux, is suggested. Daytime roof-top energy balances indicate that a significant portion of the net radiation is utilized in sensible heat transfer and in heat storage in the roof. The greatest energy is used in sensible heat transfer, which is about three times the heat storage at noon. With typical values of net radiation of 60 mWcm\u00E2\u0081\u00BB\u00C2\u00B2, the sensible heat flux is about 30 mWcm\u00E2\u0081\u00BB\u00C2\u00B2 and the heat storage 10 mWcm\u00E2\u0081\u00BB\u00C2\u00B2. The residual term (equated to latent heat transfer) is quite appreciable. It is possible that the role of latent heat transfer is important for urban energy balance considerations. The nocturnal roof-top energy balance required a latent heat term of about 15 mWcm\u00E2\u0081\u00BB\u00C2\u00B2 directed towards the active surface.\r\nThe energy balance of the surrounding urban area was deduced from measurements of sensible heat flux and net radiation at heights above the roof-top boundary layer. On the assumption that these point measurements approximately\r\nreflect areally integrated averages, partitioning of the heat between sensible and latent heat yeilds a Bowen ratio of ~ 1 at midday."@en . "https://circle.library.ubc.ca/rest/handle/2429/32331?expand=metadata"@en . "SENSIBLE HEAT FLUXES MEASURED IN AND NEAR VANCOUVER, B.C. by DAVID HAMILTON YAP B . S c , M c G i l l U n i v e r s i t y , 1966 M . S c , M c G i l l U n i v e r s i t y , 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department o f Geography We a c c e p t t h i s t h e s i s as c o n f o r m i n g to t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA March, 1973 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of Geography The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date A p r i l 24, 1973 ABSTRACT A yaw s p h e r e - t h e r m o m e t e r assembly ( Y S T ) , t o measure s e n s i b l e h e a t f l u x d e n s i t y by the eddy c o r r e l a t i o n method, was b u i l t f o l l o w i n g t h e d e s i g n o f Tanner and T h u r t e l l ( 1 9 7 0 ) . Wind t u n n e l e x p e r i m e n t s i n d i c a t e t h a t the s p h e r e c o n s t a n t s h o u l d be 1.57, which i s s i g n i f i c a n t l y l e s s than t h e p r e -v i o u s l y used t h e o r e t i c a l v a l u e o f 2.25. The e f f e c t s o f t i l t i n d i c a t e t h a t heat f l u x e s may be i n e r r o r by 5 per c e n t per d e g r e e o f t i l t i n u n s t a b l e , and up t o 11 p e r c e n t per d e g r e e i n s t a b l e c o n d i t i o n s . A m o d i f i e d thermometer assembly was found n e c e s s a r y to p r o v i d e d u r a b i l i t y . F i e l d c o m p a r i s o n s o f the heat f l u x e s measured by the yaw s p h e r e -thermometer system and a Bowen r a t i o a p p a r a t u s p r o d u c e d s a t i s f a c t o r y agreement. D i r e c t measurements o f s e n s i b l e h e a t f l u x e s o v e r a g r a s s s u r f a c e a t L a d n e r , B.C. i n d i c a t e a d i u r n a l c o u r s e v e r y s i m i l a r to t h a t o f the n e t r a d i a t i o n . In g e n e r a l , h a l f - h o u r a v e r a g i n g p e r i o d s showed no phase l a g between s e n -s i b l e h e a t and net r a d i a t i o n . F i e l d c o m p a r i s o n o f two YST systems gave good and c o n s i s t e n t agreement. A t a h e i g h t of 2 m above ground and a h o r i z o n t a l c r o s s w i n d s e p a r a t i o n i i o f 1.5 m, l e s s t h a n 5 per c e n t v a r i a b i l i t y was n o t e d i n t h e h e a t f l u x measurements from the two s y s t e m s . F o r a 19 m h o r i z o n t a l s e p a r a t i o n , the v a r i a b i l i t y was f o u n d to be l e s s t h a n 20 per c e n t . I t i s shown t h a t the p a r a m e t e r ( a ) , advanced by P r i e s t l e y and T a y l o r ( 1 9 7 2 ) , can be a u s e f u l c l i m a t i c i n d i c a t o r . The a p p l i c a b i l i t y o f t h e eddy c o r r e l a t i o n t e c h n i q u e t o t h e measurement o f s e n s i b l e h e a t t r a n s f e r between the atmosphere and the urban i n t e r f a c e i s demon-s t r a t e d f o r a l i m i t e d a r e a o f t h e c i t y o f V a n c o u v e r , B.C. D e s p i t e t h e enormous c o m p l e x i t i e s o f the t u r b u l e n t heat exchange p r o c e s s e s , t h e urban s e n s i b l e h e a t f l u x p a t t e r n , o b t a i n e d d i r e c t l y a t h e i g h t s o f 1.2, 2, 4 and 20 m above r o o f - t o p l e v e l , l a r g e l y r e f l e c t e d time and magnitude changes i n the net r a d i a t i o n f i e l d , d u r i n g t h e d a y t i m e . N o c t u r n a l urban s e n s i b l e heat f l u x e s , near r o o f - t o p l e v e l , were f o u n d to be d i r e c t e d away from the a c t i v e s u r f a c e . T h i s i s t h e r e v e r s e o f the normal r u r a l c a s e . W i t h i n the l o c a l r o o f - t o p boundary l a y e r , t h e s e n s i b l e heat f l u x was f o u n d to be a p p r o x i m a t e l y c o n s t a n t w i t h h e i g h t and s p a c e (20% v a r i a t i o n ) d u r i n g the d a y t i m e . A t n i g h t , the e x i s t e n c e o f f l u x d i v e r g e n c e and hence, n o n - c o n s t a n c y o f the h e a t f l u x , i s s u g g e s t e d . Daytime r o o f - t o p e n e r g y b a l a n c e s i n d i c a t e t h a t a s i g n i f i c a n t p o r t i o n o f th e net r a d i a t i o n i s u t i l i z e d i n s e n s i b l e h e a t t r a n s f e r and i n h e a t s t o r a g e i n the r o o f . The g r e a t e s t e n e r g y i s used i n s e n s i b l e h e a t t r a n s f e r , which i s abo u t t h r e e t i m e s t h e h e a t s t o r a g e a t noon. With t y p i c a l v a l u e s o f ne t r a d i a t i o n o f 60 mWcm\"2, the s e n s i b l e heat f l u x i s a b o u t 30 mWcm\"2 and the heat s t o r a g e 10 mWcm\"2. The r e s i d u a l term ( e q u a t e d t o l a t e n t h e a t t r a n s f e r ) i s q u i t e a p p r e c i a b l e . I t i s p o s s i b l e t h a t t h e r o l e o f l a t e n t h e a t t r a n s f e r i s i m p o r t a n t f o r urban e n e r g y b a l a n c e c o n s i d e r a t i o n s . The n o c t u r n a l r o o f - t o p e n e r g y b a l a n c e r e q u i r e d a l a t e n t h e a t term o f abo u t 15 mWcm\"2 d i r e c t e d towards t he a c t i v e s u r f a c e . The e n e r g y b a l a n c e o f the s u r r o u n d i n g urban a r e a was deduced from measurements o f s e n s i b l e h e a t f l u x and net r a d i a t i o n a t h e i g h t s above the r o o f - t o p boundary l a y e r . On t h e a s s u m p t i o n t h a t t h e s e p o i n t measurements a p p r o x i -m a t e l y r e f l e c t a r e a l l y i n t e g r a t e d a v e r a g e s , p a r t i t i o n i n g o f t h e h e a t between s e n s i b l e and l a t e n t heat y e i l d s a Bowen r a t i o o f ~ 1 a t midday. TABLE OF CONTENTS Page ABSTRACT . . . . . . . . . i i LIST OF TABLES. . .' v i i i L IST OF FIGURES i x LIST OF SYMBOLS x i i i ACKNOWLEDGEMENTS x v i C h a p t e r 1 INTRODUCTION 1 Ge n e r a l Background 1 Review. . . . . . . . . . . . . . 3 O b j e c t i v e s 15 2 SITE AND INSTRUMENTATION . . . . . . . 16 E x p e r i m e n t a l S i t e s 16 Ge n e r a l I n s t r u m e n t a t i o n and E x p e r i m e n t a l P r o c e d u r e s . . . . . . . . . . 35 Measurement Programme 39 3 THE YAW SPHERE-THERMOMETER SYSTEM. . . . . . . . 41 I n t r o d u c t i o n 41 Equipment D e s c r i p t i o n 42 v C h a p t e r Page Review o f the Yaw S p h e r e - T h e r -mometer T h e o r y 44 D e t e r m i n a t i o n o f the Sphere C o n s t a n t . . . . 50 E f f e c t o f Yaw Sphere A x i s T i l t 55 Thermometer System and F r e q u e n c y Response 60 F i e l d T e s t s R e s u l t s . . 66 4 SENSIBLE HEAT FLUX MEASUREMENTS OVER A RURAL SURFACE 72 I n t r o d u c t i o n . 72 E x p e r i m e n t a l S i t e and P r o c e d u r e s 74 D i u r n a l B e h a v i o u r o f the S e n s i b l e Heat F l u x 75 Measurements o f S p a t i a l V a r i a t i o n o f the S e n s i b l e Heat F l u x 83 P a r a m e t e r i z a t i o n o f the S e n s i b l e Heat F l u x and E v a p o r a t i o n . . . . . . . 92 5 SENSIBLE HEAT FLUXES OVER AN URBAN AREA 98 I n t r o d u c t i o n . 98 Boundary L a y e r C o n s i d e r a t i o n s . . . . . . .100 Mean V e r t i c a l V e l o c i t y C o n s i d e r a t i o n s . . .105 Samp l i n g C o n s i d e r a t i o n s 106 D i u r n a l Urban S e n s i b l e Heat F l u x P a t t e r n 115 S p a t i a l S a m p l i n g 124 6 URBAN ENERGY BALANCE 131 I n t r o d u c t i o n . . . . 131 v iC h a p t e r Page A r t i f i c i a l Heat and M o i s t u r e P r o d u c t i o n 132 R o o f - t o p Energy B a l a n c e 136 Energy B a l a n c e o f an Urban A r e a 152 7 SUMMARY OF CONCLUSIONS . 159 S u g g e s t i o n s f o r F u t u r e Work . . . . . . . . 163 REFERENCES . 1 6 6 APPENDIX A SAMPLE CALCULATION OF THE SENSIBLE HEAT FLUX 174 v i i LIST OF TABLES Tab! e Page T. Comparison o f a r t i f i c i a l e n e r g y f l u x d e n s i t y and a v e r a g e net r a d i a t i o n f o r s e l e c t e d urban a r e a s ( c . f . (SMIC, 1 9 7 1 ) ) . . . . . 10 2. Comparison o f day t i m e c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s from t h e yaw s p h e r e -thermometer (HYST) and Bowen r a t i o (H\u00E2\u0080\u009E) systems 71 3. Comparison o f a v e r a g e f l u x e s ( c . f . Dyer and H i c k s , 1972) 86 4. Comparison o f c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s from t h e yaw s p h e r e -thermometer systems (H YST/I an(^ H Y S T 2 a t 2 m above ground f o r an h o r i z o n t a l c r o s s w i n d s e p a r a t i o n o f 1.5 m . . . . . 89 5. Comparison o f c u m u l a t i v e s e n s i b l e heat f l u x d e n s i t i e s from t h e yaw s p h e r e -thermometer systems ( H y s T i a n c l H Y S T z ) a t 2 m above ground f o r an h o r i z o n t a l c r o s s w i n d s e p a r a t i o n o f 19 m . . . . . . . . . . . 91 6. Comparison o f day t i m e c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s from the yaw s p h e r e -thermometer systems ( H y s T i and H Y S T 2 ) above the urban r o o f 129 v i i i LIST OF FIGURES F i g u r e Page 1. S c h e m a t i c heat b a l a n c e o f a volume, one f a c e o f which i s the E a r t h ' s s u r f a c e ( a f t e r Suomi, 1 957) 4 2. S c h e m a t i c h e a t b a l a n c e o f urban b u i l d i n g -a i r volume . . . . . 6 3. The G r e a t e r Vancouver a r e a . 17 4. P e r c e n t a g e o f days w i t h m e a s u r e a b l e p r e c i p i -t a t i o n - Vancou v e r C i t y (1906-1955) - 7 day r u n n i n g mean ( c . f . H a r r y and W r i g h t , 1967). . . 20 5. Map o f Ladner e x p e r i m e n t a l s i t e 27 6. S k e t c h o f Lad n e r s i t e showing minimum f e t c h d i s t a n c e s 28 7. S i t e p l a n o f the urban a r e a ( V a n c o u v e r S c h o o l Board B u i l d i n g and i t s immediate e n v i r o n s ) . . . . . . . . . 31 8. The Vanc o u v e r S c h o o l Board B u i l d i n g ( p l a n view) 32 9. An example o f the l o c a t i o n o f the he a t i s l a n d c o r e s i n V a n c o u v e r , B.C . . . . 34 10. S c h e m a t i c d i a g r a m o f the r e c o r d i n g system . . . 43 11. The yaw sp h e r e - t h e r m o m e t e r a s s e m b l y . . . . . . 45 i x F i g u r e Page 12. S c h e m a t i c r e p r e s e n t a t i o n o f the a n g l e s , ty, a, 0 and the wind v e c t o r W on the yaw s p h e r e 48 13. G r a p h i c a l d e t e r m i n a t i o n o f the s p h e r e c o n s t a n t (b) and a l i g n m e n t e r r o r ( 6 ) . . 53 14. The e f f e c t o f t i l t on the geometry o f the s p h e r e 56 15. The r e s i s t a n c e thermometer . 61 16. The m o d i f i e d r e s i s t a n c e thermometer . 63 17. Comparison o f the two yaw sp h e r e - t h e r m o m e t e r systems f o r s e n s i b l e heat f l u x measurements (a) w i t h o r i g i n a l r e s i s t a n c e thermometer, (b) w i t h m o d i f i e d thermometer d e s i g n i n Y S T 1 . . . 64 18. F r e q u e n c y r e s p o n s e o f the yaw s p h e r e t u b i n g and B a r o c e l 65 19. Comparison o f s e n s i b l e h e a t f l u x d e n s i t i e s from the yaw sp h e r e - t h e r m o m e t e r system ( H Y s i O and the Bowen r a t i o system (Ho) o v e r g r a s s a t L a d n e r , B.C 67 20. Comparison o f HysT and H R a t L a d n e r , B.C. on Aug. 27, 1971. . . . . . . . . . . . . . . . . 68 21. D i u r n a l v a r i a t i o n o f H and c o m p a r i s o n o f the two YST systems 76 22. D i u r n a l v a r i a t i o n o f H and c o m p a r i s o n o f the two YST systems 77 23. D i u r n a l v a r i a t i o n o f H and c o m p a r i s o n o f the two YST systems 78 24. D i u r n a l energy b a l a n c e and s p a t i a l v a r i a t i o n o f H 79 x F i g u r e Page 25. D i u r n a l e n e r g y b a l a n c e and s p a t i a l v a r i a -t i o n o f H 80 26. An example o f l a r g e f l u c t u a t i o n s i n H w i t h 30 min a v e r a g i n g p e r i o d s 82 27. D i u r n a l v a r i a t i o n o f a (examples o f e a r l y and l a t e summer o b s e r v a t i o n s ) 94 28. R a t i o o f H/LE v s . t e m p e r a t u r e 96 29. (a) Boundary l a y e r development o v e r an a b r u p t change i n s u r f a c e r o u g h n e s s , (b) Boundary l a y e r d e v e l o p m e n t f o l l o w i n g a change from smooth t o a rough s u r f a c e where the r o u g h n e s s e l e m e n t s a r e above the s u r f a c e 101 30. S c h e m a t i c d i a g r a m o f the l o c a l boundary above a b u i l d i n g f o r a c o n s t a n t a n g l e o f a t t a c k o f the wind f l o w 103 31. Urban s e n s i b l e h e a t f l u x e s f o r h a l f - h o u r and one hour a v e r a g i n g p e r i o d s 109 32. Urban s e n s i b l e heat f l u x e s f o r h a l f - h o u r and one hour a v e r a g i n g p e r i o d s 110 33. Urban s e n s i b l e h e a t f l u x e s f o r h a l f - h o u r , one hour and two hour a v e r a g i n g p e r i o d s 113 34. Urban s e n s i b l e heat f l u x e s f o r h a l f - h o u r a v e r a g i n g p e r i o d s 114 35. D i u r n a l v a r i a t i o n o f t h e urban s e n s i b l e h e a t f l u x e s a t 1.2 m above r o o f 117a 36. D i u r n a l v a r i a t i o n o f t h e urban s e n s i b l e h e a t f l u x e s a t 1.2 m above r o o f 117b x i F i g u r e Page 37. D i u r n a l v a r i a t i o n o f t h e urban s e n s i b l e heat f l u x a t 20 m above r o o f 117c 38. E f f e c t o f shadow on the d i u r n a l b e h a v i o u r o f urban heat s t o r a g e 118 39. Urban e n e r g y b a l a n c e s (a) J u l y 7, 1972 w i t h d r y c o n d i t i o n s , (b) J u l y 13, 1972 f o l l o w i n g wet p e r i o d , ( c ) J u l y 17, 1972 5 days a f t e r wet p e r i o d . . . . . . 122 40. H o r i z o n t a l s p a t i a l v a r i a t i o n o f the urban s e n s i b l e h e a t f l u x e s 126 41. V e r t i c a l s p a t i a l v a r i a t i o n o f t h e urban s e n s i b l e h e a t f l u x e s 128 42. Daytime r o o f - t o p e n e r g y b a l a n c e 139 43. Daytime r o o f - t o p e n e r g y b a l a n c e . . 140 44. N o c t u r n a l r o o f - t o p e n e r g y b a l a n c e 151 45. N o c t u r n a l r o o f - t o p e n e r g y b a l a n c e 151 46. D i u r n a l b e h a v i o u r o f G i n v a r i o u s urban f a b r i c s . 156 47. Urban s e n s i b l e heat f l u x e s and p o i n t measurements o f Rn and G 157 48. The b r i d g e c i r c u i t 176 x i i LIST OF SYMBOLS a a n g l e between the wind v e c t o r and t h e b i s e c t o r o f the p o r t s ( C h a p t e r 3) a P r i e s t l e y and T a y l o r p a r a m e t e r ( C h a p t e r 4) b s p h e r e c o n s t a n t B b r i d g e c o n s t a n t B Bowen r a t i o (H/LE) Cp s p e c i f i c heat a t c o n s t a n t p r e s s u r e ^pb t h e r m a l c a p a c i t y o f c i t y s t r u c t u r e s d d i a m e t e r o f t h e s p h e r e D d i v e r g e n c e terms 6 t i l t e r r o r e vapour p r e s s u r e E water vapour f l u x E0 b r i d g e o u t p u t e r a t i o o f the mole w e i g h t o f water vapour to t h a t o f dr y a i r ( C h a p t e r 1) e r a t i o o f meter c o n d u c t i v i t y to medium c o n d u c t i v i t y ( C h a p t e r 6) x i i i f r a t i o o f mean f l u x d e n s i t y t h r o u g h the meter to t h e mean f l u x d e n s i t y t h r o u g h the medium F a r t i f i c i a l g e n e r a t i o n o f heat and water vapour $ c o s p e c t r u m between t h e v e r t i c a l v e l o c i t y (w) and w the a i r t e m p e r a t u r e (T) G a m p l i f i e r g a i n ( C h a p t e r 3) G s o i l h eat s t o r a g e H s e n s i b l e heat f l u x I g t r u e e f f e c t i v e o u t g o i n g r a d i a t i o n from the s u r f a c e L l a t e n t h e a t o f v a p o u r i z a t i o n LE l a t e n t h e a t f l u x M p r e s s u r e t r a n s d u c e r c o n s t a n t v k i n e m a t i c v i s c o s i t y n f r e q u e n c y p p r e s s u r e P g s t a t i c p r e s s u r e q s p e c i f i c h u m i d i t y R s p e c i f i c gas c o n s t a n t Re R e y n o l d s no. Rn net r a d i a t i o n p a i r d e n s i t y x i v a S t e f a n - B o l t z m a n n c o n s t a n t s l o p e o f the s a t u r a t i o n vapour c u r v e a t the a p p r o p r i a t e t e m p e r a t u r e T a i r t e m p e r a t u r e t e m p e r a t u r e o f c i t y s t r u c t u r e s T s s u r f a c e t e m p e r a t u r e 9 i n c l u d e d a n g l e between t h e p o r t s x n e g a t i v e momentum f l u x u h o r i z o n t a l wind v e l o c i t y component a l o n g d i r e c t i o n o f the wind IT mean wind speed V a i r speed ( C h a p t e r 3) V s t o r a g e terms i n volume ( C h a p t e r 1) V v e l o c i t y v e c t o r v c r o s s w i n d h o r i z o n t a l component o f the wind v e l o c i t y w v e r t i c a l v e l o c i t y component X J . Z J t i l t a x i s p l a n e ( \u00E2\u0080\u0094 ) time a v e r a g e a t a g i v e n p o i n t ( )' f l u c t u a t i o n a bout t h e mean V 8/8x + 8/3y XV ACKNOWLEDGEMENTS T h i s s t u d y was s u p e r v i s e d by Dr. T.R. Oke. To him I am d e e p l y i n d e b t e d f o r the encouragement, a s s i s t a n c e and c o n s t r u c t i v e i d e a s d u r i n g a l l s t a g e s o f my t h e s i s work. The a u t h o r a l s o w i s h e s to e x p r e s s h i s t h a n k s t o Dr. T.A. B l a c k and M e s s r s . K. McNaughton and R. W i l s o n o f t h e S o i l S c i e n c e Department f o r t h e i r h e l p i n t h e c o n -s t r u c t i o n and t e s t i n g o f the yaw s p h e r e - t h e r m o m e t e r s y s t e m . The main e x p e r i m e n t s were c o n d u c t e d a t C a n a d i a n F o r c e s S t a t i o n L a d n e r and the V a n c o u v e r S c h o o l Board b u i l d -i n g . P e r m i s s i o n t o use t h e s e f a c i l i t i e s a r e g r a t e f u l l y a c k n o wledged. I g r a t e f u l l y acknowledge the s u p p o r t from t h e N a t i o n a l R e s e a r c h C o u n c i l t h r o u g h a s c h o l a r s h i p d u r i n g t h e \u00E2\u0080\u00A2 p e r i o d 1970-73. x v i C h a p t e r 1 INTRODUCTION G e n e r a l Background The r e c e i p t , t r a n s f o r m a t i o n and t r a n s f e r o f e n e r g y a t t h e e a r t h - a t m o s p h e r e i n t e r f a c e i s b a s i c t o a r a t i o n a l u n d e r s t a n d i n g o f c l i m a t e s . E s t i m a t i o n o f the v e r t i c a l eddy f l u x e s o f p h y s i c a l e n t i t i e s , such as s e n s i b l e h e a t , water v a p o u r and momentum i n the a t m o s p h e r i c boundary l a y e r r e m ains a t t h e c o r e o f m i c r o m e t e o r o l o g i c a l r e s e a r c h . Knowledge o f t h e s e f l u x e s i s a l s o i m p o r t a n t i n the s t u d y o f the g e n e r a l c i r c u l a t i o n o f t h e atmosphere s i n c e t h e y d e f i n e the l o w e r boundary c o n d i t i o n s o f the l a r g e r s c a l e a t m o s p h e r i c dynamics. U n t i l v e r y r e c e n t l y , t h e f i e l d o f urban m i c r o -m e t e o r o l o g y was a l m o s t n o n - e x i s t e n t . A l t h o u g h a l a r g e body o f urban c l i m a t e l i t e r a t u r e e x i s t s ( see t h e summaries g i v e n by Brooks ( 1 9 5 2 ) , K r a t z e r ( 1 9 5 6 ) , L a n d s b e r g ( 1 9 6 1 ) , C h a n d l e r (1968) and P e t e r s o n ( 1 9 6 9 ) ) , a t t e n t i o n has been p r i m a r i l y c o n f i n e d t o t h e d e s c r i p t i o n o f t h e b a s i c n a t u r e o f c l i m a t i c e f f e c t s p r o d u c e d by urban a r e a s . The p r o c e s s e s g i v i n g r i s e 1 2 to urban c l i m a t e s remained l a r g e l y s p e c u l a t i v e . T h i s l a c k o f i n f o r m a t i o n c o n c e r n i n g the u n d e r l y i n g mechanisms g o v e r n i n g urban c l i m a t e has a t t r a c t e d many r e s e a r c h e r s , e s p e c i a l l y s i n c e t h e r e c e n t WMO Symposium on Urban C l i m a t e s (WMO, 1970). Most o f t h e work, however, seems t o be c e n t r e d on m o d e l l i n g the urban e n v i r o n m e n t ( s e e f o r example, t h e C o n f e r e n c e on Urban E n v i r o n m e n t , 1972). E x p e r i m e n t a l r e s e a r c h t o probe t h e p h y s i c a l b a s i s o f urban c l i m a t e i s s t i l l l a r g e l y d e f i c i e n t , due t o t h e enormous c o m p l e x i t y o f t h e c i t y / a t m o s p h e r e i n t e r -f a c e and t h e need f o r s o p h i s t i c a t e d measurement t e c h n i q u e s . T h i s s t u d y seeks t o a c h i e v e some i n s i g h t i n t o t h e manner i n w hich h e a t i s u t i l i z e d i n t h e urban atmosphere and i n t o t h e e n e r g e t i c s o f urban m i c r o m e t e o r o l o g y t h r o u g h d i r e c t measurements. F o r most n a t u r a l s u r f a c e s , the n a t u r e o f t h e i r e n e r g e t i c b a s i s has been e l u c i d a t e d t h r o u g h h e a t budget s t u d i e s . S i m i l a r s t u d i e s f o r c i t i e s a r e f r a g m e n t a r y o r a b s e n t . T h i s d e a r t h o f knowledge c o n c e r n i n g the e n e r g y f l u x e s i n urban a r e a s has been m e n t i o n e d by many a u t h o r s i n r e c e n t y e a r s ( e . g . Munn ( 1 9 6 6 ) , M i l l e r ( 1 9 6 8 ) , Lowry (1969) and Oke ( 1 9 6 9 ) ) . I t i s to be e x p e c t e d t h a t u r b a n i z a t i o n w i l l m a r k e d l y m o d i f y the s u r f a c e h e a t b a l a n c e . D e t e r m i n a t i o n o f t h i s a l t e r e d h e a t b a l a n c e i s one o f t he t a s k s o f urban c l i m a t o l o g y ( L a n d s b e r g , 1970). T h r o u g h o u t t h i s s t u d y , the h e a t b a l a n c e a p p r o a c h has been u t i l i z e d , and t h e r e f o r e i t i s u s e f u l to r e v i e w t h e framework h e r e . 3 Review The c o n c e p t o f heat b a l a n c e i s embodied i n the p r i n c i p l e o f c o n s e r v a t i o n o f e n e r g y : the d i f f e r e n c e between he a t i n f l o w and o u t f l o w i s the h e a t s t o r e d o r used w i t h i n the system o f c o n c e r n . The heat b a l a n c e o f a volume, one f a c e o f which i s the E a r t h ' s s u r f a c e , i s s c h e m a t i c a l l y shown i n F i g . 1. U s i n g the c o n s e r v a t i o n p r i n c i p l e , i t can be e x p r e s s e d as a g e n e r a l e q u a t i o n a t any i n s t a n t i n t i m e as f o l 1 o w s : + R n = \u00C2\u00B1 H \u00C2\u00B1 L E \u00C2\u00B1 G \u00C2\u00B1 V \u00C2\u00B1 D (1.1) where Rn, H, LE and G r e p r e s e n t the v e r t i c a l f l u x e s o f n e t r a d i a t i o n , s e n s i b l e h e a t , l a t e n t heat and s o i l h eat r e s p e c -t i v e l y . V i s the s t o r a g e o f h e a t i n the volume and D i s the h o r i z o n t a l d i v e r g e n c e o f s e n s i b l e and l a t e n t h e a t . F o r a f l a t , s o l i d s u r f a c e o r a homogeneous vege-t a t e d s u r f a c e w i t h a d e q u a t e f e t c h , the d i v e r g e n c e and volume s t o r a g e terms a r e u s u a l l y s m a l l compared w i t h the v e r t i c a l f l u x e s ( e . g . Begg et al.s 1964; Brown and Covey, 1967; Lemon, 1967), and a c c o r d i n g l y , the h e a t b a l a n c e e x p r e s -s i o n r e d u c e s t o : \u00C2\u00B1 R n = \u00C2\u00B1 H \u00C2\u00B1 LE \u00C2\u00B1 G (1.2) 4 NET RADIATION (Rn) ^ SENSIBLE HEAT TRANSFER (H) LATENT HEAT TRANSFER (LE) LATENT HEAT f\u00C2\u00B13 SENSIBLE HEAT t I I I / /6y ' STORAGE TERMS IN VOLUME (V) SOIL HEAT CONDUCTION (G) DIVERGENCE TERMS (D) LATENT HEAT SENSIBLE HEAT i F i g . 1. Sc h e m a t i c heat b a l a n c e o f a volume, one f a c e o f which i s the E a r t h ' s s u r f a c e ( a f t e r Suomi, ( 1 9 5 7 ) . 