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The mesoscale variability of insolation over the Lower Fraser Valley resolved by geostationary satellite… Benchimol, Nicole 1985

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THE MESOSCALE VARIABILITY OF INSOLATION OVER THE LOWER FRASER VALLEY RESOLVED BY \ GEOSTATIONARY SATELLITE DATA by NICOLE BENCHIMOL B . S c , The U n i v e r s i t y of B r i t i s h Columbia, 1981 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department of 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 t o the r e g u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA January 1985 © N i c o l e B e n c h i m o l , 1985 I n p r e s e n t i n g 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 o f t h e r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I agree t h a t t h e 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 r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f 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 g r a n t e d by t h e head o f my department o r by h i s o r her r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f Geography The U n i v e r s i t y o f B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date January 30, 1985. !-6 (3/81) i i ABSTRACT Assessments of the mesoscale v a r i a b i l i t y of t h e i n s o l a t i o n over the lower F r a s e r V a l l e y have been hampered by t h e inadequate s p a t i a l r e s o l u t i o n of the a v a i l a b l e p y r a n o m e t r i c d a t a . At p r e s e n t , the e s t a b l i s h m e n t of a dense ground-based o b s e r v i n g network i s e c o n o m i c a l l y i n f e a s i b l e . The a d a p t a t i o n of g e o s t a t i o n a r y s a t e l l i t e d a t a f o r e s t i m a t i n g i n s o l a t i o n i s an a t t r a c t i v e a l t e r n a t i v e . The a b i l i t y of a s i m p l e p h y s i c a l l y - b a s e d model ( G a u t i e r et a l . , 1980) t o r e s o l v e the h o u r l y mesoscale i n s o l a t i o n v a r i a b i l i t y i s e v a l u a t e d . The s a t e l l i t e - b a s e d e s t i m a t e s a r e shown t o be more coherent than t h e observ e d i n s o l a t i o n . D i s c r e p a n c i e s a r e a t t r i b u t e d t o the s p a t i a l a v e r a g i n g i n h e r e n t i n the s a t e l l i t e methodology. The e s t i m a t e s a r e found t o be i n s e n s i t i v e t o s p a t i a l a v e r a g i n g down t o a 3 x 3 p i x e l (about 2 13 km ) s c a l e . The e f f e c t s of s p a t i a l a v e r a g i n g a r e b e l i e v e d t o o ccur a t s m a l l e r s p a t i a l s c a l e s . The s a t e l l i t e - b a s e d e s t i m a t e s g e n e r a l l y d i s p l a y a good correspondence w i t h the observ e d i n s o l a t i o n . Maps of the mean h o u r l y e s t i m a t e d i n s o l a t i o n a r e o b t a i n e d w i t h a h i g h degree of a c c u r a c y due t o s m a l l s y s t e m a t i c m o d e l l i n g e r r o r s . The i n a b i l i t y of the model t o d i s t i n g u i s h between snow and c l o u d , and i t s s e n s i t i v i t y t o v a r i a t i o n s i n s u r f a c e a l b e d o i n t r o d u c e a r t i f a c t s i n maps of the c l e a r sky i n s o l a t i o n . On t h e o t h e r hand, the mesoscale v a r i a b i l i t y of i n d i v i d u a l h o u r l y f i e l d s cannot be r e s o l v e d u s i n g 'the s a t e l l i t e - b a s e d approach. E r r o r s f o r these e s t i m a t e s are so l a r g e t h a t t hey obscure the v a r i a b i l i t y of the i n s o l a t i o n f i e l d . The u s e f u l n e s s of the mapping proc e d u r e appears t o be l i m i t e d t o assessments of the average i n s o l a t i o n . TABLE OF CONTENTS PAGE ABSTRACT i i TABLE OF CONTENTS i v LIST OF FIGURES v i i LIST OF TABLES x i SYMBOLS AND ABBREVIATIONS x i i ACKNOWLEDGEMENTS xv i i i CHAPTER I INTRODUCTION 1 1 . 1 Background 1 1.2 Study O b j e c t i v e 5 1.3 T h e s i s O u t l i n e 6 CHAPTER I I A REVIEW OF GEOSTATIONARY SATELLITE-BASED METHODS FOR ESTIMATING INSOLATION 7 2.1 I n t r o d u c t i o n 7 2.2 G e o s t a t i o n a r y S a t e l l i t e - b a s e d Methods 8 2.2.1 S t a t i s t i c a l Models 8 2.2.2 P h y s i c a l l y - b a s e d Models 14 2.3 Summary and C o n c l u s i o n s 23 CHAPTER I I I DATA AND PROCESSING TECHNIQUES 26 3.1 The Study Area 26 3.1.1 G e n e r a l C l i m a t o l o g y 29 3.2 Data A r c h i v e s 30 3.2.1 S o l a r R a d i a t i o n Network Data 30 V 3.2.2 S a t e l l i t e Data 32 3.2.2.1 The GOES System 32 3.2.2.2 Image N a v i g a t i o n 33 3.2.2.3 Data C o n v e r s i o n 34 3.2.2.4 Data Merging 34 3.3 Data S t r a t i f i c a t i o n 35 3.4 The G a u t i e r A l g o r i t h m 39 3.4.1 Implementation of a Moving F l u x A v e r a g i n g A r r a y 39 3.4.2 C a l c u l a t i o n of A s t r o n o m i c a l Parameters 42 3.4.3 E s t i m a t i o n of O p t i c a l A i r Mass 43 3.4.4 E s t i m a t i o n of Water Vapour A b s o r p t i o n ........44 3.4.5 E s t i m a t i o n of R a y l e i g h S c a t t e r i n g 44 3.4.6 E s t i m a t i o n of Minimum B r i g h t n e s s 45 3.4.7 C a l c u l a t i o n of C l o u d T h r e s h o l d 46 3.4.8 E s t i m a t i o n of C l o u d A b s o r p t i o n 46 3.5 C o n c l u d i n g Remarks 47 Chapter IV SATELLITE CHARACTERIZATION OF THE MESOSCALE INSOLATION VARIABILITY 48 4.1 I n t r o d u c t i o n 48 4.2 Method of A n a l y s i s 48 4.3 R e s u l t s and D i s c u s s i o n 51 4.3.1 Network-based C o r r e l a t i o n s 51 4.3.2 S a t e l l i t e - b a s e d C o r r e l a t i o n s 53 4.3.3 Comparisons Between the Observed and E s t i m a t e d I n s o l a t i o n 55 4.3.4 I n s o l a t i o n E s t i m a t e d U s i n g 3 x 3 P i x e l A r r a y s 63 v i 4.3.5 S a t e l l i t e - b a s e d C o r r e l a t i o n s ( 3 x 3 p i x e l a r r a y s ) 66 4.4 Summary and C o n c l u s i o n s 66 Chapter V SATELLITE MAPPING OF INSOLATION 71 5.1 I n t r o d u c t i o n 71 5.2 Im p l e m e n t a t i o n of the Mapping Procedure 71 5.2.1 Minimum B r i g h t n e s s P r e d i c t i o n s 72 5.3 S a t e l l i t e - b a s e d Mean H o u r l y I n s o l a t i o n Maps 76 5.4 S p a t i a l V a r i a b i l i t y of the H o u r l y E s t i m a t e d I n s o l a t i o n 87 5.4.1 S p a t i a l C o r r e l a t i o n s 87 5.4.2 S p a t i a l Sampling Requirements f o r t h e H o u r l y E s t i m a t e d I n s o l a t i o n 88 5.5 Summary and C o n c l u s i o n s 99 Chapter VI SUMMARY AND CONCLUSIONS 101 FOOTNOTES 104 BIBLIOGRAPHY 105 APPENDIX A PROGRAM TO IMPLEMENT GAUTIER'S MODEL 112 A.1 Main Program 112 A.2 S u b r o u t i n e s 114 A.3 F u n c t i o n s 139 APPENDIX B COEFFICIENT OF DETERMINATION AND STANDARD ERROR OF ESTIMATE OF THE MINIMUM BRIGHTNESS REGRESSION MODEL 141 v i i LIST OF FIGURES F i g u r e C a p t i o n Page 2.1 The c l e a r sky model (from G a u t i e r e t a l . , 1980) ...15 2.2 The c l o u d y sky model ( a f t e r G a u t i e r e t a l . , 1980) .18 3.1 L o c a t i o n of the study a r e a 27 3.2 G e n e r a l i z e d l a n d - u s e map of the lower F r a s e r V a l l e y and i t s e n v i r o n s (from Environment Canada, 1973) 28 3.3 L o c a t i o n of the 12 s t a t i o n p y r a n o m e t r i c network ...31 3.4a,b Frequency d i s t r i b u t i o n s of the h o u r l y b r i g h t s u n s h i n e m o n i t o r e d a t Vancouver B.C. Hydro, A i r p o r t and UBC f o r : a. the p e r i o d 1 J a n u a r y 1968 - 31 December 1981 b. the data subset hours 37 3.5 The i n s o l a t i o n m o d e l l i n g sequence 41 4.1 Comparison between the i n s o l a t i o n o b s e r v e d a t A i r p o r t and a t UBC f o r the hours l i s t e d i n T a b l e 3.1 50 4.2a-d The d i s t a n c e - c o r r e l a t i o n f u n c t i o n s of the o b s e r v e d h o u r l y i n s o l a t i o n . a. a l l data b. c l e a r sky d a t a c. p a r t l y c l o u d y sky d a t a d. o v e r c a s t sky d a t a 52 v i i i 4.3a-d The d i s t a n c e c o r r e l a t i o n f u n c t i o n s of the s a t e l l i t e - e s t i m a t e d i n s o l a t i o n (based on 5 x 5 p i x e l a r r a y s ) . a. a l l d a t a b. c l e a r sky data c. p a r t l y c l o u d y sky d a t a d. o v e r c a s t d a t a 54 4.4a-m Comparisons between the o b s e r v e d and e s t i m a t e d h o u r l y i n s o l a t i o n . The l a t t e r a r e based on 5 x 5 p i x e l a r r a y s . a. a l l d a t a 56 b. Grouse Mountain d a t a c. N o r t h Vancouver d a t a d. Vancouver (B.C. Hydro B l d g . ) d a t a . e. UBC d a t a 60 f. A i r p o r t d ata g. Tsawwassen d a t a h. Langara d a t a i . A b b o t s f o r d C i t y d a t a 61 j . A b b o t s f o r d A i r p o r t d a t a k. L a n g l e y C i t y d a t a 1. P i t t Meadows da t a m. M i s s i o n C i t y d a t a 62 4.5 Comparison between the h o u r l y i n s o l a t i o n e s t i m a t e d on the b a s i s of 5 x 5 and 3 x 3 p i x e l a r r a y s 64 4.6 Comparison between the o b s e r v e d and e s t i m a t e d h o u r l y i n s o l a t i o n ( a l l d a t a ) . The l a t t e r a re based on 3 x 3 p i x e l a r r a y s 67 4.7a-d The d i s t a n c e - c o r r e l a t i o n f u n c t i o n s of the s a t e l l i t e - e s t i m a t e d i n s o l a t i o n (based on 3 x 3 p i x e l a r r a y s ) . a. a l l d a t a b. c l e a r sky d a t a c. p a r t l y c l o u d y sky d a t a d. o v e r c a s t sky d a t a 69 i x 5.1a,b The v a r i a t i o n of the c o e f f i c i e n t of d e t e r m i n a t i o n 2 (r ) of the minimum b r i g h t n e s s r e g r e s s i o n model. 2 a. h i s t o g r a m of r 2 b. s p a t i a l d i s t r i b u t i o n of r 73 5.2a-d A c t u a l and p r e d i c t e d d i u r n a l v a r i a t i o n of minimum b r i g h t n e s s f o r J u l i a n day 196/79. a. l a n d t a r g e t (38,28) b. l a n d t a r g e t (68,3) c. water t a r g e t (3,33) d. water t a r g e t (48,53) 75 5.3a-d S p a t i a l d i s t r i b u t i o n of the mean h o u r l y e s t i m a t e d i n s o l a t i o n . a. c l e a r sky da t a 77 b. p a r t l y c l o u d y sky d a t a 78 c. o v e r c a s t sky da t a 79 d. a l l data 80 5.4a-d S p a t i a l d i s t r i b u t i o n of the mean h o u r l y o b s e r v e d i n s o l a t i o n . a. c l e a r sky d a t a 81 b. p a r t l y c l o u d y sky d a t a 82 c. o v e r c a s t sky d a t a 83 d. a l l d a t a 84 5.5 L o c a t i o n s of the c e n t r a l p i x e l of 3 x 3 p i x e l a r r a y s used t o map the s a t e l l i t e - e s t i m a t e d i n s o l a t i o n , 85 5.6a-d V a r i a t i o n of the c o r r e l a t i o n of the s a t e l l i t e -based e s t i m a t e s w i t h d i s t a n c e from the c e n t r e of the study a r e a . a. c l e a r sky d a t a 89 b. p a r t l y c l o u d y sky d a t a 90 c. o v e r c a s t sky d a t a 91 d. a l l d a t a 92 X 5.7a-d V a r i a t i o n of the s t a n d a r d d e v i a t i o n of the i n s o l a t i o n d i f f e r e n c e s w i t h d i s t a n c e from the c e n t r e of the study a r e a . a. c l e a r sky d a t a 95 b. p a r t l y c l o u d y sky d a t a .96 c. o v e r c a s t sky d a t a 97 d. a l l d a t a 98 x i LIST OF TABLES Table T i t l e Page 3.1 C l a s s i f i c a t i o n of the h o u r l y d a t a i n t o c l e a r , p a r t l y c l o u d y and o v e r c a s t sky c l a s s e s 40 4.1 Comparisons between the o b s e r v e d ( K ^ Q ) and e s t i m a t e d ( K j ) i n s o l a t i o n ( t h e l a t t e r a r e based on 5 x 5 p i x e l a r r a y s ) 57 4.2 I n d i v i d u a l s t a t i o n c omparisons between the observ e d ( K ^ Q ) and e s t i m a t e d (K|) i n s o l a t i o n (the l a t t e r a r e based on 5 x 5 p i x e l a r r a y s ) ....59 4.3 Comparisons between the e s t i m a t e d i n s o l a t i o n based on 5 x 5 a r r a y s and 3 x 3 p i x e l a r r a y s ....65 4.4 Comparisons between the o b s e r v e d ( K ^ Q ) and e s t i m a t e d ( K l ) i n s o l a t i o n ( t h e l a t t e r a r e based on 3 x 3 p i x e l a r r a y s ) 68 x i i LIST OF SYMBOLS AND ABBREVIATIONS SYMBOL QUANTITY (upper case) A s u r f a c e a l b e d o ( d i m e n s i o n l e s s ) A n c l o u d a l b e d o ( d i m e n s i o n l e s s ) D d i f f e r e n c e between the i n s o l a t i o n e s t i m a t e d a t two l o c a t i o n s (kjm h ) D d i f f e r e n c e between the mean i n s o l a t i o n _ 2 -1 e s t i m a t e d a t two l o c a t i o n s (kjm h ) H t e r r a i n / s t a t i o n e l e v a t i o n (m) s a t e l l i t e - m e a s u r e d b r i g h t n e s s ( c o u n t s ) mean t a r g e t b r i g h t n e s s ( c o u n t s ) mean t a r g e t c l o u d b r i g h t n e s s ( c o u n t s ) p r e d i c t e d minimum b r i g h t n e s s ( c o u n t s ) m n o r m a l i z e d p r e d i c t e d minimum b r i g h t n e s s ( c o u n t s ) Kf u p w a r d - s c a t t e r e d r a d i a n c e observed by the s a t e l l i t e ( kJm~ 2h~ 1) _ p — i K^ t c l o u d t h r e s h o l d r a d i a n c e (kJm h ) e s t i m a t e d i n s o l a t i o n ( s o l a r i r r a d i a n c e -2 -1 a t the s u r f a c e ) (kJm h ) K l c i n s o l a t i o n f o r a c l e a r atmosphere ( k J m ~ 2 h ~ 1 ) _ 2 — 1 K j o o b s e r v e d i n s o l a t i o n (kjm h ) x i i i o K' M N T d U X, Y (lower case) a(u) a ( u 1 ) , a ( u 2 ) a ( u 1 ) f c , a ( u 1 ) f a a ( u 9 ) . , a ( u 0 ) . mean e s t i m a t e d i n s o l a t i o n (kJm h ) mean ob s e r v e d i n s o l a t i o n (kJm h ) s o l a r c o n s t a n t (kJm h ) e x t r a t e r r e s t r i a l s o l a r i r r a d i a n c e ( k Jm~ 2h~ 1) r e l a t i v e o p t i c a l a i r mass ( d i m e n s i o n l e s s ) number of o b s e r v a t i o n s or da t a p a i r s s u r f a c e dewpoint tem p e r a t u r e (°C) p r e c i p i t a b l e water vapour c o n t e n t i n a v e r t i c a l a t m o s p h e r i c column (cm) s t a t i o n v a r i a b l e names water vapour a b s o r p t i o n c o e f f i c i e n t f o r an o b l i q u e p a t h a n g l e ( d i m e n s i o n l e s s ) water vapour a b s o r p t i o n c o e f f i c i e n t s f o r s o l a r z e n i t h and s a t e l l i t e a z i m u t h a n g l e s , r e s p e c t i v e l y ( d i m e n s i o n l e s s ) water vapour a b s o r p t i o n of the incoming s o l a r r a d i a t i o n above and below c l o u d l e v e l , r e s p e c t i v e l y ( d i m e n s i o n l e s s ) water vapour a b s o r p t i o n of the s u r f a c e -r e f l e c t e d s o l a r r a d i a t i o n above and below c l o u d l e v e l , r e s p e c t i v e l y ( d i m e n s i o n l e s s ) © i n s t a n t a n e o u s E a r t h - S u n d i s t a n c e (km) x i v mean Eart h - S u n d i s t a n c e (km) f r a c t i o n a l t a r g e t c l o u d amount ( d i m e n s i o n l e s s ) Pearson product-moment c o r r e l a t i o n c o e f f i c i e n t ( d i m e n s i o n l e s s ) c o e f f i c i e n t of d e t e r m i n a t i o n ( d i m e n s i o n l e s s ) i p r e c i p i t a b l e water vapour c o n t e n t i n o b l i q u e a t m o s p h e r i c column (cm) e s t i m a t e d or ob s e r v e d i n s o l a t i o n a t s t a t i o n s X and Y, r e s p e c t i v e l y ( k J m T 2 h _ 1 ) mean e s t i m a t e d or mean observ e d i n s o l a t i o n a t s t a t i o n s X and Y, _ 2 - 1 r e s p e c t i v e l y (kJm h ) r e g r e s s i o n c o e f f i c i e n t s hour a n g l e (degrees) d i f f e r e n c e between the s a t e l l i t e s u b p o i n t l o n g i t u d e and the s t a t i o n l o n g i t u d e (degrees) z e n i t h a n g l e (degrees) c l o u d a b s o r p t i o n c o e f f i c i e n t ( d i m e n s i o n l e s s ) XV R a y l e i g h s c a t t e r i n g c o e f f i c i e n t f o r d i r e c t and d i f f u s e beam r a d i a t i o n , r e s p e c t i v e l y ( d i m e n s i o n l e s s ) a z i m u t h a n g l e between the Sun and the s a t e l l i t e (degrees) water vapour p a t h a n g l e (degrees) l a t i t u d e (degrees) c o n f i d e n c e margin of i n s o l a t i o n c o n t o u r s ( kJm~ 2h~ 1) s o l a r z e n i t h a n g l e (degrees) p r e c i p i t a b l e water vapour c o r r e c t i o n f a c t o r f o r l a t i t u d e and season ( d i m e n s i o n l e s s ) s o l a r d e c l i n a t i o n a n g l e (degrees) s t a n d a r d d e v i a t i o n of the i n s o l a t i o n o b s e r v e d over 12 p y r a n o m e t r i c s t a t i o n s _ 2 - 1 f o r a g i v e n hour (kJm h ) s t a n d a r d d e v i a t i o n of the s a t e l l i t e -measured minimum b r i g h t n e s s ( c o u n t s ) s t a n d a r d d e v i a t i o n of the e s t i m a t e d and o b s e r v e d i n s o l a t i o n , r e s p e c t i v e l y ( k J m~ 2h~ 1) s t a n d a r d d e v i a t i o n of the e s t i m a t e d or o b s e r v e d i n s o l a t i o n a t s t a t i o n s X and Y, - 2 - 1 r e s p e c t i v e l y (kJm h ) t h r e s h o l d v a l u e of the s t a n d a r d d e v i a t i o n of the i n s o l a t i o n d i f f e r e n c e s ( k J m " 2h~ 1 or %) x v i a t m o s p h e r i c t r a n s m i t t a n c e ( d i m e n s i o n l e s s ) t r a n s m i t t a n c e f o r a c l e a r atmosphere ( d i m e n s i o n l e s s ) a z i m u t h a n g l e of the Sun from s o u t h (degrees) a z i m u t h a n g l e of the s a t e l l i t e from south (degrees) X V I 1 ABBREVIATIONS GATE GARP ( G l o b a l A t l a n t i c R e s e a r c h P r o j e c t ) A t l a n t T r o p i c a l Experiment GMT Greenwich Mean Time (h) GOES G e o s t a t i o n a r y O p e r a t i o n a l E n v i r o n m e n t a l S a t e l l i t e LAT L o c a l Apparent Time (h) MBE Mean B i a s E r r o r ( k J m _ 2 h ~ 1 or %) METEOSAT M E T E O r o l o g i c a l S A T e l l i t e (a European g e o s t a t i o n a r y s a t e l l i t e ) — 2 -1 RMSE Root-Mean-Square-Error (kJm h or %) SE S t a n d a r d E r r o r of e s t i m a t e of the minimum b r i g h t n e s s ( c o u n t s ) SR S a t e l l i t e - m e a s u r e d n o r m a l i z e d r e f l e c t a n c e ( d i m e n s i o n l e s s ) VISSR V i s i b l e and I n f r a r e d Spin-Scan Radiometer cv c o e f f i c i e n t of s p a t i a l v a r i a b i l i t y (%) rpm r o t a t i o n s per minute x v i i i ACKNOWLEDGEMENTS I ex t e n d my warmest a p p r e c i a t i o n t o Dr. J.E. Hay f o r g u i d i n g t h i s s t u d y w i t h p a t i e n c e , c a r e and e n t h u s i a s m . I thank my second r e a d e r , Dr. D.G. S t e y n , f o r the many h e l p f u l s u g g e s t i o n s he has p r o v i d e d ; Mark Roseberry f o r h i s computer programming a s s i s t a n c e ; C l i f f o r d Raphael and N e i l Wanless f o r p o i n t s of a d v i c e and i n t e r e s t i n g d e b a t e . Thanks t o numerous o t h e r f r i e n d s from the Department of Geography a t U.B.C. f o r many e n j o y a b l e moments; p a r t i c u l a r l y those f i e n d s , R i c a r d o , Cleughy, S a l l y and Dan. L a s t l y , I'd l i k e t o e x t e n d a v e r y s p e c i a l t h a n k s t o D a v i d f o r h i s u n f l a g g i n g s u p p o r t . 1 CHAPTER I INTRODUCTION 1.1 Background R e s e a r c h and development of s o l a r r a d i a t i o n as a r e s o u r c e f o r energy a p p l i c a t i o n s have been c a t a l y z e d by the o i l embargo of the 1970s. A l t h o u g h w o r l d o i l p r i c e s have s i n c e d e c l i n e d , the l o n g - t e r m i n t e r e s t i n s o l a r r a d i a t i o n as an a l t e r n a t i v e and renewable energy s o u r c e remains h i g h . The i n f o r m a t i o n g e n e r a t e d over the l a s t decade has h i g h l i g h t e d both the need f o r r e l i a b l e assessements of the i n s o l a t i o n " ' a v a i l a b i l i t y and the l i m i t e d s p a t i a l coverage p r o v i d e d by c u r r e n t o b s e r v a t i o n a l networks ( S u c k l i n g and Hay, 1976; Hay and S u c k l i n g , 1979; W i l s o n , 1980; Hay, 1981; S u c k l i n g , 1982). A fundamental and r e l e v a n t f e a t u r e of the i n s o l a t i o n i s i t s s p a t i a l v a r i a b i l i t y . The i n s o l a t i o n v a r i a b i l i t y e x i s t s a t a v a r i e t y of s p a t i a l s c a l e s which a r e d e f i n e d by the s c a l e s of the phenomena t h a t c o n t r o l i t (Steyn e t a l . , 1981). Macro-5 5 s c a l e ( >10 m, >10 s) p a t t e r n s a r e p r i m a r i l y a r e s u l t of v a r i a t i o n s i n c l o u d i n e s s a s s o c i a t e d w i t h s y n o p t i c d i s t u r b a n c e s (Hanson, 1980). Topographic f a c t o r s a r e s i g n i f i c a n t a t the 2 5 2 5 mesoscale (10 - 10 m, 10 - 10 s ) . The i n s o l a t i o n v a r i a b i l may a r i s e from d i f f e r e n c e s i n s h a d i n g (Hay and S u c k l i n g , 1979) and e l e v a t i o n (Hay, 1981), or t h r o u g h o r o g r a p h i c and t h e r m a l c o n t r o l s on c l o u d d i s t r i b u t i o n ( A t w a t e r and B a l l , 1978; Bach, 1980; G r e e n l a n d , 1978; Hay, 1981). In a d d i t i o n t o topography, 2 l a r g e urban a r e a s may induce m o d i f i c a t i o n s i n the a t m o s p h e r i c p r o p e r t i e s of a r e g i o n . The a t t e n u a t i o n of s o l a r r a d i a t i o n by a i r p o l l u t a n t s and the enhancement of c i t y - c e n t e r e d c o n v e c t i v e c l o u d development are e s t a b l i s h e d e f f e c t s (Rouse et a l . , 1973; P e t e r s o n and S t o f f e l , 1980; Grosh, 1977). At the m i c r o s c a l e - 2 2 0 2 (10 - 10 m, 10 - 10 s) i n s o l a t i o n v a r i a t i o n s a r e c o n t r o l l e d by the g e ometric c h a r a c t e r i s t i c s ( i . e . s l o p e a n g l e , a z i m u t h and exposure) of the r e c e i v i n g s u r f a c e ( M o n t e i t h , 1973). The v a r i a b i l i t y of the i n s o l a t i o n a t a l l s p a t i a l s c a l e s i s , moreover, a f u n c t i o n of season and the time s c a l e over which i n s o l a t i o n i s i n t e g r a t e d (Hay and Hanson, 1984). The l a t t e r i s i n t i m a t e l y r e l a t e d t o o b s e r v a t i o n a l p r a c t i c e s . G e n e r a l l y , the h i g h e s t v a r i a b i l i t y o c c u r s over the s h o r t e s t time s c a l e s due t o random v a r i a t i o n s i n s o l a r r a d i a t i o n a s s o c i a t e d w i t h s h o r t - t e r m weather changes (Hanson, 1980). The p r a c t i c a l s i g n i f i c a n c e of t h e s e v a r i a t i o n s i s r e f l e c t e d i n the s p a t i a l r e p r e s e n t a t i v e n e s s of i n s o l a t i o n m o n i t o r i n g networks. In a r e p o r t t o the World M e t e o r o l o g i c a l O r g a n i z a t i o n , Gandin (1970a, 1970b) recommended a network 2 d e n s i t y of one s t a t i o n per 250,000 km ( s t a t i o n s e p a r a t i o n d i s t a n c e of about 500 km) t o r e s o l v e t h e m a c r o s c a l e mean monthly i n s o l a t i o n f i e l d . W h i l e t h e s e r e q u i r e m e n t s a r e r e a l i z e d i n networks o p e r a t e d by t h e Atmospheric Environment S e r v i c e i n Canada ( L a t i m e r , 1980), and the N a t i o n a l Weather S e r v i c e i n the ( c o n t i g u o u s ) U n i