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The mesoscale variability of insolation over the Lower Fraser Valley resolved by geostationary satellite… Benchimol, Nicole 1985

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THE MESOSCALE V A R I A B I L I T Y OF INSOLATION OVER THE LOWER FRASER VALLEY RESOLVED BY \  GEOSTATIONARY S A T E L L I T E DATA by NICOLE BENCHIMOL  B.Sc,  The U n i v e r s i t y  of B r i t i s h Columbia,  1981  A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Geography)  We a c c e p t t h i s t h e s i s a s c o n f o r m i n g to the reguired  standard  THE UNIVERSITY OF B R I T I S H COLUMBIA January ©  Nicole  1985  Benchimol,  1985  !-6  In p r e s e n t i n g  this  thesis i n partial  fulfilment of the  r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y of B r i t i s h Columbia, I agree that it  freely  the Library shall  a v a i l a b l e f o r r e f e r e n c e and study.  agree t h a t p e r m i s s i o n f o r extensive for  financial  copying o r p u b l i c a t i o n of t h i s  gain  Department  of  It i s thesis  s h a l l n o t be a l l o w e d w i t h o u t my  permission.  Geography  The U n i v e r s i t y o f B r i t i s h 1956 Main M a l l V a n c o u v e r , Canada V6T 1Y3  (3/81)  thesis  s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e h e a d o f my  understood that  Date  I further  copying o f t h i s  d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . for  make  January 30, 1985.  Columbia  written  i i  ABSTRACT Assessments of the mesoscale v a r i a b i l i t y over  the lower  spatial  Fraser Valley  resolution  present,  h a v e been hampered by t h e  of the a v a i l a b l e  the establishment  network i s e c o n o m i c a l l y  attractive The  et  infeasible.  for estimating insolation i s  i s evaluated.  than  the observed  at smaller s p a t i a l satellite-based  of a c c u r a c y  down t o a 3 x 3 p i x e l  insolation.  are obtained  artifacts  to variations  i n maps o f t h e c l e a r  fields  Maps o f t h e mean degree  errors.  The  b e t w e e n snow a n d c l o u d ,  i n surface albedo  sky i n s o l a t i o n .  o t h e r hand, t h e mesoscale v a r i a b i l i t y  a good  with a high  due t o s m a l l s y s t e m a t i c m o d e l l i n g  i t s sensitivity  are believed  generally display  i n a b i l i t y o f t h e model t o d i s t i n g u i s h and  (about  scales.  estimates  insolation  inherent  a r e f o u n d t o be  of s p a t i a l averaging  correspondence w i t h the observed hourly estimated  insolation.  The e s t i m a t e s  to s p a t i a l averaging The e f f e c t s  estimates are  t o the s p a t i a l averaging  the s a t e l l i t e methodology.  13 km ) s c a l e .  (Gautier  insolation  The s a t e l l i t e - b a s e d  Discrepancies are attributed  The  observing  alternative.  shown t o be more c o h e r e n t  to occur  At  The a d a p t a t i o n o f  a l . , 1980) t o r e s o l v e t h e h o u r l y m e s o s c a l e  insensitive 2  inadequate  data.  a b i l i t y of a s i m p l e p h y s i c a l l y - b a s e d model  variability  in  pyranometric  of a dense ground-based  geostationary s a t e l l i t e data an  of t h e i n s o l a t i o n  introduce  On t h e  of i n d i v i d u a l  c a n n o t be r e s o l v e d u s i n g 'the s a t e l l i t e - b a s e d  hourly approach.  Errors  f o r t h e s e e s t i m a t e s a r e so l a r g e t h a t  variability  of the i n s o l a t i o n  field.  The  m a p p i n g p r o c e d u r e a p p e a r s t o be l i m i t e d average  insolation.  they obscure the  u s e f u l n e s s of t h e  t o a s s e s s m e n t s of t h e  TABLE OF CONTENTS PAGE ABSTRACT  i i  TABLE OF CONTENTS  iv  L I S T OF FIGURES  v i i  L I S T OF TABLES  x i  SYMBOLS AND ABBREVIATIONS  x i i  ACKNOWLEDGEMENTS  xv i i i  CHAPTER  I  INTRODUCTION  1  1.1  Background  1  1.2  Study O b j e c t i v e  5  1.3  Thesis Outline  6  CHAPTER I I  A REVIEW OF GEOSTATIONARY SATELLITE-BASED METHODS FOR ESTIMATING INSOLATION  2.1  Introduction  2.2  Geostationary  2.3  3.1  3.2  7 S a t e l l i t e - b a s e d Methods  2.2.1  Statistical  2.2.2  P h y s i c a l l y - b a s e d Models  Models  8 8 14  Summary a n d C o n c l u s i o n s  CHAPTER I I I  7  23  DATA AND PROCESSING TECHNIQUES  26  The S t u d y A r e a  26  3.1.1  29  General Climatology  Data A r c h i v e s 3.2.1  S o l a r R a d i a t i o n Network  30 Data  30  V  3.2.2  S a t e l l i t e Data  32  3.2.2.1  The GOES S y s t e m  32  3.2.2.2  Image N a v i g a t i o n  33  3.2.2.3  Data Conversion  34  3.2.2.4  Data Merging  34  3.3  Data S t r a t i f i c a t i o n  35  3.4  The G a u t i e r A l g o r i t h m  39  3.4.1  Implementation Averaging  3.5 Chapter  of a Moving F l u x  Array  39  3.4.2  C a l c u l a t i o n of Astronomical  3.4.3  E s t i m a t i o n o f O p t i c a l A i r Mass  3.4.4  E s t i m a t i o n of Water Vapour A b s o r p t i o n  3.4.5  E s t i m a t i o n of R a y l e i g h S c a t t e r i n g  44  3.4.6  E s t i m a t i o n o f Minimum B r i g h t n e s s  45  3.4.7  C a l c u l a t i o n of Cloud  Threshold  46  3.4.8 E s t i m a t i o n of Cloud A b s o r p t i o n C o n c l u d i n g Remarks  46 47  IV  Parameters  42 43 ........44  S A T E L L I T E CHARACTERIZATION OF THE MESOSCALE INSOLATION V A R I A B I L I T Y  48  4.1  Introduction  48  4.2  Method o f A n a l y s i s  48  4.3  R e s u l t s and D i s c u s s i o n  51  4.3.1  Network-based C o r r e l a t i o n s  51  4.3.2  Satellite-based Correlations  53  4.3.3  Comparisons Between t h e Observed and Estimated Insolation  55  4.3.4  Insolation Estimated 3 x 3 Pixel Arrays  63  Using  vi  4.3.5  4.4 Chapter  Satellite-based Correlations ( 3 x 3 pixel arrays)  Summary a n d C o n c l u s i o n s V  S A T E L L I T E MAPPING OF INSOLATION  5.1  Introduction  5.2  Implementation 5.2.1  5.3 5.4  5.5 Chapter  66 66 71 71  of t h e Mapping Procedure  71  Minimum B r i g h t n e s s P r e d i c t i o n s  72  S a t e l l i t e - b a s e d Mean H o u r l y I n s o l a t i o n Maps S p a t i a l V a r i a b i l i t y of the Hourly Estimated Insolation  76  5.4.1  Spatial Correlations  87  5.4.2  S p a t i a l Sampling Requirements f o r t h e Hourly Estimated Insolation  88  Summary a n d C o n c l u s i o n s VI  SUMMARY AND CONCLUSIONS  87  99 101  FOOTNOTES  104  BIBLIOGRAPHY  105  APPENDIX A  PROGRAM TO IMPLEMENT GAUTIER'S MODEL  112  A.1 M a i n P r o g r a m  112  A.2 S u b r o u t i n e s  114  A.3 F u n c t i o n s  139  APPENDIX B  C O E F F I C I E N T OF DETERMINATION AND STANDARD ERROR OF ESTIMATE OF THE MINIMUM BRIGHTNESS REGRESSION MODEL  141  vii  L I S T OF  FIGURES  Figure  Caption  2.1  The  clear  2.2  The  c l o u d y sky model  3.1  L o c a t i o n of the study a r e a  3.2  G e n e r a l i z e d land-use Valley  Page s k y model  and  ( f r o m G a u t i e r e t a l . , 1980) ( a f t e r G a u t i e r e t a l . , 1980)  map  i t s environs  of the lower (from  Fraser  Environment 28  3.3  L o c a t i o n of the  3.4a,b  Frequency d i s t r i b u t i o n s  12 s t a t i o n  sunshine monitored and UBC  pyranometric  a t V a n c o u v e r B.C.  3.5  The  insolation  4.1  Comparison between t h e Table  4.2a-d  The  a. b. c. d.  bright Hydro,  - 31 December  1981  m o d e l l i n g sequence  a t UBC  insolation  f o r the hours  37 41  observed listed  at  in  3.1  50  distance-correlation  observed  ...31  for:  t h e p e r i o d 1 J a n u a r y 1968 the data subset hours  and  network  of the h o u r l y  a. b.  Airport  .18 27  C a n a d a , 1973)  Airport  ...15  hourly  f u n c t i o n s of  the  insolation.  a l l data c l e a r sky d a t a p a r t l y c l o u d y sky o v e r c a s t sky d a t a  data  52  vi i i  4.3a-d  The  distance correlation  satellite-estimated pixel a. b. c. d. 4.4a-m  insolation  insolation.  The  5 x 5  54 estimated  l a t t e r are based  on  pixel arrays.  a.  a l l data  56  b. c. d. e.  Grouse Mountain data North Vancouver data V a n c o u v e r (B.C. H y d r o B l d g . ) d a t a . UBC d a t a  60  f. g. h. i.  A i r p o r t data Tsawwassen d a t a Langara data Abbotsford C i t y data  61  j. k. 1. m.  Abbotsford Airport Langley C i t y data P i t t Meadows d a t a M i s s i o n C i t y data  62  data  Comparison between the h o u r l y i n s o l a t i o n on t h e b a s i s of 5 x 5 and  3 x 3  estimated  p i x e l arrays  C o m p a r i s o n b e t w e e n t h e o b s e r v e d and  estimated  hourly  latter  insolation  b a s e d on 4.7a-d  on  data  C o m p a r i s o n s b e t w e e n t h e o b s e r v e d and 5 x 5  4.6  (based  the  arrays).  a l l data c l e a r sky data p a r t l y c l o u d y sky overcast data  hourly  4.5  f u n c t i o n s of  The  ( a l l data).  3 x 3 pixel arrays  distance-correlation  satellite-estimated 3 x 3 a. b. c. d.  The  pixel  are 67  f u n c t i o n s of  insolation  64  (based  the on  arrays).  a l l data c l e a r sky data p a r t l y c l o u d y sky o v e r c a s t sky data  data 69  ix  5.1a,b  5.2a-d  The v a r i a t i o n o f t h e c o e f f i c i e n t o f d e t e r m i n a t i o n 2 ( r ) o f t h e minimum b r i g h t n e s s r e g r e s s i o n m o d e l . 2 a. histogram of r 2 b. s p a t i a l d i s t r i b u t i o n of r A c t u a l and p r e d i c t e d d i u r n a l  73  v a r i a t i o n o f minimum  b r i g h t n e s s f o r J u l i a n day 196/79. a. b. c. d. 5.3a-d  l a n d t a r g e t (38,28) l a n d t a r g e t (68,3) water t a r g e t (3,33) water t a r g e t (48,53)  75  S p a t i a l d i s t r i b u t i o n o f t h e mean h o u r l y  estimated  insolat ion. a. b. c. d. 5.4a-d  c l e a r sky data p a r t l y cloudy sky data overcast sky data a l l data  77 78 79 80  S p a t i a l d i s t r i b u t i o n o f t h e mean h o u r l y  observed  insolat ion. a. b. c. d. 5.5  c l e a r sky data p a r t l y cloudy sky data overcast sky data a l l data  L o c a t i o n s of the c e n t r a l  81 82 83 84  p i x e l of 3 x 3 p i x e l  a r r a y s u s e d t o map t h e s a t e l l i t e - e s t i m a t e d insolation 5.6a-d  Variation  , of the c o r r e l a t i o n  85  of t h e s a t e l l i t e -  based e s t i m a t e s w i t h d i s t a n c e from t h e c e n t r e of a. b. c. d.  the study  area.  c l e a r sky data p a r t l y cloudy sky data overcast sky data a l l data  89 90 91 92  X  5.7a-d  V a r i a t i o n o f t h e s t a n d a r d d e v i a t i o n of  the  i n s o l a t i o n d i f f e r e n c e s w i t h d i s t a n c e from c e n t r e of the study a. b. c. d.  the  area.  c l e a r sky d a t a p a r t l y c l o u d y sky d a t a o v e r c a s t sky data a l l data  95 .96 97 98  xi  L I S T OF  TABLES  Table  Title  Page  3.1  C l a s s i f i c a t i o n of the h o u r l y data partly  4.1  into  clear,  c l o u d y and o v e r c a s t s k y c l a s s e s  Comparisons estimated  between  40  t h e o b s e r v e d ( K ^ ) and Q  (Kj) insolation  (the l a t t e r are  b a s e d on 5 x 5 p i x e l a r r a y s ) 4.2  Individual observed (the  4.3  station  57  c o m p a r i s o n s between  ( K ^ ) and e s t i m