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Satellite based estimates of solar energy availability at the earth’s surface : impact of changes in… Wanless, Neil 1983

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S A T E L L I T E BASED ESTIMATES OF SOLAR ENERGY A V A I L A B I L I T Y AT THE E A R T H ' S SURFACE : IMPACT OF CHANGES IN THE CONFIGURATION OF THE S A T E L L I T E DATA By N E I L WANLESS B . S c , U n i v e r s i t y o f L i v e r p o o l , 1980 A T H E S I S SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES ( D e p a r t m e n t o f G e o g r a p h y ) 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 t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF B R I T I S H COLUMBIA December 1983 © N e i l W a n l e s s , 1983 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 a d v a n c e d d e g r e e 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 a g r e e 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 a n d s t u d y . I f u r t h e r a g r e e 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 p u r p o s e s may be g r a n t e d by t h e h e a d o f my d e p a r t m e n t o r by h i s o r h e r 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 . D e p a r t m e n t o f The 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 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5 D a t e Z3>rcV December 1^23. E - 6 (2/79) i i ABSTRACT D e s p i t e t h e e n c o u r a g i n g r e s u l t s of r e c e n t s a t e l l i t e b a s e d e s t i m a t e s o f s o l a r e n e r g y a t t h e E a r t h ' s s u r f a c e numerous q u e s t i o n s c o n c e r n e d w i t h t h e c o n f i g u r a t i o n o f t h e s a t e l l i t e d a t a u s e d i n t h e m o d e l s r e m a i n u n a n s w e r e d . The m e r i t s o f a wide r a n g e o f s a t e l l i t e d a t a c o n f i g u r a t i o n s were a s s e s s e d u s i n g a s i n g l e r e l a t i o n s h i p b e t w e e n g r o u n d - b a s e d e s t i m a t e s o f s h o r t w a v e r a d i a t i o n t r a n s m i s s i o n (T) and 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 ( T R ) . B i d i r e c t i o n a l r e f l e c t a n c e (BDR) m o d e l s were d e v e l o p e d i n an a t t e m p t t o c o r r e c t t h e s a t e l l i t e d a t a f o r t h e a n i s o t r o p i c r e f l e c t a n c e p r o p e r t i e s of t h e E a r t h - A t m o s p h e r e s y s t e m . I r r e s p e c t i v e o f t h e t y p e o f BDR m o d e l u s e d , s u c h a c o r r e c t i o n f o r a n i s o t r o p i c r e f l e c t a n c e was deemed t o be u n w a r r a n t e d . C h a n g e s t o t h e s p a t i a l c o n f i g u r a t i o n o f t h e s a t e l l i t e p i x e l a r r a y and i n c r e a s e d c o n c e n t r a t i o n o f g r o u n d b a s e d m e a s u r e m e n t s a r e a l s o f o u n d t o be o f n e g l i g i b l e i m p o r t a n c e . T h e r e f o r e , as m o d e l l i n g p r o c e d u r e s u s i n g s a t e l l i t e i n f o r m a t i o n c h a r a c t e r i s t i c a l l y i n v o l v e v o l u m i n o u s d a t a s e t s t h e a b i l i t y t o use s m a l l p i x e l a r r a y s i z e s p r e s e n t s a c o n s i d e r a b l e a d v a n t a g e . I n c r e a s i n g t h e t e m p o r a l a v e r a g i n g p e r i o d r e s u l t e d i n s u b s t a n t i a l i m p r o v e m e n t s t o t h e s t r e n g t h o f t h e r e l a t i o n s h i p be tween T and T R . The use o f a t l e a s t two images a n d a t l e a s t f o u r images p e r o n e - h o u r l y and t w o - h o u r l y t i m e p e r i o d s , r e s p e c t i v e l y , have been shown t o s a t i s f a c t o r i l y c h a r a c t e r i z e t h e o b s e r v e d r a d i a t i v e r e g i m e s . F i n a l l y , v a r i a t i o n s i n t h e c l i m a t o l o g i c a l c h a r a c t e r i s t i c s f o r t h e Lower F r a s e r V a l l e y s t u d y a r e a , h i g h l i g h t e d u s i n g s u c h a t e c h n i q u e , h a v e been e l u d e d t o . i v T A B L E OF CONTENTS Page ABSTRACT i i L I S T OF TABLES v i i L I S T OF FIGURES x ACKNOWLEDGEMENTS xv CHAPTER 1 INTRODUCTION 1 1 .1 B a c k g r o u n d 1 1.2 S p e c i f i c O b j e c t i v e s 6 CHAPTER 2 RADIATION DATA SET AND MODEL 7 2.1 S t u d y A r e a 7 2 . 2 M e a s u r e d S h o r t w a v e R a d i a t i o n 9 2 . 3 C l e a r Sky R a d i a t i o n M o d e l 9 2 . 4 P a r a m e t e r i z a t i o n u s e d i n t h e C l e a r Sky R a d i a t i o n M o d e l 12 2 . 4 . 1 Ozone A b s o r p t i o n 12 2 . 4 . 2 R a y l e i g h S c a t t e r i n g 13 2 . 4 . 3 W a t e r V a p o u r A b s o r p t i o n 13 2 . 4 . 4 A l b e d o Terms 15 2 . 4 . 5 C a l c u l a t i o n o f P o s i t i o n and T ime P a r a m e t e r s 15 2 . 4 . 6 P r e c i p i t a b l e Water D e t e r m i n a t i o n 18 2 . 5 D e r i v a t i o n o f t h e S h o r t w a v e T r a n s m i s s i o n 26 CHAPTER 3 S A T E L L I T E DATA SET 29 3.1 I n t r o d u c t i o n 29 3 .2 E a r t h - L o c a t i o n o f S a t e l l i t e Imagery 32 3 .3 P i x e l S i z e D e t e r m i n a t i o n 35 V 3 .4 V a l i d a t i o n o f t h e E a r t h - L o c a t i o n R o u t i n e 38 3 . 5 L i n e a r i t y 42 3 . 6 C o n v e r s i o n o f P i x e l C o u n t V a l u e s t o S u r f a c e R e f l e c t a n c e 47 3 . 7 M e r g i n g o f t h e S a t e l l i t e R e f l e c t a n c e and S h o r t w a v e T r a n s m i s s i o n D a t a 51 CHAPTER 4 B I D I R E C T I O N A L R E F L E C T A N C E MODELS 56 4.1 O v e r v i e w 56 4 . 2 D e f i n i t i o n s ( G e o m e t r y o f R e f l e c t a n c e ) 63 4 . 3 M o d e l l i n g P r o c e d u r e 67 4 . 3 . 1 D a t a S e l e c t i o n a n d Q u a l i t y C o n t r o l 67 4 . 3 . 1 . 1 L a n d a n d Sea S u r f a c e 67 4 . 3 . 1 . 2 C l o u d S u r f a c e 70 4 . 3 . 2 I d e n t i f i c a t i o n o f A n i s o t r o p i c 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 74 4 . 3 . 2 . 1 L a n d S u r f a c e 74 4 . 3 . 2 . 2 Sea S u r f a c e 85 4 . 3 . 2 . 3 C l o u d S u r f a c e 90 4 . 3 . 2 . 4 Summary a n d C o m p a r i s o n o f L a n d , Sea and C l o u d S u r f a c e R e f l e c t i v i t y 96 4 . 3 . 3 D e v e l o p m e n t o f BDR M o d e l s 99 4 . 3 . 3 . 1 G e n e r a l 99 4 . 3 . 3 . 2 L a n d a n d Sea S u r f a c e R e f l e c t a n c e M o d e l l i n g 103 4 . 3 . 3 . 3 C l o u d S u r f a c e R e f l e c t a n c e M o d e l l i n g 1 1 2 4 . 4 V e r i f i c a t i o n o f BDR M o d e l s 115 4 . 5 A p p l y i n g t h e BDR M o d e l s t o t h e S a t e l l i t e D a t a 124 vi CHAPTER 5 RESULTS : IMPACT OF ADJUSTMENTS TO THE S A T E L L I T E DATA 133 5.1 I n t r o d u c t i o n 133 5 . 2 D e v e l o p m e n t o f t h e R e l a t i o n s h i p Between T r a n s m i s s i o n and R e f l e c t a n c e 134 5 . 3 Impact o f A p p l y i n g t h e BDR M o d e l s 140 5 . 3 . 1 I n i t i a l S t u d y U s i n g S m a l l D a t a S e t 140 5 . 3 . 2 F u r t h e r T e s t i n g U s i n g a L a r g e r D a t a S e t 147 5 . 4 Impact o f S p a t i a l A v e r a g i n g 155 5 . 4 . 1 I n t r o d u c t i o n and A n a l y s i s o f R e s u l t s 155 5 . 4 . 2 I m p l i c a t i o n o f R e s u l t s 170 5 . 5 Impact o f T ime A v e r a g i n g 170 5 . 6 I n f l u e n c e o f S a t e l l i t e Image A v a i l a b i l i t y 174 5 . 7 V a l l e y and C o a s t a l S i t e C o m p a r i s o n 182 CHAPTER 6 CONCLUSIONS 189 REFERENCES 193 APPENDICES 2 00 APPENDIX 1 S y m b o l s i 200 APPENDIX 2 L a n d m a r k s u s e d i n t h e E a r t h - L o c a t i o n R o u t i n e 204 APPENDIX 3 E q u a t i o n s u s e d t o D e t e r m i n e t h e BDR C o r r e c t i o n s 207 v i i L I S T OF TABLES T A B L E 2.1 T r a n s m i s s i v i t y A f t e r R a y l e i g h S c a t t e r i n g . T A B L E 2 . 2 C o m p a r i s o n o f P r e c i p i t a b l e W a t e r V a l u e s D e r i v e d F r o m R a d i o s o n d e D a t a and t h e S m i t h (1966) F o r m u l a t i o n . T A B L E 2 . 3 V a r i a t i o n i n T r a n s m i s s i o n V a l u e s C a l c u l a t e d f rom P r e c i p i t a b l e Water D a t a a s D e t e r m i n e d f rom e i t h e r R a d i o s o n d e D a t a o r t h e S m i t h (1966) F o r m u l a t i o n . T A B L E 3.1 V e r i f i c a t i o n S t a t i s t i c s f o r t h e C u b i c I n t e r p o l a t i o n R o u t i n e U s e d i n t h e E a r t h - L o c a t i o n o f t h e S a t e l l i t e I m a g e r y . T A B L E 3 .2 R e s u l t s f rom t h e A s s e s s m e n t s o f L i n e a r i t y A c r o s s t h e S a t e l l i t e Image B a s e d on D a t a From T h r e e C l e a r D a y s . T A B L E 4.1 T r i g o n o m e t r i c F u n c t i o n s U s e d t o M o d e l D i u r n a l R e f l e c t a n c e P a t t e r n s f o r S u r f a c e s U n d e r C l e a r S k i e s . T A B L E 4 . 2 P e r f o r m a n c e o f t h e C l e a r Sky BDR M o d e l s i n R e p l i c a t i n g t h e T a r g e t R e f l e c t a n c e . T A B L E 4 . 3 V e r i f i c a t i o n S t a t i s t i c s f o r t h e C l e a r Sky BDR M o d e l s . T A B L E 5.1 S t a t i s t i c s S h o w i n g t h e I m p a c t o f A p p l y i n g a BDR C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T a n d T R . S a t e l l i t e D a t a a r e f o r a 7 x 7 P i x e l A r r a y C e n t r e d on U B C . T A B L E 5 . 2 S t a t i s t i c s Showing t h e Impact o f A p p l y i n g a BDR M o d e l A ( T R ) C o r r e c t i o n to t h e R e l a t i o n s h i p Between T and T R . S a t e l l i t e D a t a a r e f o r a 7 x 7 P i x e l A r r a y C e n t r e d on U B C . T A B L E 5 . 3 S t a t i s t i c s S h o w i n g t h e Impact o f A p p l y i n g a BDR M o d e l B C o r r e c t i o n to t h e R e l a t i o n s h i p Between T and T R . S a t e l l i t e D a t a a r e f o r a 7 x 7 P i x e l A r r a y C e n t r e d on U B C . Page 14 23 24 40 44 104 108 120 137 142 144 v i i i T A B L E 5 .4 S t a t i s t i c s S h o w i n g t h e Impact o f A p p l y i n g a BDR M o d e l C C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and T R . S a t e l l i t e D a t a a r e f o r a 7 x 7 P i x e l A r r a y C e n t r e d on U B C . T A B L E 5 . 5 S t a t i s t i c s S h o w i n g t h e Impact o f A p p l y i n g a BDR M o d e l C C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and T R . S a t e l l i t e D a t a a r e f o r D i f f e r e n t P i x e l A r r a y S i z e s C e n t r e d on UBC and BDR C o r r e c t i o n s a r e A p p l i e d t o A l l P i x e l s . T A B L E 5 . 6 S t a t i s t i c s S h o w i n g t h e Impact o f A p p l y i n g a BDR M o d e l C C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and T R . S a t e l l i t e D a t a a r e f o r D i f f e r e n t P i x e l A r r a y S i z e s C e n t r e d on UBC a n d BDR C o r r e c t i o n s a r e A p p l i e d t o C l e a r and O v e r c a s t P i x e l s O n l y . T A B L E 5 . 7 S t a t i s t i c s S h o w i n g t h e Impact o f A p p l y i n g a BDR M o d e l L a n d ( N ) C C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and T R . S a t e l l i t e D a t a a r e f o r a 7 x 7 P i x e l ' A r r a y C e n t r e d on A B A I R . T A B L E 5 .8 S t a t i s t i c s S h o w i n g t h e Impact of A p p l y i n g a BDR M o d e l L a n d ( S ) C C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and T R . S a t e l l i t e D a t a a r e f o r a 7 x 7 P i x e l A r r a y C e n t r e d on A B A I R . T A B L E 5 . 9 S t a t i s t i c s S h o w i n g t h e Impact o f U s i n g D i f f e r e n t A r r a y S i z e s on t h e R e l a t i o n s h i p Between T and T R . The P i x e l A r r a y s a r e C e n t r e d on U B C . T A B L E 5 . 1 0 S t a t i s t i c s S h o w i n g t h e Impact of U s i n g D i f f e r e n t A r r a y S i z e s on t h e R e l a t i o n s h i p Between T a n d T R . The P i x e l A r r a y s a r e C e n t r e d on A B A I R . T A B L E 5.11 S t a t i s t i c s S h o w i n g t h e Impact o f U s i n g D i f f e r e n t A r r a y S i z e s on t h e R e l a t i o n s h i p Between T a n d T R . The P i x e l A r r a y s a r e C e n t r e d on MAA. i x Page T A B L E 5 .12 T A B L E 5 . 1 3 T A B L E 5 .14 T A B L E 5 .15 T A B L E 5 . 1 6 S t a t i s t i c s S h o w i n g t h e Impact o f U s i n g D i f f e r e n t R e c t a n g u l a r C o n f i g u r a t i o n s on t h e R e l a t i o n s h i p Between T a n d T R . The P i x e l A r r a y s a r e C e n t r e d on UBC and A B A I R . C o m p a r a t i v e S t a t i s t i c s f o r t h e H o u r l y S h o r t w a v e R a d i a t i o n M e a s u r e m e n t s a t t h e T h r e e V a l l e y S i t e s . The Mean and S t a n d a r d D e v i a t i o n f o r H o u r l y S h o r t w a v e R a d i a t i o n M e a s u r e m e n t s a t t h e T h r e e V a l l e y S i t e s . S t a t i s t i c s S h o w i n g t h e Impact o f I n c r e a s i n g t h e Time A v e r a g i n g P e r i o d on t h e R e l a t i o n s h i p Between T and TR a t t h e U B C , ABAIR and MAA S i t e s . S t a t i s t i c s S h o w i n g t h e Impact o f Changes t o t h e Image R e q u i r e m e n t s P e r O n e - H o u r l y T ime P e r i o d on t h e R e l a t i o n s h i p Between T and TR a t t h e UBC S i t e . 163 168 169 172 176 T A B L E 5 . 1 7 T A B L E 5 .18 T A B L E 5 . 1 9 S t a t i s t i c s S h o w i n g t h e Impact o f Changes t o t h e Image R e q u i r e m e n t s P e r T w o - H o u r l y T ime P e r i o d on t h e R e l a t i o n s h i p Between T and TR a t t h e UBC S i t e . 177 S t a t i s t i c s S h o w i n g t h e Impact o f Changes t o t h e Image R e q u i r e m e n t s P e r T w o - H o u r l y T ime P e r i o d on t h e R e l a t i o n s h i p Between T and TR a t t h e ABAIR S i t e . 178 S t a t i s t i c s S h o w i n g t h e Impact o f Changes • t o t h e Image R e q u i r e m e n t s P e r T w o - H o u r l y T i m e P e r i o d on t h e R e l a t i o n s h i p Between T a n d TR a t t h e MAA S i t e . 179 X L I S T OF FIGURES FIGURE 1.1 FIGURE 2.1 FIGURE 2 .2 FIGURE 2 . 3 FIGURE 3.1 FIGURE 3 .2 FIGURE 3 .3 FIGURE 3 .4 FIGURE 3 .5 FIGURE 4.1 FIGURE 4 . 2 FIGURE 4 . 3 FIGURE 4 . 4 F l o w D i a g r a m O u t l i n i n g t h e S t e p s T a k e n t o D e v e l o p a R e l a t i o n s h i p Between S h o r t w a v e T r a n s m i s s i o n and T a r g e t R e f l e c t i v i t y . L o c a t i o n o f t h e S h o r t w a v e R a d i a t i o n M o n i t o r i n g S i t e s f o r P a r t o f t h e Lower F r a s e r V a l l e y . V a r i a t i o n o f \ W i t h L a t i t u d e and S e a s o n . S e a s o n a l V a r i a t i o n o f A F o r t h e S t u d y A r e a . 25 x 25 P i x e l A r r a y C e n t r e d on t h e UBC S i t e D e p i c t i n g Mean B r i g h t n e s s C o u n t V a l u e s B a s e d on F o r t y - N i n e Images . Map o f t h e A r e a C o v e r e d by t h e L a r g e s t S a t e l l i t e Images S h o w i n g L a n d m a r k s T y p i c a l l y U s e d i n t h e A s s e s s m e n t o f L i n e a r i t y . C a l i b r a t i o n C u r v e s f o r t h e SMS-1 and GOES-1 S a t e l l i t e R a d i o m e t e r s . A N i g h t - t i m e S u b a r r a y C e n t r e d O v e r t h e P a c i f i c O c e a n D e m o n s t r a t i n g a B a c k g r o u n d B r i g h t n e s s and S t r i p i n g Due t o t h e L a c k o f I n t e r s e c t i o n C a l i b r a t i o n . E x a m p l e o f S a t e l l i t e Image W e i g h t i n g Scheme f o r M e r g i n g S a t e l l i t e D a t a t o H o u r l y I n t e g r a t e d R a d i a t i o n D a t a . D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e O v e r a L a n d S u r f a c e F o r J u l i a n Day 2 5 6 / 7 9 . D i a g r a m o f G e o m e t r i c R e l a t i o n s Between Z e n i t h A n g l e o f t h e S u n , Z e n i t h A n g l e o f t h e R e f l e c t e d Ray and t h e S u n - S a t e l l i t e A z i m u t h A n g l e . D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e O v e r a Sea S u r f a c e f o r J u l i a n Day 2 5 6 / 7 9 . H i s t o g r a m o f C o u n t V a l u e s Showing a L a r g e S p r e a d i n t h e D a t a as a R e s u l t o f t h e P a r t l y C l o u d y C o n d i t i o n s . x i Page FIGURE 4 . 5 FIGURE 4 . 6 H i s t o g r a m o f C o u n t V a l u e s S h o w i n g a B i m o d a l D i s t r i b u t i o n Due t o a P r e d o m i n a n c e of C o m p l e t e l y C l e a r and C l o u d y P i x e l s . H i s t o g r a m S h o w i n g a S m a l l S p r e a d o f C o u n t V a l u e s S u g g e s t i n g R e l a t i v e l y Homogeneous C l o u d C o v e r C o n d i t i o n s . 72 73 FIGURE 4 . 7 FIGURE 4 . 8 D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e Over t h e L a n d ( N ) S u r f a c e f o r J u l i a n Day 2 5 6 / 7 9 . D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e O v e r t h e L a n d ( S ) S u r f a c e f o r J u l i a n Day 3 0 4 / 7 9 . 75 76 FIGURE 4 . 9 FIGURE 4 . 1 0 FIGURE 4.11 D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e O v e r t h e L a n d ( N ) S u r f a c e f o r J u l i a n Day 3 0 4 / 7 9 . D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e O v e r t h e L a n d ( S ) S u r f a c e f o r J u l i a n Day 2 0 0 / 7 9 . D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e O v e r t h e L a n d ( N ) S u r f a c e f o r J u l i a n Day 2 0 0 / 7 9 . 77 78 79 FIGURE 4 .12 FIGURE 4 . 1 3 FIGURE 4 . 1 4 FIGURE 4 . 1 5 P o l a r P l o t o f T a r g e t R e f l e c t a n c e F o r t h e L a n d ( N ) S u r f a c e . P o l a r P l o t o f T a r g e t R e f l e c t a n c e F o r t h e L a n d ( S ) S u r f a c e . D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e O v e r t h e Sea S u r f a c e f o r J u l i a n Day 2 0 0 / 7 9 . D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e O v e r t h e Sea S u r f a c e f o r J u l i a n Day 3 0 4 / 7 9 . 81 82 86 87 FIGURE 4 . 1 6 D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e Over t h e Sea S u r f a c e f o r J u l i a n Day 0 2 5 / 8 0 . 88 x i i Page FIGURE 4 . 1 7 FIGURE 4 . 1 8 FIGURE 4 . 1 9 FIGURE 4 . 2 0 FIGURE 4.21 FIGURE 4 .22 FIGURE 4 . 2 3 FIGURE 4 . 2 4 FIGURE 4 . 2 5 FIGURE 4 . 2 6 FIGURE 4 . 2 7 FIGURE 4 .28 FIGURE 4 . 2 9 FIGURE 4 . 3 0 FIGURE 4.31 P o l a r P l o t o f T a r g e t R e f l e c t a n c e F o r t h e Sea S u r f a c e . D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e O v e r an Ocean S u r f a c e f o r J u l i a n Day 2 0 0 / 7 9 . D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e O v e r a C l o u d T o p S u r f a c e f o r J u l i a n Day 1 9 7 / 8 0 . D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e O v e r a C l o u d T o p S u r f a c e f o r J u l i a n Day 2 4 5 / 8 0 . P o l a r P l o t o f T a r g e t R e f l e c t a n c e O v e r a C l o u d T o p S u r f a c e . Form o f t h e F o u r T r i g o n o m e t r i c F u n c t i o n s U s e d t o M o d e l t h e Sea and L a n d D i u r n a l R e f l e c t a n c e P a t t e r n s . BDR M o d e l F o r t h e L a n d ( N ) S u r f a c e U s i n g p V a l u e s . BDR M o d e l F o r t h e L a n d ( S ) S u r f a c e U s i n g c V a l u e s . BDR M o d e l F o r t h e Sea S u r f a c e U s i n g c V a l u e s . D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e O v e r a C l o u d T o p S u r f a c e f o r J u l i a n Day 363 /79 and a S e c o n d O r d e r P o l y n o m i a l F i t t o t h e D a t a . BDR M o d e l F o r a C l o u d T o p S u r f a c e U s i n g p V a l u e s . V e r i f i c a t i o n o f t h e Sea BDR M o d e l F o r J u l i a n Day 1 9 6 / 7 9 . V e r i f i c a t i o n o f t h e L a n d ( N ) BDR M o d e l F o r J u l i a n Day 1 2 1 / 8 0 . V e r i f i c a t i o n o f t h e L a n d ( S ) BDR M o d e l F o r J u l i a n Day 1 9 6 / 7 9 . V e r i f i c a t i o n P o l a r P l o t F o r t h e Sea S u r f a c e BDR M o d e l U s i n g P V a l u e s . 89 91 92 93 94 105 109 110 111 113 114 116 117 118 121 x i i i Page FIGURE 4 .32 FIGURE 4 . 3 3 FIGURE 4 . 3 4 FIGURE 4 . 3 5 FIGURE 4 . 3 6 FIGURE 4 . 3 7 FIGURE 5.1 FIGURE 5 .2 FIGURE 5 . 3 FIGURE 5 .4 FIGURE 5 .5 FIGURE 5 . 6 FIGURE 5 . 7 V e r i f i c a t i o n o f t h e P o l a r P l o t F o r t h e L a n d ( N ) S u r f a c e BDR M o d e l U s i n g p V a l u e s . V e r i f i c a t i o n o f t h e P o l a r P l o t F o r t h e L a n d ( S ) S u r f a c e BDR M o d e l U s i n g P V a l u e s . The R e l a t i o n s h i p Between t h e S c e n e B r i g h t n e s s and t h e C l o u d i n e s s I n d e x . D e r i v a t i o n o f a C o r r e c t e d T a r g e t R e f l e c t a n c e From t h e C l o u d i n e s s Index U s i n g M o d e l A . D e r i v a t i o n o f a C o r r e c t e d T a r g e t R e f l e c t a n c e From t h e C l o u d i n e s s Index U s i n g M o d e l B . D e r i v a t i o n of a C o r r e c t e d T a r g e t R e f l e c t a n c e From t h e C l o u d i n e s s Index U s i n g M o d e l C . S c a t t e r P l o t o f S h o r t w a v e T r a n s m i s s i o n A g a i n s t U n c o r r e c t e d S a t e l l i t e T a r g e t R e f l e c t a n c e f o r t h e UBC S i t e U s i n g a 7 x 7 P i x e l A r r a y . S c a t t e r P l o t o f S h o r t w a v e T r a n s m i s s i o n A g a i n s t U n c o r r e c t e d S a t e l l i t e T a r g e t R e f l e c t a n c e f o r t h e UBC S i t e U s i n g a 7 x 7 P i x e l A r r a y and t h e L a r g e r D a t a S e t . S c a t t e r P l o t o f S h o r t w a v e T r a n s m i s s i o n A g a i n s t U n c o r r e c t e d S a t e l l i t e T a r g e t R e f l e c t a n c e f o r t h e ABAIR S i t e U s i n g a 7 x 7 P i x e l A r r a y and t h e L a r g e r D a t a S e t . R e c t a n g u l a r S a t e l l i t e A r r a y s U s e d t o T e s t S y n o p t i c I n f l u e n c e s . S c a t t e r P l o t C o m p a r i n g H o u r l y S h o r t w a v e R a d i a t i o n T o t a l s Between A B L I B and M I S S . S c a t t e r P l o t C o m p a r i n g H o u r l y S h o r t w a v e R a d i a t i o n T o t a l s Between ABAIR and M I S S . S c a t t e r P l o t C o m p a r i n g H o u r l y S h o r t w a v e R a d i a t i o n T o t a l s Between ABAIR a n d A B L I B . 122 123 126 128 129 130 136 148 150 162 165 166 167 x i v Page FIGURE 5 .8 FIGURE 5 . 9 FIGURE 5 .10 S c a t t e r P l o t o f T w o - H o u r l y A v e r a g e d S h o r t w a v e T r a n s m i s s i o n A g a i n s t U n c o r r e c t e d S a t e l l i t e T a r g e t R e f l e c t a n c e f o r t h e UBC S i t e U s i n g a 7 x 7 P i x e l A r r a y and t h e L a r g e r D a t a S e t . C o m p a r i s o n o f t h e R e g r e s s i o n E q u a t i o n s F o r UBC a n d A B A I R . S c a t t e r P l o t o f S h o r t w a v e T r a n s m i s s i o n A g a i n s t U n c o r r e c t e d S a t e l l i t e T a r g e t R e f l e c t a n c e f o r t h e MAA S i t e U s i n g a 7 x 7 P i x e l A r r a y and t h e L a r g e r D a t a S e t . 173 184 185 FIGURE 5.11 F r e q u e n c y o f O c c u r r e n c e o f C l e a r , P a r t l y C l o u d y a n d O v e r c a s t C o n d i t i o n s a t U B C , ABAIR and MAA. 186 XV ACKNOWLEDGEMENTS I w i s h t o e x p r e s s my s i n c e r e a p p r e c i a t i o n t o my s u p e r v i s o r D r . J . E . Hay f o r h i s i n v a l u a b l e a d v i c e a n d s u p p o r t t h r o u g h o u t t h i s s t u d y . The comments and s u g g e s t i o n s on t h e f i n a l m a n u s c r i p t by D r . T . R . Oke a r e g r a t e f u l l y a c k n o w l e d g e d . D r . R . J . Woodham, t h e t h i r d member o f my c o m m i t t e e , and D r . J . A . D a v i e s ( M c M a s t e r U n i v e r s i t y ) c o n t r i b u t e d h e l p f u l t e c h n i c a l a d v i c e . M . R o s e b e r r y p r o v i d e d c o n s i d e r a b l e a s s i s t a n c e w i t h t h e c o m p u t e r p r o g r a m m i n g . I w o u l d l i k e t o e x t e n d t h a n k s t o numerous p e o p l e , b o t h i n t e r n a l and e x t e r n a l t o t h e G e o g r a p h y D e p a r t m e n t ; i n p a r t i c u l a r C . R a p h a e l f o r h i s s a l u t a r y a s s i s t a n c e i n t h e s a t e l l i t e d a t a r e s e a r c h , e s p e c i a l l y w i t h r e s p e c t t o C h a p t e r 3 w h i c h was w r i t t e n j o i n t l y . I am i n d e b t e d t o H . A . C l e u g h , C . S . B . Grimmond and C . J . S o u c h f o r t h e i r h e l p i n t h e f i n a l p r o d u c t i o n o f t h e t h e s i s . The UBC I n t e r d i s c i p l i n a r y P r o g r a m i n Remote S e n s i n g p e r m i t t e d a c c e s s t o t h e C o m t a l image p r o c e s s o r d u r i n g t h e s a t e l l i t e image a n a l y s i s . F i n a n c i a l s u p p o r t f o r t h i s s t u d y was p r o v i d e d by t h e C a n a d i a n A t m o s p h e r i c E n v i r o n m e n t S e r v i c e , c o n t r a c t DSS N o . OSE 83-00022 t o D r . J . E . H a y . F i n a l l y , I w i l l r e m a i n i n d e b t e d t o my f a m i l y and d e v o t e d f r i e n d s who h e l p e d me t h r o u g h an u n e x p e c t e d d i s t r a c t i o n d u r i n g t h e i n i t i a l r e s e a r c h p e r i o d and w i t h o u t whose c o n t i n u e d s u p p o r t t h i s p r o j e c t may n e v e r have r e a c h e d f r u i t i o n . 1 CHAPTER 1 INTRODUCTION 1 . 1 B a c k g r o u n d The i n t e r e s t i n s o l a r e n e r g y r e a c h i n g t h e E a r t h ' s s u r f a c e has i n c r e a s e d s u b s t a n t i a l l y i n r e c e n t y e a r s . A d e t a i l e d c l i m a t o l o g y o f t h e i r r a d i a n c e i s r e q u i r e d i n o r d e r t o e f f i c i e n t l y u t i l i z e t h i s r e s o u r c e and t o i m p r o v e o u r u n d e r s t a n d i n g and p r e d i c t i v e c a p a b i l i t i e s w i t h r e g a r d t o many e n v i r o n m e n t a l s y s t e m s s u c h as t h e h y d r o l o g i c c y c l e and t h e a t m o s p h e r i c c i r c u l a t i o n . The e x i s t i n g g r o u n d b a s e d n e t w o r k o f p y r a n o m e t r i c m e a s u r i n g s t a t i o n s i s i n a d e q u a t e f o r s u p p l y i n g t h e d a t a r e q u i r e d f o r t h e many d i f f e r e n t a p p l i c a t i o n s . A t t e m p t s t o mode l i r r a d i a n c e u s i n g more r e a d i l y a v a i l a b l e c l i m a t o l o g i c a l i n f o r m a t i o n have p r o v e d s u c c e s s f u l f o r c l e a r sky c o n d i t i o n s , b u t r e s u l t i n s u b s t a n t i a l e r r o r s f o r p a r t l y c l o u d y and o v e r c a s t s i t u a t i o n s ( e . g . D a v i e s and MacKay, 1 9 8 3 ) . T h i s i s t h e r e s u l t o f t h e i n a b i l i t y o f t h e m o d e l s t o a c c o u n t f o r t h e c o m p l e x r a d i a t i v e p r o p e r t i e s o f c l o u d s and t o c a p t u r e t h e s p a t i a l and t e m p o r a l v a r i a b i l i t y o f c l o u d s . A l t h o u g h t h e m o d e l l e d d a t a c a n s u p p l e m e n t t h e m e a s u r e d d a t a , t h e r e a r e s t i l l many a r e a s o f t h e w o r l d d e v o i d o f i r r a d i a n c e i n f o r m a t i o n . 2 I t a p p e a r s a t p r e s e n t t h a t s a t e l l i t e s a r e t h e o n l y p r a c t i c a l s o u r c e a v a i l a b l e t o m o n i t o r t h e c l o u d v a r i a b i l i t y . G e o s t a t i o n a r y s a t e l l i t e s i n p a r t i c u l a r p r o v i d e t h e n e c e s s a r y h i g h r e s o l u t i o n t e m p o r a l a n d s p a t i a l c o v e r a g e . The g e o s t a t i o n a r y s a t e l l i t e s have r e c e n t l y been u s e d t o p r o v i d e e s t i m a t e s o f r a d i a t i o n a t t h e E a r t h ' s s u r f a c e ( e . g . Hay and H a n s o n , 1978; T a r p l e y , 1979; G a u t i e r e t a l . , 1980; H i s e r and S e n n , 1980; B r a k k e and Kanemasu , 1981; D e d i e u e t a l . , 1 9 8 3 ) . The r e s u l t s have been e n c o u r a g i n g and r e c e n t work by R a p h a e l (1983) has c o n f i r m e d t h e a p p l i c a b i l i t y o f t h r e e o f t h e s e m o d e l s t o m e s o s c a l e i n v e s t i g a t i o n s . D e s p i t e t h e a b o v e a s s e s s m e n t s some i m p o r t a n t q u e s t i o n s r e g a r d i n g t h e c o n f i g u r a t i o n o f t h e s a t e l l i t e d a t a i n p u t o f t h e s e m o d e l s r e m a i n u n a n s w e r e d . T h i s t h e s i s w i l l a t t e m p t t o d e t e r m i n e t h e m e r i t s o f v a r i o u s s a t e l l i t e d a t a c o n f i g u r a t i o n s u s e d i n c h a r a c t e r i z i n g t h e s o l a r r a d i a t i o n r e g i m e a t t h e E a r t h ' s s u r f a c e . T h i s i s a c h i e v e d by a n a l y s i n g t h e s e n s i t i v i t y o f a s i m p l e r e l a t i o n s h i p between m e a s u r e m e n t s of s o l a r r a d i a t i o n a t t h e g r o u n d ( e x p r e s s e d as a s h o r t w a v e t r a n s m i s s i o n , T) and s a t e l l i t e b r i g h t n e s s ( e x p r e s s e d a s t a r g e t r e f l e c t a n c e , TR) t o c h a n g e s i n t h e s a t e l l i t e i n p u t d a t a . A t r a n s m i s s i o n v a r i a b l e was s e l e c t e d r a t h e r t h a n a b s o l u t e e n e r g y u n i t s ( e . g . KJm" 2 hr _ 1 ) a s i t i s a more f u n d a m e n t a l p a r a m e t e r . The s h o r t w a v e t r a n s m i s s i o n was c a l c u l a t e d u s i n g m e a s u r e d 3 p y r a n o m e t r i c d a t a and a c l e a r s k y r a d i a t i o n m o d e l ( D a v i e s e t a l . , 1 9 7 5 ) . The s h o r t w a v e t r a n s m i s s i o n c a n t h e n be r e l a t e d t o t h e s a t e l l i t e b r i g h t n e s s d a t a ( f r o m t h e SMS-2 s a t e l l i t e ) v i a an i n v e r s e r e l a t i o n s h i p ( i . e . g r e a t e r t a r g e t b r i g h t n e s s due t o t h e p r e s e n c e o f c l o u d s c o r r e s p o n d s t o l o w e r s h o r t w a v e t r a n s m i s s i o n v a l u e s a t t h e s u r f a c e , and v i s a v e r s a ) . The e x c e p t i o n t o t h i s o c c u r s w i t h snow c o v e r e d g r o u n d s u r f a c e s w h i c h r e s u l t i n v e r y h i g h r e f l e c t i v i t i e s . S u c h c o n d i t i o n s were e x c l u d e d f rom o u r a n a l y s e s . F i g u r e 1.1 shows t h e g e n e r a l s t e p s t a k e n i n d e v e l o p i n g t h e r e l a t i o n s h i p . S u c h an a p p r o a c h a l l o w s two p r o b l e m s a s s o c i a t e d w i t h t h e use o f s a t e l l i t e s t o e s t i m a t e s o l a r i r r a d i a n c e , t o be s t u d i e d . F i r s t l y t h e n a r r o w a n g l e s e n s o r t y p i c a l l y u s e d i n m e t e o r o l o g i c a l r emote s e n s i n g c a n n o t s i m u l t a n e o u s l y measure t h e r a d i a t i o n e m e r g i n g f rom many d i f f e r e n t a n g l e s . T h u s t h e a n i s o t r o p i c r e f l e c t a n c e p r o p e r t i e s o f t h e E a r t h - A t m o s p h e r e s y s t e m may r e q u i r e t h e s a t e l l i t e d a t a t o be c o r r e c t e d . The need f o r s u c h a c o r r e c t i o n w i l l be a s s e s s e d u s i n g b i d i r e c t i o n a l r e f l e c t a n c e (BDR) m o d e l s . The s e c o n d p r o b l e m i s t h a t u n d e r c l e a r sky or o v e r c a s t c o n d i t i o n s t h e r a d i a t i o n r e g i m e may be s u f f i c i e n t l y homogeneous t o be a d e q u a t e l y c h a r a c t e r i z e d by one s a t e l l i t e image f o r a g i v e n h o u r l y i n t e r v a l , w h i l e f o r p a r t l y c l o u d y c o n d i t i o n s t h e r a p i d l y c h a n g i n g r a d i a t i o n r e g i m e may w e l l r e q u i r e a g r e a t e r number o f s a t e l l i t e i m a g e s . T h u s i t i s J 4 O b s e r v e d S h o r t w a v e Wave R a d i a t i o n S a t e l l i t e B r i g h t n e s s E x t r a t e r r e s t r i a l R a d i a t i o n C l e a r Sky R a d i a t i o n M o d e l S h o r t w a v e " ^ T r a n s m i s s i o n I n v e r s e R e l a t i o n s h i p T a r g e t R e f l e c t i v i t y FIGURE 1 . 1 F l o w D i a g r a m O u t l i n i n g t h e S t e p s T a k e n t o D e v e l o p a R e l a t i o n s h i p Between S h o r t w a v e T r a n s m i s s i o n and T a r g e t R e f l e c t i v i t y . 5 i m p o r t a n t t o e s t a b l i s h t h e r e l a t i o n s h i p be tween t h e s a t e l l i t e s a m p l i n g f r e q u e n c y ( e . g . o n e , two o r t h r e e images p e r h o u r ) and t h e a b i l i t y t o e s t i m a t e t h e s o l a r i r r a d i a n c e . The s u b s t a n t i a l c o m p u t a t i o n a l r e q u i r e m e n t s a s s o c i a t e d w i t h t h e d i g i t a l image p r o c e s s i n g make i t d e s i r a b l e t o o p t i m i z e t h e number o f images u s e d t o e s t i m a t e t h e s o l a r f l u x . One o f t h e w e a k n e s s e s o f s a t e l l i t e a n a l y s e s o f s o l a r e n e r g y a r i s e s f rom t h e i n a b i l i t y o f t h e s a t e l l i t e t o c a p t u r e t h e c o m p l e x r a d i a t i v e r e g i m e f o u n d f o r p a r t l y c l o u d y c o n d i t i o n s . By v a r y i n g t h e t a r g e t s i z e a n d t e m p o r a l a v e r a g i n g p e r i o d i t may be p o s s i b l e t o m i n i m i z e t h e i n a b i l i t y o f t h e s a t e l l i t e t o c a p t u r e t h o s e c o n d i t i o n s . P r e v i o u s s a t e l l i t e s t u d i e s have a s sumed s p e c i f i c a r r a y s i z e s t o be a p p r o p r i a t e . F o r e x a m p l e , G a u t i e r e t a l . (1980) c a r r i e d out a l l t h e i r a n a l y s e s u s i n g a 16 km x 16 km s a t e l l i t e a r r a y s i z e , w h i l e T a r p l e y (1979) u s e d a 50 km x 50 km a r r a y . The a p p r o p r i a t e n e s s o f s u c h c o n f i g u r a t i o n s r e q u i r e s e x a m i n a t i o n . W i t h r e g a r d t o c h a n g i n g t h e t e m p o r a l a v e r a g i n g p e r i o d , i t i s h y p o t h e s i s e d t h a t i n c r e a s i n g t h e t i m e a v e r a g i n g w i l l r e d u c e t h e s i g n i f i c a n c e o f t h e s h o r t t e r m v a r i a b i l i t y o f t h e r a d i a n t e n e r g y w h i c h c a n n o t be c a p t u r e d by h a l f - h o u r l y i m a g e s . T h i s has l e d t o t h e f o l l o w i n g o b j e c t i v e s . 6 1.2 S p e c i f i c O b j e c t i v e s 1) To assess the impact of b i d i r e c t i o n a l r e f l e c t a n c e (BDR) on s a t e l l i t e based e s t i m a t e s of s o l a r i r r a d i a n c e a t the E a r t h ' s s u r f a c e . 2) To d e t e r m i n e the optimum s p a t i a l s a t e l l i t e a r r a y c o n f i g u r a t i o n f o r e s t i m a t i n g t a r g e t r e f l e c t a n c e . 3) To d e t e r m i n e the impact of i n c r e a s e d t e m p o r a l a v e r a g i n g . 4) To t e s t the s e n s i t i v i t y of e s t i m a t e s of s o l a r i r r a d i a n c e u s i n g s a t e l l i t e d a t a t o changes i n t he number o f s a t e l l i t e images c o n t r i b u t i n g t o t he c o m p u t a t i o n f o r a g i ven t i m e i n t e r v a l . 7 CHAPTER 2 RADIATION DATA SET AND MODEL 2 . 1 S t u d y A r e a The l o c a t i o n s a t w h i c h s o l a r r a d i a t i o n d a t a u s e d i n t h i s s t u d y have been o b s e r v e d a r e p r e s e n t e d i n F i g u r e 2 . 1 . The s o l a r r a d i a t i o n m o n i t o r i n g f a c i l i t y 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 ( s ee H a y , 1979) was s e l e c t e d as t h e i n i t i a l t e s t s i t e f o r i n v e s t i g a t i n g t h e r e l a t i o n s h i p between s h o r t wave t r a n s m i s s i o n a n d s a t e l l i t e t a r g e t r e f l e c t a n c e . F o r b r e v i t y t h i s s i t e s h a l l be r e f e r r e d t o a s U B C . Two o t h e r l o c a t i o n s a r e a l s o u s e d a t a l a t e r s t a g e , n a m e l y A b b o t s f o r d A i r p o r t (ABAIR) a n d MAA. T h e i r t o p o g r a p h i c a l p o s i t i o n p r o v i d e s a c o m p a r i s o n w i t h t h e c o a s t a l s i t e o f U B C . The MAA l o c a t i o n i s somewhat f i c t i t i o u s i n t h a t i t r e p r e s e n t s t h e a v e r a g e d r a d i a t i o n d a t a s e t s f rom A b b o t s f o r d A i r p o r t , A b b o t s f o r d C i t y and M i s s i o n C i t y , and t h e r e f o r e i t i s l o c a t e d midway be tween t h e s e t h r e e s i t e s ( s e e F i g u r e 2 . 