t e d S t a t e s ( S u c k l i n g , 1982), they are i n a d e q u a t e l y s u s t a i n e d on a g l o b a l b a s i s . Gandin's assessment i s not a p p l i c a b l e t o c o a s t a l or mountainous 3 r e g i o n s , where s i g n i f i c a n t c l i m a t o l o g i c a l g r a d i e n t s e x i s t . I n s o l a t i o n over mountainous a r e a s , i n p a r t i c u l a r , i s p o o r l y o b s e r v e d s i n c e h i g h maintenance c o s t s and d i f f i c u l t a c c e s s i b i l i t y i n h i b i t the i m p l e m e n t a t i o n of a m o n i t o r i n g programme commensurate w i t h the s p a t i a l c o m p l e x i t i e s of the r a d i a t i o n regime. Many s o l a r energy a p p l i c a t i o n s r e q u i r e d a t a a t meso- or s m a l l e r s p a t i a l s c a l e s (McVeigh, 1977). E x p e r i m e n t a l networks have been e s t a b l i s h e d t o a s s e s s the mesoscale i n s o l a t i o n v a r i a b i l i t y [Hay (1984) has r e v i e w e d s e v e r a l examples of such i n v e s t i g a t i o n s ] . U n f o r t u n a t e l y , most of t h e s e f i e l d s t u d i e s d i d not p r o v i d e a complete c h a r a c t e r i z a t i o n of s p a t i a l v a r i a b i l i t y s i n c e they were d e s i g n e d f o r s h o r t - t e r m o b s e r v a t i o n o n l y . The network e s t a b l i s h e d over th e lower F r a s e r V a l l e y of B r i t i s h Columbia i s e x c e p t i o n a l , i n s o f a r as d a t a were a c q u i r e d over a p e r i o d of 4.5 y e a r s . The v a r i a b i l i t y of the mesoscale i n s o l a t i o n over t h i s r e g i o n was noted t o have a s i g n i f i c a n t impact on the performance of d o m e s t i c hot water h e a t i n g systems (Hay, 1983). Due t o the p a u c i t y of o b s e r v a t i o n a l d a t a t h e r e a r e few, i f any, o t h e r i n v e s t i g a t i o n s of t h i s t y p e . V a r i o u s s t r a t e g i e s have been d e v e l o p e d t o e s t i m a t e i n s o l a t i o n a t l o c a t i o n s where d a t a a r e u n a v a i l a b l e . The t r a n s f e r of d a t a from i n s t r u m e n t e d s i t e s by e x t r a p o l a t i o n or i n t e r p o l a t i o n may be f e a s i b l e , depending on the r e q u i r e d a c c u r a c i e s . W i l s o n and P e t z o l d ( 1 9 7 2 ) , amongst o t h e r s , have shown t h a t i n s o l a t i o n d i f f e r e n c e s between s t a t i o n p a i r i n g s 4 i n c r e a s e w i t h s e p a r a t i o n d i s t a n c e . E r r o r s of e x t r a p o l a t i o n f o r the m a c r o s c a l e i n s o l a t i o n around network s i t e s i n B r i t i s h Columbia and A l b e r t a were d e t e r m i n e d by Hay and S u c k l i n g (1979). As an example, e x t r a p o l a t i o n t o 50 km r e s u l t e d i n an e s t i m a t e e r r o r w i t h i n 15% of the a c t u a l v a l u e b u t , i f an e r r o r of ±35% c o u l d be t o l e r a t e d , e x t r a p o l a t i o n t o . d i s t a n c e s of 400 km would be p o s s i b l e . H i g h e r a c c u r a c i e s can be a c h i e v e d u s i n g i n t e r p o l a t i o n p r o c e d u r e s . However, d a t a r e q u i r e m e n t s a r e n a t u r a l l y g r e a t e r . O p t i m a l i n t e r p o l a t i o n (Gandin, 1965; A l a k a , 1970) a c c o u n t s f o r b o t h the random e r r o r s of o b s e r v a t i o n and the s p a t i a l v a r i a b i l i t y of the i n s o l a t i o n f i e l d . T h i s method has been a p p l i e d t o assessments of the mesoscale i n s o l a t i o n over the lower F r a s e r V a l l e y (Hay, 1981). The e x i s t i n g network was found t o be i nadequate f o r the i n t e r p o l a t i o n of h o u r l y v a l u e s t o w i t h i n 10% of the o b s e r v e d mean. I t i s i m p o r t a n t t o r e a l i z e t h a t t h e s e e x t r a p o l a t i o n and i n t e r p o l a t i o n p r o c e d u r e s assume an i s o t r o p i c f i e l d and w i l l not y i e l d a p p r o p r i a t e assessments over r e g i o n s where d i r e c t i o n a l g r a d i e n t s a r e s t r o n g (Hay and S u c k l i n g , 1979). S o l a r r a d i a t i o n models based on more w i d e l y o b s e r v e d m e t e o r o l o g i c a l p a r a m e t e r s , such as b r i g h t s u n s h i n e or c l o u d i n e s s , have a l s o been used (e.g. A t w a t e r and Brown, 1974; D a v i e s e t a l . , 1975; S u c k l i n g and Hay, 1977). These models g e n e r a l l y p r o v i d e d a i l y e s t i m a t e s t o w i t h i n 11-20% of the o bserved i n s o l a t i o n . Few have been d e s i g n e d f o r h o u r l y assessments due t o u n c e r t a i n t i e s i n the s p e c i f i c a t i o n of c l o u d c h a r a t e r i s t i c s ( D a v i e s , 1980). S u c k l i n g and Hay (1979) have 5 shown t h a t a s i g n i f i c a n t improvement i n s p a t i a l coverage i s g a i n e d w i t h the i n c o r p o r a t i o n of m o d e l l i n g s i t e s , but they added t h a t such p r o c e d u r e s are i n e f f e c t i v e over l a r g e a r e a s d e v o i d of the n e c e s s a r y i n p u t p a r a m e t e r s . In t h i s r e s p e c t , m e t e o r o l o g i c a l s a t e l l i t e s r e p r e s e n t p o t e n t i a l l y u s e f u l t o o l s f o r e s t i m a t i n g i n s o l a t i o n . From a vantage p o i n t i n space, s a t e l l i t e s a r e c a p a b l e of c o l l e c t i n g r e l e v a n t i n f o r m a t i o n where c o n v e n t i o n a l network coverage i s s p a r s e or n o n - e x i s t e n t . S a t e l l i t e - b a s e d models have a l s o been shown t o p r o v i d e e s t i m a t e s w i t h a c c u r a c i e s comparable t o or b e t t e r than those d e r i v e d from ground-based p r o c e d u r e s (Raphael and Hay, 1984). 1.2 Study O b j e c t i v e The o b j e c t i v e of t h i s s tudy i s t o d e t e r m i n e whether i n s o l a t i o n e s t i m a t e s , d e r i v e d from a s a t e l l i t e - b a s e d p r o c e d u r e , can r e s o l v e the mesoscale v a r i a b i l i t y over the lower F r a s e r V a l l e y and i t s e n v i r o n s . I f t h i s approach i s s u c c e s s f u l , c e r t a i n a s p e c t s of the s a t e l l i t e - b a s e d f i e l d w i l l then be i n v e s t i g a t e d . A l t h o u g h network d e f i c i e n c i e s occur a t a l l s p a t i a l s c a l e s , the mesoscale i s w e l l - s u i t e d t o a p r e l i m i n a r y i n v e s t i g a t i o n of t h i s t y p e . I t p r o v i d e s a compromise between the s p a t i a l r e s o l u t i o n of the s e n s i n g system and the v e r y l a r g e s a t e l l i t e d a t a p r o c e s s i n g which would be r e q u i r e d t o r e s o l v e i n s o l a t i o n a t broader s p a t i a l s c a l e s . 6 1.3 T h e s i s O u t l i n e A g e n e r a l review of the methods f o r e s t i m a t i n g i n s o l a t i o n from s a t e l l i t e d a t a i s p r o v i d e d i n Chapter I I . Chapter I I I c o n t a i n s a d e s c r i p t i o n of the study a r e a , d a t a s a m p l i n g and p a r a m e t e r i z a t i o n s used i n the m o d e l l i n g p r o c e s s . The s u i t a b i l i t y of the s a t e l l i t e approach f o r mesoscale i n s o l a t i o n v a r i a b i l i t y assessments i s d e t e r m i n e d i n Chapter IV, and the mapping proc e d u r e i s a p p l i e d i n Chapter V. Chapter VI summarizes the r e s u l t s of t h i s i n v e s t i g a t i o n . 7 CHAPTER I I A REVIEW OF GEOSTATIONARY SATELLITE-BASED METHODS FOR ESTIMATING INSOLATION 2.1 I n t r o d u c t i o n S o l a r r a d i a t i o n i n c i d e n t a t the t o p of the atmosphere i s m o d i f i e d by a b s o r p t i o n and s c a t t e r i n g p r o c e s s e s w i t h i n the Earth-Atmosphere system. M e t e o r o l o g i c a l s a t e l l i t e s p r o v i d e an e x t e r n a l s e n s i n g p l a t f o r m c a p a b l e of m o n i t o r i n g the r a d i a n t energy s c a t t e r e d back t o space. However, a p r o c e d u r e i s r e q u i r e d t o deduce from these measurements the amount of s o l a r r a d i a t i o n which i s r e c e i v e d a t the E a r t h ' s s u r f a c e . The use of d e t a i l e d r a d i a t i v e t r a n s f e r models i s c i r c u m s c r i b e d by the l i m i t e d amount of i n f o r m a t i o n t h a t can be e x t r a c t e d from the s a t e l l i t e - m e a s u r e d r a d i a n c e s . C o n s e q u e n t l y , approaches have been s i m p l i f i e d f o r s a t e l l i t e a p p l i c a t i o n s t h r o u g h s t a t i s t i c a l p a r a m e t e r i z a t i o n s and s i m p l e p h y s i c a l l y - b a s e d models. Both r e q u i r e s a t e l l i t e v i s i b l e r a d i a n c e s t o i n f e r a t m o s p h e r i c a t t e n u a t i o n . S t a t i s t i c a l methods attempt t o c o r r e l a t e the s a t e l l i t e and s u r f a c e measurements, w h i l e p h y s i c a l l y - b a s e d p r o c e d u r e s e x p l i c i t l y model the r a d i a t i v e t r a n s f e r p r o c e s s e s . The more s u c c e s s f u l methods r e l y on the f r e q u e n t coverage p r o v i d e d by g e o s t a t i o n a r y s a t e l l i t e s t o account f o r d i u r n a l v a r i a t i o n s i n sky c o v e r . T h i s s t u d y w i l l a p p l y a p h y s i c a l l y - b a s e d p r o c e d u r e d e v e l o p e d by G a u t i e r e t a l . (1980). Models f o r e s t i m a t i n g 8 i n s o l a t i o n from g e o s t a t i o n a r y s a t e l l i t e d a t a w i l l be r e v i e w e d i n t h i s c h a p t e r i n o r d e r t o g a i n a p e r s p e c t i v e from which the s e l e c t i o n of the G a u t i e r approach can be a s s e s s e d . Some of these methods have been d i s c u s s e d e l s e w h e r e ; R i o r d a n and H u l s t r o m (1983) and E x e l l (1984), i n p a r t i c u l a r , p r o v i d e e x c e l l e n t summaries. 2.2 G e o s t a t i o n a r y S a t e l l i t e - b a s e d Methods 2.2.1 S t a t i s t i c a l Models These methods are g e n e r a l l y based on s i m p l e and m u l t i p l e l i n e a r r e g r e s s i o n s . Hay and Hanson (1978) used a s i m p l e r e l a t i o n s h i p between the s a t e l l i t e - m e a s u r e d n o r m a l i z e d r e f l e c t a n c e (SR)^ and a t m o s p h e r i c t r a n s m i t t a n c e , of the form: 0 = a + bSR (2.1) where, a and b a r e the r e g r e s s i o n c o e f f i c i e n t s . S i n c e 4> r e p r e s e n t s the f r a c t i o n of the e x t r a t e r r e s t r i a l s o l a r i r r a d i a n c e (K') which i s i n c i d e n t a t the s u r f a c e , E q u a t i o n 2.1 can be r e a r r a n g e d t o y i e l d i n s o l a t i o n ( K | ) : K j = K'(a + bSR) (2.1a) The model assumes an i n v e r s e l i n e a r v a r i a t i o n between i n s o l a t i o n and the s a t e l l i t e - m e a s u r e d r e f l e c t a n c e . Hence, b r i g h t e r scenes c o r r e s p o n d t o c l o u d i e r views and t h e r e b y t o a lower i n s o l a t i o n . The r e g r e s s i o n c o e f f i c i e n t s were d e v e l o p e d from d a t a 9 a c q u i r e d d u r i n g GATE (27 June - 20 September 1974) over the 2 3 3 B - s c a l e a r r a y (10 - 10 km), u s i n g s a t e l l i t e p i x e l s a t a 3 km r e s o l u t i o n . Comparisons w i t h s h i p - b o a r d o b s e r v a t i o n s showed t h a t the i n s o l a t i o n c o u l d be e s t i m a t e d t o w i t h i n 22% f o r h o u r l y v a l u e s , and 10% f o r d a i l y t o t a l s . P o o r e r r e s u l t s were o b t a i n e d when the model was v e r i f i e d f o r a m i d - l a t i t u d e l o c a t i o n (Raphael and Hay, 1984). The o r i g i n a l r e g r e s s i o n c o e f f i c i e n t s i n e f f e c t i v e l y a c c o u n t e d f o r the d i f f e r e n t p r o p e r t i e s of m i d - l a t i t u d e c l o u d s and t h e i r r e - e v a l u a t i o n was n e c e s s a r y t o improve m o d e l l i n g c a p a b i l i t i e s . H a r t and Nunez (1979) d e r i v e d s i m i l a r e x p r e s s i o n s f o r v a r i o u s l o c a t i o n s i n A u s t r a l i a . The mean a c c u r a c y of the d a i l y e s t i m a t e s was s i m i l a r t o t h a t r e p o r t e d by Hay and Hanson (1978). However, the performance of the model was found t o v a r y w i t h r e g i o n a l m e t e o r o l o g i c a l c o n d i t i o n s . E x e l l (1984) has i n d i c a t e d t h a t the s t a b i l i t y of the r e g r e s s i o n p arameters a, b ( E q u a t i o n 2.1) can be s i g n i f i c a n t l y a f f e c t e d by v a r i a t i o n s i n s u r f a c e a l b e d o and at m o s p h e r i c a e r o s o l c o n t e n t . A c o m p a r a t i v e l y s o p h i s t i c a t e d p r o c e d u r e was developed by T a r p l e y (1979) u s i n g m u l t i p l e l i n e a r r e g r e s s i o n s . The model r e q u i r e s v i s i b l e r a d i a n c e s from GOES and c o n v e n t i o n a l meteo-r o l o g i c a l ( s u r f a c e p r e s s u r e , p r e c i p i t a b l e water) o b s e r v a t i o n s . U n l i k e the Hay and Hanson approach, t h i s model a t t e m p t s t o t o account f o r v a r i a t i o n s i n the r a d i a t i v e p r o p e r t i e s of the atmosphere by s t r a t i f y i n g the d a t a a c c o r d i n g t o c l o u d amount. The h o u r l y i n s o l a t i o n i s e s t i m a t e d from the f o l l o w i n g 10 e x p r e s s i o n s : K| = a] + b^ose + c^Q + d}n + e 1 < I m / I p > 2 n < .4 (2.2a) K| = a2 + fc2cose + c 2 n ( I n / I ^ ) 2 n <_ .4 < 1.0 (2.2b) = c 3 + Jocose + c 3 ( I n / I ^ ) 2 n = 1.0 (2.2c) where 6 s o l a r z e n i t h a n g l e ^ t r a n s m i t t a n c e f o r a c l e a r atmosphere n f r a c t i o n a l t a r g e t c l o u d amount A I mean t a r g e t b r i g h t n e s s I mean t a r g e t c l o u d b r i g h t n e s s Ip p r e d i c t e d minimum b r i g h t n e s s Ip n o r m a l i z e d p r e d i c t e d minimum b r i g h t n e s s G i ' 6 i ' c i r e g r e s s i o n c o e f f i c i e n t s ( i = 1,3) d. ,e. l ' l The parameters n, I m and I a r e deduced from the s a t e l l i t e imagery; I i s e v a l u a t e d as a f u n c t i o n of the s o l a r z e n i t h and the S u n - s a t e l l i t e a z i m u t h a n g l e s (see S e c t i o n 3.4.6); I' i s d e r i v e d from I n o r m a l i z e d f o r a s o l a r z e n i t h a n g l e of p p * of 45° and a S u n - s a t e l l i t e azmuth a n g l e of 105°; ^ c i s det e r m i n e d e m p i r i c a l l y and i n c l u d e s a t t e n u a t i o n due t o R a y l e i g h s c a t t e r i n g , water vapour s c a t t e r i n g ( D a v i e s e t a l . , 1975) and water vapour a b s o r p t i o n (McDonald, 1960). The mean t a r g e t b r i g h t n e s s ( I m or I n ) and i t s p r e d i c t e d minimum v a l u e (Ip or Ip) a r e e x p r e s s e d as a r a t i o t o reduce the i n f l u e n c e of senso r 11 i n s t a b i l i t i e s ( T a r p l e y , 1979). The model uses a second-order r e l a t i o n s h i p between i n s o l a t i o n and the s a t e l l i t e - m e a s u r e d b r i g h t n e s s t o account f o r the form of the nominal c a l i b r a t i o n of the GOES v i s i b l e c h a n n e l ( J u s t u s and T a r p l e y , 1983). The c o e f f i c i e n t s of the r e g r e s s i o n e q u a t i o n s were d e v e l o p e d f o r 50 km x 50 km t a r g e t s , r e s o l v e d by 8 km p i x e l s , over the G reat P l a i n s r e g i o n of the U n i t e d S t a t e s . The h o u r l y i n s o l a t i o n was e s t i m a t e d t o w i t h i n 10%' under c l e a r s k i e s (n < . 4 ) , 30% under p a r t l y c l o u d y s k i e s (.4 ^ n < 1.0) and 50% under o v e r c a s t s k i e s (n = 1.0). D a i l y e s t i m a t e s were w i t h i n 10% of the o b s e r v e d mean i r r a d i a n c e . A l a r g e p r o p o r t i o n of the v a r i a n c e of the i n s o l a t i o n was a c c o u n t e d f o r by the cos0 term. The s a t e l l i t e - b a s e d b r i g h t n e s s r a t i o s a l s o became i m p o r t a n t parameters f o r c l o u d y c a s e s . A l t h o u g h o t h e r v a r i a b l e s ( i . e . i | / c , n) were s i g n i f i c a n t a t the 1% l e v e l , t h e i r c o n t r i b u t i o n t o the a c c u r a c y of the model was minor ( T a r p l e y , 1979). A s i m p l i f i e d v e r s i o n of t h e model based on a s i n g l e r e g r e s s i o n e q u a t i o n was s u b s e q u e n t l y produced ( T a r p l e y , 1981). The i n s o l a t i o n f o r a l l sky c o v e r c l a s s e s was e s t i m a t e d by: Kjr = a + bcosd + c ( I m / I p ) (2.3) E s t i m a t e s of the d a i l y t o t a l i n s o l a t i o n were o b t a i n e d w i t h an a c c u r a c y of ±12%. C o m p u t a t i o n a l and s u r f a c e - b a s e d d a t a r e q u i r e m e n t s were reduced at the expense of o n l y a s m a l l d e g r a d a t i o n i n e s t i m a t i o n a c c u r a c y . Brakke and Kanemasu (1981) d e v e l o p e d a s i m i l a r e x p r e s s i o n 12 f o r e s t i m a t i n g i n s o l a t i o n , where: K j = a + b(lm ~ I ) + c6 (2.4) m p The method i s based on the d i f f e r e n c e between, r a t h e r than the r a t i o of the mean t a r g e t b r i g h t n e s s and i t s e s t i m a t e d c l e a r b r i g h t n e s s . T h i s f o r m u l a t i o n appears t o be more s e n s i t i v e t o v a r i a t i o n s of b r i g h t n e s s w i t h i n a t a r g e t . The r e g r e s s i o n c o e f f i c i e n t s were d e r i v e d over the Great P l a i n s . The d a i l y i n s o l a t i o n was e s t i m a t e d t o w i t h i n 11% i n summer. Due t o c l o u d c o v e r c o n d i t i o n s which were not a d e q u a t e l y r e p r e s e n t e d by the r e g r e s s i o n , lower a c c u r a c i e s (±36%) were o b t a i n e d f o r w i n t e r e s t i m a t e s . I t must a l s o be r e c o g n i z e d t h a t , s i n c e the e r r o r s a r e r e l a t i v e , they w i l l appear l a r g e r i n w i n t e r as a r e s u l t of a lower mean i r r a d i a n c e . T a r p l e y ' s (1981) model ( E q u a t i o n 2.3) was m o d i f i e d by J u s t u s and T a r p l e y (1983) t o the form: K* = K* c + d(l2m - 1 2) (2.5) where 2 3 K^ c = acos0 + fccos d + ccos 6 (2.5a) K^ c i s t h e i n s o l a t i o n f o r a c l e a r atmosphere. T h i s v e r s i o n p r o v i d e s e s t i m a t e s of the d a i l y i n s o l a t i o n t o w i t h i n 10% of the o b s e r v e d mean and thus performs as w e l l as T a r p l e y ' s (1979) s t r a t i f i e d model. The r e g r e s s i o n models d i s c u s s e d above p a r a m e t e r i z e d i n s o l a t i o n from the s a t e l l i t e - m e a s u r e d b r i g h t n e s s . H i s e r and Senn (1981) dev e l o p e d a method which i n c o r p o r a t e s t h e s e 13 measurements s t r i c t l y as s u r r o g a t e s f o r c l o u d amount. T h e i r approach i n v o l v e d the d e r i v a t i o n of s u r f a c e - b a s e d r e l a t i o n s h i p s between i n s o l a t i o n and opaque c l o u d c o v e r . S a t e l l i t e b r i g h t n e s s was s u b s e q u e n t l y c o r r e l a t e d w i t h f r a c t i o n s of opaque c l o u d c o v e r t o e s t a b l i s h an i n d i r e c t c orrespondence between i n s o l a t i o n and s a t e l l i t e b r i g h t n e s s . The t r a n s f o r m s were p r e s e n t e d i n g r a p h i c a l f o r m a t . The method assumes t h a t the s a t e l l i t e - b a s e d measurements p r o v i d e i n f o r m a t i o n on sky cover e q u i v a l e n t t o s u r f a c e - b a s e d o b s e r v a t i o n s . However, the s a t e l l i t e b r i g h t n e s s d a t a have a d i f f e r e n t p h y s i c a l meaning. They i n t e g r a t e the e f f e c t s , not o n l y of c l o u d amount, but a l s o , c l o u d type and geometry, s u r f a c e i n t e r a c t i o n s and sensor response c h a r a c t e r i s t i c s . The i n f l u e n c e of the d i f f e r e n t o b s e r v a t i o n a l v i e w p o i n t s (above and below c l o u d l e v e l ) on the form of the r e l a t i o n s h i p i s not c o n s i d e r e d . There are a l s o a number of p o t e n t i a l s o u r c e s of e r r o r : s a t e l l i t e image n a v i g a t i o n a l o f f s e t s may i n t r o d u c e e r r o r s p a r t i c u l a r l y a t c l o u d boundaries;, c l o u d s s m a l l e r than the sensor f i e l d - o f - v i e w a r e not accounted f o r ; the use of opaque c l o u d c o v e r w i l l t e n d t o o v e r e s t i m a t e i n ' s o l a t i o n under c i r r u s c l o u d , and the a s y n c h r o n i c i t y of s a t e l l i t e and s u r f a c e o b s e r v a t i o n s may c o n t r i b u t e t o d i f f e r e n c e s i n p e r c e i v e d c l o u d c o v e r . No s y s t e m a t i c assessment of model performance i s p r o v i d e d a l t h o u g h the a u t h o r s i n d i c a t e a b i a s towards o v e r e s t i m a t i o n under o v e r c a s t c o n d i t i o n s . S t a t i s t i c a l models have been dev e l o p e d w i t h emphasis on the e f f i c i e n t p r o c e s s i n g of d a t a f o r p o t e n t i a l r o u t i n e 1 4 a p p l i c a t i o n . They p r o v i d e s i m p l e p r o c e d u r e s f o r e s t i m a t i n g i n s o l a t i o n . However, t h e s e methods p e r f o r m p o o r l y under c l o u d y c o n d i t i o n s due t o t h e i r i n a b i l i t y t o account f o r the complex r e l a t i o n s h i p s between c l o u d and a t m o s p h e r i c t r a n s m i t t a n c e . P h y s i c a l l y - b a s e d p r o c e d u r e s e x p l i c i t l y model r a d i a t i v e t r a n s f e r p r o c e s s e s and hence may p r o v i d e an improved c h a r a c t e r i z a t i o n of c l o u d i n t e r a t i o n s . Such methods a r e d e s c r i b e d i n the f o l l o w i n g s e c t i o n . 2.2.2 P h y s i c a l l y - b a s e d Models The model dev e l o p e d by G a u t i e r e t a l . (1980) i s r e p r e s e n t a t i v e of t h i s approach. The p r o c e d u r e r e q u i r e s c a l i b r a t e d GOES r a d i a n c e s a t p i x e l r e s o l u t i o n and i n f o r m a t i o n on the a b s o r p t i o n and s c a t t e r i n g p r o p e r t i e s of the atmosphere. S e p a r a t e a l g o r i t h m s a r e used t o e s t i m a t e i n s o l a t i o n f o r c l e a r and c l o u d y atmospheres. The c l e a r sky r a d i a n c e o b s e r v e d by the s a t e l l i t e ( Kt) i s c o m p r i s e d of b a c k - s c a t t e r e d and s u r f a c e - r e f l e c t e d r a d i a t i o n ( F i g u r e 2.1) and i s e x p r e s s s e d a s : Kt = K-'a + K'(1 - a ) [ l - a f u ^ J I l - a ( u 2 ) ] d - a} )A (2.6) where K' e x t r a t e r r e s t r i a l i r r a d i a n c e a, a 1 R a y l e i g h s c a t t e r i n g c o e f f i c i e n t s f o r d i r e c t and d i f f u s e beam r a d i a t i o n , r e s p e c t i v e l y a ( u 1 ) , a ( u 2 ) water vapour a b s o r p t i o n c o e f f i c i e n t s f o r s o l a r z e n i t h and s a t e l l i t e v i e w i n g a n g l e s , r e s p e c t i v e l y A s u r f a c e a l b e d o K' =K„cos0 K' a •A K ' ( l - a ) ( l - a ( u , ) ) A ( l - a , ) ( l - a ( u 2 ) ) z / \ SCATTERING \ / v y \ \ K ' ( l - a ) \ \ \ \ \ ABSORPTION \ / ABSORPTION / K ' l l - o r X l - a f u . J j A O - a , ) \ JG / N ^ K ' O - a X l - a ^ J j A a , I  SCATTERIN  \  K ' ( l - a ) ( , - a ( U l ) ) \ \ / K ' ( l - a ) ( , - a ( u , ) ) A F i g u r e 2.1 The c l e a r sky model (from G a u t i e r et a l . , 1980). R e f e r t o t e x t f o r d e f i n i t i o n of symbols. 