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

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S A T E L L I T E BASED E S T I M A T E S OF SOLAR ENERGY A V A I L A B I L I T Y AT T H E E A R T H ' S S U R F A C E : IMPACT OF CHANGES IN T H E C O N F I G U R A T I O N OF T H E S A T E L L I T E DATA By NEIL B.Sc,  A THESIS  WANLESS  University  SUBMITTED  of  IN  PARTIAL  THE REQUIREMENTS MASTER  Liverpool,  FULFILLMENT  FOR THE D E G R E E  OF  1980  OF  SCIENCE  in THE F A C U L T Y  OF GRADUATE  (Department  We a c c e p t to  this the  of  thesis  OF  December ©  Geography)  required  THE UNIVERSITY  Neil  STUDIES  as  conforming  standard  BRITISH  COLUMBIA  1983  Wanless,  1983  OF  In  presenting  requirements of  British  it  freely  agree for  this for  an  available  that  I  by  understood  that  his  that  or  be  her or  shall  Date  E-6  (2/79)  Z3>rcV  December  the  be  shall  and  study.  I  copying by  allowed  Columbia  1^23.  the  Library  publication  not  of  University  the  of  of  this  It  this  without  make  further  head  representatives.  of  The U n i v e r s i t y o f B r i t i s h 2075 W e s b r o o k P l a c e Vancouver, Canada V6T 1W5  at  granted  permission.  Department  fulfilment  the  extensive  may  copying  f i n a n c i a l gain  degree  reference  for  purposes  or  partial  agree  for  permission  scholarly  in  advanced  Columbia,  department  for  thesis  thesis  of  my  is  thesis my  written  i i  ABSTRACT  Despite  the  encouraging  estimates  of  questions  concerned  data  used  wide  range  using  a  solar  in  developed anisotropic system.  an  Irrespective  correction  for  unwarranted. satellite  pixel  measurements  the  to  considerable  time  use  resulted  and  at  periods,  characterize variations  the  increased also  in  least  four  T  the  and  images  observed  have  TR. per  data  of  to  using  of  be  of  the  ground  satellite data  sets  at  a  averaging  strength least  of two  two-hourly  satisfactorily  regimes.  characteristics  to  presents  the  to  of  a  negligible  temporal  shown  the  such  deemed  o n e - h o u r l y and  been  were  for  used,  sizes  The use  radiative  climatological  models  voluminous  improvements  of  Earth-Atmosphere  be  the  a  measured  configuration  array  Increasing  respectively, the  in  between  (BDR)  was  to  involve pixel  estimates  concentration  found  of  assessed  satellite  modelling procedures  substantial  were  BDR m o d e l  spatial  satellite  The m e r i t s  the  of  based  numerous  the  satellite  reflectance  small  advantage.  relationship  images  are  type  characteristically  ability  period  of  the  and  reflectance  properties  and  T h e r e f o r e , as  information  the  array  (T)  the  to  of  ground-based  correct  anisotropic Changes  importance.  between  of  surface  configurations  Bidirectional  reflectance  Earth's  satellite  unanswered.  transmission  to  recent  configuration  data  attempt  of  the  remain  relationship  (TR). in  at the  models  radiation  reflectance  based  with  satellite  single  shortwave  energy  the  of  results  for  Finally, the  Lower  Fraser have  Valley  been  eluded  study to.  area,  highlighted  using  such  a  technique,  iv  TABLE  OF CONTENTS Page  ABSTRACT  i i  LIST  OF T A B L E S  LIST  OF F I G U R E S  vii x  ACKNOWLEDGEMENTS  CHAPTER  CHAPTER  CHAPTER  xv  1  INTRODUCTION  1  1 .1  Background  1  1.2  Specific  6  2  RADIATION  2.1  Study  2.2  Measured  2.3  Clear  2.4  Parameterization R a d i a t i o n Model  Objectives  DATA S E T AND MODEL  7  Area  7  Shortwave  Sky  Radiation  Radiation  2.4.1  Ozone  2.4.2  Rayleigh  2.4.3  Water  2.4.4  Albedo  2.4.5  Calculation Parameters  2.4.6  Precipitable  9  Model  used  in  9 the  Clear  Sky  Absorption  13  Absorption  13  Terms  2.5  Derivation  3  SATELLITE  3.1  Introduction  3.2  Earth-Location  3.3  Pixel  Size  12  Scattering  Vapour  of  12  15 of  Position  Water the  and  Time  Determination  Shortwave  Transmission  DATA S E T  15 18 26  29 29  of  Satellite  Determination  Imagery  32 35  V  CHAPTER  3.4  Validation  3.5  Linearity  3.6  C o n v e r s i o n of P i x e l Surface Reflectance  3.7  M e r g i n g of the S a t e l l i t e R e f l e c t a n c e Shortwave T r a n s m i s s i o n Data  4  BIDIRECTIONAL  4.1  Overview  4.2  Definitions  4.3  Modelling Procedure  4.3.1  Data  of  the E a r t h - L o c a t i o n  Values  to  47 and  MODELS  51  56 56  (Geometry  Selection  4.3.1.2  Cloud  of  Reflectance)  63 67  and Q u a l i t y  Control  67  Surface  67  Surface  70  I d e n t i f i c a t i o n of A n i s o t r o p i c Reflectance Characteristics  4.3.2.1  Land  4.3.2.2  Sea  4.3.2.3  Cloud  4.3.2.4  Summary and  4.3.3.1  Count  REFLECTANCE  Land and Sea  4.3.3  38 42  4.3.1.1  4.3.2  Routine  74  Surface  74  Surface  85  Surface  90  and Comparison  Cloud  Development  Surface of  of  Land,  Reflectivity  BDR M o d e l s  99  4.3.3.2  Land and Sea  4.3.3.3  Modelling Cloud Surface  Surface  Reflectance 103  Reflectance  Modelling 4.4  V e r i f i c a t i o n of  4.5  Applying Satellite  96 99  General  the  Sea  11 2 BDR M o d e l s  BDR M o d e l s  Data  to  115 the 124  vi  CHAPTER  5  RESULTS : SATELLITE  IMPACT OF A D J U S T M E N T S DATA  5.1  Introduction  5.2  Development of the R e l a t i o n s h i p T r a n s m i s s i o n and R e f l e c t a n c e  5.3  Impact  of  TO T H E 133 133  Applying  5.3.1  Initial  Study  5.3.2  Further  Testing  the  Between  BDR M o d e l s  Using  Small  Using  a  Data  Larger  140 Set  CHAPTER  Impact  140  Data  Set 5.4  134  147 of  Spatial  5.4.1  Introduction  5.4.2  Implication  5.5  Impact  5.6  I n f l u e n c e of Availability  of  5.7  Valley  6  CONCLUSIONS  Averaging  and of  Analysis  155 of  Results  Results  170  Time A v e r a g i n g  and  Satellite  Coastal  170  Image  Site  155  174  Comparison  182  189  REFERENCES  193  APPENDICES  2 00  APPENDIX  1  Symbols  APPENDIX  2  Landmarks  i  used  in  the  Earth-Location  Routine APPENDIX  3  Equations used Corrections  200  204 to  Determine  the  BDR 207  v i i  LIST  OF T A B L E S Page  TABLE  2.1  Transmissivity  TABLE  2.2  Comparison of P r e c i p i t a b l e Water V a l u e s D e r i v e d From Radiosonde Data and the S m i t h (1966) F o r m u l a t i o n .  23  Variation in Transmission Values C a l c u l a t e d from P r e c i p i t a b l e Water Data as D e t e r m i n e d from e i t h e r Radiosonde Data or the S m i t h (1966) F o r m u l a t i o n .  24  V e r i f i c a t i o n S t a t i s t i c s for the Cubic I n t e r p o l a t i o n Routine Used i n the E a r t h - L o c a t i o n of the S a t e l l i t e Imagery.  40  R e s u l t s from the Assessments of L i n e a r i t y A c r o s s t h e S a t e l l i t e Image B a s e d on D a t a From T h r e e C l e a r D a y s .  44  TABLE  TABLE  TABLE  TABLE  TABLE  2.3  3.1  3.2  4.1  4.2  After  Rayleigh  T r i g o n o m e t r i c F u n c t i o n s Used Diurnal Reflectance Patterns Under C l e a r S k i e s . Performance Replicating  Scattering.  to Model for Surfaces  o f t h e C l e a r S k y BDR M o d e l s the Target Reflectance.  TABLE  5.1  S t a t i s t i c s Showing the Impact of A p p l y i n g a BDR C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and TR. S a t e l l i t e Data are for a 7 x 7 P i x e l A r r a y C e n t r e d on U B C .  137  S t a t i s t i c s Showing the Impact of A p p l y i n g a BDR M o d e l A ( T R ) C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and T R . Satellite Data are for a 7 x 7 Pixel Array Centred on U B C .  142  S t a t i s t i c s Showing the Impact of A p p l y i n g a BDR M o d e l B C o r r e c t i o n to t h e R e l a t i o n s h i p Between T and TR. Satellite Data are for a 7 x 7 P i x e l Array C e n t r e d on U B C .  144  5.3  Clear  Sky  108  Verification BDR M o d e l s .  TABLE  the  in  4.3  5.2  for  104  TABLE  TABLE  Statistics  14  120  viii  TABLE  5.4  S t a t i s t i c s Showing the Impact of A p p l y i n g a BDR M o d e l C C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and TR. Satellite Data are for a 7 x 7 P i x e l Array Centred on U B C .  TABLE  5.5  S t a t i s t i c s Showing the Impact of A p p l y i n g a BDR M o d e l C C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and TR. Satellite Data are for D i f f e r e n t P i x e l Array S i z e s C e n t r e d on UBC a n d BDR C o r r e c t i o n s are A p p l i e d to A l l P i x e l s .  TABLE  5.6  S t a t i s t i c s Showing the Impact of A p p l y i n g a BDR M o d e l C C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and T R . Satellite Data are for D i f f e r e n t P i x e l Array S i z e s C e n t r e d o n UBC a n d BDR C o r r e c t i o n s are A p p l i e d to C l e a r and O v e r c a s t P i x e l s O n l y .  TABLE  5.7  S t a t i s t i c s Showing the Impact of A p p l y i n g a BDR M o d e l L a n d ( N ) C C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and TR. Satellite Data are for a 7 x 7 P i x e l 'Array Centred on A B A I R .  TABLE  5.8  S t a t i s t i c s Showing the Impact of A p p l y i n g a BDR M o d e l L a n d ( S ) C C o r r e c t i o n t o t h e R e l a t i o n s h i p Between T and TR. Satellite Data are for a 7 x 7 Pixel Array Centred on A B A I R .  TABLE  5.9  S t a t i s t i c s Showing the Impact of U s i n g D i f f e r e n t A r r a y S i z e s on t h e R e l a t i o n s h i p Between T and TR. The P i x e l A r r a y s a r e C e n t r e d on U B C .  TABLE  5.10  S t a t i s t i c s Showing the Impact of U s i n g D i f f e r e n t A r r a y S i z e s on t h e R e l a t i o n s h i p Between T and TR. The P i x e l A r r a y s a r e C e n t r e d on A B A I R .  TABLE  5.11  S t a t i s t i c s Showing the Impact of U s i n g D i f f e r e n t A r r a y S i z e s on t h e Relationship Between T and T R . The P i x e l A r r a y s a r e C e n t r e d on M A A .  ix  Page TABLE  TABLE  TABLE  TABLE  TABLE  TABLE  TABLE  TABLE  5.12  5.13  5.14  5.15  5.16  5.17  5.18  5.19  S t a t i s t i c s Showing the Impact of U s i n g D i f f e r e n t R e c t a n g u l a r C o n f i g u r a t i o n s on the R e l a t i o n s h i p Between T and TR. The P i x e l A r r a y s a r e C e n t r e d o n UBC a n d A B A I R .  163  Comparative S t a t i s t i c s for the Hourly Shortwave R a d i a t i o n Measurements at the Three V a l l e y Sites.  168  T h e Mean a n d S t a n d a r d D e v i a t i o n f o r Shortwave R a d i a t i o n Measurements at Three V a l l e y Sites.  169  Hourly the  S t a t i s t i c s Showing the Impact of I n c r e a s i n g t h e Time A v e r a g i n g P e r i o d on t h e R e l a t i o n s h i p B e t w e e n T a n d TR a t the U B C , A B A I R a n d MAA S i t e s .  172  S t a t i s t i c s Showing the Impact of Changes t o t h e Image R e q u i r e m e n t s P e r O n e - H o u r l y T i m e P e r i o d on t h e R e l a t i o n s h i p B e t w e e n T a n d TR a t t h e UBC S i t e .  176  S t a t i s t i c s Showing the Impact of Changes t o t h e Image R e q u i r e m e n t s P e r T w o - H o u r l y T i m e P e r i o d on t h e R e l a t i o n s h i p B e t w e e n T a n d TR a t t h e UBC S i t e .  177  S t a t i s t i c s Showing the Impact of Changes t o t h e Image R e q u i r e m e n t s P e r T w o - H o u r l y T i m e P e r i o d on t h e R e l a t i o n s h i p B e t w e e n T a n d TR a t t h e A B A I R S i t e .  178  S t a t i s t i c s Showing the Impact of Changes • t o t h e Image R e q u i r e m e n t s P e r T w o - H o u r l y T i m e P e r i o d on t h e R e l a t i o n s h i p B e t w e e n T a n d TR a t t h e MAA S i t e .  179  X  LIST  OF F I G U R E S  FIGURE  1.1  Flow Diagram O u t l i n i n g the Steps Taken to D e v e l o p a R e l a t i o n s h i p Between Shortwave T r a n s m i s s i o n and T a r g e t Reflectivity.  FIGURE  2.1  L o c a t i o n of the Shortwave Monitoring S i t e s for Part Fraser V a l l e y .  FIGURE  2.2  Variation  FIGURE  2.3  Seasonal Area.  FIGURE  3.1  FIGURE  3.2  FIGURE  3.3  C a l i b r a t i o n C u r v e s f o r t h e SMS-1 GOES-1 S a t e l l i t e Radiometers.  FIGURE  3.4  A N i g h t - t i m e Subarray C e n t r e d Over the P a c i f i c Ocean D e m o n s t r a t i n g a Background B r i g h t n e s s a n d S t r i p i n g Due t o t h e L a c k of I n t e r s e c t i o n Calibration.  FIGURE  3.5  E x a m p l e o f S a t e l l i t e Image W e i g h t i n g Scheme f o r M e r g i n g S a t e l l i t e D a t a t o Hourly Integrated Radiation Data.  FIGURE  4.1  D i u r n a l P a t t e r n of T a r g e t Reflectance O v e r a L a n d S u r f a c e F o r J u l i a n Day 256/79.  FIGURE  4.2  Diagram of Geometric R e l a t i o n s Between Z e n i t h A n g l e of the Sun, Z e n i t h A n g l e of t h e R e f l e c t e d Ray a n d t h e Sun-Satellite Azimuth A n g l e .  FIGURE  4.3  D i u r n a l P a t t e r n of Over a Sea S u r f a c e  FIGURE  4.4  H i s t o g r a m of Count V a l u e s Showing S p r e a d i n t h e D a t a as a R e s u l t of Partly Cloudy Conditions.  of  \  With  Variation  Radiation of the Lower  Latitude of  A For  and the  Season. Study  25 x 25 P i x e l A r r a y C e n t r e d on t h e UBC S i t e D e p i c t i n g Mean B r i g h t n e s s C o u n t V a l u e s B a s e d on F o r t y - N i n e I m a g e s . Map o f t h e A r e a C o v e r e d b y t h e L a r g e s t S a t e l l i t e Images Showing Landmarks T y p i c a l l y Used i n the Assessment of Linearity. and  Target Reflectance f o r J u l i a n Day 2 5 6 / 7 9 . a Large the  xi  Page FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  4.5  4.6  4.7  4.8  4.9  4.10  4.11  4.12  4.13  4.14  4.15  4.16  H i s t o g r a m of Count V a l u e s Showing a B i m o d a l D i s t r i b u t i o n Due t o a P r e d o m i n a n c e of C o m p l e t e l y C l e a r and Cloudy P i x e l s .  72  H i s t o g r a m Showing a Small Spread of Count V a l u e s S u g g e s t i n g R e l a t i v e l y Homogeneous Cloud Cover C o n d i t i o n s .  73  D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e Over t h e L a n d ( N ) S u r f a c e f o r J u l i a n Day 256/79.  75  D i u r n a l P a t t e r n of Target R e f l e c t a n c e Over t h e L a n d ( S ) S u r f a c e f o r J u l i a n Day 304/79.  76  D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e Over t h e L a n d ( N ) S u r f a c e f o r J u l i a n Day 304/79.  77  D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e Over t h e L a n d ( S ) S u r f a c e f o r J u l i a n Day 200/79.  78  D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e Over t h e L a n d ( N ) S u r f a c e f o r J u l i a n Day 200/79.  79  P o l a r P l o t of T a r g e t Land(N) Surface.  Reflectance  81  P o l a r P l o t of T a r g e t Land(S) Surface.  Reflectance  For  For  the  the 82  D i u r n a l P a t t e r n of Target R e f l e c t a n c e Over t h e Sea S u r f a c e f o r J u l i a n Day 200/79.  86  D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e Over t h e Sea S u r f a c e f o r J u l i a n Day 304/79.  87  D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e Over t h e Sea S u r f a c e f o r J u l i a n Day 025/80.  88  xi i  Page FIGURE  FIGURE  FIGURE  FIGURE  4.17  4.18  4.19  4.20  P o l a r P l o t of Sea Surface.  Target  Reflectance  For  the  89  D i u r n a l P a t t e r n of T a r g e t Over an Ocean S u r f a c e f o r 200/79.  Reflectance J u l i a n Day  91  D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e O v e r a C l o u d T o p S u r f a c e f o r J u l i a n Day 197/80.  92  D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e O v e r a C l o u d T o p S u r f a c e f o r J u l i a n Day 245/80.  93 94  FIGURE  4.21  Polar Cloud  FIGURE  4.22  Form of the Four T r i g o n o m e t r i c F u n c t i o n s U s e d t o Model t h e Sea and Land D i u r n a l Reflectance Patterns.  105  BDR M o d e l F o r p Values.  the  109  FIGURE  4.23  P l o t of T a r g e t Top S u r f a c e .  Reflectance  Land(N)  Surface  Over  a  Using  FIGURE  4.24  BDR M o d e l F o r c Values.  the  Land(S)  FIGURE  4.25  BDR M o d e l Values.  the  Sea  FIGURE  4.26  D i u r n a l P a t t e r n of T a r g e t R e f l e c t a n c e O v e r a C l o u d T o p S u r f a c e f o r J u l i a n Day 363/79 and a Second Order P o l y n o m i a l F i t to the D a t a .  113 114  For  4.27  BDR M o d e l p Values.  FIGURE  4.28  V e r i f i c a t i o n of the J u l i a n Day 1 9 6 / 7 9 .  Sea  FIGURE  4.29  V e r i f i c a t i o n of the J u l i a n Day 1 2 1 / 8 0 .  Land(N)  V e r i f i c a t i o n of the J u l i a n Day 1 9 6 / 7 9 .  Land(S)  FIGURE  4.30  4.31  a  Cloud  Surface  FIGURE  FIGURE  For  Surface  Using  Using c  Top Surface  BDR M o d e l  111  Using  For  BDR M o d e l  110  116 For  117  Verification Polar Plot S u r f a c e BDR M o d e l U s i n g  BDR M o d e l  For  118 F o r t h e Sea P Values.  121  xi i i  Page FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  FIGURE  4.32  4.33  4.34  4.35  4.36  4.37  5.1  5.2  5.3  5.4  5.5  5.6  5.7  V e r i f i c a t i o n of Land(N) Surface  the P o l a r BDR M o d e l  P l o t For the Using p Values.  122  V e r i f i c a t i o n of Land(S) Surface  the P o l a r BDR M o d e l  P l o t For the Using P Values.  123  The R e l a t i o n s h i p Between t h e Scene B r i g h t n e s s and the C l o u d i n e s s Index.  126  D e r i v a t i o n of a C o r r e c t e d T a r g e t R e f l e c t a n c e From the C l o u d i n e s s Index U s i n g Model A .  128  D e r i v a t i o n of a C o r r e c t e d T a r g e t R e f l e c t a n c e From the C l o u d i n e s s Index U s i n g Model B.  129  D e r i v a t i o n of a C o r r e c t e d T a r g e t R e f l e c t a n c e From the C l o u d i n e s s Index U s i n g Model C.  130  S c a t t e r P l o t of Shortwave Transmission Against Uncorrected S a t e l l i t e Target Reflectance f o r t h e UBC S i t e U s i n g a 7 x 7 Pixel Array.  136  S c a t t e r P l o t of Shortwave Transmission Against Uncorrected S a t e l l i t e Target Reflectance f o r t h e UBC S i t e U s i n g a 7 x 7 P i x e l A r r a y and the L a r g e r Data Set.  148  S c a t t e r P l o t of Shortwave Transmission Against Uncorrected S a t e l l i t e Target Reflectance f o r t h e ABAIR S i t e U s i n g a 7 x 7 P i x e l A r r a y and the L a r g e r D a t a Set.  150  Rectangular S a t e l l i t e Synoptic Influences.  162  Arrays  Used  to  Test  S c a t t e r P l o t Comparing Hourly Shortwave R a d i a t i o n T o t a l s Between ABLIB and MISS.  165  S c a t t e r P l o t Comparing Hourly Shortwave R a d i a t i o n T o t a l s Between ABAIR and M I S S .  166  S c a t t e r P l o t Comparing Hourly Shortwave R a d i a t i o n T o t a l s Between ABAIR and A B L I B .  167  xiv  Page FIGURE  5.8  S c a t t e r P l o t of T w o - H o u r l y A v e r a g e d Shortwave T r a n s m i s s i o n Against Uncorrected S a t e l l i t e Target Reflectance f o r t h e UBC S i t e U s i n g a 7 x 7 P i x e l A r r a y and the L a r g e r Data Set.  173 184  FIGURE  5.9  Comparison of the R e g r e s s i o n F o r UBC a n d A B A I R .  FIGURE  5.10  S c a t t e r P l o t of Shortwave Transmission Against Uncorrected S a t e l l i t e Target Reflectance f o r t h e MAA S i t e U s i n g a 7 x 7 P i x e l A r r a y and the L a r g e r Data Set.  185  Frequency of O c c u r r e n c e o f C l e a r , Cloudy and O v e r c a s t C o n d i t i o n s at ABAIR and MAA.  186  FIGURE  5.11  Equations  Partly UBC,  XV  ACKNOWLEDGEMENTS I  wish  Dr.J.E. this  to  Hay  for  study.  Dr.R.J.  his  The  manuscript  by  M.  in  respect  Chapter  the  the  Cleugh,  final  The  UBC  satellite  image  provided  friends the  satellite  C.S.B.  I  to  this  the  and  the  OSE 8 3 - 0 0 0 2 2  to  will  indebted  me t h r o u g h period never  the  Geography  his  salutary  especially I  am  for  to  with  indebted  their  an  in  Dr.J.E. to  support  help  have  Sensing  during  for  this  Environment  the  study  Service,  Hay. my f a m i l y  unexpected and  Remote  processor  Atmospheric  Canadian  may  with  to  Souch  image  the  project  technical  thanks  for  Program  Financial  research  Dr.J.A.  thesis.  Comtal  remain  and  extend  jointly.  C.J.  final  assistance  research,  written  Grimmond of  Raphael  data  was  to  external  analysis.  who h e l p e d  initial  support  by  DSS N o .  Finally,  C.  the  helpful  would l i k e and  throughout  acknowledged.  my c o m m i t t e e ,  considerable  Interdisciplinary  access  contract  I  supervisor  on  gratefully  of  my  support  contributed  internal  production  permitted  was  member  provided  3 which  and  to  suggestions  are  particular  in  in  Oke  third  both  assistance  H.A.  and  programming.  Department;  to  advice  University)  people,  to  invaluable  Roseberry  computer  numerous  appreciation  Dr.T.R.  (McMaster  advice.  my s i n c e r e  comments  Woodham, t h e  Davies  the  express  distraction  without reached  and  whose  fruition.  devoted during  continued  1  CHAPTER 1  INTRODUCTION  1.1  Background  The has  interest  increased  in  solar  substantially  climatology  of  efficiently  utilize  understanding  and  environmental  systems  atmospheric  The  for  the  such  is  is  the  and  the  surface  A detailed  required  capabilities as  Earth's  years.  resource  in  to  with  order  to  improve regard  hydrologic  result  of  the  radiative  spatial  and data many  information.  more  (e.g.  cycle  to  our many  and  the  properties  can  of  the  clear  for  models  clouds  variability  supplement  areas  for  the  of  to and  world  sky  devoid  data  Attempts  to  conditions, cloudy  and  1983).  This  account  for  the  capture  the  Although  the  to  clouds.  measured  the  climatological  partly  and MacKay,  the  of  pyranometric  supplying  available  errors Davies  of  applications.  readily  i n a b i l i t y of  temporal  for  successful  substantial  situations  network  different  proved  in  based  inadequate  using  complex  still  this  many  have  result  modelled  recent  irradiance  ground  the  irradiance  overcast  in  predictive  stations  information but  reaching  circulation.  measuring  model  the  existing  required  energy  data, of  there  is  are  irradiance  2  It  appears  practical  source  Geostationary high  at  present  available  satellites  resolution  satellites  estimates  radiation  Hanson,  1978;  Senn, The  1980;  (1983)  have  has  models  to  mesoscale  regarding these  the the  determine used  in  encouraging  and  assessments  of  of  various the  surface.  This  a  simple  and  satellite  reflectance,  TR)  to  transmission  variable  The  KJm"2hr_1)  shortwave  necessary  recent of  The  to  provide  (e.g.  Hay  and  Hiser  and  et  al.,  work  by  three  1983). Raphael  of  as  was it  This  these  achieved  the  transmission  more  was  attempt  to  fundamental  calculated  the the  measurements  of  a  (expressed  than  at  analysing  as  satellite  rather  of  regime  between  brightness  input  configurations  by  (expressed  in  a  data  questions  data  will  radiation  selected is  thesis  satellite  ground  changes  important  satellite  relationship  T)  (e.g.  the  is  the  units  the  1980;  Dedieu  some  solar  at  transmission,  al.,  applicability  variability.  used  surface  et  1981;  unanswered.  merits  radiation  Gautier  only  coverage.  been  Earth's  the  investigations.  above  of  cloud  spatial  Kanemasu,  characterizing  sensitivity solar  1979;  are  provide  recently  the  the  remain  the  Earth's  and  configuration  models  the  particular  at  been  satellites  monitor  have  and  confirmed  Despite  in  Tarpley, Brakke  results  to  temporal  geostationary of  that  input  shortwave as  target  data.  absolute  A  energy  parameter.  using  measured  3  pyranometric  data  al.,  The  1975).  the an  satellite inverse  the  of  this  result  in from  steps  taken  developing  use  of  an  the  to  the  emerging  radiation  reflectance  system  may  require  need  for  such  for  problem  the  homogeneous image  reflectance  second  conditions  to a  solar  be given  the  require  greater  properties satellite correction (BDR)  is  shows  to  The  surfaces  conditions the  general  associated to  with  be  typically  studied. used  simultaneously  of  angles.  the  data will  to  the  in  measure Thus  the  Earth-Atmosphere be  be  corrected. assessed  The using  models.  that  under regime  clear may  characterized  interval,  changing  number  due  versa).  ground  irradiance,  cannot  adequately  rapidly  1.1  via  shortwave  Such  f r o m many d i f f e r e n t  hourly  to  satellite)  visa  covered  sensor  radiation  conditions a  a  related  lower  and  problems  angle  the  et  brightness  to  Figure  two  sensing  anisotropic  SMS-2  be  (Davies  relationship.  estimate  remote  The  the  narrow  then  target  snow  model  reflectivities.  allows  meteorological  bidirectional  with  analyses.  approach  satellites  Firstly  our  the  surface,  high  excluded  (from  can  corresponds  occurs very  radiation  greater  the  were  in  data (i.e.  at  sky  transmission  clouds  values  to  Such  clear  brightness  relationship  transmission  which  a  shortwave  presence  exception  and  of  while  radiation  satellite J  sky be by  for  or  overcast  sufficiently one  satellite  partly  regime  images.  cloudy  may Thus  well it  is  4  Extraterrestrial Radiation  Clear  Observed Shortwave Wave R a d i a t i o n  Sky R a d i a t i o n Model  Shortwave "^Transmi ssion Inverse  Satellite Brightness  Target Reflectivity  FIGURE Flow Diagram Relationship Reflectivity.  Relationship  1.1  Outlining the Steps Taken to Between Shortwave Transmission  Develop a and Target  5  important  to  establish  sampling  frequency  and  ability  the  substantial digital number  One  conditions. period  from  of  radiative  may  be  the  solar  the  to  size  for  have  assumed  specific  array  example,  Gautier  et  al.  (1980)  km  x  km s a t e l l i t e  Tarpley  16  (1979)  appropriateness With  a  regard  hypothesised  used of  to  changing  that  significance  energy  which  This  has  such  a  the  cannot  be  led  the  50  km  the  short  captured  temporal the  partly  cloudy  50  be  km  out  their  size,  while The  period,  averaging  objectives.  all  examination.  term v a r i a b i l i t y of  following  the  satellite  array.  requires  by h a l f - h o u r l y  of  appropriate.  array  averaging  time  averaging  inability  to  solar  capture  carried  x  the  to  Previous  sizes  configurations  increasing of  to  conditions.  16  of  temporal  the  those  using  the  optimize  satellite  and  minimize  to  The  with  analyses  found  target  possible  the  hour)  flux.  satellite  regime  per  associated  desirable  of  satellite  images  it  inability  the  irradiance.  capture  analyses  the  the  solar  to  studies For  make  estimate  By v a r y i n g  it  satellite  to  the  three  requirements  weaknesses  complex  two o r  estimate  used  the  arises  the  to  r e l a t i o n s h i p between one,  processing  images  of  energy  (e.g.  computational  image of  the  will the  images.  it  is  reduce radiant  6  1.2 S p e c i f i c  Objectives  1) To a s s e s s t h e on s a t e l l i t e Earth's  i m p a c t of  bidirectional  based e s t i m a t e s o f  solar  reflectance  irradiance  at  (BDR)  the  surface.  