UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The Spatial distribution of diffuse solar radiation in the sky hemisphere McArthur, Lorne John Bruce 1978

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1978_A6_7 M31.pdf [ 6.95MB ]
Metadata
JSON: 831-1.0094255.json
JSON-LD: 831-1.0094255-ld.json
RDF/XML (Pretty): 831-1.0094255-rdf.xml
RDF/JSON: 831-1.0094255-rdf.json
Turtle: 831-1.0094255-turtle.txt
N-Triples: 831-1.0094255-rdf-ntriples.txt
Original Record: 831-1.0094255-source.json
Full Text
831-1.0094255-fulltext.txt
Citation
831-1.0094255.ris

Full Text

THE SPATIAL DISTRIBUTION OF DIFFUSE SOLAR RADIATION IN THE SKY HEMISPHERE by LORNE JOHN BRUCE McARTHUR B . S c , McMaster U n i v e r s i t y , 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department o f Geography We ac c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA August 19 78 (c) Lome John Bruce McArthur, 19 78 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i lab le for reference and study. I further agree that permission for extensive copying of th i s thesis for scholar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes i s fo r f i nanc ia l gain sha l l not be allowed without my written permission. Department of Geography  The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 August 8, 19 78 Corrigendum In "The Spatial Distribution of Diffuse Solar Radiation i n the Sky Hemisphere" by Lorne John Bruce McArthur, submitted as an M.Sc. Thesis to the University of B r i t i s h Columbia, August 1978, page 88 (Figure 4.9) should be replaced with the attached page 88. Further, on page 91, the following figure references should be changed. Figure 2.7 on lines 8 and 14 should be read as Figure 2.6a. Figures 4.9 and 4.10, referenced on line 13 should read Figures 4.10 and 4.11 respectively. Figure 4.8 on line 15 should read Figure 4.9* These changes should f a c i l i t a t e a better understanding of the text. ABSTRACT A t e c h n i q u e was d e v e l o p e d t o produce maps o f 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 er the sky hemi-sphere f o r a v a r i e t y o f sky c o n d i t i o n s . T h i s p r o c e d u r e , by u t i l i z i n g b o t h a c t i n o m e t r i c and p h o t o g r a p h i c i n f o r m a t i o n , overcomes the s a m p l i n g problems o f p r e v i o u s methods. Photographs were s i m u l t a n e o u s l y exposed w i t h a c t i n o -m e t r i c measurements o f d i f f u s e s o l a r r a d i a n c e . The photographs were th e n d i g i t i z e d and the d e n s i t y v a l u e s c o r r e s p o n d i n g t o the a c t i n o m e t r i c measurements c o r r e l a t e d w i t h the known r a d i a n c e s . The e q u a t i o n produced was t h e n u t i l i z e d t o determine the r a d i a n c e f o r each d e n s i t y v a l u e f o r the e n t i r e p h o t ograph. From t h i s i n f o r m a t i o n , a map 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 er the sky hemisphere was produced. To determine the q u a l i t y o f the r a d i a n c e d i s t r i b u t i o n s , the e s t i m a t e d r a d i a n c e s were n u m e r i c a l l y i n t e g r a t e d and compared w i t h the d i f f u s e i r r a d i a n c e i n c i d e n t on a h o r i z o n t a l s u r f a c e . These were u s u a l l y found t o be w i t h i n ±10% f o r the sky c o n d i t i o n s examined. A f u r t h e r t e s t , u s i n g t h i s method to determine the d i f f u s e i r r a d i a n c e , was p erformed t o e s t i m a t e the shortwave i r r a d i a n c e on s e v e r a l s o u t h - f a c i n g i n c l i n e d s u r f a c e s . The r e s u l t s were found t o be w i t h i n ±5% o f the measured v a l u e s . i i The 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 f o r c l e a r s k i e s were a l s o compared w i t h s i m i l a r work and commented upon. T h i s t e c h n i q u e , a l t h o u g h s t i l l not p e r f e c t e d , p r o v i d e s a s u p e r i o r means f o r i n s t a n t a n e o u s l y m o d e l l i n g d i f f u s e energy.and c o u l d a l s o be u t i l i z e d i n the c o l l e c t i o n o f the da t a base n e c e s s a r y f o r t e s t i n g t h e o r e t i c a l models o f s c a t t e r i n g i n the atmosphere. i i i TABLE OF CONTENTS Page ABSTRACT , 1 ± TABLE OF CONTENTS i v LIST OF TABLES v±± LIST OF FIGURES v i i l LIST OF ILLUSTRATIONS x i ACKNOWLEDGEMENTS x i i CHAPTER ONE - INTRODUCTION 1 1.1 O b j e c t i v e s 1 1.2 Background . 2 CHAPTER TWO - EXPERIMENTAL RATIONALE 5 CHAPTER THREE - EXPERIMENTAL PROCEDURE 19 3.1 E x p e r i m e n t a l S i t e 19 3.2 View F a c t o r 20 3.3 R a d i a t i o n I n s t r u m e n t a t i o n 22 3.3-1 Pyranometers 22 3.3.2 Eppley Normal I n c i d e n c e P y r h e l i o m e t e r 25 3.3.3 L i n k e - F e u s s n e r A c t i n o m e t e r 25 3.3-4 Radiometer Maintenance 27 3.4 P h o t o g r a p h i c I n s t r u m e n t a t i o n 28 3.5 F i e l d Measurement Program 31 3.6 P h o t o g r a p h i c D i g i t i z a t i o n 36 i v Page 3.6.1 Joyce L o e b l M i c r o d e n s i t o m e t e r 36 3.6.2 D i g i t i z a t i o n s a m p l i n g c o n s i d e r a t i o n s 38 3.6.3 N e g a t i v e a l i g n m e n t 40 3.7 E r r o r A n a l y s i s 142 3.7-1 Methodology 42 3.7-2 E r r o r i n the v e r i f i c a t i o n o f the 43 p h o t o g r a p h i c t e c h n i q u e 3.7.2.1 Pyranometers 43 3.7.2.2 Normal I n c i d e n c e Eppley 43 P y r h e l i o m e t e r 3.7.2.3 R e c o r d e r e r r o r 43 3.7.2.4 Data a b s t r a c t i o n 45 3.7.2.5 T o t a l p r o b a b l e e r r o r i n the 47 p h o t o g r a p h i c v a l i d a t i o n system 3.7.3 E r r o r a s s o c i a t e d w i t h the measurement 47 o f d i f f u s e r a d i a n c e 3.7.3.1 L i n k e - F e u s s n e r A c t i n o m e t e r 47 3.7.3.2 Recorder e r r o r 48 3.7.3.3 Data a b s t r a c t i o n 49 3.7.3.4 P r o b a b l e e r r o r i n the p h o t o g r a p h i c 49 subsystem 3.7-4 E r r o r s i n the p h o t o g r a p h i c r e d u c t i o n 49 3.7.4.1 D i g i t i z a t i o n 49 3.7.4.2 P h o t o g r a p h i c system 50 3.7.5 R e l a t i v e p r o b a b l e e r r o r o f the 50 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 CHAPTER FOUR - ANGULAR DISTRIBUTION OF ;: 52 DIFFUSE RADIATION 4.1 C a l i b r a t i o n Technique 52 v Page 4.2 Curve F i t t i n g P r o c e d ures 55 4 . 3 V e r i f i c a t i o n o f C a l i b r a t i o n s 6 3 4 . 4 A p p l i c a t i o n 66 4 . 4 . 1 Case s t u d i e s 73 4 . 4 . 2 N o r m a l i z e d d i s t r i b u t i o n s 84 CHAPTER FIVE - MODELLING DIFFUSE RADIATION ON 9 8 SLOPING SURFACES 5.1 M o d e l l i n g Technique 9 8 5.2 R e s u l t s 102 CHAPTER SIX - PRELIMINARY INVESTIGATION INTO 106 GRID SIZE CHAPTER SEVEN - CONCLUSIONS AND RECOMMENDATIONS 115 BIBLIOGRAPHY 119 APPENDIX ONE - LIST OF SYMBOLS 122 APPENDIX TWO - CALIBRATION CURVES " 125 v i LIST OP TABLES TABLE Page 2.1 Energy D i s t r i b u t i o n i n the S o l a r Spectrum 10 3.1 C a l i b r a t i o n o f Kipp and Zonen CM5 Pyranometers 23 f o r Incoming Shortwave R a d i a t i o n 3.2 On S i t e Sky Cover C o n d i t i o n s 34 3.3 T y p i c a l Sequence o f A c t i n o m e t r i c Measurements 37 and P h o t o g r a p h i c Exposures 3 . 4 E r r o r Summary f o r K i p p and Zonen Pyranometer 44 3.5 R e c o r d e r E r r o r w i t h Respect t o D i f f u s e 46 R a d i a t i o n S i g n a l 4.1 E x p o n e n t i a l C u r v e - F i t t i n g S t a t i s t i c s 56 4.2 Comparison o f Measured and Computed I r r a d i a n c e 67 5.1 Comparison o f Shortwave I r r a d i a n c e on a 103 H o r i z o n t a l S u r f a c e and 3 S o u t h - F a c i n g S l o p e s 6 .1 S i z e o f Square. G r i d 108 6 .2 R e l a t i v e E r r o r o f I n t e g r a t e d F l u x e s f o r a 113 V a r i a t i o n i n Sample S i z e v i i LIST OF FIGURES FIGURE Page 2.1 A b s o r p t i o n o f r a d i a t i o n a t v a r i o u s wavelengths 7 2.2 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 r a d i a t i o n 9 2.3 D i s t r i b u t i o n o f luminous i n t e n s i t y and 13 e n e r g e t i c a l i n t e n s i t y f o r J u l y 3, 1953 2.4 Sky d i s t r i b u t i o n o f the r e l a t i v e e n e r g e t i c a l 15 i n t e n s i t y and luminous i n t e n s i t y o f d i f f u s e r a d i a t i o n 2.5a S t a n d a r d d i s t r i b u t i o n o f n o r m a l i z e d 16 sky r a d i a n c e Z = 55° 2.5b Sky luminance d i s t r i b u t i o n 16 2.6a S t a n d a r d d i s t r i b u t i o n o f n o r m a l i z e d 17 sky r a d i a n c e Z = 35° 2.6b D i s t r i b u t i o n o f luminous i n t e n s i t y and 17 e n e r g e t i c a l i n t e n s i t y f o r June 27, 1953 3.1 E q u i d i s t a n t p r o j e c t i o n o f the 21 l o c a l h o r i z o n 3.2 T r a n s m i t t a n c e f u n c t i o n o f u l t r a - v i o l e t 30 c u t - o f f f i l t e r L-1B 3.3 F i l m and f i l t e r s p e c t r a l response curves 32 4.1 I l l u s t r a t i o n o f the e f f e c t o f the removal 58 o f an o u t l i e r 4.2 S t a t i s t i c a l l y s i g n i f i c a n t curves 6l 4.3 R e p r e s e n t a t i v e n e s s o f s e l e c t e d d a t a p o i n t s 62 4.4 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 f o r a c l e a r sky 70 4.5 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 f o r a p a r t i a l l y 82 cloudy sky v i i i Page 4.6 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 f o r an 83 o v e r c a s t sky 4.7 C l e a r sky n o r m a l i z e d sky r a d i a n c e d i s t r i b u t i o n 86 f o r 12:40 February 10, 19 78 4.8 C l e a r sky n o r m a l i z e d sky r a d i a n c e d i s t r i b u t i o n 87 f o r 13:40 February 10, 1978 4.9 C l e a r sky n o r m a l i z e d sky r a d i a n c e d i s t r i b u t i o n 88 f o r 13:26 F e b r u a r y 26, 19 78 4.10 C l e a r sky n o r m a l i z e d sky r a d i a n c e d i s t r i b u t i o n 89 f o r 13:47 February 26, 19 78 4.11 C l e a r sky n o r m a l i z e d sky r a d i a n c e d i s t r i b u t i o n 90 f o r 14:11 February 26, 19 78 4.12 O v e r c a s t n o r m a l i z e d sky r a d i a n c e d i s t r i b u t i o n 93 4.13 P a r t i a l l y o v e r c a s t .normalized. d i s t r i b u t i o n 9 4 f o r 12:47 February 15, 1978 4.14 P a r t i a l l y o v e r c a s t -normalized. - d i s t r i b u t i o n 95 f o r 13:17 F e b r u a r y 15, 19 78 4.15 P a r t i a l l y o v e r c a s t normalized., d i s t r i b u t i o n 96 f o r 13:47 February 15, 19 78 6.1 The v a r i a t i o n o f R.M.S.E. due t o i n t e r p o l a t i o n 110 w i t h sample s i z e A2 .1 C a l i b r a t i o n curve f o r 12:40 LAT • , 126 February 10, 19 78 A2.2 C a l i b r a t i o n curve f o r 13:40 LAT 127 February 10, 19 78 A2 .3 C a l i b r a t i o n curve f o r 1.1:20 LAT 128 February 14, 19 78 A2 .4 C a l i b r a t i o n curve f o r 12:30 LAT 129 F e b r u a r y 14, 19 78 A2.5 C a l i b r a t i o n curve f o r 12:47 LAT 130 F e b r u a r y 15, 19 78 A2.6 C a l i b r a t i o n curve f o r 13:17 LAT 131 F e b r u a r y 15, 19 78 i x Page A2 .7 C a l i b r a t i o n curve f o r 13:22 LAT 132 February 15, 19 78 A2.8 C a l i b r a t i o n curve f o r 13=37 LAT 133 F e b r u a r y 15, 19 78 A2.9 C a l i b r a t i o n curve f o r 10:17 LAT 134 F e b r u a r y 24, 1978 A2.10 C a l i b r a t i o n curve f o r .13:26 LAT 135 February, 26, 19 78 A 2 . l l C a l i b r a t i o n curve f o r - 13:47 LAT 136 F e b r u a r y 26, 19 78 A2.12 C a l i b r a t i o n curve f o r 14:11 LAT 137 February 26, 19 78 x LIST OF ILLUSTRATIONS PLATE Page 4 . 1 E l e c t r o n i c a l l y d e n s i t y s l i c e d a l l - s k y 72 p h o t o g r a p h i c image o f 1 4 : 0 0 September 1 0 , 1 9 77 4 . 2 A l l - s k y photograph exposed a t 1 4 : 0 7 77 F e b r u a r y 1 0 , 19 78 o f a c l e a r sky 4 . 3 A l l - s k y photograph exposed a t 13:17 79 F e b r u a r y 1 5 , 1 9 7 8 o f a' p a r t i a l l y o v e r c a s t sky 4 . 4 A l l - s k y photograph exposed at 12:30 8 1 February 1 4 , 19 78 o f a c o m p l e t e l y o v e r c a s t sky x i ACKNOWLEDGEMENTS The f i n a n c i a l s u p p o r t f o r t h i s study was p r o v i d e d by the N a t i o n a l Research C o u n c i l o f Canada and the Atmospheric Environment S e r v i c e . T h e i r a s s i s t a n c e i s g r e a t l y a p p r e c i a t e d . I would l i k e t o thank my s u p e r v i s o r , Dr. J . E. Hay, f o r h i s s u p p o r t and d i r e c t i o n . I would a l s o l i k e t o thank my o t h e r committee members, Dr. T. R. Oke and Dr. M. A. Church, f o r t h e i r time i n ans w e r i n g my q u e s t i o n s and p r o v i d i n g u s e f u l feedback throughout the p r o j e c t . I would f u r t h e r l i k e t o acknowledge Mr. D. Pearce f o r a l l o w i n g me the use o f the P l a n t S c i e n c e F i e l d L a b o r a t o r y , U n i v e r s i t y o f B r i t i s h Columbia. I am a l s o most g r a t e f u l t o Mr. C. B r i c k e r o f the A l b e r t a Remote S e n s i n g Centre f o r . the use o f the Cent r e ' s e l e c t r o n i c d e n s i t y s l i c e r , and Dr. G. Walker o f the Department o f Astronomy o f the U n i v e r s i t y o f B r i t i s h Columbia f o r a l l o w i n g me the use of t h e i r e l e c t r o n i c d i g i t i z e r . I am deeply i n d e b t e d t o Mr. B. Kalanda. and Mr. 0'. Hertzman f o r the many d i s c u s s i o n s we have had c o n c e r n i n g the r e s e a r c h and the c o n t i n u o u s m o r a l s u p p o r t they have p r o v i d e d throughout t h i s t i m e . S p e c i a l a p p r e c i a t i o n and thanks go t o my w i f e , Glenda, f o r h e r mora l encouragement throughout our m a r r i a g e as I have worked on t h i s p r o j e c t . I am f u r t h e r i n d e b t e d t o h e r f o r the t y p i n g o f the f i n a l m a n u s c r i p t . x i i CHAPTER ONE INTRODUCTION 1.1 Obj e c t l v e s With the growing i n t e r e s t i n s o l a r r a d i a t i o n as a source of energy, the accurate modelling of shortwave r a d i a t i o n onto a s l o p i n g surface i s i n c r e a s i n g i n s i g n i f i c a n c e . The deter-mination of the d i f f u s e shortwave i r r a d i a n c e f o r such i n c l i n e d surfaces ( N o r r i s , : . , 1 9 6 6) has r e s u l t e d i n a need to know the s p a t i 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 over the sky hemi-sphere. In l i n e w i t h t h i s requirement, the o b j e c t i v e s of t h i s research are: 1. To c h a r a c t e r i z e the 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 over the c e l e s t i a l dome 2. For a v a r i e t y of sky conditions to i n t e g r a t e the hemisphere radiance values and compare t h i s value w i t h simultaneously measured h o r i z o n t a l d i f f u s e r a d i a t i o n 3. To use a s i m i l a r i n t e g r a t i n g procedure to map the d i f f u s e r a d i a t i o n onto 30° , 6 0 ° and 90° s o u t h - f a c i n g slopes and compare the c a l c u l a t e d and measured values 4. To produce a normalized map f o r each sky c o n d i t i o n observed f o l l o w i n g the method of Steven (19 77) 5. To undertake a p r e l i m i n a r y a n a l y s i s on the sampling density r e q u i r e d to r e t a i n a reasonable approximation of the 1 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 i n the sky hemisphere. 1.2 Background A knowledge o f the 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 i s a n e c e s s a r y p r e r e q u i s i t e f o r the e f f e c t i v e m o d e l l i n g of s o l a r r a d i a t i o n onto a s l o p i n g s u r f a c e . U n l i k e d i r e c t beam r a d i a t i o n , which can be g e o m e t r i c a l l y mapped onto any s u r f a c e w i t h known s l o p e and o r i e n t a t i o n , the d i f f u s e r a d i a t i o n cannot be p a r a m e t e r i z e d as a p o i n t s o u r c e . To overcome the problem, s e v e r a l assumptions have been made t o approximate the sky 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 . K o n d r a t y e v (1954) assumed I s o t r o p y i n d e t e r m i n i n g the d i f f u s e r a d i a t i o n from the sky dome r e c e i v e d on a s l o p i n g s u r f a c e . T h i s , however, was s u b s e q u e n t l y found t o be an u n a c c e p t a b l e assumption (Ko n d r a t y e v and Manolova, .i960). Morse and C z a r n e e k i (1958) s t a t e d t h a t most d i f f u s e r a d i a t i o n o r i g i n a t e d around the s o l a r d i s c and c o u l d be t r e a t e d i n a manner s i m i l a r t o the d i r e c t beam component. However, M o r r i s and Lawrence (1971) found t h a t f o r c l e a r sky days o n l y 57% o f the d i f f u s e component o r i g i n a t e d w i t h i n 60° o f the s o l a r d i s c . N o r r i s (1966) t e s t e d the above two a p p r o x i m a t i o n s and found t h a t n e i t h e r a d e q u a t e l y d e s c r i b e d the d i f f u s e shortwave r a d i a t i o n i n c i d e n t on a n o r t h - f a c i n g w a l l . D u f f i e and Beckman (1974) however, s t i l l f e e l t h a t the d i r e c t i o n a l a p p r o x i m a t i o n i s adequate f o r c l e a r sky and t h i n - c l o u d l a y e r 3 c o n d i t i o n s . Hay (19 77) d e v e l o p e d a means t o v a r y the p e r c e n t a g e o f d i r e c t i o n a l l y o r i e n t e d d i f f u s e r a d i a t i o n by u s i n g a d i r e c t s o l a r r a d i a t i o n t r a n s m i s s i o n c o e f f i c i e n t . T h i s approach has been t e s t e d and found s u p e r i o r t o b o t h the i s o t r o p i c and the f i x e d p e r c e n t a g e d i r e c t i o n a l approach. N o r r i s (1966) c o n c l u d e d t h a t to. a r r i v e at an "e x a c t f o r m u l a f o r c a l c u l a t i n g the d i f f u s e component 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 , i t would be n e c e s s a r y to study the a n i s o t r o p y o f the sky r a d i a t i o n " . F o l l o w i n g t h e statement o f N o r r i s (1966), i t i s e s s e n t i a l t h a t r e s e a r c h e r s have ac c e s s t o a q u a l i t y s e t o f da t a d e s c r i b i n g the a n g u l a r d i s t r i b u t i o n o f s o l a r d i f f u s e r a d i a t i o n . These d a t a can be used t o develop and t e s t an e o l o t r o p i c ( a n i s o t r o p i c ) model. S i n c e the r a d i a n t i n t e n s i t y i s not u n i f o r m , a t e c h n i q u e which p r e s e r v e s the s p a t i a l c h a r a c t e r i s t i c s must be u t i l i z e d . At p r e s e n t o n l y two t e c h n i q u e s a re a v a i l a b l e . Heimo and V a l k o (19 76) have deve l o p e d a system o f r o t a t i n g pyranometers t o measure the t o t a l i n c o m i n g shortwave r a d i a t i o n on 77 d i f f e r e n t s u r f a c e s . However, o n l y w i t h the use o f su c -c e s s i v e a p p r o x i m a t i o n t e c h n i q u e s can the r a d i a n c e o f any one p o i n t i n the sky hemisphere be. determined.. The second method i s t h a t o f Stev e n (19 77) who used a t e c h n i q u e s i m i l a r t o t h a t used by Kond r a t y e v e t a l (1955). S t e v e n (1977) used 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 34 p o i n t s o u r c e s o f d i f f u s e r a d i a t i o n i n the c e l e s t i a l dome. From t h e s e , a c o n t o u r map w i t h l i n e s o f e q u a l n o r m a l i z e d r a d i a n c e was drawn. Due t o the slow response o f the I n s t r u m e n t , the measurements spanned a time p e r i o d o f 40 m i n u t e s . T h i s l i m i t e d a l l work t o the l e s v a r i a b l e c l e a r sky s i t u a t i o n s . The t e c h n i q u e d e v e l o p e d i n the p r e s e n t study has at t e m p t e d t o overcome the problem o f response time by s u p p l e -menting t h e a c t u a l measurements w i t h a l l - s k y p h o t o g r a p h s . Because o f the r e l a t i o n s h i p between v i s i b l e and shortwave r a d i a t i o n , the a c t i n o m e t r i c measurements need o n l y s e r v e as a c a l i b r a t i o n method f o r the v i s i b l e r a d i a t i o n i n f o r m a t i o n i n the photograph. To q u a n t i f y t h i s l a t t e r i n f o r m a t i o n , a m i c r o -d e n s i t o m e t e r was employed t o d i g i t i z e the exposed n e g a t i v e s . CHAPTER TWO EXPERIMENTAL RATIONALE S o l a r energy, as I t I n t e r e s t s c l i m a t o l o g i s t s , - o c c u r s between wavelenths o f 0.2 ym and 4.0 ym (Drummond., 19 70). W i t h i n t h i s waveband, the v i s i b l e domain i s found between 0.39 ym and 0.76 ym ( P a l t r i d g e and P i a t t , 19 76). I t i s o n l y i n t h i s very s m a l l s p e c t r a l r e g i o n t h a t most p h o t o g r a p h i c f i l m i s s e n s i t i v e . Because p h o t o g r a p h i c f i l m samples l e s s than 10% o f the s o l a r spectrum, i t i s n e c e s s a r y to v a l i d a t e i t s r e p r e s e n t a t i v e n e s s as a p a r a m e t e r i z a t i o n f o r the t o t a l shortwave r a d i a t i o n - f l u x . I n the case o f s t u d y i n g the a n g u l a r d i s t r i b u t i o n o f the d i f f u s e shortwave i r r a d i a n c e over the sky hemisphere,"such a v a l i d a t i o n must a l s o c o n s i d e r changes i n the shortwave spectrum w i t h r e s p e c t t o the s o l a r z e n i t h . The c o n f i r m a t i o n o f v i s i b l e r a d i a t i o n as a p a r a m e t e r i z a t i o n o f s o l a r r a d i a t i o n w i l l be d e v e l o p e d from the e x t r a t e r r e s t i a l f l u x t o the d i f f u s e f l u x . I n the l a t t e r c a s e , t h i s p a r a m e t e r i z a t i o n w i l l a l s o be i n v e s t i g a t e d as a f u n c t i o n o f the p o s i t i o n o f the s o l a r d i s c . On a day to day b a s i s , the s p e c t r a l n a t u r e o f the e x t r a t e r r e s t i a l r a d i a t i o n remains r e l a t i v e l y c o n s t a n t . Approx-i m a t e l y 45% o f the t o t a l energy i s c o n t a i n e d w i t h i n the v i s i b l e waveband. The r e m a i n i n g 55% o f the energy i s d i s t r i b u t e d .. 