UBC Theses and Dissertations

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UBC Theses and Dissertations

The angular distribution of diffuse solar radiation over the sky hemisphere Stewart, Kathleen Elizabeth 1984

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THE ANGULAR DISTRIBUTION OF DIFFUSE SOLAR RADIATION OVER THE SKY HEMISPHERE By KATHLEEN ELIZABETH STEWART B.A., McMaster U n i v e r s i t y , 1982 THESIS SUBMITTED IN PARTIAL FULFILMENT THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department of Ge 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 BRITISH COLUMBIA J u l y 1984 © K a t h l e e n E l i z a b e t h S t e w a r t , 1984 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements fo r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for s c h o l a r l y purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission.. Department of Geofetft-ftfH^f  The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 D a t e iSri i i A b s t r a c t The use o f a v i d e o - b a s e d i m a g i n g s y s t e m i n c o n j u n c t i o n w i t h measurements o f sky r a d i a n c e made by a L i n k e - F e u s s n e r a c t i n o m e t e r p r o v i d e t h e means f o r d e t e r m i n i n g t h e a n g u l a r d i s t r i b u t i o n of d i f f u s e s o l a r r a d i a t i o n o v e r t h e sky h e m i s p h e r e . Development of t h i s f a s t - r e s p o n s e , h i g h r e s o l u t i o n measurement p r o c e d u r e a l l o w s a n a l y s e s t o be made under complex r a d i a t i v e r e g i m e s i n wh i c h e a r l i e r e x p e r i m e n t a l p r o c e d u r e s were not s a t i s f a c t o r y . I n v e s t i g a t i o n s i n t o t h e d i r e c t i o n a l d i s t r i b u t i o n o f d i f f u s e r a d i a n c e c o n f i r m t h e a n i s o t r o p y of the p a t t e r n , d i s p e l l i n g any a s s u m p t i o n t h a t t h e d i s t r i b u t i o n o v e r t h e sky h e m i s p h e r e i s i s o t r o p i c . M e asurements of d i f f u s e r a d i a n c e a c t as a c a l i b r a t i o n f o r th e b r i g h t n e s s i n f o r m a t i o n d e r i v e d from t h e v i d e o imagery of th e s k y . The a p p r o p r i a t e t r a n s f o r m a t i o n from b r i g h t n e s s t o r a d i a n c e may be d e t e r m i n e d once t h e c a l i b r a t i o n p r o c e d u r e has been a c c o m p l i s h e d . F u n c t i o n a l a n a l y s i s i s p r e s e n t e d as t h e s t a t i s t i c a l t o o l most u s e f u l f o r d e t e r m i n i n g t h e r e l a t i o n s h i p u n d e r l y i n g t h e c a l i b r a t i o n c u r v e s . T h i s s t u d y d i s c u s s e s t h e a d v a n t a g e s o f u s i n g v i d e o i m a g i n g t e c h n i q u e s i n a c l i m a t o l o g i c a l a p p l i c a t i o n and shows how t h i s t y p e o f s y s t e m c a n y i e l d v a l u a b l e i n f o r m a t i o n c o n c e r n i n g r a d i a t i v e c h a r a c t e r i s t i c s o t h e r w i s e u n a v a i l a b l e w i t h c o n v e n t i o n a l measurement t e c h n i q u e s . i i i T a b l e o f C o n t e n t s Page A b s t r a c t i i T a b l e of C o n t e n t s i i i L i s t of T a b l e s v i i i L i s t of F i g u r e s x i L i s t o f Symbols xv Acknowledgements x v i i i C h a p t e r One - I n t r o d u c t i o n 1 1.1 O b j e c t i v e s 1 1 . 2 B a c k g r o u n d 1 C h a p t e r Two - I n s t r u m e n t a t i o n 10 2.1 Measurement of D i f f u s e S o l a r 10 R a d i a t i on 2.1.1 R e c o r d i n g t h e D i f f u s e 11 R a d i a t i o n S i g n a l 2.1.2 A n a l y s i s of t h e E r r o r 12 A s s o c i a t e d w i t h t h e Measurement o f D i f f u s e S o l a r R a d i a t i o n 2.1.2.1 A n a l y s i s of t h e E r r o r 12 A s s o c i a t e d w i t h t h e S e n s o r 2.1.2.2 A n a l y s i s of t h e E r r o r 13 A s s o c i a t e d w i t h t h e R e c o r d i n g I n s t r u m e n t i v 2.1.2.3 E r r o r A s s o c i a t e d w i t h t h e Measurement of D i f f u s e S o l a r R a d i a t i o n 2.2 D e t e r m i n a t i o n o f B r i g h t n e s s V a l u e s from V i d e o Imagery 2.2.1 V i d e o Camera and M o n i t o r i n g System 2.2.1.1 V i d e o Camera, F i s h e y e L e ns and F i l t e r 2.2.1.2 V i d e o F r a m e s t o r e C h a p t e r T h r e e - E x p e r i m e n t a l P r o c e d u r e s 3.1 F i e l d Measurement S i t e 3.1.1 Sky View F a c t o r A n a l y s i s 3.2 Measurement P r o c e d u r e 3.3 E s t i m a t i o n o f t h e E r r o r i n t h e V i d e o System 3.3.1 A s s e s s m e n t of t h e E r r o r I n h e r e n t i n R e g i s t r a t i o n o f Sky C o o r d i n a t e s 3.3.2 C a l c u l a t i o n o f t h e E r r o r A s s o c i a t e d w i t h B r i g h t n e s s L e v e l D e t e r m i n a t i o n C h a p t e r F o u r - C a l i b r a t i o n P r o c e d u r e 4.1 D e t e r m i n a t i o n o f t h e R e l a t i o n s h i p between R a d i a n c e and B r i g h t n e s s V a l u e s 4.1.1 R e g r e s s i o n A n a l y s i s V Page 4.1.2 F u n c t i o n a l A n a l y s i s 50 4.2 V e r i f i c a t i o n o f t h e C a l i b r a t i o n 54 P r o c e d u r e 4.3 V a l i d i t y of A p p r o a c h u s i n g P a r t i a l 63 Scan D a t a C h a p t e r F i v e - The A n g u l a r D i s t r i b u t i o n of 73 D i f f u s e S o l a r R a d i a t i o n 5.1 D e t e r m i n i n g a Method f o r 73 T r a n s l a t i n g t h e V a l u e of a R a d i a n c e i n t h e Sky t o a P o i n t on t h e Image 5.2 The D i s t r i b u t i o n o f D i f f u s e S o l a r 76 R a d i a t i o n o v e r t h e Sky H e m i s p h e r e 5.2.1 D i s t r i b u t i o n of R a d i a n c e V a l u e s 76 f o r D i f f e r e n t Sky C o n d i t i o n s 5.3 A p p l i c a t i o n 82 5.3.1 C l e a r Sky C o n d i t i o n s 82 5.3.2 O v e r c a s t Sky C o n d i t i o n s 86 5.3.3 P a r t l y C l o u d y Sky C o n d i t i o n s 95 5.4 C o m p a r i s o n of R e s u l t s w i t h 104 P r e v i o u s S t u d i e s 5.4.1 C l e a r Sky R a d i a n c e D i s t r i b u t i o n s 104 5.4.2 O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n s 111 5.4.3 P a r t l y C l o u d y Sky R a d i a n c e 115 D i s t r i b u t i o n s C h a p t e r S i x - C o n c l u s i o n s and Recommendations 120 6.1 A s s e s s m e n t of t h e E x p e r i m e n t a l 120 v i P r o c e d u r e s 6.1.1 C r i t i c a l A s s e s s m e n t o f Measurement T e c h n i q u e s Used i n t h i s S t u d y 6.1.1.1 S i t e C o n s i d e r a t i o n s 6.1.1.2 A s s e s s m e n t of I n s t r u m e n t a t i o n 6.2 Summary of R e s u l t s 6.2.1 C l e a r Sky C a s e s 6.2.2 O v e r c a s t Sky C a s e s 6.2.3 P a r t l y C l o u d y Sky C a s e s 6.2.4 R a d i a n c e Maps 6.3 C o n c l u s i o n s and Recommendations R e f e r e n c e s A p p e n d i x I - A s s e s s m e n t of t h e C h a r a c t e r i s t i c s o f t h e F i s h e y e Camera Lens and V i d e o Imaging System A l . 1 T e s t f o r A x i a l Symmetry of F i s h e y e Camera Lens AI.1.2 T e s t t o C o n f i r m E q u i - A n g u l a r P r o j e c t i o n of F i s h e y e Camera Lens AI.2 D e t e r m i n a t i o n of t h e Shape of a V i d e o Image AI.3 D e t e r m i n a t i o n of t h e Shape of t h e A c t i n o m e t r i c F i e l d - o f - V i e w a s Seen on a V i d e o V 1 1 Page Image Ap p e n d i x II - R e g r e s s i o n R e s u l t s o f R a d i a n c e 140 V e r s u s C o r r e c t e d B r i g h t n e s s f o r C l e a r , O v e r c a s t and P a r t l y C l o u d y S k i e s v i i i L i s t Of T a b l e s T a b l e 2.1 T a b l e 2.2 T a b l e 2.3 T a b l e 3.1 T a b l e 3.2 T a b l e 4.1 T a b l e 4.2 T a b l e 4.3 T a b l e 4.4 R e c o r d e r E r r o r A s s o c i a t e d w i t h a D i f f u s e R a d i a t i o n S i g n a l P r o b a b l e R e l a t i v e E r r o r s A s s o c i a t e d w i t h Sample R a d i a n c e s (Wm~ 2sr~ 1) E n e r g y D i s t r i b u t i o n i n t h e S o l a r S p e c t r u m O u t s i d e t h e Atmosphere ( 1 0 ~ 3 c a l / c m 2 m i n ) and t h e S p e c t r a l C o m p o s i t i o n of D i f f u s e R a d i a t i o n ( 1 0 ~ 6 c a l / c m 2 m i n ) . From K o n d r a t y e v (1969) R e c o r d o f F i e l d O b s e r v a t i o n s Sequence of O b s e r v a t i o n s i n S e c o n d S a m p l i n g G r i d R e g r e s s i o n R e s u l t s f o r C l e a r S k i e s U s i n g C o r r e c t e d B r i g h t n e s s and R a d i a n c e V a l u e s ( W m " 2 s r _ 1 ) R e g r e s s i o n R e s u l t s f o r O v e r c a s t Sky D a t a U s i n g C o r r e c t e d B r i g h t n e s s and R a d i a n c e V a l u e s (Wm" 2sr~ 1) R e g r e s s i o n R e s u l t s f o r P a r t l y C l o u d y S k i e s U s i n g C o r r e c t e d B r i g h t n e s s and R a d i a n c e V a l u e s ( W m ~ 2 s r _ 1 ) R e s u l t s o f F u n c t i o n a l A n a l y s i s t o Show V a r i a t i o n between P r e d i c t e d and M e a s u r e d R a d i a n c e (Wm~ 2sr~ 1) Page 1 5 1 6 22 33 37 47 48 49 53 I X Page T a b l e 4.5 T a b l e 4.6 T a b l e 4.7 T a b l e 4.8 T a b l e 4.9 T a b l e 4.10 T a b l e 5.1 f o r C l e a r , O v e r c a s t and P a r t l y C l o u d y Sky C o n d i t i o n s R e s u l t s o f T r a n s f o r m a t i o n from B r i g h t n e s s t o R a d i a n c e f o r C l e a r Sky C o n d i t i o n s R e s u l t s of T r a n s f o r m a t i o n from B r i g h t n e s s t o R a d i a n c e f o r P a r t l y C l o u d y Sky C o n d i t i o n s R e s u l t s o f T r a n s f o r m a t i o n from B r i g h t n e s s t o R a d i a n c e f o r O v e r c a s t Sky C o n d i t i o n s R e g r e s s i o n R e s u l t s f o r C l e a r and P a r t l y C l o u d y Sky C o n d i t i o n s R e g r e s s i o n A n a l y s i s R e s u l t s f o r C l e a r Sky C o n d i t i o n s s h owing V a r i a t i o n i n D a t a as O b t a i n e d w i t h S i m u l t a n e o u s Measurements ( S ) , A s y n c h r o n o u s Measurements (N S ) . R e g r e s s i o n A n a l y s i s R e s u l t s f o r a P a r t l y C l o u d y Sky (JD339) f o r D a t a O b t a i n e d w i t h S i m u l t a n e o u s M easurements ( S ) , and A s y n c h r o n o u s (NS) M e a s u r e m e n t s . V a l u e s of M e a s u r e d and P r e d i c t e d ( U s i n g Eqn. 5.11) R a d i a n c e s (Wm~ 2sr~ 1) f o r C e r t a i n Z e n i t h A n g l e s f o r O v e r c a s t S k i e s , O b s e r v e d on J a n u a r y 20, 1984 ( Z e n i t h A n g l e 74°) 55 56 57 66 71 71 1 1 3 T a b l e A l . 1 a T a b l e A l . 1 b P i x e l C o o r d i n a t e P o s i t i o n s f o r E a c h of t h e 10° T a r g e t s V i s i b l e on t h e V i d e o Image P i x e l C o o r d i n a t e P o s i t i o n s f o r E a c h of t h e 10° T a r g e t s V i s i b l e on t h e V i d e o Image W i t h t h e Camera R o t a t e d by 90° Page 1 38 1 38 x i L i s t o f F i g u r e s F i g u r e 2.1 F i g u r e 2.2 F i g u r e 2.3 F i g u r e 3.1 F i g u r e 3.2 F i g u r e 3.3 F i g u r e 4.1 F i g u r e 4.2 F i g u r e 4.3 F i g u r e 4.4 F i g u r e 4.5 S p e c t r a l S e n s i t i v i t y C h a r a c t e r i s t i c s of t h e ER Newvicon Camera R e l a t i v e t o t h e V i d i c o n Camera V i d e o Camera and F i l t e r S p e c t r a l Response C u r v e S p e c t r a l D i s t r i b u t i o n of D i f f u s e R a d i a t i o n f o r C l e a r S k i e s View o f V i d e o Camera i n M o n i t o r i n g P o s i t i o n View of F i e l d S i t e on t h e Roof D e s i g n of S a m p l i n g G r i d C o n t o u r P l o t of D i f f e r e n c e s Between M e a s u r e d and P r e d i c t e d R a d i a n c e s f o r a C l e a r Sky C o n t o u r P l o t of D i f f e r e n c e s Between Mea s u r e d and P r e d i c t e d R a d i a n c e s f o r an O v e r c a s t Sky C o n t o u r P l o t o f D i f f e r e n c e s Between M e a s u r e d and P r e d i c t e d R a d i a n c e s f o r a P a r t l y C l o u d y Sky R e g r e s s i o n R e s u l t s f o r a C l e a r Sky Scan, December 20, 1983 R e g r e s s i o n R e s u l t s f o r a P a r t l y C l o u d y Sky, December 5, 1983 Page 18 21 24 29 30 40 58 61 62 65 68 X I 1 F i g u r e 5.1 F i g u r e 5.2 F i g u r e 5.3 F i g u r e 5.4 F i g u r e 5.5 F i g u r e 5.6 F i g u r e 5.7 F i g u r e 5.8 F i g u r e 5.9 F i g u r e 5.10 F i g u r e 5.11 Geometry of Sky H e m i s p h e r e F r e q u e n c y H i s t o g r a m s o f P r e d i c t e d R a d i a n c e f o r C l e a r S k i e s a) December 20, 1983 and b) A u g u s t 21, 1983 F r e q u e n c y H i s t o g r a m s o f P r e d i c t e d R a d i a n c e f o r O v e r c a s t S k i e s a) 1320 LAT J a n u a r y 20, 1984 b) l340 LAT J a n u a r y 20, 1984 F r e q u e n c y H i s t o g r a m s o f P r e d i c t e d R a d i a n c e f o r P a r t l y C l o u d y S k i e s a) December 5, 1983 and b) J a n u a r y 12, 1984 and c) September 13, 1983 C l e a r Sky R a d i a n c e D i s t r i b u t i o n f o r 1320 LAT August 21, 1983 C l e a r Sky R a d i a n c e D i s t r i b u t i o n f o r 1356 LAT December 20, 1983 O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n f o r 1013 LAT J a n u a r y 20, 1984 O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n f o r 1033 LAT J a n u a r y 20, 1984 O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n f o r 1126 LAT J a n u a r y 20, 1984 O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n f o r 1320 LAT J a n u a r y 20, 1984 O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n x i i i Page F i g u r e 5.12 F i g u r e 5.13 F i g u r e 5.14 F i g u r e 5.15 F i g u r e 5.16 F i g u r e 5.17 F i g u r e 5.18 F i g u r e 5.19 F i g u r e 5.20 F i g u r e 5.21 F i g u r e 5.22 F i g u r e 5.23 F i g u r e A l I . 1 f o r 1340 LAT J a n u a r y 20, 1984 P a r t l y C l o u d y Sky R a d i a n c e D i s t r i b u t i o n 96 f o r 1449 LAT J a n u a r y 12, 1984 P a r t l y C l o u d y Sky R a d i a n c e D i s t r i b u t i o n 98 f o r 1116 LAT F e b r u a r y 3, 1984 P a r t l y C l o u d y Sky R a d i a n c e D i s t r i b u t i o n 99 f o r 1148 LAT F e b r u a r y 3, 1984 P a r t l y C l o u d y Sky R a d i a n c e D i s t r i b u t i o n 101 f o r 1246 LAT December 5, 1983 P a r t l y C l o u d y Sky R a d i a n c e D i s t r i b u t i o n 103 f o r 1417 LAT September 13, 1983 C l e a r Sky Luminance D i s t r i b u t i o n s 105 f o r a) Z e n i t h A n g l e 70° and b) Z e n i t h A n g l e 50° S t a n d a r d D i s t r i b u t i o n s of N o r m a l i z e d 107 C l e a r Sky R a d i a n c e f o r a) Z e n i t h A n g l e 35° and b) Z e n i t h A n g l e 55° C l e a r Sky N o r m a l i z e d R a d i a n c e 109 D i s t r i b u t i o n s O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n 114 f o r Z e n i t h A n g l e 63° O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n s 116 R a d i a n c e D i s t r i b u t i o n s D u r i n g 117 C i r r u s C l o u d C o v e r P a r t l y C l o u d y Sky R a d i a n c e 119 D i s t r i b u t i o n f o r Z e n i t h A n g l e 64.5° R e g r e s s i o n L i n e of R a d i a n c e and 141 x i v B r i g h t n e s s f o r a C l e a r Sky 0916 LST J u l y 29,1983 F i g u r e A l l . 2 R e g r e s s i o n L i n e o f R a d i a n c e and B r i g h t n e s s f o r a C l e a r Sky 1631 LST J u l y 29, 1983 F i g u r e A l l . 3 R e g r e s s i o n L i n e o f R a d i a n c e and B r i g h t n e s s f o r a C l e a r Sky 1118 LST J u l y 30, 1983 F i g u r e A l l . 4 R e g r e s s i o n L i n e o f R a d i a n c e and B r i g h t n e s s f o r a P a r t l y C l o u d y Sky 1125 LST A u g u s t 29, 1983 F i g u r e A l l . 5 R e g r e s s i o n L i n e o f R a d i a n c e and B r i g h t n e s s f o r a P a r t l y C l o u d y Sky 1416 LST A u g u s t 27, 1983 F i g u r e A l l . 6 R e g r e s s i o n L i n e o f R a d i a n c e and B r i g h t n e s s f o r an O v e r c a s t Sky 1250 LST August 27, 1983 F i g u r e A l l . 7 R e g r e s s i o n L i n e o f R a d i a n c e and B r i g h t n e s s f o r an O v e r c a s t Sky 0921 LST A u g u s t 27, 1983 XV L i s t of Symbols Upper Case Roman A p r o j e c t e d a r e a on a h e m i s p h e r e ( m e t r e s 2 ) A' a r e a on t h e d i g i t i z e d p l a n a r image ( m e t r e s 2 ) CS a s y n c h r o n o u s r a d i a n c e and b r i g h t n e s s measurements D( z ) h o r i z o n - d a r k e n i n g f a c t o r f o r an e q u i a n g u l a r l e n s E_-^ t o t a l p r o b a b l e e r r o r o f a b r i g h t n e s s v a l u e measured under c l e a r s k i e s ( c o u n t s ) Ep_ t o t a l p r o b a b l e e r r o r of a b r i g h t n e s s v a l u e measured under p a r t l y c l o u d y s k i e s ( c o u n t s ) E Q v t o t a l p r o b a b l e e r r o r o f a b r i g h t n e s s v a l u e measured under o v e r c a s t s k i e s ( c o u n t s ) E e r r o r v a r i a n c e of b r i g h t n e s s v a l u e s ( c o u n t s ) Ey e r r o r v a r i a n c e o f d i f f u s e r a d i a n c e v a l u e s ( W i r T 2 s r ~ 1 ) LAT l o c a l a p p a r e n t t i m e ( h o u r s ) NPIX number of p i x e l s c o r r e s p o n d i n g t o a c t i n o m e t r i c f i e l d - o f - v i e w R d i s t a n c e from p o i n t t o c e n t r e on p l a n a r image ( m e t r e s ) R 0 r a d i u s o f d i g i t i z e d p l a n a r image ( m e t r e s ) R 0* semi major a x i s o f p l a n a r image ( p i x e l s ) RMS r o o t mean s q u a r e e r r o r ( W m " 2 s r _ 1 ) S a c t u a l b r i g h t n e s s of an e l e m e n t of a s c e n e ( c o u n t s ) S s y n c h r o n o u s r a d i a n c e and b r i g h t n e s s measurements SOC S t a n d a r d O v e r c a s t Sky f o r m u l a x v i T t e m p e r a t u r e (°C) X measured b r i g h t n e s s v a l u e of a s a m p l i n g p o i n t ( c o u n t s ) X' c o r r e c t e d b r i g h t n e s s v a l u e of a s a m p l i n g p o i n t ( c o u n t s ) X^ mean v a l u e o f i t h b r i g h t n e s s v a l u e ( c o u n t s ) X^_j j t h o f m r e p l i c a t e o b s e r v a t i o n s of b r i g h t n e s s v a r i a b l e X mean b r i g h t n e s s v a l u e ( c o u n t s ) Y measured d i f f u s e r a d i a n c e ( W m _ 2 s r ~ 1 ) Y' c o r r e c t e d d i f f u s e r a d i a n c e ( W m ~ 2 s r _ 1 ) Y mean d i f f u s e r a d i a n c e ( W m ~ 2 s r - 1 ) Y p r e d i c t e d d i f f u s e r a d i a n c e ( W m ~ 2 s r - 1 ) Lower Case Roman a^ i n t e r c e p t v a l u e of f u n c t i o n a l l i n e ( W m _ 2 s r ~ 1 ) a r i n t e r c e p t v a l u e of r e g r e s s i o n l i n e ( W m _ 2 s r _ 1 ) b e m p i r i c a l c o n s t a n t i n S t a n d a r d O v e r c a s t Sky f o r m u l a b^ s l o p e of f u n c t i o n a l l i n e ( W m ~ 2 s r ~ 1 ) ~ 1 b r s l o p e of r e g r e s s i o n l i n e ( W m ~ 2 s r ~ 1 ) ~ 1 c e m p i r i c a l c o n s t a n t r c o r r e l a t i o n c o e f f i c i e n t 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 x a b s c i s s a p i x e l c o o r d i n a t e on d i g i t i z e d image x 0 a b s c i s s a v a l u e o f c e n t r e c o o r d i n a t e on d i g i t i z e d image y o r d i n a t e p i x e l c o o r d i n a t e on d i g i t i z e d image y 0 o r d i n a t e v a l u e of c e n t r e c o o r d i n a t e on d i g i t i z e d image v e l e c t r i c a l o u t p u t of v i d e o camera ( V o l t s ) x v i i z z e n i t h a n g l e ( d e g r e e s ) Lower Case Greek a- a n g u l a r w i d t h of i t h a n n u l u s ( r a d i a n s ) a' t e m p e r a t u r e c a l i b r a t i o n c o e f f i c i e n t 7 gamma v a l u e o f Newvicon camera tu b e ( 7 = 1 . 0 0 ) X r a t i o of e r r o r v a r i a n c e s (j> a z i m u t h a n g l e ( d e g r e e s ) 0 _ _ R sky view f a c t o r p d i s t a n c e from t h e c e n t r e o f t h e a r e a A t o a n o r m a l p r o j e c t e d v e r t i c a l l y t h r o u g h t h e sky h e m i s p h e r e 6 e l e v a t i o n a n g l e above t h e h o r i z o n ( d e g r e e s ) x v i i i Acknowledgements I would l i k e t o g r a t e f u l l y a c k n o w l e d g e t h e g u i d a n c e and s u p p o r t g i v e n t o me be my s u p e r v i s o r , Dr. J . E . Hay, d u r i n g t h i s s t u d y . A l s o my s i n c e r e a p p r e c i a t i o n goes t o D r . D.G. S t e y n f o r h i s a d v i c e and c o n s t r u c t i v e comments. A n o t h e r s p e c i a l acknowledgement goes t o M. R o s e b e r r y whose t e c h n i c a l a s s i s t a n c e and computer programming were i n v a l u a b l e t o me. T h r o u g h o u t th e s t u d y , o t h e r s p r o v i d e d me w i t h c r i t i c a l comments and h e l p f u l s u g g e s t i o n s , namely: S. Grimmond, S. Loudon, C. R a p h a e l , R. R o b e r t s , and C. S o u c h . P o r t i o n s o f t h e r e s e a r c h were f u n d e d by a g r a n t from t h e N a t u r a l S c i e n c e s and E n g i n e e r i n g R e s e a r c h C o u n c i l and by a c o n t r a c t w i t h 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 . 1 C h a p t e r One I n t r o d u c t i o n 1.1 O b j e c t i v e s The aim of t h i s r e s e a r c h i s t o d e v e l o p a n . e x p e r i m e n t a l p r o c e d u r e f o r d e t e r m i n i n g t h e a n g u l a r d i s t r i b u t i o n of d i f f u s e s o l a r r a d i a t i o n o v e r t h e sky h e m i s p h e r e under v a r y i n g sky c o n d i t i o n s . T h i s p r o c e d u r e i n v o l v e s t h e d e v e l o p m e n t of a measurement programme c o m b i n i n g a v i d e o i m a g i n g s y s t e m w i t h a c t i n o m e t r i c o b s e r v a t i o n s w i t h t h e aim of p r o d u c i n g a f a s t - r e s p o n s e , h i g h r e s o l u t i o n means of a n a l y z i n g d i f f u s e r a d i a n c e p a t t e r n s o v e r t h e sky dome. A n o t h e r o b j e c t i v e of t h i s s t u d y i s t o a s s e s s t h i s o b s e r v a t i o n a l t e c h n i q u e and s u g g e s t any improvements t h a t a p p e a r t o be n e c e s s a r y . T h i s s t u d y a t t e m p t s t o examine t h e c h a r a c t e r i s t i c s of t h e d i s t r i b u t i o n of sky r a d i a n c e under r e l a t i v e l y s t a t i o n a r y , c l e a r sky c o n d i t i o n s and compares t h e s e r e s u l t s w i t h t h o s e of e a r l i e r s t u d i e s . A f u r t h e r aim i s t o r e c o r d o b s e r v a t i o n s under th e more complex p a r t l y c l o u d y sky c o n d i t i o n s and under o v e r c a s t s k i e s , i n an a t t e m p t t o e x t e n d t h e knowledge of d i f f u s e s o l a r r a d i a t i o n u nder more complex r a d i a t i v e r e g i m e s . A method f o r p r e d i c t i n g r a d i a n c e from t h e b r i g h t n e s s d a t a d e r i v e d f r o m t h e v i d e o i m a g e r y i s p r e s e n t e d and p o l a r c o o r d i n a t e maps a r e p r o d u c e d i n an a t t e m p t t o d i s p l a y t h e r e s u l t s of t h i s work c l e a r l y . 1.2 B a c k g r o u n d 2 I n c r e a s i n g r e s e a r c h on t h e e f f e c t i v e m o d e l l i n g o f s o l a r r a d i a t i o n i n c i d e n t on s l o p i n g s u r f a c e s has a c k n o w l e d g e d t h e f a c t t h a t t h e r o l e of d i f f u s e r a d i a t i o n , a s u b s t a n t i a l f r a c t i o n o f t h e t o t a l i n c i d e n t s h o r t w a v e l o a d , i s not y e t f u l l y u n d e r s t o o d . D e s i g n e r s o f s o l a r c o l l e c t o r s y s t e m s and t h o s e r e s e a r c h e r s i n t e r e s t e d i n c a t c h m e n t e v a p o r a t i o n o r snowmelt s t u d i e s have p a i d l i t t l e a t t e n t i o n t o t h e d i s t r i b u t i o n of i t s i n t e n s i t y a c r o s s t h e sky h e m i s p h e r e (Hooper and B r u n g e r , 1980). C u r r e n t l y t h e d e t e r m i n a t i o n o f t h e d i f f u s e component r e s t s on an assumed r a d i a n c e d i s t r i b u t i o n o v e r t h e sky h e m i s p h e r e ( M o r r i s and L a wrence, 1971). T h i s c o n t r a s t s w i t h a n a l y s e s of t h e d i r e c t beam r a d i a t i o n component w h i c h may be c a l c u l a t e d f r o m p r e c i s e e q u a t i o n s d e t e r m i n e d from g e o m e t r i c a l r e l a t i o n s h i p s between t h e Sun and t h e i n c l i n e d s u r f a c e (Hay and D a v i e s , 1980). I n v e s t i g a t i o n s i n t o t h e d i r e c t i o n a l d i s t r i b u t i o n of d i f f u s e s o l a r r a d i a t i o n have been u n d e r t a k e n w i t h v a r y i n g r e s u l t s . S e v e r a l a s s u m p t i o n s have been i n v o k e d t o a p p r o x i m a t e t h e d i s t r i b u t i o n . K o n d r a t y e v e t a l . (1955) a d o p t e d t h e a s s u m p t i o n o f an i s o t r o p i c sky r a d i a n c e p a t t e r n a s d i d G a m i e r and Ohmura ( 1 9 7 0 ) . A l t h o u g h c o n v e n i e n t m a t h e m a t i c a l l y , e m p i r i c a l a n a l y s i s d i d n o t s u p p o r t t h i s model and a more r e a l i s t i c p a t t e r n was s o u g h t . Morse and C z a r n e c k i (1958) s u g g e s t e d t h a t d i f f u s e r a d i a t i o n i s l a r g e l y c o n c e n t r a t e d i n t h e r e g i o n a r o u n d t h e Sun and hence may be a p p r o x i m a t e d as d i r e c t i o n a l r a d i a t i o n . T h i s t y p e of S u n - c e n t r e d o r h e l i o c e n t r i c model can g r e a t l y 3 o v e r e s t i m a t e t h e d i f f u s e r a d i a n c e f o r S u n - f a c i n g s l o p e s (Hooper and B r u n g e r , 1980). L a t e r s t u d i e s by N o r r i s (1966) t e s t e d t h e a s s u m p t i o n of Morse and C z a r n e c k i (1958) a g a i n s t measured v a l u e s of e n e r g y on an i n c l i n e d s u r f a c e and f o u n d t h a t the h e l i o c e n t r i c a s s u m p t i o n y i e l d s e r r o r s f o r m o n t h l y mean r a d i a n c e v a l u e s much l a r g e r t h a n t h o s e f o r d a i l y v a l u e s and t h a t t h e h i g h e s t e r r o r s were n o t e d when t h e c l o u d c o v e r was g r e a t e s t . M o r r i s and Lawrence (1971) f o u n d t h a t o n l y 57% o f t h e d i f f u s e component on a c l e a r day o r i g i n a t e d w i t h i n 60° o f t h e s o l a r d i s k . A f i x e d c o m b i n a t i o n a l model w h i c h t r e a t e d h a l f t h e sky r a d i a t i o n a s i s o t r o p i c , and t h e r e m a i n i n g h a l f a s h e l i o c e n t r i c was d e v e l o p e d by Hay ( 1 9 7 8 ) . I t was l a t e r i m p r o v e d by a s s u m i n g a v a r i a b l e r a t i o between i s o t r o p i c and h e l i o c e n t r i c d i f f u s e r a d i a t i o n . T h i s a n i s o t r o p i c model u s e d t h e 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 of t h e d i r e c t beam component as an a n i s o t r o p y i n d e x and was f o u n d t o improve b o t h b i a s and r o o t mean s q u a r e e r r o r (RMS) (Hooper and B r u n g e r , 1980). Hooper and B r u n g e r (1980) d e v e l o p e d a t h r e e component c o n t i n u o u s d i s t r i b u t i o n (TCCD) model w h i c h was c a p a b l e of d e s c r i b i n g b o t h c l e a r and o v e r c a s t sky r a d i a n c e d i s t r i b u t i o n s . T h i s model was b a s e d on t h e l i n e a r s u p e r p o s i t i o n of t h r e e f a c t o r s : an i s o t r o p i c component; a h o r i z o n b r i g h t e n i n g component; and a c i r c u m s o l a r component. T h e i r r e s u l t s seemed t o s u b s t a n t i a t e o t h e r f i n d i n g s ( e g . S t e v e n , 1 9 7 7 ) w h i c h s u g g e s t e d t h a t n o r m a l i z e d c l e a r sky r a d i a n c e d i s t r i b u t i o n s a r e s u f f i c i e n t l y s t a b l e t o a l l o w f o r c o n s i s t e n t m a t h e m a t i c a l 4 m o d e l l i n g (Hooper and B r u n g e r , 1980). As w i t h any e m p i r i c a l l y - b a s e d model, i t was l i m i t e d by t h e a c c u r a c y of t h e d a t a base w i t h w h i c h t h e model had been c a l i b r a t e d as w e l l as by not b e i n g a p p l i c a b l e t o p a r t l y c l o u d y s k i e s . As c l e a r s k i e s r e p r e s e n t an a p p r o x i m a t e l y s t e a d y s t a t e , measurement and a n a l y s e s o f t h e a n g u l a r d i s t r i b u t i o n of d i f f u s e r a d i a n c e under s u c h c o n d i t i o n s have been c a r r i e d o u t i n s e v e r a l s t u d i e s . S t e v e n (1977) a t t e m p t e d t o d e t e r m i n e t h e form of a s t a n d a r d c l e a r sky r a d i a n c e p a t t e r n . A s e r i e s of r a d i a n c e measurements were o b t a i n e d i n o r d e r t o d e f i n e s t a n d a r d d i s t r i b u t i o n s i n terms of t h e s o l a r z e n i t h a n g l e and t o i n v e s t i g a t e t h e e f f e c t s of t u r b i d i t y . T h i s s t u d y u t i l i z e d a t e c h n i q u e w h i c h p r e s e r v e d t h e s p a t i a l c h a r a c t e r i s t i c s of t h e r a d i a n t i n t e n s i t y o v e r t h e sky dome. Two o t h e r measurement programmes a t t e m p t e d a s i m i l a r p r o c e d u r e . One was t h a t d e s c r i b e d by V a l k o (1980) where r a d i a n c e was s c a n n e d a t 121 p o i n t s i n t h e sky a t v a r i o u s e l e v a t i o n s and a z i m u t h s u s i n g a s y s t e m of r o t a t i n g p y r a n o m e t e r s , s i l i c o n - d i o d e r a d i o m e t e r s , an a b s o l u t e r a d i o m e t e r and o t h e r S u n - t r a c k i n g d e v i c e s . The d a t a p r o v i d e d t h e d i r e c t i o n a l d i s t r i b u t i o n s and v a r i a t i o n s of sky r a d i a n c e . Hooper and B r u n g e r (1982) a p p r o a c h e d t h e p r o b l e m by d e v e l o p i n g an a u t o m a t i c sky s c a n n i n g s y s t e m u s i n g a s e n s i t i v e r a d i o m e t e r t o measure sky r a d i a n c e . T h i s s c a n n i n g s y s t e m was c a p a b l e of c r e a t i n