1 6 The c l e a r sky a t t e n u a t i o n i s a p p r o x i m a t e d by R a y l e i g h s c a t t e r i n g and water vapour a b s o r p t i o n . S c a t t e r i n g c o e f f i c i e n t s a r e o b t a i n e d from summaries i n C o u l s o n (1959) w h i l e a b s o r p t i o n c o e f f i c i e n t s a re c a l c u l a t e d u s i n g e m p i r i c a l f u n c t i o n s d e v e l o p e d by P a l t r i d g e (1973): a(u) = 0.099u* 3 4 u > 0.5 cm (2.7a) a(u) = 0.14u' 4 4 u < 0.5 cm- (2.7b) where u = Usecfi (2.8) U i s the p r e c i p i t a b l e water c o n t e n t i n a v e r t i c a l a t m o s p h e r i c column and seed i s the a i r mass adjustment which depends on the water vapour p a t h a n g l e ( 6 ) . E q u a t i o n 2.6 i s s o l v e d f o r the s u r f a c e a l b e d o : A = (Kt - K'a)/K'(1 " a)[1 - a ( u 1 ) ] [ l - a ( u 2 ) ] ( 1 - a,) (2.9) and the s o l a r r a d i a t i o n i n c i d e n t a t the s u r f a c e (K|) i s e s t i m a t e d by: K| = K'(1 - a ) [ l - a ( u 1 ) ] ( l + ajA) (2.10) The r a d i a t i v e t r a n s f e r s i n a c l o u d y atmosphere ,are more complex due t o a d d i t i o n a l i n t e r a c t i o n s w i t h c l o u d s ( F i g u r e 2.2). The model i s o p t i m i z e d f o r low- t o m i d - l e v e l s t r a t i f o r m c l o u d s . A tmospheric water vapour i s p a r t i t i o n e d above and below c l o u d l e v e l w i t h 70% of the t o t a l a b s o r p t i o n a p p l i e d below the c l o u d base. R a y l e i g h s c a t t e r i n g i s s p e c i f i e d above 17 the c l o u d mass o n l y . C l o u d r e f l e c t i o n p l a y s a dominant r o l e i n a t t e n u a t i n g the incoming s o l a r r a d i a t i o n and i s i n f e r r e d from the s a t e l l i t e - m e a s u r e d b r i g h t n e s s . The a t t e n u a t i o n due t o c l o u d a b s o r p t i o n i s more d i f f i c u l t t o a s s e s s s i n c e measurements a r e seldom a v a i l a b l e and m o d e l l i n g i s l i m i t e d by a poor u n d e r s t a n d i n g of c l o u d m i c r o p h y s i c s . G a u t i e r e t a l . (1980) adopted a s i m p l e a p p r o x i m a t i o n which s p e c i f i e s c l o u d a b s o r p t i o n as a l i n e a r f u n c t i o n of c l o u d b r i g h t n e s s , v a r y i n g between 0% f o r no c l o u d t o 20% f o r maximum b r i g h t n e s s . I t i s argued t h a t b r i g h t n e s s i s r e l a t e d t o c l o u d t h i c k n e s s , and t h e r e b y , t o c l o u d a b s o r p t i o n . In r e a l i t y , the r e l a t i o n s h i p i s not a s t r a i g h t o r w a r d one. The r a d i a n c e m o n i t o r e d by the s a t e l l i t e over a c l o u d y atmosphere i s g i v e n by: Kt = K'a + K'(1 - o)[1 - a ( u 1 ) f c ] A n ( l - a 1 ) [ 1 - a ( u 2 ) t ] + K'(1 - o ) [ l - a ( u 1 ) t ] ( 1 - A n ) 2 ( 1 - $ ) 2 [ 1 - a ( U l ) b ] x A[1 - a ( u 2 ) b ] ( l - c ^ H l - a ( u 2 ) t ] (2.11) where v a r i a b l e s not p r e v i o u s l y d e f i n e d a r e : a ( U j ) t , a ( u 1 ) b water vapour a b s o r p t i o n of the incoming s o l a r r a d i a t i o n above and below c l o u d l e v e l , r e s p e c t i v e l y a ( u 2 ) t , a ( u 2 ) b water vapour a b s o r p t i o n of the s u r f a c e -r e f l e c t e d s o l a r r a d i a t i o n above and below c l o u d l e v e l , r e s p e c t i v e l y $ c l o u d a b s o r p t i o n A n c l o u d a l b e d o E q u a t i o n 2.11 i s s o l v e d f o r A n, which i s then used t o c a l c u l a t e K' =K„cos0 K ' a 1 £_ K . ( i - a ) ( i -a(u 1 ) ( )A 1 1 ( l - D i 1 ) ( t -a(u j ) l ) K' ( l - a ) ( l - a ( U l ) , ) ( l - A n ) J ( l - <J> ) 2 ( l -a (u 1 ) b )A ( l -a (u 2 ) 6 ) ( l -a , ) ( l -a (u 2 ) , ) JL s i \ SCATTERING \ / v y K-(l-«) \ / \ ABSORPTION / _ / K ' ( l - a ) ( l - a ( U l ) , ) A n ( 1 - « i ) / \ SCATTERING \ / / \ ABSORPTION \ / / / / K lA( l -a ( U j )J ( l -A n ) ( l - * ) ( ! - « , ) I \ SCATTERING ABSORPTION \^  j \ / ^ K ( l - a ) ( l - a ( U l ) t ) A n « , > _ / K ' ( l - a ) ( l - a ( U l ) , ) A „ K l A ( l - a ( u 2 ) b ) ( l - A „ ) ( l - . | > ) a I K l - A ( l - a ( u 1 X ) ( l - A . X l - * ) ABSORPTION ABSORPTION K - ( l - a ) ( l - a ( u , ) , ) ( l - A j ( l - * ) \ KI'A(I-B(U. (1-a(U2)b)An / \ ABSORPTION \ \ K l = K ' ( l - a ) ( l - a ( u 1 ) , ) ( l - A „ ) * x ( l - * ) ( l - a ( u , ) b ) / K U ( l - a ( u , ) , ) ABSORPTION / / K l A F i g u r e 2.2 The c l o u d y sky model ( a f t e r G a u t i e r et a l . , 1980). R e f e r t o t e x t f o r d e f i n i t i o n of symbols. 19 the i n s o l a t i o n a c c o r d i n g t o : K| = K'(1 - O ) [ 1 - a ( u 1 ) t 3 d - A n ) ( 1 - * ) [ 1 - a ( u 1 ) b ] (2.12) To determine whether the s a t e l l i t e d a t a r e p r e s e n t c l e a r or c l o u d y v i e w s , a t h r e s h o l d i n t e n s i t y i s c a l c u l a t e d . B r i g h t n e s s v a l u e s which exceed t h i s r e f e r e n c e a r e c l a s s i f i e d as c l o u d y and a r e p r o c e s s e d through the c l o u d y sky a l g o r i t h m . O t h e r w i s e , the c l e a r sky a l g o r i t h m i s implemented. C a l c u l a t i o n s a r e performed on a p i x e l - b y - p i x e l b a s i s t o r e s o l v e s p a t i a l v a r i a t i o n s i n the i n s o l a t i o n f i e l d . These e s t i m a t e s a r e s u b s e q u e n t l y averaged over 8 x 8 p i x e l a r r a y s t o compensate f o r v a r i a t i o n s i n the s e n s i t i v i t y of the e i g h t s a t e l l i t e v i s i b l e s e n s o r s and the asynchronous n a t u r e of the s a t e l l i t e and s u r f a c e o b s e r v a t i o n s . In an attempt t o a s s e s s the u s e f u l n e s s of t h i s s t r a t e g y , Raphael (1982) compared e s t i m a t e s of the i n s o l a t i o n averaged over 8 x 8 p i x e l a r r a y s w i t h t h o s e from 5 x 5 a r r a y s . H i s r e s u l t s r e v e a l e d no s i g n i f i c a n t d i f f e r e n c e s . A number of assumptions a r e i n h e r e n t i n the G a u t i e r model: (a) i n s t a n t a n e o u s r a d i a n c e s measured by the s a t e l l i t e a r e r e p r e s e n t a t i v e of c o n d i t i o n s over t h e i n t e r v a l of o b s e r v a t i o n ( g e n e r a l l y 30 or 60 m i n u t e s ) . The assumption i m p l i e s t h a t sky c o v e r remains r e l a t i v e l y i n v a r i a n t between measurements. W h i l e t h i s c o n d i t i o n may be s u s t a i n e d f o r c l e a r or o v e r c a s t sky c o v e r s , s i g n i f i c a n t d e p a r t u r e s may occur under p a r t l y c l o u d y s k i e s which a r e more v a r i a b l e i n time and space (Diak e t a l . , 1 9 8 2 ) . 20 S p a t i a l a v e r a g i n g i s an attempt t o reduce the s i g n i f i c a n c e of t h i s p o t e n t i a l source of e r r o r ; (b) broad-band p a r a m e t e r i z a t i o n s of a t m o s p h e r i c s c a t t e r i n g and a b s o r p t i o n are a p p l i e d a l t h o u g h the s a t e l l i t e sensor response i s between .55 and .75 Mm. Both s c a t t e r i n g and a b s o r p t i o n p r o c e s s e s a r e w a v e l e n g t h - s e l e c t i v e . In f a c t , a b s o r p t i o n of s o l a r r a d i a t i o n by water vapour o c c u r s p r i m a r i l y i n the n e a r - i n f r a r e d p o r t i o n of the s o l a r spectrum, beyond the bandwidth of the s a t e l l i t e ; (c) water vapour a b s o r p t i o n and R a y l e i g h s c a t t e r i n g a r e the o n l y c o n t r i b u t o r s t o a t m o s p h e r i c a t t e n u a t i o n . S c a t t e r i n g by a e r o s o l s and a b s o r p t i o n by ozone a r e n e g l e c t e d . The m o d e l l i n g of a e r o s o l (Mie) s c a t t e r i n g i s m a t h e m a t i c a l l y complex and would r e q u i r e i n p u t parameters ( i . e . p a r t i c l e s i z e and c o n c e n t r a t i o n ) which a r e not o b s e r v e d on a r o u t i n e b a s i s . However, a t t e n u a t i o n by a e r o s o l s may be a s i g n i f i c a n t f a c t o r i n urban e n v i r o n m e n t s . Ozone a b s o r p t i o n v a r i e s between 1.5 and 3% of the t o t a l s o l a r f l u x ( K o n d r a t y e v , 1969). Ozone a t t e n u a t i o n i s most i n t e n s e i n the u l t r a - v i o l e t but weak a b s o r p t i o n bands occur i n the v i s i b l e r e g i o n between .44 and .75 nm; (d) the c l o u d y sky a l g o r i t h m assumes a p l a n e - p a r a l l e l c l o u d l a y e r . A c t u a l c o n f i g u r a t i o n s w i l l be r e l a t i v e l y complex. McKee and Cox (1976) and D a v i s e t a l . (1978) suggest t h a t l a r g e e r r o r s i n r a d i a t i v e t r a n s f e r c o m p u t a t i o n s may r e s u l t from t h i s a p p r o x i m a t i o n ; (e) the G a u t i e r model does not account f o r c l o u d s s m a l l e r 21 than the s e n s o r f i e l d - o f - v i e w . I n s o l a t i o n may be o v e r e s t i m a t e d i n such c a s e s ; ( f ) s u r f a c e s c a t t e r i n g i s assumed t o be i s o t r o p i c . However, most s u r f a c e s e x h i b i t b i d i r e c t i o n a l s c a t t e r i n g . I s o t r o p y has been shown t o be an i n a p p r o p r i a t e assumption f o r the s c a t t e r i n g b e h a v i o u r of c l o u d s (Brennan and Bandeen, 1970). A d i r e c t consequence of (d) and ( f ) i s t h a t c l o u d b r i g h t n e s s may not be a r e l i a b l e i n d i c a t o r of c l o u d a b s o r p t i o n . C louds a r e s t r o n g d i r e c t i o n a l s c a t t e r e r s and complex c l o u d geometry may cause shadowing ( G a u t i e r et a l . , 1980) and i n c r e a s e the l a t e r a l l o s s of r a d i a t i o n (McKee and Cox, 1976). A l t h o u g h such f a c t o r s modulate c l o u d b r i g h t n e s s they may be u n r e l a t e d t o c l o u d a b s o r p t i o n c h a r a c t e r i s t i c s . The model has been t e s t e d i n v a r i o u s e n v i r o n m e n t s . V e r i f i -c a t i o n by G a u t i e r e t a l . (1980) f o r E a s t e r n Canada ( M o n t r e a l , Ottawa and Toronto) has shown t h a t the d a i l y i n s o l a t i o n can be e s t i m a t e d t o w i t h i n 9% of p y r a n o m e t r i c measurements. Raphael and Hay (1984) o b t a i n e d a s i m i l a r a c c u r a c y (±8%) f o r d a i l y e s t i m a t e s over the lower F r a s e r V a l l e y . Model performance v a r i e d w i t h sky c o v e r . E s t i m a t e s were d e r i v e d t o w i t h i n 4% f o r c l e a r s k i e s , 12% f o r p a r t l y c l o u d y s k i e s and 26% f o r o v e r c a s t s k i e s (Raphael and Hay, 1984). The model tends t o o v e r e s t i m a t e the i n s o l a t i o n under c l e a r and o v e r c a s t s k i e s w h i l e i t u n d e r e s t i m a t e s under p a r t l y c l o u d y c o n d i t i o n s . G a u t i e r and Diak (1983) r e c e n t l y m o d i f i e d the model t o i n c l u d e ozone a b s o r p t i o n and p a r a m e t e r i z a t i o n s of R a y l e i g h s c a t t e r i n g w i t h i n the bandwidth of the s a t e l l i t e . Water 22 vapour a b s o r p t i o n i s removed from a l b e d o c o m p u t a t i o n s a l t h o u g h broadband c o e f f i c i e n t s f o r R a y l e i g h s c a t t e r i n g , water vapour and ozone a b s o r p t i o n a r e r e t a i n e d i n the c a l c u l a t i o n of the i n s o l a t i o n . An adjustment f o r c l o u d s s m a l l e r than the f i e l d -o f - v i e w of the s a t e l l i t e sensor i s a l s o a p p l i e d . These r e v i s i o n s r e s u l t e d i n an i n c r e a s e i n the a c c u r a c y of the d a i l y e s t i m a t e s of about ±1%. A v a r i a n t of the G a u t i e r model was de v e l o p e d by Dedieux et a l . (1983) u s i n g METEOSAT v i s i b l e r a d i a n c e d a t a . There i s no s e p a r a t i o n of c l e a r and c l o u d y v i e w s . I n s t e a d , i n s o l a t i o n i s e s t i m a t e d from a g e n e r a l e x p r e s s i o n f o r the c l e a r sky i r r a d i a n c e and a c l o u d c o v e r m o d i f i e r based on the s a t e l l i t e measurements. V e r i f i c a t i o n of the method has shown t h a t the h o u r l y i n s o l a t i o n can be d e t e r m i n e d w i t h a r e l a t i v e a c c u r a c y of ±21%. However, t h i s s t a t i s t i c i s based on com p u t a t i o n s f o r o n l y one hour (1200 GMT). A s i m i l a r method was used by Moser and Raschke (1984) t o map the d a i l y i n s o l a t i o n over Europe and the M e d i t e r r a n e a n . M o n thly averages of the d a i l y t o t a l i n s o l a t i o n were w i t h i n 5 - 6% of t h e observ e d mean w h i l e i n d i v i d u a l d a i l y v a l u e s were e s t i m a t e d w i t h a c c u r a c i e s of ±10 - 14%. H a l p e r n (1984) approached the problem of e s t i m a t i n g i n s o l a t i o n from a unique p e r s p e c t i v e . S a t e l l i t e measurements of the u p w a r d - s c a t t e r e d r a d i a t i o n a t the t o p of the atmosphere a r e compared w i t h e s t i m a t e s o b t a i n e d from a s e t of e i g h t r a d i a t i v e t r a n s f e r models d e v e l o p e d by Dave and B r a s l a u (1975). The model which p r o v i d e s the b e s t e s t i m a t e i s then used t o compute the 23 i n s o l a t i o n . The model atmospheres a r e r e s o l v e d over 50 l a y e r s , each w i t h s p e c i f i e d c o n c e n t r a t i o n s of water vapour, ozone and and a e r o s o l . Two of the e i g h t models s i m u l a t e the i n f l u e n c e of a s i n g l e c l o u d l a y e r . Model c a l c u l a t i o n s a r e a p p l i e d over 83 wavebands, f o r 9 s o l a r z e n i t h a n g l e s and 18 v a l u e s of s u r f a c e a l b e d o . S p e c t r a l e s t i m a t e s of the u p w a r d - s c a t t e r e d f l u x a r e i n t e g r a t e d over the s a t e l l i t e bandwidth f o r comparison. The s a t e l l i t e d a t a a r e used f o r model s e l e c t i o n and a r e not r e q u i r e d as i n p u t t o the i n s o l a t i o n m o d e l l i n g p r o c e s s . The d e t a i l e d c o m p u t a t i o n s a r e performed once on a f u l l range of p o s s i b l e i n p u t v a l u e s and the r e s u l t s a r e s t o r e d i n a l o o k - u p t a b l e . The p r o c e d u r e was a p p l i e d t o t h r e e days of p r e d o m i n a n t l y c l o u d - f r e e c o n d i t i o n s , one of which a l s o e x p e r i e n c e d heavy c l o u d c o v e r f o r two h o u r s . The h o u r l y i n s o l a t i o n was c a l c u l a t e d t o w i t h i n 3% of the observed v a l u e s f o r c l e a r f l u x e s , and t o w i t h i n 6% f o r the c l o u d - m o d i f i e d f l u x e s . The h i g h a c c u r a c y of the c l o u d y sky e s t i m a t e s i s e s p e c i a l l y i n t e r e s t i n g g i v e n the r e l a t i v e l y poor r e s u l t s o b t a i n e d u s i n g s i m p l e r models. Such m o d e l l i n g c a p a b i l i t i e s were t e s t e d on a l i m i t e d s e t of c o n d i t i o n s and would r e q u i r e f u r t h e r e v a l u a t i o n . 2.3 Summary and C o n c l u s i o n s Approaches t o i n s o l a t i o n m o d e l l i n g u s i n g g e o s t a t i o n a r y s a t e l l i t e d a t a were d i s c u s s e d i n the p r e v i o u s s e c t i o n . Both s t a t i s t i c a l and p h y s i c a l l y - b a s e d p r o c e d u r e s were p r e s e n t e d . S t a t i s t i c a l methods c o r r e l a t e s a t e l l i t e and s u r f a c e measurements 24 and t h e r e b y c i r c u m v e n t the need t o model the a t m o s p h e r i c r a d i a t i v e t r a n s f e r p r o c e s s e s . V a r i o u s parameters have been used. The s a t e l l i t e d a t a a r e g e n e r a l l y i n c o r p o r a t e d as an index of c l o u d i n e s s . The e s t i m a t i o n p r o c e d u r e s a r e s t r a i g h t -f o r w a r d once the r e g r e s s i o n c o e f f i c i e n t s a r e c a l c u l a t e d . However, the s e methods r e l y on the a v a i l a b i l i t y and q u a l i t y of network measurements ( G a u t i e r e t a l . , 1980; H i s e r and Senn, 1981) and produce l e s s than than o p t i m a l r e s u l t s when a p p l i e d beyond the r e g i o n s f o r which they were d e v e l o p e d . P h y s i c a l l y -based models p r o v i d e a more g e n e r a l framework f o r e s t i m a t i n g i n s o l a t i o n s i n c e they a re p a t t e r n e d on the p h y s i c a l p r o c e s s e s r a t h e r than s i t e - s p e c i f i c o b s e r v a t i o n s . These models r e q u i r e a c a l i b r a t i o n of the v i s i b l e c h a n n e l t o t r a n s f o r m b r i g h t n e s s counts i n t o r a d i a n c e s . The v i s i b l e s e n s o r s on-board GOES a r e , i n f a c t , not w e l l c a l i b r a t e d . I n - f l i g h t c a l i b r a t i o n s have been-developed by i n t e r c o m p a r i s o n of common t a r g e t s viewed by g e o s t a t i o n a r y and p o l a r - o r b i t e r or a i r c r a f t - m o u n t e d c a l i b r a t e d r a d i o m e t e r s ( S m i t h and L o r a n g e r , 1977; Smith and Vonder Haar, 1980). However, the s e o b s e r v a t i o n s a r e not n e c e s s a r i l y synchronous and t a r g e t b r i g h t n e s s may v a r y . A l l models were d e s i g n e d f o r e s t i m a t i n g i n s o l a t i o n on h o u r l y or l o n g e r t i m e - s c a l e s . The models p r o v i d e d a i l y i n t e g r a t e d e s t i m a t e s w i t h a c c u r a c i e s which a r e c o m p a t i b l e w i t h c e r t a i n user r e q u i r e m e n t s ( T a r p l e y , 1981). P o o r e r e s t i m a t e s a r e o b t a i n e d on an h o u r l y b a s i s due t o the inadequate m o d e l l i n g of c l o u d e f f e c t s . B i d i r e c t i o n a l r e f l e c t i o n (Diak e t a l . , 1982), c l o u d a b s o r p t i o n ( T a r p l e y , 1979), and c l o u d v a r i a t i o n s over a 25 time i n t e r v a l not r e s o l v a b l e by GOES ( H a l p e r n , 1984) have been i d e n t i f i e d as problem a r e a s . Of the v a r i o u s m e t h o d o l o g i e s r e v i e w e d i n t h i s c h a p t e r , the p r o c e d u r e d e r i v e d by G a u t i e r e t a l . (1980) w i l l be adopted (the r e v i s e d form of the model w i l l not be implemented s i n c e i t was i n t r o d u c e d d u r i n g the l a t e r s t a g e s of t h i s s t u d y ) . I t i n c o r p o r a t e s a p h y s i c a l a p p r o a c h , and t h e r e f o r e , no major s i t e -s p e c i f i c r e v i s i o n s a r e n e c e s s a r y f o r i t s a p p l i c a t i o n over t h e F r a s e r V a l l e y r e g i o n . The method has been v e r i f i e d over p a r t s of the study area (Raphael and Hay, 1984) and, by comparison w i t h o t h e r approaches, has been shown t o produce s u p e r i o r e s t i m a t e s of the i n s o l a t i o n under p a r t l y c l o u d y and o v e r c a s t c o n d i t i o n s . These p r e l i m i n a r y a n a l y s e s have a l s o i n d i c a t e d t h a t e s t i m a t e s o b t a i n e d u s i n g the G a u t i e r model may be s u f f i c i e n t l y a c c u r a t e f o r a s s e s s i n g the mesoscale v a r i a b i l i t y . 26 CHAPTER I I I DATA AND PROCESSING TECHNIQUES 3.1 The Study A r e a The s t u d y a r e a embraces a d i v e r s e p h y s i c a l environment e x t e n d i n g from the Coast Mountains i n sou t h w e s t e r n B r i t i s h Columbia t o the l i m i t s of the lower F r a s e r V a l l e y i n a d j a c e n t Washington S t a t e ; bounded eastward by the Cascade Mountains and westward by Howe Sound and the S t r a i t of G e o r g i a ( F i g u r e 3.1). The lower F r a s e r V a l l e y i s c h a r a c t e r i z e d by f l a t or g e n t l y r o l l i n g topography of low t o moderate r e l i e f . I t s s u r f a c e l i e s g e n e r a l l y below 150 m, a l t h o u g h i s o l a t e d h i l l s may r i s e t o over 300 m. Northward, the Coast Mountains r i s e s t e e p l y t o average summit e l e v a t i o n s between 1,500 and 2,200 m, w i t h h i g h e r peaks predominant i n n o r t h e a s t e r n a r e a s . The t e r r a i n i s rugged and i n c i s e d w i t h deep g l a c i a l l y - s c o u r e d v a l l e y s , some of which a r e o c c u p i e d by l a r g e l a k e s . A f r i n g e of the Cascade Mountains extends i n t o s o u t h e a s t e r n p a r t s of the s t udy a r e a where i t i s r e p r e s e n t e d by prominent r i d g e s of e l e v a t i o n s l e s s than 1,000 m. N e a r l y 1.5 m i l l i o n i n h a b i t a n t s r e s i d e w i t h i n the C i t y of Vancouver and s u r r o u n d i n g urban c e n t r e s . The b u i l t - u p environment o c c u p i e s r o u g h l y 15% of the l o w l a n d and i s p r e d o m i n a n t l y r e s i d e n t i a l i n n a t u r e ( F i g u r e 3.2). South of the F r a s e r R i v e r , l a n d use i s l a r g e l y a g r i c u l t u r a l , w i t h i n t e r s p e r s e d p a t c h e s of woodland, r u r a l non-farm and urban 27 F i g u r e 3.1 L o c a t i o n of the s t u d y a r e a . The shape of the study a r e a r e f l e c t s the p r o j e c t i o n of a r e c t a n g u l a r a r r a y of p i x e l s onto the s u r f a c e of the E a r t h . mmmmmmmmm •<A i Y » v > y A W » W A w . v l v . ? y - i <: 0 5 10 F i g u r e 3.2 G e n e r a l i z e d land-use map of the lower F r a s e r V a l l e y and i t s e n v i r o n s (from Environment Canada, 1973). The i n s e t i n d i c a t e s the r e l a t i o n between the a c t u a l bounds of the study area and th o s e shown on the map. t o oo 29 a r e a s . Peat bogs are widespread i n south c o a s t a l r e g i o n s and t i d a l f l a t s extend up t o 9 km from the landward edge of the F r a s e r R i v e r D e l t a . Mountain s l o p e s a r e c o v e r e d by c o n i f e r o u s woodland w i t h b r u s h , s c r u b , and b a r r e n l a n d above the t r e e l i n e or on logged-over slopes-. 