2 ) To d e t e r m i n e configuration  for  t h e optimum s p a t i a l  estimating  3) To d e t e r m i n e t h e  target  i m p a c t of  satellite  array  reflectance.  increased  temporal  averaging.  4) To t e s t irradiance satellite time  the s e n s i t i v i t y  using s a t e l l i t e  e s t i m a t e s of  solar  d a t a t o changes i n t h e number  images c o n t r i b u t i n g  interval.  of  to the computation  for  of  a given  7  CHAPTER  R A D I A T I O N DATA  2. 1 Study  The study  have  solar  radiation  at  been  for  (see  site  wave  transmission  Airport  (ABAIR)  location  is  and  site  are  a  somewhat  Abbotsford  City  i rradiances.  selected  using  the  later  the  and M i s s i o n  City,  sites  describe  calculated  to  in  as  and  site  as  the  UBC.  short  Two o t h e r  it  position T h e MAA  represents  Abbotsford  Figure  For  UBC.  therefore  sky  of  initial  between  of  it  the  Airport, is  located  2.1).  how s h o r t w a v e  clear  The  namely A b b o t s f o r d  that  from  (see  2.1.  topographical  coastal  this  reflectance.  stage,  Their  in  University  relationship  referred a  the  target  sets  will  was  used  Figure  1979)  fictitious  three  in  at  MAA. with  data  facility  data  these  Chapter  calculated  at  and  radiation  This  used  radiation  presented  satellite be  comparison  between  Hay,  shall  also  averaged  midway  are  investigating  locations  provides  solar  monitoring  test  this  which  observed  Columbia  brevity  S E T AND MODEL  Area  locations  British  2  and  transmission measured  is  solar  8  FIGURE  2.1  L o c a t i o n o f the shortwave r a d i a t i o n part of  monitoring  t h e Lower F r a s e r V a l l e y . ( The  study are i n d i c a t e d  by * ) .  sites for  s i t e s used i n t h i s  9  2.2  Measured  All  the  mesoscale from  on  stations  these  those  are  sites of  days  in  shown  (Hay,  1983a).  taken  from  Columbia. 1979  each  surface and  (1972) systems  ±5% the  and  1981  site  the  (K4-)  is  is  the  for  are  The  data  The days  measured  archives  recorded  as  an  at  a  a  the  correspond  satellite  using  of  measurements  selected  which  part  incoming shortwave  images  radiation  CM6 K i p p  hourly  and  integrated  Sky  model  originally (1975).  a  to  for  this  in  Canadian  the  recent data  Radiation  the  study used  in  Root  Mean  solar  Square  radiation  by H a y a n d W a r d l e this  study  to  be  Error  for  network (1982) within  is has  this  the  Model  chosen  developed  Subsequent  led  that  range.  Clear  The  and  claims  radiation  acceptable  'exact'  network  2.1  2  monitoring around  Section  KJ nf h r _ 1 .  Latimer  2.3  At  pyranometer  value  in  were  between  horizontal  Zonen  described  British  available. a  Radiation  pyranometric  University to  Shortwave  model study.  radiation  to at  calculate  its  Davies  sky  radiation  M c M a s t e r U n i v e r s i t y by D a v i e s  improvements  in  clear  present and  Hay  computations  in form  the  (1980) of  the  et  parameterizations  (Davies,  1981)  compared  being  this  atmosphere  by  was al. have used  model  to  Braslau  10  and  Dave  (1973)  The  global  clear  skies  and  found  radiation  (K+0)  is  extraterrestrial absorption  and  calculated has  scattering.  the  of  separate  irradiance.  Eart-h's  surface  transmittances )  constant  is  e  based  due  and (I0)  is  the  on  vapour  than  applying  =  recent  Earth's  a  depleted  under  clear  skies  the  direct  (S-l-0)  the  atmospheric energy  (K+0) and  under  after  by  shortwave  1%.  surface  residual  total  =  S+ 0 +  ozone due  cose  is  which  composed  diffuse  (D+0)  (2.1)  D+o  is  calculated  (Tr(O) to  ) and  water  it  sky  (Tr(O)  zenith  by  Rayleigh  vapourfa^),  Tr(R)  angle.  arguments,  absorptance  clear of  I0  solar  at  summation  within  to  applying scattering the  solar  that:  absorbing  The  to  absorption such  water  vapour  been  radiation  S+0  where  as  be  Hence:  direct  (Tr(R)  the  to  The  components,  K+0  The  two m e t h o d s  reaching  flux  reaches two  the  The  which  (Paltridge  multiplicatively. longer  wavelengths  diffuse  components  due  radiation to  -  au )  form  suggest and  (D+Q)  molecular  of  this  equation  subtracting  Piatt,  This than  (2.2)  is  1976) due  the  rather  to  water  ozone.  is  calculated  scattering  (Dr)  as  a  and  multiple  reflection  between  the  D+o  The  molecular  assumptions: only the  1)  half  of  ground,  radiation  scattering that the and  (Paltridge,  Dr  The  multiple  =  reflection  albedo  incident  irradiance  (as),  DS  The  term  with  for  Section  It aerosol  the  is  calculated  based  isotropic;  consequently  scattered  vapour  Tr(0)  term  (1  -  (Ds)  a l b e d o of  (S+0and  only  is  the  absorbs  on  two  reaches  direct  beam  2  (2.4)  determined  using  the  ( a b ) and  the  Thus:  Dr).  term  albedos,  /  atmosphere  - a b a s )  0  study  radiation  Tr(R))  a b a s ( S 4- +Dr)/(1  high  (Ds):  Therefore:  reflection  this  is  but  due  to  here  that  especially  this  the  is  the  (2.5)  important  least  relatively  for  important  low a l b e d o  (see  2.4.4).  should  be  noted  transmittance  exclusion. (1980)  =  multiple  surfaces  water  cose  atmosphere  (2.3)  is  Rayleigh  1973).  I0  surface  (Dr)  scattering  that  and  D r + Ds  term  total  2)  =  ground,  report  Firstly, and  these  formulations  term.  There  the  Atmospheric  Davies  (1981)  show  are  two  exclude  reasons  Environment  that  the  for  an this  Service  McMaster model  12  ignoring and  aerosol  Root  Mean  Vancouver.  and  satisfactory  the  Errors  its  determination  (WMO, 1 9 7 8 ;  Davies  used  in  and  the  smallest  for  incorporation  Parameterizations  2.4.1  yielded  Square  Secondly,  complex  2.4  effects  Mean  daily  of  an  still  Hay,  1980;  Clear  Sky  Errors  irradiances  aerosol  is  Bias  term  not  at  is  very  completely  Davies,  Radiation  1982).  Model  Ozone A b s o r p t i o n  The ozone  transmission (Tr(O)  empirical  )  is  formula  of  solar  calculated  radiation  using  the  after  Lacis  absorption  and  Hansen  by  (1974)  :  Tr(O)  =  1 -  a0  (2.6)  where:  a0  =  0.1082X1/ +  (1  +13.68XT)  0.002118X1  /  (1  +  0.00658X  + 0.042Xt+  /  (1  +  (10.36X1))  0.00000323X1) (2.7)  The  first  two  absorption  at  the  term  final  (between  0.5  terms  ultraviolet  and  for 0.7  the  of  Equation  wavelengths visible  2.7  ( < 0.35  portion  micrometers).  account  X1  for  micrometers) of  is  the the  ozone and  spectrum slant  path  13  through  ozone  through  ozone  based (u^  and  on  the  the  relative  X,  The  vertical  3.5  mm  optical Rogers  2.4.2  from  work  air  mass  (1967),  (m)  the  of  spectrum  of  spectrally  of of  a (X) u  2  al.  ozone  (1971) using  (u0)  and  a  is  the  set  8  at  relative  formula  given  by  scatter using  scattering optical the  Tr(R)  based  depth  )  by  is the  extraterrestrial  a n d Drummond ( 1 9 7 1 ) . of  (Tr(R)  Table  on  this  2.1  lists  method.  Absorption  absorption  Lacis  and  Yamamoto  =  Rayleigh  (1968)  values  vapour  results  <->  through  et  Rayleigh  Thekaekara  Water Vapour  formulation  (m) :  2.17).  after  Elterman  integrated  Water  mass  length  .  0  calculated  Equation  air  path  Scattering  from  procedure  u  optical  optical  length  is  transmissivity  calculated  the  path  -  by M c C l a t c h e y  (see  Rayleigh  The  2.4.3  optical  vertical  0.29X  Hansen  (1962)  /  ((1  is (1974)  to  water  +  14.15X)  calculated  using  who e m p i r i c a l l y path  +  the  related  (X):  0.5925X)  (2.9)  14  TABLE Transmissivity After Rayleigh Values are Dimensionless.  Relative Optical A i r Mass, m 0.5 1 .0 1 .2 1 .4 1 .6 1 .8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 10.0 30.0  2. 1  Scattering  (after  Davies,  Transmissivity After Rayleigh Scattering, Tr(R) 0.9385 0.8973 0.8830 0.8696 0.8572 0.8455 0.8344 0.8094 0.7872 0.7673 0.7493 0.7328 0.7177 0.7037 0.6907 0.6108 0.4364  1981)  15  where:  X  For  this  water (see  study  vapour,  u  Section  calculated  2.4.4  The  and  0.0685  for  free  2.4.5  The  2.17  optical  together  air  with  water  mass  is  a  pressure  the  multiple  2.4.5).  the  of  an  because  of ground  surface  albedo of  The  present  E q u a t i o n 2.5)  ground  components  use  parameters  (see  the  1974).  in  are  (as)  f i x e d at  (following  the atmosphere  latter  is  based  for  Hay,l983a)  (ab)  upon  0.20  (Lacis  the  and  Rayleigh  only.  invariant the  albedo  days  of  f o r the ground  interest  in this  surface study  is  were  snow c o v e r .  Calculation  of P o s i t i o n  and  extraterrestrial radiation  atmosphere  through  amounts of p r e c i p i t a b l e  relative  Equation  equation of  acceptable  The  albedo  albedo  The  on  length  Terms  the  scattering  (2.10)  m  w  v e r t i c a l o p t i c a l path  2.4.6).  two  reflection  u  i s based  (see S e c t i o n  Albedo  Hansen,  ,  u  using  correction  the  =  (I(o))  normal  Time  Parameters  reaching  to the s o l a r  the t o p of beam, p e r  the Earth's unit  surface  16 area,  is  determined  by:  I(o)  where to  I0 i s  mean  based  on  work  by  in  the  I0 /  R2  constant  and R i s  distance.  A solar  Thekaekara  accepted  constant  and  was  and  of  the  ratio  constant  Drummond  used  development  (2.11)  as  the  the  of of  actual  1353  Wnf2  is  It  is  (1971) .  value  McMaster  the  for  model  the  solar  (Davies  et  Sun-Earth distance  is  1975).  The  ratio  expressed (dn), day  solar  Sun-Earth  generally  al.,  the  =  of  after  ranging  the  actual  Spencer  from  number d e f i n e s  to  (1972)  0 on J a n u a r y the  mean as  1,  a  to  function  364  of  day  on D e c e m b e r  number  31.  The  angle:  9  0  =  2  IT  dn /  365  (2.12)  Then:  1 /  R  =  1.00011  + 0.034221  -0.000719  To the  calculate  atmosphere  multiplied  by  the  the for  cos80+  cos260 + 0.000077  extraterrestrial a  cosine  horizontal of  0.00128  the  zenith  surface  angle  o  sin2e0  radiation  unit  sine  (a),  at  (2.13)  the  area, which  top I(o) is  of is  17  calculated  using:  cose  where the  <j>  is  solar  latitude  the  =  sin<j> s i n 6  the l a t i t u d e ,  hour  used  angle  i s that  The  solar  hour  using:  hour  LAT  The work  =  i s the l o c a l  solar  =  site,  112.5  apparent  0.006918  at  zenith  large  The  f o r the mid-point  - LAT  of  (2.15)  time.  parameterization  - 0.399912  c o s 2 9 + 0.000907 0  relative by  interest.  49°16'N.  i s also  c o s 6 + 0 .070257 0  sin26 0  + 0.001 480  formula  of  and H i s  based  on  (1972):  -0.006759  The  (2.14)  declination  and s i t e  i s calculated  15  declination  by S p e n c e r  6  f o r the time  angle  cos 5 cosH  6 i s the solar  o f t h e UBC  H  where  + cos*  optical  Rogers  (1967)  air which  mass  (m)  allows  0.002697 sin3 6  sin6  0  cos3e  0  i s determined for refraction  0  ( 2.16)  using  a  effects  angles:  m  =  35 /  (1224 c o s  2  6 +  1 )°'  5  (2.17)  18  The  optical  pressure  by  pressure  and  kPa.  air  is  multiplying  The  p0  is  also  by  the  atmospheric  Atmospheric  p  to-the  Precipitable  Precipitable calculating  (see  Section  precipitable  /  pressure  the  amounts  water  2.4.3). water  vapour  The  data  (360  km f r o m  State  (171  temperatures surface  calculation technique an  of  error  transmission  To daily  were  obtained  from  to  the  101.3 the  station  in  site.  the  300  in  atmosphere the  tephigrams at  Port and  levels level)  the  errors  to  have  little  precipitable  water  of  for  the  Hardy  on  Quillayute  were  Possible  use  Dew-point  in  four  shown  the  involved  up t o  be  McMaster model  UBC s i t e ) .  mb  water. be  the  UBC s i t e )  fourteen  to  work  located  at the  in  from  from  determined  will  in and  atmosphere used  in  using  this  millimeters. effect  the  Such  on  the  calculation.  calculate  a  measurements  temporally  station of  absorption  km  precipitable  were  the  is  pressure  used  obtained  Island  the  p  climate  initial  Vancouver  (from  atmospheric  level  monitoring  are  stations,  bulb  sea  where  for  Water D e t e r m i n a t i o n  radiosonde  dry  ,  Service  nearest  Washington  p  values  UBC r a d i a t i o n  water  when  corrected  standard  Environment  juxtaposition  2.4.6  mass  and  at  both  spatially  value  radiosonde  (i.e.  with  for  stations  respect  to  UBC, the were solar  twice  weighted noon  for  19  the  former  resulted 04:00  and  in  Quillayute  were to  weighting  the  change  water  2%.  This  transmission  on  both  Port  distance  from  stations  represent  Hardy  Vancouver,  (1966)  Smith  strong  water  and  the  empirical  latitude  total  precipitable  In U  used  to  =  water  2.5)  was l i m i t e d  t h e model f o r  Quillayute  large  water c o n d i t i o n s  and B a l l  (1963),  (1976),  relationship  i n the study  Bolsenga  show t h a t  between t o t a l  temperature.  Smith's  radiosonde  (1965),  there  is a  precipitable  Smith's  (1966)  work  an a d j u s t m e n t  formulation  for  for  calculating  (U):  0 . 1 3 3 - I n ( X + 1) + 0 . 0 3 9 3 Td  test  to  are a s u b s t a n t i a l  the degree t o which these  and s e a s o n .  Even  doubled, the  insensitive  c o m p r e h e n s i v e and i n c o r p o r a t e s  both  changes  totals.  and  surface dew-point  most  was a l m o s t  suggests t h a t  Work by R e i t a n  and A t w a t e r  o f t h e above  f o r t h e UBC s i t e .  (see S e c t i o n  for  Various  in s i g n i f i c a n t  relatively  precipitable  is questionable.  water  This  f o r P o r t Hardy a t  permutations  amount  water  latter).  hours r e s p e c t i v e l y .  result  is  in the p r e c i p i t a b l e  Since  was  based  in the transmission value  changes  is  16:00  and  the  and 0 . 2 5 3 and 0 . 3 3 6  these d i d not r e s u l t  approximately  very  respectively,  precipitable  calculating  for  0 . 1 6 4 and 0 . 2 4 7  of  schemes  but  UBC  estimate of p r e c i p i t a b l e  the  area  from  hours  04:00  at  tested,  when  to  weightings 16:00  and  other  distance  the  appropriateness  of  (2.18)  the  measured  20  radiosonde station  data.  and  X  the  is a  time  of  temperature  (in  degrees  3.00,  and  2.76 w e r e  and  2.71 autumn  days  the  Figure for  2.3)  Td  climate  were  Smith's  results values of  In  suggest  that  the  five  of the e i g h t e e n  than  the measured  five  a l l occur  the t o t a l  amounts  this  found  difference  to  all  days  100%.  water  for  with  an the  amounts.  be a  a r e shown cases the The  and  early  water can the degree  transmissivity  indication  o f how  two  methods  of  The days  selected  are  i s an  t o 100%) u s i n g  precipitable  on  consequence  winter  i s expected  there  Service  the measured  two m e t h o d s ,  2.3 g i v e s  of cases  determining  when  the calculated  Values  totals.  of p r e c i p i t a b l e  the transmission  ( i . e .closer  may  in late  these  varied  In t h e m a j o r i t y  transmission  formulation  when  using  Table  values  precipitable  calculated  affects  be s m a l l .  transmission  clear  those  instances  as they  estimating  the  larger  (see  based  by t h e r a d i o s o n d e  factors  which  to  water  seasonal  to  abstracted.  precipitable  measured  different  were  summer  on a g r a p h  Columbia.  than  substantially  plotted  o f 2.62,  for selected  of B r i t i s h  greater  be  the  of  of the  spring,  the values  were  are  Although  2.2 v a l u e s  f o r winter,  values  a l l but  are  Figure  the Atmospheric;Environment  totals  totals  spring.  was  from  and those  2.2.  calculated  above  on t h e l a t i t u d e  and Td i s the dew-point  To d e t e r m i n e  at the U n i v e r s i t y  formula  Table  year,  Using  interpolated  calculated  based  obtained  values  obtained  station  The  in  and  the  F).  respectively. seasonal  factor  water  t o be  close  improvement i n Smith's amounts.  (1966) Only  21  FIGURE Variation From Data  2.2  of X With L a t i t u d e and P r e s e n t e d by S m i t h ( 1 9 6 6 ) .  Season.  Graph  Construe  22  2-  X  1-  J  F  M  A  M  J  J TIME  of  x  S  O  N  D  J  (Months)  FIGURE Seasonal Variation F i g u r e 2.2.  A  For  2.3 the Study  Area.  Derived  From  23  TABLE Comparison of Radiosonde Data  2.2  Precipitable Water Values and the F o r m u l a t i o n of Smith  Julian Day  Measured (Radiosonde)  Calculated (Smith Formulat ion)  196/79 200/79 255/79 256/79 257/79 276/79 293/79 304/79 361/79 012/80 025/80 030/80 105/80 121/80 171/80 183/80 185/80 261/80  18.8 21.1 19.9 21.4 23. 1 16.9 11.0 10.8 13.1 13.2 5. 1 6.2 18.1 16.9 15.3 17.6 21.7 16.3  27 .3 32.3 21.8 22.5 25.6 18.6 16.6 14.8 13.6 12.9 3.7 5.0 17.2 16.2 24.4 26.2 24. 1 25.4  (mm) D e r i v e d (1966).  %Di f ference Between Measured and Calculated 45.2 53. 1 9.5 5.1 10.8 10.1 50.9 37.0 3.8 -2.3 -27.5 -19.4 -5.0 -4. 1 59.5 48.9 11.1 55.8  24  TABLE  2.3  Variation Precipitable Data ( T ' ) or Calculations  in Transmission Values (%) Calculated from Water Data as D e t e r m i n e d from e i t h e r Radiosonde the S m i t h (1966) F o r m u l a t i o n (T''). b a s e d on F o u r C l e a r D a y s a t t h e UBC S i t e .  Hour Ending  200/79  5 6 7 8 9 10 1 1 1 2 1 3 1 4 1 5 16 1 7 18 1 9 20  Day T' 52 75 90 94 97 97 98 98 98 97 97 96 95 93 92 11 0  55 77 93 97 99 99 100 99 99 99 99 98 97 96 95 11 6  Day T'  82 93 97 98 98 98 96 94 90 84  304/79 rji l l  85 95 98 99 100 99 98 96 92 86  Day T'  92 1 32 93 89 92 75 80 70  361/79 rji I ?  92 1 32 94 89 92 75 80 70  Day T' 40 77 88 90 93 95 97 98 99 99 94 96 95 91 85 76  183/80  41 79 90 92 95 97 99 100 1 00 101 96 98 96 93 88 79  25  one an  case  out  hour  amounts  at  values  estimates  use  of  of  in  a  calculated  Smith  at  term  and  this  absolute  was  for  radiation  on e l e v e n from in  Smith  using  a  this  of  the  in  around  from  they  formulation  this  suggest  rather  total  same  from  that  study  than  of  the  the  for  radiosonde  that  than  with  dew-point study  set  the  to two  daily  of  Their  States  the  a  the  difference  by one  approaches total  solar  favoured  rather  the  than  those  earlier  work  area.  corroborate  reasons  to  rather  results  study  most  A recent  the  values the  at  showed  as  by  the McMaster  United  data  Raphael's  water  two  the  site  found  radiosonde  radiation.  formulation.  5%.  in  daily  solar  The  explained  amounts  in  estimates  remote  for  average  similar  study,  the  fully  (1976)  water an  on  be  water  appropriate.  transmission  Ball  stations  the  locations  together  and  in  based  cannot  the  precipitable  more  accounted  reduce  precipitable  results  not  calculating  difference values  appear  precipitable  (1983),  radiation  the  water  by A t w a t e r  in  used  incorporated  measured  (a  data  temperature  produced  from  transmissivities  resulted  based  Raphael  when  formula  may  Work  2.5%  radiosonde  and  they  values,  was  The  the  calculated  than  study  200/79  calculated  aerosols  95%.  measured  a deterioration  day  precipitable  since  of  less  of  on S m i t h ' s for  atmospheric model)  shows  small.  based  value  end  transmission  totals low  fifty  the  are  The  of  this  choosing method:  to  use  the  26  1)  the  version readily  2) data  of  dew-point precipitable  available;  the  radiosonde  water  is  used  more  in  easily  the  calculated  obtained  and  more  and  although from  temperature  both  same  techniques  site  are  observations  removed  from  the  study  results  than  the  use  data  in  used  for  similar  (Atwater  Port  area of  produce  Hardy  and  the  and  results  Ball,  1976),  and Q u i l l a y u t e  produce  the  are  consistently  calculated  when  far  poorer  precipitable  water  totals.  The  Tables  precipitable  water  e.g.  day  Julian  transmission within  6%  greater  at  of  85  end  atmosphere  also  increased effect  small  of  degrees.  This  on  (i.e.  the  insensitivity  the  atmospheric  solar  the  2.3  day  when  calculation  within when  the  that  by a p p r o x i m a t e l y the  confirms of  show  2%)  the  and  the 50%,  of  is  the still  z e n i t h angle  the  earlier  model  to  is  statement  changes  in  water.  D e r i v a t i o n of  The  200/79,  and  is  typically  the  precipitable  amount  the  than  concerning  2.5  is  2.2  radiation which  'Shortwave  Transmission'  transmissivity normally  survives  is  defined  incident  passage  upon  through  as  "the  the the  fraction  top  of  atmosphere  the to  27  the  Earth's  surface"  transmission'  (T)  (Huschke,  is  being  used  cloud  transmission  by  relating  solar  radiation  the  Earth's  to  that  Section  at  calculated 2.3).  for  the  Essentially  it  energy  including  is  due  the  parameter  was  this  estimate  1981);  a  actual  measured  incident  surface  (K+,  sky  see  simple  Section  conditions  K + / K +  2.2),  (K+ 0 ,  see  (2.19)  0  isolate  clouds  by  using  effects  due  model'used  here  the  depletion  measured to  the  excludes  data  of and  cloudless an  aerosol  because:  the  model  radiation  (Atmospheric  the  reflected  include  the  As  analogy,  being  describe  to  sky  of  solar  influenced  an  'shortwave  was  shown  under  clear  Environment  to  produce  sky  Service,  the  conditions 1980;  best for  Davies,  and  2) also  the  term  to  proposed  selected  form  of  Vancouver  here  clear  depletion  The c l e a r  and  =  to  atmosphere.  1)  The  Thus:  T  incident  1959).  effects  treated  transmission  by  it as  should  radiation the  of  can a  aerosols  aerosols  be  said  thin be  measured  100%  in  and the  that  clear  the  satellite  is  is  necessary  to  it  calculation  the  cloud. on a  thus  by  aerosol  Ideally day  of  is  essentially  the  devoid  T.  shortwave of  aerosols,  28  and  slightly  However ±2%  errors  less  inherent  inaccuracies  measurement Thus effects  in  of  calculated  (Davies  errors  most  than  cases  aerosol  100%  in  the  in  transmissions.  aerosols  McMaster  model  and Hay,  (Latimer, it  when  will either  1980),  1972; be the  Hay  are  present.  result  in ± 1 % or  together and  impossible satellite  with ± 5 % for  Wardle, to  1982).  isolate  data  or  the the  2 9  CHAPTER  SATELLITE  3. 1  satellite  Geostationary system  which  satellite  positioned above  al.1981).  both  are  utilized  the  satellite  subpoint  Earth's centre  resolution satellite  to 3.3.  is  surface of  the  0.8  km.  and  detectors  subpoint defined of  a  subpoint. of  at  135  spin  scan  infrared study. which  the  vector Due the  Thus  the  Vancouver, pixel  km  (Corbell  et  a  the  eight  0.8  latter  vertically  km  Phillips,  of  the  v i e w e d moves of  the  Columbia, be  1980),  the  and  the  Earth  the  from  the  study  discussed  where the  away  will  the  with  satellite of  in  resolution  intersection  curvature  will  satellite  simultaneously  resolution  size  west  SMS-2  35,800  though  are  give  and  point  British  about  images,  the  (GOES)  the  geosynchronous  and  area  of  Meteorological from  degrees  sample  the  part  Satellite  of  joining  to  as  The a c t u a l  is  are  There  (Hambrick as  Earth.  used  altitude  wavelengths  decreases  proximity  an  this  micrometer  study  Synchronous  imagery  equator  in  this  the  at  visible  visible  0.55-0.70  the  SET  Environmental  operational  provides  aligned  The  the  This  not  in  includes  (SMS).  directly  used  Operational  Satellites  the  DATA  Introduct ion  The  at  3  be in  area,  in  inferior Section  30  The acquires The  Visible  and  a  Earth  full  c o l l e c t i o n and  authorities Science the  one the  is data  the  used  The ranging  in  in  the  one  unit  the  every  data  is  line  of  (SSEC), present  quarter  of  of  0 to  being  is  converted  to  the  1000  by  the  actual  the up  the  the  are  255  8-bit  are  used  (i.e.  an  with  using  pixel area,  in  to  image  the  an  the  centred research  used  composite provided  Space  the  of  images surface,  1000  pixels  and  represents  1008  pixels  (a  in  form  a  were  of by a  on  Vancouver  could  count  targets.  The  on m a g n e t i c  tapes  count  much  25  x  in  initial  25  forty-nine of  format  system.  larger  developed  to  or  Since  area  than  extract  a  o  16'  N,  123  15'  W)  from  proceed.  of  window  (49  values  larger  processing  cover  count  with  digital  image  programs  of  brightest  the  images  form  scale),  in d i g i t a l  either  image  1008  an  provided in  study  Windows mainly  various  source  Earth's  o  which  minutes.  by  From  d i r e c t i o n and  channel data  associated  data be  sub-image  (VISSR)  Wisconsin's  study.  satellite  (N-S)  thirty  managed  which  ranging a  Radiometer  once  University  obtained  smallest  visible  satellite  the  Scan  (E-W) d i r e c t i o n .  from  can  were  point)  element  and  data  images  values  the  approximately  smaller  image  Engineering Centre  satellite  pixel  disc  Spin  a r c h i v i n g of  including  and  covering  Infrared  25  pixels  centred  investigations. images, x  25  showing  pixels  for  on  the  UBC s i t e  Figure.3.1 the  spatial  the  study  were  shows  a  coverage area.  31  62  62  61  61  62  62  62  64  67  7a  70  71  73  72  72  72  72  72  73  73  73  74  75  73  72  68  66  63  60  60  61  61  63  67  69j  70  73  73  72  71  7 1 72  72  72  72  72  72  73  73  72  70  67  64  62  62  62  63  66  69  7 1 72  73  72  71  7 1 71  70  7 1 72  7 1 71  72  73  72  72  72  72  71  7 1 70  69  70  70  7 1 7 1 71  72  73  69  66  63  62  63  64  67  59/  71  71  69  65  62  62  64  67  7  66  63  62  62  63  64  68  \  72  72  73  74  74  74  73  74  73  73  72  73  73  73  72  73  73  73  72  73  73  73  74  75  75  76  76  78  77  77  75  75  76  76  75  66  68  68  68  68  68  _72  74  76  77  78  78  77  77  77  63  62  62  62  63  63  64  61  61  61  61  61  61  61  78  78  63  63  62  63  63  64  64  65  67  6 9 s "^1  72  75  77  77  78  78  79  60  61  61  62  62  63  59  60  60  61  62  63  63  63  63  63  63  63  64  64  64  64  64  66  69>  72  74  74  73  73  74  64  64  64  65  66  68  68  67  66  66  66  67  SsJ  72  75  74  72  71  71  74 - 73  73  72  71  71  71  72  75  78  79  78  77  78  60  60  60  61  62  64  64  66  59  60  60  61  62  63  64  66  66  7t  74  76  76  75  76  78  78  78  78  ao  81  80  81  82  32  59  59  60  60  61  62  64  64  66  68  S^l  75  76  76  77  78  ao  81  81  82  31  80  82  83  33  64  65  65  68  73  75  76  78  79  80  B 1 82  81  81  82  83  83  59  59  58  59  58  58  60  60  60  59  60  59  67  Land(N)  68.  