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

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THE  ANGULAR  DIFFUSE OVER  DISTRIBUTION  SOLAR  T H E SKY  OF  RADIATION HEMISPHERE  By  KATHLEEN B.A.,  THESIS THE  ELIZABETH  STEWART  McMaster U n i v e r s i t y ,  SUBMITTED IN PARTIAL REQUIREMENTS MASTER  FOR OF  1982  FULFILMENT  THE DEGREE  OF  SCIENCE  in THE  FACULTY  OF  (Department  We  accept to  THE  this  the required  UNIVERSITY  OF  Kathleen  STUDIES  of Geography)  thesis  July  ©  GRADUATE  as  conforming  standard  BRITISH  COLUMBIA  1984  Elizabeth  Stewart,  1984  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree at the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I  further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may  be  department o r by h i s o r her  granted by  the head o f  representatives.  my  It i s  understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be  allowed without my  permission..  Department o f  Geofetft-ftfH^f  The  U n i v e r s i t y of B r i t i s h  1956  Main  Mall  Vancouver, Canada V6T 1Y3  D  a  t  e  iSri  Columbia  written  i i  Abstract  The with  use of a video-based  measurements  actinometer  of sky radiance  provide  t h e means  distribution  of d i f f u s e  hemisphere.  Development  measurement radiative not  procedure  regimes  pattern, the  dispelling  sky hemisphere Measurements brightness  the  sky.  radiance been  statistical underlying This techniques type  radiative  the sky high  t o b e made  the  confirm that  radiance  derived  resolution  under  complex  procedures  were  directional  the anisotropy  of the  the d i s t r i b u t i o n  over  a c t as a c a l i b r a t i o n f o r  from  once  useful  discusses  can y i e l d  characteristics measurement  from  imagery of  brightness to  the c a l i b r a t i o n  Functional analysis  most  the video  transformation  procedure  i s presented  f o r determining  the  has  as the  relationship  curves. the advantages  in a climatological  conventional  over  the angular  is isotropic.  the calibration  of system  Linke-Feussner  experimental  any assumption  be d e t e r m i n e d  study  earlier  information  tool  analyses  of d i f f u s e  accomplished.  in conjunction  fast-response,  radiance  The a p p r o p r i a t e may  by a  Investigations into  of diffuse  the  made  radiation  of t h i s  allows  system  f o r determining  solar  i n which  satisfactory.  distribution  imaging  application  valuable  of using  a n d shows  information  otherwise techniques.  video how  concerning  unavailable  with  imaging this  iii  Table  of  Contents  Page  Abstract Table  i i  of Contents  i i i  List  of T a b l e s  viii  List  of F i g u r e s  xi  List  of Symbols  xv  Acknowledgements Chapter 1.1  One  -  xviii  Introduction  1  Objectives  1  1 .2 Background Chapter 2.1  Two  1  - Instrumentation  Measurement  10  of D i f f u s e  Solar  10  R a d i a t i on 2.1.1  2.1.2  Recording  the D i f f u s e  Radiation  Signal  Analysis  of  Associated Measurement Solar 2.1.2.1  11  the Error with of  12  the Diffuse  Radiation Analysis  of  Associated 2.1.2.2 A n a l y s i s  Recording  with  of  Associated  the Error the  Sensor  the Error with  the  Instrument  12  13  i v  2.1.2.3  Error  Associated with  Measurement Solar 2.2  Determination from 2.2.1  of  the  Diffuse  Radiation  of  Brightness  Video  Imagery  Video  Camera  and  Values  Monitoring  System 2.2.1.1  Video Lens  Camera, and  2.2.1.2 V i d e o Chapter 3.1  Three  -  Field 3.1.1  View  Measurement  3.3  E s t i m a t i o n of Video  3.3.1  the  4.1  of  the  of with  Error  Determination  the  Error  Brightness  Procedure  of  the  Relationship  Radiance  and  Brightness  Values 4.1.1  of  Determination  Calibration  between  in  in Registration  Calculation  -  Error  Coordinates  Level Four  Analysis  System  Associated  Chapter  Site  Procedure  Inherent Sky  Procedures  Factor  Assessment  3.3.2  Framestore  Measurement  3.2  the  Filter  Experimental  Sky  Fisheye  Regression  Analysis  V  Page 4.1.2 4.2  Functional  Verification  Analysis  50  the  54  of  Calibration  Procedure 4.3  Validity Scan  Chapter  Five  of  Approach  5.2  -  The  Angular  63  the  Radiance  i n the  Point  the  on  for  Value Sky  over  73  of  to  of  the  Distribution Different  a  a  Diffuse Sky  of  Solar  Radiance  Sky  Values  76  Conditions 82  5.3.1  Clear  5.3.2  Overcast  5.3.3  Partly  Previous  76  Hemisphere  Application  Comparison  73  Image  Distribution  for  of  Radiation  Translating  5.2.1  5.4  Solar  a Method  Radiation  5.3  Distribution  Determining  The  Partial  Data  Diffuse 5.1  using  Sky  Conditions Sky  Cloudy of  82  Conditions Sky  Conditions  Results with  86 95 104  Studies  5.4.1  Clear  Sky  5.4.2  Overcast  5.4.3  Partly  Radiance Sky  Cloudy  Distributions  Radiance Sky  Distributions  Radiance  104 111 115  Distributions Chapter 6.1  Six  - C o n c l u s i o n s and  Assessment  of  the  Recommendations  Experimental  120 120  vi  Procedures 6.1.1  Critical  Assessment  Measurement in  6.2  this  Used  Study  Site  6.1.1.2  Assessment  Considerations of  Instrumentation  of R e s u l t s  6.2.1  Clear  6.2.2  Overcast  6.2.3  Partly  6.2.4  Radiance  6.3  Techniques  6.1.1.1  Summary  of  Sky  Cases Sky  Cases  Cloudy  Sky  Cases  Maps  C o n c l u s i o n s and  Recommendations  References Appendix  I - Assessment of  Lens  Imaging Test  and  Video  System  for Axial  Camera AI.1.2  Characteristics  the Fisheye  Camera  Al.1  of the  Symmetry  of Fisheye  Lens  Test  to Confirm  Projection  Equi-Angular  of F i s h e y e  Camera  Lens AI.2  Determination a  AI.3  Video  of t h e Shape of  Image  Determination  of t h e Shape of  the A c t i n o m e t r i c Field-of-View  a s Seen  on a  Video  V  11 Page  Image Appendix  II  - Regression Versus for  Corrected  Clear,  Cloudy  Results  Radiance  Brightness  Overcast  Skies  of  and  Partly  140  vi i i  List  Of  Tables  Page Table  2.1  Recorder  Error  Diffuse Table  2.2  Table  2.3  Radiation  Probable with  Radiances  Outside  3  Composition  (Wm~ sr~ ) 2  i n the Solar  From  2  3.1  Record  Table  3.2  Sequence  of O b s e r v a t i o n s  Sampling  Grid  of F i e l d  Regression  2  Table  4.2  _ 1  Table  4.3  4.4  and  Results  2  and Radiance  f o r Overcast  Brightness  Using  47  Values  Sky  and  Data  48  Radiance  1  Results  Using  Results Show  Skies  (Wm" sr~ )  Radiance Table  37  )  Regression Skies  33  i n Second  for Clear  Brightness  Corrected  Values  (1969)  Observations  Results  Regression Using  22  Kondratyev  Table  Corrected  1  of D i f f u s e R a d i a t i o n  (10~ cal/cm min). 6  1 6  and the S p e c t r a l  2  (Wm" sr  1 5  the Atmosphere  (10~ cal/cm min)  4.1  a  Signal  Distribution  Spectrum  Table  with  Relative Errors Associated  Sample  Energy  Associated  for Partly  Corrected  Values  Cloudy  B r i g h t n e s s and  (Wm~ sr 2  _ 1  )  of Functional A n a l y s i s to  Variation Measured  between  Radiance  49  Predicted (Wm~ sr~ ) 2  1  53  IX  Page for  Clear, Overcast  Cloudy Table  4.5  Results  Sky  Table  Table  4.6  4.7  of  Transformation to  of  4.8  Brightness  to  Cloudy  Conditions  Results  4.9  Sky of  Table  Table  4.10  5.1  Radiance  to  Radiance  Results  Cloudy  Regression  Data  Clear  from  for  56  Partly  Transformation  Regression  Sky  55  from  for  57  Overcast  Conditions  Partly Table  for  Transformation  Brightness  Table  Radiance  from  Conditions  Results  Sky  Partly  Conditions  Brightness Sky  and  Sky  showing  Obtained  and  66  Conditions  Analysis Results  Conditions as  for Clear  with  Measurements  (S),  Measurements  (NS).  for  Clear  Variation  in  Simultaneous  Asynchronous  Regression  Analysis Results  for a  Cloudy  (JD339)  Obtained  Sky  f o r Data  Simultaneous  Measurements  Asynchronous  (NS)  Values  of  (Using  Eqn.  for  Measured  Certain  Skies, (Zenith  5.11)  Observed Angle  (S),  on 74°)  Partly  71  with  and  Measurements. and  11 3  Predicted  Radiances  Zenith  71  Angles January  (Wm~ sr~ ) 2  for 20,  1  Overcast 1984  Page Table  Al.1 a  Pixel of  Table Al.1b  Coordinate  t h e 10° T a r g e t s  Video  Image  Pixel  Coordinate  of  Positions  Positions  t h e 10° T a r g e t s  Image W i t h  Visible  Visible  f o r Each  1 38  on t h e  f o r Each on  t h e Camera R o t a t e d  the  Video  by 9 0 °  1 38  xi  List  of  Figures  Page Figure  Figure  Figure  2.1  2.2  2.3  Spectral  Sensitivity Characteristics  of  the  to  the V i d i c o n  Video  ER  Newvicon  Camera  3.1  and  Filter  Curve  Spectral  Distribution  View  for Clear  of V i d e o  Relative  Camera  Response  Radiation Figure  Camera  18  Spectral  21  Diffuse  24  of  Skies  Camera  in  Monitoring  29  Position Figure  3.2  View  of  Figure  3.3  Design  Figure  4.1  Contour  Field of  for Figure  4.2  a  4.3  an  Figure  4.4  a  4.5  and  Cloudy  of  Sky,  40  Differences  Between  58  Radiances  Differences  Predicted  of  Between  61  Radiances  Sky Differences  Predicted  Results  December  Regression  30  Roof  Grid  P a r t l y Cloudy  Regression Scan,  Figure  and  Plot  Measured  the  Predicted  Overcast  Contour  for  of  on  Sky  Plot  Measured  Figure  and  Clear  Contour  for  Sampling  Plot  Measured  Site  62  Radiances  Sky for a  20,  Results  Between  Clear  Sky  65  1983 for a  December  5,  Partly 1983  68  1  XI  Figure  5.1  Geometry  Figure  5.2  Frequency Radiance  of Sky  Histograms for Clear  a) December  Figure  5.3  5.4  20,  Histograms f o r Overcast  Figure  Figure  Figure  Figure  5.8  5.9  5.10  5.11  Predicted  Skies  20,  1984  b) l 3 4 0  LAT  January  20,  1984  Frequency  b)  Histograms for Partly  of  Predicted  Cloudy  Skies  1983 12,  13,  1984  and  1983  Sky R a d i a n c e  1320  Clear  5,  January  September  Clear  for 5.7  of  January  for  Figure  1983  LAT  c)  5.6  and  a ) 1320  and  Figure  1983  Frequency  a) December  5.5  Predicted  Skies  21,  Radiance  Figure  of  b) A u g u s t  Radiance  Figure  Hemisphere  Distribution  LAT August  Sky R a d i a n c e  21,  1983  Distribution  1356  LAT December  20,  Overcast  Sky R a d i a n c e  Distribution  for  LAT  1013  January  Overcast  Sky R a d i a n c e  for  LAT  1033  January  Overcast  Sky R a d i a n c e  for  LAT J a n u a r y  1126  Overcast  Sky R a d i a n c e  for  LAT J a n u a r y  1320  Overcast  Sky R a d i a n c e  20,  1983  1984  Distribution 20,  1984  Distribution 20,  1984  Distribution 20,  1984  Distribution  xi i i Page for Figure  5.12  Partly for  Figure  5.13  5.14  for Figure  5.15  for Figure  5.16  for Figure  5.17  for b) Figure  Figure  5.18  5.19  a)  LAT  Cloudy  1417  Clear  LAT  Cloudy  1246  Partly  LAT  Cloudy  1148  Partly  LAT  Cloudy  1116  Partly  LAT  Cloudy  1449  Partly for  Figure  1340  LAT  Sky  Sky  Zenith  20,  January Sky  12,  Distribution  Sky  3,  Distribution  Sky  3,  Distribution  Sky  5,  Distribution  Distribution  13,  70°  103  1983  Distributions  Angle  101  1983  Radiance  September  99  1984  Radiance  December  98  1984  Radiance  February  96  1984  Radiance  February  Angle  1984  Radiance  Luminance  Zenith  Standard  January  105  and  50°  Distributions  Clear  Sky  Radiance  Angle  35°  and  Clear  Sky  Normalized  b)  of  f o r a)  Zenith  Normalized  107  Zenith  Angle  55°  Radiance  109  Distributions Figure  5.20  Overcast for  Sky  Zenith  Radiance  Angle  5.21  Overcast  Sky  Figure  5.22  Radiance  Distributions  Figure  5.23  Cloud  Partly  Cloudy  Distribution Figure  AlI. 1  Regression  114  Distributions  116  63°  Figure  Cirrus  Distribution  Radiance  During  117  Cover Sky  Radiance  for Zenith  Line  of  119  Angle  Radiance  64.5°  and  141  xi v  Brightness 0916 Figure  All.2  All.3  Brightness  for a Clear  All.4  All.5  Figure  All.6  All.7  29,  Brightness  for a Clear  LST J u l y  Sky  of Radiance  30,  Line  Brightness  for a Partly  Sky  of Radiance  1125 L S T A u g u s t  29,  Regression  Line  Brightness  for a Partly  and  Cloudy 1983  of Radiance  1416 L S T A u g u s t  27,  1983  Line  of Radiance  Brightness  f o r an O v e r c a s t  1250 L S T A u g u s t  27,  Regression  Line  of Radiance  Brightness  f o r an O v e r c a s t 27,  and  Cloudy  Regression  LST August  and  1983  Regression  0921  and  1983  Line  Sky Figure  of Radiance  Regression  Sky Figure  LST J u l y  Sky  29,1983  Line  1118 Figure  LST J u l y  Regression  1631 Figure  for a Clear  and Sky  1983  1983  and Sky  XV  List  of  Upper  Symbols  Case  Roman  A  projected area  A'  area  CS  asynchronous  D(z)  horizon-darkening  E_-^  total  probable  under  clear  total  probable  under  partly  total  probable  error  under  overcast  skies  E  error  variance  of b r i g h t n e s s  Ey  error  variance  of d i f f u s e  LAT  local  apparent  time  NPIX  number  Ep_  E  Q  v  on a h e m i s p h e r e  on t h e d i g i t i z e d  planar  radiance  skies  image  (metres ) 2  measurements  f o r an e q u i a n g u l a r  of a  lens  brightness  value  measured  brightness  value  measured  value  measured  (counts)  error  cloudy  of p i x e l s  2  and b r i g h t n e s s  factor  error  (metres )  of a skies  (counts)  of a brightness (counts) values  radiance  (counts) values  (WirT sr~ ) 2  1  (hours)  corresponding  to actinometric  field-of-view R R  distance 0  radius  from  point  of d i g i t i z e d  R * 0  semi  major  axis  RMS  root  mean  S  actual brightness  S  synchronous  SOC  Standard  to centre planar  of planar  square  error  image image  (Wm" sr 2  of an e l e m e n t  radiance  Overcast  on p l a n a r  Sky  (metres)  (metres) (pixels)  _ 1  ) of a  and b r i g h t n e s s formula  image  scene  (counts)  measurements  xvi  T  temperature  (°C)  X  measured  X'  corrected brightness  X^  mean  X^_j  j t h of m  X  mean  Y  measured  diffuse  radiance  (Wm  Y'  corrected diffuse  radiance  (Wm~ sr  Y  mean  Y  predicted diffuse  brightness  value  value  of a  value  brightness  diffuse  value  observations  value  radiance  of b r i g h t n e s s  2  - 1  _ 1  )  - 1  )  )  (Wm~ sr 2  Roman  of f u n c t i o n a l  line  (Wm  a  intercept  value  of r e g r e s s i o n  line  (Wm  b  empirical constant  b^  slope  of f u n c t i o n a l  line  (Wm~ sr~ )~  1  b  slope  of r e g r e s s i o n  line  (Wm~ sr~ )~  1  i n Standard  c  empirical  r  correlation  coefficient  coefficient  of  2  x x  0  y y v  0  variable  1  value  r  (counts)  sr~ ) 2  (Wm~ sr  Case  _ 2  intercept  r  point  (counts)  a^ r  (counts)  (counts)  radiance  Lower  point  of a sampling  of i t hbrightness  replicate  sampling  Overcast 2  2  1  1  _ 2  sr~ ) 1  _ 2  sr  _ 1  Sky  ) formula  constant  determination  abscissa  pixel  coordinate  abscissa  value  of centre  ordinate  pixel  coordinate  ordinate  value  of centre  electrical  output  on d i g i t i z e d coordinate  on d i g i t i z e d  on d i g i t i z e d coordinate  of video  camera  image image  image  on d i g i t i z e d  (Volts)  image  xvi i  z  zenith  angle  (degrees)  Lower  angular  a'  temperature  calibration  coefficient  7  gamma  value  of  camera  X  ratio  of  (j>  azimuth  p  6  R  sky  of  Greek  a-  0__  width  Case  Newvicon  error angle  view  i t h annulus  (radians)  (7 = 1 . 0 0 )  tube  variances (degrees)  factor  d i s t a n c e from  the  centre  projected  vertically  elevation  angle  above  of  through the  the  area  the  horizon  sky  A  to  a  normal  hemisphere  (degrees)  xvi i i  Acknowledgements  I  would  support this  like  given  study.  Steyn  for  special  to  advice  and  and  Loudon,  a  Natural  contract  the  helpful  C.  Portions the  be  my  and  the  Sciences with  the  s u p e r v i s o r , Dr.  the  J.E.  goes  to  M.  Roseberry  programming others  suggestions, R.  Roberts,  research and  guidance Hay, to  c o n s t r u c t i v e comments.  study,  Raphael, of  acknowledge  s i n c e r e a p p r e c i a t i o n goes  computer  Throughout  S.  my  gratefully  acknowledgement  assistance  comments  me  Also  his  to  were  were  Dr.  D.G.  Another  whose  technical  invaluable to  me.  me  with  namely:  S.  Grimmond,  C.  funded  Engineering  Canadian  during  provided  and  critical  Souch. by  Research  Atmospheric  and  a  grant  from  Council  and  Environment  by  Service.  1  Chapter  One  Introduction  1.1  Object ives The  aim  procedure solar  of  radiation  patterns  i s to  A derived  to  examine  of  sky  compares  partly attempt  under  method  more  these  i s to  cloudy to  the  extend  maps  are  results  this  work  Background  produced clearly.  the  analyzing  a with  a  diffuse  objective and  of  this  suggest  characteristics  relatively results  with  c o n d i t i o n s and the  knowledge  radiance  any  those  under  under of  of  the clear  earlier the  overcast  diffuse  solar  regimes. from  i s presented  i n an  of  stationary,  observations  radiative  imagery  of  system  producing  Another  record  sky  complex  video  imaging  sky  necessary.  under  for predicting  coordinate  1.2  aim  diffuse  varying  observational technique  radiance  of  development  of  of  dome.  attempts  i n an  of  means  be  further  from  aim  to  complex  radiation  the  appear  c o n d i t i o n s and  skies,  video  that  distribution  more  sky  a  this  study  A  resolution the  under  i n v o l v e s the  with  an.experimental  distribution  hemisphere  combining  over  develop  angular  assess  improvements  studies.  sky  procedure  high  i s to  the  observations  fast-response,  This  the  programme  actinometric  radiance  over  This  measurement  study  research  for determining  conditions.  sky  this  attempt  the  brightness  and to  polar  display  the  data  2  Increasing  research  on  the  effective  radiation  incident  on  sloping  surfaces  fact  the  of  diffuse  radiation,  of  that  the  total  role  incident  shortwave  load,  understood.  Designers  of  solar  researchers  interested  in  catchment  studies  have  paid  intensity  across  Currently  the  an  assumed  (Morris the from  beam  radiation  solar  results. the  into  radiation  the have  Several  assumptions  distribution.  Kondratyev  assumption  of  and  (1970).  Ohmura  an  isotropic  empirical  analysis  realistic  pattern  Morse  and  radiation  is  and  may  type  Sun  hence of  the  from  and  the  and  those  snowmelt  sky  of  Brunger,  component  contrasts which  fully  or  and  the fraction  distribution  (Hooper  component  the  yet  systems  diffuse  This  determined  substantial  not  the  over  solar  its 1980).  rests  on  hemisphere with  may  be  analyses  of  calculated  geometrical inclined  surface  (Hay  and  1980).  Investigations diffuse  1971).  between  to  the  distribution  equations  relationships  of  a  is  of  acknowledged  evaporation  hemisphere  determination  has  collector  attention  sky  Lawrence,  precise  Davies,  the  radiance  and  direct  little  modelling  was  not  be  been  al.  of  varying  to  approximate  adopted  pattern  convenient this  with  invoked  (1955)  radiance  support  (1958)  as  the did  Gamier  mathematically, model  suggested  concentrated  approximated  Sun-centred  undertaken  have et  distribution  and  a  more  sought.  Czarnecki  largely  been  sky  Although did  directional  or  as  in  the  that  diffuse  region  around  directional  heliocentric  model  can  radiation. greatly  the  Sun  This  3  overestimate  the d i f f u s e  and  1980).  Brunger,  assumption values  heliocentric values  much  highest Morris  Later  of Morse  of energy  by N o r r i s  were  those  noted  surface  that  day o r i g i n a t e d  (1966)  against  measured  f o r monthly  mean  values cover  only  (Hooper  tested the  that  the cloud  found  slopes  and found  for daily  when  (1971)  on a c l e a r  (1958)  yields errors  than  and Lawrence  component  studies  inclined  assumption  errors  f o r Sun-facing  and Czarnecki  on a n  larger  radiance  the radiance  and t h a t was  the  greatest.  57% o f t h e d i f f u s e  within  60° o f t h e s o l a r  disk. A  fixed  radiation  combinational  as  isotropic,  was d e v e l o p e d a  by Hay  variable  ratio  radiation.  This  transmissivity index  a n d was  error  (RMS)  (1978).  of the d i r e c t  and Brunger  describing  both  This  was  factors: component; to  an  based  (1980)  that  sufficiently  normalized  stable  developed  component;  clear  to allow  the sky  as h e l i o c e n t r i c  improved  by  assuming  the atmospheric as an  and root  a three  which  was  anisotropy mean  square  three  results  (eg. Steven,1977)  for consistent  of  brightening  Their  sky radiance  of  distributions.  superposition a horizon  component  capable  sky radiance  component.  findings  half  1980).  on t h e l i n e a r  other  bias  (TCCD) m o d e l  and a c i r c u m s o l a r  later  used  both  and overcast  isotropic  substantiate  suggested  clear  half  beam c o m p o n e n t  and Brunger,  distribution  treated  and h e l i o c e n t r i c d i f f u s e  model  t o improve  continuous  model  I t was  isotropic  anisotropic  found  which  and the remaining  between  (Hooper  Hooper  model  seemed  which  distributions are mathematical  4  modelling  (Hooper  and  empirically-based data by  base  not  with  being  As  radiance  skies  and  clear  measurements  technique  sky  the  described  obtained  points  in the  system  of  of  over  Valko sky  various  provided  the  and  directional  radiance.  Hooper  developing  an  automatic  radiometer  to  measure  capable  creating  aquisition was  system  designed  radiance  and  a  was  primarily  under  partly  Two  radiance  sky  scanning  radiance.  substantial entirely to  study  cloudy  other One was  form  and  This  was  the  that  scanned  at  121  using  a  radiometers, The  the  using  and  as  data sky by  sensitive system  the  of  of  an  problem  a  scanning  well  a  measurement  distribution  c o n d i t i o n s as  of  variations  base,  a  to  azimuths  system  of  utilized  computer-controlled. the  in several  devices.  and  diffuse  radiance  study  approached  data  as  standard  silicon-diode  (1982)  of  characteristics  Sun-tracking  Brunger  of  angle  This  distributions  sky  define  e l e v a t i o n s and  other  the  state,  out  the  series  procedure.  pyranometers,  radiometer  carried  zenith  dome.  of  well  distribution  A to  as  steady  determine  spatial  similar  accuracy  skies.  been  to  solar  sky  the  approximately  pattern.  the  any  calibrated  cloudy  turbidity.  the  a  at  absolute  been  in order  of  with  by  angular  (1980) where  rotating  of  the  the  preserved  attempted by  an  attempted  effects  intensity  had  partly  radiance  i n terms  which  programmes  model  of  As  limited  c o n d i t i o n s have  (1977)  were  distributions investigate  the  represent  such  1980).  i t was  analyses  Steven  standard  radiant  which  under  studies.  model,  a p p l i c a b l e to  clear  measurement  Brunger,  was  data This  work  diffuse under  the  5  better-documented presented  the  of the angular  overcast  Kimball  s k i e s have  and Hand  brightest  (1922)  area  a quarter  an  e m p i r i c a l formula  or less  Standard  data  pattern  range,  light  recent  to test  spectral  radiance  function  similar  significant  high  distribution atmospheric solar  energy  determining  to  Sky  have  been  spectrum t h e human  measured  frequently.  