5 The n e g l e c t o f o t h e r terms u s u a l l y i n v o l v e s an e r r o r o f l e s s than 10 per c e n t o f the net r a d i a t i o n ( D a v i e s et al.3 1969). Numerous examples o f heat b a l a n c e s t u d i e s o f t y p i c a l r u r a l s u r f a c e s ( g r a s s , c r o p s and f o r e s t ) can be c i t e d ( f o r example: L e t t a u and D a v i d s o n , 1957; W r i g h t and Lemon, 1962). Through volume c o n s i d e r a t i o n s , i t i s a l s o p o s s i b l e to f o r m u l a t e the heat b a l a n c e o f an urban a r e a . A s c h e m a t i c r e p r e s e n t a t i o n o f t h e heat b a l a n c e o f an u r b a n - b u i l d i n g a i r volume i s shown i n F i g . 2. I t may be r e p r e s e n t e d by the f o l l o w i n g e q u a t i o n ,z \u00C2\u00B1 R n \u00C2\u00B1 F = \u00C2\u00B1 H \u00C2\u00B1 L E \u00C2\u00B1 G \u00C2\u00B1 Le 3e ,_ RT 9t 6 z 9 T h b 'pb a t Sz 9T 3t Sz V H ( p u T ) 6 z Le R ue] IT J Sz (1.3) where the meaning o f the symbols i s : Cp, s p e c i f i c h eat o f a i r a t c o n s t a n t p r e s s u r e ; p, a i r d e n s i t y ; u, h o r i z o n t a l wind v e l o c i t y ; T, a i r t e m p e r a t u r e ; L, l a t e n t heat o f v a p o u r i z a -t i o n ; E, water vapour f l u x ; e, t h e r a t i o o f the mole w e i g h t NET RADIATION (Rn) SENSIBLE HEAT TRANSFER (H) LATENT HEAT TRANSFER (LE) LATENT HEAT SENSIBLE HEAT \u00E2\u0080\u00A2 C n l l D T F T F R M S IN VOI U M F f I I SOURCE E I L E 1. ART IF IC IAL H E A T G E N E R A T I O N (F\u00E2\u0080\u009E) 2. ART IF IC IAL W A T E R V A P O U R S O U R C E ( F W ) STORAGE TERMS IN VOLUME 1. H E A T S T O R A G E IN AIR\" -2. H E A T S T O R A G E IN BUILDINGS: 3. L A T E N T H E A T S T O R A G E : f*Z.C dC Jo AT 5F LATENT HEAT loo ooj SENSIBLE HEAT SOIL HEAT CONDUCTION (G) DIVERGENCE: j * L* 7H Sz DIVERGENCE, f* Cp ?H(fuT) %l F i g . 2. S c h e m a t i c heat b a l a n c e o f urban b u i l d i n g - a i r volume. 7 o f water vapour to t h a t o f d r y a i r ; R, the s p e c i f i c gas c o n s t a n t ; e, vapour p r e s s u r e ; C ^ , t h e r m a l c a p a c i t y and t e m p e r a t u r e o f c i t y s t r u c t u r e s , r e s p e c t i v e l y ; F, a r t i f i c i a l g e n e r a t i o n o f heat and water vapour and , 9/9x + 8/3y . O t h e r symbols have t h e i r meaning as b e f o r e . A l t h o u g h the g o v e r n i n g e n e r g y budget e q u a t i o n s may be r e a d i l y s p e c i f i e d f o r the urban s i t u a t i o n , the t h r e e -d i m e n s i o n a l n a t u r e o f the prob l e m i s most f o r m i d a b l e . The complex c i t y system r a i s e s s e r i o u s d i f f i c u l t i e s . In p a r -t i c u l a r , i t becomes a l m o s t i m p o s s i b l e to d e f i n e such b a s i c c o n c e p t s as the l o c a t i o n o f the ' s u r f a c e ' i t s e l f . The many b u i l d i n g s and m u l t i p l e - l e v e l s u r f a c e s p r e s e n t a complex geometry to t h e atmosphere. F u r t h e r c o m p l i c a t i o n s a r i s e from man-made p r o d u c t i o n o f h e a t and water vapour i n c i t i e s . Each e l e m e n t o f the mosaic which forms a c i t y ( t h e home, b u i l d i n g , pavement, r o a d , g a r d e n , e t c . ) c r e a t e s i t s own d i s t i n c t i v e m i c r o c l i m a t i c e n v e l o p e . One s h o u l d t h e r e f o r e e x p e c t t h a t t h e i n h o m o g e n e i t i e s ( h o r i z o n t a l l y and v e r t i c a l l y ) p r o d u c e d by t h e s e e l e m e n t s would r e s u l t i n s i g n i f i c a n t m i c r o -c l i m a t i c v a r i a b i l i t y . I t may not however be u n r e a s o n a b l e to s u g g e s t t h a t a f i r s t o r d e r u n i t y o f b u i l d i n g d e v e l o p m e n t s h o u l d g i v e a r e g i o n a l c o n t i n u i t y to t h e b a s i c urban c l i m a t e ( C h a n d l e r , 1965). Indeed, e v i d e n c e from s t u d i e s o f t h e hea t i s l a n d ( t h e c h a r a c t e r i s t i c warmth o f the c i t y ) s u p p o r t s t h i s view s i n c e t h e h o r i z o n t a l t e m p e r a t u r e p a t t e r n near s t r e e t 8 l e v e l o f t e n c l o s e l y p a r a l l e l s the urban m o r p h o l o g y , e.g. Maxwell ( 1 9 7 1 ) . Hence, by c o n f i n i n g our i n v e s t i g a t i o n i n the complex c i t y system to a l i m i t e d u r b a n - b u i l d i n g - a i r volume where b u i l d i n g s a r e o f u n i f o r m t y p e , h e i g h t , d e n s i t y and f u n c t i o n , some de g r e e o f c l i m a t i c c o n t i n u i t y may be e x p e c t e d . In d o i n g s o , we n e c e s s a r i l y r e s t r i c t t h e scope o f the r e s e a r c h to a s m a l l p o r t i o n o f the d i v e r s i f i e d urban l a n d s c a p e . A t the same time however, i t o f f e r s a r a t i o n a l a p p r o a c h towards p r o b i n g the urban atmosphere and s h o u l d e n a b l e an e l u c i d a t i o n o f t h e e n e r g e t i c b a s i s o f c i t y c l i m a t e . The c o m p l e x i t y o f the t h r e e - d i m e n s i o n a l n a t u r e o f t h e prob l e m i s e v i d e n t . I t i s not however p r o p o s e d to e v a l u a t e a l l the en e r g y terms i n d i c a t e d f o r such a volume, but r a t h e r to use t h i s framework, and t o f o c u s a t t e n t i o n p r i m a r i l y on t h e v e r t i c a l e n e r g y e x c h a n g e s . In r e c e n t y e a r s , urban heat budget s t u d i e s have a t t r a c t e d the a t t e n t i o n o f a number o f r e s e a r c h e r s . Even so i t i s not s u r p r i s i n g t h a t we know so l i t t l e a b o ut t h e components o f the he a t budget i n urban a r e a s i n view o f t h e c o m p l e x i t i e s o f the e n v i r o n m e n t and out l a c k o f a p p r o p r i a t e m e a s u r i n g t e c h n i q u e s to a s s e s s q u a n t i t a t i v e l y t h e s e e n e r g e t i c e x c h a n g e s . E x p e r i m e n t a l e v i d e n c e o f t h e urban e n e r g y com-ponents i s s t i l l f r a g m e n t a r y . The r a d i a t i o n a l a s p e c t s have now been i n v e s t i g a t e d to some e x t e n t ( e . g . Tag, 1968; Hawkins, 1969; T e r j u n g , 1970; Bach, 1970 and Oke and F u g g l e , 9 1972). The e f f e c t o f r a d i a t i v e exchanges between b u i l d i n g e l e m e n t s , and shadow a r e a s remain o u t s t a n d i n g problem a r e a s f o r i n v e s t i g a t i o n . The few a t t e m p t s made to measure the h e a t s t o r e d i n the c i t y b u i l d i n g m a t e r i a l s ( e . g . D a v i s , 1968 and T e r j u n g , 1970) o n l y p r o v i d e g r o s s e s t i m a t e s o f t h i s e n e r g y b a l a n c e component. A s p a t i a l a v e r a g i n g p r o c e d u r e t h a t i n c l u d e s g e o m e t r i c a l c o n s i d e r a t i o n s might y i e l d r e a s o n -a b l e h e a t s t o r a g e e s t i m a t e s , but has not y e t been a t t e m p t e d . E s t i m a t i o n o f the a r t i f i c i a l h eat p r o d u c e d i n c i t i e s can be f o u n d i n the l i t e r a t u r e ( e . g . Oke, 1969; SMIC, 1971). The a r t i f i c i a l e n e r g y f l u x d e n s i t y f o r v a r i o u s c i t i e s i s g i v e n i n T a b l e 1. D e t e r m i n a t i o n o f the v e r t i c a l f l u x e s o f s e n s i b l e and l a t e n t h e a t o v e r urban a r e a s remains an o u t s t a n d i n g p r o b l e m . A t t e m p t s have been made to a s s e s s t h e s e f l u x e s i n d i r e c t l y v i a t h e Bowen r a t i o / e n e r g y b a l a n c e method w i t h l i t t l e s u c c e s s ( e . g . Bach, 1970; Myrup and Morgan, 1972). F u g g l e (1971) and T e r j u n g (1971) have o b t a i n e d s t a b l e measure-ments i n t h i s r e g a r d , but o f a l i m i t e d n a t u r e . T h e r e have been no a t t e m p t s a t d i r e c t measurements o f t h e s e e n e r g y f l u x e s . I t i s thus o b v i o u s t h a t much r e s e a r c h i s s t i l l needed i n t h i s a r e a o f urban heat b a l a n c e c l i m a t o l o g y . A c c o r d i n g l y , the p r i n c i p a l aim o f t h i s r e s e a r c h w i l l be d i r e c t e d towards d i r e c t a s s e s s m e n t o f the eddy f l u x e s i n T a b l e I C o m p a r i s o n o f a r t i f i c i a l e n e r g y f l u x d e n s i t y and a v e r a g e n e t r a d i a t i o n f o r s e l e c t e d u r b a n a r e a s ( c . f . (SMIC, 1971)) C i t y A r e a ( k m 2) Popu1 a t i on I 0 6 A r t i f i c i a 1 e n e r g y f l u x d e n s i t y (mWcm - 2) A v e r a g e n e t r a d i a t i on (mWcm\" 2) A v e r a g i n g P e r i od West Ber1 i n * 234 2.3 .2.1 5.7 Y e a r Hamburg 747 1 .8 1 .3 5.5 Y e a r Moscow 878 6.4 12.7 4.2 Y e a r C i n c i n n a t i 200 0.54 2.6 Summer Los A n g e l e s 3500* 7.0 2. 1 10.8 Y e a r M a n h a t t a n , New Y o r k 59 1 .7 4.0 19.8 Summer W i n t e r F a i r b a n k s , A 1 a s k a * 37 0.03 1 .9 1 .8 Y e a r M o n t r e a 1 * 78 9.8. Y e a r B u i l d i n g a r e a o n l y . - J o B a s e d on m o d i f i e d SMIC ( 1 9 7 1 ) , Summers ( 1 9 6 4 ) and Oke ( 1 9 6 9 ) . 11 the urban c o n t e x t , and i n p a r t i c u l a r , s e n s i b l e h e a t . I t i s t h e r e f o r e u s e f u l to r e v i e w the m e a s u r i n g t e c h n i q u e . Most o f m i c r o m e t e o r o l o g i c a l r e s e a r c h has been c e n t r e d on means o f d e r i v i n g t h e f l u x e s o f h e a t , w a t e r vapour and momentum t h r o u g h i n d i r e c t methods, based on t e m p e r a t u r e , w ater vapour and wind p r o f i l e s , which n e c e s -s a r i l y i n v o l v e a s s u m p t i o n s about the c h a r a c t e r o f t h e atmo s p h e r e . A c o n s i d e r a b l e l i t e r a t u r e on p r o f i l e f o r m u l a s t o a c c o m p l i s h t h i s has been d e v e l o p e d . D i r e c t measurement o f t h e s e f l u x e s has r e c e i v e d much impetus i n r e c e n t y e a r s , as s u i t a b l e m e a s u r i n g t e c h n i q u e s have been d e v e l o p e d t o u t i l i z e such an a p p r o a c h . E x c e p t f o r the few m i l l i m e t e r o f a i r above t h e ground ( t h e l a m i n a r boundary l a y e r ) , where e n t i t i e s a r e t r a n s f e r r e d by m o l e c u l a r p r o c e s s e s , t u r b u l e n c e i s t h e p r i n c i p a l mechanism f o r a t m o s p h e r i c t r a n s p o r t near t h e E a r t h ' s s u r f a c e . The d i r e c t measurement o f e d d y - f l u x e s i s based on f l u c t u a t i o n t h e o r y . By c o n s i d e r i n g t h e v e r t i c a l t r a n s p o r t o f a p h y s i c a l e n t i t y ( s ) a c r o s s u n i t h o r i z o n t a l a r e a , i t can be shown ( e . g . Swinbank, 1951, P r i e s t l e y , 1959) t h a t the v e r t i c a l f l u x ( F g ) under c o n d i t i o n s o f s t e a d y - s t a t e and h o r i z o n t a l u n i f o r m i t y i s g i v e n by F s = (pw)s (1.4) 12 where p i s the a i r d e n s i t y ; w i s t h e v e r t i c a l wind component and t h e bar i n d i c a t e s a tim e a v e r a g e a t a g i v e n p o i n t . T h us, f o r example, t h e t u r b u l e n t heat f l u x may be w r i t t e n H = C p TpwJT (1.5) where T i s t h e a i r t e m p e r a t u r e and C p i s the s p e c i f i c h e a t a t c o n s t a n t p r e s s u r e . The v a r i a b l e s p, w and T may f u r t h e r -more be e x p r e s s e d i n terms o f a mean q u a n t i t y p l u s a f l u c -t u a t i o n a b o u t t h a t mean so t h a t H = C p [ ( p + p ' ) ( w + w')(T + T ' ) ] and i f t h e r e i s no s i g n i f i c a n t c o n v e r g e n c e o r d i v e r g e n c e ( i . e . pw - 0) the s e n s i b l e h e a t f l u x e x p r e s s i o n can be expanded to g i v e H = C p [ p w'T' + w p'T' + p'w'T'] (1.6) 13 I f the mean v e r t i c a l wind i s c l o s e to z e r o , the second term i n t h e b r a c k e t can be n e g l e c t e d . The magnitude o f t h e t h i r d term ( t h e t r i p l e moment), compared to the f i r s t term i n t h e b r a c k e t , has been shown by B u s i n g e r and Miyake (1968) e x p e r i m e n t a l l y to be a r a t i o o f about 0.0014 and t h e r e f o r e the s e n s i b l e h e a t f l u x e x p r e s s i o n r e d u c e s to H = C p p wT 7\" (1.7) In a s i m i l a r manner, t h e v e r t i c a l f l u x e s o f l a t e n t h e a t and momentum can be o b t a i n e d d i r e c t l y from t h e c o v a r i a n c e s o f w and q ( s p e c i f i c h u m i d i t y ) f l u c t u a t i o n s and w and u f l u c t u a t i o n s , r e s p e c t i v e l y . Hence LE = p L w'q' (1.8) T = -p w'u' ( T : n e g a t i v e momentum f l u x ) T h i s a p p r o a c h ( t h e eddy c o r r e l a t i o n t e c h n i q u e ) i s a f u n -damental method f o r m e a s u r i n g t u r b u l e n t t r a n s f e r , and i t p o s s e s s e s t h e adv a n t a g e o f d i r e c t l y m e a s u r i n g eddy f l u x e s . The d i r e c t m e a s u r i n g t e c h n i q u e s , however, a r e not e a s i l y a c c o m p l i s h e d s i n c e t h e y r e q u i r e v e r y f a s t - r e s p o n s e s e n s o r s t h a t must measure the p u l s a t i o n s o f t h e wind and t h e 14 a p p r o p r i a t e p h y s i c a l e n t i t y o v e r the e n t i r e f r e q u e n c y range c o n t r i b u t i n g to the f l u x . In t h i s s t u d y , a t t e n t i o n i s l i m i t e d to the use o f t h i s t e c h n i q u e i n the measurement o f s e n s i b l e h e a t . For the measurement o f H, the s t r i n g e n t r e q u i r e -ments o f the wind s e n s o r a r e h a r d e s t to meet. Two o f the most p r o m i s i n g a p p r o a c h e s a r e the s o n i c anemometer ( M i t s u t a , 1966, 1968; Kaimal et al.3 1968) and the p r e s s u r e - s p h e r e anemometer ( T h u r t e l l et al.3 1970; Wesely et al.3 1972). Comparisons o f H d e t e r m i n e d by i n s t r u m e n t s i n c o r p o r a t i n g t h e s e wind s e n s o r s have been most e n c o u r a g i n g ( e . g . Wesely et al.3 1970). R e c e n t l y Tanner and T h u r t e l l (1970) d e v e l o p e d a r e l a t i v e l y s i m p l e yaw s p h e r e - t h e r m o m e t e r (YST) system f o r the measurement o f s e n s i b l e heat f l u x i n c o r p o r a t i n g the p r e s s u r e - s p h e r e p r i n c i p l e . The yaw s p h e r e when d i r e c t e d i n t o the wind f l o w g e n e r a t e s a p r e s s u r e d i f f e r e n c e between two p o r t s t h a t i s p r o p o r t i o n a l t o the p r o d u c t o f the h o r i z o n t a l and v e r t i c a l w i n d s . The a n a l o g p r e s s u r e s i g n a l i s used to d r i v e a r e s i s t a n c e - t h e r m o m e t e r b r i d g e . The b r i d g e o u t p u t i s then d i r e c t l y r e l a t e d to the s e n s i b l e h e a t f l u x . T h i s system was chosen f o r the p u r p o s e o f our i n v e s t i g a t i o n . A s i g n i f i c a n t a s p e c t o f t h i s r e s e a r c h i n c l u d e s i n s t r u m e n t a l development and improvement, and f i e l d c o m p a r i s o n t e s t s o v e r a s i m p l e r u r a l s u r f a c e . 15 O b j e c t i ves In summary, the p r i m a r y o b j e c t i v e s o f t h i s t h e s i s can be s t a t e d as f o l l o w s : 1) t o c o n s t r u c t , c a l i b r a t e and t e s t a yaw-s p h e r e - t h e r m o m e t e r s y s t e m f o r d i r e c t m e a s u r e m e n t s o f s e n s i b l e h e a t f l u x dens i t y , 2) t o e x a m i n e t h e s p a t i a l v a r i a b i l i t y o f t h e eddy f l u x i n t h e a t m o s p h e r i c b o u n d a r y l a y e r , 3) t o d e t e r m i n e t h e m a g n i t u d e and s i g n o f t h e s e n s i b l e h e a t f l u x e s o v e r an u r b a n a r e a , 4) t o i n v e s t i g a t e t h e r o l e o f t h i s p a r a m e t e r i n t h e u r b a n e n e r g y b a l a n c e f r a m e w o r k . I t s h o u l d be emphasized t h a t some o f t h e s e o b j e c -t i v e s a r e v e r y d i f f i c u l t to a c h i e v e , and c o u p l e d w i t h l i m i t a t i o n s i n o b s e r v a t i o n must n e c e s s a r i l y c r e a t e s h o r t -comings. T h i s s t u d y i s however e x p e c t e d t o c o n t r i b u t e to our knowledge o f eddy f l u x measurement i n the a t m o s p h e r i c boundary l a y e r , and i n p a r t i c u l a r , to heat exchange p r o -c e s s e s i n the urban e n v i r o n m e n t . C h a p t e r 2 SITE AND INSTRUMENTATION E x p e r i m e n t a l S i t e s G e n e r a l a s p e c t s . For the p u r p o s e o f t h i s i n v e s t i g a t i o n , two e x p e r i -mental s i t e s were chosen i n and near V a n c o u v e r , B.C. G r e a t e r V a n c o u v e r , w i t h a p o p u l a t i o n e x c e e d i n g one m i l l i o n , c o v e r s t h e w e s t e r n m o s t p o r t i o n o f the Lower M a i n l a n d a r e a o f B r i t i s h C o l u m b i a . A map o f the r e g i o n d e p i c t i n g g e o g r a p h i c a l and p o l i t i c a l l a n d m a r k s , l a n d use and the l o c a t i o n o f the e x p e r i m e n t a l s i t e s i s shown i n F i g . 3. Dense, h i g h - r i s e b u i l d i n g s a r e c o n f i n e d p r i m a r i l y t o t h e C e n t r a l B u s i n e s s D i s t r i c t (CBD) on th e B u r r a r d P e n i n s u l a . The t o p o g r a p h y i s v a r i e d . The l a n d o v e r t h e a r e a s l o p e s g r a d u a l l y from s o u t h t o n o r t h , r i s i n g r a p i d l y from B u r r a r d I n l e t to the mountain r i d g e s a l o n g i t s n o r t h s h o r e . These mountain peaks r i s e t o h e i g h t s i n e x c e s s o f 1000 m. In the s o u t h w e s t e r n a r e a s o f Richmond and D e l t a , the l a n d i s f l a t and i s used p r i m a r i l y f o r a g r i c u l t u r e , 16 1 7 & # # & W H I T E ROCK T S A W W A S S E N U R B A N SITE (V.S.B.) \u00E2\u0080\u00A2Jf R U R A L SITE (LADNER) BUILT UP A R E A C O N T O U R I N T E R V A L 300M 10 KM J F i g . 3. The G r e a t e r V a n c o u v e r a r e a . 18 a l t h o u g h r a p i d u r b a n i z a t i o n i s becoming e v i d e n t . The S u r r e y a r e a i s one o f r o l l i n g f a r m l a n d s w i t h o c c a s i o n a l h i l l s r e a c h i n g to e l e v a t i o n s o f 100 m. In the c i t y p r o p e r , the ground s l o p e s g r a d u a l l y from the F r a s e r upwards to form a s l i g h t r i d g e between t h i s r i v e r and B u r r a r d I n l e t . Here l a n d e l e v a t i o n s r e a c h 100-150 m and c o n t a i n s e v e r a l c r e s t s . The v a r i e d t o p o g r a p h y , the c l o s e p r o x i m i t y o f the l a n d t o w a t e r b o d i e s , and the d e g r e e o f u r b a n i z a t i o n e x e r t marked i n f l u e n c e s on the l o c a l c l i m a t e . The c l i m a t e o f the r e g i o n i s b e s t d e s c r i b e d as m o d i f i e d m a r i t i m e , c h a r a c t e r i z e d by wet m i l d autumn and w i n t e r , and r e l a t i v e l y d r y c o o l summers. T e m p e r a t u r e . T e m p e r a t u r e s a r e m o d i f i e d by p r o x i m i t y to G e o r g i a S t r a i t . Mean d a i l y t e m p e r a t u r e s range from about 2-5\u00C2\u00B0C d u r i n g the months o f J a n u a r y and F e b r u a r y t o about 17-18\u00C2\u00B0C d u r i n g the months o f J u l y and A u g u s t . The t e m p e r a t u r e p a t t e r n o f the G r e a t e r V a n c o u v e r a r e a has r e c e n t l y been r e p o r t e d by E m s l i e ( 1 9 7 2 ) . L a r g e v a r i a t i o n s i n t h e s u r f a c e t e m p e r a t u r e f i e l d e x i s t . The c ause o f t h e s e v a r i a t i o n s i s a t t r i b u t e d to the f o l l o w i n g f a c t o r s : 19 a) The d i s t a n c e f r o m t h e o c e a n and i t s m o d i f y i n g e f f e c t on a i r t e m p e r a t u r e , b) s e a b r e e z e s , c ) c o l d a i r d r a i n a g e t o low a r e a s a t n i g h t , d) t h e n o r m a l d e c r e a s e o f t e m p e r a t u r e w i t h h e i g h t , e) h e a t i s l a n d e f f e c t , f ) s o u t h e r l y a s p e c t , g) s y s t e m a t i c v a r i a t i o n s i n c l o u d i n e s s , h) a t m o s p h e r i c p o l l u t i o n i n t h e downtown a r e a . P r e c i p i t a t i on. E x t r e m e l y v a r i e d p r e c i p i t a t i o n p a t t e r n s o c c u r i n th e G r e a t e r V a n c o u v e r r e g i o n as a r e s u l t o f w e s t e r l y w i n d s , c o u p l e d w i t h t h e a b r u p t t e r r a i n l e v e l changes i n t h e n o r t h e r n s e c t i o n s ( W r i g h t and T r e n h o l m , 1969). Annual p r e c i p i t a t i o n v a r i e s from < 100 cm i n the Tsawassen a r e a to > 250 cm i n p a r t s o f No r t h V a n c o u v e r . A s i m i l a r t r e n d i n c l o u d c o v e r may be i n f e r r e d from t h e p r e c i p i t a t i o n p a t t e r n . The s e a s o n a l v a r i a t i o n o f p r e c i p i t a t i o n i n Vancouver i s shown i n F i g . 4. The summer i s g e n e r a l l y d r y w i t h o n l y a few days o f r a i n , whereas the w i n t e r i s c h a r a c t e r i z e d by many days o f r a i n i n each month. F i g . 4. P e r c e n t a g e o f days w i t h m e a s u r a b l e p r e c i p i t a t i o n - Vancouver C i t y (1906-1955) - 7 day r u n n i n g mean ( c . f . H a r r y and W r i g h t , 1967). o 21 Wi nds. The p r e v a i l i n g wind d i r e c t i o n s a r e e a s t e r l y and w e s t e r l y a l o n g the a x i s o f the F r a s e r V a l l e y . E a s t e r l y winds a r e a s s o c i a t e d w i t h the development o f n i g h t time l a n d b r e e z e s and w i t h the g e n e r a l f l o w ahead o f any f r o n t a l s y s t e m . W e s t e r l i e s o c c u r as a f t e r n o o n sea b r e e z e s o r f o l l o w i n g f r o n t a l p a s s a g e s and a r e g e n e r a l l y much s t r o n g e r than the e a s t e r l y w i n d s . E a s t e r l i e s a r e p r e d o m i n a n t t h r o u g h -o u t t h e y e a r , d i m i n i s h i n g g r a d u a l l y from w i n t e r to summer. W e s t e r l i e s show an i n c r e a s e i n f r e q u e n c y o f o c c u r r e n c e from w i n t e r to summer. Mean wind speeds do n o t show much v a r i a t i o n from month t o month. The p r e s e n c e o f a l o c a l sea b r e e z e - l a n d b r e e z e c i r c u l a t i o n and v a l l e y c o n s t r i c t i o n o f t e n combine t o i n h i b i t t h e t r a n s p o r t o f a t m o s p h e r i c p o l l u t a n t s away from t h e a r e a i n p r o l o n g e d p e r i o d o f a n t i -c y c l o n i c w eather c o n d i t i o n s . V i s u a l o b s e r v a t i o n s i n d i c a t e t h a t t h e p o l l u t a n t s i n such s i t u a t i o n s a r e c a r r i e d up t h e v a l l e y d u r i n g the d a y t i m e w i t h the o n s h o r e b r e e z e , o n l y to r e t u r n to the c i t y a t n i g h t w i t h t h e l a n d b r e e z e c i r c u l a t i o n . H e a t i n g s e a s o n . H e a t i n g r e q u i r e m e n t to p r o v i d e r e a s o n a b l e c o m f o r t t h r o u g h o u t t h e y e a r i s g e n e r a l l y e x p r e s s e d i n terms o f 22 \"degree d a y s \" ( t h e number o f d e g r e e s F t h a t the mean d a i l y t e m p e r a t u r e i s below 6 5 \u00C2\u00B0 F ) . For V a n c o u v e r , on the a v e r a g e , 90 per c e n t o f the h e a t i n g s e a s o n ( h e a t i n g d e g r e e - d a y s ) o c c u r s between September and A p r i l , w i t h J a n u a r y and F e b r u a r y b e i n g the two g r e a t e s t h e a t i n g months. In c o n -t r a s t , J u l y and A u g u s t may be c o n s i d e r e d to be n o n - h e a t i n g months ( H a r r y and W r i g h t , 1967). T h i s g e n e r a l p i c t u r e p r o v i d e s the b a s i c c l i m a t e c o n t e x t w i t h i n which the m i c r o c l i m a t i c i n v e s t i g a t i o n s o f t h i s s t u d y took p l a c e . A more d e t a i l e d d e s c r i p t i o n o f the g e n e r a l c l i m a t e o f the V a n c o u v e r a r e a i s g i v e n by H a r r y and W r i g h t ( 1 9 6 7 ) . S i t e c o n s i d e r a t i o n s . E x p e r i m e n t a l s t u d i e s i n the a t m o s p h e r i c boundary l a y e r a r e s t r o n g l y i n f l u e n c e d by the s p a t i a l v a r i a b i l i t y o f m e t e o r o l o g i c a l phenomena i n both the h o r i z o n t a l and v e r t i c a l d i r e c t i o n s . To some e x t e n t , o b s e r v a t i o n s i n such an e n v i r o n m e n t can o n l y be c o n d u c t e d i m p e r f e c t l y . F o r w h i l e s p a t i a l s a m p l i n g i s h i g h l y d e s i r a b l e , e s p e c i a l l y o v e r rugged t e r r a i n , t h i s i s o f t e n d i f f i c u l t to a c h i e v e because o f p r a c t i c a l l i m i t a t i o n s . One i s then l e d to c o n s i d e r p o i n t measurements w i t h t h e i r i n h e r e n t l i m i t a t i o n s , and t o 23 l i m i t s t u d y o f the p r o c e s s e s to the time domain. P a r t i c u l a r a t t e n t i o n then must be g i v e n to the i m p o r t a n t and o f t e n d i f f i c u l t problem o f s i t e s e l e c t i o n . In c h o o s i n g the s i t e , o b j e c t i v e c r i t e r i a s h o u l d be s p e c i f i e d . P r i m a r y c o n s i d e r a t i o n s h o u l d be g i v e n t o : a) t h e p u r p o s e o f t h e i n v e s t i g a t i o n , b) t h e n a t u r e o f t h e u n d e r l y i n