g a s u b s t a n t i a l d a t a base, and t h e d a t a a q u i s i t i o n s y s t e m was e n t i r e l y c o m p u t e r - c o n t r o l l e d . T h i s work was d e s i g n e d p r i m a r i l y t o s t u d y t h e d i s t r i b u t i o n o f d i f f u s e r a d i a n c e under p a r t l y c l o u d y c o n d i t i o n s as w e l l as under t h e 5 b e t t e r - d o c u m e n t e d c l e a r sky c a s e s but few r e s u l t s have been p r e s e n t e d t h u s f a r . S t u d i e s o f t h e a n g u l a r d i s t r i b u t i o n of d i f f u s e r a d i a n c e below o v e r c a s t s k i e s have been c a r r i e d o ut l e s s f r e q u e n t l y . K i m b a l l and Hand (1922) f o u n d t h a t f o r a d e n s e l y c l o u d e d s k y , th e b r i g h t e s t a r e a was a t t h e z e n i t h and t h e r a d i a n c e d e c r e a s e d t o a q u a r t e r o r l e s s a t t h e h o r i z o n . T h i s was r e p r e s e n t e d by an e m p i r i c a l f o r m u l a by Moon and S p e n c e r (1942) and i s known as th e S t a n d a r d O v e r c a s t Sky (SOC) f o r m u l a . G r a c e (1971) r e q u i r e d d a t a on t h e d i s t r i b u t i o n of r a d i a n c e o v e r t h e sky dome w h i l e i n v e s t i g a t i n g l i g h t i n t e r c e p t i o n by p l a n t s . He f o u n d t h a t t h e mean p a t t e r n o f h i s o b s e r v a t i o n s , t a k e n o v e r a narrow s p e c t r a l r a n g e , c o r r e s p o n d e d w i t h t h e SOC f o r m u l a . He n o t e d r a p i d c h a n g e s i n t h e r a d i a n c e d i s t r i b u t i o n under o v e r c a s t c o n d i t i o n s . A more r e c e n t i n v e s t i g a t i o n by S t e v e n and U n s w o r t h ( 1 9 8 0 ) , d e s i g n e d t o t e s t t h e agreement between t h e SOC f o r m u l a and s p e c t r a l r a d i a n c e measured o v e r a b r o a d waveband, f o u n d t h a t a f u n c t i o n s i m i l a r t o t h e SOC worked w e l l but t h e r e m i g h t be s i g n i f i c a n t d i f f e r e n c e s between r a d i a n c e and l u m i n a n c e d i s t r i b u t i o n s o f o v e r c a s t s k i e s . A h i g h q u a l i t y d a t a s e t d e s c r i b i n g t h e a n g u l a r d i s t r i b u t i o n o f d i f f u s e s o l a r r a d i a t i o n under v a r y i n g a t m o s p h e r i c c o n d i t i o n s i s a f r e q u e n t r e q u i r e m e n t i n e v a l u a t i n g s o l a r e n e r g y a p p l i c a t i o n s . The immediate p r a c t i c a l use o f d e t e r m i n i n g t h e i n t e n s i t y d i s t r i b u t i o n 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 s t h a t t h i s p a r t p r o v i d e s t h e v i s u a l e n v i r o n m e n t t o t h e human eye f o r a g r e a t e r p a r t o f t h e day ( S a s t r i and 6 Manamohanan, 1975). The t e c h n i q u e s p r e s e n t e d so f a r i n v o l v e a t t e m p t s t o use c o n v e n t i o n a l r a d i o m e t r i c measurement methods. E a r l i e r r e s e a r c h by K o n d r a t y e v e t a l . (1955) d e s c r i b e d a r e l a t i o n s h i p between sky l u m i n a n c e and r a d i a n t i n t e n s i t y . They n o t e d t h a t i n t h e f i r s t a p p r o x i m a t i o n t h e r e i s a l i n e a r r e l a t i o n s h i p between t h e e n e r g e t i c a l and l u m i n o u s r a d i a t i o n f l u x e s . Hence, t h e p r o p e r t i e s of t h e a n g u l a r d i s t r i b u t i o n of t h e e n e r g e t i c a l and l u m i n o u s d i f f u s e r a d i a t i o n i n t e n s i t i e s may be d i r e c t l y compared, a l t h o u g h a q u a n t i t a t i v e c o r r e s p o n d e n c e was n o t o b s e r v e d due t o t h e d i f f e r e n t r e s p o n s e s o f t h e i n s t r u m e n t s . B e c a use of t h e s u p p o s e d l a c k of g e n e r a l a p p l i c a b i l i t y of the p h o t o m e t r i c u n i t s , t h e s t u d y by S t e v e n (1977) on t h e d e t e r m i n a t i o n of s t a n d a r d r a d i a n c e d i s t r i b u t i o n s of c l e a r s k i e s , d i d n o t a t t e m p t t o compare t h e s e p a t t e r n s w i t h t h e p r e v i o u s l y p u b l i s h e d l u m i n a n c e d i s t r i b u t i o n s . S t e v e n (1977) u s e d a L i n k e - F e u s s n e r a c t i n o m e t e r t o measure r a d i a n c e o v e r 34 p o i n t s i n a t r a n s e c t a c r o s s t h e sky h e m i s p h e r e , r e q u i r i n g a b o u t 40 m i n u t e s t o c o m p l e t e e a c h s c a n . T h e s e measurements were n o r m a l i z e d w i t h r e s p e c t t o d i f f u s 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 and were f o u n d t o be i n d e p e n d e n t of a t m o s p h e r i c t u r b i d i t y l e v e l s . T h i s e n a b l e d s t a n d a r d , c l e a r sky d i s t r i b u t i o n s b a s e d on a l o n g s e r i e s of r a d i a n c e measurements t o be p r o d u c e d f o r d i f f e r e n t s o l a r z e n i t h a n g l e s . T h i s work was t a k e n a s t e p f u r t h e r by M c A r t h u r (1978) who f o u n d t h a t d i f f u s e s h o r t w a v e r a d i a t i o n c o u l d be e s t i m a t e d a d e q u a t e l y from l u m i n a n c e b o t h s p a t i a l l y and f o r v a r y i n g a t m o s p h e r i c c o n d i t i o n s . He d e v e l o p e d a s e n s i t i v e , 7 f a s t - r e s p o n s e , p h o t o g r a p h i c t e c h n i q u e w h i c h was an a t t e m p t t o accommodate t h e s p a t i a l and t e m p o r a l c o m p l e x i t i e s o f r a p i d l y c h a n g i n g c l o u d c o n d i t i o n s and t h e l o n g r e s p o n s e t i m e of i n s t r u m e n t a t i o n which had p r e v i o u s l y r e s t r i c t e d measurements t o c l o u d l e s s c o n d i t i o n s ( M c A r t h u r and Hay, 1978). M c A r t h u r (1978) t o o k a l l - s k y p h o t o g r a p h s u s i n g a 35 mm SLR camera w i t h a f i s h e y e l e n s d u r i n g a s e q u e n c e of a c t i n o m e t r i c r a d i a n c e measurements. R e d u c t i o n o f t h e p h o t o g r a p h i c n e g a t i v e s i n t o a d i g i t a l form showed f i l m d e n s i t y t o be h i g h l y c o r r e l a t e d w i t h m e asured r a d i a n c e ( M c A r t h u r and Hay, 1978). T h i s a p p r o a c h had t h e a d v a n t a g e o v e r p r e v i o u s methods of b e i n g a b l e t o p r o v i d e an i n s t a n t a n e o u s mapping o f t h e sky dome and even t h e most complex sky c o n d i t i o n s c o u l d be r e p r e s e n t e d . The q u a n t i t a t i v e r e s u l t s p r e s e n t e d i n M c A r t h u r and Hay (1980) a r e i n good agreement w i t h c o m p u t a t i o n s f o r haze m odels by Dave ( 1 9 8 1 ) . Dave (1981) a d d r e s s e d t h e p r o b l e m of r a d i a t i v e t r a n s f e r i n t h e a t m o s p h e r e f r o m t h e v i s u a l - a i r - q u a l i t y p o i n t - o f - v i e w and f o c u s s e d on c o m p u t a t i o n s of t h e l u m i n a n c e , dominant w a v e l e n g t h and s p e c t r a l p u r i t y o f s k y r a d i a t i o n . Even t h e measurement t e c h n i q u e s d e s c r i b e d by M c A r t h u r (1978) a r e n o t w i t h o u t some i n a d e q u a c i e s . The a p p r o a c h i s r e s t r i c t e d by t h e need f o r t h e d i f f u s e r a d i a n c e measurements i n o r d e r t o c a l i b r a t e t h e p h o t o g r a p h s . T h e s e c a l i b r a t i o n s a r e o n l y a s a c c u r a t e as t h e a c t i n o m e t e r u s e d t o o b t a i n t h e measurements and h e n c e , have t h e v e r y l i m i t a t i o n s t h a t t h e p h o t o g r a p h i c t e c h n i q u e i s a t t e m p t i n g t o a v o i d (McArthur. and Hay, 1981). The d a t a r e d u c t i o n s t a g e i s hampered by t h e l e n g t h o f t i m e r e q u i r e d 8 t o d i g i t i z e p h o t o g r a p h s (1 h., 40 mins.) and t h i s l i m i t s a n a l y s i s t o s m a l l e r - s i z e d d a t a s e t s . The most r e c e n t t e c h n i q u e t o be u s e d i n c o n j u n c t i o n w i t h r a d i o m e t r i c ( a c t i n o m e t r i c ) measurement of s o l a r r a d i a t i o n i s a v i d e o - b a s e d s y s t e m o r ' f l u x m a p p e r ' u s i n g a v i d i c o n v i d e o camera e q u i p p e d w i t h an o r t h o g r a p h i c p r o j e c t i o n f i s h e y e l e n s . T h i s t y p e of p r o j e c t i o n a l l o w s o b j e c t s of e q u a l l u m i n a n c e ( d e r i v e d from t h e v i d e o image) t o be imaged w i t h t h e same d e n s i t y r e g a r d l e s s o f t h e i r l o c a t i o n w i t h i n t h e s c e n e (Cannon and Dwyer, 1981). The v i d e o s i g n a l was m o n i t o r e d and p a s s e d t h r o u g h a v i d e o f r a m e s t o r e , a u n i t c a p a b l e of d i g i t i z i n g , p r o c e s s i n g and s t o r i n g v i d e o i n f o r m a t i o n and w h i c h d i g i t i z e d a s i n g l e f i e l d o f v i d e o i n r e a l t i m e . The d a t a from t h e f r a m e s t o r e , now p r o c e s s e d i n t o d i f f e r e n t i n t e n s i t y l e v e l s , were d i s p l a y e d on a t e l e v i s i o n m o n i t o r . D i g i t i z i n g t h e v i d e o d a t a f a c i l i t a t e d r a p i d computer p r o c e s s i n g so t h e i s o - l u m i n a n c e ( i n t e n s i t y ) c o n t o u r s m ight be o b t a i n e d s h o r t l y a f t e r t h e image i s d i g i t i z e d (Cannon and Dwyer, 1981). W i t h t h i s s y s t e m , Cannon and Dwyer (1981) f o u n d t h e y c o u l d e f f e c t i v e l y map t h e e n t i r e sky h e m i s p h e r e i n s t a n t a n e o u s l y and a n a l y z e t h e d a t a i m m e d i a t e l y . D i g i t i z e d v i d e o images m i g h t be c o n v e n i e n t l y s t o r e d on m a g n e t i c t a p e f o r f u t u r e a n a l y s i s and a r c h i v i n g . The " f l u x m a p p e r " has t h e a b i l i t y t o a s s e s s n o t o n l y t h e q u a n t i t y , but a l s o , f o r d a y l i g h t i n g r e s e a r c h p u r p o s e s , t h e q u a l i t y o f l i g h t i n s p a c e (Cannon and Dwyer, 1981). Due t o t h e l i m i t a t i o n s of t h e r a d i o m e t r i c measurement t e c h n i q u e s u s e d t o g a t h e r d a t a on t h e d i r e c t i o n a l d i s t r i b u t i o n 9 o f d i f f u s e s o l a r r a d i a t i o n as d e s c r i b e d i n t h e p r e c e d i n g p a r a g r a p h s , t h e s e p r o c e d u r e s have not p r o v e d v e r y e f f i c i e n t f o r making o b s e r v a t i o n s under p a r t l y c l o u d y s k i e s or under r a p i d l y c h a n g i n g sky c o n d i t i o n s . The complex r a d i a n c e c h a r a c t e r i s t i c s of s u c h c a s e s have been a l l u d e d t o i n t h e work o f R o n d r a t y e v ( 1 9 6 9 ) , G r a c e ( 1 9 7 1 ) , S t e v e n and U n s w o r t h ( 1 9 8 0 ) . M c A r t h u r ' s (1978) s t u d y a t t e m p t e d t o overcome t h e p r o b l e m o f r e s p o n s e t i m e of i n s t r u m e n t a t i o n by s u p p l e m e n t i n g t h e c o n v e n t i o n a l r a d i o m e t r i c measurement t e c h n n i q u e s w i t h a l l - s k y p h o t o g r a p h s . Even t h e most complex d i f f u s e r a d i a t i o n d i s t r i b u t i o n s c o u l d now be mapped ( M c A r t h u r , 1978). The t e c h n i q u e d e v e l o p e d i n t h e p r e s e n t s t u d y u t i l i z e s a v i d e o - b a s e d camera s y s t e m , s i m i l a r t o t h a t d e s c r i b e d by Cannon and Dwyer ( 1 9 8 1 ) . T h i s i s a g r e a t improvement o v e r t h e p h o t o g r a p h i c d i g i t i z i n g t e c h n i q u e d i s c u s s e d i n M c A r t h u r ( 1 9 7 8 ) , s i n c e t h e r e i s a s i g n i f i c a n t r e d u c t i o n i n t i m e between when t h e v i d e o images a r e t a k e n and measured r e s u l t s a r e o b t a i n e d . B e c a u s e of t h e r e l a t i o n s h i p between v i s i b l e and t o t a l s h o r t w a v e r a d i a t i o n as d i s c u s s e d i n M c A r t h u r ( 1 9 7 8 ) , i t i s i n d e e d p o s s i b l e t o combine a c t i n o m e t r i c r a d i a n c e o b s e r v a t i o n s w i t h l u m i n a n c e i n f o r m a t i o n f r o m t h e v i d e o images and assume t h a t t h e v i d e o i n f o r m a t i o n i s r e p r e s e n t a t i v e o f t h e t o t a l s h o r t w a v e r a d i a t i o n f l u x . The p r o c e d u r e f o l l o w e d i n t h i s s t u d y w i l l a l l o w f o r a more p r e c i s e r e p r e s e n t a t i o n o f t h e a n g u l a r d i s t r i b u t i o n o f d i f f u s e r a d i a n c e p a r t i c u l a r i l y under r a p i d l y c h a n g i n g or complex sky c o n d i t i o n s . 10 C h a p t e r Two I n s t r u m e n t a t i o n 2.1 Measurement of D i f f u s e S o l a r R a d i a t i o n A K i p p and Zonen, L i n k e - F e u s s n e r a c t i n o m e t e r (Model No. 76-0319) was u s e d t o make measurements of d i f f u s e r a d i a n c e . T h e s e measurements were c a r r i e d out s o l e l y f o r p u r p o s e s o f c a l i b r a t i o n and v e r i f i c a t i o n of t h e d i s t r i b u t i o n s o f sky r a d i a n c e . The a c t i n o m e t e r i s an i n s t r u m e n t d e s i g n e d t o measure r a d i a n t e n e r g y a c c u r a t e l y under even r e l a t i v e l y t u r b u l e n t c o n d i t i o n s . B u i l t t o e n s u r e s t a b i l i t y , t h e body c o n s i s t s of s i x m a s s i v e c o p p e r r i n g s w h i c h f u n c t i o n as d i a p h r a g m s . T h e s e o p e n i n g s become p r o g r e s s i v e l y s m a l l e r t o w a r d s t h e t h e r m o p i l e and t h u s a c t t o e l i m i n a t e t u r b u l e n t a i r c u r r e n t s i n s i d e t h e body w h i c h c o u l d a f f e c t t h e t h e r m o p i l e (IGY, 1958). T h i s i n s t r u m e n t u s e s a s p e c i a l l y c o m p e n s a t e d M o l l t h e r m o p i l e w h i c h i s d i v i d e d i n t o two compartments, one o f which i s s c r e e n e d from r a d i a t i o n and so a c t s a s a c o m p e n s a t i n g d e v i c e . However, i t may s t i l l be s u b j e c t t o g u a s i - a d i a b a t i c p r e s s u r e c h a n g e s o c c u r r i n g n e a r t h e t h e r m o p i l e s u r f a c e (IGY, 1958). The r e a d i n g s of t h e i n s t r u m e n t a r e known t o be i n d e p e n d e n t of w a v e l e n g t h . The body of t h e a c t i n o m e t e r i s e q u i p p e d w i t h a d e v i c e f o r a c c u r a t e l y s i g h t i n g t h e Sun and w i t h a thermometer s e t i n s i d e t h e body t o m o n i t o r t e m p e r a t u r e f l u c t u a t i o n s w i t h i n a r a n g e of 0° t o 40°C (IGY, 1958). The i n s t r u m e n t i s mounted on a s t a n d 11 f i t t e d w i t h an a z i m u t h c i r c l e w h i c h i s d i v i d e d i n 1° i n c r e m e n t s and a c o n t r o l f o r z e n i t h a l movements, s c a l e d i n i n t e r v a l s o f 0 . 1 ° . The a c t i n o m e t e r i s w e a t h e r p r o o f e d w i t h chromium p l a t i n g . The a c t i n o m e t e r i s e q u i p p e d w i t h a b u i l t - i n f i l t e r r i n g w i t h f o u r f i l t e r p o s i t i o n s and one m e t a l s h u t t e r . F o r t h i s s t u d y , measurements were t a k e n u s i n g a q u a r t z f i l t e r made of h omogenized u l t r a s i l ; i t s t r a n s m i s s i o n p r o p e r t i e s a l l o w 92% t r a n s m i s s i o n o v e r t h e range 0.20/iin-3 . Ojum (IGY, 1958). T h i s i n s t r u m e n t shows 99% r e s p o n s e i n 8-10 s e c o n d s , a c c o r d i n g t o C o u l s o n ( 1 9 7 5 ) . The a c t i n o m e t e r was c a l i b r a t e d by 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 (AES) a t Downsview, Ont., b e f o r e t h e s t a r t of t h e e x p e r i m e n t . The c a l i b r a t i o n c o n s t a n t r e s u l t i n g from t h a t i n v e s t i g a t i o n was 1 6 . 9 A i V W _ 1 m 2 w i t h an a n g u l a r s e n s i t i v i t y t o i s o t r o p i c r a d i a n c e of 0 . 4 1 7 M V ( W m ~ 2 s r ~ 1 ) ~ 1 . T h i s c a l i b r a t i o n r e s u l t e d i n t h e d e t e r m i n a t i o n of an e q u i v a l e n t u n i f o r m a p e r t u r e and an e q u i v a l e n t s o l i d h a l f a n g l e of 5.08° and 0.0247 s r r e s p e c t i v e l y . 2.1.1.1 R e c o r d i n g t h e D i f f u s e R a d i a t i o n S i g n a l The d i f f u s e r a d i a t i o n s i g n a l was m o n i t o r e d w i t h a H e w l e t t - P a c k a r d 4 1/2 d i g i t v o l t m e t e r (Model 3466A). T h i s v o l t m e t e r has a s e n s i t i v i t y o f 1M V on a 20 mV range and t h e a c c u r a c y f o r t h i s r a n g e i s q u o t e d as ± 0 . 0 5 % + 3 d i g i t s ( H e w l e t t - P a c k a r d M a n u a l , 1979). 1 2 2.1.2 A n a l y s i s of t h e E r r o r A s s o c i a t e d w i t h t h e Measurement  of D i f f u s e S o l a r R a d i a t i o n 2.1.2.1 A n a l y s i s o f t h e E r r o r A s s o c i a t e d w i t h t h e S e n s o r The L i n k e - F e u s s n e r a c t i n o m e t e r u s e d i n t h i s s t u d y i s e s t i m a t e d t o have an a c c u r a c y of ± 1 % (IGY, 1958). However as t h e r e has been no e m p i r i c a l t e s t i n g o f t h i s a c c u r a c y e s t i m a t e , R o b i n s o n (1966) s u g g e s t s t h a t a more c o n s e r v a t i v e e s t i m a t e of ± 2 % i s more r e a s o n a b l e . The t e m p e r a t u r e dependence on t h e c a l i b r a t i o n f a c t o r f o r d i r e c t r a d i a t i o n i s e x p r e s s e d by t h e f a c t o r (1 + a ' ( T - 2 0 ) ) where T i s t e m p e r a t u r e ( i n d e g r e e s C e l s i u s ) and a'=0.002 f o r s o l a r r a d i a t i o n a t a c a l i b r a t i o n t e m p e r a t u r e of 20°C ( C o u l s o n , 1975). E m p i r i c a l s t u d i e s by P a s c o e and F o r g a n (1980) s u g g e s t t h a t t h e t e m p e r a t u r e c o e f f i c i e n t may a c t u a l l y be much s m a l l e r and so i t was not deemed n e c e s s a r y t o t e m p e r a t u r e - c o r r e c t t h e d a t a . As t h i s was n o t t e s t e d d u r i n g t h e s t u d y , t h e m a n u f a c t u r e r ' s v a l u e of t h e t e m p e r a t u r e dependence w i l l be u s e d i n t h e e r r o r a n a l y s i s . Hence c o r r e c t i o n s f o r o t h e r t e m p e r a t u r e s can a f f e c t t h e r e a d i n g s by 0.2% p e r °C. D u r i n g c a l i b r a t i o n by t h e AES, an a n a l y s i s o f t h e a n g u l a r s e n s i t i v i t y o f t h e a c t i n o m e t e r under i s o t r o p i c r a d i a t i o n c o n d i t i o n s was c a r r i e d o u t . The a n a l y s i s r e s u l t e d i n an a c c e p t a n c e a p e r t u r e o f 10.16° t o t a l a n g l e . In o t h e r words, t h e n o r m a l i z e d v e r t i c a l and h o r i z o n t a l r e s p o n s e o f t h e i n s t r u m e n t a p p r o a c h e d z e r o o u t s i d e t h e a n g u l a r l i m i t . I f however, c o n d i t i o n s of r a d i a t i v e a n i s o t r o p y s h o u l d e x i s t , t h e r e 1 3 c o u l d be an e r r o r a s s o c i a t e d w i t h e a c h measurement; t h e a c t i n o m e t e r c o u l d be s e n s i t i v e t o r a d i a t i v e s o u r c e s beyond t h e t o t a l a n g l e of a p e r t u r e and c o u l d r e s p o n d t o t h e s e s o u r c e s . D u r i n g t h i s s t u d y , t h e r e were not t h e means a v a i l a b l e t o u n d e r t a k e an a n a l y s i s o f s u c h e r r o r and i t w i l l be assumed t h a t i t would n o t be g r e a t e r t h a n t h e q u o t e d o v e r a l l a c c u r a c y of t h e a c t i n o m e t e r . A n o t h e r p o s s i b l e s o u r c e of e r r o r c o u l d a r i s e from o f f s e t s i n a l i g n m e n t o f t h e a c t i n o m e t e r . Once a g a i n , f o r i s o t r o p i c r a d i a t i o n c o n d i t i o n s , an e r r o r i n a l i g n m e n t would n o t c o n t r i b u t e t o any change i n v o l t a g e o u t p u t but t h i s would not be t r u e f o r a n i s o t r o p i c r a d i a n c e d i s t r i b u t i o n s . T h i s e r r o r was a l s o assumed t o be no g r e a t e r t h a n t h e o v e r a l l a c c u r a c y o f t h e s e n s o r . The e r r o r a n a l y s i s o u t l i n e d by Cook and R a b i n o w i c z ( 1 9 6 7 ) , i m p l i e s t h a t t h e t o t a l p r o b a b l e e r r o r c o n s i s t s of t h e r e l a t i v e e r r o r of t h e s e n s o r (±2%) and t h e t e m p e r a t u r e c o r r e c t i o n (±2% p e r ° C ) as f o l l o w s : E T = ( ( 2 ) 2 + ( 2 ) 2 ) 1 / 2 (2.1) = 2.8%. T h e r e f o r e t h e t o t a l p r o b a b l e e r r o r ( E T ) a s s o c i a t e d w i t h t h e s e n s o r i s a p p r o x i m a t e l y 3% . 2.1.2.2 A n a l y s i s of E r r o r A s s o c i a t e d w i t h t h e R e c o r d i n g  I n s t r u m e n t The a c c u r a c y of t h e v o l t m e t e r i s q u o t e d a s ± 0 . 0 5 % + 3 d i g i t s ( H e w l e t t - P a c k a r d M a n u a l ) . From t h i s , i t i s n e c e s s a r y t o 1 4 e s t a b l i s h what 3 d i g i t s r e p r e s e n t s a s an a b s o l u t e e r r o r . G i v e n t h e a c t i n o m e t r i c c a l i b r a t i o n c o n s t a n t , t h i s c o r r e s p o n d s t o an a b s o l u t e e r r o r o f ±4.91 Wm~ 2sr~ 1. T a b l e 2.1 shows t h e v a r i a t i o n i n t h e r e l a t i v e e r r o r o f t h e r e c o r d e r a s s o c i a t e d w i t h a d i f f u s e r a d i a t i o n s i g n a l . S i n c e i t i s a s i m p l e m a t t e r t o d e t e r m i n e t h e a v e r a g e d i f f u s e r a d i a n c e v a l u e p e r s c a n , t h e r e l a t i v e e r r o r o f t h e HP v o l t m e t e r c a n be c a l c u l a t e d f o r e v e r y s c a n r a t h e r t h a n u t i l i z i n g a s i n g l e r e p r e s e n t a t i v e p e r c e n t a g e e r r o r . 2.1.2.3 E r r o r A s s o c i a t e d w i t h t h e Measurement of D i f f u s e S o l a r  R a d i a t i o n The p r o b a b l e e r r o r a s s o c i a t e d w i t h t h e measurement of d i f f u s e r a d i a t i o n can be c a l c u l a t e d a s : E = Y x ( I ( E . ) 2 ) 1 / 2 i = 1 E T= Y x ( ( 0 . 0 2 ) 2 + ( 0 . 0 0 2 ) 2 + (4.91/Y ) 2 + ( . 0 0 0 5 ) 2 ) 1 / 2 (2.2) where E^ i s t h e r e l a t i v e e r r o r a s s o c i a t e d w i t h t h e i t h component of t h e measurement s y s t e m and Y i s t h e a v e r a g e sky r a d i a n c e v a l u e (Wm~ 2sr~ 1) b a s e d on n o b s e r v a t i o n s t a k e n d u r i n g a s c a n . T a b l e 2.2 shows examples o f t h e p r o b a b l e r e l a t i v e e r r o r a s s o c i a t e d w i t h v a r i o u s r a d i a n c e v a l u e s . 2.2 D e t e r m i n a t i o n of B r i g h t n e s s V a l u e s from V i d e o Imagery 1 5 T a b l e 2 . 1 R e c o r d e r E r r o r A s s o c i a t e d w i t h a D i f f u s e R a d i a t i o n S i g n a l S i g n a l (Wm 2 ) I n p u t ( M V ) A b s o l u t e E r r o r R e l a t i v e E r r o r (%) 2 5 1 0 . 4 4 ± 3 M V 1 9 . 6 4 5 0 2 0 . 8 7 o r 9 . 8 2 1 0 0 4 1 . 7 4 ± 4 . 9 1 Wm-2 4 . 9 1 1 5 0 6 2 . 6 1 3 . 2 7 2 0 0 8 3 . 4 9 2 . 4 6 2 5 0 1 0 4 . 3 6 1 . 9 6 3 0 0 1 2 5 . 2 3 1 . 6 4 1 6 T a b l e 2.2 P r o b a b l e R e l a t i v e E r r o r s A s s o c i a t e d w i t h Sample R a d i a n c e s (Wm~ 2sr~ 1) A v e r a g e R a d i a n c e P r o b a b l e E r r o r ( W m _ 2 s r _ 1 ) (%) 10 49.14 20 24.63 50 10.02 100 5.31 150 3.81 200 3.17 17 2.2.1 V i d e o Camera and M o n i t o r i n g System A v i d e o - b a s e d i m a g i n g s y s t e m was u s e d i n t h i s s t u d y f o r l u m i n a n c e a q u i s i t i o n and a n a l y s i s . E a c h component of t h e s y s t e m w i l l be d i s c u s s e d i n d i v i d u a l l y . 2.2.1 .1 V i d e o Camera, F i s h e y e Lens and F i l t e r The v i d e o camera ( P a n a s o n i c WV-1850) u s e s t h e h i g h r e s o l u t i o n , ER ( E x t e n d e d Red) Newvicon p i c k - u p t u b e . T h i s camera p r o d u c e s a c l e a r , h i g h q u a l i t y image and i s o f t e n u s e d i n a r e a s of r e s e a r c h , i n c l u d i n g s t u d i e s i n v o l v i n g TV m i c r o s c o p y . The s p e c t r a l s e n s i t i v i t y of t h e ER Newvicon t u b e i s shown i n F i g . 2.1 ( O p e r a t i n g I n s t r u c t i o n s M anual by P a n a s o n i c , 1 9 8 1 ) . The s p e c t r a l r e s p o n s e i n c r e a s e s from t h e s h o r t - w a v e end of t h e s p e c t r u m t o a maximum i n t h e n e a r - i n f r a r e d r e g i o n and c u t s o f f a t 0.940/.m. The t r a n s f e r c h a r a c t e r i s t i c s a r e s u c h t h a t i f S i s t h e a c t u a l b r i g h t n e s s of an e l e m e n t of a s c e n e , t h e e l e c t r i c a l o u t p u t , V, from t h a t p o i n t on t h e p h o t o c o n d u c t o r c a n be shown by: V = k S 7 (2.3) F o r t h i s p r o j e c t , t h e y v a l u e of t h e camera was e q u a l t o 1.0 ( P a c i f i c C o m m u n i c a t i o n s L t d . , p e r s . comm.) p r o d u c i n g l i n e a r t r a n s f e r c h a r a c t e r i s t i c s . T h e r e was not t h e means t o c h e c k t h e a c c u r a c y o f j d u r i n g t h i s s t u d y , but s i n c e t h e r e s u l t s g i v e n i n S e c t i o n 4.1.1 i n d i c a t e a l i n e a r r e l a t i o n s h i p between r a d i a n c e and b r i g h t n e s s , t h i s i n d i c a t e s t h a t t h e camera was i n d e e d 1 8 0.4 0.6 '0.8 1.0. W a v e l e n g t h (jum) F i g u r e 2.1 S p e c t r a l S e n s i t i v i t y C h a r a c t e r i s t i c s of t h e ER Newvicon Camera R e l a t i v e t o the V i d i c o n Camera ( P a n a s o n i c O p e r a t i n g M a n u a l , 1981) 19 p e r f o r m i n g as e x p e c t e d . The s t a n d a r d one i n c h Newvicon camera t u b e has a u s e f u l t a r g e t a r e a o f a bout 0.93 cm. x 1.25 cm. The c o r n e r s of t h e t a r g e t may have p o o r e r r e s o l u t i o n t h a n a t t h e c e n t r e and i t i s p o s s i b l e f o r v e r t i c a l r e s o l u t i o n t o v a r y from h o r i z o n t a l r e s o l u t i o n . T h i s p a r t i c u l a r t u b e i s r a t e d f o r a h o r i z o n t a l r e s o l u t i o n of 800 l i n e s a t c e n t r e . G e o m e t r i c d i s t o r t i o n f o r t h i s ER Newvicon i s g i v e n as l e s s t h a n 2% on e i t h e r t h e v e r t i c a l o r h o r i z o n t a l a x i s . The camera has a s i g n a l - t o - n o i s e r a t i n g of 45 dB. T h i s f i g u r e l i m i t s t h e u s e f u l dynamic range of t h e camera ( w i t h a low end s i g n a l - t o - n o i s e r a t i o of 1:1) t o a b o u t 150:1. The camera was f i t t e d w i t h an e q u i - a n g u l a r p r o j e c t i o n , c u s t o m - b u i l t f i s h e y e l e n s . D e s c r i p t i o n of t h e p r o j e c t i o n p r o p e r t i e s of t h i s l e n s and t h e t e s t s c a r r i e d out t o c o n f i r m them a r e i n A p p e n d i x I . I t was f o u n d t h a t t h e p r o p e r t i e s of t h e v i d e o i m a g i n g s y s t e m and l e n s i n c o m b i n a t i o n r e s u l t e d i n a t o t a l view of a p p r o x i m a t e l y 170°-174° of t h e sky h e m i s p h e r e ( A p p e n d i x I ) . In a d d i t i o n t o t h e f i s h e y e l e n s , i t was n e c e s s a r y t o use a n e u t r a l d e n s i t y f i l t e r i n o r d e r t o a v o i d image s a t u r a t i o n . A Kodak W r a t t e n n e u t r a l d e n s i t y ( g e l a t i n ) f i l t e r , No. 96., was u s e d f o r t h i s p u r p o s e . I t was f o u n d t h a t a n e u t r a l d e n s i t y No. 3.0 w i t h a 0.1% t r a n s m i s s i o n f a c t o r was n e c e s s a r y t o a c h i e v e s u f f i c i e n t r e d u c t i o n of l i g h t i n t e n s i t y . N e u t r a l i t y i s v a l i d f o r t h e v i s i b l e p a r t of t h e s p e c t r u m o n l y (0.400M I T I t o 0.700Mm) and so t h e s e f i l t e r s a r e not recommended f o r use i n t h e 20 u l t r a v i o l e t o r i n f r a r e d r e g i o n s . F i g . 2.2 shows t h e s p e c t r a l s e n s i t i v i t y c h a r a c t e r i s t i c s of t h e v i d e o camera and f i l t e r i n c o m b i n a t i o n , a s d e t e r m i n e d from t h e i r r e s p e c t i v e s p e c t r a l p r o p e r t i e s . I t can be seen t h a t t h e r e s p o n s e of t h e s y s t e m t o t h e v i s i b l e p o r t i o n of t h e s p e c t r u m i s much l e s s t h a n t o t h e n e a r - i n f r a r e d r e g i o n . The peak r e s p o n s e c o r r e s p o n d s t o t h o s e w a v e l e n g t h s w h i c h a r e t r a n s m i t t e d by t h e f i l t e r . From t h e l a t t e r r e s u l t s , i t was deemed n e c e s s a r y t o i n v e s t i g a t e t h e s p e c t r a l r e s p o n s e o f t h e v i d e o c a m e r a / f i l t e r c o m b i n a t i o n t o t y p i c a l c l e a r and c l o u d y sky e n e r g y d i s t r i b u t i o n s . T h i s would p r o v i d e u s e f u l knowledge when a t t e m p t i n g t o a n a l y z e a v i d e o image w i t h r e s p e c t t o l u m i n a n c e i n f o r m a t i o n . K o n d r a t y e v (1969) has p u b l i s h e d a t a b l e g i v i n g t h e e n e r g y d i s t r i b u t i o n i n t h e s o l a r s p e c t r u m f o r 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 and d i f f u s e s o l a r r a d i a t i o n ; t h i s i s p r e s e n t e d i n T a b l e 2.3. R e s u l t s from T a b l e 2.3 i n d i c a t e t h a t t h e d i f f e r e n c e between t h e e n e r g y d i s t r i b u t i o n o f d i r e c t and d i f f u s e s o l a r r a d i a t i o n must be l e s s f o r a c l o u d y s k y t h a n i n t h e c a s e of a c l e a r s k y . A n a l y s i s o f s p e c t r a l i r r a d i a n c e f o r c l o u d y p e r i o d s by B i r d e t a l . (1982) showed t h a t t h e s p e c t r a l c o m p o s i t i o n of a c l o u d y day i s v e r y s i m i l a r i n d i s t r i b u t i o n t o t h a t o f 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 a g i v e n i n T a b l e 2.3. F o r t h i s r e a s o n , t h e s p e c t r a l e n e r g y d i s t r i b u t i o n f o r t h e Sun w i l l be u s e d as an example of t h e s p e c t r a l c o m p o s i t i o n o f a t y p i c a l c l o u d y day. The s p e c t r a l e n e r g y d i s t r i b u t i o n o f a t y p i c a l c l e a r sky a l s o o r i g i n a t e s f r o m work by K o n d r a t y e v (1969) and i s d e p i c t e d i n 21 3.0 — 2.0 > co 1.0 CO CD 0.4 0.5 0.6 0.7 0.8 0.9 Wavelength (.um) F i g u r e 2.2 V i d e o Camera and F i l t e r S p e c t r a l Response C u r v e 22 T a b l e 2.3 E n e r g y D i s t r i b u t i o n i n t h e S o l a r S p e c t r u m O u t s i d e t h e Atmosphere ( 1 0 " 3 c a l / c m 2 m i n ) a n d t h e S p e c t r a l C o m p o s i t i o n of D i f f u s e R a d i a t i o n (10 6 c a 1 / c m 2 m i n ) From K o n d r a t y e v ( 1 9 6 9 ) . D X , M Sun 1 cm 3 o f 100 d r o p s 25 d r o p s 5 d r o p s c l e a n a i r r = 0 . 