1 ) . T h i s C h a p t e r w i l l d e s c r i b e how s h o r t w a v e t r a n s m i s s i o n i s c a l c u l a t e d u s i n g c a l c u l a t e d c l e a r sky and m e a s u r e d s o l a r i r r a d i a n c e s . 8 FIGURE 2.1 L o c a t i o n o f the shortwave r a d i a t i o n m o n i t o r i n g s i t e s f o r p a r t o f the Lower F r a s e r V a l l e y . ( The s i t e s used i n t h i s study are i n d i c a t e d by * ). 9 2 . 2 M e a s u r e d S h o r t w a v e R a d i a t i o n A l l t h e s t a t i o n s d e s c r i b e d i n S e c t i o n 2.1 a r e p a r t o f a m e s o s c a l e p y r a n o m e t r i c n e t w o r k ( H a y , 1 9 8 3 a ) . The measurement s f rom t h e s e s i t e s were t a k e n f rom t h e d a t a a r c h i v e s 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 . The d a y s s e l e c t e d c o r r e s p o n d t o t h o s e d a y s be tween 1979 and 1981 f o r w h i c h s a t e l l i t e images a r e a v a i l a b l e . A t e a c h s i t e t h e i n c o m i n g s h o r t w a v e r a d i a t i o n on a h o r i z o n t a l s u r f a c e (K4-) i s m e a s u r e d u s i n g a CM6 K i p p and Zonen p y r a n o m e t e r and i s r e c o r d e d as an h o u r l y i n t e g r a t e d v a l u e i n KJ nf 2 h r _ 1 . L a t i m e r (1972) c l a i m s t h a t t h e Root Mean S q u a r e E r r o r f o r m o n i t o r i n g s y s t e m s i n t h e C a n a d i a n s o l a r r a d i a t i o n n e t w o r k i s a r o u n d ± 5 % and a r e c e n t s t u d y by Hay a n d W a r d l e (1982) has shown t h e r a d i a t i o n d a t a u s e d i n t h i s s t u d y t o be w i t h i n t h i s a c c e p t a b l e r a n g e . 2 . 3 C l e a r Sky R a d i a t i o n M o d e l The m o d e l c h o s e n t o c a l c u l a t e c l e a r sky r a d i a t i o n was o r i g i n a l l y d e v e l o p e d a t M c M a s t e r U n i v e r s i t y by D a v i e s e t a l . ( 1 9 7 5 ) . S u b s e q u e n t i m p r o v e m e n t s i n t h e p a r a m e t e r i z a t i o n s have l e d t o t h e mode l i n i t s p r e s e n t fo rm ( D a v i e s , 1981) b e i n g u s e d f o r t h i s s t u d y . D a v i e s and Hay (1980) c o m p a r e d t h i s mode l t o ' e x a c t ' r a d i a t i o n c o m p u t a t i o n s o f t h e a t m o s p h e r e by B r a s l a u 10 and Dave (1973) and f o u n d t h e two methods t o be w i t h i n 1%. The g l o b a l r a d i a t i o n r e a c h i n g t h e E a r t h ' s s u r f a c e u n d e r c l e a r s k i e s (K+0) i s c a l c u l a t e d as a r e s i d u a l a f t e r t h e e x t r a t e r r e s t r i a l f l u x has been d e p l e t e d by a t m o s p h e r i c a b s o r p t i o n and s c a t t e r i n g . The t o t a l s h o r t w a v e e n e r g y w h i c h r e a c h e s t h e E a r t - h ' s s u r f a c e u n d e r c l e a r s k i e s (K+0) i s composed o f two s e p a r a t e c o m p o n e n t s , t h e d i r e c t (S-l-0) and d i f f u s e (D+0) i r r a d i a n c e . H e n c e : K+ 0 = S+0 + D+o ( 2 . 1 ) The d i r e c t r a d i a t i o n i s c a l c u l a t e d by a p p l y i n g t r a n s m i t t a n c e s due t o o z o n e ( T r ( O ) ) and R a y l e i g h s c a t t e r i n g ( T r ( R ) ) and a b s o r p t i o n due t o w a t e r v a p o u r f a ^ ) , t o t h e s o l a r c o n s t a n t ( I 0 ) s u c h t h a t : S+ 0 = I 0 c o s e ( T r ( O ) T r ( R ) - a u ) ( 2 . 2 ) where e i s t h e s o l a r z e n i t h a n g l e . The form o f t h i s e q u a t i o n i s b a s e d on r e c e n t a r g u m e n t s , w h i c h s u g g e s t s u b t r a c t i n g t h e w a t e r v a p o u r a b s o r p t a n c e ( P a l t r i d g e and P i a t t , 1976) r a t h e r t h a n a p p l y i n g i t m u l t i p l i c a t i v e l y . T h i s i s due t o w a t e r v a p o u r a b s o r b i n g a t l o n g e r w a v e l e n g t h s t h a n o z o n e . The c l e a r sky d i f f u s e r a d i a t i o n ( D + Q ) i s c a l c u l a t e d as a summat ion o f c o m p o n e n t s due t o m o l e c u l a r s c a t t e r i n g (Dr ) and m u l t i p l e r e f l e c t i o n between the g r o u n d , a n d a t m o s p h e r e ( D s ) : D+o = Dr + Ds (2.3) The m o l e c u l a r s c a t t e r i n g t e r m (Dr ) i s c a l c u l a t e d b a s e d on two a s s u m p t i o n s : 1) t h a t s c a t t e r i n g i s i s o t r o p i c ; c o n s e q u e n t l y o n l y h a l f o f t h e t o t a l R a y l e i g h s c a t t e r e d r a d i a t i o n r e a c h e s t h e g r o u n d , and 2) t h a t water v a p o u r o n l y a b s o r b s d i r e c t beam r a d i a t i o n ( P a l t r i d g e , 1 9 7 3 ) . T h e r e f o r e : Dr = I 0 c o s e T r ( 0 ) (1 - T r ( R ) ) / 2 (2.4) The m u l t i p l e r e f l e c t i o n t e r m s u r f a c e a l b e d o ( a s ) , t h e a l b e d o i n c i d e n t i r r a d i a n c e ( S + 0 a n d D r ) . (Ds) i s d e t e r m i n e d u s i n g t h e o f t h e a t m o s p h e r e (ab) and t h e T h u s : DS = a b a s ( S 4 - 0 + D r ) / ( 1 - a b a s ) (2.5) The m u l t i p l e r e f l e c t i o n t e r m i s e s p e c i a l l y i m p o r t a n t f o r s u r f a c e s w i t h h i g h a l b e d o s , but t h i s i s t h e l e a s t i m p o r t a n t t e r m f o r t h i s s t u d y due t o t h e r e l a t i v e l y low a l b e d o ( see S e c t i o n 2 . 4 . 4 ) . I t s h o u l d be n o t e d h e r e t h a t t h e s e f o r m u l a t i o n s e x c l u d e an a e r o s o l t r a n s m i t t a n c e t e r m . T h e r e a r e two r e a s o n s f o r t h i s e x c l u s i o n . F i r s t l y , the A t m o s p h e r i c E n v i r o n m e n t S e r v i c e (1980) r e p o r t a n d D a v i e s (1981) show t h a t t h e M c M a s t e r model 12 i g n o r i n g a e r o s o l e f f e c t s y i e l d e d t h e s m a l l e s t Mean B i a s E r r o r s and Root Mean S q u a r e E r r o r s f o r d a i l y i r r a d i a n c e s a t V a n c o u v e r . S e c o n d l y , i n c o r p o r a t i o n o f an a e r o s o l t e r m i s v e r y c o m p l e x and i t s d e t e r m i n a t i o n i s s t i l l n o t c o m p l e t e l y s a t i s f a c t o r y (WMO, 1978; D a v i e s and H a y , 1980; D a v i e s , 1 9 8 2 ) . 2 .4 P a r a m e t e r i z a t i o n s u s e d i n t h e C l e a r Sky R a d i a t i o n M o d e l 2 . 4 . 1 Ozone A b s o r p t i o n The t r a n s m i s s i o n o f s o l a r r a d i a t i o n a f t e r a b s o r p t i o n by o z o n e ( T r ( O ) ) i s c a l c u l a t e d u s i n g t h e L a c i s and Hansen (1974) e m p i r i c a l f o r m u l a : T r ( O ) = 1 - a 0 ( 2 . 6 ) w h e r e : a 0 = 0 . 1 0 8 2 X 1 / (1 + 1 3 . 6 8 X T ) + 0 . 0 0 6 5 8 X / (1 + ( 1 0 . 3 6 X 1 ) ) + 0 . 0 0 2 1 1 8 X 1 / (1 + 0 . 0 4 2 X t + 0 . 0 0 0 0 0 3 2 3 X 1 ) ( 2 . 7 ) The f i r s t two t e r m s of E q u a t i o n 2 . 7 a c c o u n t f o r o z o n e a b s o r p t i o n a t u l t r a v i o l e t w a v e l e n g t h s ( < 0 . 3 5 m i c r o m e t e r s ) and t h e f i n a l t e r m f o r t h e v i s i b l e p o r t i o n o f t h e s p e c t r u m (be tween 0 . 5 and 0 . 7 m i c r o m e t e r s ) . X 1 i s t h e s l a n t p a t h 13 t h r o u g h o z o n e b a s e d on t h e v e r t i c a l o p t i c a l p a t h l e n g t h t h r o u g h o z o n e (u^ and t h e r e l a t i v e o p t i c a l a i r mass (m) : X , - u 0 . <2-8> The v e r t i c a l o p t i c a l p a t h l e n g t h t h r o u g h o z o n e ( u 0 ) i s s e t a t 3 .5 mm from work by M c C l a t c h e y e t a l . (1971) and t h e r e l a t i v e o p t i c a l a i r mass (m) i s c a l c u l a t e d u s i n g a f o r m u l a g i v e n by R o g e r s ( 1 9 6 7 ) , ( see E q u a t i o n 2 . 1 7 ) . 2 . 4 . 2 R a y l e i g h S c a t t e r i n g The t r a n s m i s s i v i t y a f t e r R a y l e i g h s c a t t e r i n g ( T r ( R ) ) i s c a l c u l a t e d f rom t h e R a y l e i g h s c a t t e r o p t i c a l d e p t h by t h e p r o c e d u r e o f E l t e r m a n (1968) u s i n g t h e e x t r a t e r r e s t r i a l s p e c t r u m o f T h e k a e k a r a and Drummond ( 1 9 7 1 ) . T a b l e 2.1 l i s t s s p e c t r a l l y i n t e g r a t e d v a l u e s o f T r ( R ) b a s e d on t h i s m e t h o d . 2 . 4 . 3 W a t e r V a p o u r A b s o r p t i o n W a t e r v a p o u r a b s o r p t i o n i s c a l c u l a t e d u s i n g t h e f o r m u l a t i o n o f L a c i s and H a n s e n (1974) who e m p i r i c a l l y r e l a t e d t h e r e s u l t s o f Yamamoto (1962) t o w a t e r p a t h ( X ) : a u ( X ) = 0 . 2 9 X / ((1 + 14 .15X) + 0 .5925X) (2.9) 14 TABLE 2. 1 T r a n s m i s s i v i t y A f t e r R a y l e i g h S c a t t e r i n g ( a f t e r D a v i e s , 1981) V a l u e s a r e D i m e n s i o n l e s s . R e l a t i v e O p t i c a l T r a n s m i s s i v i t y A f t e r A i r Mass, m R a y l e i g h S c a t t e r i n g , T r ( R ) 0.5 0.9385 1 .0 0.8973 1 .2 0.8830 1 .4 0.8696 1 .6 0.8572 1 .8 0.8455 2.0 0.8344 2.5 0.8094 3.0 0.7872 3.5 0.7673 4.0 0.7493 4.5 0.7328 5.0 0.7177 5.5 0.7037 6.0 0.6907 10.0 0.6108 30.0 0.4364 15 where: X = u w m ( 2.10) F o r t h i s s t u d y t h e v e r t i c a l o p t i c a l p a t h l e n g t h t h r o u g h w a t e r v a p o u r , u u , i s b a s e d on amounts of p r e c i p i t a b l e w a t e r ( s e e S e c t i o n 2 . 4 . 6 ) . The r e l a t i v e o p t i c a l a i r mass i s c a l c u l a t e d u s i n g E q u a t i o n 2.17 t o g e t h e r w i t h a p r e s s u r e c o r r e c t i o n ( s e e S e c t i o n 2 . 4 . 5 ) . 2.4.4 A l b e d o Terms The two a l b e d o p a r a m e t e r s p r e s e n t i n t h e m u l t i p l e r e f l e c t i o n e q u a t i o n ( s e e E q u a t i o n 2.5) a r e f i x e d a t 0.20 f o r t h e a l b e d o of t h e g r o u n d s u r f a c e ( a s ) ( f o l l o w i n g H a y , l 9 8 3 a ) and 0.0685 f o r t h e a l b e d o o f t h e a t m o s p h e r e (ab) ( L a c i s and H a n s e n , 1 9 7 4 ) . The l a t t e r i s b a s e d upon t h e R a y l e i g h s c a t t e r i n g c o m p o n e n t s o n l y . The use of an i n v a r i a n t a l b e d o f o r t h e g r o u n d s u r f a c e i s a c c e p t a b l e b e c a u s e t h e days of i n t e r e s t i n t h i s s t u d y were f r e e o f g r o u n d snow c o v e r . 2.4.5 C a l c u l a t i o n o f P o s i t i o n and Time P a r a m e t e r s The e x t r a t e r r e s t r i a l r a d i a t i o n r e a c h i n g t h e t o p o f t h e E a r t h ' s a t m o s p h e r e ( I ( o ) ) n o r m a l t o t h e s o l a r beam, p e r u n i t s u r f a c e 16 a r e a , i s d e t e r m i n e d b y : I ( o ) = I 0 / R 2 ( 2 . 1 1 ) where I 0 i s t h e s o l a r c o n s t a n t and R i s t h e r a t i o o f t h e a c t u a l t o mean S u n - E a r t h d i s t a n c e . A s o l a r c o n s t a n t o f 1353 Wnf2 i s b a s e d on work by T h e k a e k a r a and Drummond (1971) . I t i s g e n e r a l l y a c c e p t e d and was u s e d as t h e v a l u e f o r t h e s o l a r c o n s t a n t i n t h e d e v e l o p m e n t o f t h e M c M a s t e r m o d e l ( D a v i e s e t a l . , 1 9 7 5 ) . The r a t i o o f t h e a c t u a l t o mean S u n - E a r t h d i s t a n c e i s e x p r e s s e d a f t e r S p e n c e r (1972) a s a f u n c t i o n o f day number ( d n ) , r a n g i n g f rom 0 on J a n u a r y 1, t o 364 on December 3 1 . The day number d e f i n e s t h e a n g l e : 9 0 = 2 IT dn / 365 ( 2 . 1 2 ) T h e n : 1 / R = 1.00011 + 0 .034221 c o s 8 0 + 0 . 0 0 1 2 8 s i n e o - 0 . 0 0 0 7 1 9 c o s 2 6 0 + 0 . 0 0 0 0 7 7 s i n 2 e 0 ( 2 . 1 3 ) To c a l c u l a t e t h e e x t r a t e r r e s t r i a l r a d i a t i o n a t t h e t o p o f t h e a t m o s p h e r e f o r a h o r i z o n t a l u n i t s u r f a c e a r e a , I ( o ) i s m u l t i p l i e d by t h e c o s i n e o f the z e n i t h a n g l e (a) , w h i c h i s 1 7 c a l c u l a t e d u s i n g : c o s e = sin<j> s i n 6 + c o s * c o s 5 cosH ( 2 . 1 4 ) where <j> i s t h e l a t i t u d e , 6 i s t h e s o l a r d e c l i n a t i o n and H i s the s o l a r hour a n g l e f o r t h e time and s i t e of i n t e r e s t . The l a t i t u d e used i s t h a t of t h e UBC s i t e , 49°16'N. The s o l a r hour a n g l e i s c a l c u l a t e d f o r t h e m i d - p o i n t of th e hour u s i n g : H = 15 112.5 - LAT ( 2 . 1 5 ) where LAT i s t h e l o c a l a p p a r e n t t i m e . The s o l a r d e c l i n a t i o n p a r a m e t e r i z a t i o n i s a l s o b a s e d on work by S p e n c e r ( 1 9 7 2 ) : 6 = 0.006918 - 0.399912 c o s 6 0 + 0 .070257 s i n 6 0 -0.006759 c o s 2 9 0 + 0.000907 s i n 2 6 0 - 0.002697 c o s 3 e 0 + 0.001 480 s i n 3 6 0 ( 2.16) The r e l a t i v e o p t i c a l a i r mass (m) i s d e t e r m i n e d u s i n g a f o r m u l a by Rogers (1967) which a l l o w s f o r r e f r a c t i o n e f f e c t s a t l a r g e z e n i t h a n g l e s : m = 35 / (1224 c o s 2 6 + 1 )°' 5 ( 2 . 1 7 ) 18 The o p t i c a l a i r mass i s a l s o c o r r e c t e d f o r a t m o s p h e r i c p r e s s u r e by m u l t i p l y i n g by p / p , where p i s t h e s t a t i o n p r e s s u r e and p 0 i s t h e s t a n d a r d sea l e v e l p r e s s u r e o f 101 .3 k P a . The a t m o s p h e r i c p r e s s u r e v a l u e s were o b t a i n e d f rom t h e A t m o s p h e r i c E n v i r o n m e n t S e r v i c e c l i m a t e s t a t i o n i n j u x t a p o s i t i o n t o - t h e UBC r a d i a t i o n m o n i t o r i n g s i t e . 2 . 4 . 6 P r e c i p i t a b l e Water D e t e r m i n a t i o n P r e c i p i t a b l e w a t e r amounts a r e u s e d i n t h e M c M a s t e r m o d e l when c a l c u l a t i n g t h e w a t e r v a p o u r a b s o r p t i o n i n t h e a t m o s p h e r e ( see S e c t i o n 2 . 4 . 3 ) . The i n i t i a l work i n v o l v e d t h e use of p r e c i p i t a b l e w a t e r d a t a o b t a i n e d f rom t e p h i g r a m s f o r t h e n e a r e s t r a d i o s o n d e s t a t i o n s , l o c a t e d a t P o r t H a r d y on V a n c o u v e r I s l a n d (360 km from t h e UBC s i t e ) and Q u i l l a y u t e i n W a s h i n g t o n S t a t e (171 km from t h e UBC s i t e ) . D e w - p o i n t and d r y b u l b t e m p e r a t u r e s a t f o u r t e e n l e v e l s i n t h e a t m o s p h e r e ( f r o m t h e s u r f a c e t o t h e 300 mb l e v e l ) were u s e d i n t h e c a l c u l a t i o n o f p r e c i p i t a b l e w a t e r . P o s s i b l e e r r o r s u s i n g t h i s t e c h n i q u e were d e t e r m i n e d t o be up t o f o u r m i l l i m e t e r s . Such an e r r o r w i l l be shown t o have l i t t l e e f f e c t on the t r a n s m i s s i o n c a l c u l a t i o n . To c a l c u l a t e a p r e c i p i t a b l e w a t e r v a l u e f o r U B C , the t w i c e d a i l y m e a s u r e m e n t s a t b o t h r a d i o s o n d e s t a t i o n s were w e i g h t e d t e m p o r a l l y and s p a t i a l l y ( i . e . w i t h r e s p e c t t o s o l a r noon f o r 19 t he fo rmer and d i s t a n c e f rom UBC f o r the l a t t e r ) . T h i s r e s u l t e d i n w e i g h t i n g s of 0 .164 and 0 .247 f o r P o r t Hardy a t 04:00 and 16:00 hours r e s p e c t i v e l y , and 0 .253 and 0 .336 f o r Q u i l l a y u t e a t 04 :00 and 16:00 hours r e s p e c t i v e l y . V a r i o u s o t h e r w e i g h t i n g schemes based on p e r m u t a t i o n s of the above were t e s t e d , but these d i d not r e s u l t i n s i g n i f i c a n t changes t o the e s t i m a t e o f p r e c i p i t a b l e water f o r the UBC s i t e . Even when the p r e c i p i t a b l e water amount was a lmos t d o u b l e d , the change i n the t r a n s m i s s i o n v a l u e (see S e c t i o n 2 . 5 ) was l i m i t e d t o a p p r o x i m a t e l y 2%. T h i s r e s u l t suggests t h a t t he model f o r c a l c u l a t i n g t r a n s m i s s i o n 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 l a r g e changes i n the p r e c i p i t a b l e water t o t a l s . S ince b o t h Por t Hardy and Q u i l l a y u t e a re a s u b s t a n t i a l d i s t a n c e f rom Vancouver , the degree t o wh ich these rad iosonde s t a t i o n s r e p r e s e n t p r e c i p i t a b l e water c o n d i t i o n s i n the s tudy area i s q u e s t i o n a b l e . Work by R e i t a n ( 1963) , Bolsenga ( 1965 ) , Smith (1966) and A twa te r and B a l l ( 1 9 7 6 ) , show t h a t t h e r e i s a v e r y s t r o n g e m p i r i c a l r e l a t i o n s h i p between t o t a l p r e c i p i t a b l e water and s u r f a c e d e w - p o i n t t e m p e r a t u r e . S m i t h ' s (1966) work i s the most comprehens ive and i n c o r p o r a t e s an a d j u s t m e n t f o r b o t h l a t i t u d e and season. S m i t h ' s f o r m u l a t i o n f o r c a l c u l a t i n g t o t a l p r e c i p i t a b l e water ( U ) : I n U = 0 .133 - I n ( X + 1) + 0 .0393 Td (2 . 1 8 ) was used t o t e s t the a p p r o p r i a t e n e s s o f t he measured 20 r a d i o s o n d e d a t a . X i s a f a c t o r b a s e d on the l a t i t u d e of t h e s t a t i o n and t h e time of t h e y e a r , and Td i s the dew - p o i n t t e m p e r a t u r e ( i n d e g r e e s F ) . U s i n g F i g u r e 2.2 v a l u e s of 2.62, 3.00, 2.71 and 2.76 were o b t a i n e d f o r w i n t e r , s p r i n g , summer and autumn r e s p e c t i v e l y . To d e t e r m i n e t h e v a l u e s f o r s e l e c t e d d a y s the s e a s o n a l v a l u e s above were p l o t t e d on a g r a p h ( see F i g u r e 2.3) and i n t e r p o l a t e d v a l u e s were a b s t r a c t e d . V a l u e s f o r Td were o b t a i n e d from t h e A t m o s p h e r i c ; E n v i r o n m e n t S e r v i c e c l i m a t e s t a t i o n a t the U n i v e r s i t y of B r i t i s h C o l u m b i a . The c a l c u l a t e d t o t a l s of p r e c i p i t a b l e water b a s e d on S m i t h ' s f o r m u l a and t h o s e measured by t h e r a d i o s o n d e a r e shown i n T a b l e 2.2. In a l l but f i v e of the e i g h t e e n c a s e s t h e c a l c u l a t e d t o t a l s a r e l a r g e r t h a n t h e measured t o t a l s . The r e s u l t s s u g g e s t t h a t t h e f i v e i n s t a n c e s when t h e measured v a l u e s a r e g r e a t e r t h a n t h o s e c a l c u l a t e d may be a c o n s e q u e n c e of s e a s o n a l f a c t o r s as th e y a l l o c c u r i n l a t e w i n t e r and e a r l y s p r i n g . A l t h o u g h the t o t a l amounts of p r e c i p i t a b l e water can be s u b s t a n t i a l l y d i f f e r e n t u s i n g t h e s e two methods, the d e g r e e t o w hich t h i s d i f f e r e n c e a f f e c t s t h e c a l c u l a t e d t r a n s m i s s i v i t y was fo u n d t o be s m a l l . T a b l e 2.3 g i v e s an i n d i c a t i o n of how the t r a n s m i s s i o n v a l u e s v a r i e d w i t h t h e two methods of e s t i m a t i n g p r e c i p i t a b l e water amounts. The days s e l e c t e d a r e a l l c l e a r days when t h e t r a n s m i s s i o n i s e x p e c t e d t o be c l o s e t o 100%. In t h e m a j o r i t y of c a s e s t h e r e i s an improvement i n the t r a n s m i s s i o n ( i . e . c l o s e r t o 100%) u s i n g S m i t h ' s (1966) f o r m u l a t i o n f o r d e t e r m i n i n g p r e c i p i t a b l e water amounts. O n l y 21 FIGURE 2 .2 V a r i a t i o n o f X W i t h L a t i t u d e and S e a s o n . G r a p h C o n s t r u e From D a t a P r e s e n t e d by S m i t h ( 1 9 6 6 ) . 22 2-X 1-J F M A M J J A S O N D J TIME ( M o n t h s ) FIGURE 2.3 S e a s o n a l V a r i a t i o n of x F o r the Study A r e a . D e r i v e d From F i g u r e 2.2. 23 TABLE 2.2 C o m p a r i s o n o f P r e c i p i t a b l e W ater V a l u e s (mm) D e r i v e d R a d i o s o n d e D a t a and t h e F o r m u l a t i o n o f S m i t h ( 1 9 6 6 ) . J u l i a n M e a s u r e d C a l c u l a t e d % D i f f e r e n c e Day ( R a d i o s o n d e ) ( S m i t h Between M e a s u r e d F o r m u l a t i o n ) and C a l c u l a t e d 196/79 18.8 27 .3 45.2 200/79 21.1 32.3 53. 1 255/79 19.9 21.8 9.5 256/79 21.4 22.5 5.1 257/79 23. 1 25.6 10.8 276/79 16.9 18.6 10.1 293/79 11.0 16.6 50.9 304/79 10.8 14.8 37.0 361/79 13.1 13.6 3.8 012/80 13.2 12.9 -2.3 025/80 5. 1 3.7 -27.5 030/80 6.2 5.0 -19.4 105/80 18.1 17.2 -5.0 121/80 16.9 16.2 -4. 1 171/80 15.3 24.4 59.5 183/80 17.6 26.2 48.9 185/80 21.7 24. 1 11.1 261/80 16.3 25.4 55.8 2 4 T A B L E 2 . 3 V a r i a t i o n i n T r a n s m i s s i o n V a l u e s (%) C a l c u l a t e d f rom P r e c i p i t a b l e Water D a t a as D e t e r m i n e d f rom e i t h e r R a d i o s o n d e D a t a ( T ' ) o r t h e S m i t h (1966) F o r m u l a t i o n ( T ' ' ) . C a l c u l a t i o n s b a s e d on F o u r C l e a r Days a t t h e UBC S i t e . Hour Day T ' 200 /79 Day 304 /79 Day 361 /79 Day 183/80 E n d i n g T ' rji l l T ' rji I ? T ' 5 52 55 40 41 6 75 77 77 79 7 90 93 88 90 8 94 97 82 85 90 92 9 97 99 93 95 92 92 93 95 10 97 99 97 98 1 32 1 32 95 97 1 1 98 100 98 99 93 94 97 99 1 2 98 99 98 100 89 89 98 100 1 3 98 99 98 99 92 92 99 1 00 1 4 97 99 96 98 75 75 99 101 1 5 97 99 94 96 80 80 94 96 16 96 98 90 92 70 70 96 98 1 7 95 97 84 86 95 96 18 93 96 91 93 1 9 92 95 85 88 20 1 1 0 1 1 6 76 79 25 one c a s e o u t o f f i f t y shows a d e t e r i o r a t i o n and t h i s was f o r an hour a t t h e end o f day 2 0 0 / 7 9 when a b s o l u t e r a d i a t i o n amounts a r e s m a l l . The t r a n s m i s s i o n c a l c u l a t e d f rom t h e p r e c i p i t a b l e w a t e r t o t a l s b a s e d on S m i t h ' s f o r m u l a a p p e a r more a p p r o p r i a t e . The low v a l u e s f o r t h e t r a n s m i s s i v i t i e s b a s e d on t h e r a d i o s o n d e e s t i m a t e s o f p r e c i p i t a b l e w a t e r c a n n o t be f u l l y e x p l a i n e d by a t m o s p h e r i c a e r o s o l s (a t e r m n o t a c c o u n t e d f o r i n t h e M c M a s t e r m o d e l ) s i n c e t h e y may r e d u c e t h e t r a n s m i s s i o n a t most t o a v a l u e o f 95%. Work by A t w a t e r and B a l l (1976) showed t h a t t h e use of c a l c u l a t e d p r e c i p i t a b l e w a t e r amounts r a t h e r t h a n m e a s u r e d v a l u e s , r e s u l t e d i n an a v e r a g e d a i l y d i f f e r e n c e o f l e s s t h a n 2.5% i n c a l c u l a t i n g t o t a l s o l a r r a d i a t i o n . T h e i r s t u d y was b a s e d on e l e v e n s t a t i o n s i n t h e U n i t e d S t a t e s w i t h r a d i o s o n d e d a t a f rom t h e same s i t e a s t h e d e w - p o i n t t e m p e r a t u r e u s e d i n t h e S m i t h f o r m u l a t i o n . A r e c e n t s t u d y by R a p h a e l ( 1 9 8 3 ) , u s i n g a s i m i l a r d a t a s e t t o t h e one i n c o r p o r a t e d i n t h i s s t u d y , f o u n d t h a t t h e two a p p r o a c h e s p r o d u c e d a d i f f e r e n c e i n e s t i m a t e s o f t h e d a i l y t o t a l s o l a r r a d i a t i o n v a l u e s o f a r o u n d 5%. R a p h a e l ' s r e s u l t s f a v o u r e d t h e c a l c u l a t e d p r e c i p i t a b l e w a t e r v a l u e s r a t h e r t h a n t h o s e m e a s u r e d a t l o c a t i o n s remote f rom t h e s t u d y a r e a . The r e s u l t s f rom t h i s s t u d y c o r r o b o r a t e t h i s e a r l i e r work and t o g e t h e r t h e y s u g g e s t two r e a s o n s f o r c h o o s i n g t o use t h e S m i t h f o r m u l a t i o n r a t h e r t h a n t h e r a d i o s o n d e m e t h o d : 26 1) t h e d e w - p o i n t t e m p e r a t u r e u s e d i n t h e c a l c u l a t e d v e r s i o n o f p r e c i p i t a b l e w a t e r i s more e a s i l y o b t a i n e d and more r e a d i l y a v a i l a b l e ; and 2) a l t h o u g h b o t h t e c h n i q u e s p r o d u c e s i m i l a r r e s u l t s when d a t a f rom t h e same s i t e a r e u s e d ( A t w a t e r and B a l l , 1 9 7 6 ) , t h e r a d i o s o n d e o b s e r v a t i o n s f o r P o r t H a r d y and Q u i l l a y u t e a r e f a r removed f rom t h e s t u d y a r e a and p r o d u c e c o n s i s t e n t l y p o o r e r r e s u l t s t h a n t h e use o f t h e c a l c u l a t e d p r e c i p i t a b l e w a t e r t o t a l s . The d a t a i n T a b l e s 2 .2 a n d 2 . 3 a l s o show t h a t when t h e p r e c i p i t a b l e w a t e r amount i s i n c r e a s e d by a p p r o x i m a t e l y 50%, e . g . J u l i a n day 2 0 0 / 7 9 , t h e e f f e c t on t h e c a l c u l a t i o n o f t h e t r a n s m i s s i o n i s t y p i c a l l y s m a l l ( i . e . w i t h i n 2%) and i s s t i l l w i t h i n 6% a t t h e end o f t h e day when t h e z e n i t h a n g l e i s g r e a t e r t h a n 85 d e g r e e s . T h i s c o n f i r m s t h e e a r l i e r s t a t e m e n t c o n c e r n i n g t h e i n s e n s i t i v i t y o f t h e mode l t o c h a n g e s i n p r e c i p i t a b l e w a t e r . 2 . 5 D e r i v a t i o n o f t h e ' S h o r t w a v e T r a n s m i s s i o n ' The a t m o s p h e r i c t r a n s m i s s i v i t y i s d e f i n e d as " t h e f r a c t i o n o f s o l a r r a d i a t i o n n o r m a l l y i n c i d e n t upon t h e t o p o f t h e a t m o s p h e r e w h i c h s u r v i v e s p a s s a g e t h r o u g h t h e a t m o s p h e r e t o 27 t h e E a r t h ' s s u r f a c e " ( H u s c h k e , 1 9 5 9 ) . The t e r m ' s h o r t w a v e t r a n s m i s s i o n ' (T) i s b e i n g u s e d h e r e t o d e s c r i b e a s i m p l e c l o u d t r a n s m i s s i o n by r e l a t i n g t h e a c t u a l m e a s u r e d i n c i d e n t s o l a r r a d i a t i o n a t t h e E a r t h ' s s u r f a c e (K+, see S e c t i o n 2 . 2 ) , t o t h a t c a l c u l a t e d f o r t h e c l e a r sky c o n d i t i o n s (K+0, see S e c t i o n 2 . 3 ) . T h u s : T = K + / K + 0 ( 2 . 1 9 ) E s s e n t i a l l y i t i s p r o p o s e d t o i s o l a t e t h e d e p l e t i o n o f i n c i d e n t e n e r g y due t o c l o u d s by u s i n g m e a s u r e d d a t a and i n c l u d i n g t h e d e p l e t i o n e f f e c t s due t o t h e c l o u d l e s s a t m o s p h e r e . The c l e a r sky m o d e l ' u s e d h e r e e x c l u d e s an a e r o s o l p a r a m e t e r and was s e l e c t e d b e c a u s e : 1) t h i s fo rm o f t h e m o d e l was shown t o p r o d u c e t h e b e s t e s t i m a t e o f s o l a r r a d i a t i o n u n d e r c l e a r sky c o n d i t i o n s f o r V a n c o u v e r ( A t m o s p h e r i c E n v i r o n m e n t S e r v i c e , 1980; D a v i e s , 1 9 8 1 ) ; and 2) t h e r e f l e c t e d r a d i a t i o n m e a s u r e d by t h e s a t e l l i t e i s a l s o i n f l u e n c e d by t h e a e r o s o l s and t h u s i t i s n e c e s s a r y t o i n c l u d e t h e e f f e c t s o f a e r o s o l s i n t h e c a l c u l a t i o n o f T . A s an a n a l o g y , i t c a n be s a i d t h a t t h e a e r o s o l i s e s s e n t i a l l y b e i n g t r e a t e d as a t h i n c l o u d . I d e a l l y t h e s h o r t w a v e t r a n s m i s s i o n s h o u l d be 100% on a c l e a r day d e v o i d o f a e r o s o l s , 28 and s l i g h t l y l e s s t h a n 100% when a e r o s o l s a r e p r e s e n t . However e r r o r s i n h e r e n t i n t h e M c M a s t e r m o d e l r e s u l t i n ± 1 % o r ± 2 % i n a c c u r a c i e s ( D a v i e s and H a y , 1 9 8 0 ) , t o g e t h e r w i t h ± 5 % f o r measurement e r r o r s ( L a t i m e r , 1972; Hay and W a r d l e , 1 9 8 2 ) . T h u s i n most c a s e s i t w i l l be i m p o s s i b l e t o i s o l a t e t h e e f f e c t s o f a e r o s o l i n e i t h e r t h e s a t e l l i t e d a t a o r t h e c a l c u l a t e d t r a n s m i s s i o n s . 2 9 CHAPTER 3 S A T E L L I T E DATA SET 3 . 1 I n t r o d u c t i o n The s a t e l l i t e u s e d i n t h i s s t u d y i s p a r t o f t h e 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 (GOES) s y s t e m w h i c h i n c l u d e s t h e S y n c h r o n o u s M e t e o r o l o g i c a l S a t e l l i t e s ( S M S ) . The i m a g e r y u s e d a r e f rom t h e SMS-2 s a t e l l i t e p o s i t i o n e d a t an a l t i t u d e o f a b o u t 3 5 , 8 0 0 km d i r e c t l y a b o v e t h e e q u a t o r a t 135 d e g r e e s wes t ( C o r b e l l e t a l . 1 9 8 1 ) . T h i s o p e r a t i o n a l s p i n s c a n g e o s y n c h r o n o u s s a t e l l i t e p r o v i d e s b o t h v i s i b l e and i n f r a r e d i m a g e s , t h o u g h t h e l a t t e r a r e no t u t i l i z e d i n t h i s s t u d y . T h e r e a r e e i g h t v e r t i c a l l y a l i g n e d v i s i b l e d e t e c t o r s w h i c h s ample s i m u l t a n e o u s l y i n t h e 0 . 5 5 - 0 . 7 0 m i c r o m e t e r w a v e l e n g t h s and g i v e a 0 . 8 km r e s o l u t i o n a t t h e s a t e l l i t e s u b p o i n t ( H a m b r i c k and P h i l l i p s , 1 9 8 0 ) , where t h e s u b p o i n t i s d e f i n e d as t h e p o i n t o f i n t e r s e c t i o n w i t h t h e E a r t h ' s s u r f a c e o f a v e c t o r j o i n i n g t h e s a t e l l i t e and t h e c e n t r e o f t h e E a r t h . Due t o t h e c u r v a t u r e o f t h e E a r t h t h e r e s o l u t i o n d e c r e a s e s as t h e a r e a v i e w e d moves away f rom t h e s a t e l l i t e s u b p o i n t . Thus t h e r e s o l u t i o n o f t h e s t u d y a r e a , i n t h e p r o x i m i t y o f V a n c o u v e r , B r i t i s h C o l u m b i a , w i l l be i n f e r i o r t o 0 .8 km. The a c t u a l p i x e l s i z e w i l l be d i s c u s s e d i n S e c t i o n 3 . 3 . 30 The V i s i b l e and I n f r a r e d S p i n S c a n R a d i o m e t e r (VISSR) a c q u i r e s a f u l l E a r t h d i s c image once e v e r y t h i r t y m i n u t e s . The c o l l e c t i o n and a r c h i v i n g o f t h e d a t a i s managed by v a r i o u s a u t h o r i t i e s i n c l u d i n g t h e U n i v e r s i t y o f W i s c o n s i n ' s S p a c e 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 ( S S E C ) , w h i c h i s t h e s o u r c e o f t h e s a t e l l i t e d a t a u s e d i n t h e p r e s e n t s t u d y . From t h e images c o v e r i n g a p p r o x i m a t e l y one q u a r t e r o f t h e E a r t h ' s s u r f a c e , s m a l l e r images were o b t a i n e d r a n g i n g up t o 1000 p i x e l s (a p i x e l i s t h e s m a l l e s t u n i t o f a s a t e l l i t e image and r e p r e s e n t s one d a t a p o i n t ) i n t h e l i n e (N-S) d i r e c t i o n and 1008 p i x e l s i n t h e e l e m e n t (E-W) d i r e c t i o n . The v i s i b l e c h a n n e l d a t a a r e i n t h e f o r m of c o u n t v a l u e s r a n g i n g f rom 0 t o 255 ( i . e . an 8 - b i t s c a l e ) , w i t h l a r g e r c o u n t v a l u e s b e i n g a s s o c i a t e d w i t h t h e b r i g h t e s t t a r g e t s . The s a t e l l i t e d a t a a r e p r o v i d e d i n d i g i t a l fo rm on m a g n e t i c t a p e s and c a n be u s e d i n e i t h e r t h e d i g i t a l c o u n t f o r m a t o r c o n v e r t e d t o an image u s i n g an image p r o c e s s i n g s y s t e m . S i n c e t h e 1000 by 1008 p i x e l images c o v e r a much l a r g e r a r e a t h a n t h e a c t u a l s t u d y a r e a , p r o g r a m s were d e v e l o p e d t o e x t r a c t a o o s u b - i m a g e c e n t r e d on V a n c o u v e r (49 16' N, 123 15' W) f rom w h i c h t h e r e s e a r c h c o u l d p r o c e e d . Windows o f 25 x 25 p i x e l s c e n t r e d on t h e UBC s i t e were m a i n l y u s e d i n i n i t i a l i n v e s t i g a t i o n s . F i g u r e . 3 . 1 shows a c o m p o s i t e o f f o r t y - n i n e i m a g e s , s h o w i n g t h e s p a t i a l c o v e r a g e p r o v i d e d by a window o f 25 x 25 p i x e l s f o r t h e s t u d y a r e a . 31 62 62 61 61 62 62 62 64 67 7a 70 71 73 72 72 72 72 72 73 73 73 74 75 73 72 68 66 63 60 60 61 61 63 67 69j 70 73 73 72 71 7 1 72 72 72 72 72 72 73 73 72 70 67 64 62 62 62 63 66 69 7 1 72 73 72 71 7 1 71 70 7 1 72 7 1 71 72 73 72 69 66 63 62 63 64 67 59/ 71 71 72 72 72 71 7 1 70 69 70 70 7 1 7 1 71 72 73 69 65 62 62 64 67 7 \ 72 72 73 74 74 74 73 74 73 73 72 73 73 73 72 73 73 73 66 63 62 62 63 64 68 72 73 73 73 74 75 75 76 76 78 77 77 75 75 76 76 75 Land(N) 63 62 62 62 63 63 64 66 68 68 68 68 68 _72 74 76 77 78 78 77 77 77 78 78 61 61 61 61 61 61 61 63 63 62 63 63 64 64 65 67 6 9 s "^1 72 75 77 77 78 78 79 60 61 61 62 62 63 63 63 63 63 63 63 64 64 64 64 64 66 69> 72 74 74 73 73 74 59 60 60 61 62 63 64 64 64 65 66 68 68 67 66 66 66 67 SsJ 72 75 74 72 71 71 60 60 60 61 62 64 64 66 67 68. 74 - 73 73 72 71 71 71 72 75 78 79 78 77 78 Point Grey 59 60 60 61 62 63 64 66 66 7t 74 76 76 75 76 78 78 78 78 ao 81 80 81 82 32 59 59 60 60 61 62 64 64 66 68 S^l 75 76 76 77 78 ao 81 81 82 31 80 82 83 33 59 59 59 59 60 62 63 64 65 65 68 73 75 76 78 79 80 B 1 82 81 81 82 83 83 58 59 59 59 60 62 63 64 65 66 68 69 72 74 76 79 81 83 83 84 82 83 84 84 58 58 59 59 60 61 62 63 64 66 68 69 70 72 75 79 83 85 85 85 84 84 83 84 Sea Land(S) 60 60 60 60 61 61 62 64 65 66 67 69 7q 72 73 75 79 82 85 86 86 85 85 85 84 59 60 60 60 60 61 6 1 63 64 65 67 68 69\ 71 72 73 75 78 8 1 33 84 84 84 84 83 59 60 59 60 60 61 62 63 64 65 67 68 68 1 7 1 72 73 74 77 8 1 83 84 85 85 84 83 60 59 59 60 60 60 61 63 64 66 67 68 691 70 72 72 74 75 78 82 82 84 85 85 85 60 60 60 61 61 62 62 64 65 67 67 70 y/o 72 73 74 73 75 78 8 1 82 83 85 85 86 60 60 60 60 61 62 62 64 66 67 69 71 72 74 74 74 74 75 77 79 80 82 84 84 60 60 61 61 63 63 64 66 67 69 70, ' 7 1 72 73 73 73 74 74 74 76 78 81 83 84 83 59 60 61 62 64 64 65 66 68 69 70| 70 7 1 72 71 72 73 73 74 75 77 80 83 84 86 60 61 62 64 64 65 67 67 68 69 70' 70 70 70 70 71 72 73 73 73 74 75 78 81 82 FIGURE 3.1 25 x 25 P i x e l A r r a y C e n t r e d on t h e UBC S i t e D e p i c t i n g Mean B r i g h t n e s s C o u n t V a l u e s B a s e d on F o r t y - N i n e Images From J u l i a n D a y s 1 9 6 / 7 9 , 2 0 0 / 7 9 , 256 /79 and 1 2 1 / 8 0 . The A r e a s U s e d t o D e v e l o p t h e S e a , L a n d ( N ) and L a n d ( S ) BDR M o d e l s a r e D e p i c t e d and a r e R e f e r r e d t o i n S e c t i o n 4 . 3 . 1 . 1 . 32 B e f o r e t h e s a t e l l i t e d a t a c a n be u s e d t h e y r e q u i r e f u r t h e r p r o c e s s i n g . T h i s w i l l be d i s c u s s e d i n t h e f o l l o w i n g s e c t i o n s . 