g s u r f a c e , c ) p r a c t i c a l l i m i t a t i o n s . In t h i s s t u d y the f o l l o w i n g g e n e r a l s i t e s e l e c t i o n c r i t e r i a were employed. a) t h e s i t e and i t s i m m e d i a t e e n v i r o n s s h o u l d be as n e a r l y as p o s s i b l e c h a r a c t e r i s t i c o f t h e a r e a , t h e c l i m a t e o f w h i c h i s t o be e x p l o r e d , b) i t s h o u l d be w i t h i n an a r e a t h a t i s f a i r l y u n i f o r m and e x t e n s i v e so a s t o m i n i m i z e s m a l l s e a I e - a d v e c t i v e i n f l u e n c e s and t o e n s u r e a d e q u a t e f e t c h , c ) p r o p e r a l l o w a n c e s h o u l d be made w i t h r e f e r e n c e t o t h e e x p o s u r e o f t h e s i t e f o r t h e e n t i t i e s t o be m e a s u r e d , d) t h e s i t e s h o u l d be a c c e s s i b l e , w i t h a d e q u a t e power and p r o t e c t i o n f r o m v a n d a l i s m . A p a r t from p r a c t i c a l l i m i t a t i o n s (see (d) a b o v e ) , an e x p e r i m e n t a l s i t e t h a t s a t i s f i e s t h e s e g e n e r a l c r i t e r i a can u s u a l l y be f o u n d i n r u r a l a r e a s . T hus, an e x t e n s i v e , u n i f o r m f l a t a r e a o r a homogeneous v e g e t a t e d s u r f a c e w i t h 24 adeq u a t e f e t c h would be a p p r o p r i a t e f o r the r u r a l e x p e r i -mental s i t e . A f i x e d s a m p l i n g p o i n t may then be c o n s i d e r e d s u f f i c i e n t l y r e p r e s e n t a t i v e o f the a r e a . S i t e s e l e c t i o n i n t h e urban e n v i r o n m e n t , to meet the above c r i t e r i a , i s e x t r e m e l y d i f f i c u l t . I n deed, i t i s i m p o s s i b l e t o d e f i n e a s a m p l i n g s i t e which c o u l d be c o n -s i d e r e d ' r e p r e s e n t a t i v e ' o f t h e c i t y as a whole, b e c a u s e t h e urban ' t o p o g r a p h y ' and the s o u r c e and s i n k d i s t r i b u -t i o n s o f h e a t , w a t er vapour and momentum i s h i g h l y i r r e g u l a r . By c o n s i d e r i n g o n l y a v e r y s m a l l p o r t i o n o f t h e urban l a n d -s c a p e (a l i m i t e d u r b a n - b u i l d i n g - a i r v o l u m e ) , i t may be p o s s i b l e t o o b t a i n a s i t e and i t s immediate e n v i r o n s t h a t i s a p p r o x i m a t e l y c h a r a c t e r i s t i c o f an urban a r e a . I f t h e a r e a p o s s e s s e s a b a s i c c o n t i n u i t y o f f o r m , c r i t e r i o n (b) may be a d e q u a t e l y s a t i s f i e d . I t s h o u l d be p o i n t e d o u t , however, t h a t where d i s t i n c t changes i n the p r o p e r t i e s o f the u n d e r l y i n g s u r f a c e o c c u r , i n t e r n a l boundary l a y e r s d e v e l o p and deepen downwind. In urban a r e a s , many changes o c c u r due t o t h e v a r i e t y o f s u r f a c e t y p e s and the n a t u r e o f the s u r f a c e geometry. S u r f a c e d i s c o n t i n u i t i e s may a l s o be c r e a t e d by t e m p e r a t u r e a n o m a l i e s ( f o r example, c o n t r a s t i n g a r e a s i n shadow and d i r e c t s u n l i g h t ) . The problem o f a c h i e v i n g s u i t a b l e h e i g h t / f e t c h r a t i o to e n s u r e r e p r e s e n t a -t i v e n e s s would become f o r m i d a b l e i f t h e s e changes r e s u l t e d 25 i n d i s t i n c t l o c a l i z e d boundary l a y e r s . Dyer (1963) i n d i c a t e s a h e i g h t / f e t c h r a t i o 1:200-300 f o r 90 per c e n t a d j u s t m e n t to a new s u r f a c e c o n d i t i o n . S u f f i c i e n t f e t c h would thus o n l y be r e a l i z e d f o r c o n d i t i o n s v e r y c l o s e t o the p a r t i c u l a r s u r f a c e o v e r which measurements were made. Such l o c a l i z e d e f f e c t s may not be v e r y s i g n i f i c a n t o v e r a r e l a t i v e l y dense u n i f o r m urban a r e a s i n c e the i n t e r n a l b o u n d a r i e s a r e l i k e l y to become d i f f u s e d t h r o u g h t u r b u l e n t m o t i o n o f t h e a i r as i t t r a v e r s e s o v e r t h e b u i l d i n g e l e m e n t s . The c h o i c e o f s i t e may thus m i n i m i z e t h i s e f f e c t . To a l l o w f o r p r o p e r e x p o s u r e a t the s i t e and to e n s u r e a r e l a t i v e l y u n i f o r m m e t e o r o l o g i c a l f i e l d , measurements i n the urban c o n t e x t s h o u l d be c o n d u c t e d above r o o f l e v e l . In c h o o s i n g t h e urban e x p e r i m e n t a l s i t e , t h e f o l l o w i n g c r i t e r i a were s p e c i f i e d : a) t h e s i t e s h o u l d be l o c a t e d i n an a r e a o f b u i l d i n g c o n t i n u i t y ( u n i f o r m t y p e , h e i g h t , d e n s i t y and f u n c t i o n ) and m e a s u r e m e n t s s h o u l d be made a b o v e r o o f -l e v e l , so as t o e n s u r e some u n i f o r m i t y i n t h e m e t e o r o l o g i c a l f i e l d s , b) t h e s i t e s h o u l d have s u i t a b l e f e t c h f r o m n o n - u r b a n s u r f a c e s so as t o a v o i d l a r g e s c a l e a d v e c t i v e i n f l u e n c e s , c ) t h e a r e a o f c o n c e r n s h o u l d be n e a r t h e c e n t r e o f t h e u r b a n h e a t i s l a n d , b u t h o r i z o n t a l t e m p e r a t u r e g r a d i e n t s s h o u l d be r e I a t i v e I y smaI I , d) t h e r e s h o u l d be no m a j o r a n o m a l y n e a r b y t h a t m i g h t s p o r a d i c a l l y a f f e c t r e s u l t s ( e x . i n d u s t r i a l p l a n t w i t h h i g h w a s t e h e a t and w a t e r v a p o u r e m i s s i o n s ) . 26 The f o l l o w i n g two s e c t i o n s d e s c r i b e the s i t e s chosen i n l i g h t o f t h e s e c r i t e r i a . The r u r a l s i t e . The r u r a l o b s e r v a t i o n a l s i t e was l o c a t e d on t h e f l a t d e l t a r e g i o n o f the F r a s e r , about 28 km s o u t h o f V a n c o u v e r ( c . f . F i g . 3 ) . The s i t e chosen was an e x t e n s i v e , f l a t g r a s s e d s u r f a c e on the abandoned a i r p o r t a t C a n a d i a n F o r c e s S t a t i o n , L a d n e r . The g e n e r a l l o c a t i o n o f the s i t e i s shown on F i g s . 5 and 6. I n t e r r u p t i o n s i n t h e g r a s s s u r f a c e p r o p e r t i e s were c r e a t e d by the a i r p o r t runways, Boundary Bay and by a s t e p change i n the g r a s s h e i g h t i n the NNE-SSE s e c t o r d u r i n g the f i e l d programme o f 1971. The g r a s s o v e r the e x p e r i m e n t a l s i t e was ~ 90 cm t a l l , g i v i n g a r o u g h n e s s l e n g t h o f ~ 10 cm based on a n a l y s i s o f n e u t r a l wind p r o f i l e s . R a d i a t i o n measurements gave a s h o r t - w a v e a l b e d o o f 0.23 and a long-wave e m i s s i v i t y o f 0.98 f o r the g r a s s s u r f a c e . H e i g h t / f e t c h r a t i o s (1:165 to 1:200) were fo u n d to be s u f f i c i e n t t o e n s u r e r e p r e s e n t a t i v e o b s e r v a t i o n s i n most i n s t a n c e s . Minimum f e t c h d i s t a n c e s , and the g e n e r a l l o c a t i o n o f t h e i n s t r u m e n t s a r e shown i n F i g . 6. The s i t e was c o n s i d e r e d s a t i s f a c t o r y i n r e s p e c t o f the g e n e r a l c r i t e r i a p r e v i o u s l y s t a t e d ( e . g . u n i f o r m i t y i n t e r r a i n F i g . 5. Map o f L a d n e r e x p e r i m e n t a l s i t e . S k e t c h o f L a d n e r s i t e showing minimum f e t c h d i s t a n c e s . 29 and v e g e t a t i o n c o v e r , freedom from v e r t i c a l o b s t r u c t i o n s , a c c e s s i b i l i t y , a v a i l a b l e power and s e c u r i t y ) . A p o s i t i v e f e a t u r e o f t h i s s i t e was the f a c t t h a t i t had been p r e -v i o u s l y used f o r e x t e n s i v e s t u d i e s o f the t u r b u l e n t t r a n s f e r mechanisms i n the a t m o s p h e r i c boundary l a y e r ( e . g . McBean and M i y a k e , 1972). The urban s i t e . The urban e x p e r i m e n t a l s i t e , c hosen f o r t h i s s t u d y was l o c a t e d i n a mixed commercial and m e d i u m - r i s e r e s i d e n t i a l d i s t r i c t . O b s e r v a t i o n s were c o n d u c t e d o v e r t h e f l a t - t o p r o o f o f a f o u r - s t o r e y b u i l d i n g ( t h e Van c o u v e r S c h o o l Board B u i l d -i n g ) i n t h e midtown a r e a ( F i g . 3 ) . The minimum f e t c h t o non-urban s u r f a c e s was a p p r o x i m a t e l y 1.5 km (N. t o F a l s e C r e e k , and NW t o E n g l i s h B a y ) . O t h e r w i s e t h e b u i l d i n g s w i t h i n a 2 km r a d i u s o f the s i t e were f a i r l y u n i f o r m i n \u00E2\u0080\u00A2 h e i g h t , d e n s i t y and f u n c t i o n ( e x c e p t i n t h e e a s t e r l y s e c t o r , where i r r e g u l a r i t i e s i n t h e s u r f a c e due t o t h e d i f f e r e n t shape and h e i g h t s o f b u i l d i n g s were n o t i c e a b l e ) . A v e r a g e b u i l d i n g h e i g h t s were ~ 10-13 m. W i t h i n a 2 km r a d i u s o f t h e e x p e r i m e n t a l s i t e , b u i l d i n g s o c c u p i e d ~ 70-80 per c e n t o f each b l o c k , e x c e p t near the p e r i p h e r y i n the n o r t h e a s t and s o u t h e r l y s e c t o r s . A p p r o x i m a t e l y 70 per c e n t o f t h e s e 30 b u i l d i n g s c o n s i s t e d o f m e d i u m - r i s e r e s i d e n t i a l d w e l l i n g s , p r i m a r i l y o f f l a t - t o p r o o f s c o v e r e d w i t h g r a v e l and t a r . A s i t e p l a n showing t h e l o c a t i o n o f the V a n c o u v e r S c h o o l Board B u i l d i n g (VSB) and i t s immediate e n v i r o n s i s shown i n F i g . 7. A s u r v e y based on l a n d uses w i t h i n the 2 km c i r c l e gave e s t i m a t e s o f i m p e r v i o u s h o r i z o n t a l s u r f a c e a r e a o f a p p r o x i -m a t e l y 70 per c e n t . C l o s e r t o the a c t u a l s i t e , t h e i m p e r v i o u s l a n d a r e a was about 80 per c e n t . The a r e a s l o p e s g r a d u a l l y downwards from s o u t h to n o r t h , d r o p p i n g a p p r o x i m a t e l y 50 m o v e r the 4 km d i s t a n c e ( i . e . s l o p e ~ 1 i n 8 0 ) . The i n f l u e n c e o f w a ter s u r f a c e s to the n o r t h ( m a i n l y E n g l i s h B a y ) , c o u l d not always to a v o i d e d a t the VSB s i t e . A i r f l o w sometimes o c c u r r e d from t h i s d i r e c t i o n . Measurements c o n d u c t e d c l o s e t o the VSB r o o f - t o p s u r f a c e would not be a f f e c t e d by t h i s i n f l u e n c e . A t g r e a t e r h e i g h t s , however, i t was r e c o g n i z e d t h a t measurements would p r o b a b l y be a f f e c t e d by the c o n t r a s t s i n w a t e r / l a n d t e m p e r a t u r e s and h u m i d i t i e s . T h i s n e c e s s i t a t e d c o n s i d e r a t i o n o f the p r e v a i l -i n g wind d i r e c t i o n d u r i n g o b s e r v a t i o n p e r i o d s . A p l a n view o f the r o o f - t o p s u r f a c e o f t h e VSB b u i l d i n g i s shown i n F i g . 8. The r o o f m a t e r i a l s c o n s i s t e d o f t a r w i t h a c o v e r i n g l a y e r o f f i n e g r a v e l which had a s h o r t - w a v e a l b e d o o f 0.21 and a long-wave e m i s s i v i t y o f 0.92. The r e s t o f t h e b u i l d i n g was c o n s t r u c t e d o f r e d b r i c k and c o n c r e t e . T h e r e were no major v e n t i l a t i o n o u t l e t s a t r o o f 31 F i g . 7. S i t e p l a n o f the urban a r e a ( V a n c o u v e r S c h o o l Board B u i l d i n g and i t s immediate e n v i r o n s ) . 1 L O C A T I O N O F RN, Y S T (20M) O N M A S T , 20M A B O V E POSITION 4 2 G R O O F < O N SUPER S T R U C T U R E ) 3 L O C A T I O N O F T A R A N D C O N C R E T E S L A B S 4 Y S T L O C A T I O N F O R M E A S U R E M E N T S A T .1.2, 2.0 A N D 4.0M MAIN EXPERIMENTAL AREA (GRAVEL AND TAR ROOF) PATIO (WOOD OVER TAR & GRAVEL) J B R O A D W A Y h L l o t h A V E ^ ~ii ir L \u00C2\u00A9 V-S.B BLDG. N \" (GRAVEL AND TAR ROOF) 4M A B O V E POSITION 4 XL T E L E S C O P I N G M A S T S U P E R -S T R U C T U R E 10M A B O V E POSITION 4 G R A V E L A N D T A R R O O F \u00E2\u0080\u00A2 I N C I N E R A T O R 10 M F i g . 8, The Vancouver S c h o o l Board B u i l d i n g ( P l a n view) 33 l e v e l e x c e p t f o r the i n c i n e r a t i o n chimney on the s u p e r s t r u c -t u r e . In g e n e r a l , d a y t i m e wind d i r e c t i o n s were p r e d o m i n a n t l y from the n o r t h , west and s o u t h e r l y s e c t o r s . A t n i g h t , t h e r e was a t e n d e n c y sometimes f o r the development o f e a s t e r l y w i n d s . The e x a c t l o c a t i o n s o f the i n s t r u m e n t s on t h e r o o f a r e shown i n F i g . 8. D u r i n g the o b s e r v a t i o n programme o f 1972, a s u r v e y o f V a n c o u v e r ' s h e a t i s l a n d was u n d e r t a k e n . I t was f o u n d t h a t the a r e a o f the e x p e r i m e n t a l s i t e was c l o s e t o one o f the c o r e s o f the h e a t i s l a n d a t n i g h t (see F i g . 9 ) . R e l a -t i v e l y s m a l l t e m p e r a t u r e g r a d i e n t s o c c u r w i t h i n t h e a r e a . A few d a y t i m e s u r v e y s i n d i c a t e d even s m a l l e r h o r i z o n t a l tem-p e r a t u r e g r a d i e n t s . I t must however be n o t e d t h a t c o n t r a s t -i n g a r e a s i n shadow and s u n l i g h t would be l i k e l y to produce l o c a l i z e d t e m p e r a t u r e g r a d i e n t s . In our a r e a , t h e s e c o u l d h a r d l y be a v o i d e d . I t w i l l be assumed t h a t t h e s e e f f e c t s a r e s m a l l , on t h e b a s i s t h a t t u r b u l e n t m i x i n g o f t h e a i r t e n d s to produce u n i f o r m i t y i n the t e m p e r a t u r e f i e l d . A l t h o u g h t h i s s i t e p o s s e s s e s o b v i o u s l i m i t a t i o n s , i t was c o n s i d e r e d a c c e p t a b l e f o r the s t u d y , based on the c r i t e r i a s p e c i f i e d p r e v i o u s l y . F i g . 9. An example of the l o c a t i o n o f the heat i s l a n d c o r e s i n V a n c o u v e r , B.C. CO 35 G e n e r a l I n s t r u m e n t a t i o n and E x p e r i m e n t a l P r o c e d u r e s The s i n g l e most i m p o r t a n t i n s t r u m e n t f o r t h i s s t u d y was the yaw s p h e r e - t h e r m o m e t e r eddy c o r r e l a t i o n s y stem t o measure s e n s i b l e heat f l u x d i r e c t l y . S i n c e the d e v e l o p m e n t , c a l i b r a t i o n and t e s t i n g o f t h i s a p p a r a t u s forms an i n t e g r a l p a r t o f the r e s e a r c h , i t w i l l be p r e s e n t e d s e p a r a t e l y i n the n e x t c h a p t e r . Here a t t e n t i o n i s l i m i t e d to o t h e r r e l e -v a n t i n s t r u m e n t a t i o n used i n the c o u r s e o f the i n v e s t i g a t i o n . Radi a t i on. Net r a d i o m e t e r s ( S w i s s t e c o P t y . L t d . , Model S I ) were used t o measure the n e t s u r f a c e a l l - w a v e r a d i a t i o n . The r a d i a t i o n s e n s o r c o n s i s t s o f a c r o s s - s h a p e d t h e r m o p i l e c o n -s t r u c t e d o f c o p p e r - p l a t e d c o n s t a n t a n w i r e . The t h e r m o p i l e s u r f a c e s a r e e n c l o s e d w i t h i n a p a i r o f molded p o l y e t h y l e n e domes, 0.5 mm i n t h i c k n e s s , which a r e t r a n s p a r e n t t o r a d i a -t i o n i n t h e w a v e l e n g t h s between 0.3 y and 100 u. The domes were kept r i g i d and f r e e o f i n t e r i o r c o n d e n s a t i o n by a c o n t r o l l e d f l o w o f d r y n i t r o g e n . A more p r a c t i c a l way t o keep the domes purged by means o f d r y a i r ( D a v i e s et al.3 1970) was a d o p t e d d u r i n g the m e a s u r i n g programme i n 1972. The r a d i o m e t e r time c o n s t a n t was 23 s, and the t h e r m o p i l e s e n s i t i v i t y was a p p r o x i m a t e l y 0.39 mv/mWcm\"2 ( c a l i b r a t i o n s 36 s u p p l i e d by N a t i o n a l R a d i a t i o n L a b o r a t o r y , Canada A E S ) . E x c e p t where n o t e d i n the t e x t , the o u t p u t s o f the r a d i o -meters were r e c o r d e d c o n t i n u o u s l y on v o l t - t i m e i n t e g r a t o r s ( L i n t r o n i c , L t d . ) , u s i n g a 30 min i n t e g r a t i o n p e r i o d . In a l l s t u d i e s c o n c e r n e d w i t h the measurement o f s u r f a c e r a d i a t i o n f l u x e s , i t i s i m p o r t a n t t h a t the r a d i a t i o n r e c e i v e d by the s e n s o r i s r e p r e s e n t a t i v e o f the s u r f a c e under s t u d y . A t the r u r a l s i t e , t h i s was not d i f f i c u l t to a c h i e v e s i n c e the s u r f a c e was r e l a t i v e l y homogeneous, and n e t r a d i a -t i o n was m o n i t o r e d a t a c o n v e n t i o n a l h e i g h t o f 1 m. A t the urban s i t e , c o r r e c t l o c a t i o n o f the s e n s o r i s i m p o r t a n t f o r view f a c t o r c o n s i d e r a t i o n s . To e n s u r e a good h o r i z o n t a l f i e l d o f view, t h e r a d i o m e t e r was mounted a p p r o x i m a t e l y 20 m above the p r i n c i p a l r o o f - t o p s u r f a c e on a f i x e d t e l e -s c o p i n g mast a t t h e p o s i t i o n shown i n F i g . 8. A t e s t o f the h e i g h t v a r i a b i l i t y i n t h e n e t r a d i a n t f l u x o v e r t h e h e i g h t range 11 to 20 m showed l e s s t h a n 5 per c e n t v a r i a t i o n d u r i n g the d a y t i m e . H o r i z o n t a l v a r i a b i l i t y o f t h e urban n e t r a d i a t i o n f i e l d was not examined. Some v a r i a t i o n s a r e to be e x p e c t e d i n measurements o v e r a r o o f as opposed t o t h o s e o v e r a canyon (between b u i l d i n g e l e m e n t s ) , p a r t i c u l a r l y when shadow a r e a s a r e e x t e n s i v e ( e . g . C r a i g and Lowry, 1972). View f a c t o r c o n s i d e r a t i o n s and the e f f e c t o f the i n t e r v e n i n g a i r l a y e r between the r a d i a t i o n s e n s o r and the r o o f - t o p s u r f a c e w i l l be examined i n C h a p t e r 6. 37 S o i l h eat s t o r a g e . S o i l h eat s t o r a g e was measured u s i n g h e a t f l u x p l a t e s ( M i d d l e t o n and C o . ) . The heat f l u x p l a t e c o n s i s t s o f two m e t a l l i c s u r f a c e p l a t e s s e p a r a t e d by a s u b s t a n c e o f known c o n d u c t i v i t y . A t h e r m o p i l e w i t h a l t e r n a t e j u n c t i o n s i n good t h e r m a l c o n t a c t w i t h one o f the s u r f a c e p l a t e s measures the t e m p e r a t u r e d i f f e r e n t i a l between the s u r f a c e s , and hence can be c a l i b r a t e d to p r o v i d e the heat f l u x d e n s i t y . A t the r u r a l l o c a t i o n , t h r e e such p l a t e s ( o f a p p r o x i m a t e l y equal c a l i b r a t i o n : 0.28 mv/mWcm\"2) were c o n n e c t e d i n s e r i e s and p l a c e d about 2.5 cm below the s o i l s u r f a c e . T h i s a r r a n g e m e n t p r o v i d e d a l a r g e r s i g n a l f o r measurements, and gave a b e t t e r s p a t i a l s a m p l i n g . S o i l f l u x d i v e r g e n c e between the 2.5 cm d e p t h and the s u r f a c e was computed v i a the c a l o r i m e t r i c ( t e m p e r a t u r e i n t e g r a l ) method (Fuchs and T a n n e r , 1968). T h i s was f o u n d t o be v e r y s m a l l i n magnitude and was s u b s e q u e n t l y n e g l e c t e d i n t h i s s t u d y . A t the urban s i t e , a heat f l u x p l a t e was embedded i n the g r a v e l and t a r r o o f , c a r e b e i n g t a k e n to e n s u r e no e x p o s u r e to s o l a r r a d i a t i o n . The p l a t e was l o c a t e d about 0.5 cm below the s u r f a c e . The measured heat f l u x p r o v i d e d an e s t i m a t e o f the amount o f heat p a s s i n g i n t o o r o u t o f the r o o f . Heat f l u x p l a t e s were a l s o embedded i n s l a b s o f t a r and c o n c r e t e and p l a c e d on the VSB r o o f i n o r d e r t o 38 p r o v i d e some u n d e r s t a n d i n g o f the way i n w hich o t h e r urban m a t e r i a l s may d i f f e r from the r o o f v a l u e . No a t t e m p t was made to e s t i m a t e the s t o r a g e by the v e r t i c a l w a l l s o f t h e b u i l d i n g . E r r o r s a s s o c i a t e d w i t h the use o f the f l u x p l a t e i n t h e r o o f w i l l be d i s c u s s e d i n C h a p t e r 6. The r o o f f l u x p l a t e o u t p u t s i g n a l was a l s o r e c o r d e d on a v o l t - t i m e i n t e g r a t o r , u s i n g a 30 min i n t e g r a t i o n p e r i o d . The p l a t e s i n t h e s l a b s o f t a r and c o n c r e t e were c o n t i n u o u s l y m o n i t o r e d on a p o t e n t i o m e t r i c r e c o r d e r (Honeywell, E l e c t r o n i k 1 9 4 ) . O t h e r i n s t r u m e n t s . The f o l l o w i n g a d d i t i o n a l equipment was u s e d : 1. F o r t h e f i e l d t e s t s o f the yaw s p h e r e - t h e r -mometer s y s t e m , c o m p a r i s o n was made a g a i n s t the Bowen r a t i o / e n e r g y b a l a n c e method. The Bowen r a t i o a p p a r a t u s used i s d e s c r i b e d i n d e t a i l i n the p a p e r by B l a c k and McNaughton ( 1 9 7 1 ) . I t i s a p s y c h r o m e t r i c a p p a r a t u s d e s i g n . f o r Bowen r a t i o d e t e r m i n a t i o n t h a t measures the wet- and d r y - b u l b d i f f e r e n c e s o v e r a v e r t i c a l d i s t a n c e o f 0.6 o r 1 m w i t h an e r r o r l e s s t h a n 0.01\u00C2\u00B0C. The t e m p e r a t u r e s e n s o r s c o n s i s t o f two matched p a i r s o f 1N2356 germanium d i o d e s . The germanium d i o d e has a l i n e a r v o l t a g e - t e m p e r a t u r e c h a r a c t e r i s t i c and 39 l a r g e s e n s i t i v i t y o f a b o u t 2.3 m v \u00C2\u00B0 C _ 1 . The time c o n s t a n t o f the s e n s i n g heads i s a p p r o x i m a t e l y 1 min. A c c o r d i n g l y , o n l y d a t a r e c o r d e d f o r t h e l a s t 10 min o f each 15-min p e r i o d i s used i n th e Bowen r a t i o c a l c u l a t i o n s . H a l f - h o u r l y Bowen r a t i o s a r e computed from the d i f f e r e n c e s between v o l t a g e a v e r a g e s from two c o n s e c u t i v e 10-min p e r i o d s . The o u t p u t s i g n a l s were c o n t i n u o u s l y m o n i t o r e d on a p o t e n t i o m e t r i c r e c o r d e r ( H o n e y w e l l , E l e c t r o n i k 1 9 4 ) . 2. S u r f a c e r o u g h n e s s c h a r a c t e r i s t i c s a t the L a d n e r s i t e were d e t e r m i n e d from p r o f i l e measurements w i t h a s i x -l e v e l s e n s i t i v e wind p r o f i l e system (C.W. T h o r n t h w a i t e A s s o c i a t e s ) . Wind speeds were measured a t 1.13, 2.00, 1.43, 1.73, 2.33 and 2.93 m above ground l e v e l . 