1M r = 0 . 5M r=1/_ 0.28-0.30 2.6 4.4 0.05 0.14 1.0 0.30-0.32 1 1 .5 14.4 0.27 0.78 4.6 0.32-0.34 21.8 21.9 0.44 1 .62 9.2 0.34-0.36 31.3 23.5 0.54 1 .78 12.8 0.36-0.38 35.2 20.8 0.51 3.52 14.6 0.38-0.40 36.0 16.9 0.45 3.78 15.1 0.42-0.44 54.3 17.2 0. 52 6.41 23.2 0.46-0.48 62.6 13.7 0.46 7.65 25.6 0.50-0.52 59.7 9.3 0.36 7.35 20.6 0.56-0.58 54.6 4.4 0.25 6.67 14.4 0.64-0.66 48 . 4 2.8 0.14 5.48 18.6 0.70-0.72 42.9 1 .8 0.09 4.29 20.0 0.78-0.80 35.3 0.8 0.05 3.04 18.0 0.86-0.88 27. 1 0.5 0.03 2.11 15.8 0.98-1.0 21.0 0.2 0.02 1 .36 12.4 23 F i g . 2.3. The p r o c e d u r e t o d e t e r m i n e how t h e v i d e o camera and f i l t e r t o g e t h e r r e s p o n d s p e c t r a l l y ( f o r a c e r t a i n waveband) t o a c l e a r and c l o u d y day i s as f o l l o w s : 1) I n t e g r a t e t h e two s p e c t r a l c u r v e s ( c l e a r s ky and c l o u d y sky) between 0 . 38/im- 1 . Oum 2) n o r m a l i z e t h e c u r v e s t o t h e same a r e a 3) m u l t i p l y the s e n s i t i v i t y of t h e c a m e r a / f i l t e r c o m b i n a t i o n by t h e c o r r e s p o n d i n g n o r m a l i z e d v a l u e of e a c h c u r v e f o r e v e r y O.lOMm i n t e r v a l between 0 . 40jum- 1 . OMITI 4) i n t e g r a t e t h e two c u r v e s and d e t e r m i n e t h e m a g n i t u d e of t h e d i f f e r e n c e s between t h e cam e r a ' s r e s p o n s e t o c l e a r and c l o u d y sky c o n d i t i o n s The f i n a l i n t e g r a t i o n of t h e c l e a r and c l o u d y c u r v e s , a f t e r a d j u s t m e n t f o r t h e c a m e r a / f i l t e r r e s p o n s e i s 11505 and 9941 ( r e l a t i v e u n i t s ) f o r the o v e r c a s t and c l e a r s k y , r e s p e c t i v e l y . T h i s r e p r e s e n t s a 15.7% d i f f e r e n c e between t h e r e s p o n s e of t h e camera s y s t e m t o a t y p i c a l c l e a r and c l o u d y s k y . G i v e n t h i s , one can e x p e c t t h e camera t o r e s p o n d 1.157 t i m e s more t o t h e t y p i c a l s p e c t r a l c o m p o s i t i o n (between 0.4(xm-1 . Oum) of an o v e r c a s t sky as compared t o a c l e a r s k y . The i m p l i c a t i o n s of t h i s f i n d i n g w i l l be c o n s i d e r e d i n S e c t i o n 4.2. F i g . 2.3 s u g g e s t s t h a t f o r c l e a r s k i e s t h e r e i s a marked d e c r e a s e i n t h e amount of e n e r g y p r e s e n t i n a p a r t i c u l a r waveband f o r l o c a t i o n s away from t h e z e n i t h . However, a l t h o u g h t h e 24 2 1 0 in F i g u r e 2.3 S p e c t r a l D i s t r i b u t i o n o f D i f f u s e S o l a r R a d i a t i o n f o r C l e a r S k i e s a t t h e (1) Z e n i t h and (2) a t a P o i n t Where the Sky Luminance i s M i n i m a l . From K o n d r a t y e v (1969) 26 v a l u e of t h a t p i x e l . The c o u n t v a l u e i s d e r i v e d from t h e v o l t a g e c o r r e s p o n d i n g t o t h e r e l a t e d p o i n t i n t h e s k y . F r o n t p a n e l c o n t r o l s i n c l u d e AC power ( o n / o f f b u t t o n ) and v i d e o l e v e l and b l a c k n e s s c o n t r o l s . The l a t t e r two c o n t r o l s may be a d j u s t e d m a n u a l l y so as t o a v o i d image s a t u r a t i o n or b l a c k n e s s . In t h i s s t u d y , an E l e c t r o h o m e v i d e o m o n i t o r (Model EVM 23AG) was l o c a t e d b e s i d e t h e v i d e o f r a m e s t o r e and p r o v i d e d c o n v e n i e n t image p r o c e s s i n g and v i e w i n g . An A p p l e II m i c r o c o m p u t e r h o s t e d t h e d i g i t a l f r a m e s t o r e and f l o p p y d i s k s were u s e d t o s t o r e images from the f r a m e s t o r e memory. In a s i m i l a r f a s h i o n , images c o u l d be t r a n s f e r r e d from t h e d i s k s t o t h e f r a m e s t o r e f o r v i e w i n g a t a l a t e r d a t e . Any b r i g h t n e s s i n f o r m a t i o n from t h e image c o u l d a l s o be a b s t r a c t e d e a s i l y and s t o r e d on t h e f l o p p y d i s k s . 25 m a g n i t u d e of t h e e n e r g y s p e c t r u m may change w i t h z e n i t h and a z i m u t h a n g l e , t h e d i s t r i b u t i o n of e n e r g y r e m a i n s t h e same. The peak of th e s p e c t r u m s t i l l r e s i d e s between 0.45-0.48Mm w h i c h a r e w a v e l e n g t h s t h a t t h e c a m e r a / f i l t e r s y s t e m i s not p a r t i c u l a r i l y s e n s i t i v e t o . The p r e c e d i n g m e t h o d o l o g y was a p p l i e d t o t h e s p e c t r a l c u r v e s d e p i c t e d i n F i g . 2.3 f o r w a v e l e n g t h s between 0.4Mm and 1.0/im t o d e t e r m i n e t h e r e s p o n s e o f t h e camera s y s t e m t o c h a n g e s i n t h e s p e c t r a l c o m p o s i t i o n w i t h c h a n g e s i n z e n i t h a n g l e . An a l t e r n a t i v e a n a l y s i s r e s u l t e d i n r e l a t i v e v a l u e s of 31.22 and 30.74 f o r c l e a r sky d i f f u s e r a d i a n c e a t t h e z e n i t h and where sky l u m i n a n c e was m i n i m a l , r e s p e c t i v e l y . Thus, no v a r i a t i o n i n r e s p o n s e of t h e v i d e o s y s t e m t o c h a n g e s i n t h e s p e c t r a l c o m p o s i t i o n due t o c h a n g e s i n t h e z e n i t h a n g l e c o u l d be d e t e c t e d . 2.2.1.2 V i d e o F r a m e s t o r e The C o l o r a d o V i d e o Model 274D v i d e o f r a m e s t o r e has a s o l i d - s t a t e memory w i t h f a s t A/i) and D/A c o n v e r t e r s . T h i s u n i t i s c a p a b l e o f d i g i t i z i n g , s t o r i n g , and d i s p l a y i n g a s i n g l e frame of v i d e o memory and t h e r e s u l t s may be v i e w e d on a s t a n d a r d v i d e o m o n i t o r . I n d i v i d u a l p i c t u r e e l e m e n t s i n t h e image known as ' p i x e l s ' can t h e n be a c c e s s e d by a com p u t e r , p r o c e s s e d and r e - d i s p l a y e d , i f d e s i r e d . An image c o n t a i n s 256 x 256 p i x e l s . A f r o n t p a n e l p u s h b u t t o n s w i t c h a l l o w s t h e image t o be v i e w e d c o n t i n u o u s l y i n r e a l t i m e and r e l e a s e o f t h i s b u t t o n r e s u l t s i n a frame ' f r e e z e ' . A s e r i e s of 8 s w i t c h e s f a c i l i t a t e s d i s p l a y of g r e y l e v e l s (256 g r e y l e v e l s i n t o t a l - 8 b i t s ) . F o r t h e p u r p o s e s o f t h i s s t u d y , t h e c o u n t v a l u e of a p i x e l w i l l be te r m e d t h e ' b r i g h t n e s s ' 27 C h a p t e r T h r e e E x p e r i m e n t a l P r o c e d u r e s 3.1 F i e l d Measurement S i t e F i e l d work f o r t h i s s t u d y was c a r r i e d out on t h e r o o f of t h e Geography Department a t t h e 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 campus a t V a n c o u v e r , B r i t i s h C o l u m b i a . T h i s l o c a t i o n i s a t a l a t i t u d e of 49.74°N and l o n g i t u d e 122.96°W and an e l e v a t i o n o f 85 m e t r e s . The s i t e i s r o u g h l y 9 km. west o f V a n c o u v e r ' s c e n t r a l b u s i n e s s d i s t r i c t . C l i m a t i c a l l y , t h e s t u d y a r e a i s i n t h e zone o f t h e m i d - l a t i t u d e w e s t e r l i e s a l t h o u g h t h e l o c a l s u r f a c e winds e x h i b i t c o n s i d e r a b l e d i r e c t i o n a l v a r i a b i l i t y (Hay and Oke, 1976). The c o a s t a l m o u n t a i n s i m m e d i a t e l y n o r t h of t h e c i t i e s of N o r t h and West V a n c o u v e r r i s e t o a p p r o x i m a t e l y 1000 m e t r e s and a r e even h i g h e r f u r t h e r t o t h e n o r t h and n o r t h w e s t . They do not s i g n i f i c a n t l y a f f e c t t h e l o c a l h o r i z o n however. T h e s e m o u n t a i n s c o n t r i b u t e c o n s i d e r a b l y t o l o c a l c l o u d r e g i m e s t h r o u g h o r o g r a p h i c u p l i f t i n g ( H e r tzman, 1979). The r o o f s i t e was a t a r and g r a v e l s u r f a c e w i t h a c c e s s t o power and s t o r a g e s p a c e f o r t h e i n s t r u m e n t s . I t was c h o s e n p r i m a r i l y t o p r o v i d e an e a s y l i n k t o computer f a c i l i t i e s r e q u i r e d by t h e v i d e o i m a g i n g s y s t e m . The v i d e o camera was h e l d i n p o s i t i o n by a p l a t e on a frame b u i l t out o f 3/4 i n c h g a l v a n i z e d s t e e l t u b i n g . T h i s frame had been l e v e l l e d and a l i g n e d due N o r t h - S o u t h , and a l l o w e d f o r s u p p o r t and c o r r e c t p o s i t i o n i n g o f t h e o c c u l t i n g 28 d i s k . When p l a c e d v e r t i c a l l y , t h e camera was l e v e l l e d w i t h a s p i r i t l e v e l and a l i g n e d i n t h e manner d e p i c t e d i n F i g . 3.1. F i g . 3.1 a l s o shows t h i s m e t a l frame and t h e camera i n i t s n o r m a l o p e r a t i n g p o s i t i o n . The a c t i n o m e t e r was p l a c e d on a l e v e l l e d p l a n e t a b l e and was a l i g n e d i n s u c h a way as t o e n s u r e b o t h t h e camera and t h e r a d i o m e t e r v i e w e d t h e same l o c a l sky h e m i s p h e r e . T h i s e n s u r e d t h a t t h e r a d i a n c e measured a t a p o i n t i n t h e sky would c o r r e s p o n d t o a mean b r i g h t n e s s v a l u e a b s t r a c t e d from a v i d e o image of t h e s k y . When t h e a c t i n o m e t e r was p l a c e d on t h e p l a n e t a b l e , i t was l e v e l l e d and t h e n t h e s i t i n g mechanism on t h e i n s t r u m e n t was u s e d t o f o c u s on a t a r g e t l o c a t e d on a r o o f v e n t w h i c h had been p r e v i o u s l y s i g h t e d w i t h a compass and deemed t o be i n l i n e w i t h t h e camera and l e n s s y s t e m . T h i s s e r v e d as a r e f e r e n c e l o c a t i o n f o r t h e a c t i n o m e t e r and e n s u r e d t h a t i t was p o s i t i o n e d i n t h e same way f o r e a c h measurement. The p l a n e t a b l e was l o c a t e d a p p r o x i m a t e l y 1.5 m e t r e s n o r t h e a s t of t h e camera and a t no t i m e was t h e a c t i n o m e t e r i n t h e f i e l d - o f - v i e w of t h e f i s h e y e camera l e n s . L i k e w i s e , t h e camera and s u p p o r t frame was n e v e r i n t h e a c t i n o m e t r i c f i e l d - o f - v i e w due t o t h e s e q u e n c e o f r a d i a n c e measurements. F i g . 3.2 i l l u s t r a t e s o t h e r d e t a i l s o f t h e e x p e r i m e n t a l s e t - u p . 3.1.1 Sky View F a c t o r A n a l y s i s The sky view f a c t o r , as d e t e r m i n e d by t h e m e t h o d o l o g y of S t e y n ( 1 9 8 0 ) , was u s e d t o d e s c r i b e t h e amount of r a d i a t i o n r e c e i v e d by t h e v i d e o camera l e n s e m a n a t i n g from a l l s o u r c e s 2 9 F i g u r e 3.1 View of V i d e o Pos i t i on Came ra Mon i t o r i n g 30 g u r e 3.2 V i e w of F i e l d M e a s u r e m e n t S i t e on t h e Roof of t h e G e o g r a p h y D e p a r t m e n t , U.B.C. 31 above th e l o c a l h o r i z o n . In t h i s a n a l y s i s , a v i d e o image of a c l o u d l e s s sky was p h o t o g r a p h e d so t h a t h o r i z o n f e a t u r e s c o u l d be i d e n t i f i e d c l e a r l y . T h i s p h o t o g r a p h was e n l a r g e d t o 20.3 x 25.4 cm. w i t h a h o r i z o n t a l r a d i u s of 9.4 cm. T h i s a l l o w s t h e p r i n t a r e a s t o be t r a n s f e r r e d o n t o p o l a r g r a p h p a p e r . The view f a c t o r ( 0 s _ r ) c a n be e x p r e s s e d as a f i n i t e sum o v e r n a n n u l i (due t o t h e s i z e of t h e image, n=41 i n t h i s c a s e ) as f o l l o w s : n 4> = 1 n E s i n ( - ( i - 1 / 2 ) ) c o s (ir( i - 1 /2 ) ) a • (3.1) 5 2 i = 1 2n 2n where a- i s t h e a n g u l a r w i d t h o f t h e i t h a n n u l u s ( S t e y n , 1980). S i n c e t h e image d i d n o t f i t e x a c t l y o n t o c o o r d i n a t e l i n e s , t h e h o r i z o n b o u n d a r i e s were t r a c e d i n a s t e p - w i s e f a s h i o n so as t o p r e s e r v e a r e a s on t h e g r a p h p a p e r . The t o t a l a n g u l a r e x t e n t of sky i n e a c h a n n u l u s was t h e n d e t e r m i n e d . I f t h i s was m u l t i p l i e d by an a d j u s t e d view f a c t o r , 0./a^, i t would g i v e t h e view f a c t o r p e r a n n u l u s as c o n t r i b u t e d t o t h e t o t a l by t h e sky ( S t e y n , 1980). The summation of a l l n e n t r i e s was t h e sky v i e w f a c t o r . C a l c u l a t i o n s i n d i c a t e d t h a t t h e view f a c t o r f o r e l e m e n t s below t h e l o c a l h o r i z o n a t t h i s e x p e r i m e n t a l s i t e was 0.023 o r 2.3%. Thus, a s s u m i n g i s o t r o p y , 97.7% of t h e t o t a l r a d i a t i o n emanated f r o m t h e sky h e m i s p h e r e above th e l o c a l h o r i z o n . As a r e s u l t o f t h i s f i n d i n g , i t was c o n c l u d e d t h a t t h e l o c a l h o r i z o n d i d n o t s i g n i f i c a n t l y a f f e c t t h i s s t u d y . 3.2 Measurement P r o c e d u r e A p r e l i m i n a r y phase o f f i e l d o b s e r v a t i o n s was c a r r i e d o u t 32 f r o m J u l y 29 t o September 13, 1983. Wind s p e e d s d i d not u s u a l l y e x c e e d 3 ms~ 1, so t h e a c t i n o m e t r i c measurements were no t a f f e c t e d by t u r b u l e n c e and t h e sky c h a r a c t e r i s t i c s were s u c h t h a t a v a r i e t y of sky c o n d i t i o n s c o u l d be examined u s i n g t h e e x p e r i m e n t a l t e c h n i q u e . The d a t a were a s s i g n e d t o t h r e e b r o a d c a t e g o r i e s : c l e a r (0/10 c l o u d ) ; p a r t l y c l o u d y (1/10 t o 8/10 c l o u d c o v e r ) ; and o v e r c a s t sky (9/10 and 10/10 c l o u d ) c o n d i t i o n s . T a b l e 3.1 p r o v i d e s a l i s t i n g o f e a c h day of o b s e r v a t i o n a l o n g w i t h t h e number o f s c a n s t a k e n , and a n o t e of t h e p r e d o m i n a t e sky c o v e r d u r i n g t h e day. M easurements were t a k e n f o r a p p r o x i m a t e l y t h e same p e r i o d of t i m e b e f o r e and a f t e r s o l a r noon i n o r d e r t o e s t a b l i s h any d e p endence i n t h e r e l a t i o n s h i p between b r i g h t n e s s and r a d i a n c e on z e n i t h a n g l e . The measurements i n c l u d e d two p r o c e d u r e s ; t h e a c t i n o m e t r i c measurement of d i f f u s e r a d i a n c e a t p r e - d e t e r m i n e d p o i n t s a c r o s s t h e sky h e m i s p h e r e , and s y n c h r o n o u s b r i g h t n e s s v a l u e s a b s t r a c t e d f r o m t h e v i d e o image a t p o i n t s c o r r e s p o n d i n g t o t h o s e s i g h t e d by t h e a c t i n o m e t e r . A s e t s a m p l i n g g r i d of z e n i t h a l and a z i m u t h a l c o o r d i n a t e s was c h o s e n b a s e d on an a t t e m p t t o o b t a i n t h e b e s t a n g u l a r r e p r e s e n t a t i o n o f t h e sky h e m i s p h e r e as v i e w e d v i a t h e f i s h e y e l e n s on t h e v i d e o m o n i t o r . The d e s i g n of t h i s s a m p l i n g g r i d a f f o r d e d h i g h s p a t i a l c o v e r a g e a t t h e z e n i t h and t o t h o s e p a r t s of t h e sky where t h e Sun would l i k e l y be p r e s e n t ( g i v e n t h e t i m e o f y e a r and day) and a l l o c a t e d l e s s samples t o a r e a s n e a r t h e h o r i z o n and o p p o s i t e t h e Sun. T h i s p a t t e r n o f s a m p l i n g was n e c e s s a r y i n o r d e r t o 33 T a b l e 3.1 R e c o r d of F i e l d O b s e r v a t i o n s Date of O b s e r v a t i o n Sky C o n d i t i o n Number o f Scans 83-08-29 C l e a r Sky 1 1 83-08-30 C l e a r Sky 9 83-08-31 P a r t l y C l o u d y . 11 83-09-01 O v e r c a s t 11 83-09-03 P a r t l y C l o u d y 10 83-09-20 C l e a r Sky 9 83-09-21 C l e a r Sky 9 83-09-22 P a r t l y C l o u d y 4 83-09-24 P a r t l y C l o u d y 8 83-09-25 O v e r c a s t 8 83-09-26 P a r t l y C l o u d y 1 83-09-27 O v e r c a s t 11 83-09-29 P a r t l y C l o u d y 5 83-10-02 O v e r c a s t 4 83-10-13 P a r t l y C l o u d y 3 34 r e p r e s e n t t h e f u l l r a n g e of r a d i a n t i n t e n s i t i e s ( f r o m h i g h t o low v a l u e s ) p r e s e n t a c r o s s t h e s k y . Between i n d i v i d u a l measurements, a c t i n o m e t r i c movement was kept t o a minimum as t h e s e q u e n c e was s u c h t h a t movement was u s u a l l y c o n f i n e d t o one z e n i t h a l o r a z i m u t h a l d i r e c t i o n o n l y . The g r i d p a t t e r n s t a r t e d w i t h a measurement a t t h e z e n i t h and t h e n t h e z e n i t h a n g l e was s e t a t 3 0 ° . K e e p i n g t h e z e n i t h a n g l e c o n s t a n t a t 3 0 ° , t h e a z i m u t h was i n c r e a s e d by 30° i n c r e m e n t s . An o b s e r v a t i o n was made a t e a c h p o s i t i o n . When an e n t i r e sweep had been c o m p l e t e d , t h e z e n i t h a n g l e was a g a i n i n c r e a s e d by 30° ( t o 60°) and a n o t h e r s c a n i n t h e a z i m u t h w i t h 30° i n c r e m e n t s was c a r r i e d o u t . Then, so as t o a v o i d c l i p p i n g on t h e v i d e o m o n i t o r , t h e z e n i t h a n g l e was c h a n g e d by 10° t o 70° and a f i n a l a z i m u t h a l sweep w i t h 60° i n t e r v a l s was c o m p l e t e d . The a c t i n o m e t e r was l e v e l l e d r o u t i n e l y b e f o r e and d u r i n g e a c h sky s c a n and t h e t i m e of t h e b e g i n n i n g and end of t h e o b s e r v a t i o n p e r i o d was r e c o r d e d . A s i n g l e a c t i n o m e t r i c o b s e r v a t i o n t o o k a p p r o x i m a t e l y 35 s e c o n d s d u r i n g w h i c h t h e m e t a l s h u t t e r was u s e d t o z e r o t h e i n s t r u m e n t and t h e a c t i n o m e t e r was s e t a t a g i v e n s a m p l i n g p o i n t ( a b o u t 20 s e c o n d s ) and 15 s e c o n d s t o a l l o w t h e i n s t r u m e n t t o e q u i l i b r a t e . An e n t i r e s c a n t o o k a p p r o x i m a t e l y 18 m i n u t e s t o c o m p l e t e . F i g u r e 3.3 i l l u s t r a t e s a t y p i c a l s c a n s e q u e n c e f o r a sample g r i d . F o r t i m e s when t h e s o l a r d i s k was p r e s e n t , i t s p o s i t i o n i n t h e sky was s i g h t e d w i t h t h e a c t i n o m e t e r ( a t b o t h t h e b e g i n n i n g and end o f a s c a n ) and i t s z e n i t h a l - and a z i m u t h a l l o c a t i o n was n o t e d . I f t h e Sun was n o t 35 v i s i b l e , a r e c o r d of o b s e r v a t i o n t i m e s a l l o w e d f o r a t h e o r e t i c a l d e t e r m i n a t i o n of i t s z e n i t h a l and a z i m u t h a l p o s i t i o n . At t h e same t i m e t h a t t h e a c t i n o m e t r i c measurements were b e i n g t a k e n , b r i g h t n e s s i n f o r m a t i o n f r o m a v i d e o image of t h e sky was b e i n g o b t a i n e d f o r t h e same s a m p l i n g p o i n t s . The camera was l e v e l l e d w i t h a s p i r i t l e v e l a t t h e s t a r t of e a c h s c a n and t h e p o s i t i o n o f t h e o c c u l t i n g d i s k was c h e c k e d t o make s u r e t h e r e would be no l e n s f l a r e . T h i s d i s k was c h e c k e d c o n t i n u a l l y and was moved as o f t e n a s n e c e s s a r y t o o c c u l t t h e d i r e c t s o l a r beam. The f i s h e y e l e n s was a l s o m o n i t o r e d i n o r d e r t o e n s u r e t h a t i t r e m a i n e d as c l e a n as p o s s i b l e . In o r d e r t o o b t a i n a s c l o s e t o an i n s t a n t a n e o u s r e p r e s e n t a t i o n of t h e b r i g h t n e s s v a l u e s a s p o s s i b l e , i t was n e c e s s a r y t o l o c a t e t h e sky h e m i s p h e r e s a m p l i n g p o i n t , on t h e d i g i t i z e d image. The b r i g h t n e s s v a l u e s c o r r e s p o n d i n g t o t h e p o r t i o n of t h e sky t h a t t h e a c t i n o m e t e r v i e w e d c o u l d t h e n be summed and s t o r e d i n t h e c o m p u t e r . The f i r s t s t e p i n l o c a t i n g t h e sky s a m p l i n g p o i n t on t h e image p l a n e was t o l o c a t e t h e c e n t r e of t h i s image and t h e n t o d e t e r m i n e t h e shape o f t h e v i d e o image. An e x p l a n a t i o n of t h e s t e p s t a k e n i n t h i s c a l c u l a t i o n i s g i v e n i n A p p e n d i x I . A t r a n s f o r m a t i o n of sky z e n i t h a l and a z i m u t h a l p o i n t s t o s c r e e n p i x e l c o o r d i n a t e s combined w i t h t h e knowledge of t h e a n g u l a r s i z e of t h e a c t i n o m e t r i c f i e l d - o f - v i e w , a l l o w e d f o r t h e d e t e r m i n a t i o n of t h e c o r r e c t shape o f t h e a c t i n o m e t r i c f i e l d - o f - v i e w e x p r e s s e d i n p i x e l c o o r d i n a t e s . T h i s shape a p p e a r e d r o u g h l y e l l i p t i c a l . 36 S i n c e t h e same se q u e n c e o f measurements was f o l l o w e d e v e r y t i m e , i t 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 t o d e s i g n a computer p r o g r a m w h i c h would l o c a t e e a c h p o i n t on t h e g r i d and draw ou t t h e p o r t i o n of t h e sky t h a t t h e a c t i n o m e t e r was ' s e e i n g ' . The sum of t h e b r i g h t n e s s v a l u e s c o r r e s p o n d i n g t o t h a t a r e a was computed, as was t h e number o f p i x e l s c o n t a i n e d w i t h i n t h e r e g i o n . T a b l e 3.2 g i v e s t h e number of p i x e l s c o r r e s p o n d i n g t o e a c h o f t h e s a m p l i n g p o i n t s . T h i s a l l o w e d f o r a d e t e r m i n a t i o n of t h e mean b r i g h t n e s s v a l u e r e p r e s e n t i n g t h a t s a m p l i n g s p o t . In o r d e r f o r t h i s p rogram t o f u n c t i o n i n r e a l t i m e ( i . e . s y n c h r o n o u s w i t h a c t i n o m e t r i c measurements) i t was n e c e s s a r y t o d e s i g n a s m a l l , h a n d - h e l d s w i t c h - b o x w h i c h c o u l d be kept a t t h e measurement s i t e on t h e r o o f and was c o n n e c t e d t o t h e c o m p u t e r . F o r e a c h o b s e r v a t i o n , by p r e s s i n g t h e b u t t o n , t h e computer was t r i g g e r e d t o f r e e z e t h e v i d e o image and r e c o r d t h e b r i g h t n e s s i n f o r m a t i o n c o r r e s p o n d i n g t o t h e p a r t i c u l a r s a m p l i n g p o i n t . E a c h t i m e t h e b u t t o n was p r e s s e d , t h e v i d e o image on t h e m o n i t o r was ' r e f r e s h e d ' . In o t h e r words, t h e r e c o r d e d b r i g h t n e s s v a l u e s c o r r e s p o n d e d t o t h e a c t u a l sky c o n d i t i o n s a t t h e t i m e o f t h e a c t i n o m e t r i c measurements. T h i s p r o c e d u r e h e l p e d t o e l i m i n a t e s u c h p r o b l e m s as t h e e f f e c t s of i n c r e a s e d a n g u l a r v e l o c i t y of o b j e c t s ( e g . c l o u d s ) a t t h e z e n i t h . I f more o b s e r v a t i o n s were n e c e s s a r y , a t t h e end o f a s c a n , t h e s a m p l i n g p r o g r a m a l l o w e d f o r t h e o p p o r t u n i t y t o m a n u a l l y e n t e r t h e z e n i t h a l and a z i m u t h a l c o o r d i n a t e s i n t o t h e computer. O t h e r w i s e , t h e s c a n n i n g p r o g r a m was a u t o m a t i c a l l y s e t t o s t a r t a n o t h e r measurement s e q u e n c e . 37 T a b l e 3.2 Sequence o f O b s e r v a t i o n s i n Second S a m p l i n g G r i d w i t h C o r r e s p o n d i n g Number of P i x e l s Z e n i t h A n g l e A z i m u t h A n g l e No. of P i x e l s ( D e g r e e s ) ( D e g r e e s )  0 0 195 30 0 201 30 60 205 30 1 20 205 30 180 201 30 240 205 30 300 205 60 0 231 60 30 235 60 60 237 60 90 237 60 120 237 60 1 50 235 60 180 231 60 210 235 60 240 237 60 270 237 60 300 237 60 330 235 70 0 259 70 30 251 70 60 253 70 90 255 70 1 20 253 70 1 50 251 70 180 259 70 210 251 70 240 253 70 270 255 70 300 253 70 330 251 38 B e f o r e t h e s t a r t of a sky s c a n , i t was n e c e s s a r y t o view t h e sky image on t h e m o n i t o r and make any a p e r t u r e , v i d e o l e v e l or b l a c k n e s s l e v e l a d j u s t m e n t s t h a t were n e c e s s a r y . I d e a l l y , one would w i s h f o r 256 g r e y l e v e l s ( t h e f u l l r a n g e ) t o be p r e s e n t i n t h e image. However, due t o t h e a c t u a l sky c o v e r c h a r a c t e r i s t i c s t h i s was not a l w a y s p o s s i b l e and so i t was n e c e s s a r y t o m a n u a l l y m a ximize t h e g r e y l e v e l r a n g e . T h i s was a c c o m p l i s h e d by a d j u s t i n g t h e v i d e o and b l a c k n e s s l e v e l s i n an a t t e m p t t o e l i m i n a t e ( o r m i n i m i z e ) b o t h s a t u r a t e d ( w h i t e ) and b l a c k r e g i o n s . T h i s p r o c e d u r e was c a r r i e d o ut b e f o r e e a c h s c a n and t h e c o n t r o l s were n e v e r a d j u s t e d once t h e measurement sequence had begun. At t h e c o m p l e t i o n of a sky s c a n , t h e most r e c e n t v i d e o sky r e p r e s e n t a t i o n was d i g i t i z e d v i a t h e f r a m e s t o r e and i t s b r i g h t n e s s c h a r a c t e r i s t i c s were n o t e d . I f t h e sky c o v e r had c h a n g e d s u b s t a n t i a l l y d u r i n g t h e s c a n , and t h e r e was a l o s s of d e t a i l i n t h e w h i t e s t o r b l a c k e s t p o r t i o n of t h e image, t h e n t h a t s c a n was not i n c l u d e d i n t h e s t u d y . When the. p r e l i m i n a r y , e x p l o r a t o r y phase of o b s e r v a t i o n had ended, some d a t a a n a l y s i s i n d i c a t e d a r e a s w i t h i n t h e m e t h o d o l o g y t h a t c o u l d be m o d i f i e d o r i m p r o v e d . Once t h e r e l a t i o n s h i p between r a d i a n c e and b r i g h t n e s s a t any p o i n t i n t h e sky had been d e t e r m i n e d ( s e e S e c t i o n 4.1) a s e c o n d a r y o b s e r v i n g phase was l a u n c h e d w i t h d a t a c o l l e c t i o n f o c u s s i n g on p a r t i c u l a r s ky c o n d i t i o n s and c a r e f u l s e l e c t i o n o f u s e f u l sky images t o be s t o r e d f o r f u r t h e r d i s p l a y and a n a l y s i s . T h e s e l a t t e r measurements were o b t a i n e d o v e r a a t h r e e month p e r i o d : December, 1983; J a n u a r y and F e b r u a r y , 1984. S i n c e t h e Sun was 39 much l o w e r on t h e h o r i z o n a t t h a t t i m e o f t h e y e a r , t h e s a m p l i n g s equence was a l t e r e d so as t o c o n t i n u e t o p r o v i d e o p t i m a l s a m p l i n g s t r a t e g y . T a b l e 3.2 i n d i c a t e s t h e d e s i g n of t h i s g r i d and F i g u r e 3.3 i l l u s t r a t e s t h e s c a n n i n g s e q u e n c e . The a c t u a l f i e l d o b s e r v a t i o n s were o b t a i n e d as d e s c r i b e d e a r l i e r . However, a t t h e end o f a sky s c a n , s e v e r a l sky images were s t o r e d w i h o u t c h a n g i n g t h e a p e r t u r e , b l a c k n e s s o r v i d e o l e v e l s . T h i s was done t o p r o v i d e a v a r i e t y of images r e p r e s e n t a t i v e of a p a r t i c u l a r sky c o n d i t i o n w i t h t h e view t h a t any image not c u r r e n t l y u t i l i z e d f o r a n a l y s i s c o u l d be a r c h i v e d f o r f u t u r e s t u d y . W i t h t h i s method, one sky s c a n ( i . e . s y n c h r o n o u s b r i g h t n e s s and r a d i a n c e measurements) p r o v i d e d t h e d a t a n e c e s s a r y t o d e t e r m i n e t h e a p p r o p r i a t e t r a n s f o r m a t i o n t o r a d i a n c e f o r a number of b r i g h t n e s s maps ( i . e . i m a g e s ) . A c a l i b r a t i o n c u r v e p r o d u c e d from a s c a n would not be a p p r o p r i a t e f o r an image t a k e n a t a l a t e r t i m e i f t h e sky s p e c t r a l c h a r a c t e r i s t i c s c h a n g e d d r a m a t i c a l l y , r e s u l t i n g i n a poor r e p r e s e n t a t i o n of t h e r e l a t i o n s h i p between r a d i a n c e and b r i g h t n e s s w i t h t h e c u r r e n t a p e r t u r e , b l a c k n e s s and v i d e o l e v e l s e t t i n g . T h i s d i d n o t seem t o pose a p r o b l e m d u r i n g t h i s s t u d y . 