3 .2 E a r t h - L o c a t i o n o f S a t e l l i t e Imagery B e f o r e t h e s a t e l l i t e d a t a c a n be u t i l i z e d i t i s i m p e r a t i v e t h a t t h e p i x e l l o c a t i o n o f e a c h image be known ( t h a t i s , w h i c h p i x e l on t h e image c o r r e s p o n d s t o a measurement s i t e o r o t h e r l a n d m a r k a t t h e E a r t h ' s s u r f a c e ) . T h i s d e t e r m i n a t i o n i s o f i m p o r t a n c e b e c a u s e any e r r o r s i n t h e E a r t h - l o c a t i o n o f t h e s a t e l l i t e i m a g e r y w i l l a f f e c t t h e r a d i a t i o n c a l c u l a t i o n s b a s e d on t h e s e d a t a . T h i s i s e s p e c i a l l y s i g n i f i c a n t u n d e r p a r t l y c l o u d y s k i e s where t h e r a d i a t i o n c h a r a c t e r i s t i c s may be c h a n g i n g r a p i d l y o v e r s h o r t d i s t a n c e s . I n i t i a l E a r t h - l o c a t i o n o f t h e s a t e l l i t e i m a g e r y was p e r f o r m e d u s i n g a m o d e l d e s c r i b e d by H a m b r i c k and P h i l l i p s ( 1 9 8 0 ) . The a l g o r i t h m s a r e b a s e d on t h e use o f b o t h s t e l l a r and t e r r e s t r i a l n a v i g a t i o n p o i n t s and a k n o w l e d g e o f t h e d e p a r t u r e o f t h e s a t e l l i t e f rom a t r u e g e o s y n c h r o n o u s o r b i t . The a c c u r a c y o f t h i s m o d e l ( s u b s e q u e n t l y r e f e r r e d t o a s " F i r s t O r d e r N a v i g a t i o n " , F . O . N , f o r b r e v i t y ) i s c l a i m e d t o be w i t h i n one p i x e l Root Mean S q u a r e a c c u r a c y . H o w e v e r , i n i t i a l 3 3 c o m p a r i s o n s o f t h e l o c a t i o n o f l a n d m a r k s d e t e r m i n e d v i a F . O . N , a n d v i s u a l n a v i g a t i o n u s i n g t h e COMTAL image p r o c e s s o r (UBC C o m p u t i n g C e n t r e ) f r e q u e n t l y r e v e a l e d much l a r g e r e r r o r s . V i s u a l n a v i g a t i o n i n v o l v e s c o m p a r i s o n between t h e p r e d i c t e d p o s i t i o n s o f a l a n d m a r k b a s e d on t h e F . O . N , and t h e a c t u a l p o s i t i o n o f t h e same l a n d m a r k as s een on t h e image p r o c e s s o r . E r r o r s were a s l a r g e a s one h u n d r e d and f i f t y - t w o p i x e l s i n t h e l i n e d i r e c t i o n ( f o r day 171/80) and s e v e n t y - t h r e e p i x e l s i n the e l e m e n t d i r e c t i o n ( f o r day 3 6 1 / 7 9 ) , w i t h e r r o r s o f t w e n t y p i x e l s and a b o v e b e i n g uncommon. S u c h e r r o r s a r e u n a c c e p t a b l e f o r t h i s s t u d y . T h e r e f o r e , ' S e c o n d O r d e r N a v i g a t i o n ' ( S . O . N . ) was d e v e l o p e d t o c o r r e c t f o r t h e E a r t h - l o c a t i o n e r r o r s s t i l l p r e s e n t f o l l o w i n g t h e F . O . N . . The o b j e c t i v e was t o a c h i e v e E a r t h - l o c a t i o n o f l a n d m a r k s t o w i t h i n one or two p i x e l s . The S . O . N , i n v o l v e d r e l a t i n g t h e l a t i t u d e and l o n g i t u d e c o o r d i n a t e s o f a l a n d m a r k ( s ee A p p e n d i x 2 f o r l a n d m a r k s u s e d i n t h e E a r t h - l o c a t i o n p r o c e d u r e ) t o t h e p i x e l c o o r d i n a t e a s v i s u a l l y d e t e r m i n e d on t h e image p r o c e s s o r s u b s e q u e n t t o t h e a p p l i c a t i o n o f F . O . N . . T h i s p r o c e d u r e i s r e p e a t e d f o r a t l e a s t t h r e e images s p r e a d t h r o u g h o u t t h e s t u d y day ( i . e . images i n t h e e a r l y m o r n i n g , n e a r noon and l a t e a f t e r n o o n ) . H o w e v e r , w h e r e v e r p o s s i b l e i t i s p r e f e r a b l e t o use one image p e r h o u r and a t l e a s t one l a n d m a r k p e r i m a g e . F o r e a c h image t h e d i f f e r e n c e ' be tween t h e p i x e l 34 c o o r d i n a t e s of t h e landmark (or an a v e r a g e of the d i f f e r e n c e i f m u l t i p l e landmarks a r e used) p r o d u c e d by t h e F.O.N, and t h e S.O.N. i s c a l c u l a t e d . T h i s d i f f e r e n c e i s t h e t r a n s l a t i o n t h a t must be a p p l i e d t o g i v e t h e ' t r u e ' l o c a t i o n of landmarks on th e image. The r e m a i n i n g images f o r a g i v e n day a r e s u b s e q u e n t l y E a r t h - l o c a t e d u s i n g a c u b i c i n t e r p o l a t i o n f u n c t i o n ( g e n e r a t e d from t h e n a v i g a t e d images) t o e s t i m a t e the c o r r e c t i o n t o be a p p l i e d t o the images which have r e c e i v e d o n l y F.O.N.. T h i s i n t e r p o l a t i o n p r o c e d u r e i s based on time and i n c o r p o r a t e s the t h r e e images t h a t have undergone S.O.N, and a r e c l o s e s t t o t h e u n n a v i g a t e d image. The t r a n s l a t i o n s a s s o c i a t e d w i t h t h e s e t h r e e images a r e used by t h e c u b i c i n t e r p o l a t i o n f u n c t i o n t o e s t i m a t e t h e t r a n s l a t i o n f o r t h e u n n a v i g a t e d image. T r a n s l a t i o n s f o r images t h a t o c c u r e a r l i e r t h a n t h e f i r s t n a v i g a t e d image, or l a t e r than t h e l a s t n a v i g a t e d image, a r e d e t e r m i n e d by e x t r a p o l a t i o n . As an example of t h e i n t e r p o l a t i o n p r o c e d u r e s : g i v e n a s u i t e of f o u r E a r t h - l o c a t e d ( n a v i g a t e d ) images (16:45, 18:15, 19:15 and 20:15) t h e e s t i m a t e d t r a n s l a t i o n s (E-W and N-S) f o r an image a t 18:45 w i l l be d e t e r m i n e d u s i n g the images a t 18:15, 19:15 and 20:15. The a c c u r a c y of t h i s i n t e r p o l a t i o n a l g o r i t h m i s d i s c u s s e d i n S e c t i o n 3.4, w h i l e t h e e x t r a p o l a t i o n e r r o r i s i n d e t e r m i n a t e due t o t h e f a c t t h a t t h e f i r s t and l a s t n a v i g a b l e images f o r e a c h day were a l w a y s used i n the E a r t h - l o c a t i o n p r o c e d u r e s . The S.O.N. p r o c e d u r e r e l i e s t o t a l l y on v i s u a l 35 i d e n t i f i c a t i o n o f l a n d m a r k s on t h e E a r t h ' s s u r f a c e and t h e r e f o r e d e p e n d s on c o m p a r a t i v e l y c l e a r s k i e s . The p r e s e n t a r e a o f i n t e r e s t i n c o r p o r a t e s p a r t o f t h e Lower F r a s e r V a l l e y where s u i t a b l e l a n d - w a t e r b o u n d a r i e s a l o n g t h e s o u t h e r n B r i t i s h C o l u m b i a c o a s t l i n e p r o v i d e c l e a r l y v i s i b l e l a n d m a r k s . H o w e v e r , c l o u d s a r e p r e v a l e n t i n t h i s a r e a and f r e q u e n t l y o b s c u r e t h e c o a s t a l l a n d m a r k s . The s a t e l l i t e images u s e d e x t e n d i n t o t h e w e s t e r n edge o f A l b e r t a and some o f t h e l a r g e r images e x t e n d i n t o n o r t h e r n B r i t i s h C o l u m b i a and s o u t h e r n O r e g o n . T h e r e f o r e , i f t h e V a n c o u v e r a r e a i s c l o u d y , a l t e r n a t i v e a r e a s may be s u f f i c i e n t l y c l e a r t o p e r m i t t h e i d e n t i f i c a t i o n o f l a n d m a r k s . T h i s p r o c e d u r e was c a r r i e d o u t by f i r s t e x a m i n i n g h a r d c o p y images a t t h e A t m o s p h e r i c E n v i r o n m e n t S e r v i c e W e a t h e r O f f i c e , V a n c o u v e r , t o l o c a t e p o s s i b l e c l o u d f r e e a r e a s and t h e n i n s p e c t i n g t h e s e a r e a s on t h e image p r o c e s s o r . I n t e r i o r l a k e s ( e . g . K o o t e n a y L a k e , B . C . and P r i e s t L a k e , I d a h o , U . S . A . ) and t h e O r e g o n c o a s t ( e . g . Cape A r a g o ) a r e e x a m p l e s o f l a n d m a r k s t h a t have been u s e d t o n a v i g a t e t h e images ( see F i g u r e 3 . 2 ) . 3 .3 P i x e l S i z e D e t e r m i n a t i o n As was n o t e d e a r l i e r ( S e c t i o n 3 . 1 . ) , t h e s p a t i a l r e s o l u t i o n f o r t h e l a t i t u d e o f t h e s t u d y a r e a i s l e s s t h a n t h a t q u o t e d f o r t h e s a t e l l i t e s u b p o i n t . The s p a t i a l r e s o l u t i o n i s r e q u i r e d f o r t r a n s l a t i n g t h e n a v i g a t i o n a l e r r o r s 36 FIGURE 3 .2 Map o f t h e A r e a C o v e r e d by the L a r g e s t S a t e l l i t e Images (1000 L i n e s x 1008 E l e m e n t s ) Showing L a n d m a r k s T y p i c a l l y U s e d i n t h e A s s e s s m e n t o f L i n e a r i t y . 37 ( q u o t e d i n p i x e l s ) i n t o d i s t a n c e e r r o r s a t t h e E a r t h ' s s u r f a c e . U s i n g t h e g e o m e t r y o f t h e s a t e l l i t e s e n s o r ( t h e i n s t a n t a n e o u s g e o m e t r i c f i e l d o f v i e w ) and v e c t o r c a l c u l u s , t h e r e s o l u t i o n was d e t e r m i n e d t o be 0 . 9 8 4 km and 1 . 5 0 km f o r t h e e a s t - w e s t a n d n o r t h - s o u t h d i r e c t i o n s r e s p e c t i v e l y ( C . R a p h a e l , p e r s o n a l c o m m u n i c a t i o n ) . T h e r e f o r e t h e s m a l l e s t a r e a r e s o l v e d by t h e s a t e l l i t e s e n s o r f o r t h e l a t i t u d e o f t h e s t u d y a r e a i s a p p r o x i m a t e l y 1 . 4 8 s q u a r e km ; o v e r t w i c e t h e s i z e o f a 0 . 8 x 0 .8 km p i x e l a t t h e s a t e l l i t e s u b p o i n t . T h u s , t h e r e s o l u t i o n f o r t h e s t u d y a r e a i s s m a l l e r t h a n t h e f o u r s q u a r e km r e s o l u t i o n e s t i m a t e d by G a u t i e r e t a l . ( l 9 8 0 ) and H a y ( l 9 8 l ) f o r 45 d e g r e e s n o r t h . T h e shape o f a p i x e l i s r e c t a n g u l a r w i t h t h e l o n g a x i s i n t h e n o r t h - s o u t h d i r e c t i o n and c o m p r e s s e d i n t h e e a s t - w e s t d i r e c t i o n ( t h e v e c t o r c a l c u l u s showed t h e r e t o be on a v e r a g e 1 2 % p i x e l u n d e r l a p a l o n g t h e n o r t h - s o u t h a x i s and 1 6 % p i x e l o v e r l a p i n t h e e a s t - w e s t d i r e c t i o n ) . S i n c e t h e s t u d y a r e a i s a g r e a t e r a n g u l a r d i s t a n c e f rom t h e s a t e l l i t e s u b p o i n t on t h e n o r t h - s o u t h t h a n t h e e a s t - w e s t a x i s , t h e d e g r a d a t i o n o f t h e r e s o l u t i o n s h o u l d be g r e a t e r f o r t h e f o r m e r ; t h i s i s b o r n e o u t by t h e a b o v e r e s u l t s . 38 3 . 4 V a l i d a t i o n o f t h e E a r t h L o c a t i o n R o u t i n e The i n t e g r i t y o f t h e r a d i a t i o n c a l c u l a t i o n s t o be p e r f o r m e d a t a s u b s e q u e n t s t a g e i n t h i s s t u d y r e l i e s h e a v i l y on t h e v a l i d i t y o f t h e E a r t h - l o c a t i o n r o u t i n e . The E a r t h - l o c a t i o n r o u t i n e i s l a r g e l y d e p e n d e n t on t h e v i s u a l p r o c e s s i n g o f a number o f images c o m b i n e d w i t h t h e use of a c u b i c i n t e r p o l a t i o n p r o c e d u r e t o a c c o u n t f o r t h o s e images t h a t have n o t been v i s u a l l y E a r t h - l o c a t e d ( see S e c t i o n 3 . 2 ) . The a c c u r a c y o f t h i s i n t e r p o l a t i o n p r o c e d u r e was a s s e s s e d u s i n g a s ample o f t h i r t y - f o u r images s e l e c t e d f rom s e v e n c l e a r d a y s . The images were s e l e c t e d s o l e l y on t h e b a s i s t h a t t h e y had n o t been p r e v i o u s l y E a r t h l o c a t e d u s i n g S . O . N . . D u r i n g t e s t i n g , l a n d m a r k s on t h e s e images were p r o c e s s e d as o u t l i n e d i n S e c t i o n 3 . 2 , and t h e o b s e r v e d t r a n s l a t i o n s c a l c u l a t e d . E s t i m a t e d t r a n s l a t i o n s were a l s o d e t e r m i n e d f o r t h e s e images u s i n g t h e c u b i c i n t e r p o l a t i o n p r o c e d u r e . Two s t a t i s t i c s , t h e Mean B i a s E r r o r ( M . B . E . ) and t h e Root Mean S q u a r e E r r o r ( R . M . S . E . ) , were u s e d as t h e i n d i c a t o r s o f t h e g o o d n e s s o f f i t o f t h e i n t e r p o l a t i o n p r o c e d u r e . T h e y a r e b a s e d on t h e r e s i d u a l s o f t h e e s t i m a t e d m i n u s t h e o b s e r v e d t r a n s l a t i o n s : n M . B . E . = T. ( F± - F ± ) / n i= 1 ( 3.1) 39 R . M . S . E . = n 2 ( i= 1 - F ± ) / n 0 . 5 ( 3 . 2 ) where F i i s t h e i t h v a l u e o f t h e e s t i m a t e d t r a n s l a t i o n s ; F i i s t h e i t h v a l u e o f t h e o b s e r v e d t r a n s l a t i o n s ; and n i s t h e s ample s i z e (n = 3 4 ) . C a l c u l a t i o n s were p e r f o r m e d f o r b o t h l i n e and e l e m e n t t r a n s l a t i o n s . From t h e r e s u l t s l i s t e d i n T a b l e 3 .1 we c a n n o t e t h a t t h e R . M . S . E . c a l c u l a t e d f o r t h e l i n e i s 1 . 0 2 6 p i x e l s w h i l s t t h e M . B . E . i s - 0 . 1 7 p i x e l s . The maximum d i f f e r e n c e be tween t h e e s t i m a t e d and o b s e r v e d t r a n s l a t i o n s i s j u s t u n d e r two p i x e l s ( 1 . 6 5 ) , w h i l e t h e minimum d i f f e r e n c e i s 0 . 0 3 p i x e l s . T h i s means t h a t i n t e r m s o f a b s o l u t e d i s t a n c e s ( u s i n g the v a l u e s o f p i x e l s i z e i n S e c t i o n 3 .3 ) we c a n e s t i m a t e t h e p o s i t i o n o f t h e l a n d m a r k i n t h e n o r t h - s o u t h d i m e n s i o n t o w i t h i n 1 .54 km. The n e g a t i v e M . B . E . means t h a t t h e t e n d e n c y w o u l d be t o e s t i m a t e a p o s i t i o n n o r t h of t h e t r u e l o c a t i o n . The R . M . S . E . c a l c u l a t e d f o r t h e e l e m e n t (E-W) i s 1 . 5 3 p i x e l s w h i l s t t h e M . B . E . i s 0 .302 p i x e l s . The maximum d i f f e r e n c e between e s t i m a t e d a n d o b s e r v e d t r a n s l a t i o n s i s j u s t u n d e r f o u r p i x e l s , w h i l e t h e minimum d i f f e r e n c e i s - 0 . 0 3 p i x e l s . The v a l u e s f o r t h e e l e m e n t c o o r d i n a t e (E-W) a r e l a r g e r i n most i n s t a n c e s t h a n t h o s e f o r t h e l i n e . T h e r e f o r e , i n t e r m s o f a b s o l u t e d i s t a n c e s ( b a s e d on a p i x e l s i z e i n t h e E-W d i r e c t i o n 40 of 0 .984 km; S e c t i o n 3 .4 ) we c a n e s t i m a t e t h e p o s i t i o n o f a l a n d m a r k t o w i t h i n 1.50 km. The p o s i t i v e M . B . E . means t h a t t h e t e n d e n c y w o u l d be t o e s t i m a t e t o t h e e a s t o f t h e a c t u a l l o c a t i o n . A ' w o r s t c a s e ' a n a l y s i s ( b a s e d on one l a n d m a r k p e r image) was c o n d u c t e d f o r t h e c u b i c i n t e r p o l a t i o n p r o c e d u r e u s i n g a s ample o f t w e n t y - f o u r i m a g e s . A g a i n t h e r e s u l t s a r e l i s t e d i n T a b l e 3.1 (numbers i n p a r e n t h e s e s ) . T h e s e r e s u l t s show t h a t , e x c e p t i n t h e c a s e o f t h e R . M . S . E . f o r t h e l i n e c o o r d i n a t e , t h e r e a r e o n l y m i n o r c h a n g e s f rom t h e r e s u l t s o f t h e p r e v i o u s a n a l y s i s . The a c c u r a c y o f t h e c u b i c i n t e r p o l a t i o n p r o c e d u r e f o r E a r t h - l o c a t i o n o f s a t e l l i t e i m a g e r y d e m o n s t r a t e d by t h e r e s u l t s i n T a b l e 3.1 i s s i m i l a r t o t h a t q u o t e d by G a u t i e r e t a l . (1980) f o r t h e i r n a v i g a t i o n p r o c e d u r e and i s c o n s i d e r e d t o be more t h a n a d e q u a t e f o r t h e p r e s e n t s t u d y . H o w e v e r , t h i s a c c u r a c y c o u l d be r e d u c e d by t h e e f f e c t s o f n o n - l i n e a r i t y a c r o s s t h e image ( s ee S e c t i o n 3 . 5 ) . A more d i r e c t t e c h n i q u e f o r t e s t i n g t h e E a r t h - l o c a t i o n p r o c e d u r e i n v o l v e d u s i n g a v a r i e t y o f l a n d m a r k s e . g . B i r c h P o i n t ( W a s h i n g t o n S t a t e ) , Moses P o i n t ( V a n c o u v e r I s l a n d ) , Cape A r a g o ( O r e g o n ) , ( s ee F i g u r e 3 . 2 ) and p r o d u c e d a t o t a l o f f i f t y - t h r e e o b s e r v a t i o n s . O n l y t h o s e images w h i c h were no t u s e d t o d e r i v e t h e S . O . N , were i n c o r p o r a t e d i n t h i s t e s t . 41 T A B L E 3 .1 V e r i f i c a t i o n S t a t i s t i c s f o r t h e C u b i c I n t e r p o l a t i o n R o u t i n e u s e d i n t h e E a r t h - L o c a t i o n o f t h e S a t e l l i t e I m a g e r y . V a l u e s a r e q u o t e d i n P i x e l s . n = 3 9 . ( V a l u e s i n b r a c k e t s a r e f rom t h e ' W o r s t C a s e ' a n a l y s i s b a s e d on o n l y one Landmark p e r Image w i t h n = 24 , See T e x t ) . L i n e (N-S) E l e m e n t (E-W) R . M . S . E . 1 . 026 ( 0 . 7 3 6 ) 1 . 53 ( 1 . 53 ) M . B . E . - 0 . 1 7 0 ( 0 . 198) 0 .302 ( 0 . 2 9 0 ) Maximum D i f f e r e n c e 1 . 65 (1 .75) 3 .77 ( 3 . 6 0 ) Minimum D i f f e r e n c e 0 .03 ( 0 . 0 3 ) - 0 . 0 3 ( - 0 . 0 2 ) 42 T h i s s e c o n d a n a l y s i s gave r e s u l t s of 0 .34 p i x e l s ( 0 . 3 3 km) and 0 .13 p i x e l s ( 0 . 2 0 km) f o r t h e M . B . E . , and 1.29 p i x e l s ( 1 . 2 7 km) and 0 . 6 3 p i x e l s ( 0 . 9 5 km) f o r t h e R . M . S . E . i n t h e e l e m e n t and l i n e d i r e c t i o n s r e s p e c t i v e l y . T h e s e r e s u l t s c o n f i r m t h o s e o f t h e p r e v i o u s n a v i g a t i o n . T h u s t h e a c c u r a c y o f t h e E a r t h - l o c a t i o n i n t e r p o l a t i o n method a p p e a r s more t h a n a d e q u a t e f o r t h e r e s e a r c h r e q u i r e m e n t s o f t h i s s t u d y . 3 . 5 L i n e a r i t y The E a r t h - l o c a t i o n o f i m a g e r y on p a r t l y c l o u d y and o v e r c a s t d a y s ( o c c a s i o n s when l a n d m a r k s i n t h e l o c a l a r e a a r e n o t v i s i b l e ) e n t a i l s t h e use o f l a n d m a r k s f r o m o t h e r a r e a s ( see A p p e n d i x 2) t h a t a r e c l o u d f r e e . I n h e r e n t i n t h i s a p p r o a c h i s t h e a s s u m p t i o n t h a t t h e t r a n s l a t i o n s a s s o c i a t e d w i t h t h e s e l a n d m a r k s c a n be a p p l i e d t o t h e s t u d y a r e a w i t h o u t any l o s s i n a c c u r a c y . T h a t i s , t h a t t h e t r a n s l a t i o n s b e h a v e i n a l i n e a r manner a c r o s s a g i v e n i m a g e . A l t e r n a t i v e l y , any n o n - l i n e a r i t y i n t r o d u c e d w i l l be o f l i t t l e i m p o r t a n c e . The i s s u e o f l i n e a r i t y i s i m p o r t a n t b e c a u s e i t i s one o f t h e s o u r c e s o f e r r o r a f f e c t i n g t h e a c c u r a t e E a r t h - l o c a t i o n o f t h e s a t e l l i t e i m a g e r y ( see S e c t i o n 3 . 2 ) . To be u s e f u l i n t h e a s s e s s m e n t o f l i n e a r i t y , images must s a t i s f y two b a s i c r e q u i r e m e n t s : 1) t h e y must be l a r g e enough t o i n c l u d e l a n d m a r k s o u t s i d e t h e s t u d y a r e a ; 2) t h e y must be 43 p r a c t i c a l l y c l o u d f r e e t o e n a b l e t h e i d e n t i f i c a t i o n o f l a n d m a r k s o v e r a l a r g e a r e a . T h e s e r e q u i r e m e n t s c o n s t r a i n t h i s a s s e s s m e n t t o c l e a r d a y s f o r w h i c h t h e l a r g e s t images (1000 l i n e s x 1008 e l e m e n t s ) were a v a i l a b l e . V a l i d a t i o n o f t h e a s s u m p t i o n o f l i n e a r i t y was a s s e s s e d u s i n g i m a g e r y f rom s e v e r a l c l e a r d a y s ( 2 7 6 / 7 9 , 121/80 and 1 8 3 / 8 0 ) . Images f rom t h e s e d a y s were E a r t h - l o c a t e d u s i n g l a n d m a r k s f rom t h e s t u d y a r e a . The t r a n s l a t i o n s d e t e r m i n e d f rom t h e s e l a n d m a r k s were a p p l i e d t o l a n d m a r k s f rom a n o t h e r a r e a o f i n t e r e s t ( F i g u r e 3 .2 shows some o f t h e l a n d m a r k s t y p i c a l l y u s e d ) . The t r a n s l a t i o n s d e t e r m i n e d f o r t h e new l a n d m a r k o u t s i d e t h e s t u d y a r e a p r o v i d e a measure o f t h e d e p a r t u r e f rom l i n e a r i t y . L i n e a r i t y was a s s e s s e d f o r b o t h t h e n o r t h - s o u t h and t h e e a s t - w e s t d i m e n s i o n s . R e s u l t s f rom t h e s e a s s e s s m e n t s a r e l i s t e d i n T a b l e 3 . 2 . A n a l y s e s f o r t h e e a s t - w e s t d i m e n s i o n a r e b a s e d on a s ample o f t h i r t e e n i m a g e s . T h e y i n d i c a t e t h a t when u s i n g l a n d m a r k s some d i s t a n c e f rom t h e s t u d y a r e a , t h e e l e m e n t p o s i t i o n o f a l a n d m a r k i n t h e s t u d y a r e a (on a v e r a g e ) c a n be e s t i m a t e d t o w i t h i n ± 5 p i x e l s ( 4 . 9 km) . The l i n e p o s i t i o n o f t h a t same l a n d m a r k c a n be e s t i m a t e d t o w i t h i n ± 4 . 6 p i x e l s ( 6 . 9 km). A n a l y s e s f o r t h e n o r t h - s o u t h d i m e n s i o n a r e b a s e d on a sample o f t w e n t y - t w o i m a g e s . T h e y i n d i c a t e t h a t t h e e l e m e n t p o s i t i o n o f a l a n d m a r k i n t h e s t u d y a r e a c a n be e s t i m a t e d t o w i t h i n ± 1 . 5 7 p i x e l s ( 1 . 5 4 km) , w h i l e t h e l i n e p o s i t i o n o f t h a t 4 4 T A B L E 3 .2 ! R e s u l t s f rom t h e A s s e s s m e n t s o f L i n e a r i t y a c r o s s t h e S a t e l l i t e Image b a s e d on D a t a f rom T h r e e C l e a r D a y s . V a l u e s a r e i n P i x e l s . L i n e E l e m e n t L i n e E l e m e n t (E-W) (E-W) (N-S) (N-S) R . M . S . E . 4 > 6 2 5 . 0 1.23 1.57 M . B . E . - 3 . 8 0 - 4 . 8 0 - 0 . 0 8 - 0 . 0 7 n 13 13 22 22 45 same l a n d m a r k c a n be d e t e r m i n e d t o w i t h i n ± 1 . 2 3 p i x e l s ( 1 . 8 5 km) . The p r e c e d i n g a n a l y s e s have been b a s e d on s m a l l d a t a s e t s . T h e i r s i z e ha s been l a r g e l y i n f l u e n c e d by t h e o c c u r r e n c e o f c l o u d c o v e r on most o f t h e a v a i l a b l e i m a g e r y . H o w e v e r , some t e n t a t i v e c o n c l u s i o n s c a n be drawn on t h e b a s i s o f t h e above r e s u l t s . 1 ) The e f f e c t s o f n o n - l i n e a r i t y a c r o s s t h e image i n t h e n o r t h - s o u t h d i m e n s i o n a r e n e g l i g i b l e . The e r r o r s d e t e r m i n e d h e r e a r e o f s i m i l a r m a g n i t u d e t o t h o s e a s s o c i a t e d w i t h t h e e a r l i e r c u b i c i n t e r p o l a t i o n p r o c e d u r e ( see S e c t i o n 3 . 4 ) . In t h e w o r s t c a s e (when i n t e r p o l a t i o n and l i n e a r i t y e r r o r s a r e a d d i t i v e ) t h e t r u e p o s i t i o n o f a l a n d m a r k w i l l be i n e r r o r by a p p r o x i m a t e l y 2 . 3 p i x e l s ( 3 . 4 5 km) i n t h e l i n e (N-S) d i r e c t i o n . 2) The e f f e c t s o f n o n - l i n e a r i t y a c r o s s t h e image i n t h e e a s t - w e s t d i r e c t i o n a r e o f g r e a t e r s i g n i f i c a n c e . T h i s i s r e f l e c t e d i n t h e l a r g e Mean B i a s E r r o r . In the w o r s t c a s e t h e t r u e p o s i t i o n o f t h e l a n d m a r k w i l l be i n e r r o r by a p p r o x i m a t e l y 3 .0 p i x e l s ( 2 . 9 5 km) i n t h e e l e m e n t (E-W) d i r e c t i o n . In t h e w o r s t c a s e (when i n t e r p o l a t i o n and l i n e a r i t y e r r o r s a r e a d d i t i v e ) t h e t r u e p o s i t i o n o f a l a n d m a r k 4 6 w i l l be i n e r r o r by up t o 1 0 . 0 km. The e r r o r s i n t h e c a l c u l a t e d r a d i a t i o n u n d e r 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 due t o e r r o r s i n E a r t h - l o c a t i o n o f the s a t e l l i t e i m a g e r y c o u l d be g r e a t e r when t h e l a n d m a r k u s e d t o E a r t h - l o c a t e t h e i m a g e r y l i e s t o t h e e a s t o f t h e s t u d y a r e a r a t h e r t h a n t o t h e n o r t h or s o u t h . R e c e n t work has s u g g e s t e d t h a t t h e n o n - l i n e a r i t y o b s e r v e d i s a f u n c t i o n o f t h e r a t e o f c h a n g e i n p i x e l s i z e a c r o s s t h e s a t e l l i t e image ( C . R a p h a e l , p e r s o n a l c o m m u n i c a t i o n ) . D e s p i t e t h e p o s s i b l e l a r g e r n a v i g a t i o n a l e r r o r s u n d e r c l o u d y c o n d i t i o n s , t h e s o l a r r a d i a t i o n r e g i m e i s l i k e l y t o be r e a s o n a b l y homogeneous w i t h w i d e s p r e a d o v e r c a s t s k i e s and t h e q u a n t i t i e s of i n c o m i n g s o l a r e n e r g y r e l a t i v e l y s m a l l . Thus t h e i m p a c t of n a v i g a t i o n a l e r r o r s i s l e s s f o r o v e r c a s t c o n d i t i o n s . The p a r t l y c l o u d y s i t u a t i o n p r o v e s t o be more o f a d i l e m m a due t o t h e r e s u l t i n g h i g h s p a t i a l v a r i a b i l i t y o f t h e i n c i d e n t s o l a r r a d i a t i o n . As a r e s u l t o f t h e s e i n v e s t i g a t i o n s , w h e r e v e r p o s s i b l e , l a n d m a r k s were s e l e c t e d e i t h e r w i t h i n o r t o t h e n o r t h ( e . g . S t u a r t L a k e , B . C . ) o r s o u t h ( e . g . W a s h i n g t o n and O r e g o n c o a s t l i n e s ) o f the s t u d y a r e a i n an a t t e m p t t o keep the n a v i g a t i o n a l e r r o r s t o a min imum. 47 3 .6 C o n v e r s i o n o f P i x e l C o u n t V a l u e s t o S u r f a c e R e f l e c t a n c e s The o r i g i n a l s a t e l l i t e d a t a a r e g i v e n as c o u n t v a l u e s r a n g i n g f rom 0-255 c o u n t s ( i . e . an 8 - b i t s c a l e ) and a r e an i n d i c a t i o n o f t h e r e l a t i v e b r i g h t n e s s . The b r i g h t n e s s v a l u e may be c o n v e r t e d t o a 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 a c a l i b r a t i o n c u r v e f o r t h e VISSR v i s i b l e c h a n n e l . Two c a l i b r a t i o n c u r v e s p r e s e n t i n t h e l i t e r a t u r e ( see F i g u r e 3 .3 ) a r e b a s e d on work by S m i t h and L o r a n g e r (1977) and S m i t h and V o n d e r H a a r (1980) f o r t h e SMS-1 a n d GOES-1 s a t e l l i t e s r e s p e c t i v e l y . The f o r m e r was b a s e d on a c o m p a r i s o n w i t h t h e NOAA-2 p o l a r o r b i t i n g s a t e l l i t e and t h e l a t t e r w i t h a i r c r a f t mounted f l u x r a d i o m e t e r s . The i m a g e r y u s e d i n t h e p r e s e n t s t u d y i s t h a t f rom t h e SMS-2 (GOES WEST) s a t e l l i t e f o r w h i c h t h e r e i s no a v a i l a b l e c a l i b r a t i o n c u r v e . T h i s i s t r u e of many o f t h e m e t e o r o l o g i c a l s a t e l l i t e s , i n c l u d i n g t h e r e c e n t GOES-4 and GOES-5 s p a c e c r a f t . The a b s e n c e o f a c a l i b r a t i o n i s o f m a j o r c o n c e r n f o r b o t h p a s t , p r e s e n t and f u t u r e m e t e o r o l o g i c a l and c l i m a t o l o g i c a l s t u d i e s w h i c h make use o f t h e s a t e l l i t e d a t a and r e q u i r e s an i m m e d i a t e r e m e d y . G i v e n t h e l a c k o f a c a l i b r a t i o n c u r v e f o r t h e SMS-2 s a t e l l i t e i t was n e c e s s a r y t o c h o o s e between t h e two a v a i l a b l e c u r v e s ( see F i g u r e 3 . 3 ) . The SMS-1 c a l i b r a t i o n c u r v e was f a v o u r e d s i n c e w i t h z e r o r e f l e c t a n c e t h e v i s i b l e c h a n n e l shows a b a c k g r o u n d c o u n t v a l u e o f s l i g h t l y above 48 8 - BIT COUNT SMS-1 COES-1 FIGURE 3 . 3 C a l i b r a t i o n C u r v e s f o r t h e SMS-1 and GOES-1 S a t e l l i t e R a d i o m e t e r s ( A f t e r S m i t h and V o n d e r H a a r , 1 9 8 0 ) . 49 t w e n t y . T h i s a g r e e d w i t h n i g h t - t i m e i m a g e r y ( i . e . z e r o r e f l e c t a n c e ) f r o m t h e SMS-2 s a t e l l i t e w h i c h a l s o had b a c k g r o u n d b r i g h t n e s s v a l u e s o f s i x t e e n t o t w e n t y - f o u r c o u n t s ( s ee F i g u r e 3 . 4 ) . On t h e o t h e r h a n d , t h e GOES-1 c a l i b r a t i o n shows a z e r o c o u n t v a l u e w i t h z e r o r e f l e c t a n c e . A p o l y n o m i a l f i t t o t h e SMS-1 c u r v e r e s u l t e d i n a c o n v e r s i o n e q u a t i o n as f o l l o w s : NR = - 0 . 0 0 4 5 8 6 3 2 - 0 .00013326D + 0 . 0 0 0 0 1 6 7 5 D 2 (3.3) where NR i s t h e n o r m a l i z e d r e f l e c t a n c e and D i s t h e d i g i t a l b r i g h t n e s s v a l u e i n c o u n t s . The f i t t i n g o f t h e c u r v e r e s u l t e d i n a s t a n d a r d e r r o r f o r e s t i m a t i n g NR o f 0 . 0033 and a c o e f f i c i e n t o f d e t e r m i n a t i o n o f 0 . 9 9 9 9 . The n o r m a l i z e d r e f l e c t a n c e v a l u e i s t h e n u s e d t o c a l c u l a t e t h e t a r g e t ( E a r t h - A t m o s p h e r e s y s t e m ) r e f l e c t i v i t e s (TR) ( f o r t h e v i s i b l e w a v e l e n g t h s , 0 . 5 5 - 0 . 7 0 m i c r o m e t e r s ) . T h i s i s d e t e r m i n e d by d i v i d i n g t h e t o t a l amount o f r e f l e c t e d e n e r g y (NR x I 0 ) by t h e t o t a l amount o f i n c o m i n g e n e r g y ( I 0 x c o s e ) g i v i n g : TR = NR / c o s e (3.4) The t a r g e t r e f l e c t i v i t y i s c a l c u l a t e d f o r e a c h p i x e l i n t h e s a t e l l i t e a r r a y ( e . g . 7 x 7 p i x e l a r r a y s were u s e d f o r much o f t h e o r i g i n a l a n a l y s e s ) , w i t h s u b s e q u e n t a v e r a g i n g t o 50 20 20 20 20 20 20 20 20 20 2 0 20 20 20 2 0 20 20 20 20 20 20 20 20 20 20 24 20 24 20 20 20 24 24 24 20 2 0 2 4 24 20 20 20 24 20 20 24 24 24 24 20 20 20 24 24 24 24 24 24 24 24 24 24 24 24 20 2 0 24 24 24 20 20 20 20 20 20 20 20 16 16 16 16 16 16 16 16 16 16 16 20 20 1 6 16 16 16 16 16 16 16 16 16 16 16 20 20 20 20 20 20 20 20 20 2 0 20 20 20 2 0 20 20 20 20 20 20 20 20 20 20 20 20 24 24 28 24 24 20 20 28 2 0 20 24 20 20 20 20 20 20 20 20 24 20 20 24 20 20 24 20 24 20 20 20 24 20 2 4 20 24 20 2 0 20 20 24 20 24 24 24 24 20 20 24 20 20 20 28 20 20 20 20 20 2 8 2 0 20 28 2 0 20 20 20 20 20 20 20 20 28 20 20 20 20 20 20 20 20 20 20 20 2 0 20 24 20 2 0 20 20 20 20 20 20 20 20 20 20 20 20 24 20 24 24 24 24 24 2 4 2 4 2 0 24 20 2 4 20 20 20 24 20 20 20 24 24 24 24 24 24 24 24 24 24 24 24 24 2 4 24 24 2 4 2 4 2 4 24 24 24 24 20 20 20 20 20 20 16 16 16 16 16 16 16 16 16 2 0 2 0 20 16 16 16 16 16 16 16 16 1 6 16 16 16 16 20 20 20 20 20 20 20 20 20 2 0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 24 24 20 20 2 0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 24 20 20 20 20 20 20 20 24 2 0 24 24 20 2 0 20 24 20 24 24 24 20 24 20 24 24 20 20 20 20 20 20 28 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 24 20 20 20 20 24 20 20 2 0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 24 24 20 20 24 24 20 20 20 24 24 20 24 24 20 20 20 20 20 24 24 24 24 24 20 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 20 20 20 16 16 28 1.6 16 16 16 16 16 2 0 20 20 16 20 16 16 16 16 16 16 16 16 16 16 16 20 20 20 20 20 20 20 20 20 2 0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 24 20 20 20 20 2 0 20 20 20 2 0 20 20 20 20 20 20 20 20 20 20 20 20 24 24 20 20 24 20 20 2 0 2 0 20 20 20 20 20 20 20 20 20 24 24 20 20 20 20 20 20 20 20 20 20 20 20 24 2 4 20 20 20 2 0 20 24 24 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 2 0 20 20 20 2 0 20 20 20 20 20 20 20 20 20 20 20 FIGURE 3 .4 A N i g h t t i m e S u b a r r a y C e n t r e d O v e r t h e P a c i f i c O c e a n A t 49 L a t i t u d e 127 L o n g i t u d e D e m o n s t r a t i n g a B a c k g r o u n d B r i g h t n e s s and S t r i p i n g Due t o t h e L a c k o f I n t e r s e c t i o n C a l i b r a t i o n . The L a t t e r i s R e f e r r e d t o i n S e c t i o n 4 . 3 . 1 . 1 . 51 d e t e r m i n e t h e mean r e f l e c t i v i t y o f t h e t a r g e t v i e w e d . The f i n a l s t a g e i n t h e i n i t i a l p r o c e s s i n g o f t h e s a t e l l i t e and r a d i a t i o n d a t a i n v o l v e d t h e m e r g i n g o f t h e s a t e l l i t e r e f l e c t a n c e d a t a w i t h t h e h o u r l y t r a n s m i s s i o n c a l c u l a t i o n s d e s c r i b e d i n C h a p t e r 2. The f o l l o w i n g s e c t i o n o u t l i n e s t h i s p r o c e d u r e . 3.7 M e r g i n g o f t h e S a t e l l i t e R e f l e c t a n c e and S h o r t w a v e T r a n s m i s s i o n D a t a The two d a t a s e t s u s e d i n t h i s s t u d y a r e b a s e d on d i f f e r e n t t i m e s c a l e s . T h e r e f o r e , t o r e l a t e t h e c a l c u l a t e d a t m o s p h e r i c t r a n s m i s s i o n s t o t h e r e f l e c t a n c e s e s t i m a t e d f rom s a t e l l i t e d a t a , i t i s n e c e s s a r y t o merge t h e two d a t a s e t s . The c a l c u l a t e d a t m o s p h e r i c t r a n s m i s s i o n s a r e an h o u r l y i n t e g r a t e d v a l u e and the s a t e l l i t e r e f l e c t a n c e d a t a a r e e s s e n t i a l l y an i n s t a n t a n e o u s measurement t a k e n e v e r y h a l f h o u r . In m a k i n g t h e d a t a s e t s c o m p a t i b l e , i t was d e c i d e d f o r two r e a s o n s t o f i t t h e s a t e l l i t e r e f l e c t a n c e d a t a t o t h e s h o r t w a v e t r a n s m i s s i o n s . F i r s t l y , t h e m a j o r i t y o f s o l a r r a d i a t i o n s t u d i e s use h o u r l y o r d a i l y q u a n t i t i e s , w h i l e i n s t a n t a n e o u s e s t i m a t e s a r e r a r e . S e c o n d l y , t h e s a t e l l i t e d a t a a r e n o t s t r i c t l y i n s t a n t a n e o u s due t o t h e s c a n t i m e of t h e s e n s o r , ( t h e y a r e i n s t a n t a n e o u s f o r a g i v e n l o c a t i o n ) . H o w e v e r , t h i s f a c t i s n e v e r e x p l i c i t l y t a k e n i n t o a c c o u n t . T h u s a s i m p l e t e c h n i q u e was d e v e l o p e d t o use t h e most 52 a p p r o p r i a t e s a t e l l i t e images t o r e p r e s e n t c o n d i t i o n s t h r o u g h t h e h o u r o v e r w h i c h t h e s o l a r r a d i a t i o n m e a s u r e m e n t s a r e i n t e g r a t e d . S i n c e t h e s a t e l l i t e images a r e t a k e n e v e r y h a l f h o u r , a c o m p l e t e d a t a s e t w i l l r e s u l t i n a maximum o f t h r e e images b e i n g u s e d . The s a t e l l i t e d a t a f o r e a c h image a r e t h e n w e i g h t e d w i t h r e s p e c t t o t i m e and t o t h e amount o f e x t r a t e r r e s t r i a l r a d i a t i o n . The . w e i g h t i n g w i t h r e s p e c t t o t i m e i s b e s t d e s c r i b e d by r e f e r e n c e t o F i g u r e 3 . 5 . Images two , t h r e e , a n d f o u r w o u l d be c h o s e n t o r e p r e s e n t c o n d i t i o n s f o r t h e h o u r between 11 :00 and 1 2 : 0 0 . Of t h e s i x t y m i n u t e p e r i o d , image two w o u l d r e c e i v e a w e i g h t i n g o f 2 4 / 6 0 , image t h r e e , 30 /60 and image f o u r 6 / 6 0 . Use o f t h e 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 w e i g h t i n g p l a c e s g r e a t e r i m p o r t a n c e on t h e images c l o s e r t o s o l a r n o o n . The r a d i a t i o n w e i g h t i n g i s b a s e d on a c a l c u l a t i o n o f t h e e x t r a t e r r e s t r i a l r a d i a t i o n a t t h e t i m e o f e a c h i m a g e . T h i s l a t t e r w e i g h t i n g scheme i s o f s e c o n d a r y i m p o r t a n c e and m o d i f i e s t h e w e i g h t b a s e d on t i m e . I f an e n t i r e s a t e l l i t e image i s u n a v a i l a b l e o r t h e r e a r e m i s s i n g d a t a o v e r t h e s t u d y a r e a , images a d j a c e n t t o t h e m i s s i n g image t i m e a r e a s s i g n e d a p p r o p r i a t e l y i n c r e a s e d w e i g h t s . F o r example i f image two ( see F i g u r e 3 . 5 ) was m i s s i n g t h e n image t h r e e w o u l d be u s e d t o r e p r e s e n t c o n d i t i o n s back t o 1 1 : 0 9 , w h i l e image one w o u l d be u s e d t o r e p r e s e n t 53 Satellite image time I Image number' r-10=39 11=09 11=39 12=09 12=39 Time 10=00 11=00 I 12=00 13=00 FIGURE 3 .5 E x a m p l e o f S a t e l l i t e Image W e i g h t i n g Scheme f o r M e r g i n g S a t e l l i t e D a t a t o H o u r l y I n t e g r a t e d R a d i a t i o n D a t a ( A r r o w s I n d i c a t e t h e Time I n t e r v a l E a c h Image R e p r e s e n t s ) . 