3.1.1 G e n e r a l C l i m a t o l o g y The l a r g e - s c a l e a t m o s p h e r i c c i r c u l a t i o n of t h i s r e g i o n i s dominated by a m o i s t w e s t e r l y f l o w o f f the P a c i f i c Ocean. The w e s t e r l y c i r c u l a t i o n tends t o be v i g o r o u s i n w i n t e r when m e r i d i o n a l temperature c o n t r a s t s a r e w e l l d e v e l o p e d (Hay and Oke, 1976). The predominant p r e s s u r e p a t t e r n i s t h a t of the A l e u t i a n Low which r e s u l t s i n a n o r t h e r l y or n o r t h w e s t e r l y f l o w . C y c l o n i c storms are f r e q u e n t i n w i n t e r . These o r i g i n a t e over the N o r t h P a c i f i c and c r o s s the c o a s t anywhere between the A l a s k a n Panhandle and n o r t h e r n C a l i f o r n i a ( S t a g e r and W a l l i s , 1966). C y c l o n e s which a f f e c t the study a r e a a r e u s u a l l y i n a deep o c c l u d e d s t a t e and t h e i r passage i s a s s o c i a t e d w i t h heavy p r e c i p i t a t i o n and c o o l t o c o l d t e m p e r a t u r e s . P r e c i p i t a t i o n over the lower F r a s e r V a l l e y i s p r e d o m i n a n t l y i n the form of r a i n . However, snow i s not uncommon i n w i n t e r . R e l a t i v e l y heavy s n o w f a l l s a r e e x p e r i e n c e d on the mid- t o upper s l o p e s of the Coast and Cascade Mountains (Hare and Thomas, 1979). W i n t e r o u t b r e a k s of m o d i f i e d A r c t i c a i r occur under the i n f l u e n c e of an i n t e n s e h i g h p r e s s u r e system c e n t e r e d over the w e s t e r n C o r d i l l e r a . Such e p i s o d e s a r e accompanied by sunny, f r i g i d weather. The 30 w e s t e r l i e s weaken i n summer and storm t r a c k s g e n e r a l l y l i e n o r t h of B r i t i s h C o l u m b i a . The n o r t h P a c i f i c H i g h b u i l d s o f f the c o a s t and summer c o n d i t i o n s a r e t y p i f i e d by extended p e r i o d s of c l e a r and mo d e r a t e l y warm weather. The mesoscale c l i m a t e i s modulated by topography and u r b a n i z a t i o n . Topographic e f f e c t s a r e observed i n the o r o g r a p h i c enhancement of c l o u d by the Coast and Cascade Mo u n t a i n s . Windward s l o p e s tend t o be c l o u d i e r , w e t t e r and r e c e i v e l e s s s o l a r r a d i a t i o n than a d j a c e n t v a l l e y l o c a t i o n s (Hay and Oke, 1976). The Vancouver I s l a n d Ranges and the Olympic Mountains which l i e t o the e a s t and s o u t h of the st u d y a r e a induce a rainshadow over the F r a s e r D e l t a . Under a n t i c y c l o n i c c o n d i t i o n s , l a n d and sea b r e e z e s t y p i c a l l y d e v e l o p . T h e i r i n f l u e n c e on the i n s o l a t i o n regime l i e s i n the t r a n s p o r t of p o l l u t a n t s w i t h i n the lower F r a s e r V a l l e y . S i n c e the sea-breeze i s b e t t e r d e v e l o p e d , t h e r e i s a tendency f o r a net t r a n s p o r t up the v a l l e y . The a t t e n u a t i o n of the incoming s o l a r r a d i a t i o n has been documented f o r v a r i o u s m i d - l a t i t u d e c i t i e s . Such an e f f e c t i s suggested f o r the case of Vancouver by Hay (1984). 3.2 Data A r c h i v e s 3.2.1 S o l a r R a d i a t i o n Network Data S o l a r r a d i a t i o n d a t a were d e r i v e d from a 12 s t a t i o n p y r a n o m e t r i c network ( F i g u r e 3.3). T h i s network was e s t a b l i s h e d as p a r t of a programme d e s i g n e d t o i n v e s t i g a t e v a r i o u s a s p e c t s 32 of the mesoscale i n s o l a t i o n over the lower F r a s e r V a l l e y (Hay, 1984). S o l a r r a d i a t i o n m o n i t o r i n g began on 1 June 1979, and t e r m i n a t e d on 1 January 1984, p r o v i d i n g a p p r o x i m a t e l y 4.5 y e a r s of c o n t i n u o u s o b s e r v a t i o n . H o u r l y o b s e r v a t i o n s of s o l a r i r r a d i a n c e and ambient a i r temperature were a v a i l a b l e a t each of the network s i t e s . S o l a r i r r a d i a n c e f o r a h o r i z o n t a l s u r f a c e was measured by a K i p p and Zonen pyranometer and i n t e g r a t e d over h o u r l y i n t e r v a l s u s i n g a Campbell S c i e n t i f i c Model CR21 da t a l o g g e r . I n s t r u m e n t a l a c c u r a c y was w i t h i n 5%, as v e r i f i e d by Hay and Wardle (1982). A d d i t i o n a l i n f o r m a t i o n on the network d e s i g n , d a t a c o l l e c t i o n , q u a l i t y c o n t r o l and a r c h i v i n g p r o c e d u r e s i s p r o v i d e d i n Hay (1984). 3.2.2 S a t e l l i t e Data 3.2.2.1 The GOES System Imagery c o v e r i n g B r i t i s h Columbia was a c q u i r e d from GOES-west, p o s i t i o n e d over the e q u a t o r a t 135°W l o n g i t u d e , a t an a l t i t u d e of a p p r o x i m a t e l y 36,000 km. The imaging system on-board the s p a c e c r a f t i s the VISSR which measures v i s i b l e r a d i a n c e s between 0.55 and 0.75 um u s i n g a l i n e a r a r r a y of e i g h t s e n s o r s . The s p a t i a l r e s o l u t i o n of the r a d i a n c e f i e l d 2 i s 0.64 km (0.8 km x 0.8 km) a t t h e n a d i r (Hambrick and P h i l l i p s , 1980). Away from t h i s p o i n t , r e s o l u t i o n d e t e r i o r a t e s and p i x e l s become d i s t o r t e d . P i x e l r e s o l u t i o n over the stu d y a r e a (50°N, 123°W) i s 1.42 km 2 (1.5 km x 0.984 km; a f t e r 33 Raphael and Hay, 1984). GOES a l s o performs i n f r a r e d imaging (10.5 - 12.6 Mm) and c u r r e n t l y has temperature sounding c a p a b i l i t i e s . Such f a c i l i t i e s were not used i n t h i s s t u d y . GOES i s s p i n - s t a b i l i z e d w i t h i t s s p i n a x i s p a r a l l e l t o the E a r t h ' s p o l a r a x i s . The s p i n of the s a t e l l i t e p r o v i d e s the w e s t - t o - e a s t motion f o r the VISSR, w h i l e the n o r t h - s o u t h motion i s o b t a i n e d by a s t e p p i n g - s c r e w mechanism. With the s a t e l l i t e r o t a t i n g a t 100 rpm, the VISSR scans the E a r t h f o r about 1/20th of each r e v o l u t i o n , and produces a f u l l E a r t h d i s c i n 18.2 minutes (Kroeck, 1976). On an o p e r a t i o n a l b a s i s , GOES p r o v i d e s imagery e v e r y h a l f - h o u r . The c h a r a c t e r i s t i c s of the GOES imaging system a re d e t a i l e d i n v a r i o u s r e p o r t s by the N a t i o n a l E n v i r o n m e n t a l S a t e l l i t e S e r v i c e ( J o h n s t o n e t a l . , 1 9 7 6 ; C o r b e l l e t a l . , 1976). F e r m e l i a (1982) d i s c u s s e s the s a t e l l i t e d e s i g n c o n f i g u r a t i o n and Crowe (1977) p r o v i d e s a summary of the d a t a p r e - p r o c e s s i n g p r o c e d u r e s . 3.2.2.2 Image N a v i g a t i o n F u l l r e s o l u t i o n s a t e l l i t e d a t a f o r the v i s i b l e c h a n n e l were o b t a i n e d i n d i g i t a l tape format from the Space S c i e n c e and E n g i n e e r i n g C e n t r e of the U n i v e r s i t y of W i s c o n s i n , a t Madison. The d a t a a r e based on an e i g h t - b i t b r i g h t n e s s s c a l e r a n g i n g from 0 - 255 c o u n t s . Image scenes were a b s t r a c t e d f o r the r e g i o n between 48° - 50°N and 121° - 125°W, c e n t e r e d on c o o r d i n a t e s (48°16'N, 123°15'W). Images were n a v i g a t e d w i t h a r e p o r t e d a c c u r a c y of ±1 p i x e l (Hambrick and P h i l l i p s , 1980). 34 N o n e t h e l e s s , the data which were r e c e i v e d from W i s c o n s i n c o n t a i n e d d i s c r e p a n c i e s f a r i n e x c e s s of t h i s v a l u e ( R a p h a e l , 1982; Wanless, 1983). The s a t e l l i t e images were r e - n a v i g a t e d u s i n g s o f t w a r e developed a t the U n i v e r s i t y of B r i t i s h C olumbia. The p r o c e d u r e r e q u i r e d the c o o r d i n a t e s of ground c o n t r o l p o i n t s which were o b t a i n e d by manual s e l e c t i o n on an image p r o c e s s o r (Comtal V i s i o n I ) . The r e s u l t a n t a c c u r a c y of n a v i g a t i o n was w i t h i n 1 - 2 p i x e l s . 3.2.2.3 Data C o n v e r s i o n The c o n v e r s i o n of the s a t e l l i t e - m e a s u r e d b r i g h t n e s s t o n o r m a l i z e d r e f l e c t a n c e was a c c o m p l i s h e d u s i n g a r e l a t i o n s h i p d e r i v e d by Smith and Vonder Haar (1980), i n the form: SR = 0.00154 + 0.000166-1 + 0.0000137-1 2 (3.1) where I i s the s a t e l l i t e b r i g h t n e s s count and SR i s i t s e q u i v a l e n t n o r m a l i z e d r e f l e c t a n c e . ' The n o r m a l i z e d r e f l e c t a n c e i s e x p r e s s e d as a d i m e n s i o n l e s s f r a c t i o n and can be t r a n s l a t e d i n t o energy u n i t s by m u l t i p l i c a t i o n w i t h the s o l a r c o n s t a n t . 3.2.2.4 Data Merging The s a t e l l i t e d a t a were c o l l e c t e d on a h a l f - h o u r l y b a s i s . However, the s o l a r i r r a d i a n c e was o b s e r v e d on an h o u r l y t i m e - s c a l e . The s a t e l l i t e - d e r i v e d e s t i m a t e s were merged or averaged over h o u r l y i n t e r v a l s t o e n a b l e comparisons between the observed and e s t i m a t e d i r r a d i a n c e s . The p r o c e d u r e i s d e s c r i b e d i n Raphael (1982) and Wanless (1983). The h a l f -35 h o u r l y e s t i m a t e s o b t a i n e d from t h r e e s u c c e s s i v e images were weighted a c c o r d i n g t o the t e m p o r a l r e p r e s e n t a t i v e n e s s over a g i v e n hour and t o t h e i r e x t r a t e r r e s t r i a l i r r a d i a n c e . T h i s l a t t e r w e i g h t i n g a t t r i b u t e s a g r e a t e r s i g n i f i c a n c e t o imagery c o l l e c t e d n e a r e r t o s o l a r noon. I f one of the s e images was not a v a i l a b l e then w e i g h t s f o r the o t h e r two were a d j u s t e d t o t o cover the hour. An e s t i m a t e was not produced f o r a g i v e n hour i f two (or more) c o r r e s p o n d i n g images were m i s s i n g . C e r t a i n problems a r i s e when e v a l u a t i n g the s a t e l l i t e e s t i m a t e s a g a i n s t p y r a n o m e t r i c o b s e r v a t i o n s . The p y r a n o m e t r i c i r r a d i a n c e s a r e broad-band h o u r l y averages o b t a i n e d from a h e m i s p h e r i c a l s e n s o r . By c o m p a r i s o n , the s a t e l l i t e e s t i m a t e s a r e based on n e a r - i n s t a n t a n e o u s r a d i a n c e o b s e r v a t i o n s , sampled over a l i m i t e d s p e c t r a l band by r a d i o m e t e r s s u b t e n d i n g a narrow f i e l d - o f - v i e w . G a u t i e r e t a l . (1980) a t t e m p t e d t o compensate f o r these d i s c r e p a n c i e s by a v e r a g i n g the e s t i m a t e d i n s o l a t i o n over 8 x 8 p i x e l a r r a y s ( S e c t i o n 2.2.2). 3.3 Data S t r a t i f i c a t i o n C o n s i d e r a t i o n s a s s o c i a t e d w i t h the c o s t and a v a i l a b i l i t y of the s a t e l l i t e d a t a have l i m i t e d t h i s study t o 31 days. These o b s e r v a t i o n s were s e l e c t e d from a range of s y n o p t i c and s e a s o n a l c o n d i t i o n s between the y e a r s 1979 and 1981. T h i s sample was t o o s m a l l t o p r o v i d e s t a t i s t i c a l l y m e a n i n g f u l assessments of the i n s o l a t i o n v a r i a b i l i t y on d a i l y or l o n g e r time s c a l e s . C o n s e q u e n t l y , a n a l y s e s were performed on h o u r l y d a t a u s i n g an e f f e c t i v e sample s i z e of 313 o b s e r v a t i o n s (see 36 be l o w ) . A n a l y s e s based on h o u r l y d a t a can be e x p e c t e d t o maximize the e s t i m a t e s of v a r i a b i l i t y . The a c c u r a c y of the p r e d i c t e d i n s o l a t i o n has been shown t o v a r y w i t h sky c o v e r . The d a t a were t h e r e f o r e s t r a t i f i e d i n t o c l e a r , p a r t l y c l o u d y and o v e r c a s t sky c l a s s e s t o a s s e s s the e f f e c t s of sky c o v e r . A g i v e n hour was c l a s s i f i e d by two i n d i c e s : (1) the c o e f f i c i e n t of s p a t i a l v a r i a b i l i t y ( c v ) , d e f i n e d by cv = a 1 2 / K| (3.2) where Kl i s t h e h o u r l y mean o b s e r v e d i n s o l a t i o n over the 12 p y r a n o m e t r i c s t a t i o n s and a 1 2 i s the s t a n d a r d d e v i a t i o n of the s e o b s e r v a t i o n s ; (2) the h o u r l y d u r a t i o n of b r i g h t s unshine (measured by a C a m p b e l l - S t o k e s r e c o r d e r ) . T h i s parameter p r o v i d e s a q u a n t i t a t i v e measure of sky c o v e r and i s more w i d e l y r e p o r t e d than the h o u r l y c l o u d amount. H o u r l y b r i g h t s u n s h i n e o b s e r v a t i o n s over t h e p e r i o d 1 January 1968 - 31 December 1981 were o b t a i n e d from the Atmospheric Environment S e r v i c e f o r Vancouver B.C Hydro, A i r p o r t and UBC ( F i g u r e 3.3). The f r e q u e n c y d i s t r i b u t i o n s drawn from t h e s e d a t a were s i m i l a r f o r the t h r e e l o c a t i o n s ( F i g u r e 3.4a), showing bimodal and s t r o n g l y p o l a r i z e d t e n d e n c i e s towards the extreme v a l u e s . A s u b s e t c o m p r i s i n g of hours used i n t h i s s t u d y were v e r i f i e d t o have s i m i l a r c h a r a c t e r i s t i c s ( F i g u r e 3.4b). On the b a s i s of t h e s e h i s t o g r a m s , the s u b s e t hours were t e n t a t i v e l y grouped i n t o a c l e a r sky c l a s s w i t h 10 6 0 0 • 5 0 0 -A V 4 0 0 -3 0 0 -2 0 0 -1 0 0 -o - ° - i r 0 1 S A M P L E S I Z E A : A I R P O R T 4 6 0 2 6 h r s V : V A N C O U V E R B C H Y D R O 4 6 0 2 6 " U : U B C 7 9 9 9 2 " A V , 2 3 4 5 6 7 8 9 1 0 B R I G H T S U N S H I N E H O U R S ( t e n t h s o f a n h o u r ) 6 0 0 5 0 0 -4 0 0 ->-o z LU O 3 0 0 -L i l tr 2 0 0 -1 0 0 -0 0 V u A : A I R P O R T V : V A N C O U V E R B C H Y D R O U : U B C S A M P L E S I Z E 3 1 3 h r s 1 2 3 4 5 6 7 8 B R I G H T S U N S H I N E H O U R S ( t e n t h s o f a n h o u r ) " T r 9 1 0 F i g u r e 3.4a,b Frequency d i s t r i b u t i o n s of the h o u r l y b r i g h t s u n s h i n e m o n i t o r e d a t Vancouver B.C. Hydro, A i r p o r t and UBC f o r : a. the p e r i o d 1 January 1968 - 31 December 1981 b. the data subset hours 38 t e n t h s of b r i g h t s u n s h i n e ; an o v e r c a s t sky c l a s s w i t h 0 t e n t h s of b r i g h t s u n s h i n e , and a p a r t l y c l o u d y sky c l a s s w i t h i n t e r m e d i a t e f r a c t i o n s of b r i g h t s u n s h i n e . S i n c e t h r e e r e f e r e n c e d i s t r i b u t i o n s were a v a i l a b l e , the f r a c t i o n of b r i g h t sunshine a t t r i b u t e d t o any g i v e n hour was d e t e r m i n e d from an average of the t h r e e v a l u e s . The above c l a s s i f i c a t i o n i n c o r p o r a t e s l i t t l e i n f o r m a t i o n on the s p a t i a l c h a r a c t e r i s t i c s of the d a t a . The b r i g h t s u n s h i n e r e c o r d s were d e r i v e d from a c o a s t a l g r o u p i n g of s t a t i o n s and may not r e p r e s e n t c o n d i t i o n s f u r t h e r i n l a n d . The c o e f f i c i e n t of v a r i a b i l i t y p r o v i d e s an a p p r o p r i a t e measure. T h i s s t a t i s t i c was computed f o r each hour u s i n g s o l a r i r r a d i a n c e o b s e r v a t i o n s from the 12 p y r a n o m e t r i c s t a t i o n s . S i n c e the c l e a r sky i n s o l a t i o n was r e l a t i v e l y u n i f o r m , c o r r e s p o n d i n g c o e f f i c i e n t s of v a r i a b i l i t y were a s s i g n e d an upper l i m i t of 10%. T h i s v a l u e was chosen t o account f o r the e f f e c t s of measurement e r r o r and minor v a r i a t i o n s i n o p t i c a l a i r mass a c r o s s the network. O v e r c a s t s k i e s a l s o t e n d t o be a s s o c i a t e d w i t h u n i f o r m c o n d i t i o n s . However, a l i m i t of 10% was judged t o o r i g o r o u s t o account f o r the e f f e c t s of a heterogeneous c l o u d c o v e r . In t h i s c a s e , a c l a s s l i m i t of 35% was a s s i g n e d . The hours which were grouped as c l e a r or o v e r c a s t by t h e b r i g h t s u n s h i n e r e c o r d s were r e v i s e d a c c o r d i n g t o t h e s e c r i t e r i a . Hours w i t h c o e f f i c i e n t s of v a r i a b i l i t y e x c e e d i n g t h e i r r e s p e c t i v e l i m i t s were r e c l a s s i f i e d as p a r t l y c l o u d y . The p r o c e s s r e s u l t e d i n a c o n s i d e r a b l e g a i n i n p a r t l y c l o u d y hours from both the c l e a r and o v e r c a s t sky c l a s s e s . 39 Samples of the s a t e l l i t e imagery a s s o c i a t e d w i t h a l l c l a s s e s were i n s p e c t e d t o determine whether any m i s c l a s s i f i c a t i o n had o c c u r e d . Only minor a d j u s t m e n t s were r e q u i r e d between the p a r t l y c l o u d y and o v e r c a s t sky c l a s s e s . The f i n a l g r o u p i n g s a r e l i s t e d i n Table 3.1. 3.4 The G a u t i e r A l g o r i t h m The g e n e r a l framework of the G a u t i e r model has been d i s c u s s e d i n S e c t i o n 2.2.2. The s p e c i f i c m o d e l l i n g p r o c e d u r e implemented i n t h i s s tudy was i d e n t i c a l t o the one d e s c r i b e d i n Raphael (1982). C e r t a i n a s p e c t s of the o r i g i n a l programme were a l t e r e d t o accomodate a more e x t e n s i v e study a r e a , but these were p u r e l y t e c h n i c a l m o d i f i c a t i o n s . The m o d e l l i n g sequence i s summarized i n F i g u r e 3.5 and a programme l i s t i n g i s p r o v i d e d i n Appendix A. 3.4.1 Implementation of a Moving F l u x A v e r a g i n g A r r a y The s t u d y a r e a conformed t o a p r i m a r y image composed of 60 x 120 p i x e l s c e n t e r e d on P i t t Meadows (49°13'N, 122°42'W). W i t h i n t h i s a r e a a secondary a r r a y c o n s i s t i n g of i x i p i x e l s ( i > 1) was s e l e c t e d as the u n i t over which f l u x a v e r a g i n g i s performed. The programme c u r r e n t l y o p e r a t e s i n two modes: Mode I g e n e r a t e s 12 secondary a r r a y s each c e n t e r e d over the network s t a t i o n s and i s analogous t o the method used by Raphael (1982); Mode I I g e n e r a t e s a secondary a r r a y which moves a c r o s s a p r i m a r y image and produces i r r a d i a n c e e s t i m a t e s f o r c o n t i g u o u s ( n o n - o v e r l a p p i n g ) a r r a y l o c a t i o n s . Computations 40 D A T E I Ml D I Y I Julian Day JUL 15 1979 196 19 200 SEP 12 255 13 256 14 257 20 263 OCT 03 20 24 31 276 293 297 304 JAN 12 1980 012 25 025 30 030 APR 14 30 MAY 20 22 JUN 01 08 19 JUL 01 03 14 15 AUG 12 18 16 105 121 141 143 153 160 171 183 185 196 197 225 231 239 SEP 01 245 09 253 17 261 MAY 22 1981 142 JUN 06 157 T I M E hour ending (LAT) 0500 0600 0700 0800 0900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 ANN N N B B D B B B B D B a a • B • B B B B B B B • • f l f l f l " " a a l l l l l l g ] a • 0 B B a a a a a a a •mi:::;;:" a a a a a a • • • • a B y " H H B H I I H 1 H a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a Q = C L E A R ; fjj = P A R T L Y C L O U D Y ; | = O V E R C A S T T O T A L S • a 12 e. 7 8 5 10 7 11 2 5 11 8 101 127 85 T O T A L : 3 1 3 h o u r s Table 3.1 C l a s s i f i c a t i o n of the h o u r l y data i n t o c l e a r , p a r t l y c l o u d y and o v e r c a s t sky c l a s s e s . The v a r i a b l e number of hours w i t h i n a day i s due t o s e a s o n a l v a r i a t i o n s i n d a y l e n g t h , m i s s i n g or poor q u a l i t y d a t a . 41 Step 1 : SELECT MODE MODE I : calculate solar fluxes for centered on the 12 network secondary arrays stations MODE I I : calculate solar fluxes for of secondary arrays of the an arbitrary grid primary image i Step 2 : INPUT PRIMARY IMAGE (60 x 120 pixels) Step 3 : SELECT SECONDARY ARRAY ( i X i ) ACCORDING TO MODE Step 4 : PROCESS SECONDARY ARRAYS a) perform quality control check b) calculate atmospheric absorption c) determine clear/cloudy pixel threshold d) calculate secondary array instantaneous solar fluxes Step 5 : REPEAT STEPS 2, 3, 4, 5 UNTIL THERE ARE NO MORE ' PRIMARY IMAGES TO PROCESS Step 6 : MERGE INSTANTANEOUS SOLAR FLUXES TO FORM HOURLY INSOLATION ESTIMATES I Step 7 : OUTPUT HOURLY INSOLATION ESTIMATES ure 3.5 The i n s o l a t i o n m o d e l l i n g sequence. 42 begin a t the t o p , l e f t - m o s t window ( f a c i n g v i e w e r ) and proceed s e q u e n t i a l l y u n t i l no more d a t a are a v a i l a b l e . The programme does not generate an a r r a y beyond the l i m i t s of the p r i m a r y image. Both these modes of a n a l y s i s were implemented i n t h i s s t u d y . 3.4.2 C a l c u l a t i o n of A s t r o n o m i c a l Parameters The s o l a r r a d i a t i o n i n c i d e n t on a h o r i z o n t a l s u r f a c e a t the t o p of the atmosphere (K') was c a l c u l a t e d from: where K* i s the s o l a r c o n s t a n t (4871 kJm h~ ) and (d/d) i s the c o r r e c t i o n f o r the d e p a r t u r e of t h e a c t u a l Earth-Sun d i s t a n c e (d) from i t s mean ( d ) . The c o s i n e of the s o l a r z e n i t h a n g l e (6) was o b t a i n e d by: $ i s the l a t i t u d e , £ i s the s o l a r d e c l i n a t i o n a n g l e , and h i s the hour a n g l e (degrees) which was d e t e r m i n e d by: K' = K * ( d / d ) 2 c o s 0 (3.3) cos0 = sin$sin£ + cos$cos^cosA (3.4) h = 15-|12 - LAT| (3.5) where LAT i s the l o c a l a pparent time i n h o u r s . The a z i m u t h a n g l e of the Sun from south (w) was c a l c u l a t e d u s i n g : (3.6) 43 The s a t e l l i t e a z i m u t h a n g l e from south (w g) was g i v e n by: a> = cos ^ s tan$ tanA/^jtan $ + (tan$/tanA) + 1} (3.7) where A i s the d i f f e r e n c e between the s a t e l l i t e s u b - p o i n t l o n g i t u d e (135°W) and the s t a t i o n l o n g i t u d e . The a z i m u t h between the sun and the s a t e l l i t e (7) was d e t e r m i n e d from the d i f f e r e n c e between co and co : s 7 = I " - " s l (3.8) S i n c e the s a t e l l i t e i s g e o s t a t i o n a r y , i t s a z i m u t h i s f i x e d f o r a g i v e n l o c a t i o n a t the E a r t h ' s s u r f a c e . The a z i m u t h a n g l e of GOES-west v i s - a - v i s P i t t Meadows was 16.1°. T h i s v a l u e was assumed t o a p p l y over the e n t i r e study a r e a . V a r i a t i o n s from t h i s v a l u e of up t o 0.8° were known t o o c c u r . However, they have been shown t o be of minor s i g n i f i c a n c e ( R a p h a e l , 1982). 3.4.3 E s t i m a t i o n of O p t i c a l A i r Mass The o p t i c a l a i r mass was r e q u i r e d i n the d e t e r m i n a t i o n of water vapour a b s o r p t i o n a t s o l a r and s a t e l l i t e - v i e w i n g z e n i t h a n g l e s . The r e l a t i v e o p t i c a l a i r mass (M) was c a l c u l a t e d from: M = exp(-H/8243)/[cos0 + 0.15(93.885 - 0 ) ~ 1 * 2 5 3 ] (3.9) where H i s the e l e v a t i o n (meters) and © i s the z e n i t h a n g l e ( d e g r e e s ) . T h i s e x p r e s s i o n a c c o u n t e d f o r the r e d u c t i o n i n o p t i c a l a i r mass w i t h e l e v a t i o n (McDonald, 1960) and i n c o r p o r a t e d a 44 c o r r e c t i o n f o r l a r g e s o l a r z e n i t h a n g l e s ( K a s t e n , 1966). The e l e v a t i o n a t a g i v e n p i x e l l o c a t i o n was e s t i m a t e d by l i n e a r i n t e r p o l a t i o n of the 4 n e a r e s t v a l u e s o b t a i n e d from a dense (1 km) ge o g r a p h i c g r i d of e l e v a t i o n p o i n t s . 