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

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THE S P A T I A L DISTRIBUTION OF DIFFUSE SOLAR RADIATION IN THE SKY HEMISPHERE by LORNE JOHN BRUCE McARTHUR B.Sc, M c M a s t e r U n i v e r s i t y , 1976  A THESIS SUBMITTED I N PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE  in THE FACULTY OF GRADUATE STUDIES Department o f Geography  We a c c e p t t h i s t h e s i s as c o n f o r m i n g to the required standard  THE UNIVERSITY OF B R I T I S H COLUMBIA A u g u s t 19 78  (c) L o m e J o h n B r u c e M c A r t h u r , 19 78  In p r e s e n t i n g  this  thesis  an advanced degree at the L i b r a r y s h a l l I  f u r t h e r agree  for  scholarly  by h i s of  this  written  make i t  freely available  that permission  for  the requirements  Columbia,  I agree  r e f e r e n c e and  f o r e x t e n s i v e copying o f  this  It  is understood that  for financial  gain shall  Geography  The U n i v e r s i t y of B r i t i s h  2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5  A u g u s t 8,  19 78  Columbia  copying or  for  that  study. thesis  purposes may be granted by the Head of my Department  permission.  Department of  fulfilment of  the U n i v e r s i t y of B r i t i s h  representatives. thesis  in p a r t i a l  or  publication  not be allowed without my  Corrigendum  In "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 Solar Radiation i n the Sky Hemisphere" by Lorne John Bruce McArthur, submitted as an M.Sc. Thesis to the U n i v e r s i t y 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 f o l l o w i n g f i g u r e references be changed. 2.6a.  should  Figure 2.7 on l i n e s 8 and 14 should be read as Figure  Figures 4.9 and 4.10, referenced on l i n e 13 should read Figures  4.10 and 4.11 r e s p e c t i v e l y . Figure 4.8 on l i n e 15 should read Figure 4.9* text.  These changes should f a c i l i t a t e a b e t t e r understanding of the  ABSTRACT A t e c h n i q u e was d i s t r i b u t i o n of  diffuse  sphere f o r a v a r i e t y by  d e v e l o p e d t o p r o d u c e maps o f s o l a r r a d i a t i o n o v e r the  o f sky  conditions.  u t i l i z i n g both actinometric  overcomes the  and  This  sky  hemi-  procedure,  photographic  sampling problems of p r e v i o u s  the  information,  methods.  P h o t o g r a p h s were s i m u l t a n e o u s l y e x p o s e d w i t h m e t r i c measurements o f  diffuse solar radiance.  w e r e t h e n d i g i t i z e d and the  actinometric  radiances.  photograph.  equation produced  radiance  the  the  conditions  examined.  to determine the  surfaces. measured  The  on  several  ii  entire solar  integrated on  within  a ±  and horizontal  10%  for  the  t e s t , u s i n g t h i s method performed to  south-facing  r e s u l t s w e r e f o u n d t o be  values.  to  of d i f f u s e  incident  d i f f u s e i r r a d i a n c e , was  shortwave i r r a d i a n c e  known  radiance d i s t r i b u t i o n s ,  f o u n d t o be  A further  the  to  produced.  q u a l i t y of the  diffuse irradiance  with  v a l u e f o r the  a map  h e m i s p h e r e was  These were u s u a l l y  photographs  then u t i l i z e d  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  surface.  the  was  f o r each d e n s i t y  determine the  compared w i t h  sky  sky  The  values corresponding  From t h i s i n f o r m a t i o n ,  r a d i a t i o n over the To  density  measurements c o r r e l a t e d  The  determine the  the  actino-  within  estimate  inclined ±  5%  of  the  The d i f f u s e  radiation  distributions  for clear  skies  were a l s o compared w i t h s i m i l a r w o r k a n d commented u p o n . This  technique,  although  still  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 e n e r g y . a n d c o u l d a l s o be u t i l i z e d data base necessary scattering  not p e r f e c t e d , modelling  diffuse  i n the c o l l e c t i o n o f the  f o r t e s t i n g t h e o r e t i c a l models o f  i n the atmosphere.  iii  provides  TABLE OF CONTENTS Page ABSTRACT  ,  TABLE OF CONTENTS  i  L I S T OF TABLES  v  L I S T OF FIGURES  v  ±± v  L I S T OF ILLUSTRATIONS  iil xi  ACKNOWLEDGEMENTS CHAPTER ONE  1 ±  x i i  -  INTRODUCTION  1  1.1  Objectives  1  1.2  Background  . 2  CHAPTER TWO  -  CHAPTER THREE  EXPERIMENTAL RATIONALE -  EXPERIMENTAL PROCEDURE  5 19  3.1  Experimental Site  19  3.2  View F a c t o r  20  3.3  Radiation Instrumentation  22  3.3-1  Pyranometers  22  3.3.2  Eppley  25  3.3.3  Linke-Feussner Actinometer  25  3.3-4  Radiometer Maintenance  27  Normal I n c i d e n c e P y r h e l i o m e t e r  3.4  Photographic Instrumentation  28  3.5  F i e l d Measurement Program  31  3.6  Photographic D i g i t i z a t i o n  36  iv  Page 3.6.1  Joyce  3.6.2  D i g i t i z a t i o n sampling  3.6.3  Negative  3.7  36  Loebl Microdensitometer considerations  alignment  38 40 142  Error Analysis  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 photographic technique  43  3.7.2.1  Pyranometers  43  3.7.2.2  Normal I n c i d e n c e Eppley Pyrheliometer  43  3.7.2.3  Recorder  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 probable e r r o r i n the photographic v a l i d a t i o n system  47  3.7.3  error  Error associated with of d i f f u s e radiance  t h e measurement  47  3.7.3.1  Linke-Feussner Actinometer  47  3.7.3.2  Recorder  48  3.7.3.3  Data  3.7.3.4  Probable e r r o r i n the photographic subsystem  3.7-4  Errors  error  49  abstraction  i n the photographic r e d u c t i o n  49 49  3.7.4.1  Digitization  49  3.7.4.2  Photographic system  50  3.7.5  CHAPTER FOUR 4.1  50  R e l a t i v e probable e r r o r o f the angular d i s t r i b u t i o n o f diffuse radiation -  ANGULAR DISTRIBUTION OF DIFFUSE RADIATION  C a l i b r a t i o n Technique v  ;  :  52 52  Page 4.2  Curve F i t t i n g P r o c e d u r e s  55  4.3  V e r i f i c a t i o n of Calibrations  63  4.4  Application  66  4.4.1  Case s t u d i e s  73  4.4.2  Normalized d i s t r i b u t i o n s  84  -  98  CHAPTER F I V E  MODELLING  DIFFUSE RADIATION ON  SLOPING 5.1  Modelling  5.2  Results  CHAPTER S I X  -  SURFACES 98  Technique  102  PRELIMINARY INVESTIGATION INTO  106  GRID S I Z E CHAPTER SEVEN  -  CONCLUSIONS AND RECOMMENDATIONS  115 119  BIBLIOGRAPHY APPENDIX ONE  -  L I S T OF SYMBOLS  APPENDIX TWO  -  CALIBRATION CURVES  vi  122 "  125  L I S T 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 K i p p and Zonen CM5 f o r Incoming Shortwave R a d i a t i o n  23  3.2  On S i t e Sky C o v e r C o n d i t i o n s  3.3  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 E x p o s u r e s  Measurements  37  3.4  E r r o r Summary f o r K i p p and Zonen P y r a n o m e t e r  44  3.5  Recorder Error with Radiation Signal  46  4.1  Exponential  4.2  Comparison o f Measured  5.1  C o m p a r i s o n o f S h o r t w a v 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 and 3 S o u t h - F a c i n g S l o p e s  103  6.1  S i z e o f Square. G r i d  108  6.2  Relative Error of Integrated V a r i a t i o n i n Sample S i z e  Pyranometers  34  Respect t o D i f f u s e  Curve-Fitting Statistics and Computed I r r a d i a n c e  vii  Fluxes f o r a  56 67  113  L I S T OF FIGURES FIGURE  Page  2.1  Absorption of radiation  2.2  Spectral distribution of diffuse  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 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,  2.4  Sky d i s t r i b u t i o n o f t h e 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 and luminous i n t e n s i t y o f d i f f u s e radiation  15  2.5a  Standard d i s t r i b u t i o n of normalized s k y r a d i a n c e Z = 55°  16  2.5b  Sky l u m i n a n c e d i s t r i b u t i o n  16  2.6a  Standard d i s t r i b u t i o n of normalized s k y r a d i a n c e Z = 35°  17  2.6b  D i s t r i b u t i o n of luminous i n t e n s i t y 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 n e 27,  3.1  Equidistant projection local horizon  3.2  Transmittance function of 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  30  3.3  Film  32  4.1  I l l u s t r a t i o n of the effect o f an o u t l i e r  4.2  Statistically  4.3  Representativeness  4.4  Diffuse radiance  distribution f o r a clear  4.5  Diffuse radiance cloudy sky  distribution  and f i l t e r  at various wavelengths  9  radiation  13  and 1953  17  and 1953  21  of the  spectral  significant  response  curves  58  o f the removal  6l  curves  62  of s e l e c t e d data p o i n t s  viii  7  sky  fora partially  70 82  Page 4.6  Diffuse radiance d i s t r i b u t i o n 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 f o r 12:40 F e b r u a r y 10, 19 78  86  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 f o r 13:40 F e b r u a r y 10, 1978  87  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 f o r 13:26 F e b r u a r y 26, 19 78  88  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 f o r 13:47 F e b r u a r y 26, 19 78  89  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 f o r 14:11 F e b r u a r y 26, 19 78  90  4.12  Overcast 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  Partially f o r 12:47  o v e r c a s t .normalized. F e b r u a r y 15, 1978  distribution  94  4.14  Partially f o r 13:17  o v e r c a s t -normalized. - d i s t r i b u t i o n F e b r u a r y 15, 19 78  95  4.15  Partially f o r 13:47  o v e r c a s t normalized., d i s t r i b u t i o n F e b r u a r y 15, 19 78  96  6.1  The v a r i a t i o n o f R.M.S.E. due w i t h sample s i z e  A2.1  C a l i b r a t i o n c u r v e f o r 12:40 F e b r u a r y 10, 19 78  LAT  A2.2  C a l i b r a t i o n c u r v e f o r 13:40 F e b r u a r y 10, 19 78  LAT  127  A2.3  C a l i b r a t i o n c u r v e f o r 1.1:20 LAT F e b r u a r y 14, 19 78  128  A2.4  C a l i b r a t i o n c u r v e f o r 12:30 F e b r u a r y 14, 19 78  LAT  129  A2.5  C a l i b r a t i o n c u r v e f o r 12:47 F e b r u a r y 15, 19 78  LAT  130  A2.6  C a l i b r a t i o n c u r v e f o r 13:17 F e b r u a r y 15, 19 78  LAT  131  ix  83  f o r an  110  to i n t e r p o l a t i o n •  ,  126  Page A2.7  C a l i b r a t i o n c u r v e f o r 13:22 F e b r u a r y 15, 19 78  LAT  132  A2.8  C a l i b r a t i o n c u r v e f o r 13=37 LAT F e b r u a r y 15, 19 78  133  A2.9  C a l i b r a t i o n c u r v e f o r 10:17 F e b r u a r y 24, 1978  LAT  134  A2.10  C a l i b r a t i o n c u r v e f o r .13:26 LAT F e b r u a r y , 26, 19 78  135  A2.ll  C a l i b r a t i o n c u r v e f o r - 13:47 F e b r u a r y 26, 19 78  LAT  136  A2.12  C a l i b r a t i o n c u r v e f o r 14:11 F e b r u a r y 26, 19 78  LAT  137  x  L I S T OF  ILLUSTRATIONS  PLATE  Page  4.1  E l e c t r o n i c a l l y density s l i c e d a l l - s k y p h o t o g r a p h i c image o f 1 4 : 0 0 S e p t e m b e r 1 0 , 1 9  4.2  A l l - s k y photograph exposed at 14:07 F e b r u a r y 1 0 , 19 78 o f a c l e a r s k y  77  4.3  A l l - s k y p h o t o g r a p h e x p o s e d a t 13:17 F e b r u a r y 1 5 , 1978 o f a' p a r t i a l l y o v e r c a s t sky  79  4.4  A l l - s k y p h o t o g r a p h e x p o s e d a t 12:30 F e b r u a r y 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  81  xi  77  72  ACKNOWLEDGEMENTS The  f i n a n c i a l support f o r t h i s  by t h e N a t i o n a l R e s e a r c h Environment  Service.  I would  Council  Their  s t u d y was p r o v i d e d  o f Canada a n d t h e A t m o s p h e r i c  assistance  i s greatly  l i k e t o t h a n k my s u p e r v i s o r ,  f o r h i s s u p p o r t and d i r e c t i o n . my o t h e r c o m m i t t e e  I would  appreciated.  D r . J . E. H a y ,  also l i k e  t o thank  members, D r . T. R. Oke a n d D r . M. A. C h u r c h ,  f o r t h e i r t i m e i n a n s w e r i n g my q u e s t i o n s a n d p r o v i d i n g feedback throughout acknowledge  the p r o j e c t .  I would  useful  further like to  Mr. D. P e a r c e f o r a l l o w i n g me t h e u s e o f t h e P l a n t  Science F i e l d Laboratory, University of 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 t h e A l b e r t a Remote S e n s i n g Centre f o r . the use o f t h e Centre's e l e c t r o n i c slicer, the  a n d D r . G. W a l k e r  University of British  of t h e i r e l e c t r o n i c  density  o f t h e Department o f Astronomy o f Columbia  f o r a l l o w i n g me t h e u s e  digitizer.  I am d e e p l y i n d e b t e d t o Mr. B. K a l a n d a . a n d Mr. 0'. H e r t z m a n f o r t h e many d i s c u s s i o n s  we h a v e h a d c o n c e r n i n g t h e r e s e a r c h  and t h e c o n t i n u o u s m o r a l s u p p o r t t h e y h a v e p r o v i d e d t h r o u g h o u t this  time. S p e c i a l a p p r e c i a t i o n a n d t h a n k s go t o my w i f e ,  Glenda,  f o r h e r m o r a l encouragement throughout o u r m a r r i a g e as I have w o r k e d on t h i s p r o j e c t . typing of the f i n a l  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 t h e  manuscript. xii  CHAPTER ONE INTRODUCTION 1.1  Obj e c t l v e s With t h e 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, t h e a c c u r a t e m o d e l l i n g o f shortwave r a d i a t i o n onto a sloping surface i s increasing i n s i g n i f i c a n c e . m i n a t i o n o f t h e d i f f u s e shortwave i r r a d i a n c e  The  deter-  f o r such i n c l i n e d  s u r f a c e s ( N o r r i s , : . , 1 9 6 6 ) has r e s u l t e d i n a need t o know 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 t i o n over t h e sky hemisphere.  In l i n e with  t h i s requirement, the objectives  of t h i s  research are: 1.  To c h a r a c t e r i z e the  2.  t h e d i s t r i b u t i o n o f d i f f u s e r a d i a t i o n over  c e l e s t i a l dome  F o r a v a r i e t y o f sky c o n d i t i o n s  to integrate  r a d i a n c e v a l u e s and compare t h i s v a l u e w i t h measured h o r i z o n t a l d i f f u s e 3.  t h e hemisphere simultaneously  radiation  To use a s i m i l a r i n t e g r a t i n g procedure t o map t h e d i f f u s e r a d i a t i o n onto 3 0 ° , 6 0 ° and 90° s o u t h - f a c i n g  s l o p e s and  compare t h e c a l c u l a t e d and measured v a l u e s 4.  To produce a n o r m a l i z e d 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 t h e method o f S t e v e n (19 77) 5.  To undertake a p r e l i m i n a r y required  a n a l y s i s on the s a m p l i n g  t o r e t a i n a reasonable approximation of the 1  density  angular d i s t r i b u t i o n o fdiffuse  radiation  i n the  sky  hemisphere. 1.2  Background A knowledge o f the  radiation  angular d i s t r i b u t i o n o f diffuse  i s a necessary p r e r e q u i s i t e  of s o l a r r a d i a t i o n  onto a s l o p i n g  f o r the  surface.  effective  U n l i k e d i r e c t beam  r a d i a t i o n , w h i c h can  be g e o m e t r i c a l l y  mapped o n t o any  w i t h known s l o p e and  orientation,  diffuse  be  parameterized as a p o i n t To  overcome the  made t o a p p r o x i m a t e t h e Kondratyev radiation  the  sky  radiation  cannot  assumptions have been  d i s t r i b u t i o n o fdiffuse  (1954) assumed I s o t r o p y from the  surface  source.  problem, several sky  modelling  radiation.  i n d e t e r m i n i n g the  dome r e c e i v e d on a s l o p i n g  diffuse  surface.  This,  h o w e v e r , was s u b s e q u e n t l y f o u n d t o b e a n u n a c c e p t a b l e a s s u m p t i o n ( K o n d r a t y e v and  M a n o l o v a , .i960).  Morse and radiation treated  Czarneeki  originated  around the  i n a manner s i m i l a r t o  H o w e v e r , M o r r i s and  solar  diffuse  found that  (1966) t e s t e d neither  shortwave r a d i a t i o n and  the  disc  and  most  diffuse  c o u l d be  d i r e c t beam c o m p o n e n t . for clear  component o r i g i n a t e d  sky  w i t h i n 60°  disc.  Norris and  solar  that  L a w r e n c e (1971) f o u n d t h a t  days o n l y 57% o f t h e of the  (1958) s t a t e d  the  above two  approximations  a d e q u a t e l y d e s c r i b e d the  incident  on a n o r t h - f a c i n g  Beckman (1974) h o w e v e r , s t i l l  f e e l that  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  the  diffuse wall.  Duffie  directional  thin-cloud  layer  3 conditions. Hay  (19 77) d e v e l o p e d  a means t o v a r y t h e p e r c e n t a g e  of 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 solar radiation  r a d i a t i o n by u s i n g a d i r e c t  transmission coefficient.  This 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 t h e i s o t r o p i c and t h e f i x e d percentage  d i r e c t i o n a l approach.  Norris  (1966)  concluded  t h a t to. a r r i v e a t a n " 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 t h e d i f f u s e component i n c i d e n t o n a n i n c l i n e d s u r f a c e , i t w o u l d b e n e c e s s a r y to study t h e a n i s o t r o p y o f t h e sky r a d i a t i o n " . F o l l o w i n g the statement essential  (1966), i t i s  of Norris  t h a t r e s e a r c h e r s have access  t oa q u a l i t y  describing the angular d i s t r i b u t i o n o fsolar These d a t a c a n be used t o d e v e l o p ( a n i s o t r o p i c ) model. a technique which be  utilized.  diffuse  s e t o f data radiation.  and t e s t a n e o l o t r o p i c  Since the r a d i a n t i n t e n s i t y i s not uniform,  preserves the s p a t i a l c h a r a c t e r i s t i c s  must  A t p r e s e n t o n l y two t e c h n i q u e s a r e a v a i l a b l e .  Heimo a n d V a l k o  (19 76) h a v e d e v e l o p e d  a system  of rotating  p y r a n o m e t e r s t o measure t h e t o t a l i n c o m i n g shortwave on 77 d i f f e r e n t s u r f a c e s .  radiation  However, o n l y w i t h t h e use o f s u 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 c a n t h e r a d i a n c e o f any one p o i n t i n t h e s k y h e m i s p h e r e be. d e t e r m i n e d . . is  that o f Steven  used by Kondratyev  The s e c o n d  method  (19 77) who u s e d a t e c h n i q u e s i m i l a r t o t h a t e t a l (1955).  Steven  (1977) u s e d a  L i n k e - F e u s s n e r A c t i n o m e t e r t o measure 34 p o i n t s o u r c e s o f diffuse  radiation  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 d r a w n .  Due t o  the slow r e s p o n s e o f t h e I n s t r u m e n t , t h e measurements spanned a t i m e p e r i o d o f 40 m i n u t e s . variable  T h i s l i m i t e d a l l work t o t h e l e s  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 t h e p r e s e n t s t u d y h a s  a t t e m p t e d t o o v e r c o m e t h e p r o b l e m o f r e s p o n s e t i m e by s u p p l e m e n t i n g t h e a c t u a l measurements w i t h a l l - s k y Because o f the r e l a t i o n s h i p between v i s i b l e  photographs. and  shortwave  r a d i a t i o n , t h e a c t i n o m e t r i c m e a s u r e m e n t s n e e d 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 t h e v i s i b l e this  radiation information i n  the photograph.  To q u a n t i f y  l a t t e r information, a micro-  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 e n e r g y , as I t I n t e r e s t s b e t w e e n w a v e l e n t h s o f 0.2  ym  Within  visible  0.39 in  t h i s waveband, the  ym  0.76  and  t h i s very  ym  its  of the  (Drummond., 19  P i a t t , 19 76).  Because photographic  photographic  f i l m samples  as a p a r a m e t e r i z a t i o n I n the  d i s t r i b u t i o n of the  70).  I t i s only  s o l a r spectrum, i t i s necessary  shortwave r a d i a t i o n - f l u x .  occurs  domain i s f o u n d between  ( P a l t r i d g e and  representativeness  angular  ym  s m a l l s p e c t r a l r e g i o n t h a t most  film is sensitive. t h a n 10%  4.0  and  climatologists,-  to  validate  f o r the  case of s t u d y i n g  d i f f u s e shortwave  less  total  the  irradiance  over the  s k y h e m i s p h e r e , " s u c h a v a l i d a t i o n must  consider  changes i n the shortwave s p e c t r u m w i t h r e s p e c t  the  solar  zenith.  a parameterization the  The  confirmation of v i s i b l e  of s o l a r r a d i a t i o n w i l l  e x t r a t e r r e s t i a l f l u x t o the  case,  diffuse  this parameterization w i l l  function  o f the p o s i t i o n of the  On  a day  t o day  basis,  a l s o be solar  the  be  flux.  also to  radiation developed In the  investigated  45%  waveband.  