3. Short-wave a l b e d o measurements were o c c a s i o n a l l y m o n i t o r e d w i t h dome s o l a r i m e t e r s ( L i n t r o n i c , L t d . ) ( M o n t e i t h , 1 959). These i n s t r u m e n t s c o n s i s t o f an e i g h t y - j u n c t i o n t h e r m o p i l e , e n c l o s e d by a t h i n - w a l l e d f r o s t e d g l a s s dome ( t r a n s p a r e n t t o r a d i a t i o n i n the w a v e l e n g t h range 0.3y t o 3.3u. Measurement Programme The o b s e r v a t i o n programme was i n i t i a l l y s t a r t e d i n t h e l a t e summer o f 1970 i n M o n t r e a l as a p r e l i m i n a r y r e s e a r c h 40 p r o j e c t . C I i m a t o l o g i c a l a p p r o a c h e s to the d e t e r m i n a t i o n o f the urban s e n s i b l e heat f l u x e s were i n v e s t i g a t e d (Oke et al.3 1972). The eddy c o r r e l a t i o n method a p p e a r e d most l i k e l y to a c h i e v e s u c c e s s i n the c o n t e x t o f the c i t y and a c c o r d i n g l y was a d o p t e d . O n l y s u b s e q u e n t work i s r e p o r t e d i n t h i s t h e s i s. The yaw s p h e r e - t h e r m o m e t e r system was c o n s t r u c t e d and c a l i b r a t e d i n 1971. L a t e r t h a t summer the f i e l d com-p a r i s o n t e s t s were c o n d u c t e d a t the r u r a l s i t e i n L a d n e r , B.C. D u r i n g the f o l l o w i n g w i n t e r , a second YST system was c o n -s t r u c t e d . The main f i e l d programme was c a r r i e d o u t a t L a d n e r and i n Vanc o u v e r d u r i n g the summer o f 1972. O b s e r v a t i o n s were c o n d u c t e d under v a r i o u s weather c o n d i t i o n s t h r o u g h o u t t h i s p e r i o d and were o n l y o m i t t e d d u r i n g s p e l l s o f wet w e a t h e r . In g e n e r a l , d u r i n g an o b s e r -v a t i o n a l s e q u e n c e , c o n t i n u o u s measurements were made t h r o u g h -out t h e day and i n the c i t y o f t e n t h r o u g h o u t t h e n i g h t as w e l l . In t h i s manner, i t was p o s s i b l e to i n v e s t i g a t e t h e d i u r n a l b e h a v i o u r o f the en e r g y f l u x e s under most weather c o n d i t i o n s t h a t t y p i c a l l y o c c u r i n Vancouver d u r i n g t h e summer. The normal s a m p l i n g i n t e r v a l was s e t a t 30 min f o r each system i n e v a l u a t i n g the heat f l u x e s . C h a p t e r 3 THE YAW SPHERE-THERMOMETER SYSTEM I n t r o d u c t i o n The p r i n c i p l e o f the yaw s p h e r e - t h e r m o m e t e r system f o r d i r e c t measurements o f s e n s i b l e h e a t f l u x d e n s i t y was b r i e f l y m e n t i o n e d i n t h e f i r s t c h a p t e r . The s p h e r e , when d i r e c t e d i n t o the f l o w , g e n e r a t e s a p r e s s u r e d i f f e r e n c e between two p o r t s t h a t i s p r o p o r t i o n a l to the p r o d u c t o f the h o r i z o n t a l and v e r t i c a l w i n d s . T h i s p r e s s u r e d i f f e r e n c e , c o n v e r t e d t o an a n a l o g s i g n a l and e l e c t r i c a l l y f i l t e r e d , i s then used t o d r i v e a r e s i s t a n c e - t h e r m o m e t e r b r i d g e . I n t e -g r a t i o n o f the o u t p u t , d i v i d e d by the mean h o r i z o n t a l wind speed y i e l d s H. F u l l d e t a i l s o f t h e c o n s t r u c t i o n and t h e o r y o f o p e r a t i o n o f the system a r e g i v e n i n Ta n n e r and T h u r t e l l (1970) and our system c l o s e l y f o l l o w e d t h e i r o r i g i n a l d e s i g n . Here, we s h a l l be p r i m a r i l y c o n c e r n e d w i t h f o u r i m p o r t a n t a s p e c t s . F i r s t l y , c e r t a i n a e r o d y n a m i c c h a r a c t e r i s t i c s on t h e b a s i s o f wind t u n n e l e x p e r i m e n t s a r e i n v e s t i g a t e d . S e c o n d l y , the e f f e c t s o f t i l t i n g the 41 42 s p h e r e a r e a n a l y s e d . T h i r d l y , the t e m p e r a t u r e s e n s o r p e r -formance i s e v a l u a t e d f o r d i f f e r e n t c o n f i g u r a t i o n s . F i n a l l y , the r e s u l t s o f a f i e l d c o m p a r i s o n between the YST system and a Bowen r a t i o a p p a r a t u s a r e p r e s e n t e d . We s h a l l p r o c e e d f i r s t w i t h a b r i e f d e s c r i p t i o n o f the i n s t r u m e n t and a r e v i e w o f the yaw s p h e r e - t h e r m o m e t e r t h e o r y . Equipment D e s c r i p t i o n The yaw s p h e r e c o n s i s t s o f two 1.59 mm d i a m e t e r h o l e s , d r i l l e d o f f - c e n t r e , t h r o u g h a 5-cm p l a s t i c s p h e r e so t h a t t h e i n c l u d e d a n g l e between the p o r t h o l e s and the c e n t r e o f t h e s p h e r e i s 4 5 \u00C2\u00B0 . A G i l l p r o p e l l e r vane (R.M. Young Co.) was m o d i f i e d so t h a t the s p h e r e c o u l d be mounted i n t h e p o s i t i o n where the p r o p e l l e r i s n o r m a l l y s i t u a t e d . Two 1.59 mm O.D. p o l y e t h y l e n e tubes were b r o u g h t t h r o u g h the stem and base o f the vane h o u s i n g and a t t a c h e d t o a c a p a c i t i v e p r e s s u r e t r a n s d u c e r ( D a t a m e t r i c s I n c . , Model 511-8 B a r o c e l ) . The p r e s s u r e t r a n s d u c e r was l o c a t e d below the vane h o u s i n g i n a t h e r m a l l y r e g u l a t e d box. A s c h e m a t i c d i a g r a m o f the r e c o r d i n g system i s shown i n F i g . 10. The e l e c t r i c a l a n a l o g o f the p r e s s u r e g e n e r a t e d between the yaw s p h e r e p o r t s (AP) i s o b t a i n e d from the B a r o c e l and i t s s i g n a l c o n d i t i o n e r . I t i s then p a s s e d t h r o u g h an a c t i v e h i - p a s s f i l t e r ( a p p r o x i m a t e l y 43 POLYETHYLENE TUBES (1.59 mm O.D.) YAW SPHERE (5 CM DIA.) BAROCEL AND ELECTRONICS ACTIVE HI-PASS FILTER (GAIN\u00C2\u00AB\u00C2\u00BB1, T = 8 MIN) 40.2 K F I / V 4 0 2 K Ql * - \u00E2\u0080\u0094 -L - V BRIDGE FAST RESPONSE RESISTANCE THERMOMETER \u00E2\u0080\u00A2w 1800 a LO-PASS FILTER DIFF \ AMP T=5 SEC INTEGRATOR / VARIABLE GAIN F i g . 10 S c h e m a t i c d i a g r a m o f the r e c o r d i n g s y s t e m . 44 u n i t y g a i n , and a time c o n s t a n t o f 8 min) t o p r o v i d e the s i g n a l o f (AP - A P ) . T h i s s i g n a l i s used to d r i v e the r e s i s t a n c e - t h e r m o m e t e r b r i d g e so t h a t the o u t p u t becomes p r o p o r t i o n a l t o AT(AP - AP), where AT i s the b r i d g e im-b a l a n c e . By p e r i o d i c a l l y b a l a n c i n g the b r i d g e , i t i s p o s s i b l e to p r e v e n t undue s a t u r a t i o n o f the o u t p u t f l u c t u -a t i o n s i n the n e x t s t a g e s o f the c i r c u i t . A d i f f e r e n t i a l a m p l i f i e r i s used to i n c r e a s e the o u t p u t s i g n a l from t h e b r i d g e . T h i s i s f o l l o w e d by a 5 sec l o - p a s s f i l t e r t o d e c r e a s e t r a n s i e n t r e s p o n s e and dynamic range r e q u i r e m e n t s b e f o r e i n t e g r a t i o n on a r e c o r d e r w i t h a b a l l and d i s c i n t e g r a t o r ( H o n e y w e l l , E l e c t r o n i k 194 and D i s c I n t e g r a t o r ) . A nearby s e n s i t i v e anemometer (C.W. T h o r n t h w a i t e A s s o c i a t e s ) wind system i s used to o b t a i n the mean h o r i z o n t a l wind speed a t the h e i g h t o f the s p h e r e . A p h o t o g r a p h o f t h e c o m p l e t e yaw s p h e r e - t h e r m o m e t e r assembly i s shown i n F i g . 11. Review of the Yaw Sphere-Thermometer T h e o r y In r e a l f l u i d f l o w , the p r e s s u r e d i s t r i b u t i o n a t p o i n t s on a s p h e r e can be w r i t t e n ( a f t e r M a r t i n o t - L a g a r d e et at., 1952) F i g . 11. The yaw s p h e r e - t h e r m o m e t e r a s s e m b l y . 45 46 P = P s + ( p / 2 ) V 2 [ l - b s i n 2 ^ ] ; if; < 60\u00C2\u00B0 (3.1) where P s i s the s t a t i c p r e s s u r e , p t h e a i r d e n s i t y , V the a i r speed and i|i i s the a n g l e between \V and the r a d i u s v e c t o r o f the p o i n t . The 'sphere c o n s t a n t ' (b) i s to be d e t e r m i n e d e x p e r i m e n t a l l y . I t i s a f u n c t i o n o f the R e y n o l d s number Re = Vd/v ( d , the d i a m e t e r o f t h e s p h e r e and v , the k i n e m a t i c v i s c o s i t y o f the f l u i d ) but i s r e l a -t i v e l y c o n s t a n t f o r 2000 < Re < 200,000. In i d e a l , i r r o t a -t i o n a l f l u i d f l o w , t h e t h e o r e t i c a l v a l u e o f b i s 2.25. On d i r e c t i n g the s p h e r e a z i m u t h l y i n t o t h e wind, the components o f the wind v e c t o r w i t h r e s p e c t to the x, z p l a n e (formed by the yaw s p h e r e p o r t s and i t s b i s e c t o r ) a r e u = |\V | cos a , v = 0 and w = |\V | s i n a where a i s the a n g l e between the wind v e c t o r and the b i -s e c t o r o f the p o r t s . The p r e s s u r e d i f f e r e n c e between the p o r t s o f the yaw s p h e r e i s then g i v e n by A P = p b ( s i n 9) u w (3.2) 47 where 6 i s the i n c l u d e d a n g l e between the p o r t s . A s c h e m a t i c d i a g r a m t o i l l u s t r a t e the a n g l e s , a and 9, and the wind v e c t o r W, i s g i v e n i n F i g . 12. The p r e s s u r e d i f f e r e n c e (AP) i s c o n v e r t e d to an a n a l o g s i g n a l and p a s s e d t h r o u g h a h i g h - p a s s f i l t e r which i s s u b s e q u e n t l y used to d r i v e a r e s i s t a n c e - t h e r m o m e t e r b r i d g e . A m p l i f i c a t i o n and i n t e g r a t i o n o f t h i s b r i d g e o u t -p u t , e x p r e s s e d i n R e y n o l d s ' n o t a t i o n , g i v e s E 0 = p b ( s i n e ) GBM (u w'T' + w u'T' + u'w'T') (3.3) where, G i s the a m p l i f i e r g a i n , B i s the b r i d g e c o n s t a n t and M, the p r e s s u r e t r a n s d u c e r c o n s t a n t . The n a t u r e o f t h i s o u t p u t s i g n a l needs c a r e f u l c o n s i d e r a t i o n . In e q u a t i o n (3.1) the moment u'T' c h a r a c -t e r i z e s the t u r b u l e n t h e a t f l o w i n t h e d i r e c t i o n o f the mean wind v e l o c i t y . One would e x p e c t t h i s q u a n t i t y t o be n e g a t i v e f o r u n s t a b l e , and p o s i t i v e f o r s t a b l e s t r a t i f i c a -t i o n (Monin and Yaglom, 1971). D i r e c t measurements show t h a t on the a v e r a g e , the r a t i o u'T'/w'T' grows w i t h i n -c r e a s i n g s t a b i l i t y ( e . g . Z u b k o v s k i i and T s v a n g , 1966; Wesely et al.3 1970; S h e p p a r d , see Monin and Yaglom, 1971) and i n d i c a t e s t h a t |u'T'| i s l a r g e r than w'T' o v e r a range 48 F i g . 12. S c h e m a t i c r e p r e s e n t a t i o n o f the a n g l e s a, 8 and the wind v e c t o r W on the yaw s p h e r e . 49 o f s t a b i l i t y . However, s i n c e w i s t y p i c a l l y v e r y s m a l l compared to u~, the term w u'T' w i l l be s m a l l compared to u w'T', and w i l l be assumed n e g l i g i b l e . I f we can assume the t r i p l e moment u'w'T' to be s m a l l when compared to the term IT w'T', t h e n , as shown by Tanner and T h u r t e l l ( 1 9 7 0 ) , the e x p r e s s i o n f o r E\"0 r e d u c e s t o E f l * p b ( s i n e) GBM u w'T (3.4) and s i n c e t h e s e n s i b l e heat f l u x can be w r i t t e n as H = pC vTV t h e n (3.5) Thus the s e n s i b l e h e a t f l u x can be d e t e r m i n e d from the \u00E2\u0080\u00A2yaw s p h e r e - t h e r m o m e t e r system o u t p u t i f u i s measured nearby a t the same h e i g h t . Kondo et al. (1970) s u g g e s t t h a t measurements w i t h cup anemometers o v e r e s t i m a t e the mean wind speed by about 4-7 per c e n t f o r the wind o v e r l a n d by day, and by about 1-3 per c e n t a t n i g h t , but more r e c e n t work by Hyson (1972) shows the o v e r e s t i m a t i o n t o be o f the o r d e r o f 1 per c e n t . S l i g h t u n d e r e s t i m a t i o n o f 50 H may t h e r e f o r e be e x p e c t e d i f u i s measured w i t h a cup anemometer. A sample c a l c u l a t i o n o f the s e n s i b l e h e a t f l u x , w i t h the a p p r o p r i a t e c o n s t a n t s i n v o l v e d , i s g i v e n i n Appe n d i x A. D e t e r m i n a t i o n o f the Sphere C o n s t a n t The s p h e r e c o n s t a n t was d e r i v e d from d a t a c o l l e c t e d i n a s e r i e s o f wind t u n n e l e x p e r i m e n t s w i t h the yaw s p h e r e . The s p h e r e p o r t s were a l i g n e d a z i m u t h l y i n t o the d i r e c t i o n o f t h e mean f l o w thus a l l o w i n g a ( t h e a n g l e o f a t t a c k o f the f l o w to the yaw s p h e r e a x i s ) , to be measured d i r e c t l y . E q u a t i o n (3.2) can be r e w r i t t e n b = 2 AP/(p|\V| 2 s i n 2a s i n e ) (3.6) For o u r s p h e r e 6, the i n c l u d e d a n g l e between the p o r t s , was 4 5 \u00C2\u00B0 . An e l e c t r i c a l a n a l o g o f the p r e s s u r e d i f f e r e n c e between the yaw s p h e r e p o r t s (AP) was m o n i t o r e d on a c h a r t r e c o r d e r . The p a r a m e t e r s p and W were known f o r each wind t u n n e l e x p e r i m e n t . T hus, knowing a l l the terms on the r i g h t hand s i d e o f e q u a t i o n (3.6) the s p h e r e c o n s t a n t c o u l d be e v a l u a t e d . F i r s t l y , f o r a c o n s t a n t a n g l e o f a t t a c k 51 o f t h e f l o w (a) , a s e r i e s o f measurements were made a t v a r i o u s wind speeds (V) w i t h 6000 < Re < 20,000. Then the a x i s o f the yaw s p h e r e probe was t i l t e d t h r o u g h a s e r i e s o f a n g l e s , | a | < 1 0 \u00C2\u00B0 . I n h e r e n t l i m i t a t i o n s o f the wind t u n n e l d i d not a l l o w l a r g e r a n g l e s o f a t t a c k , nor t o c a l i -b r a t e the s p h e r e f o r Re < 6000. The s p h e r e c o n s t a n t was o b t a i n e d from measurements i n both l a m i n a r f l o w and i n g r i d t u r b u l e n c e ( p r o d u c e d by i n t r o d u c i n g a g r i d i n t o a u n i f o r m f l o w ) . T h i s g r i d a l l o w e d g e n e r a t i o n o f a 9 per c e n t t u r -b u l e n c e l e v e l a t the yaw s p h e r e p o r t s . In the wind t u n n e l , the a n g l e o f a t t a c k (a) was measured as t h a t between the h o r i z o n t a l and the a p p a r e n t a x i s o f the yaw s p h e r e probe ( i . e . the s p h e r e and i t s s u p p o r t i n g s t e m ) . Any i n h e r e n t m i s a l i g n m e n t i n the yaw s p h e r e a x i s and s u p p o r t i n g stem would m a n i f e s t i t s e l f as a c o n s t a n t e r r o r i n the measurement o f a i n the wind t u n n e l . L e t t h i s t i l t e r r o r be 6. With the a s s u m p t i o n t h a t 26 i s s m a l l sin ( 2 a + 26) \u00C2\u00AB s i n 2a + 26 cos 2a and e q u a t i o n (3.6) becomes 52 2 b = 2 AP/- p |\V | ( s i n 2 a + 2 6 cos 2 a ) s i n 9 (3.7) The above e x p r e s s i o n w i l l be w r i t t e n t a n 2a + 26 = 1/b 2 A P/(p |\V | cos 2a s i n e (3.8) so t h a t a p l o t o f t a n 2a v e r s u s 2AP/p |\V | 2 c o s a s i ne y i e l d s a s l o p e o f 1/b, i n t e r c e p t v a l u e s o f -26 on the a b s c i s s a and 2bS on t h e o r d i n a t e . F i g . 13 r e p r e s e n t s such a g r a p h f o r V = 4 m s \" 1 and 6 m s \" 1 i n l a m i n a r f l o w . The s p h e r e c o n s t a n t o b t a i n e d was 1.57 w i t h a t i l t e r r o r o f ~ 1 \u00C2\u00B0 . T h i s v a l u e f o r b i s s i g n i f i c a n t l y l e s s than the t h e o r e t i c a l v a l u e o f 2.25. Data from the 9 per c e n t t u r b u l e n c e l e v e l e x p e r i m e n t s y i e l d e d a b e s t i m a t e w i t h i n 6 per c e n t o f t h e 1.57 v a l u e . L i t t l e emphasis i s p l a c e d on t h i s v a r i a t i o n s i n c e t h e AP t r a c e on the c h a r t r e c o r d e r c o u l d not be r e s o l v e d to b e t t e r than \u00C2\u00B110 per c e n t f o r the g r i d t u r b u l e n c e e x p e r i m e n t . F i g . 13 a l s o r e v e a l s the c o n s t a n c y o f the b v a l u e f o r v a r y i n g R e y n o l d s number. In a n o t h e r s e r i e s o f e x p e r i m e n t s i n the wind t u n n e l , the f a s t - r e s p o n s e r e s i s t a n c e thermometer (used w i t h the yaw s p h e r e to measure the s e n s i b l e h e a t f l u x ) was mounted a t the s i d e o f the s p h e r e i n i t s u s u a l p o s i t i o n f o r f i e l d 53 T A N 2 a (RADIANS) F i g . 13. G r a p h i c a l d e t e r m i n a t i o n o f the s p h e r e c o n s t a n t (b) and a l i g n m e n t e r r o r ( 6 ) . The e q u a t i o n o f t h e l i n e i s : t a n 2a = -26 + 1/b(2AP/p |\V | 2 cos 2a s i n e ) The s l o p e = 1/b = 0.638, t h e r e f o r e b = 1.57; the i n t e r c e p t = -26 = -0.023, t h e r e f o r e 5= 0 . 0 1 7 5 r a d = l 0 A l s o s i n c e 2b6 - 0.055 a g a i n b = 1.57. 54 measurements. T h i s c o n f i g u r a t i o n had no n o t i c e a b l e e f f e c t on the p r e s s u r e g e n e r a t e d a t the p o r t s , o r on the s p h e r e c o n s t a n t . A c c o r d i n g l y , a v a l u e o f b = 1.57 was c h o s e n . I t i s i n t e r e s t i n g t o note t h a t a v a l u e o f b = 1.79 has r e c e n t l y been e s t a b l i s h e d f o r the o r i g i n a l yaw s p h e r e used by Tanner and T h u r t e l l ( T a n n e r , 1971, p r i v a t e c o m m u n i c a t i o n ) . V a l u e s o f b l e s s than 2.25 have a l s o been r e p o r t e d by M a r t i n o t - L a g a r d e et al. (1952) and Wesely et al. (1972) f o r o t h e r s p h e r e s w i t h d i f f e r e n t p o r t - h o l e c o n f i g u r a t i o n s . The r e a s o n f o r t h e s e lower v a l u e s may be due t o s l i p p a g e o f the f l o w around the smooth s u r f a c e o f th e s p h e r e . T h u r t e l l ( p r i v a t e c o m m u n i c a t i o n , 1972) i n d i c a t e s t h a t r o u g h e n i n g t h e s p h e r e s u r f a c e g i v e s a b v a l u e c l o s e r t o t h a t p r e d i c t e d by t h e o r y . W h i l e i t was not p o s s i b l e t o i n v e s t i g a t e the n a t u r e o f b below Re = 6000 , we s h a l l assume ( a f t e r M a r t i n o t - L a g a r d e et al., 1952) t h a t i t behaves a p p r o x i m a t e l y c o n s t a n t down to Re = 2000. F o r our 5-cm yaw s p h e r e t h i s i m p l i e s t h a t the e x p e r i m e n t a l l y d e t e r m i n e d s p h e r e c o n s t a n t s h o u l d be used o n l y when the mean wind speed i s > 60 cm s \" 1 . In view o f t h i s , g r e a t c a u t i o n must be used i n i n t e r p r e t i n g r e s u l t s from t h e yaw s p h e r e under v e r y l i g h t wind c o n d i t i o n s , f o r i n s t a n c e a t n i g h t . 55 E f f e c t o f Yaw Sphere A x i s T i l t In s e c t i o n \" D e t e r m i n a t i o n o f the Sphere C o n s t a n t , \" i t was shown t h a t any i n h e r e n t m i s a l i g n m e n t i n the yaw s p h e r e a x i s c o u l d be d e t e r m i n e d from g e n e r a l c o n s i d e r a t i o n s of the a n g l e o f a t t a c k o f the f l o w i n c i d e n t on the s p h e r e i n a wind t u n n e l . Knowledge of t h i s c o u l d then be a p p l i e d i n a c c u r a t e l y a l i g n i n g the a x i s o f the s p h e r e h o r i z o n t a l l y i n f i e l d measurements. In p r a c t i c e , h o r i z o n t a l l e v e l l i n g o f the yaw s p h e r e a x i s may not always be a s s u r e d . Conse-q u e n t l y some e s t i m a t e o f l i k e l y e r r o r i n s e n s i b l e h e a t f l u x measurements due to a t i l t o f f - a x i s (due t o c o n s t r u c -t i o n m i s a l i g n m e n t or i n a c c u r a t e l e v e l l i n g i n the f i e l d ) i s g i v e n h e r e . L e t us assume t h a t the s p h e r e i s t i l t e d o f f - a x i s so t h a t t h e t i l t a n g l e (6) i s p o s i t i v e ( i . e . upwards, see F i g . 1 4 ) . The components o f the wind v e c t o r w i t h r e s p e c t to the x T , z T p l a n e (formed by the p o r t s and the t i l t - a x i s ) a r e u T = (u cos 6 - w s i n 6), v T = 0 and w T = (u s i n 6 + w cos 6) 56 F i g . 14. The e f f e c t o f t i l t on the geometry o f the s p h e r e . 57 I f we assume 6 to be s m a l l , then u T (u - 6w) and w T - (u6 + w). S u b s t i t u t i n g t h e s e a p p r o x i m a t i o n s o f u T and w T f o r the u and w components i n e q u a t i o n (3.1) y i e l d s E \u00C2\u00B0 ( T I L T ) ~ P b ( s i n 6 ) G B M J ( u w'T' + w u'T' + u'w'T') + 6(2u ITT7\" - 2w w^ T1\" + u' *T' - w' Z T ' ) j (3.9) S i n c e w i s t y p i c a l l y v e r y s m a l l when compared t o u , the above e x p r e s s i o n r e d u c e s to E \u00C2\u00B0 ( T I L T ) 85 P b ( s i n 9 ) G B M ( u w'T' + 26 u u'T') (3.10) i f we assume the t r i p l e moment terms t o be n e g l i g i b l e . Then ( T I L T ) = E o + E\" 6 0 ' where E 6 0 = p b ( s i n e ) G B M 26 u u T T r 58 i s t h e e r r o r c a u s e d by the t i l t . T h i s e f f e c t i v e l y p r o d u c e s an e r r o r i n the he a t f l u x 6H = C p|T>(sine)GBMJ ' E ^ / U = p C p 2 6 u'T' (3.11) For a s m a l l p o s i t i v e t i l t o f f - a x i s the YST system w i l l t h e r e f o r e p r o d u c e a he a t f l u x measurement H ( T I L T ) ^ H + 6 H = p C p | w , T ' + 2 6 u'TJ (3.12) Thus, f o r 6 = 1\u00C2\u00B0 , H 1 C = S C p j ^ T ^ + 0.035 u~T^j . From p r e v i o u s s t u d i e s c o n c e r n i n g the dependence o f u' T '/WT 1 on R i c h a r d s o n number, we note t h a t the r a t i o i n c r e a s e s from -1.4 i n u n s t a b l e t o -3.2 i n s l i g h t l y s t a b l e c o n d i t i o n s . U s i n g t h e s e r e s u l t s , we can make some e s t i m a t e o f the e r r o r 6H under d i f f e r e n t s t a b i l i t y c o n -d i t i o n s . D u r i n g the d a y t i m e w i t h m o d e r a t e l y n e g a t i v e Ri , - u'T' - 1.4 wT 1\" so t h a t H ] 0 would then e f f e c t i v e l y i n c l u d e an e r r o r o f ~ 5 per c e n t . On the o t h e r hand, under n i g h t - t i m e c o n d i t i o n s w i t h weak s t a b i l i t y , 59 u'T' = -3.2 w'T' i n the l i m i t . In t h i s c a s e would i n c l u d e an e r r o r o f ~ 11 per c e n t . I t can thus be s e e n , as an a p p r o x i m a t i o n , t h a t the e r r o r c a u s e d by a 1\u00C2\u00B0 t i l t o f f - a x i s i n the yaw s p h e r e would r e s u l t i n an e r r o r o f ~ 5 per c e n t i n the d a y t i m e , and t h a t the e r r o r would grow w i t h i n c r e a s i n g s t a b i l i t y to a p p r o a c h a v a l u e o f ~ 11 per c e n t a t n i g h t . A l t h o u g h l a r g e t i l t e r r o r s ( o f the o r d e r o f 5\u00C2\u00B0) s h o u l d not o c c u r i n p r a c t i c e , we s h a l l c o n s i d e r such an e f f e c t on o u r system to h e l p d e l i n e a t e the e r r o r magnitude a t s m a l l a n g l e s o f t i l t . F o r a 5\u00C2\u00B0 o f f - a x i s t i l t o f the s p h e r e , the e r r o r i n m e a s u r i n g the s e n s i b l e heat f l u x would be ~ 25 per c e n t i n m o d e r a t e l y u n s t a b l e s t r a t i f i c a t i o n . The above a n a l y s i s a g a i n s u g g e s t s t h a t the YST system needs c a r e f u l c o n s i d e r a -t i o n i f used a t n i g h t , when l i g h t winds and s t a b l e s t r a t i -f i c a t i o n g e n e r a l l y p r e v a i l . L a r g e t i l t s i n the yaw s p h e r e a x i s would l e a d to c o n s i d e r a b l e e r r o r s i n the measurements of the s e n s i b l e h e a t f l u x . With c o n v e n t i o n a l l e v e l i n g d e v i c e s , i t s h o u l d be p o s s i b l e to m i n i m i z e t h i s o f f - a x i s t i l t so t h a t t h i s s o u r c e o f e r r o r i n the s e n s i b l e heat f l u x measurements i s w i t h i n the range o f g e n e r a l h e a t f l u x s p a t i a l v a r i a b i l i t y . F i e l d measurements o f the t i l t e f f e c t on heat f l u x measurements w i t h the F l u x a t r o n (an eddy c o r r e l a t i o n 60 i n s t r u m e n t ) a r e r e p o r t e d i n the r e c e n t paper o f Dyer and H i c k s ( 1 9 7 2 ) . An e r r o r o f a p p r o x i m a t e l y 4 per c e n t per d e g r e e was f o u n d . I t would seem from our a n a l y s i s t h a t the YST system i s s l i g h t l y more s e n s i t i v e to l e v e l l i n g e r r o r s than the F l u x a t r o n . Thermometer System and F r e q u e n c y Response The f a s t - r e s p o n s e thermometer was i n i t i a l l y b u i l t f o l l o w i n g the d e s i g n o f Wesely et al. ( 1 9 7 0 ) . The t h e r -mometer elem e n t c o n s i s t e d o f about 65 cm o f p l a t i n u m - c o a t e d t u n g s t e n w i r e w i t h a d i a m e t e r o f 5.6y. T h i s w i r e was welded to i t s s t a i n l e s s s t e e l s i d e s u p p o r t w i t h the a i d o f a D i s a h o t - w i r e anemometer w e l d i n g a s s e m b l y . A p h o t o -g r a p h o f the r e s i s t a n c e thermometer i s shown i n F i g . 15. The t e m p e r a t u r e c o e f f i c i e n t o f r e s i s t a n c e o f the tempera-t u r e e l e m e n t was o b t a i n e d from measurements o f the t h e r -mometer r e s i s t a n c e i n a t e m p e r a t u r e - c o n t r o l l e d o i l bath o v e r the range 15\u00C2\u00B0C to 30\u00C2\u00B0C. I t was f o u n d to be 0.0033 \u00C2\u00B1 0 . 0 0 0 0 5 \u00C2\u00B0 C _ 1 . C a l c u l a t i o n s by Wesely et al. (1970) i n d i c a t e t h a t f o r the r e s i s t a n c e w i r e used i n the thermometer, the time c o n s t a n t i s a p p r o x i m a t e l y 1.5 m i l l i s e c i n \" s t i l l a i r \" and about 0.6 m i l l i s e c i n 10 m s - 1 w i n d s . Up to a F i g . 15. The r e s i s t a n c e thermometer. 62 f r e q u e n c y o f 20 Hz, r e d u c t i o n i n a m p l i t u d e s h o u l d be l e s s than 2 per c e n t and phase s h i f t about 1 0 \u00C2\u00B0 . S o l a r h e a t i n g o f the f i n e r e s i s t a n c e w i r e was shown to be n e g l i g i b l e f o r eddy f l u x c a l c u l a t i o n s . Under f i e l d c o n d i t i o n s our thermometer r e s p o n d e d w e l l , but i t s d u r a b i l i t y was n o t always s a t i s f a c t o r y . As a r e s u l t , a s l i g h t l y m o d i f i e d d e s i g n was d e v e l o p e d . The thermometer el e m e n t and s u p p o r t t e r m i n a l s remained the same. The t r i a n g u l a r frame however was e l i m i n a t e d by w i n d i n g the e l e m e n t d i r e c t l y around the s i d e s u p p o r t s which were c o v e r e d w i t h an i n s u l a t i n g l a y e r o f epoxy r e s i n . The r i g i d i t y o f the thermometer was m a i n t a i n e d by i n s e r t i n g two t h i n c e r a m i c s p a c e r s ( F i g . 1 6 ) . F i e l d t e s t s o f the two thermometer d e s i g n s i n two YST systems p l a c e d 2 m a p a r t p r o d u c e d a l m o s t i d e n t i c a l r e s u l t s (see F i g . 