54 c o n d i t i o n s between 11 :00 and 1 1 : 0 9 . H o w e v e r , t h e r e a r e l i m i t a t i o n s t o t h i s p r o c e d u r e . I f an image has t o r e p r e s e n t an i n t e r v a l g r e a t e r t h a n one h o u r , t h e h o u r l y p e r i o d i n w h i c h t h e image i s b e i n g u s e d t o r e p r e s e n t r a d i a t i o n c o n d i t i o n s i s c l a s s i f i e d a s a m i s s i n g d a t a p e r i o d . T h u s o n l y t h o s e p e r i o d s w i t h two o r more s a t e l l i t e images a v a i l a b l e p e r h o u r a r e u s e d . W i t h t h e m e r g i n g o f t h e s e two d a t a s e t s i t i s a s sumed t h a t t h e r e f l e c t a n c e d a t a a r e c o m p a r a b l e w i t h t h e t r a n s m i s s i o n v a l u e s . T h i s a s s u m p t i o n i s made d e s p i t e t h e f a c t t h a t t h e s a t e l l i t e m e a s u r e s t h e s h o r t w a v e r a d i a n c e o n l y i n t h e v i s i b l e p a r t o f t h e s p e c t r u m ( i . e . be tween 0 .55 - 0 . 7 0 m i c r o m e t e r s ) w h i l e t h e p y r a n o m e t r i c d a t a r e p r e s e n t t h e f u l l s h o r t w a v e i r r a d i a n c e (0 - 3 . 8 m i c r o m e t e r s ) . T h i s d i f f e r e n c e i s due t o t h e VISSR b e i n g o r i g i n a l l y d e s i g n e d f o r t h e p u r p o s e o f p r o d u c i n g c l o u d p i c t u r e s ( S m i t h a n d V o n d e r H a a r , 1 9 8 0 ) . The l a c k o f a s p e c i f i c t r a n s f o r m a t i o n mode l t o c o n v e r t t h e SMS-2 n a r r o w band r a d i a n c e s t o b r o a d band i r r a d i a n c e s r e s u l t s i n t h e a s s u m p t i o n f o r t h i s s t u d y t h a t t h e f o r m e r i s r e p r e s e n t a t i v e o f t h e l a t t e r . H o w e v e r , t h i s i s known t o be i n c o r r e c t f o r two r e a s o n s : 1) t h e w a v e l e n g t h d e p e n d e n c y o f a b s o r p t i o n and s c a t t e r i n g f o r s h o r t w a v e r a d i a t i o n ; 2) t h e a n i s o t r o p i c s c a t t e r i n g o f t h e s h o r t w a v e r a d i a t i o n . 55 The r e p r e s e n t a t i v e n e s s o f t h e v i s i b l e m e a s u r e m e n t s must be c o n s i d e r e d as a l i m i t a t i o n on t h e use o f s a t e l l i t e d a t a . H o w e v e r , t h e e f f e c t s of a n i s o t r o p i c s c a t t e r i n g on t h e c o n v e r s i o n f rom r a d i a n c e t o i r r a d i a n c e w i l l be i n c o r p o r a t e d v i a t h e d e v e l o p m e n t o f b i d i r e c t i o n a l r e f l e c t a n c e m o d e l s i n t h e f o l l o w i n g c h a p t e r . 56 CHAPTER 4 B I D I R E C T I O N A L REFLECTANCE MODELS 4.1 O v e r v i e w In C h a p t e r 1 i t was n o t e d t h a t t h e e n e r g y r e f l e c t e d by t h e E a r t h - A t m o s p h e r e s y s t e m i s a n i s o t r o p i c b e c a u s e o f t h e 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 o f most n a t u r a l s u r f a c e s . T h u s , due t o t h e n a r r o w a c c e p t a n c e a n g l e o f t h e SMS-2 s a t e l l i t e s e n s o r u s e d i n t h i s s t u d y , t h e r e s u l t a n t d a t a r e q u i r e s an a d j u s t m e n t . T h i s c h a p t e r w i l l d e s c r i b e t h e a p p l i c a t i o n o f b i d i r e c t i o n a l r e f l e c t a n c e ( s h o r t e n e d t o BDR f o r c o n v e n i e n c e ) m o d e l s w h i c h a t t e m p t t o c o r r e c t f o r t h e a n i s o t r o p y o f t h e r e f l e c t e d r a d i a t i o n . T h r o u g h o u t t h i s i n v e s t i g a t i o n i t i s i m p l i c i t l y a s sumed t h a t w h e r e v e r s u r f a c e r e f l e c t a n c e i s referred t o , i t a l s o i n c l u d e s t h e r e f l e c t i v i t y f r o m t h e a t m o s p h e r i c c o l u m n above t h e s u r f a c e of i n t e r e s t . F i g u r e 4.1 shows t h e marked v a r i a t i o n i n t h e r e f l e c t a n c e f o r a l a n d s u r f a c e on a c l e a r day ( J u l i a n day 2 5 6 / 7 9 ) . The r e f l e c t a n c e i s c a l c u l a t e d b a s e d on t h e s a t e l l i t e c a l i b r a t i o n f o u n d i n S e c t i o n 3 . 6 . D i u r n a l v a r i a t i o n s i n t h e r e f l e c t a n c e (as shown i n F i g u r e 4 . 1 ) a r e e x a g g e r a t e d by t h e n o r m a l i z i n g p r o c e d u r e . N o r m a l i z i n g t h e v i s i b l e b r i g h t n e s s w i t h r e s p e c t t o t h e z e n i t h a n g l e a c c e n t u a t e s t h e e x t r e m i t i e s o f t h e c u r v e due t o a d i v i s i o n by t h e c o s i n e o f t h e z e n i t h a n g l e w h i c h 57 0.08" 09:08 13:08 17:08 L.A.T. (Hours) FIGURE 4.1 D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e (TR) O v e r a L a n d S u r f a c e F o r J u l i a n Day 2 5 6 / 7 9 . D e t e r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 58 a p p r o a c h e s z e r o n e a r s u n r i s e and s u n s e t . F o r t h i s r e a s o n a d e c i s i o n was made t o l i m i t t h e a n a l y s e s t o s i t u a t i o n s where t h e s o l a r z e n i t h a n g l e i s l e s s t h a n 85 d e g r e e s . The d i u r n a l v a r i a t i o n o f r e f l e c t a n c e i s no t o n l y a f u n c t i o n o f t h e a n i s o t r o p i c p r o p e r t i e s o f t h e s u r f a c e but a l s o i n c o r p o r a t e s s c a t t e r i n g f rom t h e c o l u m n o f a t m o s p h e r e v i e w e d by t h e s a t e l l i t e . A t m o s p h e r i c s c a t t e r i n g i n c r e a s e s as t h e o p t i c a l p a t h l e n g t h i n c r e a s e s . F o r t h e f o l l o w i n g two r e a s o n s t h e s e p a r a t i o n o f t h e s e two c o m p o n e n t s i s u n n e c e s s a r y i n t h i s s t u d y . 1) G i v e n t h e c l o s e p r o x i m i t y o f t h e s u r f a c e s b e i n g m o d e l l e d u n d e r c l e a r sky c o n d i t i o n s ( see F i g u r e 3 .1 ) t h e a t m o s p h e r i c s c a t t e r i n g i s l i k e l y t o be r e a s o n a b l y c o n s i s t e n t o v e r e a c h o f t h e s u r f a c e s . T h i s w i l l a l l o w d i f f e r e n c e s i n t h e s u r f a c e r e f l e c t a n c e p a t t e r n s t o be i n f e r r e d d e s p i t e t h e a b s o l u t e c h a n g e s i n a t m o s p h e r i c r e f l e c t i o n b e i n g i n d e t e r m i n a t e . 2) In t h e d e v e l o p m e n t o f t h e r e l a t i o n s h i p between s a t e l l i t e m o n i t o r e d r e f l e c t i o n and c a l c u l a t e d t r a n s m i s s i o n t h e r e m o v a l of t h e a t m o s p h e r i c s c a t t e r i n g component f rom t h e s a t e l l i t e d a t a s e t i s u n n e c e s s a r y ( s ee C h a p t e r 5 ) . E a r l y work u s i n g s a t e l l i t e d a t a a s sumed r e f l e c t e d r a d i a t i o n t o be L a m b e r t i a n ( i . e . t h e same i n a l l d i r e c t i o n s ) 59 (Bandeen e t a l . , 1 9 6 5 ) . T h i s w o u l d l e a d t o a m i s i n t e r p r e t a t i o n o f t h e s c e n e b e i n g v i e w e d as v i r t u a l l y a l l n a t u r a l s u r f a c e s d i s p l a y some d e g r e e o f d i r e c t i o n a l r e f l e c t a n c e . The use o f t h e L a m b e r t i a n a s s u m p t i o n w o u l d s u g g e s t c h a n g e s i n t h e n a t u r e o f t h e s u r f a c e ( i n t h e c o n t e x t o f t h i s t h e s i s , s u g g e s t i n g a v a r i a t i o n i n t h e amount o f t h e s o l a r r a d i a t i o n r e a c h i n g t h e E a r t h ' s s u r f a c e ) , w h i l e i n r e a l i t y t h e c h a n g e i n b r i g h t n e s s i s a r e s u l t of t h e a n i s o t r o p i c 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 t h e s u r f a c e and a v a r i a t i o n i n a t m o s p h e r i c s c a t t e r i n g w i t h c h a n g i n g o p t i c a l p a t h l e n g t h . T h u s t o c o r r e c t l y i n t e r p r e t s a t e l l i t e d a t a , b i d i r e c t i o n a l r e f l e c t a n c e - m o d e l s a r e u sed t o c o r r e c t f o r t h e n o n - L a m b e r t i a n n a t u r e o f t h e r e f l e c t e d e n e r g y . The a b s e n c e o f h e m i s p h e r i c s e n s o r s on t h e s a t e l l i t e p l a t f o r m p r e v e n t a d i r e c t measure o f t h e a n i s o t r o p y . Thus i t was n e c e s s a r y t o r e l y on p r e s e n t knowledge o f t h e d i r e c t i o n a l n a t u r e o f t h e e n e r g y r e f l e c t e d f rom g e n e r a l i z e d s u r f a c e s t o c r e a t e a m o d e l f o r c o r r e c t i n g t h e s a t e l l i t e m e a s u r e m e n t s . I d e a l l y a m o d e l w h i c h u t i l i z e s t h e e x a c t s p e c t r o r a d i o m e t r i c c h a r a c t e r .and g e o m e t r i c p l a c e m e n t o f e v e r y i n d i v i d u a l r e f l e c t i n g component w i l l y i e l d t h e m e a s u r e d s p e c t r a l r e f l e c t a n c e o f t h e v i e w e d a r e a ( S u i t s , 1 9 7 2 a ) . The c o l l e c t i o n o f s u c h d a t a and t h e n e c e s s a r y c o m p u t a t i o n s i s u n f e a s i b l e . In a d d i t i o n , t h e use o f SMS-2 s a t e l l i t e d a t a i n t h i s s t u d y has i n h e r e n t r e s t r i c t i o n s on s u c h BDR m o d e l d e v e l o p m e n t . T h i s i s a f u n c t i o n o f t h e n a r r o w b a n d n a t u r e o f t h e v i s i b l e image d a t a 60 when c o m p a r e d t o t h e s o l a r r ad j . a t i . on s p e c t r u m and t h e r e l a t i v e l y low r e s o l u t i o n d a t a w h i c h n e c e s s i t a t e s g e n e r a l i z a t i o n s a b o u t t h e r e f l e c t i n g s u r f a c e s . In t h e a v a i l a b l e l i t e r a t u r e t h e r e i s a l a r g e range i n t h e c o m p l e x i t y o f BDR m o d e l s t h a t have been d e v e l o p e d . They v a r y f rom s i m p l e m a t h e m a t i c a l e x p r e s s i o n s , s u c h as t h a t by N k e m d i r i m ( 1 9 7 2 ) : a = a 0 exp ( b e . ) (4 .1 ) where a i s a s t a t i s t i c a l e s t i m a t e o f t h e z e n i t h a l sun o r e f l e c t i o n c o e f f i c i e n t and b i s a c o e f f i c i e n t (deg" 1) w h i c h d e s c r i b e s t h e r a t e a t w h i c h a c h a n g e s w i t h c h a n g i n g z e n i t h a n g l e , e , t o c o m p l e x n u m e r i c a l m o d e l s by S u i t s ( 1 9 7 2 a , 1972b) and Kopp and M i i l l e r ( 1 9 7 6 ) . S u i t s ( 1 9 7 2 a , 1972b) m o d e l i s b a s e d on t h e s p e c t r a l and g e o m e t r i c c h a r a c t e r o f t h e i n d i v i d u a l e l e m e n t s o f a v e g e t a t i o n c a n o p y and u se s d a t a f rom an a i r b o r n e m u l t i s p e c t r a l s c a n n e r . The Monte C a r l o s i m u l a t i o n t e c h n i q u e was a p p l i e d t o BDR m o d e l l i n g f o r c l o u d and o c e a n s u r f a c e s , by Kopp and M i i l l e r (1976) and J a c o b o w i t z e t a l . ( 1 9 7 7 ) , r e s p e c t i v e l y . D e s p i t e t h e a b u n d a n c e o f BDR m o d e l s i n t h e l i t e r a t u r e , S t e p h e n e t a l . (1981) c l e a r l y s t a t e t h a t BDR m o d e l b e h a v i o u r , a s a f u n c t i o n of Sun z e n i t h a n g l e , s a t e l l i t e v i e w i n g z e n i t h 61 a n g l e 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 , i s s t i l l p o o r l y known f o r a l l bu t s i m p l e s u r f a c e s ( e . g . o c e a n s ) . A g r e a t d e a l of work i s s t i l l n e c e s s a r y i n c l u d i n g t h e a d o p t i o n o f a s t a n d a r d n o m e n c l a t u r e . T h u s a d e c i s i o n was made t o d e v e l o p BDR m o d e l s f o r t h i s r e s e a r c h p r o j e c t , f o r two r e a s o n s : 1) t h e l a c k o f r i g o r o u s v e r i f i c a t i o n o f m o d e l s d e v e l o p e d i n v a r i o u s p a r t s o f t h e w o r l d ; a n d 2) t h e l i m i t i n g g e o m e t r i c c o n s t r a i n t s o f t h e o t h e r m o d e l s . F o r e x a m p l e , t h e M i n n i s a n d H a r r i s o n BDR m o d e l ( 1 9 8 2 a , 1982b) i s f o r d i s c r e t e Sun z e n i t h a n g l e s w h i l e t h i s s t u d y r e q u i r e s a c o n t i n u u m w i t h a f i x e d 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 . H o w e v e r , t h e work by T a r p l e y (1979) and M i n n i s and H a r r i s o n ( 1 9 8 2 a , 1982b) i n f l u e n c e d t h e d e v e l o p m e n t of t h e p r e s e n t BDR m o d e l s . The d e g r e e o f a n i s o t r o p y and t h e amount of e n e r g y r e f l e c t e d , v a r i e s f o r d i f f e r e n t s u r f a c e t y p e s ( S a l o m o n s o n and M a r l a t t , 1968; B r e n n a n and B a n d e e n , 1970; Stowe e t a l . , 1 9 8 0 ) . Thus t h r e e m o d e l s were d e v e l o p e d r e p r e s e n t i n g e a c h o f t h e g e n e r a l i z e d s u r f a c e s f o u n d i n t h e s t u d y a r e a ( i . e . s e a , l a n d and c l o u d s u r f a c e s ) . A snow s u r f a c e BDR m o d e l was not d e v e l o p e d and t h e r e f o r e t h i s s t u d y was r e s t r i c t e d t o p e r i o d s 62 w i t h o u t snow c o v e r on t h e g r o u n d . T h i s i s no t o n l y due t o t h e i n f r e q u e n c y w i t h w h i c h snow c o v e r i s p r e s e n t i n t h e s t u d y a r e a , bu t a l s o due t o t h e p r o b l e m s i n d i s t i n g u i s h i n g be tween snow and c l o u d s u r f a c e s . I d e a l l y i n t h e d e v e l o p m e n t o f BDR m o d e l s u s i n g s a t e l l i t e d a t a i t i s i m p e r a t i v e t o assume s u r f a c e and a t m o s p h e r i c h o m o g e n e i t y , b o t h s p a t i a l l y a n d t e m p o r a l l y o r t o e x p l i c i t l y remove t h e s e e f f e c t s . The Sea and L a n d BDR m o d e l s c l o s e l y a p p r o x i m a t e s u c h a s s u m p t i o n s . The s p a t i a l h e t e r o g e n e i t y o f t h e l a n d a r e a i n t h i s s t u d y i s g e n e r a l l y o f sub s a t e l l i t e r e s o l u t i o n and t h e v a r i a t i o n i n r e f l e c t a n c e due t o s u c h f a c t o r s as t h e m o i s t u r e c o n t e n t o f t h e s u r f a c e c o m p o n e n t s ( I d s o e t a l . , 1975) i s i n c o r p o r a t e d i n t h e e m p i r i c a l n a t u r e o f t h e m o d e l . H o w e v e r , due t o t h e v a r i a b l e n a t u r e o f c l o u d s and t h e l a c k o f a d e f i n i t i v e u n d e r s t a n d i n g o f t h e c o m p l e x r a d i a t i v e p r o p e r t i e s o f c l o u d s ( L i o u and W i t t m a n , 1 9 7 9 ) , a much more g e n e r a l i z e d BDR mode l has been d e v e l o p e d r e p r e s e n t i n g ' a v e r a g e ' c l o u d 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 . In t h e l i t e r a t u r e two d i f f e r e n t r a d i a n c e p a t t e r n s have been i d e n t i f i e d f o r two d i s t i n c t c l o u d c o n d i t i o n s ; i n f i n i t e ( l a y e r ) c l o u d s ( e . g . B r e n n a n and B a n d e e n , 1970; Kopp and M i i l l e r , 1 9 7 6 ) , and f i n i t e c l o u d f i e l d s ( e . g . McKee and C o x , 1974, 1 9 7 6 ) . A l s o t h e o r e t i c a l s t u d i e s ( s ee W e l c h e t a l . , 1980) show s i g n i f i c a n t d i f f e r e n c e s i n t h e r a d i a t i v e p r o p e r t i e s o f t h e s e two c l o u d c a t e g o r i e s " . . . f o r remote s e n s i n g a p p l i c a t i o n s , c l o u d o p t i c a l d e p t h , c l o u d t o p h e i g h t , c l o u d 63 d r o p s i z e d i s t r i b u t i o n and c l o u d g e o m e t r y a r e a l l i m p o r t a n t c o n t r i b u t o r s t o c l o u d b r i g h t n e s s m e a s u r e m e n t s " ( W e l c h e t a l . , 1 9 8 0 ) . T h u s , a l t h o u g h i t may be p o s s i b l e t o d e v e l o p d i s t i n c t c l o u d r e f l e c t a n c e m o d e l s f rom SMS-2 d a t a i t i s o u t s i d e t h e s c o p e o f t h i s p r e s e n t t h e s i s as " f u r t h e r r e f i n e m e n t o f t h e d e f i n i t i o n of t h e s e c a t e g o r i e s and d e v e l o p m e n t o f a u t o m a t e d c l o u d t y p e i d e n t i f i c a t i o n schemes a r e r e q u i r e d b e f o r e s u c h m o d e l s c a n be k n o w l e d g e a b l y a p p l i e d t o l a r g e d a t a s e t s " ( M i n n i s and H a r r i s o n , 1 9 8 2 b ) . F o l l o w i n g R u f f e t a l . (1968) and M i n n i s a n d H a r r i s o n ( 1 9 8 2 a , 1982b) t h e C l o u d BDR model d e v e l o p e d h e r e r e p r e s e n t s ' a v e r a g e ' c l o u d r e f l e c t a n c e w h i c h s h o u l d y i e l d b e t t e r r e s u l t s f o r c a l c u l a t i n g t h e r e f l e c t e d s o l a r e n e r g y t h a n by a s s u m i n g an i s o t r o p i c r e f l e c t i o n p a t t e r n f o r c l o u d s . 4 . 2 D e f i n i t i o n s ( G e o m e t r y of R e f l e c t i o n ) The g e o m e t r i c r e l a t i o n s h i p s i n c o r p o r a t e d i n t h e d e v e l o p m e n t o f t h e v i s i b l e BDR m o d e l s a r e d e p i c t e d i n F i g u r e 4 . 2 . T h i s f i g u r e shows a s p h e r i c a l c o o r d i n a t e s y s t e m c e n t r e d a t t h e p o i n t o f r e f l e c t i o n and d e f i n e s t h e p r i n c i p a l d i r e c t i o n s as t h e s o l a r z e n i t h a n g l e , 9 , t h e 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 ( w h i c h i s a l s o t h e z e n i t h a n g l e o f t h e r e f l e c t e d r a y ) , Z , and t h e S u n - s a t e l l i t e a z i m u t h a n g l e , ^ . G i v e n t h a t t h e SMS-2 s a t e l l i t e i s g e o s t a t i o n a r y , t h e 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 i s f i x e d . R e l a t i v e t o the UBC s i t e ( t h e c e n t r e 64 L O C A L V E R T I C A L FIGURE 4 .2 D i a g r a m of G e o m e t r i c R e l a t i o n s Between Z e n i t h A n g l e o f the S u n , e , Z e n i t h A n g l e o f t h e R e f l e c t e d R a y , z , and t h e S u n - S a t e l l i t e A z i m u t h A n g l e , ^ ( A f t e r M i n n i s and H a r r i s o n , 1 9 8 2 ) . 65 p o i n t o f r e f l e c t i o n ) , Z , has a v a l u e o f 15 d e g r e e s west ( M a c D o n a l d D e t t w i l e r and A s s o c i a t e s L t d . , p e r s o n a l c o m m u n i c a t i o n ) . In t h e p r e s e n t a p p l i c a t i o n b a c k s c a t t e r i n g i s an i m p o r t a n t p r o c e s s when t h e S u n - s a t e l l i t e a z i m u t h i s c l o s e t o 0 d e g r e e s w h i l e f o r w a r d s c a t t e r i n g i s s i g n i f i c a n t when ^ i s c l o s e t o 180 d e g r e e s . The d e g r e e t o w h i c h a s u r f a c e e x h i b i t s t h e s e f o r w a r d and b a c k s c a t t e r i n g e f f e c t s d e p e n d s n o t o n l y on t h e g e o m e t r i c p o s i t i o n i n g o f t h e S u n , s a t e l l i t e and r e f l e c t i n g s u r f a c e , but a l s o on t h e n a t u r e o f t h e r e f l e c t i n g s u r f a c e . The m i r r o r - l i k e e f f e c t o f a smooth w a t e r s u r f a c e a t s u n s e t w i t h l a r g e z e n i t h a n g l e s and l a r g e S u n - v i e w e r a z i m u t h a n g l e s i s a p r i m e example o f f o r w a r d s c a t t e r i n g o f v i s i b l e l i g h t r a y s . The ' S u n g l i n t ' phenomenon o c c u r s due t o t h e b a c k s c a t t e r i n g o f l i g h t when t h e Sun a n d s a t e l l i t e a r e i n t h e same p l a n e w i t h r e s p e c t t o t h e r e f l e c t i n g s u r f a c e and t h e s a t e l l i t e i s e s s e n t i a l l y o c c u l t i n g t h e Sun (as t h e s a t e l l i t e i s some c o n s i d e r a b l e d i s t a n c e f rom t h e r e f l e c t i n g s u r f a c e a s o l a r e c l i p s e d o e s no t o c c u r a t t h e s u r f a c e ) . F i g u r e s 4.1 and 4 . 3 show t h e v a r i a t i o n i n r e f l e c t a n c e o v e r a l a n d and sea s u r f a c e r e s p e c t i v e l y , f o r t h e same d a y . B o t h s u r f a c e s e x h i b i t a marked f o r w a r d s c a t t e r i n g a t t h e b e g i n i n g and e n d o f the d a y . I s o l a t i o n o f t h e f o r w a r d s c a t t e r i n g c o n t r i b u t i o n t o b i d i r e c t i o n a l r e f l e c t a n c e i s compounded by t h e p r o b l e m s a s s o c i a t e d w i t h t h e l a r g e s o l a r z e n i t h a n g l e s 66 256/79 0.24-0.16' TR 0.08' 09:08 13:08 17:08 L.A.T. (Hours) FIGURE 4 . 3 D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e (TR) O v e r a Sea S u r f a c e f o r J u l i a n Day 2 5 6 / 7 9 . D e t e r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 67 o c c u r r i n g a t t h e s e t i m e s and t h e i n c r e a s e d o p t i c a l p a t h l e n g t h . T h i s p r o b l e m i s a d d r e s s e d i n S e c t i o n 4 . 3 . 2 . 4 . H o w e v e r , b a c k s c a t t e r i n g a p p e a r s a s a s e c o n d a r y maximum i n t h e c u r v e a r o u n d 13 :00 h o u r s f o r t h e l a n d s u r f a c e o n l y ( see F i g u r e 4 . 1 ) . 4 . 3 M o d e l l i n g P r o c e d u r e 4 . 3 . 1 D a t a S e l e c t i o n and Q u a l i t y C o n t r o l 4 . 3 . 1 . 1 L a n d and Sea S u r f a c e The a r e a s c h o o s e n f o r d e v e l o p i n g t h e l a n d and sea s u r f a c e BDR m o d e l s a r e d e s c r i b e d i n S e c t i o n 4 . 3 . 1 . T h e y were e x t r a c t e d f rom a 25 x 25 p i x e l a r r a y c e n t r e d on t h e UBC s i t e . F i g u r e 3.1 p r e s e n t s t h e mean c o u n t v a l u e s , f o r t h e same a r r a y s i z e , b a s e d on a c o m p o s i t e o f f o r t y - n i n e images f rom f o u r c l e a r sky d a y s . The c o a s t l i n e was c i r c u m s c r i b e d i n t u i t i v e l y , u s i n g a mean c o u n t v a l u e o f 70 a s t h e t h r e s h o l d . F i g u r e 3.1 was u s e d t o d e f i n e t h e c l e a r sky BDR m o d e l l i n g a r e a s . One sea a r e a ( r e c t a n g l e l a b e l l e d Sea) and two l a n d a r e a s ( r e c t a n g l e s l a b e l l e d L a n d ( N ) and L a n d ( S ) ) were s e l e c t e d . Two l a n d a r e a s were c h o s e n due t o t h e c o n s i s t e n t l y d i f f e r e n t c o u n t v a l u e s f o u n d o v e r c e r t a i n p a r t s o f t h e a r e a d e s i g n a t e d as l a n d . The d e v e l o p m e n t o f two BDR m o d e l s f o r t h e l a n d 68 s u r f a c e w i l l show w h e t h e r t h e s e two i n d e p e n d e n t l y d e r i v e d m o d e l s a r e s i g n i f i c a n t l y d i f f e r e n t d e s p i t e t h e f a c t t h a t t h e y a r e f o r t h e same g e n e r a l i z e d s u r f a c e t y p e . T h i s w i l l be d i s c u s s e d i n C h a p t e r 5 . The e a s t - w e s t d i m e n s i o n s o f t h e s u b - a r r a y s were s e l e c t e d u n d e r t h e c o n s t r a i n t s o f t h e s u r f a c e t y p e d i s t r i b u t i o n f o u n d w i t h i n t h e 25 x 25 a r r a y . The n o r t h - s o u t h d i m e n s i o n s were c o n s t r a i n e d l i k e w i s e , bu t a r e a l s o a f u n c t i o n o f t h e e i g h t s e n s o r s w h i c h c o m p r i s e t h e SMS-2 v i s i b l e s c a n n e r . Thus t h e n o r t h - s o u t h d i m e n s i o n i s d i v i s i b l e by e i g h t . T h i s i s d e s i r a b l e s i n c e t h e i n d i v i d u a l s e n s o r s a r e n o t c a l i b r a t e d a g a i n s t e a c h o t h e r , r e s u l t i n g i n t h e e f f e c t c a l l e d ' s t r i p i n g ' . T h i s i s i d e n t i f i e d by s m a l l s y s t e m a t i c d i f f e r e n c e s i n t h e b r i g h t n e s s c o u n t v a l u e s . F i g u r e 3 .4 i s a n i g h t - t i m e image c e n t r e d o f f V a n c o u v e r I s l a n d , o v e r t h e P a c i f i c Ocean a t 49 d e g r e e s l a t i t u d e , 127 d e g r e e s l o n g i t u d e . D e s p i t e a homogeneous t a r g e t , ' s t r i p i n g ' i s c l e a r l y e v i d e n t w i t h , f o r e x a m p l e , a row o f a n o m a l o u s l y low c o u n t v a l u e s ( s i x t e e n ) e v e r y e i g h t h l i n e . The d a t a c h o s e n t o d e v e l o p t h e l a n d and sea s u r f a c e BDR m o d e l s underwent r i g o r o u s q u a l i t y c o n t r o l t o e n s u r e t h a t t h e y i n c l u d e d o n l y c l e a r sky c o n d i t i o n s . E a c h image s e l e c t e d was i n s p e c t e d f o r c l o u d c o n t a m i n a t e d p i x e l s and e r r o n e o u s p i x e l v a l u e s due t o s a t e l l i t e m a l f u n c t i o n s . T h i s t a s k was 69 i m p l e m e n t e d i n t h r e e ways : 1) i n s p e c t i o n o f g l o b a l and d i r e c t s o l a r r a d i a t i o n d a t a and b r i g h t s u n s h i n e d a t a m e a s u r e d a t t h e UBC s i t e f o r e v i d e n c e o f c l o u d ; 2) v i s u a l i n s p e c t i o n o f t h e 25 x 25 p i x e l images u s i n g t h e COMTAL image p r o c e s s o r f o r t h e o c c u r r e n c e of c l o u d ; a n d 3) i n s p e c t i o n o f t h e r e f l e c t a n c e v a l u e s f o r s p u r i o u s d i u r n a l v a r i a t i o n s . Mos t o f t h e e r r o n e o u s d a t a due t o s y s t e m m a l f u n c t i o n s c a n be r e a d i l y e l i m i n a t e d s i n c e b r i g h t n e s s v a l u e s a r e t y p i c a l l y u n u s u a l l y l a r g e o r z e r o . Of t h e f o u r t e e n d a y s w h i c h were s u b j e c t t o q u a l i t y c o n t r o l i n t h e a b o v e m a n n e r , h a l f were u s e d t o d e v e l o p t h e BDR m o d e l s ( see S e c t i o n 4 . 3 ) and h a l f were r e t a i n e d f o r i n d e p e n d e n t mode l v e r i f i c a t i o n ( see S e c t i o n 4 . 4 ) . Images f rom J u l i a n d a y s 2 0 0 / 7 9 , 2 5 6 / 7 9 , 2 7 6 / 7 9 , 3 0 4 / 7 9 , 0 1 2 / 8 0 , 0 2 5 / 8 0 , 183/80 were c h o s e n t o d e v e l o p t h e l a n d and sea s u r f a c e BDR m o d e l s . In a d d i t i o n , J u l i a n day 030 /80 was i n c o r p o r a t e d i n t h e L a n d ( S ) m o d e l . F r o m t h e s e d a t a b a s e s , t h o s e images i d e n t i f i e d as c l e a r p r o d u c e d d a t a s e t s o f 121 images f o r t h e L a n d ( N ) m o d e l , 128 images f o r t h e L a n d ( S ) m o d e l , and 131 images f o r t h e Sea 70 m o d e l . 4 . 3 . 1 . 2 C l o u d S u r f a c e The ' g e n e r a l ' c l o u d s u r f a c e BDR m o d e l was d e v e l o p e d u s i n g a 1 6 x 1 6 p i x e l s u b - a r r a y c e n t r e d on t h e UBC s i t e . The use o f a l a r g e r a r r a y s i z e c o m p a r e d t o t h a t u s e d f o r t h e o t h e r s u r f a c e s i s p r i m a r i l y t o c a p t u r e an ' a v e r a g e ' c l o u d r e f l e c t a n c e , but a l s o i s a r e s u l t o f t h e number o f s a t e l l i t e s e n s o r s ( s ee a l s o S e c t i o n 4 . 3 . 1 . 1 ) . F o l l o w i n g a r i g o r o u s q u a l i t y c o n t r o l o f t h e d a t a o n l y f i v e d a y s were a v a i l a b l e t o d e v e l o p t h e C l o u d BDR m o d e l . The s e l e c t i o n f o l l o w e d s i m i l a r c r i t e r i o n t o t h a t f o r t h e c l e a r sky m o d e l s ( see S e c t i o n 4 . 3 . 1 . 1 ) e x c e p t t h a t t h e o b j e c t i v e was t o e n s u r e c o n d i t i o n s o f c o m p l e t e c l o u d c o v e r . The q u a l i t y c o n t r o l a l s o i n c l u d e d the use o f h i s t o g r a m s d e r i v e d f rom t h e p i x e l c o u n t v a l u e s f o r t h e 25 x 25 p i x e l a r r a y s . H i s t o g r a m s were p r o d u c e d f o r e a c h i m a g e . T h e y were u s u a l l y i n s p e c t e d f o r l a r g e r a n g e s i n b r i g h t n e s s v a l u e s ( F i g u r e 4 . 4 ) o r b i m o d a l d i s t r i b u t i o n s ( F i g u r e 4 . 5 ) , b o t h i n d i c a t i n g t h e p r e s e n c e o f u n d e s i r a b l e c l e a r sky o r p a r t l y c l o u d y p i x e l s i n t h e s t u d y a r e a . F i g u r e 4 . 6 i s an example o f an a c c e p t a b l e c l o u d y image h i s t o g r a m , s i n c e i t has a s m a l l r a n g e i m p l y i n g a r e l a t i v e l y homogeneous c l o u d s u r f a c e . The J u l i a n d a y s f i n a l l y s e l e c t e d f o r t h e C l o u d BDR 71 5 On ^ 40-c n 30-3 20-o S- 1 0 H I 7 2 — i 1 i 1 1 1 92 112 132 152 172 192 Pixel Value (counts) FIGURE 4 . 4 H i s t o g r a m o f C o u n t V a l u e s S h o w i n g a L a r g e S p r e a d i n t h e D a t a a s a R e s u l t of t h e P a r t l y C l o u d y C o n d i t i o n s . B a s e d on a 25 x 25 P i x e l A r r a y C e n t r e d on the UBC S i t e F o r J u l i a n Day 160/80 a t 14 :42 L A T . 72 50i n .a c re 3 n •< 40-30 H Q. 3 fD 3 20' o 3 10-72 — i — 92 112 — i • > — 132 152 • 172 192 212 232 Pixel Value (counts) FIGURE 4 . 5 H i s t o g r a m o f C o u n t V a l u e s Showing a B i m o d a l D i s t r i b u t i o n Due t o a P r e d o m i n a n c e o f C o m p l e t e l y C l e a r and C l o u d y P i x e l s . B a s e d on a 25 x 25 P i x e l A r r a y C e n t r e d on t h e UBC S i t e F o r J u l i a n Day 185/30 a t 12 :42 L A T . 73 360T 30(H ft) C fD 3 240H ~ 180-3 fD 3 O Z3 120-1 604 i i i i i 152 172 192 212 232 Pixel Value(counts) FIGURE 4 . 6 H i s t o g r a m Showing a S m a l l S p r e a d o f C o u n t V a l u e s S u g g e s t i n g R e l a t i v e l y Homogeneous C l o u d C o v e r C o n d i t i o n s . B a s e d on a 25 x 25 P i x e l A r r a y C e n t r e d on t h e UBC S i t e F o r J u l i a n Day 185/80 a t 0 9 : 9 2 L A T . 74 m o d e l l i n g were 2 9 7 / 7 9 , 3 6 3 / 7 9 , 1 8 5 / 8 0 , 197/80 and 2 4 5 / 8 0 , g i v i n g a t o t a l o f 119 o v e r c a s t i m a g e s . ' A v e r a g e ' c l o u d r e f l e c t a n c e v a l u e s were o b t a i n e d by c o n v e r t i n g t h e b r i g h t n e s s c o u n t v a l u e s t o a t a r g e t r e f l e c t a n c e , on an i n d i v i d u a l p i x e l b a s i s , u s i n g t h e s a t e l l i t e c a l i b r a t i o n c u r v e ( see F i g u r e 3 .3 ) t o g e t h e r w i t h e q u a t i o n 3 .4 ( see S e c t i o n 3 . 6 ) a n d a v e r a g i n g o v e r a 16 x 16 p i x e l s u b - a r r a y . 4 . 3 . 2 I d e n t i f i c a t i o n o f A n i s o t r o p i c 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 4 . 3 . 2 . 1 L a n d S u r f a c e G r a p h s d e p i c t i n g t h e d i u r n a l v a r i a t i o n i n r e f l e c t a n c e f o r the s e l e c t e d d a y s have been p l o t t e d f o r t h e d i f f e r e n t s u r f a c e s . The c u r v e s f o r t h e two l a n d a r e a s f o l l o w s i m i l a r p a t t e r n s (compare F i g u r e s 4.1 and 4 . 7 , 4 . 8 w i t h 4 . 9 , and 4 . 1 0 w i t h 4 . 1 1 ) . H o w e v e r , L a n d ( S ) p r o d u c e s c o n s i s t e n t l y h i g h e r r e f l e c t a n c e v a l u e s (by a p p r o x i m a t e l y 0 .03 t o 0 .04 ) c o m p a r e d t o L a n d ( N ) . T h i s r e s u l t i s c o m p a t i b l e w i t h t h e f a c t t h a t L a n d ( S ) c o n s i s t s o f m a i n l y s u b u r b a n and u r b a n s u r f a c e s w h i l e L a n d ( N ) i n c l u d e s b o t h s u b u r b a n and f o r e s t e d a r e a s . F i g u r e s 4.1 and 4 . 7 t o 4.11 d e m o n s t r a t e a summat ion o f t h e s t r o n g a n i s o t r o p y i n t h e 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 o f t h e l a n d s u r f a c e and v a r i a t i o n s due t o a t m o s p h e r i c s c a t t e r i n g . 75 2 5 6 / 7 9 0 . 2 4 ' 0 . 1 6 TR 0 . 0 8 ' 0 9 : 0 6 1 3 : 0 6 1 7 : 0 6 L . A . T . ( H o u r s ) FIGURE 4 . 7 D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e (TR) O v e r t h e L a n d ( N ) S u r f a c e f o r J u l i a n Day 2 5 6 / 7 9 . D e t e r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 76 0 . 3 2 0 . 2 4 TR 0 . 1 6 0 . 0 8 3 0 4 / 7 9 0 9 : 1 9 1 3 : 1 9 L . A . T . ( H o u r s ) 1 7 : 1 9 FIGURE 4.8 D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e (TR) Over t h e L a n d ( S ) S u r f a c e f o r J u l i a n Day 304/79. D e t e r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 77 3 0 4 / 7 9 0 . 3 2 1 0 . 0 8 1 0 : 1 9 1 4 : 1 9 L . A . T . ( H o u r s ) FIGURE 4.9 D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e (TR) Over the Land(N) S u r f a c e f o r J u l i a n Day 304/79. D e t e r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 78 200/79 0.50i 0.40H 0.301 0 . 2 0 o . - ^ 0 7 : 2 5 1 1 : 2 5 1 5 : 2 5 L . A . T . ( H o u r s ) 1 9 : 2 5 FIGURE 4.10 D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e (TR) Over 'the Land(S) S u r f a c e f o r J u l i a n Day 200/79. D e t e r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 79 200/79 0.60 0.50H 0.40 TR 0.30 0.20 0.10 07:25 11:25 L.A.T. (Hours) FIGURE 4.11 15:25 19:25 D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e (TR) Over the Land(N) S u r f a c e f o r J u l i a n Day 200/79. D e t e r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 80 A l t h o u g h t h e s e f i g u r e s i l l u s t r a t e t h e d i u r n a l c h a r a c t e r i s t i c s of t h e r e f l e c t a n c e , the i m p o r t a n c e of t h e i n d i v i d u a l a n g l e s 9 , Z and J> ( i . e . t h e s i t u a t i o n geometry, see S e c t i o n 4.2), a r e c o n c e a l e d by t h e use of t i m e on the a b s c i s s a . Thus, p o l a r p l o t s were g e n e r a t e d t o show the v a r i a t i o n i n a n i s o t r o p i c r e f l e c t a n c e as a f u n c t i o n of t h e two a n g l e s , 8 , and i|» . F i g u r e s 4.12 and 4.13 p l o t 9 = 0 d e g r e e s a t the c e n t r e and 9 = 90 d e g r e e s a t the p e r i p h e r y of t h e c i r c l e . p l o t s as 0 d e g r e e s a t t h e s o u t h and, ±180 d e g r e e s i n the n o r t h , where^ i s p o s i t i v e when the Sun i s e a s t of the s a t e l l i t e and n e g a t i v e when t h e Sun i s west of t h e s a t e l l i t e . F i g u r e s 4.12 and 4.13 c o n t a i n d a t a f o r a l l imagery used t o d e v e l o p th e l a n d BDR m o d e l s . I t s h o u l d be n o t e d t h a t t h e i s o l i n i n g p r o c e d u r e i n c l u d e s a c e r t a i n d e g r e e of 'smoothing' of the d a t a (see UBC Computer C e n t r e D o c u m e n t a t i o n , ' S u r f a c e s ' ) . L i t t l e emphasis s h o u l d be p l a c e d on t h e d a t a p o i n t s c l o s e t o t h e p e r i p h e r y of the c i r c l e s and a l s o on e x c e p t i o n a l l y s t r o n g g r a d i e n t s . T h i s i s t h o u g h t t o be an a r t i f a c t of the n o r m a l i z i n g p r o c e d u r e which i n c l u d e s c o s e as a d e n o m i n a t o r , t h e r e b y c r e a t i n g a b n o r m a l l y l a r g e r e f l e c t a n c e v a l u e s a t l a r g e r s o l a r z e n i t h a n g l e s . The r e moval of s u c h d a t a p o i n t s or the i n c o r p o r a t i o n of more r e a l i s t i c v a l u e s has not been u n d e r t a k e n . The former would r e s u l t i n a r e d u c t i o n of the m o d e l l i n g c a p a b i l i t i e s a t l a r g e z e n i t h a n g l e s . W i t h r e s p e c t t o t h e l a t t e r , i t i s t h o u g h t t h a t the m i n i m a l m o d i f i c a t i o n of 81 180 0 (degrees) FIGURE 4.12 Polar P l o t of Target R e f l e c t a n c e (TR) For the Land(N) Surface, as a Function of the Sun Zenith Angle, e , and the S u n - S a t e l l i t e Azimuth,^ . TR i s Dimensionless, x 1 Cf2 . 82 FIGURE 4 . 1 3 P o l a r P l o t o f T a r g e t R e f l e c t a n c e (TR) F o r t h e L a n d ( S ) S u r f a c e , a s a F u n c t i o n o f t h e Sun Z e n i t h A n g l e , 9 , and t h e S u n - S a t e l l i t e A z i m u t h , <J* . TR i s D i m e n s i o n l e s s , x 1 0~ . 83 t h e d a t a s e t i s more a c c e p t a b l e e s p e c i a l l y when i t i s r e c o g n i z e d t h a t a c t u a l e n e r g y f l o w s a r e r e l a t i v e l y i n s i g n i f i c a n t a t t h e s e t i m e s . A n a l o g o u s t o t h e d i u r n a l g r a p h i c a l r e p r e s e n t a t i o n s , t h e p o l a r p l o t s o f t h e L a n d ( N ) ( F i g u r e 4 . 1 2 ) and L a n d ( S ) ( F i g u r e 4 . 