6 between the u l t r a - v i o l e t (9%) and the i n f r a r e d ( 4 6 $ ) ( P a l t r i d g e and P i a t t , 19 76). As the s o l a r r a d i a t i o n passes through a c l e a r . a t m o -s p h e r e , n e a r l y a l l the u l t r a v i o l e t r a d i a t i o n i s absorbed by ozone ( W a l l a c e and Hobbs, 19 76) and oxygen ( S i v k o v , 1968), w h i l e the i n f r a r e d p o r t i o n o f the s o l a r spectrum i s d e p l e t e d m a i n l y by wat e r vapour and carbon d i o x i d e a b s o r p t i o n ( M i l l e r and Thompson, 1970). The v i s i b l e band, however, remains r e l a t i v e l y unabsorbed ( W a l l a c e and Hobbs, 1976). The a b s o r p t i o n t h a t does, o c c u r i n the v i s i b l e c o n s i s t s o f a weak ozone a b s o r p t i o n band between 0 . 4 4 and 0.78 ym; two oxygen a b s o r p t i o n bands--one a t 0.69 pm and the more s i g n i f i c a n t between 0.76 and 0.80 i_im; and a water vapour a b s o r p t i o n band o c c u r r i n g between 0.57 and 0.70 y n u ( S i v k o v , 1968) . The l a t t e r i s i n s i g n i f i c a n t when c o n s i d e r i n g t o t a l a b s o r p t i o n o f r a d i a t i o n by w a t e r vapour ( S i v k o v , 1968). F i g u r e 2.1 g r a p h i c a l l y i l l u s t r a t e s the a b s o r p t i v i t y o f the atmosphere over the e n t i r e s o l a r spectrum. S o l a r r a d i a t i o n i s a l s o s e l e c t i v e l y d e p l e t e d by m o l e c u l a r and a e r o s o l s c a t t e r i n g . T h i s i s dependent upon the c o n s t i t u e n t s o f the atmosphere and the o p t i c a l a i r mass. For a c l e a n dry atmosphere, Kondratyev (1969) shows t h a t f o r a change i n the s o l a r z e n i t h a n g l e between 0° and 90° , the percen t a g e o f the s o l a r spectrum found i n the v i s i b l e wave-bands v a r i e s between 44.6% and 37.6%, r e s p e c t i v e l y \ Thus, the a c t u a l p e r c e n t a g e d i s t r i b u t i o n o f energy a t the s u r f a c e • ••7 ( ID 0.1 0 . 2 (.).:.! 0 . 4 ().(. 0 . 8 I 2 .1 4 5 (. 8 10 2 0 W a v e l e n g t h . ( b ) A b s o r p t i o n s p e c t r u m t o r ! l ; 0 W a v e l e n g t h , ( c ) A b s o r p t i o n s p e c t r u m f o r ; i t i n o . s p h e r e l l , 0 W a v e l e n g t h , /tm F i g u r e 2.1 A b s o r p t i o n o f r a d i a t i o n at v a r i o u s w a v elengths by (a) 0 and 0 3 ; (b) H 2 0; and (c) the p r i n c i p a l a b s o r b i n g gases (from M i l l e r and Thompson, 19 70) 8 i s - h i g h l y v a r i a b l e , even over a s i n g l e day. The s p e c t r a l d i s t r i b u t i o n o f the c l e a r sky d i f f u s e s o l a r r a d i a t i o n i s somewhat s i m i l a r t o the s o l a r s pectrum, a l t h o u g h the t o t a l i r r a d i a n c e i s of a l e s s e r magnitude. Kondratyev (1969) p r e s e n t s the da t a o f Lenz (1961) f o r a t u r b i d atmosphere showing the maximum f l u x d e n s i t y t o be at 0.451 urn a t the s o l a r , z e n i t h and, i n t h i s c a s e , s h i f t i n g down to 0.401 ym at a .point.90° : from the s o l a r d i s c . F i g u r e 2.2 p r o v i d e s s i m i l a r d a t a , a l s o c o l l e c t e d by Lenz (1961) showing the v a r i a t i o n i n the s p e c t r a l d i s t r i b u t i o n a t v a r i o u s a z i m u t h a l d i s t a n c e s from the sun. Two i m p o r t a n t p o i n t s emerging from t h i s f i g u r e a r e : (1) the maximum r a d i a n t i n t e n s i t y i s found a t 0.45 ym (K o n d r a t y e v , 1969), and (2) f o r a l l azimuths p r e s e n t e d , a l a r g e p o r t i o n o f the r a d i a t i o n o c c u r s i n the v i s i b l e w a v e l e n g t h s . The o b s e r v a t i o n a l r e s u l t s o f Lenz ( I 9 6 I ) i n d i c a t e t h a t the use o f v i s i b l e r a d i a t i o n t o e s t i m a t e s o l a r r a d i a t i o n on c l e a r sky days i s p o s s i b l e . T a b l e 2.1 ( K o n d r a t y e v , 1969) i l l u s t r a t e s the 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 r a d i a t i o n s c a t t e r e d by c l e a n dry a i r and 3 d i f f e r e n t w ater d r o p l e t s i z e s . Only i n the case o f R a y l e i g h s c a t t e r are the maxima found o u t s i d e the v i s i b l e r e g i o n o f t h e spectrum. As the s i z e of the s c a t t e r i n g s u b s t a n c e i n c r e a s e , the i n t e n s i t y o f d i f f u s e r a d i a t i o n a l s o i n c r e a s e s and the spectrum s h i f t s towards the l o n g e r w a v e l e n g t h s . T h i s l a t t e r e f f e c t l o c a t e s the maxima i n the v i s i b l e w a v e l e n g t h s . I n the case o f the l a r g e s t s c a t t e r e r i l l u s t r a t e d , b o t h a p r i m a r y and a secondary 9 F i g u r e '2 ..2... 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 at d i f f e r e n t p o i n t s o f the s o l a r a l m u c a n t h a r a t whose azim u t h v a l u e s r e l a t i v e t o t h e sun are g i v e n i n t h i s f i g u r e o f Lenz (1961) . from ( K o n d r a t y e v , (1969) TABLE 2 . 1 . — E n e r g y d i s t r i b u t i o n i n the s o l a r spectrum o u t s i d e the atmosphere ( 1 0 " 3 c a l / c m 2 m i n ) and the s p e c t r a l c o m p o s i t i o n o f 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 ) (Kondratyev, 1 9 6 9 ) D i f f u s e R a d i a t i o n by wavebands (DA,.urn) o c \ i ^ r v r > co o -=r vo m m m m m - ^ r ^ r -=r . . . . . . . . o o o o o o o o I I I I I I I I OO . _ O - C\! . . -=r VD OO CU .. ... . -=r CM m m m m m ^ r o o o o o o o o Sun 2 . 6 11.5 2 1 .8 31-3 3 5 . 2 36.0 5 4 . 3 62 .6 1 cm 3 o f c l e a n : 4 . 4 1 4 . 4 2 1 . 9 23-5 2 0 .8 16.9 1 7 . 2 13-7 dry a i r 100 d r o p l e t s 0 . 0 5 0.27 0 . 4 4 0 . 5 4 0 . 5 1 0 . 4 5 0.52 0 . 4 6 r = 0 . 1 y 25 d r o p l e t s 0 . 1 4 0.78 1 . 6 2 1.78 3-52 3-78 6 . 4 1 7.65 r = 0 . 5 y 5 d r o p l e t s 1 . 0 4 . 6 . 9 - 2 . 12 .8 1 4 . 6 15.1 2 3 . 2 25.6 r = 1 y ui IV) I—1 H CO U l O O QJ O p- 3 o II II TS o 1—1 O t l O O P "O CD • • H-c t CD H 4 CO c+ CD o -c CO •£ c+ M 01 CD P IV) U l . O —4 O VO • • • • • uo UO UO U l OA M U l -Er OA O J r - t -tr OA IV) - t C A U l M 4=-CO U l O IV) co C A -tr CO -tr OO UO OA rv> -Cr o - t O M ro o O co vo h-1 uo oo uo o o U l o o o co uo -fc- -tr OA f—1 ro IV) O o oo h-1 O U l M IV) -<] r-> no IV) 1—1 o o M -tr UO o IV) O CT\ M U l U l C A -tr uo UO rv> • • • • O OA OA o 0 .50' - 0 . 5 2 0.56 - 0.58 0 . 6 4 - 0.66 0.70 - 0.72 0.78 - 0.80 0.86 -0.88 0.98 - 1.00 % v i s i b l e r a d i a t i o n a >-•> £ cn CD £J P P. H-P c t H-O-' 3 " s;' P <! CD C p Q . CO a 3 " 12 maxima are found i n the v i s i b l e r e g i o n . I n a l l c a s e s , the v i s i b l e p o r t i o n o f the spectrum c o n t r i b u t e s a l a r g e p e r c e n t a g e o f the t o t a l energy t o the system. On the b a s i s , o f T a b l e 2.1, Kondratyev (1969) c o n c l u d e d t h a t f o r the s h o r t e r wavelengths -under a c l e a r s ky, d i f f u s e r a d i a t i o n i s more abundant than d i r e c t s o l a r r a d i a t i o n . F or an o v e r c a s t s k y , however, the d i f f e r e n c e between the s p e c t r a l c o m p o s i t i o n o f d i f f u s e r a d i a t i o n and d i r e c t s o l a r r a d i a t i o n i s l e s s ( K o n d r a t y e v , 1969). Recent r e s e a r c h i n u s i n g v i s i b l e r a d i a t i o n as a p a r a -m e t e r i z a t i o n f o r shortwave d i f f u s e r a d i a t i o n have produced c o n f l i c t i n g r e s u l t s . K o n d r a t y e v et a l (1955) measured r a d i a n c e and luminance at 30 p o i n t s o v er the c e l e s t i a l dome u s i n g a Y a n i s h e v s k y s p e c t r o m e t e r and a s e l e n i u m photometer r e s p e c t i v e l y . F o r l a r g e z e n i t h a n g l e s , he found t h a t the a n g u l a r d i s t r i b u t i o n s o f luminance and e n e r g e t i c a l i n t e n s i t y d i d not c o i n c i d e ( F i g u r e 2.3),.' However, the d i f f e r e n c e a t z e n i t h a n g l e s l e s s t h a n 26° was found t o be i n s i g n i f i c a n t . T h i s d i s c r e p a n c y may be acc o u n t e d f o r by the d i f f e r e n c e s I n the s p e c t r a l r e sponses o f the two i n s t r u m e n t s ( Z w o r y k i n and W i l s o n , 1934; Kondratyev et a l , 1955). With an i n c r e a s i n g o p t i c a l a i r mass, the 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 r a d i a t i o n a l s o i s a l t e r e d , changing the output s i g n a l s o f the t t w o i n s t r u m e n t s i n d i f f e r e n t manners. I n d o i n g s u c h , i t i s p o s s i b l e t h a t d i f f e r e n t r a d i a n c e v a l u e s c o u l d r e s u l t from the same p o r t i o n , o f the s k y , depending on the amount o f 7 s c a t t e r i n g . Moreover, the l o c a t i o n o f the minimum r a d i a n t 1 3 F i g u r e 2 . 3 D i s t r i b u t i o n o f luminous i n t e n s i t y (dashed l i n e ) and e n e r g e t i c a l i n t e n s i t y ( s o l i d l i n e ) f o r J u l y 3, 1 9 5 3 (Z = 7 4 ° ) from Kondrat y e v e t a l ( 1 9 5 5 ) .' 14 i n t e n s i t y shown i n F i g u r e 2.3 has not been s u b s t a n t i a t e d i n the o t h e r d a t a o f Kondratyev et a l (1955) nor i n the more r e c e n t work o f S t e v e n (1977). T h i s may i n d i c a t e t h a t o t h e r f a c t o r s , such as c i r r u s c l o u d , c o u l d have i n t e r f e r e d w i t h the measurements. F i g u r e 2.4 i l l u s t r a t e s the d i s t r i b u t i o n o f luminance and r a d i a n c e f o r an o v e r c a s t sky (Ko n d r a t y e v e t a l , 1955). The c o i n c i d e n c e between these two d i s t r i b u t i o n s i s r e l a t i v e l y good when compared w i t h those o f c l e a r s k i e s w i t h l a r g e s o l a r z e n i t h a n g l e s ( Z ) . T h i s f u r t h e r i n d i c a t e s t h a t the s p e c t r a l responses o f the i n s t r u m e n t s used may a f f e c t the r e s u l t s . A comparison o f the r a d i a n t i n t e n s i t i e s o f St e v e n (1977) ( F i g u r e 2.5a), who used time averaged d a t a , w i t h the luminance d i s t r i b u t i o n o f Dorno (1919) ( F i g u r e 2.5b) f o r a p p r o x i m a t e l y the. same s o l a r z e n i t h a n g l e , shows t h a t the g e n e r a l agreement i s very good. T h i s i n d i c a t e s t h a t the p r e v i o u s l y n o t e d depen-dence o f the c o i n c i d e n c e o f luminance and r a d i a n t i n t e n s i t y on the sun's z e n i t h angle i s not s i g n i f i c a n t at an g l e s as l a r g e as 35°. F u r t h e r e v i d e n c e w i t h which t o a s s e s s the i n s i g n i f i c a n c e o f z e n i t h a n g l e dependence a t medium a n g l e s can be o b t a i n e d from the work o f S t e v e n (1977) f o r Z = 55° ( F i g u r e 2.6a) and t h a t o f Kondratyev et a l (1955) f o r Z = 51° ( F i g u r e 2.6b). A l t h o u g h the methods f o r n o r m a l i z i n g the d a t a are not i d e n t i c a l ( the former u s i n g the r a t i o between D+ H and the r a d i a n t i n t e n s i t y at a given' p o s i t i o n , w h i l e the l a t t e r e x p r e s s e s the r a t i o w i t h r e s p e c t t o the i n t e n s i t y and l u m i n o s i t y at z = 0), they are 15 F i g u r e 2.4 Sky d i s t r i b u t i o n o f the r e l a t i v e e n e r g e t i c a l i n t e n s i t y ( s o l i d l i n e ) and luminous i n t e n s i t y (dashed, l i n e ) o f d i f f u s e r a d i a t i o n from o b s e r v a t i o n s on June 14, 1953 (Z = 42°, s o l i d c l o u d i n e s s ) from K o n d r a tyev e t a l (1955) 16 1*8 0 0 F i g u r e 2.5a S t a n d a r d d i s t r i b u t i o n o f n o r m a l i z e d sky r a d i a n c e o f Steve n (1977) f o r a s o l a r z e n i t h a n g l e o f 35° from. S t e v e n (1977) 100 F i g u r e 2.5b Sky luminance d i s t r i b u t i o n from C. Dorno from Robinson (1966) 180 F i g u r e 2 - : L 6'avStandard i ;distribution", o f " n o r m alized sky radiance.' o f Steven (.19 77) f o r a s o l a r z e n i t h a n g l e o f 55®. '.'Rotated:!.for comparison .with• '.Figure 2:6b from Steven (19 77)' • • F i g u r e 2.6b D i s t r i b u t i o n o f luminous i n t e n s i t y (dashed l i n e ) and e n e r g e t i c a l i n t e n s i t y ( s o l i d l i n e ) f o r June 27, 1953 (Z = 51°) from Kondratyev et a l (1955) 18 s u f f i c i e n t l y c l o s e f o r comparison. I t i s i m m e d i a t e l y apparent t h a t f o r the a r e a about the s o l a r d i s c b o t h the i n t e n s i t y and l u m i n o s i t y c o n t o u r s are o f s i m i l a r n o r m a l i z e d v a l u e s . The c o i n c i d e n c e between the two a n g u l a r d i s t r i b u t i o n s i s e x t r e m e l y good over the e n t i r e hemisphere. I n f a c t , the r e s u l t s o f Steven.(1977) compare more f a v o u r a b l y t o the luminance d i s t r i b u t i o n o f K o n d r a t yev e t a l (1955) t h a n does the i n t e n s i t y p a t t e r n o f K o n d r a t y e v e t a l (1955). A c c o r d i n g t o S t e v e n (1977), the d i s t r i b u t i o n o f d i f f u s e i n t e n s i t y f o r c l e a r sky days i s u n i v e r s a l . . T h e r e f o r e , the r a d i a n t i n t e n s i t y r e s u l t s o f K o n d r a t y e v e t a l (1955) mus.t be open t o q u e s t i o n . From t h i s work, and the g e n e r a l r e l a t i o n s h i p between the f l u x d e n s i t y found i n the v i s i b l e p o r t i o n o f the spectrum t o t h a t o f the complete shortwave spectrum, i t appears t h a t luminance i s a good e s t i m a t o r of d i f f u s e shortwave r a d i a t i o n b o t h i n a s p a t i a l manner and f o r a v a r i e t y o f atm o s p h e r i c c o n d i t i o n s . The need now i s t o f i n d a f u n c t i o n a l r e l a t i o n s h i p between the two. CHAPTER THREE EXPERIMENTAL PROCEDURE 3.1 E x p e r i m e n t a l S i t e The exposure o f the p h o t o g r a p h i c n e g a t i v e s and the a c t i n o m e t r i c measurements o f sky r a d i a n c e were u n d e r t a k e n a t the P l a n t S c i e n c e F i e l d L a b o r a t o r y on the s o u t h campus of the U n i v e r s i t y o f B r i t i s h Columbia ( L a t i t u d e 49° 15 r':N, L o n g i t u d e 123° 15' W, E l e v a t i o n 86m)7 The s i t e was chosen because measurements o f normal i n c i d e n c e s o l a r r a d i a t i o n , d i f f u s e r a d i a t i o n i n c i d e n t on a h o r i z o n t a l s u r f a c e , r e f l e c t e d shortwave r a d i a t i o n and t o t a l shortwave r a d i a t i o n f o r the h o r i z o n t a l and 30°, 60°, and 90° s o u t h - f a c i n g s l o p e s were b e i n g r o u t i n e l y t a k e n . Hay (1977) p r o v i d e s a f u l l d e s c r i p t i o n o f t h i s o b s e r v a t i o n program. The s p e c i f i c l o c a t i o n o f the camera and a c t i n o m e t e r was 35m due west o f the s o u t h - f a c i n g s e n s o r s . The two i n s t r u m e n t s were mounted on t r i p o d s w i t h i n 0.5m o f each o t h e r w i t h the a c t i n o m e t e r s e t t o the e a s t o f the camera. Both i n s t r u m e n t s were a p p r o x i m a t e l y 1.25m above the ground. The h o r i z o n t a l p r o j e c t i o n o f the camera l e n s was s e t such t h a t the a c t i n o m e t e r , when v e r t i c a l l y o r i e n t e d , c o u l d not be obs e r v e d through the v i e w f i n d e r , y e t when the a c t i n o m e t e r was o r i e n t e d a t z = 10° , the r a d i a t i o n s h i e l d o f the i n s t r u m e n t 1.9 20 c o u l d be I d e n t i f i e d through the l e n s . T h i s d i d not a f f e c t the p h o t o g r a p h i c e x p o s u r e s , however, as the r a d i a t i o n s h i e l d d i d not e x t e n d above the l o c a l h o r i z o n when o b s e r v e d t h r o u g h the v i e w f i n d e r . T h i s arrangement i n s u r e d t h a t the r e l a t i v e h e i g h t s o f the two i n s t r u m e n t s remained c o n s t a n t t h r o u g h o u t the e x p e r i m e n t . 3.2 View F a c t o r R e i f s n y d e r (1967) d e f i n e s the view f a c t o r as "the geometric f a c t o r d e s c r i b i n g the r a t i o o f r a d i a t i o n r e c e i v e d by the r a d i o m e t e r emanating from a p a r t i c u l a r s o u r c e t o the t o t a l r e c e i v e d from a l l s o u r c e s (assumed t o be r a d i a t i n g a t the same ra t e ) " . F i g u r e 3.1 g r a p h i c a l l y i l l u s t r a t e s the h o r i z o n o f the e x p e r i m e n t a l s i t e i n the form o f an e q u i d i s t a n t p r o j e c t i o n . From t h i s the average z e n i t h a n g l e f o r each 15° a r c was deter m i n e d and a view f a c t o r c a l c u l a t e d u s i n g e q u a t i o n 3-1 ( S t e y n , p e r s o n a l communication): 24" V„ = Z U/2TT ((1 + c o t 2 ( ^ / 2 • r ' / r ) ) 2 ' f i = l C t a n " 1 ( t a n IJJ/(1 + c o t 2 ( V 2 • r ^ / r ) ) ~ ^ ) ) } (3 -D where* r ' = the d i s t a n c e from the z e n i t h t o the h o r i z o n on an e q u i d i s t a n t p r o j e c t i o n (mm) r = the d i s t a n c e from the z e n i t h t o z = 7T/2 r a d i a n s ( r y r = 23/TT • r *A. f u l l l i s t o f symbols i s g i v e n i n Appendix 1.. F i g u r e 3.1 E q u i d i s t a n t p r o j e c t i o n o f the l o c a l h o r i z o n o f the e x p e r i m e n t a l s i t e as viewed t h r o u g h a 180 F i s h e y e l e n s 2-2 where 3 = mean z e n i t h a n g l e o f t h e h o r i z o n o ver a g i v e n a r c - l e n g t h 4» = t h e l e n g t h o f the a r c i n r a d i a n s a t z = ir /2 The c a l c u l a t i o n showed t h a t f o r an i s o t r o p i c s i g n a l , 98.1% o f t h e t o t a l r a d i a t i o n would emanate from t h e sky-hemisphere above t h e l o c a l h o r i z o n . The sky hemisphere i s i n f a c t not Lambertian,. F u r t h e r , F i g u r e s 2.3 t o 2.6 i n d i c a t e t h a t , a p a r t from a - s m a l l limb b r i g h t e n i n g e f f e c t , the areas o f the sky near t h e h o r i z o n a re a s s o c i a t e d w i t h r e l a t i v e l y low r a d i a n c e v a l u e s , even w i t h ' 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 r e f o r e , i t can be con c l u d e d t h a t the h o r i z o n does not s i g n i f i c a n t l y e f f e c t the e x p e r i m e n t . 3.3 R a d i a t i o n I n s t r u m e n t a t i o n 3.3-1 Pyranometers The i n s t r u m e n t s used t o r o u t i n e l y measure t h e i n c o m i n g f l u x e s o f t o t a l , d i f f u s e and r e f l e c t e d s o l a r r a d i a t i o n were Kip p and Zonen CM5 S o l a r i m e t e r s . These i n s t r u m e n t s have a nominal c a l i b r a t i o n o f 0.012 mv/Wm"2 and a temperature c o r r e c t i o n of 0.00135/°C a t 26.6 °C ( L a t i m e r , 1972). L a t i m e r (1970) and Flower s (1977) found t h a t f o r n o n - h o r i z o n t a l s u r f a c e s , a f u r t h e r c o r r e c t i o n had t o be a p p l i e d due t o the d i f f e r e n t i a l h e a t i n g o f the t h e r m o p i l e ©nee i t was removed from the h o r i z o n t a l . L a t i m e r ( p e r s o n a l communication) shows-.corrections as l a r g e " a s 1.010 ( f o r 180° t i l t ) and Flow e r s (1977) shows c o r r e c t i o n s o f 1.005 ( f o r a n g l e s between 20° and 7 0 ° ) . Table 3-1 p r o v i d e s , f o r the e x p e r i m e n t a l p e r i o d , the c a l i b r a t i o n s o f the i n s t r u m e n t s TABLE 3 - 1 - — C a l i b r a t i o n o f Ki p p and. Zonen CM5 Pyranometers f o r Incoming shortwave i r r a d i a n c e F l u x L o c a t i o n C a l i b r a t i o n * Slope Temperature Slo p e Azimuth C o r r e c t i o n * * C o r r e c t i o n * (degrees) ( d e g r e e s ) mv(Wm 2 ) 1 ( ° c " M ( f o r base o f 26.6 C) D4- 0 0 0 .0114 1.0 0 .00135 K4- 0 0 0 .0119 1.0 0 .00135 K+ 180 0 0 .0115 1.0101 0 .00135 K3 ;o 30 180 0.0116 1.003 0.00135 . 60 180 0.0112 1.005 0.00135 ho 90 180 0.0114 1.007 0.00135 * p r o v i d e d by Canadian Atmospheric Environment S e r v i c e s u p p l i e d by L a t i m e r ( p e r s o n a l communication) 24 ( p r o v i d e d by the Canadian Atmospheric Environment S e r v i c e ) , t h e i r t e m p e r a t u r e c o r r e c t i o n s , and the c o r r e c t i o n a p p l i e d due t o s l o p e . The 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 t i o n were f u r t h e r c o r r e c t e d u s i n g a m o d i f i e d form o f t h e i s o t r o p i c r a d i a t i o n c o r r e c t i o n (Drummond, 1956) t o account f o r the a r e a o f the c e l e s t i a l dome which was s c r e e n e d by the shadow band. By a d d i n g an e x t r a 4% t o t h i s v a l u e , L a t i m e r (19 72) found the a n i s o t r o p y of the sky hemisphere c o u l d be a c c o u n t e d f o r . Thus, the c o r r e c t i o n i s o f the form ( L a t i m e r , 1972): D+ = D + {2(0/iry • c o s 3 6 ( s i n <b • s i n 6 • t + c m o cos p • cos <S • s i n t 0 ) } • 1.04 (3.2) where D+ c = c o r r e c t e d d i f f u s e r a d i a t i o n • (Wm 2) D+ = measured d i f f u s e r a d i a t i o n (Wm 2 ) m oo = w i d t h o f shadow band (mm) y = r a d i u s o f shadow band (mm) 6 = s o l a r , d e c l i n a t i o n ( r a d i a n s ) <J> = l a t i t u d e ( r a d i a n s ) t n = hour ang l e o f sun at sunset ( r a d i a n s ) P.or the d u r a t i o n of. each s e t ©f f i e l d measurements, the output o f the above i n s t r u m e n t s were i n t e g r a t e d over 5 minute i n t e r v a l s and r e c o r d e d u s i n g a Campbell S c i e n t i f i c CR5 D i g i t a l R e c o r d e r . •^ 25 The d i f f u s e r a d i a t i o n s i g n a l was a l s o c o n t i n u o u s l y r e c o r d e d on a Honeywell E l e c t r o n i k 194 s t r i p c h a r t r e c o r d e r . 3-3.2 Eppley Normal I n c i d e n c e P y r h e l i o m e t e r D i r e c t beam r a d i a t i o n was measured u s i n g a tem p e r a t u r e compensated E p p l e y Normal I n c i d e n c e P y r h e l i o m e t e r a t t a c h e d t o an E p p l e y m o t o r i z e d e q u a t o r i a l mount. The p y r h e l i o m e t e r views an an g l e o f 0.009 s r . The c a l i b r a t i o n o f the i n s t r u m e n t i s 0.0079 mv/Wm~2 ( s u p p l i e d by Canadian Atmospheric Environment S e r v i c e ) w i t h a l i n e a r i t y o f response t o w i t h i n ±0.5% up t o 1400 Wm 2 . The s e n s o r o u t p u t was r e c o r d e d on a Campbell S c i e n t i f i c CR5 D i g i t a l R ecorder i n the same manner as the s i g n a l s from the pyranometers. 