3.3 E s t i m a t i o n of t h e E r r o r i n t h e V i d e o S ystem A s i m p l e e x p e r i m e n t was c a r r i e d o u t i n o r d e r t o a s s e s s t h e p r o b a b l e e r r o r a s s o c i a t e d w i t h t h e use o f t h e v i d e o s y s t e m . The v i d e o camera was p l a c e d h o r i z o n t a l l y on a t a b l e i n a room where l i g h t i n g c o n d i t i o n s c o u l d be k e p t c o n s t a n t and no g u r e 3.3 D e s i g n of S a m p l i n g G r i d . E a c h + the C e n t r e of a S a m p l i n g P o i n t R e p r e s e n t s 41 e x t e r n a l d i s t u r b a n c e s w o u l d a f f e c t o p e r a t i o n of t h e camera. The n e u t r a l d e n s i t y f i l t e r was removed from t h e f i s h e y e camera l e n s and t h e r e s u l t i n g v i d e o image was m a n i p u l a t e d ( i . e . t h e a p e r t u r e , b l a c k n e s s and v i d e o l e v e l s were a d j u s t e d ) i n o r d e r t o p r o d u c e an image w i t h h i g h c o n t r a s t ; a c o m p l e t e r e p r e s e n t a t i o n of v a r y i n g i n t e n s i t y l e v e l s from 0 t o 255. Twe l v e images were t a k e n s e q u e n t i a l l y o v e r a t i m e span of a p p r o x i m a t e l y f i f t e e n m i n u t e s , w i t h c o n d i t i o n s h e l d c o n s t a n t . T h i s i n f o r m a t i o n i n d i c a t e d t h e e x t e n t of t e m p o r a l change i n p i x e l i n t e n s i t y v a l u e s a s w e l l as t h e p r o b a b l e e r r o r i n t h e v i d e o - f r a m e s t o r e s y s t e m . I n v e s t i g a t i o n o f t h e c h a n g e s between t h e t w e l v e images showed t h a t t h e mean b r i g h t n e s s l e v e l was 92.13 ( f o r an 8 b i t s c a l e ) w i t h a s t a n d a r d d e v i a t i o n o f 4.04 f o r a s i n g l e p i x e l . Under n o r m a l o p e r a t i n g c o n d i t i o n s , t h e a c t i n o m e t r i c f i e l d - o f - v i e w a t t h e edge of a d i g i t i z e d image i n c l u d e s a b o u t 254 p i x e l s , and f o r t h i s a r e a , t h e b r i g h t n e s s was 23308 ± 0.276%. S i m i l a r i l y , f o r s a m p l i n g p o i n t s t a k e n n e a r e r t h e c e n t r e o f t h e image ( a b o u t 201 p i x e l s ) , t h e b r i g h t n e s s was 18518 ± 0.309%. These s t a n d a r d d e v i a t i o n s i n d i c a t e d t h a t t h e e r r o r i n t h e v i d e o s y s t e m i s on t h e o r d e r of l e s s t h a n 1.0%. I t was e x p e c t e d t h a t t h e mean b r i g h t n e s s w i t h i n an image would be e q u a l f o r a l l t w e l v e images. However, a n a l y s i s of t h e mean v a l u e s r e s u l t e d i n a mean b r i g h t n e s s l e v e l o f 93.5 w i t h a s t a n d a r d d e v i a t i o n o f 1.9. The c o e f f i c i e n t o f v a r i a t i o n ( t h e s t a n d a r d d e v i a t i o n e x p r e s s e d a s a p e r c e n t a g e o f t h e mean) of t h e mean b r i g h t n e s s t h e n , was 2.04%. T h i s shows t h a t o v e r t h e 42 15 m i n u t e s d u r i n g w h i c h the images were s t o r e d , t h e r e was t y p i c a l l y o n l y a 2% d i f f e r e n c e between the b r i g h t n e s s l e v e l s o f t h e t w e l v e images. 3.3.1 A s s e s s m e n t of t h e E r r o r I n h e r e n t i n R e g i s t r a t i o n of Sky  C o o r d i n a t e s L o c a t i o n of a sky s a m p l i n g p o i n t on the image i n d i c a t e d t h a t a s l i g h t , but c o n s i s t e n t o f f s e t e x i s t e d between the p o i n t ' s t r u e and c a l c u l a t e d p o s i t i o n s . T h i s w i l l be r e f e r r e d t o as a ' r e g i s t r a t i o n ' e r r o r . In o r d e r t o d e t e r m i n e what t h e m a g n i t u d e of s u c h an e r r o r would be, t h r e e images, r e p r e s e n t a t i v 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 sky c o n d i t i o n s were c h o s e n f o r t h e t e s t . A c e n t r a l 'window' ( t h e sum o f t h e b r i g h t n e s s v a l u e s o f p i x e l s w i t h i n t h e window r e g i o n was known) was o f f s e t by 2.5 p i x e l s ( t h e a p p a r e n t magnitude o f t h e m i s r e g i s t r a t i o n ) i n 8 p o s i t i o n s a r o u n d t h a t window. The window was 15 x 15 p i x e l s w h i c h a p p r o x i m a t e d t h e a c t i n o m e t r i c s a m p l i n g s p o t s i z e as computed f r o m t h e v i d e o image. The sum of t h e b r i g h t n e s s v a l u e s c o r r e s p o n d i n g t o t h e s q u a r e i n e a c h o f i t ' s 9 p o s i t i o n s (8 a t t h e edge and 1 a t t h e c e n t r e ) was computed w i t h t h e e x c l u s i o n o f windows a t t h e edge of t h e image w h i c h showed e v i d e n c e of d a r k e n i n g o r c l i p p i n g . T h i s p r o c e d u r e was c a r r i e d o u t a t a p p r o x i m a t e l y 77 p o s i t i o n s on t h e sky image. The r e s u l t s f o r t h e c l e a r s k y c a s e showed a r o o t mean s q u a r e (RMS) e r r o r o f about 4.57% w i t h t h e 2.5 p i x e l o f f s e t ; f o r t h e p a r t l y c l o u d y sky, t h e r e was a s i m i l a r RMS e r r o r of 4.73%, w i t h a RMS e r r o r of 3.17% f o r t h e o v e r c a s t sky c a s e . 43 3.3.2 C a l c u l a t i o n of t h e E r r o r A s s o c i a t e d w i t h B r i g h t n e s s  L e v e l D e t e r m i n a t i o n The t o t a l p r o b a b l e e r r o r a s s o c i a t e d w i t h b r i g h t n e s s v a l u e measurement may now be c a l c u l a t e d i n t h e f o l l o w i n g manner: E c l = 0.0457 x X (3.2) E = 0.0473 x X (3.3) pc E q v = 0.0317 x X (3.4) where X i s t h e a v e r a g e b r i g h t n e s s v a l u e f o r a s i n g l e sky s c a n and t h e s u b s c r i p t s c l , p c and ov r e p r e s e n t c l e a r , p a r t l y c l o u d y and o v e r c a s t sky c o n d i t i o n s , r e s p e c t i v e l y . The c o e f f i c i e n t s r e p r e s e n t t h e r e g i s t r a t i o n e r r o r as d e t e r m i n e d f o r 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 s k i e s . Once t h e e r r o r s a s s o c i a t e d w i t h t h e d a t a a c q u i s i t i o n s y s t e m had been c a l c u l a t e d , i t i s p o s s i b l e t o p r o c e e d w i t h t h e d e t e r m i n a t i o n o f t h e most p r o b a b l e r e l a t i o n s h i p between t h e two v a r i a b l e s , r a d i a n c e and b r i g h t n e s s . T h i s a n a l y s i s w i l l be d e s c r i b e d i n t h e f o l l o w i n g c h a p t e r . 44 C h a p t e r F o u r C a l i b r a t i o n P r o c e d u r e 4.1 D e t e r m i n a t i o n of t h e R e l a t i o n s h i p between  R a d i a n c e and B r i g h t n e s s V a l u e s 4.1.1 R e g r e s s i o n A n a l y s i s B e f o r e a d e t e r m i n a t i o n of t h e a n g u l a r d i s t r i b u t i o n of d i f f u s e r a d i a n c e o v e r t h e sky h e m i s p h e r e c o u l d be c a r r i e d o u t , i t was n e c e s s a r y t o d e f i n e t h e n a t u r e of t h e r e l a t i o n s h i p between r a d i a n c e and b r i g h t n e s s . As a f i r s t s t e p , i t was d e c i d e d t o u n d e r t a k e a s t e p - w i s e l i n e a r r e g r e s s i o n between t h e two v a r i a b l e s ; b r i g h t n e s s , (as a b s t r a c t e d f r o m t h e v i d e o image d u r i n g a sky s c a n ) and r a d i a n c e as r e c o r d e d d u r i n g t h e same measurement s e q u e n c e . F o r t h e i n i t i a l c o m p u t a t i o n s , t h e a c t i n o m e t r i c o b s e r v a t i o n s of r a d i a n c e were c h o s e n t o be t h e i n d e p e n d e n t v a r i a b l e s i n c e t h e y were deemed t h e most v a l i d r e p r e s e n t a t i o n of sky r a d i a n c e ; t h e b r i g h t n e s s v a l u e s were t h e n t h e d e p e n d e n t v a r i a b l e . P r e l i m i n a r y a n a l y s e s s u g g e s t e d a l i n e a r r e l a t i o n s h i p e x i s t e d between t h e two v a r i a b l e s and so w i t h t h i s i n mind, a more t h o r o u g h i n v e s t i g a t i o n was u n d e r t a k e n . The d a t a were a n a l y z e d u s i n g a l i n e a r r e g r e s s i o n r o u t i n e (TRP) a v a i l a b l e as a l i b r a r y programme i n 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 ' s Computing C e n t r e . The i n i t i a l r e s u l t s i n d i c a t e d w h i c h p o i n t s e x i s t e d as o u t l i e r s (an o u t l i e r i s d e f i n e d as a n o r m a l i z e d r e s i d u a l l e s s t h a n -1.96 or g r e a t e r 45 t h a n 1.96 f o r a p r o b a b i l i t y l e v e l of 5%) so i t was a s i m p l e m a t t e r t o e x c l u d e them from t h e w o r k i n g d a t a s e t . T h e s e p o i n t s were e x c l u d e d on t h e b a s i s of b e i n g s p u r i o u s d a t a p o i n t s t h a t were f o u n d t o c o r r e s p o n d w i t h an i n v a l i d b r i g h t n e s s o r r a d i a n c e measurement. The f o r m e r , r e s u l t i n g from camera s a t u r a t i o n , o r t h e camera s e n s i n g s o m e t h i n g o t h e r t h a n s h o r t w a v e r a d i a t i o n ( e g . smoke from a s m o k e s t a c k ) , and t h e l a t t e r , r e s u l t i n g p e r h a p s from t h e a c t i n o m e t e r s i g h t i n g an o b j e c t ( e g . anemometer tower) w h i c h c o u l d a f f e c t t h e v a l u e b e i n g r e c o r d e d . I t s h o u l d a l s o be n o t e d t h a t no p o i n t s w i t h b r i g h t n e s s v a l u e s g r e a t e r t h a n 240 were i n c l u d e d i n t h e a n a l y s i s s i n c e t h e camera may have been s a t u r a t i n g . The e q u i - a n g u l a r p r o j e c t i o n p r o p e r t i e s of t h e f i s h e y e l e n s made i t n e c e s s a r y t o compensate t h e a c t i n o m e t r i c v a l u e s f o r t h e z e n i t h a l - b r i g h t e n i n g and h o r i z o n - d a r k e n i n g e f f e c t s p r e s e n t a c r o s s an image. Eqn. 4.1 shows how t h i s was a c c o m p l i s h e d . Y' = (Y x 1 9 5 ) / N p i x (4.1) Y r e p r e s e n t s t h e d i f f u s e r a d i a n c e o f a s a m p l i n g p o i n t and Y' t h e 'compensated' r a d i a n c e of t h a t same p o i n t , N p ix i s t h e number o f p i x e l s r e p r e s e n t i n g Y ( N p i x > l 9 5 ) and 195 i s t h e number o f p i x e l s c o r r e s p o n d i n g t o a s a m p l i n g p o i n t l o c a t e d a t t h e z e n i t h . In o r d e r t o d e r i v e a s t r i c t l y l i n e a r r e l a t i o n s h i p , ( i . e . a c o n s t a n t s l o p e , i n t h i s c a s e 1.0, and i n t e r c e p t of 0.0) i t was n e c e s s a r y t o a d j u s t t h e b r i g h t n e s s v a l u e so as t o remove a p e r t u r e , b l a c k n e s s and v i d e o l e v e l e f f e c t s . I t i s i m p o r t a n t t o n o t e t h a t i n t h i s s t u d y , t h e l e n s a p e r t u r e was not 46 g r a d u a t e d or c a l i b r a t e d i n any manner. Hence, a l l t h a t c o u l d be a s c e r t a i n e d from o b s e r v a t i o n s was t h a t t h e a p e r t u r e and v i d e o l e v e l t o g e t h e r a f f e c t e d t h e s l o p e o f t h e r e g r e s s i o n l i n e ( b r ) ; t h e b l a c k n e s s l e v e l on t h e o t h e r hand, i n f l u e n c e d t h e i n t e r c e p t v a l u e ( a r ) . In o r d e r t o c o r r e c t t h e b r i g h t n e s s v a l u e s , an a d j u s t m e n t as d e s c r i b e d by Eqn. 4.2 was u n d e r t a k e n . X'= (X - a r ) / b r (4.2) where X i s t h e b r i g h t n e s s v a l u e f o r a s a m p l i n g p o i n t and X' i s t h e 'compensated' b r i g h t n e s s v a l u e o f t h e r e g r e s s i o n c u r v e . The t r a n s f o r m e d d a t a were r e g r e s s e d once more. Due t o t h e above m o d i f i c a t i o n s , t h e s l o p e of t h e l i n e s h o u l d have been c l o s e t o 1.0 and t h e i n t e r c e p t a p p r o x i m a t e l y z e r o i f t h e r e l a t i o n s h i p between a c t i n o m e t r i c measurements and b r i g h t n e s s measurements was l i n e a r . T a b l e 4.1 p r e s e n t s t h e r e s u l t s o f 42 c l e a r sky s c a n s w h i l e examples of t h e a c t u a l r e g r e s s i o n c u r v e s may be f o u n d i n A p p e n d i x I I . R e s u l t 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 sky s c a n s a r e g i v e n i n T a b l e s 4.2 and 4.3. I n d e e d a l i n e a r r e l a t i o n between t h e s e two v a r i a b l e s was c o n f i r m e d ( i . e . c o n s t a n t s l o p e ) . Such a r e l a t i o n s h i p between t h e two p a r a m e t e r s was t o be e x p e c t e d s i n c e a l l ' l i n k s ' i n t h e d a t a a c q u i s i t i o n s y s t e m were l i n e a r . In o t h e r words, from t h e i n i t i a l p h a s e o f r a d i a n t e n e r g y r e a c h i n g t h e camera, t o t h e d i g i t a l v a l u e s i n t h e f r a m e s t o r e ( r e c a l l t h a t t h e camera has l i n e a r t r a n s f e r c h a r a c t e r i s t i c s ) t h e r e were no n o n - l i n e a r i t i e s . S i n c e t h e aim o f t h i s e x e r c i s e was t o d e t e r m i n e t h e r e l a t i o n s h i p between r a d i a n c e and b r i g h t n e s s i n o r d e r t o p r e d i c t r a d i a n c e from a g i v e n b r i g h t n e s s v a l u e , r a d i a n c e s h o u l d 47 T a b l e 4.1 R e g r e s s i o n R e s u l t s f o r C l e a r S k i e s u s i n g C o r r e c t e d B r i g h t n e s s and R a d i a n c e V a l u e s (Wm" 2sr" 1) Scan N a b r S t . E r r r 2 S t . E r r r r of b r o f Y JD210.1 27 0.66x10" 5 1 .00 0.057 0.925 5.65 JD210.2 27 -0.73x10" 4 1 .00 0.065 0.895 1 0.95 JD210.3 28 -0.35x10" 4 1 .00 0.084 0.845 1 1 .66 JD210.4 28 -0.58x10" 5 1 .00 0.072 0.881 9.53 JD210.5 29 -0.11x10" 4 1 .00 0. 108 0.760 1 4.57 JD210.6 30 -0.85x10" 5 1 .00 0.116 0.727 1 4.20 JD210.7 31 -0.25x10" 4 1 .00 0.097 0.787 16.41 JD210.8 31 -0.31x10" 5 1 .00 0.111 0.736 16.87 JD210.9 27 1 .054 0.93 0.063 0.899 8.82 JD210.10 26 2.731 0.97 0.053 0.932 9.84 JD211.1 28 -1.186 1 .03 0.078 0.869 7.12 JD211.2 30 0.24x10" 4 1 .00 0.071 0.878 8.14 JD211.3 26 -0.302 0.98 0.072 0.884 6.81 JD211.4 30 0.47x10" 5 1 .00 0. 139 0.647 1 6.99 JD211.5 30 -0.84x10" 5 1 .00 0. 126 0.694 1 2.60 JD211.6 29 -0.55x10" 4 1 .00 0.099 0.791 14.95 JD211.7 30 0.24x10" 4 1 .00 0.077 0.858 8.97 JD211.8 28 1 .006 0.99 0.056 0.923 7.51 JD211.9 26 1 .004 0.98 0.031 0.977 4.75 JD212.1 28 -0.967 1.01 0.032 0.976 4.90 JD212.2 29 -1.952 1 .02 0.085 0.843 17.98 JD212.3 25 3.476 0.89 0.088 0.813 10.71 JD212.4 25 0.551 0.98 0.119 0.747 1 0.85 JD212.5 30 -0.42x10" 4 1 .00 0. 108 0.756 1 3.45 JD212.6 29 -11.37 1 .40 0. 128 0.817 1 3.29 JD212.7 27 -4.938 1.16 0.083 0.887 9.57 JD212.8 31 -0.33x10" 4 1 .00 0.085 0.826 1 3.76 JD212.9 28 1 .091 0.99 0.049 0.940 9.55 JD232.1 29 0.243 1 .01 0.044 0.951 8.14 JD232.2 28 0.360 1 .01 0.059 0.917 6.92 JD232.3 27 2.479 0.98 0.060 0.915 8.58 JD232.4 31 -0.95x10" 5 1 .00 0. 100 0.774 1 6.80 JD232.5 28 0.853 0.99 0.085 0.838 6.49 JD232.6 29 -1 .455 1 .09 0.074 0.889 7.24 JD232.7 30 -0.26x10" 4 1 .00 0.071 0.877 11.31 JD232.8 26 1 .671 0.98 0.045 0.951 5.20 JD233.1 27 -0.616 1 .01 0.047 0.949 4.96 JD233.2 31 0.35x10 4 1 .00 0.043 0.950 5.97 JD233.3 28 -0.112 0.97 0.680 0.886 9.25 JD233.4 29 -0.990 1 .06 0.060 0.921 5.25 JD233.5 28 -0.976 1 .06 0.053 0.940 4.86 JD233.6 28 0.835 0.99 0.064 0.901 7.31 48 T a b l e 4.2 R e g r e s s i o n R e s u l t s f o r O v e r c a s t Sky Dat a U s i n g C o r r e c t e d B r i g h t n e s s and R a d i a n c e V a l u e s ( W m " 2 s r _ 1 ) Scan N a b S t a n d . E r r r 2 S t a n d . E: r r of b r of Y JD245.3 29 2. 898 0 .955 0. 0805 0 .839 23. 84 JD239.1 28 -0. 401 0 .979 0. 461 0 .946 6. 46 JD239b.1 29 -3. 278 0 .971 0. 1 20 0 .709 70. 06 JD239d.1 25 1 . 407 0 .968 0. 056 0 .929 9. 54 JD239f.1 31 0. 42x10"' 1 .00 0. 108 0 . 746 39. 71 JD239f.2 26 2. 480 0 .975 0. 041 0 .959 9. 72 JD237.1 30 -0. 11x10" 5 1 .00 0. 042 0 .954 1 . 88 JD237.2 27 0. 890 0 .975 0. 034 0 .971 3. 45 JD237.3 26 - o . 926 1 .009 0. 045 0 .955 9. 1 4 JD213.3 29 -4. 996 1 .030 0. 1 22 0 .727 28. 1 6 JD213.4 30 - o . 40x1O -" 1 .00 0. 098 0 .789 15. 1 4 JD213.5 29 4. 091 0 .962 0. 068 0 .880 1 1 . 43 JD213.6 29 3. 427 0 .977 0. 1 34 0 .663 19. 21 JD213.7 31 0. 15x10~* 1 .00 0. 084 0 .829 20. 23 49 T a b l e 4.3 R e g r e s s i o n R e s u l t s f o r P a r t l y C l o u d y S k i e s u s i n g C o r r e c t e d B r i g h t n e s s and R a d i a n c e V a l u e s (Wm" 2sr" 1) Scan N b S t . E r r r 2 S t . E r r of b r of Y JD2 41.2 28 1 .708 0 .935 0. 103 0.761 27.23 JD241.3 31 -0.55x10" 5 1 .00 0.101 0.770 36.53 JD241.4 27 -3.393 1 .083 0.046 0.956 1 1 .64 JD239.7 27 -0.224 1 .005 0.052 0.937 11.22 JD238.2 29 0.52x10" 4 1 .00 0.086 0.834 28.91 JD238.3 28 -0.835 1 .010 0.047 0.946 6.37 JD238.4 29 0.32x10" a 1 .00 0.061 0.908 1 1 . 63 JD237.4 27 -4.018 1 . 1 46 0.097 0.848 14.13 JD237.5 29 0.46x10" 4 1 .00 0.063 0.902 13.53 JD237.6 29 -0.28x10" 4 1 .00 0.046 0.945 7.97 JD237.7 29 -0.70x10" 4 1 .00 0.059 0.915 1 1 . 58 JD237 .8 29 -3.183 1 .02 0.087 0.833 24.04 JD236.4 31 -0.70x10" 4 1 .00 0.079 0.846 21 .22 JD236.5 27 1 .401 0 .975 0.040 0.960 1 2.37 JD236.6 26 1 .609 0 .970 0.042 0.957 5.58 JD236.7 29 0.970 0 .920 0.098 0.767 1 4.59 JD234.2 28 -0.901 0 .994 0.067 0.896 1 5.23 JD234.3 27 1 .302 0 .985 0.044 0.953 7.42 JD234.4 27 -5.831 1 .062 0.062 0.921 1 3.68 JD215.1 30 0.20x10 4 1 .00 0.084 0.834 11.91 JD215.4 27 1 .547 0 .980 0.096 0.808 10.55 JD215.5 30 0.46x10" 5 1 .00 0.112 0.739 1 7.78 JD21 5.6 29 1 . 452 0 .982 0.072 0.875 1 1 .60 JD21 5.7 28 1 .405 0 .984 0.059 0.914 1 0.02 50 be a n a l y z e d as t h e d ependent v a r i a b l e . R e g r e s s i o n a n a l y s i s however, may not p r o v i d e t h e b e s t u n b i a s e d e s t i m a t e o f t h e p a r a m e t e r s o f t h e c u r v e a l t h o u g h i t has been u s e d a l m o s t u n i v e r s a l l y t o a c h i e v e t h i s (Mark and C h u r c h , 1977). I n s t e a d , a r e l a t e d s t a t i s t i c a l t o o l , f u n c t i o n a l a n a l y s i s , s h o u l d be employed i n i t s p l a c e . The r e a s o n f o r c h o o s i n g t h e l a t t e r a n a l y t i c a l t e c h n i q u e i s t o i n c o r p o r a t e e r r o r s i n b o t h t h e d e pendent and i n d e p e n d e n t v a r i a b l e so t h a t t h e most p r o b a b l e r e l a t i o n u n d e r l y i n g t h e d a t a may be e s t i m a t e d . I n most of t h e p r e s e n t a n a l y s e s , t h e c o e f f i c e n t o f d e t e r m i n a t i o n ( r 2 ) was c l o s e t o 1.0 and f o r t h e s e c a s e s Mark and C h u r c h (1977) s u g g e s t t h a t t h e d i f f e r e n c e between t h e f u n c t i o n a l r e l a t i o n s h i p and t h e r e g r e s s i o n l i n e becomes i n s i g n i f i c a n t ; t h i s however, d o e s n o t make s u c h an a n a l y s i s any l e s s u s e f u l . 4.1.2 F u n c t i o n a l A n a l y s i s Once i t had been a s c e r t a i n e d t h a t a l i n e a r r e l a t i o n s h i p e x i s t e d between r a d i a n c e and b r i g h t n e s s , t h e use o f f u n c t i o n a l a n a l y s i s t o d e t e r m i n e t h e a c t u a l c u r v e was 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 . In t h i s t y p e o f a n a l y s i s , i n f o r m a t i o n a b o u t t h e e r r o r v a r i a n c e s of N v a r i a b l e s i s r e q u i r e d . T h e s e may be d e f i n e d , a c c o r d i n g t o Mark and C h u r c h ( 1 9 7 7 ) , as m E 2= L ( x . . -X.) 2/m i=1,...,N (4.3) x j=1 1 D 1 where X^ i s t h e mean v a l u e of x^ and x ^ i s t h e j t h o f m r e p l i c a t e o b s e r v a t i o n s of x. and s i m i l a r i l y f o r E 2 . 51 When t h e and a r e n o r m a l l y d i s t r i b u t e d i t may be assumed t h a t E x 2 and E ^ 2 a r e i n d e p e n d e n t l y n o r m a l l y d i s t r i b u t e d and a p p l y e q u a l l y t o a l l o b s e r v a t i o n s and t h e r a t i o o f t h e e r r o r v a r i a n c e (X) may be w r i t t e n as X = E y 2 / E x 2 (4.4) In t h i s s t u d y , E x 2 and E ^ 2 were t h e r e l a t i v e e r r o r s a s s o c i a t e d w i t h t h e d e t e r m i n a t i o n of b r i g h t n e s s and r a d i a n c e v a l u e s r e s p e c t i v e l y , c a l c u l a t e d f o r e a c h p o i n t i n t h e s c a n . S i n c e r e g r e s s i o n a n a l y s i s had been p e r f o r m e d , a f u n c t i o n a l a n a l y s i s s l o p e p a r a m e t e r b^ was c a l c u l a t e d u s i n g b_. and r 2 ( t h e s l o p e and 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 d e r i v e d from t h e r e g r e s s i o n a n a l y s i s ) v a l u e s i n t h e f o l l o w i n g manner, (Mark and C h u r c h , ( 1 9 7 7 ) ) b f = ( ( b r 2 / r 2 - X ) + ( ( ( b _ 2 / r 2 - X ) 2 + 4 X b r 2 ) ) / 2 b r ) 2 . (4.5) From t h i s s l o p e v a l u e , an i n t e r c e p t a^ was d e t e r m i n e d . Thus Y = a^ + b^X where X r e p r e s e n t s t h e known ( u n c o r r e c t e d ) b r i g h t n e s s v a l u e s and Y i s t h e p r e d i c t e d r a d i a n c e ( W m ~ 2 s r ~ 1 ) . T h e r e f o r e t o p r e d i c t r a d i a n c e a t any p o i n t i n t h e sky from b r i g h t n e s s , a l i n e a r t r a n s f o r m a t i o n u s i n g a^ and b^ was a p p l i e d . To v e r i f y t h i s p r o c e d u r e , sample s e t s of d a t a r e p r e s e n t i n g c l e a r , o v e r c a s t and p a r t l y c l o u d y sky c o n d i t i o n s were c h o s e n . R e g r e s s i o n a n a l y s i s u s i n g e v e r y f o u r t h s a m p l i n g p o i n t o f t h e 52 e n t i r e s e q u e n c e of p o i n t s i n a s c a n was p e r f o r m e d and and r 2 v a l u e s were a b s t r a c t e d from t h e s e r e s u l t s , a l l o w i n g f o r a d e t e r m i n a t i o n of a^ and b^ p a r a m e t e r s . F o r t h e r e s t of t h e d a t a s e t ( i . e . t h o s e p o i n t s not i n c l u d e d i n t h e r e g r e s s i o n a n a l y s i s ) t h e t r a n s f o r m a t i o n was a p p l i e d and p r e d i c t e d r a d i a n c e s were c a l c u l a t e d . T h i s method had t h e a d v a n t a g e o f a l l o w i n g t h e a n a l y s i s t o be c a r r i e d out a s s u m i n g the same r e l a t i o n s h i p e x i s t e d between t h e two v a r i a b l e s i n e a c h d a t a s e t . I n o r d e r t o d e t e r m i n e t h e c o r r e l a t i o n between p r e d i c t e d and measured v a l u e s , a c o r r e l a t i o n c o e f f i c i e n t ( r ) was c a l c u l a t e d as w e l l as t h e r o o t mean s q u a r e e r r o r (RMS). T a b l e 4.4 shows t h e r e s u l t s f o r c l e a r , o v e r c a s t and p a r t l y c l o u d y d a t a . The r e s u l t s i n d i c a t e a c o n s i s t e n t l y h i g h v a l u e of r ( s i g n i f i c a n t a t t h e 95% c o n f i d e n c e l i m i t ) f o r e a c h sky c o n d i t i o n . T h i s s u g g e s t s t h a t t h e a n a l y s i s was p e r f o r m i n g s i m i l a r i l y f o r a l l sky c o v e r s . One may n o t i c e t h a t i n t h e c l e a r sky c a s e th e mean RMS i s 40% or a p p r o x i m a t e l y 9 W m ~ 2sr _ 1. S i m i l a r i l y , o v e r c a s t and p a r t l y c l o u d y c o n d i t i o n s have RMS v a l u e s of 22% (20 Wm~ 2sr" 1) and 31% (13 W m " 2 s r _ 1 ) , r e s p e c t i v e l y . The m a g n i t u d e of t h e s e e r r o r s i s due l a r g e l y t o t h e e r r o r a s s o c i a t e d w i t h t h e HP v o l t m e t e r w h i c h , as d i s c u s s e d i n S e c t i o n 2.1.3.2, r e s u l t s i n l a r g e e r r o r s f o r s m a l l m e a s u r e d f l u x e s . T h e s e f i g u r e s may be somewhat m i s l e a d i n g , however, as t h e y i n c l u d e a l l r e g i o n s of t h e sky h e m i s p h e r e . Some p o r t i o n s ( i . e . l o c a t i o n s near t h e Sun) a r e more l i k e l y t o c o r r e s p o n d t o l a r g e r e r r o r s t h a n o t h e r s . A more d e t a i l e d v e r i f i c a t i o n o f t h e c a l i b r a t i o n p r o c e d u r e f o l l o w s . T h i s i n d i c a t e s t h a t t h e 53 T a b l e 4.4 R e s u l t s of F u n c t i o n a l A n a l y s i s t o Show V a r i a t i o n Between P r e d i c t e d and M e a s u r e d R a d i a n c e s f o r C l e a r , O v e r c a s t and P a r t l y C l o u d y Sky C o n d i t i o n s Scan N r 2 RMS RMS (Wm" 2sr~ 1 ) (%) C l e a r Sky 211.1 28 0.918 6.769 31.10 211.2 30 0.937 8.107 33.00 211.3 26 0.921 9.026 38.90 211.4 30 0.805 13.805 54.98 211.5 30 0.833 13.459 54.53 211.6 29 0.926 8.031 59.03 211.7 30 0.953 8.851 31.07 211.8 28 0.978 6.328 34.32 211.9 26 0.978 6.328 23.60 O v e r c a s t Sky 239.1 25 0.923 13.150 14.57 239.2 31 0.862 38.340 39.96 239.3 26 0.954 15.090 17.01 213.3 29 0.805 29.530 30.30 213.4 30 0.901 13.190 17.12 213.5 29 0.931 12.310 15.16 213.6 29 0.761 17.320 21.71 213.7 31 0.909 19.210 18.99 P a r t l y C l o u d y Sky 237.4 27 0.944 11.430 26.76 237.5 29 0.897 15.710 38.39 237.6 29 0.951 13.650 28.96 237.7 29 0.974 8.800 25.07 237.8 29 0.952 13.800 36.54 54 m a g n i t u d e of t h e e r r o r i n h e r e n t i n t h e p r e d i c t i o n of r a d i a n c e v a r i e s a c r o s s t h e sky h e m i s p h e r e . 4.2. V e r i f i c a t i o n of t h e C a l i b r a t i o n P r o c e d u r e T h i s a n a l y s i s i n c l u d e d t h e d e r i v a t i o n of a c a l i b r a t i o n c u r v e f o r t y p i c a l c l e a r , p a r t l y c l o u d y and o v e r c a s t sky c o n d i t i o n s i n t h e manner d e t a i l e d above and a s s e s s i n g i t s v a l i d i t y u s i n g a s e t of d a t a s e p a r a t e from t h o s e d a t a i n c l u d e d i n t h e r e g r e s s i o n / f u n c t i o n a l a n a l y s i s . In o r d e r t o a c c o m p l i s h t h i s , t h e r e g r e s s i o n a n a l y s i s was p e r f o r m e d on e v e r y s e c o n d p o i n t i n t h e d a t a s e t so t h i s g r o u p o f d a t a ( i . e . t h e r e m a i n i n g o b s e r v a t i o n s ) c o u l d be a s s e m b l e d . From t h i s d e v e l o p m e n t a l d a t a s e t , t h e b and r 2 v a l u e s were a b s t r a c t e d from t h e r e g r e s s i o n r e s u l t s and were u t i l i z e d i n t h e c a l c u l a t i o n o f a^ and b^ p a r a m e t e r s . T h e s e l a t t e r v a l u e s were t h e n u s e d on t h e i n d e p e n d e n t d a t a s e t t o t r a n s f o r m t h e b r i g h t n e s s v a l u e s t o p r e d i c t e d r a d i a n c e s . T a b l e s 4.5, 4.6 and 4.7 show t h e v a l u e s f o r 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 , r e s p e c t i v e l y . The o b s e r v e d and p r e d i c t e d r a d i a n c e s a l o n g w i t h t h e r e s i d u a l s c o r r e s p o n d i n g t o e a c h p a i r of o b s e r v a t i o n s a r e p r e s e n t e d . I n e a c h c a s e , a h i g h c o r r e l a t i o n c o e f f i c i e n t (r>0.90) s u g g e s t s a s t r o n g 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 and measured r a d i a n c e s . V a r i a t i o n s i n t h e m a g n i t u d e o f t h e d i f f e r e n c e s between p r e d i c t e d and measured r a d i a n c e s a c r o s s t h e s a m p l i n g g r i d a r e i l l u s t r a t e d by t h e maps o f F i g s . 4.1, 4.2 and 4.3. F o r p u r p o s e s of c o n t o u r i n g , t h e s e a r e p r o d u c e d from a g r i d of 64x64 p i x e l s . 55 T a b l e 4.5 R e s u l t s of T r a n s f o r m a t i o n f r o m B r i g h t n e s s t o R a d i a n c e ( W m ^ s r - 1 ) f o r a C l e a r Sky, 1356 LAT December 20, 1 9 8 3 . z X Y Y Y -Y r ') (Win" ! s r - ' ; ) (Wm" : : s r " • ) ' s r 0 . 0 0 . 0 13 . 8 0 7 . 0 4 1 0 . 7 5 3 . 7 1 3 0 . 0 0 60 . C O 17 . J O 13 . 5 - ! 14 . 0 2 0 . 48 3 0 . 0 0 1 8 0 . C O 12 . 9 2 4 . 3 9 9 . 9 5 5 . 55 3 0 . 0 0 3 C 0 . 0 0 15 . 8 5 9 . 0 3 12 . 6 1 3 . 5 3 6 0 . 0 0 3 0 . 0 0 9 2 . 16 7 9 . 8 0 8 1 . 8 6 2 . 0 5 6 0 . 0 0 9 0 . 0 0 15 . 0 0 1 1 . 6 3 1 1 . 8 4 0 . 2 1 6 0 . 0 0 1 5 0 . 0 0 13 . 7 8 9 . 7 3 1 0 . 7 3 1 . 0 0 6 0 . 0 0 2 10 . 0 0 13 . 8 9 1 1 . 6 8 1 0 . 8 3 - 0 . 8 5 6 0 . O O 2 7 0 . 0 0 15 . 4 3 9 . 6 9 12 . 2 7 2 . 5 3 6 0 . 0 0 3 3 0 . 0 0 3 0 . 2 7 2 9 . 2 0 2 5 . 7 0 - 3 . SO 7 0 . 0 0 3 0 . 0 0 15 1 . 4 2 1 3 0 . 5 8 1 3 5 . 6 4 S . OS 7 0 . 0 0 1 5 0 . 0 0 15 . 2 8 12 . 8 7 12 . 0 9 - o . 7 8 7 0 . 0 0 2 10 . 0 0 14 . 9 3 14 . 7 1 1 1 . 8 2 - 2 . 8 9 7 0 . 0 0 3 3 0 . 0 0 3 7 . 4 6 3G . 7 8 3 2 . 2 2 - 4 . 5 5 3 0 . O O 0 . 0 2 0 . 5 3 17 . 5 5 16 . 8 6 - 0 . 6 9 3 0 . 0 0 1 2 0 . 0 0 13 . 7 4 9 . 0 3 1 0 . 6 9 1 . 6 5 3 0 . 0 0 2 4 0 . 0 0 15 . 17 6 . 7 7 1 1 . 9 9 5 . 2 2 6 o ! o o 0 . 0 7 9 . 8 3 8 0 . 14 7 0 . 6 7 - 9 . 47 6 0 . 0 0 6 0 . 0 0 3 2 . 8 4 2 8 . 6 0 2 8 . 0 3 - o . 5 7 6 0 . 0 0 1 2 0 . 0 0 13 . 7 8 13 . 3 5 1 0 . 7 3 - 2 . 6 2 6 0 . O O 1 8 0 . 0 0 15 . 84 9 . 7 7 12 . 6 0 2 . 8 3 6 0 . 0 0 2 4 0 .oo 13 . 34 9 . 5 3 1 0 . 3 3 0 . 8 0 6 0 . 0 0 3 C 0 . 0 0 15 . 7 9 13 . 3 5 12 . 5 5 - 0 . 8 0 7 0 . 0 0 6 0 . 0 0 4 3 . 15 3 6 . 0 7 3 7-. 3 3 1 . 3 1 7 0 . 0 0 1 2 0 . 0 0 13 . 4 3 12 . 6 3 10 . 4 7 - 2 16 7 0 . OO 1 6 0 . C O 1 4 . 13 1 4 . 10 1 1 . 0 5 - 3 . 0 5 7 0 . 0 0 3 0 0 . 0 0 IG . 9G 1 4 . 4 3 13 . 6 2 - 0 . G 1. 56 T a b l e 4.6 R e s u l t s of T r a n s f o r m a t i o n f r o m B r i g h t n e s s t o R a d i a n c e (Wm" 2sr"') f o r a P a r t l y C l o u d y Sky, 1246 LAT December 5, 1983. Z 0 X °) ( ° ) 0 . 0 0 . 0 6 5 . SO 3 0 , . 0 0 6 0 . 0 0 64 . 7 8 3 0 , . 0 0 t o o . 0 0 4 5 . 5 5 3 0 , . 0 0 3 0 0 . 0 0 9 1 . 0 2 6 0 , . 0 0 3 0 . 0 0 109 . 4 7 6 0 . 0 0 9 0 . 0 0 4 9 . 0 3 6 0 . O O 1 5 0 . 0 0 4 1 . 7 1 6 0 . O O 2 10 . 0 0 4 8 . 5 7 6 0 . 0 0 2 7 0 . 0 0 7G . 2 2 6 0 , . 0 0 3 3 0 , . 0 0 118 . 5 0 7 0 . . 0 0 3 0 , . 0 0 1 10 . 6 7 7 0 , . 0 0 1 5 0 , . 0 0 4 5 . 5 3 7 0 . . 0 0 2 1 0 . , 0 0 5 5 , . 5 1 7 0 . . 0 0 2 7 0 , , 0 0 7 8 , . 3 0 7 0 , . 0 0 3 3 0 , . 0 0 12 1 . 7 4 3 0 . . 0 0 0 , . 0 101 . 7 2 3 0 . . 0 0 1 2 0 , . 0 0 5 8 . 7 4 3 0 . . 0 0 2 4 0 , . 0 0 6 5 , . 19 G O , . 0 0 6 0 , . 0 0 7 6 . 0 2 6 0 . . 0 0 1 2 0 , . 0 0 4 0 , . 0 9 6 0 . , 0 0 1 8 0 , . 0 0 3 9 , . 8 4 G O . , 0 0 2 4 0 . . 0 0 5 5 , . 6 5 6 0 . OO 3 0 0 , . 