P o i n t Grey  59  60  62  63  59  59  60  62  63  64  65  66  68  69  72  74  76  79  81  83  83  84  82  83  84  84  59  59  60  61  62  63  64  66  68  69  70  72  75  79  83  85  85  85  84  84  83  84  60  61  61  62  64  65  66  67  69  7q  72  73  75  79  82  85  86  86  85  85  85  84  60  61  6 1 63  64  65  67  68  69\  71  72  73  75  78  8 1 33  84  84  84  84  83  85  85  84  83  60  Sea  60  17 1  Land(S)  72  73  74  77  81  83  84  691 70  72  72  74  75  78  82  82  84  85  85  85  72  73  74  73  75  78  8 1 82  83  85  85  86  72  74  74  74  74  75  77  79  80  82  84  84  73  73  74  74  74  76  78  81  83  84  83  59  60  59  60  60  61  62  63  64  65  67  68  68  60  59  59  60  60  60  61  63  64  66  67  68  60  60  60  61  61  62  62  64  65  67  67  70 y/o  60  60  60  60  61  62  62  64  66  67  69  71  60  60  61  61  63  63  64  66  67  69  70, ' 7 1  59  60  61  62  64  64  65  66  68  69  70|  70  7 1 72  71  72  73  73  74  75  77  80  83  84  86  60  61  62  64  64  65  67  67  68  69  70'  70  70  70  70  71  72  73  73  73  74  75  78  81  82  72  FIGURE  73  3.1  25 x 25 Pixel Array C e n t r e d on t h e UBC S i t e D e p i c t i n g Mean Brightness C o u n t V a l u e s B a s e d on F o r t y - N i n e I m a g e s F r o m J u l i a n Days 196/79, 200/79, 256/79 and 121/80. The Areas Used to Develop t h e S e a , L a n d ( N ) a n d L a n d ( S ) BDR Models are D e p i c t e d and are R e f e r r e d to i n S e c t i o n 4.3.1.1.  32  Before further  the  satellite  processing.  data  This  will  can be  be  used  discussed  they  in  the  require following  sections.  3.2  E a r t h - L o c a t i o n of  Before  the  imperative (that  that  is,  This  site  data  pixel  location  pixel  or  determination  Earth-location  of  the  radiation  calculations  especially  significant  radiation  on  other is  of  Imagery  satellite the  which  measurement  Satellite  can  the  be  of  each  image  landmark  importance  at  the  based  these  characteristics  partly  may  be  image  be  Earth's  because imagery  under  it  any  changing  in  affect  skies  rapidly  a  surface).  data.  cloudy  to  errors  will  is  known  corresponds  satellite on  utilized  the the  This  is  where  the  over  short  di stances.  Initial  Earth-location  performed  using  (1980).  The  and  Order one  of  accuracy  the of  Root  are  satellite  this  model  F.O.N, Mean  the  satellite  described  navigation  Navigation", pixel  model  algorithms  terrestrial  departure The  a  of  based  by H a m b r i c k a n d on  the  points  and  from a  true  (subsequently for  Square  imagery  brevity)  is  accuracy.  use a  of  was  Phillips  both  knowledge  stellar of  the  geosynchronous  orbit.  referred  to  as  "First  claimed  to  be  within  However,  initial  33  comparisons  of  and  navigation  visual  Computing Visual  of  Errors  of were  line the  twenty  pixels  'Second  the  same  as  large  the  (for  are  landmarks  to the  2  for  to  the  processor  This  procedure  the  study  near  and  late  is  preferable  landmark  For  per  to  or  and  to  the and  (UBC  errors. predicted  the  image  actual  processor.  fifty-two  pixels  seventy-three with  to at  (i.e.  afternoon).  in  pixels  errors  of  as the  to  following  The S . O . N ,  in  the  of  of  F.O.N..  images early  wherever hour  landmark  d e t e r m i n e d on  three the  of  involved  a  application  in  the  Earth-location  visually  However,  correct  Earth-location  least  per  Therefore,  developed  present  images  image  study.  coordinates  used  for  one  was  two p i x e l s .  coordinate  day  this  achieve  landmarks  use  for  longitude  repeated  the  the  361/79),  still  subsequent  throughout noon  was  pixel  is  on  day  larger  F.O.N,  and  (S.O.N.)  one  latitude  procedure) image  (for  errors  objective  Appendix  171/80)  processor  between  hundred and  unacceptable  within  much  the  seen  image  F.O.N,  b e i n g uncommon.  Earth-location  relating  day  on  as  one  Navigation'  The  COMTAL  revealed  based  as  determined via  comparison  direction  errors  Order  the  landmark  and above  F.O.N..  (see  landmark  element  landmarks  using  involves  direction  Such  for  a  of  frequently  navigation  position  in  location  Centre)  positions  the  the  and  spread  morning,  possible at  least  it one  image.  each  image  the  difference'  between  the  pixel  34  coordinates  of  if  landmarks a r e used)  multiple  S.O.N.  the  i s calculated.  must  be  the  image.  applied  function  give  be  F.O.N..  from  This the  and  are  to  closest with  interpolation unnavigated  navigated  first  at and  the  18:45  to  estimate  navigated are  are the  or  determined  by  discussed  The in  indeterminate navigable  accuracy  images  3.4,  to  the  for  each  using  of this while fact day  day  are  interpolation to estimate the have  received  i s based  on  undergone  time  S.O.N,  The t r a n s l a t i o n s used  by t h e c u b i c  translation for that  later  occur  than  given  the  last As an  a suite  18:15,  of  four  19:15  and  (E-W a n d N-S) f o r a n t h e images  image  a t 18:15,  19:15  interpolation algorithm the extrapolation that  the  were  always  the  earlier  extrapolation.  (16:45,  translations  Section due  Earth-location  images  be d e t e r m i n e d  have  f o r images  image,  given  which  image.  images  Translations  estimated  will  a  images)  that  that  o f l a n d m a r k s on  cubic  t h e images  images  three  (navigated)  20:15.  The  the navigated  of the i n t e r p o l a t i o n procedures:  Earth-located 20:15)  for a  the unnavigated  function image.  location  images  to  by t h e F.O.N, a n d t h e  i s the t r a n s l a t i o n  using  three  these  image,  example  the 'true'  of the d i f f e r e n c e  i n t e r p o l a t i o n procedure  incorporates  the  difference  applied  and  than  produced  Earth-located  to  associated  ( o r an a v e r a g e  remaining  (generated  correction  This  to  The  subsequently  only  landmark  first  is  error i s and  used  in  last the  procedures.  S.O.N.  procedure  relies  totally  on  visual  35  identification therefore area  of  depends  of  landmarks on  interest  incorporates  suitable  land-water  British  Columbia  coastline  clouds  obscure  the into  images  extend  the  Oregon.  into  identification first  possible  of  be  image  processor.  and  Priest  Lake,  Idaho,  are  examples  Cape  Arago)  navigate  3.3  the  Pixel  As  Size  was  resolution that  images  for  quoted  resolution  is  copy  areas  the  then lakes  Figure  at  and  landmarks  larger  southern  is  cloudy,  was the  permit  the  carried  out  Atmospheric to  these  Kootenay  the  used  and  Vancouver,  (e.g.  southern  the  to  inspecting  Valley  images  area  procedure  present  frequently  of  clear  images  U.S.A.) of  some  and  landmarks.  and  Columbia  Office,  and  Interior  (see  and  Vancouver  This  Weather  visible  satellite  British the  the  area  sufficiently  hard  free  The  The Fraser  along  this  Alberta  landmarks.  Service  cloud  if  Lower  clearly  in  of  northern  examining  Environment  provide  surface  skies.  the  boundaries  edge  may  Earth's  clear of  landmarks.  western  areas  part  prevalent  Therefore,  alternative  by  are  coastal  extend  the  comparatively  where  However,  on  locate areas  Lake,  B.C.  Oregon coast  that  have  been  on  (e.g.  used  to  3.2).  Determination  noted  earlier  the  latitude  for  the  required  for  (Section of  satellite  the  3.1.),  study  area  subpoint.  translating  the  the is  spatial less  The  navigational  than  spatial errors  36  FIGURE  3.2  Map of t h e A r e a C o v e r e d by t h e L a r g e s t S a t e l l i t e I m a g e s (1000 Lines x 1008 E l e m e n t s ) Showing Landmarks T y p i c a l l y Used i n the Assessment of Linearity.  37  (quoted  in  pixels)  into  distance  errors  at  the  Earth's  surface.  Using  the  instantaneous  geometry  geometric  the  resolution  the  east-west  was  personal  resolved  by  area  approximately  a  0.8  x  0.8  resolution km  resolution  for  45  The the  overlap a  greater  north-south resolution by  the  above  be  0.984  the  the  km ;  is  over  smaller  by G a u t i e r  et  the  calculus,  1.50  km  for  of  twice  the  al.(l980)  area  the  the  subpoint. than  (C.  smallest  latitude  satellite  (the  respectively  Therefore for  vector  km a n d  directions  square  area  and  sensor  study  size  Thus, four  and  of the  square  Hay(l98l)  north.  (the  in  study  estimated  of  north-south  pixel  at  satellite  view)  to  sensor  1.48  pixel  the  shape  direction 12%  km  degrees  of  communication).  satellite  for  the  north-south  Raphael,  is  field  determined  and  the  of  a  pixel  is  direction vector  underlap the  than should  and  calculus along  east-west  angular  the  be  results.  from  east-west greater  for  with  compressed showed  the  Since  in  the  former;  long the  to  axis the  satellite  axis, the  the  there  north-south  direction).  distance the  rectangular  be and  axis  in  east-west on  average  16%  study  pixel  area  is  subpoint  on  the  degradation  of  the  borne  out  this  is  38 3.4  Validation  The  the  Earth Location  integrity  performed on  of  at  the  a  of  subsequent  validity  of  Earth-location  routine  processing  a  cubic have  of  been  The using  a  days  .  had  not  sample The  in  Estimated using Mean  3.2,  cubic  Bias  Error  (R.M.S.E.), of  the  residuals  this  were  on and  were  the  to  account  the  as  the  minus  M.B.E.  T. ( F i= 1  n  ±  -  Mean  of  the are  observed  /  that  clear  that  they  During outlined  calculated. these  images  Two s t a t i s t i c s ,  Root  F± )  as  n  a  assessed  S.O.N..  for  of  seven  basis  processed  They  the  visual  images  from  translations  indicators  procedure.  =  using  determined  the  estimated  those  the  The  use  was  procedure.  and  the  be  heavily  the  procedure  were  observed also  on  3.2).  located  images  were  relies  Section  on  to  routine.  selected  solely  Earth  for  (see  images  selected  these  study  combined with  interpolation  (M.B.E.)  interpolation of  images  interpolation  used  this  dependent  Earth-located  translations  the  largely of  previously  landmarks  Section  is  in  calculations  Earth-location  thirty-four  images  been  testing,  of  of  stage  procedure  visually  accuracy  radiation  the  number  interpolation not  the  Routine  Square  goodness based  the Error  of on  fit the  translations:  (3.1)  39  R.M.S.E.  0.5  n  =  2  i= 1  where the  Fi  is  ith  sample  the  value  size  (n  ith of  =  translations. that  whilst between two  pixels  pixels. the  position within would The  (1.65),  values  means  of the  1.54  km.  to  whilst  the  M.B.E.  while  absolute  the than  the  size  a  is and  the  in  and  n  distances  Fiis is  the  3.3)  north  of  element  pixel  under  is  0.03  the  is  is  just  -0.03  in  the  to  location. pixels  difference under  four  pixels.  larger  Therefore,  size  the  tendency  1.53  T h e maximum is  (using  dimension  true  (E-W) a r e  line.  just  estimate  that  (E-W)  translations  pixels  distances  the  can  difference  is  we c a n  means  we  1.026  north-south  coordinate  on a  is  element  3.1  difference  difference  the  Table  absolute  pixels.  observed  (based  of  and  T h e maximum  M.B.E.  the  in line  minimum  position  line  translations  the  0.302  for  the  Section  for  element  for  terms in  minimum  those  listed  observed  in  calculated  pixels,  instances  that  both  pixels.  The n e g a t i v e  estimated  for  and  landmark  between  values  -0.17  estimate  R.M.S.E.  for  results  while  pixel  of  be  translations;  translations;  calculated  is  estimated  This  (3.2)  n  estimated  performed the  R.M.S.E.  M.B.E.  the  the  observed  were From  the  the  the  of  (  F± ) /  34).  Calculations  note  value  -  in  in  The most  terms  of  E-W d i r e c t i o n  40  of  0.984  km;  landmark the  to  Section within  tendency  3.4) 1.50  would  be  we c a n km.  to  estimate  the  The p o s i t i v e  estimate  to  position  M.B.E.  the  east  of  means  a  that  of  the  actual  landmark  per  image)  locat ion.  A was  'worst  conducted  sample Table  of  are  analysis. for  for  al.  in  (1980)  of  only  minor  changes  more  A  involved  (Washington  Arago  (Oregon),  to  of  is  the  the  for  State), (see  S.O.N,  of  coordinate, the  interpolation  that  that,  previous procedure  demonstrated  by  the  procedure  and  considered  to  the  present  study.  by  the  effects  is  of  However,  this  non-linearity  3.5).  for  testing  variety Point 3.2) Only  were  results  in  et  Moses  Figure  line  show  a  by G a u t i e r  technique a  listed  results  the  imagery to  are  using  quoted  Section  using  for  the  procedure  results  These  cubic  similar  observations.  derive  from  satellite  reduced  direct  the  R.M.S.E.  navigation  (see  Point  fifty-three  3.1  be  image  more  procedure  of  adequate  could  the  the  accuracy  their  than  accuracy across  for  Again  parentheses).  case  Table  on o n e  interpolation  images.  in  Earth-location  (based  cubic  the  The  results  used  the  (numbers  in  there  analysis  twenty-four  3.1  except  be  case'  of  the  landmarks  (Vancouver and  those  Earth-location  incorporated  in  Birch  Island),  produced images  e.g.  a  which  this  Cape  total were  test.  of not  41  TABLE  3.1  Verification Statistics for the Cubic I n t e r p o l a t i o n Routine used i n the E a r t h - L o c a t i o n of the S a t e l l i t e Imagery. Values are quoted in P i x e l s . n = 39. (Values in brackets are from the ' W o r s t C a s e ' a n a l y s i s b a s e d on o n l y o n e L a n d m a r k p e r Image w i t h n = 2 4 , S e e T e x t ) .  Line  (N-S)  Element  (E-W)  R.M.S.E.  1 .026 (0.736)  1 .53 ( 1 .53)  M.B.E.  -0.170 ( 0 . 198)  0.302 (0.290)  Maximum Di f ference  1 .65 (1.75)  3.77 (3.60)  Minimum Di f f e r e n c e  0.03 (0.03)  -0.03 (-0.02)  42  This km)  second  and  (1.27  0.13  km)  analysis  pixels  and  (0.20  0.63  and  confirm  those  of  Earth-location  adequate  3.5  for  overcast not  pixels  M.B.E.,  and  (0.95  km)  for  R.M.S.E.  the  respectively.  Thus  method  requirements  of  1.29  in  this  the  results  the  appears  (0.33 pixels  These  navigation.  interpolation  Earth-location days  visible)  (see  with  is  these  any  loss a  linear  non-linearity issue  of  sources satellite  To satisfy  2)  that  the  two  include  can  accuracy. manner  error  is  accuracy more  than  cloudy  and  study.  useful basic  in  a  is,  the  of  local  the the  from other  study  are  areas  in  this  associated  area  translations  without behave  Alternatively,  little  because  accurate  area  Inherent  image.  any  importance. it  is  The  one  of  the  Earth-location  of  the  3.2).  assessment  outside  the  translations  to  that  be  requirements:  landmarks  the  important  Section  in  free.  given  the  partly  landmarks  applied  will  affecting (see  that  be  across  of  cloud  That  introduced  imagery  be  are  on  landmarks  use  assumption  linearity of  imagery  when  the  landmarks in  of  (occasions entails  Appendix  approach  to  0.34  the  previous  research  of  Linearity  The  in  the  results  for  directions  of  the  km)  pixels  element  the  line  gave  the  1)  of  linearity,  they  study  images  must  be  large  area;  2)  they  must  enough must  be  43  practically landmarks  cloud over  a  this  assessment  (1000  lines  to  Validation using  183/80).  from  Images  landmarks  from  from  these  area  of  study  landmarks  interest  typically  (Figure  used).  landmark  outside  departure  from  The the  was  dimensions.  listed  Table  based  on a  using  landmarks  using  from the  another  landmarks the  new  of  the  and  the  assessments  are  a  a  Analyses  sample  of  for  measure  from  for  the  north-south  these  east-west  from  study  can  for  be the  the  (1.54  the  study (4.9  estimated  in  the  km),  to  They study while  area  km).  north-south  images.  landmark  ± 1 . 5 7 pixels  in  ±5 pixels  twenty-two a  the  distance  within  Analyses  both  some  landmark  km).  for  They  landmark  within  provide  images.  that  of  of  and  determined  determined  thirteen  to  position  some  of  estimated same  area  assessed  Earth-located  landmarks  shows  Results  3.2.  sample  of  images  121/80  translations  to  translations  was  (276/79,  were  The  3.2  assessed  east-west  position  constrain  largest  linearity  days  applied  study  the  of  linearity.  Linearity  in  which  days  area.  were  requirements  of  clear  these  identification  available.  assumption  from  the  for  were  several  the  These  days  elements)  the  enable  area.  clear  of  imagery  to  large  1008  x  free  dimension  indicate area,  (on The  within  the  average) line  area the  can  line  when  element can  be  position  of  ± 4 . 6 pixels  dimension are indicate  that  are  that be  based the  (6.9 on  element  estimated  position  a  of  to that  4 4  TABLE  3.2  !  Results from the A s s e s s m e n t s of L i n e a r i t y Image b a s e d on D a t a f r o m T h r e e C l e a r Days. Values are in P i x e l s .  Line (E-W)  R.M.S.E.  M.B.E.  n  4>62  -3.80  13  Element (E-W)  5.0  -4.80  13  Line (N-S)  across  the  Element (N-S)  1.23  1.57  -0.08  -0.07  22  22  Satellite  45  same  landmark  can  be  determined  to  within ± 1 . 2 3 pixels  (1.85  km) .  The  preceding  sets.  Their  occurrence However, of  the  of  1)  The  are  earlier the  tentative  been  based  largely  on m o s t  of  conclusions  of  dimension  on  small  influenced  the  can  non-linearity are  similar  cubic  additive)  been  cover  effects  of  worst  has  have  available  be  drawn  data  by  the  imagery.  on  the  basis  results.  north-south here  size cloud  some  above  analyses  negligible.  magnitude  interpolation  case the  (when  to  position  procedure  2.3  pixels  of  a  image  (see  and  Section  linearity  km)  will in  in  the  determined  associated  landmark  (3.45  the  The e r r o r s  those  interpolation  true  approximately  across  be  with  the  3.4).  In  errors  are  in  error  the  line  the  image  by  (N-S)  di rect ion.  2)  The  effects  east-west  direction  reflected  in  true  the  position  approximately direction. linearity  of are  large of  3.0 In  errors  non-linearity across of  Mean  Bias  the  pixels the are  greater  significance.  Error.  landmark (2.95  worst  additive)  km)  case the  In  the  will  be  in (when  true  the  in This  worst in  the  error  by  element  of  a  is  case  interpolation  position  the  (E-W) and  landmark  46  will  be  in  The and  error  by  errors  overcast  satellite  in  the  rather  to  than  change  communication  the  quantities  of  conditions. a  dilemma  incident  solar  As  a  landmarks Stuart  to  the  Lake,  east  Recent a  cloudy  landmark of  the  work  function  satellite  of  of  used  study  has  to  area  suggested  the  image  the  rate  of  (C.Raphael,  larger  solar  navigational  radiation  regime  widespread  solar  energy errors  cloudy  resulting  overcast  is  less  likely  to  and  small. for  proves  spatial  under  skies  relatively  situation high  is  errors  to  be the  Thus  overcast be  more  of  of  the  variability  radiation.  result were  the  is  the  navigational  The p a r t l y due  observed  with  incoming of  to  partly  Earth-location  when t h e  south.  across  the  homogeneous  impact  in  under  ).  reasonably  the  errors  greater  or  possible  conditions,  radiation  lies  north  size  to  be  imagery  pixel  Despite cloudy  due  could  the  km.  10.0  calculated  non-linearity  in  personal  the  imagery  the  to  conditions  Earth-locate  that  up  of  these  selected B.C.)  coastlines)  of  navigational  errors  or  the  either south  study to  a  investigations,  area  minimum.  within (e.g. in  wherever  or  to  the  Washington an  attempt  possible,  north and to  (e.g. Oregon  keep  the  47  3.6  Conversion  The  of  Pixel  original  ranging  from  counts  the  relative  may  converted  are  curves  based  Vonder  on  Haar  (1980)  polar  mounted  flux  imagery  used  WEST)  satellites,  including  absence  of  present which  a and make  satellite  channel  curves  was  a  the  is  the  (see  3.3)  Smith  and  satellites  comparison latter  a Two  Figure  and  an  value  using  GOES-1  a  are  channel.  (1977)  the  present for  true  recent  use  it  (see  was  study  which  with  with  of  many  of  the  aircraft  and  is  major  the the  satellite lack  necessary  Figure  since  background  of to  3.3).  with  meteorological spacecraft.  and  both  requires curve  between  SMS-1  reflectance of  for  climatological  calibration choose  the  available  concern  data  value  from  no  GOES-5  and  The  zero  count  a  that  is  the  GOES-4 of  is  there  meteorological  of  Given  favoured  shows  in  future  the  curve  on  and  and  reflectance  and  values  brightness  literature  based  calibration  remedy.  available  The  Loranger  satellite  This  immediate SMS-2  was  count  scale)  visible  SMS-1  satellite  curve.  studies  8-bit  as  radiometers.  (GOES  past,  and  the  former  calibration  The  the  Reflectances  given  an  VISSR  in  Smith  orbiting  are  normalized  the  for  The  NOAA-2  SMS-2  by  Surface  brightness.  a  for  to  (i.e.  present  work  respectively.  The  to  curve  calibration  data  0-255  of  calibration  Values  satellite  indication be  Count  the  an for two  calibration the  slightly  visible above  48  8 - BIT COUNT SMS-1 COES-1  FIGURE Calibration Radiometers  Curves for ( A f t e r S m i t h and  3.3  the SMS-1 and GOES-1 Vonder Haar, 1980).  Satellite  49  twenty.  This  reflectance)  with  from  background  the  brightness  (see  Figure  shows  a  3.4).  zero  A  agreed  values  value  polynomial  conversion  fit  equation  as  NR  is  brightness in  a  value  standard  coefficient The  of  target  the  visible  to  I0  hand,  the  -  by  to  also  twenty-four  the  SMS-1  GOES-1  curve  0.00013326D  had  counts  calibration  resulted  in  + 0.00001675D2  normalized reflectance in counts.  error  The  for  wavelengths,  )  which  zero  a  follows:  fitting  estimating  determination  by  (i.e.  reflectance.  of  value  of NR  is  the  the  curve  of  0.0033  the  total  the  amount  of  then  used  to  reflectivites  0.55-0.70  dividing total  and D i s  (3.3)  digital resulted and  a  0.9999.  (Earth-Atmosphere system)  determined x  sixteen  zero  normalized reflectance  the  (NR  the  of  imagery  satellite  other  with  NR = - 0 . 0 0 4 5 8 6 3 2  where  SMS-2  On t h e  count  night-time  calculate  (TR)  micrometers). amount  of  incoming  (for This  reflected  energy  (I0  is  energy x  cose)  giving:  TR  The the much  target  satellite of  the  =  NR /  reflectivity array original  (e.g.  cos  is 7  analyses),  e  (3.4)  calculated x  7 pixel with  for  each  pixel  arrays  were  used  subsequent  averaging  in for to  50  20 20 24 16 20 20 20 20 20 20 24 16 20 20 24 20 20 24 24 16 20 20 20 20 20  20 24 24 16 20 24 24 20 20 24 24 16 20 20 20 20 24 24 24 16 20 20 24 20 20  20 20 24 16 20 24 20 20 20 20 24 16 20 20 20 20 20 20 24 28 20 20 24 20 20  20 20 24 16 20 28 24 28 20 24 24 16 20 20 20 20 20 20 24 1.6 20 20 20 20 20  20 20 24 16 20 24 20 20 20 24 24 16 20 20 20 20 20 24 24 16 20 24 20 20 20  20 24 24 16 20 24 20 20 20 24 24 16 20 24 20 20 20 24 24 16 20 20 24 20 20  20 24 24 16 20 20 20 20 20 24 24 16 20 24 20 28 24 20 24 16 20 20 20 20 20  20 24 24 16 20 20 24 20 20 24 24 16 20 20 20 20 20 20 24 16 20 20 20 20 20  20 2 0 20 20 20 20 2 0 2 4 24 20 24 24 24 24 20 16 1 6 16 20 20 20 2 0 20 20 20 28 2 0 20 24 20 20 2 4 20 24 20 20 2 8 2 0 20 28 20 2 0 20 24 20 2 4 2 4 2 0 24 20 24 2 4 24 24 2 4 16 2 0 2 0 20 16 20 2 0 20 20 20 20 2 0 20 20 20 24 2 0 24 24 20 20 20 20 20 20 20 2 0 20 20 20 20 24 24 20 24 24 24 24 24 24 16 2 0 20 20 16 20 2 0 20 20 20 20 2 0 20 20 20 2 0 2 0 20 20 20 24 2 4 20 20 20 20 2 0 20 20 20  20 20 20 2 0 24 1 6 16 2 0 20 20 20 2 0 20 2 0 20 2 0 20 2 4 20 20  24  24  16 16 20 20 20 20 2 0 20 20 20 20 20 24 20 24 24 20 16 20 20 2 0 20 20 20 2 0 20 2 0 20  FIGURE  20 24 24 16 20 20 20 20 20 20 24 16 20 20 24 20 20 20 24 16 20 20 20 24 20  20 20 24 16 20 20 24 20 20 20 24 16 20 20 20 20 20 20 24 16 20 20 20 24 20  20 20 20 16 20 20 20 20 20 24 24 16 20 20 24 20 20 20 24 16 20 20 20 20 20  20 24 20 16 20 20 24 20 20 20 24 16 20 20 24 20 20 20 24 16 20 20 20 20 20  20 24 20 16 20 20 24 20 20 20 20 16 20 20 24 20 20 24 24 16 20 20 24 20 20  20 24 20 16 20 24 24 20 20 20 20 16  20 20 20 20 20 24 24 16 20 20 24 20 20  20 24 20 16 20 20 24 20 20 24 20 16 20 20 24 20 20 24 24 16 20 20 20 20 20  20 20 20 16 20 20 20 28 20 24 20 16 20 20 20 20 20 24 20 16 20 20 20 20 20  20 20 20 16 20 24 20 20 20 24 20 16 20 20 24 20 20 24 20 16 20 20 20 20 20  24 20 20 16 20 20 24 20 20 24 20 16 20 20 24 20 20 20 20 16 20 20 20 20 20  3.4  A Nighttime Subarray Centred Over the P a c i f i c Ocean A t 49 Latitude 127 Longitude Demonstrating a Background Brightness and S t r i p i n g Due t o t h e L a c k o f I n t e r s e c t i o n C a l i b r a t i o n . The L a t t e r is R e f e r r e d to in S e c t i o n 4.3.1.1.  51  determine final  the  stage  mean in  the  radiation  data  reflectance  data  described  in  reflectivity initial  the  the  Chapter  target of  merging  hourly The  2.  the  processing  involved with  of  the of  viewed.  The  satellite  and  the  transmission  following  section  satellite  calculations outlines  this  procedure.  3.7  Merging  of  Transmission  The  data  time  atmospheric satellite The  data,  it  calculated  an  In  shortwave  necessary  the  Shortwave  fit  (they  However,  this  Thus  simple  fact  is  merge  compatible,  hourly  or  daily  rare.  instantaneous instantaneous never was  are  an  hourly  data  are  it  decided  for  data  the  was  majority  half  to  of  solar  quantities,  while  due  to  for  a  developed  sets.  every  Secondly,  explicitly  from  taken  reflectance the  on  calculated  reflectance  measurement  Firstly,  technique  the  transmissions  satellite  are  the  two d a t a  the  strictly  relate  based  to  satellite  are  are  estimated  sets  use  to  study  reflectances  data  estimates  not  sensor,  a  and  studies  are  the  instantaneous  to  instantaneous  the  to  transmissions.  radiation  and  this  Therefore,  is  making the  reasons  in  atmospheric  essentially hour.  Reflectance  used  transmissions  value  data  sets  scales.  integrated  two  Satellite  Data  two  different  the  the  satellite  scan  given  taken to  the  of  location).  into use  time  account. the  most  52  appropriate the  hour  satellite over  integrated. hour,  a  images  which Since  complete being  weighted  chosen  to  to  Figure  the  weighting  of  24/60,  If  an  missing missing weights. missing back  to  weight  entire  data  conditions minute  For then  image  on  three,  the is  scheme based  the  time  are in a  for and  to  time  two,  for  each to  image the  are  every  maximum o f  on  are  three  while  is  hour  image  30/60  half three  are  then  amount  of  and  on  at  the  is  of  a time  four  between  image  closer  described  by  would 11:00  be and  two w o u l d r e c e i v e  irradiance  based  best  three,and  the  images  to  four  6/60.  weighting solar  secondary  each  places  noon.  calculation of  a  of  image.  