17) under a v a r i e t y o f wind and c l o u d c o n d i t i o n s . The new d e s i g n has p r o v e d to be more d u r a b l e . F r e q u e n c y r e s p o n s e and phase s h i f t o f t h e yaw s p h e r e t u b i n g and B a r o c e l c l o s e l y f o l l o w e d t h a t r e p o r t e d by T anner and T h u r t e l l (1970, F i g . 1 8 ) . The i n c r e a s e i n l e n g t h o f t u b i n g i n our system r e s u l t e d i n s 1 i g h t l y .more a t t e n u a t i o n . In the f r e q u e n c y domain the t u r b u l e n t h e a t f l u x c o u l d be measured to an upper f r e q u e n c y l i m i t o f ~ 8 Hz w i t h o u t s i g n i f i c a n t a t t e n u a t i o n . F i g . 16. The m o d i f i e d r e s i s t a n c e thermometer. 63 I I I I L_ 1 I I 08 10 12 14 16 18 20 22 TIME (PST) 06 08 10 12 14 16 18 20 1 I I I I I 1 I F i g . 17. Comparison o f the two yaw s p h e r e - t h e r m o m e t e r systems f o r s e n s i b l e heat f l u x measurements (a) w i t h o r i g i n a l r e s i s t a n c e thermometers (b) w i t h m o d i f i e d r e s i s t a n c e thermometer d e s i g n i n Y S T i . 65 LEGEND x RELATIVE AMPLITUDE \u00E2\u0080\u00A2 PHASE SHIFT 0 8 16 24 FREQUENCY (Hz) F i g . 18. F r e q u e n c y r e s p o n s e o f the yaw s p h e r e t u b i n g and B a r o c e l . Data p o i n t s from t h i s s t u d y ; l i n e s from r e s u l t s o f Tanner and T h u r t e l l ( 1 9 7 0 ) . 66 F i e l d T e s t s R e s u l t s T h e r e i s no s t a n d a r d t o c a l i b r a t e an i n s t r u m e n t which measures s e n s i b l e h e a t f l u x d e n s i t y . To g a i n c o n f i -dence i n the YST system however, we compared the measure-ments a g a i n s t i n d e p e n d e n t e v a l u a t i o n s o f H from a Bowen r a t i o a p p a r a t u s . The s i t e used was the e x t e n s i v e g r a s s s u r f a c e a t L a d n e r , B.C. The g r a s s was d r y , and the ground s u r f a c e c o n s i s t e d o f a dense o l d - g r a s s l i t t e r l a y e r . The i n s t r u m e n t h e i g h t s and mast l o c a t i o n s e n s u r e d adequate f e t c h / h e i g h t r a t i o s from a l l wind d i r e c t i o n s e x c e p t from the NNE-SSE s e c t o r . Winds were p r e d o m i n a n t l y SW-NW d u r i n g t h e t e s t r u n s . The c o m p l e t e YST system was mounted a p p r o x i m a t e l y 1.5 m above ground l e v e l w i t h the Bowen r a t i o a p p a r a t u s mounted a t the same h e i g h t , and 4 m from the YST s y s t e m . Net r a d i a t i o n and s o i l h eat f l u x d e n s i t y were a l s o r e c o r d e d c o n t i n u o u s l y d u r i n g d a y l i g h t hours f o r a p e r i o d o f f o u r d a y s . The r e s u l t s o f the c o m p a r i s o n e x p e r i m e n t s a r e p r e s e n t e d i n F i g s . 19 ( a - c ) and 20. C l e a r l y , w i t h the p o s s i b l e e x c e p t i o n o f Aug u s t 24, 1971 ( F i g . 1 9 ( a ) ) , the agreement between the i n d e p e n d e n t s e n s i b l e h e a t f l u x measurements (H Y - * y y f 4 I I I 1 I I I I 06 08 10 12 14 16 18 20 TIME (PST) F i g . 23. D i u r n a l v a r i a t i o n o f H and c o m p a r i s o n o f the two YST s y s t e m s . U (M/S) 4.1 4.4 5.1 5.1 4.9 5.4 5.1 5.0 4.9 5.1 4.5 3.9 2.7 1.9 2 \u00E2\u0080\u00A2 I R \u00E2\u0080\u0094 * \u00E2\u0080\u0094\u00C2\u00BB- \u00E2\u0080\u0094 ^ \u00E2\u0080\u0094 ^ \u00E2\u0080\u0094 V - > \u00E2\u0080\u0094*\" \u00E2\u0080\u0094 - > I I J I I I I I 06 08 10 12 14 16 18 20 TIME (PST) F i g . 24. D i u r n a l energy b a l a n c e and s p a t i a l v a r i a t i o n o f H. 70 r LADNER, B.C. JULY 2, 1972 ~* H Y S T * H HEIGHT : 2m HOR. SEPARATION 80 19m WIND U (M/S) 2.8 3.8 3.6 2 DIR N V \ 3.8 4.1 3.8 4.0 4.2 4.5 4.1 3.7 2.7 2.0 \ \ \ \ \ v \ \ \ \ \u00C2\u00B1 _L \u00C2\u00B1 J 06 08 10 12 14 16 18 20 TIME (PST) F i g . 25. D i u r n a l e n e r g y b a l a n c e and s p a t i a l v a r i a t i o n o f H. 81 p l a n e t a r y boundary l a y e r shows an immediate r e s p o n s e to the change o f n e t r a d i a n t energy s u p p l y a t the s u r f a c e . E x c e p t i o n s to t h i s d i s t i n c t phase r e l a t i o n s h i p were noted on two d a y s , one o f which i s shown i n F i g . 22. A f t e r 1300 PST on June 21, 1972, the net r a d i a t i o n p r o g r e s -s i v e l y d e c r e a s e d w h i l e the s e n s i b l e h e a t f l u x r e m ained c o n s i s t e n t l y h i g h f o r s e v e r a l h o u r s . The maximum v a l u e o f H o c c u r r e d a few hours a f t e r the r a d i a t i o n maximum. In a d d i t i o n , the s e n s i b l e h e a t f l u x e s do not a p p e a r to d e c l i n e as r a p i d l y w i t h the a p p r o a c h o f s u n s e t and the a n t i c i p a t e d ' t u r n o v e r ' to a downward f l u x i s c l e a r l y d e l a y e d . A s i m i l a r t r e n d was o b s e r v e d on June 30 (see F i g . 2 6 ) , a day on which sunny s k i e s p r e v a i l e d . T h i s o b s e r v e d f e a t u r e was not e v i d e n t i n t h e measurements t a k e n on the day p r e c e d i n g o r f o l l o w i n g June 30 when s i m i l a r weather c o n d i t i o n s p r e v a i l e d . The r e a s o n f o r t h e s e two e x c e p t i o n s i s not c l e a r . I t i s s u g g e s t e d t h a t t h i s b e h a v i o u r was c a u s e d by a d v e c t i v e i n f l u e n c e s from t h e runway as w e s t e r l y winds p r e v a i l e d on both o c c a s i o n s ( F i g s . 22 & 2 6 ) . While much c a r e was t a k e n i n our c h o i c e o f m e a s u r i n g h e i g h t f o r the YST systems to e n s u r e s u i t a b l e f e t c h from a l l wind d i r e c t i o n s , i t may have been p o s s i b l e t h a t t h e measurements a t the 2 m h e i g h t on t h e s e p a r t i c u l a r a f t e r n o o n s d i d n o t r e f l e c t t h e p r o c e s s e s o f t h e u n d e r l y i n g s u r f a c e . LADNER, B.C. JUNE 30, 1972 82 H H Y S T Y S T 2 HEIGHT : 2m HOR. SEPARATION 19 m - 1 0 L WIND U 2 (M/S) 4.8 4.7 4.6 3.8 DIR \u00C2\u00B1 4.1 4.3 4.6 4.8 X N> X *x I I \u00C2\u00B1 J 06 08 10 12 14 16 18 20 TIME (PST) F i g . 26. An example o f l a r g e f l u c t u a t i o n s i n H w i t h 30 min a v e r a g i n g p e r i o d s . 83 D u r i n g a s u c c e s s i o n o f days ( J u l y 1-5), c l e a r s k i e s p e r s i s t e d . The heat u t i l i z e d to warm the a i r v i a s e n s i b l e h e a t f l u x showed a p r o g r e s s i v e d e c r e a s e from J u l y 1 to J u l y 5. One would have e x p e c t e d the o p p o s i t e t r e n d i f d r y i n g out o f t h e s o i l was o c c u r r i n g , but on the c o n t r a r y , the s u r f a c e seemed to have had ample s u p p l y o f w a t e r . An e x a m i n a t i o n o f t h i s b e h a v i o u r w i l l be d i s c u s s e d i n t h e s e c t i o n \" P a r a m e t e r i z a t i o n o f the S e n s i b l e Heat F l u x and E v a p o r a t i o n . \" I t s h o u l d be n o t e d t h a t the heat s t o r a g e i n the ground i s u n u s u a l l y low d u r i n g a l l t h e s e measurements. T h i s was p r o b a b l y c r e a t e d by the t a l l g r a s s c o v e r and i t s i n s u l a t -i n g e f f e c t . In g e n e r a l , t h e r e e x i s t e d a d i u r n a l c o u r s e o f G. I t d i d not however show c l o s e s i m i l a r i t y to t h e Rn p a t t e r n on days w i t h v a r i a b l e n e t r a d i a n t e n e r g y i n p u t . Under c l e a r s k i e s a t noon, maximum v a l u e s o f G were o n l y a bout 5 per c e n t o f Rn. Measurements o f S p a t i a l V a r i a t i o n o f the S e n s i b l e Heat F l u x G e n e r a l a s p e c t s . The b a s i c a s s u m p t i o n o f much m i c r o m e t e o r o l o g i c a l r e s e a r c h i s t h a t H i s r e l a t i v e l y c o n s t a n t i n the s u r f a c e boundary l a y e r o v e r a homogeneous s u r f a c e . The j u s t i f i c a t i o n o f t h i s a s s u m p t i o n can be seen from an a n a l y s i s o f the R e y n o l d s e q u a t i o n f o r t e m p e r a t u r e . The d e v e l o p m e n t i s g i v e n 84 i n M o r d u k h o v i c h and Tsvang (1966) and i s b r i e f l y summarized below. The R e y n o l d s e q u a t i o n f o r t e m p e r a t u r e may be w r i t t e n 3T 3_uT 3v_T 3wT = 3Rni 1 (A i\ 8 t 3x 3y 3 z 3z pC where the n o t a t i o n s a r e s i m i l a r to t h o s e p r e v i o u s l y d e f i n e d . On a p p l i c a t i o n o f t h e e q u a t i o n o f c o n t i n u i t y and the assump-t i o n t h a t v~ = w = 0, e q u a t i o n (4.1) can be e x p r e s s e d as f o l l o w s 3T - 3T Su^T 1\" dV7!^ dvPTr _ dRn _]_ /. 9> 3t U 3x 3x 3y 3z 3z pC K*' d ) p F o r s t e a d y - s t a t e c o n d i t i o n s and i n the absence o f r a d i a t i v e f l u x d i v e r g e n c e , the terms ( 3 T / 3 t , 3R~n/3z) equal z e r o . Symmetry w i t h r e s p e c t t o the a v e r a g e t r a n s p o r t s u g g e s t s t h a t 3v'T'/3y s h o u l d a l s o be z e r o . A c o m p a r i s o n o f the r e m a i n i n g terms i n d i c a t e t h a t the p r i m a r y c a u s e o f a change i n H w i t h h e i g h t would be due to the a d v e c t i o n term s i n c e 3u'T'/3x << u 3T/3x . Thus, i n the a b s e n c e o f a d v e c t i o n , 85 one would e x p e c t H to be r e l a t i v e l y c o n s t a n t w i t h h e i g h t i n t h e a t m o s p h e r i c boundary l a y e r . In a s i m i l a r way, o n l y s l i g h t v a r i a t i o n i n H s h o u l d be e x p e c t e d i n the h o r i z o n t a l o v e r an e x t e n s i v e homogeneous s u r f a c e . E x p e r i m e n t a l e v i d e n c e to t e s t t h i s a s s u m p t i o n has been g a t h e r e d i n r e c e n t y e a r s t h r o u g h d i r e c t measurements o f H v i a the eddy c o r r e l a t i o n t e c h n i q u e . The r e c e n t work o f Dyer and H i c k s (1972) i n d i c a t e s a v a r i a t i o n i n H o f l e s s than 10 per c e n t f o r v e r t i c a l h e i g h t s o f 4-14 m, and h o r i z o n t a l s e p a r a t i o n o f 1-150 m, o v e r an e x t e n s i v e u n i f o r m p l a n t s u r f a c e . T h e i r r e s u l t s a r e g i v e n i n T a b l e 3. T h i s p r o v i d e s some v a l i d i t y f o r t h e t r a d i t i o n a l a s s u m p t i o n o f the c o n s t a n t f l u x l a y e r . On the o t h e r hand, the e a r l i e r works o f M o r d u k h o v i c h and Tsvang (1966) and B u s i n g e r et al. (1967) i n d i c a t e l a r g e s p a t i a l v a r i a b i l i t y i n t h e heat f l u x e s o f t h e o r d e r o f a f a c t o r o f 2. Measurements were made between the 1 and 4 m h e i g h t by M o r d u k h o v i c h and Tsvang w h i l e the r e s u l t s o f B u s i n g e r et al. were f o r a h o r i z o n t a l s e p a r a -t i o n o f 5 m. These r e s u l t s a r e most d i s t u r b i n g f o r t h e y s u g g e s t t h a t E u l e r i a n p o i n t o b s e r v a t i o n s may y i e l d ques-t i o n a b l e samples even o v e r a u n i f o r m s u r f a c e w i t h a d e q u a t e f e t c h . To e x p l a i n t h e i r d i s c r e p a n c y , B u s i n g e r et al. advanced t h e f o l l o w i n g p o s t u l a t i o n . The c o n v e c t i v e e l e m e n t s c o n t r i b u t i n g to the heat f l u x may c o n s i s t o f h o r i z o n t a l 86 T a b l e 3 C o m p a r i s o n o f a v e r a g e f l u x e s a. C o m p a r i s o n o f a v e r a g e f l u x e s (H i ^ ) a t 14 m h e i g h t w i t h a v e r a g e f l u x e s (hU) a t 4 m h e i g h t a t T s i m l y a n s k , U.S.S.R. ( c . f . D y e r and H i c k s , 1972) D a t e Du r a t i on (m i n) Hit/H 11* 16 J u l y 1970 17 J u l y 1970 300 390 0.92 1 .00 b. C o m p a r i s o n o f a v e r a g e f l u x e s ( H i and H2) t a k e n a t a n o m i n a l h e i g h t o f 4 m a t v a r i o u s c r o s s - w i n d s e p a r a t i o n s a t T s i m l y a n s k , U.S.S.R. ( c . f . D y e r and H i c k s , 1 9 7 2 ) . D a t e D u r a t i o n (mi n) S e p a r a t i o n (m) H2/H1 21 J u n e 1 970 570 1 1 .05 25 J u n e 1 970 313 1 0.98 1 2 J u l y 1 970 420 1 0 1.13 1 4 J u l y 1 970 360 1 0 0.94 3 J u l y 1 970 622 30 1 .03 5 J u l y 1 970 513 30 1.12 29 J u n e 1 970 207 60 1 .08 9 J u l y 1 970 268 60 1.14 18 J u l y 1 970 470 1 50 1 .07 87 r o l l s w i t h t h e i r l e n g t h a x i s i n the d i r e c t i o n o f t h e mean win d . These r o l l s r o t a t e s l o w l y i n o p p o s i t e d i r e c t i o n , t h e r e b y c r e a t i n g zones o f c o n v e r g e n c e and d i v e r g e n c e . Measurements i n two c o n t r a s t i n g z o n e s , even o v e r c o n s i d e r -a b l e time p e r i o d s , would thus y i e l d the no t e d v a r i a t i o n i n H. E v i d e n c e o f the o r g a n i z e d b e h a v i o u r o f t h e s e c o n -v e c t i v e e l e m e n t s has r e c e n t l y been r e p o r t e d by D a v i s o n and Miyake (1972) f o r h e i g h t s g r e a t e r than 50 m. I t i s a p p a r e n t t h a t much r e s e a r c h remains around t h i s f u n d a m e n t a l h y p o t h e s i s . The measurements r e p o r t e d h e r e , though l i m i t e d i n s c o p e , s h o u l d c o n t r i b u t e to t h e s m a l l body o f p e r t i n e n t d a t a t h a t p r e s e n t l y e x i s t s . S p a t i a l v a r i a b i l i t y e x p e r i m e n t s . In o r d e r to p r e s e r v e an adeq u a t e h e i g h t / f e t c h r a t i o a t the L a d n e r s i t e , no a t t e m p t was made to examine t h e v e r t i c a l v a r i a t i o n o f heat f l u x . O n l y measurements above the g r o u n d , a t h e i g h t s o f 2 m o r l e s s c o u l d e n s u r e s u i t a b l e f e t c h from a l l wind d i r e c t i o n s . W h i l e i t might have been p o s s i b l e to i n v e s t i g a t e v a r i a t i o n o f H between t h e 1 and 2 m h e i g h t s , the f r e q u e n c y r e s p o n s e o f t h e YST system d i d not f a v o u r such measurements. A c c o r d i n g l y , o n l y the h o r i z o n t a l v a r i a t i o n o f the s e n s i b l e heat f l u x a t a f i x e d h e i g h t o f 88 2 m above the ground was i n v e s t i g a t e d . Comparison o f the two YST systems were f i r s t made f o r a h o r i z o n t a l c r o s s w i n d s e p a r a t i o n o f 1.5 m. The two i n s t r u m e n t s were then p l a c e d 19 m a p a r t to i n v e s t i g a t e the s p a t i a l v a r i a t i o n . The 1.5 m s e p a r a t i o n p r o v i d e d a b a s i c c o m p a r i s o n between the two i n s t r u m e n t s . The s m a l l s e p a r a t i o n between i n s t r u m e n t s was to e n s u r e t h a t s a m p l i n g o c c u r r e d i n the same a i r s t r e a m . The c l o s e agreement between heat f l u x e s o b t a i n e d from the two i n s t r u m e n t s can be seen i n F i g s . 21-23. O n l y a few per c e n t v a r i a t i o n can be n o t e d . In g e n e r a l , s l i g h t l y h i g h e r v a l u e s were o b t a i n e d w i t h the Y S T 2 i n s t r u m e n t . T h i s d i f f e r e n c e a p p e a r s to be s y s t e m a t i c and may have been c a u s e d by s l i g h t d i f f e r e n c e s i n c a l i b r a t i o n c o n s t a n t s which were not t a k e n i n t o a c c o u n t . The d i f f e r e n c e i s however s m a l l enough to be c o n s i d e r e d i n s i g n i f i c a n t . C u m u l a t i v e s e n s i b l e heat f l u x e s f o r each i n s t r u m e n t , e x p r e s s e d as a r a t i o , f o r the 1.5 m h o r i z o n t a l c r o s s w i n d s e p a r a t i o n a r e g i v e n i n T a b l e 4. S a m p l i n g p e r i o d s have been a d j u s t e d to o n l y t h o s e f o r which c o m p a r i s o n i s p o s s i b l e . The d i f f e r e n c e i s g e n e r a l l y l e s s than 5 per c e n t i n the heat f l u x measurements f o r the two i n s t r u m e n t s . I n d i r e c t l y , t h i s r e s u l t a l s o s u g g e s t s s m a l l s p a t i a l v a r i a b i l i t y . F o r t h e 19 m c r o s s w i n d s e p a r a t i o n , r e l a t i v e l y good agreement was f o u n d i n the H measurements ( F i g s . 2 4 - 2 6). 89 T a b l e 4 C o m p a r i s o n o f c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s f r o m t h e yaw s p h e r e - t h e r m o m e t e r s y s t e m s ( h Y S T 1 A N D H Y S T 2 ^ a t 2 m a b o v e g r o u n d f o r an h o r i z o n t a l c r o s s w i n d s e p a r a t i o n o f 1.5 m D a t e D u r a t i o n ( m i n ) H Y S T i / H Y S T 2 1 5 J u n e 1 972 593 0.97 1 6 J u n e 1 972 170 1 .09 21 J u n e 1 972 712 1 .01 22 J u n e 1 972 274 0.99 24 J u n e 1 972 704 0.96 29 J u n e 1 972 1 1 4 0.99 90 A t t h i s l a r g e s e p a r a t i o n d i s t a n c e , the two YST systems c o u l d be p o s s i b l y s a m p l i n g i n d i f f e r e n t a i r s t r e a m s . The d e g r e e of f l u x v a r i a t i o n i s more pronounced than a t the 1.5 m s e p a r a -t i o n . T h i s i s a l s o e v i d e n t from the c u m u l a t i v e s e n s i b l e heat f l u x e s , e x p r e s s e d as a r a t i o , g i v e n i n T a b l e 5. The h o r i z o n t a l v a r i a b i l i t y i s l e s s than 20 per c e n t . a n d i s c o n s i s t e n t w i t h the h y p o t h e s i s o f the r e l a t i v e c o n s t a n c y o f the heat f l u x e s i n the s u r f a c e boundary l a y e r . These r e s u l t s t e n d to s u g g e s t t h a t r e p r e s e n t a t i v e heat f l u x e s may be a c h i e v e d by E u l e r i a n p o i n t s a m p l i n g to w i t h i n twenty per c e n t . On a few o c c a s i o n s , s h o r t - t e r m time v a r i a t i o n ( l e s s than 30 min) i n the heat f l u x measurements was n o t e d . T h i s was p a r t i c u l a r l y e v i d e n t on June 30 ( F i g . 2 6 ) . The cause o f t h e s e l a r g e f l u c t u a t i o n s i n H a r e c l e a r l y not r e l a t e d to t h e changes i n the net r a d i a t i o n f i e l d . R a t h e r , i t may be a s s o c i a t e d w i t h the c h o i c e o f an adequate s a m p l i n g i n t e r v a l . J h e use o f one-hour s a m p l i n g i n t e r v a l s would have e l m i n a t e d t h e s e s h o r t term f l u c t u a t i o n s . Smoothing o f the d a t a c a n n o t however be e a s i l y j u s t i f i e d s i n c e t h e s e f l u c t u a t i o n s may c o n t a i n p h y s i c a l s i g n i f i c a n c e . On t h i s p a r t i c u l a r day, t h e measured H f l u c t u a t i o n s o c c u r r e d a t the two s i t e s 19 m a p a r t . A f t e r n o o n , the c o u r s e o f H a t the two s i t e s i s out o f phase, a l t h o u g h the c u m u l a t i v e heat f l u x e s f o r t h a t p e r i o d remain a p p r o x i m a t e l y equal a t the two l o c a t i o n s . 91 T a b l e 5 C o m p a r i s o n o f c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s f r o m t h e yaw s p h e r e - t h e r m o m e t e r s y s t e m s (H and H ) I b l l i b i 2 a t 2 m a b o v e g r o u n d f o r an h o r i z o n t a l c r o s s w i n d s e p a r a t i o n o f 19 m D a t e D u r a t i o n (m i n ) H Y S T i / H Y S T 2 29 J u n e 1 972 60 0.98 30 J u n e 1 972 450 0.94 1 J u l y 1 972 728 0.94 2 J u l y 1 972 728 0.85 3 J u l y 1 972 331 0.83 92 Thus, i n a s t a t i s t i c a l s e n s e , t h e r e i s l i t t l e s p a t i a l v a r i -a b i l i t y f o r a l o n g - t e r m a v e r a g e . The e x i s t e n c e o f c o n v e c -t i v e r o l l s c o u l d a l s o e x p l a i n t h e s e s h o r t - t e r m f l u c t u a t i o n s . P a r a m e t e r i z a t i o n o f the S e n s i b l e Heat F l u x and E v a p o r a t i o n In i n v e s t i g a t i n g the p a r t i t i o n i n g o f energy between t h e s e n s i b l e heat f l u x and e v a p o r a t i o n , the g e n e r a l frame-work s u g g e s t e d by P r i e s t l e y and T a y l o r (1972) has been employed. The d a t a i s a n a l y z e d i n terms o f the q u a n t i t y a, d e f i n e d by a = LE/^^CH+LE)] = L E / j ^ R n - G ) ] (4.3) where y t h e p s y c h r o m e t r i c c o n s t a n t s d e f i n e d as 3 q s/3T a t the a p p r o p r i a t e t e m p e r a t u r e . The p a r a m e t e r a p r o v i d e s some measure o f the a r i d i t y o f the of the s u r f a c e . A p r i o r i , one would e x p e c t i t to be s m a l l e r f o r u n s a t u r a t e d s u r f a c e s than f o r s a t u r a t e d s u r f a c e s . The d i u r n a l b e h a v i o u r o f a a t the Ladner s i t e was examined u s i n g d a t a f o r l a t e A ugust 1971 and June 1972. The p e r i o d i n Aug u s t was p r e c e d e d by two months o f f a i r l y d r y w e a t h e r , w h i l s t i n June the a r e a had been under the 93 i n f l u e n c e o f wet weather c o n d i t i o n s f o r some t i m e . Examples f o r A u g u s t 26, 1971 and June 24, 1972 a r e shown i n F i g . 27. The v a l u e s o f LE i n e q u a t i o n 4.3 were o b t a i n e d as r e s i d u a l s from the energy b a l a n c e e q u a t i o n s i n c e the f l u x e s Rn, H and G were known. I t can be seen from the graph t h a t a was lower i n the l a t e summer o f 1971 than a t the s t a r t o f t h e summer o f 1972. E s t i m a t e s o f a f o r the days shown gave a mean v a l u e o f 0.73 on A u g u s t 26, 1971 and 1.09 on June 24, 1972 f o r the p e r i o d 1000-1600 PST. The s p r e a d o f t h e s e v a l u e s may be e x p e c t e d to r e f l e c t the n a t u r e o f the s o i l - p l a n t system water a v a i l a b i l i t y . Data from a number o f s a t u r a t e d l a n d and open water s i t e s were examined by P r i e s t l e y and T a y l o r ( 1 9 7 2 ) . From t h e s e d a t a , the b e s t e s t i m a t e o f a was f o u n d to be 1.26. I f we may use a = 1.26 f o r s a t u r a t e d s u r f a c e s (as o b t a i n e d by P r i e s t l e y and T a y l o r from mean d a i l y q u a n t i t i e s ) , a r i d i t y i n d e x e s may be computed f o r t h e s e two d a y s . The a r i d i t y i n d e x ( t h e r a t i o o f t h e a l p h a f o r n o n - s a t u r a t e d to t h a t f o r a s a t u r a t e d s u r f a c e ) would be 0.58 f o r A u g u s t 26 , 1971 and 0.87 f o r June 2.4, 1972. The u s e f u l n e s s o f the p a r a m e t e r a i n a c l i m a t o -l o g i c a l s ense a p p e a r s most e n c o u r a g i n g . I t may p r o v e a p p r o p r i a t e i n a c l a s s i f i c a t i o n scheme f o r v a r i o u s c l i m a t e s when d e t e r m i n e d on a monthly b a s i s . 94 2.0 Od= LE / { ( S / s + 7 ) ( R n - G ) } LADNER, B.C. \u00E2\u0080\u00A2 AUGUST 26, 1971 K JUNE 24, 1972 06 1.5 k 0.0 I I I I I I I 06 08 10 12 14 16 18 TIME (PST) F i g . 27. D i u r n a l v a r i a t i o n o f a (examples o f e a r l y and l a t e summer o b s e r v a t i o n s ) . 95 I t can be seen from e q u a t i o n 4.3 t h a t a i s r e l a t e d to t h e Bowen r a t i o t h r o u g h the f o l l o w i n g e q u a t i o n I t i s thus p o s s i b l e to examine the p a r t i t i o n i n g o f t h e s e n s i b l e and l a t e n t heat f l u x e s t h r o u g h the above e x p r e s s i o n . For a s a t u r a t e d s u r f a c e , a b e i n g a p p r o x i m a t e l y c o n s t a n t , one would e x p e c t 3 to show a dependence on s u r f a c e tempera-t u r e . The p r e d i c t e d p a r t i t i o n i n g o f e n e r g y between H and LE as a f u n c t i o n o f t e m p e r a t u r e i s shown i n F i g . 28 ( u s i n g a = 1.26 i n e q u a t i o n 4 . 4 ) . C u r v e s f o r a c o n s t a n t a o f 1.10 and 1.00 a r e a l s o shown. U s i n g the e n e r g y b a l a n c e measurements f o r L a d n e r , a p p r o x i m a t e Bowen r a t i o s were computed f o r a l l o b s e r v a t i o n days d u r i n g June and e a r l y J u l y 1972. These d a t a a r e p l o t t e d a g a i n s t mean d a i l y s c r e e n -l e v e l a i r t e m p e r a t u r e f o r the c o r r e s p o n d i n g days i n F i g . 28. ( I t s h o u l d be n o t e d t h a t our v a l u e s a r e o n l y a p p r o x i m a t e s i n c e the l e n g t h o f the h e a t f l u x r e c o r d s do not p r o v i d e 24 hour t o t a l s . A c c o r d i n g l y the t e m p e r a t u r e r e c o r d has been a d j u s t e d to c o n s i d e r o n l y the p e r i o d s o f f l u x measurements.) With the e x c e p t i o n o f two p o i n t s , the 3 d a t a c l e a r l y show a t e m p e r a t u r e dependence s i m i l a r to t h a t o f a 3 + 1 _H_ LE (4.4) 96 H / L E LADNER, B.C. 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 J U N E - J U L Y 1972 7 \u00E2\u0080\u00A2 1 JUNE 15 3 D 2 JUNE 16 3 JUNE 21 4 JUNE 22 5 JUNE 24 \ 6 JUNE 29 N \ 7 JUNE 30 Nx 8 JULY 1 \ 9 JULY 2 N 10 JULY 3 4 i / i Z LU a x => 5 _ i u. > O O i LU z LU 0 - 5 -10 -15 GTAR SLAB r I 1 1 1 1 1 1 06 08 10 12 14 1 16 1 8 ^ 20 1 1 T I M E (PST) 1 1 T A R S L A B IN S H A D O W F i g . 38. E f f e c t o f shadow on the d i u r n a l b e h a v i o u r o f urban r o o f heat s t o r a g e . 