1 3 ) show a marked s i m i l a r i t y . The s t r o n g i n f l u e n c e o f 6 on t h e r e f l e c t a n c e ( P a l t r i d g e and P i a t t , 1976) i s s een i n F i g u r e s 4 . 1 2 and 4 . 1 3 a s a d r a m a t i c c h a n g e i n t h e i s o l i n e g r a d i e n t t o w a r d s t h e p e r i p h e r y o f t h e h e m i s p h e r i c p r o j e c t i o n . An i n c r e a s e i n t h e a n i s o t r o p y w i t h i n c r e a s i n g z e n i t h a n g l e was a l s o shown by M i n n i s and H a r r i s o n ( 1 9 8 2 a ) . Two c h a r a c t e r i s t i c a n i s o t r o p i c r e f l e c t a n c e f e a t u r e s a r e r e v e a l e d f rom F i g u r e s 4.1 and 4 . 7 t o 4 . 1 3 , a b a c k s c a t t e r i n g and f o r w a r d s c a t t e r i n g component ( see J a c o b o w i t z , 1 9 8 1 ) . F i g u r e s 4.1 and 4 . 7 t o 4.11 show s t r o n g d i r e c t i o n a l r e f l e c t a n c e a t t h e b e g i n n i n g a n d t o w a r d s t h e end of t h e d a y . T h i s i s a f u n c t i o n o f : 1) t h e Sun z e n i t h a n g l e , w i t h i n c r e a s e d s c a t t e r i n g f rom t h e a t m o s p h e r e due t o g r e a t e r o p t i c a l p a t h l e n g t h s ; 2) an i n c r e a s e i n r e f l e c t i o n d u r i n g t h e summer as t h e g e o m e t r i c a l s i t u a t i o n f a v o u r a b l e f o r f o r w a r d s c a t t e r i n g i s a p p r o a c h e d ( t h i s i s c l e a r l y seen i n F i g u r e s 4 .12 and 4 . 1 3 wheni)) i s a t i t s g r e a t e s t and 8 i s a l s o l a r g e ) ; and 84 3) t h e n o r m a l i z i n g p r o c e d u r e . A n o t h e r peak i n r e f l e c t i o n o c c u r s i n t h e b a c k s c a t t e r i n g d i r e c t i o n . T h i s c a n be s e e n most c l e a r l y i n t h e d i u r n a l r e f l e c t a n c e c u r v e s ( F i g u r e 4.1 a n d 4 . 7 t o 4 . 1 1 ) as a peak j u s t a f t e r 13 :00 LAT when t h e S u n , s a t e l l i t e and t a r g e t a r e i n t h e same p l a n e . The b a c k s c a t t e r i n g i s s e e n as a s e c o n d a r y maximum on t h e p o l a r p l o t s when * i s c l o s e t o z e r o . F i g u r e s 4.1 and 4 . 7 t o 4.11 show a p r o g r e s s i o n a s s o c i a t e d w i t h i n c r e a s e d b a c k s c a t t e r i n g as t h e w i n t e r s o l s t i c e i s a p p r o a c h e d . T h i s i s a c o n s e q u e n c e o f a l a r g e r n o o n - t i m e z e n i t h a n g l e i n w i n t e r ( t h e i n c r e a s e i s f rom J u l i a n day 2 0 0 / 7 9 ( F i g u r e 4 . 1 1 ) , t o 256 /79 ( F i g u r e 4 . 1 ) , t o 304 /79 ( F i g u r e 4 . 9 ) ) . F i g u r e s 4 .12 and 4 . 1 3 s u g g e s t a r e f l e c t a n c e minimum a l o n g t h e 90 d e g r e e t r a n s v e r s e p l a n e when f o r w a r d s c a t t e r i n g and b a c k s c a t t e r i n g p r o c e s s e s w o u l d t e n d t o d i r e c t t h e r a d i a n t e n e r g y away f rom t h e s a t e l l i t e s e n s o r . S i m i l a r f e a t u r e s have been d e s c r i b e d by B r e n n a n and Bandeen ( 1 9 7 0 ) . The BDR model f o r v e g e t a t e d l a n d s u r f a c e s d e v e l o p e d by M i n n i s and H a r r i s o n ( 1 9 8 2 b ) , s u g g e s t s a minimum v a l u e f o r r e f l e c t a n c e i n a f o r w a r d s c a t t e r i n g d i r e c t i o n a t low Sun a n g l e s . H o w e v e r , due t o t h e n a t u r e o f t h i s s t u d y and t h e l i m i t i n g g e o m e t r i c c o n f i g u r a t i o n s , ^ i s r e s t r i c t e d t o a maximum v a l u e of 136 5 2 ' . In c o m p a r i s o n t o t h e M i n n i s and H a r r i s o n (1982b) r e s u l t s , t h e g e n e r a l i n c r e a s e i n r e f l e c t i o n seen i n t h i s s t u d y f o r t h e 85 l a r g e s t ip a n g l e s i s a r e s u l t o f t h e l a r g e 9 a s s o c i a t e d w i t h s u c h o c c a s i o n s . T h e r e f o r e any minimum v a l u e w o u l d be o v e r w h e l m e d by t h e i n c r e a s e i n r e f l e c t a n c e as a r e s u l t o f t h e l a r g e o p t i c a l p a t h l e n g t h . 4 . 3 . 2 . 2 Sea S u r f a c e B a s e d on a s e l e c t i o n o f d a y s t h r o u g h o u t t h e y e a r t h e r e a p p e a r s t o be a marked c o n s i s t e n c y i n t h e d i u r n a l p a t t e r n o f r e f l e c t a n c e f o r t h e sea s u r f a c e a s shown i n F i g u r e s 4 . 1 4 t o 4 . 1 6 . N o t e a b l e i n c r e a s e s i n t h e r e f l e c t i o n a r e s e e n w i t h l a r g e z e n i t h a n g l e s . However d i r e c t i o n a l i t y of t h e sea r e f l e c t i v i t y due t o b a c k s c a t t e r i n g i s i n d i s t i n c t . The l a t t e r c o n c l u s i o n i s c o n f i r m e d i n t h e h e m i s p h e r i c p l o t o f r e f l e c t a n c e ( F i g u r e 4 . 1 7 ) , g i v e n t h e a b s e n c e o f c u r v e d i s o l i n e s when i> = 0. B r e n n a n and Bandeen (1970) a l s o d e t e c t e d o n l y a s l i g h t b a c k s c a t t e r i n g component f o r an o c e a n s u r f a c e . H e m i s p h e r i c p l o t s were drawn f o r M i n n i s and H a r r i s o n ' s t a b u l a t e d mode l d a t a ( P . M i n n i s , p e r s o n a l c o m m u n i c a t i o n , 1982) u s i n g t h e g e o m e t r i c c o n s t r a i n t s f o r t h i s s t u d y . The r e s u l t s a l s o show a v e r y weak b a c k s c a t t e r i n g component f o r an o c e a n s u r f a c e . F i g u r e 4 . 1 7 d i s p l a y s a r e f l e c t a n c e minimum a l o n g t h e 90 d e g r e e t r a n s v e r s e p l a n e c o m p a r a b l e t o t h a t s e e n f o r t h e l a n d 86 2 0 0 / 7 9 0 . 4 8 i 0 .40H 0 . 3 2 TR 0 . 2 4 0 . 1 6 0 . 0 8 0 7 :2 8 ' 1 1 : 2 8 ' 1 5 : 2 8 ' 19^2 8 L . A . T . ( H o u r s ) FIGURE 4 . 1 4 D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e (TR) O v e r t h e Sea S u r f a c e f o r J u l i a n Day 2 0 0 / 7 9 . D e t e r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 87 3 0 4 / 7 9 0 . 3 2 1 0 . 2 4 TR 0 . 1 6 0 . 0 8 ' 0 I , , , • 1 0 : 1 9 1 4 : 1 9 L.A.J. ( H o u r s ) FIGURE 4 . 1 5 D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e (TR) O v e r t h e Sea S u r f a c e f o r J u l i a n Day 3 0 4 / 7 9 . D e t e r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 88 0 2 5 / 8 0 0 . 4 0 0 . 3 2 0 . 2 4 -TR 0 . 1 6 0 . 0 8 ' i • • i » 0 9 : 5 0 1 3 : 5 0 1 7 : 5 0 L.A.T. ( H o u r s ) FIGURE 4 . 1 6 D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e (TR) O v e r t h e Sea S u r f a c e f o r J u l i a n Day 0 2 5 / 8 0 . D e t e r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 89 1 8 0 0 ip (degrees) FIGURE 4 . 1 7 Polar Plot of Target Reflectance (TR) For the Sea Surface, as a Function of the Sun Zenith Angle, 9 , and the Sun-Satellite , <P . TR is Dimensionless , x 1 Cf2 . 90 s u r f a c e . H o w e v e r , due t o t h e weaker b a c k s c a t t e r i n g , t h i s minimum i s not s p l i t i n two a l o n g t h e =0 p l a n e , a f e a t u r e p r e s e n t f o r t h e l a n d s u r f a c e ( see F i g u r e s 4 .12 and 4 . 1 3 ) . The a r e a s e l e c t e d t o d e v e l o p t h e sea s u r f a c e BDR m o d e l was c a r e f u l l y c h o s e n t o l i m i t e f f e c t s o f t h e F r a s e r r i v e r p l u m e . H o w e v e r , due t o t h e p r o x i m i t y o f t h e s e d i m e n t plume t o t h e s t u d y a r e a a c o m p a r i s o n was made w i t h t h e d i u r n a l r e f l e c t a n c e p a t t e r n f o r an a r e a o v e r t h e P a c i f i c O c e a n , a t 49 d e g r e e s l a t i t u d e , 127 d e g r e e s l o n g i t u d e ( F i g u r e 4 . 1 8 ) . A c o m p a r i s o n o f F i g u r e s 4 .14 and 4.18 r e v e a l c o n g r u e n t r e s u l t s . The . r e f l e c t a n c e v a l u e s f o r t h e S t r a i t o f G e o r g i a ( F i g u r e 4 . 1 4 ) t e n d t o be 0 . 0 0 5 - 0.01 g r e a t e r t h a n v a l u e s f o r the P a c i f i c O c e a n ( F i g u r e 4 . 1 8 ) . I t i s t h o u g h t t h i s n e g l i g i b l e d i f f e r e n c e i s a t t r i b u t a b l e t o t h e g e n e r a l l y g r e a t e r t u r b i d i t y f o r t h e S t r a i t o f G e o r g i a r a t h e r t h a n t h e i n f l u e n c e o f the F r a s e r r i v e r p lume i t s e l f . Work by A r a n u v a c h a p u n a n d Le B l o n d (1981) seem t o c o n f i r m s u c h a h y p o t h e s i s . 4 . 3 . 2 . 3 C l o u d S u r f a c e The d i u r n a l v a r i a t i o n i n c l o u d r e f l e c t a n c e can be s e e n f rom F i g u r e s 4 . 1 9 t o 4 . 2 1 . F i g u r e s 4 . 1 9 and 4 .20 d e p i c t two d i s t i n c t d i u r n a l p a t t e r n s . C l o u d s a r e known t o p r o d u c e a v a r i e t y o f r e f l e c t a n c e p a t t e r n s ( M i n n i s a n d H a r r i s o n , 1982b) due t o t h e m u l t i f a r i o u s n a t u r e o f t h e c l o u d t o p s t r u c t u r e and 91 200/79 0.24-TR 0.16 0.08-07:28 11:28 15:28 19:28 L.A.T. (Hours) FIGURE 4 .18 D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e (TR) O v e r an Ocean S u r f a c e ( C e n t r e d a t 49 L a t i t u d e and 127 L o n g i t u d e ) f o r J u l i a n Day 2 0 0 / 7 9 . D e t e r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 92 0.8 0.6 TR 0.4 0.2 197/80 07:26 1 1:26 L.A.T. ( H o u r s ) 15:26 19:26 FIGURE 4.19 D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e (TR) Over a C l o u d Top S u r f a c e f o r J u l i a n Day 197/80. D e t e r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 93 245/80 0.8' 0.6 T R 0.4 0.2' i i i • i 08:3 2 1 2:32 1 6:3 2 L.A.T. (Hours) FIGURE 4 .2 0 D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e (TR) O v e r a C l o u d T o p S u r f a c e f o r J u l i a n Day 2 4 5 / 8 0 . D e t e r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 94 FIGURE 4.21 Polar P l o t of Target Reflectance (TR) Over a Cloud Top Surface, as a Function Of the Sun Zenith Angle. 9 , and the S u n - S a t e l l i te Azimuth Angle, i> (Dimensionless , xlO"^ ). 9 5 t h e a s s o c i a t e d shadow e f f e c t s . The d i f f e r e n t r e f l e c t a n c e p a t t e r n s s e e n i n F i g u r e s 4 . 1 9 and 4 .20 a r e l i k e l y t o be a f u n c t i o n o f t h e d i f f e r e n c e s i n c l o u d t o p s t r u c t u r e on t h e s e two d a y s . However t h e g e n e r a l t r e n d o f a l o w e r r e f l e c t a n c e w i t h i n c r e a s i n g z e n i t h a n g l e , s u g g e s t s e i s an i m p o r t a n t c o n t r o l . As 9 i n c r e a s e s , any v e r t i c a l s t r u c t u r e i n t h e c l o u d t o p s u r f a c e r e s u l t s i n g r e a t e r s h a d o w i n g and t h u s l o w e r r e f l e c t a n c e ( see F i g u r e 4 . 1 9 ) . In t h e l i t e r a t u r e b o t h b a c k s c a t t e r i n g and f o r w a r d s c a t t e r i n g f rom c l o u d s u r f a c e s have been w e l l d o c u m e n t e d . The f o r m e r w i t h r e s p e c t t o c l o u d f i e l d s w i t h v e r t i c a l s t r u c t u r e (McKee a n d C o x , 1976) a n d t h e l a t t e r r e g a r d i n g l a y e r c l o u d s ( S a l o m s o n and M a r l e t t , 1968; B r e n n a n and B a n d e e n , 1 9 7 0 ) . Due t o t h e s m a l l a z i m u t h a n g l e be tween t h e s a t e l l i t e and t h e s t u d y a r e a m e a s u r e d r e l a t i v e t o t h e N o r t h P o l e , v e r y l a r g e 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 a r e n o t a p p r o a c h e d . The f o r w a r d s c a t t e r i n g component i s t h e r e f o r e not l i k e l y t o be seen f rom t h e d a t a s e t u s e d i n t h i s t h e s i s , e s p e c i a l l y i f t h e c l o u d a l s o has s t r o n g v e r t i c a l s t r u c t u r e . H o w e v e r , a s u b t l e i n c r e a s e i n r e f l e c t a n c e a r o u n d t h e e a r l y m o r n i n g h o u r s when i> i s a t i t s l a r g e s t ( s ee F i g u r e 4 . 2 ) , s u g g e s t s a p o s s i b l e i n c r e a s e i n r e f l e c t a n c e due t o the f o r w a r d s c a t t e r i n g c o m p o n e n t . 9 6 4 . 3 . 2 . 4 Summary and C o m p a r i s o n o f L a n d , Sea a n d C l o u d S u r f a c e R e f l e c t i v i t y The s a t e l l i t e d a t a u s e d i n t h i s s t u d y a r e a measure o f t h e v i s i b l e e n e r g y l e a v i n g t h e E a r t h - A t m o s p h e r e s y s t e m . I t i s i n h e r e n t l y d i f f i c u l t t o s e p a r a t e t h e s u r f a c e r e f l e c t i o n component a n d a t m o s p h e r i c s c a t t e r i n g c o m p o n e n t . C o m p a r i s o n o f t h e r e f l e c t a n c e p a t t e r n s d e s c r i b e d f o r t h e t h r e e s u r f a c e s i n v e s t i g a t e d ( see S e c t i o n s 4 . 3 . 2 . 1 t o 4 . 3 . 2 . 3 ) a l l o w i n f e r e n c e s t o be made f o r t h e s e two m a j o r c o m p o n e n t s . The o v e r a l l r e f l e c t a n c e p a t t e r n s f o r t h e sea and l a n d s u r f a c e s a r e s i m i l a r ( compare F i g u r e s 4 . 1 , 4 . 7 - 4.11 w i t h 4 . 1 4 - 4 . 1 6 ) . The d i u r n a l p a t t e r n o f r e f l e c t a n c e f o r t h e l a n d s u r f a c e s a r e c h a r a c t e r i s t i c a l l y W - s h a p e d , and f o r t h e sea s u r f a c e , U - s h a p e d . The p r o x i m i t y o f t h e s i t e s u s e d t o d e v e l o p t h e L a n d and Sea BDR m o d e l s ( see F i g u r e 3 . 1 ) j u s t i f i e s t h e a s s u m p t i o n o f a t m o s p h e r i c h o m o g e n e i t y be tween t h e s e two a r e a s . B a c k s c a t t e r i n g i s o n l y c l e a r l y e v i d e n t f o r t h e l a n d s u r f a c e s ( see F i g u r e 4 . 1 , 4 . 7 - 4 . 1 1 ) and t h e r e f o r e i s p r o b a b l y a s u r f a c e i n d u c e d phenomenon . T h i s r e l a t i v e maximum i n t h e b a c k s c a t t e r i n g d i r e c t i o n may be a t t r i b u t e d t o v e r t i c a l s t r u c t u r e s o f t h e l a n d s u r f a c e , c r e a t i n g an a b s e n c e o f shadows when t h e Sun and v i e w i n g s e n s o r a r e a l i g n e d ( M i n n i s and H a r r i s o n , 1 9 8 2 b ) . The i n d i s t i n c t b a c k s c a t t e r i n g component o f t h e sea s u r f a c e i s p r o b a b l y a f u n c t i o n o f i t s g r e a t e r s p e c u l a r 9 7 n a t u r e r e l a t i v e t o a l a n d s u r f a c e . The g e o m e t r i c c o n s t r a i n t s o f t h i s s t u d y make i t d i f f i c u l t t o d e t e r m i n e t h e d e g r e e t o w h i c h f o r w a r d s c a t t e r i n g a c c o u n t s f o r t h e e x p o n e n t i a l a p p e a r a n c e o f t h e r e f l e c t a n c e a t t h e b e g i n n i n g and end o f a day f o r t h e l a n d and sea s u r f a c e s . As 9 i s l a r g e when i s a t a maximum ( f o r t h i s s t u d y a maximum o f 1 3 6 ° 52 ' was a c h i e v e d ) the g r e a t e r r e f l e c t i o n may be a f u n c t i o n o f t h e z e n i t h a n g l e and an a r t i f a c t o f t h e n o r m a l i z i n g p r o c e d u r e . In t h e w i n t e r months when 8 d o e s no t a p p r o a c h 90 d e g r e e s , t h e o b s e r v e d s h a r p i n c r e a s e i n r e f l e c t i o n c a n n o t be a t t r i b u t a b l e t o a f o r w a r d s c a t t e r i n g p r o c e s s . I t i s p r o b a b l y n o t a s u r f a c e r e f l e c t i v i t y phenomena as t h e same f e a t u r e i s s een f o r b o t h t h e l a n d and sea s u r f a c e . The e x t r e m i t i e s o f t h e d i u r n a l r e f l e c t i o n p a t t e r n s c o u l d be a c o m b i n a t i o n o f two f e a t u r e s w h i c h a r e i n d e p e n d e n t o f <P : 1) t h e d i v i s i o n by c o s 9 i n t h e n o r m a l i z i n g p r o c e d u r e ; a n d 2) i n c r e a s e d o p t i c a l p a t h l e n g t h s a t l a r g e z e n i t h a n g l e s p r o d u c i n g g r e a t e r a t m o s p h e r i c s c a t t e r i n g . On t h e o t h e r hand c l o u d r e f l e c t a n c e p a t t e r n s show a marked d e c r e a s e i n r e f l e c t a n c e w i t h i n c r e a s i n g e ( s ee F i g u r e 4 . 1 9 and 4 . 2 0 ) , t h e r e v e r s e o f t h a t f o r t h e l a n d and sea s u r f a c e s . T h i s m a j o r c o n t r a s t i s p r o b a b l y due t o e l e v a t i o n d i f f e r e n c e s be tween t h e c l o u d t o p s and t h e E a r t h ' s s u r f a c e . The h e i g h t o f 98 t h e c l o u d t o p e f f e c t s t h e s c e n e r e f l e c t i v i t y due t o i t s i n f l u e n c e on t h e o p t i c a l p a t h l e n g t h and s c e n e b r i g h t n e s s . W i t h r e s p e c t t o t h e f o r m e r , when m o n i t o r i n g a c l o u d t o p s u r f a c e r e l a t i v e t o t h e E a r t h ' s s u r f a c e , t h e o p t i c a l p a t h l e n g t h i s s m a l l e r . T h i s r e s u l t s i n a s u b s t a n t i a l l y r e d u c e d a t m o s p h e r i c s c a t t e r i n g c o m p o n e n t , e s p e c i a l l y as the ma jor p r o p o r t i o n o f s u c h s c a t t e r i n g o c c u r s be low t y p i c a l c l o u d h e i g h t s . Thus c l o u d s u r f a c e r e f l e c t i v i t y d o m i n a t e s o v e r t h e a t m o s p h e r i c s c a t t e r i n g c o m p o n e n t , r e s u l t i n g i n a marked d i f f e r e n t d i u r n a l r e f l e c t i v i t y p a t t e r n . The s c e n e b r i g h t n e s s a l s o i n f l u e n c e s t h e c l o u d s u r f a c e r e f l e c t i v i t y p a t t e r n a t t h e b e g i n n i n g and end o f a d a y . Compared t o the g r o u n d s u r f a c e , t h e t i m e o f s u n r i s e and s u n s e t f o r a c l o u d t o p s u r f a c e o c c u r s e a r l i e r and l a t e r r e s p e c t i v e l y . As t h e t i m e s o f s u n r i s e and s u n s e t a r e d e t e r m i n e d u s i n g t h e g e o m e t r i c a l r e l a t i o n s h i p be tween t h e E a r t h ' s s u r f a c e a n d t h e S u n , t h e c l o u d r e f l e c t i o n a p p e a r s r e l a t i v e l y h i g h . T h i s may w e l l o f f s e t the p r o b l e m a s s o c i a t e d w i t h t h e n o r m a l i z i n g p r o c e d u r e e n c o u n t e r e d when d e a l i n g w i t h the two E a r t h s u r f a c e s . I n t e r image f l u c t u a t i o n s i n r e f l e c t a n c e a p p e a r g r e a t e r f o r the c l o u d s u r f a c e t h a n f o r t h e l a n d and sea s u r f a c e s . T h i s i s a f u n c t i o n o f v a r i a b l e c l o u d t o p s t r u c t u r e and a c o n s e q u e n c e o f t h e non l i n e a r s a t e l l i t e c a l i b r a t i o n c u r v e ( see F i g u r e 99 3 . 3 ) . Changes i n b r i g h t n e s s o f t h e same m a g n i t u d e f o r l a r g e b r i g h t n e s s c o u n t v a l u e s ( t y p i c a l o f c l o u d y s c e n e s ) r e s u l t i n a g r e a t e r c h a n g e o f t h e c a l c u l a t e d t a r g e t r e f l e c t a n c e t h a n f o r r e l a t i v e l y s m a l l b r i g h t n e s s c o u n t v a l u e s ( t y p i c a l o f c l e a r sky c o n d i t i o n s ) . T h u s t h e e x p o n e n t i a l n a t u r e o f t h e c a l i b r a t i o n c u r v e p r o d u c e s g r e a t e r ' n o i s e ' i n t h e c l o u d y d a t a s e t s . T h r e e ma jor c o n c l u s i o n s may be i n f e r r e d f rom a c o m p a r i s o n o f t h e s u r f a c e r e f l e c t i o n p a t t e r n s : 1 ) b a c k s c a t t e r i n g i s a s u r f a c e i n d u c e d phenomena ; 2) t h e i n s t a b i l i t y a t l a r g e z e n i t h a n g l e s i s a f u n c t i o n o f t h e n o r m a l i z i n g p r o c e d u r e and i n c r e a s e d a t m o s p h e r i c s c a t t e r i n g ; and 3 ) t h e d i f f e r e n c e between E a r t h s u r f a c e and c l o u d s u r f a c e r e f l e c t i v i t y p a t t e r n s a t l a r g e z e n i t h a n g l e s c a n be a t t r i b u t e d , a t l e a s t i n p a r t , t o c l o u d h e i g h t w h i c h d e c r e a s e s t h e o p t i c a l p a t h and i n c r e a s e s t h e i l l u m i n a t i o n o f t h e s c e n e . 4 . 3 . 3 D e v e l o p m e n t o f BDR M o d e l s 4 . 3 . 3 . 1 G e n e r a l The s p e c u l a r t e n d e n c i e s o f n a t u r a l s u r f a c e s have been w e l l 1 0 0 d o c u m e n t e d i n t h e l i t e r a t u r e ( e . g . B a r t m a n , 1967; S a l o m o n s o n a n d M a r l a t t , 1968; R u f f e t a l . , 1968; B r e n n a n and B a n d e e n , 1970; K r i e b e l , 1976; E a t o n and D i r m h i r n , 1 9 7 9 ) . S i m i l a r a n i s o t r o p i c r e f l e c t a n c e f o r n a t u r a l s u r f a c e s has been f o u n d f o r t h e SMS-2 d a t a s e t u s e d i n t h i s s t u d y ( see S e c t i o n 4 . 3 . 2 ) . The SMS-2 s a t e l l i t e s a m p l e s u p w e l l i n g e n e r g y i n a s m a l l s e t o f c o n f i n e d s o l i d a n g l e s . A l t h o u g h t h e r e f l e c t i n g s u r f a c e and a t m o s p h e r e may r e m a i n u n i f o r m , when t h e r e f l e c t i o n c h a r a c t e r i s t i c s a r e a s sumed t o be L a m b e r t i a n t h e d i u r n a l p a t t e r n o f the s a t e l l i t e r e f l e c t a n c e d a t a s u g g e s t c h a n g e s i n t h e E a r t h - A t m o s p h e r e c o l u m n . The r e s u l t a n t e r r o r i s a f u n c t i o n o f t h e d e g r e e o f a n i s o t r o p y . , To d e t e r m i n e t h e amount o f e n e r g y r e f l e c t e d i n a l l d i r e c t i o n s i t i s n e c e s s a r y t o e i t h e r measure the r e f l e c t e d s o l a r e n e r g y i n a l l d i r e c t i o n s , o r t o make one measurement and c o m b i n e i t w i t h an u n d e r s t a n d i n g o f t h e d i r e c t i o n a l c h a r a c t e r o f t h e r e f l e c t e d e n e r g y . The SMS-2 r a d i o m e t e r d o e s no t m e a s u r e r e f l e c t e d e n e r g y i n a l l d i r e c t i o n s s i m u l t a n e o u s l y . T h u s BDR m o d e l l i n g t e c h n i q u e s have been d e v e l o p e d i n an a t t e m p t t o remove t h e a n i s o t r o p y i n t h e r e f l e c t i o n f i e l d . The c l a r i t y o f t h e S t e p h e n s e t a l . (1981) a p p r o a c h t o BDR m o d e l l i n g has been i n f l u e n t i a l on t h e f o l l o w i n g d e s c r i p t i o n o f BDR m o d e l d e v e l o p m e n t . The SMS-2 r a d i o m e t e r m e a s u r e s r e f l e c t e d s h o r t w a v e 101 r a d i a t i o n N R (8 , ^ , Z ) as a f u n c t i o n o f t h e s o l a r z e n i t h a n g l e , 9-, S u n - s a t e l l i t e a z i m u t h , , and t h e 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 , Z . The m e a s u r e d i n s t a n t a n e o u s t a r g e t r e f l e c t a n c e a t t h e s a t e l l i t e i s e s t i m a t e d b y : T R ( K ) = N R ( K , 6 v * , Z ) / C O S 8 (4 .2 ) where K i s t h e s u r f a c e t y p e and TR i s an a n i s o t r o p i c a l b e d o . The mean r e f l e c t e d r a d i a n c e (TR) o v e r a l l d i r e c t i o n s f o r a g i v e n s o l a r z e n i t h a n g l e i s c a l c u l a t e d f r o m : r2Tr TR (K) r 2 N R ( K , 6 ,<J> , Z) d C O S 8 d i> C O S 9 o J o Y ? d C 0 S 9 d * (4 .3 ) T r u e r e f l e c t i o n m e a s u r e m e n t s by a s c a n n i n g r a d i o m e t e r r e q u i r e i n t e g r a t i o n f o l l o w i n g e q u a t i o n 4 . 3 . The a n g u l a r l i m i t a t i o n s i n h e r e n t i n t h e s a t e l l i t e d a t a s e t make t h i s i n t e g r a t i o n i m p o s s i b l e . Thus a m o d i f i e d a p p r o a c h i s r e q u i r e d . A s s u m i n g t h a t b o t h t h e s u r f a c e and a t m o s p h e r i c c o n d i t i o n s do not c h a n g e , an i n t e g r a t i o n s i m i l a r t o e q u a t i o n 4 . 3 c a n be p e r f o r m e d c o v e r i n g p a r t of t h e t o t a l h e m i s p h e r e , TR* and f o r a g i v e n s a t e l l i t e z e n i t h a n g l e : TR*( K) = I I NR (K , e , +, Z) d e d i p c o s (4 .4 ) 102 where ' L ' c o v e r s t h e l i m i t s f o r t h a t p a r t o f t h e h e m i s p h e r e u s e d i n t h e i n t e g r a t i o n . D i v i d i n g E q u a t i o n 4.4 by t h e a r e a o v e r w h i c h i n t e g r a t i o n i s p o s s i b l e g i v e s : NR ( K , e , <l>, Z ) d e d i p * TR (K ) = J L J COS 9 J J d 9 d * (4.5) where T R * i s t h e mean t a r g e t r e f l e c t a n c e v a l u e . T R * a p p r o x i m a t e s t h e L a m b e r t i a n r e f l e c t a n c e v a l u e f o r a s u r f a c e (K) and t h e r e f o r e a p p r o x i m a t e s T R . To c o n v e r t TR t o TR a f u n c t i o n p ( K , e , * , Z ) i s i n t r o d u c e d s u c h t h a t : p ( K , 9 , *, 2 ) = TR(K) / TR*( K ) * TR (K ) / TR (K) (4.6) a l l o w i n g a t r u e e s t i m a t e o f the r e f l e c t a n c e by: T R ( K ) = T R ( K ) p ( K , 9 , K Z ) (4-7) The (K,9, <P , Z ) i s known as a b i d i r e c t i o n a l r e f l e c t a n c e (BDR) f u n c t i o n . TR i s e s s e n t i a l l y a BDR c o r r e c t e d TR v a l u e and h e n c e w i l l be d e f i n e d as T R ' . 103 Due t o t h e s l i g h t l y d i f f e r e n t p r o c e d u r e s f o l l o w e d i n d e v e l o p i n g t h e c l e a r sky s u r f a c e BDR m o d e l s and t h e c l o u d s u r f a c e BDR m o d e l , t h e y w i l l be o u t l i n e d s e p a r a t e l y i n t h e f o l l o w i n g two s e c t i o n s ( 4 . 3 . 3 . 2 and 4 . 3 . 3 . 3 ) . 4 . 3 . 3 . 2 L a n d and Sea S u r f a c e R e f l e c t a n c e M o d e l l i n g Two s i m i l a r a p p r o a c h e s were i n v e s t i g a t e d i n t h e d e v e l o p m e n t o f t h e c l e a r sky BDR m o d e l s . The f i r s t t e c h n i q u e was d e v e l o p e d u s i n g t h e d i u r n a l p a t t e r n s o f t a r g e t r e f l e c t a n c e ( e . g . F i g u r e s 4 . 7 t o 4.11 and 4 . 1 4 t o 4 . 1 6 ) and t h e s e c o n d t e c h n i q u e i n c o r p o r a t e d t h e p o l a r p l o t s of t a r g e t r e f l e c t a n c e ( e . g . F i g u r e s 4 . 1 2 , 4 . 1 3 and 4 . 1 7 ) . F o r t h e f o r m e r , t r i g o n o m e t r i c f u n c t i o n s b a s e d on t h e S u n , s a t e l l i t e , s u r f a c e g e o m e t r i c a l p o s i t i o n i n g were u s e d t o p r o v i d e t h e b e s t f i t t o t h e d i u r n a l c u r v e s u s i n g a s t e p w i s e m u l t i p l e r e g r e s s i o n r o u t i n e . V a r i o u s t r i g o n o m e t r i c f u n c t i o n s were t e s t e d . The s e l e c t i o n was b a s e d on b o t h known p h y s i c a l l y d e p e n d e n t f u n c t i o n s and t h o s e w h i c h v i s u a l l y r e s e m b l e d the o b s e r v e d - d i u r n a l p a t t e r n s . The s e t o f t r i g o n o m e t r i c f u n c t i o n s w h i c h p r o d u c e d t h e b e s t f i t f o r t h e l a n d and sea s u r f a c e d i u r n a l r e f l e c t a n c e p a t t e r n s a r e d e s c r i b e d i n T a b l e 4 . 1 . The forms o f t h e f u n c t i o n s a r e d e p i c t e d i n F i g u r e s 4 . 2 2 a and 4 . 2 2 b . The - c o s e and t h e s i n e 104 T A B L E 4 .1 T r i g o n o m e t r i c F u n c t i o n s u s e d t o M o d e l D i u r n a l R e f l e c t a n c e P a t t e r n s f o r S u r f a c e s U n d e r C l e a r S k i e s . The V a r i a b l e s a r e L i s t e d i n O r d e r o f I m p o r t a n c e ( i . e . t h e O r d e r i n W h i c h t h e V a r i a b l e s A p p e a r e d i n t h e S t e p w i s e R e g r e s s i o n ) . L a n d ( N ) L a n d ( S ) Sea 2 s i n e c o s 0 2 s i n e c o s i> t a n 9 t a n e t a n 9 - c o s 9 - c o s 8 - c o s 9 s i n e / 2 105 (a) 1 . 0 , L.A.T. ( H o u r s ) Cos 0 •Sin ( 6 / 2 ) S i n e C o s ^ •Tan 9 ( b ) 16 12 u. Z OO *> LU 81 1 2 L.A.T. ( H o u r s ) 1 6 20 FIGURE 4 . 2 2 Form o f t h e F o u r T r i g o n o m e t r i c F u n c t i o n s U s e d t o M o d e l t h e Sea and L a n d D i u r n a l R e f l e c t a n c e P a t t e r n s . V a l u e s Were G e n e r a t e d F o r J u l i a n Day 1 8 3 / 8 0 . 106 c o s ^ t e r m s have a p h y s i c a l b a s i s . The f o r m e r a c c o u n t s f o r t h e S u n ' s c h a n g i n g i n t e n s i t y and t h e l a t t e r s i m u l a t e s b o t h t h e b a c k s c a t t e r i n g and f o r w a r d s c a t t e r i n g c o m p o n e n t s of t h e a n i s o t r o p y . S i n c e b a c k s c a t t e r i n g i s o n l y d i s c e r n i b l e o v e r t h e l a n d s u r f a c e s (compare F i g u r e s 4.1 and 4 . 1 4 ) t h i s f u n c t i o n was f o u n d t o be of s t a t i s t i c a l i m p o r t a n c e o n l y f o r t h e l a n d s u r f a c e m o d e l s . B o t h t e r m s were i n c o r p o r a t e d i n T a r p l e y ' s (1979) minimum b r i g h t n e s s e q u a t i o n . T a r p l e y i n c l u d e d a t h i r d t e r m , c o s e c o s ip . H o w e v e r , t h i s was f o u n d t o h a v e n e g l i g i b l e i m p o r t a n c e i n t h e s t a t i s t i c a l m o d e l and i n a number of c a s e s i t s i n c l u s i o n was d e t r i m e n t a l t o m o d e l p e r f o r m a n c e . The o t h e r t r i g o n o m e t r i c f u n c t i o n s , t a n Z and - s i n e / 2 a r e s e m i - e m p i r i c a l . The f o r m e r h i g h l i g h t s t h e e x p o n e n t i a l a p p e a r a n c e o f t h e r e f l e c t a n c e when e a p p r o a c h e s 90 d e g r e e s , w h i l e t h e l a t t e r has l i t t l e known p h y s i c a l b a s i s . The s i n e / 2 t e r m i s f o u n d o n l y i n t h e sea s u r f a c e m o d e l . The f o l l o w i n g e q u a t i o n s a d e q u a t e l y r e p l i c a t e t h e d i u r n a l r e f l e c t i o n p a t t e r n s . F o r t h e Sea s u r f a c e : TR = 0 . 3 6 0 4 - 0 . 2442 c o s 9 - 0 . 3359 s i n 9 / 2 + 0 .0086 t a n 6 (4 .8) f o r t h e L a n d ( N ) s u r f a c e : TR = 0 . 0892 - 0 . 0355 c o s 9 + 0 . 1 0 0 2 s i n 9 COS 2<JJ + 0 . 0082 t a n 9 (4 .9 ) 107 a n d f o r t h e L a n d ( S ) s u r f a c e : TR = 0 . 1 2 3 6 - 0 .0400 c o s 9 + 0 . 1 0 4 5 s i n e c o s 2 <Jr+ 0 .0078 t a n 9 (4 .10 ) A c o m p a r i s o n o f t h e p r e d i c t e d t a r g e t r e f l e c t a n c e v a l u e s u s i n g t h e above e q u a t i o n s and t h e a c t u a l v a l u e s ( see T a b l e 4 . 2 ) show t h e l a n d s u r f a c e BDR m o d e l s t o be t h e most c o m p e t e n t . However t h e p e r f o r m a n c e of a l l t h r e e m o d e l s i s v e r y s a t i s f a c t o r y . E q u a t i o n s 4 .8 t o 4 . 1 0 were u s e d t o d e v e l o p BDR m o d e l s by a p p l y i n g t h e f u n c t i o n s t o h e m i s p h e r i c a l c o o r d i n a t e s and f o l l o w i n g t h e i n t e g r a t i o n p r o c e d u r e o u t l i n e d i n S e c t i o n 4 . 3 . 3 . 1 . An a l t e r n a t i v e more d i r e c t a p p r o a c h t h a n t h e p r e c e d i n g s t a t i s t i c a l - e m p i r i c a l m o d e l l i n g p r o c e d u r e was a l s o d e v e l o p e d . The s e c o n d t e c h n i q u e i s c o m p l e t e l y e m p i r i c a l and p r o v i d e s a more e x p e d i e n t a p p r o a c h i n a c c o u n t i n g f o r t h e a n i s o t r o p i c r e f l e c t a n c e . H e m i s p h e r i c p l o t s o f t h e u n c o r r e c t e d t a r g e t r e f l e c t a n c e v a l u e s ( e . g . F i g u r e s 4 . 1 2 , 4 . 1 3 and 4 . 1 7 ) were i n t e g r a t e d f o l l o w i n g t h e p r o c e d u r e o u t l i n e d i n S e c t i o n 4 . 3 . 3 . 1 . The r e s u l t i n g p ( K , 9 , , z ) f a c t o r s a r e d e p i c t e d g r a p h i c a l l y i n F i g u r e s 4 . 2 3 t o 4 . 2 5 f o r t h e L a n d ( N ) , L a n d ( S ) and Sea a r e a s , r e s p e c t i v e l y . T h o s e a r e a s where r h o (p) i s l e s s t h a n one c o r r e s p o n d t o an u n d e r e s t i m a t i o n o f r e f l e c t i o n by the s a t e l l i t e due t o r e f l e c t e d s o l a r r a d i a t i o n b e i n g 108 T A B L E 4 . 2 P e r f o r m a n c e o f t h e C l e a r Sky BDR M o d e l s i n R e p l i c a t i n g t h e T a r g e t R e f l e c t a n c e ( T R ) . V a l u e s a r e D i m e n s i o n l e s s . L a n d (N) L a n d (S) Sea Mean o f TR 0 . 1 231 0 . 1 569 0 .0888 S t a n d a r d D e v i a t i o n o f TR 0 . 0260 0 . 0268 0 .0246 C o e f f i c i e n t o f D e t e r m i n a t i o n ( r 2 ) 0 . 865 0 . 878 0 .738 S t a n d a r d E r r o r o f TR 0 . 0097 0. 0095 0 .0128 109 1 8 0 0 ip (degrees) FIGURE 4 .2 3 BDR M o d e l F o r t h e L a n d ( N ) S u r f a c e U s i n g p V a l u e s ( D i m e n s i o n l e s s , x i O " 1 ) . 110 FIGURE 4 . 2 4 BDR M o d e l F o r t h e L a n d ( S ) S u r f a c e U s i n g p V a l u e s ( D i m e n s i o n l e s s , X 1 0 ~ 1 ) . 1 1 1 180 0 t|) (degrees) FIGURE 4 . 2 5 BDR M o d e l F o r the Sea S u r f a c e U s i n g p V a l u e s ( D i m e n s i o n l e s s , x 1 0"1 ) . 112 d i r e c t e d away f rom t h e s a t e l l i t e . Thus t h e t a r g e t r e f l e c t a n c e n e e d s t o be i n c r e a s e d by d i v i d i n g by t h e r h o v a l u e ( see E q u a t i o n 4 . 7 ) . When v a l u e s o f r h o a r e g r e a t e r t h a n o n e , the s a t e l l i t e i s o v e r e s t i m a t i n g a n d t h u s d i v i s i o n by t h e r h o v a l u e w i l l r e d u c e t h e r e f l e c t i o n a p p r o p r i a t e l y . T h u s t h e r h o v a l u e s e n a b l e t h e a n i s o t r o p i c r e f l e c t a n c e p r o p e r t i e s o f t h e E a r t h ' s s u r f a c e and a t m o s p h e r e t o be r e m o v e d . 4 . 3 . 3 . 3 C l o u d S u r f a c e R e f l e c t a n c e M o d e l l i n g . Due t o t h e c o m p l e x r a d i a t i v e p r o p e r t i e s o f c l o u d s ( see S e c t i o n 4 . 1 ) , a s i m p l i f i c a t i o n o f t h e a p p r o a c h u s e d f o r t h e c l e a r sky BDR m o d e l d e v e l o p m e n t was a d o p t e d . In o r d e r t o remove t h e c o m p l e x v a r i a b i l i t y r e s u l t i n g f rom t h e g e o m e t r y o f c l o u d t o p s u r f a c e s , t h e r e f l e c t a n c e d a t a were smoothed p r i o r t o d e v e l o p i n g t h e h e m i s p h e r i c a l p l o t s . T h i s was i m p l e m e n t e d by f i t t i n g a r e l a t i v e l y s i m p l e s e c o n d o r d e r p o l y n o m i a l f u n c t i o n t o t h e r e f l e c t a n c e d a t a f o r e a c h o f t h e f i v e m o d e l l i n g d a y s ( see F i g u r e 4 . 2 6 ) . T h e s e p o l y n o m i a l f u n c t i o n s were a p p l i e d t o a h e m i s p h e r i c a l p l o t and r h o v a l u e s g e n e r a t e d ( see F i g u r e 4 . 2 7 ) , f o l l o w i n g t h e p r o c e d u r e o u t l i n e d i n S e c t i o n 4 . 3 . 3 . 1 . A c o m p a r i s o n between t h e mean i n t e g r a t e d t a r g e t r e f l e c t a n c e (TR) b a s e d on t h e s e c o n d o r d e r p o l y n o m i a l f i t and 113 0.8i 363/79 0.6-TR 0.4 0.2 Target Reflectance • '2nd Order Polynomial Fit 09:30 1 3:30 L.A.T. (Hours) 17:30 FIGURE 4 . 2 6 D i u r n a l P a t t e r n o f T a r g e t R e f l e c t a n c e O v e r a C l o u d T o p S u r f a c e f o r J u l i a n Day 363 /79 and a S e c o n d O r d e r P o l y n o m i a l F i t t o o t h e D a t a . D e t r m i n e d From SMS-2 S a t e l l i t e D a t a . TR i s D i m e n s i o n l e s s . 114 FIGURE 4 .2 7 BDR M o d e l F o r a C l o u d T o p S u r f a c e U s i n g p V a l u e s ( D i m e n s i o n l e s s , x 1 0"1 ) . 115 t h e ' r a w ' t a r g e t r e f l e c t a n c e d a t a (TR) r e s u l t e d i n s i m i l a r v a l u e s , 0 . 6 3 8 9 and 0 . 6 4 0 3 r e s p e c t i v e l y . T h i s s u g g e s t s t h a t t h e s e c o n d o r d e r p o l y n o m i a l f i t i s a d e q u a t e l y d e s c r i b i n g t h e o v e r a l 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 o f t h e c l o u d s u r f a c e w h i l e i g n o r i n g t h e n o i s e a s s o c i a t e d w i t h t h e r e f l e c t a n c e v a l u e s f o r i n d i v i d u a l i m a g e s . 4 . 