a t e d Q  (K|) i n s o l a t i o n  l a t t e r a r e b a s e d on 5 x 5 p i x e l a r r a y s )  Comparisons  between  the estimated  b a s e d on 5 x 5 a r r a y s a n d 3 x 3 4.4  the  Comparisons estimated  between  ....59  insolation  p i x e l arrays  ....65  t h e o b s e r v e d ( K ^ ) and  (Kl) insolation  Q  (the l a t t e r are  b a s e d on 3 x 3 p i x e l a r r a y s )  68  xii  L I S T OF SYMBOLS AND ABBREVIATIONS  SYMBOL (upper case)  QUANTITY  A  surface albedo  A  c l o u d albedo  n  D  (dimensionless) (dimensionless)  d i f f e r e n c e between t h e i n s o l a t i o n e s t i m a t e d a t two l o c a t i o n s ( k j m h  D  d i f f e r e n c e b e t w e e n t h e mean  )  insolation _ 2 -1  e s t i m a t e d a t two l o c a t i o n s ( k j m h H  )  t e r r a i n / s t a t i o n e l e v a t i o n (m) satellite-measured brightness  (counts)  m mean t a r g e t b r i g h t n e s s  (counts)  mean t a r g e t c l o u d b r i g h t n e s s  (counts)  p r e d i c t e d minimum b r i g h t n e s s ( c o u n t s ) n o r m a l i z e d p r e d i c t e d minimum b r i g h t n e s s (counts) Kf  upward-scattered the s a t e l l i t e  K^  t  c  2  1  _p  (kJm  insolation  Kj  o  observed  —i  )  (solar irradiance -2 -1 (kJm h )  f o r a c l e a r atmosphere  (kJm~ h~ ) 2  h  insolation  at the surface)  by  (kJm~ h~ )  cloud threshold radiance estimated  Kl  radiance observed  1  insolation  _2 — 1 (kjm h )  xi i i  mean e s t i m a t e d mean o b s e r v e d  o  insolation insolation  solar constant K'  (kJm  extraterrestrial  h  (kJm (kJm  h h  ) )  )  solar irradiance  (kJm~ h~ ) 2  M  1  relative optical  a i r mass  (dimensionless) N T  number o f o b s e r v a t i o n s o r d a t a surface dewpoint temperature  d  U  pairs  (°C)  p r e c i p i t a b l e water vapour content v e r t i c a l atmospheric  X, Y  c o l u m n (cm)  s t a t i o n v a r i a b l e names  (lower  case)  a(u)  water vapour a b s o r p t i o n c o e f f i c i e n t f o r an o b l i q u e p a t h a n g l e  1  s o l a r z e n i t h and s a t e l l i t e  2  angles, respectively  a(u ) , f c  a(u ) 1  a(u ). , a(u ). 0  azimuth  (dimensionless)  water vapour a b s o r p t i o n of the incoming f a  solar level,  9  (dimensionless)  water vapour a b s o r p t i o n c o e f f i c i e n t s f o r  a(u ), a(u )  1  ina  radiation  above and below c l o u d  respectively  (dimensionless)  water vapour a b s o r p t i o n of the s u r f a c e reflected  solar  r a d i a t i o n above and  below c l o u d l e v e l ,  respectively  (dimensionless) ©  instantaneous  Earth-Sun  d i s t a n c e (km)  xiv  mean E a r t h - S u n fractional  d i s t a n c e (km)  t a r g e t c l o u d amount  (dimensionless) Pearson  product-moment  correlation  coefficient  (dimensionless)  coefficient  of determination  (dimensionless) i  precipitable  water vapour content i n  oblique atmospheric estimated stations (kJm  T 2  h  or observed X a n d Y,  _ 1  c o l u m n (cm) insolation at  respectively  )  mean e s t i m a t e d  o r mean  observed  i n s o l a t i o n a t s t a t i o n s X a n d Y, _2 -1 r e s p e c t i v e l y (kJm h ) regression  coefficients  hour a n g l e  (degrees)  d i f f e r e n c e between t h e s a t e l l i t e subpoint longitude  l o n g i t u d e and t h e s t a t i o n (degrees)  zenith angle  (degrees)  cloud absorption coefficient (dimensionless)  XV  Rayleigh scattering direct  and  diffuse  coefficient beam  radiation,  respectively  (dimensionless)  azimuth  b e t w e e n t h e Sun  angle  satellite  for  and  the  (degrees)  water vapour path angle latitude  (degrees)  (degrees)  c o n f i d e n c e margin of  insolation  contours  (kJm~ h~ ) 2  1  solar  zenith  precipitable factor  angle  (degrees)  water vapour  f o r l a t i t u d e and  correction  season  (dimensionless) solar  declination  angle  standard  deviation  observed  over  12  (degrees)  of the  insolation  pyranometric  f o r a g i v e n hour  (kJm  standard deviation  _2  h  -1  )  of the  satellite-  m e a s u r e d minimum b r i g h t n e s s standard deviation observed  stations  (counts)  of the e s t i m a t e d  insolation,  and  respectively  (kJm~ h~ ) 2  1  standard deviation observed  of the e s t i m a t e d  insolation  respectively  (kJm  - 2  at stations h  -1  t h r e s h o l d v a l u e of the deviation (kJm" h~ 2  of t h e 1  or  %)  or  X and  Y,  ) standard  insolation  differences  xvi  atmospheric  transmittance  (dimensionless) transmittance for a clear  atmosphere  (dimensionless) a z i m u t h a n g l e o f t h e Sun  from  south  (degrees) a z i m u t h a n g l e of the s a t e l l i t e south  (degrees)  from  XVI 1  ABBREVIATIONS  GATE  GARP ( G l o b a l A t l a n t i c Tropical  Research P r o j e c t ) A t l a n t  Experiment  GMT  G r e e n w i c h Mean Time ( h )  GOES  Geostationary  Operational  Environmental  Satellite LAT  L o c a l A p p a r e n t Time ( h )  MBE  Mean B i a s E r r o r  METEOSAT  M E T E O r o l o g i c a l S A T e l l i t e (a European geostationary  (kJm h~ _ 2  1  satellite) — 2 -1 (kJm h o r %)  RMSE  Root-Mean-Square-Error  SE  Standard E r r o r of estimate  SR  o r %)  of t h e  minimum b r i g h t n e s s  (counts)  Satellite-measured  normalized  reflectance  (dimensionless)  VISSR  V i s i b l e and I n f r a r e d Spin-Scan  cv  coefficient  rpm  r o t a t i o n s per minute  Radiometer  of s p a t i a l v a r i a b i l i t y  (%)  xvi i i  ACKNOWLEDGEMENTS  I extend  my warmest  a p p r e c i a t i o n t o D r . J . E . Hay f o r  g u i d i n g t h i s s t u d y w i t h p a t i e n c e , c a r e and e n t h u s i a s m . thank  my s e c o n d  r e a d e r , D r . D.G. S t e y n ,  f o r t h e many  s u g g e s t i o n s he h a s p r o v i d e d ; Mark R o s e b e r r y  I helpful  f o r h i s computer  programming a s s i s t a n c e ; C l i f f o r d Raphael  and N e i l Wanless f o r  p o i n t s of a d v i c e and i n t e r e s t i n g debate.  T h a n k s t o numerous  other f r i e n d s  from  t h e D e p a r t m e n t o f G e o g r a p h y a t U.B.C. f o r  many e n j o y a b l e moments; p a r t i c u l a r l y t h o s e Cleughy, special  S a l l y a n d Dan. thanks  t o David  Lastly,  I'd l i k e  f o rh i sunflagging  fiends,  Ricardo,  t o extend  a very  support.  1  CHAPTER  I  INTRODUCTION 1.1  Background R e s e a r c h and development  of s o l a r r a d i a t i o n as a  f o r e n e r g y a p p l i c a t i o n s have been c a t a l y z e d o f t h e 1970s. the  Although world  resource  by t h e o i l embargo  o i l p r i c e s have s i n c e  declined,  l o n g - t e r m i n t e r e s t i n s o l a r r a d i a t i o n a s an a l t e r n a t i v e  and r e n e w a b l e e n e r g y s o u r c e r e m a i n s h i g h .  The  information  g e n e r a t e d o v e r t h e l a s t d e c a d e h a s h i g h l i g h t e d b o t h t h e need for  r e l i a b l e a s s e s s e m e n t s of t h e i n s o l a t i o n " ' a v a i l a b i l i t y and  the  l i m i t e d s p a t i a l coverage provided  networks Wilson,  1980; Hay, 1981; S u c k l i n g ,  spatial  variability.  a v a r i e t y of s p a t i a l  5 ( >10  variations  1982).  feature  of the i n s o l a t i o n i s  The i n s o l a t i o n v a r i a b i l i t y  scales which are defined  t h e phenomena t h a t c o n t r o l i t ( S t e y n  scale  observational  ( S u c k l i n g a n d Hay, 1976; Hay a n d S u c k l i n g , 1979;  A fundamental and r e l e v a n t its  by c u r r e n t  e x i s t s at  by t h e s c a l e s o f  e t a l . , 1981).  Macro-  5 m, >10  s) p a t t e r n s  i n cloudiness  a r e p r i m a r i l y a r e s u l t of  associated  with  synoptic  disturbances  (Hanson,  1980). Topographic f a c t o r s a r e s i g n i f i c a n t a t t h e 2 5 2 5 m e s o s c a l e (10 - 10 m, 10 - 10 s ) . The i n s o l a t i o n v a r i a b i l may a r i s e f r o m d i f f e r e n c e s and e l e v a t i o n  i n s h a d i n g (Hay a n d S u c k l i n g ,  (Hay, 1981), o r t h r o u g h o r o g r a p h i c  c o n t r o l s on c l o u d d i s t r i b u t i o n  ( A t w a t e r and B a l l ,  1980; G r e e n l a n d , 1978; Hay, 1 9 8 1 ) .  1979)  and t h e r m a l 1978; B a c h ,  In a d d i t i o n t o topography,  2  l a r g e u r b a n a r e a s may  induce m o d i f i c a t i o n s  p r o p e r t i e s of a r e g i o n . air  p o l l u t a n t s and  the  The  attenuation  i n the  atmospheric  of s o l a r r a d i a t i o n by  enhancement o f c i t y - c e n t e r e d  convective  c l o u d development are  e s t a b l i s h e d e f f e c t s (Rouse e t a l . ,  Peterson  and  1980;  -2  2  (10 by and  - 10  the  Stoffel, m,  10  0  - 10  2  e x p o s u r e ) of the  At  the  microscale  s) i n s o l a t i o n v a r i a t i o n s a r e c o n t r o l l e d  of the  receiving surface  insolation  (Monteith,  i n s o l a t i o n at a l l s p a t i a l  moreover, a f u n c t i o n of  s e a s o n and  i s integrated  (Hay  and  the  variability  occurs  time s c a l e over The  which latter  Generally,  s h o r t e s t time  scales  t o random v a r i a t i o n s i n s o l a r r a d i a t i o n a s s o c i a t e d  short-term The  weather changes (Hanson,  practical  reflected  i n the  monitoring  d e n s i t y of one distance  spatial  Gandin  In a r e p o r t  o f a b o u t 500  Service  i n the  they are  km)  (contiguous)  assessment i s not  Meteorological  (station  network  separation  t o r e s o l v e t h e m a c r o s c a l e mean  (Latimer,  inadequately  t o the World  250,000 km  While these requirements  i n n e t w o r k s o p e r a t e d by i n Canada  of i n s o l a t i o n  ( 1 9 7 0 a , 1970b) recommended a 2  s t a t i o n per  Service  1980).  representativeness  monthly i n s o l a t i o n f i e l d . realized  with  s i g n i f i c a n c e of t h e s e v a r i a t i o n s i s  networks.  Organization,  The  scales i s ,  Hanson, 1984).  over the  azimuth  1973).  i n t i m a t e l y r e l a t e d to observational p r a c t i c e s .  the h i g h e s t due  1977).  geometric c h a r a c t e r i s t i c s ( i . e . slope angle,  variability  is  Grosh,  1973;  the Atmospheric  1 9 8 0 ) , and United  sustained  on  Environment  the N a t i o n a l  States  (Suckling,  a global basis.  a p p l i c a b l e to c o a s t a l or  are  Weather 1982), Gandin's  mountainous  3  regions,  where s i g n i f i c a n t  Insolation  climatological gradients  over mountainous a r e a s ,  in particular, i s  o b s e r v e d s i n c e h i g h m a i n t e n a n c e c o s t s and accessibility  inhibit  the  radiation  the  poorly  difficult  i m p l e m e n t a t i o n of a  programme c o m m e n s u r a t e w i t h  exist.  monitoring  spatial complexities  of  the  regime.  Many s o l a r e n e r g y a p p l i c a t i o n s r e q u i r e d a t a a t meso- o r smaller  spatial  scales  (McVeigh, 1977).  Experimental  networks  h a v e been e s t a b l i s h e d t o a s s e s s t h e m e s o s c a l e i n s o l a t i o n variability  [Hay  investigations]. did  not  provide  (1984) has  r e v i e w e d s e v e r a l examples of  Unfortunately,  most o f t h e s e f i e l d  a c o m p l e t e c h a r a c t e r i z a t i o n of  variability  s i n c e t h e y were d e s i g n e d f o r  observation  only.  