3.3.3 L i n k e - F e u s s n e r A c t i n o m e t e 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 was used t o measure the d i f f u s e r a d i a n c e w i t h which the p h o t o g r a p h i c exposures were t o be c a l i b r a t e d . The impo r t a n c e o f th e s e measurements makes i t a p p r o p r i a t e t o d e s c r i b e the In s t r u m e n t i n d e t a i l . . 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 i s a r e l a t i v e I n s t r u m e n t , w i t h a h i g h s e n s i t i v i t y and a s t a b l e c a l i b r a t i o n (Coulson,1975) . The i n s t r u m e n t c o n t a i n s two 2 0 - j u n c t i o n manganin-constantan thermocouples connected i n o p p o s i t i o n . One t h e r m o p i l e i s exposed to r a d i a t i o n , w h i l e t h e second a c t s as.'a compensating d e v i c e by b e i n g s c r e e n e d from r a d i a t i o n , but exposed t o the same q u a s i - a d i a b a t i c p r e s s u r e changes near the t h e r m o p i l e s u r f a c e and t o s h o r t - t e r m temperature f l u c t u a t i o n s caused by a i r c u r r e n t s ( C o u l s o n , 1975; I.G.Y., 1956). The former c o n d i t i o n was found t o be a sev e r e problem i n moderate winds. Because o f t h i s , the i n s t r u m e n t cannot be used i n t u r b u l e n t c o n d i t i o n s . . The d i a m e t e r o f the s e n s i n g element i s 10mm a n d . i s p l a c e d a t the base o f a 70.3mm tube b u i l t o f 6 c o n c e n t r i c a l l y s m a l l e r d i a m e t e r copper r i n g s . T h i s d e s i g n p r o v i d e s an a p e r t u r e o f 0.025 s r . The copper r i n g s e f f e c t i v e l y reduce the h e a t i n g o f the i n s t r u m e n t over s h o r t p e r i o d s o f t i m e . For l o n g term temperature changes o f the t h e r m o p i l e due t o c o n d u c t i o n , a mercury i n g l a s s thermometer i s p l a c e d i n t h e r m a l c o n t a c t w i t h the t h e r m o p i l e c a v i t y . The tempe r a t u r e c o r r e c t i o n f a c t o r i s -0.002/°C f o r a base o f 20 °C. A b u i l t - i n r i n g c o n t a i n s 4 f i l t e r s and 1 s h u t t e r , though o n l y 1 f i l t e r was used i n the p r e s e n t e x p e r i m e n t . A S c h o t t o p t i c a l q u a r t z f i l t e r a l l o w e d measurement o f shortwave r a d i a t i o n between 0.25 and 4.0 um, w h i l e a me t a l s h u t t e r was employed t o z e r o the i n s t r u m e n t s between measurements.. The c a l i b r a t i o n o f the i n s t r u m e n t used i n the study was 0.158 mv./Wm"2 ( s u p p l i e d by Kip p and Zonen) w i t h a r e s i s t a n c e o f 6 l . l ohms.. The time r e q u i r e d by the i n s t r u m e n t t o r e a c h a 99% response i s between 8 and 10 seconds-(I.G.Y., 1956; Robinson, 1966; C o u l s o n , 1975). L e v e l l i n g o f the a c t i n o m e t e r i s c a r r i e d out u s i n g a b u i l t - i n c i r c l e b u bble at the base o f the i n s t r u m e n t . T h i s i s a c c u r a t e t o w i t h i n ±1° . An az i m u t h c i r c l e on the i n s t r u m e n t p r o v i d e s a ±1° a c c u r a c y i n a z i m u t h a l o r i e n t a t i o n , w h i l e an 27 e l e v a t i o n screw y i e l d s a- ±0.1 a c c u r a c y i n the z e n i t h . The output s i g n a l o f the a c t i n o m e t e r was r e c o r d e d . on a H o n e y w e l l E l e c t r o n i k 194 s t r i p c h a r t r e c o r d e r w i t h a f u l l s c a l e range of lOOyv. T h i s p a r t i c u l a r r e c o r d e r was used because o f i t s s h o r t response time (0.5 s e c o n d s ) , wide c h a r t and a b i l i t y t o r e c o r d a s i g n a l o f l e s s t h a n 0.1 mv. 3..'3. 4 Radiometer maintenance The pyranometers i n v o l v e d i n the r o u t i n e measurement of s o l a r r a d i a t i o n f l u x e s were c l e a n e d on a d a i l y b a s i s as a d v i s e d by L a t i m e r (1972). The l e v e l and o r i e n t a t i o n " o f these i n s t r u m e n t s was a l s o checked r o u t i n e l y . Over the course of the measurement p e r i o d no change i n o r i e n t a t i o n was found f o r any o f the s e n s o r s . The di.ffusometer shadow band was r e g u l a r l y checked t o ensure t h a t t h e t h e r m o p i l e o f the pyrano-meter was c o m p l e t e l y i n shade. The Eppley Normal I n c i d e n c e P y r h e l i o m e t e r was c l e a n e d and the s i g n a l c a b l e unwound on a d a i l y b a s i s . Whenever p o s s i b l e , the a l i g n m e n t o f the i n s t r u m e n t w i t h r e s p e c t t o the s o l a r beam was a l s o checked. The a l i g n m e n t was m a i n t a i n e d w i t h i n 2 d i a m e t e r s o f the a l i g n m e n t s i g h t o f the c e n t r e o f the t a r g e t . The e f f e c t s o f such a change i n a l i g n m e n t c o u l d not be d e t e c t e d on a 10.0 mv f u l l s c a l e analogue E s t e r l i n e Angus c h a r t r e c o r d e r which m o n i t o r e d the p y r h e l i o m e t e r s i g n a l s which were a l s o connected, t o the OR5 i n t e g r a t o r . L e v e l l i n g o f 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 was c a r r i e d out b e f o r e and. a f t e r each s e t o f o b s e r v a t i o n s . The 2 8 S c h o t t o p t i c a l q u a r t z f i l t e r was r o u t i n e l y checked f o r contam- . i n a t i o n and c l e a n e d when n e c e s s a r y . 3.4 P h o t o g r a p h i c I n s t r u m e n t a t i o n F i l m was exposed u s i n g a Canon F - l 35mm s i n g l e l e n s r e f l e x camera w i t h f u l l a p e r t u r e m e t e r i n g . The camera i s s u i t e d t o s m a l l - f o r m a t photography o f the hemisphere because of i t s c e n t r a l a r e a m e t e r i n g system. T h i s measures the amount of l i g h t e n t e r i n g t h r o u g h the c e n t r a l p o r t i o n o f the frame where i t i s n e a r l y e q u a l t o the amount, o f l i g h t t h a t exposes the ph o t o g r a p h i c f i l m ( S u z u k i , 1975). The v i e w f i n d e r i s c o n s t r u c t e d i n such a manner t h a t over 97% o f the f i e l d o f view o f the l e n s can be seen. F u r t h e r , a secondary p r i s m i n the view-f i n d e r a l l o w s one t o see the m e t e r i n g w i t h o u t moving the eye ( S u z u k i , 1975). A Canon Speed F i n d e r was a t t a c h e d t o the main camera body t o f a c i l i t a t e ease o f o p e r a t i o n when the camera was p o i n t e d toward the sky hemisphere. T h i s v i e w f i n d e r a l l o w s one t o a d j u s t the m e t e r i n g and l e n s a p e r t u r e w i t h o u t l o o k i n g through the v i e w f i n d e r a t the rear:'of the camera body. A p r i s m b u i l t i n t o the Speed F i n d e r r e f r a c t s the l i g h t r a y s 90° t o overcome t h i s d i f f i c u l t y . The l e n s u t i l i z e d i n the study was the Canon F i s h e y e 7.5mm f / 5 . 6 S.S.C. T h i s e q u i d i s t a n t l e n s has a f i e l d o f view of 180° and p r o v i d e s a c i r c u l a r exposure o f 23-143 r 0.155 mm i n d i a m e t e r on the p h o t o g r a p h i c f i l m . S u z u k i (1975) c l a i m s i t i s e x c e l l e n t f o r a z i m u t h a l phenomena. The m a g n i f i c a t i o n 29 i s 0.15X. The f o c u s i n g i s f i x e d . B u i l t i n t o the l e n s a re 6 f i l t e r s mounted i n a f i l t e r r i n g t o p r o v i d e v a r i o u s waveband t r a n s m i t t a n c e s . The u l t r a -v i o l e t c u t - o f f f i l t e r L-1B was used i n the experiment,. T h i s f i l t e r e l i m i n a t e s a l l r a d i a t i o n at wavelengths l e s s than 0.32ym and p r o v i d e s a n e a r l y f l a t t r a n s m i t t a n c e curve f o r wavelengths g r e a t e r t h a n 0.4um and l e s s than 2. 4ym ( F i g u r e 3-2). The o t h e r b u i l t - i n f i l t e r s were e i t h e r found t o cut o f f r a d i a t i o n at wavelengths w i t h i n the v i s i b l e spectrum o r had t r a n s m i t t a n c e curves which were not s u f f i c i e n t l y c o n s t a n t f o r the p r e s e n t s t u d y . The l e v e l l i n g o f the camera was checked by s e t t i n g a s p i r i t - l e v e l a c r o s s the top o f the l e n s i n two o r t h o g o n a l d i r e c t i o n s . The l e v e l was checked b e f o r e and a f t e r each d a t a s e t was r e c o r d e d . D u r i n g c o n d i t i o n s o f d i r e c t beam r a d i a t i o n an o c c u l t i n g d i s c was used t o b l o c k the s o l a r d i s c . T h i s r e d u c e d the problem o f the s p u r i o u s a d d i t i o n o f d i r e c t beam r a d i a t i o n a f f e c t i n g the o v e r a l l d e n s i t y o f the photograph, and removed the problem o f i n t e r n a l lens, f l a r e due t o the r a y s o f the sun. The d i s c was d e s i g n e d t o b l o c k a s o l i d a n g l e o f a p p r o x i m a t e l y 6° u s i n g the r a t i o s p r e s e n t e d by L a t i m e r (1972). The p h o t o g r a p h i c f i l m was I l f o r d p r o f e s s i o n a l t ype panchromatic 35mm FP4 ASA 125- T h i s i s a f i n e g r a i n e d , medium c o n t r a s t f i l m w i t h a 6-stop exposure l a t i t u d e . The s e n s i t i v i t y i s r e l a t i v e l y f l a t f o r s m a l l format f i l m s and the waveband Wavelength (ym) F i g u r e 3.2 T r a n s m i t t a n c e f u n c t i o n o f u l t r a - v i o l e t c u t - o f f f i l t e r L-( s u p p l i e d by Canon Cameras) 31 range I n which i t i s s e n s i t i v e i s the l a r g e s t o f the c o m m e r c i a l l y a v a i l a b l e s m a l l format type f i l m s i n v e s t i g a t e d . F i g u r e 3-3 p r o v i d e s the r e l a t i v e s e n s i t i v i t y o f FP4 a s s u p p l i e d by the m a n u f a c t u r e r ( I l f o r d , p e r s o n a l communication) and the e f f e c t i v e a b s o r p t i o n curve when the t r a n s m i s s i o n f a c t o r o f the f i l t e r i s added.-The exposed f i l m was p r o c e s s e d by a p r o f e s s i o n a l p r o c e s s i n g company. T h i s was f e l t t o be adequate as no i n t e r -f i l m comparisons were p l a n n e d . A study o f the d e n s i t i e s o f the unexposed p o r t i o n s o f d e v e l o p e d f i l m i n d i c a t e d t h a t use of p r o f e s s i o n a l p r o c e s s i n g would not a f f e c t i n t r a - f i l m c omparisons. 3.5 F i e l d Measurement- Program A p r e l i m i n a r y i n v e s t i g a t i o n o f the use o f a p h o t o g r a p h i c method f o r d e t e r m i n i n g the 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 was u n d e r t a k e n d u r i n g September 19 77. D u r i n g t h i s o b s e r v a t i o n a l p e r i o d , Kodachrome 64 ASA p h o t o g r a p h i c f i l m was used (McArthur and Hay, 1978). Problems a s s o c i a t e d w i t h the d i f f e r e n t response o f the c o l o u r dyes t o l i g h t i n t e n s i t y and the d i f f i c u l t y i n q u a n t i t a t i v e l y d e t e r m i n i n g the d e n s i t y a s s o c i a t e d w i t h the e l e c t r o n i c a l l y d e n s i t y s l i c e d images, produced from the c o l o u r p o s i t i v e s (see P l a t e 4.1) r e s u l t e d i n the experiment, b e i n g r e p e a t e d u s i n g p a n c h r o m a t i c f i l m . However, the a c t u a l measurement p r o c e d u r e d e v e l o p e d at t h a t time was not a l t e r e d f o r use i n the p r e s e n t s t u d y . The f i e l d measurement phase o f the d a t a c o l l e c t i o n 60 Wavelength (nm) F i g u r e 3.3 F i l m and f i l t e r s p e c t r a l response curves E q u a l energy curve f o r I l f o r d F P 4 ( s u p p l i e d by I l f o r d L t d . ) S p e c t r a l response o f f i l m and f i l t e r c o m b i n a t i o n . 33 p r e s e n t e d i n t h i s study was c a r r i e d out on 6 days over the p e r i o d F e b r u a r y 9 t o F e b r u a r y 26, 19 78. The c r i t e r i a d e s i g n e d t o s e l e c t a p a r t i c u l a r day were: (1) the wind v e l o c i t y did. not a f f e c t a c t i n o m e t r i c measurements, (2). the weather p a t t e r n would l i k e l y be c o n s i s t e n t f o r a t l e a s t 3 h o u r s , (3) the sky c h a r a c t e r i s t i c s were such t h a t the e x p e r i m e n t a l t e c h n i q u e c o u l d be t e s t e d o ver the study p e r i o d on a v a r i e t y o f sky c o n d i t i o n s . These sky co v e r c h a r a c t e r i s t i c s were c a t e g o r i z e d i n t o 3 t y p e s , dependent on the t e m p o r a l s t a b l i l i t y o f the d i f f u s e r a d i a t i o n regime. Table 3-2 p r o v i d e s the sky c o n d i t i o n f o r each day on which measurements were r e c o r d e d . A l l measurements were t a k e n w i t h i n 3 hours o f s o l a r noon. T h i s was t o a s s u r e t h a t any dependence i n the r e l a t i o n s h i p between luminance and r a d i a n t i n t e n s i t y on z e n i t h a n g l e ( K o n d r a t y e v e t a l , 1955) would be m i n i m i z e d (see Chapter 2). Each i n d i v i d u a l d a t a s e t r e q u i r e d a p e r i o d o f approx-i m a t e l y 14 minutes t o a c q u i r e . D u r i n g t h i s t i m e , 21 a c t i n o m e t r i c measurements o f d i f f u s e r a d i a t i o n were made over the sky hemi-sphere and 3 p a i r s o f photographs were exposed. The l a t t e r were at 2.0, 6.67 and 11.33 minutes from the b e g i n n i n g o f o b s e r v a t i o n . I n t h i s manner, .no • a c t i n o m e t r i c measurement was g r e a t e r t h a n 2.5 minutes from a photograph o f sky c o n d i t i o n s . P a i r s o f photographs were t a k e n to reduce the p r o b a b i l i t y o f l o s i n g f i l m d a t a due t o p r o c e s s i n g problems. The exposure o f the photographs was s e t by u s i n g the b u i l t - i n l i g h t m e t e r i n g system o f the Canon F - l . Once TABLE 3 .2 .—On s i t e sky cover c o n d i t i o n s d u r i n g the e x p e r i m e n t a l p e r i o d , F e b r u a r y 9 - February 26, 19 78 Date Sky Cover 9 3/10 a l t o c u m u l u s ; 1/10 c i r r u s 10 c l e a r 14 10/10 s t r a t u s 15 10/10 s t r a t u s 24 1/10 cumulus; 4/10 a l t o s t r a t u s 26 c l e a r 35 d e t e r m i n e d a t the b e g i n n i n g o f the f i l m , i t was not a l t e r e d . Because o f the l a t i t u d e o f the f i l m , the v a r i a t i o n i n sky c o n d i t i o n s over the time p e r i o d c o u l d be accomodated. With the use o f o n l y one exposure s e t t i n g per- o b s e r v a t i o n p e r i o d , a l l t h r e e n e g a t i v e s can be intercompared.. T h i s c o m p a t a b i l i t y r e s u l t s i n a unique r a d i a n c e f o r each d e n s i t y . Thus, when the r a d i a n c e p a t t e r n i s changing r a p i d l y , the photograph exposed n e a r e s t an a c t i n o m e t r i c measurement can p r o v i d e a r e p r e s e n -t a t i v e d e n s i t y f o r t h a t r a d i a n c e . T h i s can then be u t i l i z e d on any photograph w i t h i n the a p p r o p r i a t e o b s e r v a t i o n p e r i o d t o produce a complete and a c c u r a t e r a d i a n c e map o f the sky hemisphere. 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 c o n s i s t e d o f a p e r i o d o f 20 seconds d u r i n g which the m e t a l s h u t t e r was used t o z e r o the i n s t r u m e n t and 20 seconds when d i f f u s e r a d i a t i o n from an a r e a o f 0.025 s r was a l l o w e d t o impinge on the s e n s i n g element. The f i r s t t e n seconds o f the s h u t t e r e d p e r i o d was used t o s e t the a c t i n o m e t e r a t a g i v e n z e n i t h and a z i m u t h . The sequence o f s e n s o r o r i e n t a t i o n s was such t h a t a c t i n o m e t e r movement was kept t o a minimum. A r e g u l a r s a m p l i n g d e s i g n was f o l l o w e d which n e c e s s i t a t e d movement i n u s u a l l y o n l y one a z i m u t h a l o r z e n i t h a l d i r e c t i o n p e r s i n g l e o b s e r v a t i o n . The p a t t e r n c o n s i s t e d o f 4 z e n i t h a l measurements at 20°, 40°, 60° , and 80° f o r a g i v e n a z i m u t h . The a z i m u t h a l d i r e c t i o n was then changed by 60° and 3 z e n i t h a l o b s e r v a t i o n s were made a t 70° , 50° and.30° . The a n g u l a r sequence o f z e n i t h a l measurements 36 was dependent on the p r e v i o u s s e t o f o b s e r v a t i o n s i n the z e n i t h , k e e p i n g a c t i n o m e t r i c movement t o a minimum. Ta b l e 3.3 p r o v i d e s , a t y p i c a l sequence o f a c t i n o m e t r i c and p h o t o g r a p h i c o b s e r v a t i o n s . The s t a r t i n g a zimuth and movement i n the a z i m u t h a l d i r e c t i o n was v a r i e d f o r each s e t o f o b s e r v a t i o n s . T h i s i s based, on a proce d u r e by Ste v e n ( 1977) which i s d e s i g n e d t o reduce b i a s i n g e r r o r s i n the d a t a i f s e v e r a l s e t s of o b s e r v a t i o n s are combined. D u r i n g p e r i o d s o f o b s e r v a t i o n s when the s o l a r d i s c was v i s i b l e , the s a m p l i n g i n the h e m i s p h e r i c s e c t o r o f the sun was c a r r i e d out every 30° , w i t h 2 z e n i t h a l measurements t a k e n at each azimuth ( T a b l e 3.3)- Such a s a m p l i n g d e s i g n p r o v i d e d a b e t t e r e s t i m a t e o f the e x p o n e n t i a l i n c r e a s e o f d i f f u s e r a d i a t i o n i n t e n s i t y i n the s o l a r r e g i o n o f the sky hemisphere t h a n d i d the 60° a z i m u t h a l s a m p l i n g p a t t e r n . To reduce the problem o f i n c r e a s e d a n g u l a r v e l o c i t y o f o b j e c t s ( i n t h i s c a s e , c l o u d s ) ! n e a r the z e n i t h , a c t i n o m e t r i c measurements o f t h i s r e g i o n were made a t the same time photographs were exposed ( T a b l e 3-3). 3.6 P h o t o g r a p h i c D i g i t i z a t i o n 3.6.1 Joyce L o e b l M i c r o d e n s i t o m e t e r R e d u c t i o n o f the 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 was a c c o m p l i s h e d u s i n g a Joyce L o e b l Automatic R e c o r d i n g D e n s i t o m e t e r , Model Mk I I I C , w i t h an A u t o d e n s i d a t e r attachment. The i n s t r u m e n t i s o f the double-beam, n u l l - p o i n t t y p e , h a v i n g a r e p e a t a b i l i t y o f measurements t o w i t h i n 0.5% o f f u l l s c a l e TABLE 3 . 3 . — T y p i c a l sequence o f a c t i n o m e t r i c measurements and p h o t o g r a p h i c exposures f o r s o l a r d i s c at azimuth 19 3° and z e n i t h 65° Time Azimuth Z e n i t h P h o t o g r a p h i c Exposure 00:00 0 80 00 : 40 0 40 01:20 0 60 02 :00 0 20 02:40 60 30 03:20 60 50 04:00 60 70 04:40 120 80 05 : 20 120 40 06 :00 120 60 06 :40 120 20 07:20 180 30 08 :00 180 50 08:40 180 70 09 :20 210 80 10 :00 210 40 10 : 40 240 50 11:20 2 40 30 12:00 300 20 12:40 300 40 13:20 300 60 14:00 300 80 38 ( F r a s e r , 1978). D e t a i l e d I n f o r m a t i o n c o n c e r n i n g the o p t i c s o f the Mk I I I C can be found i n I n s t r u c t i o n Manual f o r Automatic R e c o r d i n g M i c r o d e n s i t o m e t e r Model Mk I I I C , (Joyce L o e b l ) . An o v e r v i e w o f the i n s t r u m e n t and i t s c a p a b i l i t i e s i s p r o v i d e d by F r a s e r (1978). The Autodensidater.'.attachment t o g e t h e r w i t h two servo-motors a l l o w s a n e g a t i v e o r p h o t o g r a p h i c p l a t e t o be d e n s i t i z e d i n 2 dim e n s i o n s . By programming the l e n g t h o f scan and the i n c r e m e n t a l d i s t a n c e i n b o t h X and Y d i r e c t i o n s , the m i c r o d e n s i t o m e t e r i s a b l e t o d i g i t i z e g r i d p o i n t s i n the p o s i t i v e X d i r e c t i o n . . At the end o f each scan i n the X d i r e c t i o n , the m i c r o d e n s i t o m e t e r a u t o m a t i c a l l y r e t u r n s t o the o r i g i n o f X and i n c r e m e n t s the Y d i r e c t i o n . The d i g i t i z i n g p r o c e s s i s completed when the summation o f Y inc r e m e n t s e q u a l s the l e n g t h d i m e n s i o n o f Y. The d i g i t a l o u tput o f the m i c r o d e n s i t o m e t e r was on 7 t r a c k ASCII n o - p a r i t y paper t a p e . A l l d i g i t i z a t i o n s were performed u s i n g a 0 - 3 D o p t i c a l d e n s i t y wedge as c a l i b r a t i o n . T h i s was t o m a i n t a i n c o m p a r a b i l i t y o f n e g a t i v e s o f the same p h o t o g r a p h i c exposure. The d e n s i t y range was l i n e a r l y d i v i d e d i n t o 1000 u n i t s . These d e n s i t y measurements t h e r e f o r e , have r e l a t i v e r a t h e r than a b s o l u t e s i g n i f i c a n c e . . 