4 V e r i f i c a t i o n o f BDR M o d e l s F o l l o w i n g t h e d e v e l o p m e n t o f a m o d e l , v e r i f i c a t i o n i s n e c e s s a r y t o p r o v i d e e v i d e n c e t h a t t h e m o d e l r e p l i c a t e s r e a l i t y . V e r i f i c a t i o n p r o c e d u r e s r e q u i r e an i n d e p e n d e n t d a t a s e t a g a i n s t w h i c h t h e m o d e l c a n be t e s t e d . G i v e n t h e c o n s t r a i n t s o f t h e a v a i l a b l e d a t a s e t , t h e f o l l o w i n g d a t a were s e l e c t e d . F o r t h e s ea s u r f a c e m o d e l , J u l i a n d a y s 1 9 6 / 7 9 , 2 5 5 / 7 9 , 2 5 7 / 7 9 , 2 9 3 / 7 9 , 3 6 1 / 7 9 , 0 3 0 / 8 0 , 1 2 1 / 8 0 , were c h o s e n . The same d a t a s e t , e x c l u d i n g d a y s 293 /79 and 030 /80 (as a r e s u l t of c l o u d c o n t a m i n a t i o n ) , was u s e d t o v e r i f y b o t h t h e l a n d s u r f a c e BDR m o d e l s . The v e r i f i c a t i o n d a t a s e t p r o v i d e s good t e m p o r a l c o v e r a g e a n d t h e r e f o r e a d e q u a t e l y t e s t s t h e f u l l r a n g e o f S u n - s a t e l l i t e g e o m e t r i c p o s i t i o n s . F i g u r e s 4 . 2 8 t o 4 . 3 0 show a c l o s e c o r r e s p o n d e n c e between t h e m e a s u r e d d i u r n a l t a r g e t r e f l e c t a n c e , TR ( t a k e n f rom t h e 116 0.24 oTTil ' 1 1 : 5 5 1 5 ^ 5 5 ' 77! 5 5 L . A . T . ( H o u r s ) FIGURE 4 . 2 8 V e r i f i c a t i o n o f t h e Sea BDR M o d e l F o r J u l i a n Day 1 9 6 / 7 9 . i s D i m e n s i o n l e s s . 117 FIGURE 4 . 2 9 V e r i f i c a t i o n o f t h e TR i s D i m e n s i o n l e s s . L a n d ( N ) BDR M o d e l F o r J u l i a n Day 1 2 1 / 8 0 . 118 196/79 0.4CH 0.32-0.24' TR 0.16-0.081 i i i i i i i 06:55 10:55 14:55 18:55 L.A.T. (Hours) FIGURE 4 .30 V e r i f i c a t i o n o f t h e L a n d ( S ) BDR M o d e l F o r J u l i a n Day 1 9 6 / 7 9 . TR i s D i m e n s i o n l e s s . 119 v e r i f i c a t i o n d a t a s e t ) , and t h e p r e d i c t e d mode l v a l u e s , T R , f r o m e q u a t i o n s 4 . 8 t o 4 . 1 0 . The S t a n d a r d E r r o r o f t h e m o d e l p r e d i c t i o n f o r t h e c o m p l e t e v e r i f i c a t i o n d a t a s e t was 0 . 0 1 2 , 0 . 0 1 0 and 0 .010 f o r the S e a , L a n d ( N ) and L a n d ( S ) , r e s p e c t i v e l y . T a b l e 4 . 3 p r o v i d e s a f u l l e r s e t o f s t a t i s t i c s f o r t h e v e r i f i c a t i o n . T h e s e r e s u l t s a r e c o m p a r a b l e t o t h o s e shown i n T a b l e 4 .2 and t h e r e f o r e i n d i c a t e s a t i s f a c t o r y m o d e l p e r f o r m a n c e s . V e r i f i c a t i o n u s i n g t h e h e m i s p h e r i c a l p l o t s r e v e a l e d t h e o v e r a l l m o d e l c a p a b i l i t i e s ( see F i g u r e s 4.31 t o 4 . 3 3 ) . T h i s p r o c e d u r e i n v o l v e d t h e s u b t r a c t i o n o f t h e o b s e r v e d t a r g e t r e f l e c t a n c e f rom t h e m o d e l l e d t a r g e t r e f l e c t a n c e . P o s i t i v e a r e a s c o r r e s p o n d t o m o d e l o v e r e s t i m a t i o n o f t h e t a r g e t r e f l e c t a n c e and t h e n e g a t i v e a r e a s t o m o d e l u n d e r e s t i m a t i o n . F i g u r e s 4.31 t o 4 . 3 3 show t h a t t h e mode l p e r f o r m s w e l l e x c e p t f o r t h o s e s i t u a t i o n s when 9 i s n e a r i t s maximum v a l u e . T h i s was e x p e c t e d as t h e f o r m u l a f o r c a l c u l a t i n g t a r g e t r e f l e c t a n c e becomes u n s t a b l e u n d e r t h e s e c o n d i t i o n s . S i n c e r a d i a t i o n q u a n t i t i e s a r e r e l a t i v e l y s m a l l when t h e Sun i s low i n t h e sky t h e s e e r r o r s a r e o f m i n o r i m p o r t a n c e t o t h e o v e r a l l m o d e l p e r f o r m a n c e . V e r i f i c a t i o n o f t h e c l o u d s u r f a c e m o d e l was no t p o s s i b l e due t o a l a c k o f d a t a . The t e m p o r a l and s p a t i a l v a r i a b i l i t y o f c l o u d s w i l l l i k e l y r e s u l t i n a d e t e r i o r a t i o n i n t h e 120 T A B L E 4 . 3 V e r i f i c a t i o n S t a t i s t i c s f o r t h e C l e a r Sky BDR M o d e l s . Where TR i s t h e ' r a w ' T a r g e t R e f l e c t a n c e , and TR i s t h e E s t i m a t e d T a r g e t R e f l e c t a n c e U s i n g the BDR M o d e l . V a l u e s a r e D i m e n s i o n l e s s . L a n d (N) L a n d (S) Sea Mean of TR 0 . 1 178 0 . 1518 0 .0865 Mean o f TR 0 . 1 180 0 . 1 543 0 .0845 S t a n d a r d D e v i a t i o n o f TR 0 . 0236 0 . 021 9 0 .0227 S t a n d a r d D e v i a t i o n o f TR 0 . 0217 0 . 0236 0 .021 5 C o e f f i c i e n t o f D e t e r m i n a t i o n ( r 2 ) 0 . 8036 0 . 8238 0 .7121 S t a n d a r d E r r o r o f TR 0 . 0097 0 . 01 00 0 .0116 121 \jj (degrees) FIGURE 4.31 V e r i f i c a t i o n (TR - TR) P o l a r P l o t F o r t h e Sea S u r f a c e BDR M o d e l U s i n g p V a l u e s ( D i m e n s i o n l e s s , x l O " 1 ) . 122 FIGURE 4 . 3 2 V e r i f i c a t i o n (TR - TR) o f t h e P o l a r P l o t F o r t h e L a n d ( N ) S u r f a c e BDR M o d e l U s i n g V a l u e s ( D i m e n s i o n l e s s , x 1 0"1 ) . 123 180 / * L * P -x 90 -0 V , « X • \ ') I * — " ^ l • " " \ * \ " • • M f * " I" r • " » • / M / • " S ' / / II / • • ) y 0 ip (degrees) FIGURE 4 . 3 3 V e r i f i c a t i o n (TR - TR) o f t h e P o l a r P l o t F o r t h e L a n d ( S ) S u r f a c e BDR M o d e l U s i n g p V a l u e s ( D i m e n s i o n l e s s , x 10" 1 ). 124 p e r f o r m a n c e o f the BDR m o d e l r e l a t i v e t o t h a t f o r E a r t h s u r f a c e s . V e r i f i c a t i o n o f t h e c l o u d mode l i s n e c e s s a r y t o i m p r o v e and s u b s t a n t i a t e t h e p r e s e n t C l o u d BDR m o d e l . 4 . 5 A p p l y i n g t h e BDR M o d e l s t o t h e S a t e l l i t e D a t a . BDR c o r r e c t i o n s a r e i n v a r i a b l y a p p l i e d u s i n g a c o r r e c t i o n f a c t o r , s u c h as ' r h o ' ( see S t e p h e n s e t a l . , 1981) a n d ' c h i ' ( see H a r r i s o n and M i n n i s , 1 9 8 1 ) . Such a c o n c e p t u a l a p p r o a c h was a l s o a d o p t e d i n t h i s s t u d y a l o n g w i t h a more d i r e c t m e t h o d . The l a t t e r i n c o r p o r a t e s a more f u n d a m e n t a l p a r a m e t e r , t h e t a r g e t r e f l e c t a n c e . B o t h a p p r o a c h e s a r e d e s c r i b e d i n t h i s s e c t i o n and t h e r e s u l t s c o m p a r i n g t h e two t e c h n i q u e s a r e p r e s e n t e d i n C h a p t e r 5 . E q u a t i o n 4 . 7 s u g g e s t s t h a t t h e a p p l i c a b i l i t y o f a BDR c o r r e c t i o n t o t h e s a t e l l i t e r e f l e c t a n c e i s r e l a t i v e l y s t r a i g h t f o r w a r d . H o w e v e r , d e t e r m i n i n g t h e c o r r e c t b i d i r e c t i o n a l r e f l e c t a n c e f u n c t i o n , r h o ( K , 9, ip, Z) i s more c o m p l e x . T h u s , b e f o r e t h e BDR m o d e l s c a n be u t i l i z e d i t i s n e c e s s a r y t o e s t i m a t e a c l o u d i n e s s i n d e x f rom t h e s a t e l l i t e b r i g h t n e s s . To d e r i v e s u c h an i n d e x , t h e g e o m e t r i c a l p o s i t i o n i n g o f t h e S u n , s a t e l l i t e and r e f l e c t i n g s u r f a c e a r e c a l c u l a t e d f o r the t i m e o f e a c h s a t e l l i t e image and a r e u s e d t o d e t e r m i n e a ' p r e d i c t e d ' t a r g e t r e f l e c t a n c e (TR) f o r a 125 c l o u d l e s s sky and an o v e r c a s t s k y . T h e s e p r e d i c t i o n s a r e e x t r a c t e d f rom t h e a p p r o p r i a t e p o l a r p l o t s o f t a r g e t r e f l e c t a n c e ( F i g u r e s 4 . 1 2 , 4 . 1 3 , 4 . 1 7 and 4 . 2 1 ) . A p o l a r p l o t f o r p a r t l y c l o u d y c o n d i t i o n s was n o t p r o d u c e d f o r two r e a s o n s : 1) t h e c o m p l e x n a t u r e o f t h e r e f l e c t e d r a d i a t i o n u n d e r p a r t l y c l o u d y c o n d i t i o n s ; and 2) t h e l a r g e r a n g e i n c l o u d c o v e r c o n d i t i o n s t h a t a r e c l a s s e d as b e i n g p a r t l y c l o u d y . T h e r e f o r e p a r t l y c l o u d y c o n d i t i o n s were a s sumed t o have a v a l u e i n t e r m e d i a t e be tween t h e e x t r e m e s p r e s e n t e d by c l e a r and o v e r c a s t c o n d i t i o n s . To e s t i m a t e where on t h i s c o n t i n u u m t h e p a r t l y c l o u d y BDR o c c u r r e d , t h e c l o u d i n e s s i n d e x i s u t i l i z e d . The c l o u d i n e s s i n d e x was as sumed t o be a l i n e a r r e l a t i o n s h i p between t h e p r e d i c t e d c l e a r (TRc) and o v e r c a s t (TRo) t a r g e t r e f l e c t a n c e v a l u e s . The example d e p i c t e d i n F i g u r e 4 . 3 4 i n d i c a t e s t h a t , g i v e n TRc = 0 . 1 5 and TRo = 0 . 7 , an o b s e r v e d s a t e l l i t e t a r g e t r e f l e c t a n c e (TR) o f 0 .4 i s e q u i v a l e n t t o a 45% c l o u d i n e s s i n d e x . T h i s c a n be d e t e r m i n e d m a t h e m a t i c a l l y u s i n g : C = 100 ( T r - T R c ) / (TRo - T R c ) (4 .11) where C i s t h e c l o u d i n e s s i n d e x as a p e r c e n t a g e . 126 FIGURE 4.34 The R e l a t i o n s h i p Between t h e T a r g e t B r i g h t n e s s (TR) and t h e C l o u d i n e s s I n d e x . 127 S i x m o d e l s were d e v e l o p e d t o c o r r e c t f o r BDR, t h r e e b e i n g b a s e d on r h o v a l u e s and t h r e e u s i n g t a r g e t r e f l e c t a n c e s . To d e t e r m i n e a c o r r e c t e d t a r g e t r e f l e c t a n c e f rom t h e c l o u d i n e s s i n d e x t h r e e f u n c t i o n a l forms were t e s t e d , e a c h u s i n g b o t h o f t h e a p p r o a c h e s . A l l t h r e e f u n c t i o n s a r e l i n e a r . However m o d e l A has a c o n s t a n t g r a d i e n t ( see F i g u r e 4 . 3 5 ) , w h i l e m o d e l s B and C have two t h r e s h o l d p o i n t s where t h e g r a d i e n t o f t h e f u n c t i o n c h a n g e s ( see F i g u r e 4 .36 and 4 . 3 7 ) . T h e s e two d e m a r c a t i o n s , d e f i n e d as t h e c l e a r sky t h r e s h o l d ( C T c ) and t h e c l o u d y s k y ( o r o v e r c a s t ) t h r e s h o l d ( C T o ) , were i n c o r p o r a t e d t o a l l o w f o r f l u c t u a t i o n s i n t h e b r i g h t n e s s t h a t may not be due t o c h a n g e s i n t h e c l o u d i n e s s ( G a u t i e r e t a l . , 1980, u s e d t h i s a p p r o a c h i n t h e i r d e v e l o p m e n t o f a p h y s i c a l l y b a s e d m o d e l ) . F o r e x a m p l e , w i t h m o d e l A , a s m a l l i n c r e a s e i n the p i x e l b r i g h t n e s s when t h e sky i s c o m p l e t e l y c l e a r , w o u l d p r o d u c e a m a i n l y c l e a r sky c o r r e c t i o n , but a l s o some c l o u d y c o r r e c t i o n . M o d e l s B and C were d e v e l o p e d i n an a t t e m p t t o a l l e v i a t e t h i s p r o b l e m . M o d e l B ( F i g u r e 4 . 3 6 ) i n c o r p o r a t e s a l e s s e r g r a d i e n t o u t s i d e t h e p a r t l y c l o u d y c o n d i t i o n s ( d e f i n e d as the zone be tween CTc and C T o ) , w h i l e m o d e l C ( F i g u r e 4 . 3 7 ) t r e a t s t h e s e c o n d i t i o n s as i f t h e y were c o m p l e t e l y c l e a r or c o m p l e t e l y c l o u d y . F l u c t u a t i o n s i n b r i g h t n e s s f o r o v e r c a s t c o n d i t i o n s a r e l i k e l y t o be a r e s u l t o f c h a n g i n g c l o u d t h i c k n e s s , w h i l e u n d e r c l e a r sky c o n d i t i o n s t h e s e may be due t o v a r i a t i o n s i n t h e 128 MODEL A i 20 100 60 CLOUDINESS INDEX (%) FIGURE 4 . 3 5 D e r i v a t i o n o f a C o r r e c t e d T a r g e t R e f l e c t a n c e (TR') From t h e C l o u d i n e s s Index ( D e t e r m i n e d From F i g u r e 4 . 3 4 ) U s i n g M o d e l A . 129 FIGURE 4 . 3 6 D e r i v a t i o n o f a C o r r e c t e d T a r g e t R e f l e c t a n c e (TR1) F rom the C l o u d i n e s s Index ( D e t e r m i n e d From F i g u r e 4 . 3 4 ) U s i n g M o d e l B. 130 1 . 0 , 2 0 6 0 1 0 0 C L O U D I N E S S I N D E X (%) FIGURE 4 . 3 7 D e r i v a t i o n o f a C o r r e c t e d T a r g e t R e f l e c t a n c e (TR') From t h e C l o u d i n e s s Index ( d e t e r m i n e d From F i g u r e 4 . 3 4 ) U s i n g M o d e l C . 131 a e r o s o l o p t i c a l d e p t h . The l a t t e r i s o f m i n o r i m p o r t a n c e u n d e r o v e r c a s t c o n d i t i o n s a s t h e r e l a t i v e l y h i g h b r i g h t n e s s due t o t h e c l o u d s d o m i n a t e s o v e r t h e a e r o s o l i n d u c e d s i g n a l . The p o s i t i o n i n g o f t h e c l e a r and o v e r c a s t l i m i t s a r e b a s e d on mean c l e a r and mean o v e r c a s t c o n d i t i o n s . D e p a r t u r e s f rom t h e a v e r a g e c o n d i t i o n s may r e s u l t i n p r e d i c t e d t a r g e t r e f l e c t a n c e v a l u e s o f l e s s t h a n 0% and g r e a t e r t h a n 100% c l o u d c o v e r . Such o c c u r r e n c e s a r e s t i l l v a l i d and an e x t r a p o l a t i o n p r o c e d u r e was u s e d t o e x t e n d t h e BDR m o d e l s t o i n c o r p o r a t e s u c h v a l u e s ( d e p i c t e d as a d a s h e d l i n e i n F i g u r e 4 .34 to 4 . 3 7 ) . The f i n a l e q u a t i o n s u s e d t o d e t e r m i n e t h e BDR c o r r e c t i o n s a r e g i v e n i n A p p e n d i x 3. L i s t e d a r e t h e c l e a r and o v e r c a s t t h r e s h o l d e q u a t i o n s f o r m o d e l B and C , and t h e e q u a t i o n s f o r d e r i v i n g t h e c o r r e c t e d t a r g e t r e f l e c t a n c e s f o r c l e a r , c l o u d y and p a r t l y c l o u d y c o n d i t i o n s f o r a l l t h r e e m o d e l s . The BDR c o r r e c t i o n i s a p p l i e d t o e a c h p i x e l s e p a r a t e l y w i t h i n t h e a r e a o f i n t e r e s t . In t h e i n i t i a l i n v e s t i g a t i o n o n l y t h e L a n d ( N ) and C l o u d BDR m o d e l s were t e s t e d . The fo rmer was c h o s e n i n p r e f e r e n c e t o t h e o t h e r c l e a r sky BDR m o d e l s as t h e c o u n t v a l u e s f o r t h e L a n d ( N ) a r e a a p p r o x i m a t e t h o s e seen f o r t h e UBC s i t e a t P o i n t G r e y ( see F i g u r e 3 . 1 ) , t h e i n i t i a l t e s t s i t e . 132 In summary, a p p l y i n g a BDR m o d e l i s a t w o - f o l d p r o c e s s w h i c h e n t a i l s : 1) d e t e r m i n a t i o n o f the d e g r e e o f c l o u d i n e s s f rom t h e s a t e l l i t e b r i g h t n e s s ; and 2) u se o f t h i s c l o u d i n d e x t o a p p l y t h e c o r r e c t p r o p o r t i o n o f a c l e a r c o r r e c t i o n and a c l o u d c o r r e c t i o n t o t h e o r i g i n a l s a t e l l i t e b r i g h t n e s s v a l u e . The b e n e f i t s a s s o c i a t e d w i t h t h e i n c l u s i o n o f a BDR c o r r e c t i o n may be i l l u s t r a t e d by t h e i m p a c t i t has on t h e r e l a t i o n s h i p between s a t e l l i t e b r i g h t n e s s and s h o r t w a v e r a d i a t i o n t r a n s m i s s i o n . The r e s u l t s o f t h i s a n a l y s i s a r e p r e s e n t e d i n t h e f o l l o w i n g c h a p t e r . 133 CHAPTER F I V E R E S U L T S : IMPACT OF ADJUSTMENTS TO THE S A T E L L I T E DATA 5 . 1 I n t r o d u c t i o n T h i s c h a p t e r u s e s t h e r e l a t i o n s h i p be tween s h o r t w a v e t r a n s m i s s i o n (T) and s a t e l l i t e t a r g e t r e f l e c t a n c e (TR) t o a s s e s s t h e i m p a c t o f a d j u s t m e n t s t o t h e s a t e l l i t e d a t a . The d e v e l o p m e n t o f t h e r e l a t i o n s h i p i s p r e s e n t e d i n S e c t i o n 5 . 2 . The a d j u s t m e n t s a p p l i e d t o t h e s a t e l l i t e d a t a and h e n c e t o T R , i n c l u d e a 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 o r r e c t i o n ( S e c t i o n 5 . 3 ) , s p a t i a l a v e r a g i n g ( S e c t i o n 5 . 4 ) , t e m p o r a l a v e r a g i n g ( S e c t i o n 5 . 5 ) and r e q u i r e m e n t s f o r t h e number o f s a t e l l i t e images ( S e c t i o n 5 . 6 ) . F i n a l l y , a c o m p a r i s o n i s made o f t h e r e l a t i o n s h i p s d e v e l o p e d f o r e a c h s i t e t o h i g h l i g h t some of t h e c l i m a t o l o g i c a l d i f f e r e n c e s e v i d e n t f rom t h i s a p p r o a c h . The i m p a c t t h e s e a d j u s t m e n t s have i s d e t e r m i n e d u s i n g t h e s t a n d a r d e r r o r o f t h e e s t i m a t e (SE) and t h e 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 2 ) f o r t h e r e l a t i o n s h i p between T and T R . The ' S E ' i s " t h e s t a n d a r d d e v i a t i o n o f t h e e r r o r s r e m a i n i n g a f t e r t h e p r e d i c t i o n e q u a t i o n has been f i t t e d t o t h e d a t a " and ' r ' i s " t h e p r o p o r t i o n o f t h e t o t a l sum o f s q u a r e s t h a t can be a c c o u n t e d f o r by l i n e a r r e g r e s s i o n " ( H i c k s , 1 9 8 2 ) . O t h e r s t a t i s t i c s q u o t e d a r e t h e c o n s t a n t (a) and 134 c o e f f i c i e n t (b) o f t h e r e g r e s s i o n l i n e , a l o n g w i t h t h e i r r e s p e c t i v e s t a n d a r d e r r o r s (SE o f a and SE o f b ) . T h e s e a r e p r e s e n t e d b e c a u s e t h e y have i m p o r t a n t i m p l i c a t i o n s f o r t h e s p a t i a l and t e m p o r a l a n a l y s e s ( S e c t i o n s 5 . 4 and 5 . 5 ) . G i v e n t h e e m p i r i c a l n a t u r e of t h e r e l a t i o n s h i p d e v e l o p e d between T and T R , i n most i n s t a n c e s p h y s i c a l e x p l a n a t i o n s f o r t h e r e s u l t s have n o t been o f f e r e d . F u r t h e r , i t i s r e c o g n i z e d t h a t t h o s e p r e s e n t e d a r e somewhat s p e c u l a t i v e . However t h e y do p r o v i d e a b a s i s f o r f u r t h e r i n v e s t i g a t i o n s . 5 . 2 D e v e l o p m e n t o f t h e R e l a t i o n s h i p Between T r a n s m i s s i o n a n d R e f l e c t a n c e Due t o t h e h i g h c o m p u t i n g c o s t s a s s o c i a t e d w i t h t h e p r o c e s s i n g o f t h e s a t e l l i t e d a t a t h e i n i t i a l a n a l y s i s was b a s e d on a s m a l l d a t a s e t . T h i s c o m p r i s e d t e n d a y s s e l e c t e d f rom t h r o u g h o u t t h e c a l e n d a r y e a r ( i . e . J u l i a n d a y s 2 0 0 / 7 9 , 2 5 6 / 7 9 , 2 9 7 / 7 9 , 0 3 0 / 8 0 , 1 4 3 / 8 0 , 1 5 3 / 8 0 , 1 9 6 / 8 0 , 2 2 5 / 8 0 , 245 /80 and 1 5 7 / 8 0 ) . T h e s e d a y s were c h o s e n t o p r o v i d e a v a r i e t y o f c l o u d c o v e r c o n d i t i o n s r a n g i n g f rom c l e a r t o o v e r c a s t . The d a t a s e t c o m p r i s e d 116 h o u r l y p a i r s of d a t a . The s a t e l l i t e t a r g e t r e f l e c t a n c e was c a l c u l a t e d u s i n g 7 x 7 p i x e l a r r a y s c e n t r e d on t h e UBC s i t e and t h e same a r r a y s i z e was u s e d t o i n v e s t i g a t e t h e i m p a c t o f a BDR c o r r e c t i o n a p p l i e d t o T R . 135 S c a t t e r d i a g r a m s were p l o t t e d t o d e p i c t t h e r e l a t i o n s h i p b e t w e e n T and T R . F i g u r e 5.1 shows t h a t a s i m p l e l i n e a r f u n c t i o n a d e q u a t e l y d e s c r i b e s t h e r e l a t i o n s h i p . The l i n e a r r e g r e s s i o n r e s u l t e d i n a SE of. T = 1 2 . 3 1 , w i t h 89% o f t h e v a r i a t i o n i n T b e i n g e x p l a i n e d by TR ( see T a b l e 5.1 f o r t h e c o m p l e t e s t a t i s t i c s ) . The m a j o r i t y o f t h e c l e a r sky and o v e r c a s t d a t a p o i n t s ( i . e . T >, 85% and T $ 24% r e s p e c t i v e l y ) a p p e a r t o show l e s s s c a t t e r t h a n t h e p a r t l y c l o u d y c o n d i t i o n s ( i . e . 85% < T > 24%). T h i s i s p r o b a b l y due t o t h e i n a b i l i t y o f t h e s a t e l l i t e s e n s o r s t o a d e q u a t e l y c a p t u r e t h e c h a r a c t e r i s t i c s o f t h e s h o r t w a v e r a d i a t i o n f i e l d f o r p a r t l y c l o u d y c o n d i t i o n s . P o s s i b l e r e a s o n s f o r t h i s a r e : 1) t h e c o m p l e x n a t u r e o f t h e r a d i a t i o n f i e l d u n d e r p a r t l y c l o u d y s i t u a t i o n s ; 2) t h e l o g i s t i c p r o b l e m s of c o m p a r i n g p o i n t o b s e r v a t i o n s o f T t o s a t e l l i t e m e a s u r e m e n t s a v e r a g e d o v e r 7 x 7 p i x e l a r r a y s ; and 3) E a r t h - l o c a t i o n e r r o r s ( see C h a p t e r 3 ) . The l a r g e s t r e s i d u a l s i n t h e r e l a t i o n s h i p have been l a b e l l e d i n F i g u r e 5 . 1 . R e s i d u a l s A , B and C o c c u r e a r l y o r l a t e i n t h e d a y l i g h t h o u r s ( i . e . f o r t h e h o u r e n d i n g 0 6 : 0 0 , 136 1201 0 " — i — • • - i 0.2 0.4 0.6 o.8 TR (dimensionless) FIGURE 5.1 S c a t t e r P l o t o f S h o r t w a v e T r a n s m i s s i o n (T) A g a i n s t U n c o r r e c t e d S a t e l l i t e T a r g e t R e f l e c t a n c e (TR) F o r t h e UBC S i t e U s i n g A 7 x 7 P i x e l A r r a y . Number o f O b s e r v a t i o n s = 116. 137 T A B L E 5.1 S t a t i s t i c s Showing t h e Impact o f A p p l y i n g a BDR C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and T R . S a t e l l i t e ; D a t a a r e f o r a 7 x 7 P i x e l A r r a y C e n t r e d on U B C . (Rho) a n d (TR) a r e u s e d t o D i s t i n g u i s h Between t h e BDR m o d e l s W h i c h I n c o r p o r a t e Rho V a l u e s and T a r g e t R e f l e c t a n c e s R e s p e c t i v e l y . A l l BDR M o d e l s use a C l e a r T h r e s h o l d . ( C T c ) o f 0 . 0 5 and an O v e r c a s t T h r e s h o l d (CTo) o f 0 . 8 5 . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r r ( d i m e n s i o n l e s s ) and n . M o d e l T y p e SE o f T r 2 a b SE o f a SE o f b n A ( R h o ) 14 .49 0 . 8 4 3 3 118. 5 -1 52 . 9 2.61 6 .17 1 1 6 B(Rho) 14 .33 0 . 8 4 6 7 118. 1 -151 .8 2 . 5 7 6 .05 1 1 6 C ( R h o ) 14 .35 0 .8463 118. 4 -1 52 .8 2 . 5 8 6 .10 1 1 6 A (TR) 1 3 .86 0 . 8 5 6 5 117. 9 -1 53 .3 2 . 4 7 5 .88 1 1 6 B (TR) 12 .99 0 . 8 7 4 0 121. 5 -1 67 .2 2.41 5 .94 1 1 6 C ( T R ) 12 .93 0 .8751 121. 1 -1 62 . 3 2 . 3 8 5 .74 1 1 6 NO BDR C o r r e c t i o n 12.31 0 . 8 8 6 8 114. 5 - 1 48 .5 2 . 0 7 4 . 9 7 1 1 6 138 0 7 : 0 0 and 18:00 LAT r e s p e c t i v e l y ) . H o u r s n e a r s u n r i s e a n d s u n s e t may be a s s o c i a t e d w i t h u n r e p r e s e n t a t i v e v a l u e s f o r TR f o r t h r e e r e a s o n s : 1) N a v i g a t i o n a l e r r o r s due t o t h e i n t e r p o l a t i o n p r o c e d u r e ( see C h a p t e r 3) o r t h e l a c k o f s u i t a b l e n a v i g a b l e l a n d m a r k s . 2) The s a t e l l i t e and g r o u n d s u r f a c e o b s e r v a t i o n s may be out o f s y n c h r o n i z a t i o n due t o t h e s a t e l l i t e o b s e r v i n g c l o u d s o v e r t h e g r o u n d s t a t i o n , w h i l e t h e l a t t e r i s m e a s u r i n g r a d i a t i o n i n f l u e n c e d by c l o u d s t o w a r d s t h e h o r i z o n and t h e r e f o r e o u t s i d e t h e s a t e l l i t e d a t a a r r a y . T h u s t h e two o b s e r v a t i o n s a r e i n f l u e n c e d by d i s t i n c t l y d i f f e r e n t r a d i a t i v e r e g i m e s . 3) H i g h l e v e l c l o u d s a p p e a r b r i g h t t o t h e s a t e l l i t e e v e n t h o u g h t h e Sun i s c l o s e t o t h e h o r i z o n r e l a t i v e t o t h e s u r f a c e o b s e r v a t i o n a l s i t e s . A l l t h r e e s o u r c e s o f e r r o r have been r e d u c e d h o w e v e r , by r e s t r i c t i n g t h e a n a l y s e s t o c a l c u l a t i o n s when t h e z e n i t h a n g l e o f t h e Sun i s l e s s t h a n 85 d e g r e e s . R e s i d u a l s A and B a r e a l s o f o u n d t o o c c u r u n d e r p a r t l y c l o u d y s k i e s w h i c h w i l l l i k e l y e n h a n c e t h e p r o b l e m . M o r e o v e r , i n s p e c t i o n o f t h e raw c o u n t v a l u e s i n d i c a t e t h a t r e s i d u a l s C and D o c c u r when t h e r e i s a d r a m a t i c c h a n g e i n t h e r a d i a t i o n 139 r e g i m e o v e r t h e h o u r o f i n t e r e s t . To t e s t t h e i n f l u e n c e t h a t t h e s e f o u r r e s i d u a l s have on t h e s t r e n g t h o f t h e r e l a t i o n s h i p t h e y were removed f rom t h e d a t a s e t . The r e s u l t a n t SE o f T was r e d u c e d t o 10 .84 and r 2 i n c r e a s e d t o 0 . 9 1 3 2 . D e s p i t e t h e marked improvement i n t h e s t a t i s t i c s i t was d e c i d e d t h a t t h e f o u r r e s i d u a l s s h o u l d r e m a i n i n t h e d a t a s e t f o r a l l s u b s e q u e n t a n a l y s e s f o r t h r e e r e a s o n s : 1) i f t h e s e p o i n t s a r e removed f rom t h e d a t a s e t f o r any o f t h e t h r e e r e a s o n s o u t l i n e d a b o v e , o t h e r d a t a p o i n t s ( w h i c h do n o t a p p e a r a s l a r g e r e s i d u a l s ) w o u l d l i k e w i s e have t o be r e j e c t e d f rom t h e a n a l y s i s ; 2) t h i s s t u d y i s s p e c i f i c a l l y i n t e r e s t e d w i t h t h e i m p a c t t h a t c h a n g e s t o t h e s a t e l l i t e i n p u t p a r a m e t e r have on t h e s t r e n g t h o f t h e r e l a t i o n s h i p between T and T R , and t h e r e s i d u a l s h a v e a s u b s t a n t i a l i n f l u e n c e on t h e s t a t i s t i c s ; and 3) t h e c h a n g e i n t h e l i n e a r r e g r e s s i o n e q u a t i o n i s n e g l i g i b l e ( i . e . f rom a = 1 1 5 . 1 , b = - 1 5 3 . 9 t o a = 1 1 4 . 5 , b = - 1 4 8 . 5 f o r t h e a n a l y s e s w i t h and w i t h o u t r e s i d u a l s p r e s e n t , r e s p e c t i v e l y ) . 140 5.3 Impact o f A p p l y i n g t h e BDR M o d e l s 5.3.1 I n i t i a l S t u d y U s i n g S m a l l D a t a S e t To d e t e r m i n e t h e a p p l i c a b i l i t y o f a BDR c o r r e c t i o n t h e BDR m o d e l s were a p p l i e d t o t h e same d a t a s e t as d e s c r i b e d i n S e c t i o n 5.2. The L a n d ( N ) BDR model was s e l e c t e d f o r t h e i n i t i a l a n a l y s e s a s t h e a r e a u s e d i n d e v e l o p i n g t h e model a p p e a r e d t o have a s i m i l a r r e f l e c t i v i t y t o t h a t f o r t h e UBC s i t e ( P o i n t G r e y ) , see F i g u r e 3.1. T a b l e 5.1 shows t h e r e s u l t s o f a p p l y i n g t h e t h r e e d i f f e r e n t f o r m s of t h e BDR m o d e l s ( s e e S e c t i o n 4.5), u s i n g e i t h e r r h o v a l u e s o r t a r g e t r e f l e c t a n c e s ( c o r r e c t i o n s a r e a p p l i e d t o a l l d a t a p o i n t s ) . F o r c o m p a r a t i v e p u r p o s e s t h e r e s u l t s f r o m t h e u n c o r r e c t e d d a t a have been i n c l u d e d i n T a b l e 2 5.1. I n s p e c t i o n of t h e SE of T and r s u g g e s t s t h a t i n a l l c a s e s a BDR c o r r e c t i o n has a d e t r i m e n t a l i n f l u e n c e a s j u d g e d by t h e o v e r a l l r e l a t i o n s h i p between T and TR and t h e r e f o r e i s an u n n e c e s s a r y a d d i t i o n a l c o m p u t a t i o n a l s t e p . T h i s i n i t i a l r e s u l t i s somewhat s u r p r i s i n g g i v e n t h a t many r e s e a r c h e r s u s i n g s i m i l a r s a t e l l i t e d a t a a d v o c a t e t h e need f o r a BDR c o r r e c t i o n t o t h e t a r g e t r e f l e c t a n c e ( e . g . S t e p h e n s e t a l . , 1981; M i n n i s and H a r r i s o n , 1982b; S a u n d e r s e t a l . , 1 9 8 3 ) . In l i g h t o f t h e s e r e s u l t s f u r t h e r t e s t s were made by v a r y i n g t h e c l e a r and c l o u d y s k y p i x e l t h r e s h o l d s and 141 r e s t r i c t i n g t h e BDR c o r r e c t i o n t o c e r t a i n sky c o v e r c o n d i t i o n s . T h i s w o u l d show w h e t h e r t h e above c o n c l u s i o n was s e n s i t i v e t o t h e r e l a t i v e l y s i m p l e method u s e d t o i m p l e m e n t t h e BDR m o d e l s . T a b l e 5 . 2 a p r e s e n t s t h e r e s u l t s when mode l A(TR) i s u s e d t o a p p l y c o r r e c t i o n s o n l y t o t h o s e p i x e l s deemed t o be p r e d o m i n a n t l y c l e a r o r o v e r c a s t . The c l e a r and o v e r c a s t t h r e s h o l d s (CTRc and CTRo r e s p e c t i v e l y ) a r e v a r i e d i n o r d e r t o t e s t t h e s e n s i t i v i t y o f t h e r e s u l t s t o t h e methods u s e d t o a p p l y t h e BDR c o r r e c t i o n . In a l l c a s e s t h e SE of T and r show t h e " r e l a t i o n s h i p has i m p r o v e d m a r g i n a l l y r e l a t i v e t o t h e c a s e where a l l p i x e l s were c o r r e c t e d ( T a b l e 5 . 1 ) . H o w e v e r , t h e s t a t i s t i c s f o r t h e u n c o r r e c t e d TR v a l u e s ( T a b l e 5 .1 ) s t i l l p r o d u c e a more c o h e r e n t r e l a t i o n s h i p be tween T and T R . I t a p p e a r s f rom T a b l e 5 . 2 a t h a t s t r i n g e n t t h r e s h o l d c o n t r o l s ( r e s u l t i n g i n fewer p i x e l s b e i n g c o r r e c t e d ) g i v e t h e l o w e s t SE o f T . T h i s i s f u r t h e r h i g h l i g h t e d i n T a b l e 5 . 2 b w h e r e , t o g e t h e r w i t h c l e a r and o v e r c a s t p i x e l t h r e s h o l d s , t h e r e i s a r e s t r i c t i o n t h a t t h e c o r r e c t i o n i s o n l y a p p l i e d when t h e w h o l e a r r a y ( w h i c h i n t h i s c a s e i s 7 x 7 p i x e l s ) i s d e t e r m i n e d t o be a t l e a s t 90% c l e a r o r 90% c l o u d y . - The SE o f T i s l o w e r , but a g a i n n o t s u f f i c i e n t l y t o be an improvement on t h e SE when no BDR c o r r e c t i o n i s a p p l i e d . M o d e l s B and C were t e s t e d more r i g o r o u s l y t h a n m o d e l A due t o t h e i r b e t t e r p e r f o r m a n c e as s een f rom T a b l e 5 . 1 . 142 T A B L E 5 .2 S t a t i s t i c s S h o w i n g t h e Impact o f A p p l y i n g a BDR M o d e l A ( T R ) C o r r e c t i o n to t h e R e l a t i o n s h i p Between T and T R . S a t e l l i t e D a t a a r e f o r a 7 x 7 P i x e l A r r a y C e n t r e d on U B C . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r r ( d i m e n s i o n l e s s ) a n d n . a . C o r r e c t i o n A p p l i e d t o C l e a r a n d O v e r c a s t C o n d i t i o n s O n l y . CTRc CTRo SE o f T r 2 a b SE o f a SE o f b n 0 . 2 0 0 . 8 0 13 .67 0 .8595 117. 9 -1 54 . 1 2 . 4 2 5.81 1 1 6 0 . 1 5 0 . 8 5 13.61 0 .8607 117. 7 - 1 5 3 . 9 2 . 4 0 5 . 7 7 1 1 6 0 . 1 0 0 . 9 0 1 3 .48 0 .8633 117. 5 -1 5 3 . 4 2 . 3 7 5 . 6 9 1 1 6 0 . 0 5 0 . 8 5 13 .45 0 . 8639 117. 1 -1 5 3 . 0 2 . 3 5 5 . 6 6 1 1 6 b . C o r r e c t i o n A p p l i e d t o C l e a r and O v e r c a s t C o n d i t i o n s O n l y , When 90% o f t h e P i x e l A r r a y i s Deemed t o be C l e a r o r O v e r c a s t . CTRc CTRo SE o f T r 2 a b SE o f a SE o f b n 0 . 0 5 0 . 8 5 12 .75 0 .8777 116. 2 - 1 5 2 . 4 2 . 1 9 5 .30 1 1 6 0 . 0 5 0 . 9 0 12 .65 0 .8797 115. 8 - 1 5 0 . 4 2 . 1 6 5 . 1 9 1 1 6 143 T a b l e 5.3 shows the impact on t h e r e l a t i o n s h i p of a BDR model B c o r r e c t i o n , and T a b l e 5.4 f o r a BDR model C c o r r e c t i o n . o E a c h of t h e s e two models were t e s t e d u s i n g b o t h rho and t a r g e t r e f l e c t a n c e v a l u e s , a s e l e c t i o n of c l e a r and o v e r c a s t t h r e s h o l d s , and f o r c o r r e c t i o n s t o e i t h e r a l l p i x e l s or t o t h o s e t h a t were deemed t o be c l e a r or o v e r c a s t . An e x a m i n a t i o n of t h e r e s u l t s p r e s e n t e d i n T a b l e s 5.3 and 5.4 shows a c o n s i s t e n t d e t e r i o r a t i o n i n t h e s t r e n g t h of t h e r e l a t i o n s h i p between T and TR r e l a t i v e t o when t h e r e i s no BDR c o r r e c t i o n a p p l i e d t o the s a t e l l i t e d a t a ( T a b l e 5 . 1 ) . T h e r e i s one i n s t a n c e of an improvement, a l b e i t minor, when a c o r r e c t i o n i s a p p l i e d t o c o n d i t i o n s deemed t o be 5% c l o u d y (see T a b l e 5.4d). The c o n s i s t e n t l y g r e a t e r SE of T and lower r 2 when a p p l y i n g any of the BDR model forms (see T a b l e s 5 .1 t o 5.4) s u b s t a n t i a t e s the e a r l i e r c o n c l u s i o n t h a t i t i s u n n e c e s s a r y t o a p p l y a BDR c o r r e c t i o n t o t h e s a t e l l i t e d a t a when u t i l i z i n g t h e r e l a t i o n s h i p between T and TR. W i t h a BDR c o r r e c t i o n a p p l i e d t o t h e s a t e l l i t e d a t a , a l i n e a r f u n c t i o n s t i l l a d e q u a t e l y d e s c r i b e s the r e l a t i o n s h i p . T h e r e f o r e the i n c r e a s e i n t h e SE of T i s not due t o t h e f u n c t i o n c h o s e n . I f a BDR c o r r e c t i o n i s a p p l i e d , use of t a r g e t r e f l e c t a n c e s r a t h e r t h a n rho v a l u e s i n t h e c o r r e c t i o n p r o c e d u r e does l e a d t o s t r o n g e r r e l a t i o n s h i p s . T h i s i s t r u e f o r b o t h a BDR c o r r e c t i o n a p p l i e d t o a l l p i x e l s or o n l y t o t h o s e p i x e l s deemed c l e a r and 144 T A B L E 5 . 3 S t a t i s t i c s S h o w i n g t h e Impact o f A p p l y i n g a BDR M o d e l B C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and T R . S a t e l l i t e D a t a a r e f o r a 7 x 7 P i x e l A r r a y C e n t r e d on U B C . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r r 2 ( d i m e n s i o n l e s s ) and n . a . BDR M o d e l B ( R h o ) , A l l P i x e l s C o r r e c t e d . CTRc CTRo SE o f T r 2 a b SE of a SE of •b n 0 . 0 5 0 . 8 5 14 .33 0 .8467 118. 1 -151 .8 2 . 5 7 6 . 0 5 1 1 6 0 . 1 5 0 . 8 5 14 .25 0 .8483 117. 2 -1 52 . 9 2 .52 6 . 0 6 1 1 6 0 . 1 0 0 . 8 0 14 .24 0 .8486 117. 8 -151 .9 2 . 54 6.01 1 1 6 b . BDR M o d e l B ( T R ) , A l l P i x e l s C o r r e c t e d . 0 . 0 5 0 . 8 5 12 .99 0 .8740 121 .5 - 1 6 7 . 2 2.41 5 .94 116 0 . 1 5 0 . 8 5 12 .78 0.8781 119 .8 - 1 6 5 . 7 2.31 5 .78 116 0 . 1 0 0 . 8 0 13 .02 0 .8734 120 .4 - 1 6 4 . 3 2 .38 5 . 8 6 116 c . BDR M o d e l B ( R h o ) , O n l y O v e r c a s t and C l e a r P i x e l s C o r r e c t e d . 0 . 0 5 0 . 8 5 13 .58 0 .8623 116 .8 - 1 5 2 . 7 2 .38 5.71 116 0 . 1 5 0 . 8 5 13 .84 0 . 8 5 6 9 117 .5 - 1 5 3 . 6 2 . 4 5 5 .88 116 0 . 1 0 0 . 8 0 13 .75 0 .8587 117 .5 - 1 5 3 . 4 2 . 4 3 5 .83 116 d . BDR M o d e l B ( T R ) , O n l y O v e r c a s t and C l e a r P i x e l s C o r r e c t e d . 0 . 0 5 0 . 8 5 12.51 0.8831 122.1 - 1 7 3 . 4 2 .32 5.91 116 0 . 1 5 0 . 8 5 12 .65 0 . 8 8 0 5 120 .8 - 1 7 1 . 2 2.31 5.91 116 0 . 1 0 0 . 8 0 12 .66 0 .8803 121 .2 - 1 7 0 . 6 2 . 3 3 5 . 8 9 116 145 T A B L E 5 . 4 S t a t i s t i c s Showing t h e Impact o f A p p l y i n g a BDR M o d e l C C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and T R . S a t e l l i t e D a t a a r e f o r a 7 x 7 P i x e l A r r a y C e n t r e d on U B C . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r r 2 ( d i m e n s i o n l e s s ) and n . a . BDR M o d e l C ( R h o ) , A l l P i x e l s C o r r e c t e d . CTRc CTRo SE o f T r 2 a b SE o f a SE o f b n 0 . 0 5 0 . 8 5 1 4 . 3 5 0 .8463 118. 4 -1 52 . 8 2 . 5 8 6 . 1 0 1 16 0 . 1 0 0 . 8 0 1 4 . 3 8 0 .8456 118. 5 -1 53 . 0 2 . 5 9 6.12 1 1 6 0 . 1 5 0 . 8 5 14 .53 0 .8423 118. 5 -1 52 . 4 2 . 6 2 6.18 1 1 6 0 . 1 0 0 . 8 5 14.44 0 .8443 118. 5 -1 52 . 6 2 . 6 0 6 .14 1 1 6 b . BDR M o d e l C ( T R ) , A l l P i x e l s C o r r e c t e d . 0 . 05 0 . 