Fraser  The  d a t a were a c q u i r e d variability  over a p e r i o d  4.5  years.  lower  insofar  d o m e s t i c hot  water h e a t i n g  of o b s e r v a t i o n a l  i n v e s t i g a t i o n s of t h i s Various  i m p a c t on  the performance  s y s t e m s (Hay,  data there  are  1983). few,  as  The  of the mesoscale i n s o l a t i o n over t h i s r e g i o n  n o t e d t o have a s i g n i f i c a n t  paucity  short-term  is exceptional, of  studies  spatial  network e s t a b l i s h e d over the  V a l l e y of B r i t i s h C o l u m b i a  such  Due  i f any,  was  of to  the  other  type.  s t r a t e g i e s h a v e been d e v e l o p e d t o  i n s o l a t i o n a t l o c a t i o n s where d a t a a r e  estimate  unavailable.  The  t r a n s f e r o f d a t a f r o m i n s t r u m e n t e d s i t e s by e x t r a p o l a t i o n i n t e r p o l a t i o n may accuracies. shown t h a t  be  f e a s i b l e , d e p e n d i n g on  W i l s o n and  Petzold  the  or  required  ( 1 9 7 2 ) , amongst o t h e r s ,  have  i n s o l a t i o n d i f f e r e n c e s between s t a t i o n p a i r i n g s  4  increase the  with  an  Alberta  could  be  15%  of  the  tolerated, extrapolation  possible.  naturally Alaka,  Higher accuracies  greater.  1970)  and  Optimal  This  the  km  can  be  i n t e r p o l a t i o n of h o u r l y  Solar  cloudiness,  f o u n d t o be  the  strong  a s s e s s m e n t s due charateristics  Suckling  (e.g.  and  Few  insolation  of  (Davies,  1980).  the  (Hay,  1981).  the  the  observed  and  Suckling,  1977).  i n the Suckling  will  1979).  observed  sunshine  A t w a t e r and  Hay,  and  or Brown,  1974;  These models  11-20% o f  the  hourly  s p e c i f i c a t i o n of and  and  where  h a v e been d e s i g n e d f o r  to u n c e r t a i n t i e s  are  1965;  isotropic field  (Hay  would  these e x t r a p o l a t i o n  d a i l y estimates to within  insolation.  km  of  Valley  10%  ±35%  using  assessments over regions  h a v e a l s o been u s e d  provide  400  inadequate f o r  values to w i t h i n  are  estimate  t o a s s e s s m e n t s of  p a r a m e t e r s , s u c h as b r i g h t  D a v i e s e t a l . , 1975;  observed  of  achieved  of  (1979).  e r r o r of  r a d i a t i o n m o d e l s b a s e d on more w i d e l y  meteorological  generally  i f an  lower Fraser  i n t e r p o l a t i o n p r o c e d u r e s assume an  gradients  i n an  random e r r o r s  mean. I t i s i m p o r t a n t t o r e a l i z e t h a t  y i e l d appropriate  Suckling  i n t e r p o l a t i o n (Gandin,  been a p p l i e d  e x i s t i n g n e t w o r k was  directional  resulted  spatial variability  method has  and  for  British  However, d a t a r e q u i r e m e n t s  mesoscale i n s o l a t i o n over the  not  of e x t r a p o l a t i o n  to .distances  a c c o u n t s f o r b o t h the  observation field.  t o 50  a c t u a l value but,  i n t e r p o l a t i o n procedures.  The  Errors  were d e t e r m i n e d by Hay  example, e x t r a p o l a t i o n  error within  be  distance.  m a c r o s c a l e i n s o l a t i o n around network s i t e s i n  C o l u m b i a and As  separation  Hay  cloud  ( 1 9 7 9 ) have  5  shown t h a t a s i g n i f i c a n t gained  w i t h the  improvement i n s p a t i a l c o v e r a g e i s  i n c o r p o r a t i o n of m o d e l l i n g  added t h a t s u c h p r o c e d u r e s a r e devoid  of t h e n e c e s s a r y  In t h i s potentially  sparse  better  i n f o r m a t i o n where c o n v e n t i o n a l  than those  ( R a p h a e l and  1.2  Study The  Hay,  derived  from ground-based  derived  investigated.  w o u l d be scales.  i s t o determine whether  from a s a t e l l i t e - b a s e d  i t s environs. of the  Although  over  the  I f t h i s approach i s  satellite-based field  will  network d e f i c i e n c i e s occur  s c a l e s , the mesoscale i s w e l l - s u i t e d t o a i n v e s t i g a t i o n of t h i s t y p e .  compromise between the s y s t e m and  procedures  r e s o l v e the mesoscale v a r i a b i l i t y  F r a s e r V a l l e y and  preliminary  or  1984).  o b j e c t i v e of t h i s s t u d y  spatial  network coverage i s  with a c c u r a c i e s comparable to  successful, c e r t a i n aspects  all  collecting  Objective  p r o c e d u r e , can  t h e n be  of  From a  S a t e l l i t e - b a s e d m o d e l s h a v e a l s o been  estimates  insolation estimates,  lower  represent  insolation.  i n space, s a t e l l i t e s are capable  shown t o p r o v i d e  they  over l a r g e areas  satellites  useful tools for estimating  or n o n - e x i s t e n t .  but  parameters.  respect, meteorological  vantage p o i n t relevant  input  ineffective  sites,  the very  spatial  I t provides  r e s o l u t i o n of the  large s a t e l l i t e  data  a  sensing  processing  r e q u i r e d to r e s o l v e i n s o l a t i o n at broader  which spatial  at  6  1.3  Thesis Outline A g e n e r a l r e v i e w of t h e methods f o r e s t i m a t i n g  from s a t e l l i t e  data i s p r o v i d e d i n Chapter  insolation  I I . Chapter I I I  contains a description  of t h e s t u d y a r e a , d a t a s a m p l i n g and  p a r a m e t e r i z a t i o n s used  i n the m o d e l l i n g process.  The  suitability  of the s a t e l l i t e approach  f o r mesoscale  variability  assessments  i n Chapter  mapping p r o c e d u r e  i s determined  i s applied  i n C h a p t e r V.  summarizes the r e s u l t s of t h i s  insolation  I V , and t h e  C h a p t e r VI  investigation.  7  CHAPTER I I A REVIEW OF  2.1  GEOSTATIONARY SATELLITE-BASED METHODS ESTIMATING INSOLATION  FOR  Introduction Solar  modified  r a d i a t i o n i n c i d e n t at the  by  absorption  and  Earth-Atmosphere system. external  sensing  t o p of  the atmosphere i s  s c a t t e r i n g processes within Meteorological  s a t e l l i t e s provide  p l a t f o r m c a p a b l e of m o n i t o r i n g  e n e r g y s c a t t e r e d back t o space.  the  the  radiant  However, a p r o c e d u r e i s  r e q u i r e d t o d e d u c e f r o m t h e s e m e a s u r e m e n t s t h e amount of r a d i a t i o n which i s r e c e i v e d at the Earth's The  use  circumscribed can  be  surface.  by  the  l i m i t e d amount o f  from the  information  satellite-measured  that  radiances.  C o n s e q u e n t l y , a p p r o a c h e s have b e e n s i m p l i f i e d  for  satellite  a p p l i c a t i o n s through s t a t i s t i c a l parameterizations p h y s i c a l l y - b a s e d models.  Both r e q u i r e s a t e l l i t e  to i n f e r atmospheric a t t e n u a t i o n .  methods a t t e m p t t o c o r r e l a t e the  s a t e l l i t e and  r a d i a t i v e transfer processes.  m e t h o d s r e l y on satellites This  the  frequent  The  and  visible  surface explicitly  more s u c c e s s f u l  coverage provided  by  t o account f o r d i u r n a l v a r i a t i o n s i n sky study  will  d e v e l o p e d by G a u t i e r  apply  a physically-based  et a l . (1980).  simple  Statistical  measurements, w h i l e p h y s i c a l l y - b a s e d p r o c e d u r e s model the  solar  of d e t a i l e d r a d i a t i v e t r a n s f e r models i s  extracted  radiances  an  geostationary cover.  procedure  Models f o r  estimating  8  insolation  from g e o s t a t i o n a r y s a t e l l i t e d a t a w i l l  in t h i s chapter selection  of the G a u t i e r approach  ( 1 9 8 3 ) and  excellent 2.2  can  Exell  (1984),  be a s s e s s e d .  and  provide  summaries.  Statistical  Methods  Models  T h e s e m e t h o d s a r e g e n e r a l l y b a s e d on linear  the  Some o f  Riordan  in particular,  Geostationary Satellite-based  2.2.1  reviewed  i n order to g a i n a p e r s p e c t i v e from which  t h e s e m e t h o d s have been d i s c u s s e d e l s e w h e r e ; Hulstrom  be  regressions.  Hay  s i m p l e and m u l t i p l e  and Hanson ( 1 9 7 8 ) u s e d a  simple  r e l a t i o n s h i p between t h e s a t e l l i t e - m e a s u r e d n o r m a l i z e d reflectance  ( S R ) ^ and  atmospheric  transmittance  , of  the  form: 0 = a + bSR w h e r e , a and  (2.1)  b are the r e g r e s s i o n c o e f f i c i e n t s .  represents the  fraction  of t h e e x t r a t e r r e s t r i a l  (K') w h i c h  i s i n c i d e n t at the s u r f a c e , Equation  rearranged  to y i e l d  insolation  K j = K'(a  2.1  irradiance  can  be  + bSR)  (2.1a)  m o d e l a s s u m e s an  and  the s a t e l l i t e - m e a s u r e d r e f l e c t a n c e .  The  solar  (K|):  The  correspond  S i n c e 4>  inverse linear variation  t o c l o u d i e r v i e w s and  thereby  between  insolation  Hence, b r i g h t e r t o a lower  r e g r e s s i o n c o e f f i c i e n t s were d e v e l o p e d  from  scenes  insolation. data  9  acquired B-scale  d u r i n g GATE  (27 J u n e - 20 S e p t e m b e r  2 3 (10 - 10 km), u s i n g  array  3 km r e s o l u t i o n .  1974) o v e r t h e  satellite pixels  Comparisons w i t h ship-board  3  at a  observations  showed t h a t t h e i n s o l a t i o n c o u l d be e s t i m a t e d  t o w i t h i n 22%  f o r h o u r l y v a l u e s , a n d 10% f o r d a i l y  Poorer  were o b t a i n e d location  when t h e model was v e r i f i e d  ( R a p h a e l a n d Hay, 1 9 8 4 ) .  coefficients  various  regression  i n e f f e c t i v e l y accounted f o r the d i f f e r e n t  t o improve m o d e l l i n g  Hart  results  fora mid-latitude  The o r i g i n a l  p r o p e r t i e s of m i d - l a t i t u d e c l o u d s necessary  totals.  and t h e i r  capabilities.  a n d Nunez ( 1 9 7 9 ) d e r i v e d  locations in Australia.  r e - e v a l u a t i o n was  similar  expressions f o r  The mean a c c u r a c y  of the  d a i l y estimates  was s i m i l a r  Hanson  H o w e v e r , t h e p e r f o r m a n c e o f t h e m o d e l was  (1978).  found t o vary  t o t h a t r e p o r t e d by Hay a n d  with regional meteorological  (1984) has i n d i c a t e d t h a t t h e s t a b i l i t y p a r a m e t e r s a,  b (Equation  conditions.  Exell  of t h e r e g r e s s i o n  2.1) c a n be s i g n i f i c a n t l y a f f e c t e d  by v a r i a t i o n s i n s u r f a c e a l b e d o a n d a t m o s p h e r i c a e r o s o l A comparatively Tarpley  s o p h i s t i c a t e d p r o c e d u r e was d e v e l o p e d by  (1979) u s i n g m u l t i p l e l i n e a r  requires v i s i b l e rological  content.  radiances  regressions.  The model  f r o m GOES a n d c o n v e n t i o n a l  (surface pressure,  p r e c i p i t a b l e water)  meteo-  observations.  U n l i k e t h e Hay a n d Hanson a p p r o a c h , t h i s model a t t e m p t s t o to account  f o r v a r i a t i o n s i n the r a d i a t i v e p r o p e r t i e s of the  a t m o s p h e r e by s t r a t i f y i n g The  hourly  insolation  the data  i s estimated  according  t o c l o u d amount.  