119 f l u x e s by drawing upon s t o r a g e . Thus, w h i l e the g a i n o f net r a d i a t i o n p r o g r e s s i v e l y d e c r e a s e s w i t h the a p p r o a c h o f s u n s e t , a r e l a t i v e enhancement o f s e n s i b l e h e a t f l o w may d e v e l o p . T h i s would f a v o u r the slow d e c l i n e i n H towards s u n s e t as has been n o t e d on many o c c a s i o n s . W h i l e t h i s e x p l a n a t i o n may be a p p l i c a b l e to c o n d i t i o n s above the boundary l a y e r o f the r o o f , i t would seem l e s s s a t i s f y i n g f o r c o n d i t i o n s w i t h i n the t u r b u l e n t zone. Perhaps heat r e l e a s e s from urban s t r u c t u r e s towards s u n s e t i n t o the n e i g h b o u r i n g s t r e e t canyons a r e c o u p l e d w i t h the r e t u r n f l o w onto the r o o f to p r o v i d e the n e c e s s a r y enhancement o f H as we have o b s e r v e d i n the measurements a t the 1.2 m l e v e l . I t i s i n t e r e s t i n g to note t h a t t h e s t a r t o f r a p i d growth o f the urban h e a t i s l a n d , AT ( u r b a n - r u r a l ) i s o b s e r v e d to o c c u r d u r i n g the p e r i o d near s u n s e t (Oke and E a s t , 1971; Hage, 1971; and Oke et al. , ( 1 9 7 2 ) . N i g h t - t i m e v a l u e s o f H a r e a l s o shown i n F i g s . 35-37. Wh i l e t h e r e i s l e s s c o n f i d e n c e i n the a b s o l u t e m agnitudes o f the n o c t u r n a l v a l u e s , the o b s e r v e d p a t t e r n a p p e a r s c o n s i s t e n t and i s most i n t e r e s t i n g . Near t h e r o o f s u r f a c e (1.2 m), t h e r e i s c o n s i s t e n t l y a f l o w o f h e a t away from the s u r f a c e a t n i g h t . At 4.0 m, the n o c t u r n a l v a l u e s a r e more v a r i a b l e g i v i n g f l o w s t o w a r d s , and away from the s u r f a c e d u r i n g the same n i g h t . The few n o c t u r n a l measure-ments a t 20 m show a s i m i l a r p a t t e r n to t h a t o b s e r v e d a t 120 the 4 m l e v e l ( F i g . 3 7 ) . The a p p a r e n t l a c k o f r e v e r s a l o f s e n s i b l e heat f l o w near the s u r f a c e i n the c i t y a t n i g h t (as compared to a r u r a l s i t e ) must t h e r e f o r e be c o n s i d e r e d as one o f the s o u r c e terms f o r the o b s e r v e d heat i s l a n d . The few s e n s i b l e h e a t f l u x measurements a t 20 m above the r o o f were g e n e r a l l y s m a l l e r i n magnitude than t h o s e f o u n d a t the 4 m l e v e l , both by day and by n i g h t . T h i s a p p a r e n t d i v e r g e n c e i n the heat f l u x above t h e boundary l a y e r o f t h e r o o f seems to s u g g e s t t h a t e i t h e r a d v e c t i v e i n f l u e n c e s a r e i m p o r t a n t o r e l s e c o n v e r g e n c e w i l l have warmed the a i r l a y e r . T h i s however does not p r e c l u d e the e x i s t e n c e o f a c o n s t a n t f l u x l a y e r above the r o o f - t o p boundary l a y e r s i n c e i n a d e q u a t e f e t c h / h e i g h t r a t i o may have a f f e c t e d the measurements a t 20 m, p a r t i c u l a r l y d u r i n g the d a y t i m e w i t h the p r e v a i l i n g wind from the n o r t h w e s t . I t was m e n t i o n e d e a r l i e r t h a t t h e minimum f e t c h i s a p p r o x i -m a t e l y 1.5 km from non-urban s u r f a c e s (water b o d i e s ) f o r \u00E2\u0080\u00A2 t h i s e x p e r i m e n t a l s i t e . T h i s o c c u r s f o r winds from the n o r t h w e s t . As a r e s u l t , the p r i n c i p a l boundary l a y e r d e velopment o v e r the a r e a s t u d i e d d u r i n g the daytime may be r e l a t i v e l y s h a l l o w . The measurements a t 20 m may thus be o n l y p a r t i a l l y r e p r e s e n t a t i v e o f the u n d e r l y i n g c o n d i t i o n s . U n f o r t u n a t e l y , we do not have any H d a t a f o r i n t e r m e d i a t e l e v e l s between 4 and 20 m to c o n f i r m o r r e f u t e the c o n s t a n c y o f f l u x i n the i n t e r n a l boundary l a y e r o f the c i t y . 121 A n o t h e r i n t e r e s t i n g example o f the b e h a v i o u r o f urban s e n s i b l e heat f l u x e s i s shown i n F i g . 39. F i g . 39(a) shows the d i u r n a l c o u r s e o f H on J u l y 7, 1972 f o r d r y c o n -d i t i o n s . The v a l u e s o f G shown a r e t h o s e o b t a i n e d f o r the r o o f - t o p s u r f a c e . For the d i s c u s s i o n to f o l l o w , we s h a l l assume t h a t the r e s i d u a l ( o b t a i n e d as the r e s i d u a l o f the v e r t i c a l h e a t b a l a n c e e x p r e s s i o n , e q u a t i o n 1.2 ) may be a p p r o x i m a t e l y e q u a t e d to the l a t e n t heat f l u x . F o l l o w i n g t h i s o b s e r v a t i o n day, t h e r e was a p e r i o d o f heavy r a i n which c e a s e d on J u l y 12. The r e s u l t s f o r J u l y 13 ( F i g . 39 ( b ) ) , when r o o f - t o p a r e a s were s a t u r a t e d show a r e m a r k a b l e drop i n the s e n s i b l e h e a t f l u x , which s u g g e s t s t h a t most o f the a v a i l a b l e energy was u t i l i z e d f o r e v a p o r a t i o n . In the days f o l l o w i n g , t h e r e was a p e r i o d o f d r y w e a t h e r c o n d i t i o n s . The s e n s i b l e h e a t f l u x showed a p r o g r e s s i v e i n c r e a s e so t h a t by J u l y 17 ( F i g . 3 9 ( c ) ) , i t had r e g a i n e d v a l u e s s i m i l a r to t h o s e o b s e r v e d p r i o r to the r a i n f a l l . The r e s i d u a l term, however, was s t i l l a p p r e c i a b l e , the i m p l i c a t i o n s o f which w i l l be d i s c u s s e d i n the next c h a p t e r i n the c o n t e x t o f urban energy b a l a n c e . I t i s i n t e r e s t i n g , however, to note t h a t s i g n i f i c a n t amounts o f r a i n f a l l a r e i n t e r c e p t e d by f l a t - t o p r o o f s u r f a c e s d u r i n g wet s p e l l s . An a p p r e c i a b l e q u a n t i t y does not run o f f but remains as p u d d l e s on the s u r f a c e , o r i s a b s o r b e d i n the uppermost l a y e r o f the r o o f . T h i s water th e n becomes a v a i l a b l e f o r VANCOUVER, B.C. V.S.B. BLDG. JULY 7, 1972 H : 4m ABOVE ROOF WIND U _ (M/S) 2.8 3.3 3.4 4 2.8 3.5 DIR t t t I 06 08 10 12 14 TIME (PST) I E u 3: E^ >\u00E2\u0080\u00A2 H to Z LU Q X > LU z F i g . 39. Urban energy b a l a n c e s (a) J u l y 7 1972 f o l l o w i n g wet p e r i o d . u4 0 n / S N . 9 2.0 2.0 2.8 2.5 3.9 \u00C2\u00B0>\u00C2\u00AB t f T t f t i 1 \u00E2\u0080\u0094I I I 06 08 10 12 14 TIME (PST) 1972 w i t h dry c o n d i t i o n s ; (b) J u l y 13, r o F i g . 39. Urban e n e r g y b a l a n c e ( c ) J u l y 17, 1972, 5 days a f t e r wet p e r i o d . 124 e v a p o r a t i o n i n t o the urban a tmosphere. Under such c o n d i t i o n s , energy u t i l i z a t i o n to warm the urban a i r v i a s e n s i b l e h e a t t r a n s f e r i s c l e a r l y r e t a r d e d a t the expense o f l a t e n t h e a t t r a n s f e r . T h i s b r i e f s t u d y o f the d i u r n a l p a t t e r n o f urban H v a l u e s i n d i c a t e s t h a t the eddy c o r r e l a t i o n t e c h n i q u e can be used w i t h r e l a t i v e s u c c e s s i n the urban c o n t e x t , and t h a t a number o f u n i q u e l y urban f e a t u r e s a r e e v i d e n t . S p a t i a l S a m p l i n g A l i m i t e d s t u d y o f the s p a t i a l v a r i a b i l i t y o f t h e s e n s i b l e h e a t f l u x e s o v e r a u n i f o r m g r a s s s u r f a c e was p r e -s e n t e d i n C h a p t e r 4. The r e s u l t s s u p p o r t e d the b a s i c a s s u m p t i o n o f a c o n s t a n t f l u x l a y e r , assuming l e s s than 20 per c e n t v a r i a b i l i t y to be a c c e p t a b l e . The a p p l i c a b i l i t y o f t h i s p r e m i s e i n the c o n t e x t o f the c i t y i s v e r y ques-t i o n a b l e s i n c e the mosaic o f urban s t r u c t u r e s may i n d u c e a d v e c t i v e i n f l u e n c e s t h a t r e s u l t i n the f o r m a t i o n o f a n o n - c o n s t a n t f l u x l a y e r . Where t h e r e e x i s t s a measure o f b u i l d i n g c o n t i n u i t y , some u n i f o r m i t y i n the m e t e o r o l o g i c a l f i e l d s can be a n t i c i p a t e d . A c c o r d i n g l y , s m a l l s p a t i a l v a r i a b i l i t y i n the H measurements above l o c a l r o o f - t o p boundary l a y e r s may be t a k e n to r e f l e c t the e x t e n t to which the urban a r e a s t u d i e d p o s s e s s e s b u i l d i n g c o n t i n u i t y 125 ( o u t l i n e d i n the f i r s t s e c t i o n ) . Here, we assume t h a t the measurements a r e made w i t h i n a l a r g e r s c a l e urban boundary l a y e r ( i . e . f r e e o f non-urban i n f l u e n c e s ) . A l t h o u g h i t was not p o s s i b l e to s t u d y l a r g e s c a l e a r e a l v a r i a t i o n s , a l i m i t e d s t u d y o f the s p a t i a l v a r i a b i l i t y o f H i n the immediate v i c i n i t y o f the r o o f - t o p s u r f a c e was c o n d u c t e d . As a p a r a l l e l , we might e x p e c t t h a t s p a t i a l measurements c o n d u c t e d s i m u l t a n e o u s l y w i t h i n t h e t u r b u l e n t zone o f t h e r o o f s h o u l d y i e l d c o n s i s t e n c y i f the f l o w i s p r i m a r i l y r e s p o n d i n g to the u n d e r l y i n g s u r f a c e . Measure-ments beneath and above the s u r f a c e o f s e p a r a t i o n o v e r t h e r o o f would not be e x p e c t e d t o show t h i s c o n s i s t e n c y . S i m u l t a n e o u s measurements d u r i n g t h e da y t i m e w i t h two YST systems were made f o r v e r t i c a l s e p a r a t i o n s o f 0.8 m (between 1.2 and 2.0 m), o f 2.8 m (between 1.2 and 4.0 m) and f o r h o r i z o n t a l s e p a r a t i o n s o f 2.5 and 7.0 m, a t a v e r t i c a l h e i g h t o f ~ 1.5 m. Onl y measurements a t t h e 4.0 m l e v e l can be e x p e c t e d t o be above the l o c a l r o o f - t o p boundary l a y e r . Examples o f H measurements ~ 1.5 m above the r o o f f o r a h o r i z o n t a l s e p a r a t i o n between the two YST systems o f 2.5 m a r e shown i n F i g . 4 0 ( a ) . The d i u r n a l b e h a v i o u r o f t h e two H v a l u e s e x h i b i t s c l o s e s i m i l a r i t y w i t h t h i s s m a l l s e p a r a t i o n d i s t a n c e . T h e r e i s , however, some v a r i a b i l i t y i n the i n d i v i d u a l one hour a v e r a g e s o f H from the two i n s t r u m e n t s . C u m u l a t i v e t o t a l s o f the heat 30 CN I E u 1 20 >-H t/I 2 io X Z3 >\u00E2\u0080\u00A2 o (JJ z LU - 1 0 L 06 401 CN I E | 301 >\u00E2\u0080\u00A2 | 20| X 3 >\u00E2\u0080\u00A2 10 (b) VANCOUVER, B.C. V.S.B. BLDG AUG. 24, 1972 HEIGHT ABOVE ROOF : 1.5m HOR. SEPARATION : 2.5m 126 WIND U I - 5 (M /S ) J.4 1.6 I.6 V A R I A B L E WIND D IRECTION 1.8 1.6 2.0 1.6 1.2 0.9 0.6 J_ _L J 08 10 12 14 16 Y S T 18 20 T I M E (PST) VANCOUVER, B.C. V.S.B. BLDG. AUGUST 28, 1972 HEIGHT ABOVE ROOF . 1.5m HOR. SEPARATION 7.0m WIND U J 5 (M /S) 1.0 1-2 1.6 1.7 1.6 1.4 1.6 1.7 V A R I A B L E WIND DIRECTION i . \u00C2\u00B1 J 06 08 10 12 14 16 18 20 TIME (PST) F i g . 40. H o r i z o n t a l s p a t i a l v a r i a t i o n o f the urban s e n s i b l e h eat f l u x e s . 127 f l u x e s from both i n s t r u m e n t s , e x p r e s s e d as a r a t i o ( H V C T / Y 5 T i H ) i n d i c a t e ~ 20 per c e n t v a r i a t i o n . S i m i l a r r e s u l t s were o b t a i n e d i n the H c o m p a r i s o n f o r a h o r i z o n t a l s e p a r a -t i o n o f 7.0 m ( F i g . 4 0 ( b ) ) . These r e s u l t s a r e c o n s i s t e n t f o r o t h e r o b s e r v a t i o n days on which h o r i z o n t a l c o m p a r i s o n s were made (s e e T a b l e 6 ) . While t h e y i n d i c a t e r e l a t i v e l y l a r g e h o r i z o n t a l v a r i a t i o n when compared to t h a t f o r the r u r a l g r a s s s u r f a c e , they do s u p p o r t the p r e m i s e o f a p p r o x i m a t e h o r i z o n t a l f l u x c o n s t a n c y i n the t u r b u l e n t zone of the r o o f . S i m i l a r l y , the h e i g h t v a r i a t i o n w i t h i n the boundary l a y e r o f the r o o f ( o b s e r v e d from the 1.2 and 2.0 m l e v e l s ) a p p e a r e d c o n s i s t e n t ( F i g . 4 1 ( a ) ) . L e s s than 20 per c e n t v a r i a t i o n was n o t e d . The two o b s e r v a t i o n days on which H c o m p a r i s o n s between the 1.2 and 4.0 m l e v e l s were made, showed more v a r i a b i l i t y . Good agreement was f o u n d on A u g u s t 30, 1972 ( F i g . 4 1 ( b ) ) , whereas on September 1, 1972, a 50 per c e n t r e d u c t i o n was noted i n the 4.0 m v a l u e s . T a b l e 6 g i v e s a summary o f the s p a t i a l e x p e r i m e n t a l days and the c u m u l a t i v e t o t a l s from the two YST i n s t r u m e n t s , e x p r e s s e d as a r a t i o . They s u p p o r t the p r e m i s e o f c o n s t a n c y w i t h i n the boundary l a y e r o f the r o o f , i f we c o n s i d e r 20 per c e n t v a r i a t i o n to be a c c e p t a b l e . While no measurements o f the s p a t i a l v a r i a b i l i t y o f the n o c t u r n a l f l u x e s were a t t e m p t e d , i t may be p o s s i b l e 1 28 VANCOUVER, B.C. V.S.B. BLDG. AUG. 25, 1972 H YST HYST 2 VERT. SEP. 0.8m I E u E z LU Q X > LU z LU V A R I A B L E WIND D IRECTION I 1 I _L J 06 08 2 0 r ( b ) 10 12 14 16 10 U 0 18 20 TIME (PST) VANCOUVER, B.C. V.S.B. BLDG. AUG. 30, 1972 H Y S T I (1.2m) H Y S T 2 (4.0m) VERT. SEP. 2.8m WIND 0 1 2 ( M / S ) 2.0 2.3 3.1 3.1 2.8 3.6 3.4 4.2 4.0 2.7 V A R I A B L E WIND D IRECTION 0. (M/S) 2.3 3.3 3.7 3.4 3.2 3.9 3.9 4.9 4.4 4.0 I I I I I I 3.1 06 08 10 12 14 -L J 16 18 20 TIME (PST) F i g . 41. V e r t i c a l s p a t i a l v a r i a t i o n o f the urban s e n s i b l e h eat f l u x e s . T a b l e 6 C o m p a r i s o n o f d a y t i m e c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s f r o m t h e yaw s p h e r e - t h e r m o m e t e r s y s t e m s (Hys^! and H YgT2^ above t h e u r b a n r o o f D a t e D u r a t i o n ( m i n ) u / u Y S T l YST2 Rema r k s 24 A u g u s t 1 972 584 0.79 H o r i z o n t a l s e p a r a t i o n 2.5 m a t 1.5 m 1 eve 1 a b o v e r o o f - t o p 28 29 A u g u s t A u g u s t 1 972 1 972 420 332 i .09 0.98 H o r i z o n t a l s e p a r a t i o n 7.0 m a t 1.5 m 1 eve 1 a b o v e r o o f - t o p 25 A u g u s t 1 972 682 0.88 V e r t i c a l s e p a r a t i o n 0.8 m, a t 1.2 m and 2 . 0 m I e ve 1s a bove r o o f - t o p 30 1 A u g u s t 1972 S e p t e m b e r 1972 525 426 0.88 1 .48 * V e r t t c a l s e p a r a t i o n 2.8 m, a t 1.2 m and 4.0 m l e v e l s a bove r o o f - t o p * H v c,_ a t t h e 1.2 m l e v e l and H v o _ a t t h e 2.0 and 4.0 m l e v e l s . l o l l I b l 2 130 to make some i n f e r e n c e s from the d i u r n a l b e h a v i o u r o f H p r e v i o u s l y d i s c u s s e d . C o n s i s t e n t l y , i t was f o u n d t h a t the H v a l u e s a t t h e 1.2 m l e v e l were d i r e c t e d away from the s u r f a c e a t n i g h t ( s e e F i g s . 35 and 3 6 ) . At the 4 and 20 m l e v e l s , n o c t u r n a l f l u x e s were more v a r i a b l e but s m a l l e r t h a n t h o s e a t the 1.2 m l e v e l . With the p r e s i s t e n c e o f l i g h t winds a t n i g h t , the boundary l a y e r d e velopment o v e r the r o o f - t o p s u r f a c e would not be e x p e c t e d to be as marked. As a r e s u l t , n o n - c o n s t a n c y i n the urban s e n s i b l e h e a t f l u x may be i n f e r r e d from our n i g h t - t i m e o b s e r v a t i o n s . F u g g l e (1971) a r r i v e d a t a s i m i l a r c o n c l u s i o n from s t u d i e s o f r a d i a t i v e f l u x d i v e r g e n c e i n the a i r l a y e r i m m e d i a t e l y above c i t y s t r u c t u r e s a t n i g h t . An i n c r e a s e i n r a d i a t i v e d i v e r g e n c e ( c o o l i n g ) a p p e a r e d to be p a r t i a l l y o f f s e t by a 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 n s i b l e h e a t c o n v e r g e n c e (warm-ing)-. The r e s u l t s from t h i s s t u d y a l s o i n d i c a t e s e n s i b l e h e a t f l u x c o n v e r g e n c e i n the l ower a t m o s p h e r e . Thus, the i n t e r a c t i o n o f f l u x d i v e r g e n c e i n the net r a d i a t i o n f i e l d , w i t h t h a t o f t h e v e r t i c a l t e m p e r a t u r e s t r u c t u r e c o u l d have p r o d u c e d the s e n s i b l e heat c o n v e r g e n c e . In the a bsence o f a d v e c t i v e i n f l u e n c e s , t h i s i s o f f e r e d as a p o s s i b l e e x p l a n a -t i o n f o r the n i g h t - t i m e b e h a v i o u r o f urban H v a l u e s c l o s e to the r o o f s u r f a c e . C h a p t e r 6 URBAN ENERGY BALANCE I n t r o d u c t i o n The a p p l i c a b i l i t y o f the eddy c o r r e l a t i o n t e c h n i q u e to t h e measurement o f s e n s i b l e heat t r a n s f e r between the atmosphere and the urban i n t e r f a c e was d e m o n s t r a t e d i n the p r e v i o u s c h a p t e r . D e s p i t e the enormous c o m p l e x i t i e s o f th e t u r b u l e n t heat exchange p r o c e s s e s i n the c i t y , i t was shown t h a t the urban s e n s i b l e h e a t f l u x p a t t e r n , o b t a i n e d d i r e c t l y from E u l e r i a n p o i n t measurements, l a r g e l y r e f l e c t s t ime changes i n th e net r a d i a t i o n f i e l d . Even the magnitudes o f t h e heat f l u x e s do not appear i n c o n s i s t e n t w i t h t h o s e o f the net r a d i a t i o n d u r i n g t h e d a y t i m e . In the a b s e n c e of a r t i f i c i a l l y g e n e r a t e d heat a t the s u r f a c e and a d v e c -t i o n e f f e c t s , i t s h o u l d be e x p e c t e d t h a t the amount o f heat used to warm the a i r v i a s e n s i b l e heat t r a n s f e r w i l l not exceed the net r a d i a n t heat g a i n e d a t the s u r f a c e . The i n d e p e n d e n t measurements o f urban H s u p p o r t t h i s . I t s h o u l d be emphasized t h a t t h i s r e s u l t has been d e r i v e d from c o m p l e t e l y i n d e p e n d e n t measurements o f net r a d i a t i o n 131 132 and s e n s i b l e heat f l u x . In a d d i t i o n , i t was p o s s i b l e t o make a l i m i t e d a s s e s s m e n t o f the d i u r n a l b e h a v i o u r , and s p a t i a l v a r i a b i l i t y o f H o v e r a r e s t r i c t e d urban a r e a . These r e s u l t s a r e now c o n s i d e r e d i n t h e c o n t e x t o f the ener g y b a l a n c e framework. Measurements o f H c o n c u r r e n t l y w i t h o t h e r e n e r g y components ( n e t r a d i a t i o n and s o i l h eat s t o r a g e ) p r o v i d e the b a s i s f o r a d i s c u s s i o n o f t h e urban h e a t b a l a n c e . S i n c e both Rn and G a r e o b t a i n e d from p o i n t measurements, do u b t s as t o t h e i r u s e f u l n e s s and v a l i d i t y must a r i s e when t h e y a r e used to c h a r a c t e r i z e an urban a r e a . F u r t h e r m o r e , i t i s n e c e s s a r y t o make a s s u m p t i o n s i n o r d e r t o s i m p l i f y t h e t h r e e - d i m e n s i o n a l n a t u r e o f t h e problem and the e x i s t e n c e o f a n t h r o p o g e n i c s o u r c e s o f heat and m o i s t u r e . R e c o g n i z i n g t h e s e s h o r t c o m i n g s , i t i s s t i l l p o s s i b l e to g a i n some g e n e r a l i n s i g h t s i n t o t h e e n e r g e t i c exchanges i n t h e urban e n v i r o n m e n t v i a the ene r g y b a l a n c e framework. A r t i f i c i a l Heat and M o i s t u r e P r o d u c t i o n In c i t i e s , a r t i f i c i a l h eat and m o i s t u r e a r e r e l e a s e d i n t o the atmosphere p r i m a r i l y from i n d u s t r i a l , t r a n s p o r t a t i o n and d o m e s t i c s o u r c e s . These s o u r c e s g e n e r a t e heat by com-b u s t i o n p r o c e s s e s , which then e n t e r s the atmosphere e i t h e r d i r e c t l y o r i n d i r e c t l y i n the form o f s e n s i b l e h e a t . A 133 r e l a t i v e l y s m a l l f r a c t i o n o f t h i s a r t i f i c i a l heat g e n e r a t e d w i l l be u t i l i z e d i n the e v a p o r a t i o n o f l i q u i d w a t e r and t h e r e f o r e e n t e r s t h e atmosphere i n the form o f l a t e n t h e a t . The a r t i f i c i a l heat g e n e r a t i o n can thus be e x p e c t e d to pro d u c e p r i m a r i l y a m o d i f i c a t i o n o f the n a t u r a l s e n s i b l e h e a t exchange. F o r many m e t r o p o l i t a n a r e a s , t h e magnitude o f t h i s a r t i f i c i a l e n e r g y f l u x d e n s i t y has been e s t i m a t e d ( s e e f o r example, Oke ( 1 9 6 9 ) , SMIC ( 1 9 7 1 ) ) . They i n d i c a t e t h a t man-made he a t p r o d u c t i o n has a t t a i n e d v a l u e s which a r e a s i g n i f i c a n t f r a c t i o n o f t h e n a t u r a l net r a d i a t i o n f o r many m i d - l a t i t u d e c i t i e s . In some i n s t a n c e s ( e . g . c i t i e s w i t h a c o l d w i n t e r c l i m a t e ) , t h i s term may even be l a r g e r t h a n Rn. T h i s e n e r g y , e m i t t e d d i r e c t l y o r i n d i r e c t l y i n t o t h e urban atmosphere i n t h e form o f s e n s i b l e h e a t , i s g e n e r a l l y a c c e p t e d as the prime cause f o r t h e t h r e e -d i m e n s i o n a l urban heat i s l a n d s o b s e r v e d d u r i n g the w i n t e r i n m i d - l a t i t u d e s . A r t i f i c i a l heat g e n e r a t i o n i s d i r e c t l y r e l a t e d to e n e r g y consumption and t h e r e f o r e shows a s t r o n g s e a s o n a l p a t t e r n w i t h summer v a l u e s c o n s i d e r a b l y l o w e r than t h o s e f o r the w i n t e r h e a t i n g s e a s o n . B o r n s t e i n (1968) has r e p o r t e d summer v a l u e s o f a r t i f i c i a l e n ergy f l u x d e n s i t y f o r M a n h a t t a n , New York, t h a t a r e about 1/6 o f the w i n t e r v a l u e s . S i m i l a r l y , Oke (1969) showed the summer a r t i f i c i a l h e a t p r o d u c t i o n t o be about 1/3 o f w i n t e r v a l u e s i n M o n t r e a l . T h i s p o i n t i s emphasized s i n c e the s t u d y p e r i o d here r e f e r s 134 to a summer-time s i t u a t i o n i n Va n c o u v e r . We thus a n t i c i p a t e t h a t the e f f e c t o f t h i s term w i l l d i m i n i s h from w i n t e r t o summer i n our e n e r g y b a l a n c e c o n s i d e r a t i o n s . U s i n g the p r o c e d u r e o u t l i n e d by Bach (1970) t h e av e r a g e annual a r t i f i c i a l heat p r o d u c t i o n f o r V a n c o u v e r i n 1970 was c a l c u l a t e d . The e s t i m a t e was based on u n p u b l i s h e d d a t a o f e l e c t r i c i t y , g a s , f u e l o i l , g a s o l i n e and c o a l c o n s u m p t i o n and m e t a b o l i c heat g e n e r a t i o n f o r the V a n c o u v e r a r e a i n 1970. The p r i m a r y s o u r c e s o f a r t i f i c i a l h e a t , i n d e s c e n d i n g o r d e r o f i m p o r t a n c e , were f u e l o i l , g a s , g a s o l i n e and e l e c t r i c i t y . The e s t i m a t e was found to be a p p r o x i m a t e l y 1.9 mWcm\"2 and i s somewhat s m a l l e r than t h o s e o f o t h e r mid-l a t i t u d e N o r t h A m e r i c a n c i t i e s . F o r example, Bach (1970) r e p o r t e d an a v e r a g e summer v a l u e o f 2.6 mWcm\"2 f o r C i n c i n n a t i , whi1e Summers (1964) e s t i m a t e d an a v e r a g e annual v a l u e o f 9.8 mWcm\"2 f o r M o n t r e a l ( s e e T a b l e 1 ) . The v a l u e f o r V a n c o u v e r , however, does not a p p e a r u n r e a s o n a b l e s i n c e h e a t i n g degree days here a r e l o w e r than t h o s e o f c o n t i n e n t a l m i d - l a t i t u d e c i t i e s , and c o n s e q u e n t l y may be e x p e c t e d to pro d u c e lower energy consumption demand. The s e a s o n a l v a r i a t i o n o f the a r t i f i c i a l h eat f l u x d e n s i t y f o r V a n c o u v e r showed t h a t 60 per c e n t o f the a r t i f i c i a l h e a t was p r o d u c e d i n the w i n t e r months ( O c t o b e r - M a r c h ) . For 1970, the w i n t e r and summer v a l u e s were found to be 2.3 and 1.5 mWcm-2 r e s p e c t i v e l y . 