The the This  importance  and  time.  image  study  example  image  11:09,  taken  period,  satellite  over  image  images  time  Images  radiation  weighting the  through  measurements  data  respect  weighting  extraterrestrial  modifies  conditions  radiation  result  extraterrestrial  importance  latter  will  to  3.5.  sixty  the  radiation  set  with  Of  greater  satellite  The s a t e l l i t e  represent  of  represent  radiation.  12:00.  Use  to  solar  respect  weighting  reference  the  used.  extraterrestrial  the  data  with  The.  images  is  area,  assigned  if  image  would image  unavailable  be one  images  or  there  adjacent  appropriately two  used  (see to  would  be  used  to  the  increased  Figure  represent  to  are  3.5)  was  conditions represent  53  Satellite image time I  10=39  11=09  11=39  12=09  12=39  Image number' rTime  10=00  I  11=00  FIGURE  13=00  12=00  3.5  Example of Satellite Image Weighting Scheme Satellite Data to Hourly Integrated Radiation Indicate t h e T i m e I n t e r v a l E a c h Image R e p r e s e n t s ) .  for Data  Merging (Arrows  54  conditions  between  limitations an  to  interval  the  11:00  this  is  being  classified  as  a  with  more  two o r  With the  the  This  satellite  measures  part  of  while  the  the  the  producing of  narrow  period.  Thus o n l y  those  are  the  -  3.8  cloud a  band  latter.  is  (i.e. data  pictures  this  made  represent  designed  (Smith  study  However,  broad that this  the is  the  -  model  to  former  known  to  is  used.  that  transmission fact  in  0.70  that  the  the  visible  micrometers)  full  shortwave  the  is  due  to  purpose  Haar,  1980).  convert  irradiances  which  periods  are  difference for  in  assumed  the  only  and Vonder  band  is  the  This  transformation to  with  0.55  hour  it  despite  between  period  per  sets  radiance  micrometers).  radiances for  two d a t a  comparable  originally  specific  available  shortwave  spectrum  being  assumption the  data  assumption  (0  VISSR  lack  conditions  pyranometric  irradiance  represent  radiation  these  hourly  to  represent  images  the  has  to  data  values.  image  are  used  of  hour,  an  there  one  satellite  merging  If  However,  than  missing  reflectance  11:09.  procedure.  greater  image  and  the  results  of The  SMS-2 in  is  representative  be  incorrect  for  the of two  reasons:  1) for  the  wavelength  shortwave  2)  the  dependency  of  absorption  and  scattering  radiation;  anisotropic  scattering  of  the  shortwave  radiation.  55  The  representativeness  considered  as  However,  the  effects  conversion  from  radiance  via  the  following  a  limitation  development chapter.  of  of  of to  the  visible  on  the  use  anisotropic irradiance  bidirectional  measurements of  satellite  scattering will  must  be  reflectance  be  data.  on  the  incorporated models  in  the  56  CHAPTER  BIDIRECTIONAL  4.1  REFLECTANCE  MODELS  Overview  In  Chapter  1 it  Earth-Atmosphere  was  reflectance  Thus,  to  due  satellite  an  of  convenience)  investigation reflectance the  a  (as  the is  4.1  land  in shown  in  shows  surface is  the on a  calculated  Section in  3.6.  Figure  procedure.  Normalizing  the  angle  zenith a  division  chapter  by  reflectance attempt  the  it  the  assumed also  above  the  marked clear  are  on  data  to  the  BDR f o r for  the  Throughout  that  wherever  surface  the of  in  (Julian  this  surface  reflectivity interest.  the  day  reflectance  256/79).  satellite  The  calibration  variations  in  the  reflectance  exaggerated  by  the  normalizing  visible the  cosine  SMS-2  describe  correct  includes  the  the  (shortened to  the  resultant  will  the  surfaces.  of  the  variation day  based  accentuates  angle  by of  natural  radiation.  Diurnal 4.1)  because  most  This  implicitly  column  of  study,  to,  reflected  anisotropic  this  which  referred  energy  acceptance  reflected  atmospheric  reflectance found  used  it is  Figure for  narrow  bidirectional  of  the  properties  models  anisotropy  that is  adjustment.  application  from  the  sensor  requires  noted  system  directional  to  4  brightness  extremities of  the  with of  zenith  the  respect curve  angle  to due  which  57  0.08"  09:08  13:08  17:08  L.A.T. (Hours)  FIGURE  4.1  Diurnal P a t t e r n of T a r g e t R e f l e c t a n c e (TR) O v e r a L a n d S u r f a c e For Julian Day 2 5 6 / 7 9 . D e t e r m i n e d F r o m SMS-2 S a t e l l i t e Data. TR i s D i m e n s i o n l e s s .  58  approaches  zero  near  decision  was  the  solar  zenith  The  diurnal  function  of  made  by  the  optical the  to  angle  the  incorporates  sunrise limit is  separation  of  to  the  increases.  of  reason  situations  is  the  column  of  the  two c o m p o n e n t s  not  a  where  surface  but  increases  following is  only  atmosphere  scattering For  this  degrees.  properties  from  these  85  For  reflectance  Atmospheric  length  sunset.  analyses  than  of  anisotropic  scattering  path  the  less  variation  satellite.  and  two  a  also  viewed as  the  reasons  unnecessary  in  this  study.  1)  Given  modelled  under  atmospheric over  each  surface  the  close  clear  sky  scattering of  the  changes  of  conditions  is  likely  surfaces.  reflectance  absolute  proximity  This  patterns in  to  will to  the (see  be  Figure  reasonably  allow  be  surfaces  atmospheric  3.1)  the  consistent  differences  inferred  being  in  despite  the the  reflection  being  relationship  between  indeterminate.  2)  In  satellite removal satellite  development  monitored r e f l e c t i o n of  the  data  Early radiation  the  set  work to  be  atmospheric is  of  and c a l c u l a t e d scattering  unnecessary  using  (see  satellite  Lambertian  the  (i.e.  component  Chapter  data the  transmission  same  from  the the  5).  assumed in a l l  reflected directions)  59  (Bandeen  et  al.,  misinterpretation natural  suggest  the  the  anisotropic variation  of  the  reaching change  atmospheric  bidirectional  reflectance-  non-Lambertian  nature  platform was  of  prevent  a  necessary  nature  of  create  a  Ideally  to  the model  a  such  data  addition, inherent a  of  reflected correcting  which  the  use  necessary of  restrictions  function  of  the  will  viewed area  the  SMS-2 on  are  such  narrowband  the  amount  the  the  while  in  of  the and  optical  satellite to  correct  a  path data,  for  the  energy.  sensors of  the  on  the  of  the  from g e n e r a l i z e d satellite  the  exact  placement yield  of the  (Suits,  computations  BDR m o d e l of  data  Thus  directional surfaces  to  measurements.  every  individual  measured  is in  The  spectral collection  unfeasible. this  visible  In  study  development. the  it  spectroradiometric  1972a).  satellite  satellite  anisotropy.  knowledge  nature  of  surface  changing  used  would context  result  interpret  the  utilizes  geometric  and  the  measure  energy  component  reflectance of  direct  a  all  directional  (in  the  of  with  reflected  on p r e s e n t  .and  reflecting  the  rely  model  character  models  hemispheric  for  is  a  virtually  surface),  brightness  to  assumption  in  Earth's  lead  of  surface  variation  correctly  of  the  scattering  Thus  absence  degree  characteristics  length.  The  some  as  Lambertian  the  in  to  viewed  of  a  would  being  the  nature  reflectance in  scene  suggesting  radiation  reality  use  in  thesis,  This  display  The  changes  this  solar  of  surfaces  reflectance.  of  1965).  has  This  image  is  data  60  when  compared  relatively  low  generalizations  In  the  complexity from  to  the  available of  radj.ati.on data  reflecting  literature  BDR m o d e l s  that  mathematical  which  and  the  necessitates  surfaces.  there  have  spectrum  is  been  a  large  range  developed.  expressions,  such  in  They  as  the vary  that  by  (1972):  a  where  solar  resolution  about  simple  Nkemdirim  the  is  a  a  =  a  0  statistical  exp  (be.)  estimate  (4.1)  of  the  zenithal  sun  o reflection describes angle, and  the  e,  Kopp  based  coefficient rate  at  to  complex  and  Miiller  on  the  and  which  spectral  an  multispectral  as  a  coefficient  changes  of  Suits  and  a  by  with Suits  (1972a,  geometric  vegetation  al.  abundance  Sun  is  of  the  data  from  Miiller  by  of  model  Kopp and  surfaces,  function  1972b)  t o BDR  and  (1981)  1972b)  applied  cloud  al.  (1972a,  scanner.  for  et  zenith  uses  was  the  changing  and  technique  et  which  canopy  simulation  and J a c o b o w i t z  (deg"1)  character  Carlo  Despite Stephen  a  Monte  modelling (1976)  a  (1976).  elements  The  is  n u m e r i c a l models  individual airborne  b  ocean  (1977),  of  clearly zenith  BDR state angle,  respectively.  models that  in  the  BDR m o d e l  satellite  literature, behaviour,  viewing  zenith  61  angle for  and all  work  Sun-satellite but  is  simple  still  azimuth angle,  surfaces  necessary  (e.g.  including  is  still  oceans). the  poorly  A great  adoption  of  a  known  deal  of  standard  nomenclature.  Thus  a  research  project,  the  1) in  various  2) For is  decision  parts  the  with  However, Harrison present  the  the  verification  world;  constraints  angles  satellite  work  BDR m o d e l s  for  this  by  1982b)  of  models  developed  and  and H a r r i s o n  zenith  fixed  develop  reasons:  geometric  Sun  to  the  BDR m o d e l  while  viewing  Tarpley  of  this  influenced  the  models.  (1982a,  study  zenith  (1979)  other  1982b)  requires  a  angle.  and  Minnis  development  and  of  the  BDR m o d e l s .  degree  reflected, Marlatt,  varies 1968;  three  generalized and  a  made  rigorous  Minnis  (1982a,  The  Thus  of  discrete  continuum  two  of  limiting  example, for  for  lack  the  was  cloud  developed  of  anisotropy  for  different  Brennan and  models surfaces  were  and  developed  therefore  A  in  the  snow  this  the  surface  Bandeen,  found  surfaces).  and  1970;  types Stowe  study  was  area BDR  of  energy  (Salomonson et  representing  surface  study  amount  al., each  (i.e.  restricted  1980). of  sea,  model to  and  was  the land not  periods  62  without  snow  infrequency area,  with  but  snow  and  cloud  it  these  land  factors et  the  lack  radiative much  been  is  of  for  clouds  (e.g.  Miiller,  1976),  and  1976).  to  1980)  show  applications,  due  in  to  the  two  the  study  between  cloud  of  the  in  the  variable  distinct  theoretical differences  explicitly  due  to  of  has  nature clouds  the  and  1979),  a  developed  characteristics.  patterns  the  Welch  radiative for  cloud  Kopp and  McKee  (see  and  Cox,  et  al.,  properties  remote top  have  infinite  1970;  (e.g.  studies  depth,  of  complex  been  radiance  " . . .  such  components  empirical  of  of  satellite  and W i t t m a n ,  fields  in  closely  sub  surface  Bandeen,  categories  optical  to  cloud conditions;  and  cloud  of  nature  model  different  atmospheric  heterogeneity  understanding (Liou  satellite  BDR m o d e l s  spatial  reflectance  two  or  reflectance  BDR  finite  cloud  Land  using and  generally  in  the  Brennan  significant  these  is  clouds  two  Also  and  content  cloud  literature  surface  The  generalized  (layer)  of  Sea  definitive  'average'  BDR m o d e l s  incorporated due  properties  1974,  only  present  temporally  study  moisture  a  identified  of  and  variation  1975)  of  the  not  in distinguishing  assume  The  this  the  more  In  to  spatially  However,  representing  is  is  problems  assumptions.  the  al.,  model.  This  cover  development  in  and  the  the  effects.  area  as  (Idso  snow  to  the  such  resolution  ground.  surfaces.  both  approximate the  the  imperative  homogeneity, remove  due  in  is  on  which  also  Ideally data  cover  height,  sensing cloud  63  drop  size  distribution  contributors 1980).  to  Thus,  cloud  reflectance  scope  of  this  cloud  type  models  and  energy  for  clouds.  4.2  Definitions  The  than  assuming  an  of  4.2.  figure  the  directions zenith ray), the  Z, SMS-2  zenith  the  shows  as  solar  and  (which the  is  a  spherical  reflection  is  is  fixed.  of  the  of  the  automated  before  such  data  et  al.  Cloud  sets" (1968)  BDR m o d e l  reflectance  calculating  the  which  reflected  reflection  pattern  zenith also  incorporated  BDR m o d e l s  the  are  depicted  coordinate  and  angle,  Sun-satellite  satellite  angle  cloud  isotropic  distinct  outside  large  the  al.,  Reflection)  visible  of  the  of  is  et  refinement  to  relationships  point  angle  'average' for  (Geometry  it  required  1982b)  important  develop  development are  (1982a,  all  (Welch  F o l l o w i n g Ruff  results  by  to  data  applied  better  development  at  schemes  represents  are  "further  and  1982b).  geometric  This  as  categories  Harrison  here  possible SMS-2  knowledgeably  and  yield  solar  from  geometry  measurements"  be  thesis  Harrison,  Minnis  should  models  these  be  and  developed  may  identification  can  (Minnis  it  present  of  cloud  brightness  although  cloud  definition  and  defines 9 ,  zenith  the angle  Relative  to  the  the  in  system the  the  Figure centred  principal  satellite-viewing of  azimuth angle,  geostationary,  in  the ^ .  reflected Given  that  satellite-viewing  UBC s i t e  (the  centre  64  LOCAL  VERTICAL  FIGURE Diagram of Geometric Relations Sun, e , Zenith Angle of the Sun-Satellite Azimuth Angle, ^ 1982).  4.2 Between Z e n i t h A n g l e of the Reflected Ray, z , and the ( A f t e r M i n n i s and Harrison,  65  point  of  reflection),  (MacDonald  Z,  Dettwiler  has  a  and  value  of  15 d e g r e e s  Associates  Ltd.,  west  personal  communication).  In  the  process while  application  the  Sun-satellite  when forward  degrees. and  present  scattering  The degree  backscattering  positioning  of  also  nature  on  the  effect  of  angles  and  of  a  phenomenon Sun  and  which  Sun, of  due  of  visible  to  the  are  in  surface  and  the  (as  the  the  reflecting  surface  a  close  to  0  ^  at  light  is  solar  a  is  large prime  does  example glint'  when  respect  considerable  to  the the  occulting  distance  not  but  zenith  'Sun  essentially  eclipse  forward  geometric  light  with  180  mirror-like  The of  to  surface,  with  rays.  same p l a n e  some  these  The  sunset  degrees  close  on t h e  surface.  satellite is  is  reflecting  backscattering  the  satellite  important  only  Sun-viewer azimuth angles  satellite  Sun  not  reflecting  an  exhibits  and  surface  is  is  when  surface  satellite  the  scattering  the  a  depends  smooth water  occurs  reflecting  azimuth  significant  effects  the  large  forward  to  is  backscattering  occur  from  at  the  surface).  Figures a  land  and  4.1 sea  and  4.3  surface  surfaces  exhibit  a  and  of  day.  end  contribution problems  the to  show  the  variation  respectively,  marked  forward  Isolation  for  with  the  the  scattering of  the  bidirectional reflectance  associated  in  large  is  reflectance  over  same d a y .  Both  at  the  forward  begining  scattering  c o m p o u n d e d by  solar  zenith  the  angles  66  256/79  0.24-  0.16' TR  0.08'  09:08  13:08  17:08  L.A.T. (Hours)  FIGURE  4.3  Diurnal Pattern of T a r g e t R e f l e c t a n c e (TR) O v e r a Sea Surface for Julian Day 2 5 6 / 7 9 . D e t e r m i n e d F r o m SMS-2 S a t e l l i t e Data. TR i s Dimensionless.  67  occurring  at  length.  This  However, curve  these  times  problem  is  backscattering  around  and  13:00  hours  the  increased  addressed  appears  as  for  land  the  a  in  optical  Section  secondary surface  path  4.3.2.4.  maximum  only  in  (see  the  Figure  4.1).  4.3  Modelling  4.3.1  Data  4.3.1.1  Selection  Land and  The BDR  areas  models  extracted Figure  clear  sky a  Figure areas. areas Two  as  count  3.1  values  x  25  the  value  sea  in  of  used  to  array  count of  chosen over  due  certain  development  of  centred  on  for  clear  labelled and  to  surface  the the  were  UBC  site.  same  array  images  from  four  intuitively,  threshold.  the  Land(N)  sea  They  circumscribed  the  define  and  4.3.1.  values,  was  as  land  forty-nine  (rectangle  labelled were  70  the  Section  pixel mean  area  found The  developing  composite  was  areas  Control  The c o a s t l i n e  (rectangles  land.  25  a  days.  One  land  count  a  on  mean  for  described  presents  based  Quality  Surface  choosen are  3.1  and  Sea  from  size,  using  Procedure  the  parts two  sky  BDR m o d e l l i n g  Sea)  Land(S))  and  two  land  were  selected.  consistently  different  of  the  area  BDR m o d e l s  designated  for  the  land  68  surface  will  models are  are  for  The  same  in Chapter  the  25  constrained sensors  against  each  centred  count  off  degrees  fact  type.  derived  that  This  they  will  be  also  SMS-2  individual resulting by  type  a  visible  small  the  3.4  over  the  degrees  'striping'  the  eight  Thus  the  eight.  This  is  not  calibrated 'striping'.  differences a  in  night-time  Pacific  clearly  count  were  scanner.  Ocean  longitude.  is  low  of  called  is  found  dimensions  are  systematic  Island,  anomalously  by  effect  Figure  selected  distribution  function  sensors  in  were  image at  49  Despite  a  evident  values  the  with,  (sixteen)  for  every  line.  The models  data  chosen  underwent  included  to  develop  rigorous  quality  only  clear  sky  for  cloud  contaminated  inspected values  row o f  the  sub-arrays  divisible  127  target,  a  is  the  surface  are  values.  latitude,  example,  despite  The n o r t h - s o u t h  the  Vancouver  homogeneous  eighth  other,  the  but  the  identified  brightness  independently  surface  of  array.  dimension since  is  25  comprise  north-south desirable  of  likewise,  which  different  dimensions  x  two  5.  constraints  the  these  generalized  east-west  within  This  whether  significantly  the  discussed  under  show  due  to  satellite  the  land  control  conditions.  to  Each  pixels  malfunctions.  and  sea  ensure  image and  This  surface that  selected  erroneous  task  was  BDR they was  pixel  69  implemented  1) and of  in  three  ways:  inspection  bright  of  sunshine  data  and  measured  direct at  solar  the  radiation  UBC s i t e  for  data  evidence  cloud;  2)  visual  COMTAL  image  3)  Most  inspection  processor  inspection  diurnal  the  unusually  large  the  the  (see  above  200/79,  x  25  pixel  occurrence  of  images  cloud;  values  using  the  and  for  spurious  to  days  and  (see  produced images  for  which  to  system  malfunctions  values  these data the  subject  were  used  half  were  retained  the day  were  half  276/79,  Julian  due  brightness  Section  develop  From  data  are  can  be  typically  zero.  manner,  256/79,  addition,  clear  or  4.3)  verification  model.  25  reflectance  since  fourteen  Section  chosen  the  the  erroneous  eliminated  in  the  variations.  of  Of  of  for  of  readily  128  global  4.4).  to  for  012/80,  from 025/80,  and  sea  030/80  was  incorporated  sets  bases, of  Land(S)  121  images  model,  surface  those  and  the  control  BDR m o d e l s  independent  land  data  quality  develop  Images  304/79,  to  model  Julian  days  183/80  were  BDR m o d e l s .  images  in  the  Land(S)  identified  for  the  Land(N)  131  images  for  In  as  model, the  Sea  70  model.  4.3.1.2  Cloud  The  Surface  'general'  a  16x16  pixel  a  larger  array  surfaces  size  but  compared  (see  quality  control  develop  the  also  also  the  Cloud  to  that  for  except  that  complete  cloud  cover.  25  of x  histograms 25  pixel  image.  They  brightness (Figure clear 4.6  is  since cloud  The  it  only  the  sky was  The q u a l i t y from  arrays.  the  pixel  Histograms  (Figure  4.4)  partly  example has  a  cloudy of  an  or  the  pixels  acceptable  small  range  implying  days  finally  a  (see  to  similar Section  conditions  of  included  the  large  for for  the each  ranges  in  distributions of  study  cloudy  cloud  rigorous  produced  presence the  a  values  bimodal  in  other  available  also  for  of  satellite  followed  count  were  values  indicating  were  ensure  control  inspected  both  of  models  to  the  'average'  selection  clear  for  number  days  using  The use  Following  five  The  objective  derived  an  4.3.1.1).  data  developed  used  capture of  was  UBC s i t e .  that  usually  or  an  the  to  result  the  the  on  were  4.5), sky  a  BDR m o d e l .  4.3.1.1)  use  is  to  Section  of  BDR m o d e l  centred  primarily  sensors  criterion  surface  sub-array  is  reflectance,  cloud  undesirable  area.  image  relatively  Figure  histogram, homogeneous  surface.  Julian  selected  for  the  Cloud  BDR  71  5 On  ^  40-  c n  3  30-  20-  o S-  10H  I 72  — i  92  1  112  Pixel V a l u e  FIGURE  i  132  1  152  1  172  1  192  (counts)  4.4  Histogram of Count V a l u e s Showing a Large Spread i n the Data as a R e s u l t of the P a r t l y C l o u d y C o n d i t i o n s . Based on a 25 x 25 P i x e l A r r a y C e n t r e d on t h e UBC S i t e F o r J u l i a n Day 160/80 a t 14:42 L A T .  72  50i  n  .a c  40-  re  3  n •<  30 H  Q. 3  fD 3  20'  o  3  10-  72  — i —  92  — i  112  132  Pixel V a l u e  FIGURE Histogram of Count to a Predominance of Based on a 25 x J u l i a n Day 1 8 5 / 3 0 a t  •>—  152  •  172  192  212  232  (counts)  4.5  V a l u e s Showing a Bimodal D i s t r i b u t i o n C o m p l e t e l y C l e a r and C l o u d y Pixels. 25 P i x e l A r r a y C e n t r e d on t h e UBC S i t e 12:42 L A T .  Due For  73  360T  30(H  ft)  240H  C  fD 3  ~  3  180-  fD 3 O  Z3  120-1  604  i  i  152 Pixel  172  i  192  i  212  i  232  Value(counts)  FIGURE  4.6  Histogram Showing a Small S p r e a d of Count V a l u e s Suggesting R e l a t i v e l y Homogeneous C l o u d C o v e r C o n d i t i o n s . Based on a 25 x 25 P i x e l A r r a y C e n t r e d on t h e UBC S i t e F o r J u l i a n Day 185/80 a t 0 9 : 9 2 L A T .  74  modelling  were  giving  total  a  reflectance count  using  together  with  over  x  a  4.3.2  16  of  363/79,  119  values  values  basis,  297/79,  overcast  were a  target  the  satellite  equation  calibration (see  and  245/80,  'Average'  by c o n v e r t i n g  reflectance,  3.4  197/80  images.  obtained  to  16 p i x e l  185/80,  the  brightness  on a n  individual  curve  (see  Section  3.6)  cloud  pixel  Figure  and  3.3)  averaging  sub-array.  Identification  of  Anisotropic  Reflectance  Characteristics  4.3.2.1  Land  Graphs the  Surface  depicting  selected  surfaces.  with  4.11).  Land(S) Land(N)  strong  includes  4.1  and  and  4.1  in  and  land  4.7,  is  to the  and  4.11  forested  to  to  4.9,  similar and  0.04)  with  the  for  different  follow  with  urban  demonstrate  due  the  consistently  0.03  reflectance  variations  4.8  and  reflectance  areas  compatible  suburban  in for  produces  approximately  suburban  4.7  two  Land(S)  mainly  both  plotted  the  result  of  anisotropy surface  (by  This  consists  Figures  land  values  variation  been  for  Figures  However,  Land(N).  diurnal  have  curves  (compare  reflectance to  days  The  patterns  the  4.10  higher  compared fact  surfaces  that while  areas.  a  summation  characteristics atmospheric  of  the  of  the  scattering.  75  256/79  0.24'  0.16 TR  0.08'  09:06  13:06 L.A.T.  17:06  (Hours)  FIGURE  4.7  Diurnal Pattern of Target Reflectance (TR) O v e r Surface for Julian Day 256/79. Determined S a t e l l i t e Data. TR i s Dimensionless.  the Land(N) From SMS-2  76  304/79  0.32  0.24  TR 0.16  0.08  0 9:19 L.A.T.  13:19 (Hours)  FIGURE  17:19  4.8  Diurnal Pattern of Target R e f l e c t a n c e (TR) O v e r Surface for Julian Day 304/79. Determined S a t e l l i t e Data. TR i s D i m e n s i o n l e s s .  the Land(S) From SMS-2  77  304/79 0.321  0.08  10:19 14:19 L.A.T. ( H o u r s )  FIGURE  4.9  Diurnal Pattern of Target R e f l e c t a n c e (TR) O v e r Surface for Julian Day 304/79. Determined S a t e l l i t e Data. TR i s D i m e n s i o n l e s s .  the Land(N) From SMS-2  78  200/79  0.50i  0.40H  0.301  0.20  o.-^  07:25  11:25 L.A.T.  15:25  19:25  (Hours)  FIGURE  4.10  Diurnal Pattern of Target R e f l e c t a n c e (TR) Over Surface for Julian Day 200/79. Determined S a t e l l i t e Data. TR i s D i m e n s i o n l e s s .  'the L a n d ( S ) From SMS-2  79  200/79  0.60  0.50H  0.40  TR  0.30  0.20  0.10  07:25  15:25  11:25  19:25  L.A.T. (Hours) FIGURE  4.11  Diurnal Pattern of Target R e f l e c t a n c e (TR) O v e r Surface for Julian Day 200/79. Determined S a t e l l i t e Data. TR i s D i m e n s i o n l e s s .  the Land(N) From SMS-2  80  Although of Z  the  these  reflectance,  J>  and  by  were  reflectance  =  90  as  4.12  at  the  contain  data  models.  It  includes  a  Computer  the  strong  solar  time  ±180  i s east the  latter,  the  in  that  the  The  former at  placed  circles  on and  i s thought includes large  centre  north,  and 0  negative  4.12  the  as  where^  and  and  the  isolining  to  4.13  land  BDR  procedure  data  large that  data  also be  on  an  cose  of  such  realistic would  the  (see  UBC  values  zenith  angles.  minimal  at  points has  in a  of  the  denominator,  values  data  close  exceptionally  a  result  the  points  artifact  as  reflectance  removal  i t i s thought  i|» .  'Surfaces').  be  more  the  of  polar  plots  develop  'smoothing'  are  anisotropic  the  Figures  noted  which  at  satellite  satellite.  of  in  circle.  to  abnormally  capabilities  of  the  used  This  of  degrees  imagery  the  angles.  9=0  4.2),  Thus,  8 , and  angles,  degrees  should  procedure  variation  and,  degree  of  two  Section  abscissa.  of  be  emphasis  the  9,  individual angles see  periphery  Documentation,  The  diurnal characteristics the  the  the  plot  of  should  on  show of  Sun  a l l  certain  zenith  modelling the  the  for  incorporation  to  south  creating  undertaken.  of  the  gradients.  thereby  of  4.13  at  periphery  normalizing  importance  to  i s west  Centre  Little  use  and  the  Sun  the  function  p o s i t i v e when  when  to  a  degrees  degrees is  the  illustrate  s i t u a t i o n geometry,  generated  Figures 9  the  ( i . e . the  concealed plots  figures  larger or  not  reduction With  the been  of  the  respect  modification  of  81  180  0  (degrees)  FIGURE  4.12  Polar P l o t of T a r g e t R e f l e c t a n c e (TR) For the Land(N) S u r f a c e , as a Function of the Sun Zenith Angle, e , and the S u n - S a t e l l i t e A z i m u t h , ^ . TR i s D i m e n s i o n l e s s , x 1 Cf2 .  82  FIGURE  4.13  Polar P l o t o f T a r g e t R e f l e c t a n c e (TR) F o r t h e L a n d ( S ) Surface, as a Function of the Sun Zenith Angle, 9 , and the S u n - S a t e l l i t e A z i m u t h , <J* . TR i s D i m e n s i o n l e s s , x 1 0~ .  