from t h e f o l l o w i n g  10  expressions: K| = a  ]  K| = a  2  = c  3  + b^ose  + c^  +  + c n(I /I^)  fc cose 2  + dn  Q  + e <  }  2  1  I m  /I >  2  n  + Jocose + c ( I / I ^ ) 3  n < .4  2  p  (2.2a)  n <_ .4 < 1.0  (2.2b)  n = 1.0  (2.2c)  2  n  where 6  solar zenith  ^  transmittance  n  fractional  angle f o r a c l e a r atmosphere  target cloud  amount  A  I  mean t a r g e t  I  mean t a r g e t c l o u d  brightness  Ip  p r e d i c t e d minimum  brightness  Ip  normalized  p r e d i c t e d minimum  regression  c o e f f i c i e n t s ( i = 1,3)  G  i '  6  i '  c  i  brightness  brightness  d. ,e. l'  l  The p a r a m e t e r s n, I satellite  imagery; I  m  and I  a r e deduced from t h e  i s evaluated  as a f u n c t i o n of the s o l a r  z e n i t h and t h e S u n - s a t e l l i t e a z i m u t h a n g l e s I'p i s d e r i v e d of  f r o m Ip n o r m a l i z e d  (see Section  f o r a s o l a r z e n i t h a n g*l e o f  45° a n d a S u n - s a t e l l i t e a z m u t h a n g l e o f 1 0 5 ° ; ^  c  determined e m p i r i c a l l y and i n c l u d e s a t t e n u a t i o n s c a t t e r i n g , water vapour s c a t t e r i n g (Davies water vapour a b s o r p t i o n brightness Ip)  ( M c D o n a l d , 1960).  is  due t o R a y l e i g h  e t a l . , 1975) a n d The mean  target  ( I o r I ) a n d i t s p r e d i c t e d minimum v a l u e m  n  a r e expressed as a r a t i o  3.4.6);  (Ip or  t o reduce the i n f l u e n c e of sensor  11  instabilities  (Tarpley,  1979).  The  model uses a  r e l a t i o n s h i p between i n s o l a t i o n and brightness  to account f o r the  of t h e GOES v i s i b l e c h a n n e l The for  50  c o e f f i c i e n t s of  km  x 50  km  estimated  of  (n =  1.0).  satellite-measured  the  ( J u s t u s and  the  nominal  (.4  8 km  States.  ^ n < 1.0)  Daily estimates  1983).  equations  were d e v e l o p e d  pixels, The  10%' u n d e r c l e a r s k i e s  skies  calibration  Tarpley,  regression  the U n i t e d  to w i t h i n  under p a r t l y cloudy skies  form of  t a r g e t s , r e s o l v e d by  Great P l a i n s region was  the  second-order  and  the  hourly i n s o l a t i o n (n <  50%  were w i t h i n  over  .4),  under  10%  of  30% overcast  the  o b s e r v e d mean i r r a d i a n c e . A large proportion accounted  f o r by  of the  the cos0 term.  r a t i o s a l s o became i m p o r t a n t Although other 1% l e v e l , minor  The  of t h e  i n s o l a t i o n was  s a t e l l i t e - b a s e d brightness  parameters for cloudy  v a r i a b l e s ( i . e . i | / , n) c  cases.  were s i g n i f i c a n t a t  t h e i r c o n t r i b u t i o n t o t h e a c c u r a c y of t h e m o d e l  (Tarpley,  1979).  (Tarpley,  1981).  estimated  by: Kjr  of  The  =  a  the d a i l y  an a c c u r a c y o f ±12%.  was  subsequently  i n s o l a t i o n f o r a l l sky  +  c(I  cover c l a s s e s  /Ip)  bcosd  +  total  i n s o l a t i o n were o b t a i n e d  m  C o m p u t a t i o n a l and  in estimation  B r a k k e and  was  produced was  (2.3)  surface-based  r e q u i r e m e n t s were r e d u c e d a t t h e e x p e n s e o f o n l y a degradation  the  A s i m p l i f i e d v e r s i o n of t h e model based  on a s i n g l e r e g r e s s i o n e q u a t i o n  Estimates  variance  with data  small  accuracy.  Kanemasu ( 1 9 8 1 ) d e v e l o p e d a s i m i l a r  expression  12  for estimating  insolation,  where:  K j = a + b(l The  ~ I ) + c6  m  m  (2.4)  p  method i s b a s e d on t h e d i f f e r e n c e b e t w e e n , r a t h e r  r a t i o o f t h e mean t a r g e t b r i g h t n e s s brightness.  This  formulation  to v a r i a t i o n s of b r i g h t n e s s  and i t s e s t i m a t e d  within a target.  The r e g r e s s i o n  t o w i t h i n 1 1 % i n summer.  c l o u d c o v e r c o n d i t i o n s w h i c h were n o t a d e q u a t e l y by  the r e g r e s s i o n , lower a c c u r a c i e s  winter  estimates.  they w i l l  The d a i l y Due t o represented  (±36%) were o b t a i n e d f o r  I t must a l s o be r e c o g n i z e d  errors are relative,  clear  a p p e a r s t o be more s e n s i t i v e  c o e f f i c i e n t s were d e r i v e d o v e r t h e G r e a t P l a i n s . i n s o l a t i o n was e s t i m a t e d  than t h e  that, since the  appear l a r g e r i n w i n t e r  as a  r e s u l t o f a l o w e r mean i r r a d i a n c e . Tarpley's Justus  (1981) model  and T a r p l e y  (Equation  2.3) was m o d i f i e d  by  (1983) t o t h e form: K*  = K*  c  +  d(l  2  - 1 )  (2.5)  2  m  where K^ K^  c  (2.5a)  i s t h e i n s o l a t i o n f o r a c l e a r atmosphere. T h i s  provides the  c  2 3 = a c o s 0 + fccos d + c c o s 6  estimates  of the d a i l y  version  i n s o l a t i o n t o w i t h i n 10% o f  o b s e r v e d mean a n d t h u s p e r f o r m s a s w e l l a s T a r p l e y ' s  stratified The  model.  r e g r e s s i o n models d i s c u s s e d  insolation  (1979)  above  parameterized  from the s a t e l l i t e - m e a s u r e d b r i g h t n e s s .  Senn ( 1 9 8 1 ) d e v e l o p e d a method w h i c h i n c o r p o r a t e s  H i s e r and these  13  m e a s u r e m e n t s s t r i c t l y as  surrogates  a p p r o a c h i n v o l v e d t h e d e r i v a t i o n of b e t w e e n i n s o l a t i o n and was to  subsequently  satellite  surface-based  opaque c l o u d c o v e r .  correlated with  e s t a b l i s h an  f o r c l o u d amount.  Their  relationships  Satellite  brightness  f r a c t i o n s o f opaque c l o u d  cover  i n d i r e c t c o r r e s p o n d e n c e between i n s o l a t i o n  brightness.  The  transforms  were p r e s e n t e d  and  in graphical  format. The provide  method assumes t h a t t h e i n f o r m a t i o n on  observations.  sky  cover  However, t h e  surface  i n t e r a c t i o n s and  a l s o , c l o u d type sensor  i n f l u e n c e of the d i f f e r e n t  and  below c l o u d  not  considered.  l e v e l ) on  the  There are  satellite  response  sensor  f o r m of t h e  w i l l tend  surface observations cloud cover. is provided  No  overestimation  characteristics. (above  relationship is  clouds  sources  introduce  smaller  a c c o u n t e d f o r ; t h e use  to overestimate  than of  in'solation  contribute to d i f f e r e n c e s i n  and  perceived  assessment of model performance  the authors  under o v e r c a s t  Statistical the e f f i c i e n t  may  not  geometry,  t h e a s y n c h r o n i c i t y of s a t e l l i t e  systematic  although  and  image n a v i g a t i o n a l o f f s e t s may  u n d e r c i r r u s c l o u d , and  have a  a l s o a number o f p o t e n t i a l  f i e l d - o f - v i e w are not  opaque c l o u d c o v e r  surface-based  observational viewpoints  e r r o r s p a r t i c u l a r l y at c l o u d boundaries;, the  to  They i n t e g r a t e t h e e f f e c t s ,  The  of e r r o r :  equivalent  s a t e l l i t e brightness data  d i f f e r e n t p h y s i c a l meaning. o n l y o f c l o u d amount, b u t  s a t e l l i t e - b a s e d measurements  indicate a bias  towards  conditions.  m o d e l s h a v e been d e v e l o p e d w i t h e m p h a s i s  processing  of d a t a  for potential routine  on  14  application.  They p r o v i d e  insolation.  However, t h e s e  cloudy  c o n d i t i o n s due  simple  procedures for estimating  methods p e r f o r m p o o r l y  to t h e i r  inability  c o m p l e x r e l a t i o n s h i p s b e t w e e n c l o u d and transmittance.  c h a r a c t e r i z a t i o n of c l o u d  2.2.2  i n the  and  provide  an  Such methods  model improved are  following section.  model d e v e l o p e d by G a u t i e r  r e p r e s e n t a t i v e of t h i s a p p r o a c h . c a l i b r a t e d GOES r a d i a n c e s the a b s o r p t i o n  and  Separate algorithms and  atmospheric  h e n c e may  interations.  the  P h y s i c a l l y - b a s e d Models The  on  to account for  Physically-based procedures e x p l i c i t l y  r a d i a t i v e t r a n s f e r processes  described  under  cloudy The  et a l . (1980) i s  The  at p i x e l  procedure  requires  r e s o l u t i o n and  information  s c a t t e r i n g p r o p e r t i e s of the  are  used to e s t i m a t e  atmosphere.  insolation  for clear  atmospheres.  c l e a r sky  radiance  c o m p r i s e d of b a c k - s c a t t e r e d ( F i g u r e 2.1) Kt = K-'a  and + K'(1  o b s e r v e d by and  i s expresssed - a)[l -  the  satellite  (Kt) i s  surface-reflectedradiation as:  a f u ^ J I l  - a(u )]d 2  - a )A }  (2.6)  where K' a,  extraterrestrial a  irradiance  Rayleigh scattering c o e f f i c i e n t s for direct d i f f u s e beam r a d i a t i o n , r e s p e c t i v e l y  1  and  a(u ), a(u )  water vapour a b s o r p t i o n c o e f f i c i e n t s f o r s o l a r z e n i t h and s a t e l l i t e v i e w i n g a n g l e s , r e s p e c t i v e l y  A  surface  1  2  albedo  K' =K„cos0  K'(l-a)(l- (u,))A(l-a,)(l- (u ))  K' a  a  z  •A  ABSORPTION  / \ SCATTERING \ /  v  y \ \  K'(l-a)  \ \ \  K'll-orXl-afu.JjAO-a,)  / \\ I SCATTERING JG / \ /  \ \  N^K'O-aXl-a^JjAa,  ABSORPTION \  /  \ K'(l-a)(,-a( )) U l  Figure  a  2.1  /  K'(l-a)(,-a(u,))A  \  The c l e a r s k y m o d e l ( f r o m G a u t i e r e t a l . , 1 9 8 0 ) . R e f e r t o t e x t f o r d e f i n i t i o n of symbols.  2  16  The  c l e a r sky a t t e n u a t i o n  i s a p p r o x i m a t e d by R a y l e i g h s c a t t e r i n g  and w a t e r v a p o u r a b s o r p t i o n . obtained  Scattering coefficients  from summaries i n C o u l s o n  (1959) w h i l e  are  absorption  c o e f f i c i e n t s are c a l c u l a t e d using e m p i r i c a l functions developed by P a l t r i d g e ( 1 9 7 3 ) :  a(u) = 0.099u* a(u) = 0.14u'  3 4  4 4  u > 0.5  cm  (2.7a)  u < 0.5  cm-  (2.7b)  where u = Usecfi  (2.8)  U i s the p r e c i p i t a b l e water c o n t e n t i n a v e r t i c a l column and  seed  i s t h e a i r mass a d j u s t m e n t w h i c h d e p e n d s on  the water vapour path angle ( 6 ) . the  atmospheric  E q u a t i o n 2.6  i s solved for  surface albedo:  A = (Kt - K'a)/K'(1  " a)[1 - a ( u ) ] [ l 1  - a(u )](1 2  and t h e s o l a r r a d i a t i o n i n c i d e n t a t t h e s u r f a c e estimated  - a)[l - a(u )](l 1  (K|) i s  + ajA)  r a d i a t i v e t r a n s f e r s i n a cloudy  c o m p l e x due  (2.10)  a t m o s p h e r e ,are more  to a d d i t i o n a l i n t e r a c t i o n s with clouds  The m o d e l i s o p t i m i z e d clouds.  (2.9)  by:  K| = K'(1 The  - a,)  (Figure  2.2).  f o r low- t o m i d - l e v e l s t r a t i f o r m  Atmospheric water vapour  i s p a r t i t i o n e d above  below  c l o u d l e v e l w i t h 70% o f t h e t o t a l a b s o r p t i o n  below  the c l o u d base.  Rayleigh  and  applied  scattering i s specified  above  17  t h e c l o u d mass o n l y .  