taken  by S t e v e n  by  a n d i s known a s (1971)  required while  found  that the  a narrow  spectral  He  under  noted  rapid  overcast conditions. and Unsworth  t h e SOC  well  decreased  represented  He  over  formula.  worked  clouded sky,  t h e s k y dome  by p l a n t s .  a broad  between  formula  (1980), and  waveband,  found  that  but there  might  be  radiance  and  a  luminance  skies. set describing the angular  solar  conditions i s a applications. the intensity i s that  over  between  over  t o t h e SOC  of d i f f u s e  was  Grace  the agreement  data  This  (SOC) f o r m u l a .  distribution  radiance  and the r a d i a n c e  (1942)  investigation  quality  out less  and Spencer  t h e SOC  of overcast  of d i f f u s e  f o r a densely  of radiance  with  differences  distributions A  that  of h i s observations,  designed  the  by Moon  i n the radiance  A more  carried  interception  corresponded  changes  been  at the horizon.  Overcast  investigating  distribution  found  on t h e d i s t r i b u t i o n  mean  b u t few r e s u l t s  was a t t h e z e n i t h  to  the  sky cases  thus f a r .  Studies below  clear  this  radiation  frequent The  eye f o r a greater  immediate  provides part  varying  requirement  distribution part  under  in evaluating  practical  use of  i n the v i s i b l e the visual  of t h e day  part of  environment  (Sastri  and  6  Manamohanan, attempts Earlier  to  1975). use  that  fluxes. the be  i n the  sky  first  between  et  the  energetical  and  luminous  compared,  observed  due  the  applicability  of  (1977)  d e t e r m i n a t i o n of  clear  the  skies,  previously  (1977) over  used  34  a  requiring  on  a  be  found  that  adequately atmospheric  minutes  units,  to  diffuse from  were  a  taken  a  luminance  conditions.  He  to  general by  of  distributions patterns  developed  radiation  independent standard,  of  clear  sky  measurements  McArthur  c o u l d be  a  These  angles.  by  spatially  radiance  diffuse  radiance  further  with  Steven  scan.  be  zenith  Steven  hemisphere,  enabled  radiation  both  the  to measure  respect to  solar  of  these  each  found  may  correspondence  study  sky  of  intensities  radiance  the  series  step  shortwave  the  They  radiation  distributions.  This  long  for different was  with  of  compare  across  levels.  on  lack  to complete  s u r f a c e and  methods.  distribution  responses  actinometer  normalized  based  work  involve  linear  luminous  radiation  standard  attempt  is a  angular  supposed  transect  turbidity  produced This  40  were  distributions to  in a  horizontal  atmospheric  the  Linke-Feussner  about  measurements  the  p u b l i s h e d luminance  points  far  intensity.  quantitative  photometric  d i d not  there  different  Because  of  of  a  radiant  and  diffuse  instruments.  the  of  although to  the  and  energetical  properties  on  so  a l . (1955) d e s c r i b e d a  approximation  the  not  presented  luminance  Hence,  directly  was  Kondratyev  between  relationship  techniques  c o n v e n t i o n a l r a d i o m e t r i c measurement  r e s e a r c h by  relationship noted  The  and  (1978)  estimated  for varying  sensitive,  who  7  fast-response, accommodate changing  photographic  the  spatial  cloud  took  fisheye  during  measurements. form  measured the  radiance  addressed from  the  f o r haze  the  of  Even are  the  need  accurate  for  Hay,  being  dome a n d  are  Dave  radiative  a  into  approach  able  to  the  in  and  had  provide  most  an  complex results  agreement  Dave  a  with  This  i n good  transfer  to  (1978)  correlated  (1981).  dominant  with  quantitative  point-of-view  luminance,  measurements  radiance  even  The  (1980) by  highly  of  of  negatives  1978).  represented.  some the  techniques  with  (1981)  the  atmosphere  focussed  wavelength  diffuse  photographs. actinometer  have  the  very  to  The  radiance These used  limitations  i s attempting stage  described  inadequacies.  the  reduction  be  to  rapidly  McArthur  actinometric  to  of  camera  photographic  sky  Hay  SLR  attempt  time  1978).  mm  methods  models  measurement  the  of  and  the  as  technique data  the  response  Hay,  35  density  and  of  an  and  on spectral  radiation.  without  calibrate  hence,  of  sky  the  not  problem  a  the  visual-air-quality  computations purity  be  in McArthur  computations  of  of  was  complexities  long  and  sequence  previous  mapping  which  previously restricted  (McArthur  over  the  using  film  conditions could  presented  by  a  showed  instantaneous  temporal  (McArthur  Reduction  advantage  sky  had  photographs  lens  digital  which  conditions  all-sky  and  c o n d i t i o n s and  instrumentation cloudless  technique  avoid  i s hampered  by  approach  obtain  that  the  (McArthur. by  is  measurements  calibrations to  McArthur  the  the  are  (1978)  restricted  i n order only  to  as  measurements  and  photographic and  length  Hay, of  1981). time  The  required  8  to  digitize  analysis  photographs  to  The  (1  h.,  40  s m a l l e r - s i z e d data  most  recent  mins.)  to  be  used  radiometric  ( a c t i n o m e t r i c ) measurement  video-based  system  equipped  with  type  of  from  the  video of  a  single  their The  video  processing  and  field  framestore, displayed  video  storing  of  a  video  (intensity)  contours  Cannon  and  Dwyer  entire  sky  hemisphere  immediately. stored  on  but  also,  light  has  to  techniques  the used  for  to  limitations  of  data  the on  the levels,  the  video  after  this  the  analyze be  data  image  map  the  the  data  conveniently  and  archiving.  only  purposes,  were  system,  effectively  not  a  iso-luminance  With  might  assess  Dwyer,  from  the  future analysis  research  and  gather  images  digitized  intensity  could  and  passed  which  shortly  1981).  they  video  ability  (Cannon  to  obtained  This  digitizing,  data  so  camera  density  and  of  is a  (derived  (Cannon  Digitizing  processing  found  for daylighting  in space Due  tape  the  The  different  Dwyer,  same  and  i n s t a n t a n e o u s l y and  Digitized  magnetic  "fluxmapper"  and  (1981)  information  be  luminance  capable  time.  video  fisheye lens.  scene  with  radiation  vidicon  monitored  monitor.  might  a  the  the  was  solar  equal  with  unit  into  computer  (Cannon  a  real  television  of  within  video in  using  imaged  signal  processed  rapid  digitized  be  location  facilitated  is  to  limits  in conjunction  of  projection  objects  framestore,  now  on  allows  image)  1981).  through  'fluxmapper'  orthographic  projection  regardless Dwyer,  an  this  sets.  technique  or  and  the  the  The  quantity,  quality  of  1981). radiometric the  measurement  directional  distribution  9  of  diffuse  solar  paragraphs, making  these  sky cases  have  (1969),  Grace  (1971),  of  study  Even  the  mapped The  camera  (1981).  photographic since  there  video  images  Because  of  radiation possible luminance video  the as  to  to  and  system, This  the  taken  and  distribution changing  or  more of  great  rapidly  characteristics of  of  all-sky  Rondratyev McArthur's response  time  photographs.  distributions  could  sky  that  study  utilizes  described  improvement  over  by  now  the  d i s c u s s e d i n McArthur i n time  (1978),  between  when  results  are  obtained.  between  visible  and  total  the  (1978),  i t is  a  Cannon  measured  procedure  diffuse  present  reduction  actinometric  precise  complex  with  to  d i s c u s s e d i n McArthur  i n f o r m a t i o n from  for a  for  the c o n v e n t i o n a l  i n the  technique  significant  The  under  (1980).  problem  radiation  similar  is a  relationship  flux.  work  efficient  1978).  developed  combine  or  radiance  Unsworth  overcome  preceding  very  skies  i n the  the  shortwave  indeed  radiance observations with  video  information i s representative  radiation allow  are  cloudy  technniques  digitizing is a  i n the  proved  complex  diffuse  (McArthur,  Dwyer  to  not  supplementing  complex  technique  The  alluded  measurement  video-based and  attempted  most  have  Steven  i n s t r u m e n t a t i o n by  radiometric  be  been  described  partly  conditions.  such  (1978)  as  procedures  o b s e r v a t i o n s under  changing of  radiation  images of  the  and total  followed in this  representation  of  the  radiance p a r t i c u l a r i l y conditions.  assume  that  shortwave study  will  angular under  rapidly  the  10  Chapter  Two  Instrumentat ion  2.1  Measurement A  Kipp  76-0319) These  and  was  of  Zonen,  used  and  Solar  Radiation  Linke-Feussner actinometer  t o make m e a s u r e m e n t s  measurements  calibration  Diffuse  were  carried  verification  of  of  (Model  diffuse  out  solely  the  distributions  No.  radiance.  for purposes of  of  sky  radiance. The radiant  actinometer energy  conditions. six  accurately  Built  massive  become  and  act  body  which  rings  affect  Moll  be  occurring readings  acts  subject  near of  compartments,  the  the  as  a  one  of  compensating  to guasi-adiabatic  thermopile surface  instrument are  known  the  to  This which  i s screened  from  However, i t  pressure  be  the  thermopile  device.  (IGY,  These  inside  1958).  which  of  thermopile  a i r currents  compensated  two  may  towards  specially  into  consists  diaphragms.  (IGY,  is  so  smaller  as  measure  turbulent  body  thermopile  a  and  the  function  turbulent  to  relatively  the  uses  radiation  even  stability,  which  to eliminate  instrument  still  under  progressively  could  divided  instrument designed  to ensure  copper  openings thus  i s an  changes  1958).  The  independent  of  wavelength. The  body  accurately the 0°  body to  of  the  sighting  to monitor  40°C  (IGY,  actinometer the  Sun  and  temperature  1958).  The  i s equipped with  a  a  thermometer  fluctuations  instrument  with  within  i s mounted  device set a on  for  inside range a  of  stand  11  fitted  with  increments  of  0.1°.  filter  instrument Coulson  for zenithal actinometer  positions  over  shows  were  in  movements,  1° scaled  i s weatherproofed  in  with  and  with  one  taken  a  built-in  metal  using  a  filter  shutter.  quartz  ring  For  filter  this  made  i t s transmission properties allow  the 99%  range  0.20/iin-3 . Ojum  response  actinometer  Environment  Service  experiment.  i n 8-10  was  to  calibration  resulted  (IGY,  1958).  seconds,  2.1.1.1 The  sr  and  at  of  92% This  according  to  an  diffuse  1  m  Atmospheric  Ont.,  before  constant with  2  of  an  the  resulting  start  from  angular  0.417MV(Wm~ sr~ )~ . 2  determination  equivalent  the  Diffuse  radiation  solid  voltmeter  sensitivity  a  this  (Hewlett-Packard  1/2  Radiation  signal  4  for  _  radiance  Hewlett-Packard  accuracy  Downsview,  16.9AiVW  i n the  the  of  an  half  1  This  1  equivalent  angle  of  5.08°  respectively.  Recording  has  by  calibration  isotropic  aperture  0.0247  calibrated  The  investigation  uniform  was (AES)  sensitivity  and  is divided  (1975).  The  that  which  i s equipped  ultrasil;  transmission  the  The  measurements  homogenized  of  control  actinometer  four  study,  a  circle  plating.  The with  azimuth  and  intervals chromium  an  digit  was  voltmeter of  1 M V on  range  i s quoted  Manual,  1979).  as  Signal  monitored (Model a  20  3466A).  mV  ±0.05%  with  range +  3  a This and  digits  the  12  2.1.2  A n a l y s i s of of  2.1.2.1  to  there  been  has  Robinson  i s more  temperature  the  a  ( i n degrees  s t u d i e s by  calibration  not  readings  by  0.2%  per  calibration of  the  acceptance  aperture  normalized  however,  Measurement  the  in this  Sensor  study  1958).  this  is  However  accuracy  conservative  on  the  the  as  estimate,  estimate  C e l s i u s ) and of  Forgan  the  of  by  study, will  the  approached  c o n d i t i o n s of  much  the  be  and  zero  AES,  for  (Coulson, suggest  smaller the  in  the  where  solar 1975).  that and  the  so  data.  manufacturer's  used  an  under  The  10.16°  vertical  20°C  for  a'(T-20))  a'=0.002  (1980)  be  +  factor  i t As  value  error  temperatures  can  affect  °C.  out.  of  (1  temperature-correct  actinometer  carried  calibration  factor  c o r r e c t i o n s for other  was  instrument  the  with  (IGY,  of  more  by  dependence  conditions  the  ±1%  actually  to  tested during  Hence  sensitivity  a  and  may  necessary  temperature  During  used  temperature  Pascoe  coefficient  deemed  analysis.  that  i s expressed  Empirical  the  of  dependence  at  of  accuracy  temperature  was  Associated  empirical testing  radiation  this  with  reasonable.  radiation  not  Error  actinometer  suggests  i s temperature  was  the  an  no  (1966)  The  T  have  Associated  Radiation  Linke-Feussner  estimated  direct  Error  Diffuse Solar  A n a l y s i s of  The  ±2%  the  isotropic  analysis  total  outside  the  of  In  response angular  anisotropy  the  angular  radiation  resulted  angle.  horizontal  radiative  analysis  in  other of  words,  the  limit.  should  an  If  exist,  there  1 3  could  be a n e r r o r  associated with  actinometer  could  total  of aperture  angle  During  this  undertake it  be  study,  sensitive  would  were  respond  error  than  sources  to these  n o t t h e means  of such  n o t be g r e a t e r  measurement; the  to radiative  and c o u l d  there  an a n a l y s i s  each  sources.  available  and i t w i l l  the quoted  beyond t h e  to  be a s s u m e d  overall  accuracy  that  of the  act inometer. Another in  alignment  radiation  true  also  source  an e r r o r  t o any change  for anisotropic  assumed  of e r r o r  of the actinometer.  conditions,  contribute be  possible  Once  again,  i n alignment  in voltage radiance  t o b e no g r e a t e r  could arise  output  offsets  for isotropic  would not but t h i s  distributions.  than  from  the overall  would not  This  error  accuracy  was  of the  sensor. The implies error  error that  analysis  the t o t a l  of the sensor  per°C)  as  probable  ((2)  T  = Therefore  error  and Rabinowicz  consists  (±2%) and t h e temperature  2  +  (2) ) 2  of the  (1967), relative  correction  (±2%  1  /  (2.1)  2  2.8%. the t o t a l  probable  i s approximately  2.1.2.2  by Cook  follows:  E =  sensor  outlined  3%  A n a l y s i s of E r r o r  error  ( E ) a s s o c i a t e d with T  the  .  Associated with  the  Recording  Instrument The digits  accuracy  of the voltmeter  (Hewlett-Packard  Manual).  i s quoted From  this,  as ±0.05%  + 3  i t i s necessary  to  1 4  establish the  what  3 digits  r e p r e s e n t s a s an  actinometric calibration  absolute  error  o f ±4.91 Wm~ sr~ . 2  variation  i n the r e l a t i v e  a  radiation  diffuse  determine relative scan  rather  o f t h e HP  than  radiance  voltmeter  utilizing  a  2.1  i t is a  shows  single  Given t o an  the  associated  simple  value  c a n be  error.  corresponds  of the recorder  Since  diffuse  this  Table  1  error  signal.  the average error  constant,  absolute  matter  per scan,  calculated  representative  with  to  the  f o r every percentage  error.  2.1.2.3  Error  Associated with  the Measurement  of D i f f u s e  Solar  Radiat ion The diffuse  E  probable radiation  = Y  E = T  Y +  where  E^  component  error  associated with  c a n be  x  ( I ( E . ) ) i =1  x  ((0.02)  2  (.0005) ) 2  2  +  calculated  1  (Wm~ sr~ )  a  Table  2.2  2.2  error  t h e measurement  value  error  1  shows  associated with  Determination  2  +  (4.91/Y  )  2  (2.2)  radiance scan.  as:  1 / 2  2  of  2  (0.002)  i s the r e l a t i v e of  /  t h e measurement  associated with  system  based  on  and n  Y  the i t h  i s the average  observations  taken  examples of the probable  various  radiance  sky during  relative  values.  of B r i g h t n e s s Values  from  Video  Imagery  1 5  Table  2.1  Signal  Recorder Signal  (Wm  2  )  Error  Associated  Input(MV)  with  Absolute  a  Diffuse  Error  Radiation  Relative Error  25  10.44  50  2 0 . 8 7  ±3  MV  19.64  9 . 8 2  or ± 4 . 9 1  (%)  Wm  -2  100  41.74  4.91  150  62.61  3 . 2 7  200  8 3 . 4 9  2 . 4 6  250  1 0 4 . 3 6  1.96  300  1 2 5 . 2 3  1.64  1 6  Table  2.2  Probable Relative Errors Radiances (Wm~ sr~ ) 2  Average Radiance (Wm sr ) _ 2  _ 1  Associated  with  1  Probable (%)  Error  10  49.14  20  24.63  50  10.02  100  5.31  150  3.81  200  3.17  Sample  17  2.2.1  Video A  video-based  luminance system  2.2.1  will  be  and  Camera,  The  video  camera  ER  of  Fisheye  The  (Panasonic  clear,  and  Newvicon  high  quality  studies  sensitivity  of  response  short-wave  the  spectrum  to a  The actual  region  transfer  V,  from  cuts  that  an  the  the  element  ER  point  on  the  used  TV  Newvicon  Manual  in  This  i s often  increases  tube  by  from  the  the  0.940/.m.  are  such  a  scene,  of  high  tube.  involving  maximum  off at  characteristics  b r i g h t n e s s of  output,  and  the  and  (Operating Instructions spectral  near-infrared  of  for  Filter  image  The  of  study  component  pick-up  Panasonic,1981). end  in this  WV-1850) u s e s  Red)  spectral  i n F i g . 2.1  used  Each  Lens  research, including  microscopy. shown  a  was  individually.  (Extended  produces  system  System  analysis.  discussed  Video  areas  Monitoring  imaging  .1  camera  is  and  aquisition  resolution,  in  Camera  that  i f S  the  is  the  electrical  photoconductor  can  be  shown  by: V For  this  =  kS  (2.3)  7  project,  y  the  value  (Pacific  Communications  transfer  characteristics.  accuracy  of  Section and  4.1.1  j  during  brightness,  this  the  camera  was  equal  L t d . , p e r s . comm.) p r o d u c i n g  this  indicate  of  a  There  was  not  study,  but  since  linear  indicates  the  the  relationship that  the  means  linear  results  was  1.0  t o check  between  camera  to  the  given  radiance  indeed  in  1 8  0.4  0.6 Wavelength  Figure  2.1  '0.8  1.0.  (jum)  S p e c t r a l S e n s i t i v i t y C h a r a c t e r i s t i c s of the ER N e w v i c o n C a m e r a R e l a t i v e t o t h e V i d i c o n Camera ( P a n a s o n i c O p e r a t i n g M a n u a l , 1981)  19  performing The  as  standard  target  area  target  may  possible  of  for  resolution ER  of  of  of  camera  about  45  properties are  This  (with  a  view  In  cm.  than to  tube  as  less  is  camera  figure  limits  the  centre  on  useful of  the  and  it  is  horizontal  for  a  horizontal  distortion either  has  the  a  corners  from  2%  has  The  rated  than  The  end  tube  Geometric  axis.  low  at  vary  centre.  Kodak  of  this  of  a  for  the  signal-to-noise  useful  signal-to-noise  dynamic  ratio  of  range 1:1)  to  the  and  so  lens  It  system  equi-angular  Description  and  I.  a  to  of  the  the  tests  carried  was  found  that  and  lens  in  projection, projection  out  the  of  the  to  confirm  properties  combination  170°-174°  filter  fisheye in  It  was  transmission  reduction  visible  order  density  purpose.  0.1%  these  the  neutral  this  sufficient for  lens.  an  of  resulted  sky  in  a  hemisphere  I).  Wratten  with  with  approximately  density  for  fitted  fisheye  addition  neutral  was  imaging  (Appendix  3.0  at  i s given  dB.  1.25  resolution  lines  i n Appendix  video  total  used  x  particular  800  camera  custom-built  the  cm.  camera  150:1. The  them  Newvicon  resolution  horizontal  rating the  0.93  vertical This  or  inch  poorer  Newvicon  vertical  one  about  have  resolution.  this  expected.  part  filters  light  of  the not  to  i t was  avoid  (gelatin) found factor  of  are  lens,  image  only  recommended  No.  96.,  neutral  necessary  intensity.  spectrum  a  use  to  (0.400MITI use  in  a  A was  density  No.  achieve  Neutrality  for  to  saturation.  filter,  that was  necessary  is  to  valid  0.700Mm)  the  20  ultraviolet  or  infrared  regions.  sensitivity  characteristics  of  Fig.  the  video  combination,  as  determined  properties.  It  can  be  seen  portion  of  the  spectrum  The  peak  the  visible  near-infrared wavelengths From  region. which  the  latter  investigate  the  combination  to  to  that  results,  spectral  This  their the  clear  would  analyze  a  i s much  and  provide  video  of  the  system  than  to to  necessary  video sky  useful  image  in  to  the those  filter.  the  cloudy  filter  spectral  less  deemed  of  and  spectral  corresponds  the  i t was  the  respective response  by  response  shows camera  response  transmitted  typical  distributions. attempting  are  from  2.2  with  to  camera/filter  energy  knowledge respect  when  to  luminance  information. Kondratyev distribution radiation Table  by  must  cloudy  et day  be  is  the  spectral  example The  of  spectral  originates  less  very  from  work  in  this  direct sky  the  in  than  composition of  Kondratyev  the of a  in  a  2.3. Sun  energy  and  in  difference solar  case  cloudy  of  that  of  For will  is  a  reason,  used  cloudy  clear  of  the  this be  a  periods  composition  typical  typical  (1969)  the  for  to  the  diffuse  spectral  Table  for  the  presented  that  and  distribution  given  is  irradiance  that  distribution by  of  giving  extra-terrestrial  indicate  cloudy  distribution  spectral  energy  a  showed  spectra  table  for  2.3  spectral  similar  a  radiation;  Table  for  of  energy  the  spectrum  distribution  (1982)  extra-terrestrial  published  solar  from  Analysis al.  has  solar  diffuse  energy  sky.  Bird  the  Results  the  radiation clear  and  2.3.  between  in  (1969)  sky  as day.  also  depicted  in  an  21  3.0  —  2.0  >  co  1.0  CO CD  0.4  0.5  Wavelength  Figure  2.2  Video Curve  Camera  0.6  0.7  0.8  0.9  (.um)  and  Filter  Spectral  Response  22  Table  2.3  Energy D i s t r i b u t i o n i n the Solar Spectrum Outside the Atmosphere ( 1 0 " c a l / c m m i n ) a n d the S p e c t r a l C o m p o s i t i o n o f D i f f u s e R a d i a t i o n (10 c a 1 / c m m i n ) From K o n d r a t y e v (1969). 3  2  6  DX,M  0.28-0.30 0.30-0.32 0.32-0.34 0.34-0.36 0.36-0.38 0.38-0.40 0.42-0.44 0.46-0.48 0.50-0.52 0.56-0.58 0.64-0.66 0.70-0.72 0.78-0.80 0.86-0.88 0.98-1.0  Sun  2.6 1 1 .5 21.8 31.3 35.2 36.0 54.3 62.6 59.7 54.6 48 . 4 42.9 35.3 27. 1 21.0  1 cm of clean a i r 3  4.4 14.4 21.9 23.5 20.8 16.9 17.2 13.7 9.3 4.4 2.8 1 .8 0.8 0.5 0.2  100 d r o p s r = 0 . 1M  0.05 0.27 0.44 0.54 0.51 0.45 0. 52 0.46 0.36 0.25 0.14 0.09 0.05 0.03 0.02  25 d r o p s r= 0 . 5M  0.14 0.78 1 .62 1 .78 3.52 3.78 6.41 7.65 7.35 6.67 5.48 4.29 3.04 2.11 1 .36  2  5  drops r=1/_  1.0 4.6 9.2 12.8 14.6 15.1 23.2 25.6 20.6 14.4 18.6 20.0 18.0 15.8 12.4  23  Fig.  2.3. The  procedure  together and  respond  cloudy  t o determine  spectrally  day i s as  how  (for a certain  between  2) n o r m a l i z e 3) m u l t i p l y  of  each  of  The  final  adjustment  to clear  system  expect  t h e camera  compared  to a clear  Fig. decrease for  O.lOMm  sky and c l o u d y  normalized  value  interval  and determine  between  sky c o n d i t i o n s  of the c l e a r  clear  to respond (between  sky.  the magnitude  the camera's  and cloudy  to a typical  composition  clear  of the c a m e r a / f i l t e r  and cloudy  response  15.7% d i f f e r e n c e  spectral  considered  (clear  curves,  after  i s 1 1 5 0 5 a n d 9941  f o r the overcast and c l e a r  represents a  camera can  t h e two c u r v e s  integration  units)  to a  OMITI  f o r the camera/filter  (relative This  f o r every  the differences  response  filter  area  by t h e c o r r e s p o n d i n g  0 . 