of the The  as  55%  a  disc.  s p e c t r a l nature  of  t o t a l energy i s c o n t a i n e d w i t h i n  remaining  from  latter  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 constant. imately  as  the  Approxvisible  of the energy i s d i s t r i b u t e d  .. 6 u l t r a - v i o l e t (9%) and  between the  As  the  s o l a r r a d i a t i o n passes through a clear.atmo-  sphere, nearly  a l l the  w h i l e the  u l t r a v i o l e t r a d i a t i o n i s a b s o r b e d by  H o b b s , 19 76) and  o z o n e ( W a l l a c e and  infrared portion  m a i n l y b y w a t e r v a p o u r and Thompson, 1970).  and  relatively that  o f the  a w a t e r vapour a b s o r p t i o n band 0.70 y n u ( S i v k o v , 1968) .  absorptivity  m o l e c u l a r and constituents  radiation aerosol o f the  a c l e a n dry  a change i n t h e  occurring  The l a t t e r i s  t o t a l absorption o f radiation F i g u r e 2.1  o f the  graphically  atmosphere o v e r the  bands v a r i e s actual  i s also  entire  s e l e c t i v e l y d e p l e t e d by  scattering.  a t m o s p h e r e and  T h i s i s d e p e n d e n t upon the  solar  zenith  solar  a n g l e b e t w e e n 0° and  s p e c t r u m f o u n d i n the  b e t w e e n 44.6% and  the  o p t i c a l a i r mass.  a t m o s p h e r e , K o n d r a t y e v (1969) shows t h a t  p e r c e n t a g e o f the  the  absorption  spectrum. Solar  For  o f a weak o z o n e  0.78 ym; t w o o x y g e n  w a t e r v a p o u r ( S i v k o v , 1968). the  The a b s o r p t i o n  more s i g n i f i c a n t b e t w e e n 0.76  the  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  illustrates  depleted  absorption ( M i l l e r  H o b b s , 1976).  v i s i b l e consists  b a n d s - - o n e a t 0.69 pm and  b e t w e e n 0.57 and  1968),  The v i s i b l e b a n d , h o w e v e r , r e m a i n s  does, o c c u r i n t h e  solar  s o l a r spectrum i s  u n a b s o r b e d ( W a l l a c e and  0.80 i_im; and  oxygen ( S i v k o v ,  carbon dioxide  a b s o r p t i o n b a n d b e t w e e n 0 . 4 4 and  by  (46$) (Paltridge  infrared  P i a t t , 19 76).  and  and  the  for  90°, the  v i s i b l e wave-  37.6%, r e s p e c t i v e l y \  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  Thus, surface  • ••7  (ID  0.1  0.2  (.).:.! 0 . 4  ().(.  0.8  I  2  .1  4  5 (.  8  10  20  Wavelength.  (b) Absorption spectrum  tor ! l 0 ;  Wavelength,  (c) A b s o r p t i o n s p e c t r u m for ;itino.sphere ll,0  Wavelength,  Figure  2.1  /tm  Absorption of radiation at various w a v e l e n g t h s by ( a ) 0 a n d 0 ; ( b ) H 0 ; and ( c ) t h e p r i n c i p a l a b s o r b i n g g a s e s ( f r o m M i l l e r a n d Thompson, 19 70) 3  2  8  is-highly variable, The s p e c t r a l  even over a s i n g l e day. 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 t h e s o l a r although the t o t a l irradiance  i s ofa lesser  spectrum,  magnitude.  K o n d r a t y e v (1969) p r e s e n t s t h e d a t a o f L e n z (1961) f o r a t u r b i d a t m o s p h e r e s h o w i n g t h e maximum f l u x d e n s i t y a t 0.451 urn a t t h e s o l a r , z e n i t h  and, i n t h i s case, s h i f t i n g  down t o 0.401 ym a t a . p o i n t . 9 0 ° : f r o m t h e s o l a r provides s i m i l a r data, also the  disc.  Figure  c o l l e c t e d b y L e n z (1961)  showing  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 at various  d i s t a n c e s f r o m t h e s u n . Two i m p o r t a n t p o i n t s this  figure  are:  (1)  t o be  t h e maximum r a d i a n t  2.2  azimuthal  emerging  from  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), a n d (2) f o r a l l a z i m u t h s presented, a large wavelengths. that on  portion  of the r a d i a t i o n  The o b s e r v a t i o n a l  occurs i n the v i s i b l e  r e s u l t s o f Lenz  ( I 9 6 I )  t h e 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  c l e a r s k y days i s p o s s i b l e .  illustrates scattered sizes.  the spectral  distribution ofdiffuse  by c l e a n d r y a i r and 3 d i f f e r e n t water  radiation droplet  O n l y i n t h e c a s e o f R a y l e i g h s c a t t e r are t h e maxima  of t h e s c a t t e r i n g  substance increase,  diffuse  also  radiation  the i n t e n s i t y o f  This l a t t e r e f f e c t  maxima i n t h e v i s i b l e w a v e l e n g t h s . scatterer  As t h e s i z e  i n c r e a s e s and t h e s p e c t r u m s h i f t s  towards t h e l o n g e r w a v e l e n g t h s .  largest  radiation  T a b l e 2.1 ( K o n d r a t y e v , 1969)  found o u t s i d e t h e v i s i b l e r e g i o n o f t h e spectrum.  the  indicate  locates  I n the case o f t h e  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 t h e s o l a r a l m u c a n t h a r a t whose azimuth values r e l a t i v e to the sun are g i v e n i n t h i s f i g u r e o f L e n z (1961) . f r o m ( K o n d r a t y e v , (1969)  TABLE 2 . 1 . — E n e r g y (10" cal/cm min) 3  2  distribution  i n the s o l a r spectrum outside  and t h e s p e c t r a l c o m p o s i t i o n (10~ cal/cm min) 6  2  the atmosphere  of diffuse r a d i a t i o n 1969)  (Kondratyev,  D i f f u s e R a d i a t i o n by wavebands (DA,.urn)  o m  .  c  m  o  \  .  i  o I  _  O  o  Sun 1 cm o f c l e a n dry a i r 3  :  o  o I  . . -=r  C\!  m  o  o  .  o  I  -  m  CM  co m  . .  I  OO .  ^ r v r > m m  m  I  VD  -  ^  o r  . ^ .r  o  o  o I  OO  CU  m o  vo -=r  .  o  I  m o  -=r  ^  I  .. ... . -=r  r  o  o  2.6  11.5  21.8  31-3  35.2  36.0  54.3  62.6  4.4  14.4  21.9  23-5  20.8  16.9  17.2  13-7  100 d r o p l e t s r = 0 .1 y  0.05  0.27  0.44  0.54  0.51  0.45  0.52  0.46  25  0.14  0.78  1.62  1.78  3-52  3-78  6.41  7.65  1.0  4.6  droplets r = 0.5 y  5 droplets r = 1 y  .  9-2.  12.8  14.6  15.1  23.2  25.6  ui  IV) Ul  o TS 1—  1  CD ct CO  IV) O  •  II  p-  o  Otl •  CD  -c  c+ CO  I— O O  H  1  CO  QJ O  3  II  O O • H  CD  •£ c+  01  P "O  H4  o  M  CD P  Ul.  —4  O  uo  •  •  •  Ul  UO OA  UO  VO  •  M -Er  OA  O  Jr  Ul -t  -tr  OA  IV) Ul  -t  CA  O  IV)  M  CO  Ul  CA  -tr  rv>  o  OO  UO OA  -t  O  M  O vo  co  oo  uo  o  o  o  o -fc-  o  co  -tr  IV)  O  o  hM  O IV)  Ul  1  -tr  1—  o  o  UO CT\  o  IV)  1  ct  4=-  co  -tr  0.64 -  0.66  ro  CA  0.70 - 0.72  O  •  OA  O-  '3 "  P  <! CD C Q. CO  uo Ul  uo  0.78 - 0.80  ro  a 3  0.86 -0.88  no M O  0.98 - 1.00  M  -tr UO  •  H-  s;'  Ul Ul  £J  P P. HP  -<]  r-> IV)  £ cn CD  OA  1  oo  a > • >  p  1  f—  0.56 - 0.58  -Cr  o  h-  CO  0 .50' - 0 . 5 2  •  OA  uo  %  •  radiation  rv>  o  visible  " 12 maxima a r e f o u n d i n t h e v i s i b l e  region.  visible  contributes  portion  o f the spectrum  of the t o t a l energy  a large  percentage  On t h e b a s i s , o f T a b l e 2.1,  to the system.  (1969) c o n c l u d e d t h a t  Kondratyev  I n a l l c a s e s , the  f o r the shorter  wavelengths -  u n d e r a c l e a r s k y , d i f f u s e r a d i a t i o n i s more a b u n d a n t direct  solar radiation.  difference  For an o v e r c a s t s k y , however, the  between the s p e c t r a l  r a d i a t i o n and  meterization  research i n using v i s i b l e f o r shortwave  conflicting results. r a d i a n c e and  composition o f diffuse  direct solar radiation i s less  Recent  using a Yanishevsky respectively.  r a d i a t i o n as a p a r a -  a t 30 p o i n t s  over the c e l e s t i a l  s p e c t r o m e t e r and a s e l e n i u m  For large  zenith  produced  e t a l (1955) m e a s u r e d dome  photometer  a n g l e s , he f o u n d t h a t  angular 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  the  intensity  2.3),.'  However, the d i f f e r e n c e a t  a n g l e s l e s s t h a n 26° was  f o u n d t o be i n s i g n i f i c a n t .  d i d not coincide zenith  ( K o n d r a t y e v , 1969).  d i f f u s e r a d i a t i o n have  Kondratyev  luminance  than  (Figure  T h i s d i s c r e p a n c y may b e a c c o u n t e d I n the s p e c t r a l responses  f o r by the  o f t h e two  and W i l s o n , 1934; K o n d r a t y e v  differences  instruments  e t 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, t h e s p e c t r a l d i s t r i b u t i o n o f radiation also  i s altered,  that  I ndoing such, i t  d i f f e r e n t radiance values could  t h e same p o r t i o n , o f t h e s k y , d e p e n d i n g scattering.  diffuse  changing the output s i g n a l s o f  t h e 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. is possible  Moreover,  (Zworykin  result  from  o n t h e amount o f 7  t h e l o c a t i o n o f t h e minimum  radiant  13  Figure  2.3  D i s t r i b u t i o n of luminous i n t e n s i t y ( d a s h e d l i n e ) and energetical intensity (solid line) for J u l y 3, 195 3 (Z = 7 4 ° ) from Kondratyev et a l (1955)  .' 14  2.3 h a s n o t b e e n s u b s t a n t i a t e d i n  intensity  shown i n F i g u r e  the  d a t a o f K o n d r a t y e v e t a l (1955) n o r i n t h e more  other  (1977).  r e c e n t work o f S t e v e n  f a c t o r s , such as c i r r u s  T h i s may i n d i c a t e t h a t  other  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 t h e  measurements. 2.4 i l l u s t r a t e s  Figure and  radiance  f o r an overcast  The c o i n c i d e n c e  between these  good when compared w i t h t h o s e z e n i t h angles  (Z).  This  the d i s t r i b u t i o n o f luminance  s k y ( K o n d r a t y e v e t a l , 1955). two d i s t r i b u t i o n s  i s relatively  o fclear skies with  large solar  f u r t h e r i n d i c a t e s that the s p e c t r a l  responses o f the instruments  u s e d may a f f e c t  the r e s u l t s . o f S t e v e n (1977)  A comparison o f the r a d i a n t i n t e n s i t i e s  ( F i g u r e 2.5a), who u s e d t i m e a v e r a g e d d a t a , w i t h t h e l u m i n a n c e d i s t r i b u t i o n o f Dorno  (1919)  the. same s o l a r z e n i t h a n g l e , very  good.  This  on t h e s u n ' s z e n i t h a n g l e 35°.  Further  of z e n i t h angle  approximately  shows t h a t t h e g e n e r a l  agreement i s  i n d i c a t e s t h a t t h e p r e v i o u s l y n o t e d depen-  dence o f t h e c o i n c i d e n c e  as  ( F i g u r e 2.5b) f o r  o f l u m i n a n c e and r a d i a n t i s not s i g n i f i c a n t  a t angles  evidence w i t h which to assess d e p e n d e n c e a t medium a n g l e s  intensity as l a r g e  the i n s i g n i f i c a n c e  can be o b t a i n e d  f r o m t h e w o r k o f S t e v e n (1977) f o r Z = 55° ( F i g u r e 2.6a) a n d t h a t o f K o n d r a t y e v e t a l (1955) f o r Z = 51° ( F i g u r e 2.6b). Although  t h e methods  f o r n o r m a l i z i n g the data  are not  identical  ( t h e f o r m e r u s i n g t h e r a t i o b e t w e e n D + and t h e r a d i a n t H  at a given' p o s i t i o n , w h i l e the l a t t e r expresses respect t o the i n t e n s i t y  intensity  the r a t i o  a n d l u m i n o s i t y a t z = 0), t h e y  with  are  15  Figure  2.4  Sky d i s t r i b u t i o n o f t h e r e l a t i v e energetical intensity (solid line) a n d l u m i n o u s i n t e n s i t y (dashed, l i n e ) of 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 J u n e 14, 1953 (Z = 42°, s o l i d c l o u d i n e s s ) f r o m K o n d r a t y e v e t a l (1955)  16 1*8 0  0  Figure  2.5a  Standard 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 S t e v e 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  Figure  2.5b  Sky l u m i n a n c e d i s t r i b u t i o n f r o m C. Dorno f r o m R o b i n s o n (1966)  180  F i g u r e 2-:L6'avStandardi;distribution", o f "normalized sky radiance.' o f S t e v e n (.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 c o m p a r i s o n .with• '.Figure 2:6b f r o m S t e v e n (19 77)' • •  Figure  2.6b  D i s t r i b u t i o n of 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 n e 27, 1953 (Z = 51°) f r o m K o n d r a t y e v e t a l (1955)  18 sufficiently  close f o r comparison.  I t i s immediately 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 The  contours are o f s i m i l a r normalized values.  c o i n c i d e n c e b e t w e e n t h e two  angular 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 o v e r t h e e n t i r e h e m i s p h e r e . r e s u l t s o f Steven.(1977)  In f a c t , the  compare more f a v o u r a b l y t o t h e  l u m i n a n c e d i s t r i b u t i o n o f K o n d r a t y e v 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).  According  t o S t e v e n (1977), t h e 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 s k y 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  intensity  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 b e open t o q u e s t i o n . From t h i s w o r k , and t h e g e n e r a l r e l a t i o n s h i p the  flux density  found i n the v i s i b l e p o r t i o n  to t h a t o f the complete shortwave  o f the  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  between the  that  radiation  o f atmospheric  The n e e d now i s t o f i n d a f u n c t i o n a l two.  spectrum  spectrum, i t appears  l u m i n a n c e i s a good e s t i m a t o r o f d i f f u s e s h o r t w a v e  conditions.  between  relationship  CHAPTER THREE EXPERIMENTAL PROCEDURE 3.1  Experimental The  Site  exposure  of the photographic  n e g a t i v e s and t h e  a c t i n o m e t r i c measurements o f s k y r a d i a n c e were  undertaken  a t t h e 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 t h e s o u t h of the U n i v e r s i t y Longitude  123°  C o l u m b i a ( L a t i t u d e 49°  of B r i t i s h  15'  W, E l e v a t i o n 86m)7 The s i t e was  because measurements o f n o r m a l i n c i d e n c e s o l a r  campus 15 ':N, r  chosen  radiation,  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 s h o r t w a v e r a d i a t i o n and t o t a l s h o r t w a v e r a d i a t i o n f o r t h e h o r i z o n t a l and 30°,  60°, a n d 90°  being routinely taken. of t h i s  s o u t h - f a c i n g s l o p e s were  Hay (1977) p r o v i d e s a f u l l  o b s e r v a t i o n program. The  specific  l o c a t i o n o f t h e camera and a c t i n o m e t e r  was 35m due w e s t o f t h e s o u t h - f a c i n g s e n s o r s . i n s t r u m e n t s w e r e mounted on t r i p o d s w i t h i n 0.5m other with the actinometer Both The  The two o f each  s e t t o t h e e a s t o f t h e camera.  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 t h e ground.  h o r i z o n t a l p r o j e c t i o n o f t h e camera l e n s was s e t s u c h  t h a t t h e a c t i n o m e t e r , when v e r t i c a l l y be  description  observed  through  o r i e n t e d , could not  t h e v i e w f i n d e r , y e t when t h e a c t i n o m e t e r  was o r i e n t e d a t z = 1 0 ° ,  the r a d i a t i o n s h i e l d of the instrument 1.9  20 c o u l d be I d e n t i f i e d t h r o u g h t h e l e n s .  This 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 , h o w e v e r , as t h e r a d i a t i o n  did  n o t e x t e n d a b o v e t h e 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  viewfinder.  T h i s arrangement  insured that the r e l a t i v e  h e i g h t s o f t h e two i n s t r u m e n t s r e m a i n e d the 3.2  shield  constant throughout  experiment. 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 t h e v i e w f a c t o r as " t h e  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 by t h e r a d i o m e t e r e m a n a t i n g t o t a l r e c e i v e d from a l l the  received  from a p a r t i c u l a r source t o t h e  s o u r c e s (assumed t o be r a d i a t i n g a t  same r a t e ) " . Figure  3.1  graphically illustrates  thehorizon of the  e x p e r i m e n t a l s i t e i n t h e form o f an e q u i d i s t a n t From t h i s  t h e average  projection.  z e n i t h a n g l e f o r e a c h 15° a r c was  determined 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  (Steyn, p e r s o n a l communication): 24"  V„ = f  U/2TT ((1  Z i=l tan"  + cot (^/2 2  • r'/r))  '  2  C  1  ( t a n IJJ/(1 + c o t ( V 2 2  • r^/r))~^))}  (3-D  where* r ' = t h e d i s t a n c e f r o m t h e z e n i t h t o t h e 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 r  *A. f u l l  y  r  (mm)  = t h e d i s t a n c e f r o m t h e z e n i t h t o z = /2 7T  = 23/TT • r list  o f symbols  i s g i v e n i n Appendix  1..  radians (  Figure  3.1  E q u i d i s t a n t p r o j e c t i o n of the l o c a l h o r i z o n o f t h e e x p e r i m e n t a l s i t e as v i e w e d t h r o u g h a 180 Fisheye lens  2-2 w h e r e 3 = mean z e n i t h a n g l e  o f the h o r i z o n over a given  arc-length 4» = t h e l e n g t h o f t h e a r c i n r a d i a n s a t z = i r / 2 The 98.1%  c a l c u l a t i o n showed t h a t f o r a n i s o t r o p i c  o f t h e t o t a l r a d i a t i o n w o u l d emanate f r o m t h e sky-  h e m i s p h e r e above t h e l o c a l h o r i z o n . f a c t n o t Lambertian,. t h a t , apart  The s k y h e m i s p h e r e i s i n  Further, Figures  from a - s m a l l  2.3 t o 2.6 i n d i c a t e  limb b r i g h t e n i n g e f f e c t , the areas  of the sky near t h e h o r i z o n are a s s o c i a t e d w i t h low  radiance  Therefore,  3.3  i t c a n be c o n c l u d e d  angles.  t h a t t h e h o r i z o n does n o t  e f f e c t the experiment.  Radiation  3.3-1  relatively  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  significantly  Instrumentation  Pyranometers The  instruments  fluxes of t o t a l , Kipp  signal,  u s e d t o r o u t i n e l y measure t h e i n c o m i n g  d i f f u s e a n d r e f l e c t e d s o l a r r a d i a t i o n were  a n d 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  n o m i n a l c a l i b r a t i o n o f 0.012 mv/Wm" a n d a t e m p e r a t u r e c o r r e c t i o n 2  o f 0.00135/°C a t 26.6 °C ( L a t i m e r , Flowers  1972).  Latimer  (1970) a n d  (1977) f o u n d 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 h a d t o b e a p p l i e d due t o t h e d i f f e r e n t i a l  heating  o f t h e t h e r m o p i l e ©nee i t was r e m o v e d f r o m t h e h o r i z o n t a l . Latimer  ( p e r s o n a l communication) shows-.corrections  1.010 ( f o r 180° t i l t ) 1.005 ( f o r a n g l e s  and F l o w e r s  (1977) shows c o r r e c t i o n s o f  b e t w e e n 20° a n d 7 0 ° ) .  for the experimental  as l a r g e " a s  Table  p e r i o d , the c a l i b r a t i o n s  3-1 p r o v i d e s , o fthe instruments  TABLE 3 - 1 - — C a l i b r a t i o n o f K i p p and. Zonen CM5 P y r a n o m e t e r s f o r Incoming shortwave i r r a d i a n c e  Flux  Location Slope (degrees)  Azimuth (degrees)  Slope Correction**  mv(Wm ) 2  Temperature Correction* (°c " M ( f o r b a s e o f 26.6 C)  1  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  o  30  180  0.0116  1.003  0.00135  . 60  180  0.0112  1.005  0.00135  90  180  0.0114  1.007  0.00135  K 3;  ho *  Calibration*  p r o v i d e d by C a n a d i a n A t m o s p h e r i c Environment 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)  Service  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 due  to  correction applied  slope. The  observations  of d i f f u s e r a d i a t i o n were f u r t h e r  corrected using a modified (Drummond, 1956)  correction  c e l e s t i a l dome w h i c h was a d d i n g an e x t r a 4% anisotropy  of the  Thus, the  form of the i s o t r o p i c r a d i a t i o n to account f o r the area  s c r e e n e d by  c  cos  D+ D+  p • cos  (19 72)  <b • s i n 6 • t  <S • s i n t ) } 0  m  o f shadow b a n d  y = r a d i u s o f shadow b a n d  the  o  +  (3.2)  • 1.04  = m e a s u r e d d i f f u s e r a d i a t i o n (Wm  oo = w i d t h  By  1972):  = 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  c  found  the  accounted f o r .  form ( L a t i m e r ,  3  of  shadow b a n d .  s k y h e m i s p h e r e c o u l d be  {2(0/iry • c o s 6 ( s i n  = D+ m  the  to t h i s value, Latimer  c o r r e c t i o n i s of the  D+  where  the  2  2  )  )  (mm) (mm)  6 = solar, d e c l i n a t i o n (radians) <J> = l a t i t u d e t  n  = hour angle  P.or t h e the  o f sun  at sunset  d u r a t i o n of. e a c h s e t ©f  o u t p u t o f t h e above i n s t r u m e n t s  5 minute i n t e r v a l s CR5  (radians)  Digital  and  Recorder.  recorded  (radians)  field  measurements,  were i n t e g r a t e d o v e r  u s i n g a Campbell  Scientific  •^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 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 3-3.2  194 s t r i p  continuously chart  recorder.  