135 W h i l e t h e e x a c t p a r t i t i o n i n g o f t h i s a v a i l a b l e e n e r g y i n t o s e n s i b l e and l a t e n t heat i s not known, i t i s not u n r e a s o n a b l e to s u g g e s t t h a t l e s s than 10 per c e n t e n t e r s the urban atmosphere as l a t e n t h e a t . I t i s n o t e d , f o r example, t h a t Oke and H a n n e l l (1970) e s t i m a t e d t h a t l e s s than 10 per c e n t o f the energy o u t p u t o f a s t e e l m i l l a t H a m i l t o n , O n t a r i o , e n t e r e d the atmosphere as l a t e n t h e a t . C o n s e q u e n t l y , we s h a l l i g n o r e the a r t i f i c i a l h eat c o n t r i b u t i o n to l a t e n t heat p r o c e s s e s f o r t h e Va n c o u v e r summertime s i t u a t i o n . A l t h o u g h the o v e r a l l a r t i f i c i a l h eat g e n e r a t i o n f o r summer i n Vanco u v e r i s r e l a t i v e l y s m a l l , i t s h o u l d be p o i n t e d o u t t h a t a l l e s t i m a t e s o f man-made heat p r o d u c t i o n ( i n c l u d i n g our e s t i m a t e ) r e p r e s e n t an a v e r a g e v a l u e o v e r the h o r i z o n t a l a r e a ! d i m e n s i o n s o f the c i t y . We thus e x p e c t h i g h e r v a l u e s i n the more d e n s e l y u r b a n i z e d a r e a o f t h e c i t y . F u r t h e r m o r e , the t h r e e - d i m e n s i o n a l a s p e c t o f t h e s u r f a c e and the n a t u r e o f b u i l d i n g heat exchange may cause l o c a l i z a t i o n o f t h i s heat as i t e n t e r s t h e urban a t m o s p h e r e . F o r a l i m i t e d urban b u i l d i n g - a i r volume i n the absence o f i n d u s t r i a l s o u r c e s , the p r i m a r y a r t i f i c i a l h e a t i s g e n e r a t e d by t r a n s p o r t a t i o n and d o m e s t i c s o u r c e s . Heat g e n e r a t e d by t r a n s p o r t a t i o n e n t e r s the a i r volume a t s t r e e t l e v e l , w i t h i n t h e canyon between b u i l d i n g e l e m e n t s , whereas d o m e s t i c a l l y g e n e r a t e d heat may p a r t l y e n t e r the 136 atmosphere d i r e c t l y a t r o o f - l e v e l o r t h r o u g h v e n t s on the s i d e s o f a b u i l d i n g . Some o f the heat w i l l a l s o pass i n d i r e c t l y to the atmosphere t h r o u g h the w a l l s and windows o f the i m p e r f e c t l y i n s u l a t e d b u i l d i n g . The net e f f e c t c o u l d a c c e n t u a t e th e warming between dense b u i l d i n g e l e m e n t s , p a r t i c u l a r l y a t n i g h t , when the n a t u r a l e n e r g y components a r e smal1. As an a p p r o x i m a t i o n , we s h a l l assume t h a t the v a l u e o f 1.5 mWcm\"2 can be a p p l i e d to the s t u d y a r e a . C o n s e q u e n t l y , t h e e r r o r c r e a t e d by n e g l e c t i n g t h i s e n e r g y s o u r c e term s h o u l d be i n s i g n i f i c a n t d u r i n g t h e d a y t i m e s i n c e the v a l u e i s a t l e a s t an o r d e r o f magnitude s m a l l e r than the n a t u r a l e n e r g y components. O m i s s i o n o f t h i s h eat term a t n i g h t , however, may be u n r e a s o n a b l e as the a r t i f i c i a l e n e r g y f l u x d e n s i t y i s then l i k e l y t o be an a p p r e c i a b l e f r a c t i o n o f the n a t u r a l e n e r g y components. Roof-Top Energy B a l a n c e To b e g i n d i s c u s s i o n o f the urban heat b a l a n c e , we f i r s t c o n s i d e r the s i t u a t i o n c l o s e to t he s u r f a c e , w i t h i n the l o c a l r o o f - t o p boundary l a y e r (see F i g . 3 0 ) . In d o i n g s o , we a v o i d most o f the t h r e e - d i m e n s i o n a l a s p e c t s and a t t e m p t t o view the heat b a l a n c e as b a s i c a l l y a one-dimen-s i o n a l p r o b l e m . F o r the r o o f - t o p s u r f a c e i t s e l f , we can use t h e f o l l o w i n g s i m p l e heat b a l a n c e e x p r e s s i o n 137 Rn = H + LE + G (6.1 ) S i n c e t h e n e t r a d i a t i o n ( R n ) , t h e r o o f h e a t f l u x (G) and t h e s e n s i b l e heat f l u x (H) were known v i a d i r e c t measurements, the l a t e n t h e a t f l u x (LE) i n t h e above e x p r e s -s i o n r e m a i n e d as t h e r e s i d u a l . (We s h o u l d n o t e t h a t t h i s p r o c e d u r e e n a b l e s us t o use t h e e n e r g y b a l a n c e framework b u t does not p r o v i d e a b u d g e t a r y check on t h e i n d e p e n d e n t l y measured e n e r g y p a r a m e t e r s . A h e a t b a l a n c e c h e c k i s o n l y p o s s i b l e i f we assume the r o o f - t o p s u r f a c e t o be c o m p l e t e l y d r y ( i . e . LE i s z e r o ) . ) L e t us now examine the a p p l i c a b i l i t y o f t h e e n e r g y f l u x measurements f o r the r o o f s u r f a c e . As n e t r a d i a t i o n was o n l y m o n i t o r e d c o n t i n u o u s l y a t 20 m above t h e main r o o f s u r f a c e , t h e measurements o b t a i n e d a t t h i s l e v e l w i l l be used i n t h e r o o f - t o p e n e r g y b a l a n c e c o n s i d e r a -t i o n . T h i s s h o u l d n o t be u n r e a s o n a b l e d u r i n g t h e d a y t i m e s i n c e i t was p r e v i o u s l y n o t e d t h a t the h e i g h t - v a r i a t i o n i n Rn between 11 and 20 m above the r o o f was l e s s than 5 per c e n t . The measurement o f G was made i n the uppermost g r a v e l and t a r l a y e r o f t h e r o o f . T h i s p r o v i d e d a measure o f t h e h e a t f l o w i n g i n t o o r out o f t h e r o o f s u r f a c e . I f we assume t h a t some a r t i f i c i a l h e a t p a s s e s i n d i r e c t l y to t h e atmosphere t h r o u g h t h e i m p e r f e c t l y i n s u l a t e d r o o f , t h e n t h e r o o f - t o p G measurements a l s o c o n t a i n a measure o f t h i s 138 term. D u r i n g the d a y t i m e , t h i s a r t i f i c i a l heat w i l l r e d u c e the n a t u r a l G o f the r o o f and by n i g h t , w i l l augment the n a t u r a l G. D i r e c t H measurements a t the 1.2 m l e v e l above the r o o f o n l y w i l l be used f o r the r o o f - t o p e n e r g y b a l a n c e c o n s i d e r a t i o n s . They r e p r e s e n t v a l u e s w i t h i n t h e l o c a l t u r b u l e n c e zone o f the r o o f and s h o u l d l a r g e l y r e f l e c t t h e u n d e r l y i n g s u r f a c e c o n d i t i o n s . Daytime b a l a n c e . Two examples o f t y p i c a l d a y t i m e v a r i a t i o n o f the measured e n e r g y b a l a n c e components near r o o f - l e v e l a r e g i v e n i n F i g s . 42 and 43. These r e s u l t s i n d i c a t e t h a t a s i g n i f i -c a n t p o r t i o n o f the n e t r a d i a n t e n e r g y g a i n e d a t the r o o f s u r f a c e i s u t i l i z e d i n s e n s i b l e heat t r a n s f e r and i n h e a t s t o r a g e i n t h e r o o f . Of t h e s e two t r a n s f e r p r o c e s s e s , the g r e a t e s t amount o f e n e r g y i s used i n s e n s i b l e heat t o warm the a i r ( f o r example, a t midday H i s t y p i c a l l y ~ 3 G ) . Even s o , the r e s i d u a l term ( e q u a t e d t o LE) i s q u i t e a p p r e c i -a b l e . I t s h o u l d be n o t e d t h a t the d i u r n a l c y c l e o f the r e s i d u a l term shows a morning peak on J u l y 27 ( F i g . 42) whereas on the f o l l o w i n g day ( F i g . 4 3 ) , the peak o c c u r s i n t h e l a t e e v e n i n g . The c ause o f t h i s b e h a v i o u r i s not known but i t may be r e l a t e d t o the p r e s e n c e o f a d v e c t i o n even a t the 1.2 m l e v e l above the r o o f . I f the r e s i d u a l 139 VANCOUVER, B.C. V.S.B. BLDG JULY 27, 1972 H : 1.2m ABOVE ROOF 1.9 1.9 1.5 1.4 0.8 V A R I A B L E WIND DIRECTION 06 _ J _ 08 10 12 14 16 JL J 18 20 TIME (PST) F i g . 42. Daytime r o o f - t o p e n e r g y b a l a n c e . 140 VANCOUVER, B.C. V.S.B. BLDG JULY 28, 1972 H : 1.2m ABOVE ROOF 18 20 TIME (PST) F i g . 43. Daytime r o o f - t o p e n e r g y b a l a n c e . 141 term, e q u a t e d to L E , i s r e a l , we must c o n c l u d e t h a t the r o o f - t o p s u r f a c e i s not t h o r o u g h l y d r y but t h a t i t c o n t a i n s a v a i l a b l e w a ter which i s s u b s e q u e n t l y r e l e a s e d as m o i s t u r e to the urban atmosphere and consumes l a t e n t heat o f v a p o u r i -z a t i o n . On the o t h e r hand, the r e l a t i v e l y l a r g e r e s i d u a l term may a r i s e from 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 the s u r f a c e s n e s i b l e h e a t f l u x by the eddy c o r r e l a t i o n i n s t r u -ment, as w e l l as from u n d e r e s t i m a t i o n o f the s u r f a c e n e t r a d i a t i o n and s o i l h e a t s t o r a g e t e r m s . These p o s s i b i l i t i e s a r e examined f u r t h e r below. T h e o r e t i c a l c o n s i d e r a t i o n s i n d i c a t e t h a t n e t r a d i a t i o n measurements become i n c r e a s i n g l y l e s s r e p r e s e n t a -t i v e o f s u r f a c e c o n d i t i o n s w i t h i n c r e a s i n g h e i g h t above the s u r f a c e when s u r f a c e t e m p e r a t u r e s a r e 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 a t o f t he ambient a i r . E x p e r i m e n t a l l y , t h i s e f f e c t was f o u n d to c r e a t e a 7 per c e n t d i s c r e p a n c y between net r a d i a t i o n measured a t 50 cm above a d r y , bare s o i l and t h a t measured a t 215 cm f o r d a y l i g h t hours ( I d s o and C o o l e y , 1971). A s i m i l a r e f f e c t can be a n t i c i p a t e d i n t h e n e t r a d i a t i o n measurements above the urban r o o f s u r f a c e , when s u r f a c e t e m p e r a t u r e s a r e s i g n i f i c a n t l y warmer than t h e ambient a i r t e m p e r a t u r e s . Measurements o f t r u e r o o f - t o p s u r f a c e t e m p e r a t u r e were made w i t h a Barnes s e n s o r d u r i n g the d a y t i m e by i s o l a t i n g the s u r f a c e from sky r a d i a t i o n and a l l o w i n g i t to r a d i a t e as an a p p a r e n t b l a c k b o d y . The 142 method used i s d e s c r i b e d by Fuchs and Ta n n e r ( 1 9 6 6 ) . The r o o f - s u r f a c e t e m p e r a t u r e s t h u s o b t a i n e d were f o u n d to be l a r g e r t h a n 40\u00C2\u00B0C, w h i l e s c r e e n h e i g h t a i r t e m p e r a t u r e s were ~ 20\u00C2\u00B0C. The maximum e f f e c t o f a i r - r o o f s u r f a c e t e m p e r a t u r e d i f f e r e n c e s on t h e e f f e c t i v e o u t g o i n g r a d i a t i o n c o u l d then be d e t e r m i n e d a p p r o x i m a t e l y from the e m p i r i c a l r e l a t i o n s h i p ( b a s e d on t h e d a t a o f R i d e r and Ro b i n s o n (1951)) when s c r e e n h e i g h t i s 1 m and the s u r f a c e e m i s s i v i t y i s assumed e q u a l t o one. ! s \" 1 s = 0.205 (upper l i m i t ) (6.2) a T * - T* where a S t e f a n - B o l t z m a n n c o n s t a n t I i s the t r u e e f f e c t i v e o u t g o i n g r a d i a t i o n from t h e s u r f a c e I i s t h e t r u e e f f e c t i v e o u t g o i n g r a d i a t i o n a t s c r e e n h e i g h t T s t e m p e r a t u r e o f the s u r f a c e T ambient t e m p e r a t u r e a t s c r e e n h e i g h t I f we assume a maximum a i r - r o o f s u r f a c e t e m p e r a t u r e d i f f e r e n c e o f 30\u00C2\u00B0C and an ambient t e m p e r a t u r e o f 20\u00C2\u00B0C, i t can be seen t h a t I i s a p p r o x i m a t e l y 4 mWcm\"2 g r e a t e r than I. The e f f e c t o f such l a r g e a i r - r o o f s u r f a c e t e m p e r a t u r e d i f f e r e n c e s can then be e x p e c t e d t o produce an o v e r e s t i m a t i o n o f t h e 143 s u r f a c e net r a d i a t i o n o f 4 mWcm\"2 when net r a d i a t i o n measure-ments a t the 1 m l e v e l a r e e x t r a p o l a t e d t o the r o o f s u r f a c e . F u r t h e r m o r e , i f we assume t h a t Rn measurements a t the 20 m l e v e l a r e g r e a t e r than t h o s e a t 1 m by 5 per c e n t , t h e net e f f e c t would y i e l d a maximum o v e r e s t i m a t i o n o f r o o f -s u r f a c e Rn o f ~ 7 mWcm\"2 when Rn measurements a t 20 m a r e used to r e p r e s e n t s u r f a c e c o n d i t i o n s . Thus, the r e l a t i v e l y l a r g e r e s i d u a l term, d e r i v e d from the heat b a l a n c e e x p r e s -s i o n , can be p a r t l y a t t r i b u t e d t o the e x t r a p o l a t i o n o f Rn a t 20 m to the r o o f s u r f a c e . In t h e r o o f - t o p s u r f a c e e n e r g y b a l a n c e , G v a l u e s were o b t a i n e d from a f l u x p l a t e embedded i n the uppermost g r a v e l and t a r l a y e r o f the r o o f , a p p r o x i m a t e l y 0.5 cm below the s u r f a c e . A c c o r d i n g l y , an u n d e r e s t i m a t i o n o f s u r f a c e G w i l l a r i s e from d i v e r g e n c e e f f e c t s i n the 0.5 cm l a y e r between the p l a t e and the s u r f a c e , d u r i n g t h e da y t i m e . The r o o f s u r f a c e G can be e x p r e s s e d i n the f o l l o w -i n g manner roof s u r f a c e 0-0.5 cm (6.3) + G heat f l u x p l a t e at 0.5 cm where AG i s the change i n heat s t o r a g e i n the top 0.5 cm. No a t t e m p t was made to measure AG. I t s c o n t r i b u t i o n to the 144 r o o f - s u r f a c e v a l u e , however, i s u n l i k e l y to be s i g n i f i c a n t . I t i s n o t e d , f o r i n s t a n c e , t h a t T u r n e r (1969) o b t a i n e d AG v a l u e s f o r the top 0.5 cm i n a c o n c r e t e s l a b t h a t were ~ 10 per c e n t o f the f l u x p l a t e G v a l u e s a t the 0.5 cm de p t h , d u r i n g the d a y t i m e . Thus, i f we assume a s i m i l a r o r d e r o f magnitude e f f e c t f o r the top 0.5 cm o f the r o o f , the use o f G measurements a t the 0.5 cm depth t o r e p r e s e n t s u r f a c e v a l u e s would produce a maximum u n d e r e s t i m a t i o n o f ~ 1 mWcm-2 d u r i n g the d a y t i m e . In a d d i t i o n to d i v e r g e n c e e f f e c t s , e r r o r s o f G may a r i s e from d i f f e r e n c e s i n t h e r m a l c o n d u c t i v i t i e s o f the f l u x p l a t e and the g r a v e l and t a r r o o f medium. The magnitude o f t h i s e f f e c t can be d e t e r m i n e d a p p r o x i m a t e l y from the f o r m u l a g i v e n by P h i l l i p (1961) f = 1/[1 - a r ( l - e \" 1 ) ] (6 where f r a t i o o f mean f l u x d e n s i t y t h r o u g h t h e m e t e r t o t h e f l u x d e n s i t y t h r o u g h t h e med i urn e r a t i o o f m e t e r c o n d u c t i v i t y t o medium c o n d u c t i v i t y r r a t i o o f t h e mean m e t e r t h i c k n e s s i n t h e g e n e r a l d i r e c t i o n o f t h e h e a t f l o w t o t h e s q u a r e r o o t o f t h e mean c r o s s -s e c t i o n t h e m e t e r p r e s e n t s n o r m a l t o t h e d i r e c t i o n a a c o n s t a n t , e q u a l t o 1.70 145 For t h e heat f l u x p l a t e , the th e r m a l c o n d u c t i v i t y i s ~ 84.0 mWcm\" l 0K - 1 and the v a l u e o f r i s 0.13. I f we assume a ther m a l c o n d u c t i v i t y o f the g r a v e l and t a r medium o f ~ 25.2 mWcnr^K\"\" 1, the above e q u a t i o n y i e l d s a v a l u e o f f = 1.18. Thus, the heat f l u x measured by the meter i s 18 per c e n t l a r g e r than t h a t t h r o u g h the g r a v e l and t a r medium. S i n c e peak f l u x p l a t e G v a l u e s measured d u r i n g the d a y t i m e were ~ 10 mWcm-2, maximum o v e r e s t i m a t i o n o f G f o r the r o o f - t a r and g r a v e l medium would be ~ 2 mWcm - 2. I t can thu s be seen t h a t e r r o r s o f the r o o f - s u r f a c e G from the use o f the h e a t f l u x p l a t e embedded a t 0.5 cm i n the g r a v e l and t a r medium a r e l i k e l y to be n e g l i g i b l e . The p o s s i b i l i t y o f 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 s u r f a c e s e n s i b l e h e a t f l u x e s by the eddy c o r r e l a t i o n i n s t r u -ment a t 1.2 m above t h e r o o f s u r f a c e d u r i n g t h e d a y t i m e c o u l d n ot be r e a d i l y a s s e s s e d . Some u n c e r t a i n t i e s must e x i s t i n the use o f H v a l u e s a t the 1.2 m l e v e l t o r e p r e -s e n t s u r f a c e c o n d i t i o n s . The complex n a t u r e o f the f l o w i n t h e t u r b u l e n t zone o f the r o o f , i n c l u d i n g a r e t u r n f l o w onto t h e r o o f from n e i g h b o u r i n g s t r e e t canyons may c r e a t e d i f f i c u l t i e s i n the a c t u a l measurement o f the s e n s i b l e h e a t f l o w o f f the r o o f . I t i s not known, however, i f t h i s e f f e c t would produce a s y s t e m a t i c u n d e r e s t i m a t i o n o f H d u r i n g the d a y t i m e . In u s i n g the eddy c o r r e l a t i o n t e c h -n q i u e , i t i s n e c e s s a r y to assume t h a t the v e r t i c a l v e l o c i t y , 146 a v e r a g e d f o r a s u f f i c i e n t time p e r i o d , i s c l o s e to z e r o o v e r the r o o f s u r f a c e . A l t h o u g h some a t t e m p t s were made to d e t e r m i n e w w i t h a v e r t i c a l anemometer, l i t t l e c o n f i d e n c e can be p l a c e d on the a c t u a l m a g nitudes as t h e s e v a l u e s (\u00C2\u00B1 10 c m s - 1 ) were w i t h i n the r e s o l u t i o n c a p a b i l i t y o f the i n s t r u m e n t . I t a p p e a r e d , however, t h a t t h e r e was a t e n d e n c y towards s l i g h t d o w n d r a f t c o n d i t i o n s d u r i n g the d a y t i m e near the r o o f s u r f a c e . A c c o r d i n g l y eddy f l u x measurements o f s e n s i b l e heat would be u n d e r e s t i m a t i n g the s e n s i b l e heat t r a n s p o r t from the r o o f . On the o t h e r hand, the n a t u r e o f t h e o u t p u t from th e yaw s p h e r e - t h e r m o m e t e r a s s e m b l y s u g g e s t s a s l i g h t o v e r e s t i m a t i o n o f the eddy f l u x o f s e n s i b l e h e a t d u r i n g t h e d a y t i m e w i t h s m a l l n e g a t i v e mean v e r t i c a l v e l o c i t i e s . Thus, the e x i s t e n c e o f s m a l l n e g a t i v e w may not have a f f e c t e d the s e n s i b l e heat f l u x measurements to any a p p r e c i a b l e e x t e n t . As an a p p r o x i m a t i o n , i t may thus n o t be u n r e a s o n a b l e to assume no s y s t e m a t i c u n d e r e s t i m a t i o n o f H f o r t h e r o o f s u r f a c e d u r i n g the d a y t i m e . The p r e c e d i n g a n a l y s i s o f e r r o r s a s s o c i a t e d w i t h the use o f Rn, G and H measurements to r e p r e s e n t r o o f s u r f a c e c o n d i t i o n s d u r i n g the d a y t i m e can thus e x p l a i n o n l y p a r t o f the l a r g e r e s i d u a l term n o t e d from the heat b a l a n c e c o n s i d e r a t i o n s . A maximum p o s s i b l e c o n t r i b u t i o n t o t h e r e s i d u a l term from t h e s e e r r o r s i s l i k e l y to be ~ 7 mWcm-2. The r e m a i n i n g p o r t i o n o f the r e s i d u a l term ( e q u a t i o n to LE) 147 would s t i l l be a p p r e c i a b l e . A c c o r d i n g l y , the p o s s i b i l i t y o f l a t e n t heat t r a n s f e r from the r o o f - t o p s u r f a c e i s examined f u r t h e r below. I t i s o f t e n s t a t e d i n t h e l i t e r a t u r e t h a t t h e c i t y has l i t t l e a v a i l a b l e water f o r e v a p o r a t i o n ( f o r example, C h a n d l e r , ( 1 9 6 5 ) , P e t e r s o n ( 1 9 6 9 ) ) . T h i s a s s e s s m e n t i s o f f e r e d on t h e b a s i s t h a t the r e p l a c e m e n t o f n a t u r a l spongy r u r a l s u r f a c e by urban m a t e r i a l s r e n d e r s the s u r f a c e more i m p e r v i o u s to w a t e r . I t i s s u g g e s t e d t h a t p r e c i p i t a t i o n then l e a d s p r i m a r i l y to more r a p i d r u n - o f f . Lacy (1972, p r i v a t e c o m m u n i c a t i o n ) , however, i n d i c a t e s t h a t q u a n t i t a t i v e measurements do not s u p p o r t t h i s . He c i t e s examples from the r e s u l t s o f measurements i n a number o f E n g l i s h towns which show t h a t , on the a v e r a g e , r u n - o f f i s o n l y 40 per c e n t o f the t o t a l r a i n f a l l . Over a t e s t d i s t r i c t , 95 p e r c e n t paved, the r u n - o f f was a bout 50 per c e n t o f t h e r a i n -f a l l . T hese r e s u l t s s u g g e s t t h a t a l a r g e f r a c t i o n o f t h e r a i n f a l l i s a b s o r b e d by unpaved g r o u n d s , by porous m a t e r i a l s o r r e m a i n s as p u d d l e s . T h i s water would s u b s e q u e n t l y be a v a i l a b l e as a s o u r c e f o r e v a p o r a t i o n . I t would th u s seem t h a t the w i d e l y h e l d a s s u m p t i o n t h a t LE << H o v e r an urban a r e a i s u n f o u n d e d . The r e c e n t work o f Oke et al. (1972) i n M o n t r e a l s h o u l d a l s o be n o t e d i n t h i s r e g a r d . The p a r t i t i o n i n g o f e n e r g y between H and LE o v e r a r o o f - t o p s u r f a c e was d e r i v e d 148 from the Bowen r a t i o method, u s i n g t e m p e r a t u r e and wet-b u l b g r a d i e n t s between 2, 4 and 6 m above the r o o f s u r f a c e , and assuming s i m i l a r i t y i n the t r a n s f e r c o e f f i c i e n t s f o r h e a t and water v a p o u r . T h e i r r e s u l t s i n d i c a t e t h a t a g r e a t e r p o r t i o n o f e n e r g y i s used f o r l a t e n t h e a t t r a n s f e r than f o r s e n s i b l e h e a t ( i . e . B < 1) d u r i n g most o f the day-t i m e , and hence LE was found to be an i m p o r t a n t term i n the urban e n e r g y b a l a n c e . . In view o f t h e s e e x p e r i m e n t a l f i n d i n g s , i t i s a p p a r e n t t h a t one may not be j u s t i f i e d i n assuming t h a t the r o l e o f l a t e n t heat t r a n s f e r i n the c i t y i s i n s i g n i f i c a n t . The e x t e n t to which one can g e n e r a l i z e urban a r e a l a t e n t h e a t t r a n s f e r to i n d i v i d u a l r o o f - t o p s u r f a c e s must remain somewhat s p e c u l a t i v e . A l t h o u g h t h e r e were no q u a n t i t a t i v e measurements o f the m o i s t u r e s t a t e o f the r o o f s u r f a c e , i t seems d u b i o u s i f not u n r e a s o n a b l e to e x p e c t such l a r g e l a t e n t h e a t f l o w s d u r i n g the d a y t i m e as shown i n F i g s . 42 and 43. A t the same t i m e , we must e x p e c t some l a t e n t heat t r a n s f e r from the r o o f i f i t i s not t h o r o u g h l y d r y . The l a r g e r e s i d u a l term o b t a i n e d from our r o o f -top e n e r g y b a l a n c e c o n s i d e r a t i o n s may t h e r e f o r e p a r t l y a r i s e from t h e p r e s e n c e o f l a t e n t heat t r a n s f e r and p a r t l y from e r r o r s a s s o c i a t e d w i t h the use o f Rn, 6 and H measurements a t a f i n i t e d i s t a n c e from the a c t u a l r o o f s u r f a c e . 149 In g e n e r a l , t h e r o o f - t o p e n e r g y b a l a n c e showed t h a t t h e major p a r t i t i o n i n g o f the a v a i l a b l e n e t r a d i a t i o n a t midday was i n t o s e n s i b l e h e a t t r a n s f e r . F o r a net r a d i a n t i n p u t o f 60 mWcm\"2, G was t y p i c a l l y 10 mWcm\"2 and H about 30 mWcm\"2. I f the r e s i d u a l e n e r g y was c o n v e r t e d t o l a t e n t h e a t , we o b t a i n a Bowen r a t i o o f 1.5. T h i s v a l u e i s a p p r o x i m a t e l y t w i c e t h a t o f the maximum v a l u e o b t a i n e d f o r the L a d n e r g r a s s s u r f a c e , a t midday. On the o t h e r hand, o v e r e s t i m a t i o n o f s u r f a c e Rn by 7 mWcm\"2 would y i e l d midday v a l u e f o r t h e r e s i d u a l term o f 13 mWcm\"2. T y p i c a l Bowen r a t i o s f o r the r o o f s u r f a c e would th e n be 2.3, i f t h i s r e s i d u a l e n e r g y was c o n v e r t e d t o l a t e n t h e a t . N o c t u r n a l b a l a n c e . The a p p l i c a b i l i t y o f the n o c t u r n a l e n e r g y f l u x measurements f o r t h e r o o f s u r f a c e needs c a r e f u l c o n s i d e r a -t i o n s . The e x i s t e n c e o f r a d i a t i v e f l u x d i v e r g e n c e a t n i g h t ( e . g . F u g g l e , 1971) p r e s e n t s a d i f f i c u l t y i n e x t r a p o l a t i n g Rn measurements a t 20 m above t h e r o o f t o t h a t o f the r o o f -s u r f a c e . S i m i l a r l y , s e n s i b l e h e a t f l u x d i v e r g e n c e would i n v a l i d a t e a t t e m p t s t o use the H measurements a t the 1.2 m l e v e l as r e p r e s e n t a t i v e o f the u n d e r l y i n g s u r f a c e . I t s h o u l d be no t e d t h a t t h e YST i n s t r u m e n t i s l e s s r e l i a b l e a t 150 n i g h t i f l i g h t winds p r e v a i l . With t h e s e l i m i t a t i o n s i n mind, a b r i e f a s s e s s m e n t o f the n o c t u r n a l s i t u a t i o n i s p r e s e n t e d below. Two examples o f t y p i c a l n o c t u r n a l v a r i a t i o n o f the measured he a t b a l a n c e components a r e shown i n F i g s . 