3.4.4 E s t i m a t i o n of Water Vapour A b s o r p t i o n F o l l o w i n g G a u t i e r e t a l . (1980), water vapour a b s o r p t i o n was c a l c u l a t e d u s i n g f u n c t i o n s d e v e l o p e d by P a l t r i d g e (1973). The p r e c i p i t a b l e water (U) was p a r a m e t e r i z e d i n terms of s u r f a c e dewpoint temperature ( T ^ ) , based on Smith's (1966) r e l a t i o n s h i p : 0 = F T T exp(0.0707-T d) (3.10) where U i s i n cm; T^ i s i n °C; X i s a d i m e n s i o n l e s s c o r r e c t i o n f a c t o r f o r s t a t i o n l a t i t u d e and season and i s o b t a i n e d from Smith (1966). S i n c e the G a u t i e r model i s r e l a t i v e l y i n s e n s i t i v e t o v a r i a t i o n s i n p r e c i p i t a b l e water ( R a p h a e l , 1982), dewpoint t e m p e r a t u r e s observed by the Atmospheric Environment S e r v i c e a t UBC were assumed t o r e p r e s e n t c o n d i t i o n s elsewhere i n the v a l l e y . P r e c i p i t a b l e water f o r mountainous r e g i o n s ( d e f i n e d by e l e v a t i o n s g r e a t e r than 500 m) was a s s i g n e d a v a l u e 20% lower than the v a l l e y e s t i m a t e . 3.4.5 E s t i m a t i o n of R a y l e i g h S c a t t e r i n g S c a t t e r i n g c o e f f i c i e n t s f o r d i r e c t (a) and d i f f u s e (e^) beam r a d i a t i o n were based on d a t a from C o u l s o n (1959). The d i f f u s e beam s c a t t e r i n g c o e f f i c i e n t was assumed t o be 45 independent of the s o l a r z e n i t h a n g l e and was a s s i g n e d a c o n s t a n t v a l u e of 0.076. D i r e c t beam s c a t t e r i n g i s a f u n c t i o n of the s o l a r z e n i t h a n g l e . I t was c a l c u l a t e d u s i n g the f o l l o w i n g e x p r e s s i o n : a = 0.0467563 + 0.0014173-0 + 0.00005258•8 2 + 0.000000651•0 3 (3.11) where 6 i s i n degr e e s . T h i s e x p r e s s i o n was v a l i d f o r a range of s o l a r z e n i t h a n g l e s of up t o 85°. 3.4.6 E s t i m a t i o n of Minimum B r i g h t n e s s The minimum b r i g h t n e s s (*p) o f a t a r g e t r e p r e s e n t s the t a r g e t ' s b r i g h t n e s s under c l o u d - f r e e c o n d i t i o n s . I t was e s t i m a t e d from an e q u a t i o n d e v e l o p e d by T a r p l e y (1979): 2 I = a + bcosd + c c o s 7 s i n 0 + dcos 7 s i n 0 (3.12) where 8 s o l a r z e n i t h a n g l e (degrees) 7 S u n - s a t e l l i t e a z i m u t h a n g l e (degrees) a, b, r e g r e s s i o n c o e f f i c i e n t s c, d The r e g r e s s i o n c o e f f i c i e n t s were d e r i v e d u s i n g imagery c o r r e s p o n d i n g t o the c l e a r sky hours l i s t e d i n T a b l e 3.1. P r i o r t o t h e s e c a l c u l a t i o n s a q u a l i t y c o n t r o l check was performed on the 60 x 120 p i x e l p r i m a r y images t o remove m i s s i n g and c l o u d - c o n t a m i n a t e d p i x e l s from t h i s s e t . The mean b r i g h t n e s s of each c o n t i g u o u s 5 x 5 p i x e l a r r a y was a s s e s s e d f o r each p r i m a r y image. A g i v e n a r r a y was not 46 e n t e r e d i n t o subsequent c a l c u l a t i o n s i f more than 33% of i t s p i x e l s were m i s s i n g (due t o e x c l u s i o n d u r i n g q u a l i t y c o n t r o l ) . The mean b r i g h t n e s s v a l u e s were r e g r e s s e d a g a i n s t s o l a r z e n i t h and S u n - s a t e l l i t e a z i m u t h a n g l e s u s i n g the T r i a n g u l a r R e g r e s s i o n Package a v a i l a b l e from the U n i v e r s i t y of B r i t i s h Columbia Computing C e n t r e L i b r a r y . The s t a n d a r d e r r o r of e s t i m a t e and the c o e f f i c i e n t of d e t e r m i n a t i o n computed w i t h each e q u a t i o n d i s p l a y e d i n t e r e s t i n g s p a t i a l v a r i a t i o n s and a r e d i s c u s s e d i n Chapter V. 3.4.7 Calculation of Cloud Threshold The c l o u d t h r e s h o l d c o n t r o l s the d e c i s i o n t o p r o c e s s the s a t e l l i t e d a t a t h r o u g h e i t h e r the c l e a r or the c l o u d y sky a l g o r i t h m s . I t was e v a l u a t e d u s i n g E q u a t i o n 2.6. The s u r f a c e a l b e d o was e s t i m a t e d from the minimum b r i g h t n e s s and was incremented by a c o n f i d e n c e margin of 0.0056 ( e q u i v a l e n t t o 12 c o u n t s ; a f t e r R a p h a e l , 1982) t o accomodate s m a l l v a r i a t i o n s i n s u r f a c e a l b e d o , a t m o s p h e r i c water vapour and a e r o s o l con-t e n t . The r a d i a n c e observed by the s a t e l l i t e was compared w i t h t h i s t h r e s h o l d v a l u e . I f the o b s e r v e d r a d i a n c e was g r e a t e r than the t h r e s h o l d , then the c l o u d y sky a l g o r i t h m was used. O t h e r w i s e , c a l c u l a t i o n s were based on the c l e a r sky a l g o r i t h m . 3.4.8 Estimation of Cloud Absorption C l o u d a b s o r p t i o n was a p p r o x i m a t e d as a l i n e a r f u n c t i o n of c l o u d b r i g h t n e s s , v a r y i n g from 0.0 f o r no c l o u d , t o 0.2 (20%) 47 f o r the b r i g h t e s t c l o u d s . The s o l a r r a d i a t i o n which was s c a t t e r e d back t o space by a c l o u d l a y e r was c a l c u l a t e d as the d i f f e r e n c e between the r a d i a n c e m o n i t o r e d by the s a t e l l i t e (KT) and the e s t i m a t e d c l o u d t h r e s h o l d r a d i a n c e ( K t t > . The maximum p o s s i b l e s c a t t e r i n g was assumed t o be the d i f f e r e n c e between the e x t r a t e r r e s t r i a l i r r a d i a n c e (K') and the c l o u d t h r e s h o l d . Thus, $ was e s t i m a t e d by: 'KT - Kt, K' - K1\ x 0.2 (3.13) 3.5 C o n c l u d i n g Remarks T h i s c h a p t e r has o u t l i n e d the r e g i o n a l c o n t e x t , the d a t a and m o d e l l i n g p r o c e d u r e s used t o d e r i v e e s t i m a t e s of the i n s o l a t i o n . The o v e r v i e w of the G a u t i e r model emphasized the m o d i f i c a t i o n s a p p l i e d t o the a l g o r i t h m s used by Raphael (1982) and Raphael and Hay (1984). The r e a d e r i s d i r e c t e d t o Raphael (1982) f o r more d e t a i l e d d i s c u s s i o n s of s p e c i f i c c o m p u t a t i o n a l p r o c e d u r e s . 48 Chapter IV SATELLITE CHARACTERIZATION OF THE MESOSCALE INSOLATION VARIABILITY 4.1 Introduction The s t u d y a r e a d e s c r i b e d i n S e c t i o n 3.1 d i s p l a y s .a complex s o l a r r a d i a t i o n c l i m a t e a s s o c i a t e d w i t h mountain-l o w l a n d , c o a s t a l - i n l a n d and u r b a n - r u r a l c o n t r a s t s (Hay, 1984). The f e a s i b i l i t y of u s i n g s a t e l l i t e d a t a t o e s t i m a t e i n s o l a t i o n over t h e lower F r a s e r V a l l e y ( v i a the G a u t i e r model) was i n i t i a l l y e v a l u a t e d by Raphael (1982). H i s a n a l y s e s were based on t i m e - s e r i e s comparisons between the s a t e l l i t e e s t i m a t e s and the ob s e r v e d i n s o l a t i o n a t s e l e c t e d network s t a t i o n s . However, the i n d i v i d u a l s t a t i o n assessments p r o v i d e almost no i n f o r m a t i o n on the a b i l i t y of the s a t e l l i t e e s t i m a t e s t o r e p l i c a t e t he s p a t i a l c h a r a c t e r i s t i c s of the obs e r v e d f i e l d . The o b j e c t i v e of t h i s c h a p t e r i s t o determine whether such a c a p a b i l i t y e x i s t s . 4.2 Method of Analysis The i n s o l a t i o n v a r i a b i l i t y was a s s e s s e d by d e t e r m i n i n g the i n t e r s t a t i o n c o r r e l a t i o n s , u s i n g h o u r l y d a t a measured a t , or e s t i m a t e d f o r , the 12 p y r a n o m e t r i c s t a t i o n s . The d i s t a n c e -c o r r e l a t i o n f u n c t i o n s d e r i v e d from t h e observed and e s t i m a t e d i n s o l a t i o n were s u b s e q u e n t l y compared i n o r d e r t o e v a l u a t e the a b i l i t y of the s a t e l l i t e - b a s e d approach t o d e s c r i b e t h e s p a t i a l v a r i a b i l i t y . 49 The Pearson product-moment c o r r e l a t i o n c o e f f i c i e n t ( r ) p r o v i d e d a q u a n t i t a t i v e measure of the c o n c o m i t a n t v a r i a t i o n of i n s o l a t i o n f o r a g i v e n s t a t i o n p a i r . I t was c a l c u l a t e d as f o l l o w s : £ ( x . - x) (y. - y) r = ^ 1 (4.1) No o x y where N i s the number of p a i r e d o b s e r v a t i o n s ( x ^ , y ^ ) ; x and y are the mean i n s o l a t i o n a t s t a t i o n s X and Y; a and a a r e the ' x y r e s p e c t i v e s t a n d a r d d e v i a t i o n s . The c o r r e l a t i o n method assumed t h a t the s t a t i o n i n s o l a t i o n p a i r i n g s were l i n e a r l y r e l a t e d . F i g u r e 4.1 shows t h a t t h i s c o n d i t i o n was approximated by d a t a from the UBC and A i r p o r t s t a t i o n s . Other s t a t i o n p a i r i n g s were a l s o known t o d i s p l a y s i m i l a r c h a r a c t e r i s t i c s (Hay, p e r s . comm., 1984). The v a r i a t i o n of the i n t e r s t a t i o n c o r r e l a t i o n w i t h d i s t a n c e has been used t o d e f i n e the s p a t i a l coherence of numerous c l i m a t o l o g i c a l f i e l d s ( e . g . A l a k a , 1970; L o n g l e y , 1974; Hay, 1981). T h i s approach was adopted i n t h e p r e s e n t a n a l y s i s s i n c e i t o f f e r e d a c o n c i s e and c o n v e n i e n t r e p r e s e n t a t i o n . However, a corr e s p o n d e n c e between the d i s t a n c e - c o r r e l a t i o n f u n c t i o n s of the o b s e r v e d and e s t i m a t e d f i e l d s d i d not c o n s t i t u t e a complete assessment of the s a t e l l i t e methodology as o n l y r e l a t i v e v a r i a t i o n s were c o n s i d e r e d . The obse r v e d and e s t i m a t e d d a t a may v a r y i n u n i s o n though they may not n e c e s s a r i l y r e p r e s e n t the same s p a t i a l d i s t r i b u t i o n . Hence, comparisons of the a b s o l u t e i n s o l a t i o n were a l s o undertaken t o e v a l u a t e the a c c u r a c y 50 U B C I N S O L A T I O N ( k J m ^ h - 1 ) Figure 4 . 1 Comparison between the i n s o l a t i o n o bserved at A i r p o r t and at UBC f o r the hours l i s t e d i n Table 3.1. 51 of the model p r e d i c t i o n s . The r e s u l t s of b oth t h e s e a n a l y s e s s h o u l d p r o v i d e c o n c l u s i v e e v i d e n c e w i t h which t o a s s e s s the m o d e l l i n g p r o c e d u r e . The c a l c u l a t i o n s were performed u s i n g the i n s o l a t i o n data f o r the hours l i s t e d i n T a b l e 3.1. S i n c e the a n a l y s e s i n v o l v e d 12 s t a t i o n l o c a t i o n s , 66 p a i r i n g s were p o s s i b l e . These p a i r i n g s c o r r e s p o n d e d t o a range of s t a t i o n s e p a r a t i o n d i s t a n c e s between 4 and 74 km. The i n s o l a t i o n f o r each s t a t i o n was i n i t i a l l y e s t i m a t e d on the b a s i s of 5 x 5 p i x e l a r r a y s . These c o m p r i s e d the s m a l l e s t a r r a y d i m e n s i o n s a s s e s s e d f o r s p a t i a l s c a l e dependence by Raphael (1982) [ S e c t i o n 2.2.2]. Yet s m a l l e r a r r a y s would be p r e f e r r e d f o r a more d e t a i l e d r e s o l u t i o n of the s p a t i a l f i e l d . The 3 x 3 p i x e l a r r a y r e p r e s e n t e d the f i n e s t r e s o l u t i o n a t t a i n a b l e w i t h i n the c o n s t r a i n t s of n a v i g a t i o n a l a c c u r a c y ( S e c t i o n 3.2.2.2). I t s i m p l e m e n t a t i o n would r e l y on the i n s e n s i t i v i t y of the s a t e l l i t e e s t i m a t e s t o a r e d u c t i o n i n s p a t i a l a v e r a g i n g . T h i s i s s u e w i l l be examined i n S e c t i o n 4.3.4. 4.3 Results and Discussion 4.3.1 Network-based Correlations F i g u r e 4.2a i l l u s t r a t e s , f o r the network d a t a , the h o u r l y i n t e r s t a t i o n c o r r e l a t i o n s as a f u n c t i o n of s e p a r a t i o n d i s t a n c e . The c o r r e l a t i o n s d i s p l a y a g r a d u a l d e c r e a s e w i t h s t a t i o n s e p a r a t i o n , c o n f i r m i n g our e x p e c t a t i o n t h a t s t a t i o n s 52 10-0-8-* * <%> 10-08-10-0-8-8 0-6-| z o 0 <j, « . © « «• ©© £ 10-0 8-© © © © » © * © O <is 0 <!> © * # © © © © © 0-6-0-4-+ + 0:2-OBSERVED 00 -+ Grouse Mountain pairings 10 I 20 30 40 50 STATION SEPARATION (km) 60 70 80 F i g u r e 4.2a-d The d i s t a n c e - c o r r e l a t i o n f u n c t i o n s of the ob s e r v e d h o u r l y i n s o l a t i o n . a. a l l d a t a b. c l e a r sky da t a c. p a r t l y c l o u d y sky da t a d. o v e r c a s t sky da t a 53 l o c a t e d i n c l o s e r p r o x i m i t y t e n d t o e x h i b i t a s i m i l a r v a r i a b i l i t y . The i n s o l a t i o n f i e l d appears g e n e r a l l y w e l l c o r r e l a t e d throughout the network. S y s t e m a t i c a l l y lower c o r r e l a t i o n s a r e observed f o r s t a t i o n p a i r i n g s a s s o c i a t e d w i t h the Grouse Mountain s i t e . T h i s f e a t u r e i s a t t r i b u t e d t o d i f f e r e n c e s i n c l o u d i n e s s between mountain and l o w l a n d r e g i o n s and i s c o n s i s t e n t w i t h r e l a t i o n s h i p s noted p r e v i o u s l y by Hay (1981). Comparable p l o t s were produced f o r the c l e a r , p a r t l y c l o u d y and o v e r c a s t sky c l a s s e s ( F i g u r e 4.2b - d ) . The c l e a r sky d a t a d i s p l a y a h i g h l y c o h e r e n t f i e l d . In t h e absence of c l o u d , Grouse Mountain p a i r i n g s do not e x h i b i t anomalously lower c o r r e l a t i o n s . The p a r t l y c l o u d y and o v e r c a s t sky d a t a a r e more v a r i a b l e , as judged by the more r a p i d d e c r e a s e of c o r r e l a t i o n s w i t h d i s t a n c e and the g r e a t e r s c a t t e r of p o i n t s about the g e n e r a l t r e n d . The Grouse Mountain p a i r i n g s a r e d i s t i n c t i n b o t h these c a s e s . 4.3.2 S a t e l l i t e - b a s e d C o r r e l a t i o n s The d i s t a n c e - c o r r e l a t i o n f u n c t i o n s f o r the i n s o l a t i o n e s t i m a t e d u s i n g 5 x 5 p i x e l a r r a y s a r e shown i n F i g u r e 4.3a -d. The s p a t i a l coherence of t h e s e f i e l d s i s s i m i l a r t o t h a t of t h e i r network c o u n t e r p a r t s . However, f o r a g i v e n s e p a r a t i o n d i s t a n c e , the s a t e l l i t e - b a s e d c o r r e l a t i o n s a r e l e s s v a r i a b l e . In p a r t i c u l a r , the Grouse Mountain p a i r i n g s do not d i s p l a y the anomaly observed i n the network s e t . T h i s d i s c r e p a n c y i s r e l a t e d t o the f a c t t h a t .while th e network d a t a 54 1-0-0 - 8 -1 0 ' 0 8 -1 - 0 -gO-8-rx cr O o 2 o +" ° * ^ «, » «, 0 6 -I 1-0-0 - 8 -0 - 6 -* + + 0 4 -0 - 2 -ESTIMATED ( 5 x 5 pixel arrays) -+- Grouse Mountain pairings 0 0 -1 0 2 0 3 0 4 0 5 0 STATION SEPARATION (km) 6 0 I 7 0 8 0 F i g u r e 4.3a-d The d i s t a n c e c o r r e l a t i o n f u n c t i o n s of the s a t e l l i t e - e s t i m a t e d i n s o l a t i o n (based on 5 x 5 p i x e l a r r a y s ) . a. a l l d a t a b. c l e a r sky d a t a c. p a r t l y c l o u d y sky d a t a d. o v e r c a s t d a t a 55 c o r r e s p o n d t o p o i n t o b s e r v a t i o n s , the s a t e l l i t e - b a s e d e s t i m a t e s a r e s p a t i a l averages (the a v e r a g i n g o c c u r s d u r i n g the s a t e l l i t e o b s e r v a t i o n and i n s o l a t i o n m o d e l l i n g p r o c e s s e s ) . S i n c e the s a t e l l i t e e s t i m a t e s r e p r e s e n t a s p a t i a l l y - s m o o t h e d f i e l d , random d i f f e r e n c e s between s t a t i o n p a i r i n g s a r e reduced. 4.3.3 Comparisons Between the Observed and E s t i m a t e d I n s o l a t i o n The o b s e r v e d and e s t i m a t e d i n s o l a t i o n a r e compared i n F i g u r e 4.4a. The p l o t i n c l u d e s 3756 d a t a p a i r s d e r i v e d from 313 h o u r l y v a l u e s a t each of the 12 network s t a t i o n s . The cor r e s p o n d e n c e between the two s e t s i s summarized i n Ta b l e 4.1. The l o n g - t e r m ( i . e . s y s t e m a t i c ) e r r o r i n h e r e n t i n the model i s q u a n t i f i e d by the m e a n - b i a s - e r r o r (MBE): MBE = K| - K| o (4.2) where, K| i s the mean h o u r l y e s t i m a t e d i n s o l a t i o n and i s i t s o b s e r v e d c o u n t e r p a r t . The s h o r t - t e r m a c c u r a c y of the model i s e v a l u a t e d by the root-mean-square e r r o r (RMSE): V : dU - KA ) 2 RMSE | — N (4.3) where K\ and K| a r e the h o u r l y e s t i m a t e d and observ e d d a t a , and N i s the number of d a t a p a i r s . F i g u r e 4.4a i n d i c a t e s a g e n e r a l l y good agreement between the o b s e r v e d and e s t i m a t e d d a t a . The magnitude of the MBE i s s m a l l (+0.4%) r e l a t i v e t o the p y r a n o m e t r i c c a l i b r a t i o n a c c u r a c y (±2%; a f t e r L a t i m e r , 1980). The MBE's a s s o c i a t e d 56 O B S E R V E D INSOLATION ( M m - 2 ^ 1 ) F i g u r e 4.4a Comparisons between the observed and e s t i m a t e d h o u r l y i n s o l a t i o n . The l a t t e r a r e based on 5 x 5 p i x e l a r r a y s . a. a l l data DATA 1 GROUPING N o a "o/KJo a/Kl r MBE MBE% RMSE RMSE% CLEAR 1212 2125 2 2187 1 719 2 748 6 30 30 0 .978 +61. 9 +2 9 127 .7 6. 0 PARTLY CLOUDY 1524 1023 1 978 1 888 8 774 4 90 80 0 862 -44. 9 -4 4 337 .8 33 .0 OVERCAST 1020 541 9 567 7 513 9 413 2 70 70 0 810 +25. 8 +4 8 220 .4 40 .0 ALL DATA 3756 1205 7 1210 3 969 6 940 9 80 80 0 927 +4. 6 +0 4 261 .8 21 .7 N : sample size — - 2 - 1 Kl : observed mean insolation (kJm h ) - -2 -1 K| : estimated mean insolation (kjm h ) -2 -1 fj : standard deviation of the observed insolation (kjm h ) ° -2-1 CT : standard deviation of the estimated insolation (kjra h ) MBE: Mean Bias Error (kJm~ 2h - 1 or %) -2 -1 RMSE: Root-Mean-Square Error (kJm h or %) rela t i v e errors are determined with respect to the observed mean insolation Table 4.1 Comparisons between the observed (M 0) and e s t i m a t e d ( K l ) i n s o l a t i o n ( the l a t t e r are based on 5 x 5 p i x e l a r r a y s ) . 58 w i t h i n d i v i d u a l s t a t i o n d a t a a r e , i n most c a s e s , i n s i g n i f i c a n t ( T a ble 4.2). These r e s u l t s c o n f i r m t h a t on a v e r a g e , the model i s d e s c r i b i n g the o b s e r v e d f i e l d . The RMSE ( f o r a l l d a t a ) i s w i t h i n 21.7%. The d i f f e r e n c e s which e x i s t between i n d i v i d u a l d a t a p a i r s a r e n o n - s y s t e m a t i c s i n c e the o v e r a l l b i a s of the model i s n e g l i g i b l e . However, the s c a t t e r i s not s t a t i s t i c a l l y random; o v e r e s t i m a t i o n i s - 2 — 1 predominant at low i r r a d i a n c e s (<1200 kJm h ) w h i l e under-e s t i m a t i o n g e n e r a l l y o c c u r s a t h i g h e r i r r a d i a n c e s (1200 -- 2 -1 2750 kJm h ). The i n d i v i d u a l s t a t i o n d a t a comparisons ( F i g u r e 4.4b - m; T a b l e 4.2), i n a d d i t i o n , r e v e a l t h a t the Grouse Mountain p a i r i n g s a r e the prime c o n t r i b u t o r s t o the o v e r e s t i m a t i o n . U n d e r e s t i m a t i o n appears t o be a f e a t u r e of a l l s t a t i o n s . G a u t i e r e t a l . (1980) found t h a t the model o v e r e s t i m a t e d the o b s e r v e d i n s o l a t i o n when c l o u d a l b e d o was h i g h (>0.75). T h i s tendency was enhanced when s o l a r z e n i t h a n g l e s were a l s o l a r g e . G a u t i e r (1982) a t t r i b u t e d t h i s type of e r r o r t o the i n a b i l i t y of the model t o account f o r shadowing by uneven c l o u d t o p s and a n i s o t r o p i c b a c k - s c a t t e r i n g by water d r o p l e t s . Raphael and Hay (1984) a l s o s u g g ested the i n a d e q u a t e parameter-i z a t i o n of c l o u d a b s o r p t i o n . Presumably, the i n s o l a t i o n c a l c u l a t e d f o r Grouse Mountain i s more s u s c e p t i b l e t o o v e r e s t i m a t i o n as a r e s u l t of the more f r e q u e n t o c c u r r e n c e of c l o u d over t h a t s t a t i o n . Raphael and Hay (1984) a t t r i b u t e d the tendency f o r model u n d e r e s t i m a t i o n t o c l o u d t h r e s h o l d e r r o r s . The G a u t i e r STATION GROUPING N a • < V K | O O"/KJ 2 r MBE MBE% RMSE RMSE% GROUSE MTN 313 1174 .0 1226 .6 1019 9 951 0 87 78 0 871 +52 6 +4 5 370 .9 31 6 N. VANCOUVER 313 1173 9 1177 3 965 1 927 9 82 79 0 939 +3 4 +0 3 239 9 20 4 VANCOUVER B . C . HYDRO BLDG 313 1174 0 1198 2 964 0 915 5 82 76 0 951 +24 2 +2 1 215. 8 18 4 AIRPORT 313 1264 9 1240 2 987 0 940 3 78 76 0 920 -24 7 - 2 0 280 0 22 1 TSAWWASSEN 313 1326 .6 1320 .8 1019 4 998 6 77 76 0 962 - 5 8 - 0 4 199 0 15 0 PITT MEADOWS 313 1171 .3 1164 1 954 3 940 4 81 81 0 919 -7 2 - 0 6 273 0 23 3 MISSION CITY 313 1169 5 1180 1 933 6 925 2 80 78 0 912 +10 6 +0 9 278 6 23 .8 ABBOTSFORD CITY 313 1185 0 1194 3 934 6 926 1 79 78 0 915 +9 3 +0 8 274 6 23 2 ABBOTSFORD AIRPORT 313 1214 7 1201 2 937 3 924 4 77 77 0 930 - 1 3 . 5 ' -1 1 249 2 20 5 LANGLEY CITY 313 1175 1 1195 0 938 2 932 9 80 78 0. 921 +19 9 +1 7 265 9 22 6 LANGARA 313 1144 0 1166 .2 934 4 940 3 82 81 0 940 +22 0 +1 9 231 .2 20 2 UBC 313 1290 4 1257 6 1035 0 970 5 80 77 0. 953 - 3 2 8 - 2 5 227 1 17 .6 relative errors are determined with respect to the observed mean insolation T a b l e 4.2 I n d i v i d u a l s t a t i o n comparisons between the observe d ( K J Q ) and e s t i m a t e d ( K j ) i n s o l a t i o n (the l a t t e r a r e based on 5 x 5 p i x e l a r r a y s ) . 60 O B S E R V E D I N S O L A T I O N ( k J m ^ r f 1 ) F i g u r e 4.4b-e Comparisons between the observed and e s t i m a t e d h o u r l y i n s o l a t i o n . The l a t t e r a re based on 5 x 5 p i x e l a r r a y s . b. Grouse Mountain d a t a c. N o r t h Vancouver d a t a d. Vancouver (B.C. Hydro Bldg.) d a t a . e. UBC dat a 61 F i g u r e 4 . 