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 m e a s u r e d u s i n g a t e m 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  v i e w s a n a n g l e o f 0.009 s r . The c a l i b r a t i o n o f t h e i n s t r u m e n t is  0.0079 mv/Wm~  2  ( s u p p l i e d by Canadian Atmospheric  Service) with a l i n e a r i t y 1400 Wm . 2  Scientific signals 3.3.3  Environment  o f r e s p o n s e t o w i t h i n ±0.5% up t o  The s e n s o r o u t p u t was r e c o r d e d o n a C a m p b e l l CR5 D i g i t a l R e c o r d e r i n t h e same manner as t h e  from the pyranometers. Linke-Feussner Actinometer 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 u s e d t o m e a s u r e  the d i f f u s e  radiance w i t h which the photographic exposures  were t o be c a l i b r a t e d .  The i m p o r t a n c e o f t h e s e m e a s u r e m e n t s  makes i t a p p r o p r i a t e t o d e s c r i b e t h e I n 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 with a high sensitivity  and a s t a b l e c a l i b r a t i o n  The i n s t r u m e n t c o n t a i n s t w o 2 0 - j u n c t i o n thermocouples  connected i n o p p o s i t i o n .  Instrument,  (Coulson,1975).  manganin-constantan One t h e r m o p i l e i s  e x p o s e d t o r a d i a t i o n , w h i l e t h e s e c o n d a c t s as.'a c o m p e n s a t i n g 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 , b u t exposed t o t h e same q u a s i - a d i a b a t i c p r e s s u r e changes n e a r t h e 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 t e m p e r a t u r e by a i r c u r r e n t s  fluctuations  ( C o u l s o n , 1975; I.G.Y., 1956).  caused  The f o r m e r  c o n d i t i o n was f o u n d t o be a s e v e r e p r o b l e m i n m o d e r a t e winds.  Because o f t h i s ,  the instrument  c a n n o t be u s e d i n  turbulent conditions.. The  diameter  o f t h e s e n s i n g e l e m e n t i s 10mm a n d . i s  p l a c e d a t t h e b a s e o f a 70.3mm t u b e 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 diameter  copper r i n g s .  a p e r t u r e o f 0.025 s r .  This design provides an  The c o p p e r r i n g s e f f e c t i v e l y  the h e a t i n g o f the i n s t r u m e n t For long term temperature  reduce  over s h o r t periods o f time.  changes o f t h e 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 thermal  contact w i t h the t h e r m o p i l e  cavity.  The t e m p e 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 b a s e o f 20 °C. A b u i l t - i n r i n g contains 4 f i l t e r s t h o u g h o n l y 1 f i l t e r was  and  1 shutter,  used i n the p r e s e n t experiment.  Schott o p t i c a l quartz f i l t e r r a d i a t i o n b e t w e e n 0.25 and  A  a l l o w e d measurement o f s h o r t w a v e  4.0 um, w h i l e a m e t a l  s h u t t e r was  e m p l o y e d t o z e r o t h e i n s t r u m e n t s b e t w e e n measurements.. The was  c a l i b r a t i o n o f the instrument  0.158 mv./Wm" ( s u p p l i e d b y K i p p and 2  of 6l.l a 99%  ohms..  response  Robinson,  i s b e t w e e n 8 and  1966; C o u l s o n ,  is  c i r c l e bubble  t o reach  10 s e c o n d s - ( I . G . Y . ,  1956;  1975). i s c a r r i e d out  using  a t the base o f the i n s t r u m e n t .  accurate to w i t h i n ±1°.  p r o v i d e s a ±1° a c c u r a c y  study  Zonen) w i t h a r e s i s t a n c e  The t i m e r e q u i r e d b y t h e i n s t r u m e n t  L e v e l l i n g o f the a c t i n o m e t e r a built-in  used i n the  An a z i m u t h  circle  on the  This  instrument  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 a- ±0.1  e l e v a t i o n screw y i e l d s The  output  on a H o n e y w e l l full  accuracy  194  Electronik  s c a l e range o f lOOyv.  strip  T h i s p a r t i c u l a r r e c o r d e r was  Latimer  (1972).  The  t h e measurement p e r i o d no any  of the sensors .  The  completely i n shade. Eppley  the s i g n a l  to ensure  The  Over the  The  a l i g n m e n t was  of the alignment  d e t e c t e d on a 10.0  chart r e c o r d e r which  of such mv  was pyrano-  cleaned  Whenever  of the instrument w i t h r e s p e c t to  a l s o checked.  effects  course found  t h a t the thermopile of the  c a b l e unwound on a d a i l y b a s i s .  w i t h i n 2 diameters target.  routinely.  N o r m a l I n c i d e n c e P y r h e l i o m e t e r was  p o s s i b l e , the alignment s o l a r beam was  orientation"of  d i . f f u s o m e t e r shadow b a n d  m e t e r was  be  mv.  change i n o r i e n t a t i o n was  checked  The  l e v e l and  a l s o checked  regularly  and  seconds), wide c h a r t  p y r a n o m e t e r s i n v o l v e d i n t h e r o u t i n e measurement  t h e s e i n s t r u m e n t s was  for  (0.5  time  used  s o l a r r a d i a t i o n f l u x e s w e r e 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  of  a  Radiometer maintenance The  of  recorded.  chart recorder with  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  ability  3..'3. 4  zenith.  s i g n a l o f t h e a c t i n o m e t e r was  because of i t s s h o r t response and  i n the  s i g h t of the  maintained centre of  a change i n a l i g n m e n t  full  monitored  were a l s o c o n n e c t e d , t o t h e OR5  the  c o u l d not  s c a l e analogue E s t e r l i n e  Angus  the p y r h e l i o m e t e r s i g n a l s  which  integrator.  L e v e l l i n g of the Linke-Feussner  Actinometer  the  was  c a r r i e d o u t b e f o r e and. a f t e r e a c h s e t o f o b s e r v a t i o n s .  The  28 Schott o p t i c a l quartz  f i l t e r was r o u t i n e l y  i n a t i o n a n d c l e a n e d when 3.4  Photographic  checked f o r contam- .  necessary.  Instrumentation  F i l m was e x p o s e d u s i n g a Canon F - l 35mm s i n g l e r e f l e x camera w i t h f u l l suited t o small-format  aperture metering.  it  e n t e r i n g through  in  system.  the  T h i s measures the  c e n t r a l p o r t i o n o f the  i s n e a r l y e q u a l t o t h e amount, o f l i g h t  photographic  film  The c a m e r a i s  photography o f the hemisphere because  of i t s c e n t r a l area metering of l i g h t  lens  ( S u z u k i , 1975).  amount  f r a m e where  t h a t exposes t h e  The v i e w f i n d e r i s c o n s t r u c t e d  s u c h a manner t h a t o v e r 97% o f t h e f i e l d o f v i e w o f t h e  lens  can b e s e e n .  F u r t h e r , a secondary  f i n d e r a l l o w s one t o see (Suzuki,  p r i s m i n the  the metering w i t h o u t  view-  moving the eye  1975). A Canon S p e e d F i n d e r was a t t a c h e d t o t h e m a i n camera  body t o f a c i l i t a t e e a s e o f o p e r a t i o n when t h e c a m e r a was p o i n t e d toward the sky hemisphere. one  t o a d j u s t the m e t e r i n g  through  lens aperture without  looking  t h e v i e w f i n d e r a t t h e r e a r : ' o f t h e camera b o d y .  prism b u i l t 90°  and  This viewfinder allows  i n t o the Speed F i n d e r r e f r a c t s  t o overcome t h i s The  the l i g h t  o f 180° and p r o v i d e s  rays  difficulty.  l e n s u t i l i z e d i n t h e s t u d y was t h e  7.5mm f / 5 . 6 S.S.C.  A  Canon  This e q u i d i s t a n t lens has a f i e l d a circular  on the p h o t o g r a p h i c  Fisheye o f view  e x p o s u r e o f 23-143 r 0.155 mm  in  diameter  film.  Suzuki  it  i s e x c e l l e n t f o r a z i m u t h a l phenomena.  (1975)  claims  The m a g n i f i c a t i o n  29 is  0.15X.  The f o c u s i n g i s f i x e d . i n t o the lens are 6 f i l t e r s  Built  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 . violet  cut-off  filter  filter  e l i m i n a t e s a l l r a d i a t i o n a t wavelengths  L-1B was u s e d i n t h e experiment,.  0.32ym a n d p r o v i d e s a n e a r l y f l a t  The o t h e r b u i l t - i n at wavelengths curves which  f i l t e r s were e i t h e r  within  less  This  than  t r a n s m i t t a n c e curve f o r  g r e a t e r t h a n 0.4um a n d l e s s  wavelengths  The u l t r a -  than found  the v i s i b l e spectrum  2. 4ym ( F i g u r e  3-2).  t o cut o f f r a d i a t i o n  o r had t r a n s m i t t a n c e  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 t h e p r e s e n t  study. The l e v e l l i n g o f t h e c a m e r a was c h e c k e d  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 t h e t o p o f t h e l e n s i n two o r t h o g o n a l directions.  The l e v e l was c h e c k e d  before anda 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 occulting  d i s c was u s e d t o b l o c k t h e s o l a r  the problem o f the s p u r i o u s a d d i t i o n  disc.  an This  o f d i r e c t beam  reduced  radiation  a f f e c t i n g t h e o v e r a l l d e n s i t y o f t h e photograph, and removed t h e p r o b l e m o f i n t e r n a l l e n s , f l a r e due t o t h e r a y s o f t h e s u n . 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 angle o f approximately  6° u s i n g t h e r a t i o s p r e s e n t e d b y L a t i m e r The p h o t o g r a p h i c panchromatic  (1972).  f i l m was I l f o r d p r o f e s s i o n a l  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 . is  relatively flat  type  f o r s m a l l format  The s e n s i t i v i t y  f i l m s and t h e waveband  Wavelength Figure  3.2  Transmittance  (ym)  function of u l t r a - v i o l e t  ( s u p p l i e d by Canon Cameras)  c u t - o f f f i l t e r L-  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 of the  commercially a v a i l a b l e s m a l l format type f i l m s Figure  3-3  p r o v i d e s the r e l a t i v e  by t h e m a n u f a c t u r e r effective  sensitivity  investigated.  o f FP4 a s  ( I l f o r d , p e r s o n a l communication)  supplied  and  a b s o r p t i o n c u r v e when t h e t r a n s m i s s i o n f a c t o r  the f i l t e r  the of  i s added.-  The  exposed  f i l m was  p r o c e s s i n g company. f i l m comparisons the unexposed  p r o c e s s e d by a p r o f e s s i o n a l  T h i s was  were p l a n n e d .  portions  f e l t t o be a d e q u a t e  as no  inter-  A study of the d e n s i t i e s  of developed f i l m i n d i c a t e d that  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  of use  intra-film  comparisons. 3.5  F i e l d Measurement- P r o g r a m A preliminary  i n v e s t i g a t i o n o f t h e 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 t h e 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 t i o n was  u n d e r t a k e n d u r i n g S e p t e m b e r 19 77.  o b s e r v a t i o n a l p e r i o d , Kodachrome 64 was  used  ( M c A r t h u r and Hay,  the d i f f e r e n t response and t h e d i f f i c u l t y  ASA  1978).  During  photographic  Problems  o f t h e c o l o u r dyes  i n quantitatively  to l i g h t  produced  ( s e e P l a t e 4.1)  t i m e was  not a l t e r e d The  density  images, resulted  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 H o w e v e r , t h e a c t u a l measurement p r o c e d u r e  with  intensity  d e t e r m i n i n g the  density s l i c e d  this  film  associated  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 from the colour p o s i t i v e s  diffuse  film.  developed at  that  f o r use i n t h e p r e s e n t s t u d y .  f i e l d measurement p h a s e o f t h e d a t a  collection  60  Wavelength  Figure  3.3  (nm)  F i l m and f i l t e r s p e c t r a l r e s p o n s e c u r v e s E q u a l e n e r g y c u r v e 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 S p e c t r a l r e s p o n s e o f f i l m and f i l t e r c o m b i n a t i o n  Ltd.)  . 33 presented i n this  s t u d y was  c a r r i e d o u t on 6 days o v e r t h e  period February 9 to February  26,  t o s e l e c t a p a r t i c u l a r day w e r e :  19 78.  The c r i t e r i a  (1) t h e w i n d v e l o c i t y d i d .  n o t a f f e c t a c t i n o m e t r i c m e a s u r e m e n t s , (2). would  designed  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  the weather  3 hours,  (3)  pattern the sky  c h a r a c t e r i s t i c s were such t h a t t h e 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 v e r t h e s t u d y p e r i o d on a v a r i e t y conditions. into  These s k y c o v e r c h a r a c t e r i s t i c s w e r e c a t e g o r i z e d  3 t y p e s , d e p e n d e n t on t h e t e m p o r a l s t a b l i l i t y  r a d i a t i o n regime. each  o f sky  Table  3-2  of the d i f f u s e  p r o v i d e s the sky c o n d i t i o n f o r  day on w h i c h m e a s u r e m e n t s w e r e r e c o r d e d . 3 hours  A l l measurements were t a k e n w i t h i n noon.  of solar  T h i s was t o a s s u r e t h a t any d e p e n d e n c e i n t h e 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  ( K o n d r a t y e v e t a l , 1955)  on z e n i t h  w o u l d be m i n i m i z e d  angle  (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 approximately  14 m i n u t e s  to acquire.  t i m e , 21  During t h i s  actinometric  m e a s u r e m e n t s o f d i f f u s e r a d i a t i o n were made o v e r t h e s k y h e m i sphere and 3 p a i r s o f photographs were a t 2.0, observation.  6.67  minutes  The  latter  from the b e g i n n i n g of  I n t h i s manner, .no • a c t i n o m e t r i c measurement  g r e a t e r t h a n 2.5 Pairs  a n d 11.33  were exposed.  minutes  of photographs  from a photograph  were t a k e n t o r e d u c e  was  o f sky c o n d i t i o n s . the p r o b a b i l i t y  of  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 p r o b l e m s . The e x p o s u r e built-in  o f the photographs  was  s e t by u s i n g t h e  l i g h t m e t e r i n g s y s t e m o f t h e Canon F - l .  Once  TABLE 3 . 2 . — O n s i t e s k y c o v e r conditions during the experimental p e r i o d , F e b r u a r y 9 - F e b r u a r y 26, 19 78  Date  9  Sky  Cover  3/10  altocumulus;  10  clear  14  10/10  stratus  15  10/10  stratus  24  1/10  26  clear  c u m u l u s ; 4/10  1/10  cirrus  altostratus  35 determined  at the beginning  of the f i l m ,  Because o f the l a t i t u d e o f the f i l m ,  i t was n o t a l t e r e d .  the v a r i a t i o n i nsky  c o n d i t i o n s o v e r t h e t i m e p e r i o d c o u l d be a c c o m o d a t e d .  With  t h e use o f o n l y one e x p o s u r e 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 , all  three negatives  c a n be i n t e r c o m p a r e d . .  This compatability  r e s u l t s i n a unique radiance  f o r each d e n s i t y .  radiance p a t t e r n i s changing  r a p i d l y , the photograph  nearest  T h u s , when t h e  a n a c t i n o m e t r i c measurement c a n p r o v i d e a  tative density f o r that radiance.  This  exposed  represen-  c a n t h e n be u t i l i z e d  on any p h o t o g r a p h w i t h i n t h e 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 to  produce a complete and a c c u r a t e  r a d i a n c e map o f t h e s k y  hemisphere. A single actinometric observation consisted of a p e r i o d o f 20 s e c o n d s d u r i n g w h i c h t h e m e t a l to  zero the instrument  s h u t t e r was u s e d  a n d 20 s e c o n d s when d i f f u s e  radiation  f r o m a n a r e a o f 0.025 s r was a l l o w e d t o i m p i n g e on t h e s e n s i n g element.  The f i r s t  t e n s e c o n d s o f t h e 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 The  sequence o f sensor  movement was k e p t  a t a g i v e n z e n i t h and  o r i e n t a t i o n s was s u c h t h a t  t o a minimum.  azimuth. actinometer  A r e g u l a r sampling  d e s i g n was  f o l l o w e d w h i c h 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 azimuthal or zenithal d i r e c t i o n per single observation. 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 a t 20°, and  80°  f o r a given azimuth.  The  40°, 6 0 ° ,  The a z i m u t h a l d i r e c t i o n was  then  c h a n g e d by 60° a n d 3 z e n i t h a l o b s e r v a t i o n s w e r e made a t 7 0 ° , 50° a n d . 3 0 ° .  The a n g u l a r  sequence o f z e n i t h a l measurements  36 was d e p e n d e n t on t h e 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 t h e 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.  Table  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 observations.  The s t a r t i n g a z i m u t h  a n d movement i n t h e  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 e a c h T h i s i s based, on a p r o c e d u r e  by S t e v e n  set of observations. ( 1977)  which i s  designed t o reduce b i a s i n g e r r o r s i n the data i fs e v e r a l s e t s of o b s e r v a t i o n s a r e combined.  During periods of observations  when t h e s o l a r d i s c was v i s i b l e ,  the sampling i n the hemispheric  s e c t o r o f t h e s u n was c a r r i e d o u t e v e r y measurements t a k e n a t each  azimuth  30°,  with 2 zenithal  ( T a b l e 3.3)-  Such a  sampling design provided a b e t t e r estimate of the exponential increase of diffuse radiation intensity  i n the s o l a r r e g i o n  o f t h e s k y h e m i s p h e r e t h a n d i d t h e 60° a z i m u t h a l  sampling  pattern. To r e d u c e  the problem  of o b j e c t s ( i n t h i s  3.6 3.6.1  r e g i o n w e r e made a t t h e same  were exposed  Photographic Joyce  Loebl  velocity  case, clouds)!near 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 photographs  of increased angular  (Table  time  3-3).  Digitization Microdensitometer  Reduction of the photographic negatives into a f o r m was a c c o m p l i s h e d Densitometer, The  u s i n g a Joyce  Loebl Automatic  M o d e l Mk I I I C , w i t h a n A u t o d e n s i d a t e r  digital  Recording attachment.  i n s t r u m e n t i s o f t h e double-beam, n u l l - p o i n t t y p e , h a v i n g  a repeatability  o f m e a s u r e m e n t s t o w i t h i n 0.5% o f f u l l  scale  TABLE 3 . 3 . — T y p i c a l s e q u e n c e o f a c t i n o m e t r i c measurements a n d p h o t o g r a p h i c e x p o s u r e s f o r s o l a r d i s c a t a z i m u t h 19 3° a n d z e n i t h 65°  Time  Azimuth  Zenith  00:00  0  80  00 : 40  0  40  01:20  0  60  02 :00  0  20  02:40  30 50  04:00  60 60 60  04:40  120  80  05 : 20 06 :00  120  40  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  300 300  60  03:20  14:00  70  80  Photographic Exposure  38 ( F r a s e r , 1978).  Detailed Information concerning the optics  o f t h e Mk I I I C c a n b e f o u n d i n I n s t r u c t i o n M a n u a l f o r 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 M o d e l Mk I I I C , ( J o y c e An o v e r v i e w  Loebl).  o f t h e 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 provided  (1978).  by F r a s e r The  servo-motors  Autodensidater.'.attachment  t o g e t h e r w i t h two  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 dimensions.  By p r o g r a m m i n g t h e l e n g t h o f  s c a n and t h e 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 microdensitometer i s able t o d i g i t i z e p o s i t i v e X direction..  g r i d points i n the  A t t h e end o f each s c a n i n t h e X  d i r e c t i o n , the microdensitometer a u t o m a t i c a l l y returns t o the o r i g i n o f X and i n c r e m e n t s t h e 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 c o m p l e t e d when t h e s u m m a t i o n o f Y i n c r e m e n t s the l e n g t h d i m e n s i o n The  o f Y.  d i g i t a l o u t p u t o f t h e m i c r o d e n s i t o m e t e r was o n  7 t r a c k ASCII n o - p a r i t y paper All  tape.  d i g i t i z a t i o n s were p e r f o r m e 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 .  using a 0 - 3 D  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 t h e same p h o t o g r a p h i c The  equals  d e n s i t y r a n g e was l i n e a r l y  divided into  exposure.  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 t h a n absolute 3.6.2  significance..  D i g i t i z a t i o n sampling considerations The  The  s a m p l i n g p r o c e d u r e was b a s e d on s e v e r a l  criteria.  minimum number o f p o i n t s t o b e s a m p l e d was d e p e n d e n t o n  39 the requirement  o f the computer's  p o i n t data base t o smoothly format was  ( C o u l t h a r d , 19 75).  g r a p h i c s - f o r a t l e a s t a 2500  interpolate  c u r v e s i n a 2.54 x 254mm  The maximum number o f d a t a p o i n t s  d e p e n d e n t o n t h e s i z e o f t h e a r e a o f t h e n e g a t i v e t o be  d e n s i t i z e d a n d t h e i n c r e m e n t b e t w e e n d e n s i t y measurements.. A l s o when c o n s i d e r i n g s a m p l e s i z e , t h e t i m e r e q u i r e d t o t a k e an i n d i v i d u a l measurement must be c o n s i d e r e d . . The  photographic  f i l m u s e d has  b e t w e e n 0.49um and 0.93um.  