83  the  data  set  is  recognized  that  insignificant  at  Analogous polar  plots  4.13)  show  the  and  towards  the  increase also  a  the  and  forward  Figures  This  is  1)  a  at  Sun  an  its  greatest  it  is  relatively  in  is  the  seen  of  in  isoline  6 on  Figures gradient  projection.  increasing  zenith  An  angle  was  features  are  (1982a).  anisotropic  reflectance  4.1  to  and  4.7  component to  (Figure  influence  hemispheric  with  Land(S)  the  4.11  4.13,  a  backscattering  (see  Jacobowitz,  show  strong  directional  the  of  towards  end  1981).  the  day.  scattering  from  of:  zenith to  is  angle,  greater  in  situation (this  are  and  1976)  change  b e g i n n i n g and  increase  geometrical  at  due  4.12)  Piatt,  the  4.7  the  function  the  approached  and  when  representations,  The s t r o n g  and H a r r i s o n  scattering  atmosphere  2)  of  Figures  4.1  reflectance  and  dramatic  characteristic from  (Figure  anisotropy  shown by M i n n i s  revealed  is  as  flows  graphical  similarity.  periphery  in  Two  diurnal  (Paltridge  4.13  energy  Land(N)  marked  especially  times.  the the  reflectance  4.12  the  these  of  acceptable  actual  to  a  more  optical  reflection favourable  clearly  and  with  8 is  seen also  increased path  during for  in  lengths;  forward  Figures  large);  the  and  4.12  summer  as  the  scattering and  4.13  is  wheni))  84  3)  the  normalizing procedure.  Another  peak  direction.  This  reflectance after the  same  4.1  to  a  256/79  Figures the  90  backscattering energy been for  away  (1982b),  a  a  4.9)).  suggest  a  plane would  minimum  low  sensor.  developed for  study restricted  In  to  the  Minnis  in  reflection  and  to  a  the  and  in  this  and  radiant have  Harrison  in a  maximum v a l u e  seen  along  T h e BDR m o d e l  forward  due  limiting  (1982b)  in  4.11),  features  However,  Harrison  angle  scattering  by M i n n i s  the  with  minimum  (1970).  in  Figures  (Figure  reflectance  and  are  approached.  direct  angles.  just  secondary  zenith  Similar  Bandeen  a  is  forward to  peak  target  reflectance  tend  Sun  a  zero.  solstice  when  value  as  diurnal  associated  (Figure  304/79  is  increase  progression winter  the  as  to  200/79  ^  general  close  day  configurations, comparison  is  seen  Julian  satellite  at  *  is  in  and  from  surfaces  this  satellite  noon-time  Brennan and  direction of  when  4.11)  larger  4.13  land  suggests  scattering  is  processes  vegetated  to  a  and  by  4.7  Sun,  backscattering  clearly  of  to  the  and  the  the  4.1),  from  most  in  as  transverse  described  nature  show  4.12  degree  the  4.11  increase  (Figure  4.1  plots  consequence  (the  seen  polar  to  occurs  backscattering  backscattering  is  winter  when The  the  4.7  increased This  LAT  on  be  (Figure  plane.  and  reflection  can  curves  13:00  maximum  in  to  the  geometric of  136  results, study  for  52'. the the  85  largest such  ip  angles  is  occasions.  overwhelmed large  by  optical  4.3.2.2  Sea  Based appears  on  a be  zenith  conclusion  is  large  9 associated  minimum  reflectance  using  to  and  in  value as  a  with  would  result  throughout  the  absence  Bandeen  (1970)  component  data  for  an  were  be  of  the  show  a  very  diurnal  shown  there  pattern  in Figures  4.14  of to  seen  with  directionality  of  the  sea  is  indistinct.  of  also  ocean  plot  curved  The  of  latter  reflectance  isolines  detected  only  when a  i> =  slight  surface.  for  Minnis  personal  constraints  weak  year  are  Minnis,  geometric  the  reflection  drawn  (P.  the  hemispheric  the  plots  as  backscattering in  in  the  However  given  the  also  days  surface  increases  model  for  backscattering  and  Harrison's  communication, this  study.  The  component  for  an  minimum a l o n g  the  90  surface.  Figure degree  in  of  sea  confirmed  Hemispheric  ocean  the  due  backscattering  results  any  marked c o n s i s t e n c y  angles.  Brennan  1982)  the  length.  a  4.17),  tabulated  increase  selection  for  reflectivity  0.  the  Noteable  (Figure  of  Surface  reflectance  large  result  Therefore  path  to  4.16.  a  4.17  transverse  displays plane  a  reflectance  comparable  to  that  seen  for  the  land  86  200/79 0.48i  0.40H  0.32  TR  0.24  0.16  0.08  0 7:2 8  '  11:28  '  15:28  '  19^2 8  L.A.T. (Hours)  FIGURE  4.14  Diurnal Pattern of Target Reflectance (TR) Over the Sea Surface for Julian Day 200/79. Determined From SMS-2 S a t e l l i t e Data. TR i s Dimensionless.  87  304/79 0.321  0.24  TR  0.16  0.08'  0  I  ,  ,  ,  •  10:19  L.A.J.  14:19 (Hours)  FIGURE  4.15  Diurnal Pattern of Target Reflectance (TR) Over the Sea Surface for Julian Day 304/79. Determined From SMS-2 S a t e l l i t e Data. TR i s Dimensionless.  88  025/80  0.40  0.32  0.24TR  0.16  0.08'  i • • 09:50 1 3:50 L.A.T. (Hours)  FIGURE  i  » 1 7:50  4.16  Diurnal Pattern of Target Reflectance (TR) Over the Sea Surface for Julian Day 025/80. Determined From SMS-2 S a t e l l i t e Data. TR i s Dimensionless.  89  180  ip  0  (degrees)  FIGURE  4.17  Polar Plot of Target R e f l e c t a n c e (TR) For the Sea Surface, as a Function of the Sun Zenith Angle, 9 , and the S u n - S a t e l l i t e , <P . TR i s Dimensionless , x 1 Cf2 .  90  surface.  However,  minimum  is  present  for  The  area  a  127  to  Ocean is  (Figure  Strait  of  river seem  plume to  4.3.2.3  The from  distinct  4.12  the  surface  0.01 is  the  sediment  plume  to  (Figure  4.18).  thought  than  diurnal  congruent  values  the  49  results.  for  influence  The  (Figure the  of  Le  4.14)  Pacific  difference  turbidity  by A r a n u v a c h a p u n a n d  degrees  A comparison  negligible  greater  the  reflectance  at  Georgia  this  was  plume.  Ocean,  than  4.13).  river  the  of  feature  Fraser  Pacific  Strait  a  this  BDR m o d e l  the  generally  Work  the  and  with  greater  the  a  of  plane,  made  the  It  sea  of  for  the  the  Fraser  Blond  (1981)  hypothesis.  Surface  variation  4.19  diurnal  to  4.21.  in  cloud  reflectance  Figures  4.19  Clouds  are  patterns.  variety  of  reflectance  patterns  due  the  multifarious  nature  to  Figures  reveal  rather  such  diurnal  Figures  4.18  -  to  =0  effects  was  for  itself.  confirm  Cloud  develop  backscattering,  the  longitude  and  Georgia  (see  over  4.18).  attributable  weaker  proximity  degrees  0.005  the  two a l o n g  limit  area  values  be  to  the  4.14  .reflectance  in  comparison an  Figures  to  surface  to  to  for  latitude,  tend  land  selected  due  pattern  split  chosen  However,  of  the  area  carefully  study  not  due  of  (Minnis the  and  can  4.20  known  to  depict  top  seen two  produce  and H a r r i s o n ,  cloud  be  a  1982b)  structure  and  91  200/79  0.24-  TR 0.16  0.08-  07:28  11:28 L.A.T. (Hours)  FIGURE Diurnal Pattern of Surface (Centred at Julian Day 200/79. is Dimensionless.  15:28  19:28  4.18  Target Reflectance (TR) Over an O c e a n 49 Latitude and 127 Longitude) for D e t e r m i n e d F r o m SMS-2 S a t e l l i t e D a t a . TR  92  197/80  0.8  0.6  TR  0.4  0.2  07:26  15:26  1 1:26  19:26  L.A.T. ( H o u r s )  FIGURE  4.19  Diurnal Pattern of Target R e f l e c t a n c e (TR) O v e r a C l o u d Top Surface for Julian Day 197/80. Determined From SMS-2 S a t e l l i t e Data. TR i s D i m e n s i o n l e s s .  93  245/80  0.8'  0.6  T R  0.4  0.2'  i  08:3 2  i  i  1 2:32 L.A.T. (Hours)  FIGURE  •  i  1 6:3 2  4.2 0  Diurnal Pattern of Target Reflectance (TR) O v e r Surface for Julian Day 245/80. Determined S a t e l l i t e Data. TR i s Dimensionless.  a C l o u d Top From SMS-2  94  FIGURE  4.21  Polar Plot of Target Reflectance (TR) Over a Cloud Surface, as a Function Of the Sun Z e n i t h A n g l e . 9 , and S u n - S a t e l l i te A z i m u t h A n g l e , i> ( D i m e n s i o n l e s s , xlO"^ ).  Top the  95  the  associated  patterns  seen  function  of  two  surface  reflectance  In  (McKee  and  (Salomson  area  respect Cox,  and  small  scattering the  data  set  has  strong  largest  azimuth  due  to  is  structure  the  to  to on  be  a  these  reflectance an  important  in  the  and  the  the are  thesis,  early  forward  well  with  latter  cloud  thus  lower  vertical  and  However, a morning  if  a  scattering  The be  the  subtle  hours  the  Due study  very  approached. to  clouds  1970).  Pole,  likely  The  structure  layer  Bandeen,  especially  forward  documented.  satellite  not  suggests  and  regarding  North  not  therefore  4.2),  been  fields  between  structure.  the  lower  e  B r e n n a n and  angles  this  Figure  a  backscattering  the  1968;  is  in  around  (see  reflectance  and  relative  used  likely  structure  shadowing  have  cloud  1976)  vertical  reflectance  surfaces to  component  of  vertical  both  azimuth angle  Sun-satellite  top  trend  greater  are  reflectance  4.19).  Marlett,  measured  4.20  suggests  any  literature cloud  different  in cloud  angle,  in  Figure  from  with  the  results  and  general  9 increases,  the  former  to  zenith  (see  scattering  the  The  4.19  differences  increasing As  effects.  Figures  However  control. top  in the  days.  with  shadow  component.  forward  seen  from  cloud  also  increase  when i> i s  possible  large  at  increase  in its in  9 6  4.3.2.4  Summary a n d C o m p a r i s o n o f  Land,  Sea  and Cloud  Surface  Reflectivity  The  satellite  visible  energy  inherently component the  inferences  to  be  are  made  surface,  U-shaped.  assumption  of  Sea  Backscattering (see  Figure  surface  is  when  the  Harrison, the  sea  of  patterns  Sun  and  1982b). surface  is  of  Figure  clearly -  land  may  surface,  probably  a  are  3.1)  for  an  of  -  4.11  land with  the  land  the  to  these  two  land is  aligned  the  areas.  surfaces  probably  maximum i n to  absence  sea  develop  justifies  the  its  and  for  used  backscattering  function  allow  for  attributed  creating  indistinct  sites  relative  be  sensor  4.7  therefore  This  viewing The  and  surfaces  sea  and  between  evident  4.11)  reflection  three  reflectance  homogeneity  is  Comparison of  the  W-shaped,  (see  the  It  4.3.2.3)  4.1,  BDR  direction the  for  the  models  system.  the to  of  components.  Figures  pattern  phenomenon.  backscattering  for  The p r o x i m i t y of  4.7  measure  component.  two m a j o r  (compare  only  4.1,  induced  structures  these  atmospheric  a  surface  4.3.2.1  characteristically  and  are  the  described  The d i u r n a l  are  Land  scattering  reflectance  surfaces  the  for  study  Earth-Atmosphere  Sections  similar  4.16).  this  separate  patterns  overall  surfaces -  to  and atmospheric  (see  in  the  difficult  reflectance  The  used  leaving  investigated  4.14  data  a  the  vertical of  shadows  (Minnis  and  component  of  greater  specular  97  nature  relative  The to  the  is  136° of  large 52'  the  degrees,  the  diurnal  two  features  1)  the  2)  On  a  4.20),  the major  between  the  which  for  study  forward of  the  land  the  greater  and  an  winter  sharp  and  this  increase  scattering  in  which  are  other  patterns  independent  by c o s  optical  path  atmospheric  hand  cloud  reflectance reverse  tops  maximum o f a  function  approach cannot  is  same  90 be  probably  feature  is  The e x t r e m i t i e s  of  a  normalizing  lengths  at  increasing for  probably  and  As  c o m b i n a t i o n of  <P :  reflectance  that  is  the  be  the  procedure;and  large  zenith  angles  patterns  show a  marked  scattering.  with  of  contrast cloud  9 in  surface.  of  It  the  at  normalizing  not  process.  could  a  reflection  sea  reflection  accounts  surfaces.  the  8 does  the  and  difficult  may be  of  phenomena as  land  sea study  reflection  when  it  reflectance  artifact  months  make  scattering  the  reflectivity  greater  in  this  maximum ( f o r  forward  division  the  decrease  This  to  increased  producing  a  observed  both  the  the  day  at  angle  surface for  a  achieved)  In  attributable  seen  is  to  of  appearance  end of  zenith  a  degree  when  was  surface.  constraints  the  and  procedure.  not  land  exponential  beginning 9  a  geometric  determine  for  to  the  e  the due  Earth's  (see  land  to  Figure  and  sea  elevation  surface.  4.19  and  surfaces. differences  The h e i g h t  of  98 the  cloud  influence  on  With surface length  top the  to  the  Earth's  smaller.  such  atmospheric different  reflectivity  brightness pattern  the  ground  cloud  top  surface  times  geometrical the  of  occurs  offset  procedure  and  the  the  especially  encountered  cloud  optical  as  below  top path  reduced  the  major  typical  cloud  dominates  resulting  in  sunset  are  over  the  a  marked  cloud  surface  end  sunrise later  dealing  of  a  and  sunset  Earth's  with  using  surface high. the  with  day.  respectively.  determined  relatively  associated when  of  and  the  the  and  time  earlier  appears  problem  the  influences  between  reflection  a  substantially  beginning  surface,  sunrise  a  its  pattern.  the  relationship cloud  in  to  brightness.  surface,  reflectivity  also  at  due  when m o n i t o r i n g  component,  reflectivity  scene  occurs  surface  to  the  and  results  scattering  scattering  scene  reflectivity  component,  cloud  diurnal  Compared  This  scattering  Thus  well  length  relative  heights.  Sun,  path  former,  of  As  optical  the  proportion  a  scene  to  atmospheric  for  the  respect  is  The  effects  the  and  the  This  may  normalizing  the  two  Earth  surfaces.  Inter the a of  image  cloud  surface  function the  fluctuations  non  of  than  for  variable  linear  in  the  cloud  satellite  reflectance land top  and  sea  structure  calibration  appear  greater  surfaces. and  a  curve  This  for is  consequence (see  Figure  99  Changes  3.3).  brightness greater  count  change  relatively  small  of  the  major  surface  2)  the  the  the  3)  reflection  is  optical  4.3.3  The  values  the  may  be  result  reflectance (typical  nature  of  cloudy  data  inferred  large  of  the  in  a  than  for  clear  sky  calibration  sets.  from a  comparison  patterns:  a  at  surface  large  induced  zenith  procedure  difference  between  patterns at path  Development  4 . 3 . 3 . 1  target  scenes)  for  and  phenomena;  angles  is  a  increased  function  of  atmospheric  and  reflectivity attributed,  in  same m a g n i t u d e  cloudy  exponential  'noise'  instability  of  count  conclusions  normalizing  scattering;  the  the  backscattering  1)  the  calculated  brightness  greater  of  (typical  the  Thus  produces  Three  brightness  values of  conditions). curve  in  least and  of  in  at part,  increases  Earth  surface  large to the  cloud  and  zenith height  cloud  angles which  i l l u m i n a t i o n of  the  surface can  be  decreases scene.  BDR M o d e l s  General  specular  tendencies  of  natural  surfaces  have  been  well  100  documented and  in  Marlatt,  1970;  the  set and  1976;  data  SMS-2  of  characteristics of  used  To  satellite  solar  the  is in  combine  it  with  of  the  reflected  energy.  measure  reflected  energy  BDR  attempt clarity modelling BDR m o d e l  The  an  remove  of has  the been  to  directions,  in  et  influential  a  reflecting the  found  4.3.2).  in  small  surface  reflection the  suggest  diurnal  changes  error  measure  is  one  in a  SMS-2  radiometer  the  the  character  developed  does  in  field.  approach  following  and  not  simultaneously.  reflection  (1981)  all  reflected  measurement  directional  been  in  the  the  al. on  energy  directions  in  been  reflected  make  have  anisotropy  Stephens  of  all  techniques  the  to  The  Similar  ,  energy  or  has  resultant  either  understanding  modelling to  of  Bandeen,  Section  when  data  The  amount  and  Lambertian  reflectance  necessary  all  be  anisotropy.  energy  Thus  to  column. of  (see  the  Salomonson  1979).  upwelling  uniform,  degree  it  study  remain  determine  directions  this  samples  assumed  Brennan  surfaces  may are  the  natural  in  1967;  Dirmhirn,  Although  the  of  1968;  angles.  Earth-Atmosphere  function  al., and  for  Bartman,  solid  atmosphere  the  Eaton  set  (e.g.  et  satellite  confined  pattern  Ruff  reflectance  SMS-2  The  literature  1968;  Kriebel,  anisotropic for  the  to  description  an The BDR of  development.  SMS-2  radiometer  measures  reflected  shortwave  101  radiation 9-,  Sun-satellite  angle, the  NR(8, ^ ,Z)  Z .  The  K  is  is  mean  given  estimated  the  =  ,  type  is  make  this  measurements  following  limitations  do  4.3  performed  and  for  be a  given  and  /  angle,  viewing  zenith  reflectance  at  (TR)  (4.2)  COS 8  TR i s  not  that change,  an  over  0  S  by  9  a  =  anisotropic all  albedo.  directions  for  a  from:  d C O S 8 d i>  *  (4.3)  scanning  radiometer  require  4.3.  an  in  the  Thus a  both  the  part  of  satellite  modified  surface  integration  zenith  I  d  inherent  covering  satellite  TR*( K)  C  impossible.  Assuming  conditions can  equation  integration  required.  zenith  COS 9  oJoY?d  angular  target  N R ( K , 6 ,<J> , Z)  TR (K)  The  satellite  calculated  r 2  integration  solar  by:  radiance  zenith angle  reflection  the  the  instantaneous  r2Tr  True  and  of  NR(K,6v*,Z)  surface  reflected  solar  function  measured  TR(K)  where  a  azimuth,  The  satellite  as  the  and  similar total  data  set  approach  is  atmospheric to  equation  hemisphere,  TR*  angle:  I NR ( K , e , +, Z) cos  dedip (4.4)  102  where  'L'  used  in  over  covers the  which  the  limits  integration.  integration  is  for  that  Dividing  possible  part  Equation  TR (K )  where  TR*  approximates (K)  is  therefore  To  convert  J  the  the  and  such  =  L  J  JJ  mean  4.4 by  the  (4.5)  TR a  reflectance  reflectance  value  value. for  a  allowing  a  true  =  surface  TR.  function  estimate  TR(K)  of  TR(K)  p(K,e,*,Z)  is  introduced  the  /  TR*( K )  *  reflectance  =  TR (K ) /  TR (K)  ( K , 9 , <P , Z )  function. will  TR be  is is  defined  known  as  TR(K)  a  essentially as  TR'.  (4.6)  by:  p(K,9,KZ)  hence  TR*  that:  p ( K , 9 , *, 2 )  The  area  dedip  d 9 d *  target  approximates  to  hemisphere  COS 9  Lambertian  TR  the  gives:  NR ( K , e , <l>, Z )  *  of  bidirectional a  (4-7)  reflectance  BDR c o r r e c t e d  (BDR)  TR v a l u e  and  103  Due  to  the  developing surface  the  BDR  following  4.3.3.2  developed  (e.g.  technique  For  the  multiple were  the  observed  The  4.7  and  the  polar  and  4.17).  geometrical  -diurnal  of  the  are  described in  4.14  surface  to  the  routine.  selection  was  followed and  separately  cloud in  the  Modelling  investigated The of  to  plots  target  4.16) of  and  based  positioning  on  were  trigonometric  which  both  using  known  visually  second  reflectance  Various  on  technique  the  curves  based  the  reflectance  target  functions  in  first  diurnal  those  the  in  4.3.3.3).  patterns  trigonometric  and  outlined  BDR m o d e l s .  4.11  functions  for  sky  former,  The  models  were  to  fit  BDR  Reflectance  diurnal  regression  set  and  the  4.13  best  fit  depicted  clear  using  tested.  dependent  be  approaches  4.12,  satellite, provide  (4.3.3.2  incorporated  Figures  will  Surface  the  Figures  (e.g.  Sea  procedures  surface  they  similar of  different  sky  sections  Land and  development was  clear  model,  two  Two  slightly  the used  a  Sun, to  stepwise functions  physically  resembled  the  patterns.  trigonometric  land in  and  sea  Table  Figures  functions  surface 4.1.  4.22a  and  which  diurnal  The  forms  4.22b.  produced  reflectance of  The  the  the  patterns  functions  - c o s e and  best  the  are sine  104  TABLE  4.1  Trigonometric Functions used to Model Diurnal Reflectance P a t t e r n s f o r S u r f a c e s Under C l e a r Skies. The V a r i a b l e s are L i s t e d in Order of I m p o r t a n c e ( i . e . the Order in Which the V a r i a b l e s Appeared i n the Stepwise Regression). Land(N)  Land(S) 2  sin  e  tan  -cos  cos e  8  Sea 2  0  sin  e  c o s i>  tan  9  9  tan  9  -cos  -cos  9  sin  e/2  105  (a) 1.0,  L.A.T.  (Hours)  Cos 0 •Sin ( 6 / 2 ) Sine C o s ^ •Tan 9  (b)  16  12 u.  Z  OO  81 *> LU  12 L.A.T. ( H o u r s )  FIGURE  16  20  4.22  Form of the Four T r i g o n o m e t r i c F u n c t i o n s and Land Diurnal Reflectance Patterns. F o r J u l i a n Day 1 8 3 / 8 0 .  Used to Model the Sea V a l u e s Were G e n e r a t e d  106  cos  ^  terms  the  Sun's  have  changing  backscattering anisotropy. land  to  surface  of  in  inclusion  The  was  However,  The  of  while  latter  sine  /  2 term  The  is  =  -  were  this  model  to  known  in  the  equations  0.2442  the  sea  cos 9 -  of  the  over  the  function  was  for in  a  have  land  Tarpley's  included  to  in  the  a  third  negligible  number  of  cases  performance.  tanZ  and  -sine  the  90  physical surface  /  2  are  exponential  e approaches  adequately Sea  only  highlights  has  For  and  functions,  little  this  found  model  former  only  4.14)  Tarpley  was  the  discernible  incorporated  when  patterns.  0.3604  and  for  both  components  only  reflectance  found  following  reflection  TR  the  is  accounts  simulates  importance  statistical  trigonometric  former  latter  equation.  detrimental  appearance  the  4.1  terms  brightness  semi-empirical.  the  Figures  Both  The  scattering  statistical  the  other  and  backscattering  c o s ip .  cos e  basis.  forward  (compare  be  importance its  Since  minimum  term,  intensity  models.  (1979)  physical  and  surfaces  found  a  degrees,  basis.  The  model.  replicate  the  diurnal  surface:  0 . 3359  sin9/2  +  0 .0086  tan 6 (4.8)  for  the  TR  =  Land(N)  0 . 0892  -  surface:  0 . 0355  cos 9 +  0.1002  sin9  COS <JJ 2  +  0.0082  tan 9 (4.9)  107  and  for  TR  =  the  Land(S)  0.1236  -  surface:  0.0400  cos 9 +  0.1045  sine  c o s 2 <Jr+ 0 . 0 0 7 8  tan 9 (4.10)  A  comparison  of  using  the  equations  4.2)  show  above the  competent. very  the  land  However  predicted and  surface the  target  the BDR  reflectance  actual  values  models  performance  of  to all  values  (see  Table  the  most  be three  models  is  BDR m o d e l s  by  satisfactory.  Equations applying  4.8  the  following  to  4.10  functions  the  were to  integration  used  to  develop  hemispherical procedure  coordinates  outlined  in  and  Section  4.3.3.1.  An  alternative  more  statistical-empirical The more  second  reflectance. reflectance integrated  graphically  less by  the  (e.g.  in  Figures  one  plots  the  to  to  the  4.12,  to  preceding  also  developed.  and the  4.13  the  areas  solar  a  anisotropic  and  target  4.17)  were  in  Section  are  depicted  Land(N), where  underestimation  reflected  provides  uncorrected  factors  for  Those an  the  outlined  ,z)  4.25  was  for  procedure  4.23  correspond due  of  p(K,9,  than  empirical  accounting  respectively.  satellite  procedure  Figures  resulting  areas,  than  in  Hemispheric values  approach  completely  approach  The  Sea  is  following  4.3.3.1.  and  modelling  technique  expedient  direct  of  rho  Land(S) (p) i s  reflection  radiation  being  108  TABLE Performance of the Clear Sky Target Reflectance (TR). Values  Land Mean  of  TR  Standard Deviation  of  TR  Coefficient of Determination  Standard Error o f TR  (r2)  (N)  4.2 BDR M o d e l s i n R e p l i c a t i n g are Dimensionless.  Land  (S)  Sea  0 . 1 231  0 . 1 569  0 .0888  0 . 0260  0 . 0268  0 .0246  0 . 865  0 . 878  0 .738  0 . 0097  0. 0095  0 .0128  the  109  180  0  ip (degrees)  FIGURE BDR Model (Dimensionless,  For the x i O " 1 ).  4.2 3  Land(N)  Surface  Using  p  Values  110  FIGURE BDR Model (Dimensionless,  For the X10~1).  4.24  Land(S)  Surface  Using  p  Values  111  180  0 t|) ( d e g r e e s )  FIGURE BDR M o d e l F o r t h e S e a ( D i m e n s i o n l e s s , x 1 0" 1  Surface ).  4.25  Using  p  Values  112  directed needs  away  to  be  Equation  is  reduce the  surface  and  4.3.3.3  Cloud  Due  clear remove cloud to  atmosphere  Surface  the a  the  by  modelling  days  These plot  and  the a  to  be  Figure  A  comparison (TR)  than  by  Thus  the the  (see  one, rho  rho  the  value values  of  the  Earth's  of  clouds  of  the was  approach  used  for  adopted.  In  order  to  geometry  of  resulting  from  data  plots.  the  were This  second  data  (see  smoothed  the  prior  was  implemented  order  polynomial  for  each  applied  to  of  the  five  4.26).  functions generated Section  between based  greater  properties  simple  (see  in  rho v a l u e  properties  reflectance  reflectance  outlined  reflectance  Modelling.  development  the  procedure  the  division  radiative  relatively  rho v a l u e s  target  removed.  Reflectance  the  by  appropriately.  hemispherical  polynomial  reflectance  thus  variability  surfaces,  function  and  the  rho are  simplification  complex  fitting  to  model  developing  of  reflectance  complex  BDR  top  values  reflection  Thus  dividing  overestimating  4.1), sky  by  anisotropic  to  Section  satellite.  When  the  enable  the  increased  4.7).  satellite will  from  on t h e  were (see  Figure  a  4.27),  hemispherical following  the  4.3.3.1.  the second  mean  integrated  order  polynomial  target fit  and  113  363/79  0.8i  0.6-  TR  0.4  Target Reflectance •  ' 2 n d Order Polynomial Fit  0.2  09:30  1 3:30  17:30  L.A.T. (Hours)  FIGURE  4.26  Diurnal P a t t e r n of T a r g e t R e f l e c t a n c e Over a C l o u d Top S u r f a c e for Julian Day 363/79 and a Second Order P o l y n o m i a l F i t too the Data. Detrmined From SMS-2 Satellite Data. TR i s Dimensionless.  114  BDR Model (Dimensionless ,  For x 1 0" 1  a ).  FIGURE  4.2 7  Cloud  Top  Surface  Using  p  Values  115  the  'raw'  values, the  target  0.6389  second  overall  and  order  0.6403  the  individual  noise  Verification  the  of  the  against  development  provide  which  constraints  of  selected.  For  same  and  data  of  cloud  surface  suggests  that  describing  cloud  surface  reflectance  sea  model,  that  data  361/79,  excluding  be  set,  surface  the  require  can  the  while  values  for  was  model an  the  is  replicates  independent  data  Given  the  data  were  following  model,  days  verification  tested.  030/80,  contamination),  verification  Julian  days  196/79,  121/80,  were  chosen.  293/79 used  and  to  030/80  verify  (as  both  a  the  data  adequately  set  tests  provides  good  the  range  full  temporal of  coverage  Sun-satellite  positions.  Figures the  the  similar  BDR m o d e l s .  therefore  geometric  model  293/79, set,  a  procedures  available  the  of  evidence  the  the  257/79,  The  with  This  in  BDR M o d e l s  Verification  land  resulted  adequately  associated  reality.  result  is  of  to  The  fit  characteristics  necessary  255/79,  (TR)  images.  Following  set  data  respectively.  