Cloud  r e f l e c t i o n p l a y s a dominant  role  i n a t t e n u a t i n g t h e incoming s o l a r r a d i a t i o n and i s i n f e r r e d from t h e s a t e l l i t e - m e a s u r e d b r i g h t n e s s . due  to cloud absorption  i s more d i f f i c u l t  The a t t e n u a t i o n to assess  measurements a r e seldom a v a i l a b l e and m o d e l l i n g a poor understanding  of cloud microphysics.  (1980) a d o p t e d a s i m p l e absorption  as a l i n e a r  approximation  since  i s l i m i t e d by  Gautier  et a l .  which s p e c i f i e s  cloud  f u n c t i o n of c l o u d b r i g h t n e s s ,  varying  b e t w e e n 0% f o r no c l o u d t o 2 0 % f o r maximum b r i g h t n e s s . i s argued that b r i g h t n e s s thereby,  It  i s r e l a t e d t o c l o u d t h i c k n e s s , and  to cloud absorption.  In r e a l i t y ,  the r e l a t i o n s h i p  i s not a s t r a i g h t o r w a r d one. The  radiance  m o n i t o r e d by t h e s a t e l l i t e o v e r a  cloudy  atmosphere i s g i v e n by: K t = K'a + K'(1 - o ) [ 1 - a ( u ) 1  f c  ]A (l - a )[1 n  1  + K'(1 - o ) [ l - a ( u ) ] ( 1 - A ) ( 1  - $) [1 - a (  2  1  x A[1 - a ( u ) ] ( l 2  b  t  a(u ) ] 2  2  n  - c^Hl - a(u ) ] 2  t  U l  t  ) ] b  (2.11)  where v a r i a b l e s n o t p r e v i o u s l y d e f i n e d a r e : a(Uj) ,  a(u )  b  a(u ) ,  a(u )  b  t  2  t  $ A  n  Equation  1  2  water vapour a b s o r p t i o n of t h e incoming s o l a r r a d i a t i o n above and below c l o u d l e v e l , respectively water vapour a b s o r p t i o n of t h e s u r f a c e r e f l e c t e d s o l a r r a d i a t i o n above and below cloud l e v e l , respectively cloud  absorption  cloud  albedo  2.11 i s s o l v e d f o r A , w h i c h i s t h e n u s e d t o c a l c u l a t e n  K  K' =K„cos0  . (i- )(i-a(u ) )A (l-Di )(t-a(uj) ) a  1  (  11  1  l  JL  £_  /  s i  K' ( l - a ) ( l - a ( ) , ) ( l - A ) ( l - <J> ) ( l - a ( u ) ) A ( l - a ( u ) ) ( l - a , ) ( l - a ( u ) , ) J  U l  \  SCATTERING \ /  y  _  /  \ 1  U l  2  \  /  /  n  /  I  KlA(l-a( )J(l-A )(l - * )(!-«,) n  U j  \  SCATTERING \^ j  ABSORPTION /  b  /  K'(l-a)(l-a( ),)A ( -«i)  / \ SCATTERING \ /  \  1  ABSORPTION  /  K-(l-«) \  2  n  /  ABSORPTION  \  v  1  K'a  ^K(l-a)(l-a(  U l  ) )A «, t  n  >  _ KlA(l-a(u ) )(l-A„)(l-.|>)a 2  b  I  K'(l-a)(l-a( ),)A„  /  U l  Kl-A(l-a(u X)(l-A.Xl-*) 1  ABSORPTION  ABSORPTION  ( - ( )b) n  K-(l-a)(l-a(u,),)(l-Aj(l-* ) \  1 a U KI'A(I-B(U.  A  2  /  \  /  KU(l-a(u,),)  ABSORPTION ABSORPTION \  /  \  Kl=K'(l-a)(l-a(u ),)(l-A„)  *  1  /  KlA  x(l-*)(l- (u,) ) a  Figure  2.2  b  The c l o u d y s k y model ( a f t e r G a u t i e r e t a l . , 1 9 8 0 ) . R e f e r t o t e x t f o r d e f i n i t i o n of symbols.  6  2  19  the  insolation according t o :  K| = K'(1 - O ) [ 1 - a ( u ) 3 d 1  To d e t e r m i n e  - A )(1 - *)[1 - a ( u ) ]  t  n  1  whether the s a t e l l i t e  or cloudy views, a t h r e s h o l d i n t e n s i t y B r i g h t n e s s values which  exceed  as c l o u d y and a r e p r o c e s s e d Otherwise,  the clear  this  estimates are subsequently  i s calculated.  the cloudy sky a l g o r i t h m .  on a p i x e l - b y - p i x e l  i n the i n s o l a t i o n  averaged  t o compensate f o r v a r i a t i o n s  over  8 x 8  visible  satellite  and s u r f a c e o b s e r v a t i o n s .  basis  field. pixel  i n the s e n s i t i v i t y  satellite  These  arrays  of the e i g h t  s e n s o r s and t h e a s y n c h r o n o u s n a t u r e of t h e  the u s e f u l n e s s of t h i s  I n an a t t e m p t  s t r a t e g y , Raphael  e s t i m a t e s of the i n s o l a t i o n averaged  significant  clear  sky a l g o r i t h m i s implemented.  to resolve s p a t i a l v a r i a t i o n s  from  represent  reference are c l a s s i f i e d  through  C a l c u l a t i o n s are performed  w i t h those  data  (2.12)  b  5 x 5  arrays.  to assess  (1982) compared  over  His results  8 x 8  pixel  arrays  r e v e a l e d no  differences.  A number o f a s s u m p t i o n s  are inherent i n the Gautier  model: (a)  i n s t a n t a n e o u s r a d i a n c e s m e a s u r e d by t h e s a t e l l i t e a r e  r e p r e s e n t a t i v e of c o n d i t i o n s over (generally cover  30 o r 60 m i n u t e s ) .  remains  relatively  the i n t e r v a l  The a s s u m p t i o n  invariant  which  i m p l i e s that sky  between measurements.  t h i s c o n d i t i o n may be s u s t a i n e d f o r c l e a r significant  of observation  or overcast sky c o v e r s ,  d e p a r t u r e s may o c c u r u n d e r p a r t l y c l o u d y  a r e more v a r i a b l e  i n time and space  While  skies  (Diak e t a l . , 1 9 8 2 ) .  20  S p a t i a l averaging  i s an a t t e m p t t o r e d u c e t h e s i g n i f i c a n c e of  t h i s p o t e n t i a l source (b) and  of e r r o r ;  broad-band p a r a m e t e r i z a t i o n s absorption  are a p p l i e d although  r e s p o n s e i s between  .55  and  .75  processes  absorption  o f s o l a r r a d i a t i o n by  satellite  In  water vapour  i n t h e n e a r - i n f r a r e d p o r t i o n of t h e  water vapour a b s o r p t i o n  of a e r o s o l  absorption  (Mie)  s o l a r spectrum,  satellite; and  Rayleigh  s c a t t e r i n g are  s c a t t e r i n g i s mathematically  which are not  and  3% of t h e t o t a l  attenuation absorption and (d)  .75  complex and  i n the  1969).  ultra-violet  i n the v i s i b l e  factor  v a r i e s between  (Kondratyev,  1.5  Ozone  but  weak  r e g i o n between  .44  sky a l g o r i t h m assumes a p l a n e - p a r a l l e l c l o u d  Actual configurations w i l l  McKee and errors  size  and  nm;  the cloudy  layer.  solar flux  bands occur  modelling  be a s i g n i f i c a n t  Ozone a b s o r p t i o n  i s most i n t e n s e  The  o b s e r v e d on a r o u t i n e b a s i s .  H o w e v e r , a t t e n u a t i o n by a e r o s o l s may i n urban environments.  the  S c a t t e r i n g by  by o z o n e a r e n e g l e c t e d .  would r e q u i r e input parameters ( i . e . p a r t i c l e concentration)  fact,  occurs  only c o n t r i b u t o r s to atmospheric a t t e n u a t i o n . a e r o s o l s and  sensor  B o t h s c a t t e r i n g and  are wavelength-selective.  beyond the bandwidth of the (c)  the  Mm.  absorption  primarily  of a t m o s p h e r i c s c a t t e r i n g  Cox  (1976) and  Davis  be  relatively  complex.  e t a l . (1978) s u g g e s t t h a t  i n r a d i a t i v e t r a n s f e r c o m p u t a t i o n s may  result  from  approximation; (e)  t h e G a u t i e r model d o e s n o t  account f o r clouds  smaller  large this  21  than the in  sensor  such  (f)  field-of-view.  I n s o l a t i o n may  be  overestimated  cases;  surface  s c a t t e r i n g i s assumed t o be  most s u r f a c e s e x h i b i t b i d i r e c t i o n a l  isotropic.  scattering.  However,  Isotropy  has  been shown t o be an  i n a p p r o p r i a t e assumption f o r the s c a t t e r i n g  behaviour  ( B r e n n a n and  of c l o u d s  A direct  consequence of  b r i g h t n e s s may Clouds are  not  strong d i r e c t i o n a l cause shadowing  i n c r e a s e the  lateral  Although  (d) and  be a r e l i a b l e  g e o m e t r y may  m o d e l has  c a t i o n by G a u t i e r O t t a w a and estimated  T o r o n t o ) has t o w i t h i n 9%  complex  of p y r a n o m e t r i c a similar  the  Estimates  and  Cox,  they  1976).  may  Hay,  1984).  (±8%)  The  (Montreal,  for  overcast  daily  the  4%  for to  skies  conditions.  parameterizations  s c a t t e r i n g w i t h i n t h e b a n d w i d t h of  26%  the model of  satellite.  be  Raphael  model t e n d s  (1983) r e c e n t l y m o d i f i e d and  Verifi-  i n s o l a t i o n can  s k i e s and  under p a r t l y c l o u d y  i n c l u d e ozone a b s o r p t i o n  be  Model performance  i n s o l a t i o n u n d e r c l e a r and  Diak  Canada  were d e r i v e d t o w i t h i n  for p a r t l y cloudy  i t underestimates Gautier  and  measurements.  accuracy  Fraser V a l l e y .  s k i e s ( R a p h a e l and  overestimate  cloud  characteristics.  shown t h a t t h e d a i l y  lower  c l e a r s k i e s , 12%  while  s c a t t e r e r s and  absorption.  been t e s t e d i n v a r i o u s e n v i r o n m e n t s .  v a r i e d w i t h sky c o v e r .  overcast  i n d i c a t o r of c l o u d  e t a l . (1980) f o r E a s t e r n  over the  cloud  l o s s o f r a d i a t i o n (McKee and  (1984) o b t a i n e d  estimates  for  (f) i s that  such f a c t o r s modulate c l o u d b r i g h t n e s s  The  Hay  1970).  ( G a u t i e r e t a l . , 1980)  unrelated to cloud absorption  and  Bandeen,  to  Rayleigh Water  22  v a p o u r a b s o r p t i o n i s removed f r o m a l b e d o broadband c o e f f i c i e n t s and  computations  f o rRayleigh scattering,  although  water  ozone a b s o r p t i o n a r e r e t a i n e d i n t h e c a l c u l a t i o n  insolation. of-view  An a d j u s t m e n t f o r c l o u d s  of the s a t e l l i t e  resulted  sensor  s m a l l e r than  i s also applied.  i n an i n c r e a s e i n t h e a c c u r a c y  vapour of the  the f i e l d These  of the d a i l y  revisions  estimates  of a b o u t ± 1 % . A v a r i a n t o f t h e G a u t i e r m o d e l was d e v e l o p e d et  a l . ( 1 9 8 3 ) u s i n g METEOSAT v i s i b l e  no  s e p a r a t i o n of c l e a r  is estimated  by D e d i e u x  radiance data.  and c l o u d y v i e w s .  Instead,  There i s insolation  from a g e n e r a l e x p r e s s i o n f o r t h e c l e a r sky  i r r a d i a n c e a n d a c l o u d c o v e r m o d i f i e r b a s e d on t h e s a t e l l i t e measurements. hourly  V e r i f i c a t i o n o f t h e method h a s shown t h a t t h e  insolation  of ±21%.  c a n be d e t e r m i n e d  However, t h i s s t a t i s t i c  o n l y one h o u r  with a r e l a t i v e  i s b a s e d on c o m p u t a t i o n s f o r  ( 1 2 0 0 GMT).  A s i m i l a r method was u s e d by M o s e r a n d R a s c h k e map t h e d a i l y  accuracy  insolation  over  Monthly averages of the d a i l y 5 - 6% o f t h e o b s e r v e d  (1984) t o  Europe and t h e M e d i t e r r a n e a n . total  insolation  were w i t h i n  mean w h i l e i n d i v i d u a l d a i l y  values  were e s t i m a t e d w i t h a c c u r a c i e s o f ±10 - 14%. Halpern insolation  (1984) a p p r o a c h e d t h e p r o b l e m o f e s t i m a t i n g  from a unique p e r s p e c t i v e .  of t h e u p w a r d - s c a t t e r e d  radiation  models developed  measurements  a t the t o p of t h e atmosphere  a r e compared w i t h e s t i m a t e s o b t a i n e d transfer  Satellite  from a s e t o f e i g h t  by Dave a n d B r a s l a u ( 1 9 7 5 ) .  which provides the best estimate  radiative  The m o d e l  i s t h e n u s e d t o compute t h e  23  insolation.  The  model atmospheres a r e  r e s o l v e d over  50  layers,  e a c h w i t h s p e c i f i e d c o n c e n t r a t i o n s of w a t e r v a p o u r , o z o n e and  aerosol.  