3.6.2 D i g i t i z a t i o n s a m p l i n g c o n s i d e r a t i o n s The s a m p l i n g p r o c e d u r e was based on s e v e r a l c r i t e r i a . The minimum number o f p o i n t s t o be sampled was dependent on 39 the r e q u i r e m e n t o f the computer's graphics-for a t l e a s t a 2500 p o i n t d a t a base t o smoothly i n t e r p o l a t e curves i n a 2.54 x 254mm format ( C o u l t h a r d , 19 75). The maximum number o f d a t a p o i n t s was dependent on the s i z e o f the a r e a o f the n e g a t i v e t o be d e n s i t i z e d and the i n c r e m e n t between d e n s i t y measurements.. A l s o when c o n s i d e r i n g sample s i z e , the time r e q u i r e d t o tak e an i n d i v i d u a l measurement must be considered.. The p h o t o g r a p h i c f i l m used has a g r a i n s i z e range between 0.49um and 0.93um. T h i s l i m i t s the a v e r a g i n g a r e a over which a d e n s i t y measurement i s t a k e n t o a p p r o x i m a t e l y 25um2. F u r t h e r , the s m a l l e r the a v e r a g i n g a r e a , the p o o r e r the r e s o l v i n g power o f the i n s t r u m e n t because o f the s m a l l amount o f l i g h t i n c i d e n t on the p h o t o m u l t i p l i e r . Joyce L o e b l  B u l l e t i n 54/8B (1954) suggests t h a t the l a r g e s t p o s s i b l e i l l u m i n a t e d a r e a be.used when i n t e g r a t i n g p h o t o g r a p h i c e m u l s i o n s i n o r d e r t o reduce the e r r o r i n t r o d u c e d by the g r a i n s i z e d i s t r i b u t i o n . The t h e o r e t i c a l upper l i m i t i n t h i s case would be the i n t e g r a t e d a r e a o f the o b s e r v a t i o n s o f 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 as r e p r e s e n t e d on the n e g a t i v e . T h i s , however, i s an o r d e r o f magnitude l a r g e r than the l a r g e s t i l l u m i n a t e d a r e a a v a i l a b l e on the i n s t r u m e n t and i s t h e r e f o r e , o f no con c e r n . An i l l u m i n a t e d a r e a of 75 x 75ym was adopted f o r the s t u d y . T h i s i s 225 times l a r g e r t h a n the minimum a v e r a g i n g a r e a , so s h o u l d p r o v i d e h i g h r e s o l u t i o n d e n s i t y measurements. I t r e q u i r e d a p p r o x i m a t e l y 1 second per d e n s i t y measurement u s i n g the above i l l u m i n a t e d a r e a . A f u r t h e r 40 : 40 seconds was n e c e s s a r y at the end o f a l i n e f o r the m i c r o -d e n s i t o m e t e r t o r e s e t t o b e g i n the next scan l i n e . W i th these time r e q u i r e m e n t s , i t would r e q u i r e 32 hours t o a c c u r a t e l y determine the d e n s i t y over t h e e n t i r e n e g a t i v e i f the e n t i r e n e g a t i v e was covered.by the 75 * 75ym i l l u m i n a t e d a r e a . T h i s would produce a d a t a base o f over 102 thousand v a l u e s f o r each photograph. The most c o n v e n i e n t minimum number o f data p o i n t s was found t o r e s u l t i n a sample every 400um i n b o t h the X and Y d i r e c t i o n s . T h i s p r o v i d e d 3600 d a t a p o i n t s over a 24 x 24mm square g r i d and 2629 p o i n t s w i t h i n the exposed a r e a o f the n e g a t i v e . T h i s s a m p l i n g procedure d e t e r m i n e d the d e n s i t y o f o f the t o t a l g r i d a r e a . The time r e q u i r e d i n d i g i t i z i n g i s a p p r o x i m a t e l y 1 hour 40 minutes per n e g a t i v e . 3.6.3 N e g a t i v e a l i g n m e n t To m a i n t a i n the r e q u i r e d c o m p a t a b i l i t y amongst the p h o t o g r a p h i c n e g a t i v e s , a method was d e s i g n e d t o p r o v i d e each d a t a p o i n t ( X^,Y^) w i t h a unique and i d e n t i f i a b l e l o c a t i o n on every n e g a t i v e . T h i s was a c h i e v e d t h r o u g h the l o c a t i o n i n b o t h azimuth a n d . z e n i t h o f a p o i n t on the n e g a t i v e , such t h a t a c h o r d p a s s i n g t h r o u g h the o b j e c t b i s e c t s the c e l e s t i a l concave t h r o u g h the z e n i t h . A l l p o i n t s can then;foe d e f i n e d w i t h r e s p e c t t o t h i s a x i s . From a knowledge of the z e n i t h a n g l e o f the o b j e c t and by s e t t i n g the s c a n such t h a t a s a m p l i n g p o i n t c o i n c i d e s w i t h the same o b j e c t , a l l g r i d p o i n t s can be d e f i n e d a l o n g a second o r t h o g o n a l a x i s . To a f i x the n e g a t i v e on the m i c r o d e n s i t o m e t e r , a"'square t e m p l a t e was c o n s t r u c t e d t o se c u r e the n e g a t i v e by the edges w i t h o u t c o v e r i n g the exposed p o r t i o n . The use o f such a cov e r s l i p e l i m i n a t e s the e f f e c t s o f Newtonian r i n g s . Once the n e g a t i v e i s s e c u r e , the o b j e c t w i t h known p o s i t i o n can be l o c a t e d v i a the image p r o j e c t e d onto the a p e r t u r e p l a t e o f the m i c r o d e n s i t o m e t e r . F i n e a l i g n m e n t o f the o b j e c t i s t h e n f a c i l i t a t e d u s i n g s t e p p i n g c o n t r o l s i n the X and Y d i r e c t i o n s and a hand c o n t r o l i n a r o t a t i o n a l mode. A secondary a l i g n m e n t check w i t h r e s p e c t t o c e n t e r i n g was c a r r i e d out by t e s t i n g t he r a d i u s o f the n e g a t i v e i n b o t h p o s i t i v e and n e g a t i v e X d i r e c t i o n s . . I t i s e s t i m a t e d t h a t t h e g r i d p o i n t s can be d e f i n e d t o w i t h i n ±25ym i n the X d i r e c t i o n and t o w i t h i n ±10ym i n the Y d i r e c t i o n by u s i n g t h i s method. An e r r o r o f ±25ym r e p r e s e n t s l e s s t h a n a 0 .2° e r r o r i n the z e n i t h and i n the azimuth a t 60° . I n t e r n a l c o n s i s t e n c y w i t h i n the i n s t r u m e n t i n r e t u r n i n g t o the same p o s i t i o n , once a l i g n e d , i s l e s s than ±5ym. I n the p r e s e n t s t u d y , the o b j e c t used t o determine uniqueness was the m e t a l s u p p o r t o f the s e n s o r . T h i s was known t o be p e r p e n d i c u l a r t o the s u r f a c e . Because o f the n a t u r e o f the F i s h e y e l e n s , a chord drawn th r o u g h any o b j e c t p e r p e n d i c u l a r t o the h o r i z o n t a l p r o j e c t i o n o f the l e n s passes t h r o u g h the z e n i t h . The azimuth d i r e c t i o n o f the p o s t w i t h r e s p e c t t o the camera was due e a s t . T h i s c o n v e n i e n t l y p r o v i d e d the b a s i s f o r an e a s t - w e s t , n o r t h - s o u t h g r i d on the n e g a t i v e . 3.7 E r r o r A n a l y s i s 3.7-1 Methodology The a n a l y s i s p e r f ormed t o determine the p r o b a b l e e r r o r f o l l o w s t h a t l a i d out by Cook and R a b i n o w i c z (1963). Assuming the e r r o r s i n components o f the system are independent and n o r m a l l y d i s t r i b u t e d , the p r o b a b l e r e l a t i v e e r r o r i n measuring a q u a n t i t y can be d e t e r m i n e d by e q u a t i o n 3.3: e = ( ? . ( e . ) z ) h (3.3) i = l x where e T = 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 the measured q u a n t i t y {%) = the 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 the i t h component o f the measurement system (%) The e r r o r s w i t h i n the p r e s e n t experiment have been d i v i d e d , i n t o t h r e e components: (1) the e r r o r a s s o c i a t e d w i t h the measurement o f i n c o m i n g s o l a r r a d i a t i o n used i n the v a l i d -a t i o n o f the p h o t o g r a p h i c t e c h n i q u e , (2) the p r o b a b l e e r r o r i n v o l v e d i n the measurement o f d i f f u s e r a d i a n c e used i n the c a l i b r a t i o n o f the p h o t o g r a p h i c n e g a t i v e , (3) 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 the p h o t o g r a p h i c component o f the e x p e r i m e n t . Both o f the f i r s t two subsystems can be f u r t h e r d i v i d e d i n t o 3 s e c t i o n s : (1) the e r r o r a s s o c i a t e d w i t h the s e n s o r , (2) the e r r o r r e s u l t i n g from the e l e c t r i c a l o u tput s i g n a l , 43 and (3) the e r r o r i n t r o d u c e d by d i g i t i z i n g a n a l o g d a t a . 3.7.2 E r r o r i n the v e r i f i c a t i o n o f the p h o t o g r a p h i c t e c h n i q u e 3.7.2.1 Pyranometers The 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 the K i p p and Zonen Pyranometers are found I n Table 3.4. These are a p p l i c a b l e t o each o f the shortwave f l u x e s . A f u r t h e r ±2% e r r o r i s a s s o c i a t e d w i t h the d i f f u s e f l u x because o f the e m p i r i c a l shadow band c o r r e c t i o n ( L a t i m e r , 1972). The r e l a t i v e p r o b a b l e e r r o r f o r the i n s t r u m e n t as r e p o r t e d by L a t i m e r (19 72) i s 3.6%. For the measurement of d i f f u s e r a d i a t i o n , t h i s i s i n c r e a s e d t o 4.1%. 3.7.2.2 Normal I n c i d e n c e E p p l e y P y r h e l i o m e t e r The normal i n c i d e n c e p y r h e l i o m e t e r has a l i n e a r i t y o f response o f ±0.5% up t o 1400 Wm~2. A f u r t h e r ±1% e r r o r i s a s s o c i a t e d w i t h the e r r o r i n a l i g n m e n t o f the i n s t r u m e n t w i t h the s o l a r beam. T h i s e s t i m a t e i s c o n s e r v a t i v e over a range of 2 s i g h t i n g d i a m e t e r s . The t o t a l p r o b a b l e r e l a t i v e e r r o r i s 1.12%. 3.7.2.3 R e c o r d e r E r r o r Two r e c o r d e r s were used t o m o n i t o r the d i f f u s e f l u x ; t he Honeywell . E l e c t r o n i k 194 and t h e Campbell S c i e n t i f i c CR5 I n t e g r a t i n g R e c o r d e r . A l l o t h e r s e n s o r s used f o r v e r i f -i c a t i o n were m o n i t o r e d on the Campbell S c i e n t i f i c CR5 a l o n e . The Honeywell r e c o r d e r has a r e f e r e n c e a c c u r a c y o f ±0.25% o f span o r l u v , w h i c h e v e r i s g r e a t e r . The f u l l s c a l e range used f o r the d i f f u s e f l u x was 5 mv. T h e r e f o r e , the 44 TABLE 3 . 4 . - — E r r o r summary f o r Ki p p and Zonen Pyranometer ( f r o m L a t i m e r , 1972) L i n e a r i t y o f response ±1% Cosine response ±5% ( a t 10° e l e v a t i o n ) Temperature response ( u n c o r r e c t e d ) ±2.5% Temperature response ( c o r r e c t e d ) ±1.5% O v e r a l l c o s i n e and azimuth e r r o r ±3% O v e r a l l p r o b a b l e e r r o r o f i n s t r u m e n t ( t e m p e r a t u r e c o r r e c t e d ) ±3.6% a b s o l u t e e r r o r i s found t o be ±0.0125 mv. The Campbell S c i e n t i f i c a c c u r a t e l y i n t e g r a t e s o v er a time span t o w i t h i n ±1 count. By the manner o f i n t e g r a t i o n , t h i s i s d i r e c t l y c o n v e r t i b l e t o the a b s o l u t e e r r o r o f the mean f l u x o v e r t h e i n t e g r a t i n g p e r i o d . Thus, t h e r e l a t i v e e r r o r o f the r e c o r d e r i s dependent on the s i z e o f the i n p u t s i g n a l . T a b l e 3.5 p r o v i d e s c a l c u l a t i o n s o f the a b s o l u t e and r e l a t i v e e r r o r f o r b o t h r e c o r d e r s over the range o f d i f f u s e r a d i a t i o n f l u x e s e n c o u n t e r e d . F o r a mean d i f f u s e i r r a d i a n c e o f 200 Wm~2 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 the Hone y w e l l E l e c t r o n i k 194 i s ±0.55%. For the same i r r a d i a n c e , the p r o b a b l r e l a t i v e e r r o r f o r the Campbell S c i e n t i f i c i s ±0.44%. F o r a mean shortwave i r r a d i a n c e o f 535 Wm 2 the 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 the Campbell S c i e n t i f i c i s ±0.16%. S i m i l a r i l y , f o r the mean d i r e c t beam i r r a d i a n c e o f 650 Wm-2 the p r o b a b l e r e l a t i v e e r r o r i s ±0.19%. The apparent d i s c r e p a n c y between these two e r r o r s i s due t o the d i f f e r e n c e i n the c a l i b r a t i o n o f the i n s t r u m e n t s . 3.7.2.4 Data A b s t r a c t i o n . D a ta, r e c o r d e d i n st e a d y r a d i a t i v e c o n d i t i o n s , can be e a s i l y a b s t r a c t e d from a Honeywell s t r i p c h a r t t o w i t h i n +0.25 d i v i s i o n s . For a d i f f u s e i r r a d i a n c e o f 200 Wm-2, as used above, 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 the removal o f data'.-is ±0.50%. TABLE 3 - 5 . — R e c o r d e r e r r o r 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 s i g n a l I n s t r u m e n t S i g n a l Input A b s o l u t e R e l a t i v e (Wm - 2) (mv) (counts) E r r o r E r r o r {%) Hon e y w e l l 50 0.57 . ±0.0125mv 2.19 E l e c t r o n i k 194 100 1 . 1 4 1.10 150 1.71 0.73 200 2.28 0.55 250 2.85 0.44 300 3 . 4 2 0.36 350 3.99 0.31 Campbell S c i e n t i f i c 50 57 ±1 count 1.75 100 114 0.88 150 171 0.58 200 228 0.44 250 285 0.35 300 3 4 2 0.29 350 399 0.25 47 3 . 7 - 2 . 5 T o t a l P r o b a b l e E r r o r i n the P h o t o g r a p h i c V a l i d a t i o n System For an average d i f f u s e i r r a d i a n c e , t he p r o b a b l e r e l a t i v e e r r o r i s c a l c u l a t e d a s : e T = ( ( 4 . 1 ) 2 + ( 0 . 5 5 ) 2 + ( 0 . 2 5 ) 2 ) 1 ' 2 ( 3 . 4 ) = 4 . 1 4 % F o r a t y p i c a l i n c o m i n g shortwave i r r a d i a n c e , t he p r o b a b l e r e l a t i v e e r r o r i s : e T = ( ( 3 . 6 ) 2 + {Q.l6)2)h ( 3 . 5 ) s = 3 . 6 1 % F i n a l l y , f o r an average d i r e c t beam i r r a d i a n c e , t he pr o b a b l e r e l a t i v e e r r o r i s : £ T = ( ( 1 . 1 2 ) 2 + ( 0 . 1 9 ) 2 ) s 2 \h ( 3 . 6 ) = 1 . 1 3 % I t must be no t e d t h a t these a re f o r average i r r a d i a n c e v a l u e s . F o r 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 c o n s t a n t a b s o l u t e e r r o r s , the s i z e o f the s i g n a l b e i n g measured i s i n v e r s e l y p r o p o r t i o n a l t o the s i z e o f the r e l a t i v e e r r o r . 3 . 7 . 3 E r r o r a s s o c i a t e d w i t h t he measurement o f d i f f u s e r a d i a n c e 3 . 7 . 3 . 1 L i n k e - F e u s s n e r A c t i n o m e t e 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 i s e s t i m a t e d t o be 48 a c c u r a t e t o w i t h i n ±1% ( D a v i e s , p e r s o n a l communication). F o r s m a l l f l u x e s however, Robinson (1966) q u e s t i o n s the a c c u r a c y o f the i n s t r u m e n t because no t e s t s have been performed. A more c o n s e r v a t i v e e s t i m a t e o f ±2% has t h e r e f o r e been adopted. The p r e s e n t i n s t r u m e n t i s not temperature compensated and c a v i t y temperature can o n l y be a s c e r t a i n e d t o ±0.5 °C. T h i s adds a f u r t h e r r e l a t i v e e r r o r o f 0.25%. A f i n a l s i g n i f i c a n t e r r o r i s found i n the a l i g n m e n t o f the system. As o f y e t , no t e s t s have been c a r r i e d out t o determine the magnitude o f t h i s e r r o r . I t i s assumed t o be no g r e a t e r t h a n the a c c u r a c y o f the s e n s o r though, p r o b a b l y between 1 and 2%. Assuming the l a r g e s t i n d i v i d u a l e r r o r s f o r the v a r i o u s components, the p r o b a b l e r e l a t i v e e r r o r i s : e T = ((2) 2.+ (2) 2 + (0.25)2)h (3.7) = 2.84% 3.7.3.2 R e c o r d e r E r r o r Due t o the very s m a l l f l u x e s b e i n g measured by the a c t i n o m e t e r , the f u l l s c a l e range o f the H o n e y w e l l E l e c t r o n i k 194 was lOOuv. F o r t h i s r a n g e , the r e c o r d e r c l a i m s no g r e a t e r a c c u r a c y i n r e c o r d i n g the i n p u t s i g n a l t h a n ±lyv. Thus, the r e l a t i v e e r r o r s i n r e c o r d i n g v a r y between ±1.25% f o r the most i n t e n s e f l u x e s and up t o ±35% f o r the weakest s i g n a l s on c l e a r sky days. The l a r g e s t e r r o r s o c c u r f o r a p p r o x i m a t e l y 5% o f a l l d a t a , w h i l e the mean e r r o r a s s o c i a t e d 49 w i t h r e c o r d i n g i s 5%• 3.7.3.3 Data A b s t r a c t i o n The t r a n s p o s i n g 0 f the d i f f u s e r a d i a n c e measurementv d a t a are s i m i l a r 'to t h a t - f o r '• d i f f u s e i r r a d i a n c e v a l u e s . The mean e r r o r a s s o c i a t e d w i t h the a b s t r a c t i o n o f th e s e d a t a I s 1.25%. 3.7.3.4 P r o b a b l e E r r o r i n the P h o t o g r a p h i c C a l i b r a t i o n Subsystem . The t o t a l p r o b a b l e e r r o r i n v o l v e d i n the measurement of d i f f u s e r a d i a n c e r e q u i r e d f o r the c a l i b r a t i o n o f the photo-g r a p h i c n e g a t i v e s I s : e T = ( (2 .84) 2 •+ (5) 2 + (1.25) 2) 3 5 (3-8) = 5 - 88% Once a g a i n i t must be noted, t h a t t h i s i s an average e r r o r and t h a t f o r low r a d i a n c e the e r r o r w i l l i n c r e a s e s i g n i f i c a n t l y . I n the case o f a r e c o r d e r e r r o r o f 35%, the a b s t r a c t i o n e r r o r w i l l be 8.75%. T h i s w i l l g i v e a p r o b a b l e r e l a t i v e e r r o r f o r the system o f 36.13%. 3.7.4 E r r o r s i n p h o t o g r a p h i c r e d u c t i o n 3.7.4.1 D i g i t i z a t i o n T h i s i s the o n l y p o r t i o n o f the p h o t o g r a p h i c r e d u c t i o n i n which any p r e v i o u s e r r o r e s t i m a t i o n has been c a l c u l a t e d . F r a s e r (1978) s t a t e s the r e p e a t a b i l i t y o f measurements can be gua r a n t e e d t o 0.5% o f f u l l s c a l e , d e f l e c t i o n . S i n c e the d e n s i t y measurements are u s u a l l y u t i l i z e d as r e l a t i v e v a l u e s , 50 o n l y the r e l a t i v e a c c u r a c y o f the i n s t r u m e n t has been p u b l i s h e d . 3.7.4.2 P h o t o g r a p h i c System The e r r o r a s s o c i a t e d w i t h the p h o t o g r a p h i c system i s p o o r l y known. T h e r e f o r e , e r r o r a n a l y s i s i s i n t e n d e d t o p r o v i d e o n l y an o r d e r of. magnitude e s t i m a t e o f the e r r o r I n the system. To determine t h i s e r r o r f o r the e n t i r e system, 2 photographs of a p a r t i a l l y c l o u d y sky. were t a k e n a p p r o x i m a t e l y 8 seconds a p a r t . These were d i g i t i z e d u s i n g the normal p r o c e d u r e s and compared u s i n g c o r r e l a t i o n a n a l y s i s . The b e s t f i t l i n e was f o r c e d t h r o u g h the o r i g i n t o determine the v a r i a t i o n from the t h e o r e t i c a l 1:1 l i n e . The s l o p e o f the curve was found t o be. 1.018 w i t h a s t a n d a r d e r r o r o f 4.988 x 10 -1* and a c o r r e l a t i o n c o e f f i c i e n t o f 0.9976. The 1.8% d i f f e r e n c e i n the s l o p e from the 1:1 curve i s a c o m b i n a t i o n o f a l l s y s t e m a t i c e r r o r s i n the system. The r e l a t i v e e r r o r f o r i n d i v i d u a l d e n s i t y d e t e r m i n a t i o n s was found t o be so s m a l l as t o be i r r e l e v a n t . . From the above, i t appears t h a t an e r r o r o f ±2% i s not u n r e a s o n a b l e . 3.7.5 R e l a t i v e P r o b a b l e E r r o r o f the 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 The above t h r e e subsystems are i n t r i c a t e l y l i n k e d i n the d e t e r m i n a t i o n o f the a n g u l a r v a r i a t i o n i n r a d i a n t i n t e n s i t y . The f i r s t subsystem p r o v i d e s the d a t a w i t h which the i n t e g r a t e d r a d i a n c e v a l u e s are compared, the second system s e r v e s as, the v a l u e s r e q u i r e d t o c a l i b r a t e the p h o t o g r a p h , w h i l e the t h i r d system i n d i c a t e s the c o n f i d e n c e w i t h which the luminance p a t t e r n can be i n t e r p r e t e d . The t y p i c a l e r r o r i n the system i s t h e r e -51 f o r e a f u n c t i o n o f the t y p i c a l p r o b a b l e e r r o r s . l n the t h r e e subsystems: e T = ( ( 4 . 1 4 ) 2 + (5.88) 2 + ( 2 ) 2 ) h ( 3 - 9 ) = 7 . 4 6 % T h i s p r o b a b l e r e l a t i v e e r r o r i s approximate f o r an average s e t o f measurements.. N e v e r t h e l e s s , the magnitude of the e r r o r i s w i t h i n a c c e p t a b l e l i m i t s when c o n s i d e r i n g the number o f i n s t r u m e n t s used. A l s o , when one c o n s i d e r s t h i s i s a f i r s t attempt a t t h i s t e c h n i q u e and t h a t improvements are p o s s i b l e , the e r r o r i s r e l a t i v e l y low. When comparing t h i s e r r o r w i t h the p r o b a b l e e r r o r o f the u s u a l method f o r d e t e r m i n i n g d i f f u s e r a d i a t i o n ( 4 - 2 - 4 . 