40jum- 1 .  4) i n t e g r a t e  waveband)  curves  t o t h e same  the s e n s i t i v i t y  curve  between  and  0 . 38/im- 1 . Oum  the curves  combination  camera  follows:  1) I n t e g r a t e t h e t w o s p e c t r a l sky)  the video  between  sky, r e s p e c t i v e l y . the response  and cloudy  sky.  1.157 t i m e s  0.4(xm-1 . Oum)  The i m p l i c a t i o n s  more  of the  Given  this,  to the typical  o f an o v e r c a s t of t h i s  one  sky as  finding  will  be  i n S e c t i o n 4.2. 2.3 s u g g e s t s  i n t h e amount  locations  away  from  that  forclear  of energy  skies  present  the zenith.  there  i s a  marked  in a particular  However,  waveband  although the  24  210  in  Figure  2.3  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 Solar Radiation f o r Clear S k i e s at the (1) Z e n i t h and (2) a t a P o i n t Where t h e Sky Luminance i s M i n i m a l . From Kondratyev (1969)  26  value  of that  corresponding controls  In was  the  this  The  study,  beside  transferred  easily  latter image  the video  and f l o p p y In a  the disks  Any b r i g h t n e s s  abstracted  (on/off  i s derived  i n the sky. button)  saturation  similar  and s t o r e d  on  be  panel  level  monitor  used  fashion,  (Model  images  23AG)  hosted  images  could  f o r viewing  disks.  EVM  convenient  to store  t h e image  the floppy  and  adjusted  II microcomputer  were  from  may  voltage  blackness.  to the framestore  information  the  Front  and p r o v i d e d  An A p p l e disks  or  video  framestore  from  and v i d e o  two c o n t r o l s  an E l e c t r o h o m e  memory.  from  value  point  and viewing.  framestore  framestore  date.  power  so as t o a v o i d  processing  digital  AC  controls.  located  image  The c o u n t  to the r e l a t e d  include  blackness manually  pixel.  could  from  be  at a  also  the  be  later  25  magnitude angle, the  of t h e energy  the d i s t r i b u t i o n  spectrum  wavelengths sensitive spectral and in  that  resides  1.0/im t o d e t e r m i n e  clear  response  The  capable video  'pixels'  can then  front  continuously  Model fast  i s not p a r t i c u l a r i l y was a p p l i e d  changes  tothe  values  at the zenith Thus,  t o changes  between  system  in zenith  in relative  0.4Mm  t o changes  angle.  An  o f 31.22 a n d 30.74  a n d where s k y no v a r i a t i o n i n  i n the spectral  angle  could  be d e t e c t e d .  274D  video  framestore  composition  picture  be a c c e s s e d  i fdesired. panel  in real  'freeze'.  time  A series  levels  (256 g r e y  levels  study,  the count  value  and d i s p l a y i n g  may  be v i e w e d  elements  allows  of 8 switches  of a p i x e l  will  frame o f video  known a s  2 5 6 x 256 t h e image button  facilitates  bits).  unit i s  processed and  and r e l e a s e of t h i s  in total-8  a single  i n t h e image  contains  switch  This  on a s t a n d a r d  by a c o m p u t e r ,  An i m a g e  pushbutton  has a  A / i ) a n d D/A c o n v e r t e r s .  storing,  and the r e s u l t s  Individual  re-displayed,  frame  with  of d i g i t i z i n g ,  monitor.  A  system  Video  memory  memory  which a r e  o f t h e camera  respectively.  azimuth  Framestore  Colorado  solid-state  with  i n the zenith  Video  system  and  The peak of  i n F i g . 2.3 f o r w a v e l e n g t h s  radiance  was m i n i m a l ,  zenith  t h e same.  methodology  resulted  sky d i f f u s e  with  0.45-0.48Mm  the response  of the video  2.2.1.2  between  composition  analysis  t o changes  remains  the camera/filter  depicted  the spectral  may c h a n g e  of energy  The p r e c e d i n g  curves  luminance  due  still  to.  alternative for  spectrum  pixels.  t o be  viewed  results  ina  display  For the purposes  be t e r m e d  of grey of  this  the 'brightness'  27  Chapter  Three  Experimental  3.1  Field  Measurement  Field the  Geography  campus  at  latitude of  work  85  the  surface and  of  of  metres  and  do  primarily required  are  even  built  frame  had  the  out  an of  the  to  although  the  the  considerably  to  surface  an  camera  for  the  easy  3/4  levelled and  and  to  of  It  computer  however.  cloud  regimes  with  access  was  chosen  facilities  i n p o s i t i o n by  galvanized aligned  correct  due  steel  a  plate  tubing.  North-South,  p o s i t i o n i n g of  the  the  1000  system.  held  inch  instruments.  link  imaging was  gravel  (Hay  northwest.  horizon  and  in  local  north  and  local  a  is  approximately  was  tar  area  variability  1979).  a  Columbia  Vancouver's  the  north  local  of  elevation  study  (Hertzman,  video  support  and  west  to  roof  l o c a t i o n i s at  immediately  rise  further  the  British  directional  mountains  affect  on  uplifting  space  of  km.  westerlies  Vancouver  higher  provide  been  for  9  Climatically,  contribute  site  video  frame  West  This  122.96°W  i s roughly  coastal  out  U n i v e r s i t y of  longitude  significantly  storage  by  The  allowed  The and  to  and  carried  Columbia.  mid-latitude  North  roof  and  the  British  site  orographic  The  at  was  exhibit considerable  mountains  through  power  the  not  study  district.  1976).  cities  These  The  winds  Oke,  They  49.74°N  business  zone  this  Vancouver, of  Site  Department  metres.  central  for  Procedures  on  a  This and  occulting  to  28  disk.  When  spirit  level  Fig.  3.1  normal  the  of  table,  the  instrument  be  had  reference  located  and  of  fisheye  frame  was  sequence details  3.1.1  of  Sky  by  on  to  at  a  a  the and  then  focus  on  and  f o r the same  sky  with  in Fig.  camera  a  3.1.  in i t s  the a  was  the  lens.  i n the  1.5  table  camera  sky  was  siting  a  located  on  compass  and  This  metres  actinometer  a  the  plane  the  roof  vent  deemed  to  that The  video  as i t  a was  plane of  the  field-of-view  camera  and  support  actinometric field-of-view  due  to  measurements.  the  a  on  northeast i n the  ensured  served  ensured  measurement.  Likewise,  on  mechanism  and  the  would  placed  system.  and  and  This  a b s t r a c t e d from  target  f o r each  the  i n the  actinometer  way  plane  hemisphere.  point  lens  approximately time  F i g . 3.2  illustrates  the other  set-up.  Factor Analysis  view was  the  the  both  actinometer  experimental  View  levelled  levelled  ensure  local  camera  camera  the  sky  and  brightness value  radiance  (1980),  received  no  never  of  The Steyn  at  as  same  to  the  i n the  camera the  way  When  location  was  frame  was  depicted  previously sighted with  with  positioned table  mean  used  been  in line  a  levelled  was  camera  manner  placed  measured  sky.  i t was  metal  was  the  radiance a  i n the  this  i n such  to  the  position.  viewed  correspond  which  shows  actinometer  radiometer  image  vertically,  aligned  operating  aligned  that  and  also  The was  placed  factor,  as  used  describe  video  to  camera  determined  lens  the  by  the  amount  emanating  methodology of  from  of  radiation a l l sources  29  Figure  3.1  V i e w o f V i d e o Came r a P o s i t i on  Mon i t o r i n g  30  gure  3.2  View Roof  o f F i e l d M e a s u r e m e n t S i t e on of the Geography D e p a r t m e n t ,  the U.B.C.  31  above  the In  local  this  analysis,  photographed clearly. a  so  This  horizontal  be  of  be  radius  video  horizon  as  of  polar a  of  features  was  9.4  image  a  cloudless  could  enlarged to  cm.  This  graph  finite  over  n  x  the  The  25.4  cm.  print  view  annuli  was  identified  20.3  allows  paper.  sum  be  sky  with  areas  factor  (due  to  to  (0 _ ) s  the  n=41 i n t h i s case) as f o l l o w s : n = 1 n E s i n ( - ( i - 1 / 2 ) ) c o s (ir( i - 1 /2 ) ) a • 2 i =1 2n 2n i s the angular width of the i t h annulus (Steyn,  r  size  image,  4> 5  where  a-  Since  the  horizon  image  d i d not  boundaries  preserve  areas  i n each  multiplied view  onto  expressed  the  sky  that  a  photograph  transferred  can  horizon.  the  annulus by  factor  (Steyn,  on  were  an  per  1980).  onto  traced  step-wise  fashion  so  The  angular  extent  of  the  in a  paper.  then  The  as  coordinate lines,  total  determined.  a d j u s t e d view annulus  1980).  f i t exactly  graph  was  (3.1)  factor,  contributed  summation  of  a l l n  If this  the  as  to  was  0./a^,  i t would  give  to  total  by  the  sky  the  sky  view  the  entries  was  factor. Calculations below  the  2.3%.  Thus,  emanated result did  3.2  local  not  horizon  assuming  from  of  this  the  sky  significantly  at  that this  the  97.7%  hemisphere i t was  affect  view  factor  for  experimental site  isotropy,  finding,  Measurement A  indicated  above  of  the  concluded  this  the  total  local  that  was  elements 0.023  radiation  horizon.  the  or  local  As  horizon  study.  Procedure  preliminary  phase  of  field  o b s e r v a t i o n s was  a  carried  out  32  from  July  usually not  to  exceed  affected  such the  29  that  a  September 3 ms~ ,  by  variety  (0/10  data  overcast  sky  provides  a  number  of  during  the  time  on  abstracted  the  sighted and  The  a  of  taken  note  8/10  were were  examined  using  categories: cloud  the  clear  cover);  conditions.  of  and  Table  along  3.1  with  predominate  by  solar  obtain  the  of  this  of  the  the  azimuthal  noon  in order  between  diffuse  video  the  sky  cover  best via  sampling to  those  be  (given  the  of  time  allocated  less  samples  to  areas  the  This  pattern  of  sampling  at  lens  the  of  near  the  the  the  corresponding grid on  of  an  the  sky  video  monitor.  spatial  coverage  where  and  radiance  brightness  based  high  sky  year  was  on  any  pre-determined  sampling  chosen  period  procedures;  points  set  afforded  parts  two  and  r e p r e s e n t a t i o n of  fisheye grid  A  was  angular  the  at  same  establish  synchronous  image  coordinates  to  radiance  and  the  brightness  included  actinometer.  z e n i t h and present  for approximately  hemisphere,  from  The  Sun.  be  observation  measurements  sky  viewed  likely  not  characteristics  broad  to  cloud)  relationship  as  the  three  (1/10  day  and  after  hemisphere  at  each  measurement  values  design  to  10/10  were  i n the  across  to  of  and  points  attempt  sky  did  measurements  conditions could  cloudy  taken,  zenith angle.  zenithal  the  speeds  day.  before  those  sky  and  listing  actinometric  to  actinometric  assigned  (9/10  scans  dependence  of  partly  Measurements of  the and  Wind  technique.  were  cloud);  1983.  turbulence  experimental The  so  1  13,  the  day)  horizon  necessary  and  Sun  would  and opposite  in order  to  33  Table  Date  3.1  Record  of O b s e r v a t i o n  of F i e l d  Observations  Sky  Condition  Number o f Scans  83-08-29  Clear  Sky  1 1  83-08-30  Clear  Sky  9  83-08-31  Partly  83-09-01  Cloudy  Overcast  11 11  83-09-03  Partly  83-09-20  Clear  Sky  9  83-09-21  Clear  Sky  9  83-09-22  Partly  Cloudy  4  83-09-24  Partly  Cloudy  8  83-09-25 83-09-26 83-09-27 83-09-29 83-10-02 83-10-13  Cloudy  .  Overcast Partly  Cloudy  Overcast Partly  Cloudy  Overcast Partly  Cloudy  10  8 1 11 5 4 3  34  represent low  the  values)  full  present  measurements, the  sequence  zenithal with set  a  or  made  each  completed,  zenith  with  levelled of  the  at  the the  zenith  scan so  angle  intensities  sky.  Between  zenith  was  60°  to  30°  angle  changed  intervals  routinely  beginning  and  an  end  and  with  to  the  pattern  zenith at  as to  had  video  70°  and  a  the  30°  was  (to  was  the  azimuthal  actinometer  sky  60°)  carried  monitor,  final  The  was  been  increments  the  one  started  angle  30°,  i n c r e a s e d by  each  to  minimum  observation  sweep  30°  high  confined  on  during  the  a  grid  An  completed.  and  to  constant  again  10°  of  then  entire  clipping  was  before  usually  increments.  was  by  was  angle  azimuth  avoid  kept  The  (from  individual  was  only.  zenith  When  in the  as  movement  direction  position.  the  Then,  radiant the  that  i n c r e a s e d by  another  sweep  such  Keeping  was  at  across  azimuthal  azimuth  out.  was  30°.  of  a c t i n o m e t r i c movement  measurement  at  and  range  scan  and  observation period  was  the  time  was  recorded. A  single  seconds  during  instrument point  actinometric observation which  and  (about  the  20  to  equilibrate.  to  complete.  for  a  sample  present,  the  z e n i t h a l - and  s h u t t e r was  actinometer  seconds) An  Figure grid.  (at both  and  entire 3.3 For  i t s position  actinometer  metal  azimuthal  15  set  seconds took  illustrates  i n the the  was  scan  times  took  when sky  beginning  location  was  to  used a  to  zero  given allow  a  typical  the 18  scan  minutes sequence  was  sighted with  the  end  noted.  of If  a  the  instrument  disk  and  solar  35  sampling  approximately  the  was  at  approximately  scan) the  Sun  and was  its not  35  visible,  a record  theoretical  of observation  determination  times  of i t s  allowed  zenithal  for a  and  azimuthal  position. At being sky  t h e same  taken,  was  camera  obtained  levelled  and t h e p o s i t i o n  sure  there  would  direct order  solar  beam.  to ensure In  order  digitized  image.  the  and s t o r e d  video  of t h i s image.  calculation  The b r i g h t n e s s  point  explanation  i s given  and a z i m u t h a l  combined  with  the in  correct pixel  t h e knowledge field-of-view,  shape  I.  This  corresponding  first  shape  was  could step  on t h e to the  then  to locate the  taken  of the  in this of sky  coordinates  size  of the  f o r the determination field-of-view  appeared  be  in locating  the shape  pixel  of the angular allowed  i t was  transformation  to screen  in  point,  viewed  A  of the actinometric  coordinates.  sampling  plane  the  as p o s s i b l e .  as p o s s i b l e ,  The  t o make  to occult  values  values  each  checked  instantaneous  of the steps  points  of  t o an  to determine  i n Appendix  The  checked  was  were  of the  a l s o monitored  as clean  t h e image  and then  was  disk  was  the actinometer  on  image  points.  as necessary  i n the computer.  image An  disk  This  lens  as close  a video  at the start  the sky hemisphere  zenithal  actinometric  flare.  i t remained  of the sky that  sky sampling  centre  level  of the b r i g h t n e s s  to locate  summed  lens  The f i s h e y e  necessary  portion  spirit  measurements  sampling  of the o c c u l t i n g  to obtain  representation  a  moved a s o f t e n  that  from  f o r t h e same  be no  a n d was  the actinometric  information  with  scan  continually  that  brightness  being was  time  roughly  of  expressed elliptical.  36  Since time,  the  same  i t relatively  program  which  out  the  p o r t i o n of  The  sum  of  computed, region. each  the as  of  the  the  In  order  synchronous  time  was  brightness time  helped  more  enter  the by  the  button  the  pixels  number This  pixels  allowed  representing  to  function  switch-box and  video  was  to  in  image the  to  of  problems  the  real  the  objects  were  and  scanning  clouds)  necessary,  to  to the  computer. was  brightness  image  the  on  recorded sky  c o n d i t i o n s at  This  procedure  the  of  increased  zenith.  azimuthal  coordinates  into  sequence.  at  point.  to  measurement  kept  computer  the  opportunity  was  spot.  necessary  the  the  the  program  the  to  (i.e.  be  of  for  at  time  effects at  the  sampling  the  was  determination  end  allowed  zenithal  (eg.  area  within  could  actual  the  that  sampling  record  words,  'seeing'.  i t was  video  draw  corresponding  button,  and  as  to  that  particular  other  corresponded  was  connected  the  and  for a  which  was  pressed, In  grid  contained  of  every  computer  actinometer  a c t i n o m e t r i c measurements.  program  another  on  followed  a  corresponding  pressing  'refreshed'.  the  of  roof  corresponding  observations  the  values  value  e l i m i n a t e such  Otherwise, start  on  velocity  sampling  the  points.  hand-held  the  that  the  program  values  of  to  angular  gives  freeze  the  point  was  design  a c t i n o m e t r i c measurements)  site  to  information  the  this  measurements  each  number  observation,  triggered  monitor  3.2  with  measurement  Each  the  small,  each  sky  brightness  for  a  the  sampling  mean  design  locate  brightness  was  of  s t r a i g h t f o r w a r d to  would  Table  of  For  sequence  a  scan,  If the  manually the  automatically set  computer. to  37  Table  3.2  Sequence of O b s e r v a t i o n s i n Second Sampling G r i d w i t h C o r r e s p o n d i n g Number o f P i x e l s Zenith Angle (Degrees)  0 30 30 30 30 30 30 60 60 60 60 60 60 60 60 60 60 60 60 70 70 70 70 70 70 70 70 70 70 70 70  Azimuth Angle (Degrees )  0 0 60 1 20 180 240 300 0 30 60 90 120 1 50 180 210 240 270 300 330 0 30 60 90 1 20 1 50 180 210 240 270 300 330  No.  of  195 201 205 205 201 205 205 231 235 237 237 237 235 231 235 237 237 237 235 259 251 253 255 253 251 259 251 253 255 253 251  Pixels  38  Before the  s k y image  level  one would  present  black and  video  of  was  ended,  adjusted  At the completion  a  had changed  loss  then  that  was  could  relationship  between  sky had been phase  be m o d i f i e d  radiance  determined was  launched  areas  scan  t h e most  noted.  the scan,  or blackest  If and  portion study.  of o b s e r v a t i o n had  within the  or improved.  Once t h e  and b r i g h t n e s s a t any p o i n t i n  (see Section with  data  sky c o n d i t i o n s and c a r e f u l  images  t o be s t o r e d  for further  latter  measurements  were  1983; J a n u a r y  were  during  the. p r e l i m i n a r y , e x p l o r a t o r y p h a s e  that  each  v i athe  not included i n the  indicated  and  t h e measurement  digitized  i n the whitest  scan  methodology  December,  out before  was  i n an  (white)  of a sky scan,  substantially  of d e t a i l  This  levels  saturated  once  sky cover  range.  and blackness  carried  was  range) t o  a n d s o i t was  level  procedure  analysis  particular  the grey  both  never  necessary.  (the f u l l  possible  (or minimize)  data  observing  levels  t o view  video  due t o t h e a c t u a l  not always  some  the  were  and i t s b r i g h t n e s s c h a r a c t e r i s t i c s  t h e image, When  However,  necessary  any a p e r t u r e , that  f o r 256 g r e y  s k y r e p r e s e n t a t i o n was  sky cover  there  a n d make  maximize  were  had begun.  i t was  adjustments  was  This  the c o n t r o l s  framestore the  this  to eliminate  sequence  sky scan,  by a d j u s t i n g t h e v i d e o  regions.  recent  wish  t o manually  accomplished attempt  level  i n t h e image.  characteristics necessary  of a  on t h e m o n i t o r  or blackness  Ideally, be  the start  over  and February,  secondary  collection selection  display  obtained  4.1) a  f o c u s s i n g on  of useful  and a n a l y s i s . a a three  1984.  month  Since  sky  These period:  t h e Sun  was  39  much  lower  sampling  The  sampling  grid  and  actual  earlier. were  the  levels.  Figure  any  image  was  not  for  future  of  for a  representation  level  at  a  with  the  the  setting.  radiance the  from  a  scan  time  did  not  seem  to  view  be  archived  provided  transformation  not  sky  be  in a  radiance  a  the to  A  appropriate  spectral  blackness pose  that  scan ( i . e .  would  between  aperture,  video  ( i . e . images).  i f the  relationship  the  could  measurements)  maps  or  images  images  dramatically, resulting  current  This  of  sky  of  sequence.  blackness  appropriate  design  s e v e r a l sky  for analysis one  provide  described  condition with  method,  later  changed of  sky  as  scan,  the  the  scanning  variety  brightness  produced  taken  characteristics  and  the  aperture, a  to  indicates  sky  a  year,  continue  of  utilized  of  3.2  provide  determine  number  to  the  obtained  the  this  of  were  particular  With  curve  image  brightness  a  to  end  to  currently  necessary  an  done  as  illustrates  the  brightness  calibration for  3.3  so  time  Table  changing  study.  synchronous  altered  at  wihout  representative  that  observations  However,  This  radiance  was  at  strategy.  field  stored  data  horizon  sequence  optimal this  on  and  problem  poor and video during  this  study.  3.3  Estimation A  simple  probable The  video  where  error  of  experiment  Error was  i n the  Video  System  carried  out  in order  associated with  camera  lighting  the  was  placed  the  use  of  horizontally  conditions could  be  kept  the on  a  to  assess  video  system.  table  in a  constant  and  no  the  room  gure  3.3  Design of Sampling G r i d . the C e n t r e of a S a m p l i n g  Each + Point  Represents  41  external The  disturbances  neutral density  lens  filter  and the r e s u l t i n g  aperture, to  blackness  produce  an  image  representation Twelve  images  This pixel  intensity  scale)  with  a  0.276%. centre  standard operating  ± 0.309%.  error  in the video  mean  values  of temporal  area,  (about  These  span of constant.  change i n  error  i n the  the twelve  images  level  was  92.13 for a  ( f o r an 8 b i t single  that  201  points  pixel.  pixels),  i n a mean  d e v i a t i o n of  1.9.  standard  deviation expressed  the  brightness  brightness  level  This  was  that the 1.0%.  an  analysis  image of the  o f 93.5 w i t h  a  of v a r i a t i o n (the  as a percentage 2.04%.  ±  the  than  within  However,  The c o e f f i c i e n t  was  nearer  of l e s s  about  23308  indicated  brightness  images.  was  the brightness  deviations  t h e mean  includes  taken  i s on t h e o r d e r  f o r a l l twelve  then,  image  the brightness  standard  system  resulted  between  of a d i g i t i z e d  standard  mean  a time  as the probable  f o r sampling  expected  be e q u a l  0 t o 255.  conditions, the actinometric  and f o r t h i s  18518  would  from  over  d e v i a t i o n o f 4.04  a t t h e edge  o f t h e image  was  as well  i n order  complete  conditions held  the extent  camera  ( i . e . the  adjusted)  levels  with  brightness  Similarily,  It  were  sequentially  of the changes  t h e mean  pixels,  intensity  minutes,  the fisheye  system.  that  field-of-view  high  of the camera.  was m a n i p u l a t e d  contrast; a  taken  showed  normal  image  from  with  indicated  Investigation  Under  removed  levels  values  video-framestore  was  operation  and v i d e o  fifteen  information  affect  video  of v a r y i n g were  approximately  254  would  o f t h e mean) o f  shows  that  over  the  42  15  minutes  typically the  during only  twelve  3.3.1  which  a  2%  of  slight,  a  sky  but  to  'registration'  magnitude  of  an  of  sum  of  brightness  was  k n o w n ) was  the  misregistration)  of  was  the  it's  with  showed  x  15  square the  4.73%,  as  (8  at  RMS  the  there  was  brightness  levels  This  of  of  of  the  from  about sky,  error  the  and  of  will  referred  1 at  77  sky  4.57%  or  overcast  that  the  the  edge  there  was  a  3.17%  for  the  2.5  of  This  on a  the root  pixel  s i m i l a r RMS overcast  of  The  actinometric  centre)  showed  region  magnitude  square  positions  (the  window  image.  