This l i m i t s  a grain size  range  the a v e r a g i n g  area  o v e r w h i c h 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 25um . 2  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  poorer  t h e r e s o l v i n g power o f t h e i n s t r u m e n t b e c a u s e o f t h e s m a l l amount o f l i g h t  i n c i d e n t on t h e p h o t o m u l t i p l i e r .  B u l l e t i n 54/8B (1954) s u g g e s t s  Joyce  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 b e . u s e d when i n t e g r a t i n g p h o t o g r a p h i c i n order t o reduce distribution.  the e r r o r i n t r o d u c e d by the g r a i n  The t h e o r e t i c a l u p p e r l i m i t  i n this  be t h e i n t e g r a t e d a r e a o f t h e o b s e r v a t i o n s o f t h e Actinometer  Loebl  a s r e p r e s e n t e d on t h e n e g a t i v e .  emulsions size  case  would  Linke-Feussner  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  illuminated  a r e a a v a i l a b l e o n t h e i n s t r u m e n t a n d i s t h e r e f o r e , o f no c o n c e r n . An i l l u m i n a t e d a r e a o f 75  x  75ym was a d o p t e d f o r t h e  study.  T h i s i s 225 t i m e s l a r g e r t h a n t h e minimum a v e r a g i n g a r e a , s o 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 required approximately  1 second per d e n s i t y  measurement u s i n g t h e above i l l u m i n a t e d a r e a .  A further  40 :  40 s e c o n d s was n e c e s s a r y  a t t h e end  of a l i n e  f o r the  densitometer t o r e s e t to b e g i n the next scan l i n e . t h e s e t i m e r e q u i r e m e n t s , i t w o u l d r e q u i r e 32 determine  covered.by  t h e 75  *  hours  75ym i l l u m i n a t e d  T h i s w o u l d p r o d u c e a d a t a b a s e o f o v e r 102 f o r each p h o t o g r a p h . d a t a p o i n t s was  The  to accurately  area of the n e g a t i v e . of  values  2629 p o i n t s w i t h i n t h e  This sampling procedure  d i g i t i z i n g i s approximately  400um i n  T h i s p r o v i d e d 3600 d a t a p o i n t s  g r i d and  of the t o t a l  Negative  area.  thousand  found t o r e s u l t i n a sample every  o v e r a 24 x 24mm s q u a r e  grid area.  The  per negative.  alignment  d a t a p o i n t ( ^,Y^) w i t h a unique X  on e v e r y n e g a t i v e .  T h i s was  the  designed to provide and i d e n t i f i a b l e  achieved through  location  the l o c a t i o n i n  a n d . z e n i t h o f a p o i n t on t h e n e g a t i v e , s u c h  a chord passing through concave through  the  time r e q u i r e d i n  1 h o u r 40 m i n u t e s  p h o t o g r a p h i c n e g a t i v e s , a method was  both azimuth  exposed  determined  To m a i n t a i n t h e r e q u i r e d c o m p a t a b i l i t y amongst  each  entire  most c o n v e n i e n t minimum number o f  b o t h t h e X and Y d i r e c t i o n s .  3.6.3  With  the d e n s i t y over the e n t i r e n e g a t i v e i f the  n e g a t i v e was  density  micro-  the o b j e c t b i s e c t s  the z e n i t h .  with respect to t h i s  the  that  celestial  A l l p o i n t s can then;foe d e f i n e d  axis.  From a k n o w l e d g e o f t h e z e n i t h a n g l e o f t h e o b j e c t and by  s e t t i n g the scan such t h a t a sampling p o i n t c o i n c i d e s  w i t h t h e same o b j e c t , a l l g r i d p o i n t s c a n be second  orthogonal  axis.  defined along a  To a f i x t h e n e g a t i v e template without slip  on t h e m i c r o d e n s i t o m e t e r ,  was c o n s t r u c t e d t o s e c u r e  t h e n e g a t i v e by t h e edges  c o v e r i n g t h e exposed p o r t i o n .  The u s e o f s u c h a  e l i m i n a t e s t h e e f f e c t s o f Newtonian Once t h e n e g a t i v e  a"'square  rings.  i s secure, the object with  known  position  c a n be l o c a t e d v i a t h e image p r o j e c t e d o n t o t h e  aperture  plate of the microdensitometer.  of the o b j e c t i s then  cover  Fine  alignment  f a c i l i t a t e d using stepping controls  i n t h e 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 alignment  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 o u t b y t e s t i n g t h e r a d i u s o f t h e n e g a t i v e p o s i t i v e and n e g a t i v e  X directions..  I t i s estimated  i n both that the  g r i d p o i n t s c a n be d e f i n e d t o w i t h i n ±25ym i n t h e X d i r e c t i o n and  t o w i t h i n ±10ym i n t h e Y d i r e c t i o n b y u s i n g t h i s  An e r r o r o f ±25ym r e p r e s e n t s z e n i t h and i n t h e azimuth w i t h i n the instrument aligned, i s less  l e s s than  a t 60°.  a 0.2° e r r o r i n t h e  Internal consistency  i n r e t u r n i n g t o t h e same p o s i t i o n ,  once  t h a n ±5ym.  In the present  study,  u n i q u e n e s s was t h e m e t a l  the o b j e c t used t o determine  support  of the  sensor.  was known t o be p e r p e n d i c u l a r t o t h e s u r f a c e . nature  method.  of the Fisheye  l e n s , a chord  This  Because o f t h e  drawn t h r o u g h any  object perpendicular t o the h o r i z o n t a l p r o j e c t i o n of the lens passes through  the zenith.  The a z i m u t h  w i t h r e s p e c t t o t h e c a m e r a was due e a s t . provided  t h e b a s i s f o r an e a s t - w e s t ,  d i r e c t i o n o f the post This  north-south  conveniently g r i d on t h e  negative. 3.7  Error  3.7-1  Analysis  Methodology The  follows the  a n a l y s i s performed to determine the  that  l a i d out  by  Cook and  e r r o r s i n components o f t h e  normally d i s t r i b u t e d , the a quantity  e  where  e  can be  =  ( ?  i =l  z  The  independent  and  3.3:  (3.3)  h  with  r e l a t i v e error associated  e r r o r s w i t h i n the  divided, i n t o three  the  measured  {%)  component o f t h e  with  the  measurement s y s t e m  i  t  h  (%)  p r e s e n t e x p e r i m e n t have been  components:  (1)  the  error associated  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 u s e d i n t h e  a t i o n of the involved  p h o t o g r a p h i c t e c h n i q u e , (2)  i n the  error associated  the  photographic negative,  with  Both of the 3 sections:  the  probable  the  first (1)  the  (3)  s u b s y s t e m s can be  error associated  e r r o r r e s u l t i n g from the  valid-  the  the r e l a t i v e  p h o t o g r a p h i c component o f t h e two  with  error  measurement o f d i f f u s e r a d i a n c e u s e d i n  c a l i b r a t i o n o f the  (2)  equation  = probable error associated  T  = the  into  system are  Assuming  x  quantity  the  R a b i n o w i c z (1963).  error  probable r e l a t i v e e r r o r i n measuring  d e t e r m i n e d by  .(e.) )  probable  with  further the  experiment. divided  sensor,  e l e c t r i c a l output s i g n a l ,  43 and  (3) t h e e r r o r i n t r o d u c e d b y d i g i t i z i n g a n a l o g  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  3.7.2.1  technique  Pyranometers The  relative  e r r o r s a s s o c i a t e d w i t h the Kipp  Zonen P y r a n o m e t e r s a r e f o u n d I n T a b l e to  data.  each o f the shortwave  f l u x because o f the  ( L a t i m e r , 1972).  shadow b a n d c o r r e c t i o n  These a r e  applicable  A f u r t h e r ±2% e r r o r i s  fluxes.  a s s o c i a t e d w i t h the d i f f u s e  3.4.  and  empirical  The r e l a t i v 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 F o r t h e measurement o f d i f f u s e r a d i a t i o n , t h i s  probable  (19 72) i s 3.6%. i s increased  t o 4.1%. 3.7.2.2  Normal I n c i d e n c e Eppley The  response  Pyrheliometer  n o r m a l i n c i d e n c e p y r h e l i o m e t e r has  o f ±0.5%  up t o 1400  Wm~ . 2  A f u r t h e r ±1%  a s s o c i a t e d w i t h the e r r o r i n alignment t h e s o l a r beam. of  a linearity of error i s  o f the instrument w i t h  This 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  2 s i g h t i n g diameters.  The t o t a l p r o b a b l e r e l a t i v e  error  i s 1.12%. 3.7.2.3  Recorder Two  Error  r e c o r d e r s were u s e d t o m o n i t o r  the d i f f u s e  t h e H o n e y w e l l . E l e c t r o n i k 194 and t h e C a m p b e l l CR5  I n t e g r a t i n g Recorder.  i c a t i o n were m o n i t o r e d The  Honeywell  r e c o r d e r has  ±0.25% o f s p a n o r l u v , w h i c h e v e r range used  f o r the d i f f u s e  Scientific  A l l o t h e r sensors used  on t h e C a m p b e l l  for verif-  S c i e n t i f i c CR5 a l o n e .  a reference accuracy o f  i s greater.  f l u x was  flux;  5 mv.  The f u l l  Therefore,  scale the  44  TABLE 3 . 4 . - — E r r o r summary f o r K i p p a n d Zonen (from Latimer, 1972)  Linearity  of response  Pyranometer  ±1%  Temperature response  (uncorrected)  ±5% ( a t 10° elevation) ±2.5%  Temperature response  (corrected)  ±1.5%  Cosine response  Overall  c o s i n e and a z i m u t h e r r o r  Overall probable error of instrument (temperature corrected)  ±3% ±  3.6%  absolute  e r r o r i s f o u n d t o be ±0.0125 mv. The  Campbell S c i e n t i f i c  accurately  a t i m e s p a n t o w i t h i n ±1 c o u n t . this  i sdirectly  convertible  over  By t h e manner o f i n t e g r a t i o n ,  to the absolute  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 . error of the recorder  integrates  error of the  Thus, t h e r e l a t i v e  i s dependent on t h e s i z e o f t h e i n p u t  signal. Table relative  3.5  provides  c a l c u l a t i o n s o f t h e absolute and  error f o r both recorders  r a d i a t i o n fluxes encountered. o f 200 Wm~  2  Electronik  over the range o f d i f f u s e  F o r a mean d i f f u s e  the probable error associated 194 i s ±0.55%.  with  i s ±0.44%.  a mean s h o r t w a v e i r r a d i a n c e o f 535 Wm  relative  error associated  ±0.16%.  Similarily,  650 Wm  t h e 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%.  -2  with  the  f o r t h e mean d i r e c t beam i r r a d i a n c e o f  i n the c a l i b r a t i o n o f the Data  2  the Campbell S c i e n t i f i c i s  d i s c r e p a n c y b e t w e e n t h e s e two e r r o r s  3.7.2.4  the Honeywell  F o r t h e same i r r a d i a n c e , t h e p r o b a b l  r e l a t i v e e r r o r f o rthe Campbell S c i e n t i f i c For  irradiance  The a p p a r e n t  i s due t o t h e d i f f e r e n c e  instruments.  Abstraction.  Data, recorded i n steady r a d i a t i v e c o n d i t i o n s , can be  easily abstracted  from a Honeywell s t r i p  chart  to within  +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  used above, t h e p r o b a b l e e r r o r a s s o c i a t e d  data'.-is ±0.50%.  with  as  the removal o f  TABLE 3 - 5 . — R e c o r d e r e r r o r w i t h  Instrument  Signal (Wm ) -2  Honeywell Electronik  194  Campbell S c i e n t i f i c  respect to diffuse r a d i a t i o n  Input (mv)  Absolute  (counts) E r r o r  Error  0.57  100  1.14  1.10  150 200 250 300  1.71 2.28 2.85 3.42  0.73 0.55 0.44 0.36  350  3.99  0.31 57  ±0.0125mv  Relative  50  50  .  signal  ±1 c o u n t  2.19  1.75  100  114  0.88  150 200  171 228  0.58 0.44  250 300  285 342  0.35 0.29  350  399  0.25  {%)  47 3.7-2.5  Total  Probable Error  Validation  i n the Photographic  System  For an average d i f f u s e i r r a d i a n c e , t h e probable r e l a t i v e error  i s calculated as:  eT  = ((4.1)2  + (0.55)  2  + (0 . 2 5 ) 2 ) 1 ' 2  (3.4)  = 4.14%  For a t y p i c a l incoming  shortwave i r r a d i a n c e , t h e  probable r e l a t i v e error i s :  e  T  s  = ((3.6)2  + {Q.l6) ) 2  (3.5)  h  = 3.61%  Finally,  f o r a n a v e r a g e d i r e c t beam i r r a d i a n c e , t h e  probable r e l a t i v e error i s :  £  T  s  = ((1.12) =  2  + ( 0 . 1 9 )2 )\h  1.13%  I t must b e n o t e d t h a t values.  (3.6)  2  For r e l a t i v e errors  these a r e f o r average associated  with  irradiance  constant absolute  e r r o r s , t h e s i z e o f t h e s i g n a l b e i n g measured i s i n v e r s e l y proportional  t o the size o f the r e l a t i v e error.  3.7.3  associated  3.7.3.1  Error  Linke-Feussner The  with  t h e measurement o f d i f f u s e  radiance  Actinometer  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 c o m m u n i c a t i o n ) . s m a l l f l u x e s h o w e v e r , R o b i n s o n (1966) q u e s t i o n s t h e  For  accuracy  o f t h e i n s t r u m e n t b e c a u s e no t e s t s h a v e b e e n p e r f o r m e d . more c o n s e r v a t i v e e s t i m a t e o f ±2% The  present  cavity  instrument  temperature  t h e r e f o r e been adopted.  i s not temperature  compensated  e r r o r o f 0.25%.  i n the alignment  A final  o f the system.  no t e s t s h a v e b e e n c a r r i e d o u t t o d e t e r m i n e of t h i s  error.  accuracy  and  c a n o n l y b e a s c e r t a i n e d t o ± 0 . 5 °C.  adds a f u r t h e r r e l a t i v e e r r o r i s found  has  the  though, probably  This  significant As o f y e t , magnitude  I t i s assumed t o be no g r e a t e r t h a n  of the sensor  the  b e t w e e n 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 components, the p r o b a b l e  e  = ((2) .+ (2) 2  T  =  3.7.3.2  was  error i s :  + (0.25) ) 2  (3.7)  h  Error  t o the very s m a l l f l u x e s b e i n g measured by the  actinometer, 194  2  various  2.84%  Recorder Due  relative  A  the  lOOuv.  full  s c a l e range o f the Honeywell  For t h i s range,  greater accuracy  Electronik  t h e r e c o r d e r c l a i m s no  i n r e c o r d i n g the i n p u t s i g n a l than  ±lyv.  T h u s , t h e 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 b e t w e e n ±1.25% f o r t h e most i n t e n s e f l u x e s and s i g n a l s on c l e a r sky days. approximately  up t o ±35% f o r t h e w e a k e s t  The l a r g e s t e r r o r s o c c u r  for  5% o f a l l d a t a , w h i l e t h e mean e r r o r a s s o c i a t e d  49 with recording 3.7.3.3  Data  i s 5%• Abstraction  The t r a n s p o s i n g data  0  f the d i f f u s e radiance  are s i m i l a r 'to that  - f o r '• d i f f u s e i r r a d i a n c e  The mean e r r o r a s s o c i a t e d w i t h  Is  measurementv values.  the a b s t r a c t i o n o f these  data  1.25%.  3.7.3.4  Probable E r r o r i n the Photographic 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 t h e measurement of d i f f u s e radiance graphic  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-  negatives I s :  e  = ( ( 2 . 8 4 ) •+ (5) 2  T  2  + (1.25) ) 2  (3-8)  35  = 5 - 88%  Once a g a i n  i t must b e n o t e d , t h a t t h i s  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 s an average e r r o r and  increase  significantly.  I n the case o f a r e c o r d e r  e r r o r o f 35%, t h e a b s t r a c t i o n e r r o r  w i l l b e 8.75%.  give a probable r e l a t i v e error f o r  the  This w i l l  s y s t e m o f 36.13%.  3.7.4  Errors i n photographic  3.7.4.1  Digitization This  i s the only p o r t i o n o f the photographic  i n w h i c h any p r e v i o u s Fraser  reduction  reduction  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 .  (1978) s t a t e s t h e r e p e a t a b i l i t y o f m e a s u r e m e n t s c a n  be g u a r a n t e e d t o 0.5% o f f u l l  scale,deflection.  Since  d e n s i t y m e a s u r e m e n t s a r e u s u a l l y u t i l i z e d as r e l a t i v e  the values,  50 only the r e l a t i v e 3.7.4.2  accuracy  Photographic The  o f t h e i n s t r u m e n t has  been p u b l i s h e d .  System  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  p o o r l y known.  Therefore, error analysis  system  i s intended to provide  o n l y a n o r d e r of. m a g n i t u d e e s t i m a t e o f t h e e r r o r I n t h e To  determine  apart.  system.  2 photographs  t h i s e r r o r f o r the e n t i r e system,  of a p a r t i a l l y  is  c l o u d y sky. w e r e t a k e n a p p r o x i m a t e l y  8 seconds  These were d i g i t i z e d u s i n g the n o r m a l 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 . forced through  the o r i g i n to determine  t h e o r e t i c a l 1:1 l i n e .  The  b e s t f i t l i n e was  the v a r i a t i o n from  the  The s l o p e o f t h e c u r v e was f o u n d 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 * and a c o r r e l a t i o n -1  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 t h e s l o p e  t h e 1:1 c u r v e i s a c o m b i n a t i o n system. was it  o f a l l s y s t e m a t i c e r r o r s i n the  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  found t o be s o s m a l l as t o be i r r e l e v a n t . . a p p e a r s t h a t a n e r r o r o f ±2% i s n o t  3.7.5  from  R e l a t i v e Probable  From t h e  above,  unreasonable.  E r r o r o f the Angular  Distribution  of D i f f u s e R a d i a t i o n The  above t h r e e subsystems a r e i n t r i c a t e l y  linked 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  first  subsystem provides the data w i t h which  r a d i a n c e v a l u e s are compared, the second values required to c a l i b r a t e system  system  the photograph,  i n d i c a t e s the confidence w i t h which  c a n be i n t e r p r e t e d .  the i n t e g r a t e d s e r v e s as, t h e  w h i l e the  the luminance  The t y p i c a l e r r o r i n t h e s y s t e m  third pattern  i s there-  51 fore a f u n c t i o n o f the t y p i c a l probable e r r o r s . l n the three subsystems:  eT  = ((4.14)2  +  (5.88)  2  +  (2) ) 2  (3-9)  h  = 7.46%  This  p r o b a b l e r e l a t i v e e r r o r i s a p p r o x i m a t e f o r an  a v e r a g e s e t o f measurements..  Nevertheless,  t h e magnitude  o f t h e 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 the  number o f i n s t r u m e n t s u s e d .  this are  i sa first  attempt a t t h i s  A l s o , when one c o n s i d e r s technique and that  possible, the error i s r e l a t i v e l y  this  error with  improvements  l o w . When c o m p a r i n g  the probable error o f the usual  determining diffuse r a d i a t i o n (4-2 it  considering  method f o r  4.6%) (Latimer,  i s o f t h e same m a g n i t u d e , y e t t h e p r e s e n t s y s t e m  1972), also  provides the angular 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 4 .1  Calibration  OF DIFFUSE  Technique  Theoretically  the radiance  can be r e l a t e d t o p h o t o g r a p h i c  F(6OJ)  =  from a s o l i d  negative  a n g l e (6co)  density by.the f u n c t i o n :  f { v , D}  (4.1)  F(6w) = the r a d i a n t i n t e n s i t y  where  RADIATION  v = atmospheric  from t h e s o l i d  a n g l e 6to  conditions  D = density n  f{e,  where  n ."x.,}  1=1  e = exposure IIX^  = product  of the properties of the  photographic  system  Since the c h a r a c t e r i s t i c s a r e unknown, sities  conversion of the density values  c o u l d o n l y be a c c o m p l i s h e d  radiant flux  o f many o f t h e s e v a r i a b l e s to actual inten-  by r e g r e s s i o n a g a i n s t m e a s u r e d  values.  Before  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  angle  c a l c u l a t i o n must be p e r f o r m e d .  •53 The  e q u i d i s t a n t l e n s used i n the data c o l l e c t i o n  area.  Thus, f o r a square  r e p r e s e n t e d by  preserves  sampling p a t t e r n , the s o l i d  angle  a single point i s :  6u) = 2ir/n  where  (4.2)  n = t h e number o f p o i n t s w i t h i n t h e e x p o s e d 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 of the hemis p h e r i c photographs the e q u i v a l e n t s o l i d angle by  e a c h p o i n t was 2.39 The  represented  *• 1 0 ~ s r . 3  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  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 t h e n e g a t i v e , t h e d e n s i t y o f 13 was  averaged..  The  angle  data p o i n t s  c e n t r e of 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 t h e r e s p e c t i v e a c t i n o m e t r i c observation. and  The  t h e r e f o r e 24%  a r e a r e p r e s e n t e d by  l a r g e r t h a n t h e a r e a s e n s e d by  T h u s , t h e a p p r o a c h p r o v i d e d some s m o o t h i n g o f t h e I n the a v e r a g i n g p r o c e s s , t o reduce f l a w s and  0.031  t h i s m e t h o d was the  actinometer.  data.  e r r o r s due  from the d e n s i t y value of the c e n t r a l p o i n t  was  instituted.  