0 0 7 3 . 9 1 7 0 . , 0 0 1 2 0 . . 0 0 3 5 , . 7 6 7 0 . 0 0 1 8 0 . 0 0 4 1 , . 5 6 7 0 . 0 0 2-10. . 0 0 54 , , 2 9 7 0 . G O 3 0 0 . 0 0 7 5 , , 2 9 Y Y Y -Y >m"*s r"') (Wm~ : s r ' 1 ) (Wn" 3 1 . 1 4 3 1 . G4 0 . 5 0 3 1 . 9 0 3 0 . 4 9 - 1 . 4 1 16 . 27 12 . 1 1 - 4 . 16 4 5 . 5 8 5 5 . 5 8 1 0 . 0 0 6 9 . 5 7 7 3 . 2 2 3 . 6 5 2 3 . 6 5 15 . 4 4 - 8 . 2 1 15 . 9 0 8 . 4 4 - 7 . 4 6 13 . 9 1 15 . O O 1 . 0 9 2 9 . 5 7 4 1 . 4 3 1 1 . 8 6 7 3 . 5 5 8 1 . 8 5 8 . 3 0 7 6 . 3 1 7 4 . 3 7 - 1 . 94 16 . 7 5 12 . 0 9 - 4 . 6 6 18 . 6 1 2 1 . 6 3 3 . 0 2 2 5 . 6 5 4 3 . 9 0 18 . 2 5 7 6 . 3 1 8 4 . 9 5 8 . 64 6 7 . 4 0 6 5 . 8 1 - 1 . 5 9 2 7 . 3 5 2 4 . 7 2 - 2 . 6 3 2 2 . 7 9 3 0 . 8 9 8 . 10 4 9 . 2 8 4 1 . 2 4 - 8 . 0 4 13 . 8 0 6 . 8 9 - 6 . 9 1 14 . 16 6 . 6 5 - 7 . 5 1 2 1 . 6 8 2 1 . 7 7 0 . 0 9 2 7 . 6 0 3 9 . 2 2 1 1 . 6 2 12 . 9 2 2 . 7 5 - 1 0 . 17 18 . 0 4 8 . 3 0 - 9 . 7 4 2 0 . 3 1 2 0 . 4 7 0 . 16 2 9 . 54 4 0 . 5 4 1 1 . 0 0 57 T a b l e 4.7 R e s u l t s of T r a n s f o r m a t i o n from B r i g h t n e s s t o R a d i a n c e ( W m " 2 s r - 1 ) f o r an O v e r c a s t Sky, 1033 LAT J a n u a r y 20, 1984. z X Y Y Y-Y ( ° ) D s r " ' ) (Wm_ ' s r " ' ) (WnT 1 sr 0 . 0 0 . 0 2 0 4 . 19 2 8 . 17 2 5 . 9 3 - 2 . 2 4 3 O . 0 0 6 0 . 0 0 1 8 0 . 8 6 2 4 . 8 2 2 3 . 2 0 - 1 . 6 2 3 0 . 0 0 1 8 0 . 0 0 1 7 6 . 7 7 19 . 7 4 2 2 . 7 2 2 . 9 8 3 0 . 0 0 3 0 0 . 0 0 1 7 9 . 8 2 24 . 8 2 2 3 . 0 8 - 1 . 7 4 6 0 . 0 0 3 0 . 0 0 1 2 3 . 9 9 1 5 . 5 7 16 . 5 4 0 . 9 7 6 0 . 0 0 9 0 . 0 0 15 1. 6 6 2 1 . 3 2 19 . 7 8 - 1 . 5 4 6 0 . 0 0 1 5 0 . 0 0 1 4 4 . 3 7 17 . 5 2 18 . 9 3 1 . 4 1 6 0 . 0 0 2 10 . 0 0 12 1 . 9 3 17 . 5 2 16 . 3 1 - 1 . 2 1 6 0 . 0 0 2 7 0 . 0 0 1 0 8 . 2 3 17 . 4 5 14 . 7 0 - 2 . 7 5 6 0 . 0 0 3 3 0 . 0 0 1 2 5 . 4 0 17 . 5 2 16 . 7 1 - 0 . 8 1 7 0 . 0 0 3 0 . 0 0 1 1 1 . 7 7 14 . 7 1 15 . 1 1 0 . 4 0 7 0 . 0 0 2 10 . 0 0 1 1 5 . 2 7 14 . 7 1 15 . 5 2 0 . 8 1 7 0 . 0 0 3 3 0 . 0 0 1 0 3 . 9 8 12 . 8 7 14 . 2 0 1 . 3 3 58 F i g u r e 4 . 1 Contour P l o t of D i f f e r e n c e s Between Measured and P r e d i c t e d Radiances (Wm~ 2sr~ 1) f o r a C l e a r Sky, 1356 LAT December 20, 1 9 8 3 59 F o r t h e c l e a r sky c a s e , a s c a n t a k e n on December 20, 1983, one c an see t h a t t h e r e i s a n o t i c e a b l e r e g i o n o f u n d e r e s t i m a t i o n of p r e d i c t e d r a d i a n c e s i n t h e r e g i o n of t h e s o l a r a u r e o l e . T h i s u n d e r p r e d i c t i o n i s on t h e o r d e r of 8 Wm _ 2sr" 1 or a b o u t 12% (of t h e measured v a l u e ) and i s most l i k e l y t o be a m a n i f e s t a t i o n of t h e d i f f e r e n c e s i n r e s p o n s e of t h e a c t i n o m e t e r and v i d e o camera t o r a d i a n t e n e r g y i n t h a t r e g i o n . The i n t e n s e s c a t t e r i n g a t s h o r t e r w a v e l e n g t h s n e a r t h e Sun would c a u s e an i n c r e a s e i n r e s p o n s e of t h e a c t i n o m e t e r , but th e camera i s not a s s e n s i t i v e t o r a d i a t i o n i n t h i s s p e c t r a l r e g i o n and so an u n d e r p r e d i c t i o n r e s u l t s . The o t h e r e x t r e m e , t h e r e g i o n o f minimum r a d i a n t i n t e n s i t y , a p p r o x i m a t e l y 90° away from t h e s o l a r d i s k , c o r r e s p o n d s t o an a r e a o f o v e r p r e d i c t i o n o f a b o u t 5 Wm~ 2sr~ 1 ( o r 4 % ) . The human eye s e n s e s t h i s r e g i o n as a d a r k e r , more b l u e a r e a , b u t a s i t r e p r e s e n t s t h e s c a t t e r i n g minimum ( G h a z i , 1971) t h e a c t i n o m e t e r would not r e s p o n d t o t h i s s p e c t r a l c o m p o s i t i o n t o t h e same e x t e n t as t h e v i d e o camera and hence , an o v e r p r e d i c t i o n r e s u l t s . At z e n i t h a n g l e s of 70° ( t h e o u t e r edge s i n c e t h e i s o l i n e s do not e x t e n d t o t h e h o r i z o n ) t h e r e a p p e a r s t o be an u n d e r p r e d i c t i o n of 1-2 Wm~ 2sr~ 1. P o r t i o n s of t h e sky w h i c h c o r r e s p o n d t o o b s e r v e d r a d i a n c e v a l u e s of l e s s t h a n 10 wm~ 2sr" 1, o f t e n have d i f f e r e n c e s between p r e d i c t e d and measured r a d i a n c e s r a n g i n g between 30% and 50%. T h i s i s due m a i n l y t o t h e a b s o l u t e e r r o r a s s o c i a t e d w i t h u s i n g t h e HP v o l t m e t e r t o measure s u c h s m a l l f l u x e s . O t h e r w i s e t h e RMS can be as low as 3% w h i c h i s w i t h i n t h e a c c u r a c y o f t h e a c t i n o m e t e r and v i d e o s y s t e m . 60 The p a r t l y c l o u d y sky r e s u l t ( F i g . 4.2) i s l e s s easy t o i n t e r p r e t ; t h e r e i s a p r o m i n a n t r e g i o n of o v e r p r e d i c t i o n , a s h i g h a s 18 Wm~ 2sr~ 1 ( 7 1 % o f t h e measured v a l u e ) a t t h e t o p of t h e image. A n a l y s i s o f t h e image c o r r e s p o n d i n g t o t h i s s c a n , does not p r o v i d e an o b v i o u s r e a s o n f o r t h i s o v e r p r e d i c t i o n . However, t h e s t e e p c o n t o u r s s u g g e s t t h a t i t i s a f u n c t i o n o f a s i n g l e d a t a p o i n t . The c o n t o u r p l o t a p p e a r s t o have two major p o r t i o n s ; one c o r r e s p o n d s t o o v e r p r e d i c t i o n ( t h e upper h a l f ) and t h e o t h e r t o u n d e r p r e d i c t i o n ( t h e lower h a l f ) . I t i s not c e r t a i n what u n d e r l i e s t h i s phenomenon. The c o n t o u r s i n t h e upper h a l f of t h e image have a s t e e p e r g r a d i e n t t h a n t h o s e i n th e l o w e r h a l f , and a r e i n f l u e n c e d s t r o n g l y by t h e v a l u e o f t h e v a r i a t i o n s between p r e d i c t e d and measured r a d i a n c e s a t a z e n i t h a l a n g l e o f 30° and a z i m u t h a l a n g l e s o f 240° and 3 0 0 ° . The i s o l i n e s i n t h e l o w e r h a l f o f t h e image i n d i c a t e u n d e r p r e d i c t i o n s r a n g i n g from -1 t o -9 Wm~ 2sr~ 1. A p o s s i b l e r e a s o n f o r t h e h i g h l y s y s t e m a t i c d i s t r i b u t i o n o f e s t i m a t i o n d i f f e r e n c e s i s an e q u a l l y s y s t e m a t i c a r r a n g e m e n t o f c l o u d s or a t m o s p h e r i c phenomena a t t h e t i m e o f o b s e r v a t i o n . I t i s u n l i k e l y t h a t t h i s c o n f i g u r a t i o n of v a l u e s i s r e l a t e d t o i n s t r u m e n t a t i o n s i n c e no o t h e r c a s e shows a s i m i l a r p a t t e r n . F i g . 4.3 i s t h e c o n t o u r map r e p r e s e n t i n g an o v e r c a s t s ky c o n d i t i o n . T h e r e i s a v e r y s m a l l r a n g e of r a d i a n c e s i n t h i s low c o n t r a s t image; t h i s i s m a n i f e s t e d i n t h e s m a l l e r d i f f e r e n c e s between p r e d i c t e d and measured r a d i a n c e s f o u n d on t h i s p l o t a s compared t o t h e p r e v i o u s two p l o t s . T h e r e i s a low g r a d a t i o n of c o n t o u r s w i t h no d i f f e r e n c e between p r e d i c t e d 61 F i g u r e 4.2 C o n t o u r P l o t of D i f f e r e n c e s Between M e a s u r e d and P r e d i c t e d R a d i a n c e s (Wm" 2sr" 1) f o r a P a r t l y C l o u d y Sky, 1246 LAT, December 5, 1983 6 2 E W F i g u r e 4.3 C o n t o u r P l o t of D i f f e r e n c e s Between M e a s u r e d and P r e d i c t e d R a d i a n c e s (Wm" 2sr"') f o r an O v e r c a s t Sky, 1320 LAT J a n u a r y 20, 1984 63 and measured r a d i a n c e s b e i n g g r e a t e r t h a n 3 Wm - 2sr~ 1. An a r e a of u n d e r p r e d i c t i o n by 2 Wm~ 2sr~ 1 ( 8 % of t h e measured v a l u e ) a t th e z e n i t h c o r r e s p o n d s t o t h e b r i g h t e s t p a r t of t h e s k y . Most of t h e image c o r r e s p o n d s t o an u n d e r p r e d i c t i o n of ab o u t 1 Wm _ 2sr~ 1 ( 5 % ) . The r e g i o n s of o v e r p r e d i c t i o n c o u l d be a s s o c i a t e d w i t h t h o s e p a t c h e s of e s p e c i a l l y dense or t h i c k c l o u d w h i c h s c a t t e r o r r e f l e c t r a d i a t i o n i n s u c h a manner t h a t t h e a c t i n o m e t e r would show l e s s r e s p o n s e r e l a t i v e t o t h e camera ( g r e a t e r s c a t t e r i n g e f f e c t s of wa t e r d r o p l e t s c o u l d r e s u l t i n a s h i f t i n t h e e n e r g y s p e c t r u m t o l o n g e r w a v e l e n g t h s ) . T h i s i s i n k e e p i n g w i t h t h e f i n d i n g s o f S e c t i o n 2.2.1.1. The c o n t o u r p l o t s s e r v e t o i l l u s t r a t e how t h e v a l u e o f t h e v a r i a t i o n s between p r e d i c t e d and measured r a d i a n c e s a r e d i s t r i b u t e d o v e r a sky image. The c a l i b r a t i o n m e t h o d o l o g y i s c a p a b l e o f p r e d i c t i n g r a d i a n c e w i t h i n 5% a t b e s t , b u t may a l s o r e s u l t , i n o v e r / u n d e r p r e d i c t i o n s o f 50% or g r e a t e r due t o t h e e r r o r a s s o c i a t e d w i t h u s i n g t h e d i g i t a l v o l t m e t e r f o r m e a s u r i n g low r a d i a n c e s and t h e s p e c t r a l l y , v a r y i n g r e s p o n s e o f t h e camera as compared t o t h e a c t i n o m e t e r . 4.3 V a l i d i t y of A p p r o a c h u s i n g P a r t i a l Scan D a t a A t y p i c a l measurement s c a n i n c l u d e d 31 s a m p l i n g p o i n t s a s d e s c r i b e d i n S e c t i o n 3.2. V a r i o u s t e s t s were p e r f o r m e d t o judg e t h e a p p r o p r i a t e n e s s of t h i s s a m p l i n g g r i d and t o a s c e r t a i n i f a g r i d c o n t a i n i n g fewer s a m p l i n g p o i n t s c o u l d be u t i l i z e d a t l e a s t i n t h e s t e a d y s t a t e c o n d i t i o n s of c l e a r s k i e s . 64 On December 20,1983, a c l o u d l e s s day, t h e r a d i a n c e a t 62 p o i n t s on t h e sky was measured i n s t e a d of t h e u s u a l 31. A t t h e end o f t h e s c a n , an image was s t o r e d f o r a n a l y s i s . F i g . 4.4 shows t h e r e g r e s s i o n l i n e f o r t h i s d a t a s e t w h i l e T a b l e 4.8 g i v e s t h e p e r t i n e n t i n f o r m a t i o n on t h e r e s u l t s of t h e r e g r e s s i o n a n a l y s i s f o r t h e 62 d a t a p o i n t s ( J D 3 5 4 a ) . Not o n l y i s 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 ) v e r y h i g h (and s i g n i f i c a n t t o t h e 99% c o n f i d e n c e l e v e l ) , but t h e s t a n d a r d e r r o r of Y, a measure o f t h e d e p a r t u r e of p r e d i c t e d v a l u e s from t h e r e g r e s s i o n l i n e , i s o n l y about 2%, w h i c h i s w i t h i n t h e r e l a t i v e e r r o r of t h e a c t i n o m e t e r . A l s o , as can be n o t e d from T a b l e 4.8, t h e s t a n d a r d e r r o r s of a r and b r a r e b o t h v e r y low, f u r t h e r e v i d e n c e o f t h e c l o s e f i t o f t h e d a t a t o t h e p r e d i c t e d c u r v e . T h e s e r e s u l t s have been o b t a i n e d u s i n g 62 s a m p l i n g p o i n t s . A n o t h e r r e g r e s s i o n a n a l y s i s was c a r r i e d o u t , t h i s t i m e u s i n g o n l y e v e r y f o u r t h p o i n t i n t h e d a t a s e t . B e c a u s e t h e p r e v i o u s r e s u l t s were so f a v o u r a b l e and r 2 ( s i g n i f i c a n t a t t h e 99% l e v e l ) was so h i g h , i t i s not s u r p r i s i n g t h a t i n c o r p o r a t i n g o n l y 13 d a t a p o i n t s s t i l l r e s u l t s i n a s t r o n g p o s i t i v e c o r r e l a t i o n between a c t i n o m e t r i c measurements and b r i g h t n e s s measurements as e v i d e n c e d by t h e JD354b r e s u l t s i n T a b l e 4.8. The s t a n d a r d e r r o r of Y has i n c r e a s e d o n l y s l i g h t l y t o 2.5% and t h e s t a n d a r d e r r o r s o f a r and b r a r e s t i l l m i n i m a l ; r 2 has i n c r e a s e d i n t h i s c a s e . These r e s u l t s seem t o s u g g e s t t h a t f o r a c l e a r s k y , when n e a r l y s t e a d y s t a t e r a d i a t i v e c o n d i t i o n s e x i s t , o n l y a m i n i m a l number of s a m p l i n g p o i n t s need be t a k e n i n o r d e r t o r e t a i n v a l i d p r e d i c t i v e c a p a b i l i t i e s . I t must be 65 Br i g h t n e s s *Note - 4-, 2 r e p r e s e n t t h e number and l o c a t i o n of d a t a po i n t s F i g u r e 4.4 R e s u l t s of R e g r e s s i n g B r i g h t n e s s and R a d i a n c e ( W m ~ 2 s r _ 1 ) f o r a C l e a r Sky, 1356 LAT December 20, 1983 66 T a b l e 4 .8 R e g r e s s i o n R e s u l t s f o r C l e a r and P a r t l y C l o u d y Sky Scan a r b_. St . E r r o r S t . E r r o r S t . E r r o r r 2 N of a_. of b r of Y JD354a -1 .77 0.907 0.592 0 .014 3.324 0.989 62 JD354b -2 .62 0.912 0.371 0 .022 3.866 0.994 1 3 JD339 -26 .87 0.891 2.374 0 .031 7. 198 0.941 62 JD339a -27 .33 0.904 2.866 0 .036 6. 1 93 0.963 31 JD339b -30 .18 0.961 3.756 0 .042 7.351 0.977 1 3 67 n o t e d however t h a t i n t h i s c a s e , t h e use of e v e r y f o u r t h s a m p l i n g p o i n t c o i n c i d e d w i t h a u n i f o r m r e p r e s e n t a t i o n of d i f f e r e n t r e g i o n s of t h e sky h e m i s p h e r e , ( i . e . from t h e b r i g h t e s t r e g i o n s u r r o u n d i n g t h e Sun t o t h e a r e a o f l e a s t r a d i a n t i n t e n s i t y ) . I f t h i s had n o t been t h e c a s e , t h e s l o p e o f t h e r e g r e s s i o n c u r v e c o u l d be v e r y d i f f e r e n t t o t h a t of t h e c u r v e d e r i v e d from use of t h e f u l l d a t a s e t and a d i f f e r e n t t r a n s f o r m a t i o n would have r e s u l t e d . T h i s would be e s p e c i a l l y t r u e i n t h e more complex p a r t l y c l o u d y sky c a s e s . T h e r e f o r e when o n l y a p a r t i a l d a t a s e t i s u s e d , i t i s n e c e s s a r y t o e n s u r e t h a t t h o s e d a t a a r e r e p r e s e n t a t i v e o f a l l z o n e s i n t h e s k y . The same p r o c e d u r e was c a r r i e d o u t f o r a p a r t l y c l o u d y sky example o b t a i n e d on December 5, 1983 ( J D 3 3 9 ) . F i g . 4.5 shows t h e r e g r e s s i o n l i n e b a s e d on 62 d a t a p o i n t s w h i l e T a b l e 4.8 g i v e s t h e r e s u l t of t h i s r e g r e s s i o n a n a l y s i s ( N o t e - a l l r 2 v a l u e s a r e s i g n i f i c a n t t o t h e 99% c o n f i d e n c e l e v e l ) . In t h i s c a s e , one c a n see t h e g r e a t e r amount o f s c a t t e r p r e s e n t and t h i s i s m a n i f e s t e d i n t h e l a r g e r s t a n d a r d e r r o r o f Y v a l u e , namely 5% f o r JD339. The s t a n d a r d e r r o r o f b r , t h e s l o p e p a r a m e t e r i s a l s o s l i g h t l y l a r g e r t h a n f o r t h e c l e a r sky c a s e . P a r t o f t h i s i n c r e a s e d s c a t t e r was due t o t h e v a r y i n g r e s p o n s e o f t h e c a m e r a / f i l t e r s y s t e m a s compared t o t h e a c t i n o m e t e r , a s t h e f o r m e r v i e w e d a l t e r n a t i n g b l u e s k y and c l o u d r e g i o n s . P a r t l y c l o u d y sky c o n d i t i o n s r e p r e s e n t t h e most complex sky r a d i a n c e d i s t r i b u t i o n s and a r e i n h e r e n t l y more d i f f i c u l t t o map due t o s p a t i a l and t e m p o r a l v a r i a b l i l i t y . B e c a u s e of t h i s , 68 F i g u r e 4.5 R e s u l t s of R e g r e s s i n g B r i g h t n e s s and R a d i a n c e ( W m ~ 2 s r _ 1 ) f o r a P a r t l y C l o u d y Sky, 1246 LAT December 5,1983 69 two d i f f e r e n t s a m p l i n g a p p r o a c h e s were examined. F i r s t l y , e v e r y s e c o n d p o i n t out of t h e 62 o r i g i n a l s a m p l i n g p o i n t s (JD339a) was i n c l u d e d i n t h e r e g r e s s i o n , and t h e n o n l y e v e r y f o u r t h p o i n t (JD339b) was i n c l u d e d . 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 4.8. In b o t h c a s e s , r 2 has i n c r e a s e d from i t s o r i g i n a l v a l u e due t o t h e r e d u c e d s c a t t e r r e s u l t i n g from t h e r e m o v a l of c e r t a i n d a t a p o i n t s . F o r JD339a, b o t h t h e s t a n d a r d e r r o r of Y (now o n l y 45% o f t h e range o f p r e d i c t e d r a d i a n c e s ) and b have d e c r e a s e d w h i l e t h e s l o p e and i n t e r c e p t v a l u e s have not c h a n g e d s i g n i f i c a n t l y . JD339b however, shows a d i f f e r e n t s l o p e and i n t e r c e p t v a l u e from t h e o r i g i n a l c a s e and has l a r g e r s t a n d a r d e r r o r v a l u e s f o r a r , b r and Y. Once a g a i n , t h e s a m p l i n g p o i n t s were r e p r e s e n t a t i v e of t h e r a n g e of i n t e n s i t i e s p r e s e n t i n t h e sky a t t h e t i m e of o b s e r v a t i o n s and so t h e change i n t h e s l o p e p a r a m e t e r was m i n i m i z e d . By s t u d y i n g F i g . 4.5 c l o s e l y , one can d i s c e r n t h a t a t l e a s t two t r e n d s a r e p r e s e n t i n t h e d a t a ( t h e r e c o u l d have been a change i n t h e s p e c t r a l c o m p o s i t i o n of e n e r g y d u r i n g t h e d a t a c o l l e c t i o n w h i c h r e s u l t e d i n two d i f f e r e n t r e s p o n s e s by t h e camera t o t h a t e n e r g y d i s t r i b u t i o n ) and so d e p e n d i n g on w h i c h of t h e 62 s a m p l i n g p o i n t s had been i n c l u d e d i n t h e p a r t i a l d a t a s e t , q u i t e d i f f e r e n t r e s u l t s may have been o b t a i n e d . T h i s e m p h a s i z e s t h e need f o r c a r e f u l c h o i c e of s a m p l i n g p o i n t s . S i n c e t h e a c c u r a c y of t h e r e s u l t s d o e s n o t seem t o d e c r e a s e s i g n i f i c a n t l y w i t h use of a s m a l l e r s a m p l i n g g r i d as l o n g a s t h e p o i n t s a r e r e p r e s e n t a t i v e of t h e range o f e n e r g y i n t e n s i t i e s p r e s e n t i n t h e s k y , i t a p p e a r s t h a t t h e g r i d 70 u s e d i n t h i s s t u d y was r e a s o n a b l e and one b a s e d on fewer d a t a p o i n t s c o u l d have been e q u a l l y s a t i s f a c t o r y . One v e r y i m p o r t a n t f e a t u r e common t o b o t h o f t h e above examples i s t h a t t h e a c t i n o m e t r i c measurements and t h e b r i g h t n e s s o b s e r v a t i o n s were r e c o r d e d s i m u l t a n e o u s l y so t h a t b o t h would be i n s t a n t a n e o u s r e p r e s e n t a t i o n s of t h e same sky c o n d i t i o n s . S i n c e t h e images t a k e n d u r i n g , o r a t t h e end of a s c a n were s t o r e d on f l o p p y d i s k s , i t was p o s s i b l e t o d e t e r m i n e how t h e r e s u l t s would be a f f e c t e d by b e i n g r e c o r d e d a s y n c h r o n o u s l y . T a b l e 4.9 g i v e s t h e r e g r e s s i o n r e s u l t s f o r d a t a o b t a i n e d under c l e a r s k i e s , on December 20, 1983. The p r i m a r y s c a n d a t a were c o l l e c t e d s i m u l t a n e o u s l y ( i . e . a c t i n o m e t r i c and b r i g h t n e s s o b s e r v a t i o n s were o b t a i n e d s i m u l t a n e o u s l y ) . Once an image had been s t o r e d , i t was a r e l a t i v e l y s i m p l e p r o c e d u r e t o run t h e b r i g h t n e s s s a m p l i n g programme so t h a t b r i g h t n e s s d a t a c o u l d be a b s t r a c t e d f r o m t h e s t o r e d image and c o u l d be compared w i t h t h e p r e v i o u s l y o b t a i n e d r a d i a n c e measurements ( i . e . t h i s r e s u l t s i n a s y n c h r o n o u s o b s e r v a t i o n s ) . C o m p a r i s o n s of t h e r e s u l t s o b t a i n e d w i t h use o f s i m u l t a n e o u s o b s e r v a t i o n s (S) w i t h r e s u l t s f o r a s y n c h r o n o u s (NS) o b s e r v a t i o n s , i n d i c a t e a s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e ( a t 95% c o n f i d e n c e l e v e l ) between t h e two d a t a s e t s . I t c an be n o t e d t h a t r 2 d e c r e a s e d and t h e r e was a s i g n i f i c a n t change i n t h e s l o p e (t> r) and i n t e r c e p t (a_.) o f t h e r e g r e s s i o n l i n e . The s t a n d a r d e r r o r o f Y i n c r e a s e d from 2% t o a l m o s t 5% and t h e s t a n d a r d e r r o r o f a and b a p p r o x i m a t e l y d o u b l e d . 71 T a b l e 4.9 R e g r e s s i o n A n a l y s i s R e s u l t s f o r C l e a r Sky C o n d i t i o n s (JD354) Showing V a r i a t i o n i n D a t a a s O b t a i n e d w i t h S i m u l t a n e o u s Measurements ( S ) , and A s y n c h r o n o u s (NS) Measurements. S (N=56) NS (N=56) a r -1.769 0.8842 b r 0.9073 0.8312 S t a n d a r d E r r o r of a r 0.592 1 .252 S t a n d a r d E r r o r of b r 0.0135 0.0278 S t a n d a r d E r r o r of Y 3.324 7.347 r 2 0.9885 0.9429 T a b l e 4.10 R e g r e s s i o n A n a l y s i s R e s u l t s f o r a P a r t l y C l o u d y Sky (JD339) f o r D a t a O b t a i n e d U s i n g S i m u l t a n e o u s Measurements (S) and A s y n c h r o n o u s (NS) M e a s u r e m e n t s . S t a n d a r d E r r o r of S t a n d a r d E r r o r o f S t a n d a r d E r r o r o f S (N=56) -26.870 0.8914 2.374 0.0307 7.1980 0.9410 NS (N=54) •24.740 0.7467 3.362 0.0397 0.8722 0.8722 72 T h e r e was not s u c h a s t r o n g c o r r e l a t i o n between a c t i n o m e t r i c and b r i g h t n e s s o b s e r v a t i o n s when t h e r e a d i n g s were r e c o r d e d a s y n c h r o n o u s l y . F o r t h e c l e a r sky c a s e , i t w o u l d seem t h a t t h e r e s u l t s c o u l d be a f f e c t e d most by u s i n g a s y n c h r o n o u s a c t i n o m e t r i c and b r i g h t n e s s o b s e r v a t i o n s . In t h e c a s e of t h e more complex p a r t l y c l o u d y sky, T a b l e 4.10 i n d i c a t e s t h a t a s u b s t a n t i a l i n c r e a s e i n a l l o f t h e s t a n d a r d e r r o r v a l u e s o c c u r s when a s y n c h r o n o u s o b s e r v a t i o n s a r e compared t o t h o s e o b t a i n e d i n s i m u l t a n e o u s measurements. I n d e e d , t h e d i f f e r e n c e s between t h e r e g r e s s i o n r e s u l t s a r e s i g n i f i c a n t a t t h e 95% c o n f i d e n c e l e v e l . The s t a n d a r d e r r o r of Y i n c r e a s e s from a b o u t 4.6% t o 7% i n t h i s c a s e , a l o n g w i t h a d r o p i n t h e r 2 v a l u e f r o m 0.94 t o 0.89. These f i n d i n g s s u g g e s t t h a t f o r t h e c a s e of p a r t i a l c l o u d i n e s s , i t i s i m p o r t a n t t o c o l l e c t s i m u l t a n e o u s measurements o f b r i g h t n e s s and r a d i a n c e i n o r d e r t o b e s t r e p r e s e n t sky c o n d i t i o n s and f o r a c c u r a t e p r e d i c t i o n of d i f f u s e r a d i a n c e . 73 C h a p t e r F i v e The A n g u l a r D i s t r i b u t i o n of D i f f u s e S o l a r R a d i a t i o n Once t h e l i n e a r n a t u r e of t h e r e l a t i o n s h i p between r a d i a n c e and b r i g h t n e s s had been d e t e r m i n e d and v e r i f i e d , i t was p o s s i b l e t o u n d e r t a k e an a n a l y s i s of t h e a c t u a l a n g u l a r d i s t r i b u t i o n of d i f f u s e s o l a r r a d i a t i o n a c r o s s t h e sky h e m i s p h e r e . As m e n t i o n e d i n S e c t i o n 3.2, a s e t of f i e l d o b s e r v a t i o n s was c a r r i e d out i n December, 1983 and J a n u a r y and F e b r u a r y , 1984. The r e s u l t s o f t h i s work, i n c l u d i n g some a d d i t i o n a l summer d a t a , w i l l f o r m t h e b a s i s f o r t h e a n a l y s e s i n t h e f o l l o w i n g s e c t i o n s . 5.1 D e t e r m i n i n g a Method f o r T r a n s l a t i n g t h e V a l u e of a  R a d i a n c e i n t h e Sky t o a P o i n t on t h e Image As p a r t of t h e m e t h o d o l o g y u s e d t o d e t e r m i n e a f and b^,. t h e i n t e r c e p t and s l o p e r e s p e c t i v e l y , o f t h e l i n e a r t r a n s f o r m a t i o n w h i c h r e s u l t s i n t h e p r e d i c t i o n o f r a d i a n c e v a l u e s f r o m b r i g h t n e s s v a l u e s , a c o r r e c t i o n was a p p l i e d t o t h e a c t i n o m e t r i c measurements ( s e e S e c t i o n 4 . 1 . 1 ) . T h i s was t o compensate f o r t h e e f f e c t s of t h e e q u i - a n g u l a r p r o p e r t i e s o f t h e f i s h e y e l e n s on t h e b r i g h t n e s s v a l u e s ( b r i g h t n e s s v a l u e s were not a d j u s t e d b e c a u s e t h i s w o u l d i m p l i c i t l y assume knowledge of t h e r e l a t i o n s h i p between r a d i a n c e and b r i g h t n e s s , w h i c h i s what was b e i n g d e t e r m i n e d ) . S i n c e t h i s c o r r e c t i o n had been a p p l i e d t o t h e measured d i f f u s e r a d i a n c e s , an a d j u s t m e n t must be p e r f o r m e d i n o r d e r t o t r a n s f o r m any b r i g h t n e s s v a l u e on 74 t h e sky image t o a r a d i a n c e , e s t i m a t e d u s i n g t h e f u n c t i o n a l a n a l y s i s m e t h o d o l o g y . An a n a l y t i c a l a p p r o a c h has been u t i l i z e d t o d i s c o v e r what form t h i s t r a n s f o r m a t i o n s h o u l d h a v e . L e t dA be t h e p r o j e c t i o n o n t o a h e m i s p h e r e of r a d i u s R 0 of an e l e m e n t i n t h e sky ( F i g . 5 . 1 ) . S i n c e dA = R 0 d z p 6\<p (5.1) where p = R 0 s i n z (5.2) and z = z e n i t h a n g l e $ = a z i m u t h a n g l e p = d i s t a n c e from t h e c e n t r e of t h e a r e a t o a n o r m a l p r o j e c t e d v e r t i c a l l y t h r o u g h t h e sky h e m i s p h e r e . Then, dA = (5.3) (5.4) R 0 2 s i n z dz d<p . On t h e image p l a n e , R/R 0 =2 z/ir or R = 2R 0 z/n and t h e r e f o r e , dR = 2R 0 d z / i r . (5.5) L e t dA' be t h e e l e m e n t a l a r e a on t h e image p l a n e so t h a t dA' = R dR dt5 =4 R 0 2 z dz ae/n2 T h e r e f o r e , dA'/dA = (4 R 0 2 z dz 69/n2 ) / ( R 0 2 s i n z dz d<j>) = 4 / 7 r 2 x z / s i n z s i n c e d0=d</>. (5.6) (5.7) (5.8) F i g u r e 5.1 Geometry of Sky H e m i s p h e r e 76 N o r m a l i z i n g w i t h r e s p e c t t o t h e v a l u e a t t h e z e n i t h ( 4 / 7 r 2 ) , y i e l d s D ( z ) , t h e h o r i z o n - d a r k e n i n g f a c t o r . T h e r e f o r e a t th e z e n i t h (z=0), D ( 0 ° ) = l i m z / s i n z = 1.0 ~Zr*o and a t z e n i t h a n g l e 9 0 ° , D ( 9 0 ° ) = i r / 2 . Thus, i t has been d e t e r m i n e d t h a t t h e v a l u e s o f p r e d i c t e d r a d i a n c e s h o u l d be m u l t i p l i e d by z / s i n z i n o r d e r t o t r a n s f o r m a b r i g h t n e s s map ( i . e . a sky image) t o a r a d i a n c e map and c o r r e c t l y r e p r e s e n t t h e r a d i a n c e v a l u e s . 5.2 The D i s t r i b u t i o n o f D i f f u s e S o l a r R a d i a t i o n o v e r  t h e Sky He m i s p h e r e 5.2.1 D i s t r i b u t i o n of R a d i a n c e V a l u e s f o r D i f f e r e n t  Sky C o n d i t i o n s F i g u r e s . 5.2, 5.3 and 5.4 p r e s e n t f r e q u e n c y h i s t o g r a m s i l l u s t r a t i n g t h e c h a r a c t e r i s t i c s o f t h e d i s t r i b u t i o n of r a d i a n c e s f o r t y p i c a l c l e a r , o v e r c a s t and p a r t l y c l o u d y sky c o n d i t i o n s . An example o f a c l e a r sky d i s t r i b u t i o n (December 20,1983) i s g i v e n i n F i g . 5.2a. From t h i s f i g u r e , one c a n n o t e t h a t t h e mode o f t h e d i s t r i b u t i o n l a y between 4-12 Wm _ 2sr~ 1. I n d e e d a l m o s t 81% o f t h e p r e d i c t e d v a l u e s were l e s s t h a n 28 Wm~ 2sr - 1. The l a r g e r v a l u e s , 160-248 Wm" 2sr" 1, c o r r e s p o n d e d t o p o i n t s l o c a t e d n e a r t h e Sun. The h i s t o g r a m was p o s i t i v e l y skewed w i t h a mean r a d i a n c e o f 29.13 Wm~ 2sr~ 1 and a s t a n d a r d d e v i a t i o n o f 77 b) in CD -ico CU o O Z on CD a, o z VO CM Q3 T O VO CM CO O a) u") r~ oo o CM m if> *o co oo — — — — — . _ <NI CM R a d i a n c e (Wm'^sr" 1) O VO CM D O ^ r O <i) N CO R a d i a n c e (Wm" 3-sr" i) * N o t e - C l a s s i n t e r v a l s a r e r e p r e s e n t e d by the m i d p o i n t of each c l a s s F i g u r e 5.2 F r e q u e n c y H i s t o g r a m s o f P r e d i c t e d R a d i a n c e (wm 2 s r " ' ) f o r C l e a r S k i e s a) 1356 LAT December 2 0 , 1 9 8 3 and b) 1320 LAT A u g u s t 2 1, 1983 78 49.80 Wm~ 2sr~ 1. T h i s h i s t o g r a m would be t y p i c a l of a c l e a r s k y , w i n t e r t i m e p a t t e r n w i t h t h e Sun low on t h e h o r i z o n ( z e n i t h a n g l e 7 7 ° ) . Most of t h e v a l u e s a r e i n d i c a t i v e of t h e low c o n t r a s t , c l e a r r e g i o n of t h e sky r e g i s t e r i n g no a u r e o l e e f f e c t s . F i g . 5.2b i l l u s t r a t e s t h e f r e q u e n c y d i s t r i b u t i o n f o r a c l e a r sky ( A u g u s t 21,1983; z e n i t h a n g l e 4 0 . 4 ° ) r e p r e s e n t a t i v e o f summertime r a d i a t i v e c o n d i t i o n s . As i n t h e above c a s e , most v a l u e s r e s i d e d between 4-28 Wm~ 2sr~ 1 w i t h a p p r o x i m a t e l y 70% of th e measured r a d i a n c e s below 28 W m~ 2sr _ 1. The mean r a d i a n c e was 27.06 Wm~ 2sr~ 1 w i t h a s t a n d a r d d e v i a t i o n o f 26.40 Wm~ 2sr" 1. The v a l u e of skewness was l e s s f o r t h i s d i s t r i b u t i o n ; 2.26 r a t h e r t h a n 3.13 f o r F i g . 