the  the  the  sky  window.  clipping.  with  what  'window'  the  the  at  case  be  images,  video to  windows  darkening  clear  the  apparent  around  Sky  between  central  (the  of  indicated  determine  approximated  approximately  for  A  image  pixels within  edge of  to  and  corresponding  the  the  three  test.  8 positions  computed  Registration  existed  be,  pixels  2.5  exclusion  error  a  would  by  at  p a r t l y cloudy with  on  order  of  in  evidence  (RMS)  In  values  values  the  results  for  in  positions.  p i x e l s which  size  c a r r i e d out The  for  spot  offset  9 positions  which was  15  chosen  brightness  computed  the  c l e a r , p a r t l y cloudy  were  the  point  offset  error.  error  conditions  sampling  stored,  Inherent  sampling  calculated  such  representative  window  between  Error  consistent  true  a  and  the  point's as  were  images.  Location a  images  difference  Assessment of Coordinates  that  the  The in  each  of  was the  image  procedure sky  image.  mean offset;  error sky  sum  of  case.  43  3.3.2  C a l c u l a t i o n of the E r r o r Level Determination The  total  measurement  E E E  c  where  (3.2)  =  0.0473  x X  (3.3)  v  =  0.0317  x X  (3.4)  X  i s the average  overcast  represent  cl,pc  the data  sky c o n d i t i o n s ,  and  overcast  ov  to proceed between  brightness.  This  with  for a  represent  system  had  been  analysis  variables,  will  be  sky  partly  associated i t is  t h e most  radiance  described  cloudy  for clear,  calculated, of  scan  coefficients  the errors  the determination  t h e two  The  as determined Once  manner:  single  clear,  respectively.  skies.  acquisition  relationship  chapter.  and  value  the r e g i s t r a t i o n error  cloudy  possible  brightness  i n the following  value  x X  and  with  brightness  0.0457  the s u b s c r i p t s  calculated  with  =  l  be  associated  Brightness  now  and  partly  error  with  may  pc q  probable  Associated  probable  and  in the  following  44  Chapter  Four  Calibration  4.1  Determination Radiance  4.1.1  diffuse was  a  linear  first  from  recorded  initial were  step,  the  the  be  most  brightness  video the  between  two  the  thorough  data  available  British  defined  as  Columbia's  indicated as  which a  decided  to  the  be  of  carried  out,  relationship  then  during  a  measurement  the  suggested  was  library  Computing  points  normalized  undertake  variables;  actinometric  analyzed a  two  image  v a r i a b l e s and  were  distribution  could  of  so  scan)  sequence.  variable since  linear with  step-wise  brightness,  sky  sky  dependent a  a  radiance  For  the  of  they  radiance were  radiance;  the  variable.  relationship  this  (as  and  observations  r e p r e s e n t a t i o n of  investigation  The  nature  independent  were  analyses  angular  hemisphere  the  same the  the  Preliminary  the  the  i t was  valid  values  of  brightness.  computations, to  Values  sky  define  and  during  chosen  deemed  (TRP)  the  r e g r e s s i o n between  abstracted  between  Analysis  to  radiance a  Relationship  Brightness  over  necessary  As  the  determination  radiance  between  as  and  Regression Before  it  of  Procedure  i n mind,  existed a  more  undertaken. using  a  linear  programme Centre.  e x i s t e d as residual  i n The The  outliers less  regression  than  routine  U n i v e r s i t y of  initial (an -1.96  results  outlier or  is  greater  45  than  1.96  matter  for a  to  probability  exclude  them  from  were  excluded  on  were  found  correspond  to  measurement. the  camera  (eg.  tower)  which  be  than  240  have  been  of  from  from  also  the  The  a  the  values  how Y'  Y  =  was  (Y  195)/Npix  x  the  with  spurious  data  points  than the  a  brightness camera  an  (eg.  radiance or  anemometer It  values  since  that  radiation  recorded.  brightness  the  should  greater  camera  projection  to  or  points  resulting  object  being  simple  saturation,  shortwave latter,  analysis  may  properties  compensate  the  z e n i t h a l - b r i g h t e n i n g and  present  across  an  image.  Eqn.  4.1  accomplished. (4.1) radiance  radiance  of  of  that  of  pixels  representing Y  number  of  pixels  corresponding  a  sampling  same p o i n t ,  (Npix>l95) to  a  Npix  and  sampling  point  195  and  is is  point  Y'  the the  located  at  zenith. In  order  constant  to  slope,  derive in  this  a  strictly  case  1.0,  necessary  to  adjust  the  brightness  aperture,  blackness  and  video  to  These  from  value  number  the  set.  equi-angular  the  diffuse  'compensated'  data  i t necessary  effects  this  represents  the  for  i t was  sighting  the  The  so  invalid  and  i n the  f i s h e y e l e n s made  horizon-darkening shows  an  other  points  included  5%)  working  resulting  affect no  of  being  with  actinometer  saturating.  actinometric  of  smokestack),  that  were  the  something  could  noted  basis  former,  sensing  smoke  perhaps  the  level  note  that  in this  study,  linear and  the  intercept  value  level lens  relationship,  so  as  effects. aperture  of to  It was  0.0)  (i.e. a i t  was  remove is  important  not  46  graduated be  or  calibrated  ascertained  video  level  (b );  the  r  X'= where the  X  together  value  affected level  (a ).  an  adjustment  (X  -  r  i s the  as  to  the  relationship  between  measurements  was  may  be  found  overcast linear  relation  constant  was  acquisition  phase  digital  values  linear  the  relationship predict  of  II.  these a  regression  influenced  line  the  brightness  by  was  of  between from  the  Eqn.  4.2  undertaken.  the  two  In  more.  should  between  (recall there  words, the  was  to  brightness  42  and a  (i.e.  two  in the from  data  the to  camera  the has  non-linearities.  determine in order  value,  of  curves  confirmed  the  no  brightness  the  Indeed  camera,  that  were  been  cloudy  the  the  brightness  4.3.  a l l 'links'  reaching  to  regression  and  is  curve.  results  for partly 4.2  X'  Due  if  and  the  and  have  zero  actual  other  exercise  given  once  v a r i a b l e s was  since  and  point  regression  line  in Tables  energy  radiance  the  presents  Results  linear.  this  sampling  measurements  of  framestore  a  a of  4.1  characteristics)  radiance  and  c o r r e c t the  relationship  expected  radiant  aim  hand,  could  aperture  the  approximately  Table  given  were  i n the  transfer  Since  be  system  initial  are  Such  to  of  examples  between  slope).  parameters  slope  actinometric  while  scans  the  of  regressed  intercept  i n Appendix  sky  for  value  were  linear.  scans  other to  value  data  close  sky  slope  described  brightness  m o d i f i c a t i o n s , the  clear  that  a l l that  (4.2)  above  and  the  Hence,  r  transformed  1.0  was  the  order  brightness  'compensated' The  on  In  r  a )/b  manner.  observations  blackness  intercept values,  from  i n any  the to  radiance  should  47  Table  4.1  Regression Results f o r Clear Skies using C o r r e c t e d B r i g h t n e s s and Radiance V a l u e s (Wm" sr" ) 2  Scan  JD210.1 JD210.2 JD210.3 JD210.4 JD210.5 JD210.6 JD210.7 JD210.8 JD210.9 JD210.10 JD211.1 JD211.2 JD211.3 JD211.4 JD211.5 JD211.6 JD211.7 JD211.8 JD211.9 JD212.1 JD212.2 JD212.3 JD212.4 JD212.5 JD212.6 JD212.7 JD212.8 JD212.9 JD232.1 JD232.2 JD232.3 JD232.4 JD232.5 JD232.6 JD232.7 JD232.8 JD233.1 JD233.2 JD233.3 JD233.4 JD233.5 JD233.6  N  27 27 28 28 29 30 31 31 27 26 28 30 26 30 30 29 30 28 26 28 29 25 25 30 29 27 31 28 29 28 27 31 28 29 30 26 27 31 28 29 28 28  1  a  b  r  0.66x10" -0.73x10" -0.35x10" -0.58x10" -0.11x10" -0.85x10" -0.25x10" -0.31x10" 1 .054 2.731 -1.186 0.24x10" -0.302 0.47x10" -0.84x10" -0.55x10" 0.24x10" 1 .006 1 .004 -0.967 -1.952 3.476 0.551 -0.42x10" -11.37 -4.938 -0.33x10" 1 .091 0.243 0.360 2.479 -0.95x10" 0.853 -1 .455 -0.26x10" 1 .671 -0.616 0.35x10 -0.112 -0.990 -0.976 0.835  5 4 4 5 4 5 4 5  4  5 5 4 4  4  4  5  4  4  r  r  1 .00 1 .00 1 .00 1 .00 1 .00 1 .00 1 .00 1 .00 0.93 0.97 1 .03 1 .00 0.98 1 .00 1 .00 1 .00 1 .00 0.99 0.98 1.01 1 .02 0.89 0.98 1 .00 1 .40 1.16 1 .00 0.99 1 .01 1 .01 0.98 1 .00 0.99 1 .09 1 .00 0.98 1 .01 1 .00 0.97 1 .06 1 .06 0.99  St. E r r of b r  r  2  0.057 0.925 0.065 0.895 0.084 0.845 0.072 0.881 0. 108 0.760 0.727 0.116 0.097 0.787 0.111 0.736 0.063 0.899 0.053 0.932 0.078 0.869 0.071 0.878 0.072 0.884 0.647 0. 139 0. 126 0.694 0.099 0.791 0.077 0.858 0.056 0.923 0.977 0.031 0.032 0.976 0.085 0.843 0.088 0.813 0.119 0.747 0. 108 0.756 0. 128 0.817 0.887 0.083 0.085 0.826 0.049 0.940 0.044 0.951 0.917 0.059 0.060 0.915 0. 100 0.774 0.085 0.838 0.074 0.889 0.071 0.877 0.045 0.951 0.047 0.949 0.043 0.950 0.680 0.886 0.921 0.060 0.053 0.940 0.064 0.901  St. E r r of Y 5.65 1 0.95 1 1 .66 9.53 1 4.57 1 4.20 16.41 16.87 8.82 9.84 7.12 8.14 6.81 1 6.99 1 2.60 14.95 8.97 7.51 4.75 4.90 17.98 10.71 1 0.85 1 3.45 1 3.29 9.57 1 3.76 9.55 8.14 6.92 8.58 1 6.80 6.49 7.24 11.31 5.20 4.96 5.97 9.25 5.25 4.86 7.31  48  Table  4.2  R e g r e s s i o n R e s u l t s f o r O v e r c a s t Sky Data C o r r e c t e d B r i g h t n e s s and Radiance V a l u e s (Wm" sr ) 2  Scan  JD245.3 JD239.1 JD239b.1 JD239d.1 JD239f.1 JD239f.2 JD237.1 JD237.2 JD237.3 JD213.3 JD213.4 JD213.5 JD213.6 JD213.7  N  29 28 29 25 31 26 30 27 26 29 30 29 29 31  Using  _ 1  a  b  r  2. 898 - 0 . 401 - 3 . 278 1 .407 0. 4 2 x 1 0 " ' 2. 480 -0. 11x10" 0. 890 - o . 926 - 4 . 996 - o . 40x1O " 4. 091 3. 427 0. 1 5 x 1 0 ~ * 5  -  r  0 .955 0 .979 0 .971 0 .968 1 .00 0 .975 1 .00 0 .975 1 .009 1 .030 1 .00 0 .962 0 .977 1 .00  Stand. of  Err b  r 2  r  0. 0805 0. 461 0. 1 20 0. 056 0. 108 0. 041 0. 042 0. 034 0. 045 0. 1 22 0. 098 0. 068 0. 1 34 0. 084  0 0 0 0 0 0 0 0 0 0 0 0 0 0  .839 .946 .709 .929 . 746 .959 .954 .971 .955 .727 .789 .880 .663 .829  S t a n d . E: of Y  2 3 . 84 6. 46 7 0 . 06 9. 54 3 9 . 71 9. 72 1 .88 3. 45 9. 1 4 28. 1 6 15. 1 4 1 1 .43 19. 21 2 0 . 23  49  Table  4.3  Regression Results f o r P a r t l y Cloudy Skies C o r r e c t e d B r i g h t n e s s and Radiance Values (Wm" sr" ) 2  Scan  JD2 41.2 JD241.3 JD241.4 JD239.7 JD238.2 JD238.3 JD238.4 JD237.4 JD237.5 JD237.6 JD237.7 J D 2 3 7 .8 JD236.4 JD236.5 JD236.6 JD236.7 JD234.2 JD234.3 JD234.4 JD215.1 JD215.4 JD215.5 JD21 5.6 JD21 5.7  N  28 31 27 27 29 28 29 27 29 29 29 29 31 27 26 29 28 27 27 30 27 30 29 28  using  1  r  1 .708 -0.55x10" 5 -3.393 -0.224 0.52x10" 4 -0.835 0.32x10" a -4.018 0.46x10" 4 -0.28x10" 4 -0.70x10" 4 -3.183 -0.70x10" 4 1 .401 1 .609 0.970 -0.901 1 .302 -5.831 0.20x10 4 1 .547 0.46x10" 5 1 . 452 1 .405  b  r  0 .935 1 .00 1 .083 1 .005 1 .00 1 .010 1 .00 1 . 1 46 1 .00 1 .00 1 .00 1 .02 1 .00 0 .975 0 .970 0 .920 0 .994 0 .985 1 .062 1 .00 0 .980 1 .00 0 .982 0 .984  St. E r r of b  r  0. 103 0.101 0.046 0.052 0.086 0.047 0.061 0.097 0.063 0.046 0.059 0.087 0.079 0.040 0.042 0.098 0.067 0.044 0.062 0.084 0.096 0.112 0.072 0.059  0.761 0.770 0.956 0.937 0.834 0.946 0.908 0.848 0.902 0.945 0.915 0.833 0.846 0.960 0.957 0.767 0.896 0.953 0.921 0.834 0.808 0.739 0.875 0.914  2  r  St. of  E Y  27.23 36.53 1 1 .64 11.22 28.91 6.37 1 1 . 63 14.13 13.53 7.97 1 1 . 58 24.04 21 .22 1 2.37 5.58 1 4.59 1 5.23 7.42 1 3.68 11.91 10.55 1 7.78 1 1 .60 1 0.02  50  be  analyzed  however,  as  may  parameters  not  of  universally a  related  employed  dependent  close that  achieve  technique and  1.0  such  for  line an  i t has and  reason  been  used  data  that  should the  be  estimated.  coefficent  of  determination  between  the  becomes  Mark  and  any  less  Church  functional  insignificant;  In  be  latter  most  may  cases  Instead,  in both  the  the  almost  analysis,  incorporate errors so  of  1977).  for choosing  variable  analysis  estimate  Church,  functional  these  analysis  unbiased  (Mark  The  independent  and  best  Regression  the  probable most  (r ) 2  of was  (1977)  suggest  relationship  this  however,  the  and  does  the  not  useful.  Functional Analysis Once  existed  i t had  been  between  analysis  to  error  defined,  ascertained that  radiance  determine  straightforward. the  this  i s to  difference  regression  the  tool,  the  variable.  although  i t s place.  analyses,  to  4.1.2  curve  u n d e r l y i n g the  the  make  provide  statistical  analytical  present  dependent  the  to  in  relation  the  In  the  N  type  curve  of  and  was  analysis,  variables  t o Mark  linear  b r i g h t n e s s , the  actual  this  v a r i a n c e s of according  and  a  relationship  use  of  relatively information  is required.  Church  functional  (1977),  These  about may  be  as  m E  2  =  x  where  X^  replicate  L j=1  (x..  i s the  1  D  -X.) /m  i=1,...,N  2  (4.3)  1  mean  value  observations  of  of x.  x^ and  and  x^  i s the  similarily  j t h of  for E  2  .  m  51  When  the  that  E  apply  and and  2 x  equally  variance  X  In  (X)  = E  this  with  E^  2 y  to  /E  From Y  =  f  i t may  normally and  the  be  assumed  distributed  ratio  of  and  the  error  as  (4.4)  2 x  of  E  2 x  calculated  were  2  the  for  parameter  coefficient  b^  of  relative  brightness each  was  and  point  r e g r e s s i o n a n a l y s i s had  slope  i n the  the  values  scan.  performed,  calculated  determination  analysis) values  radiance in  been  errors associated  as  a  functional  using  b_. a n d  r  derived  from  the  f o l l o w i n g manner,  (the  2  (Mark  and  (1977))  =  ((b  this a^  written  determination  regression  b  be  E^  and  distributed  independently  and  Since  Church,  normally  a l l observations  may  respectively,  analysis  are  2  study,  the  slope  are  +  2 r  /r -X)+(((b_ /r -X) +4Xb 2  slope b^X  brightness Therefore  2  value,  where  values to  brightness,  X  a  linear  2  intercept  represents  and  predict  an  2  Y  i s the  radiance  the  2 r  a^  ))/2b )  was  known  predicted at  any  transformation  .  2  r  (4.5)  determined.  Thus  (uncorrected) radiance  point using  in a^  (Wm~ sr~ ). 2  the and  sky b^  1  from was  applied. To clear,  verify overcast  Regression  this and  procedure, partly  analysis using  sample  cloudy every  sets  of  data  sky  conditions  fourth  sampling  representing  were point  chosen. of  the  52  entire  sequence  values  were  set  of  the  radiances  were  allowing  the  In  4.4  shows  data.  The  condition.  sky  Wm~ sr 2  have  _ 1  RMS  clear,  in  indicate a 95%  the  values  of The  22%  associated  Section  2.1.3.2,  they  These  include  (i.e. larger  with  a l l regions  errors  than  regression  had  the  the  may or  and  be of  in  Sun) A  follows.  each  and  large  errors  somewhat sky  more  each  that  in 9  conditions Wm" sr 2  which, for  as  misleading,  indicates  _ 1  ),  largely  measured  however,  Some  as  portions  correspond  that  to  discussed  small  to  the  detailed verification  This  r  sky  i s due  likely  of  performing  hemisphere.  more  Table  cloudy  value  (13  errors  voltmeter  are  (RMS).  was  31%  data  was  partly  for  of  predicted  (r)  notice  and  the  same  approximately  these  HP  the  the  p a r t l y cloudy  1  of  in  of  advantage  error  analysis  2  predicted  assuming  square  One  2  the  others.  procedure  the  variables  Wm~ sr" )  results  near  in and  r  a  rest  limit)  the  overcast (20  for  the  overcast  i s 40%  f i g u r e s may  locations  calibration  RMS  magnitude  error  fluxes.  that  and  For  c o n s i s t e n t l y high  covers.  mean  Similarily,  mean  confidence  suggests  a l l sky  case  allowing  correlation coefficient  for  the  two  and  c o r r e l a t i o n between  results  respectively. the  the  root  for  .  the  the  at  method  c a r r i e d out  between  a  results,  applied  as  This  similarily  be  determine  results  (significant  clear  to  performed  included  This  well  the  not  calculated. to  was  parameters.  was  values,  as  scan  transformation  order  calculated  b^  a  these  points  existed  measured  in  from  and  analysis  relationship  and  a^  ( i . e . those  analysis)  set.  points  abstracted  determination data  of  the  of  to the  53  Table  4.4  R e s u l t s o f F u n c t i o n a l A n a l y s i s t o Show V a r i a t i o n Between P r e d i c t e d and Measured R a d i a n c e s f o r Clear, O v e r c a s t and P a r t l y C l o u d y Sky Conditions  Scan  N  r  2  RMS (Wm" sr~ 2  Clear  )  RMS (%)  Sky 211.1 211.2 211.3 211.4 211.5 211.6 211.7 211.8 211.9  Overcast  28 30 26 30 30 29 30 28 26  0.918 0.937 0.921 0.805 0.833 0.926 0.953 0.978 0.978  6.769 8.107 9.026 13.805 13.459 8.031 8.851 6.328 6.328  31.10 33.00 38.90 54.98 54.53 59.03 31.07 34.32 23.60  25 31 26 29 30 29 29 31  0.923 0.862 0.954 0.805 0.901 0.931 0.761 0.909  13.150 38.340 15.090 29.530 13.190 12.310 17.320 19.210  14.57 39.96 17.01 30.30 17.12 15.16 21.71 18.99  0.944 0.897 0.951 0.974 0.952  11.430 15.710 13.650 8.800 13.800  26.76 38.39 28.96 25.07 36.54  Sky 239.1 239.2 239.3 213.3 213.4 213.5 213.6 213.7  Partly  1  Cloudy 237.4 237.5 237.6 237.7 237.8  Sky 27 29 29 29 29  54  magnitude varies  4.2.  of  across  error  the  sky  Verification This  curve  for  typical  validity the  in  the  using  the  point  in  the  the  results  prediction  Calibration  included  the  b  and  and  were  cloudy  overcast  manner  detailed  of  set  data  so  and  above  separate  be  and  to  radiances.  for  clear,  The  observed  partly and  corresponding case,  a  were  latter  set  group  data  In  order  to  cloudy  of  each  high  this  were  and  pair  of  between  and  used  on  the  4.7  values  show  conditions, with are  the  b^  to values  respectively.  the  residuals  presented.  (r>0.90)  p r e d i c t e d and  data  regression  a^  and  coefficient  remaining  of  4.6  observations  the  the  brightness  along  second  developmental  the  overcast  accomplish  every  from  then  included  ( i . e . the  values  correlation  relationship  data  From  predicted radiances  to  on  calculation  4.5,  sky  those  i n the  Tables  calibration  from  abstracted  transform  a  assessing i t s  performed  assembled.  utilized  data  was  this  values  2  These  independent predicted  r  radiance  Procedure of  partly  could  of  derivation  clear,  set  data  parameters.  strong  the  regression analysis  observations)  each  i n the  regression/functionalanalysis.  this,  set,  a  inherent  hemisphere.  of  analysis  conditions  in  the  In  suggests  a  measured  radiances. Variations predicted  and  illustrated of  by  contouring,  i n the  magnitude  of  measured  radiances  across  the  maps o f  these  are  Figs.  produced  the  4.1, from  differences the  4.2 a  sampling  and grid  4.3. of  between grid For  64x64  are purposes  pixels.  55  Table  4.5  R e s u l t s of Transformation from Brightness to Radiance ( W m ^ s r ) f o r a C l e a r Sky, 1356 L A T D e c e m b e r 2 0 , 1 9 8 3 . - 1  z  X  r') 0.0 30.00 30.00 30.00 60.00 60.00 60.00 60.00  6 0 . OO 60.00 70.00 70.00 70.00 70.00 30.OO 30.00 30.00  6o!oo 60.00 60.00 60.OO 60.00 60.00 70.00 70. 00 7 0 . OO 70.00  0 .0 .CO 180 .CO 3C0 .00 30 .00 90 .00 150 . 0 0 2 10 . 0 0 270 .00 330 .00 30 .00 150 . 0 0 2 10 . 0 0 330 .00 0 .0 120 .00 240 .00 0 .0 60 .00 120 . 0 0 180 . 0 0 2 4 0 .oo 3C0 .00 60 .00 120 . 0 0 160 .CO 300 .00  60  13 17 12 15 92 15 13 13 15 30 15 1 15 14 37 20 13 15 79 32 13 15 13 15 43 13  . 80 .JO .92 .85 . 16 .00 .78 .89 . 43 .27 .42 . 28 . 93 .46 .53 .74 . 17 . 83 .84 . 78 . 84 . 34 . 79 . 15 . 43 . 13 1IG . 9 G  4  Y  Y  (Win" ! s r - ' ; )  ( W m " :: s r " • )  7 .04 13 . 5 - ! 4 .39 9 .03 79 . 8 0 1 1. 6 3 9 .73 1 1. 6 8 9 . 69 29 . 2 0 130 . 58 12 . 8 7 14 . 7 1 3G . 7 8 17 . 5 5 9 .03 6 .77 8 0 . 14 28 . 6 0 13 . 3 5 9 .77 9 . 53 13 . 3 5 36 .07 12 . 6 3 . 10 . 43 1  10. 75 14 . 0 2 9 . 95 12 . 6 1 8 1 . 86 1 1 .8 4 10. 73 10. 83 12 . 2 7 25. 70 135 . 64 12 . 0 9 1 1 .8 2 32 . 22 16 . 8 6 10. 69 99 1 7 0 . 67 28 . 03 10. 73 12 . 6 0 10. 33 12 . 5 5 3 7-. 3 3 10 . 4 7 1 1 .0 5 13 . 6 2  14 4  1.  Y-Y 'sr  3 .71 0 . 48 5 . 55 3 . 53 2 . 05 0. 1 . 02 0 - 0 . 85 2 . 53 - 3 . SO S . OS - o . 78 - 2 . 89 -4 . 55 - 0 . 69 65 5 .22 - 9 . 47 - o . 57 -2 . 62 2 . 83 0. 80 - 0 . 80 1 . 3 - 2 16 -3 . 05 - 0 . G 1.  1  1.  1  56  Table  4.6  R e s u l t s of T r a n s f o r m a t i o n f r o m B r i g h t n e s s to Radiance (Wm" sr"') f o r a P a r t l y C l o u d y S k y , 1246 LAT D e c e m b e r 5, 1983. 2  Z  0  °)  (°)  0 30, 30, 30, 60, 60 60 60 60 60, 70. 70, 70. 70. 70, 30. 30. 30. GO, 60. 60. GO. 60. 70. 70. 70. 70.  .0 .00 .00 .00 .00 .00 .OO .OO .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 ,00 ,00 OO ,00 00 00 GO  0 .0 60 .00 t o o .00 300 .00 30 .00 90 .00 150 . 0 0 2 10 . 0 0 270 .00 330, .00 30, .00 150, .00 2 1 0 ., 0 0 270, ,00 330, .00 0, .0 120, .00 240, .00 60, .00 120, .00 180, .00 240. .00 300, .00 120. .00 180. 00 2-10. . 0 0 300. 00  X  Y >m"*sr " ' )  6 5 . SO 64 . 7 8 45 . 55 9 1 .02 109 . 4 7 49 . 0 3 4 1 .7 1 48 . 57 7G . 22 118 . 5 0 1 10 . 6 7 45 . 53 5 5 ,. 5 1 7 8 ,. 3 0 12 1 . 7 4 101 . 7 2 58 . 74 6 5 , . 19 76 .02 40, .09 3 9 ,. 8 4 5 5 ,. 6 5 73 .9 1 3 5 , . 76 4 1 .,5 6 5 4 ,, 2 9 7 5 ,, 2 9  3 1 . 14 3 1 . 90 16 . 27 45 . 58 6 9 . 57 23 . 65 15 . 9 0 13 . 9 1 29 . 57 73 . 55 76 . 3 1 16 . 7 5 18 . 6 1 25 . 65 76 . 3 1 67 . 4 0 27 . 35 22 . 79 49 . 28 13 . 8 0 14 . 16 2 1 . 68 27 . 6 0 12 . 9 2 18 . 0 4 20. 3 1 2 9 . 54  Y -Y  Y (Wm~ 3 1 30 12 55 73 15 8 15 4 1 8 1 74 12 2 1 43 84 65 24 30 4 1 6 6 2 1 39 2 8 20 40  :  sr' )  . G4 .49 . 11 . 58 .22 . 44 .44 .OO .43 .85 .37 .09 . 63 .90 . 95 . 8 1 .72 . 89 . 24 . 89 .65 .77 . 22 .75 .30 .47 . 54  1  (Wn" 0 . 50  - 1 . 4 1  - 4 . 16 10. 00 3 . 65 -8 . 2 1 -7 . 46 1 . 09 1 1 . 86 8 . 30 - 1 . 94 - 4 . 66 3 . 02 18 . 2 5 8 . 64 - 1 . 59 -2 . 63 8 . 10 -8 . 04 -6 . 9 1 -7 . 5 1 0 . 09 1 1 . 62 - 1 0 . 17 - 9 . 74 0 . 16 1 1 .00  57  Table  4.7  R e s u l t s of T r a n s f o r m a t i o n from Brightness t o R a d i a n c e ( W m " s r ) f o r an O v e r c a s t Sky, 1033 L A T J a n u a r y 2 0 , 1 9 8 4 . 2  z (°) 0.0 3O.00 30.00 30.00 60.00 60.00 60.00 60.00 60.00 60.00 70.00 70.00 70.00  Y  Y  X  sr"')  D 0 .0 60 180 300 30 90 150 2 10 270 330 30 2 10 330  - 1  .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00  204 . 180. 176. 179. 123 . 15 1 . 144 .  19 86 77  82 99 66 37 12 1 . 9 3 108 . 23 125 . 40 111. 77 1 15. 27 103 . 98  2 8 . 17 24 . 82 19 . 7 4 24 . 8 2 15. 57 2 1 . 32 17 . 5 2 17 . 5 2 17 . 4 5 17 . 5 2 14 . 7 1 14 . 7 1 12 . 8 7  (Wm ' s r " ' ) _  25 23 22 23 16 19 18 16 14 16 15 15 14  . 93 .20 .72 .08 . 54 . 78 . 93 .3 1 .70 . 71 . 1 1 . 52 . 20  Y-Y 1  (WnT s r -2 .24 - 1 .62 2 . 98 -1.74 0.97 - 1 .54 1.41 -1.21 -2.75 -0.8 1 0.40 0.8 1 1 .33  58  Figure  4.1  C o n t o u r P l o t of D i f f e r e n c e s Between M e a s u r e d and P r e d i c t e d R a d i a n c e s ( W m ~ s r ~ ) f o r a C l e a r S k y , 1356 LAT December 20, 1 9 8 3 2  1  59  For one  the clear  can see that  sky case,  there  of p r e d i c t e d  solar  This  Wm  _ 2  sr"  likely the  or about  1  region.  would  the  camera  region  o f minimum  about  as  a darker,  respond  2  more  to this  spectral  radiance  there  Portions  1  values  differences  between  with  accuracy  of 8  a n d i s most  energy  results.  