4 f - i Comparisons between the observed and e s t i m a t e d h o u r l y i n s o l a t i o n . The l a t t e r a r e based on 5 x 5 p i x e l a r r a y s . f . A i r p o r t d a t a g. Tsawwassen d a t a h. Langara d a t a i . A b b o t s f o r d C i t y d a t a 62 O B S E R V E D I N S O L A T I O N ) M m " 2 I T 1 ) F i g u r e 4.4j-m Comparisons between the o b s e r v e d and e s t i m a t e d h o u r l y i n s o l a t i o n . The l a t t e r a re based on 5 x 5 p i x e l a r r a y s . j . A b b o t s f o r d A i r p o r t d a t a k. L a n g l e y C i t y d a t a 1 . P i t t Meadows da t a m. M i s s i o n C i t y d a t a 63 model c l a s s i f i e s each p i x e l as c l e a r or c l o u d y by comparing the p i x e l r e f l e c t a n c e ( c o n v e r t e d t o energy u n i t s , as d e s c r i b e d i n S e c t i o n 3.2.2.3) w i t h a t h r e s h o l d v a l u e . A c l e a r p i x e l may be m i s c l a s s i f i e d as c l o u d y i f the t h r e s h o l d f a i l s t o account f o r the i n h e r e n t v a r i a b i l i t y i n the minimum b r i g h t n e s s f i e l d ( i . e . the c l o u d t h r e s h o l d i s too l o w ) . T h i s would l e a d t o the p r o c e s s i n g of p i x e l s by the c l o u d y sky model and, i n e v i t a b l y , t o the u n d e r e s t i m a t i o n of the i n s o l a t i o n . P a r t l y c l o u d y f i e l d s a r e p a r t i c u l a r l y s e n s i t i v e t o c l o u d t h r e s h o l d e r r o r s . The d a t a subset s t a t i s t i c s ( T a b l e 4.1) a r e c o n s i s t e n t w i t h the p r e v i o u s assessments. The model o v e r e s t i m a t e s under c l e a r and o v e r c a s t s k i e s w h i l e i t u n d e r e s t i m a t e s under p a r t l y c l o u d y c o n d i t i o n s . The s h o r t - t e r m a c c u r a c y of the model i s -2 -1 v a r i a b l e , r a n g i n g from ±6% (127.7 kJm h ) f o r the c l e a r sky - 2 - 1 i n s o l a t i o n t o ±40% (220.4 kJm h ) f o r the o v e r c a s t sky e s t i m a t e s . The RMSE's a r e p r i m a r i l y n o n - s y s t e m a t i c i n n a t u r e . 4 . 3 . 4 I n s o l a t i o n E s t i m a t e d U s i n g 3 x 3 P i x e l A r r a y s In o r d e r t o det e r m i n e whether s i g n i f i c a n t d i f f e r e n c e s i n e s t i m a t i o n o c c u r w i t h a r e d u c t i o n i n s p a t i a l a v e r a g i n g , the h o u r l y i n s o l a t i o n d e r i v e d from 3 x 3 p i x e l a r r a y s a r e compared w i t h t h o s e from 5 x 5 a r r a y s . The comparisons shown i n F i g u r e 4.5 and Ta b l e 4.3 i n d i c a t e t h a t the two s e t s of e s t i m a t e s a r e almost i d e n t i c a l . The MBE i s 0% i n a l l c a s e s and the RMSE i s l e s s than ±1%. The a c c u r a c y of the model i s a p p a r e n t l y u n a f f e c t e d by the s e changes i n s p a t i a l a v e r a g i n g . As might t h e r e f o r e be a n t i c i p a t e d , the network d a t a and 64 ESTIMATED INSOLATION ( k J m ^ r r 1 ) ( 5 x 5 pixel arrays) F i g u r e 4.5 Comparison between the h o u r l y i n s o l a t i o n e s t i m a t e d on the b a s i s of 5 x 5 and 3 x 3 p i x e l a r r a y s . DATA GROUPING N *o K l a 0-/KJ 2 r MBE MBE% RMSE RMSE% CLEAR 1212 2187 1 2192 2 748 . 6 753 9 30 30 0 .995 +5 .1 0 0 52 .2 0 . 0 PARTLY CLOUDY 1524 9 7 8 . 1 9 9 1 . 7 774 . 4 773 . 9 80 80 0 .960 +13 .6 0 . 0 156 .0 0 . 2 OVERCAST 1020 567 . 7 578 . 7 4 1 3 . 2 435 3 70 70 0 .947 +11 . 0 0 . 0 99 .6 0 . 2 A L L DATA 3756 1210. 3 1221 . 9 9 4 0 . 9 942 7 80 80 0 .984 +11 .6 0 . 0 119 .3 0 . 1 r e l a t i v e e r r o r s a r e d e t e r m i n e d w i t h r e s p e c t t o t h e e s t i m a t e d m e a n i n s o l a t i o n b a s e d o n 5 x 5 p i x e l a r r a y s T a b l e 4.3 Comparisons between the e s t i m a t e d i n s o l a t i o n based on 5 x 5 a r r a y s and 3 x 3 p i x e l a r r a y s . 66 the 3 x 3 a r r a y e s t i m a t e s ( F i g u r e 4.6; T a b l e 4.4) d i s p l a y an agreement s i m i l a r t o t h a t o b t a i n e d u s i n g the 5 x 5 a r r a y ( F i g u r e 4.4a). Comparisons i n d i c a t e a s l i g h t i n c r e a s e i n the magnitudes of the e r r o r s f o r a l l but the p a r t l y c l o u d y sky d a t a . In t h i s l a t t e r s i t u a t i o n , , a r e d u c t i o n i n b o t h the s h o r t - and l o n g - t e r m e r r o r s i s n o t e d . 4.3.5 S a t e l l i t e - b a s e d C o r r e l a t i o n s ( 3 x 3 p i x e l a r r a y s ) The i n t e r s t a t i o n c o r r e l a t i o n s f o r e s t i m a t e s d e r i v e d from 3 x 3 p i x e l a r r a y s a r e i l l u s t r a t e d i n F i g u r e s 4.7a - d. The c o r r e l a t i o n p a t t e r n f o r each s e t of e s t i m a t e s i s comparable t o the c o r r e s p o n d i n g 5 x 5 a r r a y r e s u l t s . The i m p l i e d s p a t i a l coherence of the i n s o l a t i o n f i e l d i s r e l a t i v e l y u n a l t e r e d by t h i s r e d u c t i o n i n s p a t i a l a v e r a g i n g . T h i s would suggest t h a t the average v a r i a b i l i t y w i t h i n the 5 x 5 and 3 x 3 p i x e l a r r a y s does not d i f f e r s u f f i c i e n t l y t o induce s i g n i f i c a n t changes i n the s p a t i a l c h a r a c t e r i s t i c s of the d e r i v e d i n s o l a t i o n f i e l d s . 4.4 Summary and C o n c l u s i o n s Two i s s u e s a r e i n v e s t i g a t e d i n t h i s c h a p t e r . The f i r s t c o ncerned the a b i l i t y of the s a t e l l i t e e s t i m a t e s t o r e s o l v e the mesoscale i n s o l a t i o n v a r i a b i l i t y over the 12 s t a t i o n p y r a n o m e t r i c network. The c o r r e l a t i o n a n a l y s e s and the s c a t t e r p l o t comparisons i n d i c a t e a good agreement between the network d a t a and the s a t e l l i t e e s t i m a t e s . The c o r r e l a t i o n a n a l y s e s a l s o r e v e a l t h a t the s a t e l l i t e - b a s e d f i e l d s ( n o t a b l y 67 O B S E R V E D , INSOLATION( W i n ^ h - 1 ) F i g u r e 4.6 Comparison between the observ e d and e s t i m a t e d h o u r l y i n s o l a t i o n ( a l l d a t a ) . The l a t t e r a r e based on 3 x 3 p i x e l a r r a y s . DATA o GROUPING N KJ 0 c W K l z r MBE MBE% RMSE RMSE% CLEAR 1212 2125 2 2192 .2 719 .2 753 .9 30 30 0 .976 +67 .0 +3 2 137 .2 6 .5 PARTLY CLOUDY 1524 1023. 1 991 7 888. 8 773. 9 90 90 0 875 -31 .4 -3. 1 321 8 31 0 OVERCAST 1020 541. 9 578. 7 513. 1 432. 3 90 70 0 794 +36 .8 +6. 8 228. 4 42 0 ALL DATA 3756 1205. 7 1221. 9 969. 6 942. 7 80 80 0. 931 +16 .2 +1. 3 255. 7 21 0 relative errors are determined with respect to the observed mean insolation T a b l e 4.4 Comparisons between the observed and e s t i m a t e d ( K l ) i n s o l a t i o n (the l a t t e r a r e based on 3 x 3 p i x e l a r r a y s ) . 69 1 0 -0 - 8 ' *»7 1 0 -0 8 -1 0 -0 8 -0 6 -cc 1 - 0 ' 0 - 8 -A © 4 + T © © © © © + © © S© « 0 6 -0 - 4 -0 2 -E S T I M A T E D (3x3 p i x e l a r r a y s ) + G r o u s e M o u n t a i n p a i r i n g s OO-I 1 -7 0 —f 8 0 1 0 I 2 0 I I I 3 0 4 0 5 0 S T A T I O N S E P A R A T I O N ( k m ) 6 0 F i g u r e 4.7a-d The d i s t a n c e - c o r r e l a t i o n f u n c t i o n s of the s a t e l l i t e - e s t i m a t e d i n s o l a t i o n (based on 3 x 3 p i x e l a r r a y s ) . a. a l l d a t a b. c l e a r sky d a t a c. p a r t l y c l o u d y sky da t a d. o v e r c a s t sky d a t a 70 t h o s e r e p r e s e n t i n g c l o u d y c o n d i t i o n s ) are more homogeneous. T h i s e f f e c t i s a t t r i b u t e d t o the s p a t i a l a v e r a g i n g i n h e r e n t i n the s a t e l l i t e methodology. Comparisons between the o b s e r v e d and the s a t e l l i t e - b a s e d i n s o l a t i o n show t h a t the model i s , on a v e r a g e , p r o v i d i n g an a c c u r a t e c h a r a c t e r i z a t i o n of the observed f i e l d . However, the s h o r t - t e r m a c c u r a c y of the model i s c o m p a r a t i v e l y poor. Though the h o u r l y m o d e l l i n g e r r o r s a r e l a r g e , the v a r i a b i l i t y of the e s t i m a t e d i n s o l a t i o n (as d e f i n e d by a/ K|; T a b l e 4.4) i s l a r g e r . The e s t i m a t e s a r e t h e r e f o r e m e a n i n g f u l . The second i s s u e c o n s i d e r e d the f e a s i b i l i t y of u s i n g 3 x 3 p i x e l a r r a y s t o r e s o l v e the s p a t i a l f i e l d . The d i f f e r e n c e s between the 5 x 5 and 3 x 3 a r r a y e s t i m a t e s a r e minor. Whil e the e f f e c t s of s p a t i a l a v e r a g i n g would imply t h a t the 3 x 3 a r r a y e s t i m a t e s s h o u l d d i s p l a y a g r e a t e r s i m i l a r i t y w i t h the network d a t a than shown by the 5 x 5 a r r a y e s t i m a t e s , such i s not the c a s e . T h i s r e d u c t i o n i n s p a t i a l a v e r a g i n g appears t o have l i t t l e impact on the e s t i m a t e d f i e l d . S i n c e d i f f e r e n c e s i n the c oherence of the observed and s a t e l l i t e - e s t i m a t e d f i e l d s o c c u r as a r e s u l t of s p a t i a l a v e r a g i n g , i t i s assumed t h a t most of the v a r i a b i l i t y o r i g i n a t e s a t s p a t i a l s c a l e s f i n e r than t h a t of the 3 x 3 p i x e l a r r a y . A l t h o u g h the G a u t i e r model c a l c u l a t e s i n s o l a t i o n on a p i x e l - b y - p i x e l b a s i s , t h i s v a r i a b i l i t y cannot be a s s e s s e d due t o l i m i t a t i o n s imposed by t h e n a v i g a t i o n a l e r r o r s . 71 Chapter V SATELLITE MAPPING OF INSOLATION 5.1 I n t r o d u c t i o n The p r e c e d i n g a n a l y s e s c o n f i r m the c a p a b i l i t y of the s a t e l l i t e - b a s e d methodology t o map i n s o l a t i o n a t the m esoscale. A l t h o u g h t h i s p o t e n t i a l had been r e c o g n i z e d i n e a r l i e r m o d e l l i n g e f f o r t s (e.g. Vonder Haar and E l l i s , 1978), few examples of mesoscale maps e x i s t beyond those produced by G a u t i e r (1982), f o r the S t . Lawrence - Lake O n t a r i o r e g i o n . In t h i s c h a p t e r , e s t i m a t e s of the h o u r l y i n s o l a t i o n over the lower F r a s e r V a l l e y , and i t s e n v i r o n s , a r e mapped and c e r t a i n a s p e c t s of the mesoscale v a r i a b i l i t y a re d i s c u s s e d . 5.2 Implementation of the Mapping Procedure The G a u t i e r model was implemented a c c o r d i n g t o the Mode I I p r o c e d u r e ( S e c t i o n 3.4.1), u s i n g c o n t i g u o u s 3 x 3 p i x e l a r r a y s t o r e s o l v e the i n s o l a t i o n over a 60 x 120 p i x e l f i e l d . Minimum b r i g h t n e s s was e s t i m a t e d by E q u a t i o n 3.12. In an e f f o r t t o reduce c a l c u l a t i o n s , t h e c o e f f i c i e n t s of the r e g r e s s i o n e q u a t i o n were e v a l u a t e d on the b a s i s of 5 x 5 p i x e l a r r a y s i n s t e a d of the 3 x 3 a r r a y s used i n the i n s o l a t i o n m o d e l l i n g . Such m o d i f i c a t i o n s a r e not e x p e c t e d t o have a s i g n i f i c a n t i n f l u e n c e on the minimum b r i g h t n e s s e s t i m a t e s s i n c e the c l e a r sky i n s o l a t i o n d e r i v e d from 3 x 3 and 5 x 5 a r r a y s has been shown t o d i f f e r by i n s i g n i f i c a n t amounts 72 (Table 4.3). The r e g r e s s i o n c o e f f i c i e n t s were s t o r e d by the c o o r d i n a t e s of the c e n t r a l p i x e l of the 5 x 5 a r r a y s . Minimum b r i g h t n e s s was e s t i m a t e d a t th e s e g r i d l o c a t i o n s and s u b s e q u e n t l y e x t r a p o l a t e d t o the c e n t r a l p i x e l c o o r d i n a t e s of 3 x 3 a r r a y s u s i n g the n e a r e s t - n e i g h b o u r method ( L i l l e s a n d and K i e f e r , 1979). 5.2.1 Minimum B r i g h t n e s s P r e d i c t i o n s The s t a n d a r d e r r o r of the e s t i m a t e (SE) and the 2 c o e f f i c i e n t of d e t e r m i n a t i o n (r ) were computed f o r each e q u a t i o n t o a s s e s s the performance of the minimum b r i g h t n e s s p r e d i c t i o n s . These measures d i s p l a y e d a h i g h v a r i a b i l i t y w i t h 2 ranges of SE and r between 1.61 - 7.37 c o u n t s and 0.229 -0.975, r e s p e c t i v e l y (Appendix B ) . The r e g r e s s i o n model a p p a r e n t l y p r o v i d e s an i n f e r i o r a p p r o x i m a t i o n of the minimum 2 b r i g h t n e s s i n c e r t a i n c a s e s . A h i s t o g r a m of r v a l u e s r e v e a l s t h a t the d i s t r i b u t i o n i s bimodal ( F i g u r e 5.1a). The lower 2 c o e f f i c i e n t s ( i . e . r < 0.650, the m i d p o i n t of the 0.600 -0.699 c l a s s i n t e r v a l ) t e n d t o be a s s o c i a t e d w i t h l a r g e water dominated s u r f a c e s , i n c l u d i n g p o o r l y d r a i n e d t e r r a i n i n s o u t h e a s t e r n p a r t s of the l o w l a n d ( F i g u r e 5.1b). E r r o r s of p r e d i c t i o n a r e a l s o h i g h e r over t h e s e s u r f a c e s (note t h a t 2 2 SE i s r e l a t e d t o r by the e x p r e s s i o n , SE = a^/[1 - r ] , where i s the s t a n d a r d d e v i a t i o n of the minimum b r i g h t n e s s ) . The g e n e r a l form of the r e g r e s s i o n model ( S e c t i o n 3.4.6) i s based on t h r e e g e o m e t r i c f u n c t i o n s : cos0 a c c o u n t s f o r the e f f e c t s of a ch a n g i n g sun a n g l e ; c o s 0 s i n 7 a c c o u n t s f o r s u r f a c e 74 2 s h a d i n g and cos 7Sin0 s i m u l a t e s the b i d i r e c t i o n a l r e f l e c t a n c e p r o p e r t i e s of the s u r f a c e . The s i g n i f i c a n c e of the second term i s q u e s t i o n a b l e as i t s i n c l u s i o n was found t o have a n e g l i g i b l e impact on the performance.of the r e g r e s s i o n (Wanless, 1983). The p o o r e r f i t p r o v i d e d by the r e g r e s s i o n model over water dominated s u r f a c e s i s r e l a t e d t o the i n a b i l i t y of the l a s t term t o account f o r the s u r f a c e s c a t t e r i n g a n i s o t r o p y . Land and water s u r f a c e s e x h i b i t d i f f e r e n t s c a t t e r i n g c h a r a c t e r i s t i c s (Brennan and Bandeen, 2 1970). W h i l e the cos 7 s i n 0 term was shown t o be an a p p r o p r i a t e d e s c r i p t o r of the minimum b r i g h t n e s s over l a n d , i t was i n e f f e c t u a l i n the case of water (Wanless, 1983). T h i s i s s u e i s e x e m p l i f i e d i n F i g u r e 5.2a - d, which d i s p l a y s the a c t u a l and p r e d i c t e d minimum b r i g h t n e s s v a r i a t i o n s over l a n d and water t a r g e t s d u r i n g J u l i a n day 196/79. I t i s e v i d e n t t h a t a b e t t e r a p p r o x i m a t i o n of b r i g h t n e s s v a r i a t i o n s i s o b t a i n e d over l a n d . The d i u r n a l asymmetry e x h i b i t e d by water i s not repr o d u c e d by the model. The r e f l e c t a n c e c h a r a c t e r i s t i c s of water dominated s u r f a c e s moreover e x h i b i t day-to-day v a r i a t i o n s which a r e not acc o u n t e d f o r by the parameters of the r e g r e s s i o n . These i n c l u d e changes a s s o c i a t e d w i t h t i d a l c y c l e s , s e a s o n a l v a r i a t i o n s of the sediment d i s c h a r g e i n t o the S t r a i t of G e o r g i a and of the m o i s t u r e c o n t e n t of bogs and o t h e r p o o r l y d r a i n e d l a n d a r e a s . A l t h o u g h the r e g r e s s i o n model i s shown t o be an i n a p p r o p r i a t e p r e d i c t o r of the minimum b r i g h t n e s s of water dominated s u r f a c e s , the c o n f i d e n c e margin of 12 c o u n t s added t o the c l o u d t h r e s h o l d ( S e c t i o n 3.4.7) L A N D T A R G E T S 100 W A T E R T A R G E T S 6 0 2 40 c 3 o o w CO UJ f. 100 I o m 80 60-40 • \ \ 3: ( 5 x 5 array central pixel coordinate: 38,28) is * s s \ V \ \ \ \ \ \ \ \ t>* ( 5 x 5 array central pixel coordinate: 68, 3 ) 8 10 12 14 TIME ( L A T ) 16 18 100 80 60 40-CO CO U J 100 z 1-I o rx m 80 60 40-0 ^ ( 5 x 5 array central pixel coordinate : 3,33) Ch(5x5 array central pixel coordinate; 48,53) predicted - a c t u a l 10 12 14 TIME ( L A T ) —r— 16 - T * 18 F i g u r e 5.2a-d A c t u a l and p r e d i c t e d d i u r n a l v a r i a t i o n of minimum b r i g h t n e s s f o r J u l i a n day 196/79 76 i s s u f f i c i e n t l y l a r g e t o accomodate the e r r o r s of p r e d i c t i o n . A d justments t o the model are t h e r e f o r e judged t o be un n e c e s s a r y . 5.3 S a t e l l i t e - b a s e d Mean H o u r l y I n s o l a t i o n Maps The mean h o u r l y i n s o l a t i o n e s t i m a t e s f o r c l e a r , p a r t l y c l o u d y , o v e r c a s t and a l l c o n d i t i o n s a r e mapped i n F i g u r e 5.3a - d. T h e i r network-based c o u n t e r p a r t s a r e shown i n F i g u r e 5.4a - d. The l o c a t i o n s of the d a t a p o i n t s used t o c o n t o u r the e s t i m a t e d f i e l d a r e d i s p l a y e d i n F i g u r e 5.5. The d e n s i t y and e x t e n t of the s p a t i a l s a m p l i n g c o n t r a s t s w i t h t h a t p r o v i d e d by the 12 s t a t i o n network and h i g h l i g h t s the u t i l i t y of the s a t e l l i t e approach, p a r t i c u l a r l y over mountainous t e r r a i n where measurements are l a r g e l y n o n - e x i s t e n t . For -2 -1 c o n s i s t e n c y between maps, a c o n t o u r i n t e r v a l of 100 kJm h i s a p p l i e d i n a l l c a s e s . The c o n f i d e n c e margin a s s o c i a t e d w i t h the p o s i t i o n (or magnitude) of an i s o l i n e w i l l depend on the a c c u r a c y of the r e p r e s e n t e d f i e l d ( T a b l e 4.4). S i n c e the n o n - s y s t e m a t i c e r r o r s c a n c e l out i n the a v e r a g i n g p r o c e s s , t h e e r r o r i n h e r e n t i n each map c o r r e s p o n d s t o the MBE of the d i s t r i b u t i o n . The c o n f i d e n c e margin a s s i g n e d t o the c o n t o u r s of a g i v e n f i e l d i s de t e r m i n e d by: where ±2% i s the p y r a n o m e t r i c c a l i b r a t i o n u n c e r t a i n t y . A l l The c l e a r sky e s t i m a t e d and ob s e r v e d i n s o l a t i o n d i s p l a y comparable ranges over t h o s e r e g i o n s m o n i t o r e d by b o t h the e ( % ) (5. 1 ) v a l u e s of e a r e w i t h i n 100 kJm h (see c o r r e s p o n d i n g maps). F i g u r e 5 . 3 a S p a t i a l d i s t r i b u t i o n of the mean h o u r l y e s t i m a t e d i n s o l a t i o n ( c l e a r sky d a t a ) . F i g u r e 5.3b S p a t i a l d i s t r i b u t i o n of the mean h o u r l y e s t i m a t e d i n s o l a t i o n ( p a r t l y c l o u d y sky d a t a ) . F i g u r e 5.3c S p a t i a l d i s t r i b u t i o n of the mean h o u r l y e s t i m a t e d i n s o l a t i o n ( o v e r c a s t sky d a t a ) . F i g u r e 5.3d S p a t i a l d i s t r i b u t i o n of the mean h o u r l y e s t i m a t e d i n s o l a t i o n ( a l l d a t a ) . F i g u r e 5 . 4 a S p a t i a l d i s t r i b u t i o n of the mean h o u r l y observed i n s o l a t i o n ( c l e a r sky d a t a ) . 0 0 contour interval 1 0 0 K J m " 2 h - 1 km 0 5 10 20 + Network Station F i g u r e 5.4b S p a t i a l d i s t r i b u t i o n of the mean h o u r l y observed i n s o l a t i o n ( p a r t l y c l o u d y sky d a t a ) . F i g u r e 5.4c S p a t i a l d i s t r i b u t i o n of the mean h o u r l y observed i n s o l a t i o n ( o v e r c a s t sky d a t a ) . O O Network Station F i g u r e 5.4d S p a t i a l d i s t r i b u t i o n of the mean h o u r l y observed i n s o l a t i o n ( a l l d a t a ) . • location of the central pixel of 3x3 pixel array 0 5 10 F i g u r e 5.5 L o c a t i o n s of the c e n t r a l p i x e l of 3 x 3 p i x e l a r r a y s used t o map the s a t e l l i t e - e s t i m a t e d i n s o l a t i o n . CD 86 s a t e l l i t e and the network. The r e l a t i v e v a r i a n c e of the i n s o l a t i o n i s s m a l l . The l o w e s t i n s o l a t i o n o c c u r s i n n o r t h e r l y r e g i o n s where snow has been i n t e r p r e t e d as c l o u d by the G a u t i e r model. T h i s e r r o n e o u s a r t i f a c t i s enhanced i n r e g i o n s of p e r s i s t e n t s n o w f i e l d s , but d e c r e a s e s southward w i t h the more s e a s o n a l n a t u r e of the snow c o v e r . L a r g e r r a d i a t i v e i n t e n s i t i e s would have been a n t i c i p a t e d a t h i g h e r a l t i t u d e s due t o a s m a l l e r o p t i c a l a i r mass. W h i l e t h i s t r e n d i s d i s c e r n a b l e i n the network map, i t i s not e v i d e n t i n the s a t e l l i t e - b a s e d d i s t r i b u t i o n . Presumably, the i n t e n s i t y of the e s t i m a t e d i n s o l a t i o n i s s u p p r e s s e d by the e f f e c t s of snow c o n t a m i n a t i o n i n these r e g i o n s . The s p a t i a l p a t t e r n s i n mountainous a r e a s d i s p l a y a n o r t h - s o u t h a l i g n m e n t c o i n c i d e n t w i t h the g e n e r a l a x i s of r i d g e s and v a l l e y s and a r e p o s s i b l y r e l a t e d t o t o p o g r a p h i c s h a d i n g . By c o m p a r i s o n , the l o w l a n d i n s o l a t i o n i s l e s s s t r u c t u r e d . The d e t a i l o b s e r v e d a l o n g the c o a s t i s p r i m a r i l y an a r t i f a c t of the m o d e l l i n g p r o c e d u r e ( i . e . n o i s e ) i n d u c e d by the h i g h l y v a r i a b l e b r i g h t n e s s of s u r f a c e s such as bogs and t i d a l f l a t s . The i n s o l a t i o n under p a r t l y c l o u d y s k i e s e x h i b i t s a wider range of v a l u e s . The d i s t r i b u t i o n i s c o n t r o l l e d by o r o g r a p h i c e f f e c t s , as shown by the g r a d u a l d e c r e a s e of i n s o l a t i o n towards the Coast M o u n t a i n s . The i n s o l a t i o n f i e l d i s r e l a t i v e l y u n i f o r m under o v e r c a s t s k i e s due t o the e x t e n s i v e n a t u r e of the s y n o p t i c - s c a l e c l o u d f e a t u r e s . The p a t t e r n s which o c c u r a l o n g the mountain f r o n t may be a t t r i b u t e d t o a d d i t i o n a l o r o g r a p h i c e f f e c t s . Comparisons 87 w i t h the c o r r e s p o n d i n g network-based map i n d i c a t e s t h a t the g e n e r a l tendency f o r o v e r e s t i m a t i o n under o v e r c a s t c o n d i t i o n s i s e s p e c i a l l y s i g n i f i c a n t i n t h i s r e g i o n ( S e c t i o n 4.3.3). The s p a t i a l g r a d i e n t between mountain and l o w l a n d r e g i o n s p e r s i s t s i n the d i s t r i b u t i o n f o r a l l c o n d i t i o n s . A lower i n s o l a t i o n i s r e c e i v e d over mountainous t e r r a i n due t o a t t e n u a t i o n by o r o g r a p h i c a l l y enhanced c l o u d . The i n f l u e n c e of snow may be i n c o r p o r a t e d i n t h e s e p a t t e r n s . A weak c o a s t a l - i n l a n d g r a d i e n t i s a l s o e v i d e n t . H i g h e r i r r a d i a n c e s o c c u r a t the c o a s t w h i l e the g e n e r a l l y p a t c h y d i s t r i b u t i o n of lower i r r a d i a n c e s found i n l a n d a r e a t t r i b u t e d t o the e f f e c t s of enhanced c o n v e c t i v e a c t i v i t y a t those l o c a t i o n s (Hay, 1984). 