Two  of the e i g h t models s i m u l a t e the  of a s i n g l e c l o u d l a y e r . over  f l u x are The  Spectral estimates  i n t e g r a t e d over  satellite  r e q u i r e d as  of t h e  the s a t e l l i t e  and  18 v a l u e s  bandwidth f o r comparison.  d a t a a r e u s e d f o r m o d e l s e l e c t i o n and  input to the  insolation modelling  i n p u t v a l u e s and  the  of  upward-scattered  r e s u l t s are  are  not  process.  d e t a i l e d c o m p u t a t i o n s a r e p e r f o r m e d o n c e on a f u l l possible  influence  Model c a l c u l a t i o n s are a p p l i e d  83 w a v e b a n d s , f o r 9 s o l a r z e n i t h a n g l e s  surface albedo.  and  The  r a n g e of  stored in a  look-up  table. The  p r o c e d u r e was  a p p l i e d t o t h r e e days of  c l o u d - f r e e c o n d i t i o n s , one cloud cover  f o r two  of w h i c h a l s o e x p e r i e n c e d  hours.  The  hourly  c a l c u l a t e d t o w i t h i n 3% o f t h e o b s e r v e d f l u x e s , and  t o w i t h i n 6%  high accuracy  s i m p l e r models.  Summary and  relatively  Such m o d e l l i n g  heavy  was  for clear fluxes.  The  is especially  poor r e s u l t s o b t a i n e d  using  c a p a b i l i t i e s were t e s t e d on  a  would r e q u i r e f u r t h e r e v a l u a t i o n .  Conclusions  Approaches to i n s o l a t i o n m o d e l l i n g satellite  values  sky e s t i m a t e s  l i m i t e d s e t of c o n d i t i o n s and 2.3  insolation  f o r the c l o u d - m o d i f i e d  of t h e c l o u d y  i n t e r e s t i n g given the  predominantly  d a t a were d i s c u s s e d  using  i n the p r e v i o u s  statistical  and  Statistical  methods c o r r e l a t e s a t e l l i t e  geostationary section.  p h y s i c a l l y - b a s e d p r o c e d u r e s were and  Both  presented.  s u r f a c e measurements  24  and  thereby  circumvent  t h e need t o model t h e a t m o s p h e r i c  radiative t r a n s f e r processes. used.  V a r i o u s p a r a m e t e r s h a v e been  The s a t e l l i t e d a t a a r e g e n e r a l l y i n c o r p o r a t e d a s an  index  of c l o u d i n e s s .  forward  The e s t i m a t i o n p r o c e d u r e s a r e s t r a i g h t -  once t h e r e g r e s s i o n c o e f f i c i e n t s a r e c a l c u l a t e d .  However, t h e s e methods r e l y on t h e a v a i l a b i l i t y  and q u a l i t y  of n e t w o r k m e a s u r e m e n t s ( G a u t i e r e t a l . , 1980; H i s e r a n d Senn, 1981)  and produce l e s s than  than  beyond t h e r e g i o n s f o r which they  o p t i m a l r e s u l t s when a p p l i e d were d e v e l o p e d .  Physically-  b a s e d m o d e l s p r o v i d e a more g e n e r a l  framework f o r e s t i m a t i n g  insolation  on t h e p h y s i c a l  s i n c e they a r e p a t t e r n e d  r a t h e r than  site-specific  a calibration counts  observations.  of the v i s i b l e  into radiances.  The v i s i b l e  in f a c t , not w e l l c a l i b r a t e d . developed  channel  by i n t e r c o m p a r i s o n  These models r e q u i r e  to transform sensors  In-flight  processes  brightness  o n - b o a r d GOES a r e ,  c a l i b r a t i o n s h a v e been-  o f common t a r g e t s v i e w e d  by g e o s t a t i o n a r y a n d p o l a r - o r b i t e r o r a i r c r a f t - m o u n t e d calibrated  radiometers  Vonder Haar, necessarily All  1980).  m o d e l s were d e s i g n e d time-scales.  integrated estimates  obtained  However, t h e s e  user  1977; S m i t h a n d  observations a r e not  s y n c h r o n o u s a n d t a r g e t b r i g h t n e s s may v a r y .  hourly or longer  certain  (Smith and L o r a n g e r ,  f o r e s t i m a t i n g i n s o l a t i o n on The m o d e l s p r o v i d e  w i t h a c c u r a c i e s which a r e compatible  requirements  ( T a r p l e y , 1981).  Poorer  on a n h o u r l y b a s i s due t o t h e i n a d e q u a t e  cloud effects. cloud absorption  daily  Bidirectional  reflection  with  estimates are m o d e l l i n g of  (Diak e t a l . , 1982),  ( T a r p l e y , 1979), and c l o u d v a r i a t i o n s over a  25  time i n t e r v a l  not  r e s o l v a b l e by GOES ( H a l p e r n ,  i d e n t i f i e d as problem Of  the v a r i o u s methodologies reviewed  introduced  during  the  later  not  r e v i s i o n s are necessary  Fraser Valley region. of the  study  with other estimates  area  The  a p p r o a c h e s , has of the  conditions.  sufficiently  implemented of t h i s  Hay,  1984)  and,  accurate  since  study).  by  been shown t o p r o d u c e  using  adopted  been v e r i f i e d o v e r  i n s o l a t i o n under p a r t l y cloudy  obtained  be  t h e r e f o r e , no m a j o r  These p r e l i m i n a r y a n a l y s e s  that estimates  chapter,  f o r i t s a p p l i c a t i o n over  m e t h o d has  ( R a p h a e l and  be  stages  i n c o r p o r a t e s a p h y s i c a l a p p r o a c h , and specific  in this  e t a l . (1980) w i l l  ( t h e r e v i s e d f o r m o f t h e model w i l l was  have been  areas.  t h e p r o c e d u r e d e r i v e d by G a u t i e r  it  1984)  sitethe parts  comparison superior  and  overcast  have a l s o i n d i c a t e d  t h e G a u t i e r model may  for assessing  It  be  the mesoscale v a r i a b i l i t y .  26  CHAPTER I I I DATA AND PROCESSING TECHNIQUES 3.1  The S t u d y A r e a The  s t u d y a r e a embraces a d i v e r s e p h y s i c a l  extending  from the Coast Mountains  environment  i n southwestern  British  Columbia t o the l i m i t s of the lower F r a s e r V a l l e y  i n adjacent  Washington  Mountains  S t a t e ; b o u n d e d e a s t w a r d by t h e C a s c a d e  and w e s t w a r d  by Howe Sound a n d t h e S t r a i t  3.1).  The l o w e r F r a s e r V a l l e y  gently  rolling  surface l i e s  of G e o r g i a  i s c h a r a c t e r i z e d by f l a t o r  topography o f low t o moderate  g e n e r a l l y below  may r i s e t o o v e r 300 m.  of the of  hills rise  1,500 a n d 2,200 m,  i n northeastern areas.  i s rugged and i n c i s e d w i t h deep  The  glacially-scoured  some o f w h i c h a r e o c c u p i e d by l a r g e l a k e s .  A  fringe  the Cascade Mountains extends i n t o s o u t h e a s t e r n p a r t s of s t u d y a r e a where i t i s r e p r e s e n t e d by p r o m i n e n t  ridges  e l e v a t i o n s l e s s t h a n 1,000 m. Nearly  of  Its  Northward, the Coast Mountains  w i t h h i g h e r peaks predominant  valleys,  relief.  150 m, a l t h o u g h i s o l a t e d  s t e e p l y t o a v e r a g e summit e l e v a t i o n s between  terrain  (Figure  Vancouver  1.5 m i l l i o n  inhabitants reside within the City  and s u r r o u n d i n g urban c e n t r e s .  The b u i l t - u p  e n v i r o n m e n t o c c u p i e s r o u g h l y 15% o f t h e l o w l a n d a n d i s predominantly r e s i d e n t i a l the  i n nature (Figure 3.2). South of  F r a s e r R i v e r , l a n d use i s l a r g e l y a g r i c u l t u r a l ,  i n t e r s p e r s e d patches of woodland,  r u r a l non-farm  with  and urban  27  Figure  3.1  L o c a t i o n of the s t u d y a r e a . The shape o f t h e study area r e f l e c t s the p r o j e c t i o n of a r e c t a n g u l a r a r r a y of p i x e l s o n t o t h e s u r f a c e of the E a r t h .  to  oo  mmmmmmmmm •<A i Y » v > y A W » W A w . v v . ? y - i <: l  0  Figure  3.2  5  10  G e n e r a l i z e d l a n d - u s e map o f t h e l o w e r F r a s e r V a l l e y and i t s e n v i r o n s ( f r o m E n v i r o n m e n t Canada, 1973). The i n s e t i n d i c a t e s t h e r e l a t i o n b e t w e e n t h e a c t u a l bounds o f t h e s t u d y a r e a and t h o s e shown on t h e map.  29  areas. tidal  P e a t bogs a r e w i d e s p r e a d flats  e x t e n d up t o 9 km  Fraser River Delta.  Mountain  i n south c o a s t a l  from the l a n d w a r d  r e g i o n s and  edge o f  s l o p e s a r e c o v e r e d by c o n i f e r o u s  w o o d l a n d w i t h b r u s h , s c r u b , and b a r r e n l a n d a b o v e t h e or  the  treeline  on l o g g e d - o v e r s l o p e s - .  3.1.1  General Climatology The  l a r g e - s c a l e atmospheric c i r c u l a t i o n  dominated  by a m o i s t w e s t e r l y f l o w o f f t h e P a c i f i c  westerly circulation  1976).  The  A l e u t i a n Low flow.  Cyclonic  contrasts are well developed  predominant  which  Ocean.  The  t e n d s t o be v i g o r o u s i n w i n t e r when  m e r i d i o n a l temperature Oke,  of t h i s r e g i o n i s  results  pressure pattern  (Hay  and  i s t h a t of  the  i n a n o r t h e r l y or n o r t h w e s t e r l y  storms are frequent i n w i n t e r .  These  o r i g i n a t e o v e r t h e N o r t h P a c i f i c and c r o s s t h e c o a s t a n y w h e r e between the A l a s k a n Panhandle and W a l l i s , usually  1966).  and n o r t h e r n C a l i f o r n i a  C y c l o n e s which a f f e c t  i n a d e e p o c c l u d e d s t a t e and  (Stager  the study area are  t h e i r passage  is  a s s o c i a t e d w i t h h e a v y p r e c i p i t a t i o n and c o o l t o c o l d temperatures. predominantly  Precipitation  i n the form of r a i n .  uncommon i n w i n t e r .  Cascade Mountains  H o w e v e r , snow i s n o t  R e l a t i v e l y heavy s n o w f a l l s a r e  e x p e r i e n c e d on t h e m i d -  of  over the lower F r a s e r V a l l e y i s  t o upper  s l o p e s of the Coast  ( H a r e and Thomas, 1 9 7 9 ) .  Winter  and  outbreaks  m o d i f i e d A r c t i c a i r o c c u r u n d e r t h e i n f l u e n c e o f an i n t e n s e  h i g h p r e s s u r e system  c e n t e r e d over the western  S u c h e p i s o d e s a r e a c c o m p a n i e d by s u n n y , f r i g i d  Cordillera. weather.  The  30  w e s t e r l i e s weaken i n summer and s t o r m t r a c k s g e n e r a l l y l i e north of B r i t i s h Columbia.  The n o r t h P a c i f i c  High b u i l d s o f f  t h e c o a s t a n d summer c o n d i t i o n s a r e t y p i f i e d by e x t e n d e d p e r i o d s o f c l e a r a n d m o d e r a t e l y warm The m e s o s c a l e urbanization.  climate  weather.  i s modulated  by t o p o g r a p h y a n d  Topographic e f f e c t s are observed i n the  o r o g r a p h i c e n h a n c e m e n t o f c l o u d by t h e C o a s t a n d C a s c a d e Mountains.  W i n d w a r d s l o p e s t e n d t o be c l o u d i e r , w e t t e r a n d  receive less solar  radiation  (Hay a n d Oke, 1 9 7 6 ) .  than a d j a c e n t v a l l e y  The V a n c o u v e r  locations  I s l a n d Ranges and t h e  O l y m p i c M o u n t a i n s w h i c h l i e t o t h e e a s t and s o u t h o f t h e s t u d y area  induce a rainshadow over the Fraser D e l t a .  anticyclonic develop.  conditions,  Their  l a n d and sea b r e e z e s  i n f l u e n c e on t h e i n s o l a t i o n  Under  typically  regime  lies  t r a n s p o r t of p o l l u t a n t s w i t h i n t h e lower F r a s e r V a l l e y . the sea-breeze  i s b e t t e r developed, t h e r e i s a tendency  net t r a n s p o r t up t h e v a l l e y . solar  Such an e f f e c t  Since fora  The a t t e n u a t i o n o f t h e i n c o m i n g  r a d i a t i o n has been documented f o r v a r i o u s  cities.  