6 % ) ( L a t i m e r , 1 9 7 2 ) , i t i s o f the same magnitude, y e t the p r e s e n t system a l s o p r o v i d e s t h e a n g u l a r d i s t r i b u t i o n o f the d i f f u s e r a d i a t i o n . CHAPTER FOUR ANGULAR DISTRIBUTION OF DIFFUSE RADIATION 4 .1 C a l i b r a t i o n Technique T h e o r e t i c a l l y the r a d i a n c e from a s o l i d a n g l e (6co) can be r e l a t e d t o p h o t o g r a p h i c n e g a t i v e d e n s i t y by.the f u n c t i o n : F(6O J ) = f { v , D} (4.1) where F(6w) = the r a d i a n t i n t e n s i t y from the s o l i d a n g l e 6to v = a t m o s p h e r i c c o n d i t i o n s D = d e n s i t y n f{e, n ."x.,} 1=1 where e = exposure IIX^ = p r o d u c t o f the p r o p e r t i e s o f the p h o t o g r a p h i c system S i n c e the c h a r a c t e r i s t i c s o f many o f thes e v a r i a b l e s are unknown, c o n v e r s i o n o f the d e n s i t y v a l u e s t o a c t u a l i n t e n -s i t i e s c o u l d o n l y be a c c o m p l i s h e d by r e g r e s s i o n a g a i n s t measured r a d i a n t f l u x v a l u e s . B e f o r e comparing r a d i a n c e t o d e n s i t o m e t r i c measurements, an e q u i v a l e n t a r e a t o s o l i d a n g l e c a l c u l a t i o n must be performed. •53 The e q u i d i s t a n t l e n s used i n the d a t a c o l l e c t i o n p r e s e r v e s a r e a . Thus, f o r a square s a m p l i n g p a t t e r n , t h e s o l i d a n g l e r e p r e s e n t e d by a s i n g l e p o i n t i s : 6u) = 2ir/n (4.2) where n = the number o f p o i n t s w i t h i n the exposed r e g i o n For the g r i d s i z e used i n d i g i t i z a t i o n o f the hemi-s p h e r i c photographs the e q u i v a l e n t s o l i d a n g l e r e p r e s e n t e d by each p o i n t was 2.39 *• 1 0~ 3sr. The a c t i n o m e t e r measured r a d i a n c e over a s o l i d a n g l e o f 0.025 s r . To determine a r e p r e s e n t a t i v e d e n s i t y f o r an e q u i v a l e n t a r e a on the n e g a t i v e , the d e n s i t y o f 13 d a t a p o i n t s was averaged.. The c e n t r e o f each a v e r a g i n g a r e a had the same a n g u l a r p o s i t i o n as t h a t o f the r e s p e c t i v e a c t i n o m e t r i c o b s e r v a t i o n . The a r e a r e p r e s e n t e d by t h i s method was 0.031 s r , and t h e r e f o r e 24% l a r g e r t h a n the a r e a sensed by the a c t i n o m e t e r . Thus, the approach p r o v i d e d some smoothing o f the d a t a . I n the a v e r a g i n g p r o c e s s , t o reduce e r r o r s due t o f l a w s and dust i n t r o d u c e d i n p r o c e s s i n g , a c u t - o f f o f ±75 d e n s i t y u n i t s from the d e n s i t y v a l u e o f the c e n t r a l p o i n t was i n s t i t u t e d . I n t u r n , t o i n s u r e the m i d - p o i n t i t s e l f was not f l a w e d , the number of p o i n t s used I n the a v e r a g i n g p r o c e s s was c o n s i d e r e d . I f t h i s v a l u e was l e s s t h a n 7, the c e n t r a l p o i n t was manually checked and I f n e c e s s a r y , removed 54 and the average r e c a l c u l a t e d . . ' Two methods o f curve f i t t i n g were u t i l i z e d t o produce p r e d i c t i v e e q u a t i o n s f o r the r e l a t i o n s h i p between r a d i a n c e and d e n s i t y . The i n i t i a l method was n o n - l i n e a r r e g r e s s i o n a n a l y s i s . T h i s was p r e f e r e n t i a l f o r two r e a s o n s : (1) the s t a t i s t i c a l e v i d e n c e p r o v i d e d an e s t i m a t e o f the s i g n i f i c a n c e of the c o r r e l a t i o n and (2) the a n a l y s i s produced a " b e s t - f i t " e q u a t i o n t o the d a t a . When a f u n c t i o n c o u l d not be found.to a d e q u a t e l y d e s c r i b e t h e d a t a , a b e s t - f i t curve was drawn by hand. The c r i t e r i a used i n c u r v e - f i t t i n g a re d i s c u s s e d more f u l l y i n S e c t i o n 4.2. The c u r v e - f i t t i n g procedure,was implemented by c o r r e -l a t i n g the complete a c t i n o m e t r i c d a t a s e t w i t h each o f the averaged d a t a s e t s f o r the c o r r e s p o n d i n g 3 photographs. The approach was t h e n r e p e a t e d u s i n g a d a t a s e t which c o n s i s t e d of the a c t i n o m e t r i c measurements b e i n g p a i r e d w i t h the averaged d e n s i t y measurements from the n e a r e s t photograph only.. I n t h i s l a t t e r c a s e , the f i r s t 7 a c t i n o m e t r i c measurements would be p a i r e d w i t h the d e n s i t y measurements d e t e r m i n e d from the f i r s t p h o t o g r a p h , the next 7 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 averaged d e n s i t y v a l u e s from the second photograph and s i m i l -a r i l y . the l a s t 7 a c t i n o m e t r i c measurements w i t h v a l u e s from the t h i r d p h o t ograph. T h i s l a t t e r method w i l l be r e f e r r e d t o as the 'bombined t e c h n i q u e " . The r e s u l t s u s i n g the combined t e c h n i q u e ( S e c t i o n 3-5) were i n c o n c l u s i v e . F o r c l e a r sky p h o t o g r a p h s , the b e s t s t a t i s -.55 t i c a l f i t was found by c o r r e l a t i n g the a c t i n o m e t r i c measurements w i t h t h e photograph exposed midway, through the * measurement' •'" p e r i o d ( T a b l e 4.1). The c o r r e l a t i o n s u s i n g the combined method were o n l y s l i g h t l y l e s s s i g n i f i c a n t , and e q u i v a l e n t t o those using:, e i t h e r the f i r s t o r l a s t photograph i n the d a t a s e t . I t appears t h a t i n the case o f very s t a b l e c o n d i t i o n s , such as a c l o u d l e s s s k y , the e r r o r i n t r o d u c e d by v a r i a t i o n s i n the f i l m and i n the d e n s i t o m e t r i e a n a l y s i s o f f s e t s any gains made by the combined t e c h n i q u e . I n s i t u a t i o n s where the c l o u d p a t t e r n o v e r the c e l e s t i a l dome was more complex, the combined t e c h n i q u e was found t o be s u p e r i o r . T able 4.1 a l s o p r o v i d e s an. example f o r the f i t t i n g o f an e x p o n e n t i a l curve t o an o v e r c a s t sky c o n d i t i o n . The s u p e r i o r i t y o f the combined t e c h n i q u e was not u n i v e r s a l , however. Changes i n sky c o n d i t i o n s do not o c c u r at the same r a t e . Thus, a l t h o u g h a measurement may have been made w i t h i n minutes o f one pho t o g r a p h , i t may be b e t t e r c o r r e l a t e d w i t h a d i f f e r e n t p h o t o g r a p h , r e d u c i n g the e f f e c t i v e n e s s o f the >. combined t e c h n i q u e . T h i s problem i s d i r e c t l y r e l a t e d t o the time r e q u i r e d t o produce a r e p r e s e n t a t i v e sample o f a c t i n o m e t r i c measurements, over a c o n t i n u a l l y changing sky hemisphere, v e r s u s the i n s t a n t a n e o u s n e s s o f a photograph. Because o f the i n c o n -s i s t e n c y i n the combined t e c h n i q u e , i t was d e c i d e d t h a t i n d i v i d u a l c a l i b r a t i o n s f o r each photograph would be u t i l i z e d . 4.2 Curve F i t t i n g Procedures-F o r a d a t a s e t o f 20 p o i n t s , 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 56 TABLE 4 . 1 . — E x p o n e n t i a l c u r v e - f i t t i n g s t a t i s t i c s f o r a c l e a r sky ( 1 4 : 1 1 F e b r u a r y 26, 19 78) and an o v e r c a s t sky c o n d i t i o n (11:20 February 1 4 , 1978) Sky C o n d i t i o n P h o t o g r a p h ( s ) F R a t i o 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 C l e a r 1 2 3 Combination 81.420 117. 700. 102.100 101.400 0.8358 0.8803 0 .8645 0 . 8637 10/10 S t r a t u s • 1 2 3 Combination 4.526 0 .1919 6.874 30.830 0.1924 0 .0100 0 .2657 o .6187 : 57 curve i s d e f i n e d as h a v i n g a c o r r e l a t i o n c o e f f i c i e n t o f O..56I a t the 0.01 c o n f i d e n c e l e v e l ( S o k a l and R o h i f , 1973). S i m i l a r i l y , f o r 15 p o i n t s , a c o r r e l a t i o n c o e f f i c i e n t o f 0.606 i s n e c e s s a r y . The average number o f p o i n t s used i n the c o r r e l a t i o n s was 19. The r e d u c t i o n i n the number o f da t a p o i n t s between the o b s e r -v a t i o n s o f r a d i a n c e and the c a l i b r a t i o n o f the d e n s i t y v a l u e s was because the measured f l u x was e i t h e r too s m a l l o r too l a r g e t o be a c c u r a t e l y r e c o r d e d by; -the H o n e y w e l l E l e c t r o n i k 194 r e c o r d e r a t the lOOuv s c a l e o r because d a t a p o i n t s were removed as u n r e p r e s e n t a t i v e . The removal o f da t a o c c u r r e d when i t was found t h a t ' c e r t a i n p o i n t s d i d not f o l l o w the g e n e r a l t r e n d o f the o b s e r v a t i o n . F i g u r e 4.1 p r o v i d e s an example of such a case f o r a c l e a r sky day. An a r b i t r a r y d e c i s i o n was made such t h a t an i n t e r i o r o b s e r v a t i o n . p o i n t which d i f f e r e d from the p r e d i c t e d r a d i a n c e f o r the same d e n s i t y by g r e a t e r t h a n ±50% was r e j e c t e d . The r e g r e s s i o n e q u a t i o n was then r e c a l c u l a t e d . I f more tha n two p o i n t s were found t o be o u t s i d e t h i s range,, none was r e j e c t e d . There were 2 reasons why u n r e p r e s e n t a t i v e d a t a p o i n t s might o c c u r . The f i r s t was because o f an e r r o r i n measurement, e i t h e r d u r i n g o b s e r v a t i o n o f r a d i a n c e o r d u r i n g the d i g i t i z i n g o f the photograph. I n the c l e a r sky c a s e , the v a l i d i t y o f an a c t i n o m e t r i c o b s e r v a t i o n c o u l d be dete r m i n e d by n o r m a l i z i n g the o b s e r v a t i o n and c h e c k i n g i t a g a i n s t the u n i v e r s a l d i s t r i -b u t i o n s o f Stev e n (1977). I n a l l o t h e r cases o f t h i s t ype o f e r r o r , no f u r t h e r e x p l a n a t i o n can be g i v e n . The second Density Figure 4.1 I l l u s t r a t i o n of the effect of the removal of an o u t l i e r for 13:26 February 26, 1978 C a l i b r a t i o n curve before o u t l i e r removed ( c i r c l e d point) Calculated EH = 58.562 Wm 2 C a l i b r a t i o n curve with o u t l i e r removed Calculated D-i- = 55-059 Wm Actual D4 = 52.55 Wm 2 0 0 •59 r e a s o n f o r the r e j e c t i o n o f a p o i n t i s based on the knowledge t h a t w i t h a r a p i d v a r i a t i o n i n h e m i s p h e r i c c o n d i t i o n s , a g i v e n a r e a may not be. r a d i a t i n g a t the same f l u x d e n s i t y when measured by the a c t i n o m e t e r as when photographed. Such a d i f f e r e n c e i n v a l u e s can o f t e n be r e c o g n i z e d by comparing the d i f f u s e i r r a d i a n c e o b s e r v e d a t the time o f the a c t i n o m e t r i c measurement w i t h the d i f f u s e i r r a d i a n c e a t the time o f the photograph. I n d e t e r m i n i n g the r e g r e s s i o n e q u a t i o n s used i n mapping r a d i a n c e f o r the sky hemisphere, i t was hoped t h a t a common form o f e q u a t i o n c o u l d be found t o f i t a l l r a d i a n c e d i s t r i -b u t i o n s . I n the attempt t o f i n d such a form, i t was assumed t h a t a s i g n i f i c a n t c o r r e l a t i o n c o e f f i c i e n t j u s t i f i e d the use of t h a t e q u a t i o n . t o p r e d i c t the a n g u l a r d i s t r i b u t i o n o f r a d i -ance. Thus, when a form o f e q u a t i o n was found t o be s i g n i f i c a n t f o r one sky c o n d i t i o n , i t was t e s t e d o v e r a v a r i e t y o f sky c o n d i t i o n s . I f t h e s e a l s o r e s u l t e d i n s i g n i f i c a n t c o r r e l a t i o n c o e f f i c i e n t s , the r a d i a n c e v a l u e s were p r e d i c t e d over the e n t i r e hemisphere and the i r r a d i a n c e c a l c u l a t e d ( S e c t i o n 4.3). T h i s was t h e n compared, t o the ob s e r v e d i r r a d i a n c e . T h i s attempt y i e l d e d no s i n g l e form o f e q u a t i o n which a d e q u a t e l y p r e d i c t e d i r r a d i a n c e f o r even s i m i l a r sky c o n d i t i o n s . However, b e s i d e s i n d i c a t i n g the c o m p l e x i t y o f the problem b e i n g d e a l t w i t h , i t d i d produce a methodology a p p l i c a b l e t o i n d i v i d u a l c a s e s . T h i s methodology d e v e l o p e d t h r e e b a s i c g u i d e l i n e s by which curves c o u l d be f i t t o the c a l i b r a t i o n d a t a : (1) the cu r v e , 60 i f d e t e r m i n e d u s i n g r e g r e s s i o n , a n a l y s i s , had t o have a c o r r e l a t i o n c o e f f i c i e n t s i g n i f i c a n t a t the 0.01 l e v e l . (2) I t was found t h a t i n n e a r l y a l l cases any r e g r e s s i o n e q u a t i o n p r o v i d e d a. c o r r e l a t i o n c o e f f i c i e n t t h a t was s t a t i s -t i c a l l y s i g n i f i c a n t , y e t the g e n e r a l form o f t h i s f u n c t i o n o f t e n bore l i t t l e p h y s i c a l resemblance t o the t r e n d o f the dat a ( F i g u r e 4.2). T h e r e f o r e , the curve a l s o had t o f o l l o w the g e n e r a l form o f the d a t a b e f o r e b e i n g a c c e p t e d . (3) I t was found t h a t the d i s t r i b u t i o n o f d e n s i t y v a l u e s f o r a n t e n t i r e n e g a t i v e d i d not. always f o l l o w the same d i s t r i b u t i o n as those d e n s i t i e s used i n the c a l i b r a t i o n c u r v e . I n such c a s e s , c e r t a i n p o i n t s i n the c a l i b r a t i o n o b s e r v a t i o n s r e p r e -s e n t e d a l a r g e p e r c e n t a g e o f d e n s i t y v a l u e s . When t h i s o c c u r r e d , i t was d e s i r a b l e t h a t the c a l i b r a t i o n curve p r e d i c t the r a d i a n c e a t t r i b u t e d , t o these d a t a p o i n t s a c c u r a t e l y w h i l e s t i l l f u l f i l l i n g the f i r s t two c r i t e r i a . . F i g u r e 4.. 3 i l l u s t r a t e s two c u r v e s , b o t h meeting the f i r s t two g u i d e -l i n e s but o n l y one o f which meets - the t h i r d , f o r a c l e a r sky c a s e . By more a c c u r a t e l y p r e d i c t i n g the a r e a o f the curve which r e p r e s e n t s the...greater number o f d e n s i t y v a l u e s , the e s t i m a t e d i r r a d i a n c e changes.from 62.3 Wm 2 t o 59-9 Wm 2 . T h i s i s a s i g n i f i c a n t Improvement as the ob s e r v e d i r r a d i a n c e was 56 .5 Wm"2 . The l a s t two g u i d e l i n e s f o r the curve f i t t i n g were s u b j e c t i v e l y d e f i n e d as b e i n g met when the form o f the curve f o l l o w e d the t r e n d o f the d a t a f o r over 90% o f the range o f 1 h 0 ' , / Density Figure 4.2 S t a t i s t i c a l l y significant curves i l l u s t r a t i n g variation i n quality of f i t (14:11 LAT February 26, 1978) £ = -71. 404 + 0.278 X correlation coefficient =0.84 — = Exp {-0.2833 + 8.649 x 10 3 X} correlation coefficient = 0.94 St a t i s t i c a l l y significant correlation coefficient at the 0.01 level = 0.54 o crj •H 1 4 0 1 2 0 1 0 01 8 0 R GO 4 0 2 0 16% of population represented by. 10% of c a l i b r a t i o n data i:8% of population representee} by 5% df calibration data 2"0.0 (! 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 D e n s i t y F i g u r e 4.3 R e p r e s e n t a t i v e n e s s o f s e l e c t e d data p o i n t s w i t h r e s p e c t t o the t o t a l p o p u l a t i o n o f d e n s i t y v a l u e s f o r 13:40 LAT February 10, 19 78 curve not a c c o u n t i n g f o r the d i s t r i b u t i o n o f the t o t a l p o p u l a t i o n , e s t i m a t e d d i f f u s e i r r a d i a n c e o f 62.3 Wm-2 curve which r e p r e s e n t s t o t a l p o p u l a t i o n d i s t r i b u t i o n , e s t i m a t e d d i f f u s e i r r a d i a n c e of 59.9 Wm-2 ro A c t u a l d i f f u s e i r r a d i a n c e 56.5 Wm-2 6:3 the t o t a l p o p u l a t i o n o f d e n s i t y v a l u e s . When a r e g r e s s i o n f u n c t i o n c o u l d not be found t o ad e q u a t e l y meet these g u i d e l i n e s , a smooth hand-drawn f u n c t i o n was u t i l i z e d . The curve f o l l o w e d the g e n e r a l t r e n d o f the dat a a t t e m p t i n g t o i n t e r c e p t as many p o i n t s as p o s s i b l e t a k i n g i n t o c o n s i d e r a t i o n the g e n e r a l s c a t t e r o f the o b s e r v a t i o n s and the r e p r e s e n t a t i v e n e s s o f each d e n s i t y v a l u e . The curve was t h e n d i g i t i z e d and a p o l y n o m i a l f u n c t i o n f i t t e d t o t h e s e p o i n t s . The hand-drawn curve was e x t r a p o l a t e d beyond the c a l i b r a t i o n d a t a u s i n g the' knowledge o f p r e v i o u s s t a t i s t i c a l l y f i t t e d c urves found, i n s i m i l a r s i t u a t i o n s . Although, t h e s e data d i d not s i g n i f i c a n t l y a f f e c t a l a r g e p o r t i o n o f the t o t a l p o p u l a t i o n , i t ensured t h a t a f u n c t i o n would be c o n t i n -u o u s l y d e f i n e d , o v e r the o p e r a t i n g range in'.both i n t e n s i t y and d e n s i t y terms. The f i t t i n g o f t h e p o l y n o m i a l t o t h e hand-drawn curve was u t i l i z e d t o e x p e d i a t e the co m p u t a t i o n o f both the r a d i a n c e f o r the t o t a l p o p u l a t i o n and the i r r a d i a n c e . 4 . 3 V e r i f i c a t i o n , o f C a l i b r a t i o n s . To t e s t the p r e d i c t i v e a b i l i t y o f the r e s u l t i n g b e s t -f i t c u r v e s , the method o u t l i n e d i n S t e v e n (1977) was f o l l o w e d . T h i s assumes a unique r e l a t i o n s h i p between the: a n 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 and the ob s e r v e d d i f f u s e i r r a d i a n c e . Thus, i f the c a l c u l a t e d i r r a d i a n c e .was found t o approximate the o b s e r v e d , the a n g u l a r d i s t r i b u t i o n was c o r r e c t . The i n t e g r a t e d i r r a d i a n c e s o f Ste v e n (1977) f o r c l e a r sky cond-i t i o n s o v e r e s t i m a t e d the o b s e r v e d i r r a d i a n c e s by a mean 64 e r r o r o f 6%. I n the p r e s e n t study the p r e d i c t i v e f u n c t i o n s were a p p l i e d t o the 2629 i n d i v i d u a l d e n s i t y o b s e r v a t i o n s and the r e s u l t i n g r a d i a n c e s were n u m e r i c a l l y i n t e g r a t e d . B e f o r e the i n t e g r a t i o n , the f i v e d e n s i t y v a l u e s n e a r e s t t o t h e p o s i t i o n o f the s o l a r d i s c were removed. T h i s was t o a v o i d contam-i n a t i o n by d e n s i t y measurements which might i n t u r n be i n f l u e n c e d by e i t h e r the o c c u l t i n g d i s c , when p r e s e n t , o r l e n s f l a r e a s s o c i a t e d w i t h - t h e s o l a r d i s c . These f i v e p o i n t s r e p r e s e n t a s o l i d a n g l e o f 0 . 011 sr., I n the cases where the sun was o b s c u r e d by c l o u d s , t h e s e p o i n t s were not removed. The n u m e r i c a l i n t e g r a t i o n - e q u a t i o n used t o r e l a t e r a d i a n c e and the i r r a d i a n c e f o r a h o r i z o n t a l s u r f a c e f o l l o w s the i n t e g r a l o u t l i n e d i n P a l t r i d g e and P i a t t ( 1 9 7 7 ) : n = E L. • cos 0 . • Sco ( 4 . 2 ) p 1=1 x x p r e d i c t e d - d i f f u s e i r r a d i a n c e on a h o r i z o n t a l s u r f a c e (Wm - 2) r a d i a n c e from the p o i n t i ( W m - 2 s r - 1 ) s o l i d a n g l e r e p r e s e n t e d by each d e n s i t y ( s r ) z e n i t h a n g l e f o r each r a d i a n c e v a l u e ( r a d i a n s ) I n the p r e s e n t form, e q u a t i o n 4 . 3 assumes t h a t the measured d e n s i t y i s r e p r e s e n t a t i v e o f i t s immediate surroun--. d i n g s . A st u d y d e s c r i b e d i n Chapter S i x i n d i c a t e s t h i s i s a where. D+p = \ = 6co = 0. = 65 r e a s o n a b l e a ssumption. Because o f the time r e q u i r e d t o d i g i t i z e each i n d i v i d u a l p h o t o g r a p h , the t e c h n i q u e has been t e s t e d on o n l y 11 o f the 30 s e t s o f f i e l d o b s e r v a t i o n s . On the b a s i s o f the method-ology f o r d e t e r m i n i n g a b e s t - f i t curve ( S e c t i o n 4.2), 9 o f th e s e 11 d a t a s e t s p r e d i c t e d the h o r i z o n t a l s u r f a c e d i f f u s e i r r a d i a n c e t o w i t h i n ±10% o f the ob s e r v e d i r r a d i a n c e . Of thes e 95 5 were p r e d i c t e d f o l l o w i n g the i n i t i a l p r o c e d u r e ( S e c t i o n 4.2) and the f u n c t i o n found t o b e s t p r e d i c t the i r r a d i a n c e was e x p o n e n t i a l . The 5 c o n s i s t e d o f 3 c l e a r sky s e t s o f o b s e r v a t i o n s , 13:26, 13:47 and 14:11 f o r February 26, 1978 and 2 p a r t i a l l y c l o u d y s e t s o f o b s e r v a t i o n s 13=17 and 13 = 37 f o r F e b r u a r y 15, 1978. Data f o r 13:22. Febr u a r y 15 were a l s o found, t o f o l l o w an e x p o n e n t i a l c u r v e , b u t . t h i s i n v o l v e s the use o f the same a c t i n o m e t r i c d a t a as f o r the 13:17 s e t o f o b s e r v a t i o n s . . The v a l u e s o f the c o n s t a n t s and the form o f the curves f o r a l l d a t a s e t s can be found i n Appendix 2. The two da t a s e t s , which n e c e s s i t a t e d the more e l a b o r a t e c a l i b r a t i o n methodology and s t i l l d i d not p r e d i c t i r r a d i a n c e t o w i t h i n ±10% were t a k e n d u r i n g f l u c t u a t i n g r a d i a t i o n c o n d i t i o n s . This, may be p a r t i a l l y r e s p o n s i b l e f o r the poor agreement. One case was f o r a p a r t i a l l y c l o u d y c o n d i t i o n , w h i l e the o t h e r was f o r an o v e r c a s t s i t u a t i o n . I n the . f i r s t c a se, F e b r u a r y 24, i t was found t h a t a l a r g e p e r c e n t a g e o f the a c t i n o m e t r i c o b s e r v a t i o n s o c c u r r e d w i t h i n a s m a l l range 66 o f d e n s i t y v a l u e s ( F i g u r e A2.9). I n the second c a s e , 11 : 4 7 February 14, no f u r t h e r e x p l a n a t i o n c o n c e r n i n g t h e ; t e m p o r a l v a r i a b i l i t y i n the d i f f u s e i r r a d i a n c e can be o f f e r e d a t t h i s t i m e . Table 4.2 p r o v i d e s a comparison o f the computed and o b s e r v e d d i f f u s e i r r a d i a n c e f o r each d a t a s e t on which the a n a l y s i s was performed. The d i f f e r e n c e i n the q u a l i t y o f the e s t i m a t e o f d i f f u s e i r r a d i a n c e i s a r e s u l t o f the v a r i a t i o n i n the goodness o f f i t o f the curve t o the c a l i b r a t i o n d a t a . T h i s i s p a r t i c u l a r l y the case f o r 12 : 4 7 F e b r u a r y 1 5 , where t h e r e was a l a r g e s c a t t e r o f p o i n t s i n the c a l i b r a t i o n d a t a ( F i g u r e A2. 5 ) . O v e r a l l t h e r e l a t i v e e r r o r i s v e r y s m a l l and must be seen i n l i g h t o f the p r o b a b l e r e l a t i v e e r r o r o f 7 . 4 6 % ( S e c t i o n 3 - 7 . 5 ) . F u r t h e r , p a r t o f t h i s e r r o r i s due t o the s e n s i n g o f r a d i a t i o n r e f l e c t e d by s u r f a c e s above the theor^"' e M c a l h o r i z o n on the case o f the o b s e r v e d v a l u e s . T h i s was not c o n s i d e r e d on the c a l c u l a t e d i r r a d i a n c e . Thus, a l t h o u g h a s i n g l e form o f e q u a t i o n cannot be used I n d e t e r m i n i n g the 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 , c a l i b r a t i o n curves t h a t f i t t h e form o f the d a t a p o i n t s can produce u s e f u l r a d i a n c e d i s t r i b u t i o n s f o r i n d i v i d u a l sky c o n d i t i o n s . 4 . 4 A p p l i c a t i o n S i n c e the prime o b j e c t o f t h i s s tudy was t o map the 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 , the r e s u l t s are p r e s e n t e d i n two forms of map. The f i r s t p r e s e n t e d , TABLE 4 . 2 . — Comparison of. measured and computed d i f f u s e i r r a d i a n c e Time . Date Sky C o n d i t i o n A c t u a l Computed A b s o l u t e % (LAT) D4-(Wm~2) D+.(Wm~2) Diff(Wm" 2) D i f f e r e n c e 12: 40 Feb . 10 c l e a r 65 .730 . ' 6 8 .467 2 .737 4 .16 13: 40 Feb . 10 c l e a r 56 .480 . 59 .896 3 .416 6 .05 11: 20 Feb . 14 10/10St 88 .566 76 .199 12 .367 13 .96 12: 30 Feb . 14 10/10St 63 .346 62 .090 1 .256 : 1 .98 12: 47 Feb . 15 8/10Ac 291 .657 265 .807 25 .850 8 .86 13: 17 Feb . 15 4/10Ac3/10Ci 162 .552 167 .802 5 .25 3 .23 13: 22 Feb . 15 4/10Ac3/10Ci 141 .118 129 .481 11 .637 8 .25 13: 47 . Feb . 15 3/10Acl/10Ci 91 .561 90 .586 0 .975 1 .06 10 : 07 Feb . 24 l/10Ac5 /10As3/10Ci 199 .108 165 .000 34 .10 8 17 .13 13: 26 Feb . 26 c l e a r 52 .550 55 .059 2 • 509 4 • 77 13: 47 Feb . 26 c l e a r 51 .590 50 • 715 0 .875 1 .70 14: 11 Feb . 