intensity,  T h e human  in this  extreme,  approximately  This  eye senses  this  region  but as i t represents the would not  t o t h e same  since  extent  the isolines  correspond  10 w m ~ s r " , 2  often  1  i s due m a i n l y  do n o t e x t e n d  to  radiances  observed  ranging  to the absolute  t o measure  and video  o f 1-2  have  such  c a n b e a s l o w a s 3% w h i c h  of the actinometer  as the  At z e n i t h  t o be an u n d e r p r e d i c t i o n  t h e HP v o l t m e t e r  t h e RMS  9 0 ° away  of overprediction  an o v e r p r e d i c t i o n r e s u l t s .  than  but  spectral  The o t h e r  t o an a r e a  composition  edge  near t h e  of the actinometer,  to radiation  of  i n that  wavelengths  p r e d i c t e d and measured  using  Otherwise  value)  1971) t h e a c t i n o m e t e r  appears  of l e s s  of the  i s on t h e o r d e r  to radiant  of t h e sky which  30% and 50%.  associated fluxes.  area,  of 70° ( t h e outer  Wm~ sr~ .  between  (or 4%).  (Ghazi,  i n the region  at shorter  corresponds  blue  region of  i n response  radiant  and hence,  the horizon) 2  1  minimum  camera  angles  disk,  5 Wm~ sr~  scattering  the  scattering  a n d s o an u n d e r p r e d i c t i o n  the solar  video  camera  an i n c r e a s e  on December 20, 1983,  of the d i f f e r e n c e s i n response  i s not as s e n s i t i v e  of  to  and video  cause  region  from  underprediction  12% ( o f t h e m e a s u r e d  The i n t e n s e  Sun  the  radiances  t o be a m a n i f e s t a t i o n  actinometer  taken  i s a noticeable  underestimation aureole.  a scan  system.  error  small  i s within  60  The  partly  interpret; high the  image.  portions;  certain upper  half  lower  half,  variations  The  angle  isolines  i n the lower ranging  f o rthe highly  i s an e q u a l l y  atmospheric  phenomena  that  this  instrumentation Fig.  4.3  condition. low  contrast  differences this low  plot  i s a very  image; between  this  small  the  those i n of the  and 300°.  indicate 1  A  possible  estimation  arrangement of clouds  of observation. of values  i s related to  representing range  or  I ti s  shows a s i m i l a r  i s manifested  with  in  at a  o f 240°  2  pattern.  an overcast  of radiances  sky  in this  i n the smaller  and measured  to the previous  of contours  half)  by t h e v a l u e  t o -9 W m ~ s r ~ .  case  map  predicted  as compared  gradation  no o t h e r  than  d i s t r i b u t i o n of  a t the time  of a  I t i s not  radiances  angles  systematic  i s the contour  There  -1  configuration  since  gradient  o f t h e image  systematic  differences  unlikely  from  scan,  two m a j o r  The c o n t o u r s  and measured  half  t o have  half).  strongly  o f 30° and a z i m u t h a l  underpredictions reason  predicted  to this  ( t h e upper  ( t h e lower  and a r e i n f l u e n c e d  between  appears  a steeper  a t t h e t o pof  i t i s a function  phenomenon.  have  as  overprediction.  to overprediction  this  o f t h e image  that  plot  to underprediction underlies  value)  forthis  suggest  easy t o  of o v e r p r e d i c t i o n ,  corresponding  reason  The c o n t o u r  one c o r r e s p o n d s  what  zenithal  contours  point.  the other  region  o f t h e image  an o b v i o u s  the steep  data  ( F i g . 4.2) i s l e s s  (71% of t h e measured  1  Analysis  not provide  single  sky r e s u l t  i s a prominant  2  However,  the  there  a s 18 W m ~ s r ~  does  and  cloudy  radiances  two p l o t s .  no d i f f e r e n c e  found  There  between  on  i sa  predicted  61  Figure  4.2  C o n t o u r P l o t of D i f f e r e n c e s Between Measured and P r e d i c t e d Radiances (Wm" sr" ) f o r a P a r t l y Cloudy S k y , 1246 L A T , D e c e m b e r 5, 1983 2  1  62  E  W  Figure  4.3  C o n t o u r P l o t of D i f f e r e n c e s Between Measured and P r e d i c t e d Radiances ( W m " s r " ' ) f o r an O v e r c a s t S k y , 1320 L A T J a n u a r y 2 0 , 1984 2  63  and of  measured  underprediction  the of Wm  radiances  _ 2  sr~  2  associated cloud the  which  those  scatter  actinometer  (greater  a shift  This  contour  variations  plots  over  spectrum  a s k y image. radiance  low  a s s o c i a t e d with  radiances  camera  4.3  Validity A  typical  described judge  utilized  of Approach measurement  i n Section  i fa grid at least  a manner  that  t o t h e camera result  how  2.2.1.1. the value  of the  radiances are methodology i s  5% a t b e s t ,  o f 50% o r g r e a t e r  the d i g i t a l  thick  voltmeter  varying  response  b u t may  also  due t o t h e f o r measuring of the  to the actinometer.  3.2.  the appropriateness  ascertain  skies.  using  or  wavelengths).  The c a l i b r a t i o n  and the s p e c t r a l l y ,  as compared  dense  t o longer  Most  be  droplets could  within  value) at  of about 1  relative  to illustrate  area  of the sky.  the findings of Section serve  An  1  i n such  response  of water  result, in over/underpredictions error  radiation  p r e d i c t e d and measured  of predicting  sr~ .  ( 8 % of t h e measured  1  of e s p e c i a l l y  less  effects  with  between  distributed capable  show  i n the energy  i s i n keeping The  patches  would  - 2  of o v e r p r e d i c t i o n could  or r e f l e c t  scattering  3 Wm  t o an u n d e r p r e d i c t i o n  The r e g i o n s  with  than  to the brightest part  corresponds  (5%).  1  greater  by 2 W m ~ s r ~  zenith corresponds t h e image  in  being  using scan  Partial included  Various of t h i s  containing  i n the steady  tests  Scan  31 s a m p l i n g were  sampling  fewer  Data  performed t o  grid  sampling  points as  and t o  points  could  state c o n d i t i o n s of c l e a r  be  64  On  December  points  on  end  the  of  the  20,1983,  sky  scan,  was an  image  the  regression line  gives  the  pertinent  is  the  significant  to  error  a  the  of  Y,  of  the  measure  Table  error  4.8,  of  the  evidence  curve.  These  points. using  only  previous 99%  every  results  level)  only  13  was  data  correlation  so  error  the  standard  errors  in  order  have  results  points (r )  very  2  level),  about  which  2%,  r  f i t of  been  so  when  favourable i t i s not  still  results  as  can  b  the  data  and  are  r  set. 2  of  Y  of  by  has a  r  the  and  b  case.  These  nearly  steady  number  valid  of  r  are  still  results state  seem  predictive  predicted  sampling out,  this  time  the at  the  that incorporating positive and  brightness  in Table  slightly  to  minimal;  r  to  radiative  sampling  low,  Because  results  increased only  very  (significant  strong  JD354b  the from  the  62  from  noted  both  carried  surprising in a  only  standard  be  to  using  r  Not (and  the  a c t i n o m e t r i c measurements  minimal  retain  in the  the  is within  and  obtained  4.8  predicted values  Also, a  the  4.4  Table  of  62  At  Fig.  high  but  at  31.  (JD354a).  of  of  usual  while  departure  close  evidenced  in this  to  the  errors  high,  between  a  data  actinometer.  the  were  standard  only  the  data  The  exist,  on  set  fourth point  points  sky,  data  the  radiance  analysis.  was  as  clear  62  for  regression analysis  measurements  increased  this  i s only  results  Another  for  confidence of  the  of  stored  the  standard  further  was  determination  99%  regression line,  relative  a  for  the  i n s t e a d of  information  analysis  coefficient  c l o u d l e s s day,  measured  shows  regression  a  points  2  suggest  4.8.  2.5%  and  has that  for  conditions need  capabilities.  be  taken  I t must  be  65  Br i g h t n e s s  *Note  Figure  - 4-, 2 r e p r e s e n t po i n t s  4.4  t h e number  and  location  R e s u l t s of R e g r e s s i n g Brightness Radiance (Wm~ sr ) f o r a Clear Sky, 1356 L A T D e c e m b e r 2 0 , 1983 2  _ 1  of  and  data  66  Table  Scan  4 .8  a  Regression  r  b_.  Results  St .  Error  o f a_.  for  Clear  St.  Error  of  b  r  and  P a r t l y Cloudy  St. of  Error  r  2  Sky  N  Y  JD354a  -1 .77  0.907  0.592  0 .014  3.324  0.989  62  JD354b  -2 .62  0.912  0.371  0 .022  3.866  0.994  1 3  JD339  -26 .87  0.891  2.374  0 .031  7. 198  0.941  62  JD339a  -27 .33  0.904  2.866  0 .036  6. 1 93  0.963  31  JD339b  -30 .18  0.961  3.756  0 .042  7.351  0.977  1 3  67  noted  however  sampling  that  point  regions  brightest  region  of  the  curve  of  from  i n the  more  when  only  partial  that  those The  example  data  same  are  on  the are  In  and  value,  this  namely  Part  response  of  of  the  actinometer, cloud  of  case,  parameter  case.  of  as  not  been  full  resulted.  set  cloudy  i s used,  carried  area  the  set  This  for a  based  62  data  points  one  can  99%  see  the in  f o r JD339.  increased  the  The  slightly  greater  scatter  former  viewed  as  sky.  cloudy  F i g . 4.5  sky  shows  Table  of  4.8 r  2  scatter  standard error  than  was  partly  ensure  level).  larger  larger  to  i n the  amount  standard  the  especially  (Note-all  confidence  of  Therefore  while  regression analysis  slope  different  be  a l l zones  (JD339).  the  a  the  i t is necessary  1983  to  least  that  cases.  5,  this  of  to  and  December on  the  case,  would  sky  out  c a m e r a / f i l t e r system the  the  different  data  r e p r e s e n t a t i v e of  is also this  very  fourth  ( i . e . from  had be  every  r e p r e s e n t a t i o n of  to  the  was  of  Sun  i s manifested 5%  uniform  partly  data  use  the  could  have  significant  this  present  slope  result  a  the  hemisphere,  this  procedure  obtained  sky  complex  regression line  values  Y  a  use  would  true  gives  If  regression curve  transformation  the  the  surrounding  intensity).  derived  case,  c o i n c i d e d with  different  radiant  in this  due  b ,  of  the  r  for  the  clear  to  the  varying  compared  alternating  of  error  to  blue  sky  the sky  and  regions. Partly  cloudy  sky  radiance  map  due  to  sky  conditions represent  distributions  spatial  and  and  temporal  are  the  most  i n h e r e n t l y more  variablility.  complex  difficult  Because  of  to  this,  68  Figure  4.5  R e s u l t s of R e g r e s s i n g B r i g h t n e s s and Radiance (Wm~ sr ) f o r a P a r t l y C l o u d y S k y , 1246 L A T D e c e m b e r 5,1983 2  _ 1  69  two  different  every  second  (JD339a)  was  fourth  point  Table  4.8. In  due  to  both the  certain (now  point  (JD339b)  was  cases,  r  of  parameter  For  discern could  that  slope  the r  Y.  the  range  two  change  the  data  collection  the  depending  on  which  the  partial  obtained. sampling  camera  data  This  seem  to  decrease  grid  as  long  to  the  the  that 62  the  the  intensities  p o i n t s are present  sampling  so  the  F i g . 4.5 present  energy  with  i n the  use  of  may  smaller  r e p r e s e n t a t i v e of  i n the  sky,  can  (there energy  and  i t appears  the  so  included have  choice  results a  slope one  of  been  results  the  the  different  had  for careful of  in  data  distribution)  different  points  closely,  i n two  points  standard  i n the  composition  resulted  have  and  present  change  Y  changed  slope  the  spectral  accuracy  not  again,  intensities  of  b  larger  are  need  and  has  sampling  significantly the  and  error  have  different  of  and  studying  set, quite  Since  of  which  emphasizes  points.  as  of  in  standard  in  value  removal  values  a  case  Once  trends  a  by  energy  and  been  responses  shows  observations  least  the  intercept  original  By  both  every  presented  predicted radiances)  however,  minimized. at  of and  have  during  in  JD339a,  range  r  was  are  the  the  of  Results  only  from  for a ,b  time  included.  then  resulting  r e p r e s e n t a t i v e of the  r e g r e s s i o n , and  points  scatter  from  at  sampling  its original  intercept  sky  original  Firstly,  from  JD339b  were  examined.  increased  the  value  62  were  has  2  points.  while  values  the  i n the  significantly.  error  of  included  45%  decreased  approaches  out  reduced  data  only  sampling  been  of  does  not  sampling range  that  the  of grid  70  used  in this  points  study  could  One  have  very  examples  was  reasonable  been  equally  important  i s that  the  both  be  scan how  were the  were  instantaneous Since  the  s t o r e d on  results  based  floppy  would  recorded  to  both  of  be  fewer  taken  disks,  data  during,  by  the  or  at  above  the  simultaneously  i t was  affected  the  and  r e p r e s e n t a t i o n s of  images  on  satisfactory.  a c t i n o m e t r i c measurements  observations  conditions.  one  f e a t u r e common  brightness would  and  so  same the  sky  end  p o s s i b l e to  being  that  of  a  determine  recorded  asynchronously. Table under were  4.9  clear  gives  skies,  collected  on  regression results  December  simultaneously  observations  were  been  i t was  stored,  the  obtained a  programme  abstracted  from  stored  previously  obtained  (NS)  It  can  be  (at  line.  The  the  95%  noted  i n the  and  the  so  that and  Once  procedure  brightness could  measurements  results  observations  change  simple  image  radiance  of  observations,  difference  primary  be  scan  brightness  an  image  to  run  data  had  the  could  compared  (i.e. this  data  be  with  the  results  in  observations).  Comparisons simultaneous  The  obtained  ( i . e . a c t i n o m e t r i c and  relatively  sampling  asynchronous  1983.  simultaneously).  brightness  the  20,  for data  standard  standard  indicate  with  a  r  (t> ) r  error  error  of  and  results  level)  decreased  2  with  intercept  of  Y  a  and  there (a_.)  increased b  of  asynchronous  significant  between  and  use  for  statistically  confidence  that  slope  (S)  obtained  the  two  data  sets.  was  a  significant  of  the  regression  from  2%  approximately  to  almost  doubled.  5%  71  Table  4.9  R e g r e s s i o n A n a l y s i s R e s u l t s f o r C l e a r Sky C o n d i t i o n s (JD354) Showing V a r i a t i o n i n Data as Obtained with Simultaneous Measurements ( S ) , a n d A s y n c h r o n o u s (NS) M e a s u r e m e n t s .  S (N=56) a  -1.769  r  r Standard  Error  of  Standard  Error  of  Standard  Error  of  b  r  2  Table  4.10  a  r  r Y b  NS (N=56) 0.8842  0.9073  0.8312  0.592  1 .252  0.0135  0.0278  3.324  7.347  0.9885  0.9429  Regression Analysis Results for a Partly Sky (JD339) f o r D a t a O b t a i n e d U s i n g S i m u l t a n e o u s Measurements (S) and A s y n c h r o n o u s (NS) M e a s u r e m e n t s .  S (N=56) -26.870  NS (N=54) •24.740  0.8914  0.7467  Standard  Error  of  2.374  3.362  Standard  Error  of  0.0307  0.0397  Standard  Error  of  7.1980  0.8722  0.9410  0.8722  Cloudy  72  There and  was  not  such  brightness  a  strong  correlation  observations  when  the  between  readings  actinometric  were  recorded  asynchronously. For could  be  the  affected  brightness In 4.10  clear  sky most  the  case  of  the a  standard  error values  compared  to  those  the  at  Y  from  increases in  that  for  collect order  to  the  r  the  more  seem  that  asynchronous  the  results  actinometric  complex  2  the  case  occurs  asynchronous  about  of  best of  when  in  simultaneous the  and  regression  results  4.6%  7%  in  case,  to  0.89.  partial  measurements sky  this  cloudiness, of  are  are  standard along  error with  These  findings  it is  important  brightness  c o n d i t i o n s and  radiance.  the  measurements.  The  0.94  Table  observations  level.  to  sky,  i n a l l of  confidence  from  represent diffuse  cloudy  increase  95%  value  partly  substantial  obtained  simultaneous  prediction  using  d i f f e r e n c e s between  significant  drop  by  i t would  observations.  indicates that  Indeed,  case,  for  and  a  suggest to  radiance  accurate  of  in  73  Chapter The  Angular  Once radiance was  the and  Distribution  linear  nature  brightness  possible  to  undertake  distribution  of  diffuse  hemisphere.  As  mentioned  observations  was  carried  February,  1984.  additional the  Radiance  the  in of  transformation from  compensate the were  not  which  slope  the  lens  of  i s what  been  applied  must  be  form  for to  a  the  verified,  actual  set  sky  of  field  and  January  including  basis  for  i t  angular  the  1983  work,  the  Point  the  on  used  in  values, (see of  the a  the  and  some analyses  in  being  the  performed  determine  would  in order  to  diffuse  a  and  f  This  properties  implicitly radiance  any  the  to of  values  assume and  this  radiances,  to  was  (brightness  Since  b^,.  radiance  applied  4.1.1).  transform  a  linear  equi-angular  determined).  measured  the  values  of  Image  p r e d i c t i o n of  Section the  this  Value  c o r r e c t i o n was  brightness  because  the  the  to  r e l a t i o n s h i p between  was to  a  results  effects  on  Translating  r e s p e c t i v e l y , of  measurements  adjusted  knowledge  the  3.2,  this  methodology  which  for  fisheye  and  radiation across  of  will  Sky  brightness  actinometric  of  i n December,  results  Method  the  i n t e r c e p t and  values  determined  Section  out  Radiation  r e l a t i o n s h i p between  analysis  in  Solar  sections.  a  part  an  Diffuse  the  been  solar  data,  Determining  As the  summer  following  5.1  The  of  of  had  Five  brightness,  correction an  had  adjustment  brightness  value  on  74  the  s k y image  analysis to  discover  what  dA  be  an e l e m e n t dA  radiance,  methodology.  Let of  to a  An  form  estimated  analytical  this  = R dz  the  approach  transformation  the p r o j e c t i o n onto i n the sky  using  h a s been  should  a hemisphere  ( F i g . 5.1).  functional utilized  have. of radius  0  Since  p 6\<p  0  R  (5.1)  where p =  R sinz  (5.2)  0  and z  = zenith  $  = azimuth  angle angle  p = distance  from  projected  the centre  vertically  of the area  through  the sky  to a  normal  hemisphere.  Then, dA On  sinz  2 0  (5.3)  plane,  =2  0  d z d<p .  z/ir o r R = 2 R  0  z/n  (5.4)  therefore, dR  Let  R  t h e image R/R  and  =  dA' dA'  =  2R  be  dz/ir  0  .  (5.5)  the elemental  area  on  t h e image  plane  so  = R dR dt5 =4  R  2 0  that (5.6)  z dz  (5.7)  ae/n  2  Therefore, dA'/dA  since  d0=d</>.  =  (4 R  =  4/7r2  z d z 69/n  2 0  x  z/sinz  2  )/(R  2 0  sinz  dz  d<j>)  (5.8)  Figure  5.1  Geometry  of  Sky  Hemisphere  76  Normalizing yields the  with  respect  to the value  D(z), the horizon-darkening  zenith  (4/7r2),  at the zenith  factor.  Therefore at  (z=0),  D(0°)  = l i mz/sinz  =  1.0  ~Zr*o and  a t z e n i t h angle 90°, D(90°)  Thus,  ir/2.  i t h a s been  radiance  should  brightness correctly  5.2  =  map  determined  be m u l t i p l i e d  5.2.1  the values  by z / s i n z  ( i . e . a s k y image)  represent  the radiance  The D i s t r i b u t i o n the  that  of predicted  i n order  to a radiance  t o transform  a  map a n d  values.  of Diffuse Solar  Radiation  over  Sky Hemisphere  Distribution Sky  Values  for Different  Conditions  Figures. illustrating radiances  of Radiance  5.2, 5.3 a n d 5.4 p r e s e n t the c h a r a c t e r i s t i c s  f o rtypical  clear,  frequency  histograms  of the distribution  overcast  and p a r t l y  of  cloudy sky  conditions. An is  given  mode  The  of a clear  i n F i g . 5.2a.  mean  this  figure,  l a y between  81% of the p r e d i c t e d values  larger  located  sky d i s t r i b u t i o n  From  of the d i s t r i b u t i o n  almost  a  example  values,  near  160-248  t h e Sun.  radiance  Wm" sr" , 2  1  The h i s t o g r a m  o f 29.13 Wm~ sr~ 2  1  20,1983)  one c a n note  4-12 W m  were  (December  less  _ 2  sr~ .  than  corresponded  1  28  Indeed Wm~ sr 2  - 1  .  to points  was p o s i t i v e l y  and a standard  that the  skewed  with  deviation of  77  b)  on in  CD  CD - i c o  a, CU  o  o z  O Z  3o T O VO CM CO a) u") CMr~ Q oo CM m i f> *o co Ooo — — — — — . _ <NI CM  VO  Radiance  *  Note  (Wm'^sr" )  5.2  VO  CM  D O ^ r O  Radiance  1  -Class intervals of each class  Figure  O  are represented  by  <i) N  CO  (Wm" -sr" ) 3  the m i d p o i n t  Frequency Histograms of P r e d i c t e d R a d i a n c e (wm s r " ' ) f o r C l e a r Skies a) 1356 L A T D e c e m b e r 2 0 , 1 9 8 3 a n d b) 1320 L A T A u g u s t 2 1, 1983 2  i  78  49.80 W m ~ s r ~ . 2  sky,  This  1  wintertime  angle  77°).  contrast,  histogram  pattern  Most  clear  with  would  of a  clear  t h e Sun low on t h e h o r i z o n  of the values  region  be t y p i c a l  are indicative  of the sky r e g i s t e r i n g  (zenith  of t h e low no  aureole  e f fects. Fig. clear of  5.2b i l l u s t r a t e s  sky (August  summertime  values  21,1983;  radiative  resided  between  the  measured  was  27.06 Wm~ sr~  The  value  than  values  was m u c h  higher  2  below  with  2  scatter,  values  than  - 1  with  Vancouver,  B.C., a s c o m p a r e d  state rain  during  exists and wind  clear  after  example.  levels  of  months  2  1  2.26  as  - 1  Due t o to  Greater  turbidity  conditions at  i n the winter.  of aerosol  the winter  Wm~ sr" .  slightly  t o t h e u s u a l l y lower  conditions  70% o f  radiance  sky case.  anticyclonic  the flushing  during  2  most  the range o f  a t 160 W m ~ s r  clear  higher  t h e summertime  example,  i s shifted  i n the previous  associated  turbidity  For this  the distribution  r e s u l t ' from  T h e mean  distribution;  f o r the winter  could  case,  d e v i a t i o n o f 26.40  a maximum  scattering  representative  approximately  .  _ 1  forthis  3.13 f o r F i g . 5 . 2 a . less,  with  1  2  a standard  40.4°)  f o ra  As i n t h e above  28 W m ~ s r  was l e s s  t o 248 W m ~ s r  increased  conditions.  with  of skewness  rather  compared  1  distribution  zenith angle  4-28 W m ~ s r ~  radiances 2  the frequency  values of The  particles  latter  by t h e  ( a s i n Hay a n d D a r b y ,  1984). The 1984 range  histogram  (LAT 1320),  representing  depicted  of r a d i a n c e s ;  only  an o v e r c a s t  sky f o rJanuary  i n F i g . 5.3a h a d a n e v e n 30 W m ~ s r 2  - 1  ,  smaller  concentrated'in  class  20,  79  b)  1 0 0 0  -  1 0 0 0  So o  10  _>oo  0)  cu  u-i O  loo  O  s o  So-  8  16 24  Radiance  *  Note  igure  -loo  32  8  (Wm~ sr 2  -Class intervals of each class  5.3  - 1  )  1 6  Radiance  a r e r e p r e s e n t e d by  (Wm  - ; z  sr~  )  the m i d p o i n t  Frequency Histograms of Predicted R a d i a n c e (Wm" sr"') f o r O v e r c a s t S k i e s a ) l 3 2 0 L A T J a n u a r y 2 0 , 1984 b) 13 4 0 L A T J a n u a r y 2 0 , 1984 2  l  80  intervals Wm  _ 2  between  sr~ ).  12-28 W m ~ s r ~ 2  Approximately  1  between  12-36 W m ~ s r ~ .  example  was 2 1 . 0 6 W m ~ s r ~  2  2  the  This  1  left  angle  7 4 ° ) shows  radiances; Wm" sr~ 2  latter  was o n l y  was - 0 . 0 6 ) .  being  have  shifted 2  a distribution  frequency  location  distributions  of the clouds were  made  the  radiance  pattern  5.4a.  The range  of the radiances  vary  under  of values  to  forthis  the presence  right mainly Sun  _ 1  less  with  exhibiting  clear  sky with  a n d was o b t a i n e d  strongly  skewed  partly  5,  7/10  1 9 8 3 , when  a s shown i n  4-208 W m ~ s r ~ 2  32 W m ~ s r 2  values  This  o f 1.63. cirrus  to the right  distribution  patches  12, 1 9 8 4 .  