was  n o t f l a w e d , t h e number o f p o i n t s u s e d I n t h e  p r o c e s s was  to ±75  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 of  density units  sr,  In t u r n , to i n s u r e the mid-point  considered.  c e n t r a l p o i n t was  I f this  manually  v a l u e was  checked  and  itself averaging  l e s s t h a n 7,  I f necessary,  the  removed  54 and t h e a v e r a g e  recalculated..'  Two methods o f c u r v e f i t t i n g w e r e u t i l i z e d t o p r o d u c e 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 . analysis. statistical of  The i n i t i a l  method was n o n - l i n e a r  regression  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 :  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 t h e s i g n i f i c a n c e  t h e c o r r e l a t i o n and (2) t h e a n a l y s i s p r o d u c e d a  equation to the data.  hand.  "best-fit"  When a f u n c t i o n c o u l d n o t be f o u n d . t o  adequately describe the data, a b e s t - f i t  c u r v e was  drawn by  The c r i t e r i a u s e d i n c u r v e - f i t t i n g a r e d i s c u s s e d more  fully  i n Section  4.2.  The c u r v e - f i t t i n g p r o c e d u r e , w a s lating  the complete a c t i n o m e t r i c  averaged data sets  implemented  by  corre-  d a t a s e t w i t h each o f the  f o r the corresponding 3 photographs.  a p p r o a c h 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 w h i c h of  (1) t h e  The  consisted  t h e 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 t h e a v e r a g e d  d e n s i t y measurements from t h e n e a r e s t p h o t o g r a p h this  latter  case, the f i r s t  only..  7 a c t i n o m e t r i c measurements  In would  be p a i r e d w i t h t h e d e n s i t y m e a s u r e m e n t s d e t e r m i n e d f r o m t h e f i r s t photograph, 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 t h e second photograph and s i m i l arily. the l a s t the  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  t h i r d photograph.  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 t h e 'bombined t e c h n i q u e " . The r e s u l t s were i n c o n c l u s i v e .  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)  F o r c l e a r sky photographs, the best  statis-  .55 tical  f i t was f o u n d b y c o r r e l a t i n g t h e a c t i n o m e t r i c  measurements  w i t h t h e p h o t o g r a p h e x p o s e d midway, t h r o u g h t h e * measurement' •'" period  (Table  4.1).  method w e r e o n l y  The c o r r e l a t i o n s u s i n g t h e c o m b i n e d  slightly  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  t h o s e using:, e i t h e r t h e f i r s t set.  or l a s t photograph i n the data  I t appears t h a t i n t h e case o f very  s u c h as a c l o u d l e s s s k y ,  conditions,  t h e 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 t h e f i l m and i n t h e d e n s i t o m e t r i e gains  stable  made b y t h e c o m b i n e d  a n a l y s i s o f f s e t s any  technique.  I n s i t u a t i o n s where t h e c l o u d p a t t e r n o v e r t h e c e l e s t i a l dome was more c o m p l e x , t h e c o m b i n e d t e c h n i q u e superior.  T a b l e 4.1 a l s o p r o v i d e s  o f an e x p o n e n t i a l superiority however. rate.  an. e x a m p l e f o r t h e f i t t i n g  curve t o an o v e r c a s t  o f t h e combined t e c h n i q u e  Changes i n s k y c o n d i t i o n s  Thus, a l t h o u g h  was f o u n d t o be  sky c o n d i t i o n .  The  was n o t u n i v e r s a l , do n o t o c c u r a t t h e same  a measurement may h a v e b e e n made w i t h i n  m i n u t e s o f one p h o 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 photograph, reducing combined t e c h n i q u e .  This  t h e e f f e c t i v e n e s s o f t h e >.  problem i s d i r e c t l y  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  r e l a t e d to the  sample o f a c t i n o m e t r i c  measurements, o v e r a c o n t i n u a l l y c h a n g i n g s k y h e m i s p h e r e , v e r s u s the  instantaneousness  o f a photograph.  s i s t e n c y i n t h e combined t e c h n i q u e , individual 4.2  i t was d e c i d e d  that  c a l i b r a t i o n s f o r e a c h p h o t o g r a p h w o u l d be u t i l i z e d .  Curve F i t t i n g For  Because o f t h e i n c o n -  a data  Proceduress 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  significant  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 s k y ( 1 4 : 1 1 F e b r u a r y 26, 19 78) a n d a n o v e r c a s t s k y c o n d i t i o n (11:20 F e b r u a r y 1 4 , 1978)  Sky C o n d i t i o n  Clear  F Ratio  Coeffi cient of Determination  1  81.420  0.8358  2  117. 700.  0.8803  102.100  0.8645  101.400  0 . 8637  Photograph(s)  3 Combination 10/10 S t r a t u s  • 1 2 3 Combination  4.526  0.1924  0 .1919  0 .0100  6.874  0 .2657  30.830  o .6187  57 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 :  curve  i s d e f i n e d as h a v i n g  a t t h e 0.01 c o n f i d e n c e for  ( S o k a l a n d R o h i f , 1973).  level  Similarily,  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 a v e r a g e number  o f p o i n t s u s e d i n t h e 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 t h e number o f d a t a p o i n t s b e t w e e n t h e  obser-  vations o f radiance  values  and t h e c a l i b r a t i o n o f t h e d e n s i t y  was b e c a u s e t h e m e a s u r e d f l u x was e i t h e r t o o s m a l l o r t o o l a r g e to  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 t h e lOOuv s c a l e o r b e c a u s e d a t a p o i n t s were r e m o v e d as u n r e p r e s e n t a t i v e .  The r e m o v a l o f d a t a  occurred  when i t was f o u n d t h a t ' c e r t a i n p o i n t s d i d n o t f o l l o w t h e general trend o f the observation.  Figure  4.1 p r o v i d e s a n  e x a m p l e o f s u c h a c a s e f o r a c l e a r s k y day. d e c i s i o n was made s u c h t h a t a n i n t e r i o r  observation.point  which d i f f e r e d from the p r e d i c t e d radiance by  g r e a t e r t h a n 50% was r e j e c t e d . ±  was t h e n r e c a l c u l a t e d .  An a r b i t r a r y  f o r t h e same d e n s i t y  The r e g r e s s i o n  I f more t h a n  equation  two p o i n t s were f o u n d 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 . T h e r e were 2 r e a s o n s why u n r e p r e s e n t a t i v e might occur.  of the photograph.  o r during the d i g i t i z i n g  I n the c l e a r sky case, the v a l i d i t y  actinometric observation  o f S t e v e n (1977).  o f an  c o u l d be d e t e r m i n e d b y n o r m a l i z i n g  o b s e r v a t i o n and c h e c k i n g  butions  points  The f i r s t was b e c a u s e o f a n e r r o r i n m e a s u r e m e n t ,  either during observation o fradiance  the  data  i t against the u n i v e r s a l  I na l l other  cases o f t h i s  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 c a n be g i v e n .  distritype  The s e c o n d  Density Figure 4.1  I l l u s t r a t i o n o f the e f f e c t of the removal of an o u t l i e r f o r 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) C a l c u l a t e d EH = 58.562 Wm C a l i b r a t i o n curve w i t h o u t l i e r removed Calculated D-i- = 55-059 Wm A c t u a l D4 = 52.55 Wm 2  2  0 0  •59 reason f o r the r e j e c t i o n of a point that with given  i s b a s e d on t h e k n o w l e d g e  a rapid v a r i a t i o n i n hemispheric  conditions, a  a r e a may n o t be. r a d i a t i n g a t t h e same f l u x  density  when m e a s u r e d by t h e a c t i n o m e t e r as when p h o t o g r a p h e d . a d i f f e r e n c e i n values the  c a n o f t e n be r e c o g n i z e d  Such  by c o m p a r i n g  d i f f u s e i r r a d i a n c e observed 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. In determining radiance  butions.  c o u l d be f o u n d t o f i t a l l r a d i a n c e  distri-  I n t h e a t t e m p t t o f i n d s u c h a f o r m , i t was assumed  a significant  of that equation.to ance.  e q u a t i o n s used i n mapping  f o r t h e s k y h e m i s p h e r e , i t was h o p e d t h a t a common  form o f equation  that  the regression  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 t h e use p r e d i c t the angular d i s t r i b u t i o n o f r a d i -  T h u s , when a f o r m o f e q u a t i o n  was f o u n d t o be  significant  f o r one s k y 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 s k y conditions.  I f these also 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 radiance  values  w e r e p r e d i c t e d over t h e e n t i r e  hemisphere and t h e 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). was t h e n compared, t o t h e o b s e r v e d i r r a d i a n c e . y i e l d e d no s i n g l e f o r m o f e q u a t i o n irradiance  which adequately  f o r even s i m i l a r sky c o n d i t i o n s .  i n d i c a t i n g the complexity  This  This  attempt predicted  However, b e s i d e s  of the problem being  dealt with, 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 cases. This  methodology developed three  b a s i c g u i d e l i n e s by w h i c h  c u r v e s c o u l d be f i t t o t h e c a l i b r a t i o n d a t a :  (1) t h e c u r v e ,  60 if  determined  correlation (2)  u s i n g r e g r e s s i o n , a n a l y s i s , h a d t o have a  coefficient  I t was f o u n d  s i g n i f i c a n t a t t h e 0.01  t h a t i n n e a r l y a l l cases  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 tically  any r e g r e s s i o n  coefficient  t h a t was  statis-  s i g n i f i c a n t , y e t t h e 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 data  level.  little  ( F i g u r e 4.2).  p h y s i c a l resemblance t o the t r e n d o f the T h e r e f o r e , the curve a l s o had t o f o l l o w (3)  the g e n e r a l form o f the data b e f o r e b e i n g accepted.  It  was f o u n d t h a t t h e 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 entire  n e g a t i v e d i d not. a l w a y s  as t h o s e  densities  f o l l o w t h e same  used i n the c a l i b r a t i o n  distribution  curve.  I n such  cases, c e r t a i n points i n the c a l i b r a t i o n observations represented a l a r g e percentage  of density values.  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 t h e c a l i b r a t i o n  curve  predict  the r a d i a n c e a t t r i b u t e d , t o these  data p o i n t s a c c u r a t e l y  while 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 . .  illustrates  two c u r v e s , b o t h m e e t i n g  l i n e s b u t o n l y one o f w h i c h  F i g u r e 4.. 3  the f i r s t  meets - t h e t h i r d ,  two g u i d e f o r a c l e a r sky case.  By more a c c u r a t e l y p r e d i c t i n g t h e a r e a o f t h e c u r v e  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 , t h e e s t i m a t e d irradiance  c h a n g e s . f r o m 62.3  Wm  2  t o 59-9  s i g n i f i c a n t I m p r o v e m e n t as t h e o b s e r v e d  56 .5 Wm"  2  Wm  2  .  This i s a  irradiance  was  .  The l a s t two g u i d e l i n e s f o r t h e c u r v e subjectively  fitting  were  d e f i n e d as b e i n g met when t h e f o r m o f t h e c u r v e  f o l l o w e d t h e t r e n d o f t h e d a t a f o r o v e r 90% o f t h e r a n g e o f  1  h0 '  ,  /  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 X} correlation coefficient = 0.94 S t a t i s t i c a l l y significant correlation coefficient at the 0.01 level = 0.54 3  14  i:8% of population representee} by 5% df  0  120  calibration  data 10  01  80  16% of population represented by. 10% of c a l i b r a t i o n data  R  o crj •H  GO  40  20  2"0.0  (!  30  0  40  0  5 0  60  0  7 0  0  0  Density Figure  4.3  R e p r e s e n t a t i v e n e s s of s e l e c t e d data p o i n t s w i t h respect to 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 F e b r u a r y 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 curve which represents 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 o f 59.9 Wm 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  -2  -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  values.  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 n o t b e f o u n d t o adequately was  meet t h e s e  utilized.  The c u r v e  data attempting into  g u i d e l i n e s , a smooth h a n d - d r a w n f u n c t i o n followed the general trend o f the  t o i n t e r c e p t a s many p o i n t s a s p o s s i b l e t a k i n g  consideration the general s c a t t e r of the observations  and  the representativeness  was  then  o f each d e n s i t y v a l u e .  d i g i t i z e d and a p o l y n o m i a l  points.  f u n c t i o n f i t t e d t o these  The h a n d - d r a w n c u r v e was e x t r a p o l a t e d b e y o n d t h e  c a l i b r a t i o n data u s i n g the' knowledge o f p r e v i o u s fitted  The c u r v e  curves  found, i n s i m i l a r s i t u a t i o n s .  data d i d not s i g n i f i c a n t l y  statistically  Although, these  a f f e c t a large p o r t i o n of 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 uously density  defined, over terms.  t h e o p e r a t i n g range in'.both i n t e n s i t y and  The f i t t i n g o f t h e p o l y n o m i a l  drawn c u r v e was u t i l i z e d t o e x p e d i a t e both  the radiance  4.3  Verification, of Calibrations. To  fit  t o t h e hand-  the computation o f  f o r t h e t o t a l p o p u l a t i o n and t h e i r r a d i a n c e .  t e s t the p r e d i c t i v e a b i l i t y  o fthe r e s u l t i n g  best-  c u r v e s , t h e 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 u n i q u e r e l a t i o n s h i p b e t w e e n the: a n g u l a r d i s t r i b u t i o n of radiance  and t h e observed  diffuse irradiance.  T h u s , i f t h e c a l c u l a t e d i r r a d i a n c e .was f o u n d t o a p p r o x i m a t e the  observed,  the angular  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 S t e v e n (1977) f o r c l e a r s k y c o n d itions  overestimated  the observed  i r r a d i a n c e s b y a mean  64 e r r o r o f 6%. In the present  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 t h e 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 a n d t h e 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 . i n t e g r a t i o n , the five  Before the  density values nearest to the p o s i t i o n  o f t h e s o l a r d i s c were removed.  T h i s was t o a v o i d c o n t a m -  i n a t i o n by d e n s i t y m e a s u r e m e n t s w h i c h m i g h t i n t u r n be i n f l u e n c e d by e i t h e r t h e o c c u l t i n g d i s c , when p r e s e n t , o r lens f l a r e  associated with-the  represent a s o l i d angle s u n was o b s c u r e d  solar disc.  These f i v e  points  o f 0 . 0 1 1 s r . , I n t h e c a s e s where t h e  by c l o u d s , t h e s e p o i n t s w e r e n o t r e m o v e d .  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 u s e d t o r e l a t e r a d i a n c e and t h e i r r a d i a n c e f o r a h o r i z o n t a l s u r f a c e 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  p  where.  n = E L. • c o s 0 . 1=1 x  x  (1977):  (4.2)  • Sco  D+p = 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 surface  \  =  radiance  (Wm ) -2  from the p o i n t i  (Wm  - 2  sr  - 1  )  6co = s o l i d a n g l e r e p r e s e n t e d by e a c h d e n s i t y ( s r ) 0. = z e n i t h a n g l e  In the present  f o r each r a d i a n c e v a l u e  form,  equation  (radians)  4 . 3 assumes t h a t t h e  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 dings.  A study  d e s c r i b e d i n Chapter  surroun--.  Six indicates this  is a  65 reasonable  assumption.  Because o f the time r e q u i r e d t o d i g i t i z e  each  p h o t o g r a p h , t h e t e c h n i q u e h a s b e e n t e s t e d on o n l y 30 s e t s o f f i e l d o b s e r v a t i o n s . ology  f o r determining  t h e s e 11 d a t a  On t h e b a s i s  a best-fit  individual  11 o f t h e  o f t h e method-  ( S e c t i o n 4.2),  curve  sets p r e d i c t e d the h o r i z o n t a l surface  9 of diffuse  i r r a d i a n c e t o w i t h i n ±10% o f t h e o b s e r v e d i r r a d i a n c e . t h e s e 95 5 were p r e d i c t e d f o l l o w i n g t h e i n i t i a l ( S e c t i o n 4.2)  and t h e f u n c t i o n found t o b e s t  i r r a d i a n c e was e x p o n e n t i a l .  1978  and 2 p a r t i a l l y  cloudy  13 = 37 f o r F e b r u a r y 15,  1978.  a n d 14:11  the  f o r F e b r u a r y 26, 13=17  D a t a f o r 13:22. F e b r u a r y  i n v o l v e s t h e u s e o f t h e same a c t i n o m e t r i c s e t of observations..  p r e d i c t the  sets of observations  were a l s o found, t o f o l l o w a n e x p o n e n t i a l  13:17  procedure  The 5 c o n s i s t e d o f 3 c l e a r s k y  13:26, 13:47  sets of observations,  Of  The v a l u e s  form o f the curves f o r a l l data  curve, data  and 15  but.this as f o r t h e  of the constants  sets  and  c a n be f o u n d i n  A p p e n d i x 2. The two d a t a  s e t s , w h i c h n e c e s s i t a t e d t h e more  c a l i b r a t i o n methodology and s t i l l t o w i t h i n ±10% w e r e t a k e n d u r i n g conditions. agreement. while  elaborate  d i d not p r e d i c t i r r a d i a n c e fluctuating radiation  T h i s , may be p a r t i a l l y  responsible  One c a s e was f o r a p a r t i a l l y  t h e o t h e r was f o r a n o v e r c a s t  cloudy  situation.  f o r the poor condition, In the . f i r s t  c a s e , F e b r u a r y 2 4 , i t was f o u n d t h a t a l a r g e p e r c e n t a g e o f the  actinometric  observations  occurred  within a small  range  66  of density values 11:47  14,  February  variability  (Figure A2.9). no  I n the second  case,  further explanation concerning  i n the d i f f u s e  irradiance  c a n be  the;temporal  o f f e r e d at  this  time. Table observed  4.2  diffuse  a n a l y s i s was  p r o v i d e s a comparison irradiance  performed.  estimate of diffuse in  computed  and  f o r e a c h d a t a s e t on w h i c h  the  The  d i f f e r e n c e i n the q u a l i t y  irradiance  the goodness o f f i t o f the  This i s p a r t i c u l a r l y t h e r e was  the case  i s a result curve  f o r 12:47  seen i n l i g h t (Section  o f the probable  3-7.5).  e M c a l h o r i z o n on  relative  data.  where  calibration  data  the case  form  form  values.  to  c a n n o t be  This  Thus,  the  was  although  used I n d e t e r m i n i n g  radiance, calibration  o f the d a t a p o i n t s can produce  radiance d i s t r i b u t i o n s  be  s u r f a c e s above t h e t h e o r ^ " '  o f the observed  d i s t r i b u t i o n of diffuse  f i t the  e r r o r i s due  calculated irradiance.  of equation  must  7.46%  e r r o r of  Further, part of this  c o n s i d e r e d on t h e  a single  4.4  15,  e r r o r i s v e r y s m a l l and  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  that  the  variation  calibration  February  a l a r g e s c a t t e r o f p o i n t s i n the  O v e r a l l the r e l a t i v e  angular  t o the  of the  of  A2.5).  (Figure  not  of the  the  curves  useful  f o r i n d i v i d u a l sky c o n d i t i o n s .  Application S i n c e the prime o b j e c t of t h i s  s t u d y was  to  the angular 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 , the are presented  i n two  f o r m s o f map.  The  first  map results  presented,  TABLE 4 . 2 . — C o m p a r i s o n of. m e a s u r e d a n d 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  (LAT)  Computed  D4-(Wm~ ) 2  12: 40  Feb . 10  clear  13: 40 11: 20  Feb . 10  clear  Feb . 14  10/10St  12: 30 12: 47  Feb . 14  10/10St  Feb . 15 Feb . 15  8/10Ac  13: 17  Actual  13: 22 Feb . 13: 47 . Feb . 10 : 07 Feb . 13: 26 Feb .  4/10Ac3/10Ci  15 15  4/10Ac3/10Ci  24  l/10Ac5/10As3/10Ci  3/10Acl/10Ci  26  clear  13: 47  Feb . 26  clear  14: 11  Feb . 26  clear  65 .730 56 .480 88 .566 63 .346 291 .657 162 .552 141 .118 91 .561 199 .108 52 .550 51 .590 49 .680  Absolute  D+.(Wm~ ) D i f f ( W m " ) 2  .467 . 59 .896 76 .199 62 .090 . ' 6 8  265 .807 167 .802 129 .481 90 .586 165 .000 55 .059 50 • 715 49 .088  2  2 .737  3 .416 12 .367 1 .256 25 .850 5 .25 11 .637 0 .975 34 .10 8  % Difference  4 .16 6 .05 13 .96 : 1.98 8 .86 3 .23 8 .25 1 .06  2 • 509  17 .13 4 • 77  0 .875  1 .70  0 .592  1 .19  68 a r e r a d i a n c e maps f o r t h e s k y h e m i s p h e r e as s e e n o n a n The i s o l i n e s r a n g e b e t w e e n 5 a n d  equidistant projection. 