26 c l e a r 49 .680 49 .088 0 .592 1 .19 68 are r a d i a n c e maps f o r the sky hemisphere as seen on an e q u i d i s t a n t p r o j e c t i o n . The i s o l i n e s range between 5 and 130 Wm~ 2sr - 1 w i t h i n t e r m e d i a t e v a l u e s o f 10, 20, 30, 40, 60, 80., and 105 Wm 2 s r _ 1 . These v a l u e s were f e l t t o p r o v i d e the b e s t coverage o f the c e l e s t i a l dome f o r b o t h c l e a r and cloudy c o n d i t i o n s . The i r r e g u l a r s t e p s p r o v i d e the n e c e s s a r y means t o c o n t o u r , w i t h a minimum o f i s o l i n e s , b o t h t h e very low r a d i a n c e v a l u e s 90° from the sun and the h i g h v a l u e s around the s o l a r d i s c . The second s e t o f ' a n a l y s e s t o b e ' p r e s e n t e d are n o r m a l i z e d maps u s i n g the e q u i v a l e n t f l u x d e n s i t y r e l a t i o n s h i p o f Unsworth and M o n t e i t h (19 75). The c l e a r sky. maps p r e s e n t e d i n t h i s form a re d i r e c t l y comparable t o thos e o f St e v e n (1977). The i s o l i n e s were s e t 0.5 s r - 1 a p a r t , s i m i l a r t o thos e o f Ste v e n . Both s e t s o f maps were drawn on an e l e c t r o m e c h a n i c a l p L . t t e r ( C o c k l e , 1976) w i t h i n d i v i d u a l pen movements o f 0.254mm i n the X and Y d i r e c t i o n s and 0.359mm i n a d i a g o n a l d i r e c t i o n . The sky r a d i a n c e maps p r e s e n t e d a re 6,63. times l a r g e r t h a n the o r i g i n a l p h o tograph. T h i s spaces i n d i v i d u a l d a t a p o i n t s a p p r o x i m a t e l y 2 .5mm a p a r t . The c o n t o u r i n g , program u t i l i z e d i n the i s o l i n i n g ( C o u l t h a r d , 1 9 7 5 ) ' uses a s i m p l e l i n e a r i n t e r p o l a t i o n t e c h n i q u e between each 2 p o i n t s t o draw the c o n t o u r . The c o m b i n a t i o n o f the d i s c r e t e pen movements, the s p a c i n g between d a t a p o i n t s and the i n t e r p o l a t i o n t e c h n i q u e w i l l produce a curve w i t h a c e r t a i n amount o f n o i s e . 69 The a c t u a l amount, however, cannot be e a s i l y a s c e r t a i n e d . To q u a l i t i t i v e l y determine the h i g h f r e q u e n c y v a r i a -b i l i t y due t o the methodology used i n . p r o d u c i n g ' t h e s e maps, a comparison was made between 2 c l e a r sky days d e n s i - t i z e d i n d i f f e r e n t manners.. P l a t e 4.1 i s a f a l s e c o l o u r r e p r e s e n -t a t i o n o f the n e a r l y c l e a r sky luminance p a t t e r n f o r 14:00 September 10, 19 77. T h i s was produced u s i n g an e l e c t r o n i c d e n s i t y s l i c e r and d i s p l a y e d on a c o l o u r v i d i c o n t u b e . Each c o l o u r r e p r e s e n t s a r e g i o n o f s i m i l a r d e n s i t y ( t h e d a r k e r the c o l o u r , the g r e a t e r the d e n s i t y o f the p o s i t i v e ) , w h i l e the boundary between. 2 c o l o u r s i s a d e n s i t y i s o l i n e (MeArthur and Hay, 1978). Though the e l e c t r o n i c d e n s i t y s l i c e r d e t e r -mines d e n s i t y o ver the e n t i r e a r e a o f ' t h e p h o t o g r a p h , th e d a r k e s t and w h i t e s t , r e g i o n s o f the p l a t e are areas i n w h i c h the d e n s i t y range c o u l d not be a d e q u a t e l y d i s p l a y e d by t h i s t e c h n i q u e . F i g u r e 4.4 i s the c l e a r sky r a d i a n c e p a t t e r n f o r 14:07 F e b r u a r y 10, 19 78. T h i s was t r a c e d by the e l e c t r o -m e c h a n i c a l p l o t t e r . I f i t i s assumed t h a t the c o m p u t e r i z e d d e n s i t y s l i c e r produces a " t r u e " d i s t r i b u t i o n o f sky l u m i n a n c e , one i s a b l e t o determine the f r e q u e n c y above w h i c h the v a r i a t i o n i s s o l e l y due t o the c o m p u t e r i z e d mapping t e c h n i q u e . A l t h o u g h p r e v i o u s work ( S t e v e n , 1977) has produced smooth, d e n s i t y i s o l i n e s , b o t h e l e c t r o n i c and m e c h a n i c a l mappings o f the d i s t r i b u t i o n o f luminance and r a d i a n c e r e s p e c t i v e l y , i n d i c a t e 70 N E S Figure 4.4 D i f f u s e radiance d i s t r i b u t i o n f o r a c l e a r sky (13:40 February 10, 19 78) as produced from the photographic negative (VJm~ 2sr- 1) (Z = 67 .6° ) PLATE 4.1 . E l e c t r o n i c a l l y d e n s i t y s l i c e d a l l - s k y p h o t g r a p h i c image o f 14:00 September 10, 19 77 73 t h a t t h i s i s not the case. Only the s m a l l e s t p e r t u r b a t i o n s , a p p a r e n t l y caused by i n d i v i d u a l pen movements, are not a l s o found i n the e l e c t r o n i c a l l y d e n s i t y s l i c e d luminance d i s t r i -b u t i o n . I t i s o b s e r v e d i n b o t h methods o f mapping t h a t i n the d a r k e r areas o f the sky hemisphere, areas o f g r e a t e r i n t e n s i t y are found w i t h i n areas o f l e s s e r i n t e n s i t y . I t s h o u l d be n o t e d t h a t an a r e a where t h i s i s a p p a r e n t l y found on the e l e c t r o n i c a l l y produced image (top l e f t , P l a t e 4.1) i s due t o the presence o f c l o u d . The r e a l i t y o f t h i s c l e a r sky p a t t e r n may s t i l l r emain i n q u e s t i o n w i t h r e s p e c t t o the r e s u l t s o f the 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 u s i n g s i n g l e s c a t t e r i n g t h e o r y ( A t r o s h e n k o e t a l , 1962) and the m u l t i p l e s c a t t e r i n g approx-i m a t i o n s o f Dave (1975). However, at t h i s t i m e , t h e r e i s no r e a s o n to doubt the t e c h n i c a l a s p e c t s o f the work. One p o s s i b l e r e a s o n f o r t h i s apparent c o n t r a d i c t i o n between t h e o r y and measurement was the q u a l i t y o f the f i l m s used i n the s t u d y . T h i s i s u n l i k e l y , however, as b o t h f i l m s behaved s i m i l a r l y , and the method employed ( S e c t i o n 3.6.2) c o n s i d e r e d t h i s problem. U n t i l f u r t h e r t e s t s prove o t h e r w i s e , t h e s e l a r g e r p e r t u r b a t i o n s cannot be i g n o r e d . 4.4.1 Case s t u d i e s Of the t e n d a t a s e t s upon which t h i s study i s b a s e d , f i v e are f o r 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 ; 2 are f o r t o t a l l y o v e r c a s t s i t u a t i o n s , w h i l e the r e m a i n i n g 3 r e p r e s e n t the more complex p a r t i a l l y c l oudy c o n d i t i o n which i s o f so much i n t e r e s t . 74 The r e a s o n f o r the l a r g e number o f c l e a r sky cases i s t o show t h e i r g e n e r a l c o m p a r a b i l i t y t o p r e v i o u s work; At p r e s e n t , one can o n l y assume t h a t i f t h e s e c l e a r sky cases are comparable, the o t h e r more complex d i s t r i b u t i o n s are a l s o r e a l i s t i c , w i t h i n the a c c u r a c y w i t h which they are p r e p a r e d . P l a t e s 4.2 - 4.4 p r o v i d e t h e p h o t o g r a p h i c images c o r r e s p o n d i n g t o F i g u r e s 4.4 t o 4.6 r e s p e c t i v e l y . As e x p e c t e d , the p a r t i a l l y c l o u d y c o n d i t i o n ( F i g u r e 4.5) i s by f a r the most complex, w h i l e the l e a s t complex d i s t r i b u t i o n i s f o r the o v e r c a s t s i t u a t i o n ( F i g u r e 4.6). By i n t e r c o m p a r i n g t h e s e t h r e e f i g u r e s one i s a b l e t o note the change i n the r a d i a n c e d i s t r i b u t i o n from t o t a l l y c l e a r t o t o t a l l y o v e r c a s t s k y c o n d i t i o n s . In. the c l e a r s k y . c a s e , the l e a s t i n t e n s e r a d i a n c e i s found a p p r o x i m a t e l y 90° from the s o l a r d i s c w i t h i n t e n s i t y i n c r e a s i n g from t h e r e out t o t h e h o r i z o n . T h i s i n c r e a s e f o l l o w s a n e a r l y e l l i p t i c a l p a t t e r n u n t i l i t i s i n f l u e n c e d by the c i r c u m s o l a r r e g i o n ( M o r r i s and. Lawrence, 1971). At t h i s p o i n t , the i s o l i n e s o f r a d i a n c e ( i s o r a d s ) are i n f l u e n c e d more by the s o l a r d i s c and b e g i n t o f o l l o w c o n c e n t r i c p a t t e r n s , around the sun. This i s p a r t i c u l a r l y w e l l i l l u s t r a t e d i n . P l a t e 4.1. I n the p a r t i a l l y o v e r c a s t c o n d i t i o n , the l o w e s t i n t e n s i t y o c c u r s i n the same r e g i o n . However, the magnitude o f the i n t e n s i t y has i n c r e a s e d due t o the g r e a t e r s c a t t e r i n g e f f e c t o f the w a t e r d r o p l e t s . The i n t e n s i t y i n c r e a s e s b o t h PLATE 4.2 * A l l - s k y photograph exposed a t 14:07 F e b r u a r y 10, 19 78 o f a c l e a r s k y . F i g u r e 4.4 p r o v i d e s the sky r a d i a n c e map produced from the exposed n e g a t i v e . w E N ORIENTATION OF PHOTOGRAPHS PLATE 4 . 3 A l l - s k y photograph exposed a t 13:17 F e b r u a r y 15, 19 78 o f an p a r t i a l l y o v e r c a s t s k y. F i g u r e 4.5 p r o v i d e s t h e sky r a d i a n c e map produced form the exposed n e g a t i v e . PLATE 4.4 A l l - s k y photograph exposed at 12:30 F e b r u a r y 14, 1978. o f a c o m p l e t e l y o v e r c a s t s k y. F i g u r e 4.6 p r o v i d e s the sky r a d i a n c e map produced from the exposed n e g a t i v e . 82 F i g u r e 4.5 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 f o r a p a r t i a l l y c loudy sky (13:17 F e b r u a r y 15, 19 78) as produced from the p h o t o g r a p h i c n e g a t i v e (Wm _ 2sr- 1) (Z = 64 . 5 ° ) 83 F i g u r e 4.6 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 f o r an o v e r c a s t sky (12:30 F e b r u a r y 14, 19 78) as produced from the photographic-n e g a t i v e (Wm- 2sr- 1) (Z = 63 .0° ) 84 towards the h o r i z o n and the s o l a r d i s c , but not i n the same c o n s i s t e n t p a t t e r n as the c l e a r sky case. I n a d d i t i o n , the a r e a around the s o l a r d i s c i s not the o n l y a r e a o f the hemi-sphere where r a d i a n c e i s g r e a t e r t h a n 130 Wm _ 2sr~ 1. T h i s i l l u s t r a t e s the h i g h r e f l e c t i v i t y o f c l o u d s and the added c o m p l e x i t y which i t c r e a t e s i n the m o d e l l i n g o f d i f f u s e i r r a d i a n c e . O v e r a l l , the g r a d i e n t has d e c r e a s e d between the l e a s t i n t e n s e and most i n t e n s e r a d i a n t areas o f the c e l e s t i a l dome . For the o v e r c a s t case ( F i g u r e 4.6), t h e g r a d i e n t has almost c o m p l e t e l y d i m i n i s h e d and the s o l a r p o s i t i o n i s not even e v i d e n t . Kondratyev .(.1969) s t a t e s , " t h a t { f o r } a dense n o n - t r a n s p a r e n t c l o u d i n e s s , the a z i m u t h a l dependence o f d i f f u s e r a d i a t i o n i n t e n s i t y i s not marked enough and a somewhat mono-tonous i n c r e a s e o f the i n t e n s i t y from the h o r i z o n z e n i t h w a r d i s o b s e r v e d " . A l t h o u g h the i s o t r o p i c a s sumption i s not met i n any o f the above c a s e s , F i g u r e 4.6 i n d i c a t e s t h a t f o r dense c l o u d the a p p r o x i m a t i o n i s r e a s o n a b l y v a l i d o v er the c e n t r a l p o r t i o n o f the s k y . I n a l l o t h e r sky c o n d i t i o n s , however, t h i s i s i l l u s t r a t e d as not b e i n g the case. 4.4.2 N o r m a l i z e d d i s t r i b u t i o n s At p r e s e n t , t h e more u s e f u l p r e s e n t a t i o n o f data: i s as f l u x e s n o r m a l i z e d t o the d i f f u s e r a d i a t i o n i n c i d e n t on a h o r i z o n t a l s u r f a c e . I n the case o f the p h o t o g r a p h i c t e c h n i q u e , a l l measurements were e f f e c t i v e l y t a k e n i n s t a n t a n e o u s l y . 85-T h e r e f o r e , t h e i r r a d i a n c e measured a t t h e t i m e o f t h e photo-graph i s used, as the n o r m a l i z i n g parameter. T h i s a v o i d s the problem i n v o l v e d i n the work o f S t e v e n (19 77) where the d i f f u s e f l u x i s e i t h e r the average i r r a d i a n c e o ver th e p e r i o d , or the d i f f u s e i r r a d i a n c e i s measured f o r each i n d i v i d u a l a c t i n o -m e t r i c o b s e r v a t i o n . A l t h o u g h t h i s d i f f i c u l t y may be s m a l l i n the case o f c l e a r s k i e s , i t would become a l i m i t i n g f a c t o r f o r more v a r i a b l e sky c o n d i t i o n s . Figures 4.7 t o 4.11 p r e s e n t the 5 c l e a r sky n o r m a l i z e d sky r a d i a n c e d i s t r i b u t i o n s , comparable t o the d i s t r i b u t i o n s p r e s e n t e d by Steven((1977) ( F i g u r e . 2 . 5 and 2.7). One immed-i a t e l y n o t i c e s the g r e a t e r c o m p l e x i t y o f the p r e s e n t work, a l t h o u g h the more g e n e r a l agreement i s good. The main f a c t not c o n s i d e r e d by Steven, (19 77) i s the magnitude o f t h e i n c r e a s e i n b r i g h t n e s s near the h o r i z o n . T h i s may be p a r t i a l l y due t o t h e r e l a t i v e l y few p o i n t s and the s a m p l i n g d e s i g n t h a t he used. When c o n s i d e r i n g t h e two diagrams : o f S t e v e n (Z = 35° , 2 = 55°) and the g e n e r a l p a t t e r n o f the n o r m a l i z e d d i s t r i b u t i o n f o r Z = 65° ( F i g u r e 4.11) as a p r o g r e s s i o n , a number o f apparent d i f f e r e n c e s can be e x p l a i n e d . As the 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 , i t appears t h a t the g e n e r a l form o f the 1.0 s r - : 1 i s o l i n e changes from b e i n g c i r c u m s o l a r t o encompassing the r e g i o n o f the sky hemisphere o f l e a s t i n t e n s i t y . T h i s i n d i c a t e s t h a t as the s o l a r p a t h i n c r e a s e s , the limb b r i g h t -e n i n g becomes r e l a t i v e l y more i m p o r t a n t w i t h the i n c r e a s e i n "86 Figure 4.7 Clear sky normalized sky radiance d i s t r i b u t i o n ( s r x) f o r 12:40 February 10, 1978 as produced from the photographic negative (Z = 64.5°) 8,7, F i g u r e 4.8 C l e a r sky n o r m a l i z e d sky r a d i a n c e d i s t r i b u t i o n ( s r _ 1 ) f o r 13:40 February 10, 1978 as produced from the p h o t o g r a p h i c n e g a t i v e (Z = 67 .6° ) Figure 4.9 Clear sky normalized sky radiance distribution (sr _ 1) for 13:26 February 26, 1978 as produced from the photographic negative (Z = 61.0°) F i g u r e 4.9 C l e a r sky n o r m a l i z e d sky r a d i a n c e d i s t r i b u t i o n ( s r - 1 ) f o r 13:26 F e b r u a r y 26, 1978 as produced from the p h o t o g r a p h i c n e g a t i v e {Z = 61 .0° ) F i g u r e 4.10 C l e a r sky n o r m a l i z e d sky r a d i a n c e d i s t r i b u t i o n ( s r l) f o r 13:4 7 F e b r u a r y 26, 19 78 as produced from the p h o t o g r a p h i c n e g a t i v e (Z = 62.8 ) F i g u r e 4.11 C l e a r sky n o r m a l i z e d sky r a d i a n c e d i s t r i b u t i o n ( s r ]) f o r 1*4:11 February 26, 1978 as produced from the p h o t o g r a p h i c n e g a t i v e "(Z = 65 .0° ) 91 s c a t t e r i n g mass. C o r r e s p o n d i n g l y , the magnitude o f the i s o l i n e c l o s e s t t o t h e ' s o l a r d i s c i n c r e a s e s w i t h the i n c r e a s e i n the s o l a r z e n i t h a n g l e . T h i s a l s o i s e x p e c t e d due t o the i n c r e a s i n g s c a t t e r i n g mass and the s t r o n g f o r w a r d peak o f Mie s c a t t e r about the s o l a r d i s c . As the s o l a r z e n i t h a n g l e approaches 90° , the p a t t e r n o f c l e a r sky r a d i a n c e becomes more complex. T h i s i s i l l u s t r a t e d by F i g u r e 2.7 a n d . F i g u r e s 4.9 t o 4.11 where the s o l a r z e n i t h a n g l e s are 55°, 6 l ° , 62.8° and 65° r e s p e c t i v e l y . F o r a s o l a r z e n i t h a n g l e o f . 5 5 ° the c i r c u m s o l a r r e g i o n i s w e l l d e f i n e d by con t i n u o u s i s o l i n e s . However, by a s o l a r z e n i t h angle o f 6 l ° , o n l y the 5 s r ~ - c i r c u m s o l a r i s o l i n e i s c o n t i n u o u s . I n the norm-a l i z e d maps o f s o l a r z e n i t h a n g l e s g r e a t e r t h a n Z = 6 l ° ( F i g u r e s 4.9 and 4.10), no continuous, c i r c u m s o l a r i s o l i n e s are ob s e r v e d . The 4.5 s r - 1 i s o l i n e i n F i g u r e 2.7 i s seen t o be c o n t i n u o u s , w h i l e w i t h a 6° i n c r e a s e i n s o l a r z e n i t h ( F i g u r e 4.8), i t i s d i s c o n t i n u o u s and i n f l u e n c e d by limb, b r i g h t e n i n g . By Z = 62.8° ( F i g u r e 4.10), the 5 s r - 1 i s o l i n e i s a l s o found t o be a f f e c t e d by s c a t t e r i n g near the h o r i z o n . W i t h a s o l a r z e n i t h angle o f 65° ( F i g u r e 4.11), the i n c r e a s e d s c a t t e r i n g o f r a d i a t i o n due t o the l a r g e o p t i c a l a i r mass commences t o dominate the s c a t t e r i n g w i t h i n the c i r c u m s o l a r r e g i o n i n d i c a t i n g i t s e v e n t u a l t o t a l breakdown ( M o r r i s and Lawrence, 1971). As the s o l a r z e n i t h angle i n c r e a s e s , the d i f f u s e r a d i a n c e emanating from the r e g i o n about the h o r i z o n i s 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 the d i f f u s e i r r a d i a n c e . 92 Though, f o r the d i f f u s e r a d i a t i o n maps f o r cl o u d y c o n d i t i o n s , no d i r e c t comparison can be made w i t h p r e v i o u s r e s u l t s , a few p o i n t s are noteworthy n o n e t h e l e s s . F i g u r e 4.12, f o r an o v e r c a s t c o n d i t i o n , i l l u s t r a t e s t h a t t h e r e i s near i s o t r o p y i n r a d i a n t i n t e n s i t y - over the c e l e s t i a l dome f o r heavy c l o u d . The s i m p l i c i t y o f t h i s r a d i a n c e d i s t r i b u t i o n i s i n d i r e c t c o n t r a s t t o the r a d i a n c e d i s t r i b u t i o n o f a p a r t i a l l y c l o u d y sky ( F i g u r e 4.13). F i g u r e s 4.13 t o 4.15 i l l u s t r a t e , f o r a p a r t i a l l y c l oudy sky hemisphere, the r a p i d change i n c o n d i t i o n s o v e r a p e r i o d o f an hour. The s t r o n g e s t g r a d i e n t s i n thes e maps are found between c l e a r sky and r e l a t i v e l y t h i n c l o u d s , p a r t i c - ' u l a r l y ; near the s o l a r d i s c . F i g u r e 4.13 i l l u s t r a t e s the r a d i a n c e p a t t e r n f o r a sky c o n d i t i o n o f b r o k e n a l t o c u m u l u s ' i n the c e n t r a l p o r t i o n o f the sky hemisphere. To the west, the sky remains c l e a r , w h i l e sweeping around the h o r i z o n from the no r t h w e s t t o the ea s t , : i s a band o f a l t o s t r a t u s . G n e - h a l f hour l a t e r ( F i g u r e 4.14), a l a r g e band o f t h i n a l t o s t r a t u s i s c o v e r i n g the r e g i o n o f the s o l a r d i s c and e x t e n d i n g e a s t w a r d around the h o r i z o n . As i t approaches the e a s t , i t b e g i n s t o break up, becoming a l t o c u m u l u s . The c e n t r a l p o r t i o n o f the sky i s a m i x t u r e o f c l e a r s k y , t h i n a l t o c u m u l u s and c i r r u s c l o u d . On the n o r t h e r n h o r i z o n , a band o f a l t o s t r a t u s r emains. By 13:37, the c e n t r a l p o r t i o n o f the sky hemisphere i s c l e a r , w h i l e a l t o s t r a t u s c l o u d s r i n g the e a s t e r n h o r i z o n . The t y p i c a l c l e a r sky r a d i a n c e 93 F i g u r e 4.12 O v e r c a s t n o r m a l i z e d sky r a d i a n c e d i s t r i b u t i o n ( s r *) f o r 11:20 F e b r u a r y 14, 1978 as produced from the p h o t o g r a p h i c n e g a t i v e (Z = 63.2°) 94 F i g u r e 4.13 P a r t i a l l y o v e r c a s t s k y ; n o r m a l i z e d d i s t r i b u t i o n ( s r l) f o r 12:47 F e b r u a r y 15, 19 78 as produced from the p h o t o g r a p h i c n e g a t i v e . ( Z = 63 -1° ) 95 Figure 4.14 P a r t i a l l y overcast s k y n o r m a l i z e d d i s t r i b u t i o n ( s r 1) f o r 13:17 February 15, 1978 as produced from the photographic negative (Z-64.5 ) 9 96 F i g u r e 4.15 P a r t i a l l y o v e r c a s t -.sky; n o r m a l i z e d d i s t r i b u t i o n (sr~ 1)•1 3 : 4 7 F e b r u a r y 15, 1978 as produced from the p h o t o g r a p h i c n e g a t i v e (Z=66 .5° ) 97 p a t t e r n i s now b e g i n n i n g t o emerge. The r e g i o n o f the s o l a r d i s c i s a l s o c l e a r , but a l t o c u m u l u s c l o u d s are found between the sun and the z e n i t h . A l l t h r e e maps i n d i c a t e the s p a t i a l problems i n v o l v e d i n m o d e l l i n g d i f f u s e i r r a d i a n c e a c c u r a t e l y . Combined, they a l s o i n d i c a t e the t e m p o r a l problems which must be overcome by r e s e a r c h e r s a t t e m p t i n g t o e s t i m a t e d i f f u s e i r r a d i a n c e o v er t i m e . The d a t a p r e s e n t e d i n t h i s study are p o t e n t i a l l y u s e f u l i n a i d i n g i n the s o l u t i o n o f b o t h the s p a t i a l and t e m p o r a l problems found i n d i f f u s e r a d i a t i o n m o d e l l i n g . However, i t i s f e l t t h a t a g r e a t e r use o f t h i s t e c h n i q u e w i l l be found i n energy u t i l i z a t i o n models concerned w i t h the amount o f d i f f u s e r a d i a t i o n i n c i d e n t on n o n - h o r i z o n t a l s u r f a c e s . As an example o f such an a p p l i c a t i o n , Chapter F i v e a ttempts t o use the d i s t r i b u t i o n i n f o r m a t i o n t o e s t i m a t e i n c o m i n g energy on s e v e r a l s o u t h - f a c i n g s u r f a c e s . CHAPTER FIVE MODELLING DIFFUSE RADIATION ON SLOPING SURFACES 5.1 M o d e l l i n g Technique To determine the t o t a l shortwave 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 , t h r e e s e p a r a t e components must be c o n s i d e r e d ; the d i r e c t beam r a d i a t i o n , the d i f f u s e r a d i a t i o n emanating from the sky hemisphere and t h i r d