with  t h e modal  with  has  shifted  was 5 1 . 5 2  scattering  i s skewed  F i g . 5.4b i s t y p i c a l  cloud  on J a n u a r y  ( t h e mean  increased  with  1  ( t h e modal  _ 1  the distribution  indicating  cloudy  altocumulus,  distribution  than  higher  of clouds.  a skewness  during sky  When F i g . 5 . 4 a i s c o m p a r e d  1  example)  This  on t h e a m o u n t a n d  was b e t w e e n  5.2a a n d b, one c a n s e e t h a t  2  was 1 1 . 1 3 1  complex  approximately  Figs.  Wm" sr  lower  T h e mean  On D e c e m b e r  had a frequency  12-28 W m " s r " ) .  radiances  (JD20b.2:zenith  observed  depending  was  more  skewed t o  2  o f t h e more  class  2  o f 6.85  o f 3.91 W m ~ s r ~ .  i n the sky.  being  were  cover.  histograms  observations  to  1  represents  cloud  deviation  t o even  4-24 Wm~ sr"' .  20-28  for this  F i g . 5.3b  result  dense  values  slightly  deviation  with  being  value  a standard  a standard  radiance  38%  radiance  with  1  The  Fig.  with  the values  t h e range  conditions  sky  1  distribution  (skewness value  class  75% o f t h e measured T h e mean  1  2  Wm" sr~ .  ( t h e modal  1  due  tothe  of a  i n the region  of the  The d i s t r i b u t i o n i s class  b e i n g 12-20  a )  1coo -  .—I CD X  a,  t o o  U-4  So  O  O  2  CO cNi**ir»r-coori<"itr»*i>coo ^rOvO^CO^OVOnco^pO^OtMCO — _ —  Radiance  — —  —  — fN <N  <N  (Wm -sr- ) _2  1  b)  c)  £00  to  r-1 CD  X  CD  •too  -io«  50  a  o  o  2  ft xfy  Radiance Figure  VO  vo co o  n  (Wm-2-sr" ) 1  Radiance  CM  OO  iS) vo cO  (Wm^sr  o O  - 1  Frequency Histograms of P r e d i c t e d Radiance ( W i r T ^ r ) f o rP a r t l y Cloudy S k i e s a ) 1 2 4 6 LAT D e c e m b e r 5,1983 b) 14 4 9 L A T J a n u a r y 1 2 , 1 9 8 4 a n d c ) 1 4 1 7 LAT S e p t e m b e r 13,1983 - 1  )  82  Wm~ sr  _ 1  .  The range  Wm~ sr  _ 1  ,  the higher  2  2  reflecting of  cloud  large  The  mean  The  o f 44.38 W m ~ s r ~ .  of a p a r t l y mean  value  standard skewed  2  2  histograms  may a s s u m e .  radiance  type  1  indicate  of  under  a  evident.  standard  distribution,  i n F i g . 5.4c,  example,  i s  clouds.  with  The d i s t r i b u t i o n  a  was  The range o f  but the d i s t r i b u t i o n has  1  radiance.  the distributions  a clear,  and r e f l e c t i o n ,  2  5/10 o f c u m u l u s  to classes of higher  The presence  t o dominate  with  _ 1  72%  Wm~ sr~',  i s clearly  forthis  1  32  (skewness=1. 1 0).  250 Wm~ sr"  a s s o c i a t e d with  scattering  overcast  of cloud  causes these  which t h e  or partly  cloudy  and t h e r e s u l t a n t  higher  values  of  diffuse  conditions.  Application As  method  i n Steven  (1977)  of presenting  radiation  5.3.1  about  102.02 W m ~ s r ~  considerably  radiances  polar  sky with  to the right  i s still  These  5.2  A third  1  2  radiances  sky  sr  d e v i a t i o n o f 49.20 W m ~ s r ~ .  slightly  shifted  _ 2  4-252  As almost  than  13, 1983 a n d d e p i c t e d  cloudy  was  aureole.  intensity  was 3 4 . 2 0 W m  was  to the brightly  t o be l e s s  radiant  2  histogram  corresponding  estimated  value  on S e p t e m b e r  forthis  as the s o l a r  of l e a s t  radiance  obtained that  were  region  deviation  values  as well  the radiances  the  of values  across  and McArthur  the angular  Clear  distribution  the sky hemisphere  coordinates.  Sky C o n d i t i o n s  (1978),  the primary of diffuse  i s radiance  maps  using  83  Fig. (zenith polar  5.5  represents  angle  40.4°)  coordinate  representation contouring  image clear  (note  that  to  radiance  over  the  intervals  have  been  features  a s s o c i a t e d with  diffuse  radiance  under  and  value  there  circular of  steep  configuration in forward away  from  (gradient  lessens)  increases,  with  horizon  the  of  shortwave  The  minimum  located  which  radiation value  of  values  This  angle  conditions  with  of  the  Sun  contour  from  greater  with  an  (approximately  there  of to  the the  sky  a  is  and 30  clear  horizon.  be  of  length.  2  )  _ 1  Sun  which  spectrum  (to  located  recognized  by  is  and  Trees,  the  lower  scattering  Wm~ sr the  gradual  on  the  the  Wm~ sr~ . 2  1  sky  distribution on  indicative on  from  result  and  path  s e n s i t i v e ) are  may  obtained  low  10  )  Sun  upper  optical  - 1  lines  the  of  region  is a  is a  is a  was  and  There  This  increased  maximum 2  effect  of  of  almost  the  result  the  Wm" sr  an  on  about  image  77°)  zone.  the  (150  with  This  near-infrared part  of  Sun  distance  of  distribution  brightening  horizon  example  the  pattern  is particularily  northeastern  5.6.  (zenith  from  irregular  Firstly,  region.  angular of  to  1983  best  dome,  angular  in this  radiance  i n the  camera  Another Fig.  of  opposite  highly  presence  the  21,  contoured  the  isolines  coherent  evidence  increases  the  upper,  as  image.  i n the  radiance  this  August  i n d i c a t e s some  the  of  this  scattering  departure  of  sky  conditions.  gradient  on  This  obtain  i s located adjacent  is a  strong  reflect  such  skies.  used)  primary  radiance  obtained  under  map  of  an  the  December of  typical  horizon  i s given  20,  in  1983  winter  (in contrast  climatic to  the  Figure  5.5  C l e a r Sky R a d i a n c e D i s t r i b u t i o n (Wm 1320 L A T A u g u s t 2 1 , 1 9 8 3 (z=40.4°)  2  sr"')  for  85  Figure  5.6  C l e a r Sky R a d i a n c e D i s t r i b u t i o n (Wm" sr f o r 1356 L A T D e c e m b e r 2 0 , 1 9 8 3 (z=77°) 2  ')  86  previous  example  Once  again,  coincident although (i.e. and  with  the region the solar  in this  case  so t h e v a l u e s f o r about  a steep,  encompass pattern here  the solar  since  lines  (about  From  with  this  to the horizon. radiances  that  than  associated effect  sequence  such  The  From  bending  effect  10 W m ~ s r 2  region,  )  zone  there,  there  slightly  to  of the c i r c u l a r  forming  the majority 2  with  i s located  the values  30 W m ~ s r  sky.  a conditon  finally  - 1  the isolines  extreme  obtained  first  as previously  This  framestore  _ 1  .  a large  about  9 0 ° away  a pattern  of radiance  around increase  of t h e sky corresponds  Due t o t h e i n c r e a s e d optical  along  airmass,  a  horizon  the horizon.  Conditions  over  of changing  layer  of i s o l i n e s  c a n be n o t e d  Sky  opposite  were  disk.  present  of the  ' c l i p p e d ' a t 250).  The f u l l  Again  o f an o v e r c a s t  images  cloud  less  Overcast  represent  of s a t u r a t i o n  the threshold  the solar  1  The r e g i o n o f  point.  The  2  t h e Sun i s so low on t h e h o r i z o n .  this  5.2.2  250 W m ~ s r ~ ) ,  i s not evident  the solar disk  brightening  intensity i s  noted  intensity  scattering  than  been  disk.  (about  i s a zone  gradation  from  to  aureole  15° f r o m  smooth  o f maximum r a d i a n t  there  have  of contour  minimum  out  i n t h e summer).  t h e s k y was b r i g h t e r  extends is  observed  cloud  from Figs.  Fig.  cloudless  skyi s  5 . 7 , 5.8, 5 . 9 , 5.10 a n d 5.11  as viewed a 3 hour patterns  dominated  image,  an c o m p l e t e l y  on J a n u a r y period until  20, 1984.  These  and i l l u s t r a t e the a dense,  stratiform  the field-of-view.  5 . 7 , was o b t a i n e d  under  2 layers of  87  88  altocumulus isolines The  with  formed  obscured  resulting was  from  an e l l i p t i c a l  gradient form  a concentric  Sun.  (about  Once  this  area  pattern, that  from low  In f a c t ,  contrast  was  angle  convoluted clouds  Wm~ sr~ ) 2  form  minutes  across  zenith  1  effect  later,  as 50°  t h e s k y was o f  2  from  from  a r e never  of approximately  1  A  very  noticeable  increased  ( F i g . 5.8) m o r e  the sky especially was 7 4 . 4 ° ) .  pattern located  near  was s t i l l  radiaton  This  was e v i d e n c e d  t h e Sun.  located in this  cirrus  i n the solar  of the i s o l i n e s  of the i s o l i n e s  visible  from t h e  t o a c l e a r sky  40 W m " s r " .  resulting  to  d i s t r i b u t i o n and  the gradients  of only  disbanding  to increase  similar  to the f a rhorizon,  a range  gentle  9 0 ° away  this  distance  a  There  scattering  on t h e h o r i z o n .  Twenty moved  with  brightening  present  was t h a t  area.  o f minimum  tended  Although  a t an a n g u l a r  t h e Sun e x t e n d i n g  horizon  of radiance  the  influence  gradually  approximately  1  in  which,  with  the region  d i f f e r e n c e between  sky case  an  of i s o l i n e s  around  out to the horizon. t h e major  was 7 5 . 1 ° )  exerted  and the  of a c l e a r s k y .  was f o u n d  1  region,  10 W m ~ s r ~ ) values  cloud  scattering in this  aureole  2  of that  sr~ )  _ 2  angle  still  forward  pattern  again,  of a c l e a r  steep.  zenith  configuration  i n the solar  intensity  150 W m  by c l o u d ,  intense  o f 2/10 c i r r u s  reminiscent  (about  o f t h e Sun ( s o l a r  although  level  a pattern  maximum r a d i a n c e  region  of  an upper  near  which  disk  cloud had region  (solar  b y t h e more  conform  to the pattern  T h e maximum r a d i a n c e  (150  t h e Sun b u t t h e g r a d i e n t a n d  region  o f f of the clouds  had a l t e r e d . resulted  R e f l e c t i o n of  i n areas  of  higher  Figure  5.8  Overcast f o r 1033  Sky LAT  Radiance D i s t r i b u t i o n (Wm J a n u a r y 20,1984 (z=74.4°)  2  sr  1  )  90  radiance absence away is  (about  from  radiance  There  that  with  the  radiances  lengths  a t the horizon  with  higher  the following minutes,  place  ( t h e amount  increasing) radiance maximum  pattern 2  and from  clouds  with  were  a  there  steep  clouds  solar  region,  gradient  corresponded radiance  at the opposite  can  previously)  found  the near  than  region  by t h e p r e s e n c e expected  droplets  be e v i d e n c e d  There  was s t i l l  (zenith  them.  angle  the form  radiances. an even  of the near t h e  values  of cloud  30  The p a t t e r n o f was  obviously  in slightly  The s c a t t e r i n g  e f f e c t s of  of d i f f u s e  of radiance  steep  of about  resulting  values  From t h e  less  p o r t i o n o f t h e image  by a c o m p a r i s o n  of  The c l o u d s  of the sky.  i n higher  a  and the b r i g h t e r p o r t i o n s of  (with  radiances.  resulted  b u i l d u p had  continually  followed  t o minimum  i n the northeastern  influenced  water  in  a r e not evident  cloud  was  to the higher  decreased  Wm" sr"  contours  more  disk  between  the radiation  than  higher  values  there  scattering  resulted  effects  again.  the isolines  gradient 1  once  at the solar  1  reflecting  these  2  from  b y F i g . 5.9 a n d a s a r e s u l t t h e  had changed  (150 Wm" sr" )  still  of altocumulus  as evidenced  74.2°)  Sun  brightening  It  o f minimum  a n d more  path  Horizon  horizon.  i n radiance  by c l o u d  the  image.  In taken  increase  in  i n radiance  region  optical  z e n i t h or Sun. this  decrease  was n o p a r t i c u l a r  Attenuation  longer  be p r e s e n t  the sky t o the opposite  no c o r r e s p o n d i n g  with  would  was a g r a d u a l  there  to the horizon.  lower  than  1  t h e Sun, a c r o s s  associated  on  2  of cloud.  noteworthy  out  130 W m " s r " )  values  radiance for clear  as  91  92  skies the  i n the region  image)  radiance due  with  those  increases  to scattering Eventually,  2/10  to  located there from  cover  formed  no l o n g e r  than  p r e v i o u s l y ; now o n l y  optical cover  depth  of the c l o u d  of radiance  course,  was c o m p l e t e l y  decrease  being  i n radiance  For this  a reasonable  sides  became  type  and bases  between under more  of values 2  was _ 1  .  conditions.  simplified  to 2 layers  results  10-32 W m ~ s r  these  from  attenuation of  ( F i g . 5.11).  t o between  as the The c l o u d  ( 1 / 1 0 a n d 4/10  10-20 W m  - 2  sr~  1  The with the  a t t h e z e n i t h o f t h e sky ( t h eSun, of obscured).  There  was a  outwards  to the horizon  of cloud  cover,  approximation  thicker  less  was  at longer  a n d 5/10 o f a l t o s t r a t u s .  decreased  values  clouds  even  i n radiance  The range  increased  of altocumulus  largest  case.  became  b y 1340 L A T was c h a n g i n g  respectively) range  was n o t e v i d e n t  intensity  by c l o u d  while  at the zenith.  resemblance  of radiances  of radiation  less  had any  decrease  at the horizon,  distribution  clouds  c l o u d and  of highest  distribution  occurs  position  of  of sky  t h e s k y ( F i g . 5.10) a n d t h e  a gradual  attenuation  lengths  over  beam  solar  The d i s t r i b u t i o n  the presence  The r e g i o n  This  portion of  by t h e c l o u d s .  solar  This  is  sky. with  of radiance  t o the. h o r i z o n .  path  ( i . e . upper  1320 L A T , 8/10 o f a l t o c u m u l u s  patterns.  the greater  much The  by  at the zenith with  optical the  of a cloudy  i n complexity  distribution  the previous  intensity  and r e f l e c t i o n  cirrostratus  angular  of lower  to real  and formed  diminished  constant  as i n t h e above  the isotropic  assumption  sky c o n d i t i o n s .  a more  i n importance  continuous a n d most  As t h e  cover,  their  of the l i g h t  ure  5.10  Overcast f o r 1320  Sky LAT  Radiance D i s t r i b u t i o n (Wm J a n u a r y 20,1984 (2=72.5°)  2  s r  _  1  )  94  Figure  5.11  Overcast f o r 1340  Sky LAT  Radiance D i s t r i b u t i o n (Wm" sr~') J a n u a r y 20,1984 (z=73.8°) 2  95  was  s c a t t e r e d o f f the t o p of t h e c l o u d  resulting  i n t h e low range  gradation  of energy  energy  was b e i n g  symmetry  5.3.3  Partly In  to  Cloudy  portion  Figs.  as t h e even  of the radiant  5.10 a n d 5.11  show  Sky C o n d i t i o n s  cloudy  o f t h e amount  first  sky c o n d i t i o n , the presence  distribution  of d i f f u s e  The e x t e n t  of c l o u d  January  example  with  cumulus  of t h i s  of cloud  solar  radiation  complexity  and i t s l o c a t i o n  with  and from  1  forthis  the intensity t h e Sun.  clouds  were  edges  higher  lessens (about  image  80.5°);  again,  i sa respect  region,  or sides  from  a t these  the steep  14 W m " s r " ) 2  1  with  angular  points.  gradients  dissipates.  near  disk  distance  where  away  towards cirrus  and s c a t t e r i n g o f f  t h e Sun r e s u l t e d i n  The s i d e s  of the clouds  of the i s o l i n e s ; The area  was l o c a t e d a b o u t  (230-250  g e n e r a l l y curve  reflecting  clouds  value  1/10  of the solar  t o be c o n t o r t e d  The l i g h t  of these  as the cloud  the location  decreased  tend  cover  1/10 s t r a t o f r a c t u s ,  the isolines  they  present.  was  obtained  during the  The c l o u d  T h e maximum r a d i a n c e  rapidly  Although  radiances  apparent  angle  was c o i n c i d e n t w i t h  aureole  a s k y ( F i g . 5 . 1 2 ) was  t h e Sun l o w on t h e h o r i z o n .  a n d 1/10 c i r r u s .  Wm~ sr~ ) 2  of such  12, 1984 ( z e n i t h  characteristics  the  Both  as w e l l  t h e Sun.  winter,  the  a smaller  a n d Cox, 1974)  the zenith.  the sky hemisphere.  The on  levels;  i n an i r r e g u l a r  function  of radiances  transmitted.  the partly  results over  about  (McKee  the gradient  o f minimum  90° from  were  intensity  the solar  disk  Figure  5.12  P a r t l y C l o u d y Sky R a d i a n c e Distribution ( W m " s r ) f o r 1449 L A T J a n u a r y 12,1984 (z=80.5°) 2  _ 1  97  and to  as i n the clear the horizon.  more  In general,  convoluted  than  presence  of cloud  droplets  which  diffuse image  similar  occasions first  results  clouds  resulted maximum  there were  was v i s i b l e a steep  and  then  Sun  the gradient  gradually However, Fig.  of  lessen  of cloud  solar  located  disk  corresponds  to values  ice  that  point  on t w o  values  increase  more  horizon  of both  of radiance  area.  The  t h e Sun  the isolines  the solar  aureole  60° from t h e values  the opposite near  horizon.  the horizon.  distribution  and c i r r u s )  higher  amount  in this  again,  again  complex  i n increased  F o rt h e  cloud  and radiance  towards  of the  noted.  coincided with Once  of  f r a c t u s a n d 2/10  of approximately  decreases  slightly  on t h e upper  c a n be  This  in to delimit  (stratocumulus  and hence,  )  examples.  distance  resulted  or  a t t h e edges  cumulus  t h e Sun.  _ 1  appear  that the  was o b s e r v e d  of the isolines  curving  5.14 h a s a s l i g h t l y  light  near  2  sharply from  airmass  low l e v e l  250 W m " s r  i n both  the radiance  presence the  present  a t an a n g u l a r  image  1984 ( F i g . 5.13 a n d 5 . 1 4 ) .  was some  gradient  by w a t e r  brightening  of sky radiance  (about  in this  there out  of the d i s t r i b u t i o n  scattering  3,  from  indicating  in scattering  i n the deformation radiance  cases,  in variations  pattern  increased  the contours  Some h o r i z o n  on F e b r u a r y  example,  cirrus  form  results  radiance.  radiance  i n previous  due t o t h e g r e a t e r A  which  sky case,  since the  i n the region of  scattering radiances.  and r e f l e c t a n c e Cirrus  cloud  F i g . 5.13 a n d 5.14  from  35 t o 50  Wm" sr" , 2  1  respect ively. The  presence  of the high,  thin  i c eclouds  ( i . e . cirrus) can  98  Figure  5 . 1 3  P a r t l y C l o u d y Sky R a d i a n c e Distribution (WITT s r " ' ) f o r 1 1 1 6 L A T February 3 , 1 9 8 4 2  ( z = 7 5 . 9 ° )  Figure  5.14  P a r t l y C l o u d y Sky R a d i a n c e Distribution ( W m ~ s r ~ ) f o r 1148 L A T F e b r u a r y 3,1984 (z=72.7°) 2  1  100  still  permit  the t r a n s f e r of v i s i b l e  substantial of  radiance.  thicker hence, 5.15  This  the cloud  this  case  previous  from  the typical  i s exemplified elements,  the greater  represents  For in  departure  sky c o n d i t i o n s  examples,  clear  by F i g s .  the greater  the variation  the cloud  r a d i a t i o n without  cover  as observed was a b o u t  isolines  forming  region.  The d e f o r m a t i o n  density  t o these  of radiance  magnitude angular uneven in  which  of the cloud.  correspond values  patterns  i n contours are a  changes relating  of the predicted  distance  from  values  scattering at different  generally  higher  values  as compared  to a clear  sky case.  (less  than  sr  found  of  the sky.  increase in  - 2  _ 1  A horizon  )  were  brightening  i n s c a t t e r i n g mass  i s most  with  this  irregular  i nthe  intensities with  densities. with  The a l t o c u m u l u s  of d i f f u s e  dipping  of changes  decreased  regions  As  1  enclosing  density,  image  30 W m  steeply  i n radiant  to greater  t h e Sun.  2  corresponds  in cloud  5, 1 9 8 3 .  (190 Wm~ sr~ )  pattern  function  Variations  pattern. F i g .  on December  radiance  contorted  The  7/10 a l t o c u m u l u s .  a t t h e l o c a t i o n of t h e Sun, with  scattering  5.7-5.9.  the s c a t t e r i n g and  occurred  a slightly  sky d i s t r i b u t i o n  i n the radiance  t h e maximum  a  higher The  increasing cover  caused  of the sky and r e s u l t e d radiation across the The minimum  values  i n the northwestern effect  resulting  clearly  portion  from an  evident  F i g . 5.15. The  becomes with  angular most  strongly  distribution  complex  of d i f f u s e  i n the case  reflecting  cumulus  solar  of a clear clouds.  radiation  sky superimposed  This  condition i s  Figure  5.15  P a r t l y C l o u d y Sky R a d i a n c e Distribution ( W m " s r " M f o r 1246 L A T D e c e m b e r 5,1983 ( Z = 71 . 7 ° ) 2  1 02  complex  f o r two m a i n  distinct 2)  cloud  because  study  elements  on t h e o t h e r .  hence,  appear system  elements  very  were  bright.  information  very  low c o n t r a s t ) . radiance  example,  However, point.  I t was  under  cases,  i f one s t u d i e s  were  These  l o c a t i o n s coincided with  reflectance the  cloud  change  points  which  which  play  elements  i n radiance  not to lose too  values  i n values  conforming There  coincident with  Where  present,  the isolines  T h e minimum  value  2  1  of the  to the rapid  droplets  from  Wm~ sr~ .  The i s o l i n e s d e l i n e a t i n g  of scattering  away  that  in directional  i s a f u n c t i o n o f t h e amount  radiance  from  carefully,  radiance  conformed  For this  a n d some b a s e s  of a cloud.  the cloud.  of  of theSun.  o f 130-160  role  gradients  in this  had  1  pattern  values.  of radiance  2  the sides  a side  i t  the complexity  coherent  decreasing  the cloud  (250 Wm~ sr~ )  decrease  of l i g h t .  had steep along  where  the location  an i m p o r t a n t  and s c a t t e r i n g  in this  to adjust the  the distribution  show  and  r e f l e c t i v e and  sky c o n d i t i o n s .  radiance with  there  clouds  such  was n o t a c o n s t a n t  many  time,  used  t h e c l o u d l e s s s k y ( i . e . where  predicted  as i n other  Indeed,  cumulus  difficult  sky;  and the b r i g h t  are highly  F i g . 5.16 i l l u s t r a t e s  distribution  there  system  saturation i n the region  regarding  the highest  coincided,  sides  l o c a t e d , a n d a t t h e same  much  the  the video  clear  s k y on t h e one h a n d ,  The c l o u d  to avoid  p r o p e r t i e s of  i n an o t h e r w i s e  i n which  t o the blue  clouds  video  present  o f t h e manner  responds  Othe s c a t t e r i n g  reasons:  example.  to their  t h e Sun w i t h  of p r e d i c t e d  Instead, the  there  usual  i s no  of water  was n o c l o u d  pattern of  an even  radiance  gradation of  under  these  103  Figure  5.16  Partly  Cloudy  (Wm" sr 2  _ 1  (z=50.8°)  )  for  Sky  Radiance  1417  LAT  Distribution  September  13,  1983  1 04  conditions northern this  was  70 W m ~ s r ~ 2  horizon.  type  No  the s c a t t e r i n g  zenith  angles  5.4  Comparison  5.4.1  Clear The  well  and  visible  cloudless a  along the  solar  approximately (1975)  utilized  luminance  5.17a  line  His results  of a  radiance  the scattering radiance  o f minimum  t h e Sun.  results, contours  were r o u g h l y  gradient around  presented on p o l a r  luminance  symmetrical  azimuth  through  of i s o l i n e s  map,  gradient was  showed peaking  located at  a n d Manamohanan  across  to record  the sky  as equi-luminance diagrams  appear  maps  illustrated  about  the solar  the solar  t h e Sun a n d a d e c r e a s e  for a  intensity lay  Sastri  conforming  to  ultraviolet  positions  of constant  pattern  i n the  spectrum.  T h e maximum  designed  at different  Their  large  correspond  changes  a n d 5.17b.  steepest  of s k y l i g h t  with  from  study  t e l e p h o t o photometer  equi-luminance  contours  in this  sky-scanning  Their  at  Studies  a  hemisphere. with  elements  particles  spectrophotometer  and the r e g i o n  9 0 ° away  found f o r  research.  i n t h e form  vertical.  