5.2a. F o r t h i s example, t h e r a n g e o f v a l u e s was much l e s s , w i t h a maximum a t 160 Wm~ 2sr - 1 as compared t o 248 Wm~ 2sr - 1 f o r t h e w i n t e r example. Due t o i n c r e a s e d s c a t t e r , t h e d i s t r i b u t i o n i s s h i f t e d s l i g h t l y t o h i g h e r v a l u e s t h a n i n t h e p r e v i o u s c l e a r s ky c a s e . G r e a t e r s c a t t e r i n g c o u l d r e s u l t ' from h i g h e r l e v e l s o f t u r b i d i t y a s s o c i a t e d w i t h t h e summertime a n t i c y c l o n i c c o n d i t i o n s a t V a n c o u v e r , B.C., as compared t o t h e u s u a l l y l o w e r v a l u e s o f t u r b i d i t y d u r i n g c l e a r c o n d i t i o n s i n t h e w i n t e r . The l a t t e r s t a t e e x i s t s a f t e r t h e f l u s h i n g of a e r o s o l p a r t i c l e s by t h e r a i n and wind d u r i n g t h e w i n t e r months (as i n Hay and Da r b y , 1984). The h i s t o g r a m r e p r e s e n t i n g an o v e r c a s t s k y f o r J a n u a r y 20, 1984 (LAT 1320), d e p i c t e d i n F i g . 5.3a had an even s m a l l e r r a n g e of r a d i a n c e s ; o n l y 30 Wm~ 2sr - 1, c o n c e n t r a t e d ' i n c l a s s 79 b) 1 0 0 0 - 1 0 0 0 So o l o o 10 0) cu u-i O O _>oo - l o o s o So-8 16 24 32 R a d i a n c e ( W m ~ 2 s r - 1 ) 8 1 6 R a d i a n c e (Wm - ; zsr~ l ) * N o t e - C l a s s i n t e r v a l s a r e r e p r e s e n t e d by the m i d p o i n t of each c l a s s i g u r e 5.3 F r e q u e n c y H i s t o g r a m s o f P r e d i c t e d R a d i a n c e (Wm" 2sr"') f o r O v e r c a s t S k i e s a) l320 LAT J a n u a r y 20, 1984 b) 13 4 0 LAT J a n u a r y 20, 1984 80 i n t e r v a l s between 12-28 Wm~ 2sr~ 1 ( t h e modal c l a s s b e i n g 20-28 W m _ 2 s r ~ 1 ) . A p p r o x i m a t e l y 75% o f t h e measured v a l u e s were between 12-36 Wm~ 2sr~ 1. The mean r a d i a n c e v a l u e f o r t h i s example was 21.06 Wm~ 2sr~ 1 w i t h a s t a n d a r d d e v i a t i o n of 6.85 Wm" 2sr~ 1. T h i s d i s t r i b u t i o n was o n l y s l i g h t l y skewed t o the l e f t (skewness v a l u e was - 0 . 0 6 ) . F i g . 5.3b ( J D 2 0 b . 2 : z e n i t h a n g l e 74°) shows t h e v a l u e s have s h i f t e d t o even l o w e r r a d i a n c e s ; t h e range b e i n g 4-24 Wm~2sr"'1. The mean was 11.13 Wm" 2sr~ 1 w i t h a s t a n d a r d d e v i a t i o n o f 3.91 Wm~ 2sr~ 1. T h i s l a t t e r r e s u l t r e p r e s e n t s a d i s t r i b u t i o n o b s e r v e d d u r i n g sky c o n d i t i o n s w i t h dense c l o u d c o v e r . The f r e q u e n c y h i s t o g r a m s o f t h e more complex p a r t l y c l o u d y sky r a d i a n c e d i s t r i b u t i o n s v a r y d e p e n d i n g on t h e amount and l o c a t i o n o f t h e c l o u d s i n t h e s k y . On December 5, 1983, when o b s e r v a t i o n s were made under a p p r o x i m a t e l y 7/10 a l t o c u m u l u s , t h e r a d i a n c e p a t t e r n had a f r e q u e n c y d i s t r i b u t i o n a s shown i n F i g . 5.4a. The ran g e of v a l u e s was between 4-208 Wm~ 2sr~ 1 w i t h 38% of t h e r a d i a n c e s b e i n g l e s s t h a n 32 Wm~ 2sr _ 1 ( t h e modal c l a s s was 12-28 W m " 2 s r " 1 ) . When F i g . 5.4a i s compared w i t h F i g s . 5.2a and b, one c a n see t h a t t h e d i s t r i b u t i o n has s h i f t e d t o more r a d i a n c e s e x h i b i t i n g h i g h e r v a l u e s ( t h e mean was 51.52 Wm" 2sr _ 1 f o r t h i s example) i n d i c a t i n g i n c r e a s e d s c a t t e r i n g due t o t h e p r e s e n c e of c l o u d s . T h i s d i s t r i b u t i o n i s skewed t o t h e r i g h t w i t h a skewness o f 1.63. F i g . 5.4b i s t y p i c a l o f a m a i n l y c l e a r sky w i t h c i r r u s c l o u d p a t c h e s i n t h e r e g i o n of t h e Sun and was o b t a i n e d on J a n u a r y 12, 1984. The d i s t r i b u t i o n i s s t r o n g l y skewed t o t h e r i g h t w i t h t h e modal c l a s s b e i n g 12-20 1coo -.—I CD X t o o a, U-4 So O O 2 a ) CO ^ rOvO^CO^OVOnco^pO^OtMCO cNi**ir»r-coori<"itr»*i>coo — _ — — — — — fN <N <N R a d i a n c e (Wm _ 2-sr- 1 ) b) to r-1 CD X a o 2 £00 •too 50 CD - i o « o c) ft xfy vo co o V O C M OO o n iS) vo cO O R a d i a n c e (Wm-2-sr"1 ) F i g u r e R a d i a n c e ( W m ^ s r - 1 ) F r e q u e n c y H i s t o g r a m s o f P r e d i c t e d R a d i a n c e ( W i r T ^ r - 1 ) f o r P a r t l y C l o u d y S k i e s a ) 1 2 4 6 LAT December 5,1983 b) 14 4 9 LAT J a n u a r y 12,1984 and c ) 1 4 1 7 LAT S e p t e m b e r 1 3 , 1 9 8 3 82 W m ~ 2sr _ 1. The ran g e o f v a l u e s f o r t h i s h i s t o g r a m was 4-252 Wm~ 2sr _ 1, t h e h i g h e r v a l u e s c o r r e s p o n d i n g t o t h e b r i g h t l y r e f l e c t i n g c l o u d as w e l l as t h e s o l a r a u r e o l e . As a l m o s t 72% of t h e r a d i a n c e s were e s t i m a t e d t o be l e s s t h a n 32 Wm~ 2sr~', th e l a r g e r e g i o n of l e a s t r a d i a n t i n t e n s i t y i s c l e a r l y e v i d e n t . The mean r a d i a n c e v a l u e was 34.20 W m _ 2 s r _ 1 w i t h a s t a n d a r d d e v i a t i o n of 44.38 Wm~ 2sr~ 1. A t h i r d t y p e o f d i s t r i b u t i o n , o b t a i n e d on September 13, 1983 and d e p i c t e d i n F i g . 5.4c, i s t h a t of a p a r t l y c l o u d y sky w i t h a b o u t 5/10 o f cumulus c l o u d s . The mean v a l u e was 102.02 Wm~ 2sr~ 1 f o r t h i s example, w i t h a s t a n d a r d d e v i a t i o n o f 49.20 Wm~ 2sr~ 1. The d i s t r i b u t i o n was skewed s l i g h t l y t o t h e r i g h t (skewness=1. 1 0 ) . The range o f r a d i a n c e s i s s t i l l 250 Wm~ 2sr" 1 b u t t h e d i s t r i b u t i o n has s h i f t e d c o n s i d e r a b l y t o c l a s s e s o f h i g h e r r a d i a n c e . T h e s e h i s t o g r a m s i n d i c a t e t h e d i s t r i b u t i o n s w h i c h t h e r a d i a n c e s a s s o c i a t e d w i t h a c l e a r , o v e r c a s t o r p a r t l y c l o u d y sky may assume. The p r e s e n c e o f c l o u d and t h e r e s u l t a n t s c a t t e r i n g and r e f l e c t i o n , c a u s e s h i g h e r v a l u e s of d i f f u s e r a d i a n c e t o d o m i n a t e under t h e s e c o n d i t i o n s . 5.2 A p p l i c a t i o n As i n S t e v e n (1977) and M c A r t h u r ( 1 9 7 8 ) , t h e p r i m a r y method of p r e s e n t i n g t h e a n g u l a r d i s t r i b u t i o n o f d i f f u s e r a d i a t i o n a c r o s s t h e sky h e m i s p h e r e i s r a d i a n c e maps u s i n g p o l a r c o o r d i n a t e s . 5.3.1 C l e a r Sky C o n d i t i o n s 83 F i g . 5.5 r e p r e s e n t s an image o b t a i n e d on A u g u s t 21, 1983 ( z e n i t h a n g l e 40.4°) under c l e a r s k i e s . T h i s c o n t o u r e d p o l a r c o o r d i n a t e map ( n o t e t h a t t o o b t a i n t h e b e s t r e p r e s e n t a t i o n of r a d i a n c e o v e r t h e sky dome, i r r e g u l a r c o n t o u r i n g i n t e r v a l s have been used) i n d i c a t e s some of t h e p r i m a r y f e a t u r e s a s s o c i a t e d w i t h t h e a n g u l a r d i s t r i b u t i o n of d i f f u s e r a d i a n c e under s u c h c o n d i t i o n s . F i r s t l y , t h e maximum r a d i a n c e v a l u e i s l o c a t e d a d j a c e n t t o t h e Sun (150 W m " 2 s r - 1 ) and t h e r e i s a s t e e p g r a d i e n t o f i s o l i n e s w i t h an a l m o s t c i r c u l a r c o n f i g u r a t i o n i n t h i s r e g i o n . T h i s e f f e c t i s a r e s u l t o f s t r o n g f o r w a r d s c a t t e r i n g i n t h i s z o ne. T h e r e i s a g r a d u a l d e p a r t u r e away from t h i s c o h e r e n t p a t t e r n o f c o n t o u r l i n e s ( g r a d i e n t l e s s e n s ) as t h e a n g u l a r d i s t a n c e f r o m t h e Sun i n c r e a s e s , w i t h e v i d e n c e o f b r i g h t e n i n g on t h e upper and l o w e r h o r i z o n of t h e image. T h i s i s a r e s u l t of g r e a t e r s c a t t e r i n g o f s h o r t w a v e r a d i a t i o n w i t h an 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 . The minimum v a l u e o f r a d i a n c e ( a p p r o x i m a t e l y 10 W m ~ 2 s r _ 1 ) i s l o c a t e d i n t h e o p p o s i t e r e g i o n o f t h e sky f r o m t h e Sun and r a d i a n c e i n c r e a s e s from t h e r e t o t h e h o r i z o n . T r e e s , w h i c h r e f l e c t h i g h l y i n t h e n e a r - i n f r a r e d p a r t of t h e s p e c t r u m ( t o w h i c h t h e camera i s p a r t i c u l a r i l y s e n s i t i v e ) a r e l o c a t e d on t h e u p p e r , n o r t h e a s t e r n h o r i z o n and may be r e c o g n i z e d by t h e p r e s e n c e o f v a l u e s of a b o u t 30 Wm~ 2sr~ 1. A n o t h e r example o f a c l e a r sky d i s t r i b u t i o n i s g i v e n i n F i g . 5.6. T h i s image was o b t a i n e d on December 20, 1983 ( z e n i t h a n g l e 77°) and i s i n d i c a t i v e of t y p i c a l w i n t e r c l i m a t i c c o n d i t i o n s w i t h t h e Sun low on t h e h o r i z o n ( i n c o n t r a s t t o t h e F i g u r e 5.5 C l e a r Sky R a d i a n c e D i s t r i b u t i o n (Wm 2 s r " ' ) f o r 1320 LAT A u g u s t 21,1983 (z=40.4°) 85 F i g u r e 5.6 C l e a r Sky R a d i a n c e D i s t r i b u t i o n (Wm" 2sr ') f o r 1356 LAT December 20,1983 (z=77°) 86 p r e v i o u s example o b s e r v e d i n t h e summer). Once a g a i n , t h e r e g i o n of maximum r a d i a n t i n t e n s i t y i s c o i n c i d e n t w i t h t h e s o l a r a u r e o l e ( a b o u t 250 W m ~ 2 s r ~ 1 ) , a l t h o u g h i n t h i s c a s e t h e r e i s a zone of s a t u r a t i o n p r e s e n t ( i . e . t h e sky was b r i g h t e r t h a n t h e t h r e s h o l d o f t h e f r a m e s t o r e and so t h e v a l u e s have been ' c l i p p e d ' a t 2 5 0 ) . T h i s zone e x t e n d s f o r ab o u t 15° from t h e s o l a r d i s k . From t h e r e , t h e r e i s a s t e e p , smooth g r a d a t i o n o f i s o l i n e s b e n d i n g s l i g h t l y t o encompass t h e s o l a r d i s k . The f u l l e f f e c t of t h e c i r c u l a r p a t t e r n of c o n t o u r l i n e s a s p r e v i o u s l y n o t e d i s n o t e v i d e n t h e r e s i n c e t h e Sun i s so low on t h e h o r i z o n . The r e g i o n o f minimum i n t e n s i t y ( a b o u t 10 W m ~ 2 s r - 1 ) i s l o c a t e d a b o u t 90° away from t h e s o l a r d i s k w i t h t h e i s o l i n e s f o r m i n g a p a t t e r n a r o u n d t h i s p o i n t . From t h i s r e g i o n , t h e v a l u e s of r a d i a n c e i n c r e a s e out t o t h e h o r i z o n . A g a i n t h e m a j o r i t y of t h e sky c o r r e s p o n d s t o r a d i a n c e s l e s s t h a n 30 W m~ 2sr _ 1. Due t o t h e i n c r e a s e d s c a t t e r i n g a s s o c i a t e d w i t h a l a r g e o p t i c a l a i r m a s s , a h o r i z o n b r i g h t e n i n g e f f e c t c a n be n o t e d a l o n g t h e h o r i z o n . 5.2.2 O v e r c a s t Sky C o n d i t i o n s The o p p o s i t e e xtreme from an c o m p l e t e l y c l o u d l e s s s ky i s t h a t o f an o v e r c a s t s k y . F i g s . 5.7, 5.8, 5.9, 5.10 and 5.11 r e p r e s e n t s u c h a c o n d i t o n as v i e w e d on J a n u a r y 20, 1984. Th e s e images were o b t a i n e d o v e r a 3 hour p e r i o d and i l l u s t r a t e t h e sequence o f c h a n g i n g c l o u d p a t t e r n s u n t i l a d e n s e , s t r a t i f o r m c l o u d l a y e r f i n a l l y d o m i n a t e d t h e f i e l d - o f - v i e w . The f i r s t image, F i g . 5.7, was o b t a i n e d under 2 l a y e r s o f 87 88 a l t o c u m u l u s w i t h an upper l e v e l of 2/10 c i r r u s c l o u d and t h e i s o l i n e s formed a p a t t e r n r e m i n i s c e n t of t h a t of a c l e a r s k y . The maximum r a d i a n c e ( a b o u t 150 W m _ 2 s r ~ 1 ) was f o u n d i n t h e r e g i o n of t h e Sun ( s o l a r z e n i t h a n g l e was 75.1°) w h i c h , a l t h o u g h o b s c u r e d by c l o u d , s t i l l e x e r t e d an i n f l u e n c e r e s u l t i n g f r o m i n t e n s e f o r w a r d s c a t t e r i n g i n t h i s a r e a . T h e r e was an e l l i p t i c a l c o n f i g u r a t i o n of i s o l i n e s w i t h a g e n t l e g r a d i e n t i n t h e s o l a r a u r e o l e r e g i o n , g r a d u a l l y d i s b a n d i n g t o form a c o n c e n t r i c p a t t e r n a r o u n d t h e r e g i o n of minimum i n t e n s i t y ( a b o u t 10 Wm~ 2sr~ 1) a p p r o x i m a t e l y 90° away from t h e Sun. Once a g a i n , v a l u e s of r a d i a n c e t e n d e d t o i n c r e a s e f r o m t h i s a r e a o u t t o t h e h o r i z o n . A l t h o u g h s i m i l a r t o a c l e a r sky p a t t e r n , t h e major d i f f e r e n c e between t h i s d i s t r i b u t i o n a nd t h a t of a c l e a r sky c a s e was t h a t t h e g r a d i e n t s a r e n e v e r a s s t e e p . In f a c t , a t an a n g u l a r d i s t a n c e of a p p r o x i m a t e l y 50° from t h e Sun e x t e n d i n g t o t h e f a r h o r i z o n , t h e sky was of v e r y low c o n t r a s t w i t h a ra n g e of o n l y 40 Wm" 2sr" 1. A n o t i c e a b l e h o r i z o n b r i g h t e n i n g e f f e c t r e s u l t i n g from i n c r e a s e d s c a t t e r i n g was p r e s e n t on t h e h o r i z o n . Twenty m i n u t e s l a t e r , ( F i g . 5.8) more c i r r u s c l o u d had moved a c r o s s t h e s k y e s p e c i a l l y i n t h e s o l a r d i s k r e g i o n ( s o l a r z e n i t h a n g l e was 7 4 . 4 ° ) . T h i s was e v i d e n c e d by t h e more c o n v o l u t e d p a t t e r n o f t h e i s o l i n e s w h i c h c o n f o r m t o t h e p a t t e r n of c l o u d s l o c a t e d n e a r t h e Sun. The maximum r a d i a n c e (150 Wm~ 2sr~ 1) was s t i l l l o c a t e d n e a r t h e Sun but t h e g r a d i e n t and form of t h e i s o l i n e s i n t h i s r e g i o n had a l t e r e d . R e f l e c t i o n o f v i s i b l e r a d i a t o n o f f of t h e c l o u d s r e s u l t e d i n a r e a s o f h i g h e r F i g u r e 5.8 O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n (Wm 2 s r 1) f o r 1033 LAT J a n u a r y 20,1984 (z=74.4°) 90 r a d i a n c e ( a b o u t 130 Wm" 2sr" 1) th a n would be p r e s e n t i n t h e a b s e n c e o f c l o u d . T h e r e was a g r a d u a l d e c r e a s e i n r a d i a n c e away from t h e Sun, a c r o s s t h e sky t o t h e o p p o s i t e h o r i z o n . I t i s n o t e w o r t h y t h a t t h e r e was no p a r t i c u l a r r e g i o n of minimum r a d i a n c e w i t h no c o r r e s p o n d i n g i n c r e a s e i n r a d i a n c e from t h e r e out t o t h e h o r i z o n . A t t e n u a t i o n by c l o u d and more s c a t t e r i n g a s s o c i a t e d w i t h l o n g e r o p t i c a l p a t h l e n g t h s r e s u l t e d i n t h e lowe r r a d i a n c e s a t t h e h o r i z o n w i t h h i g h e r v a l u e s f o u n d n e a r t h e z e n i t h o r Sun. H o r i z o n b r i g h t e n i n g e f f e c t s a r e not e v i d e n t on t h i s image. In t h e f o l l o w i n g m i n u t e s , s t i l l more c l o u d b u i l d u p had t a k e n p l a c e ( t h e amount of a l t o c u m u l u s was c o n t i n u a l l y i n c r e a s i n g ) a s e v i d e n c e d by F i g . 5.9 and as a r e s u l t t h e r a d i a n c e p a t t e r n had ch a n g e d once a g a i n . T h e r e was s t i l l a maximum (150 Wm" 2sr" 1) a t t h e s o l a r d i s k ( z e n i t h a n g l e of 74.2°) and f r o m t h e r e t h e i s o l i n e s f o l l o w e d t h e f o r m of t h e c l o u d s w i t h a s t e e p g r a d i e n t between them. The c l o u d s n e a r t h e Sun were r e f l e c t i n g t h e r a d i a t i o n and t h e b r i g h t e r p o r t i o n s of t h e s e c l o u d s c o r r e s p o n d e d t o t h e h i g h e r r a d i a n c e s . From t h e s o l a r r e g i o n , r a d i a n c e d e c r e a s e d ( w i t h an even l e s s s t e e p g r a d i e n t t h a n p r e v i o u s l y ) t o minimum v a l u e s of a b o u t 30 Wm" 2sr" 1 a t t h e o p p o s i t e r e g i o n o f t h e s k y . The p a t t e r n o f c o n t o u r s i n t h e n o r t h e a s t e r n p o r t i o n o f t h e image was o b v i o u s l y i n f l u e n c e d by t h e p r e s e n c e of c l o u d r e s u l t i n g i n s l i g h t l y h i g h e r t h a n e x p e c t e d r a d i a n c e s . The s c a t t e r i n g e f f e c t s of water d r o p l e t s r e s u l t e d i n h i g h e r v a l u e s of d i f f u s e r a d i a n c e as can be e v i d e n c e d by a c o m p a r i s o n o f r a d i a n c e v a l u e s f o r c l e a r 91 92 s k i e s i n t h e r e g i o n of low e r i n t e n s i t y ( i . e . upper p o r t i o n o f th e image) w i t h t h o s e o f a c l o u d y s k y . The d i s t r i b u t i o n o f sky r a d i a n c e i n c r e a s e s i n c o m p l e x i t y w i t h t h e p r e s e n c e of c l o u d s due t o s c a t t e r i n g and r e f l e c t i o n by t h e c l o u d s . E v e n t u a l l y , by 1320 LAT, 8/10 o f a l t o c u m u l u s c l o u d and 2/10 c i r r o s t r a t u s c o v e r formed o v e r t h e sky ( F i g . 5.10) and t h e a n g u l a r d i s t r i b u t i o n of r a d i a n c e no l o n g e r had any r e s e m b l a n c e t o t h e p r e v i o u s p a t t e r n s . The r e g i o n of h i g h e s t i n t e n s i t y was l o c a t e d a t t h e z e n i t h w i t h a g r a d u a l d e c r e a s e i n r a d i a n c e from t h e r e t o the. h o r i z o n . T h i s d i s t r i b u t i o n of r a d i a n c e s r e s u l t s from t h e g r e a t e r a t t e n u a t i o n o f r a d i a t i o n by c l o u d a t l o n g e r o p t i c a l p a t h l e n g t h s a t t h e h o r i z o n , w h i l e l e s s a t t e n u a t i o n o f the s o l a r beam o c c u r s a t t h e z e n i t h . The ran g e of v a l u e s was much l e s s t h a n p r e v i o u s l y ; now o n l y between 10-32 Wm~ 2sr _ 1. The s o l a r p o s i t i o n was n o t e v i d e n t under t h e s e c o n d i t i o n s . T h i s d i s t r i b u t i o n became even more s i m p l i f i e d a s t h e o p t i c a l d e p t h of t h e c l o u d i n c r e a s e d ( F i g . 5.11). The c l o u d c o v e r by 1340 LAT was c h a n g i n g t o 2 l a y e r s (1/10 and 4/10 r e s p e c t i v e l y ) of a l t o c u m u l u s and 5/10 of a l t o s t r a t u s . The range o f r a d i a n c e d e c r e a s e d t o between 10-20 Wm - 2sr~ 1 w i t h t h e l a r g e s t v a l u e s b e i n g a t t h e z e n i t h o f t h e sky ( t h e Sun, of c o u r s e , was c o m p l e t e l y o b s c u r e d ) . T h e r e was a c o n s t a n t d e c r e a s e i n r a d i a n c e o u t w a r d s t o t h e h o r i z o n as i n t h e above c a s e . F o r t h i s t y p e o f c l o u d c o v e r , t h e i s o t r o p i c a s s u m p t i o n i s a r e a s o n a b l e a p p r o x i m a t i o n t o r e a l s ky c o n d i t i o n s . As t h e c l o u d s became t h i c k e r a nd formed a more c o n t i n u o u s c o v e r , t h e i r s i d e s and b a s e s d i m i n i s h e d i n i m p o r t a n c e and most of t h e l i g h t ure 5.10 O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n (Wm 2 s r _ 1 ) f o r 1320 LAT J a n u a r y 20,1984 ( 2 = 7 2 . 5 ° ) 9 4 F i g u r e 5.11 O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n (Wm" 2sr~') f o r 1340 LAT J a n u a r y 20,1984 (z=73.8°) 95 was s c a t t e r e d o f f t h e t o p of t h e c l o u d (McKee and Cox, 1974) r e s u l t i n g i n t h e low range of r a d i a n c e s as w e l l a s t h e even g r a d a t i o n of e n e r g y l e v e l s ; a s m a l l e r p o r t i o n o f t h e r a d i a n t e n e r g y was b e i n g t r a n s m i t t e d . B o t h F i g s . 5.10 and 5.11 show symmetry a b o u t t h e z e n i t h . 5.3.3 P a r t l y C l o u d y Sky C o n d i t i o n s In t h e p a r t l y c l o u d y sky c o n d i t i o n , t h e p r e s e n c e of c l o u d r e s u l t s i n an i r r e g u l a r d i s t r i b u t i o n of d i f f u s e s o l a r r a d i a t i o n o v e r t h e sky h e m i s p h e r e . The e x t e n t of t h i s c o m p l e x i t y i s a f u n c t i o n of t h e amount of c l o u d and i t s l o c a t i o n w i t h r e s p e c t t o t h e Sun. The f i r s t example of s u c h a s k y ( F i g . 5.12) was o b t a i n e d on J a n u a r y 12, 1984 ( z e n i t h a n g l e 8 0 . 5 ° ) ; a g a i n , d u r i n g t h e w i n t e r , w i t h t h e Sun low on t h e h o r i z o n . The c l o u d c o v e r c h a r a c t e r i s t i c s f o r t h i s image was 1/10 s t r a t o f r a c t u s , 1/10 cumulus and 1/10 c i r r u s . The maximum r a d i a n c e v a l u e (230-250 Wm~ 2sr~ 1) was c o i n c i d e n t w i t h t h e l o c a t i o n o f t h e s o l a r d i s k and t h e i n t e n s i t y r a p i d l y d e c r e a s e d w i t h a n g u l a r d i s t a n c e away from t h e Sun. A l t h o u g h t h e i s o l i n e s g e n e r a l l y c u r v e t o w a r d s t h e a u r e o l e r e g i o n , t h e y t e n d t o be c o n t o r t e d where c i r r u s c l o u d s were p r e s e n t . The l i g h t r e f l e c t i n g a nd s c a t t e r i n g o f f t h e edges o r s i d e s of t h e s e c l o u d s n e a r t h e Sun r e s u l t e d i n h i g h e r r a d i a n c e s a t t h e s e p o i n t s . The s i d e s o f t h e c l o u d s were a p p a r e n t f r o m t h e s t e e p g r a d i e n t s o f t h e i s o l i n e s ; t h e g r a d i e n t l e s s e n s a s t h e c l o u d d i s s i p a t e s . The a r e a o f minimum i n t e n s i t y ( a b o u t 14 Wm" 2sr" 1) was l o c a t e d a b o u t 90° from t h e s o l a r d i s k F i g u r e 5.12 P a r t l y C l o u d y Sky R a d i a n c e D i s t r i b u t i o n ( W m " 2 s r _ 1 ) f o r 1449 LAT J a n u a r y 12,1984 (z=80.5°) 97 and a s i n t h e c l e a r sky c a s e , r a d i a n c e i n c r e a s e d from t h e r e out t o t h e h o r i z o n . In g e n e r a l , t h e c o n t o u r s i n t h i s image a p p e a r more c o n v o l u t e d t h a n i n p r e v i o u s c a s e s , i n d i c a t i n g t h a t t h e p r e s e n c e o f c l o u d r e s u l t s i n s c a t t e r i n g by water o r i c e d r o p l e t s w h i c h r e s u l t s i n v a r i a t i o n s of t h e d i s t r i b u t i o n of d i f f u s e r a d i a n c e . Some h o r i z o n b r i g h t e n i n g a t t h e edges of t h e image due t o t h e g r e a t e r s c a t t e r i n g a i r m a s s c a n be n o t e d . A s i m i l a r p a t t e r n of sky r a d i a n c e was o b s e r v e d on two o c c a s i o n s on F e b r u a r y 3, 1984 ( F i g . 5.13 and 5.14). F o r t h e f i r s t example, t h e r e was some low l e v e l cumulus f r a c t u s and 2/10 c i r r u s c l o u d s were p r e s e n t n e a r t h e Sun. T h i s c l o u d amount r e s u l t e d i n t h e d e f o r m a t i o n o f t h e i s o l i n e s i n t h i s a r e a . The maximum r a d i a n c e ( a b o u t 250 W m " 2 s r _ 1 ) c o i n c i d e d w i t h t h e Sun wh i c h was v i s i b l e i n b o t h e x a m p l e s . Once a g a i n , t h e i s o l i n e s form a s t e e p g r a d i e n t c u r v i n g i n t o d e l i m i t t h e s o l a r a u r e o l e and t h e n a t an a n g u l a r d i s t a n c e of a p p r o x i m a t e l y 60° from t h e Sun t h e g r a d i e n t s h a r p l y d e c r e a s e s and r a d i a n c e v a l u e s g r a d u a l l y l e s s e n f r o m t h a t p o i n t t o w a r d s t h e o p p o s i t e h o r i z o n . However, t h e r a d i a n c e v a l u e s i n c r e a s e a g a i n n e a r t h e h o r i z o n . F i g . 5.14 has a s l i g h t l y more complex d i s t r i b u t i o n s i n c e t h e p r e s e n c e of c l o u d ( s t r a t o c u m u l u s and c i r r u s ) i n t h e r e g i o n of th e s o l a r d i s k r e s u l t e d i n i n c r e a s e d s c a t t e r i n g and r e f l e c t a n c e of l i g h t a nd hence, s l i g h t l y h i g h e r r a d i a n c e s . C i r r u s c l o u d l o c a t e d on t h e upper h o r i z o n of b o t h F i g . 5.13 and 5.14 c o r r e s p o n d s t o v a l u e s of r a d i a n c e f r o m 35 t o 50 Wm" 2sr" 1, r e s p e c t i v e l y . The p r e s e n c e of t h e h i g h , t h i n i c e c l o u d s ( i . e . c i r r u s ) c a n 98 F i g u r e 5 . 1 3 P a r t l y C l o u d y Sky R a d i a n c e D i s t r i b u t i o n ( W I T T 2 s r " ' ) f o r 1 1 1 6 L A T F e b r u a r y 3 , 1 9 8 4 ( z = 7 5 . 9 ° ) F i g u r e 5.14 P a r t l y C l o u d y Sky R a d i a n c e D i s t r i b u t i o n (Wm~ 2sr~ 1) f o r 1148 LAT F e b r u a r y 3,1984 (z=72.7°) 100 s t i l l p e r m i t t h e t r a n s f e r of v i s i b l e r a d i a t i o n w i t h o u t a s u b s t a n t i a l d e p a r t u r e from t h e t y p i c a l c l e a r sky d i s t r i b u t i o n o f r a d i a n c e . T h i s i s e x e m p l i f i e d by F i g s . 5.7-5.9. The t h i c k e r t h e c l o u d e l e m e n t s , t h e g r e a t e r t h e s c a t t e r i n g and hence, t h e g r e a t e r t h e v a r i a t i o n i n t h e r a d i a n c e p a t t e r n . F i g . 5.15 r e p r e s e n t s sky c o n d i t i o n s as o b s e r v e d on December 5, 1983. F o r t h i s c a s e t h e c l o u d c o v e r was a b o u t 7/10 a l t o c u m u l u s . As i n p r e v i o u s e x amples, t h e maximum r a d i a n c e (190 Wm~ 2sr~ 1) o c c u r r e d a t t h e l o c a t i o n of t h e Sun, w i t h s t e e p l y d i p p i n g i s o l i n e s f o r m i n g a s l i g h t l y c o n t o r t e d p a t t e r n e n c l o s i n g t h i s r e g i o n . The d e f o r m a t i o n i n c o n t o u r s c o r r e s p o n d s w i t h i r r e g u l a r s c a t t e r i n g p a t t e r n s w h i c h a r e a f u n c t i o n of c h a n g e s i n t h e d e n s i t y o f t h e c l o u d . V a r i a t i o n s i n r a d i a n t i n t e n s i t i e s c o r r e s p o n d t o t h e s e c h a n g e s i n c l o u d d e n s i t y , w i t h h i g h e r v a l u e s of r a d i a n c e r e l a t i n g t o g r e a t e r d e n s i t i e s . The ma g n i t u d e of t h e p r e d i c t e d v a l u e s d e c r e a s e d w i t h i n c r e a s i n g a n g u l a r d i s t a n c e from t h e Sun. The a l t o c u m u l u s c o v e r c a u s e d uneven s c a t t e r i n g a t d i f f e r e n t r e g i o n s of t h e sky and r e s u l t e d i n g e n e r a l l y h i g h e r v a l u e s of d i f f u s e r a d i a t i o n a c r o s s t h e image as compared t o a c l e a r sky c a s e . The minimum v a l u e s ( l e s s t h a n 30 W m - 2 s r _ 1 ) were f o u n d i n t h e n o r t h w e s t e r n p o r t i o n o f t h e s k y . A h o r i z o n b r i g h t e n i n g e f f e c t r e s u l t i n g from an i n c r e a s e i n s c a t t e r i n g mass i s most c l e a r l y e v i d e n t i n F i g . 5.15. The a n g u l a r d i s t r i b u t i o n of d i f f u s e s o l a r r a d i a t i o n becomes most complex i n t h e c a s e o f a c l e a r sky s u p e r i m p o s e d w i t h s t r o n g l y r e f l e c t i n g cumulus c l o u d s . T h i s c o n d i t i o n i s F i g u r e 5.15 P a r t l y C l o u d y Sky R a d i a n c e D i s t r i b u t i o n ( W m " 2 s r " M f o r 1246 LAT December 5,1983 ( Z = 71 .7°) 1 02 complex f o r two main r e a s o n s : Othe s c a t t e r i n g p r o p e r t i e s of d i s t i n c t c l o u d e l e m e n t s p r e s e n t i n an o t h e r w i s e c l e a r s k y ; and 2) b e c a u s e of t h e manner i n w h i c h t h e v i d e o s y s t e m u s e d i n t h i s s t u d y r e s p o n d s t o t h e b l u e sky on t h e one hand, and t h e b r i g h t c l o u d s on t h e o t h e r . The c l o u d s i d e s a r e h i g h l y r e f l e c t i v e and hence, a p p e a r v e r y b r i g h t . I t was d i f f i c u l t t o a d j u s t t h e v i d e o s y s t e m t o a v o i d s a t u r a t i o n i n t h e r e g i o n where t h e c l o u d e l e m e n t s were l o c a t e d , and a t t h e same t i m e , n o t t o l o s e t o o much i n f o r m a t i o n r e g a r d i n g t h e c l o u d l e s s sky ( i . e . where i t had v e r y low c o n t r a s t ) . F i g . 5.16 i l l u s t r a t e s t h e c o m p l e x i t y o f th e r a d i a n c e d i s t r i b u t i o n under s u c h sky c o n d i t i o n s . F o r t h i s example, t h e h i g h e s t p r e d i c t e d r a d i a n c e (250 Wm~ 2sr~ 1) c o i n c i d e d , as i n o t h e r c a s e s , w i t h t h e l o c a t i o n of t h e Sun. However, t h e r e was not a c o n s t a n t d e c r e a s e i n v a l u e s f r o m t h a t p o i n t . I n d e e d , i f one s t u d i e s t h e d i s t r i b u t i o n c a r e f u l l y , t h e r e were many p o i n t s w h i c h show v a l u e s of 130-160 Wm~ 2sr~ 1. The s e l o c a t i o n s c o i n c i d e d w i t h t h e s i d e s and some b a s e s o f t h e cumulus c l o u d s w h i c h p l a y an i m p o r t a n t r o l e i n d i r e c t i o n a l r e f l e c t a n c e and s c a t t e r i n g of l i g h t . The i s o l i n e s d e l i n e a t i n g t h e c l o u d e l e m e n t s had s t e e p g r a d i e n t s c o n f o r m i n g t o t h e r a p i d change i n r a d i a n c e a l o n g a s i d e o f a c l o u d . T h e r e i s no c o h e r e n t p a t t e r n o f r a d i a n c e i n t h i s example. I n s t e a d , t h e r a d i a n c e i s a f u n c t i o n o f t h e amount o f s c a t t e r i n g o f water d r o p l e t s c o i n c i d e n t w i t h t h e c l o u d . Where t h e r e was no c l o u d p r e s e n t , t h e i s o l i n e s c o n f o r m e d t o t h e i r u s u a l p a t t e r n o f d e c r e a s i n g r a d i a n c e away from t h e Sun w i t h an even g r a d a t i o n of v a l u e s . The minimum v a l u e of p r e d i c t e d r a d i a n c e under t h e s e 103 F i g u r e 5 .16 P a r t l y C l o u d y Sky R a d i a n c e D i s t r i b u t i o n ( W m " 2 s r _ 1 ) f o r 1417 LAT September 13, 1983 (z=50.8°) 1 04 c o n d i t i o n s was 70 Wm~ 2sr~ 1 and t h i s was f o u n d a l o n g t h e n o r t h e r n h o r i z o n . No h o r i z o n b r i g h t e n i n g e f f e c t was f o u n d f o r t h i s t y p e of sky c o v e r s i n c e t h e p r e s e n c e of c l o u d e l e m e n t s masked t h e s c a t t e r i n g e f f e c t of a t m o s p h e r i c p a r t i c l e s a t l a r g e z e n i t h a n g l e s 5.4 C o m p a r i s o n of R e s u l t s w i t h P r e v i o u s S t u d i e s 5.4.1 C l e a r Sky R a d i a n c e D i s t r i b u t i o n s The c l e a r sky r e s u l t s p r e s e n t e d i n t h i s s t u d y c o r r e s p o n d w e l l w i t h t h e r e s u l t s of p r e v i o u s r e s e a r c h . G h a z i (1971) d e v e l o p e d a s p e c t r o p h o t o m e t e r d e s i g n e d t o s t u d y t h e s p e c t r a l d i s t r i b u t i o n of s k y l i g h t i n t h e u l t r a v i o l e t and v i s i b l e r e g i o n s o f t h e s o l a r s p e c t r u m . H i s r e s u l t s f o r a c l o u d l e s s day, p r e s e n t e d i n t h e form of a r a d i a n c e map, showed a s y m m e t r i c a l d i s t r i b u t i o n w i t h t h e s c a t t e r i n g g r a d i e n t p e a k i n g a l o n g t h e s o l a r v e r t i c a l . The maximum r a d i a n c e was l o c a t e d a t t h e s o l a r p o i n t and t h e r e g i o n o f minimum i n t e n s i t y l a y a p p r o x i m a t e l y 90° away from t h e Sun. S a s t r i and Manamohanan (1975) u t i l i z e d a s k y - s c a n n i n g t e l e p h o t o p h o t o m e t e r t o r e c o r d l u m i n a n c e c h a n g e s a t d i f f e r e n t p o s i t i o n s a c r o s s t h e sky h e m i s p h e r e . T h e i r r e s u l t s , p r e s e n t e d as e q u i - l u m i n a n c e maps w i t h e q u i - l u m i n a n c e c o n t o u r s on p o l a r d i a g r a m s a p p e a r i n F i g s . 