polynomial  reflectance  ignoring  4.4  reflectance  measured  4.28  to  diurnal  4.30  show a  target  close  correspondence  reflectance,  TR ( t a k e n  between from  the  116  0.24  oTTil  '  11:55 L.A.T.  the  Sea  77! 5 5  '  (Hours)  FIGURE Verification of is Dimensionless.  15^55  4.28  BDR M o d e l  For  Julian  Day  196/79.  117  FIGURE Verification of the TR i s Dimensionless.  Land(N)  4.29 BDR M o d e l  For  Julian  Day  121/80.  118  196/79  0.4CH  0.32-  0.24' TR  0.16-  0.081  i  06:55  i  i  FIGURE Verification of the TR i s D i m e n s i o n l e s s .  i  i  i  10:55 14:55 L.A.T. (Hours)  Land(S)  i  18:55  4.30 BDR M o d e l  For  Julian  Day  196/79.  119  verification from  data  equations  prediction 0.010  for  and  the  shown  and  4.8  to  the  complete  4.3  verification.  in  Table  4.2  verification the  Sea,  provides  These  and  predicted  The S t a n d a r d  for  Table  the  4.10.  0.010  respectively. for  set),  Error data  a  fuller are  values, of  set  Land(N)  results  therefore  model  the was  and  set  model 0.012,  Land(S),  of  statistics  comparable  indicate  TR,  to  those  satisfactory  model  performances.  Verification overall  model  procedure  Figures except This  for was  radiation the  model  and  of  the  model  negative  to  those  situations  these  4.33  as  becomes  (see  modelled  to  Figures  errors  target  the  observed  model  that  the  9 is  near  formula  of  for  under  minor  4.33).  reflectance.  show  relatively  are  to  to  when  revealed  4.31  areas  the  are  of  plots  overestimation  unstable  quantities  sky  hemispherical  subtraction  4.31  these small  of  the This  target  Positive the  target  underestimation.  model its  performs maximum  calculating  value. target  conditions. when  importance  the to  Since  Sun the  well  is  low  overall  performance.  Verification due  the  expected  reflectance  in  from  the  correspond  reflectance  the  capabilities  involved  reflectance areas  using  to  a  lack  clouds  will  of of  the data.  likely  cloud  surface  The t e m p o r a l result  in  a  model and  was  spatial  not  possible  variability  deterioration  in  the  120  TABLE  4.3  V e r i f i c a t i o n S t a t i s t i c s f o r t h e C l e a r S k y BDR M o d e l s . Where TR is the 'raw' Target Reflectance, and TR i s Estimated Target Reflectance U s i n g t h e BDR M o d e l . V a l u e s Dimensionless.  Land  (N)  Land  (S)  Sea  Mean  of  TR  0 . 1 178  0 . 1518  0 .0865  Mean  of  TR  0 . 1 180  0 . 1 543  0 .0845  0 . 0236  0 . 021 9  0 .0227  0 . 0217  0 . 0236  0 .021 5  C o e f f i c i e n t of Determination (r2)  0 . 8036  0 . 8238  0 .7121  Standard Error o f TR  0 . 0097  0 . 01 00  0 .0116  Standard Deviation  of  TR  Standard Deviation  of  TR  the are  121  \jj ( d e g r e e s )  FIGURE Verification (TR Model U s i n g p Values  4.31  TR) Polar Plot For the (Dimensionless, xlO"1 ).  Sea  Surface  BDR  122  FIGURE Verification (TR TR) S u r f a c e BDR M o d e l U s i n g  4.3 2  of the Polar P l o t For the Land(N) Values (Dimensionless, x 1 0"1 ).  123  180 90  /*  L*  Px  \  0  X  V,  f " I"  • ')  I  *  —"^l  •  "  * \  "  •  •  r  "  • " \  *  «  •  M  » • " S /  •  •)  ' II  M  y  /  / /  /  0 ip (degrees)  FIGURE  4 . 3 3  Verification (TR TR) of the Polar P l o t For the Land(S) S u r f a c e BDR M o d e l U s i n g p V a l u e s ( D i m e n s i o n l e s s , x 10" ) . 1  124  performance  of  surfaces.  Verification  improve  4.5  and  factor, (see was  the  such  as  Harrison also  target  section  and  the  to  forward. reflectance  Thus, necessary  the  (see  study  incorporates  more  comparing  that  satellite  reflectance  r h o ( K , 9, ip, Z)  the  estimate  BDR a  the  is  models  cloudiness  derive  such  of  the  Sun,  satellite  for  the  time  of  a  correction  1981)  and  with  a  are  direct  parameter,  described  two  'chi'  approach  more  fundamental  in  this  techniques  'predicted'  each  applicability is  the  To  determine  to  are  5.  function,  positioning  a  conceptual  the  suggests  before  necessary  using  al., a  Both approaches  determining  to  et  along  a  Earth  Data.  applied  Such  is  for  BDR m o d e l .  Satellite  Stephens  that  model  Cloud  1981).  this  to  cloud  the  However,  brightness.  to  to  results  4.7  the  invariably  reflectance.  Equation  calculated  in  relative  present  Minnis,  in Chapter  correction  the  are  latter  and  presented  of  'rho'  adopted The  model  BDR M o d e l s  corrections  method. the  BDR  substantiate  Applying  BDR  the  an  relatively  correct  complex.  can  be  index index,  target  the  the  reflecting  satellite  straight  utilized from  image  reflectance  a BDR  bidirectional  more  and  of  it  is  satellite  geometrical surface and  are  (TR)  are used  for  a  125  cloudless  sky  and  an  extracted  from  reflectance  (Figures  for  partly  1) partly  the  classed  as  being  Therefore value  overcast partly  cloudy  an  partly  of  in  the  the  index the  reasons:  under  that  ,  45% c l o u d i n e s s  this  assumed  given  assumed  index  The  target  are  TRc =  continuum  the  utilized.  be  and  (TR)  index.  can  This  a  and  example  reflectance  a  and  (TRc)  0.15  have  by c l e a r  is  to  to  overcast  depicted TRo = of  be  linear  0.4  in 0.7, is  determined  using:  C  the  cloudiness  values.  satellite  C is  on  clear  observed  where  plot  radiation  presented  predicted  that  mathematically  two  conditions  were  where  was  indicates  a  cover  extremes  To e s t i m a t e  reflectance  to  target  A polar  for  reflected  conditions  4.34  equivalent  the  of  4.21).  produced  cloud  cloudy  BDR o c c u r r e d ,  target  not  plots  are  and  between  between  and  predictions  cloudy.  cloudiness  relationship  Figure  partly  conditions.  The  (TRo)  nature  range  intermediate  was  These polar  4.12,4.13,4.17  conditions;  large  sky.  appropriate  conditions  complex  cloudy  2)  the  cloudy  the  overcast  =  100  (Tr  cloudiness  -  TRc)  index  as  /  (TRo -  a  TRc)  percentage.  (4.11)  126  FIGURE The Relationship Cloudiness Index.  Between  the  4.34 Target  Brightness  (TR)  and  the  127  Six based  models on  rho  determine index the  were  a  values  models the  has  B and  C have  two  changes  demarcations,  defined  allow to  sky  (or  for  approach For  in  with  when  the  sky  Models  B  C were  Model  B  in  sky  is  (Figure  between  CTc and C T o ) , w h i l e as  if  cloudy  they  of  a  et  small  but  also  i n an  some  incorporates  model  were  C  may  and  not  1980,  be  used  based in  the to due this  model).  the  would  to  pixel  produce  a  alleviate lesser  (defined  (Figure  completely  two  a  cloudy correction.  attempt  conditions  These  (CTc)  increase clear,  of  incorporated  that al.,  while  gradient  4.37).  were  of  However  4.35),  the  physically  completely  4.36)  the  (CTo),  brightness  a  developed  and  both  linear.  Figure  To  cloudiness  using  threshold  (Gautier  A,  outside  conditions  the  correction,  partly  sky  the  each  where  4.36  being  reflectances.  are  points  clear  BDR, t h r e e  from  (see  threshold  model  clear and  the  target  tested,  Figure  development  mainly  problem.  as  for  functions  cloudiness  their  example,  brightness  the  were  gradient  (see  overcast)  in  using  threshold  fluctuations  changes  correct  reflectance  three  constant  function  cloudy  three  forms  A l l  a  to  target  functional  approaches. A  and  corrected  three  model  developed  as  4.37) clear  gradient the  treats or  this  zone these  completely  cloudy.  Fluctuations likely clear  to sky  be  a  in result  conditions  brightness of  changing  these  may  for  overcast  cloud be  conditions  thickness,  due  to  while  variations  are  under in  the  128  MODEL A i 20  60  100  CLOUDINESS INDEX (%)  FIGURE Derivation Cloudiness  of a Corrected Index ( D e t e r m i n e d  4.3 5  Target Reflectance (TR') F r o m t h e From F i g u r e 4 . 3 4 ) U s i n g Model A .  129  FIGURE Derivation Cloudiness  of a Corrected Index ( D e t e r m i n e d  4.36  Target Reflectance (TR 1 ) F r o m t h e From F i g u r e 4.34) U s i n g Model B.  130  1.0,  20  60 CLOUDINESS  FIGURE Derivation Cloudiness  INDEX  100 (%)  4.37  of a Corrected Target Reflectance (TR') F r o m t h e Index ( d e t e r m i n e d From F i g u r e 4.34) U s i n g Model C.  131  aerosol  optical  under  overcast  due  the  to  The on  clouds  clear  cover.  values  the  mean  of  used  to  over  the  aerosol  may  and  than are  as  importance  high  brightness  0% a n d  in  the  based  predicted than  and  an  BDR m o d e l s  dashed  are  Departures  greater  valid  signal.  limits  conditions.  still  a  minor  induced  overcast  result  extend  (depicted  of  relatively  clear  less  is  the  overcast  occurrences  was  values  of  latter  as  conditions  Such  procedure such  dominates  and  average  reflectance  The  conditions  positioning  mean  the  depth.  line  target  100%  cloud  extrapolation to  in  from  incorporate  Figure  4.34  to  4.37).  The are  final  given  in  threshold  the  partly  The within only  used  Appendix  3.  equations  deriving and  equations  corrected  cloudy  BDR the  the  chosen  the  count  for  the  test  site.  in  of  site  at  are  all  In  to the  BDR m o d e l s  the Point  the  (see  each  overcast  the  equations  for  clear,  pixel  initial  for  cloudy  sky  The  former  BDR m o d e l s  approximate  Figure  separately  investigation  tested.  clear  area  and  models.  were  other  Land(N) Grey  and  three  BDR c o r r e c t i o n s  clear  reflectances  applied  to  the  the  B and C ,  interest.  preference for  for  is  and C l o u d  values UBC  model  conditions  area  determine  Listed  target  correction  Land(N)  was  for  to  3.1),  those the  as  seen  initial  132  In which  summary,  a  BDR  model  is  a  two-fold  process  entails:  1)  determination  satellite  2) of  applying  a  brightness;  use  of  clear  satellite  The  this  may  relationship radiation presented  index and  to  cloudiness  apply  the  correct  cloud  correction  with  the  illustrated  between  the  of  from  the  to  proportion  the  original  value.  transmission. in  a  associated be  degree  and  correction  benefits  the  cloud  brightness  correction  of  following  by  satellite The  the  impact  brightness  results  chapter.  inclusion  of  it and  this  of  a  has  on  BDR the  shortwave  analysis  are  133  CHAPTER  RESULTS:  FIVE  IMPACT OF ADJUSTMENTS  TO T H E S A T E L L I T E  DATA  5. 1 I n t r o d u c t i o n  This  chapter  transmission assess  (T)  the  and  impact  development The  of  adjustments  spatial  averaging  (Section  to  requirements  differences  standard  these  error  of (r2)  'SE'  standard  the is  is  "the  prediction "the  accounted  Other  for  by  presented data  temporal number  site  to  have  is  (SE)  relationship  deviation has the  of  been  total  regression"  quoted  sum  to of  (Hicks,  are  5.2.  hence  TR,  the  to  5.3),  (Section  made  images of  some  the  of  the  using  the  approach.  the  errors  fitted  Section  satellite  between  the  The  averaging  is  to  data.  determined  and  (TR)  (Section  highlight  adjustments  the  and  of  comparison  estimate  in  correction  this  of  statistics  each  shortwave  satellite  from  for  linear  the  evident  equation  proportion  a  between reflectance  satellite  the  for  the  determination  is  5.4),  Finally,  climatological  to  reflectance  for  developed  impact  the  (Section  relationships  The  target  relationship  bidirectional  5.6).  relationship  adjustments  applied  a  and  the  satellite  of  the  include  5.5)  uses  the  coefficient T and  TR.  remaining data"  squares  of  after  and  that  The  'r  can  ' be  1982).  constant  (a)  and  134  coefficient  (b)  respective presented spatial  because  Given  the  do  the T  provide  5.2  they  TR,  have  a  (SE  have  analyses  empirical  and  those  regression  errors  temporal  results  that  the  standard  and  between  of  a  and  (Sections  of  with  b).  and  their  These  implications  5.4  the  along  SE o f  important  nature  i n most  of  line,  for  relationship  developed  physical  explanations  Further,  it  been  offered.  presented  are  somewhat  basis  for  further  Development of  the  Relationship  the  5.5).  instances  not  are  is  speculative.  for  recognized  However  they  investigations.  Between  Transmission  and  Reflectance  Due  to  the  processing based  on  from  a  the small  throughout  256/79, and  of  297/79,  157/80).  cloud data  cover set  target centred  high  satellite data  the  030/80, These  investigate  the the  This  was  UBC impact  (i.e.  chosen  ranging  from  hourly  pairs  116  calculated  ten  to  of  using  and  of  BDR c o r r e c t i o n  days  to  variety  The  7 x 7  same a r r a y  245/80  overcast.  data.  size  applied  of The  satellite  pixel was to  was  200/79,  225/80, a  the  selected  days  provide  clear  with  analysis  Julian  196/80,  site a  the  initial  comprised  153/80,  were  associated  the  year  143/80,  days  conditions  reflectance  set.  costs  data  calendar  comprised  on  computing  arrays used  TR.  to  135  Scatter between  diagrams  T  function  and  complete  in  T  5.1 the  in  of.  being  SE  explained  depict  shows  describes a  to  the  that  a  relationship simple  relationship. T =  by TR  12.31, (see  with  Table  linear  The  linear  89%  of  the  for  the  5.1  statistics).  The  majority T  >, than  24%).  This  sensors  to  T $  the  clear 24%  partly  probably  radiation reasons  1)  and  the is  the  adequately  shortwave Possible  of  85%  scatter  cloudy  plotted  Figure  resulted  variation  for  complex  sky  overcast  respectively)  cloudy due  to  field  inability  the  for  data  appear  conditions  the  capture  this  and  to  show  (i.e. of  85%  the  cloudy  less < T >  satellite  characteristics  partly  points  of  the  conditions.  are:  nature  of  the  radiation  field  of  comparing  point  measurements  averaged  over  under  partly  situations;  2) of  TR.  adequately  regression  (i.e.  were  the  T  to  arrays;  logistic satellite  problems  observations 7 x 7  pixel  and  3)  Earth-location  The  largest  labelled  in  late  the  in  errors  (see  residuals  Figure  5.1.  daylight  in  Chapter  the  relationship  Residuals  hours  (i.e.  3).  A , B and  for  the  have  C occur  hour  been  early  ending  or  06:00,  136  1201  0"  —i  0.2  —  •  •  0.4  0.6  -  i  o.8  TR (dimensionless)  FIGURE  5.1  Scatter P l o t of S h o r t w a v e T r a n s m i s s i o n (T) A g a i n s t U n c o r r e c t e d S a t e l l i t e T a r g e t R e f l e c t a n c e ( T R ) F o r t h e UBC S i t e U s i n g A 7 x 7 Pixel Array. Number o f O b s e r v a t i o n s = 1 1 6 .  137  TABLE  5.1  Statistics Showing t h e I m p a c t o f A p p l y i n g a BDR C o r r e c t i o n t o the R e l a t i o n s h i p Between T and TR. S a t e l l i t e ; Data are for a 7 x 7 P i x e l A r r a y C e n t r e d on U B C . (Rho) and ( T R ) a r e u s e d t o D i s t i n g u i s h B e t w e e n t h e BDR m o d e l s Which Incorporate Rho Values and Target Reflectances Respectively. A l l BDR M o d e l s u s e a C l e a r T h r e s h o l d . ( C T c ) o f 0.05 and an O v e r c a s t T h r e s h o l d (CTo) o f 0 . 8 5 . A l l Values are Percentages Except for r (dimensionless) and n .  Model Type A(Rho)  SE  of T 14.49  r  0.8433  118. 5  -1 52 . 9  a 2.61  B(Rho)  14.33  0.8467  118. 1  -151 . 8  C(Rho)  14.35  0.8463  118. 4  A (TR)  1 3.86  0.8565  B (TR)  12.99  C(TR) NO BDR Correct ion  a  b  SE  of  SE  n  of b 6.17  11 6  2.57  6.05  11 6  -1 52 . 8  2.58  6.10  11 6  117. 9  -1 53 . 3  2.47  5.88  11 6  0.8740  121. 5  -1 67 . 2  2.41  5.94  11 6  12.93  0.8751  121. 1  -1 62 . 3  2.38  5.74  11 6  12.31  0.8868  114. 5  - 1 48. 5  2.07  4.97  11 6  2  138  07:00  and  sunset for  may  three  1) (see  be  associated  3)  The  of  respectively). with  Hours  near  unrepresentative  sunrise  values  and  for  TR  reasons:  Chapter  over  LAT  Navigational  2) out  18:00  or  errors  the  lack  satellite  ground  radiation therefore  are  interpolation navigable  surface  the  the  clouds  landmarks.  latter  data  is  the  array.  i n f l u e n c e d by d i s t i n c t l y  may  observing  towards  satellite  procedure  observations  satellite  while  by  the  the  suitable  to  station,  outside  to  ground  due  influenced  observations  of  and  synchronization the  due  be  clouds  measuring  horizon  and  Thus  two  different  the  radiative  regimes.  3) though  High the  level Sun  observational  All  three  the  Sun  the is  skies  inspection and  D  of  occur  appear  to  the  bright  horizon  to  the  relative  satellite to  the  even  surface  sites.  Residuals cloudy  close  sources  restricting of  is  clouds  of  error  analyses  less  A  than  and  which the when  to  85  B  will  been  calculations  reduced when  the  however, zenith  by  angle  degrees.  are  also  likely  raw c o u n t there  have  is  a  found  enhance values  to  the  occur  problem.  indicate  dramatic  under  change  that in  partly  Moreover, residuals  the  C  radiation  139  regime  over  To the  the  test  the  strength  data  hour  the  The  increased  to  interest.  influence  of  set.  of  it  resultant  was  remain  in  the  if  these  SE o f  Despite  decided  data  these  relationship  0.9132.  statistics  that  they  T was the  that  four  set  for  all  points  are  removed  were  removed  reduced  marked  the  residuals  to  have from  10.84  improvement  four  subsequent  analyses  the  and in  residuals  on  r2  the  should  for  three  reasons:  1) of  the  three  do  not  appear  rejected  2) that  from  this  to  of  residuals  have  -148.5  the  the  for  a  the  respectively).  above,  residuals)  the  other would  data  data  set  for  points  likewise  any  (which  have  to  be  analysis;  is the  specifically satellite  relationship substantial  change (i.e.  outlined  large  study  strength  negligible  as  the  changes  3)  reasons  from  in  from  analyses  =  input between  influence  the a  interested  linear  115.1, with  on  with  parameter T the  and  and w i t h o u t  have  TR,  to  impact on  and  statistics;  regression  b = -153.9  the  the and  equation a  =  114.5,  residuals  the  is b =  present,  140 5.3  Impact  5.3.1  of  Applying  Initial  To  Study  determine  models  were  initial  analyses  (Point Grey),  Table  5.1  different either  rho to  results  from  same BDR  a BDR data  model  area  used  Figure  3.1.  the or  results  BDR  models  target  of  to  (see  For  data  the  selected for  that  the  f o r the  the  UBC  three using  (corrections  comparative  the  model  S e c t i o n 4.5),  have been  BDR  described in  applying  reflectances  points).  uncorrected  s e t as  in developing  see  the  correction  was  reflectivity  data  the  of  similar  of  a l l  the  Set  a  values  applied  Data  the  shows  forms  Small  Land(N)  as  have  Models  to  The  to  BDR  applicability  applied  5.2.  site  Using  the  Section  appeared  the  purposes  included in  are the  Table  2  5.1.  Inspection  cases  a  BDR  the  overall  an  unnecessary is  using  1981; In  varying  the  and  light the  these  clear  that  in a l l  a d e t r i m e n t a l i n f l u e n c e as  judged  T and  and  r  suggests  between T and computational  data  target  Harrison,  of  of  surprising  satellite  to  Minnis  has  additional  similar  SE  relationship  somewhat  correction  the  correction  by  result  of  given  TR  step.  that  advocate  the  r e f l e c t a n c e (e.g. 1982b; S a u n d e r s  results cloudy  further sky  and  therefore is This  many  initial  researchers  need  for a  BDR  Stephens et a l . ,  et a l . , 1983). tests  pixel  w e r e made  thresholds  by and  141  restricting  the  conditions.  This  would  show  whether  the  relatively  simple  sensitive the  to  BDR  to  Table  5.2a  apply  corrections  thresholds test  clear  the  BDR  the  case  where  all  a  appears  from  T.  together  in  again  of  certain  the  above  method  sky  cover  conclusion  used  Models  has  to  was  implement  pixels  in  this clear  their  is  and  give  to  7 x  be  an  Table  applied  7 pixels)  cloudy.  the  - The  is  SE  improvement  to  still  lowest  T is  on  the  SE  where,  there  when  It  controls  the  determined  of  r  the  TR.  5.2b  thresholds,  only  T and  T and  corrected)  is  to  5.1)  being  pixel  used  However,  threshold  is  90%  5.1).  (Table  in  to  SE o f  between  highlighted  order  relative  (Table  TR v a l u e s  in  stringent  correction  or  the  be  overcast  methods  marginally  corrected  overcast  case  the  used  to  and  varied  cases  is  deemed  that  further  sufficiently  B  improved  to  relationship  fewer  the  all  A(TR)  clear  are  results  uncorrected  5.2a  that  pixels The  In  were  and  when m o d e l  those  the  Table  clear  90%  not  to  to  respectively)  coherent  with  BDR c o r r e c t i o n  due  CTRo  the  is  (which  least  for  This  restriction  to  overcast.  pixels  more  (resulting  at  and  results  correction.  statistics  array  or  "relationship  produce  the  only  sensitivity  show  the  presents  (CTRc  the  apply  correction  models.  predominantly  of  BDR  is  a  whole to  be  lower,  but  SE when  no  applied.  C  better  were  tested  performance  more as  rigorously seen  from  than  model A  Table  5.1.  142  TABLE  5.2  Statistics Showing the Impact o f A p p l y i n g a BDR M o d e l A ( T R ) Correction to the Relationship Between T and T R . Satellite Data are for a 7 x 7 P i x e l A r r a y C e n t r e d on U B C . A l l V a l u e s are Percentages Except for r ( d i m e n s i o n l e s s ) and n .  a. CTRc 0.20 0.15 0.10 0.05  b.  Correction Conditions CTRo 0.80 0.85 0.90 0.85  SE  Applied Only.  of  T 13.67 13.61 1 3.48 13.45  to  r2 0 0 0 0  .8595 .8607 .8633 .8639  C o r r e c t i o n A p p l i e d to C o n d i t i o n s O n l y , When Deemed t o be C l e a r o r  CTRc  CTRo  0.05 0.05  0.85 0.90  SE  of T 12.75 12.65  r  2  0 .8777 0 .8797  Clear  a 117. 117. 117. 117.  and  Overcast  b 9 7 5 1  -1 5 4 . -153. -1 5 3 . -1 5 3 .  SE 1 9 4 0  of a 2.42 2.40 2.37 2.35  C l e a r and O v e r c a s t 90% o f t h e P i x e l A r r a y Overcast. a  b  116. 2 115. 8  -152.4 -150.4  SE  of a 2.19 2.16  SE  of b 5.81 5.77 5.69 5.66  n 11 11 11 11  6 6 6 6  is  SE  of b 5.30 5.19  n 11 6 11 6  143  Table B  5.3  shows  correction,  Each  of  and  these  two  reflectance  that  An 5.4  and were  shows  a  correction one  models  is  of  be  to of  an  earlier  apply  correction  BDR  relationship to  adequately SE  correction rho  values  C  BDR  model  correction.  rho  clear  and  and  target overcast  a l l pixels  or  to  overcast.  in to  in Tables  the  data  there  (Table  albeit  conditions  deemed  5.3  strength  when  improvement,  the  is in  T  i s not  applied, the This  to  or  pixels  the  SE  model  to T  T  forms  the  to  the  i s no  BDR  5.1).  be  and  of  There  minor,  (see  when  5%  TR.  data,  a  use  to of  i s true to  the  a  cloudy  for  both  those  data  With linear  5.1  a  when BDR  pixels  5.4) to  utilizing  the  lead  If  a  rather to  BDR than  stronger  correction deemed  still increase  chosen.  does BDR  to  correction  reflectances  a  when  2  function  Therefore  procedure  r  i s unnecessary  function  target  lower  Tables  it  satellite  relationship. due  and  that  and  correction  only  of  conclusion  satellite  describes of  BDR  between  relationships. a l l  or  relative  greater  the  the  both  either  satellite  to  substantiates  in  TR  the  the  applied  of  to  clear  model  using  deterioration  of  the  BDR  results presented  and  applied  any  a  tested  selection  the  T  consistently  applying  to  a  a  5.4d).  Table  The  r e l a t i o n s h i p of  for o  were  consistent  instance  the  corrections  deemed  applied  on 5.4  a  for  between  correction (see  Table  examination  relationship  is  impact  values,  thresholds, those  the  applied  clear  and  144  TABLE  5.3  Statistics Showing the Impact of Applying a BDR M o d e l B Correction to the R e l a t i o n s h i p Between T and T R . Satellite Data are f o r a 7 x 7 P i x e l A r r a y C e n t r e d on U B C . A l l V a l u e s a r e P e r c e n t a g e s Except f o r r 2 ( d i m e n s i o n l e s s ) and n .  a.  BDR M o d e l  CTRc  CTRo  0.05 0.15 0.10  0.85 0.85 0.80  b. 0.05 0.15 0.10  c.  0.05 0.15 0.10  d.  0.05 0.15 0.10  SE  0.85 0.85 0.80  13.58 13.84 13.75  0.85 0.85 0.80  12.51 12.65 12.66  121.5 119.8 120.4  Only  0.8623 0.8569 0.8587  BDR M o d e l B ( T R ) , Corrected.  118. 1 117. 2 117. 8  A l l Pixels  0.8740 0.8781 0.8734  BDR M o d e l B ( R h o ) , Corrected.  Corrected.  a  0 .8467 0 .8483 0 .8486  B(TR),  12.99 12.78 13.02  A l l Pixels  r2  of  T 14.33 14.25 14.24  BDR M o d e l 0.85 0.85 0.80  B(Rho),  Only  0.8831 0.8805 0.8803  b -151 . 8 -1 52 . 9 -151 . 9  -167.2 -165.7 -164.3  2.41 2.31 2.38  and C l e a r  -152.7 -153.6 -153.4  Overcast  122.1 120.8 121.2  of a 2.57 2.52 2.54  SE o f •b 6.05 6.06 6.01  n 11 6 11 6 11 6  5.94 5.78 5.86  116 116 116  Corrected.  Overcast  116.8 117.5 117.5  SE  2.38 2.45 2.43  and C l e a r  -173.4 -171.2 -170.6  2.32 2.31 2.33  Pixels  5.71 5.88 5.83  116 116 116  Pixels  5.91 5.91 5.89  116 116 116  145  TABLE  5.4  Statistics Showing the Impact of Applying a BDR M o d e l C Correction to the R e l a t i o n s h i p Between T and T R . Satellite Data are f o r a 7 x 7 P i x e l A r r a y C e n t r e d on U B C . A l l V a l u e s are Percentages Except for r2 ( d i m e n s i o n l e s s ) and n .  a.  BDR M o d e l  CTRc  CTRo  0.05 0.10 0.15 0.10  0.85 0.80 0.85 0.85  0. 0. 0. 0.  SE  C(Rho),  r2  of  T 1 4.35 1 4.38 14.53 14.44  0 0 0 0  BDR M o d e l  05 10 15 1 0  0.85 0.80 0.85 0.85  c.  BDR M o d e l C ( R h o ) , Corrected.  0.05 0.10 0.15  d.  0.05 0.10 0.15 0.10 0.10 0.05  0.85 0.80 0.85  C(TR),  13.47 13.69 13.79  12.20 12.36 12.36 12.34 12.32 12.19  118. 118. 118. 118.  4 5 5 5  121.1 119.8 118.9 119.8  Only  0.8644 0.8602 0.8579  Only  0.8888 0.8859 0.8859 0.8863 0.8867 0.8891  Corrected.  SE  b  A l l Pixels  0.8751 0.8736 0.8824 0.8791  BDR M o d e l C ( T R ) , Corrected. 0.85 0.80 0.85 0.85 1 .00 1 .00  a  .8463 .8456 .8423 .8443  b.  12.93 13.01 12.55 12.72  A l l Pixels  -1 5 2 . -1 5 3 . -1 5 2 . -1 5 2 .  8 0 4 6  of a 2.58 2.59 2.62 2.60  -1 62 -1 58 -161 -161  .3 .7 . 2 .3  2 . 38 2.36 2.24 2 . 30  -153.3 -154.4 -154.5  2.36 2.43 2.46  O v e r c a s t and C l e a r  121.4 120.5 120.0 120.6 120.5 121.3  of b 6.10  n  6.12 6.18 6.14  1 16 11 6 11 6 11 6  5.74 5.66 5.51 5.60  11 11 11 11  Corrected.  O v e r c a s t and C l e a r  117.0 117.8 118.0  SE  -169.6 -166.5 -167.2 -168.2 -168.6 -170.0  2 . 24 2.25 2.23 2.25 2.24 2.24  6 6 6 6  Pixels  5.69 5.83 5.89  116 116 116  Pixels  5.62 5 . 60 5.62 5.64 5.64 5.62  11 11 11 11 11 11  6 6 6 6 6 6  146  overcast.  Although the  BDR  model  the  correction  chosen,  appropriate  5.4).  generally rho  better  thresholds  or  models  B  conditions model  preliminary  improve  the only  C(TR)  relationship  used,  best  the the  A,  =  0.85  outperform  a  the  model  same  stronger  applied  (see  Table  5.4d).  