point  a  of the solar  distribution  the solar  presented  of p r e v i o u s  day, p r e s e n t e d  symmetrical  Previous  the  was  of c l o u d  of atmospheric  distribution  regions  along  Distributions  developed  the s p e c t r a l  found  brightening effect  with  sky r e s u l t s  (1971)  was  the presence  effect  of R e s u l t s  the r e s u l t s  Ghazi  since  Sky R a d i a n c e  clear  with  study  horizon  of sky cover  masked  and t h i s  1  in Figs.  that  the  vertical  position)  t o an  maps  with the  elliptical  i n luminance  (a  with  105  Figure  5.17  C l e a r Sky L u m i n a n c e D i s t r i b u t i o n s for a ) Z e n i t h " A n g l e 70° and b ) Z e n i t h Angle 50°. From S a s t r i and Manamohanan (1975)  106  increasing study, which the  F i g . 5.5 does  solar  unseen time  angular  distance  presents  vertical.  This  or aerosol  of o b s e r v a t i o n .  particular  symmetry  about  that  the solar  of a wintertime  altitude,  appear  Ghazi  (1971) The  was  tended  to increase  Manamohanan isolines  (1975)  bounding  encompassed  Standard for  the  normalization radiance  clear  sky radiance  t h e Sun  pattern away  note  that  the area  maps,  that  appoximately  radiance The  9 0 ° away  from  lower  disk  solar  region  5.17a a n d b) and  values  Sastri  and  zenith angles,  the  intensity  clear  been  These  sky  radiance  presented  maps  value)  by  disk  of  t o produce v e r s i o n s of  show  the p o s i t i o n  and i l l u s t r a t e  increasing angular  o f minimum  Steven  As a r e s u l t  used  'smoothed'  the solar  by  map.  procedures  with  solar  as d e s c r i b e d  (inFigs.  radiant  radiance  from t h e  F i g . 5.6,  5.18a a n d 5.18b.  distributions.  in a  (1975).  the solar  represent  of  at the  a departure  of normalized  in Figs.  point.  result  symmetry  for large  about  of the presence  sky with  such  of l e a s t  ( i . e . t h e maximum  o f symmetry  vertical.  of the luminance  they  distribution  to the horizon.  and a v e r a g i n g  of decreasing  from  causes  of 35° and 55° have  a n d a r e shown  these  of  there  distributions  zenith angles  (1977)  from  from  the centre  could  brightness  9 0 ° away  In the present  i n the atmosphere  a n d Manamohanan  o f minimum  approximately  result  clear  to exhibit  and S a s t r i  region  be a  features  representative does  sky radiance  particles  regime  the sun.  to the notion  could  These  scattering  from  a clear  n o t seem t o c o n f o r m  cirrus  expected  away  radiance  the  distance lies  and t h e i s o l i n e s  form  1 07  (b)  Figure  5.18  S t a n d a r d D i s t r i b u t i o n of N o r m a l i z e d C l e a r Sky R a d i a n c e f o r a ) Z e n i t h A n g l e 35° and b ) Z e n i t h A n g l e 55° F r o m S t e v e n ( 1 977 )  108  a  pattern,  larger  encompassing  solar  results  z e n i t h angle  i n an  corresponds  increased  about  the solar  the  rapidly  diffuse the  examples,  not  cloudless region about  found  given  near  the  symmetrical  by a  a modelled  thought  and s l o w l y  90° from  a n d Hay  that f o r  result  of  of h i s  Ground  caused  reflection  study,  given  was  the  site.  of a  changed As  varying  map  for a  strong by a  aureole factor  of  i n the other radiance  was  t h e Sun.  diffuse (1981)  angular  t o have  radiance  radiance  with  isolines  of 4 as a  in zenith angle.  o f minimum  a t an  F o r some  the presence  also  or h o r i z o n t a l ) the  factor  was  the  found  i n the present  i n which  sky normalized  by M c A r t h u r  Valko  the horizon.  depicted  at approximately  t h e minimum  was  coincident  there  o f t h e measurement  30° change  the region  Clear  As e x p e c t e d ,  radiance  (i.e. vertical  important  t h e Sun a  mass  This  sky radiance  and from  the Sun.  differ  presented  sky which  10 w i t h  cases,  t o be  of c l e a r  reflection  values  (1981)  around  to a  a n d Manamohanan  are also  of sky r a d i a n c e .  characteristics  Dave  (1977)  until  exposures  ground  radiance  surface  from  anisotropy  suspected  effect.  study.  T h e maximum  in value  surface  high  of t h i s  isolines,  i r r a d i a n c e s may  strong  higher  by  o f 9 0 ° away  different  brightening  of Steven  (1980).  bounded  decreased  distance  scattering  f i n d i n g s of S a s t r i  distribution  by V a l k o  S u n was  F i g . 5.18b c o r r e s p o n d s  vertical.  angular  measured  horizon  as the r e s u l t s  distributions  The  area.  and t h e i n c r e a s e d  to the e a r l i e r  (1975) a s w e l l radiance  this  radiance  distributions  and a r e d e p i c t e d  were  i n F i g . 5.19.  1  Figure  5.19  09  C l e a r Sky N o r m a l i z e d R a d i a n c e Distributions ( s r ) f o r a ) l 2 4 0 LAT F e b r u a r y 10,1978; b ) l 3 4 0 LAT F e b r u a r y 10,1978; c ) l 3 2 6 LAT F e b r u a r y 26,1978; d ) l 3 4 7 LAT F e b r u a r y 26,1978. From McArthur a n d Hay ( 1 9 8 1 ) -  1  1 10  These  maps  show  video-based apparent with the  imaging  that  solar  scattering this  region  the  in  angle.  of  from  radiant  the  isolines  closest  to  the  Fig.  horizon)  5.6.  diffuse  Hence,  (McArthur  radiation  Hay,  show  encompassing provide  with  greater  radiances those  of  are to  increasing zenith  angles,  discontinuous  (as  the  This  solar  zenith  angle  the  percentage  can  of  Sun  the  the  is  be  seen  region  diffuse  lower  horizon  increases,  horizon  the  isolines  s t r o n g l y by  1981).  reasons  angular  the  from  the  encompass  with  clear  sky  the  distributions  with  latter  those  have  sky  radiance  entire  sky  hemisphere  detail i t was  observed  and not  accuracy  p o s s i b l e to  i n the  during  from and  than  McArthur  of  results  the  of  observed  disk  Hay,  that  forward  change  solar  increases  state  complex,  agreement  values  Unfortunately, the  good  the  Sun  also  in  the  becomes  an  irradiance  1981).  However,  instantaneous  then  larger  emanating  examples  study.  the  solar  with  the  strong  the  i t is  (1981)  i n f l u e n c e d more  and  significant  and  These  For  Hay  using  5.19,  near  the  the  isolines  being  as  radiation  about  becoming  and  and  and  produced  Figure  radiance  becomes more  (McArthur  increasingly  this  Sun  of  intensity  Sun.  of  brightening  The  those  From  mass  characteristics  least  to  McArthur  scattering  pattern  the  technique.  phenomenon.  distance  on  similarity  magnitude  zenith  increase  for  close  advantage  of  a  data  digital as  a  compare  this.study, since  in  being base  result  the  Hay  solar  produced  previous  and  diffuse  results. magnitude  (1981)  in both  study cases,  of  111  there  was  not  conclusions sky  (or  Overcast Grace  days  (SOC)  Spencer the  (1942)  horizon.  The  given L  obviously,  formula  natural  the  the of  from  and  environment  showed  radiant  decreasing  empirical  1/3L  that  Standard  chamber)  the  mean  Overcast  brightness)  of  Sky  Moon  intensity  located  there  to  referred  to  out  as  the  on  and  at  the  SOC  formula  (1+2sin0)  (5.10)  Z  u  where  to  highest  radiance  an  results  distribution  the  more  by:  =  a  His  under  used  corresponded  with  z e n i t h and  radiance  skies.  and  significant  Distributions  ( i . e . he  ( i . e . the  statistically  same.  Radiance  radiance  formula  derive  distributions)  measured  overcast  of  to  the  environments  with  pattern  not  Sky  (1971)  controlled  data  standard  c o n d i t i o n s were  5.4.2  is  enough  L„  i s the  brightness  at  any  angle  6 above  the  1971).  He  horizon;  L  u  is  the  that  brightness  instantaneous  under  such  skies.  at  the  zenith  (Grace,  radiance  distributions  This  studied  agreement  the  luminance  sky  the  SOC  formula.  cloud  and  dense  Steven  and  Unsworth  (1980) d e s c r i b e  of  overcast  skies  distribution N(0) where  b  = is a  to  verify  between  thick  attempted  Sastri  (1975)  distribution They  foggy  of  found  the good  the  individual agreement  N  and  overcast for  very  conditions.  by  an  the  equation  radiance of  the  N ( o ) ( 1 + b c o s t 9 ) / ( 1+b) constant,  noted  highly variable  f u r t h e r by  Manamohanan  and  who  was  were  also  i s measured  form (5.11)  radiance  at  any  angle  6  Z  112  above  the  value  of  horizon the  and  Unsworth,  and  5.11,  and  a  N(o)  coefficient  satisfactorily  using  and  but  i s the  b  has  For  of  b=1.5  Unsworth,1980).  measured  radiances  hemisphere compared  Generally,  The at  variety  the  radiances  the  equation  see  of  tends  to  a  An  (1981)  no  gradient  stated  where  the  of  solar  study.  The  and  as  are the  radiance  Steven  5.1,  the  show  sky  may  be  radiance  zenith  and  this  angle.  these  hemisphere  that  the  azimuthal i s not  findings sky  are  in accord  only  small  range  (1980)  agreed  as  measured  studied  the  almost  the  over  the  overcast  with  of  They  the  those in  of  this  Figs.  McArthur  radiances  isotropy across  also  of  depicted  results  and  with  under  i n agreement  of  and  ( F i g . 5.20).  dependence  the  McArthur  visible  pronounced  with  by  i s reasonable  and  distributions  approximates  Valko  are  not  values  approximation  sky  overcast  gradient  hemisphere.  in  5.11.  presented  was  the  radiance  These  5.11,  (1981)  Eqn.  5.10  performs  These  data,  was  position  between  isotropic  sky  conditions.  slight  the  (1969)  intensity  Hay  distribution  p o r t i o n of  Kondratyev  5.10  sky  existed  that  central  on  (Steven  in Figs.  in Table  underpredict  increasing  2.0  presented  angles. using  and  5.11  positions  overcast  The  findings.  overcast  Hay  of  zenith.  shown  Eqn.  values  estimated  paucity  1.0  presented  zenith  However,  preliminary  well  azimuthal  increases with  to  how  the  determined  between  from  underprediction due  be  results,  two  been  at  distributions  (chosen  for a  to  to  the  i t i s p o s s i b l e to value  not  i s thought  1980).  radiance  and  and  the  sky  characteristics  of  a  11 3  Table  5.1  V a l u e s o f M e a s u r e d a n d P r e d i c t e d ( U s i n g E q n . 5.11) Radiances (Wm" sr ) f o r Certain Zenith Angles f o r O v e r c a s t S k i e s O b s e r v e d on J a n u a r y 2 0 , 1984 (Zenith Angle 74°) 2  Zenith Angle (Degrees)  Meas. Rad 0° A z i m u t h (Wm" • s r )  - 1  Meas. Rad 180° Azimuth (Wm" sr )  Predicted Radiance (Wm~ sr~ ) 2  JD20b.1 20 40 60 70  32 32 22 18  32 31 26 23  30.84 27.51 22.40 1 9.37  20 40 60 70  18 1 7 1 4 1 3  18 1 7 1 6 1 4  17.35 15.47 12.60 1 0.89  JD20b.2  1  114  gure  5.20  O v e r c a s t Sky R a d i a n c e (Wm" sr"') D i s t r i b u t i o n f o r 1230 L A T F e b r u a r y 14,1978 (z = 63°). From M c A r t h u r and Hay (1981) 2  1 15  radiance  distribution  illustrates of  a  stratus  symmetry in  the  of  azimuthal  5.4.3  layer  cloudy  the  radiometric  as  about to  found  Sky  Radiance  well  the  long  r a d i a n c e measurements,  diffuse  r a d i a n c e under  Research typical  those  by  diffuse  such  Valko solar  the  radiance distribution  the  resulting  bright of  areas  radiance  distribution on  the  observed  when  patterns observed  these  cases, (Valko,  findings  of  the  1980). this  This  study  illustrated  by  Figs.  differences  between  as  5.16 the  (Valko,1980).  of  partly  typically  used  to  obtain  have  of  the  been  distribution  attempted  that  the  irregular  F i g . 5.22  cirrus  clouds  cloud  well  to  shows were  structure,  the  that  dark  a  similar  to  values  of  radiance  were  and  both  clear with  d i s c u s s e d i n S e c t i o n 5.3.2 There  and  resembled  For a  by  distributions  present,  conditions.  5.8.  of  is disturbed  observation corresponds  and  less  regularity  turbid form  of  conditions.  distributions  the  p a t t e r n s had  of  the  shows  under  lack  the  decrease  of  corresponds  clouds.  those  case  of  A  the  time  sky  radiation  and  notes  response  skies  (1980)  zenith,  complexity  studies  for other  (1980)  effect  Distributions  temporal  systems  5.21  r e p r e s e n t s the Valko  exist  and  measurement  than  to  Fig.  horizon.  spatial  diffuse  frequently  which  the  the  was  as  skies.  underlying fog.  zenith  Cloudy  the  skies  overcast case  with  dependence  to  overcast  distribution  from  Partly Due  fully  the  radiance  under  sky the  and  smaller  for surfaces  facing  Figure  5.21  O v e r c a s t Sky R a d i a n c e D i s t r i b u t i o n s under A l t o s t r a t u s C l o u d . From V a l k o  (Wm ) (1980) - 2  1 1  Figure  5.22  7  Radiance D i s t r i b u t i o n s During Cirrus Cloud C o v e r F r o m V a l k o ( 1 9 8 0 ) (Wm~ ) 2  1 18  towards, the  or  cloud  away  cover  from  becomes  component  i s depleted  intensity  may  be  shifted  zenithal  no  symmetry and  distributions photographic complexity  locally  higher  Hay  (1981  the  from  manner Hay  diffuse  the  the  radiances.  as  a  clear  (1981)  sky  same  the  case  under  validity  scattering  of  individual  cloud  distribution  The  visible  of  of of  was  the that  elements radiance  as  in  may  perfect  and  of  Fig.  conclusion. the  in a sky  their  lowest  the  clear  increase in  the  1981). the  to 5.17 The  sides highly  the  resulted  Hay,  clouds.  using  scattering  not  skies  the  but  radiance  the  to  cloudy  across  Sun,  illustrates  droplets  complexity  results  of  cloudiness  although  radiation off  the  examples  found  (McArthur  beam  radiant  Almost  Increased  region  direct  As  sky.  l o c a t i o n of  Sun,  partly  around  clearly  water  radiance  and  properties  the  5.23  the  cirrus.  maximum  a  partial  of  a t t r i b u t e d the  radiance  reflective affirms  horizon  such  of  1980).  ) provided  Fig.  and  of  (Valko,  for  presence  Sun)  region  during  the  presence  however,  distribution.  in approximately  towards  and  to  dense  zenith noted  a  the  concentrated  was  such  due  (90°  the  in  the  be  technique.  effects  was  and  obtained  of  Sun  more  longer  towards  McArthur  the  in intensity  sky  both same McArthur  pattern  the  cases  of  highly  exemplifies reflection and  bases  irregular  hemisphere.  and of  and  Figure  5.23  P a r t l y C l o u d y Sky R a d i a n c e Distribution f o r 1317 L A T F e b r u a r y 1 5 , 1 9 7 8 , F r o m M c A r t h u r a n d Hay ( 1 9 8 1 >  1 20  Chapter Six Conclusions  6.1  Assessment  6.1.1  Assessment  Technique Site  For roof  s e t of observations Department  however,  i t would  since  framestore  unit  a more  remote  an  experimental  major  camera  field site  will  allow  a video  geographical/climatological  images  representative  studies  This  The  range  would  Assessment necessity  abstracted  from  a t such  be o f  to studies a  such  flexibility system  settings  of sky  on t h e e f f e c t s o f t u r b i d i t y  luminance/radiance  6.1.1.2  of a  roof  a  in  t o be  so as t o  computer choosing  located in record  luminance  i n t e r e s t f o r example, i n on t h e s k y  distribution.  of  Instrumentation  to c a l i b r a t e the brightness  a video  image  easy  a r e a v a i l a b l e and the  This  varied  characteristics.  to locate  i t was  in selecting  For future  i n t e r f a c e d with  location.  system,  the necessity  link.  microcomputers be e a s i l y  the video  consideration  was  n o t be m a n d a t o r y  could  c a r r i e d o u t on t h e  at a location allowing  and framestore  portable  at  Another  f o r the video  a computer  using  the equipment  and s e r v i c i n g .  maintain  site,  Study  Considerations  to operate  location  Procedures  of Measurement  in this  of the Geography  access that  Used  the i n i t i a l  necessary  Recommendations  of the Experimental  Critical  6.1.1.1  and  of the sky using  values measured  121  radiances to  obtained  be a p r o c e d u r e  eliminated The  time  longer  which  than  radiative would  would  desired  e s p e c i a l l y i fthe  manually  particularily were  could  change  to obtain  to record  recorded  since  diffuse  shorter  when  was  interval.  during  time.  under  Also,  by  the  i s longer rapidly  the instrument  It  relatively  be a c c o m p l i s h e d  (8-10 s e c o n d s ) radiance  of  the  the scan  could  solar  The l e n g t h  (18 m i n u t e s )  ideal  within  This  i n a much  conditions  low.  measurements  of the instrument  or windy  even  to operate  be c o n s i d e r e d  observations  time  or  of d i f f u s e  observations  what  improved  proved  f o r t h e measurement  spectral conditions.  response  skies  were  conditions  collecting  that  sluggish  be p r e f e r a b l e  constant  be much  actinometer  research. used  temperatures  over  could  in further  proved  the Linke-Feussner  that  actinometer  radiation outside  with  than  changing  operates  less  ef f e c t i v e l y . Ideally, had a  a  i t would  smaller  smaller  total  solid  be d e s i r a b l e  aperture  angle  t o use an  i n order  and so r e c o r d  instrument  t o measure  which  radiance  a more a c c u r a t e  over  point  est imate. If for  measurements  calibration  sky-scanning  purposes  system  actinometer.  of d i f f u s e  Such  i n future  would a  solar  be an  system  studies,  improvement  could  of d i f f u s e  radiance,  much  time  (as i n Hooper  could  be b u i l t  span,  with  a smaller  an  completing  over  angle  a  required  automatic  automatically  observations shorter  radiation are  the use of the record  sky scan  in a  and Brunger,1982) and  of aperture.  This  type of  122  system the  would  undoubtedly  Linke-Feussner The  result (i.e.  less  minimize  relative  than  this  error  when  i t would  advisable  t o have  The for  the c o l l e c t i o n  with of The  ER N e w v i c o n  the desired  t h e camera  instance,  an may no  even  i t would  t o be a u s e f u l  A neutral  that  density  allowed  radiant  characteristics  tube  In order  to  be  device  filter  the operation  intensities.  of t h e camera radiance  and  made a n  brightness  various distortions and i t s e l e c t r o n i c s .  For  v a r i a t i o n s o f 1 0 % may b e a t t r i b u t e d t o t h e n o n l i n e a r  may o c c u r  evidence  t h e image  and even  larger  of temperature  dependent)  (Franck  solar  during during  noon)  the r e s o l u t i o n of the video appeared  saturated.  This  a  would  this  size  Although study,  intense  'blooming'  image  across  ( i . e . image  e t a l . , 1983).  For instance,  ( e g .about  variations  drift  d i s t o r t i o n s was f o u n d  d i dexist.  conditions where  system,  because  of such  problems  occurred  proved  the highest  the video  signals  the d i g i t a l  study,  properties  i t i s known  with  be t e m p e r a t u r e  radiative  and  under  was f o u n d t o  to further use.  o f sky images.  of the video  image  other  camera  transmission  However  associated  effects  prior  this  o f t h e r e l a t i o n s h i p between  possible. are  video  s p e c t r a l response  analysis  done  study.  to amplify the  Although  was n o t c a l i b r a t e d d u r i n g  small  2.1.2.2).  be a d v i s a b l e  voltmeter  this  and t h i s  _ 1  recording  by t h e a c t i n o m e t e r .  of  radiation signal  (See S e c t i o n  2  produced  solar 2  errors  operation  i n the present  o f ±4.91 W m ~ s r  10 W m " s r ~ ' )  problem  t o t h e manual  as used  of the d i f f u s e  an a b s o l u t e  in large  signal  actinometer  recording  involved  be s u p e r i o r  effect  deteriorated  last  until the  1 23  radiative filter  regime  could  had  resumed  operate  more  a  level  where  effectively,  and  the  camera  the  image  and was  restored. A the  better  video  improve  correspondence  system  the  and  and  result  This  eliminate  interpretation coordinate  Newvicon of for  the  would  should checked  could  be  to  distribution  of  in  the  the the  polar  camera of  shorter  particularily  alternate  would  and  independent  video  of  equation.  from  properties  i s not an  is  the  i n s e n s i t i v e to  and  energy  radiance  uncertainty  spectral  studies  of  calibration  actinometer  This  response  of should  the  ER  wavelengths desirable  spectral  response  improvement. lens,  a  its optical further  check  deemed  for  custom-built properties  use.  geometric  performed  to  present  well  system  in  must  various  be  lens  tests  d i s t o r t i o n s , none  Although  this  camera  study, made  in  this  case,  professionally tested  Though  conclusive.  system the  the  response  spectrum.  before  performed  the  relatively  fisheye  have  of  present  radiation an  The  The  spectral  between  improved  radiance  spectral  energy  be  the  the i t .  an  much  Since  are  solar  in  maps.  wavelength, complement  of  the  spectral distribution  r e l a t i o n s h i p obtained  brightness would  the  between  the an  lens  and  important  before  further  or  were of  these  camera modification research  is  attempted. The or  present  calibrated in  further  use.  It  aperture  on  any  manner  was  not  the and  fisheye this  possible  to  lens  should discern  i s not  be by  graduated  remedied how  much  before the  1 24  aperture be  was  being  p o s s i b l e to  been  and  adjusting effects gives  for  the  the  be  necessary as  change  clear,  be  every  6.2  The  of  level,  the  as  values) Once  the  this  signal  this the  had  been  blackness  each  partly  having  to  an  carried  radiation  of  procedure sky  cover  cloudy)  but  this  determine  a  described  i t would  level  of  the  this  would  be  not  controls not sort  conditions  calibration  may ( i .e.  an  curve  for  scan.  of  Results  Sky  Cases distribution  c o n d i t i o n s has  study  are  found  been to  be  of  diffuse  well  solar  documented  in close  Radiance  maps  of  such  c o i n c i d e n t with with  solar  increasing angular  radiance  usually  lies  disk  and  distance  and  Valko,  conditions consistently the  radiation  agreement  Steven,1977 ; McArthur,1978;  minimum  out,  which  would  that  c o n d i t i o n s do  (eg.  values  aperture  to  video  research  value  after  brightness,  similar  and  between  limits  and  have  oscilloscope,  and  manner  calibration  for  on  voltage  in a  spectral  and  angular  sky  video between  adjust  over  Clear  clear  video  i t might  could  relationship  level,  to  Summary  6.2.1  the  known,  This  blackness  overcast,  sky  system.  spectral  followed  improvement  been  given  dramatically. A  to  video  this  within  4.1.1.  long  the  had  brightness  latter  Section  and  determining  relationship  in  again  by  (monitoring  provide  have  calibrate  accomplished  radiance  adjusted  a  approximately  with  the 90°  results previous  1980).  show  sharp  from  the  under  a  maximum  decrease Sun. from  in  A the  solar  1 25  disk  and  values  generally  increase  from  there  out  to  the  hor i z o n . Since  these  distributions  regardless  of  of  energy,  radiant  Section  6.1.1.2  collecting provide with  a  a  such of the  to  It  and  not  be  of and  previous  work  that  results  during  this  study  6.2.3  Partly  By and  f a r the analyze  of  to  the  indicate  Cloudy most  Sky  complex  i s that  data  composition  described of  set  which  earlier  in  efficiently  under  overcast  system  could  clear  skies  studies.  to  collect  a  data  compare Steven  overcast good  these  a  highly under  s i z e a b l e data future quality  best  results  overcast  be  possible the  with (1980).  