i n the  mid-latitude  i s suggested f o r t h e case of Vancouver  by Hay ( 1 9 8 4 ) . 3.2 3.2.1  Data A r c h i v e s S o l a r R a d i a t i o n Network Solar radiation  p y r a n o m e t r i c network  Data  d a t a were d e r i v e d (Figure  f r o m a 12 s t a t i o n  3.3). T h i s network  was e s t a b l i s h e d  a s p a r t o f a programme d e s i g n e d t o i n v e s t i g a t e v a r i o u s a s p e c t s  32  of t h e m e s o s c a l e i n s o l a t i o n 1984).  Solar radiation monitoring  terminated years  over t h e lower  on 1 J a n u a r y  of c o n t i n u o u s Hourly  F r a s e r V a l l e y (Hay,  began on 1 J u n e  1984, p r o v i d i n g a p p r o x i m a t e l y  observations  of s o l a r i r r a d i a n c e and ambient a i r sites.  i r r a d i a n c e f o r a h o r i z o n t a l s u r f a c e was m e a s u r e d by a  K i p p a n d Zonen p y r a n o m e t e r a n d i n t e g r a t e d o v e r i n t e r v a l s using a Campbell S c i e n t i f i c Instrumental Wardle data  4.5  observation.  t e m p e r a t u r e were a v a i l a b l e a t e a c h o f t h e n e t w o r k Solar  1979, a n d  accuracy  (1982).  hourly  M o d e l CR21 d a t a  was w i t h i n 5%, a s v e r i f i e d  logger.  by Hay a n d  A d d i t i o n a l i n f o r m a t i o n on t h e n e t w o r k  design,  c o l l e c t i o n , q u a l i t y c o n t r o l and a r c h i v i n g procedures i s  provided 3.2.2  i n Hay  Satellite  3.2.2.1  (1984). Data  The GOES S y s t e m  I m a g e r y c o v e r i n g B r i t i s h C o l u m b i a was a c q u i r e d  from  GOES-west, p o s i t i o n e d o v e r t h e e q u a t o r a t 135°W l o n g i t u d e , a t an a l t i t u d e o f a p p r o x i m a t e l y system on-board the s p a c e c r a f t visible  radiances  of e i g h t s e n s o r s . 2 is  0.64 km  Phillips, and area  36,000 km.  i s t h e VISSR w h i c h measures  b e t w e e n 0.55 a n d 0.75 um u s i n g a l i n e a r The s p a t i a l  r e s o l u t i o n of the r a d i a n c e  ( 0 . 8 km x 0.8 km) a t t h e n a d i r 1980).  The i m a g i n g  array field  (Hambrick and  Away f r o m t h i s p o i n t , r e s o l u t i o n d e t e r i o r a t e s  p i x e l s become d i s t o r t e d . (50°N, 123°W) i s 1.42 km  Pixel 2  r e s o l u t i o n over the study  ( 1 . 5 km x 0.984 km;  after  33  Raphael (10.5  a n d Hay, 1 9 8 4 ) .  GOES a l s o p e r f o r m s  infrared  - 12.6 Mm) a n d c u r r e n t l y h a s t e m p e r a t u r e  capabilities.  Such f a c i l i t i e s  were n o t u s e d  imaging  sounding  in this  study.  GOES i s s p i n - s t a b i l i z e d w i t h i t s s p i n a x i s p a r a l l e l t o the E a r t h ' s p o l a r a x i s . the west-to-east motion motion  disc  With the  r o t a t i n g a t 100 rpm, t h e V I S S R s c a n s t h e E a r t h f o r  1/20th o f each i n 18.2 m i n u t e s  GOES p r o v i d e s i m a g e r y The  provides  f o r t h e VISSR, w h i l e t h e n o r t h - s o u t h  i s o b t a i n e d by a s t e p p i n g - s c r e w m e c h a n i s m .  satellite about  The s p i n o f t h e s a t e l l i t e  r e v o l u t i o n , and produces (Kroeck,  1976).  a full  Earth  On an o p e r a t i o n a l b a s i s ,  every h a l f - h o u r .  c h a r a c t e r i s t i c s o f t h e GOES i m a g i n g  system a r e  detailed  i n v a r i o u s r e p o r t s by t h e N a t i o n a l E n v i r o n m e n t a l  Satellite  S e r v i c e (Johnston e t al.,1976; C o r b e l l e t a l . ,  Fermelia  (1982) d i s c u s s e s t h e s a t e l l i t e  design  1976).  configuration  and Crowe (1977) p r o v i d e s a summary o f t h e d a t a p r e - p r o c e s s i n g procedures. 3.2.2.2  Image N a v i g a t i o n  Full  resolution  satellite  were o b t a i n e d i n d i g i t a l  data for the v i s i b l e  tape format  channel  from t h e Space S c i e n c e  and E n g i n e e r i n g C e n t r e o f t h e U n i v e r s i t y o f W i s c o n s i n , a t Madison. ranging  The d a t a a r e b a s e d from  0 - 255 c o u n t s .  on a n e i g h t - b i t Image s c e n e s  brightness scale  were a b s t r a c t e d f o r  t h e r e g i o n b e t w e e n 48° - 50°N a n d 121° - 125°W, c e n t e r e d on coordinates  (48°16'N, 123°15'W).  r e p o r t e d a c c u r a c y o f ±1 p i x e l  Images were n a v i g a t e d w i t h a  (Hambrick  and P h i l l i p s ,  1980).  34  Nonetheless,  t h e d a t a w h i c h were r e c e i v e d f r o m  contained d i s c r e p a n c i e s f a r i n excess 1982;  Wanless,  using software The  procedure  1983).  The  developed  satellite  Wisconsin  of t h i s v a l u e images were  (Raphael,  re-navigated  a t the U n i v e r s i t y of B r i t i s h  r e q u i r e d the c o o r d i n a t e s of ground  Columbia.  control  p o i n t s w h i c h were o b t a i n e d by m a n u a l s e l e c t i o n on an  image  processor  of  (Comtal  n a v i g a t i o n was 3.2.2.3  Data  The  Vision  I).  within 1 - 2  The  r e s u l t a n t accuracy  pixels.  Conversion  c o n v e r s i o n of t h e s a t e l l i t e - m e a s u r e d b r i g h t n e s s t o  normalized  r e f l e c t a n c e was  d e r i v e d by S m i t h SR  accomplished  and V o n d e r H a a r  (1980),  using a i n the  = 0.00154 + 0.000166-1 + 0.0000137-1  where I i s t h e s a t e l l i t e equivalent normalized i s expressed  b r i g h t n e s s c o u n t and  r e f l e c t a n c e . ' The  as a d i m e n s i o n l e s s  relationship  SR  form: (3.1)  2  is its  normalized reflectance  f r a c t i o n and  can  be  i n t o e n e r g y u n i t s by m u l t i p l i c a t i o n w i t h t h e s o l a r 3.2.2.4 The  constant.  Data Merging s a t e l l i t e d a t a were c o l l e c t e d on a h a l f - h o u r l y b a s i s .  However, t h e s o l a r time-scale. averaged over the observed described  translated  The  i r r a d i a n c e was  satellite-derived  observed  estimated  i n Raphael  irradiances.  (1982) and  hourly  e s t i m a t e s were m e r g e d o r  hourly i n t e r v a l s to enable and  on an  c o m p a r i s o n s between The  procedure  Wanless (1983).  The  is half-  35  hourly estimates obtained weighted  f r o m t h r e e s u c c e s s i v e images were  according t o the temporal  representativeness  a g i v e n hour and t o t h e i r e x t r a t e r r e s t r i a l latter  irradiance.  This  w e i g h t i n g a t t r i b u t e s a g r e a t e r s i g n i f i c a n c e t o imagery  c o l l e c t e d nearer not a v a i l a b l e to  over  cover  t o s o l a r noon.  then weights  the hour.  I f one o f t h e s e  i m a g e s was  f o r t h e o t h e r two were a d j u s t e d t o  An e s t i m a t e was n o t p r o d u c e d f o r a g i v e n  h o u r i f two ( o r more) c o r r e s p o n d i n g  i m a g e s were m i s s i n g .  C e r t a i n p r o b l e m s a r i s e when e v a l u a t i n g t h e s a t e l l i t e estimates against pyranometric  observations.  The  pyranometric  i r r a d i a n c e s a r e broad-band h o u r l y averages o b t a i n e d  from a  hemispherical sensor.  estimates  By c o m p a r i s o n ,  a r e b a s e d on n e a r - i n s t a n t a n e o u s over  a limited  the s a t e l l i t e  r a d i a n c e o b s e r v a t i o n s , sampled  s p e c t r a l b a n d by r a d i o m e t e r s  narrow f i e l d - o f - v i e w .  subtending  G a u t i e r e t a l . (1980) a t t e m p t e d  c o m p e n s a t e f o r t h e s e d i s c r e p a n c i e s by a v e r a g i n g insolation  over  3.3  Stratification  Data  8 x 8  pixel arrays  (Section  T h e s e o b s e r v a t i o n s were s e l e c t e d  this  2.2.2).  study  assessments of the i n s o l a t i o n v a r i a b i l i t y Consequently,  d a t a u s i n g an e f f e c t i v e  t o 31  1979 a n d 1981.  s a m p l e was t o o s m a l l t o p r o v i d e s t a t i s t i c a l l y  scales.  availability days.  from a range o f s y n o p t i c and  s e a s o n a l c o n d i t i o n s between t h e y e a r s  time  to  the estimated  C o n s i d e r a t i o n s a s s o c i a t e d w i t h t h e c o s t and o f t h e s a t e l l i t e d a t a have l i m i t e d  a  This  meaningful  on d a i l y o r l o n g e r  a n a l y s e s were p e r f o r m e d on h o u r l y  s a m p l e s i z e o f 313 o b s e r v a t i o n s ( s e e  36  below).  A n a l y s e s based  on h o u r l y d a t a c a n be e x p e c t e d  to  maximize t h e e s t i m a t e s of v a r i a b i l i t y . The a c c u r a c y o f t h e p r e d i c t e d i n s o l a t i o n to vary w i t h sky cover. into clear, partly  h a s been shown  The d a t a were t h e r e f o r e s t r a t i f i e d  c l o u d y and o v e r c a s t s k y c l a s s e s t o a s s e s s  the e f f e c t s of sky c o v e r .  A g i v e n h o u r was c l a s s i f i e d  by two  indices: (1)  the c o e f f i c i e n t  of s p a t i a l v a r i a b i l i t y cv = a  where Kl  1 2  / K|  i s t h e h o u r l y mean o b s e r v e d  pyranometric  s t a t i o n s and a  ( c v ) , d e f i n e d by (3.2)  i n s o l a t i o n over  t h e 12  i s t h e s t a n d a r d d e v i a t i o n of  1 2  these o b s e r v a t i o n s ; (2)  t h e h o u r l y d u r a t i o n of b r i g h t  a Campbell-Stokes  recorder).  sunshine  T h i s parameter  ( m e a s u r e d by provides a  q u a n t i t a t i v e m e a s u r e o f s k y c o v e r a n d i s more w i d e l y r e p o r t e d t h a n t h e h o u r l y c l o u d amount. Hourly bright 1 January Atmospheric  1968 - 31 December Environment  A i r p o r t a n d UBC drawn f r o m  sunshine o b s e r v a t i o n s over  1981 w e r e o b t a i n e d f r o m t h e  S e r v i c e f o r V a n c o u v e r B.C  ( F i g u r e 3.3).  The f r e q u e n c y  t h e s e d a t a were s i m i l a r  (Figure 3.4a),  showing bimodal  towards  the extreme v a l u e s .  in this  s t u d y were v e r i f i e d  (Figure 3.4b).  the period  Hydro,  distributions  f o r the three  locations  and s t r o n g l y p o l a r i z e d  tendencies  A subset c o m p r i s i n g of hours t o have s i m i l a r  used  characteristics  On t h e b a s i s o f t h e s e h i s t o g r a m s , t h e s u b s e t  h o u r s were t e n t a t i v e l y  grouped i n t o a c l e a r  sky c l a s s w i t h  10  6 0 0  60  • S A M P L E A: A  50  0 -  40  0 -  V  A I R P O R T  46026  V:  V A N C O U V E R  U:  U B C  B C H Y D R O  0  SIZE  S A M P L E  hrs  46026  "  79992  "  A:  50  0 -  40  0-  3 0  0 -  20  0 -  V  AIRPORT  313  V:  V A N C O U V E R  U:  U B C  B C  SIZE hrs  H Y D R O  u  >-  o z  LU  30  O  0 A V ,  20  10  0 -  0 -  o-°-i  Lil  tr  10  0  r  0 1  2  3  BRIGHT  Figure  4  5  S U N S H I N E  6 H O U R S  3.4a,b  7  8  9  ( t e n t h s of a n h o u r )  10  0 -  0 1  2  3 BRIGHT  4  5  SUNSHINE  6 H O U R S  Frequency d i s t r i b u t i o n s of the hourly b r i g h t s u n s h i n e m o n i t o r e d a t V a n c o u v e r B.C. H y d r o , A i r p o r t a n d UBC f o r : a. b.  t h e p e r i o d 1 J a n u a r y 1968 - 31 December 1981 t h e data subset hours  7  8  "T 9  ( t e n t h s of a n h o u r )  10  r  38  t e n t h s of b r i g h t s u n s h i n e ; of b r i g h t s u n s h i n e , intermediate  an o v e r c a s t  and a p a r t l y c l o u d y  sky c l a s s  f r a c t i o n s of b r i g h t s u n s h i n e .  