even  show  is  Some  minor  without  a  conclusion  is  that,  application  of  a  BDR  and  BDR  most  overcast  appears C,  5.2  to  the  and  to  using  give  either  latter  case,  favourable.  A and  when  is  comparing  the  latter  between  T and  applied  to  all  by  BDR m o d e l  clear  and  overcast  of  results  the  improvement  of  correction  does  between  using  over  correction.  irrespective  relationship  BDR  5% c l o u d i n e s s  provided  to  the  also  C(Rho)  of  the  Tables  relationship  correction  the  of  of to  thresholds,  performance  a  as  (see  B and  are  form  clear  In  overall  of  made  85% c l o u d i n e s s  when m o d e l  strength  be  (CTRc)  is  developed  the  models  models  CTRo  with  exception  The with  and  provides  The  for  on  reflectances.  C both C  of  can  inappropriateness  optimum  threshold  (CTRo)  = 0.15  and  consistently  C(TR)  different  results  and  B  pixels.  the  target  CTRc  Models  The  clear  the  dependent  use.  threshold  values  TR'.  a  not  that  remarks  for  However,  show  summary  to  vary  overcast  is  some  form  thresholds  an  results  the  Thus the  model  little  T and TR.  a  to  147  5.3.2  Further  To was  Testing  substantiate  decided  that should  abbreviated  set  data  set  Section  Larger  findings  the  tested  spatial the  plus  using  using This  and  days  Julian  Data  Set  the  smaller  significant  analyses.  includes 5.1)  a  most  be  of  with  the the  conclusions  proceeding  Using  was  the  larger  it  set  a n d an  deemed n e c e s s a r y  before  the  255/79,  set  preceding  data  temporal analyses. from  days  a  of  data  smaller  257/79,  The  data  larger  set  276/79,  (see  293/79,  304/79,  319/79,  361/79,  363/79,  009/80,  012/80,  025/80,  105/80,  121/80,  126/80,  141/80,  160/80,  171/80,  183/80,  185/80,  197/80,  Figure (without 332.  5.2 a  Once  the  and  presents  a  simple  relationship.  The  again  of  partly  80% s h o r t w a v e  synoptic  Columbia,  clear  overcast  The section  the  types  for  the  linear  cloudy  a  to  between data  diagram data,  (see  set,  shows  especially  can  be  select  the  describes a  smaller  b e t w e e n 40%  in  of  Hay a n d O k e ,  the  where n =  attributed  experienced  using  T a n d TR  adequately  preponderance  analyses used  function  This  commonly  conditions  were  larger  scatter  giving  preliminary 5.1)  relationship  transmission.  weather  British or  261/80.  BDR c o r r e c t i o n )  concentration and  239/80  south  either  the west  mainly  1976).  smaller most  to  data  set  (see  a p p r o p r i a t e BDR  148  120  100 FORMAT  s e e FIGURE 5 . 1  80  T (%) 60  40  11 1  20  1 1  — I  0.2  1 1 1 1 > * 2 1 1111 1 N. 2 2 i i 11 1 r> 1 i "V* n i i 1 >«• 12 11 1 111111 i \ 1 1 1 1 1 2 1 1 2 11 3 \ 1 1 1111 *V 11 3 1 1  0.6  0.4  0.8  TR (dimensionless)  FIGURE  5.2  Scatter P l o t of S h o r t w a v e T r a n s m i s s i o n (T) A g a i n s t U n c o r r e c t e d Satellite Target Reflectance ( T R ) F o r t h e UBC S i t e U s i n g A 7 x 7 Pixel Array and the Larger Data Set. Number o f O b s e r v a t i o n s = 332.  149  models in  the  the x  for  testing  majority  UBC s i t e 7,  and  used  in  the  of  using  larger  the  tests.  three to  15 x  15,  the  preliminary  determine  Further  testing  Abbotsford  Airport  (ABAIR)  was  for  ABAIR  more  model  (see  Land(N) for  Figure  and  the  ABAIR  ABAIR  and  5.5a  a  Tables -  carried  out  sizes,  5 x 5 , 7  was  biasing  Inspection  of  the  reflectivity to  develop  were  included  shows  a  (without  in  a  the  count site  Land(S)  BDR  both  the  scatter  the  this  purposes,  for  array  from raw  at  the  used  the  data  comparative  TR  of  of  the  5.3  size  use  used  For  5.7a  T and  sites,  5.5(b e)  difference the  area  -  for  g)  the  based is  SE  that  of  T  (compare  Tables  5.7(b  -  e),  are  small  a  the  analyses  plot  for  the  BDR c o r r e c t i o n )  for  TR w i t h o u t  a  BDR c o r r e c t i o n  The  larger  and  5.6  for  site.  The  the  smaller  few  more  of  r2  the  5.7a  in  to  Where the  set  results data  to  are  Tables  the  for  from  in  Table  substantiate  show  The  an  improvements regression  do  the only  improvement  uncorrected  5.5(b  the  presented  and  set.  the  for  obtained  UBC s i t e  tests  compared  and  results data  the  on  changes  statistics  the  respectively). and  the  to  ABAIR  and 5.5a  list  respectively.  BDR c o r r e c t i o n  conclusions  in  that  and  and  between  ABAIR  applying  5.7(b  site.  Figure T  were  the  was  site.  relationship  in  whether  BDR m o d e l s  site.  C(TR)  array  i n c l u d e d the  3.1).  between  Tables  UBC  the  Land(S)  relationship the  to  pixel  Model  investigations  revealed  similar  set.  Analyses  different  results.  values  data  g),  cases  5.6  and  occur  they  equations  are  150  TR (dimensionless)  FIGURE  5.3  Scatter P l o t of S h o r t w a v e T r a n s m i s s i o n (T) A g a i n s t U n c o r r e c t e d S a t e l l i t e Target Reflectance (TR) F o r t h e ABAIR S i t e U s i n g A 7 x 7 Pixel Array and the Larger Data Set. Number o f O b s e r v a t i o n s = 331.  151  TABLE  5.5  Statistics Showing the Impact of Applying a BDR M o d e l C Correction to. the R e l a t i o n s h i p Between T and T R . Satellite Data are for Different P i x e l A r r a y S i z e s C e n t r e d o n UBC a n d BDR Corrections are Applied to A l l P i x e l s . A l l Values are P e r c e n t a g e s Except f o r r 2 ( d i m e n s i o n l e s s ) and n .  a.  Without  Array Size 5 x 5 7 x 7 1 5x 1 5  b.  CNRo  0.05  0.85  0.05 0.10 0.15  d . 0.05  e . 0.05 0.10 0 . 1.5. . f . 0.05  of  T 11.02 10.94 11.17  BDR M o d e l  CNRc  c  SE  a  SE  of T 12.08  BDR M o d e l 0.85 0.80 0.85  10.95 11.06 10.89  BDR M o d e l 0.85  12.02  BDR M o d e l 0.85 0.80 0.85  10.91 11.01 10.84  BDR M o d e l 0.85  11.97  BDR  Correction a  b  113.9 113.5 113.7  -147.6 -147.4 -148.4  r2 0.9092 0.9108 0.9071  C(Rho),  5 x  5 Pixel  0.8912  C(TR),  b  115.9  -149.2  5 x  0.9106 0.9088 0.9116  C(Rho),  7  C(Rho), 0.8931  x  7  - 157.3 -154.0 -156.0  118.5 117.4 116.7  15 x  333 332 331  SE of a 1. 26  SE  of b 2 . 87  n 332  1. 1 6 1. 1 6 1. 1 3  2 . 71 2 . 69 2 . 68  332 332 332  1. 24  2 . 85  332  1. 1 6 1. 16 1. 1 3  2 . 72 2 . 69 2 . 68  332 332 332  2 . 87  329  Arrays.  - 158.1 -155.0 -157.0  15 P i x e l  115.7  n  Arrays.  -148.9  Pixel  of b 2 . 57 2 . 54 2 . 62  Arrays.  7 Pixel  115.4  7 x  0.9113 0.9097 0.9124  Pixel  118.3 117.1 116.5  0.8922  C(TR),  5  SE  Arrays.  a  r2  SE o f a 1. 1 1 1 . 09 1. 1 2  Arrays •  -150.2  1. 25  152  TABLE  g. 0.05 0.10 0.15  BDR M o d e l 0.85 0.80 0.85  10.94 10.97 10.83  C(TR),  5.5  15 x  0.9106 0.9100 0.9124  (continued)  15 P i x e l  119.3 118.1 117.4  Arrays.  -160.3 -157.2 -159.0  TTT8 1.17 1.14  2777 2.73 2.72  33~0 330 330  153  TABLE  5.6  Statistics Showing the Impact of Applying a BDR M o d e l C Correction to the Relationship Between T and T R . Satellite Data are for Different P i x e l A r r a y S i z e s C e n t r e d o n UBC a n d BDR C o r r e c t i o n s a r e A p p l i e d to C l e a r and O v e r c a s t P i x e l s O n l y . All Values are Percentages Except for r2 ( d i m e n s i o n l e s s ) and n.  a.  BDR M o d e l  CNRc  CNRo  0 . 05  0.85  b. 0 . 05 0. 1 0 0. 1 5  c. 0 . 05  d. OOO  05 1 0 1 5  e. 0 . 05  f . 0 . 05 0 . 10 0. 1 5  SE  of  T 11.68  BDR M o d e l 0.85 0.80 0.85  10.72  10.89  10.76  BDR M o d e l 0.85  1 1 .57  BDR M o d e l 0.85 0.80 0.85  10.67 10.82 10.73  BDR M o d e l 0.85  11.53  BDR M o d e l 0.85 0.80 0.85  10.85 10.92 10.88  C(Rho), r  5 x  -148.5  C(Rho),  5 Pixel  117.8  0.9136  117.4  7 x  0.9001  C(Rho),  7  118.8 118.0 117.7  15 x  0.9008  0.9121 0.9109 0.9116  -160.7  - 148.3  of b 2 . 75  332  1 .1 5  2 . 74 2 . 74 2 . 72  332 332 332  1 .1 8  2 . 72  332  1 .1 4 1. 1 5 1. 1 3  2 . 74 2 . 74 2 . 73  332 332 332  2 . 75  329  2 . 84 2 . 80 2 . 81  330 330 330  1 .1 5  1. 1 3  Arrays.  -163.5 -160.6 -161.6  Arrays •  -149.7  15 P i x e l  119.6 118.7 118.3  SE  Arrays.  15 P i x e l  114.8  15 x  -162.8  -159.8  Pixel  n  SE of a 1 .20  Arrays.  7 Pixel  114.5  7 x  0.9151 0.9127 0.9142  C(TR),  114.9  118.7  0.9143  C(TR),  b  5 x  0.9117  Arrays.  a  2  0.8983  C(TR),  5 Pixel  1 . 18  Arrays.  -165.5 -162.3 -163.3  1. 1 8 1 .1 7 1 .1 6  154  TABLE  5.7  Statistics Showing t h e I m p a c t o f A p p l y i n g a BDR M o d e l L a n d ( N ) C Correction t o the R e l a t i o n s h i p Between T and TR. Satellite Data are for a 7 x 7 P i x e l A r r a y C e n t r e d on A B A I R . A l l Values are Percentages Except for r 2 ( d i m e n s i o n l e s s ) and n .  a.  Without  CNRc  CNRo  -  b.  0.05  c. 0.05 0.10  d.  0.05  e.  0.05 0.10  SE  a of  T 13.87  BDR M o d e l 0.85  14.67  BDR M o d e l 0.85 0.80  13 . 1 0 13.24  BDR C o r r e c t i o n rz 0.8366  C(Rho),  14.28  0 .8543 0.8513  0.85 0.80  13.13 13.17  -143.5  116.7  116.1 112.8  Only  0.8270  BDR M o d e l C ( T R ) , Corrected.  114.2  A l l Pixels  BDR M o d e l C ( R h o ) , Corrected. 0.85  b  A l l Pixels  0.8175  C(TR),  a  Only  0.8538 0.8529  -147.7  of b 3.50  n 331  1.72  3.85  331  3.41 3.29  331 331  Corrected. -149.7 -142.9  and  -145.0  Overcast  117.6 115.3  SE  Corrected.  Overcast  114.7  SE o f a 1.56  and  -156.4 -151.3  1 . 50 1.45  Clear  1.62  Clear  1.53 1.49  Pixels  3.66  331  Pixels  3.57. 3.46  331 331  155  negligible. different  It pixel  statistics. not  the  The  use  ABAIR  of  sets  a  it  appears  this to  5.6)  a  Impact  5.4.1  of  Previous  used  have  model  small  that  the  of  a the  and  a  to in  was  all  a  to  TR,  and  on  the  array  did  BDR m o d e l s  for  pixel  consistently  of but  5.3 a  1)  generally T and  analyses  use  only large  and  large  BDR c o r r e c t i o n  BDR c o r r e c t i o n  the  similar  BDR c o r r e c t i o n .  between  further  made  using  impact  provide  improvement  apply  that  produced  (Section  relationship  leads  TR. to  Thus TR  (Sections  the data  for 5.4  relationship set.  Averaging  Analysis  of  radiation a  5.8)  incorporation  minor  minor  Land(S)  does  the  5.6  corrections.  and  both  analyses  system  5.7  and  7 x 7  or  from  Spatial  the  BDR  Land(N)  Tables  uncorrected  characterize  the  without  Therefore,  Introduction  of  the  Land(S)  produces  an  of  similar  and  decision  T and  a  use  the  inappropriate  study.  has  5.5  with  deterioration  between  5.4  errors,  show  occasionally  testing  the  Tables  the  (compare  results  to  sizes  either  However,  standard  The data  initial  site  results. lower  array  from  Therefore  bias  the  appears  wide  of  Results  the  ability  regime range  of of  the  of  satellites  to  Earth-Atmosphere  satellite  array  sizes.  156  TABLE  5.8  Statistics Showing t h e I m p a c t o f A p p l y i n g a BDR M o d e l L a n d ( S ) C Correction t o t h e R e l a t i o n s h i p Between T and T R . Satellite Data are for a 7 x 7 P i x e l A r r a y C e n t r e d on A B A I R . A l l Values are Percentages Except for r 2 ( d i m e n s i o n l e s s ) and n .  a.  BDR M o d e l  CNRc  CNRo  0 . 05  0.85  b. 0 . 05 0. 1 0  c.  0 . 05  d.  0 . 05 0. 1 0  SE o f T 14.10  BDR M o d e l 0.85 0.80  12.76 12.96  C(Rho),  A l l Pixels  r2 0.8306  C(TR),  BDR M o d e l C ( R h o ) , Corrected. 0.85  14.04  0.85 0.80  12.77 12.82  b  115.9  -146.8  118.0 116.5  Only  0.8322  BDR M o d e l C ( T R ) , Corrected.  a  A l l Pixels  0.8612 0.8570  -153.6 -149.8  and  -146.6  Overcast  119.2 117.8  SE o f a 1.63  SE o f b 3.66  n 330  3.40 3.38  330 330  Corrected.  Overcast  115.6  Only  0.8611 0.8601  Corrected.  and  -159.7 -156.0  1.50 1.49  Clear  1.61 Clear  1.52 1.50  Pixels  3.63  330  Pixels  3.54 3.47  330 330  157  Examples km  include  pixels)  array  (2  impact  km  of  using the  and  were  were and  detailed  5.11  show  The  number  3  increased.  x  3  results  of  in  results  and  two  the  data  8 x  8  (8  pixel  investigate array  the again of  optimum s i z e  and  target  set  arrays  The d i m e n s i o n s  the  individual  station  reflectance.  stations, MAA ( s e e  from to  to  (n)  gradually  19 x  in  as  a of  UBC a n d  Chapter  2  in  (evident  changes  'b') in  each  as  Tables from  of  the  the  with  test as  of  the  arrays  Tables  5 . 9 to  varies  for  array the  size  size  the is  increased  pixel  such  of  values, the  data  are  not  indicate  that  data  T and TR.  5.9 the  initial  pixel  the  erroneous  between  the  a n d MAA r e s p e c t i v e l y .  containing  relationship  in  19 p i x e l s .  result  malfunctions,  and  tested  decreases  occurrence  presented  'a'  was  used  Images  the  adopted  U B C , ABAIR  occurs  the  strength  insensitive  for  for  images  increases.  (evident  calculating  an  pixel  TR.  determine  pixels  satellite  the  for  to  satellite T and  relationship  This  incorporated  the  pixel  who u s e d  decided  configuration the  sites  by  was  7 x 6  descriptions).  of  probability  of  to  three  the  different  it  between  for  from  The  size  out  of  while  the  the  al.  Thus  carried  development  array  (1980)  required  square  caused  et  altered  The  ranging  Gautier  pixels).  configuration  for  who u s e d  relationship  array  ABAIR,  (1979)  changing  the  Tests  Tarpley  -  5.11  SE a n d  r  )  relationship  are  configuration  of  and  nature  relatively the  array,  158  TABLE  5.9  Statistics Showing the Impact of U s i n g D i f f e r e n t A r r a y S i z e s on the Relationship Between T and TR. The P i x e l A r r a y s a r e Centred on UBC. A l l values are Percentages Except for the Array Size (pixels), r2 ( d i m e n s i o n l e s s ) and n .  Array Size 3 x 3  SE  5 x  of  T 11.74  r2  a  b  0.8968  113.7  5  1 1 .02  0.9092  7 x  7  1 0.94  9 x  9 1 1  SE  -145.9  of a 1.18  of b 2.72  334  113.9  -147.6  1.11  2.57  333  0.9108  113.5  -147.4  1 .09  2.54  332  10.91  0.9112  113.2  -147.2  1 .09  2.53  332  1 0.94  0.9108  113.2  -147.4  1 .09  2.54  332  1 5 x 1 5  11.17  0.9071  113.7  -148 . 4  1.12  2.62  331  1 9 x 19  1 1 .54  0.9008  113.9  -148.7  1.17  2.72  331  11 X  SE  n  159  TABLE  5.10  Statistics Showing the Impact of U s i n g D i f f e r e n t A r r a y S i z e s on the Relationship Between T and TR. The P i x e l A r r a y s a r e Centred on ABAIR. A l l Values are Percentages Except for the Array Size ( p i x e l s ) , r2 ( d i m e n s i o n l e s s ) and n .  Array Size 3 x 3  SE  of T 14.32  r2  a  0.8260  113.6  5 x  5,  1 4.22  0.8284  7 x  7  13.87  9 x  9 1 1  b  SE  -141 .0  of a 1 .60  of b 3.57  331  113.7  - 1 41. 6  1 .59 .  3.55  331  0.8366  114.2  -1 43 . 5  1 .56  3.50  331  1 3.82  0.8379  114.3  - 1 4 3 .8  1 .55  3.49  331  1 3.68  0.841 1  114.4  -1 44 . 3  1 .54  3.46  331  1 5 x 1 5  13.54  0.8442  114.5  -1 44 . 6  1 .53  3.43  330  19 x  13.42  0.8470  114.6  - 1 44 . 9  1 .52  3.40  330  11 x  19  SE  n  160  TABLE  5.11  Statistics Showing the Impact of U s i n g D i f f e r e n t A r r a y Sizes on the Relationship Between T and TR. The P i x e l A r r a y s a r e Centred on MAA. A l l Values are Percentages Except for the Array Size ( p i x e l s ) , r2 ( d i m e n s i o n l e s s ) and n .  Site Array Size 3 x 3  Total Array Size 1 1 x 1 0  5 x  5  1 3X  7 x  7  9 x  SE  of  r2  a  b  SE  114. 2 - 1 4 2 . 9  of a 1 .57  of b 3.52  330  0 .8354  114. 3 - 1 4 3 . 3  1 .57  3.52  329  13.80  0 .8379  114. 4 - 1 4 3 . 4  1 .55  3.49  329  1 6  13.70  0 .8408  114. 4 - 1 4 3 . 5  1 . 54  3.46  328  19 X  18  13.65  0 .8412  1 1 4 . 4 -1 4 3 . 4  1 .54  3.46  327  1 5 x 1 5  23  X  22  13.58  0 .8425  113. 9 - 1 4 2 . 7  1 . 53  3.43  325  1 9 x 19  27  X  26  1 3 . 50  0 .8442  113. 7 - 1 4 2 . 7  1.51  3.40  325  11 X  T 13.98  0 .8342  1 2  13.91  1 5X  1 4  9  1 7 X  1 1  SE  n  161  there  is  site  a  the  ABAIR  optimum  and  larger, sites at  suggestion  sites  appears  most  these  Sect ion  a  sites  ABAIR  and  of  in  the  and of  size.  For  array,  19 p i x e l  different  array,  synoptic  cloud  t h e UBC  while and  The d i f f e r e n c e  for  the  possibly  between  the  characteristics  weather  5.12  south the  For  conditions  indicate  prevailing  site  the  there  the  (see  at  gives  the  are  to  the  the  5.12) to  5.11), little  the lowest  in  away  the  from of  the  lowest  both with difference.  standard  the  site  for  of  west  and Oke, with  T is  a  not  rectangular  using  square  and w i t h o u t a It  is  rectangle  error  the  movement  of  the  those  the  of  in  results  rectangle SE  the  terms  direction  (Hay  using  UBC s i t e  the  directions  systems  to  from  described  direction  for  end of  away  preferred  preferred  for  pixels  the  elongated  results  appears  that  a  reason  providing  5.1  is  8 x 1 4  Inspection  weather  (Table  (Tables  however,  projection  relation  comparing  correction,  the  synoptic  arrays  configurations  there  were  project  and w e s t ) .  that  some  ABAIR  was  they  UBC s i t e  projection When  satellite  which  investigated  towards  The r e c t a n g l e s  south  the  also  positioned  rectangle  5.4).  suggest  At the  clear.  were  in  were  The r e c t a n g l e s  the  east,  site.  northerly  west  arrays  array  9 pixel  x  the  pixel  Figure  Table  noting,  of  certain  direction  1976).  BDR  19  under  that  north,  each  9 x  appropriate.  sites  so  (see  (i.e.  a  the  sites.  the  rectangle site  optimum  5.6).  and  size  an  is  function  Rectangular UBC  size  MAA  may be  of  for  all  worth with  a  tests  162  NORTH  Ground WEST  EAST  Station  SOUTH  Scale  FIGURE Rectangular  Satellite  Arrays  Used  (Pixels)  5.4 to  Test  Synoptic  Influences.  163  TABLE  5.12  Statistics Showing the Impact of U s i n g D i f f e r e n t R e c t a n g u l a r Configurations on the Relationship Between T and TR. The Pixel Arrays are C e n t r e d on a ) UBC a n d b) A B A I R . A l l Values are P e r c e n t a g e s Except f o r r 2 ( d i m e n s i o n l e s s ) and n .  a.  UBC  Array Projection North East South West b.  SE o f T 12.42 11.76 10.97 10.59  r2  a  0.8850 0 . 8968 0 . 9101 0 . 91 63  113.0 115.5 113.1 111.9  0. 0. 0. 0.  115.1 113.8 113.7 114.4  b  SE  SE  -145.2 -149.7 -147.9 -146.3  of a 1 .25 1.21 1 .09 1 .03  of b 2.88 2.80 2.56 2.43  n 332 332 333 332  -145.0 -142.3 -142.8 -143.8  1 1 1 1  3.34 3.54 3.49 3.50  328 330 330 328  ABAIR  North East South West  13.12 14.06 13.86 13.79  8528 831 7 8363 8383  .49 .58 .55 .56  164  (see  Table  the of  satellite clouds  The over of  in  array for  If  size the  in be  due  measured  radiation  5.13);  2) the  of  to  the  advantages  the  of  predominant  ABAIR,  for  ABAIR  site  relating movements  these  and  are  nature  5.13  once  the  the  it  a  two  sites  the  pixel 11  similar  appears  for  size  that  the  gives  the  (Tables  5.10  and  regimes  used  for  MAA  and  5.14  comparable  suggest  because  of  the  scatter  an  almost  1:1  linear  of  the  a  general  radiation the  x  overall  consistently  reason  5.11)  than  actual  to  the  in  stations Tables  data  density  MAA ( T a b l e  greater  2)  5.10),  based  similarity  regimes  around  for  is  column  relationship  increased  5.10)  between  However,  results the  (Table  (Table  the  for  stations  5.11,  in  the  results  made  ground  error.  5.7  is  (Table  of  despite  The  ABAIR  to  improvement  individual  MAA  symmetric  5.7)  to  data.  pyranometric  5.5  to  little  comparison  the  Figures  5.5  the  standard  three  1)  site  density  may  the  a  for  similarity 5.11)  shows  those  single  increased greater  site  around  pixels.  the  area.  than  size  highlights  configuration  measurement  worse  array  the  single  network  This  array  MAA  the  are  11  5.12a).  at  site.  that  the  of:  plots  (see  relationship  Figures (Table  and  the  similarity  different  sites  (Table  means  5.14).  and  standard  deviations  for  165  FIGURE Scatter Between  Plot Comparing Hourly ABLIB and MISS. Number o f  5.5 Shortwave Radiation O b s e r v a t i o n s = 421.  Totals  166  FIGURE Scatter Between  Plot Comparing Hourly ABAIR a n d M I S S . Number o f  5.6 Shortwave Radiation O b s e r v a t i o n s = 418.  Totals  167  FIGURE Scatter Between  Plot Comparing ABAIR and A B L I B .  5.7  Hourly Shortwave Radiation Number o f O b s e r v a t i o n s = 4 1 6 .  Totals  168  TABLE  5.13  Comparative Statistics f o r the Hourly Shortwave Radiation Measurements at the Three Valley Sites. A l l Values are Percentages Except f o r r ( d i m e n s i o n l e s s ) and n. 2  Stat ion Compari son  r  2  a  b  n  ABAIR  v. ABLIB  0 .9677  24. 29  0 .9932  416  ABAIR  v . MISS  0 .9288  4 7 . 36  0 .9788  418  ABLIB  v . MISS  0 .9467  28. 21  0 .9793  421  169  TABLE The Mean a n d Measurements  5.14  Standard D e v i a t i o n for Hourly Shortwave Radiation at the Three V a l l e y S i t e s . Values are in k j m _ 2 h r _ :  Site  Mean o f K+-  Standard D e v i a t i o n of  ABAIR  9 1 4 . .6  8 6 8 . .8  ABLIB  8 9 3 . .2  8 5 9 . .5  MISS  881 .. 1  8 5 3 . .0  K+  170  .Inspection the is  of  regression little  the  equations  change  in  array  configuration  5.4.2  Implication  Section optimum small  satellite  modelling  for  the  TR i m p l y data  small  5.9  the  coefficients  to  5.12  show  relationship  three  error  test  as  (b)  for  that  there  the  pixel  changes  in  have  little  the  the  in  the  However,  the  relationship  spatial  data  as  information  sets,  presents  averaging  Therefore  satellite  voluminous sizes  for  impact.  using  array  differences sites.  statistics  that  involve  pixel  substantial  the  procedures  characteristically use  form of  revealed  in  of  the  and  Tables  and  Results  configurations  T  (a)  altered.  5.4.1  variations  in  the  is  of  between  to  constants  a  the  ability  considerable  advantage.  5.5  Impact  Random documented affect at  the the  of  Time  Averaging  fluctuations (see  Hay  ability Earth's  in  and of  solar Hanson,  models surface.  to  radiation 1983).  estimate  have  These  been  well  fluctuations  the  solar  irradiance  Increased  time  averaging  171  significantly  improves  et  Suckling,  al.,1975;  consider  the  relationship  impact between  Two-hourly  sites  For  the  and  to  per  Therefore,  four  two-hourly  tests  (see The  of  the  comparing  (see  the  is, 'a'  and  'b'  developed  one-hourly reduction conditions, partly  not  the  cloudy  (see  and  of  overcast  for  in  to  again  the  shortwave  U B C , ABAIR  one-hourly  the  images TR  for  the  it  increased  when  equations  that  the  to  results.  regression  suggesting  on  5.15.  T show  one-hourly  influencing  value.  Table  estimating  the  are  discussion  in  has  and  results.  necessary  further  the  in  the  satellite  r2  5.15),  the  form  large  of  the  for  the  T and TR.  is  much  comparison Figure  throughout  majority  the  deemed  to  scatter in  for  presented  change  between  scale  scatter the  tests  Table  averaging  in  are  greatly  shows  time  5.6  while  relationship  two-hourly  Section  the  more  were  reduced,  in  (Davies  appropriate and  calculate  errors  are  5.8  to  standard  residuals  Figure  or  images  little  is  at  with  two  period  ' two-hourly  models  averaging,  reflectances  results  however,  it  calculated  comparison  more  such  used.  were  tests,  or  substantially  There  a  hourly  topic).  be  TR i s  target  of  Thus  temporal  T and  one-hourly  Inspection  1977).  of  provide  required  this  performance  r u n n i n g means  transmissions MAA  the  the  5.2). the  to  the  While full  reduction  conditions  reduced  equivalent  there  range  of  appears  to  (i.e.  below  is  80%  some cloud  be  for  clear  172  TABLE  5.15  Statistics Showing t h e Impact of I n c r e a s i n g t h e Time A v e r a g i n g Period on t h e R e l a t i o n s h i p B e t w e e n T a n d TR a t t h e T h r e e S i t e s a) UBC, b) ABAIR and c) MAA. A l l Values are Percentages Except f o r the A r r a y S i z e ( p i x e l s ) , r 2 ( d i m e n s i o n l e s s ) and n .  a.  UBC.  Time Array Period Size (Hours) 7 x 7 1 7 x 7 2 1 5 x 1 5 1 1 5 x 1 5 2 8 x 14(W) 1 8 x 14(W) 2  b. 7 7 1 5 1 5 8 8  X X X X X X  C. 7 7 15 1 5  X X X X  SE  of T 1 0.94 8.87 11.17 9.29 10.59 8.56  1 2 1 2 1 2  1 2 1 2  2  SE  of a 1 .09 0.94 1.12 1 .00 1 .03 0.89  SE  of b 2.54 2.19 2.62 2.34 2.43 2.10  n 332 291 331 282 332 288  -143.5 -146.9 -144.6 -147. 1 -142.8 -146.8  1 .56 1 .32 1 .53 1 .23 1 .55 1.31  3.50 2.94 3.43 2.76 3.49 2.96  331 286 330 277 330 277  -143.4 -146.6 -142.7 -146.3  1 . 55 1 .31 1.53 1.26  3.49 2.92 3.43 2.80  329 282 325 269  r 0 .91 08 0 .9407 0 .9071 0 .9349 0 .9163 0 .9449  a 1 1 3. 5 1 1 3. 6 1 1 3. 7 1 1 3. 7 1 1 1. 9 1 1 1. 9  b -147 -1 48 -1 48 -1 48 -1 46 -1 46  1 3.87 10.93 1 3.54 10.12 1 3.86 10.82  0.8366 0.8977 0.8442 0.9117 0.8363 0.8994  114.2 115.8 114.5 115.8 113.7 115.1  1 3.80 10.79 1 3.58 10.17  0.8379 0.8998 0.8425 0.9110  114.4 115.9 113.9 115.6  .4 .0 .4 .2 .3 .8  ABAIR. 7 7 1 1 1 1  5 5 4 (S) 4 (S)  MAA. 7 7 1 5 1 5  173  1201  i 0  .——  1 0.2  1 0.4  • — — 0.6  1 0.8  TR (dimensionless)  FIGURE  5.8  Scatter P l o t of T w o - H o u r l y A v e r a g e d Shortwave T r a n s m i s s i o n (T) Against Uncorrected S a t e l l i t e Target Reflectance (TR) F o r t h e UBC Site Using A 7 x 7 P i x e l A r r a y and the L a r g e r Data Set. Number p f O b s e r v a t i o n s = 2 9 1 .  174  sky in  transmission). the  one-hourly  probably nature  a of  the  the  the  the  target  image  equivalent  will  investigate required  Influence  also  carry  longer the  partly  reduces  up  to  period  latter  the  importance  present  evident.  This  more  the  a  and  scatter less  for  overcast as  a  of  the  while is  following  number o f  represent  a  one  on  one-hourly  maximum w e i g h t the  images  weight  50% w e i g h t i n g ,  the  is  inhomogeneous  cloudy  (i.e.  reasoning,  adequately  residuals  p e r i o d have  value  this  the  maximum  one-hourly and  Satellite  5.5  images  influenced  3.7)  of  Section  satellite  was  under  reflectance  may  to  no  large  or  for  25%).  section satellite  two-hourly  period.  In  The  to  are  half-hourly  two-hourly  respect  5.6  field  a  the  smoothing of  Such a v e r a g i n g  resultant  images  the  radiation  With  time  of  may m i s r e p r e s e n t  period  many o f  averaging  result  situations. that  Thus  strength  number o f  and five  were  became  required  images  needed  the  satellite time  Availability  evident time  the  that  interval  relationship images period,  respectively.  somewhat for  per  of  two-hourly  stipulated,  images  it  Image  are  to  number  of  calculate  TR  between could three  T and TR.  represent (see  Throughout t h i s  subjectively, one-hourly  that  the  that  averaging  at  Section study  least  period.  a  it two  This  175  was  a  compromise  if  1) hourly  at  not  (especially  if  2) set  For images four.  least  periods  probably  data  given  three  the  the  partly  images  w o u l d be  image  changes  per  hour  in  was  were  those  was  available  would  the  radiation  regime  conditions);  hour  required,  and  required,  the  size  of  the  reduced.  