analysis carried with  set  research,  fits  Unsworth  agreement  been  radiance  i t would  which  sky  a  high  and  in  for  set,  equation  by  but  providng  s k i e s have  provides  variations  study,  of  the  distribution as  the  such  radiance  preliminary  video  this  capable  form  under  feasible  With  such  as  capable  than  form  spectral  radiance  accuracy  the  during  for analysis. the  system  of  or  sysem  significant  recording  was  would  level  in  Cases  of  images  determine  a  distributions  means  sky  system  data  Sky  consistency  video  distribution  frequently,  skies.  such  provide  resolution  less  successful  calibrated  would  radiance  studied  turbidity  statistically  Overcast As  a  standard  better  6.2.2  location,  show  earlier  The out  work.  Cases radiance  obtained  under  distribution partly  cloudy  to  both  skies.  record Due  to  1 26  the  rapidly  scattering had  been  of  regime  made  radiance impeded  changing  cloudy  have  technique  under  in this  characteristics  f o r a more  radiance  distribution.  s e t should  the scattering  cloudy  useful  information  radiative  skies.  transfer  Some  on c l o u d i n cloudy  of c l e a r  intensities  skies This  present  spectral  procedures  arose  an a u t o m a t i c  measuring  interval  time,  as well  response  of the video  observations  distribution  mapping  of the  requires  of shortwave  preserved  that  useful  a  results  radiation  similarily  large  under  provide  and t h i c k n e s s  a n d on  atmospheres. during  attempts  individual  radiance  as a better  elements  range  were  of radiant  and o f t h e c o n t i n u a l l y  radiative  instrument)  t o record sky  cloud  of the large  an image  diffuse  camera  many  f o r making  s k y image,  to derive  would  has been  instruments  a radiance  i n order  of those  for procuring  a  distributions  was a r e s u l t  nature  area  synchronous  and a c c u r a t e  on w h i c h  i n such  of sky  The measurement  from  geometry  progress  t o be u s e f u l  skies.  of such  data  little  in this  utilizing  regime  These  difficulties  superimposed.  of  of such  be c o l l e c t e d  partly  varying  detailed  complexity  concerning  study  very  radiometric  too long  cloudy  and the complex  distribution  Progress  and b r i g h t n e s s  allowing  The  times  partly  radiance  complex  images  the angular  skies.  response  used  diffuse  data  them,  by t h e u s e o f c o n v e n t i o n a l  which  the  of clouds  associated with  in studying  under  observations  of  distribution  and energy  Improved  measurements  with  match  regimes.  a  shorter  between  ( i . e . use  scan  the spectral  distribution,  would  1 27  minimize  6.2.4  this  Radiance It  radiance  illustrating  distribution  not  values  used  radiance  6.3  concerned over  sky  real-time  simple  they  were  The measurement  i s better  to best  of the video  of  radiance  accuracy  than  1978).  Irregular  express  the v a r i a t i o n s  and accurate  determination  brightness  technique of d i f f u s e  be d o u b t e d .  and the d i g i t i z i n g  between  imaging  distribution  cannot  efficient  t h e s k y dome.  i n that  study  Recommendations  a n a l y s i s of the data.  established  over  and  the angular  for fast,  found  the  in this  for prediction  (eg. McArthur,  over  of the  produced  more d e t a i l e d .  which  polar  successful in  intensity  attempts  allowed  of a  t h e s k y dome.  usefulness  hemisphere  study  were  the sky hemisphere  allows  proved  T h e maps  previous  reported  across  with  values.  ± 2 % i n some c a s e s  Conclusions The  maps  i n t h e form  of the radiant  a n d were  intervals  was  of p r e s e n t i n g the  as the c h a r a c t e r i s t i c s  in this  studies  contouring  These  over  values  within  earlier  in  as w e l l  of those  averaged  method  of radiances  map.  improvement  technique  the best  the magnitude  hemisphere  an  that  distribution  coordinate  were  Maps  was d e c i d e d  predicted  sky  problem.  mapping  facilities The l i n e a r  and radiance  of the p r e d i c t e d  This  i n research radiation  type  of  system  of the e n t i r e  allow f o r relationship values  radiance  allows  fora  distribution  1 28  As video of  system  i s its ability  monitoring  would  even  of dynamic  be u s e f u l  types  transitional clear the  stages  which  to overcast)  angular  entail  would  image allowing  This  technique  continuous  monitoring  collecting  images of  provide  data  extreme  radiance  showing the  to another  one t o s t u d y  of d i f f u s e  of the  instantaneous  or motions.  involving  allow  advantage  sky c o n d i t i o n s ,  one s k y c o v e r  and would  distribution  an  complex  would  This  from  a major  processes  i n a programme  of sky cover.  6.2,  to provide  t h e most  the sky hemisphere  all  of  out i n Section  the sky under  for  of  pointed  (eg.  the changes i n  over  a  continuum  conditions. The  many the  potential  of such  researchers given  a system  that  the r e s u l t s  a n i s o t r o p y of the d i s t r i b u t i o n  Models  incorporating  radiation true  must  Future  initial  procedure  continually.  could  system  will  study  solar  confirm  radiation.  characteristics  more  process  of d i f f u s e  then have  the  measurement  not  overly  would  of  solar  r e p r e s e n t a t i v e of the  benefit  f o r the video  The weakest  be r e f i n e d  procedure,  of t h i s  to  regime.  calibration  measurement  a n d made  s t u d i e s however,  calibration  be o f i n t e r e s t  of diffuse  the d i r e c t i o n a l  be r e f i n e d  radiative  would  which  link  from  system;  would  in this  an  preferably  not have study  was  t o be  radiation  and i f that  or assigned  a minimal  role  and very  useful  important  been system  optimistic  developed.  These  require l i t t l e to envision  this  repeated  process  i n t h e measurement  final  data  acquisition  refinements  development video  an  i n the  solar  an  improved  to  and so i t  imaging  i s  technique  129  in  wider  use  i n the  very  near  future.  130  References  B i r d , R.E., R.L. 1982. Solar environment,  H u l s t r o m , A.W. K l i m a n , a n d H.G. Eldering, s p e c t r a l measurements i n the terrestrial A p p l i e d O p t i c s , 21,8, 1430-1436.  C a n n o n , T.W., a n d L.D. D w y e r , 1981. l u m i n a n c e mapper f o r d a y l i g h t i n g the S i x t h N a t i o n a l P a s s i v e S o l a r O r e g o n , S e p t . 8-12, 855-859.  An a l l - s k y video-based research, P r o c e e d i n g s of Energy Conference, Portland  C o o k , N.H., a n d E.H. R a b i n o w i c z , 1967. A n a l y s i s , Addison-Wesley P u b l i s h i n g C o u l s o n , K.L., 1975. and M e a s u r e m e n t s ,  P h y s i c a l Measurement Co. I n c . , 29-68.  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 : M e t h o d s A c a d e m i c P r e s s , New Y o r k , 322 pp.  Dave, J.V., 1981. Transfer atmosphere, Atmospheric  of v i s i b l e r a d i a t i o n i n the E n v i r o n m e n t , 15, 1820-1905.  F r a n c k , J.B., P.N. K e l l e r , R.A. S w i n g , a n d G. S i l b e r b e r g , Process for producing laser-formed video calibration m a r k e r s , A p p l i e d O p t i c s , 22,16, 2481-2483. G a r n i e r , B., a n d A. O h m u r a , 1970. variations in solar radiation G h a z i , A., 1971. distribution, 52,11 , 1161.  and  1983.  The e v a l u a t i o n o f surface income, S o l a r Energy,13,21-34  S p e c t r a l measurements of sky radiance B u l l e t i n American M e t e o r o l o g i c a l Society,  G r a c e , J . , 1971. The d i r e c t i o n a l d i s t r i b u t i o n o f l i g h t i n n a t u r a l and c o n t r o l l e d e n v i r o n m e n t c o n d i t i o n s , J . A p p l . Ecology, 8, 155-164. Hay,  J.E., 1978. Measurement and m o d e l l i n g of shortwave r a d i a t i o n on i n c l i n e d s u r f a c e s . T h i r d C o n f e r e n c e on Atmospheric Radiation, American M e t e o r o l o g i c a l Society, D a v i s , C a l i f o r n i a , June 28-30, 150-153.  Hay,  J . E . , a n d T.R. Oke, 1976. The C l i m a t e T a n t a l u s R e s e a r c h L t d . , V a n c o u v e r , B.C.,  Hay,  J . E . , a n d J . A . D a v i e s , 1980. C a l c u l a t i o n of s o l a r r a d i a t i o n i n c i d e n t on an i n c l i n e d s u r f a c e , P r o c e e d i n g s of the F i r s t Canadian S o l a r R a d i a t i o n Data Workshop, J . E . Hay a n d T.K. Won, Eds. Canadian Atmospheric Environment S e r v i c e s , Downsview, O n t a r i o , 166 pp.  Hay,  J.E.,  and  R.  Darby,  1984.  El  Chichon  of V a n c o u v e r , 49 pp.  -  impact  on  aerosol  131  o p t i c a l d e p t h and d i r e c t , i r r a d i a n c e s at Vancouver, Hertzman, Using M.Sc.  d i f f u s e and t o t a l solar B.C., Atmosphere-Ocean,in  press.  0., 1979. C l o u d Mapping f o r the E a r t h ' s S u r f a c e an I n f r a r e d R a d i a n c e C o n t r a s t T e c h n i q u e . Unpub. T h e s i s , U n i v . o f B r i t i s h C o l u m b i a , 141 pp.  H e w l e t t - P a c k a r d , 1979. Manual, 62-63.  Electronic  I n s t r u m e n t s and  Systems  H o o p e r , F.C., a n d A.P. B r u n g e r , 1980. A model f o r the a n g u l a r d i s t r i b u t i o n of sky r a d i a n c e , J o u r n a l of S o l a r Energy E n g i n e e r i n g , 102, 196-202. H o o p e r , F.C., a n d A.P. B r u n g e r , 1982. E x p e r i m e n t a l o b s e r v a t i o n and c h a r a c t e r i z a t i o n of the s k y - d i f f u s e component of the shortwave s o l a r r a d i a t i o n at the earth's s u r f a c e , F i n a l R e p o r t f o r t h e A t m o s p h e r i c E n v i r o n m e n t S e r v i c e , D.S.S. C o n t r a c t No. O S U 7 9 - 0 0 2 1 0 , T o r o n t o , C a n a d a , 155 p p . IGY,  1958. I n s t r u c t i o n Manual of the G e o p h y s i c a l Year, V I . , R a d i a t i o n I n s t r u m e n t s and Measurements, Annals IGY, P e r g a m m o n P r e s s , New Y o r k , 3 6 7 - 4 6 6 .  K i m b a l l , H.H., a n d I . F . Hand, 1922. h o r i z o n t a l , v e r t i c a l and s l o p i n g Review, 50,12, 615-628. K o n d r a t y e v , K. Y a . , Academic P r e s s ,  Part of the  D a y l i g h t i l l u m i n a t i o n on s u r f a c e s , Monthly Weather  1969. R a d i a t i o n i n the New Y o r k , 912 pp.  Atmosphere,  K o n d r a t y e v , K. Y a . , L . A . K u d r i a v t z e v a , a n d M.P. Manolova, 1955. D i s t r i b u t i o n of 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 of d i f f u s e atmospheric r a d i a t i o n over the c e l e s t i a l sphere, B u l l . L e n i n g r a d U n i v . , 119-129. M a r k , D.M., a n d M. C h u r c h , 1 9 7 7 . On t h e m i s u s e o f r e g r e s s i o n i n e a r t h s c i e n c e , M a t h e m a t i c a l G e o l o g y , 9,1, 63-75. M c A r t h u r , L.B., 1978. The s p a t i a l d i s t r i b u t i o n o f d i f f u s e s o l a r r a d i a t i o n i n t h e s k y h e m i s p h e r e , M.Sc. T h e s i s , Dept. of Geography, U n i v e r s i t y of B r i t i s h Columbia, Vancouver, Canada, 137 p p . M c A r t h u r , L.B., a n d J . E . Hay, 1978. On t h e a n i s o t r o p y d i f f u s e s o l a r r a d i a t i o n , B u l l e t i n of the American M e t e o r o l o g i c a l S o c i e t y , 59,11, 1442-1443.  of  M c A r t h u r , L.B., a n d J . E . Hay, 1 9 8 0 . An a s s e s s m e n t o f t h e techniques f o r d e t e r m i n i n g the d i s t r i b u t i o n of d i f f u s e solar r a d i a n c e f o r the sky hemisphere, S o l a r E n e r g y , 25,6,573-574. McArthur,  L.B.,  and  J . E . Hay,  1981.  A  technique for  1 32  mapping the d i s t r i b u t i o n of d i f f u s e s o l a r r a d i a t i o n over sky h e m i s p h e r e , J o u r n a l o f A p p l i e d M e t e o r o l o g y , 20,4,421-429. McKee, T.B., a n d r a d i a t i o n by  S.K. C o x , 1 9 7 4 . Scattering of v i s i b l e f i n i t e c l o u d s , J . Atmos. S c i . , 31, 1885-1892.  M o o n , P., a n d D . E . S p e n c e r , 1 9 4 2 . non-uniform sky. Trans. Ilium Morris, sky  Illumination from a E n g . S o c . , 37, 7 0 7 - 7 2 6 .  C.W., a n d J.H. L a w r e n c e , 1971. The a n i s o t r o p y o f c l e a r d i f f u s e r a d i a t i o n , ASHRAE T r a n s . , 7 7 , P a r t I I , 1 3 6 - 1 4 2 .  M o r s e , R.N. a n d J . T . C z a r n e c k i , 1 9 5 8 . Flat plate solar absorbers: t h e e f f e c t on i n c i d e n t r a d i a t i o n of i n c l i n a t i o n and o r i e n t a t i o n , CSIRO D i v i s i o n o f M e c h a n i c a l E n g i n e e r i n g , R e p o r t E.D.6., 28pp. N o r r i s , D . J . , 1966. Solar radiation S o l a r E n e r g y , 10,2, 7 2 - 7 6 . Panasonic, Series  on  inclined  surfaces,  1981. Operating Instructions M a n u a l f o r WV C a m e r a s , S e c a u c u s , New J e r s e y , 13pp.  -  1800  P a s c o e , D . J . , a n d B.W. F o r g a n , 1980. An i n v e s t i g a t i o n o f t h e Linke-Feussner pyrheliometer temperature c o e f f i c i e n t , Solar E n e r g y , 25, 191-192. Robinson, York,  N., 347  1966. pp.  Solar  Radiation,  Elsevier  Pub.  Co.,  New  S a s t r i , V . D . P . , a n d S.B. M a n a m o h a n a n , 1 9 7 5 . A sky-scanning photometer f o r the luminance d i s t r i b u t i o n of sky, Pure and A p p l i e d G e o p h y s i c s , 113, 3 7 3 - 3 8 7 . S e a r s , F.W., 1949. Addison-Wesley  Optics. The P r i n c i p l e s o f P h y s i c s Publishing C o . I n c . , 386 p p .  Series,  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 s o f c l e a r s k y radiance, Quarterly Journal of the Royal M e t e o r o l o g i c a l Society, 103, 4 5 7 - 4 6 5 . S t e v e n , M.D., a n d M.H. U n s w o r t h , 1 9 8 0 . Angular d i s t r i b u t i o n i n t e r c e p t i o n of d i f f u s e s o l a r r a d i a t i o n below o v e r c a s t s k i e s , Q u a r t e r l y J o u r n a l of the Royal M e t e o r o l o g i c a l Society, 106, 5 7 - 6 1 . S t e y n , D.G., 1980. The c a l c u l a t i o n of view f a c t o r s fisheye l e n s p h o t o g r a p h s , A t m o s p h e r e - O c e a n , 18,  from 254-258.  S w o k o w s k i , E . W. , 1 9 7 5 . C a l c u l u s w i t h A n a l y t i c Geometry, P r i n d l e , Weber a n d S c h m i d t I n c . , B o s t o n , M a s s a c h u s e t t s , 854 p p .  and  1 33  V a l k o , P., 1 9 8 0 . Some e m p i r i c a l p r o p e r t i e s o f s o l a r r a d i a t i o n and r e l a t e d p a r a m e t e r s . I n : An I n t r o d u c t i o n t o M e t e o r o l o g i c a l Measurements and Data H a n d l i n g f o r S o l a r E n e r g y Application (DOE/ER-0084), S w i s s M e t e o r o l o g i c a l Institute, Z u r i c h , 46 p p .  1 34  Appendix Assessment  of  the  C h a r a c t e r i s t i c s of and  Al.1  Test The  for  custom-built geometric in  Axial  fisheye  order  the  experimental  at  UBC. A  levelled  targets,  each  theodolite,  targets  had  and  video  system to  was  avoid  of  axial  at  an  of  the  that  carefully  levelled  was and  flare.  were  roof  in  the  occulting  The  brightness  enough  contrast  could  identified  easily  on  digitized  image  separation symmetry  AI.1.2  and  of  was  Test  the  were  targets  angular  a  indeed  It  be  disk  The  so  was  preserved  within of  was  the the  removed  camera  and  up  on  the  monitor  a l l of  the  This  viewed  found and  in  lens  set  image. as  the  was  that  that  were  targets  image on  order  was  the the  hence,  angular  axial  confirmed.  to  Confirm  Equi-Angular  Projection  of  at  four  position  theodolite  made  Department  sight  would  was  the  performed  around  the  distances  determined. was  90°  levels  video  test  was  to  i t s place.  provide  recorded  of  Since  Geography  used  Once  to  then  was  a  work  the  targets  adjusted be  This  was  lens.  Lens  Lens  study  unknown,  of  marked,  the  Camera  laboratory-calibrated.  the  put  Camera  this  distance  camera  camera  in  theodolite  sure  Fisheye  System  symmetry.  on  the  Fisheye  lens  angular  the  of used  been the  Sokisha  been  lens  lens  not  site,  making  field-of-view  the  had  confirm  Imaging  Symmetry  properties to  Video  camera  and  I  Fisheye  135  Camera  Lens  The  f i s h e y e camera  lens  equi-angular  projection.  the  of  is  distance directly  in  order  in  the  to to  sky  This set  up,  was  so  the  that  confirm  from  video  each  the  p o s s i b l e to 10°  vertical It pixels  per  not  i n the  at  same  level  The  as  on  the  by  this  location  of  a  study  the  sampling  spot  An  height  A  tripod  chosen  a  as  placed  where  as  of  noting  and  be  the  level  the  ( a l l marks  until  hung  90°  down noted  placed  a  in  horizontal fisheye lens  was  had  video  i t was  pixels  was  was  carefully  in a  of  the  taken  interval  was  could  centre  number  point  level  plumb-line  its position  was  lens  automatic  anticlockwise  was  was  image.  i n an  a  it  camera  height,  spot  vertical  In  image  the  10°  The  well  circular  of  an  projection,  every  on  the  angle  indoors.  camera  exact  the  have  point,  and  camera  of  p r o p e r t i e s of  r e f e r e n c e mark.  been.  found  A  that i t  corresponding  to  number-of-pixel were  located at  the  same  image. that  division  varying  zenith  a  to  equi-angular  centre  video  out  this  discovered 10°  the  the  aimed  count  height) was  the  accurate  markings  interval  variations  spot  10°  true  assumed  field-of-view.  levelled.  i n the  a  angular  on  the  position.  of  the  From  the  and  the  the  and  automatic  positioned  from  carried  o f f at  orientation  was  was  point.  the  similar  image  evaluate  levelled  direction  in  hemisphere  marked  from  point  test  reference  point  With  p r o p o r t i o n a l to  corresponding necessary  a  i s normally  more  there  with than  the  were  approximately  vertical  2 pixels.  dimension I t was  17±2 of  noted  each that  the  1 36  90°  marker  not  confirm  the  image. The  and in  was  was  camera  and  10°  the  image  had  On  determine  the  basis  perimeter  the of  pixels  rather this  to  than  confirmed  f o r each the  analysis,  of  the  Shape  of  85°  on  axis  was 10°  of  pixels  suggested  as  to  the  number  i t was  and  image  of  This  circular  image  could  consistency  Another  14.  video  one  i t s horizontal  position,  the  the  2  from may  +  Cy  that  initially possible  locate  to  sampling  image,  Dx  the  +  Ey  presented  centre, image  scanning  +  equation  the  Image  coordinates  equation  of  the  along  the  ellipse  could  performed  to  f i t the  data  the  to  in  F  = of  0  .  the  (AI.1) ellipse  with  non-rotated  as:  2  digitized  pixel  Video  f o l l o w i n g method.  (X-133.4) /(120.6) the  x,y  a  1975):  +  2  this, be  the  r e g r e s s i o n was  (Swokowski, Ax  of  video  by  Multiple  video  found  in this  of  check  fact,  approximately  about  of  values  the  determined  where  past  location.  were  17  In  within i t .  Given  axes  marker  camera's  from  shape  image.  plumbline  elliptical the  the  r o t a t e d 90°  camera  Determination  form  a  coordinates  the  was  A  the  on  of  then  changed  assumed.  points  of  pixel For  per  and  was  re-levelled.  markers.  AI.2  visible  visiblility  replication  taken  be  not  2  +  screen  appears process.  (y-124.9) /(l45.3) 2  coordinates,  elliptical This  due  results  to in  is an the  2  =  1  (AI.2)  (133,126). asymmetry lens'  The in  the  circular  1 37  image of  being  camera  was  positioned with  image lens  was  taken  using  positions  for  The  another  image  From  this  the  y  then  set  up  direction  of  camera was  by  a  constant  i t can  ±1  pixel  image  Al.3  Determination Field-of-View  aperture AES.  10.16°  Given  the  actinometer's located  on  factor  r  =  2/TT  be  Table seen  of as  projection pixel  were  90°,  An  of  the  coordinate  visible  on  re-levelled  shows  the  these  the  and  results.  equi-angular  i s confirmed which  (133,126).  the  that  AI.1b  that  the Shape S e e n on a  used  with  i s the  variations  resolution  of  of the  as  of the A c t i n o m e t r i c V i d e o Image  in this  determined and  study during  azimuth the  image  translation a  shows  r o t a t e d by  accuracy  digitized  The  of  re-levelled  monitor.  zenith  firstly  coordinates,  markers  field-of-view,  the  principles. involves  the  actinometer of  10°  fisheye lens  video  The  on  Al.1 a  then  and  equi-angular  Table  the  was  horizontally coordinates  the  analysed.  the  than  centre  confirm  each  of  the  centre.  study,  projection more  to  this  image.  not  in  1.21. The  and  stretched  conversion  of  a  total  calibration  the  centre  corresponding  plane  of  has  sky  from  using to  sky  of  pixel  angle at  of  the  the can  be  geometric  screen (z,a)  coordinates to  polar ( r , 8 )  where Z  R * 0  ( A l .4)  1 38  Table  AI.1a  Pixel Coordinate Positions o f t h e 10° T a r g e t s V i s i b l e V i d e o Image Marker  Position  (°)  f o r Each on t h e  Pixel  0 10 20 30 40 50 60 70 80  Table  AI.1b  131 131 131 131 131 131 131 131 131  Same a s T a b l e A I . 1 a f o r a V i d e o Camera by 9 0 ° Marker  Position 0 1 0 20 30 40 50 60  coordinates  (°)  1 33 1 47 , 161 , 1 75 , 189 , 203 21 7 230 ,243 r  r  p  r  Rotation  Pixel  of  Coordinates 130,132 146,132 163,132 180,132 197,132 214,132 231,132  1 39  and =  6  a.  R *  i s the  the  sky  0  semi-minor  zenithal  translating  from  coordinates  (x,y)  0  +  rsinc? x  x  =  x  0  +  xcosfl  0  0  image. from  mean  the  are  the  planar  angles  coordinates  image  and  z  respectively.  ( t , 8 )  to  a  and  are  Then  cartesian  gives,  y  planar  the  polar  =  (x ,y )  of  azimuthal  y  where  5.08°  and  axis  1 .21  (Al.6)  the  centre  A l l pixels central  brightness  ( A l . 5)  of  corresponding  point the  coordinates  are  sample  of to  included area.  the sky  in  digitized points  the  less  than  computation  of  1 40  Appendix Regression  Results Clear,  of  Radiance  Overcast  and  II  versus  Corrected  Partly  Cloudy  Brightness  Skies  for  1 4 1  Radiance  *Note  Figure  -  1,2 r e p r e s e n t points  AlI.1  (Wm" sr"') 2  t h e number a n d l o c a t i o n  of  data  Regression Line of Radiance (Wm" sr"') and B r i g h t n e s s f o r a C l e a r Sky 0916 L S T J u l y 2 9 , 1 9 8 3 2  1 42  158.0  17;  Radiance  Figure  All.2  (Wm~ sr 2  ')  Regression Line of Radiance (Wm~ sr and B r i g h t n e s s f o r a C l e a r Sky 1631 L S T J u l y 2 9 , 1 9 8 3 2  _ 1  )  Figure  All.3  Regression L i n e of R a d i a n c e (Wm" sr"') and B r i g h t n e s s f o r a C l e a r Sky 1118 LST J u l y 30,1983 2  1 44  -60.00 -30.OO  40.00  100.0  Radiance  Figure  All.4  ISO.O  (Wm  2  sr  220.0  ' )  R e g r e s s i o n L i n e of Radiance and B r i g h t n e s s f o r a P a r t l y 1125 L S T A u g u s t 29,1983  (Wm~ sr"') C l o u d y Sky 2  2S0  145  Figure  All.5  Regression L i n e of R a d i a n c e and B r i g h t n e s s for a Partly 1416 L S T A u g u s t 2 7 , 1983  (Wm sr"') C l o u d y Sky 2  146  I 10.0  19  Radiance  Figure  All.6  (Wm~ sr 2  _ 1  )  Regression L i n e of Radiance (Wm sr"') and B r i g h t n e s s f o r an O v e r c a s t Sky 1250 L S T A u g u s t 27,1983 _ 2  1 47  Figure  All.7  Regression L i n e of Radiance (Wm~ sr~') and B r i g h t n e s s f o r an O v e r c a s t Sky 0921 L S T A u g u s t 2 7 , 1 9 8 3 2  

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