130 W m ~ s r 2  60,  - 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, 4 0 ,  80., a n d 105 Wm  the best cloudy  2  sr  _  1  .  These v a l u e s w e r e f e l t  coverage o f the c e l e s t i a l  conditions.  dome f o r b o t h  t o provide c l e a r and  The i r r e g u l a r s t e p s p r o v i d e t h e 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 low r a d i a n c e v a l u e s 90° f r o m around the s o l a r  t h e sun and t h e h i g h  t h e very values  disc.  The s e c o n d 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 normalized  maps u s i n g t h e 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 in  (19 75).  The c l e a r sky. maps  t h i s form a r e d i r e c t l y comparable t o those  The i s o l i n e s were s e t 0.5 s r  -  1  presented  o f Steven  (1977).  apart, s i m i l a r t o those o f  Steven. Both pL.tter  s e t s o f maps w e r e drawn on a n e l e c t r o m e c h a n i c a l  ( C o c k l e , 1976) w i t h i n d i v i d u a l p e n movements o f  0.254mm i n t h e X a n d Y d i r e c t i o n s direction. larger  T h e s k y r a d i a n c e maps p r e s e n t e d  than the o r i g i n a l photograph.  data p o i n t s approximately program u t i l i z e d simple  a n d 0.359mm i n a d i a g o n a l  2.5mm a p a r t .  a r e 6,63. t i m e s  This spaces  individual  The c o n t o u r i n g ,  i n t h e i s o l i n i n g ( C o u l t h a r d , 1975)' uses  a  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 t h e c o n t o u r . movements,  The c o m b i n a t i o n  o f the d i s c r e t e pen  t h e s p a c i n g between data p o i n t s and t h e i n t e r p o l a t i o n  technique w i l l  p r o d u c e a c u r v e 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, h o w e v e r , c a n n o t be To q u a l i t i t i v e l y  bility  due  determine the h i g h  ascertained.  frequency  varia-  t o the methodology used i n . p r o d u c i n g ' t h e s e  maps,  a c o m p a r i s o n was  made b e t w e e n 2 c l e a r s k y  i n d i f f e r e n t manners..  P l a t e 4.1  t a t i o n of the n e a r l y  c l e a r sky  S e p t e m b e r 10,  T h i s was  19 77.  d e n s i t y s l i c e r and colour represents c o l o u r , the  easily  days d e n s i - t i z e d  i s a false  colour  luminance p a t t e r n f o r  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 . a region of s i m i l a r density  g r e a t e r the  1978).  Hay,  the  Each  (the darker  d e n s i t y of the p o s i t i v e ) , w h i l e  Though t h e  and w h i t e s t , r e g i o n s  d e n s i t y r a n g e c o u l d n o t be  adequately  the  deter-  of'the photograph,  of the p l a t e are  the  (MeArthur  electronic density s l i c e r  mines d e n s i t y o v e r t h e e n t i r e a r e a darkest  14:00  p r o d u c e d u s i n g an e l e c t r o n i c  b o u n d a r y 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 and  represen-  the  areas i n which  d i s p l a y e d by  this  technique. Figure 14:07  February  mechanical  4.4  i s the  c l e a r sky  19 78.  T h i s was  10,  radiance t r a c e d by  computerized density  produces a " t r u e " d i s t r i b u t i o n o f sky to determine the due  previous  the e l e c t r o -  plotter.  I f i t i s assumed t h a t t h e  solely  pattern for  to the  l u m i n a n c e , one  slicer i s able  f r e q u e n c y above w h i c h t h e v a r i a t i o n i s c o m p u t e r i z e d mapping t e c h n i q u e .  work ( S t e v e n ,  1977)  has  Although  p r o d u c e d 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  d i s t r i b u t i o n o f l u m i n a n c e and  radiance  the  respectively, indicate  70 N  E  S  F i g u r e 4.4  Diffuse radiance d i s t r i b u t i o n f o r a clear sky (13:40 February 10, 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 (VJm~ sr- ) (Z = 6 7 . 6 ° ) 2  1  PLATE  4.1  .Electronically all-sky  photgraphic  S e p t e m b e r 1 0 , 19 77  density  sliced  image o f  14:00  73 that this  i s not the case.  apparently  c a u s e d by  Only  i n d i v i d u a l pen  found i n the e l e c t r o n i c a l l y bution.  I t i s observed  the d a r k e r areas intensity  the s m a l l e s t p e r t u r b a t i o n s , movements, a r e n o t  density sliced  o f the sky h e m i s p h e r e , areas  are found w i t h i n areas  on t h e e l e c t r o n i c a l l y p r o d u c e d due  t o the presence The  remain sky  reality  i s apparently  image ( t o p  left  of t h i s  e t a l , 1962)  c l e a r s k y p a t t e r n may  for this  measurement was  study.  4.1)  still  of the  and  the m u l t i p l e s c a t t e r i n g  However, at t h i s  apparent  the q u a l i t y  clear theory approx-  t i m e , t h e r e i s no  to doubt the t e c h n i c a l a s p e c t s o f the work.  p o s s i b l e reason  found  , Plate  d i s t r i b u t i o n of radiance using single s c a t t e r i n g  reason  It  of cloud.  i m a t i o n s o f Dave ( 1 9 7 5 ) .  and  of greater  of l e s s e r i n t e n s i t y .  i n q u e s t i o n w i t h r e s p e c t to the r e s u l t s  (Atroshenko  distri-  i n b o t h methods o f m a p p i n g t h a t i n  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  is  luminance  also  One  c o n t r a d i c t i o n between  theory  o f the f i l m s used i n the  T h i s i s u n l i k e l y , h o w e v e r , as b o t h  films  behaved  s i m i l a r l y , and  t h e method e m p l o y e d ( 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  l a r g e r p e r t u r b a t i o n s cannot 4.4.1  be  otherwise,  these  ignored.  Case s t u d i e s Of t h e t e n d a t a s e t s upon w h i c h  this  study  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 ;  i s based,  2 are  for totally  o v e r c a s t s i t u a t i o n s , w h i l e the remaining  3 r e p r e s e n t t h e more  complex p a r t i a l l y  i s o f so much  cloudy  c o n d i t i o n which  interest.  74 The  reason  f o r t h e l a r g e number o f c l e a r s k y  cases  i s to  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 w o r k ; p r e s e n t , one are  c a n o n l y assume t h a t i f t h e s e  At  c l e a r sky  cases  c o m p a r a b l e , t h e o t h e r more c o m p l e x d i s t r i b u t i o n s  a l s o r e a l i s t i c , w i t h i n the accuracy  w i t h which they  are are  prepared. Plates corresponding expected,  4.2  -  4.4  provide the photographic  t o F i g u r e s 4.4  the p a r t i a l l y  t o 4.6  f a r t h e most c o m p l e x , w h i l e t h e  is  f o r the o v e r c a s t s i t u a t i o n  radiance  f i g u r e s one  r a d i a n c e i s found with intensity  In. t h e  least  i s able to note  90°  approximately  distribution intercomparing  change i n t h e  clear to t o t a l l y  c l e a r sky. case, the  is  least  overcast  intense  from the s o l a r  disc  i n c r e a s i n g from t h e r e out t o the h o r i z o n .  i n f l u e n c e d by  1971).  By  the  This increase follows a nearly e l l i p t i c a l is  As  complex  ( F i g u r e 4.6).  d i s t r i b u t i o n from t o t a l l y  sky c o n d i t i o n s .  respectively.  c o n d i t i o n ( F i g u r e 4.5)  cloudy  by  these three  images  the  pattern until i t  c i r c u m s o l a r r e g i o n ( M o r r i s and. L a w r e n c e ,  At t h i s p o i n t , the i s o l i n e s  a r e i n f l u e n c e d more by  of radiance  (isorads)  t h e 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 , a r o u n d t h e s u n . This i s p a r t i c u l a r l y illustrated In intensity  4.1.  in. Plate  the p a r t i a l l y occurs  overcast  c o n d i t i o n , the  i n t h e same r e g i o n .  o f t h e i n t e n s i t y has  well  i n c r e a s e d due  e f f e c t of the water d r o p l e t s .  The  lowest  However, the  t o the g r e a t e r intensity  magnitude scattering  increases  both  PLATE * at  A l l - s k y photograph 14:07  exposed  F e b r u a r y 10, 19 78 o f a  c l e a r sky. the  4.2  Figure  sky r a d i a n c e  from the exposed  4.4  map  provides produced  negative.  w  E  N  ORIENTATION OF PHOTOGRAPHS  PLATE 4 . 3 A l l - s k y photograph a t 13:17 partially provides  F e b r u a r y 15, overcast  exposed 19 78  o f an  sky. Figure  the sky r a d i a n c e  produced form the exposed  4.5  map negative.  PLATE  4.4  A l l - s k y photograph a t 12:30  F e b r u a r y 14,  completely  exposed 1978.  of a  overcast sky. Figure  4.6  p r o v i d e s the sky r a d i a n c e  map  produced  negative.  from the exposed  82  F i g u r e 4.5  Diffuse radiance 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 l o u d y s k y (13:17 F e b r u a r y 15, 19 78) as p r o d u c e d f r o m t h e p h o t o g r a p h i c n e g a t i v e ( W m s r - ) (Z = 6 4 . 5 ° ) _2  1  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 s k y (12:30 F e b r u a r y 1 4 , 19 78) as p r o d u c e d f r o m t h e p h o t o g r a p h i c n e g a t i v e ( W m - s r - ) (Z = 6 3 . 0 ° ) 2  1  84 t o w a r d s t h e h o r i z o n a n d t h e s o l a r d i s c , b u t n o t i n t h e same c o n s i s t e n t p a t t e r n as t h e c l e a r s k y c a s e .  In a d d i t i o n , the  area around the s o l a r d i s c i s not the only area o f the hemis p h e r e where r a d i a n c e i s g r e a t e r t h a n illustrates  the high r e f l e c t i v i t y  130  Wm sr~ . _ 2  1  This  o f c l o u d s and t h e added  complexity 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 irradiance.  O v e r a l l , t h e g r a d i e n t has d e c r e a s e d  l e a s t i n t e n s e a n d most i n t e n s e r a d i a n t a r e a s  between the  of the  celestial  dome . For the overcast almost  completely  even e v i d e n t .  .(.1969) s t a t e s ,  i s n o t m a r k e d enough a n d 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  zenithward  observed". Although  the i s o t r o p i c  t h e above c a s e s , F i g u r e 4.6 the a p p r o x i m a t i o n of the sky. illustrated 4.4.2  " t h a t { f o r } a dense  c l o u d i n e s s , t h e a z i m u t h a l dependence o f d i f f u s e  radiation intensity  is  t h e g r a d i e n t has  d i m i n i s h e d and t h e s o l a r p o s i t i o n i s n o t  Kondratyev  non-transparent  ( F i g u r e 4.6),  case  a s s u m p t i o n i s n o t met i n any o f  i n d i c a t e s t h a t f o r dense c l o u d  i s reasonably  v a l i d over  the c e n t r a l p o r t i o n  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 as n o t b e i n g t h e  Normalized  case.  distributions  A t 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 d a t a : i s as f l u x e s n o r m a l i z e d  t o t h e 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  horizontal surface.  I n the case  a l l measurements were e f f e c t i v e l y  of the photographic  technique,  taken instantaneously.  Therefore,  85photo-  the i r r a d i a n c e measured a t the time o f the  g r a p h i s used, as t h e n o r m a l i z i n g p a r a m e t e r .  This  p r o b l e m i n v o l v e d i n t h e work o f S t e v e n (19 77)  avoids  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 over the p e r i o d , the  observation.  Although t h i s  Figures 4.7 radiance  presented iately  by  t o 4.11  present  be  5 c l e a r sky  the  d i s t r i b u t i o n s , comparable to the ( F i g u r e . 2 . 5 and  Steven((1977)  n o t i c e s the g r e a t e r t h e more g e n e r a l  f a c t not  considered  to the r e l a t i v e l y  complexity  small i n factor  p o i n t s and  distributions One  of the present The  immedwork,  main  i s the magnitude o f  near the h o r i z o n . few  normalized  2.7).  agreement i s good.  S t e v e n , (19 77)  by  increase i n brightness  he  may  conditions.  although  due  difficulty  c a s e o f c l e a r s k i e s , i t w o u l d become a l i m i t i n g  f o r more v a r i a b l e s k y  sky  or  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 -  metric the  the  T h i s may  the  be  the  partially  sampling design  that  used. When c o n s i d e r i n g t h e two  2 = 55°)  and  f o r Z = 65°  the  d i a g r a m s o f S t e v e n (Z =  g e n e r a l p a t t e r n of the normalized  ( F i g u r e 4.11)  as a p r o g r e s s i o n ,  a p p a r e n t d i f f e r e n c e s can be  explained.  angle  i n c r e a s e s , i t appears that the  1.0  -  sr :  1  isoline  the r e g i o n of the  :  changes f r o m b e i n g  As  distribution  a number o f the s o l a r z e n i t h  general  form of  circumsolar to  s o l a r path i n c r e a s e s , the  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  the  encompassing  sky hemisphere o f l e a s t i n t e n s i t y .  i n d i c a t e s t h a t as t h e  35°,  This  limb b r i g h t increase  in  "86  F i g u r e 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 ( s r ) f o r 12:40 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 = 64.5°) x  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 distribution (sr ) for 13:40 F e b r u a r y 10, 1978 as p r o d u c e d f r o m t h e p h o t o g r a p h i c n e g a t i v e (Z = 6 7 . 6 ° ) _ 1  Figure 4.9  Clear sky normalized sky radiance distribution ( s r ) for 13:26 February 26, 1978 as produced from the photographic negative (Z = 61.0°) _1  Figure  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 distribution (sr- ) for 13:26 F e b r u a r y 26, 1978 as p r o d u c e d f r o m t h e p h o t o g r a p h i c n e g a t i v e {Z = 6 1 . 0 ° ) 1  Figure  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 ) f o r 13:4 7 F e b r u a r y 26, 19 78 as p r o d u c e d f r o m t h e p h o t o g r a p h i c n e g a t i v e (Z = 62.8 l  )  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 F e b r u a r y 26, 1978 as p r o d u c e d f r o m t h e p h o t o g r a p h i c n e g a t i v e "(Z = 6 5 . 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 ,  t h e magnitude o f t h e i s o l i n e  closest t o the'solar disc increases with the increase i n the s o l a r zenith angle.  This  a l s o i s e x p e c t e d due t o t h e i n c r e a s i n g  s c a t t e r i n g mass a n d t h e 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 t h e s o l a r d i s c . As  the s o l a r z e n i t h angle  of c l e a r sky radiance by  Figure  angles  becomes more c o m p l e x .  This  a r e 55°,  continuous  6 l ° , 6 2 . 8 ° a n d 65° r e s p e c t i v e l y .  isolines.  However, by a s o l a r z e n i t h angle  the 5 s r ~ - circumsolar  isoline  i s continuous.  -  1  isoline  i n Figure  w h i l e w i t h a 6° i n c r e a s e discontinuous  by  i n solar zenith (Figure  -  1  I n t h e norm-  are observed.  2.7 i s s e e n t o be c o n t i n u o u s ,  a n d i n f l u e n c e d b y limb, b r i g h t e n i n g .  ( F i g u r e 4.10), t h e 5 s r  isoline  s c a t t e r i n g near the h o r i z o n .  65°  ( F i g u r e 4.11), t h e i n c r e a s e d  the  large optical  4.8), i t i s By Z = 6 2 . 8 °  i s a l s o found t o be a f f e c t e d With a s o l a r z e n i t h angle o f s c a t t e r i n g o f r a d i a t i o n due t o  a i r mass commences t o d o m i n a t e t h e s c a t t e r i n g  w i t h i n the circumsolar region i n d i c a t i n g i t s eventual b r e a k d o w n ( M o r r i s a n d L a w r e n c e , 1971). angle  of 6l°,  greater than Z = 6l° (Figures  4.9 a n d 4.10), no c o n t i n u o u s , c i r c u m s o l a r i s o l i n e s 4.5 s r  Fora solar  o f . 5 5 ° t h e 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  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  The  i s illustrated  2.7 a n d . F i g u r e s 4.9 t o 4.11 where t h e s o l a r z e n i t h  z e n i t h angle  only  approaches 90°, t h e p a t t e r n  increases, the d i f f u s e radiance  As t h e s o l a r z e n i t h emanating from t h e  r e g i o n about t h e h o r i z o n i s an i n c r e a s i n g l y percentage o f the d i f f u s e i r r a d i a n c e .  total  significant  92 Though, f o r t h e d i f f u s e r a d i a t i o n maps f o r c l o u d y c o n d i t i o n s , no d i r e c t  c o m p a r i s o n c a n be made w i t h  previous  r e s u l t s , a few p o i n t s a r e n o t e w o r t h y n o n e t h e l e s s . f o r an o v e r c a s t  condition, illustrates  Figure  4.12,  t h a t there 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 - o v e r t h e c e l e s t i a l dome f o r heavy c l o u d . is  The s i m p l i c i t y  of this  radiance  i n d i r e c t contrast to the radiance  partially  cloudy  Figures cloudy  sky (Figure  distribution of a  4.13).  4.13 t o 4.15 i l l u s t r a t e ,  for a partially  s k y h e m i s p h e r e , t h e 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  gradients  found between c l e a r sky and r e l a t i v e l y u l a r l y ; near the s o l a r d i s c . radiance  Figure  i n these  thin clouds,  4.13  p a t t e r n f o r a sky c o n d i t i o n o f broken  sky remains c l e a r , w h i l e  maps a r e partic-'  i l l u s t r a t e s the  i n the c e n t r a l p o r t i o n o f the sky hemisphere. the  distribution  altocumulus' To t h e w e s t ,  sweeping around the h o r i z o n  from t h e northwest t o the east,: i s a band o f a l t o s t r a t u s . Gne-half hour l a t e r altostratus extending the  ( F i g u r e 4.14), a l a r g e b a n d o f t h i n  i s c o v e r i n g t h e r e g i o n o f t h e s o l a r d i s c and  eastward around the h o r i z o n .  east, i t begins  As i t a p p r o a c h e s  t o b r e a k up, becoming a l t o c u m u l u s .  c e n t r a l p o r t i o n o f the sky i s a mixture altocumulus  and c i r r u s  cloud.  band o f a l t o s t r a t u s remains.  of clear sky, thin  On t h e n o r t h e r n h o r i z o n , a By 13:37, t h e c e n t r a l p o r t i o n  of the sky hemisphere i s c l e a r , w h i l e r i n g the eastern horizon.  The  The t y p i c a l  a l t o s t r a t u s clouds c l e a r sky radiance  93  F i g u r e 4.12  Overcast 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 p r o d u c e d f r o m t h e p h o t o g r a p h i c n e g a t i v e (Z = 63.2°)  94  Figure  4.13  P a r t i a l l y overcast sky; normalized distribution (sr ) for 12:47 F e b r u a r y 15, 19 78 as p r o d u c e d f r o m the photographic n e g a t i v e . ( Z = 63-1°) l  95  F i g u r e 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 ) f o r 13:17 February 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-64.5 ) 1  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~ )•13:47 F e b r u a r y 15, 1978 as p r o d u c e d 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°) 1  97 pattern  i s now b e g i n n i n g t o emerge.  disc i s also the  c l e a r , but altocumulus  sun and t h e z e n i t h .  problems i n v o l v e d  The r e g i o n  of the s o l a r  clouds are found between  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  i n modelling diffuse irradiance  accurately.  Combined, they a l s o  indicate  the temporal 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 irradiance  over  diffuse  time.  The d a t a p r e s e n t e d i n t h i s s t u d y are p o t e n t i a l l y  useful  i n a i d i n g i n t h e s o l u t i o n o f b o t h t h e 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 . is  felt  that  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  i n energy u t i l i z a t i o n  models c o n c e r n e d w i t h  diffuse radiation incident  on n o n - h o r i z o n t a l s u r f a c e s .  the d i s t r i b u t i o n information  on s e v e r a l  south-facing  surfaces.  found  t h e amount o f  an e x a m p l e o f s u c h an a p p l i c a t i o n , C h a p t e r F i v e use  However, i t  As  attempts to  t o e s t i m a t e incoming energy  CHAPTER F I V E MODELLING DIFFUSE RADIATION ON SLOPING SURFACES 5.1  Modelling To  Technique  determine the t o t a l shortwave r a d i a t i o n  on a n 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 considered;  incident  components must be  t h e d i r e c t beam r a d i a t i o n , t h e d i f f u s e  radiation  emanating from t h e sky hemisphere and t h i r d l y , t h e r a d i a t i o n r e f l e c t e d from adjacent The radiation  conversion  disc  S+  where  o f t h e n o r m a l i n c i d e n c e d i r e c t beam  t o t h a t f o r a n i n c l i n e d s u r f a c e was  using the geometric solar  surfaces.  relationship  between the p o s i t i o n  and t h e normal t o t h e s l o p e  = I.cos  (Sellers,  where  1965):  (5.1)  - surface :  incident  on a  sloping  (Wm ) -2  I = normal Incidence cos  of the  i  S4- = d i r e c t s h o r t w a v e r a d i a t i o n s I  accomplished  d i r e c t beam r a d i a t i o n  (Wm  i = cos s ••• c o s z + s i n s • s i n z • cos ( a - b ) s = angle  of slope  z = zenith  angle  (radians)  of radiation  a = azimuth  of radiation  b = azimuth  of slope  source  source  (radians)  (radians.)  (radians)  2  )  99 The  photographic  technique  used i n the present  permitted the determination of the normal incidence  study  diffuse  r a d i a t i o n f r o m a l a r g e number o f p o s i t i o n s o v e r t h e c e l e s t i a l dome.  This enabled  to determine  t h e summation o f e q u a t i o n  5.1 t o be u s e d  t h e 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 t h e  inclined surfaces: n  D+  where D  =  s  D4-  g  N  i  £ (D • 6co) • c o s i i =l i N  = diffuse  (5.2)  ±  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 ' s u r f a c e ( W m ) -2  -60) = the normal i n c i d e n c e d i f f u s e at a p o i n t r e p r e s e n t i n g the s o l i d angle  (Wm  -2  n = t h e number o f g r i d p o i n t s o v e r With  ( 6co • s r ) ~ ) 1  the c e l e s t i a l  the i n c r e a s i n g slope angle, r a d i a t i o n  dome  from the  a r e a b e t w e e n t h e t h e o r e t i c a l a n d l o c a l h o r i z o n s becomes more important.  The p h o t o g r a p h i c  not account  f o r the radiance emanating from t h i s  f o r e an a p p r o x i m a t i o n site, is  was n e c e s s a r y .  as d e s c r i b e d , does area.  c a u s e d 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 d e c i d u o u s  0.14.  The a l b e d o  There-  F o r the' e x p e r i m e n t a l  t h e d i f f e r e n c e between t h e t h e o r e t i c a l and l o c a l  c o n i f e r o u s woods.  oak  technique,  horizons  and  o f t h e a r e a was assumed t o be  T h i s i s t h e a r i t h m e t i c mean f o r r e p o r t e d a l b e d o e s  (0.18) and f i r (0.10) ( K o n d r a t y e v ,  the r a d i a t i o n emanating from t h i s  1969).  of  To a c c o u n t f o r  a r e a , i t was f u r t h e r assumed  t h a t t h e woods r e f l e c t e d t h e i n c o m i n g  shortwave f l u x  isotro-  100 pically. and  T h i s I s a commonly a c c e p t e d a s s u m p t i o n  P i a t t , 1976).  below the a c t u a l the  diffuse  D  n E  1= 1  {0.14 • (K + /2ir)  horizon,  by:  (5-3)  • 6u> . c o s i . } 1  = the r e f l e c t e d diffuse the  i n the r e g i o n  h o r i z o n a n d above t h e t h e o r e t i c a l  r a d i a n c e was c a l c u l a t e d  =  where  T h u s , f o r any g r i d p o s i t i o n  (Paltridge  irradiance  (Wm~ ) f r o m • 2  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 f r o m w h i c h t h e d i f f u s e  radiation 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 = t h e number o f p o s i t i o n s  w i t h i n . .the„region  The i m p o r t a n c e o f t h e 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 d e p e n d e n t on i t s a n g l e o f i n c i d e n c e on  the slope. For  a clear  sky condition,'/'this  increased the t o t a l d i f f u s e as  f l u x on a h o r i z o n t a l  measured u s i n g the p h o t o g r a p h i c  1.0 Wm  2  when D4- i s g e n e r a l l y  reflected  not been e x t e n s i v e l y  a r o u n d 60.0  reflected radiation  studied.  i s isotropic  surface,  t e c h n i q u e , by l e s s -2  from  I t i s usually (Paltridge  surfaces assumed  a sloping  surface  that  a n d P i a t t , 1976).  The e q u a t i o n u s e d t o d e t e r m i n e t h e amount o f e n e r g y on  than  Wm .  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 has  radiation  received  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 infinite  r  where  and h o r i z o n t a l  s  r  =  r  hor  '  s  l  n  '  2  surface i s (Kondratyev,  a / 2  ( 5  = reflected radiation  s  1969):  on ah i n c l i n e d  -  4 )  surface  o f a n g l e or r, hor  = reflected radiation facing horizontal  incident  on a downward  surface  C o m b i n i n g t h e above c o m p o n e n t s , t h e t o t a l  shortwave  f l u x o n t o a n 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 t h e  photographic  technique, i s :  K+  = S+  +  + D s  where  K+ S4D+  D  s  s s  r. s r  p  = shortwave i r r a d i a n c e  s  on an i n c l i n e d s u r f a c e  = direct solar radiation = the diffuse  P  (5.5)  + r  radiation  incident  radiation  on t h e s l o p e  technique  surface  integrated values.  (Wm  f r o m an a d j a c e n t  horizon horizontal  (Wm ) -2  M e a s u r e m e n t s o f K+  (Wm  ) 2  )  )  r e f l e c t e d from the r e g i o n  between t h e t h e o r e t i c a l and t h e a c t u a l = reflected radiation  2  emanating from t h e sky las.  measured u s i n g t h e p h o t o g r a p h i c = the diffuse  (Wm  a n d I were r e c o r d e d as 5 m i n u t e s B e c a u s e o f t h i s , o n l y mean i r r a d i a n c e s  (Wm  102 c o u l d be u t i l i z e d i n t h e d e t e r m i n a t i o n 5.5-  equation  I n determining  and t e s t i n g o f  the quality  o f these  a h o r i z o n t a l s u r f a c e , i t was f o u n d t h a t l a r g e e x i s t e d between  when m e a s u r e d d i r e c t l y  data f o r  discrepencies  a n d when c a l c u l a t e d  using:  (5-6)  K+ = I • c o s z + D+  where D+ was an i n s t a n t a n e o u s  measurement.  O n l y i n t h e 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 t h e s u m m a t i o n o f t h e 5 m i n u t e mean d i r e c t beam r a d i a t i o n a n d t h e 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 t h e i r r a d i a n c e m e a s u r e d by t h e pyranometer. 5.2  Results The c o m p u t a t i o n a l  technique  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 and  90°  to the h o r i z o n t a l .  T a b l e 5.1.  o f 30°,  60°,  The r e s u l t s a r e p r e s e n t e d - i n  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 b e t w e e n t h e  mean i r r a d i a n c e o v e r 5 m i n u t e s and. t h e 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 t h e i n t e g r a t i o n p e r i o d and  t h e t o t a l s h o r t w a v e 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 -  tropic  d i f f u s e r a d i a t i o n m o d e l ( H a y , 1978).  This  m o d e l h a s b e e n f o u n d , t o more a c c u r a t e l y 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 t h a n t h e t h r e e more w i d e l y the  latter the shortwave  used models;  i s o t r o p i c model, t h e c i r c u m s o l a r model and t h e  m o d e l ( H a y , 19 78) .  combination  TABLE 5 . 1 . — C o m p a r i s o n o f s h o r t w a v e I r r a d i a n c e o n a h o r i z o n t a l s u r f a c e a n d three south-facing slopes  Time o f  Slope  Photograph (LAT)  (degrees)  12:40  Of 30  60  13:40  13:26  13:47  14  :11  90 0  30 60  90 0 30 60 90 0 30  Measured* :. I r r a d i a n c e  Calculated  (Wm )  (Wm )  460 . 4 1 849.68  440.76  -2  1018.26 944.37  383.29  734.90 866.42  852.60  525.12  874 . 0 3 995 . 0 4  891.61 494.78  830.76  60  959.29  60  763.25 870.94  90 0 30 90  Photographic  850.52 449 . 4 7  792.69  Technique Difference  -2  802.54 973.65 902.79 381.88 710.75  871.56 815.66  507.33  847.0 7 986.35  888.72 475.74  809.90  941.99 847.0 3 433.97  715.85 868.68  800.42  (%)  -4.26** . -5.54  -4.38  -4.40-  -0.37 -3.29  0.59 -4.33 -3.38 -3.08  A n i s o t r o p i c Model:. Calculated (Wm ) -2  440.76 799 . 2 4  963.79 890 .28 381.88  710 . 2 4 '  865.99 80 7.39  -0.87  507.33 843.62 974.65  -3.85  475.74  -0.32  -2.51 -1.80 -0 .41 -3.45 -2.28 -0 .24  0.98  872.38  802.87 924.56  Difference (%)  -4.26** -5.94 -5.35  -5.73 -0.37  -3.35 -0.05 -5-30 -3-38 -3.47  -2.05 -2.16 -3.85  -3.36 -3.62  824.81 433.97  -3.02 -3.45  781.48  -1.41  740.56 845-98  -2.97 -2.87  * a l l measured values  a r e 5 m i n mean f l u x e s f o r t h e p e r i o d o f t h e p h o t o g r a p h  * a l l negative  i n d i c a t e an  values  underestimation  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 t h e c l e a r s k y c o n d i t i o n i s t h e most s t a t e , the photographic  technique c o n s i s t e n t l y  t h e a n i s o t r o p i c m o d e l on a 5 m i n u t e a v e r a g e 15 m o d e l l e d  cases, the photographic  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%• model, a r e l a t i v e occasions. 28.03 Wm  -2  stable  outperformed  basis.  Of t h e  t e c h n i q u e o n l y once h a d For the anisotropic  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  The R.M.S.E. f o r t h e p h o t o g r a p h i c  t e c h n i q u e was  w h i l e f o r t h e a n i s o t r o p i c m o d e l , i t was 38.37  Wm . -2  T h i s r e p r e s e n t s a n 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 t h e 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 Even g r e a t e r advantages  o f the photographic  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  beam). technique f a c e away  from t h e s o l a r d i s c  ( e . g . , n o r t h ) a n d f o r more c o m p l e x  cloudy  I n such  conditions.  technique can determine  partially  cases, only the photographic  t h e amount o f e n e r g y  available to  s u r f a c e s due t o t h e r e f l e c t i o n a n d 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 a n e x a m p l e where  the r a d i a n c e f o r an area o f t h e northwestern sky i s e q u i v a l e n t t o that o f an area i n the southwestern c e l e s t i a l dome n e a r t h e s o l a r d i s c .  portion o f the  Hay ( p e r s o n a l c o m m u n i c a t i o n )  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, t h e a n i s o t r o p i c m o d e l does n o t p e r f o r m w e l l due t o p r o b l e m s o f radiation reflected topography. are a v a i l a b l e  from clouds a s s o c i a t e d w i t h t h e l o c a l  U n f o r t u n a t e l y , a t p r e s e n t , no a p p r o p r i a t e d a t a f o r a thorough  evaluation.  A f u r t h e r advantage o f t h e photographic technique i s  105 Its  ability  from areas  to determine  above a h o r i z o n t a l s u r f a c e .  p l i s h e d , e i t h e r by m e a s u r e d by technique  t h e amount o f r a d i a t i o n  d e t e r m i n i n g the  This  c a n be  the  determining a p p r o p r i a t e albedoes  v a r i o u s s u r f a c e s above t h e h o r i z o n and energy u s i n g e q u a t i o n  5.3.  the m o d e l l i n g of d i f f u s e  The  accom-  d i f f e r e n c e i n irradian'ce  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  o r by  reflected  photographic f o r the  m o d e l l i n g the  reflected  l a t t e r method c o u l d l e a d t o  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 a b o v e t h e t h e o r e t i c a l are important  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  for that surface. the photographic  This r a i s e s the q u e s t i o n of the a b i l i t y technique  i n t h e same manner as. s k y  of the p r e s e n t  diffuse irradiance.  estimates  decided  beyond the  of the r e s u l t s presented,  t h a t the photographic  can a l s o be  I t was  scope  study.  From t h e q u a l i t y  a u s e f u l map  of  t o measure r e f l e c t e d i r r a d i a n c e  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  apparent  horizon  technique  can n o t  i t is only  provide  of d i f f u s e r a d i a n c e over the sky hemisphere u t i l i z e d to provide accurate  instantaneous  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 .  p r e s e n t , however, the u s e f u l n e s s of t h i s technique accurately provide  l o n g term  to  a v e r a g e s i s h i n d e r e d by  l o g i s t i c a l p r o b l e m s o f d a t a a c q u i s i t i o n and  At  the  processing.  but  CHAPTER S I X PRELIMINARY INVESTIGATION INTO GRID S I Z E One o f t h e m a j o r p r o b l e m s i n v o l v e d i n t h e m a p p i n g o f a "surface" i s the design of a sampling  procedure.  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 i c a n t due t o t h e r a p i d l y over  time  and space.  signif-  v a r y i n g d i s t r i b u t i o n o f energy  Krumbein and G r a y b i l l  both  (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 a p p a r e n t is  utilized,  Is  the square  as i n t h i s  regularity.  c a s e , t h e most o b v i o u s  design  t h e sample d e n s i t y  ( i . e . , t h e s a m p l e s i z e ) must b e c o n s i d e r e d . consideration of previous constants  sampling  grid.  Once t h e d e s i g n i s d e t e r m i n e d ,  time  I f digitizing  research i n this  The p r i m e  sampling  a r e a has been t h e  o f t h e measurement i n s t r u m e n t s .  The  present  w o r k , h o w e v e r , i s n o t c o n s t r a i n e d i n t h i s manner a n d t h u s i t was p o s s i b l e t o d e t e r m i n e  an o p t i m u m g r i d  density with  greater  obj e c t i v i t y . A s e c o n d p r o b l e m i n v o l v e d i n t h e 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 t h e a c c u r a c y (1977) " c o n f i r m e d "  the accuracy  of the d i s t r i b u t i o n .  of the c l e a r sky radiance  d i s t r i b u t i o n s he p r o d u c e d by i n t e g r a t i n g t h e s e and  radiance  comparing the r e s u l t i n g i r r a d i a n c e t o the observed  106  Steven  values diffuse  10 7 • Irradiance. verify still  This  method was  the p r e s e n t d i s t r i b u t i o n s . remained as to whether the  r e p r e s e n t e d the  a c c u r a c y o f the  A preliminary the  followed  The q u e s t i o n ,  however,  above c o m p a r i s o n  truly  radiance  i n v e s t i g a t i o n was  magnitude of e r r o r s i n t r o d u c e d  various dome.  g r i d spacings  pattern.  undertaken to  by i n t e r p o l a t i o n  ( i . e . , sample s i z e s ) over the  By i n t e g r a t i o n o f t h e  radiance,  p r e s e n t v a l i d a t i o n methodology c o u l d  the  i n s a m p l i n g ; the tively. down t o point  the  and  celestial the  a partially  to r e p r e s e n t the  highly  variable  case,  The s a m p l e d e n s i t i e s e x a m i n e d v a r i e d f r o m 1800 36 p o i n t s .  Each o f these s e t s  are  f o r the  easy d e t e r m i n a t i o n  for  each data p o i n t .  the  sample s i z e of the  and  S t e v e n (1977).  and  the  the  a c t u a l number o f g r i d p o i n t s  The s m a l l e s t  less.  respecpoints .  This  representative  sample a l s o  area  approximated  p r e v i o u s w o r k o f K o n d r a t y e v e t a l . (1955)  As t h e  g r i d represents  e x p o s e d n e g a t i v e has  p r o c e d u r e was  of the  extrema  s u b s e t s o f the' 3600  d a t a s e t whose r e s u l t a n t i s i n e v e n i n t e g e r s .  allowed  using  a l s o b e d e t e r m i n e d . The  These w e r e b e l i e v e d  c o h e r e n t and  determine  q u a l i t y of  a n a l y s i s was p e r f o r m e d f o r b o t h a c l e a r s k y cloudy s i t u a t i o n .  4.3 t o  i n Section  a s q u a r e o f 24 x 24mm  a . d i a m e t e r o f a p p r o x i m a t e l y 23mm, u t i l i z e d i n the  T a b l e 6.1 p r o v i d e s t h e  of g r i d points used to determine the  integration  a c t u a l number  i r r a d i a n c e f o r each  grid. Prom t h e points  c o m p l e t e dat  coinciding with  set  (36OO  p o i n t s ) , 20 g r i d  c a l c u l a t e d r a d i a n c e s were  obtained.  TABLE 6 . 1 . — S i z e o f s q u a r e g r i d c o r r e s p o n d i n g number o f g r i d  with  points  l o c a t e d w i t h i n the exposed area o f the  negative  Grid size  Grid points within exposed area  3600 1800 1200 900 600  2629 1298  . 400  225 100  36  865 649  432 288 162  72 26  109The  s e l e c t i o n was s u c h  t o any o f t h e s u b s e t s  t h a t t h e s e p o i n t s w e r e n o t common on w h i c h t h e a n a l y s i s was t o be p e r f o r m e d  Thus, o n l y e s t i m a t e d v a l u e s  f o r these  l o c a t i o n s c o u l d be  o b t a i n e d from t h e subsets.  T h i s e s t i m a t e d r a d i a n c e was  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 f r o m t h e c l o s e s t o f known r a d i a n c e i n t h e s u b s e t . is  data p o i n t s  An e x a m p l e o f t h i s  Assume t h e r a d i a n c e a t a p o i n t (36,  useful.  d a t a s e t (3600) p o i n t s .  of a f u l l  g r i d o f 900  data p o i n t s the four nearest neighbours  (35, 8,  25), 12,  (37,  25,  23)  a n d (37,  25).  procedure  24) i s 10 Wm  i n t h e case  t h e same g r i d i d e n t i f i c a t i o n ) w o u l d be f o u n d  cal-  a t (35,  (using 23),  T h e s e may h a v e r a d i a n c e s o f  a n d 27 W m s r ~ R e s p e c t i v e l y .  Thus, t h e i n t e r -  - 2  (36,  f o r the l o c a t i o n of point  18 W m  The r o o t mean s q u a r e e r r o r (R.M.S.E.) was t h e n  sr  - 1  .  s  However, f o r a  polated value - 2  2  24) w o u l d be  c a l c u l a t e d u s i n g t h e d i f f e r e n c e s b e t w e e n t h e 20 known a n d 20 i n t e r p o l a t e d r a d i a n c e s n R.M.S.E. = {( E  1=1 R  where R  f o r each o f t h e 8 sampling  R C  - R-  ) /n} 2  densities:  (6.1)  h  i  = known r a d i a n c e  (Wm s r ) 2  ;  = interpolated radiance  x  (Wm s r ) 2  :  1  n = 20  F i g u r e 6.1 both  provides the results  c l e a r and p a r t i a l l y  cloudy  t h e R.M.S.E. i s o f i n t e r e s t .  of the analysis f o r  conditions.  I n both  cases  The t r e n d o f there appears t o  _1_  3  0,0)  6 0 0'  9-0 0  120  0  1500  180  0  Sample S i z e  Figure  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 sample s i z e p a r t i a l l y c l o u d y sky case c l e a r sky case  with  Ill be a " t h r e s h o l d " number o f d a t a p o i n t s r e q u i r e d t o p r o d u c e 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 . all  For the c l e a r sky case,  s a m p l e 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 h a v e a R.M.S.E.  o f u n d e r 2.0 Wm s r . 2  sample s i z e s  1  less  T h i s i n c r e a s e s t o o v e r 5 Wm~ sr" f o r 2  t h a n 225 p o i n t s .  1  For the p a r t i a l l y  cloudy  c o n d i t i o n , t h e " t h r e s h o l d " , a l t h o u g h n o t as d e f i n i t e  as i n  t h e c l e a r s k y c a s e , i s 600 p o i n t s .  larger  The s a m p l e s i z e s  t h a n t h i s h a v e a mean R.M.S.E. o f a p p r o x i m a t e l y 6.0 Wm~ s r " , 2  1  w h i l e f o r s m a l l e r s a m p l e s i z e s , t h e mean R.M.S.E. i s o v e r  11 Wm~ s r 2  _ 1  .  I n d i v i d u a l l y , t h e v a r i a t i o n i n R.M.S.E. p r o v i d e s useful insights  i n d e t e r m i n i n g optimum sample s i z e s .  The  more c o h e r e n t 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 t h e number of g r i d p o i n t s necessary significantly is  less  t o p r o v i d e a s t a b l e R.M.S.E. i s  than f o r the cloudy case.  225 p o i n t s t o a minimum o f 600 p o i n t s .  (i.e., all-sky  The d i f f e r e n c e  However, i f r o u t i n e  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 u s e d , t h e 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 t h e most c o m p l e x c a s e , u n l e s s a n o p t i m u m 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 t h e g r i d s i z e i s  o p t i m i z e d f o r t h e most c o m p l e x c a s e , t h e s i z e o f t h e e r r o r associated with 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 b e up t o  5 t i m e s a s g r e a t a s 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 . Kondratyev determine  e t a l (1955) u s e d 30 o b s e r v a t i o n s t o  the d i s t r i b u t i o n o fdiffuse radiation  of sky c o n d i t i o n s .  Steven  f o r a l l types  (1977) made 34 m e a s u r e m e n t s  over  112 the  sky hemisphere t o produce c l e a r sky n o r m a l i z e d  distributions.  B o t h sample s i z e s a r e an o r d e r o f magnitude  l e s s thaft t h e . d e f i n e d brings  into question  associated  with  c l e a r sky threshold  a radiance value at a given  horizontal surface.  the  to provide  This  point, and t h e  the f l u x received  on a  Can .the R.M.S.E. be p a r a m e t e r i z e d b y  e r r o r found i n the i n t e g r a t e d The  values.  t h e r e l a t i o n s h i p between the e r r o r  summation o f t h e p o i n t s  the  radiance  flux?  a s s u m p t i o n was made t h a t  each g r i d p o i n t  represented  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 t h e c e l e s t i a l  inversely proportional  t o t h e sample s i z e .  The L a m b e r t i a n  r e s p o n s e was d e t e r m i n e d f o r t h e p o s i t i o n o f t h e g r i d I f one assumes t h a t  a g r i d o f 3600 p o i n t s  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  dome  point.  