l y , t he r a d i a t i o n r e f l e c t e d from a d j a c e n t s u r f a c e s . The c o n v e r s i o n o f the normal i n c i d e n c e d i r e c t beam r a d i a t i o n t o t h a t f o r an i n c l i n e d s u r f a c e was a c c o m p l i s h e d u s i n g the g e o m e t r i c r e l a t i o n s h i p between the p o s i t i o n o f the s o l a r d i s c and the normal to the s l o p e ( S e l l e r s , 1965): S+ = I.cos i (5.1) where S4- = d i r e c t shortwave r a d i a t i o n i n c i d e n t on a s l o p i n g s I -: s u r f a c e (Wm - 2) I = normal I n c i d e n c e d i r e c t beam r a d i a t i o n (Wm 2) cos i = cos s ••• cos z + s i n s • s i n z • cos (a-b) where s = angle o f s l o p e ( r a d i a n s ) z = z e n i t h a n g l e o f r a d i a t i o n source (radians.) a = azimuth o f r a d i a t i o n source ( r a d i a n s ) b = azimuth o f s l o p e ( r a d i a n s ) 99 The p h o t o g r a p h i c t e c h n i q u e used i n the p r e s e n t study p e r m i t t e d the d e t e r m i n a t i o n o f the normal i n c i d e n c e d i f f u s e r a d i a t i o n from a l a r g e number o f p o s i t i o n s over the c e l e s t i a l dome. T h i s e n a b l e d the summation o f e q u a t i o n 5.1 t o be used t o determine the t o t a l d i f f u s e r a d i a t i o n i n c i d e n t on the i n c l i n e d s u r f a c e s : n D+ s = £ ( D N • 6co) • cos i ± (5.2) i = l i where D4-g = d i f f u s e i r r a d i a n c e i n c i d e n t on i n c l i n e d ' surface(Wm - 2) D N - 6 0 ) = the normal i n c i d e n c e d i f f u s e a t a p o i n t r e p r e s -i e n t i n g the s o l i d a n g l e (Wm - 2 ( 6co • s r ) ~ 1) n = the number o f g r i d p o i n t s over the c e l e s t i a l dome With the i n c r e a s i n g s l o p e a n g l e , r a d i a t i o n from the a r e a between the t h e o r e t i c a l and l o c a l h o r i z o n s becomes more i m p o r t a n t . The p h o t o g r a p h i c t e c h n i q u e , as d e s c r i b e d , does not account f o r the r a d i a n c e emanating from t h i s a r e a . There-f o r e an a p p r o x i m a t i o n was n e c e s s a r y . F o r the' e x p e r i m e n t a l s i t e , the d i f f e r e n c e between the t h e o r e t i c a l and l o c a l h o r i z o n s i s caused g e n e r a l l y by r e g i o n s o f s t a n d i n g deciduous and c o n i f e r o u s woods. The albedo o f the a r e a was assumed t o be 0.14. T h i s i s the a r i t h m e t i c mean f o r r e p o r t e d albedoes o f oak (0.18) and f i r (0.10) ( K o n d r a t y e v , 1969). To account f o r the r a d i a t i o n emanating from t h i s a r e a , i t was f u r t h e r assumed t h a t the woods r e f l e c t e d the i n c o m i n g shortwave f l u x i s o t r o -100 p i c a l l y . T h i s I s a commonly a c c e p t e d assumption ( P a l t r i d g e and P i a t t , 1976). Thus, f o r any g r i d p o s i t i o n i n the r e g i o n below the a c t u a l h o r i z o n and above the t h e o r e t i c a l h o r i z o n , the d i f f u s e r a d i a n c e was c a l c u l a t e d by: n D = E {0.14 • (K + /2ir) • 6u> . cos i . } (5-3) 1 = 1 1 where = the r e f l e c t e d d i f f u s e i r r a d i a n c e (Wm~2) from • the r e g i o n between t h e o r e t i c a l and l o c a l h o r i z o n s 6o) = s o l i d a n g l e from which t h e d i f f u s e r a d i a t i o n i s emanating ( S r ) 2TT = number o f s t e r r a d i a n s i n a hemisphere i = the number o f p o s i t i o n s w i t h i n . .the„region The im p o r t a n c e o f the r e f l e c t e d r a d i a t i o n from t h i s a r e a was t h e r e f o r e s o l e l y dependent on i t s a n g l e o f i n c i d e n c e on the s l o p e . For a c l e a r sky c o n d i t i o n , ' / ' t h i s r e f l e c t e d r a d i a t i o n i n c r e a s e d the t o t a l d i f f u s e f l u x on a h o r i z o n t a l s u r f a c e , as measured u s i n g the p h o t o g r a p h i c t e c h n i q u e , by l e s s than 1.0 Wm 2 when D4- i s g e n e r a l l y around 60.0 Wm-2. The s p e c u l a r r e f l e c t i o n o f r a d i a t i o n from s u r f a c e s has not been e x t e n s i v e l y s t u d i e d . I t i s u s u a l l y assumed t h a t r e f l e c t e d r a d i a t i o n i s i s o t r o p i c ( P a l t r i d g e and P i a t t , 1976). The e q u a t i o n used t o determine the amount o f energy r e c e i v e d on a s l o p i n g s u r f a c e from an i s o t r o p i c a l l y r e f l e c t i n g a d j a c e n t , 101 i n f i n i t e and h o r i z o n t a l s u r f a c e i s ( K o n d r a t y e v , 1969): r s = r h o r ' s l n 2 ' a / 2 ( 5 - 4 ) where r = r e f l e c t e d r a d i a t i o n on ah i n c l i n e d s u r f a c e s of an g l e or r, = r e f l e c t e d r a d i a t i o n i n c i d e n t on a downward hor f a c i n g h o r i z o n t a l s u r f a c e Combining the above components, the t o t a l shortwave f l u x onto an i n c l i n e d s u r f a c e , when u t i l i z i n g the p h o t o g r a p h i c t e c h n i q u e , i s : K+ = S+ + + D + r (5.5) s p where K+ = shortwave i r r a d i a n c e on an i n c l i n e d s u r f a c e (Wm 2 ) s S4- = d i r e c t s o l a r r a d i a t i o n i n c i d e n t on the s l o p e (Wm 2 ) s D+ = the d i f f u s e r a d i a t i o n emanating from the sky las. s P measured u s i n g the p h o t o g r a p h i c t e c h n i q u e (Wm ) D = the d i f f u s e r a d i a t i o n r e f l e c t e d from the r e g i o n r. s between the t h e o r e t i c a l and the a c t u a l h o r i z o n (Wm r = r e f l e c t e d r a d i a t i o n from an a d j a c e n t h o r i z o n t a l s s u r f a c e (Wm - 2) Measurements o f K+ and I were r e c o r d e d as 5 minute s i n t e g r a t e d v a l u e s . Because o f t h i s , o n l y mean i r r a d i a n c e s 102 c o u l d be u t i l i z e d i n the d e t e r m i n a t i o n and t e s t i n g o f e q u a t i o n 5.5- I n d e t e r m i n i n g the q u a l i t y o f t h e s e d a t a f o r a h o r i z o n t a l s u r f a c e , i t was found t h a t l a r g e d i s c r e p e n c i e s e x i s t e d between when measured d i r e c t l y and when c a l c u l a t e d u s i n g : K+ = I • cos z + D+ (5-6) where D+ was an i n s t a n t a n e o u s measurement. Only i n the most s t a b l e r a d i a t i o n c o n d i t i o n s was the summation o f t h e 5 minute mean d i r e c t beam r a d i a t i o n and the i n s t a n t a n e o u s l y measured d i f f u s e r a d i a t i o n w i t h i n 5% o f the i r r a d i a n c e measured by the pyranometer. 5.2 R e s u l t s The c o m p u t a t i o n a l t e c h n i q u e d e s c r i b e d above was t e s t e d on 3 s o u t h - f a c i n g s u r f a c e s w i t h i n c l i n a t i o n s o f 30° , 60° , and 90° t o the h o r i z o n t a l . The r e s u l t s a re presented- i n Table 5.1. The t a b l e a l s o i n c l u d e s d i f f e r e n c e s between the mean i r r a d i a n c e over 5 minutes and. the i r r a d i a n c e c a l c u l a t e d u s i n g t h e photograph" exposed d u r i n g the i n t e g r a t i o n p e r i o d and the t o t a l shortwave i r r a d i a n c e s c a l c u l a t e d u s i n g an a n i s o -t r o p i c d i f f u s e r a d i a t i o n model (Hay, 1978). T h i s l a t t e r model has been found, t o more a c c u r a t e l y e s t i m a t e the shortwave d i f f u s e i r r a d i a n c e than the t h r e e more w i d e l y used models; the i s o t r o p i c model, the c i r c u m s o l a r model and the c o m b i n a t i o n model (Hay, 19 78) . TABLE 5 . 1 . — C o m p a r i s o n o f shortwave I r r a d i a n c e on a h o r i z o n t a l s u r f a c e and t h r e e s o u t h - f a c i n g s l o p e s Time o f Slo p e Measured* P h o t o g r a p h i c Technique A n i s o t r o p i c Model:. Photograph :. I r r a d i a n c e C a l c u l a t e d D i f f e r e n c e C a l c u l a t e d D i f f e r e n c e (LAT) ( d e g r e e s ) (Wm - 2) (Wm - 2) (%) (Wm - 2) (%) 1 2 : 4 0 O f 4 6 0 . 4 1 4 4 0 . 7 6 - 4 . 2 6 * * . 4 4 0 . 7 6 - 4 . 2 6 * * 30 8 4 9 . 6 8 802.54 - 5 . 5 4 799 . 2 4 - 5 . 9 4 60 1018.26 973.65 - 4 .38 963.79 - 5 . 3 5 9 0 9 4 4 .37 902.79 - 4 . 4 0 - 8 9 0 .28 - 5 .73 13 :40 0 383.29 381 .88 - 0 .37 381 .88 - 0 .37 30 7 3 4 . 9 0 710 .75 - 3 .29 710 . 2 4 ' - 3 . 3 5 60 8 6 6 . 4 2 8 7 1 . 5 6 0 . 5 9 865 .99 - 0 . 0 5 9 0 852.60 8 1 5 . 6 6 - 4 . 3 3 80 7.39 - 5 - 3 0 1 3 : 2 6 0 525 .12 507 .33 - 3 . 3 8 5 0 7 . 3 3 - 3 - 3 8 30 8 7 4 . 0 3 8 4 7 . 0 7 - 3 . 0 8 8 4 3 . 6 2 - 3 . 4 7 60 9 9 5 . 0 4 9 8 6 . 3 5 - 0 .87 9 7 4 . 6 5 - 2 .05 9 0 8 9 1 .61 888 .72 - 0 . 3 2 872.38 - 2 .16 13 :47 0 4 9 4 .78 4 7 5 . 7 4 - 3 .85 4 7 5 . 7 4 - 3 . 8 5 30 830.76 809 .90 - 2 . 5 1 802 .87 - 3 .36 60 9 5 9 .29 9 4 1 . 9 9 - 1 . 8 0 924 .56 - 3 .62 9 0 8 5 0 . 5 2 8 4 7 . 0 3 - 0 . 4 1 8 2 4 . 8 1 - 3 . 0 2 14 : 1 1 0 449 . 4 7 4 3 3 . 9 7 - 3 . 4 5 4 3 3 . 9 7 - 3 . 4 5 30 763.25 715.85 - 2 . 2 8 740.56 - 2 .97 60 870.94 8 6 8 . 6 8 - 0 . 2 4 845-98 - 2 .87 9 0 792 .69 800 .42 0.98 7 8 1 . 4 8 - 1 . 4 1 * a l l measured v a l u e s are 5 min mean f l u x e s f o r the p e r i o d o f the photograph * a l l n e g a t i v e v a l u e s i n d i c a t e an u n d e r e s t i m a t i o n t 0 ° i s d e f i n e d as a h o r i z o n t a l s u r f a c e 10 4 A l t h o u g h the c l e a r sky c o n d i t i o n i s the most s t a b l e s t a t e , the p h o t o g r a p h i c t e c h n i q u e c o n s i s t e n t l y o u t p e r f o r m e d the a n i s o t r o p i c model on a 5 minute average b a s i s . Of the 15 m o d e l l e d c a s e s , the p h o t o g r a p h i c t e c h n i q u e o n l y once had a r e l a t i v e e r r o r o f g r e a t e r than. 5%• For the a n i s o t r o p i c model, a r e l a t i v e e r r o r o f g r e a t e r t h a n 5% o c c u r r e d on f i v e o c c a s i o n s . The R.M.S.E. f o r the p h o t o g r a p h i c t e c h n i q u e was 28.03 Wm-2 w h i l e f o r the a n i s o t r o p i c model, i t was 38.37 Wm-2. T h i s r e p r e s e n t s an i n c r e a s e i n e r r o r o f 0.6% i n e s t i m a t i n g the t o t a l mean I r r a d i a n c e ( i . e . , i n c l u d i n g d i r e c t beam). Even g r e a t e r advantages o f the p h o t o g r a p h i c t e c h n i q u e are b e l i e v e d t o be found on s l o p e s t h a t g e n e r a l l y f a c e away from the s o l a r d i s c ( e . g . , n o r t h ) and f o r more complex p a r t i a l l y c l o udy c o n d i t i o n s . I n such c a s e s , o n l y the p h o t o g r a p h i c t e c h n i q u e can determine the amount o f energy a v a i l a b l e t o s u r f a c e s due t o the r e f l e c t i o n and s c a t t e r i n g o f s o l a r r a d i a t i o n by c l o u d s . F i g u r e 4.15 p r o v i d e s an example where the r a d i a n c e f o r an a r e a o f the n o r t h w e s t e r n sky i s e q u i -v a l e n t t o t h a t o f an a r e a i n the s o u t h w e s t e r n p o r t i o n o f the c e l e s t i a l dome near the s o l a r d i s c . Hay ( p e r s o n a l communication) found t h a t f o r a n o r t h - f a c i n g v e r t i c a l w a l l i n Vancouver, the a n i s o t r o p i c model does not p e r f o r m w e l l due t o problems o f r a d i a t i o n r e f l e c t e d from c l o u d s a s s o c i a t e d w i t h the l o c a l t opography. U n f o r t u n a t e l y , at p r e s e n t , no a p p r o p r i a t e d a t a are a v a i l a b l e f o r a thorough e v a l u a t i o n . A f u r t h e r advantage o f the p h o t o g r a p h i c t e c h n i q u e i s 105 I t s a b i l i t y t o determine the amount o f r a d i a t i o n r e f l e c t e d from areas above a h o r i z o n t a l s u r f a c e . T h i s can be accom-p l i s h e d , e i t h e r by d e t e r m i n i n g the d i f f e r e n c e i n i r r a d i a n ' c e measured by a h o r i z o n t a l s e n s o r w i t h t h a t by the p h o t o g r a p h i c t e c h n i q u e or by d e t e r m i n i n g a p p r o p r i a t e albedoes f o r the v a r i o u s s u r f a c e s above the h o r i z o n and m o d e l l i n g the r e f l e c t e d energy u s i n g e q u a t i o n 5.3. The l a t t e r method c o u l d l e a d t o the m o d e l l i n g o f d i f f u s e f l u x e s onto n o n - h o r i z o n t a l s u r f a c e s i n s i t u a t i o n s where p r o t r u s i o n s above the t h e o r e t i c a l h o r i z o n are i m p o r t a n t f a c t o r s i n d e t e r m i n i n g the t o t a l i r r a d i a n c e f o r t h a t s u r f a c e . T h i s r a i s e s the q u e s t i o n o f the a b i l i t y o f the p h o t o g r a p h i c t e c h n i q u e t o measure r e f l e c t e d i r r a d i a n c e i n the same manner as. sky d i f f u s e i r r a d i a n c e . I t was d e c i d e d t h a t i n v e s t i g a t i o n o f t h i s p o s s i b i l i t y was beyond the scope o f the p r e s e n t s t u d y . From the q u a l i t y o f the r e s u l t s p r e s e n t e d , i t i s apparent t h a t the p h o t o g r a p h i c t e c h n i q u e can not o n l y p r o v i d e a u s e f u l map of d i f f u s e r a d i a n c e over the sky hemisphere bu t can a l s o be u t i l i z e d t o p r o v i d e a c c u r a t e i n s t a n t a n e o u s e s t i m a t e s o f d i f f u s e i r r a d i a n c e on i n c l i n e d s u r f a c e s . At p r e s e n t , however, the u s e f u l n e s s of t h i s t e c h n i q u e t o a c c u r a t e l y p r o v i d e l o n g term averages i s h i n d e r e d by the l o g i s t i c a l problems of d a t a a c q u i s i t i o n and p r o c e s s i n g . CHAPTER SIX PRELIMINARY INVESTIGATION INTO GRID SIZE One o f the major problems i n v o l v e d i n the mapping o f a " s u r f a c e " i s the d e s i g n o f a s a m p l i n g p r o c e d u r e . I n the mapping o f d i f f u s e r a d i a n c e t h i s problem I s e s p e c i a l l y s i g n i f -i c a n t due t o the r a p i d l y v a r y i n g d i s t r i b u t i o n o f energy b o t h over time and space. Krumbein and G r a y b i l l (1965) I n d i c a t e t h a t a s y s t e m a t i c d e s i g n o r a g r i d i s advantageous i n a complex v a r i a b l e p a t t e r n w i t h no apparent r e g u l a r i t y . I f d i g i t i z i n g i s u t i l i z e d , as i n t h i s c a s e , the most o b v i o u s s a m p l i n g d e s i g n I s the square g r i d . Once the d e s i g n i s d e t e r m i n e d , the sample d e n s i t y ( i . e . , t h e sample s i z e ) must be c o n s i d e r e d . The prime s a m p l i n g c o n s i d e r a t i o n o f p r e v i o u s r e s e a r c h i n t h i s a r e a has been the time c o n s t a n t s o f the measurement i n s t r u m e n t s . The p r e s e n t work, however, i s not c o n s t r a i n e d i n t h i s manner and thus i t was p o s s i b l e t o determine an optimum g r i d d e n s i t y w i t h g r e a t e r obj e c t i v i t y . A second problem i n v o l v e d i n the p r e s e n t method o f a n a l y s i s was d e t e r m i n i n g the a c c u r a c y o f the d i s t r i b u t i o n . S t e v e n (1977) " c o n f i r m e d " the a c c u r a c y o f the 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 he produced by i n t e g r a t i n g t h e s e r a d i a n c e v a l u e s and comparing the r e s u l t i n g i r r a d i a n c e t o the ob s e r v e d d i f f u s e 106 10 7 • I r r a d i a n c e . T h i s method was f o l l o w e d i n S e c t i o n 4.3 t o v e r i f y the p r e s e n t d i s t r i b u t i o n s . The q u e s t i o n , however, s t i l l remained as to whether the above comparison t r u l y r e p r e s e n t e d the a c c u r a c y o f the r a d i a n c e p a t t e r n . A p r e l i m i n a r y i n v e s t i g a t i o n was u ndertaken t o determine the magnitude o f e r r o r s i n t r o d u c e d by i n t e r p o l a t i o n u s i n g v a r i o u s g r i d s p a c i n g s ( i . e . , sample s i z e s ) over the c e l e s t i a l dome. By i n t e g r a t i o n o f the r a d i a n c e , the q u a l i t y o f the p r e s e n t v a l i d a t i o n methodology c o u l d a l s o be det e r m i n e d . The a n a l y s i s was performed f o r b o t h a c l e a r sky and a p a r t i a l l y c l o u d y s i t u a t i o n . These were b e l i e v e d t o r e p r e s e n t the extrema i n s a m p l i n g ; the coherent and the h i g h l y v a r i a b l e c a s e , r e s p e c -t i v e l y . The sample d e n s i t i e s examined v a r i e d from 1800 p o i n t s . down t o 36 p o i n t s . Each o f thes e s e t s are s u b s e t s o f the' 3600 p o i n t d a t a s e t whose r e s u l t a n t i s i n even i n t e g e r s . T h i s a l l o w e d f o r the easy d e t e r m i n a t i o n o f the r e p r e s e n t a t i v e a r e a f o r each d a t a p o i n t . The s m a l l e s t sample a l s o a p p r o x i m a t e d the sample s i z e o f the p r e v i o u s work o f K o n d r a t y e v et a l . (1955) and S t e v e n (1977). As the g r i d r e p r e s e n t s a square o f 24 x 24mm and the exposed n e g a t i v e has a.diameter o f a p p r o x i m a t e l y 23mm, the a c t u a l number o f g r i d p o i n t s u t i l i z e d i n the i n t e g r a t i o n p r o c e d u r e was l e s s . T able 6.1 p r o v i d e s the a c t u a l number o f g r i d p o i n t s used t o determine the i r r a d i a n c e f o r each g r i d . Prom the complete dat s e t ( 3 6 O O p o i n t s ) , 20 g r i d p o i n t s c o i n c i d i n g w i t h c a l c u l a t e d r a d i a n c e s were o b t a i n e d . TABLE 6 . 1 . — S i z e o f square g r i d w i t h c o r r e s p o n d i n g number o f g r i d p o i n t s l o c a t e d w i t h i n the exposed a r e a o f the n e g a t i v e G r i d s i z e G r i d p o i n t s w i t h i n exposed a r e a 3600 2629 1800 1298 1200 865 900 649 600 432 . 400 288 225 162 100 72 36 26 109-The s e l e c t i o n was such t h a t t h e s e p o i n t s were not common to any o f the s u b s e t s on which the a n a l y s i s was t o be performed Thus, o n l y e s t i m a t e d v a l u e s f o r t h e s e l o c a t i o n s c o u l d be o b t a i n e d from the s u b s e t s . T h i s e s t i m a t e d r a d i a n c e was c a l -c u l a t e d by l i n e a r i n t e r p o l a t i o n from the c l o s e s t d a t a p o i n t s o f known r a d i a n c e i n the s u b s e t . An example o f t h i s p r o c e d u r e i s u s e f u l . Assume the r a d i a n c e a t a p o i n t (36, 24) i s 10 Wm 2 s i n the case o f a f u l l d a t a s e t (3600) p o i n t s . However, f o r a g r i d o f 900 d a t a p o i n t s the f o u r n e a r e s t n e i g h b o u r s ( u s i n g the same g r i d i d e n t i f i c a t i o n ) would be found a t (35, 23), (35, 25), (37, 23) and (37, 25). These may have r a d i a n c e s o f 8, 12, 25, and 27 W m - 2 s r ~ R e s p e c t i v e l y . Thus, the i n t e r -p o l a t e d v a l u e f o r the l o c a t i o n o f p o i n t (36, 24) would be 18 W m - 2 s r - 1 . The r o o t mean square e r r o r (R.M.S.E.) was then c a l c u l a t e d u s i n g the d i f f e r e n c e s between the 20 known and 20 i n t e r p o l a t e d r a d i a n c e s f o r each o f the 8 s a m p l i n g d e n s i t i e s : n )2/n}h R.M.S.E. = {( E R - R-1 = 1 C i (6.1) where R = known r a d i a n c e (Wm 2 s ; r x) R = i n t e r p o l a t e d r a d i a n c e (Wm 2 s : r 1) n = 20 F i g u r e 6.1 p r o v i d e s the r e s u l t s o f the a n a l y s i s f o r bo t h c l e a r and p a r t i a l l y c l o u d y c o n d i t i o n s . The t r e n d o f the R.M.S.E. i s o f i n t e r e s t . I n b o t h cases t h e r e appears t o _1_ 3 0,0) 6 0 0' 9-0 0 120 0 1 5 0 0 180 0 Sample S i z e F i g u r e 6.1 The v a r i a t i o n o f R.M.S.E. due t o i n t e r p o l a t i o n w i t h sample s i z e p a r t i a l l y c loudy sky case c l e a r sky case I l l be a " t h r e s h o l d " number o f da t a p o i n t s r e q u i r e d t o produce a s t a b l e e r r o r due t o i n t e r p o l a t i o n . F o r the c l e a r sky c a s e , a l l sample s i z e s l a r g e r t h a n 225 d a t a p o i n t s have a R.M.S.E. of under 2.0 Wm 2 s r 1 . T h i s i n c r e a s e s t o over 5 Wm~ 2sr" 1 f o r sample s i z e s l e s s t h a n 225 p o i n t s . F o r the p a r t i a l l y c l o u d y c o n d i t i o n , the " t h r e s h o l d " , a l t h o u g h not as d e f i n i t e as i n the c l e a r sky c a s e , i s 600 p o i n t s . The sample s i z e s l a r g e r t h a n t h i s have a mean R.M.S.E. o f a p p r o x i m a t e l y 6.0 Wm~2 s r " 1 , w h i l e f o r s m a l l e r sample s i z e s , t h e mean R.M.S.E. i s over 11 Wm~2 s r _ 1 . I n d i v i d u a l l y , the v a r i a t i o n i n R.M.S.E. p r o v i d e s u s e f u l i n s i g h t s i n d e t e r m i n i n g optimum sample s i z e s . The more coherent p a t t e r n f o r c l e a r s k i e s means t h a t the number of g r i d p o i n t s n e c e s s a r y t o p r o v i d e a s t a b l e R.M.S.E. i s s i g n i f i c a n t l y l e s s than f o r the c l o u d y case. The d i f f e r e n c e i s 225 p o i n t s t o a minimum o f 600 p o i n t s . However, i f r o u t i n e ( i . e . , a l l - s k y c o n d i t i o n s ) measurements and automated d i g i t i z i n g a r e t o be used, the g r i d s i z e s h o u l d be d e s i g n e d f o r the most complex ca s e , u n l e s s an optimum g r i d s i z e f o r each type o f case i s a v a i l a b l e . Even i f the g r i d s i z e i s o p t i m i z e d f o r the most complex c a s e , the s i z e o f the e r r o r a s s o c i a t e d w i t h the p a r t i a l l y c l o u d y c o n d i t i o n may be up t o 5 times as g r e a t as t h a t f o r a more r e g u l a r 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) used 30 o b s e r v a t i o n s t o determine the 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 f o r a l l types of sky c o n d i t i o n s . S t e v e n (1977) made 34 measurements over 112 the sky hemisphere t o produce 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 . B oth sample s i z e s a re an o r d e r o f magnitude l e s s thaft t h e . d e f i n e d c l e a r sky t h r e s h o l d v a l u e s . T h i s b r i n g s i n t o q u e s t i o n the r e l a t i o n s h i p between the e r r o r a s s o c i a t e d w i t h a r a d i a n c e v a l u e a t a g i v e n p o i n t , and the summation o f the p o i n t s t o p r o v i d e the f l u x r e c e i v e d on a h o r i z o n t a l s u r f a c e . Can .the R.M.S.E. be p a r a m e t e r i z e d by the e r r o r found i n the i n t e g r a t e d f l u x ? The assumption was made t h a t each g r i d p o i n t r e p r e s e n t e d the i s o t r o p i c d i f f u s e f l u x f o r an a r e a o f the c e l e s t i a l dome i n v e r s e l y p r o p o r t i o n a l t o the sample s i z e . The L a m b e r t i a n response was det e r m i n e d f o r the p o s i t i o n o f the g r i d p o i n t . I f one assumes t h a t a g r i d o f 3600 p o i n t s p r o v i d e s the c o r r e c t a n g u l a r d i s t r i b u t i o n and i n t e g r a t e d i r r a d i a n c e , a comparison can be made between the R.M.S.E. and the r e l a t i v e e r r o r o f the i n t e g r a t e d v a l u e s f o r each s u b s e t o f g r i d p o i n t s . T a b l e 6.2 p r o v i d e s b o t h the R.M.S.E.'s and t h e r e l a t i v e e r r o r o f the i n t e g r a t e d f l u x e s f o r each sample s i z e . I n comparing the two measures o f the a c c u r a c y o f the 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 , l i t t l e c o n f i d e n c e can be p l a c e d i n the r e l a t i v e e r r o r o f the i n t e g r a t e d f l u x as a p a r a m e t e r i z a t i o n o f the e r r o r due t o i n t e r p o l a t i o n . I n the c l e a r sky c a s e , t h e r e I s a g e n e r a l i n c r e a s e i n the r e l a t i v e e r r o r w i t h the i n c r e a s e o f the R.M.S.E. f o r l a r g e ..changes o f g r i d s p a c i n g . However, t h e r e i s no s i m p l e correspondence between the d i r e c t i o n s and the changes i n magnitude o f the two e r r o r s . From the d a t a 113 TABLE 6 . 