5.4 S p a t i a l V a r i a b i l i t y of the H o u r l y E s t i m a t e d I n s o l a t i o n 5.4.1 S p a t i a l C o r r e l a t i o n s The c o r r e l a t i o n a n a l y s e s u n d e r t a k e n i n S e c t i o n 4.3 p r o v i d e an assessment of the c o v a r i a t i o n of the h o u r l y i n s o l a t i o n about the mean. However, they do not emphasize the c a n i s o t r o p y i n the c o r r e l a t i o n f i e l d which r e s u l t s from t o p o g r a p h i c v a r i a t i o n s w i t h i n the study a r e a . The e x t e n t of t h i s a n i s o t r o p y can be f u r t h e r i n v e s t i g a t e d by mapping the c o r r e l a t i o n s over t w o - d i m e n s i o n a l space. F o l l o w i n g an approach employed by Hay (1981), i n s o l a t i o n e s t i m a t e s from c o n t i g u o u s 3 x 3 a r r a y s were c o r r e l a t e d w i t h t h o s e from an a r b i t r a r i l y s e l e c t e d a r r a y l o c a t e d a t the c e n t r e of the s t u d y a r e a . The r e s u l t s of t h i s a n a l y s i s were mapped, as shown i n 88 F i g u r e 5.6a - d. The c l e a r sky f i e l d d i s p l a y s a h i g h coherence throughout the study a r e a . The c o r r e l a t i o n s d e c r ease s l i g h t l y i n n o r t h e r n p a r t s of the s t u d y a r e a but t h i s i s l i k e l y due t o a r t i f a c t s of the snow c o v e r . The s p a t i a l p a t t e r n s of the p a r t l y c l o u d y and o v e r c a s t f i e l d s p r o v i d e a marked c o n t r a s t . The c o r r e l a t i o n s are g e n e r a l l y h i g h about the c e n t e r and d e c r e a s e r a p i d l y towards c o a s t a l and mountainous r e g i o n s . The p a r t l y c l o u d y f i e l d e x h i b i t s a s t r o n g g r a d i e n t a l o n g the mountain f r o n t , r e f l e c t i n g the importance of o r o g r a p h i c c o n t r o l s under t h e s e c o n d i t i o n s . The c o r r e l a t i o n s over the l o w l a n d approximate i s o t r o p i c c h a r a c t e r i s t i c s . However, i t i s a pparent t h a t the p a t t e r n s a r e modulated by the p h y s i c a l c o n f i g u r a t i o n of the lower F r a s e r V a l l e y . The f i e l d i s c o m p a r a t i v e l y complex and h i g h l y a n i s o t r o p i c over mountainous t e r r a i n . S i m i l a r , though l e s s pronounced d i f f e r e n c e s between mountain and l o w l a n d r e g i o n s a r e d i s p l a y e d under a l l c o n d i t i o n s . The map a l s o r e v e a l s some i n t e r e s t i n g d e t a i l . E s p e c i a l l y noteworthy a r e the h i g h e r c o r r e l a t i o n s a s s o c i a t e d w i t h the deeper mountain v a l l e y s . 5.4.2 S p a t i a l Sampling Requirements f o r the H o u r l y E s t i m a t e d I n s o l a t i o n E s t i m a t e s of the h o u r l y i n s o l a t i o n were o b t a i n e d over a g r i d of 800 sample p o i n t s . These d a t a p r o v i d e the most i n t e n s i v e s p a t i a l coverage p o s s i b l e w i t h i n the a c c u r a c y of image n a v i g a t i o n . The d e r i v e d f i e l d p e r m i t s an i n i t i a l e v a l u a t i o n of s p a t i a l p a t t e r n s , h i t h e r t o unknown over l a r g e F i g u r e 5.6a V a r i a t i o n of the c o r r e l a t i o n of the s a t e l l i t e -based e s t i m a t e s w i t h d i s t a n c e from the c e n t r e of the study a r e a ( c l e a r sky d a t a ) . F i g u r e 5.6b V a r i a t i o n of the c o r r e l a t i o n of the s a t e l l i t e -based e s t i m a t e s w i t h d i s t a n c e from the c e n t r e of the study a r e a ( p a r t l y c l o u d y sky d a t a ) . F i g u r e 5.6c V a r i a t i o n of the c o r r e l a t i o n of the s a t e l l i t e -based e s t i m a t e s w i t h d i s t a n c e from the c e n t r e of the study a r e a ( o v e r c a s t sky d a t a ) . contour interval 0 0 5 + central 3 x 3 array ( central pixel coordinate 6 2 , 3 2 ) F i g u r e 5.6d V a r i a t i o n of the c o r r e l a t i o n of the s a t e l l i t e -based e s t i m a t e s w i t h d i s t a n c e from the c e n t r e of the study a r e a ( a l l d a t a ) . 48 45 1 2 1 ° 51' 93 p a r t s of the study a r e a . Due t o the l a r g e amount of d a t a p r o c e s s i n g r e q u i r e d t o d e f i n e the f i e l d , a r e d u c t i o n i n the s p a t i a l s a m p l i n g d e n s i t y c o u l d have a b e n e f i c i a l e f f e c t . T h i s can be a s s e s s e d by e x amining the r e l a t i o n s h i p between e x t r a p o l a t i o n e r r o r and d i s t a n c e . The approach i n v o l v e s the c a l c u l a t i o n of the s t a n d a r d d e v i a t i o n of the h o u r l y i n s o l a t i o n d i f f e r e n c e s between the e s t i m a t e f o r the c e n t r a l a r r a y ( K | 6 2 , 3 2 ) and a l l o t h e r e s t i m a t e s (K-^,..): (5.2) where, D i . j " K * i . : " K ' " ' M J A I J 3 2 3 2 (5.2a) (5.2b) I f the f i e l d i s assumed t o be homogeneous ( i . e . v a r i a n c e s a r e independent of l o c a t i o n ) , XID. • = 0, and E q u a t i o n 5.1 11 J becomes: (5.2c) The s p a t i a l d i f f e r e n c e s i n the l o n g - t e r m average i n s o l a t i o n over the lower F r a s e r V a l l e y have been shown t o be s m a l l (Hay, 1984). The assumption of homogeneity i s hence a v a l i d one. The a n a l y s i s was performed on each of the d a t a g r o u p i n g s and the r e s u l t s are i l l u s t r a t e d i n F i g u r e 5.7a - d. A c c o r d i n g t o W i l s o n and P e t z o l d (1972), d i f f e r e n c e s between two sample 94 e s t i m a t e s a re not s i g n i f i c a n t u n l e s s they exceed a v a l u e : 2" a t ( % ) = y |V'(RMSE%) (5.3) The r e l e v a n t t h r e s h o l d i s shown on each map. The c l e a r sky e s t i m a t e s d i s p l a y s m a l l d i f f e r e n c e s over the study a r e a . The l a r g e r e r r o r s which o c c u r i n mountainous r e g i o n s i n c o r p o r a t e m o d e l l i n g a r t i f a c t s a s s o c i a t e d w i t h snow c o v e r . The map i n d i c a t e s t h a t the i n s o l a t i o n can be e x t r a p o l a t e d from the c e n t e r t o any o t h e r l o c a t i o n , w i t h e r r o r s r e m a i n i n g — 2 - 1 below ofc = 9.2% of the mean e s t i m a t e ( i . e . 196 kjm h ). Thus one sample would a d e q u a t e l y d e f i n e the f i e l d . L a r g e r v a r i a t i o n s o c c u r i n the p a r t l y c l o u d y f i e l d . However, d i f f e r e n c e s of up t o _ 2 — i 43.8% of the mean ( i . e . 448 kjm h ) a r e not s i g n i f i c a n t . The i n s o l a t i o n a t the c e n t e r can be e x t r a p o l a t e d t hroughout t h e l o w l a n d , e x c l u d i n g c o a s t a l l o c a t i o n s . The o v e r c a s t f i e l d i s c h a r a c t e r i z e d by both s m a l l i n s o l a t i o n d i f f e r e n c e s and l a r g e e s t i m a t e e r r o r s . S i n c e d i f f e r e n c e s of up t o 59.4% of the mean _ 2 -1 ( i . e . 322 kJm h ) are i n s i g n i f i c a n t , e x t r a p o l a t i o n i s p o s s i b l e over the e n t i r e study a r e a and o n l y one sample i s r e q u i r e d . Under a l l c o n d i t i o n s , the i n s o l a t i o n can be e x t r a p o l a t e d t o - 2 - 1 w i t h i n 29.7% of the mean ( i . e . 358 kJm h ) w i t h no s i g n i f i c a n t l o s s of i n f o r m a t i o n . T h i s c o r r e s p o n d s t o a r e g i o n which encompasses the l o w l a n d and p a r t of the mountain f r o n t . The a n a l y s i s s u g g e s t s t h a t the i n i t i a l s a m p l i n g d e n s i t y can be s u b s t a n t i a l l y reduced. The c l e a r sky i n s o l a t i o n i s homogeneous over the study a r e a and i s a d e q u a t e l y c h a r a c t e r i z e d by the e s t i m a t e f o r the c e n t r a l a r r a y . In c o n t r a s t , the F i g u r e 5 . 7 a V a r i a t i o n of the s t a n d a r d d e v i a t i o n of the i n s o l a t i o n d i f f e r e n c e s w i t h d i s t a n c e from the c e n t r e of the study area ( c l e a r sky d a t a ) . F i g u r e 5.7b V a r i a t i o n of the s t a n d a r d d e v i a t i o n of the i n s o l a t i o n d i f f e r e n c e s w i t h d i s t a n c e from the c e n t r e of the study area ( p a r t l y c l o u d y sky d a t a ) . - f central 3x3 array ( central pixel coordinate 62,32^ oi = 322 kJrrr 2 rf 1 ( ± 59.4% of the observed mean insolation ) F i g u r e 5.7c V a r i a t i o n of the st a n d a r d d e v i a t i o n of the i n s o l a t i o n d i f f e r e n c e s w i t h d i s t a n c e from the c e n t r e of the study area ( o v e r c a s t sky d a t a ) . F i g u r e 5.7d V a r i a t i o n of the s t a n d a r d d e v i a t i o n of the i n s o l a t i o n d i f f e r e n c e s w i t h d i s t a n c e from the c e n t r e of the study area ( a l l d a t a ) . 99 the i n s o l a t i o n p a t t e r n s under c l o u d y c o n d i t i o n s a r e h i g h l y v a r i a b l e but the l a r g e m o d e l l i n g e r r o r s p r e v e n t an assessment of the s p a t i a l d i s t r i b u t i o n . The poor s h o r t - t e r m a c c u r a c y of the model p r e c l u d e s any c o n s i d e r a t i o n of the p r e c i s e sampling r e q u i r e m e n t s . 5 . 5 Summary a n d C o n c l u s i o n s G e o s t a t i o n a r y s a t e l l i t e d a t a were used t o map the mesoscale i n s o l a t i o n over t h e lower F r a s e r V a l l e y and the a d j a c e n t Coast M o u n t a i n s . The mapping p r o c e d u r e r e q u i r e d e s t i m a t e s of minimum b r i g h t n e s s . These were d e r i v e d u s i n g T a r p l e y ' s (1979) r e g r e s s i o n e q u a t i o n . The r e l a t i o n s h i p p r o v i d e d a good c h a r a c t e r i z a t i o n of the minimum b r i g h t n e s s over l a n d s u r f a c e s . I t f a i l e d t o reproduce the b r i g h t n e s s v a r i a t i o n s over water dominated s u r f a c e s due to the in a d e q u a t e "modelling of the b i d i r e c t i o n a l r e f l e c t a n c e p r o p e r t i e s . The mean h o u r l y s a t e l l i t e - b a s e d maps d i s p l a y e d the m o u n t a i n - l o w l a n d d i f f e r e n c e s which had been p r e v i o u s l y i n f e r r e d from the network d a t a . However, the g r e a t e r s p a t i a l coverage p r o v i d e d by the s a t e l l i t e c l e a r l y d e f i n e s t h e s e p a t t e r n s . The maps c o m p i l e d by G a u t i e r (1982) l i k e w i s e showed t h a t the d i s t r i b u t i o n of the mesoscale i n s o l a t i o n was i n f l u e n c e d by l o c a l topography though her d a t a were based on l a r g e r time and space s c a l e s . S p a t i a l c o r r e l a t i o n s were mapped t o a s s e s s the coherence of the h o u r l y i n s o l a t i o n f i e l d . The c l e a r sky c o r r e l a t i o n s were i s o t r o p i c and homogeneous throughout the study a r e a 100 ( e x c l u d i n g r e g i o n s a s s o c i a t e d w i t h a r t i f a c t s of the snow c o v e r ) . The p a r t l y c l o u d y and o v e r c a s t f i e l d s were more v a r i a b l e . Both d i s p l a y e d d i s t i n c t p a t t e r n s over mountain and l o w l a n d r e g i o n s . The c o r r e l a t i o n s r e v e a l e d some degree of i s o t r o p y over the l o w l a n d but were h i g h l y a n i s o t r o p i c i n mountainous r e g i o n s . C e r t a i n a r t i f a c t s of the m o d e l l i n g p r o c e d u r e were noted i n t h i s c h a p t e r . The i n a b i l i t y of the p r e s e n t i n s o l a t i o n model t o d i s t i n g u i s h between snow and c l o u d d i s t o r t e d the c l e a r sky p a t t e r n s . E r r o r s due t o snow were not apparent i n p r e v i o u s assessments i n v o l v i n g the Grouse Mountain s t a t i o n (Chapter IV) s i n c e t h e s e e r r o r s a r e a s s o c i a t e d w i t h more n o r t h e r l y l o c a t i o n s where snow c o v e r tends t o be p e r s i s t e n t . The s t a n d a r d d e v i a t i o n of the h o u r l y i n s o l a t i o n d i f f e r e n c e s was d e t e r m i n e d i n an attempt t o e v a l u a t e the f e a s i b i l i t y of r e d u c i n g the s p a t i a l s a m p l i n g d e n s i t y . The c l e a r f i e l d was a d e q u a t e l y r e p r e s e n t e d by one sample. Any assessment of the mesoscale v a r i a b i l i t y of the c l o u d y f i e l d s was hampered by the low a c c u r a c y of the model. Though maps of the average h o u r l y i n s o l a t i o n a re m e a n i n g f u l , i t w i l l not be p o s s i b l e t o account f o r the v a r i a b i l i t y of i n d i v i d u a l h o u r l y f i e l d s u n t i l the s h o r t - t e r m a c c u r a c y of the G a u t i e r model i s improved. 101 Chapter VI SUMMARY AND CONCLUSIONS The aim of t h i s t h e s i s was t o a s s e s s the a b i l i t y of a GOES-based procedure t o r e s o l v e the mesoscale v a r i a b i l i t y of the i n s o l a t i o n over the lower F r a s e r V a l l e y and a d j a c e n t mountainous r e g i o n . A s i m p l e p h y s i c a l l y - b a s e d model developed by G a u t i e r et a l . (1980) was used t o map the i n s o l a t i o n . A p r i o r v e r i f i c a t i o n f o r the s t u d y a r e a (Raphael and Hay, 1984) had demonstrated the s u p e r i o r i t y of t h i s approach over a l t e r n a t i v e methods. The c o r r e l a t i o n a n a l y s e s ( S e c t i o n 4.3.2) have shown t h a t t h e e s t i m a t e d d i s t r i b u t i o n s were more co h e r e n t than c o r r e s p o n d i n g network-based f i e l d s . T h i s was e s p e c i a l l y e v i d e n t i n the case of c l o u d y s k i e s and was a t t r i b u t e d t o the i n f l u e n c e of s p a t i a l a v e r a g i n g i n the s a t e l l i t e - b a s e d p r o c e d u r e . Comparisons between the o b s e r v e d and e s t i m a t e d i n s o l a t i o n ( S e c t i o n 4.3.3) c o n f i r m e d the p o t e n t i a l c a p a b i l i t y f o r the s a t e l l i t e - b a s e d mapping of the mesoscale f i e l d . Though the RMSE of the h o u r l y e s t i m a t e s were l a r g e , the MBE was s m a l l , i n d i c a t i n g t h a t the e s t i m a t e s were, on ave r a g e , p r o v i d i n g an a c c u r a t e r e p r e s e n t a t i o n of the o b s e r v e d i n s o l a t i o n . The model d i s p l a y e d a tendency towards o v e r e s t i m a t i o n under o v e r c a s t c o n d i t i o n s . These d i s c r e p a n c i e s were most f r e q u e n t l y a s s o c i a t e d w i t h e s t i m a t e s f o r the Grouse Mountain l o c a t i o n due t o the h i g h e r i n c i d e n c e of o r o g r a p h i c c l o u d over mountainous r e g i o n s . U n d e r e s t i m a t i o n o c c u r r e d under p a r t l y c l o u d y c o n d i t i o n s , 102 i r r e s p e c t i v e of s t a t i o n l o c a t i o n . I n s o l a t i o n e s t i m a t e s d e r i v e d from 3 x 3 p i x e l a r r a y s d i d not d i f f e r s i g n i f i c a n t l y from th o s e u s i n g 5 x 5 a r r a y s ( S e c t i o n s 4.3.4 and 4.3.5). These r e s u l t s d emonstrated the f e a s i b i l i t y of a p p l y i n g the 3 x 3 p i x e l a r r a y s t o r e s o l v e the s p a t i a l f i e l d . I n t e r e s t i n g l y , the 3 x 3 a r r a y e s t i m a t e s d i d not e x h i b i t any i n c r e a s e d s i m i l a r i t y w i t h the network o b s e r v a t i o n s , a s i t u a t i o n which might be a n t i c i p a t e d as a r e s u l t of the r e d u c t i o n i n s p a t i a l a v e r a g i n g . T h i s i m p l i e s t h a t most of the i n s o l a t i o n v a r i a b i l i t y o c c u r s a t s m a l l e r s c a l e s . The e f f e c t s of s p a t i a l a v e r a g i n g a r e t h e r e f o r e e x p e r i e n c e d p r i m a r i l y between the p o i n t and the 3 x 3 p i x e l s c a l e s . A more s p e c i f i c i n v e s t i g a t i o n of s p a t i a l a v e r a g i n g was not undertaken s i n c e n a v i g a t i o n a l e r r o r s r e s t r i c t t he use of s m a l l e r a r r a y s . A r e g r e s s i o n d e v e l o p e d by T a r p l e y (1979) was used t o map the minimum b r i g h t n e s s f i e l d ( S e c t i o n 5.2.1). The performance 2 of the model, as det e r m i n e d by r and SE, was p o o r e r f o r water dominated s u r f a c e s . Assessments i n d i c a t e d t h a t the b i d i r e c t i o n a l r e f l e c t a n c e c h a r a c t e r i s t i c s of such s u r f a c e s were i n a d e q u a t e l y p o r t r a y e d by the model. The s p a t i a l p a t t e r n s of the mean h o u r l y e s t i m a t e d i n s o l a t i o n ( S e c t i o n 5.3) were dominated by m o u n t a i n - l o w l a n d d i f f e r e n c e s . The maps d i s p l a y e d c e r t a i n a r t i f a c t s of the m o d e l l i n g p r o c e d u r e . In p a r t i c u l a r , they showed the i n a b i l i t y of the s a t e l l i t e - b a s e d i n s o l a t i o n model t o d i f f e r e n t i a t e between snow and c l o u d and the s e n s i t i v i t y of the m o d e l l e d 103 i n s o l a t i o n t o v a r i a t i o n s i n s u r f a c e a l b e d o . Maps of the c o r r e l a t i o n of the h o u r l y i n s o l a t i o n ( S e c t i o n 5.4.1) showed t h a t the c l e a r f i e l d was h i g h l y c o h e r e n t . The lower c o r r e l a t i o n s o b t a i n e d i n n o r t h e r l y l o c a t i o n s were due t o m o d e l l i n g a r t i f a c t s caused by the occ u r e n c e of snow i n the s e r e g i o n s . The p a t t e r n s d i s p l a y e d by the c l o u d y sky d i s t r i b u t i o n s were c o n t r o l l e d by topography. The c o r r e l a t i o n s e x h i b i t e d a c e r t a i n degree of i s o t r o p y over the l o w l a n d , but d e c r e a s e d r a p i d l y toward the mountains where p a t t e r n s were r e l a t i v e l y complex. The s t a n d a r d d e v i a t i o n of the h o u r l y i n s o l a t i o n d i f f e r e n c e s ( S e c t i o n 5.4.2) i n d i c a t e d t h a t the mesoscale v a r i a b i l i t y of i n d i v i d u a l h o u r l y f i e l d s cannot be r e s o l v e d u s i n g the s a t e l l i t e -based approach. The h o u r l y m o d e l l i n g e r r o r s ( p a r t i c u l a r l y t h o s e a s s o c i a t e d w i t h c l o u d y f i e l d s ) were so l a r g e as t o obscure the v a r i a b i l i t y of the e s t i m a t e d f i e l d . The u s e f u l n e s s of the mapping p r o c e d u r e appears t o be l i m i t e d t o assessments of the average i n s o l a t i o n , f o r which m o d e l l i n g e r r o r s a r e s m a l l . However, i t i s a l s o n o t e d t h a t e s t i m a t e s of the h o u r l y i n s o l a t i o n under c l o u d y c o n d i t i o n s have l i k e w i s e been d e r i v e d w i t h poor a c c u r a c i e s u s i n g methods based on s u r f a c e d a t a ( D a v i e s , 1980). The l a c k of d i s t i n c t i o n between snow and c l o u d s u r f a c e s poses an a d d i t i o n a l l i m i t a t i o n i n mountainous and temperate environments where p e r s i s t e n t or s e a s o n a l snow c o v e r i s e x p e r i e n c e d . For such r e g i o n s , t h i s problem needs t o be r e s o l v e d i f s a t e l l i t e - b a s e d mapping i s ex p e c t e d t o y i e l d r e l i a b l e e s t i m a t e s of the i n s o l a t i o n a v a i l a b i l i t y . 1 04 FOOTNOTES CHAPTER I 7 The terms " i n s o l a t i o n " and " s o l a r i r r a d i a n c e " a r e used i n t e r c h a n g e a b l y throughout t h i s t h e s i s . They a r e both d e f i n e d a s , "the r a d i a n t f l u x per u n i t a r e a i n c i d e n t upon a s u r f a c e " (Hay, 1980). CHAPTER I I 1 SR i s the r a t i o of the r a d i a n t energy r e f l e c t e d by a s u r f a c e t o t h a t i n c i d e n t upon i t , n o r m a l i z e d f o r an overhead sun, as d e s c r i b e d i n S e c t i o n 3.2.2.3. 2 R e f e r t o L i s t of Symbols and A b b r e v i a t i o n s f o r the ex p a n s i o n of acronyms. 3 A p i x e l ( p i c t u r e element) c o r r e s p o n d s t o the p r o j e c t i o n on the ground of the i n s t a n t a n e o u s f i e l d - o f - v i e w of the s a t e l l i t e . 4 The term " b r i g h t n e s s " i s a r e l a t i v e measure of the i n t e n s i t y of the r a d i a t i o n emerging from an image p l a n e . 105 BIBLIOGRAPHY A l a k a , M.A., 1970: T h e o r e t i c a l and P r a c t i c a l C o n s i d e r a t i o n s f o r Network D e s i g n . 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T h e s i s , 209 pp. W i l s o n , R.G., 1980: R a d i a t i o n Network Assessment and D e s i g n . P r o c e e d i n g s , F i r s t Canadian S o l a r R a d i a t i o n Data Workshop, J.E. Hay and T.K. Won ( e d s ) , Canadian Atmospheric Environment S e r v i c e , Downsview, O n t a r i o , 105-117. W i l s o n R.G. and D.E. P e t z o l d , 1972: D a i l y S o l a r R a d i a t i o n D i f f e r e n c e s Between S t a t i o n s i n Southern Canada: A p r e l i m i n a r y A n a l y s i s . C l i m a t o l o g i c a l B u l l e t i n , 11, M c G i l l U n i v e r s i t y , 15-22. i 1 1 2 APPENDIX A PROGRAM TO IMPLEMENT GAUTIER'S MODEL Modified by M.D.R. 7/8 3 A . l Main Program U n i t a s s i g n m e n t s : S a t e l l i t e d a t a windows read from UNIT 8 E l e v a t i o n m a t r i x read from UNIT 4 R e g r e s s i o n c o e f f i c i e n t s read from UNIT 3 L i m i t s r e a d from UNIT 2 C o n t r o l i n f o r m a t i o n r e a d from UNIT 5 P r e d i c t e d f l u x e s , e t c p r i n t e d on UNIT 7 P r e d i c t e d h o u r l y i n s o l a t i o n v a l u e s p r i n t e d on UNIT 10 I f par=reg s p e c i f i e d , d a t a f o r b r i g h t n e s s r e g r e s s i o n output on UNIT 9 COMMON /REG/ RDATA(50,50),RFLAG LOGICAL RFLAG Determine secondary image s i z e , e t c CALL INIT(NRS,NCS,JR,JC,MODE,RFLAG) Read i n a primary image and deter m i n e a n g l e s , e t c , 5 CALL INPUT(NAVTIM,XLAPT,NRP,NCP,X1,X2,X3,MODE,&5,&99) CALL GETLIM(NAVTIM,&5) For each secondary image: 1) p e r f o r m d a t a q u a l i t y c o n t r o l check 2) c a l c u l a t e a t m o s p h e r i c a b s o r p t i o n 3) c a l c u l a t e minimum b r i g h t n e s s 4) d e t e r m i n e n o r m a l i z e d r e f l e c t a n c e 5) d e t e r m i n e minimum r e f l e c t a n c e 6) c a l c u l a t e the s o l a r f l u x e s 7) s t o r e t h e d a t a by secondary image p o s i t i o n IF(MODE.EQ.2) GOTO 20 MODE I p r o c e s s i n g : 12 s t a t i o n network DO 10 ISTN=1,12 CALL GETPOS(ISTN,NR,NC,IR,IC,MODE) CALL QCHECK(NAVTIM,NR,NC,ISTN,ISTN,&10) CALL ABS1(X1,IR,IC,ALT) CALL B1(X1,X2,X3,ISTN,BMIN) RMIN=RNORM(BMIN,X1)*1353.0*X1 CALL THRESH(X1,X2,X3,RMIN,ALBS,THR) 1 1 3 CALL CALC(X1,X2,X3,THR,ALBS,XKD,NCLDY,XKDO,XKDC) IF(RFLAG) CALL RSTORE(ISTN,ISTN) CALL STORE(ISTN,ISTN,XKD) 10 CONTINUE CALL PRINT1 IF(RFLAG) CALL RPR1(X1,X2,X3) GOTO 5 MODE II p r o c e s s i n g -- moving g r i d 20 DO 30 NR=1,NRP,JR ISR=(NR-1)/JR+1 DO 25 NC=1,NCP,JC ISC=(NC-1)/JC+1 CALL GETPOS(0,NR+NRS/2,NC+NCS/2,IR,IC,MODE) CALL QCHECK(NAVTIM,NR,NC,ISR,ISC,& 2 5) C CALL ABS1(X1,IR,IC,ALT) CALL B2(X1,X2,X3,NR+NRS/2,NC+NCS/2,ALT,BMIN) C CALL STORE(ISR,ISC,BMIN) C RMIN=RNORM(BMIN,X1)* 1353.0*X1 C CALL THRESH(X1,X2,X3,RMIN,ALBS,THR) C CALL CALC(X1,X2,X3,THR,ALBS,XKD,NCLDY,XKDO,XKDC) C IF(RFLAG) CALL RSTORE(ISR,ISC) C CALL STORE(ISR,ISC,XKD) 25 CONTINUE 30 CONTINUE CALL PRINT2(JR,JC,NRP,NCP) IF(RFLAG) CALL RPR2(JR,JC,NRP,NCP,X1,X2,X3) GO TO 5 99 CALL SPAN CALL MERGE((NRP-1)/JR+1,(NCP-1)/JC+1) IF(MODE.EQ.2) CALL FPRINT(JR,JC,NRP,NCP) STOP END 1 1 4 A. 2 S u b r o u t i n e s SUBROUTINE ABS1(COSZZ,IR,IC,ALT) Input p r e c i p i t a b l e water ( i f n e c e s s a r y ) and c a l c u l a t e a t m o s p h e r i c a b s o r p t i o n . INTEGER L I S T ( 1 ) / ' * ' / REAL ELEV(120,60)/7200*0.0/ COMMON/ATTEN/ABSUN,ABSAT,ABSUNT,ABSUNB,BREFL,ABSATT, *ABSATB,DENOM LOGICAL FIRST/.TRUE./,WARN/.TRUE./ I f f i r s t pass - read i n p r e c i p . water and e l e v a t i o n m a t r i x IF(.NOT.FIRST) GOTO 23 FIRST=.FALSE. WRITE(6,20) 20 FORMATC INPUT PRECIP.WATER IN MM.') READ(5,LI ST) W READ(4) ELEV 23 ALT=ELEV(60+IC,30+IR) C WRITE(6,661) IR,IC,ALT C661 FORMATC *** ' , 21 5 ,F9. 