8 5 12 .93 0 .8751 121.1 -1 62 . 3 2 . 38 5 .74 1 1 6 0 . 10 0 . 8 0 13.01 0 . 8 7 3 6 1 1 9 . 8 -1 58 . 7 2 . 3 6 5 . 6 6 1 1 6 0 . 15 0 . 8 5 12 .55 0 .8824 118 .9 -161 . 2 2 . 2 4 5.51 1 1 6 0 . 1 0 0 . 8 5 12 .72 0.8791 119 .8 -161 .3 2 . 30 5 . 6 0 1 1 6 c . BDR M o d e l C ( R h o ) , O n l y O v e r c a s t and C l e a r P i x e l s C o r r e c t e d . 0 . 0 5 0 . 8 5 13 .47 0 .8644 117 .0 - 1 5 3 . 3 2 . 3 6 5 . 6 9 116 0 . 1 0 0 . 8 0 13 .69 0 .8602 117 .8 - 1 5 4 . 4 2 . 4 3 5 . 8 3 116 0 . 1 5 0 . 8 5 13 .79 0 . 8 5 7 9 118 .0 - 1 5 4 . 5 2 . 4 6 5 . 8 9 116 d . BDR M o d e l C ( T R ) , O n l y O v e r c a s t and C l e a r P i x e l s C o r r e c t e d . 0 . 0 5 0 . 8 5 12 .20 0 .8888 121 .4 - 1 6 9 . 6 2 . 24 5 .62 1 1 6 0 . 1 0 0 . 8 0 12 .36 0 . 8 8 5 9 120 .5 - 1 6 6 . 5 2 . 2 5 5 . 60 1 1 6 0 . 1 5 0 . 8 5 12 .36 0 . 8 8 5 9 120 .0 - 1 6 7 . 2 2 . 2 3 5 .62 1 1 6 0 . 1 0 0 . 8 5 12 .34 0 .8863 120 .6 - 1 6 8 . 2 2 . 2 5 5 .64 1 1 6 0 . 1 0 1 .00 12.32 0 .8867 1 2 0 . 5 - 1 6 8 . 6 2 . 2 4 5 .64 1 1 6 0 . 0 5 1 .00 12 .19 0 .8891 121 .3 - 1 7 0 . 0 2 . 2 4 5 .62 1 1 6 146 o v e r c a s t . A l t h o u g h t h e r e s u l t s show t h a t t h e i n a p p r o p r i a t e n e s s o f t h e BDR c o r r e c t i o n i s n o t d e p e n d e n t on t h e form o f t h e BDR m o d e l c h o s e n , some summary r e m a r k s c a n be made as t o t h e most a p p r o p r i a t e form t o u s e . The opt imum c l e a r and o v e r c a s t t h r e s h o l d s v a r y f o r t h e d i f f e r e n t m o d e l s ( see T a b l e s 5 .2 t o 5 . 4 ) . H o w e v e r , a c l e a r t h r e s h o l d (CTRc) o f 5% c l o u d i n e s s and an o v e r c a s t t h r e s h o l d (CTRo) of 85% c l o u d i n e s s a p p e a r s t o g i v e g e n e r a l l y b e t t e r r e s u l t s f o r m o d e l s A , B and C , u s i n g e i t h e r r h o v a l u e s o r t a r g e t r e f l e c t a n c e s . In t h e l a t t e r c a s e , t h r e s h o l d s CTRc = 0 . 1 5 and CTRo = 0 . 8 5 a r e a l s o f a v o u r a b l e . M o d e l s B and C b o t h o u t p e r f o r m mode l A and when c o m p a r i n g m o d e l s B and C w i t h t h e same t h r e s h o l d s , t h e l a t t e r c o n s i s t e n t l y p r o v i d e s a s t r o n g e r r e l a t i o n s h i p be tween T and T R ' . The e x c e p t i o n i s when mode l C (Rho) i s a p p l i e d t o a l l p i x e l s . The b e s t o v e r a l l p e r f o r m a n c e i s p r o v i d e d by BDR mode l C ( T R ) w i t h t h e c o r r e c t i o n a p p l i e d t o c l e a r and o v e r c a s t c o n d i t i o n s o n l y ( see T a b l e 5 . 4 d ) . Some o f t h e r e s u l t s u s i n g m o d e l C ( T R ) even show a m i n o r improvement o v e r the r e l a t i o n s h i p d e v e l o p e d w i t h o u t a BDR c o r r e c t i o n . Thus a p r e l i m i n a r y c o n c l u s i o n i s t h a t , i r r e s p e c t i v e of t h e mode l u s e d , t h e a p p l i c a t i o n o f a BDR c o r r e c t i o n does l i t t l e t o i m p r o v e t h e s t r e n g t h o f t h e r e l a t i o n s h i p between T and T R . 1 4 7 5 . 3 . 2 F u r t h e r T e s t i n g U s i n g a L a r g e r D a t a Se t To s u b s t a n t i a t e t h e f i n d i n g s u s i n g t h e s m a l l e r d a t a s e t i t was d e c i d e d t h a t t h e most s i g n i f i c a n t o f t h e p r e c e d i n g c o n c l u s i o n s s h o u l d be t e s t e d u s i n g a l a r g e r d a t a s e t and an a b b r e v i a t e d s e t o f a n a l y s e s . T h i s was deemed n e c e s s a r y b e f o r e p r o c e e d i n g w i t h t h e s p a t i a l and t e m p o r a l a n a l y s e s . The l a r g e r d a t a s e t i n c l u d e s t h e d a y s f rom t h e s m a l l e r d a t a s e t ( see S e c t i o n 5 . 1 ) p l u s J u l i a n d a y s 2 5 5 / 7 9 , 2 5 7 / 7 9 , 2 7 6 / 7 9 , 2 9 3 / 7 9 , 3 0 4 / 7 9 , 3 1 9 / 7 9 , 3 6 1 / 7 9 , 3 6 3 / 7 9 , 0 0 9 / 8 0 , 0 1 2 / 8 0 , 0 2 5 / 8 0 , 1 0 5 / 8 0 , 1 2 1 / 8 0 , 1 2 6 / 8 0 , 1 4 1 / 8 0 , 1 6 0 / 8 0 , 1 7 1 / 8 0 , 1 8 3 / 8 0 , 1 8 5 / 8 0 , 1 9 7 / 8 0 , 239/80 and 2 6 1 / 8 0 . F i g u r e 5 .2 p r e s e n t s t h e r e l a t i o n s h i p be tween T and TR ( w i t h o u t a BDR c o r r e c t i o n ) f o r t h e l a r g e r d a t a s e t , where n = 332 . Once a g a i n a s i m p l e l i n e a r f u n c t i o n a d e q u a t e l y d e s c r i b e s t h e r e l a t i o n s h i p . The s c a t t e r d i a g r a m shows a s m a l l e r c o n c e n t r a t i o n o f p a r t l y c l o u d y d a t a , e s p e c i a l l y be tween 40% and 80% s h o r t w a v e t r a n s m i s s i o n . T h i s c a n be a t t r i b u t e d t o t h e s y n o p t i c w e a t h e r t y p e s commonly e x p e r i e n c e d i n s o u t h west B r i t i s h C o l u m b i a , g i v i n g a p r e p o n d e r a n c e o f e i t h e r m a i n l y c l e a r o r o v e r c a s t c o n d i t i o n s ( see Hay and O k e , 1 9 7 6 ) . The p r e l i m i n a r y a n a l y s e s u s i n g t h e s m a l l e r d a t a s e t ( see s e c t i o n 5 . 1 ) were u s e d t o s e l e c t t h e most a p p r o p r i a t e BDR 148 120 100 80 T (%) 60 40 20 F O R M A T see FIGURE 5 .1 — I 0.2 11 1 1 1 1 > * 2 1 1 1111 1 N . 2 2 1 i i 11 1 r> 1 i "V* n i i 1 1 > « • 1 2 1 1 1 1 1 1 1 1 1 i \ 1 1 1 1 1 1 2 1 1 2 11 3 \ 1 1 1 1 1 1 *V 11 3 1 0.4 TR (dimensionless) 0.6 0.8 FIGURE 5 . 2 S c a t t e r P l o t of S h o r t w a v e T r a n s m i s s i o n (T) A g a i n s t U n c o r r e c t e d S a t e l l i t e T a r g e t R e f l e c t a n c e (TR) F o r t h e UBC S i t e U s i n g A 7 x 7 P i x e l A r r a y and t h e L a r g e r D a t a S e t . Number o f O b s e r v a t i o n s = 332 . 149 m o d e l s f o r t e s t i n g t h e l a r g e r d a t a s e t . M o d e l C ( T R ) was u s e d i n t h e m a j o r i t y of t h e t e s t s . A n a l y s e s were c a r r i e d o u t f o r t h e UBC s i t e u s i n g t h r e e d i f f e r e n t p i x e l a r r a y s i z e s , 5 x 5 , 7 x 7, and 15 x 15, t o d e t e r m i n e w h e t h e r t h e s i z e o f t h e a r r a y u s e d i n t h e p r e l i m i n a r y i n v e s t i g a t i o n s was b i a s i n g t h e r e s u l t s . F u r t h e r t e s t i n g i n c l u d e d t h e use of d a t a f rom t h e A b b o t s f o r d A i r p o r t (ABAIR) s i t e . I n s p e c t i o n of t h e raw c o u n t v a l u e s f o r ABAIR r e v e a l e d t h a t t h e r e f l e c t i v i t y a t t h i s s i t e was more s i m i l a r t o t h e a r e a u s e d t o d e v e l o p t h e L a n d ( S ) BDR m o d e l ( see F i g u r e 3 . 1 ) . F o r c o m p a r a t i v e p u r p o s e s , b o t h t h e L a n d ( N ) and L a n d ( S ) BDR m o d e l s were i n c l u d e d i n t h e a n a l y s e s f o r t h e ABAIR s i t e . F i g u r e 5 .3 shows a s c a t t e r p l o t f o r t h e r e l a t i o n s h i p be tween T and TR ( w i t h o u t a BDR c o r r e c t i o n ) f o r t h e ABAIR s i t e . T a b l e s 5 . 5 a and 5 . 7 a l i s t t h e s t a t i s t i c s f o r t h e r e l a t i o n s h i p be tween T and TR w i t h o u t a BDR c o r r e c t i o n f o r t h e UBC and ABAIR s i t e s , r e s p e c t i v e l y . The r e s u l t s o b t a i n e d f r o m a p p l y i n g a BDR c o r r e c t i o n t o t h e l a r g e r d a t a s e t a r e p r e s e n t e d i n T a b l e s 5 . 5 ( b - g) and 5 . 6 f o r t h e UBC s i t e and i n T a b l e 5 . 7 ( b - e) f o r t h e ABAIR s i t e . The r e s u l t s s u b s t a n t i a t e t h e c o n c l u s i o n s b a s e d on t h e s m a l l e r d a t a s e t . The o n l y d i f f e r e n c e i s t h a t a few more of t h e t e s t s show an improvement i n t h e SE o f T and r 2 c o m p a r e d t o t h e u n c o r r e c t e d c a s e s ( compare T a b l e s 5 . 5 a and 5 . 7 a t o T a b l e s 5 . 5 ( b - g ) , 5 . 6 and 5 . 7 ( b - e ) , r e s p e c t i v e l y ) . Where i m p r o v e m e n t s do o c c u r t h e y a r e s m a l l and c h a n g e s i n t h e r e g r e s s i o n e q u a t i o n s a r e 150 TR (dimensionless) FIGURE 5 . 3 S c a t t e r P l o t o f S h o r t w a v e T r a n s m i s s i o n (T) A g a i n s t U n c o r r e c t e d S a t e l l i t e T a r g e t R e f l e c t a n c e (TR) F o r t h e ABAIR S i t e U s i n g A 7 x 7 P i x e l A r r a y and t h e L a r g e r D a t a S e t . Number of O b s e r v a t i o n s = 3 3 1 . 1 5 1 T A B L E 5 . 5 S t a t i s t i c s Showing t h e Impact o f A p p l y i n g a BDR M o d e l C C o r r e c t i o n to. t h e R e l a t i o n s h i p Between T a n d T R . S a t e l l i t e D a t a a r e f o r D i f f e r e n t P i x e l A r r a y S i z e s C e n t r e d on UBC and BDR C o r r e c t i o n s a r e A p p l i e d t o A l l P i x e l s . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r r 2 ( d i m e n s i o n l e s s ) and n . a . W i t h o u t a BDR C o r r e c t i o n A r r a y S i z e SE o f r 2 T a b SE o f a SE o f b n 5 7 1 5 x 5 x 7 x 1 5 11 .02 0 .9092 10.94 0 .9108 11 .17 0 .9071 113 .9 - 1 4 7 . 6 1 . 113 .5 - 1 4 7 . 4 1 . 113 .7 - 1 4 8 . 4 1. 1 1 09 1 2 2 . 2 . 2 . 57 54 62 333 332 331 b . BDR M o d e l C ( R h o ) , 5 x 5 P i x e l A r r a y s . CNRc CNRo SE o f r 2 T a b SE o f a SE o f b n 0 . 0 5 0 . 8 5 12 .08 0 .8912 115 .9 - 1 4 9 . 2 1. 26 2 . 87 332 c BDR M o d e l C ( T R ) , 5 x 5 P i x e l A r r a y s . 0 . 0 5 0 . 1 0 0 . 1 5 0 . 8 5 0 . 8 0 0 . 8 5 10 .95 0 . 9 1 0 6 11 .06 0 . 9 0 8 8 10 .89 0 . 9 1 1 6 118 .3 - 157 .3 1. 117.1 - 1 5 4 . 0 1. 116 .5 - 1 5 6 . 0 1. 1 6 1 6 1 3 2 . 2 . 2 . 71 69 68 332 332 332 d . BDR M o d e l C ( R h o ) , 7 x 7 P i x e l A r r a y s . 0 . 0 5 0 . 8 5 12 .02 0 .8922 115 .4 - 1 4 8 . 9 1. 24 2 . 85 332 e . BDR M o d e l C ( T R ) , 7 x 7 P i x e l A r r a y s . 0 . 0 5 0 . 1 0 0 . 1.5. 0 . 8 5 0 . 8 0 . 0 . 8 5 10.91 0 .9113 11.01 0 . 9 0 9 7 10.84 0 .9124 118.5 - 158.1 1. 117 .4 - 1 5 5 . 0 1. 116.7 - 1 5 7 . 0 1. 1 6 16 1 3 2 . 2 . 2 . 72 69 68 332 332 332 f . BDR M o d e l C ( R h o ) , 15 x 15 P i x e l A r r a y s • 0 . 0 5 0 . 8 5 11 .97 0 .8931 115 .7 - 1 5 0 . 2 1. 25 2 . 87 329 152 T A B L E 5 . 5 ( c o n t i n u e d ) g . BDR M o d e l C ( T R ) , 15 x 15 P i x e l A r r a y s . 0 . 0 5 0 . 8 5 10 .94 0 . 9 1 0 6 119 .3 - 1 6 0 . 3 TTT8 2777 33~0 0 . 1 0 0 . 8 0 10 .97 0 .9100 118.1 - 1 5 7 . 2 1.17 2 .73 330 0 . 1 5 0 . 8 5 10 .83 0 .9124 117 .4 - 1 5 9 . 0 1.14 2 .72 330 153 T A B L E 5 . 6 S t a t i s t i c s Showing t h e Impact o f A p p l y i n g a BDR M o d e l C C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and T R . S a t e l l i t e D a t a a r e f o r D i f f e r e n t P i x e l A r r a y S i z e s C e n t r e d on UBC and BDR C o r r e c t i o n s a r e A p p l i e d t o C l e a r and O v e r c a s t P i x e l s O n l y . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r r 2 ( d i m e n s i o n l e s s ) and n . a . BDR M o d e l C ( R h o ) , 5 x 5 P i x e l A r r a y s . CNRc CNRo SE o f r 2 T a b SE o f a SE o f b n 0 . 05 0 . 8 5 11 .68 0 . 8 9 8 3 114 .9 - 1 4 8 . 5 1 . 20 2 . 75 332 b . BDR M o d e l C ( T R ) , 5 x 5 P i x e l A r r a y s . 0 . 0 . 0 . 05 1 0 1 5 0 . 8 5 0 . 8 0 0 . 8 5 10.72 0 .9143 10 .89 0.9117 10 .76 0 . 9 1 3 6 118.7 - 1 6 2 . 8 1 . 117.8 -159.8 1 . 117.4 - 1 6 0 . 7 1 . 1 5 1 5 1 3 2 . 2 . 2 . 74 74 72 332 332 332 c . BDR M o d e l C ( R h o ) , 7 x 7 P i x e l A r r a y s . 0 . 05 0 . 8 5 1 1 .57 0 .9001 114 .5 - 148 .3 1 . 1 8 2 . 72 332 d . BDR M o d e l C ( T R ) , 7 x 7 P i x e l A r r a y s . OOO 05 1 0 1 5 0 . 8 5 0 . 8 0 0 . 8 5 10 .67 0 .9151 10 .82 0 . 9 1 2 7 10 .73 0 .9142 118.8 - 1 6 3 . 5 1 . 118 .0 - 1 6 0 . 6 1 . 117 .7 - 1 6 1 . 6 1. 1 4 1 5 1 3 2 . 2 . 2 . 74 74 73 332 332 332 e . BDR M o d e l C ( R h o ) , 15 x 15 P i x e l A r r a y s • 0 . 05 0 . 8 5 11 .53 0 . 9 0 0 8 114.8 - 1 4 9 . 7 1 . 18 2 . 75 329 f . BDR M o d e l C ( T R ) , 15 x 15 P i x e l A r r a y s . 0 . 0 . 0 . 05 10 1 5 0 . 8 5 0 . 8 0 0 . 8 5 10 .85 0 .9121 10 .92 0 . 9 1 0 9 10 .88 0 . 9 1 1 6 119 .6 - 1 6 5 . 5 1 . 118 .7 - 1 6 2 . 3 1 . 118 .3 - 1 6 3 . 3 1 . 1 8 1 7 1 6 2 . 2 . 2 . 84 80 81 330 330 330 154 T A B L E 5 . 7 S t a t i s t i c s Showing t h e Impact o f A p p l y i n g a BDR M o d e l L a n d ( N ) C C o r r e c t i o n t o the R e l a t i o n s h i p Between T and T R . S a t e l l i t e D a t a a r e f o r a 7 x 7 P i x e l A r r a y C e n t r e d on A B A I R . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r r 2 ( d i m e n s i o n l e s s ) a n d n . a . W i t h o u t a BDR C o r r e c t i o n CNRc CNRo SE o f r z a b SE o f T a SE o f b n - - 13 .87 0 . 8 3 6 6 114 .2 - 1 4 3 . 5 1.56 3 .50 331 b . BDR M o d e l C ( R h o ) , A l l P i x e l s C o r r e c t e d . 0 . 0 5 0 . 8 5 14 .67 0 . 8 1 7 5 116 .7 - 1 4 7 . 7 1.72 3 . 8 5 331 c . BDR M o d e l C ( T R ) , A l l P i x e l s C o r r e c t e d . 0 . 0 5 0 . 1 0 0 . 8 5 0 . 8 0 13 .10 0 .8543 116.1 - 1 4 9 . 7 1 . 50 13 .24 0 .8513 112 .8 - 1 4 2 . 9 1.45 3.41 3 .29 331 331 d . BDR M o d e l C ( R h o ) , O n l y O v e r c a s t and C l e a r C o r r e c t e d . P i x e l s 0 . 0 5 0 . 8 5 14 .28 0 .8270 114 .7 - 1 4 5 . 0 1.62 3 . 6 6 331 e . BDR M o d e l C ( T R ) , O n l y O v e r c a s t and C l e a r C o r r e c t e d . P i x e l s 0 . 0 5 0 . 1 0 0 . 8 5 0 . 8 0 13 .13 0 .8538 1 1 7 . 6 - 1 5 6 . 4 1.53 13 .17 0 . 8 5 2 9 115 .3 - 1 5 1 . 3 1.49 3 . 5 7 . 3 . 4 6 331 331 155 n e g l i g i b l e . I t a p p e a r s f rom T a b l e s 5 . 5 and 5 . 6 t h a t u s i n g d i f f e r e n t p i x e l a r r a y s i z e s has a s i m i l a r m i n o r i m p a c t on t h e s t a t i s t i c s . T h e r e f o r e t h e use o f t h e 7 x 7 p i x e l a r r a y d i d n o t b i a s t h e i n i t i a l t e s t i n g o f t h e BDR c o r r e c t i o n s . The use o f e i t h e r t h e L a n d ( N ) o r L a n d ( S ) BDR m o d e l s f o r t h e ABAIR s i t e (compare T a b l e s 5 .7 and 5 . 8 ) p r o d u c e d s i m i l a r r e s u l t s . H o w e v e r , t h e L a n d ( S ) m o d e l d o e s p r o v i d e c o n s i s t e n t l y l o w e r s t a n d a r d e r r o r s , w i t h and w i t h o u t a BDR c o r r e c t i o n . The r e s u l t s f rom b o t h t h e s m a l l ( S e c t i o n 5 . 3 1) and l a r g e d a t a s e t s show t h a t t h e i n c o r p o r a t i o n o f a BDR c o r r e c t i o n o c c a s i o n a l l y p r o d u c e s a m i n o r i m p r o v e m e n t bu t g e n e r a l l y l e a d s t o a d e t e r i o r a t i o n o f t h e r e l a t i o n s h i p be tween T and T R . T h u s i t a p p e a r s i n a p p r o p r i a t e t o a p p l y a BDR c o r r e c t i o n t o TR f o r t h i s s t u d y . T h e r e f o r e , i n a l l f u r t h e r a n a l y s e s ( S e c t i o n s 5 .4 t o 5 . 6 ) a d e c i s i o n was made t o use o n l y t h e r e l a t i o n s h i p be tween T and an u n c o r r e c t e d T R , and t h e l a r g e d a t a s e t . 5 . 4 Impact o f S p a t i a l A v e r a g i n g 5 . 4 . 1 I n t r o d u c t i o n and A n a l y s i s o f R e s u l t s P r e v i o u s a n a l y s e s o f t h e a b i l i t y o f s a t e l l i t e s t o c h a r a c t e r i z e t h e r a d i a t i o n r e g i m e o f t h e E a r t h - A t m o s p h e r e s y s t e m have u s e d a wide r a n g e o f s a t e l l i t e a r r a y s i z e s . 156 T A B L E 5 .8 S t a t i s t i c s Showing t h e Impact o f A p p l y i n g a BDR M o d e l L a n d ( S ) C C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and T R . S a t e l l i t e D a t a a r e f o r a 7 x 7 P i x e l A r r a y C e n t r e d on A B A I R . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r r 2 ( d i m e n s i o n l e s s ) and n . a . BDR M o d e l C ( R h o ) , A l l P i x e l s C o r r e c t e d . CNRc CNRo SE o f r 2 a b SE o f SE o f n T a b 0 . 05 0 . 8 5 14 .10 0 . 8 3 0 6 115 .9 - 1 4 6 . 8 1.63 3 .66 330 b . BDR M o d e l C ( T R ) , A l l P i x e l s C o r r e c t e d . 0 . 0 . 05 1 0 0 . 8 5 12 .76 0 .8612 118 .0 - 1 5 3 . 6 1.50 0 . 8 0 12 .96 0 .8570 116 .5 - 1 4 9 . 8 1.49 3 .40 3 .38 330 330 c . BDR M o d e l C ( R h o ) , O n l y O v e r c a s t and C l e a r C o r r e c t e d . P i x e l s 0 . 05 0 . 8 5 14 .04 0 .8322 115 .6 - 1 4 6 . 6 1.61 3 .63 330 d . BDR M o d e l C ( T R ) , O n l y O v e r c a s t and C l e a r C o r r e c t e d . P i x e l s 0 . 0 . 05 1 0 0 . 8 5 12 .77 0.8611 119 .2 - 1 5 9 . 7 1.52 0 . 8 0 12 .82 0 .8601 117 .8 - 1 5 6 . 0 1.50 3 .54 3 .47 330 330 157 E x a m p l e s i n c l u d e T a r p l e y (1979) who u s e d 7 x 6 p i x e l a r r a y s (8 km p i x e l s ) and G a u t i e r e t a l . (1980) who u s e d an 8 x 8 p i x e l a r r a y (2 km p i x e l s ) . T h u s i t was d e c i d e d t o i n v e s t i g a t e t h e i m p a c t o f c h a n g i n g t h e s i z e o f t h e s a t e l l i t e p i x e l a r r a y a g a i n u s i n g t h e r e l a t i o n s h i p be tween T and T R . The d i m e n s i o n s o f t h e a r r a y were a l t e r e d t o d e t e r m i n e t h e opt imum s i z e and c o n f i g u r a t i o n r e q u i r e d f o r c a l c u l a t i n g t h e t a r g e t r e f l e c t a n c e . T e s t s were c a r r i e d o u t f o r two i n d i v i d u a l s t a t i o n s , UBC and A B A I R , and f o r t h e t h r e e s t a t i o n d a t a s e t MAA ( see C h a p t e r 2 f o r d e t a i l e d d e s c r i p t i o n s ) . The s q u a r e c o n f i g u r a t i o n a d o p t e d i n t h e i n i t i a l d e v e l o p m e n t o f t h e r e l a t i o n s h i p was t e s t e d w i t h p i x e l a r r a y s r a n g i n g f rom 3 x 3 p i x e l s t o 19 x 19 p i x e l s . T a b l e s 5 . 9 t o 5.11 show t h e r e s u l t s f o r U B C , ABAIR and MAA r e s p e c t i v e l y . The number o f images (n) u s e d i n e a c h t e s t v a r i e s f o r the d i f f e r e n t s i t e s and g r a d u a l l y d e c r e a s e s a s t h e a r r a y s i z e i s i n c r e a s e d . T h i s o c c u r s a s a r e s u l t o f t h e i n c r e a s e d p r o b a b i l i t y o f t h e o c c u r r e n c e o f e r r o n e o u s p i x e l v a l u e s , c a u s e d by s a t e l l i t e m a l f u n c t i o n s , as t h e s i z e o f t h e d a t a a r r a y i n c r e a s e s . Images c o n t a i n i n g s u c h d a t a a r e not i n c o r p o r a t e d i n t h e r e l a t i o n s h i p between T a n d T R . The r e s u l t s p r e s e n t e d i n T a b l e s 5 . 9 - 5.11 i n d i c a t e t h a t w h i l e t h e s t r e n g t h ( e v i d e n t f rom t h e SE a n d r ) a n d n a t u r e ( e v i d e n t f rom ' a ' and ' b ' ) o f t h e r e l a t i o n s h i p a r e r e l a t i v e l y i n s e n s i t i v e t o c h a n g e s i n t h e c o n f i g u r a t i o n o f t h e a r r a y , 158 T A B L E 5 . 9 S t a t i s t i c s Showing t h e Impact o f U s i n g D i f f e r e n t A r r a y S i z e s on t h e R e l a t i o n s h i p Between T and T R . The P i x e l A r r a y s a r e C e n t r e d on U B C . A l l v a l u e s a r e P e r c e n t a g e s E x c e p t f o r t h e A r r a y S i z e ( p i x e l s ) , r 2 ( d i m e n s i o n l e s s ) a n d n . A r r a y S i z e SE o f T r 2 a b SE o f a SE o f b n 3 x 3 11 .74 0 . 8 9 6 8 113 .7 - 1 4 5 . 9 1.18 2 .72 334 5 x 5 1 1 .02 0 . 9 0 9 2 113 .9 - 1 4 7 . 6 1.11 2 . 5 7 333 7 x 7 1 0 .94 0 . 9 1 0 8 113 .5 - 1 4 7 . 4 1 .09 2 .54 332 9 x 9 10.91 0 . 9 1 1 2 113.2 - 1 4 7 . 2 1 .09 2 .53 332 1 1 X 1 1 1 0 . 9 4 0 . 9 1 0 8 113.2 - 1 4 7 . 4 1 . 09 2 .54 332 1 5 x 1 5 11 .17 0 .9071 113 .7 -148 . 4 1.12 2 .62 331 1 9 x 19 1 1 .54 0 . 9 0 0 8 113 .9 - 1 4 8 . 7 1.17 2 .72 331 159 T A B L E 5 . 1 0 S t a t i s t i c s S h o w i n g t h e Impact o f U s i n g D i f f e r e n t A r r a y S i z e s on t h e R e l a t i o n s h i p Between T and T R . The P i x e l A r r a y s a r e C e n t r e d on A B A I R . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r t h e A r r a y S i z e ( p i x e l s ) , r 2 ( d i m e n s i o n l e s s ) and n . A r r a y S i z e SE o f T r 2 a b SE o f a SE o f b n 3 x 3 14 .32 0 .8260 113 .6 -141 .0 1 .60 3 .57 331 5 x 5 , 1 4 . 2 2 0 .8284 113 .7 - 1 41 .6 1 .59 . 3 . 55 331 7 x 7 13 .87 0 . 8 3 6 6 114 .2 -1 43 .5 1 .56 3 .50 331 9 x 9 1 3 .82 0 . 8 3 7 9 114 .3 -143 .8 1 .55 3 . 4 9 331 1 1 x 1 1 1 3 .68 0.841 1 114 .4 -1 44 .3 1 .54 3 .46 331 1 5 x 1 5 13 .54 0 .8442 114 .5 -1 44 .6 1 .53 3 .43 330 19 x 19 13 .42 0 .8470 114 .6 - 1 44 . 9 1 .52 3 .40 330 160 T A B L E 5.11 S t a t i s t i c s S h o w i n g t h e Impact o f U s i n g D i f f e r e n t A r r a y S i z e s on t h e R e l a t i o n s h i p Between T and T R . The P i x e l A r r a y s a r e C e n t r e d on MAA. A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r t h e A r r a y S i z e ( p i x e l s ) , r 2 ( d i m e n s i o n l e s s ) and n . S i t e A r r a y S i z e T o t a l A r r a y S i z e SE o f T r 2 a b SE o f a SE o f b n 3 x 3 1 1 x 1 0 13 .98 0 .8342 114. 2 - 1 4 2 . 9 1 .57 3 .52 330 5 x 5 1 3 X 1 2 13.91 0 .8354 114. 3 - 1 4 3 . 3 1 .57 3 .52 329 7 x 7 1 5 X 1 4 13 .80 0 . 8379 114. 4 - 1 4 3 . 4 1 .55 3 . 4 9 329 9 x 9 1 7 X 1 6 13 .70 0 .8408 114. 4 - 1 4 3 . 5 1 . 54 3 . 4 6 328 1 1 X 1 1 19 X 18 13 .65 0 .8412 114. 4 -1 4 3 . 4 1 .54 3 .46 327 1 5 x 1 5 23 X 22 13 .58 0 .8425 113. 9 - 1 4 2 . 7 1 . 53 3 .43 325 1 9 x 19 27 X 26 1 3 . 50 0 .8442 113. 7 - 1 4 2 . 7 1.51 3 .40 325 161 t h e r e i s a s u g g e s t i o n o f an opt imum a r r a y s i z e . F o r t h e UBC s i t e the opt imum s i z e i s a 9 x 9 p i x e l a r r a y , w h i l e f o r t h e ABAIR and MAA s i t e s t h e 19 x 19 p i x e l a r r a y , and p o s s i b l y l a r g e r , a p p e a r s most a p p r o p r i a t e . The d i f f e r e n c e be tween t h e s i t e s may be a f u n c t i o n o f t h e d i f f e r e n t c l o u d c h a r a c t e r i s t i c s a t t h e s e s i t e s u n d e r c e r t a i n s y n o p t i c w e a t h e r c o n d i t i o n s ( see S e c t i o n 5 . 6 ) . R e c t a n g u l a r p i x e l a r r a y s were a l s o i n v e s t i g a t e d f o r t h e UBC and ABAIR s i t e s . The r e c t a n g l e s were 8 x 1 4 p i x e l s i n s i z e and t h e s i t e s were p o s i t i o n e d t o w a r d s t h e end o f t h e r e c t a n g l e so t h a t t h e r e c t a n g l e was e l o n g a t e d away f rom t h e s i t e ( see F i g u r e 5 . 4 ) . The r e c t a n g l e s a r e d e s c r i b e d i n t e rms o f t h e d i r e c t i o n i n w h i c h t h e y p r o j e c t away f rom t h e s i t e ( i . e . n o r t h , e a s t , s o u t h and w e s t ) . I n s p e c t i o n o f t h e r e s u l t s i n T a b l e 5 . 1 2 s u g g e s t t h a t t h e r e i s a p r e f e r r e d d i r e c t i o n f o r e a c h s i t e . F o r t h e UBC s i t e t h e p r e f e r r e d d i r e c t i o n s o f west and s o u t h i n d i c a t e some r e l a t i o n t o t h e d i r e c t i o n o f movement o f t h e p r e v a i l i n g s y n o p t i c w e a t h e r s y s t e m s (Hay and O k e , 1 9 7 6 ) . A t t h e ABAIR s i t e t h e r e a s o n f o r t h e r e c t a n g l e w i t h a n o r t h e r l y p r o j e c t i o n p r o v i d i n g t h e l o w e s t SE o f T i s no t c l e a r . When c o m p a r i n g t h e r e s u l t s u s i n g t h e r e c t a n g u l a r s a t e l l i t e a r r a y s ( T a b l e 5 . 1 2 ) t o t h o s e u s i n g s q u a r e c o n f i g u r a t i o n s ( T a b l e s 5.1 t o 5 . 1 1 ) , b o t h w i t h and w i t h o u t a BDR c o r r e c t i o n , t h e r e a p p e a r s l i t t l e d i f f e r e n c e . I t i s w o r t h n o t i n g , h o w e v e r , t h a t a t t h e UBC s i t e t h e r e c t a n g l e w i t h a west p r o j e c t i o n g i v e s t h e l o w e s t s t a n d a r d e r r o r f o r a l l t e s t s 1 6 2 N O R T H W E S T G r o u n d S t a t i o n E A S T S O U T H S c a l e ( P i x e l s ) FIGURE 5.4 R e c t a n g u l a r S a t e l l i t e A r r a y s U s e d t o T e s t S y n o p t i c I n f l u e n c e s . 163 T A B L E 5 .12 S t a t i s t i c s Showing t h e Impact o f U s i n g D i f f e r e n t R e c t a n g u l a r C o n f i g u r a t i o n s on t h e R e l a t i o n s h i p Between T and T R . The P i x e l A r r a y s a r e C e n t r e d on a) UBC and b) A B A I R . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r r 2 ( d i m e n s i o n l e s s ) and n . a . UBC A r r a y SE o f r 2 a b SE o f SE o f n P r o j e c t i o n T a b N o r t h 12 .42 0. 8850 113 .0 - 1 4 5 . 2 1 .25 2 . 8 8 332 E a s t 11 .76 0 . 8968 115 .5 - 1 4 9 . 7 1.21 2 . 8 0 332 S o u t h 10 .97 0 . 9101 113.1 - 1 4 7 . 9 1 . 09 2 . 5 6 333 West 10 .59 0 . 91 63 111 .9 - 1 4 6 . 3 1 .03 2 .43 332 b . ABAIR N o r t h 13 .12 0 . 8528 115.1 - 1 4 5 . 0 1 . 49 3 .34 328 E a s t 14 .06 0 . 831 7 113 .8 - 1 4 2 . 3 1 .58 3 .54 330 S o u t h 13 .86 0 . 8363 113 .7 - 1 4 2 . 8 1 .55 3 .49 330 West 13 .79 0 . 8383 114 .4 - 1 4 3 . 8 1 .56 3 .50 328 164 ( s ee T a b l e 5 . 1 2 a ) . T h i s h i g h l i g h t s t h e a d v a n t a g e s o f r e l a t i n g t h e s a t e l l i t e a r r a y c o n f i g u r a t i o n t o t h e p r e d o m i n a n t movements o f c l o u d s i n t h e a r e a . The MAA s i t e shows l i t t l e i m p r o v e m e n t i n t h e r e l a t i o n s h i p o v e r t h e s i n g l e s i t e o f A B A I R , d e s p i t e t h e i n c r e a s e d d e n s i t y o f n e t w o r k measurement d a t a . The r e s u l t s f o r MAA ( T a b l e 5 . 1 1 ) a r e worse t h a n t h o s e f o r ABAIR ( T a b l e 5 . 1 0 ) once t h e p i x e l a r r a y s i z e a r o u n d t h e i n d i v i d u a l s t a t i o n s i s g r e a t e r t h a n 11 x 11 p i x e l s . I f a c o m p a r i s o n i s made be tween t h e a c t u a l o v e r a l l a r r a y s i z e f o r MAA ( T a b l e 5 . 1 1 , c o l u m n 2) t o a s i m i l a r s i z e f o r t h e s i n g l e ABAIR s i t e ( T a b l e 5 . 1 0 ) , i t a p p e a r s t h a t t h e i n c r e a s e d d e n s i t y o f g r o u n d b a s e d d a t a c o n s i s t e n t l y g i v e s a g r e a t e r s t a n d a r d e r r o r . H o w e v e r , t h e r e a s o n f o r t h e g e n e r a l s i m i l a r i t y i n t h e r e s u l t s f o r t h e s e two s i t e s ( T a b l e s 5 .10 and 5 . 1 1 ) may be due t o t h e s i m i l a r i t y i n t h e r a d i a t i o n r e g i m e s a t t h e t h r e e p y r a n o m e t r i c s t a t i o n s u s e d f o r t h e MAA s i t e . F i g u r e s 5 . 5 t o 5 . 7 a n d T a b l e s 5 . 1 3 and 5 .14 s u g g e s t t h a t t h e m e a s u r e d r a d i a t i o n r e g i m e s a r e c o m p a r a b l e b e c a u s e o f : 1) t h e s y m m e t r i c n a t u r e o f t h e s c a t t e r p l o t s ( see F i g u r e s 5 . 5 t o 5 . 7 ) a r o u n d an a l m o s t 1:1 l i n e a r r e l a t i o n s h i p ( T a b l e 5 . 1 3 ) ; a n d 2) t h e s i m i l a r i t y o f t h e means and s t a n d a r d d e v i a t i o n s f o r t h e d i f f e r e n t s i t e s ( T a b l e 5 . 1 4 ) . 165 FIGURE 5 . 5 S c a t t e r P l o t C o m p a r i n g H o u r l y S h o r t w a v e R a d i a t i o n T o t a l s Between A B L I B and M I S S . Number o f O b s e r v a t i o n s = 4 2 1 . 166 FIGURE 5 . 6 S c a t t e r P l o t C o m p a r i n g H o u r l y S h o r t w a v e R a d i a t i o n T o t a l s Between ABAIR a n d M I S S . Number o f O b s e r v a t i o n s = 418 . 167 FIGURE 5 .7 S c a t t e r P l o t C o m p a r i n g H o u r l y S h o r t w a v e R a d i a t i o n T o t a l s Between ABAIR and A B L I B . Number o f O b s e r v a t i o n s = 416 . 168 TABLE 5.13 C o m p a r a t i v e S t a t i s t i c s f o r t h e H o u r l y Shortwave R a d i a t i o n Measurements a t t h e T h r e e V a l l e y S i t e s . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r r 2 ( d i m e n s i o n l e s s ) and n. S t a t i o n Compar i son r 2 a b n ABAIR v. ABLIB 0 .9677 24. 29 0 .9932 416 ABAIR v. MISS 0 .9288 47. 36 0 .9788 418 ABLIB v. MISS 0 .9467 28. 21 0 .9793 421 169 T A B L E 5 .14 The Mean and S t a n d a r d D e v i a t i o n f o r H o u r l y S h o r t w a v e R a d i a t i o n M e a s u r e m e n t s a t t h e T h r e e V a l l e y S i t e s . V a l u e s a r e i n k j m _ 2 h r _ : Mean S t a n d a r d S i t e of K+- D e v i a t i o n o f K+ ABAIR 914. .6 868. .8 A B L I B 893. .2 859. .5 MISS 881 . . 1 853. .0 170 . I n s p e c t i o n o f t h e c o n s t a n t s (a) and c o e f f i c i e n t s (b) f o r t h e r e g r e s s i o n e q u a t i o n s i n T a b l e s 5 . 9 t o 5 .12 show t h a t t h e r e i s l i t t l e c h a n g e i n t h e f o r m o f t h e r e l a t i o n s h i p as t h e p i x e l a r r a y c o n f i g u r a t i o n i s a l t e r e d . 5 . 4 . 2 I m p l i c a t i o n o f R e s u l t s S e c t i o n 5 . 4 . 1 r e v e a l e d s u b s t a n t i a l d i f f e r e n c e s i n t h e opt imum c o n f i g u r a t i o n s f o r t h e t h r e e t e s t s i t e s . H o w e v e r , t h e s m a l l v a r i a t i o n s i n t h e e r r o r s t a t i s t i c s f o r t h e r e l a t i o n s h i p be tween T and TR i m p l y t h a t c h a n g e s i n t h e s p a t i a l a v e r a g i n g o f t h e s a t e l l i t e d a t a have l i t t l e i m p a c t . T h e r e f o r e a s m o d e l l i n g p r o c e d u r e s u s i n g s a t e l l i t e i n f o r m a t i o n c h a r a c t e r i s t i c a l l y i n v o l v e v o l u m i n o u s d a t a s e t s , t h e a b i l i t y t o use s m a l l p i x e l a r r a y s i z e s p r e s e n t s a c o n s i d e r a b l e a d v a n t a g e . 5 . 5 Impact o f T i m e A v e r a g i n g Random f l u c t u a t i o n s i n s o l a r r a d i a t i o n h a v e been w e l l d o c u m e n t e d ( see Hay and H a n s o n , 1 9 8 3 ) . T h e s e f l u c t u a t i o n s a f f e c t t h e a b i l i t y o f m o d e l s t o e s t i m a t e t h e s o l a r i r r a d i a n c e a t t h e E a r t h ' s s u r f a c e . I n c r e a s e d t i m e a v e r a g i n g 171 s i g n i f i c a n t l y i m p r o v e s t h e p e r f o r m a n c e o f s u c h m o d e l s ( D a v i e s e t a l . , 1 9 7 5 ; S u c k l i n g , 1 9 7 7 ) . T h u s i t i s a p p r o p r i a t e t o c o n s i d e r t h e i m p a c t o f t e m p o r a l a v e r a g i n g , and a g a i n t h e r e l a t i o n s h i p be tween T and TR i s u s e d . T w o - h o u r l y r u n n i n g means were c a l c u l a t e d f o r t h e s h o r t w a v e t r a n s m i s s i o n s and t a r g e t r e f l e c t a n c e s a t t h e UBC, ABAIR and MAA s i t e s t o p r o v i d e a c o m p a r i s o n w i t h t h e o n e - h o u r l y r e s u l t s . F o r t h e o n e - h o u r l y t e s t s , two or more s a t e l l i t e images a r e r e q u i r e d p e r h o u r l y p e r i o d t o c a l c u l a t e t h e TR v a l u e . T h e r e f o r e , f o u r o r more images were deemed n e c e s s a r y f o r t h e t w o - h o u r l y t e s t s ( s ee S e c t i o n 5 . 6 f o r f u r t h e r d i s c u s s i o n on t h i s t o p i c ) . The r e s u l t s a r e p r e s e n t e d i n T a b l e 5 . 1 5 . I n s p e c t i o n o f t h e s t a n d a r d e r r o r s i n e s t i m a t i n g T show i t t o be s u b s t a n t i a l l y r e d u c e d , w h i l e r 2 ha s i n c r e a s e d when c o m p a r i n g t h e ' t w o - h o u r l y t e s t s t o t h e o n e - h o u r l y r e s u l t s . T h e r e i s , h o w e v e r , l i t t l e c h a n g e i n t h e r e g r e s s i o n e q u a t i o n s ( see ' a ' and ' b ' i n T a b l e 5 . 1 5 ) , s u g g e s t i n g t h a t t h e l a r g e r e s i d u a l s a r e n o t g r e a t l y i n f l u e n c i n g t h e form o f t h e r e l a t i o n s h i p d e v e l o p e d between T a n d T R . F i g u r e 5 .8 shows t h e s c a t t e r i s much r e d u c e d f o r t h e t w o - h o u r l y a v e r a g i n g i n c o m p a r i s o n t o t h e e q u i v a l e n t o n e - h o u r l y t i m e s c a l e ( see F i g u r e 5 . 2 ) . W h i l e t h e r e i s some r e d u c t i o n i n s c a t t e r t h r o u g h o u t t h e f u l l r a n g e o f c l o u d c o n d i t i o n s , t h e m a j o r i t y o f t h e r e d u c t i o n a p p e a r s t o be f o r 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 ( i . e . be low 80% c l e a r 172 T A B L E 5 . 1 5 S t a t i s t i c s S h o w i n g t h e Impact o f I n c r e a s i n g t h e T ime A v e r a g i n g P e r i o d on t h e R e l a t i o n s h i p Between T and TR a t t h e T h r e e S i t e s a) UBC, b) ABAIR and c ) MAA. A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r t h e A r r a y S i z e ( p i x e l s ) , r 2 ( d i m e n s i o n l e s s ) and n . a . U B C . T i m e A r r a y P e r i o d S i z e ( H o u r s ) SE o f T 2 r a b SE o f a SE o f b n 7 x 7 1 1 0 .94 0 .91 08 1 1 3 .5 -147 .4 1 .09 2 .54 332 7 x 7 2 8 . 8 7 0 .9407 1 1 3 .6 -1 48 .0 0 . 9 4 2 . 1 9 291 1 5 x 1 5 1 11 .17 0 .9071 1 1 3 .7 -1 48 .4 1.12 2 .62 331 1 5 x 1 5 2 9 . 2 9 0 . 9349 1 1 3 .7 -1 48 .2 1 .00 2 .34 282 8 x 14(W) 1 10 .59 0 . 9163 1 1 1 . 9 -1 46 .3 1 .03 2 . 4 3 332 8 x 14(W) 2 8 . 5 6 0 . 9449 1 1 1 . 9 -1 46 .8 0 . 8 9 2 .10 288 b . A B A I R . 7 X 7 1 1 3 .87 0 . 8 3 6 6 114 .2 - 1 4 3 . 5 1 .56 3 .50 331 7 X 7 2 10 .93 0 . 8 9 7 7 115 .8 - 1 4 6 . 9 1 .32 2 .94 286 1 5 X 1 5 1 1 3 .54 0 .8442 114 .5 - 1 4 4 . 6 1 .53 3 .43 330 1 5 X 1 5 2 10 .12 0 . 9 1 1 7 115 .8 - 1 4 7 . 1 1 .23 2 .76 277 8 X 1 4 (S) 1 1 3 .86 0 . 8 3 6 3 113 .7 - 1 4 2 . 8 1 .55 3 .49 330 8 X 1 4 (S) 2 10 .82 0 .8994 115.1 - 1 4 6 . 8 1.31 2 . 9 6 277 C . MAA. 7 X 7 1 1 3 .80 0 . 8 3 7 9 114 .4 - 1 4 3 . 4 1 . 55 3 .49 329 7 X 7 2 10 .79 0 .8998 115 .9 - 1 4 6 . 6 1 .31 2 .92 282 15 X 1 5 1 1 3 .58 0 . 8 4 2 5 113 .9 - 1 4 2 . 7 1 .53 3 .43 325 1 5 X 1 5 2 10 .17 0 . 9 1 1 0 115 .6 - 1 4 6 . 3 1 .26 2 .80 269 173 1201 i .—— 1 1 • — — 1 0 0.2 0.4 0.6 0.8 TR (dimensionless) FIGURE 5 . 8 S c a t t e r P l o t o f T w o - H o u r l y A v e r a g e d S h o r t w a v e T r a n s m i s s i o n (T) A g a i n s t U n c o r r e c t e d S a t e l l i t e T a r g e t R e f l e c t a n c e (TR) F o r t h e UBC S i t e U s i n g A 7 x 7 P i x e l A r r a y and t h e L a r g e r D a t a S e t . Number p f O b s e r v a t i o n s = 2 9 1 . 174 s k y t r a n s m i s s i o n ) . Thus many o f t h e l a r g e r e s i d u a l s p r e s e n t i n t h e o n e - h o u r l y a v e r a g i n g a r e no l o n g e r e v i d e n t . T h i s i s p r o b a b l y a r e s u l t o f t h e s m o o t h i n g o f t h e more i n h o m o g e n e o u s n a t u r e o f t h e r a d i a t i o n f i e l d u n d e r p a r t l y c l o u d y and o v e r c a s t s i t u a t i o n s . Such a v e r a g i n g a l s o r e d u c e s t h e s c a t t e r as images t h a t may m i s r e p r e s e n t a h a l f - h o u r l y p e r i o d have l e s s w e i g h t on t h e r e s u l t a n t t a r g e t r e f l e c t a n c e v a l u e ( i . e . f o r a o n e - h o u r l y p e r i o d t h e image may c a r r y up t o a 50% w e i g h t i n g , w h i l e f o r t h e e q u i v a l e n t t w o - h o u r l y p e r i o d t h e maximum w e i g h t i s 25%). W i t h r e s p e c t t o t h i s l a t t e r r e a s o n i n g , t h e f o l l o w i n g s e c t i o n w i l l i n v e s t i g a t e t h e i m p o r t a n c e o f t h e number o f s a t e l l i t e images r e q u i r e d t o a d e q u a t e l y r e p r e s e n t a one o r t w o - h o u r l y t i m e p e r i o d . 5 . 6 I n f l u e n c e o f S a t e l l i t e Image A v a i l a b i l i t y In S e c t i o n 5 . 5 i t became e v i d e n t t h a t t h e number o f s a t e l l i t e images r e q u i r e d p e r t i m e i n t e r v a l t o c a l c u l a t e TR i n f l u e n c e d the s t r e n g t h o f t h e r e l a t i o n s h i p be tween T and T R . The maximum number o f s a t e l l i t e images t h a t c o u l d r e p r e s e n t a o n e - h o u r l y and t w o - h o u r l y t i m e p e r i o d , a r e t h r e e ( see S e c t i o n 3 . 