2 . — R e l a t i v e e r r o r {%) o f I n t e g r a t e d f l u x e s f o r a v a r i a t i o n i n sample s l z e : a n d R.M.S.E. f o r i n t e r p o l a t e d v a l u e s Sample s i z e C l e a r sky P a r t l y c l o u d y sky ( p o i n t s ) R.M.S.E. R e l a t i v e R.M.S.E. R e l a t i v e e r r o r e r r o r 1800 1.485 0.33 6.842 0.14 1200 1.423 0 .42 5.372 0 .68 900 1.944 1.02 7.059 1.42 600 1. 731 1.13 5.649 2.24 400 1.894 1.84 9.278 1.68 225 2.10 7 1.37 10.000 5.44 ; 100 6.758 4.47 13.591 0 .12 36 . 6.173 5.41 12.653 6.31 114 p r e s e n t e d , I t appears t h a t f o r an i n t e g r a t i o n e r r o r o f <1%, the R.M.S.E. c o u l d be e s t i m a t e d t o be a p p r o x i m a t e l y 2 W m - 2 s r - 1 . Steven (1977) r e p o r t s an e r r o r o f 6% f o r h i s i n t e g r a t e d i r r a d i a n c e f o r c l e a r s k i e s . From the r e s u l t s p r e s e n t e d , the R'. M.S:.E .: f o r ..his d i s t r i b u t i o n would.be over 6 Wm"2sr_1 when the n o r m a l i z e d v a l u e s were a p p r o p r i a t e l y r e d u c e d . The p a r t i a l l y c l o u d y s i t u a t i o n has no r e l a t i o n s h i p between the measurements o f e r r o r . The g r i d s i z e o f 100 p o i n t s produced the l a r g e s t R.M.S.E. and y e t i t b e s t e s t i m a t e d the i r r a d i a n c e f o r the h o r i z o n t a l s u r f a c e . T h i s i n d i c a t e s t h a t t o use the method d e s c r i b e d by Stev e n (1977) t o determine the ac c u r a c y o f the a n g u l a r d i s t r i b u t i o n i n more complex cases than the c l e a r sky c o n d i t i o n i s not a p p r o p r i a t e . T h i s a n a l y s i s s e r i o u s l y q u e s t i o n s the use o f the i n t e -g r a t e d f l u x t e c h n i q u e f o r s t a t i n g t h a t the d e r i v e d 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 i s a c c u r a t e . The use o f t h i s method s h o u l d be a v o i d e d i n cases o f complex sky c o n d i t i o n s . F u r t h e r r e s e a r c h t o p r o v i d e a more p r e c i s e e r r o r e s t i m a t e a n a l y s i s f o r such a v a r i a b l e system i s o b v i o u s l y needed. Because o f the i n f i n i t e v a r i e t y o f c l o u d c o m b i n a t i o n s , the approach:-.may have t o be e m p i r i c a l w i t h the t e s t i n g o f i n t e r p o l a t e d v a l u e s u s i n g a wide v a r i e t y o f sky c o n d i t i o n s and g r i d s i z e s . CHAPTER SEVEN CONCLUSIONS AND RECOMMENDATIONS The study d e s c r i b e d , • p r e s e n t s •= a t e c h n i q u e t o determine the 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 i n the sky hemisphere. The advantages o f t h i s method over t h a t o f p r e v i o u s methods ( K o n d r a t y e v , 1955; S t e v e n , 1977) a r e : (1) the p r e s e n t t e c h n i q u e p r o v i d e s an i n s t a n t a n e o u s mapping of the c e l e s t i a l dome. Even the most complex d i f f u s e r a d i a n c e cond-i t i o n s can now be mapped.. (2) The sample s i z e employed i s two o r d e r s o f magnitude l a r g e r t h a n t h a t used i n p r e v i o u s s t u d i e s . T h e r e f o r e , the maps produced u s i n g t h i s method p r o v i d e g r e a t e r d e t a i l and are s i g n i f i c a n t l y more p r e c i s e than those p r e v i o u s l y p u b l i s h e d . (3) The d i f f u s e r a d i a n c e d a t a base i s i n d i g i t a l form and i s e v e n l y and d e n s e l y d i s t r i b u t e d o v er the sky hemisphere a l l o w i n g i t t o be used t o determine the d i f f u s e i r r a d i a n c e on i n c l i n e d s u r f a c e s w i t h l i t t l e m o d i f i c a t i o n . The t e c h n i q u e , however, has not y e t been p e r f e c t e d , nor are the r e s u l t s comprehensive enough f o r g e n e r a l i z a t i o n s t o be made. The recommendations o f t h i s s tudy can t h e r e f o r e be c l a s s i f i e d i n t o two main c a t e g o r i e s : (1) those recommen-d a t i o n s c o n c e r n i n g the t e c h n i c a l a s p e c t s of. the measurement and d a t a r e d u c t i o n p r o c e d u r e and (2) those f o r f u t u r e s t u d i e s 115 116 u s i n g t h i s t e c h n i q u e . The g r e a t e s t problem a t p r e s e n t i s i n the c o l l e c t i o n o f the d i f f u s e r a d i a n c e d a t a r e q u i r e d f o r the c a l i b r a t i o n o f the photographs. 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 has f o u r major l i m i t a t i o n s : (1) the response time o f the i n s t r u m e n t i s too slow t o a d e q u a t e l y sample I n a s h o r t time p e r i o d a l l the r e g i o n s o f the c e l e s t i a l dome n e c e s s a r y to p r o v i d e -comprehensive c a l i b r a t i o n data.. The I d e a l i n s t r u m e n t would have a response time o f a. second o r l e s s . (2) The manual adjustment o f the a c t i n o m e t e r i n c r e a s e s the r e q u i r e d time t o t a k e an adequate number o f o b s e r v a t i o n s . I t i s recommended t h a t an e n t i r e c a l i b r a t i o n sequence t a k e l e s s than 2 m i n u t e s . A l t h o u g h t h i s i s l e s s i m p o r t a n t f o r c l e a r sky o b s e r v a t i o n s ! f o r the more complex c o n d i t i o n s , i t i s e s s e n t i a l . (3) 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 i s too s e n s i t i v e t o windy c o n d i t i o n s . I f r o u t i n e measurements are t o be made, an i n s t r u m e n t w i t h g r e a t e r p r e s s u r e s t a b i l i t y i s n e c e s s a r y . (4) The ou t p u t s i g n a l o f t h e i n s t r u m e n t used was i n a d e q u a t e . The minimum output s h o u l d p r o v i d e a s i g n a l t h a t i s e a s i l y m o n i t o r e d . I f such an i n s t r u m e n t cannot be found, i t i s recommended t h a t the s i g n a l be a m p l i f i e d b e f o r e e n t e r i n g an a n a l o g r e c o r d e r . I t would be advantageous i n the d a t a r e d u c t i o n s t a g e of the experiment t o be a b l e t x r d i g i t i z e photographs more q u i c k l y u s i n g a s m a l l e r g r i d s p a c i n g . A l a r g e r sample s i z e c o u l d o n l y improve the a c c u r a c y o f mapping r a d i a n c e over the sky hemisphere f o r c l o u d y c o n d i t i o n s by r e d u c i n g the i n t e r -117 p o l a t i o n e r r o r between, g r i d p o i n t s . T h i s c o n c l u s i o n f o l l o w s from the r e s u l t s o f Chapter S i x . F o r the p r e s e n t s t u d y , the camera equipment was found adequate. However, i f a l a r g e r format p h o t o g r a p h i c system was u s e d , . - s p e c i a l l y d e s i g n e d s c i e n t i f i c f i l m s and p l a t e s would become a v a i l a b l e . T h i s c o u l d improve the a c c u r a c y o f the c a l i b r a t i o n c u r v e s . B e f o r e 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 r a d i a n c e f o r complex sky c o n d i t i o n s can be p a r a m e t e r i z e d , a c o l l e c t i o n o f r a d i a n c e maps f o r a l l such c o n d i t i o n s w i l l be n e c e s s a r y . With t h e s e , g e n e r a l c h a r a c t e r i s t i c s o f the d i f f u s e d i s t r i b u t i o n may be discovered... I t i s t h e r e f o r e recommended t h a t a d a t a base be c o l l e c t e d and a r c h i v e d . T h i s would a l s o be advan-tageous to r e s e a r c h e r s i n the t e s t i n g o f b o t h e m p i r i c a l and t h e o r e t i c a l l y based models e v a l u a t i n g the 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 . The use o f t h e p h o t o g r a p h i c t e c h n i q u e combined w i t h the d i r e c t beam r a d i a t i o n p r o v i d e s a methodology t o a c c u r a t e l y d e t e r m i n e , by r e s i d u a l , r a d i a t i o n r e f l e c t e d from a d j a c e n t s u r f a c e s . From t h i s i n f o r m a t i o n , the p r e s e n t l y used i s o t r o p i c a ssumption can be t e s t e d and, i f n e c e s s a r y , more a c c u r a t e models dev e l o p e d . As a l l u d e d t o i n Chapter F i v e , a t e c h n i q u e i s now a v a i l a b l e f o r d e t e r m i n i n g the d i f f u s e r a d i a t i o n i n c i d e n t upon s u r f a c e s i n s i t u a t i o n s where the h o r i z o n becomes a s i g n i f i c a n t f a c t o r . F u r t h e r s t u d y i s r e q u i r e d f o r b o t h t h e s e a s p e c t s o f " p h o t o g r a p h i c r a d i a t i o n s e n s i n g " . 118 A t e c h n i q u e i s now a v a i l a b l e t o q u a n t i t a t i v e l y determine the 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 i n the sky hemisphere. When p e r f e c t e d and used w i t h i m a g i n a t i o n , i t i s b e l i e v e d t h a t the d a t a base p r o v i d e d w i l l a i d i n the s o l u -t i o n o f a v a r i e t y o f shortwave r a d i a t i o n problems. BIBLIOGRAPHY Atroshenko, V.S., K.S. Glazova, S.Y. Kogan, T.D. Koronatov, M.A. Kuznetzov, M.S. Malkevich and E.M. Feugelson, 1962: Computation of the atmospheric l i g h t b rightness i n u n i s o t r o p i c s c a t t e r i n g . Proc. I n s t . Atmospheric  Phys., No.3, Acad. S c i . 3 Moscow, U.S.S.R. Cook, N.H. and E:.. Rabinowicz, 1963: P h y s i c a l Measurement  and A n a l y s i s . Addison-Wesley, London, 312pp. Coulson, 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 Measurements. Academic Press, New York, 322pp. Coulthard, W.J., 1975: Contouring a G r i d . U n i v e r s i t y of B r i t i s h Columbia Computing Centre, 10pp.7 Dave, J.V., 19 75: A d i r e c t s o l u t i o n of the s p h e r i c a l harmonics approximation to the r a d i a t i v e t r a n s f e r equation f o r an a r b i t r a r y s o l a r e l e v a t i o n . Part I I : R e s u l t s . J . Atmos. S c i . , 32, 1463-1474. Dorno, C., 1919: V e r f o f f e n t l . Preuss. Meteorol. I n s t . Abandhl. , 8, 303-Drummond, A.J., 1956: On the measurement of sky r a d i a t i o n . Arch. Met. Geophys. B i o k l . B ,7 , 413-436. Drummond, A.J., 1970: P r e c i s i o n radiometry and i t s s i g n i -f i cance i n atmospheric and space physics . Advances  i n Geophysics, V o l . 14, Academic Press, New York, 1-52. D u f f l e , J.A. and W.A. Beckman, 1974: S o l a r Energy Thermal  Processes. John Wiley and Sons, Toronto, 386pp. Flowers, E., 1977: Test and e v a l u a t i o n of the performance of s o l a r r a d i a t i o n sensors at i n c l i n a t i o n from the h o r i z o n t a l under laboratory and f i e l d c o n d i t i o n s . Report ERDA-NOAA IAA (49-26) - l 4 p l , TOO3, Environmental Research Laboratory NOAA, Boulder, Colorado, 1-19. Fraser, I . , 19 78: E v a l u a t i n g images q u a n t i t a t i v e l y . Canadian Research, January/February, 27-2 8, 39. Hay, J.E., 19 77: Shortwave 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 . F i n a l Report September, 1976 - August, 1977, Contract DSS 05576-02095-119 120 Hay, J.E., 19 77: Measurement and m o d e l l i n g of shortwave 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 . P r e p r i n t s T h i r d  Conference on Atm o s p h e r i c R a d i a t i o n , Am. Met. S o c , 150-153. Heimo, A. and P. Valko, 19 76: F i r s t r e s u l t s o b t a i n e d from the Swiss M o b i l e System f o r s o l a r r a d i a t i o n measurements. Working Reports o f the Swiss Meteor-o l o g i c a l I n s t i t u t e , No. 63, 1-8. IGY I n s t r u c t i o n Manual, 1958: R a d i a t i o n I n s t r u m e n t s and Measurements, P a r t V I , Pergamon P r e s s , London, 39 4-401. Joyce I n s t r u m e n t a t i o n , 1954: Double Beam A u t o m a t i c R e c o r d i n g M i c r o d e n s i t o m e t e r Mark I I I . B u l l e t i n 54/8B, 8pp. Joyce L o e b l : I n s t r u c t i o n Manual f o r Automatic R e c o r d i n g  M i c r o d e n s i t o m e t e r Model Mk I I I C , Joyce L o e b l and Co., L t d . , E n g l a n d . K o n d r a t y e v , K.Ya., 1969: R a d i a t i o n i n the Atmosphere, Academic P r e s s , New Yor k , 912pp. 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. Manolova, 1955: D i s t r i b u t i o n o f the 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 over the 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. K o n d r a t y e v , K.Ya. and M.P. Manolova, I960: The r a d i a t i o n b a l a n c e o f s l o p e s . S o l a r Energy, 4, 14-19. Krumbein, W.C. and F.A. G r a y b i l l , 1965: An I n t r o d u c t i o n t o  S t a t i s t i c a l Models i n Geology, M c G r a w - H i l l Book Co., Toronto, 475PP• L a t i m e r , J.R., .1970: I n v e s t i g a t i o n o f S o l a r R a d i a t i o n I n s t r u m e n t s a t the N a t i o n a l R a d i a t i o n Centre o f the  Canadian M e t e o r o l o g i c a l S e r v i c e , Paper No. 3/1, 19 70 I n t e r n a t i o n a l S o l a r Energy C o n f e r e n c e , Melbourne, 6 pp. L a t i m e r , J.R., 1972: R a d i a t i o n measurement. IFYGL T e c h n i c a l  Manual S e r i e s , No. 2, 53pp. Long, K., 1961: Uber das S t r e u s p e k t r u m der Atmosphare. O p t l k und S p e k t r o s k o p l e a l l e r W e l l e n l a n g e n , Akademie V e r l a g , B e r l i n . McArthur L.B. and J.E. Hay, 1978:. On the 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 from the sky hemisphere. B u l l . Am.  Met. Soc., ( i n p r e s s ) . 121 M i l l e r , A. and J.C. Thompson, 19 70: Elements of Meteorology, C.E. M e r r i l l Pub. Co., Columbus, Ohio, 402 pp. Mo r r i s , C.W. and J.H. Lawrence, 1971: The anisotropy of c l e a r sky d i f f u s e s o l a r r a d i a t i o n . Ashrae Transactions 19 71, Part I I , 136-141. Morse, R.N. and J.T. Czarnecki, 1958: F l a t P l a t e S o l a r  Absorbers: The E f f e c t on Incident R a d i a t i o n of  I n c l i n a t i o n and Slope, CSIRO Engineering S e c t i o n , Report E.D.6., 2opp. N o r r i s , D.J.,:1966: S o l a r 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 . S o l a r Energy, 10, 72-76. P a l t r i d g e , G..W. and C.M.R. P i a t t , 1976: Radiative.Processes i n Meteorology and Climatology. Developments i n Atmospheric Science, No. 5, E l s e v i e r S c i e n t i f i c Pub. Co., New York, 3l8pp. Reifsnyder, W., 1967: R a d i a t i o n geometry i n the measurement and i n t e r p r e t a t i o n of the r a d i a t i o n balance. A g r i c . Meteor., 4, 255-256. Robinson, N., 1966: S o l a r R a d i a t i o n , E l s e v i e r Pub. Co., New York, 347 pp. S e l l e r s , W.D., 1965: P h y s i c a l Climatology, Univ. of Chicago Press, Chicago, 272pp. Sivkov, S.I., 1968: Computation of S o l a r R a d i a t i o n C h a r a c t e r i s t i c s , I s r a e l Program f o r S c i e n t i f i c T r a n s l a t i o n s , 19 71. l85pp. S o k a l , R.R. and F.J. Rohlf, 19 73: I n t r o d u c t i o n to B i o s t a t - 1 : . . i s t i c s , W.H. Freeman and Co., San F r a n c i s c o , 368pp. Steven, M.D., 1977: Standard d i s t r i b u t i o n of c l e a r sky radiance. Quart. J . R. Meteor. S o c , 103, 457-465. Suzuki, T., 19 75: An I n t r o d u c t i o n to the Canon F - l , Canon Inc., Tokyo, 15 3pp. Unsworth, M.H. and J.L. Montelth, 1975: Longwave r a d i a t i o n at the ground. Quart J . R. Meteor. S o c , 101, 13-24. Wallace, J.M. and P.V. Hobbs, 1977: Atmospheric Science: An Introductory Survey, Academic Press, New York, 467pp. Zworykin, W.K. and E.D. Wilson, 19 34: P h o t o c e l l s and Their A p p l i c a t i o n , John Wiley and Son, Inc., New York, 348pp. APPENDIX ONE NOTATION UPPER CASE ROMAN d e n s i t y c o r r e c t e d d i f f u s e r a d i a t i o n measured d i f f u s e r a d i a t i o n normal i n c i d e n t d i f f u s e from <5co p r e d i c t e d d i f f u s e i r r a d i a n c e on a h o r i z o n t a l s u r f a c e d i f f u s e i r r a d i a n c e 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 r e f l e c t e d d i f f u s e i r r a d i a n c e r a d i a n t i n t e n s i t y normal i n c i d e n c e d i r e c t beam r a d i a t i o n i n c o m i n g shortwave i r r a d i a n c e r e f l e c t e d shortwave i r r a d i a n c e shortwave i r r a d i a n c e i n c i d e n t on a 30° s l o p e shortwave i r r a d i a n c e i n c i d e n t on a 60° s l o p e shortwave i r r a d i a n c e i n c i d e n t on a 90° s l o p e shortwave i r r a d i a n c e 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 r a d i a n c e d i m e n s i o n l e s s Wm-2 Wm-2 Wm-2 (6w • s r ) - 1 Wm-2 Wm-2 Wm-2 Wm-2 Wm-2 Wm-2 Wm-2 Wm-2 Wm"2 Wm-2 Wm~ 2 Wm-2 s r _ 1 122 123 known r a d i a n c e i n t e r p o l a t e d r a d i a n c e d i r e c t shortwave r a d i a t i o n i n c i d e n t on a s l o p i n g s u r f a c e view f a c t o r s o l a r z e n i t h angle Wm s r - 2 - 1 Wm s r - 2 Wm d i m e n s i o n l e s s d e g r e e s , r a d i a n s LOWER CASE ROMAN azimuth o f r a d i a t i o n source azimuth o f s l o p e exposure number o f p o i n t s i n an exposed •area ( c e l e s t i a l dome) d i s t a n c e from the z e n i t h t o z = T r/2 r a d i a n s d i s t a n c e from the z e n i t h t o the h o r i z o n on an e q u i d i s t a n t p r o j e c t i o n r e f l e c t e d r a d i a t i o n i n c i d e n t on a downward f a c i n g h o r i z o n t a l s u r f a c e r e f l e c t e d r a d i a t i o n on an i n c l i n e d . s u r f a c e angle a angle o f s l o p e : hour ang l e o f sun at sunset z e n i t h angle r a d i a n s r a d i a n s d i m e n s i o n l e s s d i m e n s i o n l e s s mm mm _ 2 Wm Wm-2 r a d i a n s •radians r a d i a n s UPPER CASE GREEK z e n i t h a n g l e f o r the i r a d i a n c e v a l u e r a d i a n s 12 LOWER CASE GREEK angle of I n c l i n e d surface mean z e n i t h angle of the hor i z o n over a given arc length length of the arc of 3 at z = ir / 2 l a t i t u d e the 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 the i component of the measurement system probable e r r o r a s s o c i a t e d with the measured qua n t i t y probable e r r o r a s s o c i a t e d with the measured quantity f o r a subsystem. atmospheric conditions radius of shadow band s o l a r d e c l i n a t i o n s o l i d angle represented by each density 1 t h property of the photographic system radians radians mm radians dimensionless mm radians s r dimensionless APPENDIX TWO CALIBRATION CURVES 125 1 4 0 120 I 10 0 u m I 80 CD O c CO 6 0 •H T3 Cti CC 4 0 2 0 20 0 30 0 4 0 0 5 0 0 6 0 0 70 0 D e n s i t y F i g u r e A2.2 C a l i b r a t i o n curve f o r 13:40 LAT February 10, 19 78 L = Exp {-0.2708 + 3.0598 In (-0.7935 + 7.943 * 10 3 D)} C o r r e l a t i o n C o e f f i c i e n t = 0.9470 ro 2 0 0 30 0 4 0 0 50 0 6 0 0 70 0 D e n s i t y F i g u r e A2 . 3 C a l i b r a t i o n curve f o r 11:2 0 LAT February 14, 19 78 Hand drawn curve P o l y n o m i a l f i t : L = -134.602 + 1.642 D - 6.01 x 10 2 + 7-55 * 10 F i g u r e A2.4 C a l i b r a t i o n c urve f o r 12:30 LAT_Pebruary 14, 19 78 L = 39.051 - 0.326 D + 9.2 x 10 * D 2 C o r r e l a t i o n C o e f f i c i e n t 0.739 280 240 >.0 0 CO 1 6 0 CD O C aj 120 •H •T3 PC 80 40 20 0 30 0 4 0 0 5 0 0 6 0 0 70 0 D e n s i t y •Figure A2.5 C a l i b r a t i o n curve f o r 12:47 LAT February 15, 19 7 8 Hand drawn curve P o l y n o m i a l f i t : L = 149-937 - 0.945 D + 1 . 86 x 10"3D2 uo o •00 300 >t00 500 600 70 0 D e n s i t y F i g u r e A2 .6 C a l i b r a t i o n curve f o r 13:17_LAT February 15, 19 78 L = Exp {1.059 + 7-724 x 10 3 D} C o r r e l a t i o n c o e f f i c i e n t 0.728 Radiance (Wm 2 s r 1) H" (R C H CD > ro o r 1 o o II M CD x 4 P3 C+ c t H* ^ H-O H O • 3 U l o VO O o ro p CD Mi + < '-*> CD H- U l O • >-*> H- LO O CD - J ^ »-< »—• c o c + O X LO CD O .. 3 h-> ro co -<! o ro H-LO ! <rt «< O > CD c r !~$ H U l cx> o o 2£l Radiance (Wm 2 s r ~ 1 ) c CD > co o tr1 o o CD h-1 p X3 c t O 3 CD II i — 1 H-M cr p c t H> O 3 o O H O O Ul c CD H-O H-CD 4 CD • OA O — J 4 3 O ct I-1 X uo o • H U J co o U D I I— 1 w t - 1 > CD O" 4 a CD a cn H-ct P Ul i— 1 C O 1 4 0 20 0 30 0 40 0 5 0 0 6 0 0 D e n s i t y F i g u r e A 2 . 1 1 C a l i b r a t i o n curve f o r 13:47 LAT February 26 , 1978 L = Exp { -0 .6874 +9 -352 x i o 3D} C o r r e l a t i o n c o e f f i c i e n t 0 .946 14 0 120 h D e n s i t y F i g u r e A2.12 C a l i b r a t i o n curve f o r 14:11 LAT February 26, 19 78 L = Exp {-0.2833 + 8.649 x 10 3D} C o r r e l a t i o n c o e f f i c i e n t 0.94 r— 1 U O —q 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0094255/manifest

Comment

Related Items