1 ) IF(ALT.GE.O.O) GOTO 25 IF(WARN) WRITE(6,100) WARN=.FALSE. ALT=0.0 25 COSZ=COSZZ IF(COSZZ.LT.O.O) COSZZ= 0.009 ZED=ARCOS(COSZZ)*180.0/3.14159 C IF(ZED.GT.90.0) ZED=90.0 Kas t e n ' s a i r mass a l g o r i t h m AMSUN=EXP(-ALT/8243.0)/(COSZZ+0.15/((93.885-ZED)** 1.253)) U1 = W IF(ALT.GT.500.0) U1=U1*0.8 ABSUN=YAM(U1,AMSUN) (Note: 56.4 i s the s a t e l l i t e z e n i t h a n g l e f o r Vancouver l a t i t u d e ) AMSAT=EXP(-ALT/8 2 4 3.0)/(COS(56.4*3.14159/180.0)+0.15/ * ((93.885-56.4)**1.253)) ABSAT=YAM(U1,AMSAT) U2=U1*0.3 ABSUNT=YAM(U2,AMSUN) ABSATT=YAM(U2,AMSAT) 1 1 5 U2=U1*0.7 ABSUNB=YAM(U2,AMSUN) BREFL=COUL(COSZ) ABSATB=YAM(U2,AMSAT) RETURN 100 FORMATC0*** WARNING <ABS 001> *** NO ELEVATION DATA', 1 ' AVAILABLE FOR ONE',/,' ' , 3 1 X, ' OR MORE LOCATIONS', 2 ' - 0 ASSUMED.') END 1 1 6 SUBROUTINE B l ( X I , X 2 , X 3 , N S , B ) R e t u r n s the p r e d i c t e d t a r g e t c l e a r b r i g h t n e s s . The minimum b r i g h t n e s s c o e f f i c i e n t s a re based on a n a l y s i s of c l e a r images i n a l l seasons (no snow). REAL A(12)/37.698,39.345,41.494,40.534,40.540,41.877,40. *529,39.763,40.389,40.716,39.636,40.132/ REAL BAB(12)/39.842,42.952,42.043,49.969,52.102,30.195,5 *0.239,51.981,53.205,50.7 55,50.7 08,37.713/ REAL C(12)/6.921,8.256,9.533,8.33 7,9.061,3.004,7.483,5.3 *95,5.352,5.119,7.560,7.488/ REAL D(12)/15.438,13.046,10.896,10.564,9. 1 69,2.457,9.334 , *13.134,11.348,12.853,10.586,7.207/ B=A(NS)+BAB(NS)*X1+C(NS)*X2+D(NS)*X3 C WRITE(6,100) B C100 FORMAT(' BMIN : ',F8.2) RETURN END 1 1 7 SUBROUTINE B2(Xl,X2,X3,IR,IC,ALT,B3) Computes t a r g e t c l e a r b r i g h t n e s s g i v e n r e l a t i v e g r i d l o c a t i o n , u s i n g r e g r e s s i o n f o r n e a r e s t c e n t r a l p i x e l of 5x5 a r r a y INTEGER ISROW(12)/-12,-8,-5,1,14,0,6,12,14,7,-1,-5/,NW */288/ INTEGER ISCOL(12)/-38,-35,-39,-41,-33,0,38,41,35,8,-36, *-50/ REAL C1(300),C2(300),C3(300),C4(300) LOGICAL FIRST/.TRUE./ IF(.NOT.FIRST) GOTO 5 READ(3,100) ( C 1 ( I ) , C 2 ( I ) , C 3 ( I ) , C 4 ( I ) , 1 = 1 , N W ) FIRST=.FALSE. 5 IR5=(IR-1)/5+1 IC5=(IC-1)/5+1 I=(IR5-1)*24+IC5 B3=C1(I)+C2(I)*X1+C3(I)*X2+C4(I)*X3 C WRITE(6,88) IR,IC 88 FORMAT(' ',215) C I S= 1 C IF(ALT.GT.500.0) GOTO 15 C DMIN=9999.9 C DO 10 I = 1 , 12 C D = ( I R - I S R 0 W ( I ) ) * * 2 + ( l C - I S C O L ( l ) ) * * 2 C IF(D.GE.DMIN) GOTO 10 C DMIN=D C IS=I C10 CONTINUE C15 CALL B1(X1,X2,X3,IS,BVAL) C B3=BVAL RETURN 100 FORMAT(4E13.6) END 118 SUBROUTINE CALC(XI,X2,X3,THR,ALBS,KDOWN,NCLDY,KDOWNO, KDOWNC) C a l c u l a t e the p r e d i c t e d s o l a r f l u x e s : (1) c l e a r ("KDOWNO") (2) c l o u d y ("KDOWNC") (3) average ("KDOWN") INTEGER VALS(50,50) COMMON /ATTEN/ ABSUN,ABSAT,ABSUNT,ABSUNB,BREFL,ABSATT, * ABSATB,DENOM COMMON /SEC/ VALS,NR,NC REAL KDOWN 0,KDOWNC,KDOWNT,KDOWN LOGICAL CLR/.FALSE./ I n i t i a l i z e . NCLEAR=0 NCLDY=0 KDOWNC=0.0 NVALS=NR*NC AVALBS=0.0 RKO = 1353.0 * XI KDOWN0=0.0 KDOWNT=0.0 IF(RKO.LT.0.0) GOTO 50 KDOWN0=RK0*(1.0-BREFL)*(1.0-ABSUN)*(1.0+ALBS*0.076)*3.60 DO 25 I=1,NR DO 20 J=1,NC Conv e r t c o u n t s t o n o r m a l i z e d r e f l e c t a n c e and compare w i t h t h r e s h o l d . RVAL = VAL S ( I , J ) REFL=RNORM(RVAL,X1)*RK0 IF(REFL.GE.THR) GO TO 10 Count number of c l e a r p i x e l s NCLEAR=NCLEAR+1 GO TO 20 Cloudy p i x e l c a l c u l a t i o n s : (1) c a l c u l a t e c l o u d a b s o r p t i v i t y ("CLABS") (2) c a l c u l a t e c l o u d a l b e d o ("CLREFL") (3) d e t e r m i n e f l u x i n c l o u d y p i x e l and add t o "KDOWNC" 10 NCLDY=NCLDY+1 STEP=(RKO-THR)/2 0.0 CLABS=((REFL-THR)/STEP)* 0.01 PHI=RK0*(1.0-BREFL)*(1.0-ABSUNT)*(1.0-ABSUNB)*ALBS* 1 (1.0-ABSATT)*((1.0-CLABS)**2)*(1.0-ABSATB)*(1.0 119 2 -0.076) BETA=RK0*(1.0-BREFL)*(1.0-ABSUNT)*(1.0-0.076)*(1.0 1 -ABSATT) GAMMA=RKO*BREFL SW=REFL GEE=BETA-2.0*PHI EFF=(GAMMA+PHI-SW)*PHI ROOT=SQRT(GEE*GEE-4.0*EFF) GEE=GEE*(-1.0) ALBCL1=(GEE+ROOT)/(2.0*PHI) ALBCL2=(GEE-ROOT)/(2.0*PHI) CLREFL=ALBCL1 IF(CLREFL.GT.0.85) CLREFL=0.85 KDOWNT=RK0*(1.0~BREFL)*(1.0-ABSUNT)*(1.0-CLREFL) 1 *(1.0-CLABS)*(1.0-ABSUNB)*3.60 KDOWNC=KDOWNC+KDOWNT 20 CONTINUE 25 CONTINUE IF(NCLDY.GT.O) GO TO 40 I f no c l o u d a c t u a l s o l a r f l u x = c l e a r sky v a l u e KDOWN=KDOWN0 GO TO 50 I f c l o u d i n image then weight f o r c l e a r and c l o u d y p i x e l s , c l o u d y p i x e l s 40 KDOWN=(KDOWN0*NCLEAR+KDOWNC)/(NCLEAR+NCLDY) 50 RETURN END 120 SUBROUTINE FPRINT(JR,JC,NRP,NCP) P r i n t s out a g r i d of p r e d i c t e d f l u x e s on UNIT 10. COMMON /MDATA/ TIM1(40),TIM2(40),FLG(40),HFLUX(50,50,20) *,IH1,IH2 COMMON /SEC/ SIM(50,50),NRS,NCS COMMON /PDATA/ FLUX(50,50,40),NTIMS(40) NR=NRP/JR NC=NCP/JC KC1=1+NCS/2 KC2=NCP-NCS/2 KR1=1+NRS/2 KR2=NRP-NRS/2 IDATE=NTIMS(1)/l0000 IF(MOD(NTIMS(1),10000).LT.800) IDATE=IDATE-1 IF(MOD(IDATE,1000).NE.999) GOTO 2 IDATE=IDATE/1000*1000+365 IF(M0D(IDATE/1000,4).EQ.0) IDATE=IDATE+1 2 DO 20 IH=IH1,IH2 WRITE(10,100) IDATE,IH,NRS,NCS,(I,I=KC1,KC2,JC) 1 = 0 DO 5 IR=KR1,KR2,JR 1 = 1 + 1 WRITE(10,101) IR,(HFLUX(I,J,IH),J=1,NC) 5 CONTINUE 20 CONTINUE RETURN 100 FORMATC- PREDICTED INSOLATION FOR ',15,' HOUR ENDING ', 1 I2,':00 GAUTIER''S MODEL (FLUX AVERAGING) - K J / ' 2 ,'M2/HR',/,' SECONDARY WINDOW SIZE : ',13,' BY' 3 ,13,/,' ',5016) 101 FORMATC ',I3,50F6.0) END 121 SUBROUTINE GETLIM(NAVTIM, ) Reads i n b r i g h t n e s s t h r e s h o l d s f o r t h i s image from UNIT 2. COMMON /LIM/ LIM1,LIM2 COMMON /REG/ RDATA(50,50),RFLAG LOGICAL RFLAG IF(.NOT.RFLAG) GOTO 88 ILINE=M0D(NAVTIM/10,10000000) FIND(2'ILINE) READ(2,100,END= 99) NT,LIM1,LIM2 IF(NT.NE.NAVTIM) GOTO 99 RETURN 88 LIM1=-1 LIM2=256 RETURN 99 RETURN 1 100 FORMAT(110,215) END 122 SUBROUTINE GETPOS(ISTN,NR,NC,IR,IC,MODE) Determines image p o s i t i o n and s t o r a g e l o c a t i o n f o r next s t a t i o n . COMMON / P R I / VALS(250,250),NRP,NCP,ICSTN COMMON /SEC/ SIM(50,50),NRS,NCS INTEGER ISROW(l2)/-12,-8,-5,1,14,0,6,12,14,7,-1,-5/ INTEGER ISCOL(12)/-38,-35,-39,-41,-33,0,38,41,35,8,-36,-50/ IF(MODE.EQ.2) GOTO 10 IR=ISR0W(ISTN) IC=ISC0L(ISTN) NR=ISROW(ISTN)-ISROW(ICSTN)+NRP/2-NRS/2+1 NC=ISCOL(ISTN)-ISCOL(ICSTN)+NCP/2-NCS/2+1 RETURN 10 IR=NR-NRP/2+ISROW(lCSTN) IC=NC-NCP/2+ISCOL(lCSTN) RETURN END 1 23 SUBROUTINE INIT(NR,NC,JR,JC,MODE,RFLAG) Reads i n s i z e of secondary images & de t e r m i n e s MODE.(from UNIT 5) COMMON /SEC/ IVALS(50,50),NRS,NCS INTEGER L I S T ( 1 ) / ' * ' / LOGICAL RFLAG LOGICAL* 1 PRSTROOO) MODE=1 RFLAG=.FALSE. CALL PAR(PRSTR, I PL,100) CALL FINDST(PRSTR,I PL,'MODE2',5,1,1POS) IF(IPOS.NE.O) MODE=2 CALL FINDST(PRSTR,I PL,'REG' ,3,1,IPOS) IF(IPOS.NE.O) RFLAG=.TRUE. WRITE(6,100) READ(5,LI ST) NRS,NCS NR=NRS NC=NCS IF(MODE.NE.2) RETURN WRITE(6,101) READ(5,LI ST) JR,JC RETURN 100 FORMATC ENTER SIZE OF SECONDARY WINDOWS (NROWS, NCOLS)') 101 FORMATC ENTER ROW AND COLUMN WINDOW SPACING') END 124 SUBROUTINE INPUT(NAVTIM,XLAPT,NRP,NCP,XI,X2,X3,MODE, , ) Reads i n a p r i m a r y image and computes s o l a r a n g l e s . INTEGER VALS(250,250),NTIM/0/ REAL*8 STAT,FSTAT,FNAV COMMON /PDATA/ FLUX(50,50,40),NTIMS(40),XLATS(40),NIMS COMMON / P R I / VALS,NR,NC,ICSTN COMMON /SEC/ IVALS(50,50),NRS,NCS LOGICAL FIRST/.TRUE./ IF(.NOT.FIRST) GOTO 5 FIRST=.FALSE. NIMS=0 Input image s i z e , time and s t a t i o n name 5 READ(8,100,END= 44) NR,NC,NAVTIM,STAT IF(NAVTIM.EQ.NTIM) GO TO 15 NTIM=NAVTIM Determine LAT and a n g l e s CALL SGEOM(NAVTIM,0.0,XLPT,Y1,Y2,Y3) XLAPT=XLPT X1=Y1 X2=Y2 X3=Y3 Input b r i g h t n e s s c o u n t s 15 DO 20 1=1,NR READ(8,101) (VALS(I,J),J=1,NC) 20 CONTINUE NRP=NR NCP=NC ICSTN=ISTNUM(STAT) IF((NR.LT.NRS).OR.(NC.LT.NCS)) GOTO 30 IF(X1.LE.0.0) GOTO 55 WRITE(7,102) NAVTIM,XLAPT,NR,NC,STAT,NRS,NCS IF(((MOD(NR,NRS).NE.0).OR.(MOD(NC,NCS).NE.0)).AND.(MODE 1.EQ.2)) WRITE(6,103) NR,NC,NAVTIM NIMS=NIMS+1 NTIMS(NIMS)=NAVTIM XLATS(NIMS)=XLAPT RETURN 30 WRITE(6,104) NR,NC,NAVTIM RETURN 1 44 RETURN 2 55 WRITE(6,105) NAVTIM,XLAPT RETURN 1 100 F0RMAT(I4,4X,I3,I10,14X,A8) 101 FORMAT(4(64I3)) 125 102 FORMAT('-NAVTIM : ',110,' L.A.T. : ',F6.2,/, 1 ' PRIMARY IMAGE : ',14,' BY' ,14, 2 ' CENTERED ON *,A8,' SECONDARY IMAGE SIZE : ',13, 3 ' BY',13) 103 FORMATC0*** WARNING <INPUT 001> *** PRIMARY IMAGE ', 1 'SIZE', ' (',14,' BY',14,')', 2 /,' IS NOT AN INTEGRAL MULTIPLE OF SECONDARY IMAGE' 3 ,' SIZE.',/,' PERIPHERAL DATA WILL BE IGNORED.' 4 ,'NAVTIM : ',110) 104 FORMAT('0**** ERROR <INPUT 001> **** PRIMARY IMAGE ' 1 ,'SIZE (',14,' BY',14,')', 2 A ' IS LESS THAN SECONDARY IMAGE SIZE.', 3 /,' IMAGE IGNORED. NAVTIM : ',110) 105 FORMATC0*** NOTE <INPUT 001> *** NAVTIM = ',110, 1 * L.A.T. = ',F6.2,/,* 2 ,'SUN BELOW HORIZON - IMAGE IGNORED') END 126 SUBROUTINE MERGE(NR,NC) Merges the i n s t a n t a n e o u s f l u x p r e d i c t i o n s t o form h o u r l y i n s o l a t i o n p r e d i c t i o n s . COMMON /PDATA/ FLUX(50,50,40),NTIMS(40),XLATS(40),NIMS COMMON /MDATA/ TIM1(40),TIM2(40),SFLG(40),HFLUX(50,50,20) , 1 IH1,IH2 LOGICAL SFLG Determine e a r l i e s t p o s s i b l e s t a r t i n g hour IH1=TIM1(1)+2.0 IH2=TIM2(NIMS) Now compute h o u r l y v a l u e s f o r each l o c a t i o n DO 70 IR=1,NR DO 60 IC=1,NC DO 50 IH=IH1,IH2 TST=IH-1.0 DO 10 IM=1,NIMS IM1=IM IF(TIM2(IM).GT.TST+0.001 ) GO TO 15 10 CONTINUE 15 IF((.NOT.SFLG(IM1)).OR.(FLUX(IR,IC,IM1).EQ.-9.999) 1 .OR.'(TIM2 (IM1 ) . LE. TST) ) GOTO 25 TFRAC=0.0 XDBAR=0.0 20 IF((IM1.GT.NIMS).OR.(FLUX(IR,IC,IM1).EQ.-9.999)) 1 - GO TO 25 IF(.NOT.SFLG(IM1)) GOTO 25 T1=TIM1(IM1) T2=TIM2(IM1) C WRITE(6,90) T1,T2 90 FORMAT( 'T1=',F9.3,2X,'T2=*,F9.3) Determine w e i g h t s f o r each image i n hour TIME=AMIN1(T2,FLOAT(IH))-AMAX1(T1,TST) FRAC=TIME/(T2-T1) TFRAC=TFRAC+FRAC Weight the i n s t a n t a n e o u s p r e d i c t i o n s XDBAR=XDBAR+FRAC *FLUX(IR,IC,IM1) IM1=IM1+1 IF(T2.LT.FLOAT(IH)) GO TO 20 127 Convert t o k j m h XDBAR=XDBAR/TFRAC S t o r e c a l c u l a t e d v a l u e s f o r hour and l o c a t i o n IF(XDBAR.LT.O.O) XDBAR=0.0 HFLUX(IR, IC , IH )=XDBAR GO TO 50 25 HFLUX(lR,IC,IH)=-9.999 50 CONTINUE 60 CONTINUE 70 CONTINUE 99 RETURN END 1 28 SUBROUTINE PRINT1 P r i n t s out p r e d i c t e d f l u x e s f o r 12 s t a t i o n s on UNIT 7. COMMON /PDATA/ FLUX(50,50,40),NTIMS(40),XLATS(40),NIMS REAL*8 NAMES(12)/'GRSMT ' , 'NRTHMT ' ,'BCHYDRO ' , * 'VANAIR ','FERRY ','PITMED ','MISSHAB * 'ABBLIB ','ABBAIR ','LANGLEY ','LANGA ','CLISTN '/ WRITE(7,100) (NAMES(I),1=1,12) WRITE(7,101) (FLUX(I,I,NIMS),I=1,12) RETURN 100 FORMAT('0 ',12A8) 101 FORMAT(' ' ,12F8. 1) END 129 SUBROUTINE PRINT2(JR,JC,NRP,NCP) P r i n t s out a g r i d of p r e d i c t e d f l u x e s on UNIT 7. COMMON /PDATA/ FLUX(50,50,40),NTIMS(40),XLATS(40),NIMS COMMON /SEC/ SIM(50,50),NRS,NCS NR=NRP/JR NC=NCP/JC K1=1+NCS/2 K2=NCP-NCS/2 WRITE(7,100) (I,I=K1,K2,JC) K1=1+NRS/2 K2=NRP-NRS/2 1 = 0 DO 5 IR=K1,K2,JR 1 = 1 + 1 WRITE(7,101) IR,(FLUX(I,J,NIMS),J=1,NC) 5 CONTINUE RETURN 100 FORMAT(' *,5016) 101 FORMAT(' ',I3,50F6.0) END 1 30 SUBROUTINE QCHECK(NAVTIM,NR,NC,ISR,ISC, ) E x t r a c t s secondary image s t a r t i n g a t (NR,NC) from p r i m a r y image and performs q u a l i t y c o n t r o l check. 5 1 0 22 33 100 101 GOTO 33 GOTO 22 INTEGER PIM,SIM COMMON /SEC/ SIM(50,50),NRS,NCS COMMON / P R I / PIM(250,250),NRP,NCP IF((NR.LT.1).OR.(NC.LT.1)) GOTO 33 ITOT=0 NVAL=0 DO 10 1=1,NRS DO 5 J=1,NCS NI=NR+I-1 NJ=NC+J-1 IF((NI.GT.NRP).OR.(NJ.GT.NCP)) IVAL=PIM(NR+I-1,NC+J-1) ITOT=ITOT+IVAL IF((IVAL.GT.255).OR.(IVAL.LT.12)) NVAL=NVAL+1 SIM(I,J)=IVAL CONTINUE CONTINUE CALL STORE(ISR,ISC,FLOAT(ITOT/NVAL)) RETURN WRITE(6,100) NAVTIM,NR,NC CALL STORE(ISR,ISC,-9.999) CALL RSTORE(-ISR,-ISC) RETURN 1 WRITE(6,101) NAVTIM,NR,NC,ISR CALL STORE(lSR,ISC,-9.999) CALL RSTORE(-ISR,-ISC) RETURN 1 FORMATC 0*** WARNING <QCHECK 1 ,' FAILURE',/,' NAVTIM 2 ,'REFERENCE : ',214) FORMATC0*** WARNING <QCHECK 002> 1 ,'OUTSIDE PRIMARY IMAGE BOUNDS',/,' NAVTIM 2 110,' PRIMARY IMAGE REFERENCE : ',214,' 3 ,'ION : ',12) END 001> *** ' ,no,' *** QUALITY CONTROL' PRIMARY IMAGE ' SECONDARY IMAGE STAT' 131 SUBROUTINE R P R 1 ( X l , X 2 , X 3 ) P r i n t s out d a t a f o r c l e a r b r i g h t n e s s r e g r e s s i o n on UNIT 9. (MODE I ) COMMON /REG/ RDATA(50,50) WRITE(9,100) X1,X2,X3,(RDATA(I,1),1=1,12) RETURN 100 FORMAT(3F7.4,/,12F6.1) END 1 32 SUBROUTINE RPR2(JR,JC,NRP,NCP,XI,X2,X3) P r i n t s out da t a f o r c l e a r b r i g h t n e s s r e g r e s s i o n on UNIT 9. (MODE II.) COMMON /REG/ RDATA(50,50) NR=NRP/JR NC=NCP/JC WRITE(9,100) X1,X2,X3,((RDATA(I,J),J=1,NC),I=1,NR) RETURN 100 FORMAT(3F7.4,/,10(12F6.1,/)) END 133 SUBROUTINE RSTORE(NR,NC) S t o r e s r e g r e s s i o n i n f o r m a t i o n . INTEGER SIM,ITALLY(256) COMMON /SEC/ SIM(50,50),NRS,NCS COMMON /REG/ RDATA(50,50) COMMON /LIM/ LIM1,LIM2 F i r s t check f o r m i s s i n g data i n d i c a t i o n IF(NR.LT.O) GOTO 20 Compute median and mode of secondary window d a t a and s t o r e the l e s s e r of the two DO 2 1=1,256 ' ITALLY(I)=0 2 CONTINUE NP=0 DO 10 IR=1,NRS DO 5 IC=1,NCS IV=SIM(IR,IC)+1 IF((IV.LT.LIM1).OR.(IV.GE.LIM2)) GOTO 5 ITALLY(IV)=ITALLY(IV)+1 NP=NP+1 5 CONTINUE 10 CONTINUE PP=NRS*NCS IF(NP/PP.LT.0.67) GOTO 17 IC = 0 XMED=-1.0 IMODE=0 IH=NP/2 DO 15 1=1,256,4 IT=ITALLY(I) IC=IC+IT IF(IT.GT.ITALLY(IMODE+1)) IMODE=I"1 IF((IC.LT.IH).OR.(XMED.GE.0.0)) GOTO 15 XMED=FLOAT(I-1) IF(MOD(NP,2).NE.0) XMED=XMED+2.0 15 CONTINUE XREG=FLOAT(IMODE) IF(XMED.LT.XREG) XREG=XMED RDATA(NR,NC)=XREG RETURN 17 RDATA(NR,NC ) = - 9 . 9 RETURN 20 RDATA(-NR,-NC ) = - 9 . 9 RETURN END 134 SUBROUTINE SGEOM(NAVTIM,XPT,XLAPT,XI,X2,X3) Computes l o c a l apparent time and v a r i o u s g e o m e t r i c v a l u e s REAL CLAT/49.217/,SATAZ/15.0/ F i r s t compute d e c l i n a t i o n , s o l a r z e n i t h a n g l e , and s o l a r a z i m u t h f o r t h i s t i m e . RADDEG=3.14159/180.0 C1=279.457*RADDEG C2=0.985647*RADDEG YR=NAVTIM/10000000 JD=MOD(NAVTIM,10000000)/l0000 IF(XPT.EQ.0.0) GOTO 5 XLAPT=XPT GOTO 10 5 TI=FTM(NAVTIM) X=AINT((YR-65)*365.251)+JD+Tl/24.0 G=C1+C2*X X=X/365.2422 'EQ' i s e q u a t i o n of time v a l u e EQ=(-102.5-0.142*X)*SIN(G)+(-429.8+.033*X)*COS(G)+596 1*SIN(2*G)-2.0*COS(2*G)+4.2*SIN(3*G)+19.3*COS(3*G)-12.8 2*SIN(4*G) EQ=EQ/3600 'XLAPT' i s l o c a l apparent time i n hours ( c o n s t a n t s v a r y w i t h c e n t r a l l o c a t i o n ) XLAPT=TI-8.0+EQ-10.8/60.0 IF(XLAPT.LT.0.0) XLAPT=XLAPT+ 24.0 10 HA=15.0*(XLAPT-12.0)*RADDEG PSI=2*3.14159*(JD-1)/365.0 'DEC i s s o l a r d e c l i n a t i o n DEC=0.006918-0.399912*COS(PSI)+0.070257*SIN(PSI) * -0.006758*COS(2*PSI)+0.000907*SIN(2*PSI)-0.002697*COS * (3*PSI)+0.00l480*SIN(3*PSI) 'COSZ' and 'SINZ' a re s i n and cos of s o l a r z e n i t h a n g l e and 'CA' i s cos of s o l a r a z i m u t h COS Z = SIN(CLAT* RADDEG)*SIN(DEC)+COS(CLAT* RADDEG)* COS( * DEC)*COS(HA) SINZ=SIN(ARCOS(COSZ)) CA=(SIN(CLAT*RADDEG)*COS Z~SIN(DEC))/(COS(CLAT*RADDEG) *SINZ) 135 Now compute the 3 parameters of i n t e r e s t SIGN=1 IF(XLAPT.LT.12.0) SIGN = - i SSA=ABS(SATAZ*RADDEG-SIGN*ARCOS(CA)) X1=COSZ X2=SINZ*COS(SSA) X3=X2*COS(SSA) RETURN END 136 SUBROUTINE SPAN Computes the time span f o r which the images a re v a l i d . COMMON /PDATA/ FLUX(50,50,40),NTIMS(40),XLATS(40),NIMS COMMON /MDATA/ TIM1(40),TIM2(40),SFLG(40) LOGICAL SFLG TIM1(1)=XLATS(1)-0.25 TIM2(NIMS)=XLATS(NIMS)+0.2 5 DO 30 IM=2,NIMS TIM1(IM)=(XLATS(IM-1)+XLATS(lM))/2.0 TIM2(IM-1)=TIM1(IM) 30 CONTINUE DO 40 IM=1,NIMS IF((TIM2(IM)-TIM1(IM)).LE.1.0) GOTO 35 SFLG(IM)=.FALSE. GOTO 40 35 SFLG(IM)=.TRUE. 40 CONTINUE RETURN END 1 37 SUBROUTINE STORE(NR,NC,VAL) S t o r e s the p r e d i c t e d f l u x i n the p r i n t o u t a r r a y . COMMON /PDATA/ FLUX(50,50,40),NTIMS(40),XLATS(40),NIMS FLUX(NR,NC,NIMS)=VAL RETURN END 138 SUBROUTINE THRESH(X1,X2,X3,RMIN,ALBS,THR) Determines the minimum b r i g h t n e s s t h r e s h o l d . COMMON/ATTEN/ABSUN,ABSAT,ABSUNT,ABSUNB,BREFL,ABSATT, *ABSATB,DENOM RK0=1353.0*X1 DENOM=(1.0-BREFL)*(1.0-ABSUN)*(1.0-ABSAT)*(1.0-0.076) ALBS=(RMIN-RKO*BREFL)/(DENOM*RKO) ALBP=ALBS+0.00566/X1 THR=RK0*(BREFL+ALBP*DENOM) IF(ALBS.LT.0.0) XX=XY~X2 C WRITE(6,66) THR C66 FORMAT(' THRESH : ',F8.3) RETURN END 1 39 A.3 F u n c t i o n s FUNCTION COUL(COSZ) C a l c u l a t e s C o u l s o n ' s beam s c a t t e r i n g . ZEDD=ARCOS(COSZ)*l80.0/3.14159 COUL=0.0467563+0.0014173*ZEDD-0.00005258*(ZEDD**2)+ *0.000000651*(ZEDD**3) IF(COUL.LT.0.046) COUL=0.046 RETURN END FUNCTION FTM(NVTIM) Re t u r n s f l o a t i n g p o i n t time i n h r s . IT=MOD(NVTIM,10000) FTM=IT/100+MOD(IT,100)/60.0 RETURN END FUNCTION ISTNUM(STAT) Re t u r n s the number of a p a r t i c u l a r s t a t i o n 'STAT'. REAL* 8 STAT,NAMES(12)/'GRSMT ' ,'NRTHMT ' ,'BCHYDRO ' , * 'VANAIR ','FERRY ','PITMED ','MISSHAB ', * 'ABBLIB ','ABBAIR ','LANGLEY *,'LANGA ','CLISTN LOGICAL EQCMP DO 10 1=1,12 J=I IF(EQCMP(8,STAT,NAMES(I))) GOTO 15 IF(I.EQ.12) WRITE(6,100) 10 CONTINUE 15 ISTNUM=J RETURN 100 FORMATC HELLLP!... THERE IS AN UNKNOWN STATION SOMEWH 1 ERE' ) END 1 40 FUNCTION RNORM(BMIN,Xl) C o n v e r t s c o u n t s t o n o r m a l i z e d r e f l e c t a n c e u s i n g second o r d e r p o l y n o m i a l . RIR=0.00154+BMIN*0.000166+BMIN*BMIN*0.0000137 RNORM=RIR/X1 RETURN END FUNCTION YAM(UT,AM) C a l c u l a t e s Yamamoto's a b s o r p t i v i t i e s f o r water vapour. (Note: C o n v e r s i o n from mm t o c o r r e c t u n i t s e.g: i f r e l a t i o n s h i p f o r U i n cm then use U=UT/10.0) U=(UT/10.0) * AM IF(U.GT.0.5) YAM=0.099*U**0.34 IF(U.LE.0.5) YAM= 0.14*U**0.44 RETURN END APPENDIX B C o e f f i c i e n t of determination (r ) and the standard error of estimate (SE) of the minimum brightness regression model, indexed according to the coordinates of the ce n t r a l p i x e l of contiguous 5 x 5 p i x e l arrays. SE i n units of counts. r 8 1 3 1 8 2 3 2 8 3 3 3 8 4 3 4 8 5 3 5 8 0.617 4.49 0.456 5.28 0.486 4.38 0.423 4.61 0.403 5.06 0.347 5.33 0.311 6.05 0.421 5.54 0.802 3.76 0.723 4.62 0.619 5.30 0.763 3.87 0.354 5.42 0.423 5.55 0.397 5.71 0.616 4.79 1 3 0.797 3.81 0.809 3.92 0.846 3.38 0.820 3.41 0.393 4.98 0.565 5.11 0.585 4.89 0.690 4.38 1 8 0.839 3.54 0.773 4.U 0.833 3.37 0.811 3.23 0.499 5.67 0.865 2.81 0.661 4.15 0.752 3.82 2 3 0.797 3.88 0.756 4.30 0.785 3.84 0.807 3.55 0.723 4.07 0.901 2.34 0.828 3.01 0.530 5.18 2 8 0.856 2.88 0.870 2.58 0.803 3.40 0.649 4.60 3 3 3 8 4 3 4 8 5 3 5 8 6 3 6 8 7 3 7 8 8 3 8 8 93 9 8 1 0 3 1 0 8 1 1 3 1 1 8 767 0. .781 0. .907 0. .906 0. .740 0. .800 0. .748 0. .902 0. .940 0. ,902 0, .847 0. .920 0. .934 0. .934 0, ,950 0. .889 0. .904 0. .737 0. .734 24 3. ,87 2. .64 2. ,82 4. ,35 3. 82 4. .05 2. 64 2. 65 2. 78 3. 45 2. 57 2. .85 2. 57 2. 33 3. .24 2. 87 3. 20 4. 15 784 0. .791 0. .760 0. ,809 0. .772 0. .942 0. .834 0. .819 0. .813 0. .949 0. .866 0. .935 0. .874 0. .915 0 .796 0. .828 0. .948 0. .866 0. .789 83 4. .19 4, .18 3. .95 4. .01 2. 26 3. 55 3. .68 3. .74 2. 02 3. .38 2. .50 3. .30 2. .88 3. .90 3. .62 2. 42 3. 30 3. 76 849 0. ,749 0. .804 0. .820 0. .791 0. ,751 0. .859 0. .826 0. ,734 0. ,799 0. .856 0. .840 0. .857 0. .863 0. .797 0. .975 • 0. 947 0. .855 0. 853 , 50 3. .32 3, .78 3. .74 3. ,85 4. 20 3. 30 3. .55 3. .60 3. 79 3. 41 3. ,45 3. 47 3. 25 3. ,75 1. .61 2. 19 3. .54 3. 30 -* 863 0. ,825 0. .830 0. .783 0. .758 0. ,805 0. 860 0. .821 0. ,563 0. 785 0. ,842 0. 787 0. .786 0. 572 0. ,813 0. 856 0. 873 0. 804 0. 801 91 3. .27 3. .03 3. .73 3. ,75 3. 64 3. 39 3. 46 3. 99 4. 03 3. 23 3. 95 3. ,84 4. 68 3. .51 3. 27 3. 20 3. 92 3. ,71 0.712 3.97 0.839 3.04 0.810 3.04 0.652 4.22 0.630 4.49 0.869 2.89 0.815 3.12 0.511 5.97 0.828 3.19 0.851 3.18 0.870 2.82 0.374 7.37 0.838 0.838 3.20 3.20 0.908 0.895 2.37 2.44 0.856 0.860 2.94 .2.98 0.725 0.772 4.04 3.54 0.811 3.40 0.861 2.66 0.796 3.23 0.711 3.62 0.758 3.50 0.778 3.40 0.883 2.63 0.859 2.83 0.834 3.24 0.866 2.86 0.834 2.93 0.781 3.49 0.863 3.15 0.854 2.89 0.828 3.16 0.808 3.28 0.861 2.98 0.850 2.87 0.900 2.42 0.823 3.16 0.828 3.34 0.872 2.71 0.858 2.83 0.836 3.05 0.801 3.63 0.814 3.07 0.828 2.83 0.804 3.32 0.555 4.55 0.820 3.97 0.870 2.62 0.786 3.19 0.792 3.67 0.870 2.64 0.876 2.70 0.852 2.65 0.829 3.55 0.816 3.36 0.772 3.64 0.734 3.74 0.846 3.40 0.862 3.22 0.770 3.64 0.811 3.31 0.857 3.26 0.802 3.79 0.757 3.78 0.939 2.22 0.869 3.14 0.790 3.48 0.703 0.660 4.11 4.4G 0. 508 0. 596 0. .611 0. 559 0. .579 0. .552 0. 619 0. 450 0. ,549 0. 512 0. 385 0. 454 0. ,824 0. ,860 0. 831 0. .777 0. 837 0. 713 0. 794 0. ,830 0. ,729 0. .566 0. 491 0. 735 4. .41 4. .20 4. .56 5, .04 4. .69 4. .28 5. .41 4. .60 3. .82 3, .86 6. .32 6. .35 3. .09 2. .80 2. .93 3. ,52 3. .05 3. .62 3. .27 2, .98 3, .40 3. .92 4. .84 3. .78 0. 484 0. .424 0. .511 0. .483 0. 509 0. .546 0. .501 0. .450 0. ,464 0. 401 0. .467 0. .406 0. .646 0. .755 0. .804 0. .776 0. 753 0. .759 0. ,577 0. .563 0. ,663 0. .718 0. ,872 0. .844 4. 38 5. . 16 4. .27 4. .55 4. .45 4. .17 4. .11 3. .71 3. .93 4. 55 4. ,07 5. .50 5. .51 3. .66 3. .23 3. ,16 4. 40 4. .19 4. ,27 4. ,94 4. .72 4. .13 2. ,85 3. .14 0. 503 0. 516 0. ,572 0. 529 0. .534 0. ,423 0. 525 0. .476 0. ,465 0. .419 0. 437 0. .442 0. 229 0. ,691 0. 858 0. .824 0. 811 0. 655 0. .638 0. .822 0. .771 0. .833 0. ,883 0. .880 4. 34 4. .51 4. ,62 4. ,75 3. ,95 4, .56 4. .03 4. .35 4. .29 4. 20 4. , 14 4. 34 6. ,65 4. ,26 2. .67 3. .09 3. ,48 4. ,19 4. .55 3. .29 3. .43 3. ,31 2. ,76 2. ,71 0. 844 0. .565 0. .456 0. 516 0. 559 0. .599 0. 491 0. ,503 0. .450 0. 501 0. 510 0. .547 0. .481 0. .464 0. 358 0. .709 0. 684 0. 835 0. .863 0. .860 0. .841 0. .853 0. .936 0. .860 3. .09 4. .91 3. .92 6. .31 4. .03 4. .59 4. .84 4. .03 4. . 17 4. .08 3. .58 3. .38 3. .60 4. . 16 6. .96 4, .15 4. .40 3. . 18 2. .81 2 .95 2. .96 3. .02 2. .10 2. .97 

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