44 and 45. As p r e v i o u s l y n o t e d i n C h a p t e r 5, the n o c t u r n a l s e n s i b l e h e a t f l u x e s remain d i r e c t e d away from the a c t i v e r o o f s u r f a c e t h r o u g h o u t the c o u r s e o f the n i g h t . The mag-n i t u d e s were t y p i c a l l y 5 to 10 mWcm\"2. I f we assume t h a t a l l the measured e n e r g y components a r e a p p l i c a b l e t o the r o o f s u r f a c e , i t i s n e c e s s a r y t o s u g g e s t a l a r g e f l o w o f l a t e n t heat to the a c t i v e s u r f a c e a t n i g h t (~ 10 to 15 mWcm\"2). T h i s would p r e s u m a b l y r e s u l t i n s i g n i f i c a n t dew f o r m a t i o n on the r o o f s u r f a c e . W h i l e the o c c u r r e n c e o f e x t e n s i v e dew f o r m a t i o n on the r o o f s u r f a c e was o b s e r v e d d u r i n g the l a t t e r p a r t o f Augu s t 1972, t h e r e was no v i s i b l e e v i d e n c e d u r i n g the o b s e r v a t i o n program i n J u l y . The a p p a r e n t l y l a r g e l a t e n t heat t r a n s f e r t o the s u r f a c e a t n i g h t may have a r i s e n from the i n a p p l i c a b i l i t y o f our measurements o f Rn and H f o r s u r f a c e c o n d i t i o n s . However based on the r e s u l t s o f F u g g l e (1971) the Rn d i v e r g e n c e and H c o n v e r g e n c e would te n d to be c o m p l i m e n t a r y . I t i s i n t e r e s t i n g to note t h a t the heat f l o w towards the r o o f s u r f a c e (6) was nev e r g r e a t e r than 3 mWcm\"2. T h i s v a l u e i n c l u d e s a measure o f the a r t i f i c i a l h eat f l o w towards 151 20 CN I E u E 10 to LLl Q X 0 >-ai. ULi - 1 0 VANCOUVER, B.C. V.S.B. BLDG. JULY 24-25, 1972 H: 1.2m ABOVE ROOF / RESIDUAL (LE) | WIND U 1 - 2 (m/s) -201-1.5 1.1 1-2 1.1 1.2 1.1 1.1 1.1 1.3 1-5 DIR MISSING L 20 22 J U L Y 24 24 02 04 06 J U L Y 25 J F i g . 44 CN I E o E^ > to z X Z3 > LU 20 10 - 1 0 08 10 TIME (PST) N o c t u r n a l r o o f - t o p e n e r g y b a l a n c e . VANCOUVER, B.C. V.S.B. BLDG. JULY 27-28, 1972 H : 1.2 m ABOVE ROOF _ S RESIDUAL (LE) WIND -20 L 1 2 0.5 0.5 0.8 0.6 0.5 0.5 0.5 0.5 0.8 0.5 DIR MISSING I 1 1 1 I L 20 22 24 J U L Y 27 02 04 J U L Y 28 06 \u00C2\u00B1 J 08 10 TIME (PST) F i g . 45. N o c t u r n a l r o o f - t o p e n e r g y b a l a n c e . 152 the r o o f s u r f a c e , and hence i t can be c o n c l u d e d t h a t a r t i -f i c i a l h eat t h r o u g h t he r o o f does not s i g n i f i c a n t l y c o n -t r i b u t e to t h e r o o f - t o p e n e r g y b a l a n c e a t n i g h t . Energy B a l a n c e o f an Urban A r e a A l t h o u g h we may r e a d i l y s p e c i f y the g o v e r n i n g e n e r g y b a l a n c e e x p r e s s i o n f o r a l i m i t e d u r b a n - b u i l d i n g a i r volume, the t h r e e - d i m e n s i o n a l n a t u r e o f the p r o b l e m remains most f o r m i d a b l e ( s e e F i g . 2 ) . Some o f t h e s e c o m p l e x i t i e s may be a v o i d e d i f we can assume t h a t h o r i z o n t a l a d v e c t i o n and a r t i f i c i a l h eat g e n e r a t i o n a r e s m a l l w i t h i n the a r e a o f c o n c e r n . As an a p p r o x i m a t i o n , t h e s e a s s u m p t i o n s do not a p p e a r u n r e a s o n a b l e based on the s i t e c h a r a c t e r i s t i c s and a r t i f i c i a l h e a t c o m p u t a t i o n s . E x p e r i m e n t a l measurements of the e n e r g y b a l a n c e components o v e r a l i m i t e d urban a r e a t h e n become b a s i c a l l y a s p a t i a l p r o b l e m and a l l terms i n the h e a t b a l a n c e e x p r e s s i o n must r e f e r t o s p a t i a l l y i n t e g r a t e d a v e r a g e s . T h i s , however, i s s t i l l e x t r e m e l y d i f f i c u l t t o a c h i e v e , p a r t i c u l a r l y i n the measurement o f Rn and 6. M e a n i n g f u l e s t i m a t e s o f Rn s h o u l d i n c l u d e measurements above the s t r e e t canyons and r o o f s u r f a c e s . S i m i l a r l y , the measurement o f G must r e p r e s e n t an i n t e g r a t e d v a l u e f o r the v a r i o u s c i t y f a b r i c s o v e r the t h r e e - d i m e n s i o n a l s o l i d s u r f a c e a r e a . On the o t h e r hand, measurement o f LE 1 o r H o v e r the l i m i t e d urban a r e a may be a c h i e v e d from p o i n t measurements, p r o v i d e d t h a t t h e s e a r e made a t a h e i g h t above the l o c a l r o o f - t o p boundary l a y e r . At t h i s h e i g h t , we assume t h a t l o c a l i n h o m o g e n e i t i e s i n t h e s e n s i b l e and l a t e n t heat f l u x e s become i n s i g n i f i c a n t i n c o m p a r i s o n to t h e m e s o - s c a l e urban boundary l a y e r f l u x e s . The t u r b u l e n t eddy f l u x e s s h o u l d then be r e p r e s e n t a t i v e o f s p a t i a l l y i n t e g r a t e d v a l u e s . We s h a l l now examine our measurements i n t h i s c o n t e x t . In t h i s s t u d y , both Rn and G were d e r i v e d from p o i n t measurements. A c c o r d i n g l y , t h e i r u s e f u l n e s s i n t h e e n e r g y b a l a n c e e x p r e s s i o n f o r an urban a r e a a p p e a r s some-what d o u b t f u l . The measurement o f Rn a t 20 m above the urban r o o f s u r f a c e does p r o v i d e a good h o r i z o n t a l f i e l d -o f - v i e w t h a t i n c l u d e s the urban r o o f s u r f a c e , as w e l l as s t r e e t c a n y o n s , but the r a d i a n t e n e r g y r e c e i v e d by the s e n s o r from below r e f l e c t s p r i m a r i l y t h a t f r a c t i o n e m i t t e d by the immediate u n d e r l y i n g s u r f a c e , namely, the r o o f - t o p . The h o r i z o n t a l a r e a c o n t r i b u t i n g to 90 per c e n t o f the f l u x measured by the net r a d i o m e t e r a t 20 m above the r o o f en-compasses a c i r c l e o f r a d i u s equal to 60 m. G e n e r a l i z a t i o n o f t h e s e Rn r e s u l t s to t h a t o v e r the s t r e e t canyons may not be j u s t i f i e d , e s p e c i a l l y i n s i t u a t i o n s where l a r g e shadow a r e a s o c c u r a t s t r e e t l e v e l . As the net r a d i a t i o n f i e l d above s t r e e t canyons has not been p r e v i o u s l y i n v e s t i g a t e d i n any d e p t h , i t s c o n t r i -b u t i o n to the s p a t i a l l y i n t e g r a t e d Rn v a l u e o v e r an urban a r e a can o n l y be t r e a t e d q u a l i t a t i v e l y . The r e c e n t model o f the e f f e c t o f the t r a p p i n g o f s o l a r r a d i a t i o n by the c a nyon, advanced by C r a i g and Lowry ( 1 9 7 2 ) , s u g g e s t s t h a t the canyon l o w e r s the urban a l b e d o . Hence, we m i g ht e x p e c t an i n c r e a s e i n the e f f e c t i v e net s o l a r r a d i a t i o n above the s t r e e t canyon compared w i t h t h a t o v e r an open h o r i z o n t a l r o o f s u r f a c e . S i m i l a r l y , the e f f e c t i v e o u t g o i n g long-wave r a d i a t i o n from the canyon can be e x p e c t e d to be somewhat r e d u c e d i n c o m p a r i s o n w i t h t h a t o f an open h o r i z o n t a l s u r f a c e b ecause o f the v e r t i c a l w a l l s (Munn, 1966). These two p r o c e s s e s a r e l i k e l y to enhance the net r a d i a t i o n above the s t r e e t c a n y o n . In the a bsence o f q u a n t i f i a b l e e s t i m a t e s o f t h e s e e f f e c t s , we can o n l y s u g g e s t t h a t our p o i n t - m e a s u r e -ment o f Rn above the r o o f s u r f a c e i s l i k e l y to be some-what lower than t h a t o f a s p a t i a l l y i n t e g r a t e d a v e r a g e Rn f o r t h e s u r r o u n d i n g urban a r e a . The r o o f - t o p G measurements a r e o n l y i n d i c a t i v e o f one urban f a b r i c i n a h o r i z o n t a l p o s i t i o n , and c a n n o t be used s o l e l y to a r r i v e a t an e s t i m a t e o f s p a t i a l l y i n t e -g r a t e d v a l u e s o f G f o r the t h r e e - d i m e n s i o n a l s y s t e m . A s p a t i a l l y i n t e g r a t e d a v e r a g e o f G i s t h e r e f o r e v e r y d i f f i c u l t to a c h i e v e , but s i n c e we do have s i m u l t a n e o u s measurements 155 o f G i n t a r and c o n c r e t e s l a b s , p l a c e d h o r i z o n t a l l y on t h e urban r o o f s u r f a c e , we may be a b l e to i n d i c a t e upper l i m i t s to an a v e r a g e G v a l u e f o r the urban a r e a . An example o f the d i u r n a l b e h a v i o u r o f G i n v a r i o u s u rban f a b r i c s i s shown i n F i g . 46. The v a l u e s f o r c o n c r e t e and t a r were o b t a i n e d from s o i l heat f l u x p l a t e s embedded i n s l a b s o f the r e s p e c t i v e m a t e r i a l s p l a c e d on the urban r o o f s u r f a c e . I t can be seen t h a t the heat s t o r e d i n the t a r b l o c k i s q u i t e a p p r e c i a b l e ( a p p r o x i m a t e l y 70 per c e n t h i g h e r than t h a t o f the urban r o o f s u r f a c e ) . On t h i s p a r t i c u l a r day, G i n t h e t a r b l o c k was about 25 per c e n t o f the n e t r a d i a t i o n a t midday. I t i s n o t u n r e a s o n a b l e to s u g g e s t t h a t the G v a l u e f o r the t a r b l o c k p r o v i d e s an upper l i m i t to the amount o f e n e r g y t h a t can be s t o r e d o v e r the t h r e e - d i m e n s i o n a l s o l i d s u r f a c e d u r i n g the d a y t i m e . The a c t u a l s p a t i a l l y a v e r a g e d G w i l l be s i g n i f i c a n t l y l ower than t h i s upper l i m i t when the urban f a b r i c s o f v a r y i n g t h e r m a l c a p a c i t i e s a r e a l l t a k e n i n t o a c c o u n t . The s e n s i b l e heat f l u x v a r i a t i o n a t h e i g h t s o f 4 and 20 m above the urban r o o f s u r f a c e was p r e s e n t e d i n the p r e v i o u s c h a p t e r . As t h e s e measurements were c o n d u c t e d above the l o c a l r o o f - t o p boundary l a y e r , t h e y may be assumed i n d i c a t i v e o f s p a t i a l l y i n t e g r a t e d a v e r a g e s . A n o t h e r example o f the H measurements f o r the 4 m l e v e l above the r o o f i s g i v e n i n F i g . 47, a l o n g w i t h the p o i n t measurements F i g . 46. D i u r n a l b e h a v i o u r urban f a b r i c s . o f G i n v a r i o u s VANCOUVER, B.C. V.S.B. BLDG. JULY 5, 1972 Rn H : 4m ABOVE ROOF U R B A N A -I R O O F -10*- WIND U 4 (M/S) 2.1 2.7 3.2 3.1 2 . 2 2.9 2.5 1.9 2.1 1.8 1.4 I 1 1 1 1 I I I 06 08 10 12 14 16 18 20 TIME (PST) F i g . 47. Urban s e n s i b l e heat f l u x e s and p o i n t measurements o f Rn and G. 158 o f Rn and o f the r o o f - t o p G. In g e n e r a l , midday v a l u e s o f urban H were ~ 20 to 25 mWcm-2, when Rn was 60 mWcm\"2. I f we c o n s i d e r t h i s p o i n t measurement o f Rn t o be the lo w e r l i m i t o f an a r e a l l y i n t e g r a t e d a v e r a g e , we can p e r f o r m t h e f o l l o w i n g a n a l y s i s f o r the ene r g y b a l a n c e o f the urban a r e a . As an extreme c a s e , l e t us assume the upper l i m i t o f an av e r a g e G i d e n t i c a l to t h a t t y p i c a l l y i n the t a r b l o c k a t midday ( i . e . ~ 15 mWcm - 2). The urban e n e r g y b a l a n c e then y i e l d s a r e s i d u a l term ( t a k e n to be LE) o f - 20 t o 25 mWcm-2. Thus, the r e s u l t would i n d i c a t e a p p r o x i m a t e l y equal p a r t i t i o n i n g o f the heat u t i l i z a t i o n between s e n s i b l e and l a t e n t h e a t t r a n s f e r ( i . e . B ~ 1) aroun d noon. These v a l u e s o f Rn and G a r e c o n s i d e r e d extreme l i m i t s . A c c o r d -i n g l y * i f we assume H to be c o r r e c t , we can a n t i c i p a t e LE to be s l i g h t l y l a r g e r than H i n the r e a l s i t u a t i o n f o r the urban a r e a a t midday. T h i s b r i e f a n a l y s i s p r o v i d e s some i n s i g h t i n t o t h e energy p a r t i t i o n i n g o v e r an urban a r e a . The r e s u l t s a r e c o n s i s t e n t w i t h s i m i l a r f i n d i n g s from the ene r g y b a l a n c e e s t i m a t i o n s o v e r M o n t r e a l (Oke et al. 3 1 97 2 ) . C h a p t e r 7 SUMMARY OF CONCLUSIONS A yaw s p h e r e - t h e r m o m e t e r assembly ( Y S T ) , to measure s e n s i b l e h e a t f l u x d e n s i t y by the eddy c o r r e l a t i o n method, was b u i l t f o l l o w i n g t h e d e s i g n o f T a n n e r and T h u r t e l l ( 1 9 7 0 ) . From wind t u n n e l e x p e r i m e n t s the 'sphere c o n s t a n t ' was d e t e r m i n e d to be 1.57. T h i s v a l u e i s s i g n i f i c a n t l y l e s s than t h a t p r e d i c t e d t h e o r e t i c a l l y , namely, 2.25. I t i s i m p o r t a n t t h a t the yaw s p h e r e a p p r o a c h be m o d i f i e d to i n c l u d e an e x p e r i m e n t a l l y d e t e r m i n e d 'sphere c o n s t a n t . ' A n a l y s i s o f t h e e f f e c t s o f t i l t i n g t h e yaw s p h e r e a x i s i n d i c a t e s t h a t an e r r o r f o a p p r o x i m a t e l y 5 per c e n t per d e g r e e o f t i l t i s l i k e l y w i t h m o d e r a t e l y u n s t a b l e c o n d i t i o n s . T h i s e r r o r may a t t a i n 11 per c e n t per d e g r e e i n v e r y s t a b l e c o n d i t i o n s . A m o d i f i e d thermometer assembly was f o u n d n e c e s s a r y to p r o v i d e d u r a b i l i t y i n the f i e l d . In the f r e -quency domain the t u r b u l e n t heat f l u x c o u l d be measured t o an upper f r e q u e n c y l i m i t o f 8 Hz w i t h o u t s i g n i f i c a n t a t t e n u -a t i o n . F i e l d c o m p a r i s o n s o f the heat f l u x e s measured by the yaw s p h e r e - t h e r m o m e t e r system and a Bowen r a t i o a p p a r a t u s 159 160 p r o d u c e d s a t i s f a c t o r y agreement. Daytime c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s i n d i c a t e t h a t the d i f f e r e n c e between the two methods i s g e n e r a l l y l e s s than 10 per c e n t . D i r e c t measurements o f s e n s i b l e heat f l u x e s o v e r a g r a s s s u r f a c e a t L a d n e r , B.C. i n d i c a t e a d i u r n a l c o u r s e v e r y s i m i l a r to t h a t o f the net r a d i a t i o n . In g e n e r a l , h a l f - h o u r a v e r a g i n g p e r i o d s showed no phase l a g between s e n s i b l e heat and net r a d i a t i o n . F i e l d c o m p a r i s o n o f two YST systems gave good and c o n s i s t e n t agreement. A t a h e i g h t o f 2 m above ground and a h o r i z o n t a l c r o s s w i n d s e p a r a -t i o n o f 1.5 m, l e s s than 5 per c e n t v a r i a b i l i t y was n o t e d i n the heat f l u x measurements from the two systems. F o r a 19 m h o r i z o n t a l s e p a r a t i o n , the v a r i a b i l i t y was f o u n d t o be l e s s t h a n 20 per c e n t . These r e s u l t s g i v e s u p p o r t t o the b a s i c a s s u m p t i o n t h a t the s e n s i b l e heat f l u x i s r e l a -t i v e l y c o n s t a n t i n t he a t m o s p h e r i c boundary l a y e r . I t i s shown t h a t the p a r a m e t e r (a), advanced by P r i e s t l e y and T a y l o r ( 1 9 7 2 ) , can be a u s e f u l c l i m a t i c i n d i c a t o r , and hence l a r g e s c a l e p a r a m e t e r i z a t i o n o f s u r f a c e heat f l u x e s a p p e a r s e n c o u r a g i n g . The p a r t i t i o n i n g o f e n e r g y between s e n s i b l e and l a t e n t heat ( i . e . the Bowen r a t i o ) d u r i n g June and e a r l y J u l y 1972 shows a t e m p e r a t u r e dependence s i m i l a r to t h a t o f a s a t u r a t e d s u r f a c e w i t h an a l p h a v a l u e between a p p r o x i m a t e l y 1.00 and 1.10. 161 The a p p l i c a b i l i t y o f the eddy c o r r e l a t i o n t e c h n i q u e to the measurement o f s e n s i b l e heat t r a n s f e r between the atmosphere and the urban i n t e r f a c e i s d e m o n s t r a t e d f o r a l i m i t e d a r e a o f the c i t y o f V a n c o u v e r , B.C. D e s p i t e t h e enormous c o m p l e x i t i e s o f the t u r b u l e n t heat exchange p r o -c e s s e s , the urban s e n s i b l e heat f l u x p a t t e r n , o b t a i n e d d i r e c t l y a t h e i g h t s o f 1.2, 2, 4 and 20 m above r o o f - t o p l e v e l , l a r g e l y r e f l e c t e d time and magnitude changes i n the net r a d i a t i o n f i e l d d u r i n g the d a y t i m e . N o c t u r n a l urban s e n s i b l e heat f l u x e s , near r o o f - t o p l e v e l , were f o u n d t o be d i r e c t e d away from the a c t i v e s u r f a c e . T h i s i s r e v e r s e of t h e normal r u r a l c a s e . W i t h i n the l o c a l r o o f - t o p boundary l a y e r , t h e s e n s i b l e heat f l u x was f o u n d t o be a p p r o x i m a t e l y c o n s t a n t w i t h h e i g h t and space (20 per c e n t v a r i a t i o n ) d u r i n g t h e d a y t i m e . A t n i g h t , the e x i s t e n c e of f l u x d i v e r g e n c e and hence, n o n - c o n s t a n c y o f the heat f l u x , i s s u g g e s t e d . Daytime r o o f - t o p e n e r g y b a l a n c e i n d i c a t e s t h a t a s i g n i f i c a n t p o r t i o n o f the net r a d i a t i o n i s u t i l i z e d i n s e n s i b l e h e a t t r a n s f e r and i n hea t s t o r a g e i n the r o o f . The g r e a t e s t e n e r g y i s used i n s e n s i b l e heat t r a n s f e r , which i s about t h r e e times the heat s t o r a g e a t noon. A r t i f i c i a l e n e r g y f l u x d e n s i t y a p p e a r s to be i n s i g n i f i c a n t . With t y p i c a l v a l u e s o f net r a d i a t i o n o f 60 mWcm\"2, the s e n s i b l e heat f l u x i s about 30 mWcm-2 and the heat s t o r a g e 162 10 mWcm\"2. The r e s i d u a l term ( e q u a t e d t o l a t e n t h e a t ) i s a p p r e c i a b l e . On t h e o t h e r hand, t h e e r r o r s a s s o c i a t e d w i t h t h e use o f ne t r a d i a t i o n measurements to r e p r e s e n t a c t u a l s u r f a c e c o n d i t i o n s c o u l d have r e s u l t e d i n an o v e r e s t i m a t i o n o f t h e r e s i d u a l term up t o 7 mWcm-2. A c c o r d i n g l y , i f the s e n s i b l e h e a t f l u x measurements a r e n o t s y s t e m a t i c a l l y b i a s e d and the s t o r a g e term e r r o r s a r e s m a l l , the r e s i d u a l e n e r g y , c o n v e r t e d t o l a t e n t h e a t , would be 13 mWcm\"2 a t midday. T h i s would the n y i e l d a Bowen r a t i o f o r t h e r o o f -top s u r f a c e o f 2.3. I t would seem t h a t t h e r o l e o f l a t e n t h e a t t r a n s f e r f o r t h e r o o f - s u r f a c e needs f u r t h e r i n v e s t i -g a t i o n . The n o c t u r n a l r o o f - t o p e n e r g y b a l a n c e r e q u i r e d a l a t e n t h e a t term o f about 15 mWcm\"2 d i r e c t e d towards the a c t i v e s u r f a c e . The e n e r g y b a l a n c e o f the s u r r o u n d i n g a r e a was deduced from measurements o f s e n s i b l e h e a t f l u x and net r a d i a t i o n a t h e i g h t s above the r o o f - t o p boundary l a y e r . On t h e a s s u m p t i o n t h a t t h e s e p o i n t measurements a p p r o x i -m a t e l y r e f l e c t a r e a l l y i n t e g r a t e d a v e r a g e s , p a r t i t i o n i n g o f t h e heat between s e n s i b l e and l a t e n t heat y i e l d s a Bowen r a t i o o f ~ 1 a t midday. The c i t y does not app e a r to a c t as a \" d e s e r t \" as has sometimes been s u g g e s t e d . I t would seem t h a t t h e r o l e o f l a t e n t h e a t t r a n s f e r i s impor-t a n t f o r urban e n e r g y b a l a n c e c o n s i d e r a t i o n s . The a c c u r a t e d e t e r m i n a t i o n o f the e n e r g y b a l a n c e f o r an urban a r e a 163 remains o u t s t a n d i n g . T h i s t a s k can o n l y be a c c o m p l i s h e d by some means o f o b t a i n i n g s p a t i a l l y i n t e g r a t e d a v e r a g e s o f a l l the ene r g y b a l a n c e components. Such a f o r m i d a b l e and e s s e n t i a l t a s k was beyond the scope o f t h i s r e s e a r c h u n d e r t a k i ng. S u g g e s t i o n s f o r F u t u r e Work From t h i s r e s e a r c h , many q u e s t i o n s have been r a i s e d which w a r r a n t more a t t e n t i o n . Some o f t h e s e a r e o f f e r e d here as s u g g e s t i o n s f o r f u t u r e work. 1. The s p a t i a l v a r i a b i l i t y o f s e n s i b l e h e a t f l u x e s i n the a t m o s p h e r i c boundary l a y e r o v e r a f l a t u n i f o r m s u r f a c e s h o u l d be f u l l y examined. E x t e n s i v e and r e l i a b l e d a t a a r e r e q u i r e d to t e s t t h e f u n d a m e n t a l h y p o t h e s i s o f t h e c o n s t a n t f l u x l a y e r . 2. The pa r a m e t e r ( a ) , advanced by P r i e s t l e y and T a y l o r (1972) s h o u l d be i n v e s t i g a t e d f u r t h e r , to d e t e r m i n e i t s u s e f u l n e s s as a c l i m a t i c i n d i c a t o r and i n l a r g e s c a l e p a r a m e t e r i z a t i o n o f s u r f a c e h e a t f l u x e s o v e r v a r i o u s s u r f a c e s . T h i s c o u l d p r o v e most u s e f u l i n n u m e r i c a l m o d e l i n g o f t h e l a r g e r s c a l e a t m o s p h e r i c d y n a m i c s . 164 3. The s i g n i f i c a n t f r e q u e n c y domain f o r urban s e n s i b l e h e a t f l u x e s remains o u t s t a n d i n g . A d e t a i l e d s t u d y of the urban s e n s i b l e heat f l u x c o s p e c t r u m v i a o t h e r eddy c o r r e l a t i o n i n s t r u m e n t s ( e . g . a c o u s t i c anemometer-thermometer) i s s u g g e s t e d . F u r t h e r m o r e , the i n t e g r a t e d urban c o s p e c t r u m c o u l d then be compared w i t h s i m u l t a n e o u s measurements from the yaw s p h e r e - t h e r m o m e t e r s y s t e m . 4. The e f f e c t o f r a d i a t i v e exchanges between b u i l d i n g e l e m e n t s , and shadow a r e a s remain a r e a s f o r i n -v e s t i g a t i o n . E x t e n s i v e r a d i a t i o n measurements, w i t h i n an urban c a n y o n , may p r o v i d e i n s i g h t i n t o t h i s f o r m i d a b l e p r o b l e m . 5. Heat s t o r a g e o r r e l e a s e i n the v a r i o u s c i t y b u i l d i n g m a t e r i a l s ( i n c l u d i n g shadow a r e a s ) d e s e r v e s much a t t e n t i o n . A s p a t i a l a v e r a g i n g p r o c e d u r e , o v e r t h e t h r e e -d i m e n s i o n a l s u r f a c e o f an urban c a n y o n , i s s u g g e s t e d as an i n i t i a l a p p r o a c h t o t h i s t a s k . 6. S t u d i e s o f t h e c o u p l i n g between the e n e r g e t i c p r o c e s s e s a t s t r e e t l e v e l and t h o s e a t r o o f - l e v e l and above, a r e r e q u i r e d . 165 7. In t h i s s t u d y , the m agnitudes o f d i v e r g e n c e t e r m s , h e a t s t o r a g e i n the a i r and l a t e n t heat s t o r a g e f o r the l i m i t e d urban b u i l d i n g - a i r volume were c o n s i d e r e d n e g l i g i b l e . The v a l i d i t y o f t h e s e a s s u m p t i o n s needs to be e x p l o r e d . 8. The r o l e o f l a t e n t heat t r a n s f e r i n urban e n e r g y b a l a n c e s t u d i e s w a r r a n t s more a t t e n t i o n . 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H * C p C b C s i n e j G B M ] \" 1 E 0 / u where C : the s p e c i f i c heat a t c o n s t a n t p r e s s u r e p (1 .01 J g - l 0 K - M b : sp h e r e c o n s t a n t (1.57) 6 : the i n c l u d e d a n g l e between t h e p o r t s (45\u00C2\u00B0) G : a m p l i f i e r g a i n B : b r i d g e c o n s t a n t M : t r a n s d u c e r c o n s t a n t E\"0 : i n t e g r a t e d o u t p u t v o l t a g e from the b r i d g e u : mean h o r i z o n t a l wind speed T r a n s d u c e r C o n s t a n t (M) T h i s c o n s t a n t i s o b t a i n e d from t h e s p e c i f i c a t i o n s o f the B a r o c e l and i t s e l e c t r o n i c s . I t i s g i v e n by the f o l l o w i n g e x p r e s s i o n 174 175 f u l l s c a l e M = ( r a n g e s w i t c h p o s i t i o n ) ( p r e s s u r e r a n g e ) where f u l l s c a l e = 10 v o l t s p r e s s u r e range = 10 mb = 101* dyne cm\" range s w i t c h p o s i t i o n ( e . g . 0.03, 0.01, 0.003, 0.001) Thus, f o r a range s w i t c h p o s i t i o n o f 0.003 B r i d g e C o n s t a n t (B) The b r i d g e c i r c u i t i s shown i n F i g . 48. i s the v o l t a g e a p p l i e d to the b r i d g e ( i . e . the h i - p a s s f i l t e r e d a n a l o g p r e s s u r e s i g n a l ) and E 0 i s t h e b r i d g e o u t p u t ( t h e i m b a l a n c e ) . A c c o r d i n g l y , M = 1/3 v o l t s cm 2dyne -1 AT E. Ri + Ri\u00C2\u00BB + R 3 where a To = c o e f f i c i e n t o f r e s i s t a n c e o f the thermometer at T 0 (0.0033 \u00C2\u00B0 K \" 1 ) 176 177 B _ Ri, + R 3 (where R r e f e r s to t h e Ri + Ri* + R 3 a p p r o p r i a t e r e s i s t a n c e s shown i n F i g . 48) Thus, f o r a b r i d g e b a l a n c e o f Ri\u00C2\u00BB = 650ft ( i . e . the thermometer r e s i s t a n c e o f 1950ft) B = 1.53 x 10\"\" \u00C2\u00B0 K - 1 Example U s i n g the v a l u e s o f M and B above and an a m p l i f i c a t i o n g a i n (G) o f 290 H * 614 x 1 0 2 % u E 0 i n v o l t s fu\" i n cms\" 1 H i n mWcm\"2 Thus, w i t h a 30 min a v e r a g e E 0 v a l u e o f 0.0901 v o l t s and a mean wind speed (u) o f 296 cms\" 1 a t noon H = 18.6 mWcnr 2 "@en . "Thesis/Dissertation"@en . "10.14288/1.0101037"@en . "eng"@en . "Geography"@en . "Vancouver : University of British Columbia Library"@en . "University of British Columbia"@en . "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en . "Graduate"@en . "Sensible heat fluxes measured in and near Vancouver, B.C."@en . "Text"@en . "http://hdl.handle.net/2429/32331"@en .