5.17a and 5.17b. T h e i r l u m i n a n c e maps i l l u s t r a t e d t h a t t h e c o n t o u r s were r o u g h l y s y m m e t r i c a l a b o u t t h e s o l a r v e r t i c a l (a l i n e o f c o n s t a n t a z i m u t h t h r o u g h t h e s o l a r p o s i t i o n ) w i t h t h e s t e e p e s t g r a d i e n t o f i s o l i n e s c o n f o r m i n g t o an e l l i p t i c a l p a t t e r n a r o u n d t h e Sun and a d e c r e a s e i n l u m i n a n c e w i t h 105 F i g u r e 5.17 C l e a r Sky L u m i n a n c e D i s t r i b u t i o n s f o r a ) Z e n i t h " A n g l e 70° and b ) Z e n i t h A n g l e 50°. From S a s t r i and Manamohanan (1975) 106 i n c r e a s i n g a n g u l a r d i s t a n c e away from t h e sun. In t h e p r e s e n t s t u d y , F i g . 5.5 p r e s e n t s a c l e a r sky r a d i a n c e d i s t r i b u t i o n w h i c h does not seem t o c o n f o r m t o t h e n o t i o n o f symmetry a b o u t t h e s o l a r v e r t i c a l . T h i s c o u l d be a r e s u l t of t h e p r e s e n c e of unseen c i r r u s o r a e r o s o l p a r t i c l e s i n t h e a t m o s p h e r e a t t h e t i m e of o b s e r v a t i o n . T h e s e f e a t u r e s c o u l d r e s u l t i n a p a r t i c u l a r s c a t t e r i n g r e g i m e t h a t c a u s e s a d e p a r t u r e from t h e e x p e c t e d symmetry a b o u t t h e s o l a r v e r t i c a l . F i g . 5.6, r e p r e s e n t a t i v e of a w i n t e r t i m e c l e a r sky w i t h l o w e r s o l a r a l t i t u d e , does a p p e a r t o e x h i b i t s u c h symmetry as d e s c r i b e d by G h a z i (1971) and S a s t r i and Manamohanan ( 1 9 7 5 ) . The r e g i o n o f minimum b r i g h t n e s s ( i n F i g s . 5.17a and b) was a p p r o x i m a t e l y 90° away from t h e s o l a r d i s k and v a l u e s t e n d e d t o i n c r e a s e from t h e r e t o t h e h o r i z o n . S a s t r i and Manamohanan (1975) n o t e t h a t f o r l a r g e s o l a r z e n i t h a n g l e s , t h e i s o l i n e s b o u n d i n g t h e a r e a of l e a s t r a d i a n t i n t e n s i t y encompassed t h e c e n t r e of t h e l u m i n a n c e map. S t a n d a r d d i s t r i b u t i o n s of n o r m a l i z e d c l e a r sky r a d i a n c e f o r z e n i t h a n g l e s of 35° and 55° have been p r e s e n t e d by S t e v e n (1977) and a r e shown i n F i g s . 5.18a and 5.18b. As a r e s u l t of t h e n o r m a l i z a t i o n and a v e r a g i n g p r o c e d u r e s u s e d t o p r o d u c e t h e s e r a d i a n c e maps, t h e y r e p r e s e n t 'smoothed' v e r s i o n s of c l e a r sky r a d i a n c e d i s t r i b u t i o n s . T h e s e maps show t h e p o s i t i o n o f t h e Sun ( i . e . t h e maximum r a d i a n c e v a l u e ) and i l l u s t r a t e t h e p a t t e r n of d e c r e a s i n g r a d i a n c e w i t h i n c r e a s i n g a n g u l a r d i s t a n c e away from t h a t p o i n t . The r e g i o n o f minimum r a d i a n c e l i e s a p p o x i m a t e l y 90° away from t h e s o l a r d i s k and t h e i s o l i n e s form 1 07 (b) F i g u r e 5.18 S t a n d a r d D i s t r i b u t i o n of N o r m a l i z e d C l e a r Sky R a d i a n c e f o r a ) Z e n i t h A n g l e 35° and b ) Z e n i t h A n g l e 55° From S t e v e n ( 1 977 ) 108 a p a t t e r n , e n c o m p a s s i n g t h i s a r e a . F i g . 5.18b c o r r e s p o n d s t o a l a r g e r s o l a r z e n i t h a n g l e and t h e i n c r e a s e d s c a t t e r i n g mass r e s u l t s i n an i n c r e a s e d h o r i z o n b r i g h t e n i n g e f f e c t . T h i s c o r r e s p o n d s t o t h e e a r l i e r f i n d i n g s o f S a s t r i and Manamohanan (1975) as w e l l as t h e r e s u l t s o f t h i s s t u d y . As e x p e c t e d , t h e r a d i a n c e d i s t r i b u t i o n s of S t e v e n (1977) a r e a l s o s y m m e t r i c a l a b o u t t h e s o l a r v e r t i c a l . The a n g u l a r d i s t r i b u t i o n of c l e a r sky r a d i a n c e was a l s o measured by V a l k o ( 1 9 8 0 ) . The maximum r a d i a n c e c o i n c i d e n t w i t h t h e Sun was bounded by i s o l i n e s , and from t h e r e t h e i s o l i n e s r a p i d l y d e c r e a s e d i n v a l u e u n t i l t h e minimum a t an a n g u l a r d i s t a n c e of 90° away from t h e Sun. V a l k o f o u n d t h a t f o r d i f f e r e n t s u r f a c e e x p o s u r e s ( i . e . v e r t i c a l or h o r i z o n t a l ) t h e d i f f u s e i r r a d i a n c e s may d i f f e r by a f a c t o r o f 4 as a r e s u l t o f t h e s t r o n g a n i s o t r o p y o f sky r a d i a n c e . F o r some of h i s examples, h i g h g r o u n d r e f l e c t i o n was t h o u g h t t o have c a u s e d h i g h e r r a d i a n c e v a l u e s n e a r t h e h o r i z o n . G r o u n d r e f l e c t i o n was no t s u s p e c t e d t o be i m p o r t a n t i n t h e p r e s e n t s t u d y , g i v e n t h e s u r f a c e c h a r a c t e r i s t i c s o f t h e measurement s i t e . Dave (1981) p r e s e n t e d a m o d e l l e d r a d i a n c e map f o r a c l o u d l e s s s k y w h i c h d e p i c t e d t h e p r e s e n c e o f a s t r o n g a u r e o l e r e g i o n a r o u n d t h e Sun i n w h i c h r a d i a n c e c h a n g e d by a f a c t o r o f ab o u t 10 w i t h a 30° change i n z e n i t h a n g l e . As i n t h e o t h e r c a s e s , t h e r e g i o n of minimum and s l o w l y v a r y i n g r a d i a n c e was f o u n d a t a p p r o x i m a t e l y 90° from t h e Sun. C l e a r sky n o r m a l i z e d d i f f u s e r a d i a n c e d i s t r i b u t i o n s were g i v e n by M c A r t h u r and Hay (1981) and a r e d e p i c t e d i n F i g . 5.19. 1 0 9 F i g u r e 5.19 C l e a r Sky N o r m a l i z e d R a d i a n c e D i s t r i b u t i o n s ( s r - 1 ) f o r a ) l 2 4 0 LAT F e b r u a r y 10,1978; b ) l 3 4 0 LAT F e b r u a r y 10,1978; c ) l 3 2 6 LAT F e b r u a r y 26,1978; d ) l 3 4 7 LAT F e b r u a r y 26,1978. From M c A r t h u r and Hay (1981 ) 1 10 T h e s e maps show c l o s e s i m i l a r i t y t o t h o s e p r o d u c e d u s i n g t h e v i d e o - b a s e d i m a g i n g t e c h n i q u e . From F i g u r e 5.19, i t i s a p p a r e n t t h a t t h e m a g n i t u d e of r a d i a n c e n e a r t h e Sun i n c r e a s e s w i t h s o l a r z e n i t h a n g l e . M c A r t h u r and Hay (1981) s t a t e t h a t t h e i n c r e a s e i n s c a t t e r i n g mass and t h e s t r o n g f o r w a r d s c a t t e r i n g c h a r a c t e r i s t i c s a b o u t t h e s o l a r d i s k a r e t h e r e a s o n s f o r t h i s phenomenon. The i s o l i n e s t h e n change t o encompass t h e r e g i o n of l e a s t r a d i a n t i n t e n s i t y w i t h i n c r e a s i n g a n g u l a r d i s t a n c e from t h e Sun. F o r l a r g e r s o l a r z e n i t h a n g l e s , t h e p a t t e r n of i s o l i n e s becomes more complex, w i t h t h e i s o l i n e s c l o s e s t t o t h e Sun becoming d i s c o n t i n u o u s (as t h e Sun i s l o w e r on t h e h o r i z o n ) and b e i n g i n f l u e n c e d more s t r o n g l y by h o r i z o n b r i g h t e n i n g ( M c A r t h u r and Hay, 1981). T h i s can be s e e n a l s o i n F i g . 5.6. Hence, as t h e s o l a r z e n i t h a n g l e i n c r e a s e s , t h e d i f f u s e r a d i a t i o n e m a n a t i n g from t h e h o r i z o n r e g i o n becomes an i n c r e a s i n g l y s i g n i f i c a n t p e r c e n t a g e o f t h e d i f f u s e i r r a d i a n c e ( M c A r t h u r and Hay, 1981). T h e s e examples of c l e a r sky d i s t r i b u t i o n s of d i f f u s e s o l a r r a d i a t i o n show good agreement w i t h t h o s e r e s u l t s p r o d u c e d i n t h i s s t u d y . However, t h e l a t t e r have t h e a d v a n t a g e of b e i n g i n s t a n t a n e o u s v a l u e s of sky r a d i a n c e from a d i g i t a l d a t a base e n c o m p a s s i n g t h e e n t i r e sky h e m i s p h e r e and as a r e s u l t p r o v i d e g r e a t e r d e t a i l and a c c u r a c y t h a n p r e v i o u s r e s u l t s . U n f o r t u n a t e l y , i t was n o t p o s s i b l e t o compare t h e m a g n i t u d e of t h e r a d i a n c e s o b s e r v e d i n t h e M c A r t h u r and Hay (1981) s t u d y w i t h t h o s e o b s e r v e d d u r i n g t h i s . s t u d y , s i n c e i n b o t h c a s e s , 111 t h e r e was n o t enough d a t a t o d e r i v e s t a t i s t i c a l l y s i g n i f i c a n t c o n c l u s i o n s ( o r s t a n d a r d d i s t r i b u t i o n s ) and more o b v i o u s l y , t h e sky c o n d i t i o n s were not t h e same. 5.4.2 O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n s G r a c e (1971) measured r a d i a n c e under n a t u r a l and c o n t r o l l e d e n v i r o n m e n t s ( i . e . he u s e d an e n v i r o n m e n t chamber) on d a y s w i t h o v e r c a s t s k i e s . H i s r e s u l t s showed t h a t t h e mean p a t t e r n o f r a d i a n c e c o r r e s p o n d e d t o t h e S t a n d a r d O v e r c a s t Sky (SOC) f o r m u l a ( i . e . t h e d i s t r i b u t i o n of b r i g h t n e s s ) of Moon and S p e n c e r (1942) w i t h t h e h i g h e s t r a d i a n t i n t e n s i t y l o c a t e d a t t h e z e n i t h and r a d i a n c e d e c r e a s i n g f r o m t h e r e o u t t o t h e h o r i z o n . The e m p i r i c a l f o r m u l a r e f e r r e d t o as t h e SOC f o r m u l a i s g i v e n by: L a = 1/3L ( 1 + 2 s i n 0 ) (5.10) u Z where L„ i s t h e b r i g h t n e s s a t any a n g l e 6 above t h e h o r i z o n ; L u Z i s t h e b r i g h t n e s s a t t h e z e n i t h ( G r a c e , 1971). He a l s o n o t e d t h a t i n s t a n t a n e o u s r a d i a n c e d i s t r i b u t i o n s were h i g h l y v a r i a b l e under s u c h s k i e s . T h i s was s t u d i e d f u r t h e r by S a s t r i and Manamohanan (1975) who a t t e m p t e d t o v e r i f y t h e agreement between t h e l u m i n a n c e d i s t r i b u t i o n o f t h e i n d i v i d u a l o v e r c a s t sky and t h e SOC f o r m u l a . They f o u n d good agreement f o r v e r y t h i c k c l o u d and dense f o g g y c o n d i t i o n s . S t e v e n and U n s w o r t h (1980) d e s c r i b e t h e r a d i a n c e d i s t r i b u t i o n o f o v e r c a s t s k i e s by an e q u a t i o n o f t h e form N(0) = N(o) ( 1+bcost9)/( 1+b) (5.11) where b i s a c o n s t a n t , N i s measured r a d i a n c e a t any a n g l e 6 112 above t h e h o r i z o n and N(o) i s t h e r a d i a n c e a t t h e z e n i t h . The v a l u e of t h e c o e f f i c i e n t b has n o t been d e t e r m i n e d s a t i s f a c t o r i l y but i s t h o u g h t t o be between 1.0 and 2.0 ( S t e v e n and U n s w o r t h , 1980). F o r t h e d i s t r i b u t i o n s shown i n F i g s . 5.10 and 5.11, i t i s p o s s i b l e t o see how w e l l Eqn. 5.11 p e r f o r m s u s i n g a v a l u e o f b=1.5 ( c h o s e n from v a l u e s p r e s e n t e d i n S t e v e n and U n s w o r t h , 1 9 8 0 ) . The r e s u l t s , p r e s e n t e d i n T a b l e 5.1, show measured r a d i a n c e s a t two a z i m u t h a l p o s i t i o n s on t h e sky h e m i s p h e r e f o r a v a r i e t y of z e n i t h a n g l e s . T h e s e may be compared t o t h e r a d i a n c e s e s t i m a t e d u s i n g Eqn. 5.11. G e n e r a l l y , t h e e q u a t i o n t e n d s t o u n d e r p r e d i c t r a d i a n c e and t h i s u n d e r p r e d i c t i o n i n c r e a s e s 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 . However, due t o a p a u c i t y of o v e r c a s t d a t a , t h e s e a r e o n l y p r e l i m i n a r y f i n d i n g s . An o v e r c a s t sky d i s t r i b u t i o n was p r e s e n t e d by M c A r t h u r and Hay (1981) where t h e s o l a r p o s i t i o n was not v i s i b l e and a l m o s t no g r a d i e n t e x i s t e d between r a d i a n c e v a l u e s ( F i g . 5.20). They s t a t e d t h a t t h e i s o t r o p i c a p p r o x i m a t i o n i s r e a s o n a b l e o v e r t h e c e n t r a l p o r t i o n of t h e sky h e m i s p h e r e and a g r e e d w i t h K o n d r a t y e v (1969) t h a t t h e a z i m u t h a l d e pendence of t h e i n t e n s i t y of sky r a d i a n c e i s not p r o n o u n c e d under o v e r c a s t c o n d i t i o n s . T h e s e f i n d i n g s a r e i n agreement w i t h t h o s e of t h i s s t u d y . The o v e r c a s t sky d i s t r i b u t i o n s as d e p i c t e d i n F i g s . 5.10 and 5.11, a r e i n a c c o r d w i t h t h e r e s u l t s o f M c A r t h u r and Hay (1981) as t h e s m a l l r a n g e of measured r a d i a n c e s and t h e s l i g h t g r a d i e n t a p p r o x i m a t e s i s o t r o p y a c r o s s t h e sky h e m i s p h e r e . V a l k o (1980) a l s o s t u d i e d t h e c h a r a c t e r i s t i c s o f a 1 1 3 T a b l e 5.1 V a l u e s of M e a s u r e d and P r e d i c t e d ( U s i n g Eqn. 5.11) R a d i a n c e s ( W m " 2 s r - 1 ) f o r C e r t a i n Z e n i t h A n g l e s f o r O v e r c a s t S k i e s O b s e r v e d on J a n u a r y 20, 1984 ( Z e n i t h A n g l e 74°) Z e n i t h A n g l e ( D e g r e e s ) Meas. Rad 0° A z i m u t h Meas. Rad 180° A z i m u t h (Wm" • s r ) (Wm" s r ) P r e d i c t e d R a d i a n c e (Wm~ 2sr~ 1) JD20b.1 JD20b.2 20 32 32 30.84 40 32 31 27.51 60 22 26 22.40 70 18 23 1 9.37 20 18 18 17.35 40 1 7 1 7 15.47 60 1 4 1 6 12.60 70 1 3 1 4 1 0.89 1 1 4 g u r e 5.20 O v e r c a s t Sky R a d i a n c e (Wm" 2sr"') D i s t r i b u t i o n f o r 1230 LAT F e b r u a r y 14,1978 (z = 63°). From M c A r t h u r and Hay (1981) 1 15 r a d i a n c e d i s t r i b u t i o n under o v e r c a s t s k i e s . F i g . 5.21 i l l u s t r a t e s t h e f u l l y o v e r c a s t c a s e w h i c h r e p r e s e n t s t h e e f f e c t o f a s t r a t u s l a y e r w i t h u n d e r l y i n g f o g . V a l k o (1980) n o t e s t h e symmetry of t h e d i s t r i b u t i o n a b o u t t h e z e n i t h , and t h e d e c r e a s e i n r a d i a n c e from t h e z e n i t h t o t h e h o r i z o n . A l a c k of a z i m u t h a l dependence was f o u n d t o e x i s t ( V a l k o , 1 9 8 0 ) . 5.4.3 P a r t l y C l o u d y Sky R a d i a n c e D i s t r i b u t i o n s Due t o t h e s p a t i a l and t e m p o r a l c o m p l e x i t y of p a r t l y c l o u d y s k i e s as w e l l as t h e l o n g r e s p o n s e t i m e o f t h e r a d i o m e t r i c measurement s y s t e m s t y p i c a l l y u s e d t o o b t a i n d i f f u s e r a d i a n c e measurements, s t u d i e s of t h e d i s t r i b u t i o n of d i f f u s e r a d i a n c e under s u c h s k i e s have been a t t e m p t e d l e s s f r e q u e n t l y t h a n t h o s e f o r o t h e r sky c o n d i t i o n s . R e s e a r c h by V a l k o (1980) shows t h a t t h e r e g u l a r i t y of t y p i c a l d i f f u s e s o l a r r a d i a t i o n d i s t r i b u t i o n s i s d i s t u r b e d by t h e r a d i a n c e d i s t r i b u t i o n of t h e i r r e g u l a r c l o u d s t r u c t u r e , and t h e r e s u l t i n g d i s t r i b u t i o n c o r r e s p o n d s w e l l t o t h e d a r k and b r i g h t a r e a s on t h e c l o u d s . F i g . 5.22 shows t h a t d i s t r i b u t i o n s o f r a d i a n c e o b s e r v e d when c i r r u s c l o u d s were p r e s e n t , r e s e m b l e d t h o s e p a t t e r n s o b s e r v e d under t u r b i d c o n d i t i o n s . F o r b o t h t h e s e c a s e s , t h e p a t t e r n s had a form s i m i l a r t o a c l e a r sky c a s e ( V a l k o , 1980). T h i s o b s e r v a t i o n c o r r e s p o n d s w i t h t h e f i n d i n g s o f t h i s s t u d y a s d i s c u s s e d i n S e c t i o n 5.3.2 and i l l u s t r a t e d by F i g s . 5.16 and 5.8. T h e r e were s m a l l e r d i f f e r e n c e s between t h e v a l u e s o f r a d i a n c e f o r s u r f a c e s f a c i n g F i g u r e 5.21 O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n s (Wm - 2) und e r A l t o s t r a t u s C l o u d . From V a l k o ( 1 9 8 0 ) 1 1 7 F i g u r e 5.22 R a d i a n c e D i s t r i b u t i o n s D u r i n g C i r r u s C o v e r From V a l k o (1980) (Wm~2) C l o u d 1 18 t o w a r d s , o r away from t h e Sun i n t h e p r e s e n c e of c i r r u s . As t h e c l o u d c o v e r becomes more dense however, t h e d i r e c t beam component i s d e p l e t e d and t h e r e g i o n of maximum r a d i a n t i n t e n s i t y may no l o n g e r be c o n c e n t r a t e d a r o u n d t h e Sun, but may be s h i f t e d t o w a r d s t h e z e n i t h ( V a l k o , 1980). A l m o s t p e r f e c t z e n i t h a l symmetry was n o t e d f o r s u c h a s k y . M c A r t h u r and Hay (1981 ) p r o v i d e d examples of r a d i a n c e d i s t r i b u t i o n s o b t a i n e d d u r i n g p a r t i a l c l o u d i n e s s u s i n g t h e i r p h o t o g r a p h i c t e c h n i q u e . F i g . 5.23 c l e a r l y i l l u s t r a t e s t h e c o m p l e x i t y o f s u c h a d i s t r i b u t i o n . I n c r e a s e d s c a t t e r i n g e f f e c t s due t o t h e p r e s e n c e o f w ater d r o p l e t s r e s u l t e d i n l o c a l l y h i g h e r r a d i a n c e s . The l o c a t i o n o f t h e l o w e s t i n t e n s i t y was i n a p p r o x i m a t e l y t h e same r e g i o n as i n t h e c l e a r sky c a s e s (90° from t h e Sun) and r a d i a n c e was f o u n d t o i n c r e a s e b o t h t o w a r d s t h e h o r i z o n and t h e Sun, a l t h o u g h not i n t h e same manner as a c l e a r sky c a s e ( M c A r t h u r and Hay, 1981). M c A r t h u r and Hay (1981) a t t r i b u t e d t h e c o m p l e x i t y of t h e p a t t e r n of d i f f u s e r a d i a n c e under p a r t l y c l o u d y s k i e s t o t h e h i g h l y r e f l e c t i v e p r o p e r t i e s of t h e c l o u d s . F i g . 5.17 e x e m p l i f i e s and a f f i r m s t h e v a l i d i t y of t h a t c o n c l u s i o n . The r e f l e c t i o n and s c a t t e r i n g o f v i s i b l e r a d i a t i o n o f f t h e s i d e s and b a s e s of i n d i v i d u a l c l o u d e l e m e n t s r e s u l t s i n a h i g h l y i r r e g u l a r d i s t r i b u t i o n o f r a d i a n c e a c r o s s t h e sky h e m i s p h e r e . F i g u r e 5.23 P a r t l y C l o u d y Sky R a d i a n c e D i s t r i b u t i o n f o r 1317 LAT F e b r u a r y 15,1978, From M c A r t h u r and Hay (1981 > 1 20 C h a p t e r S i x C o n c l u s i o n s and Recommendations 6.1 A s s e s s m e n t of t h e E x p e r i m e n t a l P r o c e d u r e s 6.1.1 C r i t i c a l A s s e s s m e n t of Measurement  T e c h n i q u e Used i n t h i s S t u d y 6.1.1.1 S i t e C o n s i d e r a t i o n s F o r t h e i n i t i a l s e t of o b s e r v a t i o n s c a r r i e d o ut on t h e r o o f of t h e Geography Department u s i n g t h e v i d e o s y s t e m , i t was n e c e s s a r y t o o p e r a t e t h e equipment a t a l o c a t i o n a l l o w i n g e a s y a c c e s s and s e r v i c i n g . A n o t h e r m a j o r c o n s i d e r a t i o n i n s e l e c t i n g t h a t l o c a t i o n f o r t h e v i d e o camera was t h e n e c e s s i t y t o m a i n t a i n a computer and f r a m e s t o r e l i n k . F o r f u t u r e s t u d i e s however, i t would n o t be ma n d a t o r y t o l o c a t e a t s u c h a r o o f s i t e , s i n c e p o r t a b l e m i c r o c o m p u t e r s a r e a v a i l a b l e and t h e f r a m e s t o r e u n i t c o u l d be e a s i l y i n t e r f a c e d w i t h s u c h a computer a t a more remote f i e l d l o c a t i o n . T h i s f l e x i b i l i t y i n c h o o s i n g an e x p e r i m e n t a l s i t e w i l l a l l o w a v i d e o s y s t e m t o be l o c a t e d i n v a r i e d g e o g r a p h i c a l / c l i m a t o l o g i c a l s e t t i n g s so as t o r e c o r d images r e p r e s e n t a t i v e o f a ra n g e o f sky l u m i n a n c e c h a r a c t e r i s t i c s . T h i s would be o f i n t e r e s t f o r example, i n s t u d i e s on t h e e f f e c t s o f t u r b i d i t y on t h e sky l u m i n a n c e / r a d i a n c e d i s t r i b u t i o n . 6.1.1.2 A s s e s s m e n t of I n s t r u m e n t a t i o n The n e c e s s i t y t o c a l i b r a t e t h e b r i g h t n e s s v a l u e s a b s t r a c t e d f r o m a v i d e o image o f t h e sky u s i n g measured 121 r a d i a n c e s o b t a i n e d w i t h t h e L i n k e - F e u s s n e r a c t i n o m e t e r p r o v e d t o be a p r o c e d u r e t h a t c o u l d be much im p r o v e d o r even e l i m i n a t e d i n f u r t h e r r e s e a r c h . The a c t i n o m e t e r u s e d f o r t h e measurement o f d i f f u s e s o l a r r a d i a t i o n p r o v e d s l u g g i s h t o o p e r a t e m a n u a l l y e s p e c i a l l y i f t h e o u t s i d e t e m p e r a t u r e s were p a r t i c u l a r i l y low. The l e n g t h of t i m e o v e r w h i c h o b s e r v a t i o n s were r e c o r d e d (18 m i n u t e s ) was l o n g e r t h a n what would be c o n s i d e r e d i d e a l s i n c e t h e r a d i a t i v e c o n d i t i o n s c o u l d change w i t h i n t h e s c a n i n t e r v a l . I t would be p r e f e r a b l e t o o b t a i n measurements d u r i n g r e l a t i v e l y c o n s t a n t s p e c t r a l c o n d i t i o n s . T h i s c o u l d be a c c o m p l i s h e d by c o l l e c t i n g o b s e r v a t i o n s i n a much s h o r t e r t i m e . A l s o , t h e r e s p o n s e t i m e of t h e i n s t r u m e n t (8-10 s e c o n d s ) i s l o n g e r t h a n t h a t d e s i r e d t o r e c o r d d i f f u s e r a d i a n c e under r a p i d l y c h a n g i n g s k i e s or windy c o n d i t i o n s when t h e i n s t r u m e n t o p e r a t e s l e s s e f f e c t i v e l y . I d e a l l y , i t would be d e s i r a b l e t o use an i n s t r u m e n t w h i c h had a s m a l l e r t o t a l a p e r t u r e i n o r d e r t o measure r a d i a n c e o v e r a s m a l l e r s o l i d a n g l e and so r e c o r d a more a c c u r a t e p o i n t e s t i m a t e . I f measurements of d i f f u s e s o l a r r a d i a t i o n a r e r e q u i r e d f o r c a l i b r a t i o n p u r p o s e s i n f u t u r e s t u d i e s , an a u t o m a t i c s k y - s c a n n i n g s y s t e m would be an improvement o v e r t h e use of t h e a c t i n o m e t e r . Such a s y s t e m c o u l d a u t o m a t i c a l l y r e c o r d o b s e r v a t i o n s o f d i f f u s e r a d i a n c e , c o m p l e t i n g a sky s c a n i n a much s h o r t e r t i m e span, (as i n Hooper and B r u n g e r , 1 9 8 2 ) and c o u l d be b u i l t w i t h a s m a l l e r a n g l e o f a p e r t u r e . T h i s t y p e of 122 s y s t e m would u n d o u b t e d l y be s u p e r i o r t o t h e manual o p e r a t i o n of th e L i n k e - F e u s s n e r a c t i n o m e t e r as u s e d i n t h e p r e s e n t s t u d y . The r e c o r d i n g of t h e d i f f u s e s o l a r r a d i a t i o n s i g n a l i n v o l v e d an a b s o l u t e e r r o r of ±4.91 Wm~ 2sr _ 1 and t h i s was f o u n d t o r e s u l t i n l a r g e r e l a t i v e e r r o r s when r e c o r d i n g s m a l l s i g n a l s ( i . e . l e s s t h a n 10 Wm" 2sr~') (See S e c t i o n 2 . 1 . 2 . 2 ) . In o r d e r t o m i n i m i z e t h i s p r o b l e m i t would be a d v i s a b l e t o a m p l i f y t h e s i g n a l p r o d u c e d by t h e a c t i n o m e t e r . A l t h o u g h t h e d i g i t a l v o l t m e t e r was not c a l i b r a t e d d u r i n g t h i s s t u d y , i t would be a d v i s a b l e t o have t h i s done p r i o r t o f u r t h e r u s e . The ER Newvicon v i d e o camera p r o v e d t o be a u s e f u l d e v i c e f o r t h e c o l l e c t i o n o f sky images. A n e u t r a l d e n s i t y f i l t e r w i t h t h e d e s i r e d t r a n s m i s s i o n p r o p e r t i e s a l l o w e d t h e o p e r a t i o n of t h e camera under even t h e h i g h e s t r a d i a n t i n t e n s i t i e s . The s p e c t r a l r e s p o n s e c h a r a c t e r i s t i c s of t h e camera made an a n a l y s i s o f t h e r e l a t i o n s h i p between r a d i a n c e and b r i g h t n e s s p o s s i b l e . However i t i s known t h a t v a r i o u s d i s t o r t i o n s a r e a s s o c i a t e d w i t h t h e v i d e o t u b e and i t s e l e c t r o n i c s . F o r i n s t a n c e , v a r i a t i o n s of 10% may be a t t r i b u t e d t o t h e n o n l i n e a r e f f e c t s of t h e v i d e o s y s t e m , and even l a r g e r v a r i a t i o n s a c r o s s an image may o c c u r b e c a u s e o f t e m p e r a t u r e d r i f t ( i . e . image s i z e may be t e m p e r a t u r e d e p e n d e n t ) ( F r a n c k e t a l . , 1983). A l t h o u g h no e v i d e n c e o f su c h d i s t o r t i o n s was f o u n d d u r i n g t h i s s t u d y , o t h e r p r o b l e m s d i d e x i s t . F o r i n s t a n c e , d u r i n g i n t e n s e r a d i a t i v e c o n d i t i o n s ( e g . ab o u t s o l a r noon) a ' b l o o m i n g ' e f f e c t o c c u r r e d where t h e r e s o l u t i o n of t h e v i d e o image d e t e r i o r a t e d and t h e image a p p e a r e d s a t u r a t e d . T h i s w o u l d l a s t u n t i l t h e 1 23 r a d i a t i v e r e g i m e had resumed a l e v e l where the camera and f i l t e r c o u l d o p e r a t e more e f f e c t i v e l y , and t h e image was r e s t o r e d . A b e t t e r c o r r e s p o n d e n c e between t h e s p e c t r a l r e s p o n s e o f t h e v i d e o s y s t e m and t h e s p e c t r a l d i s t r i b u t i o n o f e n e r g y would improve t h e r e l a t i o n s h i p o b t a i n e d between r a d i a n c e and b r i g h t n e s s and r e s u l t i n an i m p r o v e d c a l i b r a t i o n e q u a t i o n . T h i s would e l i m i n a t e much of t h e u n c e r t a i n t y i n t h e i n t e r p r e t a t i o n o f t h e r a d i a n c e d i s t r i b u t i o n f r o m t h e p o l a r c o o r d i n a t e maps. S i n c e t h e a c t i n o m e t e r i s i n d e p e n d e n t o f w a v e l e n g t h , t h e s p e c t r a l r e s p o n s e o f t h e v i d e o camera s h o u l d complement i t . The p r e s e n t s p e c t r a l p r o p e r t i e s of t h e ER Newvicon 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 t h e s h o r t e r w a v e l e n g t h s of t h e e n e r g y s p e c t r u m . T h i s i s not p a r t i c u l a r i l y d e s i r a b l e f o r s o l a r r a d i a t i o n s t u d i e s and an a l t e r n a t e s p e c t r a l r e s p o n s e would be an improvement. The f i s h e y e l e n s , a c u s t o m - b u i l t camera l e n s i n t h i s c a s e , s h o u l d have i t s o p t i c a l p r o p e r t i e s p r o f e s s i o n a l l y t e s t e d or c h e c k e d b e f o r e f u r t h e r u s e . Though v a r i o u s t e s t s were p e r f o r m e d t o c h e c k f o r g e o m e t r i c d i s t o r t i o n s , none of t h e s e c o u l d be deemed c o n c l u s i v e . A l t h o u g h t h e l e n s and camera s y s t e m p e r f o r m e d w e l l i n t h i s s t u d y , an i m p o r t a n t m o d i f i c a t i o n t o t h e p r e s e n t s y s t e m must be made b e f o r e f u r t h e r r e s e a r c h i s a t t e m p t e d . The p r e s e n t a p e r t u r e on t h e f i s h e y e l e n s i s n o t g r a d u a t e d o r c a l i b r a t e d i n any manner and t h i s s h o u l d be r e m e d i e d b e f o r e f u r t h e r u s e . I t was n o t p o s s i b l e t o d i s c e r n by how much t h e 1 24 a p e r t u r e was b e i n g a d j u s t e d and had t h i s been known, i t might be p o s s i b l e t o c a l i b r a t e t h e v i d e o s y s t e m . T h i s c o u l d have been a c c o m p l i s h e d by d e t e r m i n i n g t h e r e l a t i o n s h i p between r a d i a n c e and b r i g h t n e s s w i t h i n g i v e n s p e c t r a l l i m i t s a f t e r a d j u s t i n g f o r b l a c k n e s s l e v e l , v i d e o l e v e l , and a p e r t u r e e f f e c t s ( m o n i t o r i n g t h e v i d e o s i g n a l on an o s c i l l o s c o p e , w h i c h g i v e s t h e r e l a t i o n s h i p between v o l t a g e and b r i g h t n e s s , would p r o v i d e t h e l a t t e r v a l u e s ) i n a manner s i m i l a r t o t h a t d e s c r i b e d i n S e c t i o n 4.1.1. Once t h i s had been c a r r i e d o u t , i t would not be n e c e s s a r y t o a d j u s t t h e b l a c k n e s s and v i d e o l e v e l c o n t r o l s a g a i n as l o n g as the s p e c t r a l r a d i a t i o n c o n d i t i o n s do not change d r a m a t i c a l l y . A c a l i b r a t i o n p r o c e d u r e of t h i s s o r t may have t o be f o l l o w e d f o r e a c h o f t h e sky c o v e r c o n d i t i o n s ( i .e. c l e a r , o v e r c a s t , and p a r t l y c l o u d y ) but t h i s w ould be an improvement o v e r h a v i n g t o d e t e r m i n e a c a l i b r a t i o n c u r v e f o r e v e r y sky s c a n . 