provides the correct  i r r a d i a n c e , a comparison  can be made b e t w e e n t h e R.M.S.E. a n d t h e r e l a t i v e e r r o r o f the  integrated  v a l u e s f o r each subset o f g r i d p o i n t s .  Table  6.2  p r o v i d e s b o t h t h e R.M.S.E.'s a n d t h e r e l a t i v e e r r o r o f t h e integrated  fluxes  f o r each sample s i z e .  I n c o m p a r i n g t h e two  measures o f t h e a c c u r a c y o f t h e a n g u l a r d i s t r i b u t i o n o f d i f f u s e radiation, l i t t l e  c o n f i d e n c e c a n be p l a c e d  error of the integrated  f l u x as a p a r a m e t e r i z a t i o n  e r r o r due t o i n t e r p o l a t i o n . a general the  ofthe  I n the c l e a r sky case, there I s  i n the r e l a t i v e error with  the increase of  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 .  there the  increase  i n ther e l a t i v e  However,  i s no s i m p l e c o r r e s p o n d e n c e b e t w e e n t h e d i r e c t i o n s a n d  c h a n g e s i n m a g n i t u d e o f t h e two e r r o r s .  From t h e d a t a  113  TABLE 6 . 2 . — R e l a t i v e  error  {%) o f I n t e g r a t e d  v a r i a t i o n i n sample s l z e : a n d  Sample s i z e  Clear  (points)  R.M.S.E.  1800  1.485  1200  1.423 1.944  fluxes  for a  R.M.S.E. f o r i n t e r p o l a t e d  sky Relative error  values  P a r t l y cloudy sky R.M.S.E.  Relative error  0.33 0 .42  6.842  0.14  5.372  0 .68  1.02  7.059  1.42  1.13 1.84  5.649  2.24  400  1. 731 1.894  9.278  1.68  225  2.10 7  1.37  10.000  5.44  ; 100  6.758  4.47  13.591  0 .12  6.173  5.41  12.653  6.31  900 600  36 .  114 p r e s e n t e d , I t appears that the  R.M.S.E. c o u l d  Steven  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  (1977) r e p o r t s  irradiance  f o r an i n t e g r a t i o n e r r o r  o f <1%, 2 Wm  f o r clear skies.  - 1  .  From t h e r e s u l t s p r e s e n t e d , t h e 2  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 The p a r t i a l l y  sr  a n e r r o r o f 6% f o r h i s i n t e g r a t e d  R'. M.S:.E .: f o r ..his d i s t r i b u t i o n w o u l d . b e o v e r 6 Wm" sr the  - 2  _1  when  reduced.  c l o u d y s i t u a t i o n h a s no r e l a t i o n s h i p  b e t w e e n t h e measurements  of error.  The g r i d s i z e o f 100 p o i n t s  p r o d u c e d t h e l a r g e s t R.M.S.E. a n d y e t i t b e s t e s t i m a t e d t h e irradiance  f o r the h o r i z o n t a l  t o u s e t h e method d e s c r i b e d  surface.  This indicates  that  b y S t e v e n (1977) t o d e t e r m i n e t h e  a c c u r a c y o f t h e a n g u l a r d i s t r i b u t i o n i n more c o m p l e x c a s e s the  c l e a r sky condition This analysis  i s not  than  appropriate.  s e r i o u s l y q u e s t i o n s t h e use o f t h e i n t e -  grated f l u x technique f o r s t a t i n g that  the derived  d i s t r i b u t i o n o f diffuse radiation i s accurate.  angular  The u s e o f  t h i s method s h o u l d b e a v o i d e d i n c a s e s o f c o m p l e x s k y conditions. 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 estimate analysis needed. the  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  Because o f t h e i n f i n i t e  variety o f cloud  approach:-.may h a v e t o b e e m p i r i c a l w i t h  interpolated values using and  grid sizes.  error  combinations,  the t e s t i n g o f  a wide v a r i e t y o f sky c o n d i t i o n s  CHAPTER SEVEN CONCLUSIONS AND The  study  RECOMMENDATIONS  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  to  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 hemisphere.  The  are:  (1)  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 m a p p i n g o f  the  c e l e s t i a l dome. itions two  sky  advantages o f t h i s method o v e r 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 , present  determine  can now  1955;  1977)  Steven,  E v e n t h e most c o m p l e x d i f f u s e r a d i a n c e be mapped..  (2)  The  the  cond-  sample s i z e employed i s  orders of magnitude l a r g e r than t h a t used i n p r e v i o u s  studies.  T h e r e f o r e , t h e maps p r o d u c e d  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 (3)  than those p r e v i o u s l y p u b l i s h e d . data base i s i n d i g i t a l  using this  f o r m and  The  method  more p r e c i s e  diffuse  i s e v e n l y and  radiance  densely  d i s t r i b u t e d o v e r t h e s k y h e m i s p h e r e a l l o w i n g i t t o be to determine  t h e 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  used  surfaces  with l i t t l e modification. The  t e c h n i q u e , h o w e v e r , has  nor are the r e s u l t s t o be made. be  classified  dations and  The  not y e t been p e r f e c t e d ,  c o m p r e h e n s i v e enough f o r g e n e r a l i z a t i o n s  recommendations o f t h i s  into  two  study  m a i n c a t e g o r i e s : (1)  can t h e r e f o r e  those  recommen-  c o n c e r n i n g t h e t e c h n i c a l a s p e c t s of. t h e measurement  data r e d u c t i o n procedure  and  115  (2)  those  for future studies  116 using this The of  technique. g r e a t e s t problem  the diffuse  radiance data r e q u i r e d f o r the c a l i b r a t i o n of  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 h a s f o u r  major l i m i t a t i o n s : is  at present i s i n the c o l l e c t i o n  (1)  the response  too slow t o adequately  sample I n a s h o r t time p e r i o d a l l  the regions o f the c e l e s t i a l comprehensive  calibration  have a r e s p o n s e adjustment  time o f the instrument  dome n e c e s s a r y  data..  The I d e a l i n s t r u m e n t w o u l d  t i m e o f a. s e c o n d  (2)  or less.  The m a n u a l  o f the actinometer 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 a d e q u a t e number o f o b s e r v a t i o n s . t h a t an e n t i r e Although  to provide -  calibration  this i s less  I t i s recommended  sequence t a k e l e s s  important f o r clear  than 2 minutes.  sky o b s e r v a t i o n s !  f o r t h e more c o m p l e x c o n d i t i o n s , i t i s e s s e n t i a l . Linke-Feussner Actinometer  i s too sensitive  (3)  t o windy  The conditions.  I f r o u t i n e m e a s u r e m e n t s a r e t o be made, an i n s t r u m e n t w i t h greater pressure s t a b i l i t y signal  i s necessary.  (4)  The o u t p u t  o f t h e i n s t r u m e n t u s e d was i n a d e q u a t e .  output should provide a s i g n a l  that i s easily  The minimum monitored.  I f s u c h an i n s t r u m e n t c a n n o t be f o u n d , i t i s recommended t h a t t h e 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 w o u l d be a d v a n t a g e o u s i n t h e d a t a r e d u c t i o n s t a g e of  the experiment  quickly  t o be a b l e t x r d i g i t i z e p h o t o g r a p h s  using a smaller grid  c o u l d o n l y improve  spacing.  A larger  more sample  size  t h e a c c u r a c y o f mapping r a d i a n c e over t h e  s k y h e m i s p h e r e 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 t h e 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 . from the r e s u l t s  of Chapter  For the present adequate. was  study, the  This  scientific  system  f i l m s and p l a t e s w o u l d  c o u l d improve the accuracy  of  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  f o r complex sky  c o n d i t i o n s c a n be  o f r a d i a n c e maps f o r a l l s u c h  may  photographic  b a s e be  the  parameterized,  c o n d i t i o n s w i l l be  radiance a  discovered...  collection  necessary.  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 be  found  curves.  Before  With  c a m e r a e q u i p m e n t was  However, i f a l a r g e r format  become a v a i l a b l e .  conclusion follows  Six.  used,.-specially designed  calibration  This  distribution  I t i s t h e r e f o r e recommended t h a t a  c o l l e c t e d and  archived.  T h i s w o u l d a l s o be  tageous to r e s e a r c h e r s i n the t e s t i n g of both  advan-  e m p i r i c a l and  t h e o r e t i c a l l y b a s e d models e v a l u a t i n g the d i s t r i b u t i o n diffuse  data  of  radiance. The  use  of the photographic  technique  combined w i t h  t h e 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 m e t h o d o l o g y t o a c c u r a t e l y determine,  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  surfaces.  From t h i s  a s s u m p t i o n c a n be models d e v e l o p e d . i s now  i n f o r m a t i o n , the p r e s e n t l y used  t e s t e d and, As  adjacent  i f necessary,  more  a l l u d e d to i n Chapter  a v a i l a b l e f o r determining the d i f f u s e  isotropic  accurate  Five, a  technique  radiation  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 t h e h o r i z o n becomes a significant aspects  factor.  Further study  of "photographic  radiation  i s r e q u i r e d f o r both  sensing".  these  118 A t e c h n i q u e i s now the  angular d i s t r i b u t i o n  hemisphere.  available  to quantitatively  determine  of d i f f u s e r a d i a t i o n i n the sky  When p e r f e c t e d and u s e d 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 t i o n of a variety  of shortwave r a d i a t i o n  a i d i n the  problems.  solu-  BIBLIOGRAPHY A t r o s h e n k o , V.S., K.S. G l a z o v a , S.Y. Kogan, T.D. Koronatov, M.A. Kuznetzov, M.S. M a l k e v i c h and E.M. F e u g e l s o n , 1962: Computation o f t h e atmospheric l i g h t b r i g h t n e s s i n u n i s o t r o p i c s c a t t e r i n g . P r o c . I n s t . Atmospheric Phys., No.3, Acad. S c i . Moscow, U.S.S.R. 3  Cook, N.H. and E:.. R a b i n o w i c z , 1963: P h y s i c a l Measurement and A n a l y s i s . Addison-Wesley, London, 312pp. C o u l s o n , K.L., 1975: S o l a r and T e r r e s t r i a l R a d i a t i o n : Methods and Measurements. Academic P r e s s , New Y o r k , 322pp. C o u l t h a r d , W.J., 1975: C o n t o u r i n g a G r i d . U n i v e r s i t y o f B r i t i s h Columbia Computing C e n t r e , 10pp. 7  Dave, J.V., 19 75: A d i r e c t s o l u t i o n o f t h e s p h e r i c a l harmonics a p p r o x i m a t i o n t o t h e r a d i a t i v e t r a n s f e r e q u a t i o n 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 : Results. J . Atmos. S c i . , 32, 1463-1474. Dorno, C., 1919: V e r f o f f e n t l . P r e u s s . M e t e o r o l . I n s t . Abandhl. , 8, 303Drummond, A . J . , 1956: On t h e measurement o f sky r a d i a t i o n . A r c h . Met. Geophys. B i o k l . B , 7 , 413-436. Drummond, A . J . , 1970: P r e c i s i o n r a d i o m e t r y and i t s s i g n i f i c a n c e i n atmospheric and space p h y s i c s . Advances i n G e o p h y s i c s , V o l . 14, Academic P r e s s , New Y o r k , 1-52. D u f f l e , J.A. and W.A. Beckman, 1974: S o l a r Energy Thermal P r o c e s s e s . John W i l e y and Sons, T o r o n t o , 386pp. F l o w e r s , E., 1977: Test and e v a l u a t i o n o f t h e performance of s o l a r r a d i a t i o n s e n s o r s a t i n c l i n a t i o n from t h e h o r i z o n t a l under l a b o r a t o r y 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, E n v i r o n m e n t a l Research L a b o r a t o r y NOAA, B o u l d e r , C o l o r a d o , 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 R e s e a r c h , J a n u a r y / F e b r u a r y , 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, C o n t r a c t DSS 05576-02095119  120 Hay,  J . E . , 19 77: Measurement a n d m o d e l l i n g of s h o r t w a v e r a d i a t i o n on i n c l i n e d s u r f a c e s . Preprints Third C o n f e r e n c e on A t m o s p h e r i c R a d i a t i o n , Am. M e t .  Soc,  150-153.  H e i m o , A. a n d 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 Mobile System f o r s o l a r r a d i a t i o n measurements. Working Reports o f t h e Swiss Meteoro 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 M a n u a l , 1958: R a d i a t i o n Instruments and M e a s u r e m e n t s , P a r t V I , Pergamon P r e s s , L o n d o n , 39 4-401.  J o y c e I n s t r u m e n t a t i o n , 1954: D o u b l e 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 Loebl: 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 M o d e l Mk I I I C , J o y c e L o e b l a n d 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, A c a d e m i c P r e s s , New Y o r 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 a n d M.P. M a n o l o v a , 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 atmospheric r a d i a t i o n over t h e c e l e s t i a l s p h e r e . B u l l . L e n i n g r a d U n i v . , 119-129. K o n d r a t y e v , K . Y a . a n d M.P. M a n o l o v a , I960: The r a d i a t i o n balance o f slopes. S o l a r E n e r g y , 4, 14-19. K r u m b e i n , W.C. a n d 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 M o d e l s i n G e o l o g y , 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 Instruments a t the N a t i o n a l R a d i a t i o n Centre o f the C a n a d i a n M e t e o r o l o g i c a l S e r v i c e , P a p e r No. 3/1, 19 70 I n t e r n a t i o n a l S o l a r E n e r g y C o n f e r e n c e , M e l b o u r n e , 6 pp. L a t i m e r , J . R . , 1972: R a d i a t i o n measurement. M a n u a l S e r i e s , No. 2, 53pp.  IFYGL T e c h n i c a l  L o n g , K., 1961: U b e r das S t r e u s p e k t r u m d e r A t m o s p h a r e . 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 . M c A r t h u r L.B. a n d J . E . H a y , 1978:. On t h e a n i s o t r o p y o f d i f f u s e s o l a r r a d i a t i o n from the sky hemisphere. B u l l . Am. Met. S o c . , ( i n p r e s s ) .  121  M i l l e r , A. and J.C. Thompson, 19 70: Elements o f M e t e o r o l o g y , C.E. M e r r i l l Pub. Co., Columbus, Ohio, 402 pp. M o r r i s , C.W. and J.H. Lawrence, 1971: The a n i s o t r o p y o f 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 T r a n s a c t i o n s 19 71, P a r t I I , 136-141. Morse, R.N. and J.T. C z a r n e c k i , 1958: F l a t P l a t e S o l a r A b s o r b e r s : The E f f e c t on I n c i d e n t R a d i a t i o n o f I n c l i n a t i o n and S l o p e , CSIRO E n g i n e e r i n g 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 o l a r Energy, 10, 72-76.  surfaces.  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 C l i m a t o l o g y . Developments i n Atmospheric S c i e n c e , No. 5, E l s e v i e r S c i e n t i f i c Pub. Co., New Y o r k , 3l8pp. R e i f s n y d e r , 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 o f the r a d i a t i o n b a l a n c e . Agric. Meteor., 4, 255-256. R o b i n s o n , 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 Y o r k , 347 pp. S e l l e r s , W.D., 1965: P h y s i c a l C l i m a t o l o g y , Chicago P r e s s , C h i c a g o , 272pp.  Univ. o f  S i v k o v , S . I . , 1968: Computation o f 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 . R o h l f , 19 73: I n t r o d u c t i o n t o B i o s t a t - : . . i s t i c s , W.H. Freeman and Co., San F r a n c i s c o , 368pp. 1  S t e v e n , M.D., 1977: S t a n d a r d d i s t r i b u t i o n o f c l e a r sky radiance. Quart. J . R. Meteor. S o c , 103, 457-465. S u z u k i , T., 19 75: An I n t r o d u c t i o n t o t h e Canon F - l , Canon I n c . , Tokyo, 15 3pp. Unsworth, M.H. and J.L. M o n t e l t h , 1975: Longwave r a d i a t i o n at t h e ground. Quart J . R. Meteor. S o c , 101, 13-24. W a l l a c e , J.M. and P.V. Hobbs, 1977: Atmospheric S c i e n c e : An I n t r o d u c t o r y Survey, Academic P r e s s , New Y o r k , 467pp. Z w o r y k i n , W.K. and E.D. W i l s o n , 19 34: P h o t o c e l l s and T h e i r A p p l i c a t i o n , John W i l e y and Son, I n c . , New Y o r k , 348pp.  APPENDIX ONE NOTATION UPPER CASE ROMAN dimensionless  density corrected diffuse  Wm  -2  Wm  -2  Wm  -2  predicted diffuse irradiance on a h o r i z o n t a l s u r f a c e  Wm  -2  diffuse irradiance incident on a n i n c l i n e d s u r f a c e  Wm  -2  reflected diffuse  Wm  -2  Wm  -2  Wm  -2  Wm  -2  measured d i f f u s e normal i n c i d e n t  radiation radiation  d i f f u s e from  <5co  irradiance  radiant intensity normal i n c i d e n c e beam r a d i a t i o n  direct  incoming shortwave  irradiance  r e f l e c t e d shortwave  irradiance  Wm  -2  shortwave i r r a d i a n c e on a 30° s l o p e  incident  Wm  -2  shortwave i r r a d i a n c e on a 60° s l o p e  incident  Wm"  shortwave i r r a d i a n c e on a 90° s l o p e  incident  Wm  2  -2  shortwave i r r a d i a n c e i n c i d e n t on a n i n c l i n e d s u r f a c e  Wm~  radiance  Wm  122  (6w • s r )  -2  2  sr  _1  - 1  123 known  Wm  radiance  interpolated  radiance  Wm  sr - 2  sr  -1  - 2  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  Wm  view  dimensionless  factor  solar zenith  degrees,radians  angle  LOWER CASE ROMAN azimuth  of radiation  azimuth  o f slope  source  radians radians  exposure  dimensionless  number o f p o i n t s i n a n e x p o s e d •area ( c e l e s t i a l dome)  dimensionless  d i s t a n c e from t h e z e n i t h t o z = /2 r a d i a n s  mm  d i s t a n c e from t h e z e n i t h t o t h e h o r i z o n on a n e q u i d i s t a n t projection  mm  reflected radiation incident on a downward f a c i n g h o r i z o n t a l surface  Wm  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  Wm  angle  :  radians  o f sun a t sunset  •radians  Tr  o f slope  hour angle zenith  angle  _ 2  -2  radians  UPPER CASE GREEK zenith angle f o r the i radiance value  radians  12 LOWER CASE GREEK  angle o f I n c l i n e d s u r f a c e  radians  mean z e n i t h angle o f the h o r i z o n over a g i v e n a r c l e n g t h  radians  l e n g t h o f the a r c o f 3 a t z = i r / 2  mm  latitude  radians  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 o f t h e measurement system probable e r r o r associated with the measured q u a n t i t y probable e r r o r a s s o c i a t e d with the measured q u a n t i t y f o r a subsystem. atmospheric conditions  dimensionless  r a d i u s o f shadow band  mm  solar declination  radians  s o l i d angle r e p r e s e n t e d by each d e n s i t y  sr  1 property system  dimensionless  t h  o f the photographic  APPENDIX  TWO  CALIBRATION CURVES  125  140  120  I  10 0  u m  I 80 CD O  c  CO •H T3 Cti CC  6 0  4 0  2 0  20 0  30 0  5 00  4 0 0  70 0  6 0 0  Density Figure  A2.2 C a l i b r a t i o n c u r v e f o r 13:40 LAT F e b r u a r y 10, 19 78 L = Exp {-0.2708 + 3.0598 I n (-0.7935 + 7.943 * 10 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 3  ro  2 0 0  30  0  4 0 0  50  0  6 0 0  70  0  Density F i g u r e A2 . 3  C a l i b r a t i o n c u r v e f o r 11:2 0 LAT F e b r u a r y 14, 19 78 Hand drawn c u r v e Polynomial 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 u r v e f o r 12:30 LAT_Pebruary L = 39.051 - 0.326 D + 9.2 x 10 * D C o r r e l a t i o n C o e f f i c i e n t 0.739 2  14, 19 78  280  240  >.0 0 CO  16 0 CD O  C  aj •H •T3  120  PC  80  40  20 0  30 0  400  50 0  70 0  600  Density • F i g u r e A2.5 C a l i b r a t i o n c u r v e f o r 12:47 LAT F e b r u a r y 15, 19 7 8 Hand drawn c u r v e P o l y n o m i a l f i t : L = 149-937 - 0.945 D + 1 . 8 6 x 10" D 3  uo o 2  •00  300  >t00  500  600  Density F i g u r e A2 .6  C a l i b r a t i o n c u r v e f o r 13:17_LAT F e b r u a r y L = E x p {1.059 + 7-724 x 10 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 3  15, 19 78  70 0  Radiance  H"  (R C H  CD  >  ro  o o  r  o  1  M  II  CD  P3  4  x  H* ^  ct H-  O  O  C+  H  •  o o  3  Ul VO O ro p  CD Mi + < CD '-*> H- U l O • >-*> H- LO O CD - J ^ »-< »—•  c+  c o  X LO  O .. h-> r o -<! o r o ! LO O  O  CD 3  co H<rt  «<  >  CD cr  ~$  !  H Ul  cx>  o o  2£l  (Wm s r 2  1  )  Radiance  c CD >  co  o tr o 1  o  CD h-  CD i—  II  1  H-  M cr  1  X3  p  p  ct  ct H> O  O 3  o  3  O H O  c  O Ul  4  CD  CD  HO H-• OA O CD — J 4 3 O ct IX uo  1  o •  H  co o  UD I—  1  w  a  CD UJ I t >  - 1  CD O" 4 P  Ul  i—  1  C O  a  cn Hct  (Wm s r ~ ) 2  1  140  20 0  30 0  40 0  500  600  Density F i g u r e A2.11  C a l i b r a t i o n c u r v e f o r 13:47 LAT F e b r u a r y L = Exp { - 0 . 6 8 7 4 + 9 - 3 5 2 x i o D} Correlation coefficient 0.946 3  26,  1978  14 0  120 h  Density  F i g u r e A2.12  C a l i b r a t i o n c u r v e f o r 14:11 LAT F e b r u a r y L = Exp {-0.2833 + 8.649 x 10 D} C o r r e l a t i o n c o e f f i c i e n t 0.94 3  26,  19 78  r— UO  1  —q  

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