7 ) and f i v e images r e s p e c t i v e l y . T h r o u g h o u t t h i s s t u d y i t was s t i p u l a t e d , somewhat s u b j e c t i v e l y , t h a t a t l e a s t two images were n e e d e d f o r t h e o n e - h o u r l y a v e r a g i n g p e r i o d . T h i s 175 was a c o m p r o m i s e g i v e n t h e f o l l o w i n g : 1 ) i f a t l e a s t one image p e r h o u r was r e q u i r e d , t h o s e h o u r l y p e r i o d s when o n l y one image was a v a i l a b l e w o u l d p r o b a b l y n o t c a p t u r e t h e c h a n g e s i n t h e r a d i a t i o n r e g i m e ( e s p e c i a l l y u n d e r p a r t l y c l o u d y c o n d i t i o n s ) ; and 2) i f t h r e e images p e r h o u r were r e q u i r e d , t h e s i z e of t h e d a t a s e t w o u l d be r e d u c e d . F o r t h e t w o - h o u r l y t i m e p e r i o d , ' t h e minimum number o f images r e q u i r e d p e r t i m e i n t e r v a l was d o u b l e d t o a t l e a s t f o u r . T h e r e f o r e i t was d e c i d e d t o a s s e s s t h e e f f e c t on t h e r e l a t i o n s h i p o f c h a n g i n g t h e c o n s t r a i n t on t h e number o f images r e q u i r e d , f o r b o t h t h e o n e - h o u r l y and t w o - h o u r l y t i m e i n t e r v a l s . The t e s t s were c a r r i e d o u t f o r a l l t h r e e s i t e s , U B C , ABAIR a n d MAA, u s i n g a s e l e c t i o n of p i x e l a r r a y c o n f i g u r a t i o n s . ABAIR and MAA were o n l y t e s t e d u s i n g t h e t w o - h o u r l y r u n n i n g mean d a t a . I n s p e c t i o n o f T a b l e s 5 . 1 6 t o 5 . 1 9 r e v e a l s s u b s t a n t i a l r e d u c t i o n s i n t h e s t a n d a r d e r r o r f o r e s t i m a t i n g T and l i k e w i s e an i n c r e a s e i n t h e c o e f f i c i e n t o f d e t e r m i n a t i o n as t h e number o f images r e q u i r e d f o r e i t h e r o n e - h o u r l y o r t w o - h o u r l y t i m e i n t e r v a l s i n c r e a s e s . 176 T A B L E 5 . 1 6 S t a t i s t i c s S h o w i n g t h e Impact o f C h a n g e s t o t h e Image R e q u i r e m e n t s P e r O n e - H o u r l y T i m e P e r i o d on t h e R e l a t i o n s h i p Between T and TR a t t h e UBC S i t e . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r t h e A r r a y S i z e ( p i x e l s ) , r 2 ( d i m e n s i o n l e s s ) a n d n . A r r a y S i z e Number o f Imaqes SE of T r 2 a b SE o f a SE o f b n 7 x 7 > 1 14 .62 0 .8378 111 . 5 -141 .0 1 .40 3 . 2 0 379 7 x 7 >2 1 0 .94 0 .9108 113. 5 -147 .4 1 . 09 2 . 5 4 332 7 x 7 3 10.51 0 . 9207 113. 8 -1 47 .8 1.14 2 . 6 2 277 15 x 1 5 > 1 1 4 . 56 0 .8395 112. 0 -143 .3 1.41 3 .24 376 15 x 1 5 >2 11 .17 0 .9071 113. 7 -1 48 .4 1.12 2 . 6 2 331 1 5 x 1 5 3 10 .86 0 .91 53 114. 1 - 1 48 . 9 1 .20 2 . 7 8 268 8 x 1 4 (W) > 1 14 .33 0 .8444 1 10. 2 -140 . 6 1 . 35 3.11 378 8 x 1 4(W) >2 10 .59 0 .9163 111 . 9 -1 46 . 3 1 . 03 2 . 4 3 332 8 x 1 4(W) 3 9 . 9 5 0 . 9289 112. 2 -1 46 .6 1 .06 2 . 4 6 275 8 x 1 4 (S) > 1 14 .44 0 .841 9 111. 4 -141 .9 1 .38 3 .17 378 8 x 1 4 ( S ) >2 10 .97 0 .9101 113 . 1 -1 47 . 9 1 .09 2 . 5 6 333 8 x 1 4 (S ) 3 10 .17 0 .9254 113. 5 -1 48 .5 1.10 2 . 5 7 271 177 T A B L E 5 . 1 7 S t a t i s t i c s S h o w i n g t h e Impact o f C h a n g e s t o t h e Image R e q u i r e m e n t s P e r T w o - H o u r l y T ime P e r i o d on t h e R e l a t i o n s h i p Between T and TR a t t h e UBC S i t e . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r t h e A r r a y S i z e ( p i x e l s ) and r 2 ( d i m e n s i o n l e s s ) a n d n . Number A r r a y S i z e o f Images SE o f T r 2 a b SE o f a SE o f b n 7 x 7 >2 11 .37 0 .8984 1 12 .6 -1 4 4 . 1 1.12 2 . 57 357 7 x 7 >3 10 .03 0 .9232 1 1 3 . 1 - 1 4 7 . 3 1.01 2 . 32 337 7 x 7 >4 8 . 8 7 0 .9407 1 1 3 .6 -1 4 8 . 0 0 . 9 4 2 . 1 9 291 7 x 7 5 8 . 5 8 0 .9466 1 1 4 .3 -1 4 9 . 1 1 .03 2 . 39 221 1 5 x 1 5 >2 11 .44 0 .8971 1 1 2 .8 - 1 4 5 . 3 1.13 2 . 61 357 1 5 x 1 5 >3 10 .26 0 .91 94 1 1 3 . 1 -148. 1 1 .03 2 . 41 334 1 5 x 1 5 >4 9 . 2 9 0 .9349 1 1 3 .7 -1 48 . 2 1 .00 2 . 34 282 1 5 x 1 5 5 8 . 9 2 0 .9418 1 1 4 .6 -1 5 0 . 1 1 .09 2 . 58 2 1 2 8 x 1 4 (W) >2 11 .24 0 .9008 1 1 0 . 9 - 1 4 2 . 7 1 .08 2 . 51 357 8 x 1 4(W) >3 9 . 6 5 0 .9290 1 1 1 .6 -1 46 . 3 0 .94 2 . 21 337 8 x 1 4(W) >4 8 . 5 6 0 .9449 1 1 1 . 9 -1 46 . 8 0 . 8 9 2 . 1 0 288 8 x 1 4(W) 5 8.11 0 .9523 1 1 2 .5 - 1 4 7 . 8 0 . 9 5 2 . 25 219 1 7 8 T A B L E 5 . 1 8 S t a t i s t i c s S h o w i n g t h e Impact o f C h a n g e s t o t h e Image R e q u i r e m e n t s P e r T w o - H o u r l y T i m e P e r i o d on t h e R e l a t i o n s h i p Between T and TR a t t h e ABAIR S i t e . A l l V a l u e s a r e P e r c e n t a g e s E x c e p t f o r t h e A r r a y S i z e ( p i x e l s ) , r 2 ( d i m e n s i o n l e s s ) and n . A r r a y S i z e Number o f Images SE o f T r 2 a b SE o f a SE o f b . n 7 x 7 >2 1 2 . 9 3 0 . 8499 114. 2 -1 4 2 . 8 1 .43 3 .19 355 7 x 7 >3 12.81 0 .8538 1 14. 1 -1 4 2 . 3 1 .46 3 .24 332 7 x 7 >4 1 0 . 9 3 0 .8977 115. 8 - 1 4 6 . 9 1 .32 2 .94 286 7 x 7 5 9 . 8 6 0 .91 80 117. 0 -1 4 9 . 0 1 .38 3 .07 212 1 5 x 1 5 >2 12 .62 0 . 8573 114. 4 -1 4 3 . 7 1 .40 3 .13 353 15 x 1 5 >3 12 .43 0 .8632 1 14. 5 - 1 4 3 . 5 1 .42 3 .15 330 1 5 x 1 5 >4 10 .12 0 . 9117 115. 8 -1 4 7 . 1 1 .23 2 . 7 6 277 1 5 x 1 5 5 9 . 6 6 0 . 9209 117. 4 -1 4 9 . 8 1 .43 3.19 191 179 T A B L E 5 . 1 9 S t a t i s t i c s Showing t h e Impact o f C h a n g e s t o t h e Image R e q u i r e m e n t s Per T w o - H o u r l y T i m e P e r i o d o n , t h e R e l a t i o n s h i p Between T and TR a t t h e MAA S i t e . A r r a y S i z e Number o f Images SE o f T r 2 a b SE o f a SE o f b n 7 x 7 >2 12 .78 0 .8536 114 .3 -1 4 3 . 0 1.41 3 .15 355 7 x 7 >3 1 2 . 6 6 0 .8570 114 .2 -1 4 2 . 4 1 .44 3 . 2 2 329 7 x 7 >4 10 .79 0 .8998 115 .9 - 1 4 6 . 6 1 .31 2 .92 282 7 x 7 5 9 . 8 9 0 .91 68 1 17 .4 - 1 4 9 . 3 1 .43 3 .20 200 15 x 1 5 >2 1 2 . 6 2 0 .8572 113 .8 -1 4 2 . 1 1 .39 3 . 0 9 354 15 x 1 5 >3 12.51 0 . 8613 113 .9 -1 4 2 . 0 1 .42 3 .18 323 1 5 x 1 5 >4 10 .17 0 .9110 115 .6 - 1 4 6 . 3 1 .26 2 . 8 0 269 180 I n c r e a s i n g t h e number o f s a t e l l i t e images r e q u i r e d r e s u l t s i n r e m o v i n g t h o s e t i m e p e r i o d s when : 1) t h e r e a r e an i n s u f f i c i e n t number o f s a t e l l i t e images t o a d e q u a t e l y r e p r e s e n t t h e r a d i a t i o n r e g i m e t h r o u g h t h e t i m e i n t e r v a l ; and 2) t h e r e i s a l a r g e r w e i g h t i n g a p p l i e d t o images t h a t may m i s r e p r e s e n t t h e r a d i a t i o n c o n d i t i o n s ( see S e c t i o n 5 . 5 ) . As more images a r e r e q u i r e d p e r t i m e i n t e r v a l , t h e r e i s a marked r e d u c t i o n i n t h e number o f d a t a p o i n t s (n) u s e d t o d e v e l o p t h e r e l a t i o n s h i p be tween T and T R . H o w e v e r , t h e i m p r o v e m e n t s i n t h e SE o f T and r s u g g e s t t h e i n c r e a s e d t e m p o r a l s a m p l i n g f r e q u e n c y f o r t h e s a t e l l i t e d a t a i s i n s t r u m e n t a l i n i m p r o v i n g t h e r e l a t i o n s h i p be tween T and T R . The o n e - h o u r l y t i m e a v e r a g i n g ( T a b l e 5 . 1 6 ) shows a marked i m p r o v e m e n t i n t h e r e l a t i o n s h i p when t h e s a t e l l i t e image r e q u i r e m e n t s a r e i n c r e a s e d f rom a t l e a s t one image , t o a t l e a s t two f o r e a c h h o u r l y p e r i o d . When t h r e e images a r e deemed n e c e s s a r y , t h e i m p r o v e m e n t i s no t as p r o n o u n c e d . F o r t h e t w o - h o u r l y a v e r a g i n g a t t h e UBC s i t e ( T a b l e 5 . 1 7 ) t h e l a r g e s t i m p r o v e m e n t s i n t h e s t a t i s t i c s a r e f o u n d when i n c r e a s i n g t h e image r e q u i r e m e n t s t o a t l e a s t t h r e e , and a t 181 l e a s t f o u r i m a g e s . The s m a l l e s t i m p r o v e m e n t s o c c u r when t h e r e q u i r e m e n t s a r e i n c r e a s e d t o f i v e i m a g e s , t h e maximum number o f images p o s s i b l e f o r a t w o - h o u r l y p e r i o d . The s t a t i s t i c s f o r t h e v a l l e y s i t e s o f ABAIR ( T a b l e 5 . 1 8 ) and MAA ( T a b l e 5 . 1 9 ) show most i m p r o v e m e n t when t h e image r e q u i r e m e n t s a r e i n c r e a s e d t o a t l e a s t f o u r images and o n l y m i n o r i m p r o v e m e n t f o r i n c r e a s e s t o a t l e a s t t h r e e o r t o f i v e i m a g e s . The d i f f e r e n c e i n t h e improvement s e e n a t t h e v a l l e y s i t e s c o m p a r e d t o t h e UBC s i t e may be due t o t h e g r e a t e r o c c u r r e n c e o f p a r t l y c l o u d y c o n d i t i o n s a t t h e v a l l e y s i t e s ( see S e c t i o n 5 . 7 ) . T h u s a t t h e v a l l e y s i t e s more images a r e deemed n e c e s s a r y ( i . e . a t l e a s t f o u r images ) . b e f o r e t h e r e i s a l a r g e i m p r o v e m e n t i n t h e s t r e n g t h o f t h e r e l a t i o n s h i p . The r e s u l t s f rom t h i s s e c t i o n s u g g e s t t h a t t h e most c o h e r e n t r e l a t i o n s h i p be tween T and TR may be d e v e l o p e d when u s i n g o n l y t h o s e t i m e p e r i o d s f o r w h i c h t h e maximum number o f p o s s i b l e images a r e a v a i l a b l e ( i . e . t h r e e images and f i v e images f o r t h e o n e - h o u r l y and t w o - h o u r l y t i m e p e r i o d s r e s p e c t i v e l y ) . H o w e v e r , o n l y m i n o r d e t e r i o r a t i o n s i n t h e s t r e n g t h o f t h e r e l a t i o n s h i p o c c u r s when u s i n g a t l e a s t two images f o r t h e o n e - h o u r l y , and a t l e a s t f o u r images f o r t h e t w o - h o u r l y t i m e p e r i o d . T h u s i t c a n be c o n c l u d e d t h a t t h e image r e q u i r e m e n t s u s e d t h r o u g h o u t t h i s s t u d y p r o v i d e a d e q u a t e v a l u e s f o r t h e t a r g e t r e f l e c t a n c e . 182 5 .7 V a l l e y and C o a s t a l S i t e C o m p a r i s o n From t h e r e s u l t s p r e s e n t e d e a r l i e r i n t h i s c h a p t e r some i n t e r e s t i n g c o m p a r i s o n s i n t h e r a d i a t i o n r e g i m e s b e t w e e n t h e c o a s t a l s i t e , U B C , a n d t h e v a l l e y s i t e s , ABAIR and MAA, c a n be d e d u c e d . The two v a l l e y s i t e s show c o n s i s t e n t l y s i m i l a r r e s u l t s and p r o d u c e a weaker r e l a t i o n s h i p be tween T and TR t h a n t h o s e f o r t h e c o a s t a l s i t e . The r e a s o n f o r t h e f o r m e r i s l i k e l y due t o t h e d a t a f o r ABAIR b e i n g i n c o r p o r a t e d i n t h e MAA s i t e , and the p r o x i m i t y of t h e t h r e e s i t e s u s e d t o d e r i v e MAA. The r e a s o n f o r t h e d i f f e r e n c e s between t h e c o a s t a l and v a l l e y s i t e s a r e p r o b a b l y a f u n c t i o n o f l o c a l c l i m a t o l o g i c a l phenomena b e c a u s e a l l s i t e s i n t h i s s t u d y e x p e r i e n c e t h e same s y n o p t i c w e a t h e r c o n d i t i o n s . The d i f f e r e n c e s a r e most p r o n o u n c e d u n d e r s p e c i f i c s y n o p t i c f l o w p a t t e r n s when m e s o s c a l e i n h o m o g e n e i t i e s a r e b e s t d e v e l o p e d w i t h r e s p e c t t o a t m o s p h e r i c a e r o s o l c o n c e n t r a t i o n s and p a r t i c u l a r l y t o c l o u d c o n d i t i o n s . U n d e r p e r s i s t e n t a n t i c y c l o n i c w e a t h e r , a t m o s p h e r i c a e r o s o l c o n c e n t r a t i o n s a r e known t o be g r e a t e r f u r t h e r i n l a n d d u r i n g d a y l i g h t h o u r s as a r e s u l t o f t h e l a n d and sea b r e e z e c i r c u l a t i o n s y s t e m i n t h e Lower F r a s e r V a l l e y (Hay and O k e , l 9 7 6 ) . The i m p a c t w i l l be g r e a t e s t f o r c l e a r sky c o n d i t i o n s and t h e r e f o r e has a s t o n g c o n t r o l on where t h e l i n e a r r e l a t i o n s h i p i n t e r c e p t s t h e Y - a x i s . H o w e v e r , F i g u r e 183 5 . 9 shows t h a t t h e d i f f e r e n c e i n t h e Y - i n t e r c e p t f o r t h e c o a s t a l and v a l l e y s i t e s i s s m a l l , a s i s t h e d i f f e r e n c e be tween t h e g r a d i e n t s of t h e r e g r e s s i o n l i n e s . I t i s d i f f i c u l t t o draw any f i n a l c o n c l u s i o n s f rom F i g u r e 5 . 9 p a r t l y b e c a u s e o f t h e unknown r a d i a t i v e p r o p e r t i e s o f a e r o s o l s and t h e g r e a t e r r e f l e c t i v i t y o f t h e g r o u n d s u r f a c e a t t h e v a l l e y s i t e . H o w e v e r , i t i s a p p a r e n t t h a t s u c h m e s o s c a l e d i f f e r e n c e s have l i t t l e i m p a c t on t h e n a t u r e o f t h e r e g r e s s i o n r e l a t i o n s h i p . A c o m p a r i s o n o f F i g u r e s 5 . 2 , 5 . 3 a n d 5 . 1 0 show t h e two v a l l e y s i t e s , ABAIR ( F i g u r e 5 . 3 ) and MAA ( F i g u r e 5 . 1 0 ) , t o have a g r e a t e r p r e p o n d e r a n c e o f p a r t l y c l o u d y d a t a p o i n t s t h a n a t t h e UBC s i t e ( F i g u r e 5 . 2 ) . T h i s i s a l s o shown q u a n t i t a t i v e l y i n F i g u r e 5 . 1 1 . T h i s d i f f e r e n c e i s p r o b a b l y a f u n c t i o n o f more a c t i v e c o n v e c t i v e p r o c e s s e s e x p e r i e n c e d f u r t h e r away f rom t h e m o d e r a t i n g e f f e c t o f t h e s e a . S u c h c o n v e c t i v e p r o c e s s e s w i l l i n f l u e n c e t h e c l o u d c h a r a c t e r i s t i c s i n two w a y s : 1) U n d e r o t h e r w i s e c l e a r s k y c o n d i t i o n s , d i s c r e t e c e l l u l a r c l o u d s ( c u m u l u s ) w i l l f o rm as a r e s u l t o f t h e h e a t i n g o f t h e g r o u n d s u r f a c e . T h i s p r o c e s s i s more p r o n o u n c e d a t t h e v a l l e y s i t e s a s a r e s u l t o f g r e a t e r h e a t i n g and t h e p r o x i m i t y of a sea b r e e z e f r o n t w h i c h d e v e l o p s u n d e r s u c h c o n d i t i o n s . T h e c l o u d s t e n d t o d i s s i p a t e a s t h e y a r e c a r r i e d away f rom t h e i r s o u r c e s o f h e a t and m o i s t u r e by t h e s y n o p t i c w i n d s above t h e 184 T (%) 1.0 FIGURE 5 . 9 C o m p a r i s o n o f t h e R e g r e s s i o n E q u a t i o n s F o r UBC a n d A B A I R . The R e g r e s s i o n E q u a t i o n s a r e B a s e d on t h e L a r g e r D a t a Set W i t h o u t a BDR C o r r e c t i o n t o T R . TR i s D i m e n s i o n l e s s . 185 TR (dimensionless) FIGURE 5 . 1 0 S c a t t e r P l o t o f S h o r t w a v e T r a n s m i s s i o n (T) A g a i n s t U n c o r r e c t e d S a t e l l i t e T a r g e t R e f l e c t a n c e (TR) F o r t h e MAA S i t e U s i n g A 7 x 7 P i x e l A r r a y and t h e L a r g e r D a t a S e t . Number o f O b s e r v a t i o n s = 3 2 9 . 186 5 0 i U B C A B A I R M A A ° 2 g o £ c m Z z n n -< 3 0' 10^ C I r PC O C I r PC C I r P C C l e a r - C I r - T r a n s m i s s i o n > 8 5 % P a r t l y C l o u d y - PC - 8 5 % < T r a n s m i s s i o n > 2 4 % O v e r c a s t - O - 2 4 % ^ T r a n s m i s s i o n FIGURE 5.11 F r e q u e n c y o f O c c u r e n c e o f 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 C o n d i t i o n s a t U B C , ABAIR and MAA. B a s e d on T r a n s m i s s i o n V a l u e s U s i n g t h e L a r g e r D a t a s e t . 187 sea b r e e z e s y s t e m ( L y o n s , 1 9 7 5 ) . T h i s f u r t h e r e n h a n c e s t h e d i f f e r e n c e s between t h e c o a s t a l a n d i n l a n d s i t e s . 2) W i t h r e l a t i v e l y t h i n c o n t i n u o u s low l e v e l c l o u d w h i c h d e v e l o p s a l o n g t h e c o a s t a l s t r e t c h e s , t h e more a c t i v e c o n v e c t i v e and o r o g r a p h i c p r o c e s s e s i n t h e F r a s e r V a l l e y c a u s e t h e c l o u d t o t h i n and b r e a k u p , r e s u l t i n g i n p a r t l y c l o u d y c o n d i t i o n s . I t a p p e a r s f rom F i g u r e 5.11 t h a t t h e i n c r e a s e i n p a r t l y c l o u d y c o n d i t i o n s e x p e r i e n c e d a t ABAIR and MAA c o m p a r e d t o U B C , i s more a t t h e e x p e n s e of t h e c l e a r sky s i t u a t i o n s r a t h e r t h a n t h o s e w h i c h a r e o v e r c a s t ( i . e . p r o c e s s 1 i s more i m p o r t a n t t h a n p r o c e s s 2 ) . The more v a r i a b l e n a t u r e o f t h e r a d i a t i v e r e g i m e a s s o c i a t e d w i t h p a r t l y c l o u d y c o n d i t i o n s , l i k e l y e x p l a i n s t h e c o n s i s t e n t l y l o w e r c o e f f i c i e n t o f d e t e r m i n a t i o n and l a r g e r s t a n d a r d e r r o r s f o r t h e v a l l e y s i t e s ( e . g . T a b l e s 5 .10 and 5 . 1 1 ) c o m p a r e d t o t h e UBC s i t e ( e . g . T a b l e 5 . 9 ) . T h i s c h a p t e r has u t i l i z e d t h e r e l a t i o n s h i p between s h o r t w a v e t r a n s m i s s i o n and t a r g e t r e f l e c t a n c e t o i n v e s t i g a t e t h e i m p a c t o f v a r i o u s m o d i f i c a t i o n s t o t h e s a t e l l i t e i n p u t d a t a . The i m p a c t o f a BDR c o r r e c t i o n , d i f f e r i n g s p a t i a l and t e m p o r a l a v e r a g i n g , and s a t e l l i t e image a v a i l a b i l i t y have 188 h i g h l i g h t e d t h e s e n s i t i v i t y and opt imum c o n d i t i o n s f o r s u c h a r e l a t i o n s h i p . The c o n c l u s i o n s f rom t h i s s t u d y a r e p r e s e n t e d i n C h a p t e r 6 . 189 CHAPTER 6 CONCLUSIONS The i n t e n t i o n o f t h i s s t u d y was t o use a s i m p l e r e l a t i o n s h i p be tween s a t e l l i t e and g r o u n d m e a s u r e d s o l a r r a d i a t i o n t o i n v e s t i g a t e t h e i m p a c t o f d i f f e r e n t c o n f i g u r a t i o n s o f t h e s a t e l l i t e d a t a on t h e a b i l i t y t o c h a r a c t e r i z e t h e s o l a r r a d i a t i o n r e g i m e a t t h e E a r t h ' s s u r f a c e . The s a t e l l i t e d a t a s e t was shown t o be s a t i s f a c t o r i l y E a r t h - l o c a t e d f o l l o w i n g p r o c e d u r e s o u t l i n e d i n C h a p t e r 3 . E r r o r s u s i n g t h i s p r o c e d u r e were d e t e r m i n e d t o be ± 1 . 5 4 km i n t h e n o r t h - s o u t h d i r e c t i o n and ± 1 . 5 0 km f o r t h e e a s t - w e s t d i r e c t i o n . The a s s u m p t i o n o f l i n e a r i t y ( see S e c t i o n 3 .5 ) may i n c r e a s e t h e s e e r r o r s u n d e r 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 when n a v i g a b l e l a n d m a r k s a r e l o c a t e d away f rom t h e s t u d y s i t e . T h i s i s e s p e c i a l l y t h e c a s e w i t h l a n d m a r k s l o c a t e d t o t h e e a s t o f t h e s t u d y s i t e . B i d i r e c t i o n a l r e f l e c t a n c e (BDR) m o d e l s were d e v e l o p e d i n C h a p t e r 4 and u s e d t o c o r r e c t t h e s a t e l l i t e d a t a f o r t h e a n i s o t r o p i c r e f l e c t a n c e p r o p e r t i e s o f t h e E a r t h - A t m o s p h e r e s y s t e m . . C h a p t e r 4 r e v e a l e d t h a t t h e d i f f e r i n g d i u r n a l r e f l e c t a n c e p a t t e r n s f o r t h e s u r f a c e s v i e w e d by t h e s a t e l l i t e 190 r e q u i r e d t h e d e v e l o p m e n t o f f o u r i n d i v i d u a l BDR m o d e l s ( v i z . , a c l o u d , a sea and two l a n d s u r f a c e m o d e l s ) . In C h a p t e r 5 an i n v e r s e l i n e a r f u n c t i o n was f o u n d t o a d e q u a t e l y d e s c r i b e t h e r e l a t i o n s h i p between s h o r t w a v e t r a n s m i s s i o n (T) and s a t e l l i t e t a r g e t r e f l e c t a n c e ( T R ) . T h i s r e l a t i o n s h i p was u s e d t o a s s e s s t h e i m p a c t o f m o d i f y i n g t h e s a t e l l i t e d a t a and l e d t o t h e f o l l o w i n g c o n c l u s i o n s : 1 ) In a p p l y i n g a b i d i r e c t i o n a l r e f l e c t a n c e (BDR) c o r r e c t i o n t o t h e s a t e l l i t e d a t a , t h o s e BDR m o d e l s d e v e l o p e d u s i n g a more f u n d a m e n t a l p a r a m e t e r ( i . e . t a r g e t r e f l e c t a n c e s , r a t h e r t h a n a c o n c e p t u a l a p p r o a c h u s i n g r h o v a l u e s w h i c h a r e d e r i v e d f rom t h e t a r g e t r e f l e c t a n c e s ) , r e s u l t e d i n a c o n s i s t e n t l y s t r o n g e r r e l a t i o n s h i p be tween T and T R . The o v e r a l l b e s t p e r f o r m a n c e o c c u r r e d when u s i n g a BDR m o d e l t h a t i n c o r p o r a t e s a c l e a r and o v e r c a s t t h r e s h o l d (be tween w h i c h a l i n e a r c o m b i n a t i o n o f b o t h a c l e a r sky and o v e r c a s t c o r r e c t i o n i s made and o u t s i d e o f w h i c h a c o m p l e t e l y c l e a r o r c o m p l e t e l y o v e r c a s t c o r r e c t i o n i s a p p l i e d ) . 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 o r r e c t i o n s a p p l i e d t o o n l y t h o s e p i x e l s deemed p r e d o m i n a n t l y c l e a r and o v e r c a s t a r e f a v o u r e d o v e r a c o r r e c t i o n a p p l i e d t o a l l p i x e l s . T h i s h i g h l i g h t s b o t h t h e c o m p l e x r a d i a t i v e r e g i m e f o r p a r t l y c l o u d y c o n d i t i o n s and a l s o t h a t a c o m b i n a t i o n o f t h e BDR m o d e l s ( f o r c o m p l e t e l y c l e a r o r c l o u d y c o n d i t i o n s ) c a n n o t c a p t u r e t h e c o m p l e x i t i e s o f t h e p a r t l y c l o u d y c a s e s . 191 H o w e v e r , d e s p i t e t h e s e i n i t i a l c o n c l u s i o n s , t h e o v e r a l l r e s u l t s s u g g e s t t h a t i r r e s p e c t i v e o f t h e t y p e o f m o d e l u s e d , i n most c a s e s t h e a p p l i c a t i o n o f a 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 o r r e c t i o n t o t h e s a t e l l i t e d a t a does n o t s t r e n g t h e n t h e r e l a t i o n s h i p be tween T and T R . In t h e few s i t u a t i o n s where t h e r e l a t i o n s h i p a p p e a r s s t r o n g e r , t h e i m p r o v e m e n t s were n e g l i g i b l e and t h u s a BDR c o r r e c t i o n a p p e a r s u n w a r r a n t e d . 2) A l t h o u g h t h e opt imum c o n f i g u r a t i o n f o r a s a t e l l i t e p i x e l a r r a y a p p e a r s t o be r e l a t e d t o t h e d i r e c t i o n o f movement o f t h e p r e v a i l i n g s y n o p t i c w e a t h e r s y s t e m s , i t i s c o n c l u d e d t h a t c h a n g e s i n t h e s p a t i a l a v e r a g i n g o f t h e s a t e l l i t e d a t a has l i t t l e i m p a c t on t h e r e l a t i o n s h i p be tween T and T R . 3) I r r e s p e c t i v e o f t h e s a t e l l i t e a r r a y s i z e , i n c r e a s i n g t h e number o f p y r a n o m e t r i c s t a t i o n s f o r e s t i m a t i n g t h e t r a n s m i s s i o n has l i t t l e e f f e c t on t h e r e l a t i o n s h i p be tween T and T R . 4) I n c r e a s i n g t h e t i m e a v e r a g i n g p e r i o d r e s u l t s i n a s u b s t a n t i a l i m p r o v e m e n t i n t h e s t r e n g t h of t h e r e l a t i o n s h i p be tween T and T R , w i t h l i t t l e c h a n g e i n t h e n a t u r e o f t h e r e l a t i o n s h i p . 5 ) F o r b o t h t h e one and t w o - h o u r l y a v e r a g i n g p e r i o d s , i n c r e a s i n g the number o f images u s e d t o c a l c u l a t e t h e t a r g e t b r i g h t n e s s f o r e a c h t i m e i n t e r v a l r e s u l t s i n a s t r e n g t h e n e d 192 r e l a t i o n s h i p be tween T and T R . The use o f a t l e a s t two i m a g e s , and a t l e a s t f o u r images p e r o n e - h o u r l y and t w o - h o u r l y t i m e p e r i o d , r e s p e c t i v e l y , a p p e a r s t o p r o d u c e a l m o s t as s t r o n g a r e l a t i o n s h i p be tween T and TR as when o n l y t h o s e t i m e p e r i o d s w i t h t h e maximum number o f images ( t h r e e f o r t h e o n e - h o u r l y and f i v e f o r t h e t w o - h o u r l y p e r i o d ) a r e u s e d . 6 ) The s t r e n g t h o f t h e r e l a t i o n s h i p be tween T and TR i s c o n s i s t e n t l y g r e a t e r a t t h e c o a s t a l s i t e t h a n f o r i n l a n d v a l l e y s i t e s . 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J o u r n a l o f t h e A t m o s p h e r i c S c i e n c e s . 19, 182-188. 200 APPENDIX 1 S y m b o l s UPPER CASE ROMAN ABAIR A b b o t s f o r d A i r p o r t A B L I B A b b o t s f o r d L i b r a r y BDR 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 C l o u d i n e s s Index (%) CTc C l e a r Sky T h r e s h o l d (%) CTo O v e r c a s t Sky T h r e s h o l d (%) D D i g i t a l B r i g h t n e s s V a l u e ( c o u n t s ) Dr Component o f t h e C l o u d l e s s Sky D i f f u s e Sky R a d i 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 (k JnT 2 hr _ 1 ) Ds Component o f t h e C l o u d l e s s Sky D i f f u s e R a d i a t i o n Due t o M u l t i p l e R e f l e c t i o n s Between t h e G r o u n d a n d t h e A t m o s p h e r e (k jm ' 2 hr _ 1 ) D+Q D i f f u s e 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 U n d e r C l o u d l e s s S k i e s (kJm" 2 hr ) F i i t h V a l u e o f t h e O b s e r v e d T r a n s l a t i o n s F i i t h V a l u e o f t h e E s t i m a t e d T r a n s l a t i o n s F . O . N . F i r s t O r d e r N a v i g a t i o n 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 H S o l a r Hour A n g l e ( d e g r e e s ) Io S o l a r C o n s t a n t (1353 Wm 2) I ( o ) E x t r a t e r r e s t r i a l R a d i a t i o n R e a c h i n g t h e T o p o f t h e E a r t h ' s A t m o s p h e r e N o r m a l t o t h e S o l a r Beam, p e r U n i t S u r f a c e A r e a (kjrn^hr" 1 ) K+ S h o r t w a v e 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 (k jm^hr" 1 ) K4-Q S h o r t w a v e 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 U n d e r C l e a r S k i e s (kJm" 2 hr" x ) 201 L L i m i t s o f I n t e g r a t i o n L A T L o c a l A p p a r e n t T ime ( H o u r s ) MAA A v e r a g e d R a d i a t i o n D a t a S e t s From A b b o t s f o r d A i r p o r t , A b b o t s f o r d C i t y and M i s s i o n C i t y M.B.E. Mean B i a s E r r o r NOAA N a t i o n a l O c e a n i c a n d A t m o s p h e r i c A d m i n i s t r a t i o n NR N o r m a l i z e d R e f l e c t a n c e R E a r t h ' s R a d i u s V e c t o r ( t h e R a t i o o f A c t u a l Mean S u n - E a r t h D i s t a n c e ) R.M.S.E. R o o t Mean S q u a r e E r r o r SE S t a n d a r d E r r o r SMS S y n c h r o n o u s M e t e o r o l o g i c a l S a t e l l i t e S . O . N . S e c o n d O r d e r N a v i g a t i o n SSEC S p a c e 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 S+0 D i r e c t 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 U n d e r C l o u d l e s s S k i e s ( k j n i ^ h r 1 ) T S h o r t w a v e T r a n s m i s s i o n (%) T ' S h o r t w a v e T r a n s m i s s i o n C a l c u l a t e d U s i n g P r e c i p i t a b l e W a t e r D a t a D e t e r m i n e d From R a d i o s o n d e D a t a (%) T " S h o r t w a v e T r a n s m i s s i o n C a l c u l a t e d U s i n g P r e c i p i t a b l e W a t e r D a t a D a t e r m i n e d From t h e S m i t h (1966) F o r m u l a t i o n (%) TR T a r g e t R e f l e c t a n c e TRTc C l e a r Sky T a r g e t R e f l e c t a n c e T h r e s h o l d TRTo O v e r c a s t T a r g e t R e f l e c t a n c e T h r e s h o l d TRc C l e a r Sky T a r g e t R e f l e c t a n c e T R c o P a r t l y C l o u d y T a r g e t R e f l e c t a n c e TRo O v e r c a s t T a r g e t R e f l e c t a n c e T d D e w - P o i n t T e m p e r a t u r e ( D e g r e e s F) T r ( O ) T r a n s m i s s i o n due t o Ozone 202 T r ( R ) T r a n s m i s s i o n due t o R a y l e i g h S c a t t e r i n g U T o t a l P r e c i p i t a b l e Water (mm) UBC U n i v e r s i t y of B r i t i s h C o l u m b i a VISSR V i s i b l e I n f r a r e d S p i n Scan R a d i o m e t e r X S l a n t P a t h T h r o u g h Water (cm) X j S l a n t P a t h T h r o u g h Ozone (mm) LOWER CASE ROMAN a 0 A b s o r p t i v i t y of Ozone a w Water Vapour A b s o r p t a n c e b R e g r e s s i o n C o e f f i c i e n t dn Daynumber m R e l a t i v e O p t i c a l A i r Mass n Sample S i z e p S t a t i o n P r e s s u r e (kPa) p 0 S t a n d a r d Sea L e v e l P r e s s u r e (101.3kPa) r 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 u 0 V e r t i c a l P a t h L e n g t h Through Ozone (3.5mm) u w V e r t i c a l O p t i c a l P a t h L e n g t h Through Water Vapour (cm) GREEK ab A t m o s p h e r i c A l b e d o f o r 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 as S u r f a c e A l b e d o ao S t a t i s t i c a l E s t i m a t e of t h e Z e n i t h a l Sun R e f l e c t i o n Coef f i c i e n t <S S o l a r D e c l i n a t i o n ( d e g r e e s ) Z 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 ( d e g r e e s ) 203 9 Solar Zenith Angle (degrees) 6 0 Angular Representation of Day Number (degrees) X Factor Based on L a t i t u d e and Time of Year P Rho Value P T C Rho Value for Clear Sky Threshold P T O Rho Value for Overcast Sky Threshold pc C l e a r Sky Rho Value po. Overcast Rho Value <t> L a t i t u d e (degrees) S u n - S a t e l l i t e Azimuth Angle (degrees) OTHERS P r e d i c t e d or Estimated Value Mean Value ' Corrected Value * P a r t i a l Value 204 APPENDIX 2 L a n d m a r k s u s e d i n E a r t h - L o c a t i o n R o u t i n e Landmark Name L a t i t u d e (N) D M S L o n g i t u d e (W) D M S L o c a t i o n Moses P o i n t 4 8 ° 41 ' 40" 1 2 3 ° 28 ' 54" S a a n i c h P e n i n s u l a V a n c o u v e r I s l a n d B e a c h y Head 4 8 ° 18' 54" 1 2 3 ° 38' 39 " V a n c o u v e r I s l a n d C h u r c h P o i n t 4 8 ° 18' 56" 1 2 3 ° 34 ' 18" V a n c o u v e r I s l a n d T e x a d a I s l a n d ( S o u t h T i p ) 4 9 ° 29 ' 26" 1 2 4 ° 08 ' 0 3 " V a n c o u v e r I s l a n d L a k e Okanagan ( S o u t h End) 4 9 ° 30 ' 00" 1 1 9 ° 34 ' 24" B r i t i s h C o l u m b i a ( S o u t h C e n t r a l ) L a k e Okanagan ( N o r t h E n d , West Arm) 5 0 ° 19' 54" 1 1 9 ° 17' 24" B r i t i s h C o l u m b i a ( S o u t h C e n t r a l ) K o o t e n a y L a k e (Cape H o r n ) 4 go 35 ' 4 8 " 1 1 6 ° 4 9 ' 12" B r i t i s h C o l u m b i a ( S o u t h E a s t ) K o o t e n a y L a k e ( N o r t h End) 5 0 ° 10* 18" 1 1 6 ° 55 ' 48 " B r i t i s h C o l u m b i a ( S o u t h E a s t ) K o o t e n a y L a k e ( S o u t h End) 4 9 ° 1 1 ' 34" 1 1 6 ° 39* 29" B r i t i s h C o l u m b i a ( S o u t h E a s t ) S l o c a n L a k e ( S o u t h End) 4 9 ° 46 ' 13" 1 1 7 ° 28 ' 12" B r i t i s h C o l u m b i a ( S o u t h E a s t ) W i l l i s t o n L a k e ( E a s t Arm) 5 5 ° 56 ' 30 " 1 2 2 ° 08 ' 24" B r i t i s h C o l u m b i a ( N o r t h ) S t u a r t L a k e ( S o u t h E a s t ) 5 4 ° 23 ' 30" 1 2 4 ° 16' 54" B r i t i s h C o l u m b i a ( N o r t h ) B i r c h P o i n t 4 8 ° 56 ' 12" 1 2 2 ° 48 ' 36" W a s h i n g t o n ( N o r t h West ) Cape F l a t t e r y ( O l y m p i c P e n i n s u l a ) 4 8 ° 22 ' 50 " 1 2 4 ° 4 3 ' 48" W a s h i n g t o n ( N o r t h West ) Hood C a n a l (Puge t Sound) 4 7 ° 20 ' 12" 1 2 3 ° 07 ' 06 " W a s h i n g t o n ( N o r t h West ) 205 Landmark Name L a t i t u d e (N) D M S L o n g i t u d e (W) D M S L o c a t i o n G r a y s H a r b o u r 4 6 ° 56 ' 36" ( N o r t h S p i t ) Banks L a k e ( N o r t h End) Banks L a k e ( S o u t h End) 4 7 ° 55 ' 57" 4 7 ° 37 ' 04" P r i e s t R a p i d s 4 6 ° 38 ' 08" L a k e ( S o u t h End) Wanapum L a k e 4 6 ° 52 ' 05" ( S o u t h End) P o t h o l e s R e s e r v o i r ( S o u t h End) P r i e s t L a k e ( S o u t h End) L a k e Pend O r e i l l e ( E a s t End) L a k e Pend O r e i l i e ( S o u t h Wes t ) 4 6 ° 5 9 ' 19" 4 8 ° 28 ' 59 " 4 8 ° 0 9 ' 24" C o e u r D ' A l e n e 4 7 ° 26 ' 58" L a k e (West End) C o l u m b i a R i v e r 4 6 ° 14' 12" M o u t h ( S o u t h S p i t ) T i l l a m o o k Bay 4 5 ° 2 9 ' 34" (Head o f Bay) 1 2 4 ° 0 9 ' 12" 1 1 9 ° 05 ' 48 " 1 1 9 ° 17' 13" 1 1 9 ° 53 ' 0 3 " 1 1 9 ° 57 ' 09 " 1 1 9 ° 17' 18" 1 1 6 ° 51 ' 52" 1 1 6 ° 14' 06 " 4 7 ° 58 ' 0 1 " 1 1 6 ° 32 ' 04' Coos Bay ( N o r t h End) 4 3 ° 2 1 ' 09 " 116° 54 ' 55" 1 2 4 ° 00 ' 00 " 1 2 3 ° 53 ' 05" 124 19' 18" W a s h i n g t o n (West ) W a s h i n g t o n ( C e n t r a l ) W a s h i n g t o n ( C e n t r a l ) W a s h i n g t o n ( C e n t r a l ) W a s h i n g t o n ( C e n t r a l ) W a s i n g t o n ( C e n t r a l ) I d a h o ( N o r t h ) I d a h o ( N o r t h ) I d a h o ( N o r t h ) I d a h o (West ) O r e g o n ( N o r t h Wes t ) O r e g o n ( N o r t h Wes t ) O r e g o n ( S o u t h Wes t ) 206 Landmark Name L a t i t u d e (N) L o n g i t u d e (W) D M S D M S C o o s Bay ( S o u t h End) Cape A r a g o 4 3 ° 20 ' 0 1 " 1 2 4 ° 19' 0 5 " 4 3 ° 17' 54" 1 2 4 ° 2 3 ' 18" Cape B l a n c o 4 2 ° 50 ' 27" 1 2 4 ° 30 ' 33 " F e r n R i d g e R e s e r v o i r ( N o r t h Wes t ) Waldo L a k e ( S o u t h End) 4 4 ° 07 ' 25" 1 2 3 ° 18' 18" 4 3 ° 4 1 ' 14" 1 2 2 ° 06 ' 3 1 " L o c a t i o n O r e g o n ( S o u t h West ) O r e g o n ( S o u t h Wes t ) O r e g o n ( S o u t h Wes t ) O r e g o n (West ) O r e g o n ( C e n t r a l ) 207 APPENDIX 3 E q u a t i o n s u s e d t o d e t e r m i n e t h e BDR c o r r e c t i o n s MODEL A P I X E L CORRECTION U s i n g P V a l u e s TR' = TR / (pc + C (po - Pc) ) U s i n g T a r g e t R e f l e c t a n c e s TR' = TRc + C (TRO - TRc) MODEL B P I X E L CORRECTION U s i n g P V a l u e s V a l u e a t t h e C l e a r Sky T h r e s h o l d : pTc = P C (1 - C T c ) + CTc (TR / T R c ) V a l u e a t t h e O v e r c a s t Sky T h r e s h o l d : pTo = po (CTo) + (1 - CTo) TR / T R o P a r t l y C l o u d y P i x e l C o r r e c t i o n : T R c o = pTc + (pTo - p T c ) (C - C T c ) / (CTo - C T c ) O v e r c a s t P i x e l C o r r e c t i o n : TRb = P 0 . C + ( 1 - C ) T R / TRo C l e a r P i x e l C o r r e c t i o n : TRc = p c ( 1 - O + C . T R / TRc U s i n g T a r g e t R e f l e c t a n c e s T a r g e t R e f l e c t a n c e V a l u e a t t h e C l e a r Sky T h r e s h o l d : TRTc = TRc (1 - C T c ) + ( C T c ) (TR) 208 T a r g e t r e f l e c t a n c e V a l u e a t t h e O v e r c a s t Sky T h r e s h o l d : TRTo = TRo . CTo + (1 - CTo) TR P a r t l y C l o u d y P i x e l C o r r e c t i o n : TRCO = TRTc + (TRTo - T R T c ) (C - C T c ) / (CTo - C T c ) O v e r c a s t P i x e l C o r r e c t i o n : TRo = TRo . C + (1 - C) TR C l e a r P i x e l C o r r e c t i o n : TRc = TRc (1 - C) + C . TR MODEL C P I X E L CORRECTION U s i n g P V a l u e s V a l u e a t t h e C l e a r Sky T h r e s h o l d : pTc = P C ' V a l u e a t t h e O v e r c a s t T h r e s h o l d : p T o = P O ' P a r t l y C l o u d y P i x e l C o r r e c t i o n : T R c o = TR / ( (C - C T c ) P o + (CTo - C) P c / (CTo - C T c ) ) O v e r c a s t P i x e l C o r r e c t i o n : TRo = TR / po C l e a r P i x e l C o r r e c t i o n : TRc = TR / pc 209 U s i n g T a r g e t R e f l e c t a n c e s T a r g e t R e f l e c t a n c e V a l u e a t t h e C l e a r Sky T h r e s h o l d : TRTc = TRc T a r g e t R e f l e c t a n c e V a l u e a t t h e O v e r c a s t Sky T h r e s h o l d : TRTo = TRo P a r t l y C l o u d y P i x e l C o r r e c t i o n : T R c o = ( ( C - C T c ) TRo + (CTo - C) T R c ) / (CT o - CTc ) O v e r c a s t P i x e l C o r r e c t i o n : TR'o = TRo C l e a r P i x e l C o r r e c t i o n : TRc = TRc 

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