required  per  of  per  one  cloudy  two-hourly  relationship  image  only  capture  under  following:  one  when  Therefore  images  the  time  time  it  interval  was  decided  changing  required,  for  period,'  the  both  to  the was  minimum number doubled  assess  constraint  the  the on  one-hourly  to  effect the  and  at  of  least on  the  number  two-hourly  of  time  intervals.  The and  tests  MAA,  using  ABAIR  and  mean  data.  as  selection  were  only  reductions  number  two-hourly  out  Inspection  likewise the  carried  a  MAA  substantial and  were  time  an  in  increase of  intervals  all  of  pixel  tested  three  using  of  Tables  the  standard  in  images  for  the  array the  error  increases.  for  U B C , ABAIR  configurations.  two-hourly  5.16  coefficient  required  sites,  to for of  either  5.19  running reveals  estimating  T  determination one-hourly  or  176  TABLE  5.16  Statistics Showing the Impact Requirements Per One-Hourly Time Between T a n d TR a t t h e UBC S i t e . Except for the Array Size ( p i x e l s ) ,  Array Size 7 x 7  Number of Imaqes > 1  7 x  7  >2  7 x  7  3  SE  of Changes to the Image P e r i o d on t h e R e l a t i o n s h i p A l l Values are Percentages r 2 ( d i m e n s i o n l e s s ) and n .  of T 14.62  r2 0 .8378  a 111. 5  b -141 . 0  1 0.94  0 .9108  113. 5  10.51  0 . 9207  SE  of a 1 .40  SE  of b 3.20  n 379  -147 .4  1 .09  2.54  332  113. 8  -1 47 . 8  1.14  2.62  277  15 x  1 5  >1  1 4 . 56  0 .8395  112. 0  -143 .3  1.41  3.24  376  15 x  1 5  >2  11.17  0 .9071  113. 7  -1 48 . 4  1.12  2.62  331  1 5 x 1 5  3  10.86  0 .91 53  114. 1  - 1 48. 9  1 .20  2.78  268  8 x  1 4 (W)  >1  14.33  0 .8444  1 10. 2  -140 . 6  1 . 35  3.11  378  8 x  1 4(W)  >2  10.59  0 .9163  111. 9  -1 46 . 3  1 . 03  2.43  332  8 x  1 4(W)  3  9.95  0 .9289  112. 2  -1 46 . 6  1 .06  2.46  275  8 x  1 4 (S)  >1  14.44  0 .841 9  111. 4  -141 . 9  1 .38  3.17  378  8 x  1 4(S)  >2  10.97  0 .9101  113. 1  -1 47 . 9  1 .09  2.56  333  8 x  1 4(S)  3  10.17  0 .9254  113. 5  -1 48 . 5  1.10  2.57  271  177  TABLE  5.17  Statistics Showing the Impact of Changes to the Image Requirements Per Two-Hourly Time P e r i o d on t h e R e l a t i o n s h i p Between T a n d TR a t t h e UBC S i t e . A l l Values are Percentages Except for the A r r a y S i z e ( p i x e l s ) and r 2 ( d i m e n s i o n l e s s ) and n.  Array Size 7 x 7  Number of Images >2  SE  of T 11.37  r2 0 .8984  a 1 12 . 6  b -1 4 4 . 1  SE  of a 1.12  SE  of b 2 . 57  n 357  7  >3  10.03  0 .9232  1 1 3. 1  -147. 3  1.01  2 . 32  337  7 x 7  >4  8.87  0 .9407  1 1 3. 6  -1 4 8 . 0  0.94  2. 1 9  291  7  5  8.58  0 .9466  1 1 4. 3  -1 4 9 . 1  1 .03  2 . 39  221  1 5 x 1 5  >2  11.44  0 .8971  1 1 2. 8  -145. 3  1.13  2 . 61  357  1 5 x 1 5  >3  10.26  0 .91 94  1 1 3. 1  -148. 1  1 .03  2 . 41  334  1 5 x 1 5  >4  9.29  0 .9349  1 1 3. 7  -1 48 . 2  1 .00  2 . 34  282  1 5 x 1 5  5  8.92  0 .9418  1 1 4. 6  -1 5 0 . 1  1 .09  2 . 58  21 2  8 x  1 4 (W) >2  11.24  0 .9008  1 1 0. 9  -142. 7  1 .08  2 . 51  357  8 x  1 4(W)  >3  9.65  0 .9290  1 1 1. 6  -1 4 6 . 3  0.94  2 . 21  337  8 x  1 4(W)  >4  8.56  0 .9449  1 1 1. 9  -1 4 6 . 8  0.89  2. 1 0  288  8 x  1 4(W)  5  8.11  0 .9523  1 1 2. 5  -147. 8  0.95  2 . 25  219  7 x  7 x  178  TABLE  5.18  Statistics Showing the Impact of Changes to the Image Requirements Per Two-Hourly Time P e r i o d on t h e R e l a t i o n s h i p Between T and TR at the ABAIR Site. A l l Values are Percentages Except for the Array Size (pixels), r2 ( d i m e n s i o n l e s s ) and n .  Array Size 7 x 7  Number of Images >2  SE  of T 1 2.93  r2 0 .8499  a 114. 2  b -1 4 2 . 8  SE  of a 1 .43  SE  of b . 3.19  n 355  7 x  7  >3  12.81  0 .8538  1 14. 1  -1 4 2 . 3  1 .46  3.24  332  7 x  7  >4  1 0.93  0 .8977  115. 8  -146. 9  1 .32  2.94  286  7 x  7  5  9.86  0 .91 80  117. 0  -1 4 9 . 0  1 .38  3.07  212  1 5 x 1 5  >2  12.62  0 .8573  114. 4  -1 4 3 . 7  1 .40  3.13  353  15 x  1 5  >3  12.43  0 .8632  1 14. 5  -143. 5  1 .42  3.15  330  1 5 x 1 5  >4  10.12  0 .9117  115. 8  -1 4 7 . 1  1 .23  2.76  277  1 5 x 1 5  5  9.66  0 .9209  117. 4  -1 4 9 . 8  1 .43  3.19  191  179  TABLE  5.19  Statistics Showing the Impact Requirements Per Two-Hourly Time B e t w e e n T a n d TR a t t h e MAA S i t e .  Array Size 7 x 7  Number of Images >2  7 x 7 7 x 7 x  SE  of Changes to the Image Period on,the Relationship  of T 12.78  r2 0 .8536  a 114.3  b -1 4 3 . 0  >3  1 2.66  0 .8570  114.2  7  >4  10.79  0 .8998  7  5  9.89  SE  of a 1.41  SE  of b 3.15  n 355  -1 4 2 . 4  1 .44  3.22  329  115.9  -146. 6  1 .31  2.92  282  0 .91 68  1 17.4  -149. 3  1 .43  3.20  200  15 x  1 5  >2  1 2.62  0 .8572  113.8  -1 4 2 . 1  1 .39  3.09  354  15 x  1 5  >3  12.51  0 .8613  113.9  -1 4 2 . 0  1 .42  3.18  323  1 5 x 1 5  >4  10.17  0 .9110  115.6  -146. 3  1 .26  2.80  269  180  Increasing in  removing  1)  2)  are  misrepresent  more  is the  satellite  periods  the  images  required  results  when:  insufficient  a  the  temporal  larger  radiation  images  improvements  are  number  radiation  in  of  satellite  regime  in  the  the  SE  in  requirements  in are  least  two  deemed  necessary,  the  largest  increasing  for  images  through  T  the  time  the  the  increased each the  to  time  image  and  TR.  the  at  is  at  the  requirements  5.16)  least When  not  the  as  a to  the  increased data  T and  is  TR.  a  marked  satellite  image  one  to  image,  three  images  at are  pronounced.  UBC s i t e  at  is  used  shows  statistics to  (n)  the  between  the  period.  there  satellite  (Table  may  However,  suggest  when  averaging in  points  for  that  5.5).  data  relationship  improvement  improvements  interval,  r  from  hourly  time  and  relationship  images  Section  T  averaging  to  (see  of  between  frequency  two-hourly  the  per  number  of  improving  applied  conditions  relationship  one-hourly  improvement  weighting  required  sampling  instrumental  the  an  reduction  develop  For  time  of  and  there  marked  number  represent  interval;  The  those  there  adequately  As  the  least  (Table  are  5.17)  found  three,  when  and  at  181  least  four  images.  requirements of  are  images  for  the  5.19)  valley  increased  difference compared of  to  partly  5.7).  (i.e.  improvement  in  images  images  for  strength images  for  two-hourly  the  image  four  images  and  only  least  three  or  valley  least  are  the time  of  the  for  available one-hourly  one-hourly, period.  requirements  values  for  used  target  which  and  Section  is  Thus throughout  be  deemed a  large  the  most  the  developed  images time  when u s i n g  least  it  can  this  and  be  four  at  study  provide  five  in  the  least  two  images  concluded  of  periods  deteriorations  at  when  maximum number  two-hourly  occurs and  that  three  minor  reflectance.  sites  are  there  The  occurrence  (see  images  TR may  (i.e.  only  valley  sites  suggest  T and  periods  are  images.  greater  .before  (Table  relationship.  section  between  five  more  images)  relationship  image  the  four  this  However, the  sites  MAA  improvement  the  valley  number  requirements  the  the  the  statistics  and  at  at  when  maximum  minor  to  seen  occur  The  5.18)  conditions  the  of  (Table  to  time  the  period.  due  from  respectively).  ABAIR  strength  those  possible  two-hourly  be  the  the  images,  may  relationship  only  five  improvement  at  results  coherent using  at  improvements  when  UBC s i t e  cloudy  necessary  The  at  the  the  Thus  a of  least  to  in  to  improvement  at  increases  for  sites  most to  smallest  increased  possible  show  for  The  for  the  that  the  adequate  182  5.7  Valley  From  and C o a s t a l  the  interesting coastal  Site  results  presented  comparisons  site,  Comparison  UBC, and  in the  earlier  the  in  radiation  valley  sites,  this  chapter  regimes  ABAIR  some  between  and MAA, c a n  the be  deduced.  The  two v a l l e y  produce  a  weaker  sites  show c o n s i s t e n t l y  relationship  between  T and  for  former  the  coastal  site.  The  the  data  for  ABAIR  being  incorporated  proximity  of  the  three  sites  for  the  differences  probably all  a  sites  this  conditions. specific are  and  concentrations daylight  are  hours  circulation  system  Oke,l976). conditions linear  as  The and  a  impact  therefore  relationship  to  be  result in  coastal  the  the  cloud  of  the  Lower  will has  intercepts  a  are  because  synoptic  weather under  inhomogeneities aerosol  atmospheric  further  greatest  the  the  conditions.  land  stong  to  phenomena  pronounced  Fraser  be  for  reason  sites  atmospheric  weather, greater  due and  The  valley  same  to  likely  MAA.  and  those  MAA s i t e ,  and  most  respect  to  is  when m e s o s c a l e  anticyclonic known  the  results  TR t h a n  derive  are  patterns  particularly  persistent  to  experience  with  in  climatological  differences  flow  the  used the  local  study  developed  concentrations  Under  of  The  synoptic  best  between  function in  reason  similar  and  for  during  sea  Valley  control  Y-axis.  inland  aerosol  breeze  (Hay  and  clear  sky  on w h e r e  the  However,  Figure  183  5.9  shows  coastal  that  and  between  the  of  sites  gradients  to  because  difference  valley  the  difficult  the  draw the  greater  any  of  unknown  However,  have  little  it  is  as  conclusions  of  the  apparent on  Y-intercept is  regression  radiative  impact  the  small,  the  final  reflectivity  site.  is  in  lines.  properties  that  of  surface  such  It 5.9  of  is  partly  aerosols at  the  mesoscale  nature  the  difference  from F i g u r e  ground  the  the  for  and  valley  differences  the  regression  relat ionship.  A  comparison  valley  of  Figures  5.2,  5.3  sites,  ABAIR  (Figure  5.3)  a n d MAA ( F i g u r e  greater  preponderance  have  a  at  the  UBC  quantitatively function further  two  1)  in  away  from  the  processes  Under  otherwise  surface. as  a  breeze  sources  influence  the  of  cloud  points  is  two  5.10),  also  processes  effect  the  to  than shown  probably  a  experienced  the  sea.  Such  characteristics  ways:  ground  clouds  will  is  difference  convective  show  data  This  This  moderating  5.10  cloudy  5.2).  5.11.  active  (cumulus)  sea  Figure  more  clouds  sites  partly  (Figure  of  convective in  site  of  and  will This  result front  tend  to  of  heat  clear  form as process  of  dissipate  conditions, a  is  greater  which  and  sky  result more  as  moisture  they by  and  under are the  the  the  such  carried synoptic  cellular  heating  pronounced at  heating  develops  of  discrete  the  of  valley  proximity  of  conditions. away winds  from  the  a  The their  above  the  184  T  (%)  1.0  FIGURE  5.9  Comparison o f t h e R e g r e s s i o n E q u a t i o n s F o r UBC a n d Regression Equations a r e B a s e d on t h e L a r g e r D a t a a BDR C o r r e c t i o n t o T R . TR i s D i m e n s i o n l e s s .  ABAIR. The Set W i t h o u t  185  TR (dimensionless)  FIGURE  5.10  Scatter P l o t of S h o r t w a v e T r a n s m i s s i o n (T) A g a i n s t U n c o r r e c t e d S a t e l l i t e Target Reflectance ( T R ) F o r t h e MAA S i t e U s i n g A 7 x 7 Pixel Array and the Larger Data Set. Number of O b s e r v a t i o n s = 329.  186  50i  ° 2 go  UBC  ABAIR  MAA  3 0'  £ c m Z  z n n -<  10^  CIr  Clear  Partly  PC  CIr  O  - CIr -  Cloudy  Overcast  -  O  PC  Transmission  - PC -  CIr  >  PC  85%  8 5 % < Transmission  > 24%  - 2 4 % ^ Transmission  FIGURE Frequency of Occurence of Conditions at UBC, ABAIR V a l u e s U s i n g the Larger Data  5.11  C l e a r , Partly Cloudy and MAA. B a s e d on set.  and O v e r c a s t Transmission  187  sea  breeze  system  differences  between  2)  With  (Lyons, the  1975).  coastal  relatively  and  thin  inland  continuous  coastal  further  enhances  the  sites.  low  level  convective  and  orographic  processes  in  the  to  thin  break  resulting  in  partly  cloudy  increase  in  partly  cloudy  up,  the  the  which  along  and  stretches,  cloud  develops  cloud  the  This  more  Fraser  active  Valley  cause  conditions.  It  appears  conditions more  at  those  from F i g u r e  5.11  experienced  at  the  expense  which  process  are  more  associated  standard  errors  This  clear  to  for  The  of  the  MAA c o m p a r e d  sky  situations  1 is  has  averaging,  of  a and  of  (e.g.  utilized and  of  more  the  conditions,  valley  UBC s i t e  various  impact  cloudy  the  transmission  impact  nature  coefficient  chapter  shortwave  temporal  partly  lower  compared  data.  and  (i.e.process  variable  with  consistently  the  ABAIR the  overcast  the  to  UBC,  is  rather  than  important  than  2 ) .  The  5.11)  of  that  target  likely  determination sites  (e.g.  Table  the  and  Tables  to ,  the  larger  5.10  and  5.9).  reflectance  BDR c o r r e c t i o n  regime  explains  relationship  modifications  satellite  radiative  the  to  investigate  satellite  differing  image  between  spatial  availability  input and have  188  highlighted  the  relationship. in  Chapter  6.  sensitivity The  and  conclusions  optimum c o n d i t i o n s from  this  study  are  for  such  a  presented  189  CHAPTER  6  CONCLUSIONS  The  intention  relationship  of  between  radiation  to  this  study  satellite  and  investigate  configurations  of  characterize  the  the  to  use  ground  the  satellite  solar  was  radiation  simple  measured  impact data  a  on  of the  regime  solar  different ability  at  the  to  Earth's  surface.  The  satellite  data  Earth-located  following  Errors  this  the  using  north-south  direction.  conditions  when  site.  located  to  errors  This  the  east  4  anisotropic system.. reflectance  and  is of  were and of  to  reflectance Chapter  4  patterns  ±1.50  (BDR)  revealed  to  Chapter  be  for  3.  ± 1 . 5 4 km i n  the  east-west  Section  3.5)  may  cloudy  and  overcast  located  away  from  case  with  the  landmarks  site.  correct  the  are  satisfactorily in  (see  the  models  the  properties  for  km  partly  landmarks  study  be  determined  especially  the  to  outlined  linearity  reflectance used  shown  under  navigable  Bidirectional Chapter  procedure  The a s s u m p t i o n these  was  procedures  direction  increase  study  set  of  that  surfaces  were  satellite the the  developed data  for  in the  Earth-Atmosphere differing  v i e w e d by  the  diurnal satellite  190  required a  the  cloud,  In  a  development  sea  and  two  5  an  Chapter  land  describe  transmission  (T)  and  relationship  was  used  data  In  1) correction using  a  rather  the  more than  the  incorporates  a  made  overcast  of  data,  parameter approach  both  a  correction  is  applied).  to  only  overcast  all  pixels.  This  for  partly  cloudy  the  BDR  models  capture  the  are  a  highlights  target  using  rho  both  pixels  the  and  completely  complexities  and  of  a  clear the  developed  values  T  which  a  and  are  in  a  TR.  The  BDR m o d e l  that  (between  which  a  overcast  correction  clear  completely  deemed  or  that or  partly  reflectance  predominantly  correction  complex  also  (BDR)  resulted  between  over  the  reflectances,  Bidirectional  those  conditions  (for  (i.e.  sky  This  modifying  BDR m o d e l s  completely  favoured  (TR).  reflectance  threshold  clear  which  and  of  to  conclusions:  when u s i n g  overcast  of  applied  impact  found  shortwave  those  relationship  and  reflectance  reflectances),  occurred  was  between  bidirectional  and o u t s i d e  corrections  cannot  a  the  following  target  clear  combination  target  assess  the  performance  function  relationship  satellite  stronger  best  linear  to  conceptual  from  overall  to  (viz.,  models).  linear  satellite  fundamental a  consistently  clear  led  i n d i v i d u a l BDR m o d e l s  surface  the  applying to  derived  is  and  four  inverse  adequately  satellite  of  applied  radiative a  regime  combination  cloudy cloudy  to  of  conditions) cases.  191  However, results in  despite  suggest  most  pixel  array  the  that has  the  a  in  on  transmission  of  related  In  little  few  the  to  the  situations  the  where were  unwarranted.  for  of  a  it  the  between  the  used,  reflectance  direction  satellite  of is  movement concluded  satellite  data  T and TR.  array  stations on  model  strengthen  systems,  satellite  overall  improvements  appears  averaging  effect  of  not  the  weather  the  the  bidirectional does  relationship  of  type  configuration  spatial  the  the  stronger,  pyranometric  has  a  TR.  synoptic  Irrespective number  and  be  the  impact  of data  optimum to  conclusions, of  BDR c o r r e c t i o n  the  prevailing  little  T  appears  appears  changes  3)  and  satellite  thus  Although  2)  irrespective  between  and  initial  application  the  relationship  negligible  of  the  to  relationship the  that  cases  correction  these  size,  for  increasing  estimating  relationship  the  between  T  TR.  4)  Increasing  substantial between  T  the  time  improvement and  TR,  in  with  averaging the  little  period  strength change  of in  results  the the  in  a  relationship nature  of  the  relat ionship.  5)  For  both  the  increasing  the  number  brightness  for  each  one of time  and images  two-hourly used  interval  to  averaging  calculate  results  in  a  periods,  the  target  strengthened  192  relationship images, time a  and  between at  period,  least  with  one-hourly  6)  and  The  between  radiative  images  maximum  five  for  and  the  greater  at  the  regimes)  appears  partly  produce as  of  coastal  cloudy  occurring  at  be  a  the  inland  least  are  between  as  strong  those  time  for  the  used.  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J o u r n a l o f t h e A t m o s p h e r i c S c i e n c e s . 19, 182-188.  200  APPENDIX 1 Symbols  UPPER CASE  ROMAN  ABAIR  Abbotsford  Airport  ABLIB  Abbotsford  Library  BDR  Bidirectional  C  Cloudiness  CTc  Clear  CTo  Overcast  D  Digital  Dr  Component of the C l o u d l e s s Due t o R a y l e i g h S c a t t e r i n g  Ds  C o m p o n e n t o f t h e C l o u d l e s s S k y D i f f u s e R a d i a t i o n Due to M u l t i p l e R e f l e c t i o n s Between the Ground and the Atmosphere (kjm'2hr_1)  D+ Q  Diffuse Irradiance for a H o r i z o n t a l Surface C l o u d l e s s S k i e s (kJm"2hr )  Fi  i t h Value  of  the  Observed  Fi  i t h Value  of  the  Estimated  F.O.N.  First  GOES  Geostationary  H  Solar  Hour  Io  Solar  Constant  I(o)  E x t r a t e r r e s t r i a l R a d i a t i o n R e a c h i n g the Top of the E a r t h ' s A t m o s p h e r e N o r m a l t o t h e S o l a r Beam, p e r Unit Surface Area (kjrn^hr"1)  K+  Shortwave R a d i a t i o n Surface (kjm^hr"1)  K4-Q  Shortwave R a d i a t i o n I n c i d e n t Under C l e a r S k i e s (kJm"2hr"x)  Sky  Reflectance  Index  (%)  Threshold Sky  Threshold  Brightness  Order  (%) (%)  Value  (counts) Sky D i f f u s e (kJnT2hr_1)  Sky  Radiation  Under  Translations Translations  Navigation Operational  Angle  Environmental  Satellite  (degrees)  (1353  Wm 2 )  Incident  on a H o r i z o n t a l  on  a  Horizontal  Surface  201  L  Limits  of  Integration  LAT  Local  MAA  A v e r a g e d R a d i a t i o n D a t a S e t s From A b b o t s f o r d A i r p o r t , A b b o t s f o r d C i t y and M i s s i o n C i t y  M.B.E.  Mean  NOAA  National  NR  Normalized  R  E a r t h ' s Radius Vector Sun-Earth Distance)  R.M.S.E.  Root  SE  Standard  SMS  Synchronous  S.O.N.  Second  SSEC  Space  S+0  D i r e c t Irradiance for a Horizontal Cloudless Skies (kjni^hr1)  T  Shortwave  T'  Shortwave T r a n s m i s s i o n C a l c u l a t e d U s i n g P r e c i p i t a b l e Water Data D e t e r m i n e d From R a d i o s o n d e D a t a (%)  T"  Shortwave T r a n s m i s s i o n C a l c u l a t e d U s i n g P r e c i p i t a b l e Water D a t a D a t e r m i n e d From the S m i t h (1966) Formulation (%)  TR  Target  TRTc  Clear  TRTo  Overcast  TRc  Clear  TRco  Partly  TRo  Overcast  Td  Dew-Point Temperature  Tr(O)  Transmission  Apparent  Bias  Mean  Time  (Hours)  Error Oceanic  and  Atmospheric Administration  Reflectance  Square  (the  Ratio  of  Actual  Mean  Error  Error Meteorological  Order Science  Satellite  Navigation and  Engineering  Transmission  Centre Surface  (%)  Reflectance Sky  Sky  Target Target Target  Cloudy  Reflectance Reflectance  Target  due  Threshold Threshold  Reflectance  Target  Reflectance  Reflectance  to  Under  (Degrees  Ozone  F)  202  Tr(R)  T r a n s m i s s i o n due t o R a y l e i g h  U  Total  UBC  University  VISSR  Visible  X  Slant  Path  Through  Water  (cm)  Xj  Slant  Path  Through  Ozone  (mm)  LOWER C A S E  P r e c i p i t a b l e Water of B r i t i s h  Infrared  Spin  Scan  Absorptivity  o f Ozone  a  w  Water  Absorptance  Vapour  b  Regression Coefficient  dn  Daynumber  m  Relative  n  Sample  p  Station  r  Optical  u  0  u  w  A i r Mass  Size Pressure (kPa)  Standard  Sea L e v e l  Coefficient  2  Radiometer  ROMAN  0  0  (mm)  Columbia  a  p  Scattering  Vertical  P r e s s u r e (101.3kPa)  of Determination  Path  Length  Vertical Optical V a p o u r (cm)  Path  Through Length  Ozone  (3.5mm)  Through  Water  GREEK ab  Atmospheric  as  Surface  ao  Statistical Coef f i c i e n t  <S  Solar  Z  Satellite  Albedo  f o rSurface Reflected  Radiation  Albedo Estimate of the Zenithal  Declination Viewing  Sun R e f l e c t i o n  (degrees) Zenith  Angle  (degrees)  203  9 6  Solar 0  Z e n i t h Angle  Angular  (degrees)  R e p r e s e n t a t i o n o f Day Number  (degrees)  X  F a c t o r Based on L a t i t u d e and Time of Year  P  Rho V a l u e  PTC  Rho V a l u e  for Clear  PTO  Rho V a l u e  f o r O v e r c a s t Sky T h r e s h o l d  pc  Clear  po.  O v e r c a s t Rho V a l u e  <> t  Sky T h r e s h o l d  Sky Rho V a l u e  Latitude  (degrees)  Sun-Satellite  Azimuth Angle  OTHERS Predicted Mean  or E s t i m a t e d Value  Value  '  C o r r e c t e d Value  *  Partial  Value  (degrees)  204  APPENDIX Landmarks  Landmark Moses  Name  Point  used  in  2  Earth-Location  Latitude (N) D M S 4 8 ° 41' 40"  Longitude (W) D M S 1 2 3 ° 28' 54"  Routine  Location Saanich Peninsula Vancouver Island  Beachy  Head  48°  18'  54"  1 2 3 ° 38'  39"  Vancouver  Island  Church  Point  48°  18'  56"  1 2 3 ° 34'  18"  Vancouver  Island  Texada (South  Island Tip)  49°  29'  26"  124°  08'  03"  Vancouver  Island  Lake Okanagan (South End)  49°  30'  00"  119°  34'  24"  B r i t i s h Columbia (South Central)  Lake Okanagan (North End, W e s t Arm)  50°  19' 5 4 "  1 19°  17'  24"  B r i t i s h Columbia (South Central)  Kootenay Lake (Cape Horn)  4  go  35'  48"  116°  49'  12"  B r i t i s h Columbia (South East)  Kootenay Lake ( N o r t h End)  50°  10*  18"  1 1 6 ° 55'  48"  B r i t i s h Columbia (South East)  Kootenay Lake (South End)  49°  1 1'  34"  116°  39*  29"  B r i t i s h Columbia (South East)  Slocan (South  49°  46'  13"  1 17°  28'  12"  B r i t i s h Columbia (South East)  W i l l i s t o n Lake ( E a s t Arm)  55°  56'  30"  1 2 2 ° 08'  24"  B r i t i s h Columbia (North)  Stuart (South  54°  23 '  30"  124°  16'  54"  B r i t i s h Columbia (North)  48°  56'  12"  1 2 2 ° 48'  36"  Washington ( N o r t h West)  Cape Flattery (Olympic Peninsula)  48°  22'  50"  124°  43'  48"  Washington ( N o r t h West)  Hood C a n a l (Puget Sound)  47°  20'  12"  1 2 3 ° 07'  06"  Washington (North West)  Birch  Lake End)  Lake East) Point  205  Landmark  Name  Latitude (N) D M S 4 6 ° 56' 36"  L o n g i t u d e (W) D M S 124° 09' 12"  Banks Lake ( N o r t h End)  47°  55'  57"  119°  05'  48"  Washington (Central)  Banks Lake (South End)  47°  37'  04"  119°  17'  13"  Washington (Central)  Priest Lake (South  46°  38'  08"  119°  53'  03"  Washington (Central)  Wanapum L a k e (South End)  46°  52'  05"  119°  57'  09"  Washington (Central)  Potholes Reservoi r (South End)  46°  59'  19"  119°  17'  18"  Wasington (Central)  Priest (South  48°  28'  59"  116°  51'  52"  Idaho (North)  Lake Pend Oreille ( E a s t End)  48°  09'  24"  116°  14'  06"  Idaho (North)  Lake Pend Oreilie (South West)  47°  58'  01"  1 1 6 ° 32'  04'  Idaho (North)  Coeur D ' A l e n e 47° L a k e (West End)  26'  58"  116° 5 4 '  55"  Idaho (West)  Columbia River Mouth (South S p i t )  46°  14'  12"  124°  00'  00"  Oregon ( N o r t h West)  T i l l a m o o k Bay (Head of Bay)  45°  29'  34"  123°  53'  05"  Oregon ( N o r t h West)  C o o s Bay ( N o r t h End)  43°  21'  09"  124  19'  18"  Oregon (South West)  Grays Harbour (North S p i t )  Rapids End)  Lake End)  Locat ion Washington (West)  206  Landmark  Name  C o o s Bay (South End)  L a t i t u d e (N) D M S 4 3 ° 20' 01"  L o n g i t u d e (W) D M S 1 2 4 ° 19' 05"  Locat ion Oregon (South West)  Cape  Arago  43°  17'  54"  124°  23'  18"  Oregon (South West)  Cape  Blanco  42°  50'  27"  124°  30'  33"  Oregon (South West)  Fern Ridge Reservoi r (North West)  44°  07'  25"  123°  18' 18"  Waldo Lake (South End)  43°  41'  14"  1 2 2 ° 06'  31"  Oregon (West)  Oregon (Central)  207  APPENDIX Equations  used  to determine  MODEL A P I X E L Using  t h e BDR c o r r e c t i o n s  CORRECTION  Values  P  TR' = TR /  Using  3  Target  (pc  + C (po  -  Pc) )  Reflectances TR' = T R c + C (TRO - T R c )  MODEL B P I X E L Using  P Values  Value  at  the Clear pTc  Value  at  =  Sky  the Overcast  Cloudy TRco  Overcast  Pixel  Pixel  Target  Target  Threshold:  (CTo) +  (1  -  C T o ) TR / T R o  (pTo - pTc)  (C -  CTc) /  (CTo - C T c )  =  P  0 . C + ( 1 - C ) T R /  TRo  Correction: TRc  Using  Sky  C T c ) + C T c (TR / T R c )  Correction: TRb  Clear  -  Correction:  = pTc +  Pixel  Threshold:  (1  P C  pTo = po Partly  CORRECTION  =pc(1  - O + C . T R /  TRc  Reflectances  Reflectance TRTc  Value  at  = T R c (1  the Clear -  CTc) +  Sky  Threshold:  (CTc) (TR)  208  Target  reflectance  Value  TRTo  Partly  Cloudy  Overcast  = TRo  Pixel  TRCO = T R T c  Pixel  +  Pixel  the  .  Overcast  CTo +  (TRTo  -  TRTc)  = TRo  .  (C  CTo)  TR  -  CTc)  /  (CTo  -  CTc)  (1 - C) TR  C +  Correction:  (1 - C )  = TRc  MODEL C P I X E L  + C  .  TR  CORRECTION  P Values  Value  at  the  Clear  Sky  Threshold: pTc  Value  at  the  Overcast  Partly  Cloudy  TRco  Overcast  Pixel  = TR /  Pixel  Pixel  ((C  =  P C '  Threshold: pTo  Clear  -  Threshold:  Correction:  TRc  Using  (1  Sky  Correction:  TRo  Clear  at  =  P O '  Correction: -  CTc)  P  o  +  (CTo  -  Correction: TRo  = TR /  po  TRc  = TR /  pc  Correction:  C)  P  c  /  (CTo  -  CTc))  209  Using Target  Target  Reflectances  Reflectance  Value  at  the  TRTc  Target  Reflectance  Value  at  Cloudy  TRco  Overcast  Clear  =  ((C  Pixel  Pixel  Pixel -  Sky  Threshold:  = TRc  the  TRTo  Partly  Clear  Overcast  Sky  Threshold:  = TRo  Correction:  CTc)  TRo +  (CTo  -  Correction: TR'o  = TRo  TRc  = TRc  Correction:  C)  TRc)  /  (CT o  -  CTc  )  

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