6.2 Summary of R e s u l t s 6.2.1 C l e a r Sky C a s e s The a n g u l a r d i s t r i b u t i o n of d i f f u s e s o l a r r a d i a t i o n under c l e a r s k y c o n d i t i o n s has been w e l l documented and t h e r e s u l t s o f t h i s s t u d y a r e f o u n d t o be i n c l o s e agreement w i t h p r e v i o u s r e s e a r c h ( e g . Steven,1977 ; M c A r t h u r , 1 9 7 8 ; V a l k o , 1980). R a d i a n c e maps of s u c h c o n d i t i o n s c o n s i s t e n t l y show a maximum v a l u e c o i n c i d e n t w i t h t h e s o l a r d i s k and a s h a r p d e c r e a s e i n v a l u e s w i t h i n c r e a s i n g a n g u l a r d i s t a n c e from t h e Sun. A minimum r a d i a n c e u s u a l l y l i e s a p p r o x i m a t e l y 90° f r o m t h e s o l a r 1 25 d i s k and v a l u e s g e n e r a l l y i n c r e a s e f r o m t h e r e o u t t o t h e h o r i z o n . S i n c e t h e s e d i s t r i b u t i o n s show c o n s i s t e n c y i n form r e g a r d l e s s o f l o c a t i o n , t u r b i d i t y l e v e l o r s p e c t r a l c o m p o s i t i o n of r a d i a n t e n e r g y , a c a l i b r a t e d v i d e o sysem a s d e s c r i b e d i n S e c t i o n 6.1.1.2 would p r o v i d e a s y s t e m c a p a b l e of e f f i c i e n t l y c o l l e c t i n g a s t a t i s t i c a l l y s i g n i f i c a n t d a t a s e t w h i c h c o u l d p r o v i d e a s t a n d a r d d i s t r i b u t i o n o f r a d i a n c e under c l e a r s k i e s w i t h b e t t e r r e s o l u t i o n and a c c u r a c y t h a n e a r l i e r s t u d i e s . 6.2.2 O v e r c a s t Sky C a s e s As r a d i a n c e d i s t r i b u t i o n s u nder o v e r c a s t s k i e s have been s t u d i e d l e s s f r e q u e n t l y , t h e v i d e o s y s t e m p r o v i d e s a h i g h l y s u c c e s s f u l means of r e c o r d i n g t h e v a r i a t i o n s i n r a d i a n c e under s u c h s k i e s . I t was not f e a s i b l e t o c o l l e c t a s i z e a b l e d a t a s e t of s u c h sky images d u r i n g t h i s s t u d y , but f o r f u t u r e r e s e a r c h , t h e s y s t e m w o u l d be c a p a b l e o f p r o v i d n g h i g h q u a l i t y o v e r c a s t d a t a f o r a n a l y s i s . W i t h s u c h a d a t a s e t , i t would be p o s s i b l e t o d e t e r m i n e t h e f o r m of t h e e q u a t i o n w h i c h b e s t f i t s t h e r a d i a n c e d i s t r i b u t i o n and t o compare t h e s e r e s u l t s w i t h p r e v i o u s work su c h as t h a t by S t e v e n and U n s w o r t h ( 1 9 8 0 ) . The p r e l i m i n a r y r e s u l t s of t h e o v e r c a s t sky a n a l y s i s c a r r i e d out d u r i n g t h i s s t u d y i n d i c a t e good agreement w i t h e a r l i e r work. 6.2.3 P a r t l y C l o u d y Sky C a s e s By f a r t h e most complex r a d i a n c e d i s t r i b u t i o n t o b o t h r e c o r d and a n a l y z e i s t h a t o b t a i n e d under p a r t l y c l o u d y s k i e s . Due t o 1 26 th e r a p i d l y c h a n g i n g d i s t r i b u t i o n of c l o u d s and t h e complex s c a t t e r i n g r egime a s s o c i a t e d w i t h them, v e r y l i t t l e p r o g r e s s had been made i n s t u d y i n g t h e a n g u l a r d i s t r i b u t i o n of sky r a d i a n c e under c l o u d y s k i e s . P r o g r e s s i n t h i s a r e a has been impeded by t h e use of c o n v e n t i o n a l r a d i o m e t r i c i n s t r u m e n t s many of w h i c h have r e s p o n s e t i m e s t o o l o n g t o be u s e f u l f o r making o b s e r v a t i o n s under p a r t l y c l o u d y s k i e s . The measurement t e c h n i q u e u s e d i n t h i s s t u d y u t i l i z i n g s y n c h r o n o u s o b s e r v a t i o n s of d i f f u s e r a d i a n c e and b r i g h t n e s s from a sky image, p r e s e r v e d t h e complex c h a r a c t e r i s t i c s of s u c h a r a d i a n c e d i s t r i b u t i o n a l l o w i n g f o r a more d e t a i l e d and a c c u r a t e mapping of t h e r a d i a n c e d i s t r i b u t i o n . The c o m p l e x i t y o f s u c h d i s t r i b u t i o n s r e q u i r e s t h a t a l a r g e d a t a s e t s h o u l d be c o l l e c t e d i n o r d e r t o d e r i v e u s e f u l r e s u l t s c o n c e r n i n g t h e s c a t t e r i n g r e g i m e o f s h o r t w a v e r a d i a t i o n under p a r t l y c l o u d y s k i e s . T h e s e d a t a would s i m i l a r i l y p r o v i d e u s e f u l i n f o r m a t i o n on c l o u d geometry and t h i c k n e s s and on r a d i a t i v e t r a n s f e r i n c l o u d y a t m o s p h e r e s . Some d i f f i c u l t i e s a r o s e d u r i n g a t t e m p t s t o r e c o r d s k y images of c l e a r s k i e s on w h i c h i n d i v i d u a l c l o u d e l e m e n t s were s u p e r i m p o s e d . T h i s was a r e s u l t o f t h e l a r g e range o f r a d i a n t i n t e n s i t i e s p r e s e n t i n s u c h an image and o f t h e c o n t i n u a l l y v a r y i n g s p e c t r a l n a t u r e o f t h o s e r a d i a t i v e r e g i m e s . Improved p r o c e d u r e s f o r p r o c u r i n g d i f f u s e r a d i a n c e measurements ( i . e . use of an a u t o m a t i c m e a s u r i n g i n s t r u m e n t ) w i t h a s h o r t e r s c a n i n t e r v a l t i m e , a s w e l l a s a b e t t e r match between t h e s p e c t r a l r e s p o n s e o f t h e v i d e o camera and e n e r g y d i s t r i b u t i o n , w o u l d 1 27 m i n i m i z e t h i s p r o b l e m . 6.2.4 R a d i a n c e Maps I t was d e c i d e d t h a t t h e b e s t method of p r e s e n t i n g t h e p r e d i c t e d d i s t r i b u t i o n of r a d i a n c e s was i n t h e form of a p o l a r c o o r d i n a t e r a d i a n c e map. Th e s e maps p r o v e d s u c c e s s f u l i n i l l u s t r a t i n g t h e m a g n i t u d e o f t h e r a d i a n t i n t e n s i t y o v e r t h e sky h e m i s p h e r e as w e l l as t h e c h a r a c t e r i s t i c s of t h e d i s t r i b u t i o n of t h o s e v a l u e s . The maps p r o d u c e d i n t h i s s t u d y were an improvement o v e r p r e v i o u s a t t e m p t s i n t h a t t h e y were not a v e r a g e d v a l u e s and were more d e t a i l e d . The measurement t e c h n i q u e u s e d i n t h i s s t u d y a l l o w e d f o r p r e d i c t i o n o f r a d i a n c e v a l u e s w i t h i n ± 2 % i n some c a s e s w h i c h i s b e t t e r a c c u r a c y t h a n e a r l i e r s t u d i e s r e p o r t e d ( e g . M c A r t h u r , 1978). I r r e g u l a r c o n t o u r i n g i n t e r v a l s were f o u n d t o b e s t e x p r e s s t h e v a r i a t i o n s i n r a d i a n c e a c r o s s t h e sky dome. 6.3 C o n c l u s i o n s and Recommendations The u s e f u l n e s s of t h e v i d e o i m a g i n g t e c h n i q u e i n r e s e a r c h c o n c e r n e d w i t h t h e a n g u l a r d i s t r i b u t i o n o f d i f f u s e r a d i a t i o n o v e r t h e sky h e m i s p h e r e c a n n o t be d o u b t e d . T h i s t y p e o f s y s t e m a l l o w s f o r f a s t , e f f i c i e n t and a c c u r a t e mapping of t h e e n t i r e sky h e m i s p h e r e and t h e d i g i t i z i n g f a c i l i t i e s a l l o w f o r r e a l - t i m e a n a l y s i s of t h e d a t a . The l i n e a r r e l a t i o n s h i p e s t a b l i s h e d between b r i g h t n e s s and r a d i a n c e v a l u e s a l l o w s f o r a s i m p l e d e t e r m i n a t i o n of t h e p r e d i c t e d r a d i a n c e d i s t r i b u t i o n o v e r t h e sky dome. 1 28 As p o i n t e d o ut i n S e c t i o n 6.2, a major a d v a n t a g e of t h e v i d e o s y s t e m i s i t s a b i l i t y t o p r o v i d e an i n s t a n t a n e o u s image of t h e sky under even t h e most complex sky c o n d i t i o n s , a l l o w i n g f o r m o n i t o r i n g of dynamic p r o c e s s e s o r m o t i o n s . T h i s t e c h n i q u e would be u s e f u l i n a programme i n v o l v i n g c o n t i n u o u s m o n i t o r i n g of t h e sky h e m i s p h e r e w h i c h would e n t a i l c o l l e c t i n g images of a l l t y p e s o f sky c o v e r . T h i s would p r o v i d e d a t a showing t h e t r a n s i t i o n a l s t a g e s from one sky c o v e r extreme t o a n o t h e r ( e g . c l e a r t o o v e r c a s t ) and would a l l o w one t o s t u d y t h e c h a n g e s i n t h e a n g u l a r d i s t r i b u t i o n o f d i f f u s e r a d i a n c e o v e r a c o n t i n u u m of c o n d i t i o n s . The p o t e n t i a l of s u c h a s y s t e m w o u l d be of i n t e r e s t t o many r e s e a r c h e r s g i v e n t h a t t h e r e s u l t s of t h i s s t u d y c o n f i r m t h e a n i s o t r o p y of t h e d i s t r i b u t i o n o f d i f f u s e s o l a r r a d i a t i o n . M o d e l s i n c o r p o r a t i n g t h e d i r e c t i o n a l c h a r a c t e r i s t i c s o f s o l a r r a d i a t i o n must be r e f i n e d and made more r e p r e s e n t a t i v e of t h e t r u e r a d i a t i v e r e g i m e . F u t u r e s t u d i e s however, would b e n e f i t f r o m an i m p r o v e d c a l i b r a t i o n p r o c e d u r e f o r t h e v i d e o s y s t e m ; p r e f e r a b l y an i n i t i a l c a l i b r a t i o n p r o c e s s w h i c h would not have t o be r e p e a t e d c o n t i n u a l l y . The weakest l i n k i n t h i s s t u d y was i n t h e measurement o f d i f f u s e s o l a r r a d i a t i o n and i f t h a t p r o c e s s c o u l d be r e f i n e d o r a s s i g n e d a m i n i m a l r o l e i n t h e measurement p r o c e d u r e , t h e n an i m p o r t a n t and v e r y u s e f u l d a t a a c q u i s i t i o n s y s t e m w i l l have been d e v e l o p e d . T h e s e f i n a l r e f i n e m e n t s t o t h e measurement s y s t e m r e q u i r e l i t t l e d e v e l o p m e n t and so i t i s not o v e r l y o p t i m i s t i c t o e n v i s i o n t h i s v i d e o i m a g i n g t e c h n i q u e 129 i n w i d e r use i n t h e v e r y near f u t u r e . 130 R e f e r e n c e s B i r d , R.E., R.L. H u l s t r o m , A.W. K l i m a n , and H.G. E l d e r i n g , 1982. S o l a r s p e c t r a l measurements i n t h e t e r r e s t r i a l e n v i r o n m e n t , A p p l i e d O p t i c s , 21,8, 1430-1436. Cannon, T.W., and L.D. Dwyer, 1981. An a l l - s k y v i d e o - b a s e d l u m i n a n c e mapper f o r d a y l i g h t i n g r e s e a r c h , P r o c e e d i n g s of t h e S i x t h N a t i o n a l P a s s i v e S o l a r E n e r g y C o n f e r e n c e , P o r t l a n d O regon, S e p t . 8-12, 855-859. Cook, N.H., and E.H. R a b i n o w i c z , 1967. P h y s i c a l Measurement and  A n a l y s i s , A d d i s o n - W e s l e y P u b l i s h i n g Co. I n c . , 29-68. C o u l s o n , K.L., 1975. S o l a r and T e r r e s t r i a l R a d i a t i o n : Methods  and M easurements, Academic P r e s s , New Y o r k , 322 pp. Dave, J.V., 1981. T r a n s f e r of v i s i b l e r a d i a t i o n i n t h e a t m o s p h e r e , A t m o s p h e r i c E n v i r o n m e n t , 15, 1820-1905. F r a n c k , J.B., P.N. K e l l e r , R.A. Swing, and G. S i l b e r b e r g , 1983. P r o c e s s f o r p r o d u c i n g l a s e r - f o r m e d v i d e o c a l i b r a t i o n m a r k e r s , A p p l i e d O p t i c s , 22,16, 2481-2483. G a r n i e r , B., and A. Ohmura, 1970. The e v a l u a t i o n o f s u r f a c e v a r i a t i o n s i n s o l a r r a d i a t i o n income, S o l a r Energy,13,21-34 G h a z i , A., 1971. S p e c t r a l measurements of sky r a d i a n c e d i s t r i b u t i o n , B u l l e t i n A m e r i c a n M e t e o r o l o g i c a l S o c i e t y , 52,11 , 1161. G r a c e , J . , 1971. The d i r e c t i o n a l d i s t r i b u t i o n o f l i g h t i n n a t u r a l and c o n t r o l l e d e n v i r o n m e n t c o n d i t i o n s , J . A p p l .  E c o l o g y , 8, 155-164. Hay, J . E . , 1978. Measurement and m o d e l l i n g of s h o r t w a v e r a d i a t i o n on i n c l i n e d s u r f a c e s . T h i r d C o n f e r e n c e on A t m o s p h e r i c R a d i a t i o n , A m e r i c a n M e t e o r o l o g i c a l S o c i e t y , D a v i s , C a l i f o r n i a , June 28-30, 150-153. Hay, J . E . , and T.R. Oke, 1976. The C l i m a t e of V a n c o u v e r , T a n t a l u s R e s e a r c h L t d . , V a n c o u v e r , B.C., 49 pp. Hay, J . E . , and J.A. D a v i e s , 1980. C a l c u l a t i o n o f s o l a r r a d i a t i o n i n c i d e n t on an i n c l i n e d s u r f a c e , P r o c e e d i n g s of t h e F i r s t C a n a d i a n S o l a r R a d i a t i o n D a t a Workshop, J . E . Hay and T.K. Won, E d s . 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 s , Downsview, O n t a r i o , 166 pp. Hay, J . E . , and R. D a r b y , 1984. E l C h i c h o n - impact on a e r o s o l 131 o p t i c a l d e p t h and d i r e c t , d i f f u s e and t o t a l s o l a r i r r a d i a n c e s a t V a n c o u v e r , B.C., A t m o s p h e r e - O c e a n , i n p r e s s . Hertzman, 0., 1979. C l o u d Mapping f o r t h e E a r t h ' s S u r f a c e U s i n g an I n f r a r e d R a d i a n c e C o n t r a s t T e c h n i q u e . Unpub. M.Sc. T h e s i s , U n i v . o f B r i t i s h C o l u m b i a , 141 pp. H e w l e t t - P a c k a r d , 1979. E l e c t r o n i c I n s t r u m e n t s and Systems M a n u a l , 62-63. Hooper, F.C., and A.P. B r u n g e r , 1980. A model f o r t h e a n g u l a r d i s t r i b u t i o n of sky r a d i a n c e , J o u r n a l of S o l a r E n e r g y  E n g i n e e r i n g , 102, 196-202. Hooper, F.C., and A.P. B r u n g e r , 1982. E x p e r i m e n t a l o b s e r v a t i o n and c h a r a c t e r i z a t i o n of t h e s k y - d i f f u s e component of t h e s h o r t w a v e 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 , F i n a l R e p o r t f o r 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 , D.S.S. C o n t r a c t No. OSU79-00210, T o r o n t o , C a n a d a , 155 pp. IGY, 1958. I n s t r u c t i o n Manual of t h e G e o p h y s i c a l Y e a r , P a r t V I . , R a d i a t i o n I n s t r u m e n t s and Measurements, A n n a l s o f t h e  IGY, Pergammon P r e s s , New Y o r k , 367-466. K i m b a l l , H.H., and I . F . Hand, 1922. D a y l i g h t i l l u m i n a t i o n on h o r i z o n t a l , v e r t i c a l and s l o p i n g s u r f a c e s , M o n t h l y Weather  Review, 50,12, 615-628. K o n d r a t y e v , K. Ya., 1969. R a d i a t i o n i n t h e Atmosphere, Academic P r e s s , New Y o r k , 912 pp. K o n d r a t y e v , K. Ya., L.A. K u d r i a v t z e v a , and M.P. M a n o l o v a , 1955. D i s t r i b u t i o n of t h e e n e r g e t i c a l and l i g h t i n t e n s i t y o f d i f f u s e a t m o s p h e r i c r a d i a t i o n o v e r t h e c e l e s t i a l s p h e r e , B u l l . L e n i n g r a d U n i v . , 119-129. Mark, D.M., and M. C h u r c h , 1977. On t h e m i s u s e o f r e g r e s s i o n i n e a r t h s c i e n c e , M a t h e m a t i c a l G e o l o g y , 9,1, 63-75. M c A r t h u r , L.B., 1978. The s p a t i a l d i s t r i b u t i o n o f d i f f u s e s o l a r r a d i a t i o n i n t h e sky h e m i s p h e r e , M.Sc. T h e s i s , D e p t . o f G e o g r a p h y , 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 , V a n c o u v e r , Canada, 137 pp. M c A r t h u r , L.B., and J . E . Hay, 1978. On t h e a n i s o t r o p y o f d i f f u s e s o l a r r a d i a t i o n , B u l l e t i n o f t h e A m e r i c a n  M e t e o r o l o g i c a l S o c i e t y , 59,11, 1442-1443. M c A r t h u r , L.B., and J . E . Hay, 1980. An a s s e s s m e n t o f t h e t e c h n i q u e s f o r d e t e r m i n i n g t h e d i s t r i b u t i o n o f d i f f u s e s o l a r r a d i a n c e f o r t h e sky h e m i s p h e r e , S o l a r E n e r g y , 25,6,573-574. M c A r t h u r , L.B., and J . E . Hay, 1981. A t e c h n i q u e f o r 1 32 mapping t h e d i s t r i b u t i o n of d i f f u s e s o l a r r a d i a t i o n o v e r sky h e m i s p h e r e , J o u r n a l of A p p l i e d M e t e o r o l o g y , 20,4,421-429. McKee, T.B., and S.K. Cox, 1974. 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S t a n d a r d d i s t r i b u t i o n s o f c l e a r sky r a d i a n c e , Q u a r t e r l y J o u r n a l o f t h e R o y a l M e t e o r o l o g i c a l  S o c i e t y , 103, 457-465. S t e v e n , M.D., and M.H. U n s w o r t h , 1980. A n g u l a r d i s t r i b u t i o n and i n t e r c e p t i o n o f d i f f u s e s o l a r r a d i a t i o n below o v e r c a s t s k i e s , Q u a r t e r l y J o u r n a l of t h e R o y a l M e t e o r o l o g i c a l  S o c i e t y , 106, 57-61. S t e y n , D.G., 1980. The c a l c u l a t i o n of view f a c t o r s f r o m f i s h e y e l e n s p h o t o g r a p h s , A t m o s p h e r e - O c e a n , 18, 254-258. Swokowski, E. W. , 1975. C a l c u l u s w i t h A n a l y t i c Geometry, P r i n d l e , Weber and S c h m i d t I n c . , B o s t o n , M a s s a c h u s e t t s , 854 pp. 1 33 V a l k o , P., 1980. Some e m p i r i c a l p r o p e r t i e s of s o l a r r a d i a t i o n and r e l a t e d p a r a m e t e r s . I n : An I n t r o d u c t i o n t o M e t e o r o -l o g i c a l Measurements and D a t a H a n d l i n g f o r S o l a r E n e r g y A p p l i c a t i o n (DOE/ER-0084), S w i s s M e t e o r o l o g i c a l I n s t i t u t e , Z u r i c h , 46 pp. 1 34 A p p e n d i x I A s s e s s m e n t o f t h e C h a r a c t e r i s t i c s of t h e F i s h e y e Camera Lens and V i d e o Imaging System A l . 1 T e s t f o r A x i a l Symmetry of F i s h e y e Camera Lens The f i s h e y e camera l e n s u s e d i n t h i s s t u d y was c u s t o m - b u i l t and had not been l a b o r a t o r y - c a l i b r a t e d . S i n c e t h e g e o m e t r i c p r o p e r t i e s of t h e l e n s were unknown, a t e s t was made i n o r d e r t o c o n f i r m a x i a l symmetry. T h i s work was p e r f o r m e d a t t h e e x p e r i m e n t a l s i t e , on t h e r o o f of t h e Geography Department a t UBC. A l e v e l l e d S o k i s h a t h e o d o l i t e was u s e d t o s i g h t f o u r t a r g e t s , e a c h a t an a n g u l a r d i s t a n c e of 90° a r o u n d t h e t h e o d o l i t e , making s u r e t h a t t h e t a r g e t s would be w i t h i n t h e f i e l d - o f - v i e w of t h e camera l e n s . Once t h e p o s i t i o n of t h e t a r g e t s had been c a r e f u l l y marked, t h e t h e o d o l i t e was removed and t h e v i d e o camera was p u t i n i t s p l a c e . The camera and l e n s s y s t e m was l e v e l l e d and t h e o c c u l t i n g d i s k was s e t up i n o r d e r t o a v o i d l e n s f l a r e . The b r i g h t n e s s l e v e l s on t h e m o n i t o r were a d j u s t e d t o p r o v i d e enough c o n t r a s t so t h a t a l l of t h e t a r g e t s c o u l d be i d e n t i f i e d e a s i l y on a v i d e o image. T h i s image was t h e n r e c o r d e d and t h e a n g u l a r d i s t a n c e s as v i e w e d on t h e d i g i t i z e d image were d e t e r m i n e d . I t was f o u n d t h a t t h e a n g u l a r s e p a r a t i o n of t a r g e t s was i n d e e d p r e s e r v e d and h e n c e , a x i a l symmetry was c o n f i r m e d . AI.1.2 T e s t t o C o n f i r m E q u i - A n g u l a r P r o j e c t i o n o f F i s h e y e 135 Camera L e n s The f i s h e y e camera l e n s i s n o r m a l l y assumed t o have an e q u i - a n g u l a r p r o j e c t i o n . W i t h a t r u e e q u i - a n g u l a r p r o j e c t i o n , t h e d i s t a n c e of a p o i n t from t h e c e n t r e of t h e c i r c u l a r image i s d i r e c t l y p r o p o r t i o n a l t o t h e z e n i t h a n g l e of t h e c o r r e s p o n d i n g p o i n t i n t h e f i e l d - o f - v i e w . In t h i s s t u d y i t was n e c e s s a r y t o e v a l u a t e t h e a n g u l a r p r o p e r t i e s of t h e camera l e n s i n o r d e r t o c o n f i r m t h e a c c u r a t e l o c a t i o n of a s a m p l i n g p o i n t i n t h e sky h e m i s p h e r e on t h e v i d e o image. T h i s t e s t was c a r r i e d out i n d o o r s . An a u t o m a t i c l e v e l was s e t up, l e v e l l e d and aimed a t a s p o t h e i g h t c h o s e n as a r e f e r e n c e p o i n t . From t h i s p o i n t , e v e r y 10° i n t e r v a l u n t i l 90° was marked o f f a t t h e same h e i g h t , i n an a n t i c l o c k w i s e d i r e c t i o n from t h e r e f e r e n c e mark. A plumb-line was hung down from t h e a u t o m a t i c l e v e l and i t s p o s i t i o n was c a r e f u l l y n o t e d so t h a t t h e v i d e o camera on a t r i p o d c o u l d be p l a c e d i n a s i m i l a r p o s i t i o n . The camera was p l a c e d i n a h o r i z o n t a l o r i e n t a t i o n and l e v e l l e d . The c e n t r e o f t h e f i s h e y e l e n s was p o s i t i o n e d i n t h e e x a c t s p o t where t h e l e v e l had been. A v i d e o image of t h e 10° m a r k i n g s was t a k e n and i t was f o u n d t h a t i t was p o s s i b l e t o c o u n t t h e number o f p i x e l s c o r r e s p o n d i n g t o e a c h 10° i n t e r v a l as w e l l as n o t i n g t h e n u m b e r - o f - p i x e l v a r i a t i o n s i n t h e v e r t i c a l ( a l l marks were l o c a t e d a t t h e same v e r t i c a l h e i g h t ) on t h e image. I t was d i s c o v e r e d t h a t t h e r e were a p p r o x i m a t e l y 17±2 p i x e l s p e r 10° d i v i s i o n w i t h t h e v e r t i c a l d i m e n s i o n o f e a c h s p o t n o t v a r y i n g by more t h a n 2 p i x e l s . I t was n o t e d t h a t t h e 1 36 90° marker was n o t v i s i b l e on t h e image. In f a c t , one c o u l d not c o n f i r m v i s i b l i l i t y of a marker p a s t a p p r o x i m a t e l y 85° on t h e image. The camera was t h e n r o t a t e d 90° a b o u t i t s h o r i z o n t a l a x i s and was r e - l e v e l l e d . A p l u m b l i n e c h e c k c o n f i r m e d c o n s i s t e n c y i n r e p l i c a t i o n o f t h e camera's l o c a t i o n . A n o t h e r image was t a k e n and p i x e l c o o r d i n a t e s were f o u n d f o r e a c h o f t h e 10° m a r k e r s . F o r t h e camera i n t h i s p o s i t i o n , t h e number of p i x e l s p e r 10° had c h a n g e d from 17 p i x e l s t o 14. T h i s s u g g e s t e d t h a t t h e image was e l l i p t i c a l r a t h e r t h a n c i r c u l a r as i n i t i a l l y assumed. On t h e b a s i s of t h i s a n a l y s i s , i t was p o s s i b l e t o d e t e r m i n e t h e shape of t h e v i d e o image and t o l o c a t e s a m p l i n g p o i n t s w i t h i n i t . AI.2 D e t e r m i n a t i o n of t h e Shape o f a V i d e o Image G i v e n t h e v a l u e s of t h e x,y p i x e l c o o r d i n a t e s a l o n g t h e p e r i m e t e r of t h e v i d e o image, t h e e q u a t i o n of t h e e l l i p s e c o u l d be d e t e r m i n e d by t h e f o l l o w i n g method. M u l t i p l e r e g r e s s i o n was p e r f o r m e d t o f i t t h e d a t a t o t h e f o r m (Swokowski, 1975): A x 2 + C y 2 + Dx + Ey + F = 0 . ( A I . 1 ) and f r o m t h i s , t h e e q u a t i o n o f t h e e l l i p s e w i t h n o n - r o t a t e d a x e s may be p r e s e n t e d a s : ( X - 1 3 3 . 4 ) 2 / ( 1 2 0 . 6 ) 2 + ( y - 1 2 4 . 9 ) 2 / ( l 4 5 . 3 ) 2 = 1 (AI.2) where t h e c e n t r e , i n s c r e e n c o o r d i n a t e s , i s ( 1 3 3 , 1 2 6 ) . The d i g i t i z e d image a p p e a r s e l l i p t i c a l due t o an asymmetry i n t h e v i d e o s c a n n i n g p r o c e s s . T h i s r e s u l t s i n t h e l e n s ' c i r c u l a r 1 37 image b e i n g s t r e t c h e d i n t h e y d i r e c t i o n by a c o n s t a n t f a c t o r o f 1.21. The camera was t h e n s e t up h o r i z o n t a l l y and r e - l e v e l l e d and p o s i t i o n e d w i t h t h e c e n t r e c o o r d i n a t e s of ( 1 3 3 , 1 2 6 ) . An image was t a k e n t o c o n f i r m t h e e q u i - a n g u l a r p r o j e c t i o n of t h e l e n s u s i n g t h i s c e n t r e . T a b l e A l . 1 a shows t h e p i x e l c o o r d i n a t e p o s i t i o n s f o r e a c h of t h e 10° m a r k e r s t h a t were v i s i b l e on t h e image. The camera was t h e n r o t a t e d by 9 0 ° , r e - l e v e l l e d and a n o t h e r image was a n a l y s e d . T a b l e AI.1b shows t h e s e r e s u l t s . From t h i s s t u d y , i t c a n be seen t h a t t h e e q u i - a n g u l a r p r o j e c t i o n of t h e f i s h e y e l e n s i s c o n f i r m e d w i t h v a r i a t i o n s of n o t more t h a n ±1 p i x e l a c c u r a c y w h i c h i s t h e r e s o l u t i o n o f t h e v i d e o image on t h e m o n i t o r . A l . 3 D e t e r m i n a t i o n of t h e Shape o f t h e A c t i n o m e t r i c  F i e l d - o f - V i e w as Seen on a V i d e o Image The a c t i n o m e t e r u s e d i n t h i s s t u d y has a t o t a l a n g l e o f a p e r t u r e o f 10.16° as d e t e r m i n e d d u r i n g c a l i b r a t i o n a t t h e AES. G i v e n t h e z e n i t h and a z i m u t h of t h e c e n t r e of t h e a c t i n o m e t e r ' s f i e l d - o f - v i e w , t h e c o r r e s p o n d i n g p i x e l can be l o c a t e d on t h e d i g i t i z e d image p l a n e u s i n g g e o m e t r i c p r i n c i p l e s . The t r a n s l a t i o n of sky t o s c r e e n c o o r d i n a t e s i n v o l v e s f i r s t l y a c o n v e r s i o n from sky ( z , a ) t o p o l a r ( r , 8 ) c o o r d i n a t e s , where r = 2/TT Z R 0* ( A l .4) 1 38 T a b l e A I.1a P i x e l C o o r d i n a t e P o s i t i o n s f o r E a c h of t h e 10° T a r g e t s V i s i b l e on t h e V i d e o Image M a r k e r P o s i t i o n (°) P i x e l c o o r d i n a t e s 0 131 r 1 33 10 131 r 1 47 20 131 , 161 30 131 , 1 75 40 131 , 189 50 131 , 203 60 131 p 2 1 7 70 131 r230 80 131 ,243 T a b l e AI.1b Same as T a b l e A I . 1 a f o r V i d e o Camera by 90° a R o t a t i o n of M a r k e r P o s i t i o n (°) P i x e l C o o r d i n a t e s 0 1 0 20 30 40 50 60 130,132 146,132 163,132 180,132 197,132 214,132 231,132 1 39 and 6 = a. R 0* i s t h e s e m i - m i n o r a x i s of t h e p l a n a r image and z and a a r e t h e sky z e n i t h a l and a z i m u t h a l a n g l e s r e s p e c t i v e l y . Then t r a n s l a t i n g f r o m p o l a r c o o r d i n a t e s ( t , 8 ) t o c a r t e s i a n c o o r d i n a t e s ( x , y ) g i v e s , y = y 0 + rsinc? x 1 .21 ( A l . 5) x = x 0 + xcosfl ( A l . 6 ) where ( x 0 , y 0 ) a r e t h e c e n t r e c o o r d i n a t e s of t h e d i g i t i z e d p l a n a r image. A l l p i x e l s c o r r e s p o n d i n g t o sky p o i n t s l e s s t h a n 5.08° from t h e c e n t r a l p o i n t a r e i n c l u d e d i n t h e c o m p u t a t i o n o f t h e mean b r i g h t n e s s of t h e sample a r e a . 1 40 A p p e n d i x I I R e g r e s s i o n R e s u l t s o f R a d i a n c e v e r s u s C o r r e c t e d B r i g h t n e s s f o r C l e a r , O v e r c a s t and P a r t l y C l o u d y S k i e s 1 4 1 R a d i a n c e (Wm" 2sr"') *Note - 1,2 r e p r e s e n t t h e number and l o c a t i o n of d a t a p o i n t s F i g u r e A l I . 1 R e g r e s s i o n L i n e of R a d i a n c e (Wm" 2sr"') and B r i g h t n e s s f o r a C l e a r Sky 0916 LST J u l y 29,1983 1 42 158.0 17; R a d i a n c e (Wm~ 2sr ') F i g u r e A l l . 2 R e g r e s s i o n L i n e of R a d i a n c e ( W m ~ 2 s r _ 1 ) and B r i g h t n e s s f o r a C l e a r Sky 1631 LST J u l y 29,1983 F i g u r e A l l . 3 R e g r e s s i o n L i n e of R a d i a n c e (Wm" 2sr"') and B r i g h t n e s s f o r a C l e a r Sky 1118 LST J u l y 30,1983 1 44 -60.00 -30.OO 40.00 100.0 ISO.O 220.0 2S0 R a d i a n c e (Wm 2 s r ' ) F i g u r e A l l . 4 R e g r e s s i o n L i n e of R a d i a n c e (Wm~ 2sr"') and B r i g h t n e s s f o r a P a r t l y C l o u d y Sky 1125 LST A u g u s t 29,1983 145 F i g u r e A l l . 5 R e g r e s s i o n L i n e of R a d i a n c e (Wm 2 s r " ' ) and B r i g h t n e s s f o r a P a r t l y C l o u d y Sky 1416 LST A u g u s t 27, 1983 146 I 10.0 19 R a d i a n c e ( W m ~ 2 s r _ 1 ) F i g u r e A l l . 6 R e g r e s s i o n L i n e of R a d i a n c e (Wm _ 2sr"') and B r i g h t n e s s f o r an O v e r c a s t Sky 1250 LST A u g u s t 27,1983 1 47 F i g u r e A l l . 7 R e g r e s s i o n L i n e of R a d i a n c e (Wm~ 2sr~') and B r i g h t n e s s f o r an O v e r c a s t Sky 0921 LST A u g u s t 27,1983 

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