r e f e r e n c e d i s t r i b u t i o n s were a v a i l a b l e , sunshine  sky c l a s s w i t h 0 t e n t h s  attributed  a v e r a g e of t h e t h r e e  Since  three  the f r a c t i o n of b r i g h t  t o any g i v e n h o u r was d e t e r m i n e d  f r o m an  values.  The a b o v e c l a s s i f i c a t i o n  incorporates l i t t l e  on t h e s p a t i a l c h a r a c t e r i s t i c s o f t h e d a t a . sunshine  with  information  The b r i g h t  r e c o r d s were d e r i v e d f r o m a c o a s t a l g r o u p i n g  of  s t a t i o n s a n d may n o t r e p r e s e n t c o n d i t i o n s f u r t h e r i n l a n d . coefficient  of v a r i a b i l i t y  This s t a t i s t i c  p r o v i d e s an a p p r o p r i a t e m e a s u r e .  was c o m p u t e d f o r e a c h h o u r u s i n g  solar  i r r a d i a n c e o b s e r v a t i o n s f r o m t h e 12 p y r a n o m e t r i c Since the c l e a r corresponding upper l i m i t  s k y i n s o l a t i o n was r e l a t i v e l y  c o e f f i c i e n t s of v a r i a b i l i t y  o f 10%.  were a s s i g n e d an  T h i s v a l u e was c h o s e n t o a c c o u n t  a i r mass a c r o s s t h e n e t w o r k .  Overcast  associated with uniform conditions. too r i g o r o u s t o account  heterogeneous c l o u d cover. was a s s i g n e d .  cloudy.  their  in optical  s k i e s a l s o t e n d t o be  However, a l i m i t  o f 10%  f o r the e f f e c t s of a o f 35%  were g r o u p e d a s c l e a r o r  o v e r c a s t by t h e b r i g h t s u n s h i n e  exceeding  f o r the  In t h i s case, a c l a s s l i m i t  The h o u r s w h i c h  to these c r i t e r i a .  stations.  uniform,  e f f e c t s o f measurement e r r o r a n d m i n o r v a r i a t i o n s  was j u d g e d  The  r e c o r d s were r e v i s e d a c c o r d i n g  Hours w i t h c o e f f i c i e n t s of v a r i a b i l i t y  r e s p e c t i v e l i m i t s were r e c l a s s i f i e d as p a r t l y  The p r o c e s s  resulted  c l o u d y hours from both  i n a considerable gain i n p a r t l y  t h e c l e a r and o v e r c a s t sky c l a s s e s .  39  S a m p l e s of t h e s a t e l l i t e  imagery  were i n s p e c t e d t o d e t e r m i n e occured.  associated with a l lclasses  w h e t h e r any  Only minor adjustments  misclassification  were r e q u i r e d b e t w e e n  p a r t l y c l o u d y and o v e r c a s t s k y c l a s s e s . are l i s t e d 3.4  i n Table  The  final  Gautier Algorithm  The  g e n e r a l f r a m e w o r k of t h e G a u t i e r model h a s i n S e c t i o n 2.2.2.  The  s t u d y was  i n Raphael  C e r t a i n a s p e c t s of the o r i g i n a l  (1982).  identical  t o t h e one  s e q u e n c e i s s u m m a r i z e d i n F i g u r e 3.5 i s p r o v i d e d i n Appendix Implementation The  been procedure described programme  t o a c c o m o d a t e a more e x t e n s i v e s t u d y a r e a ,  t h e s e were p u r e l y t e c h n i c a l m o d i f i c a t i o n s .  3.4.1  groupings  specific modelling  implemented i n t h i s  were a l t e r e d  the  3.1.  The  discussed  had  The  but  modelling  and a programme  listing  A.  of a Moving F l u x A v e r a g i n g  study area conformed t o a primary  Array  image composed o f  60 x 120 p i x e l s c e n t e r e d on P i t t Meadows (49°13'N, 122°42'W). Within t h i s area a secondary (i  > 1) was  s e l e c t e d as t h e u n i t over which  i s performed.  The  Mode I g e n e r a t e s  12 s e c o n d a r y  i n two  t o t h e method u s e d  ( 1 9 8 2 ) ; Mode I I g e n e r a t e s a s e c o n d a r y  contiguous  averaging  a r r a y s each c e n t e r e d over  i s analogous  moves a c r o s s a p r i m a r y for  flux  programme c u r r e n t l y o p e r a t e s  n e t w o r k s t a t i o n s and Raphael  a r r a y c o n s i s t i n g of i x i p i x e l s  image and p r o d u c e s  array  irradiance  (non-overlapping) array l o c a t i o n s .  modes: the  by which estimates Computations  40 DATE  T O T A L S  TIME  0500 0600 0700 0800 0900 1000 1100  200  SEP 12  255  13  256  14  257  20  263  OCT 03  276  20  293  24  297  31  304  1200  1300 1400  1500 1600 1700  1800 1900  2000  BB BBBB B a a •B  A  JUL 15 1979 196 19  •a  hour ending (LAT)  I Ml D I Y I Julian Day  N N N  D  D  12  e.  N  7 8 5  JAN 12 1980 012 25  025  30  030  APR 14  105  30  121  MAY 20  141  22  143  JUN 01  153  08  160  19  171  JUL 01  183  03  185  14  196  15  197  AUG 12  225  18  231  16  239  SEP 01  245  09  253  17  261  MAY 22 1981 142 JUN 06  157  a B B •BBBBBBB 0 a a a ••flflfl"" a l l l l l l g ] a a •  a  a a  10 7  •mi:::;;:" a aaaa a a B y • ••• a a  "HHBHIIH1H a a a a a a a a a a aaa a a a a a a a a a a a a aaa a Q  T a b l e 3.1  = C L E A R ;  fjj  = PARTLY  CLOUDY ; |  =  cloudy and o v e r c a s t  variable  to seasonal v a r i a t i o n s or poor q u a l i t y  data.  into  sky c l a s s e s .  number o f h o u r s w i t h i n  8  11  2 5  101  TOTAL:  OVERCAST  C l a s s i f i c a t i o n of t h e h o u r l y data partly  11  127  313  clear, The  a d a y i s due  i ndaylength,  missing  85  hours  41  Step 1 :  SELECT MODE  MODE I :  c a l c u l a t e s o l a r f l u x e s f o r secondary arrays centered on the 12 network s t a t i o n s  MODE I I :  c a l c u l a t e s o l a r f l u x e s f o r an a r b i t r a r y g r i d of secondary a r r a y s of theprimary image  i Step 2 :  INPUT PRIMARY IMAGE (60 x 120 p i x e l s )  Step 3 :  SELECT SECONDARY ARRAY ( i X i ) ACCORDING TO MODE  Step 4 :  PROCESS SECONDARY ARRAYS a) b) c) d)  Step 5 :  perform q u a l i t y c o n t r o l check c a l c u l a t e atmospheric absorption determine c l e a r / c l o u d y p i x e l threshold c a l c u l a t e secondary array instantaneous solar fluxes  REPEAT STEPS 2, 3, 4, 5 UNTIL THERE ARE NO MORE PRIMARY IMAGES TO PROCESS  '  Step 6 : MERGE INSTANTANEOUS SOLAR FLUXES TO FORM HOURLY INSOLATION ESTIMATES  I Step 7 :  u r e 3.5  OUTPUT HOURLY INSOLATION ESTIMATES  The i n s o l a t i o n m o d e l l i n g  sequence.  42  b e g i n a t t h e t o p , l e f t - m o s t window sequentially  until  ( f a c i n g v i e w e r ) and p r o c e e d  no more d a t a a r e a v a i l a b l e .  The  programme  d o e s n o t g e n e r a t e an a r r a y b e y o n d t h e l i m i t s o f t h e p r i m a r y image.  B o t h t h e s e modes o f a n a l y s i s  were i m p l e m e n t e d  in this  study. 3.4.2  Calculation  of A s t r o n o m i c a l Parameters  The s o l a r r a d i a t i o n i n c i d e n t the  t o p of the atmosphere K' =  where K* the  ( K ' ) was c a l c u l a t e d  from: (3.3)  2  h~ ) and ( d / d )  f o r t h e d e p a r t u r e of t h e a c t u a l  is  Earth-Sun  ( d ) f r o m i t s mean ( d ) . The c o s i n e o f t h e s o l a r  zenith angle  (6)  was o b t a i n e d b y :  c o s 0 = sin$sin£ + $ i s the l a t i t u d e , the  surface at  K*(d/d) cos0  i s t h e s o l a r c o n s t a n t (4871 kJm  correction  distance  on a h o r i z o n t a l  hour a n g l e  cos$cos^cosA  (3.4)  £ i s t h e s o l a r d e c l i n a t i o n a n g l e , and h i s  ( d e g r e e s ) w h i c h was d e t e r m i n e d b y : h = 15-|12 - LAT|  where LAT i s t h e l o c a l a p p a r e n t  (3.5)  time i n hours.  The a z i m u t h a n g l e o f t h e Sun f r o m s o u t h (w) was calculated  using: (3.6)  43  The s a t e l l i t e  azimuth  a> = c o s ^ s  angle  from south  ( w ) was g i v e n g  tan$ tanA/^jtan  (3.7)  + 1}  $ + (tan$/tanA)  where A i s t h e d i f f e r e n c e b e t w e e n t h e s a t e l l i t e longitude  by:  (135°W) and t h e s t a t i o n  b e t w e e n t h e sun and t h e s a t e l l i t e  longitude. (7)  sub-point  The  azimuth  was d e t e r m i n e d  from t h e  d i f f e r e n c e b e t w e e n co and co : s 7  Since the s a t e l l i t e a given  = I  " - "  s  l  i s g e o s t a t i o n a r y , i t sazimuth  l o c a t i o n at the Earth's  surface.  GOES-west v i s - a - v i s P i t t Meadows was assumed  (3.8)  t o a p p l y over  the e n t i r e  t h i s v a l u e o f up t o 0.8°  The a z i m u t h  16.1°.  a n g l e of  This value  study area.  was  V a r i a t i o n s from  were known t o o c c u r .  have been shown t o be o f m i n o r s i g n i f i c a n c e 3.4.3  i s fixed for  However,  (Raphael,  they  1982).  E s t i m a t i o n o f O p t i c a l A i r Mass The o p t i c a l  a i r mass was r e q u i r e d i n t h e d e t e r m i n a t i o n o f  water v a p o u r a b s o r p t i o n a t s o l a r and s a t e l l i t e - v i e w i n g z e n i t h angles.  The r e l a t i v e  o p t i c a l a i r mass (M) was  calculated  from: M = e x p ( - H / 8 2 4 3 ) / [ c o s 0 + 0.15(93.885 - 0 ) ~ * 1  where H i s t h e e l e v a t i o n ( m e t e r s ) (degrees). air  2 5 3  ]  (3.9)  and © i s t h e z e n i t h a n g l e  This expression accounted  f o r the r e d u c t i o n i n o p t i c a l  mass w i t h e l e v a t i o n ( M c D o n a l d , 1960) a n d i n c o r p o r a t e d a  44  correction elevation  for large solar  angles  of t h e 4 nearest  (1 km) g e o g r a p h i c  values obtained  g r i d of e l e v a t i o n  E s t i m a t i o n o f Water Vapour  was c a l c u l a t e d  by l i n e a r  from a dense  water vapour a b s o r p t i o n by P a l t r i d g e  (U) was p a r a m e t e r i z e d  s u r f a c e dewpoint temperature  The  Absorption  using f u n c t i o n s developed  p r e c i p i t a b l e water  1966).  points.  F o l l o w i n g G a u t i e r e t a l . (1980),  The  (Kasten,  a t a g i v e n p i x e l l o c a t i o n was e s t i m a t e d  interpolation  3.4.4  zenith  (1973).  i n terms of  ( T ^ ) , b a s e d on S m i t h ' s  (1966)  relationship: 0  =  F T T  exp(0.0707-T )  (3.10)  d  where U i s i n cm; T^ i s i n °C; X i s a d i m e n s i o n l e s s factor Smith  correction  f o r s t a t i o n l a t i t u d e and season and i s o b t a i n e d (1966).  to v a r i a t i o n s temperatures  S i n c e t h e G a u t i e r model i s r e l a t i v e l y i n p r e c i p i t a b l e water observed  (Raphael,  by t h e A t m o s p h e r i c  insensitive  1982), dewpoint  Environment S e r v i c e  a t UBC were assumed t o r e p r e s e n t c o n d i t i o n s e l s e w h e r e valley.  P r e c i p i t a b l e water f o r mountainous r e g i o n s  by e l e v a t i o n s g r e a t e r t h a n lower 3.4.5  than  the valley  i nthe (defined  500 m) was a s s i g n e d a v a l u e 2 0 %  estimate.  E s t i m a t i o n of R a y l e i g h Scattering  from  Scattering  coefficients fordirect  beam r a d i a t i o n were b a s e d on d a t a  (a) and d i f f u s e ( e ^ )  from Coulson  (1959).  d i f f u s e beam s c a t t e r i n g c o e f f i c i e n t was assumed t o be  The  45  i n d e p e n d e n t of t h e s o l a r constant  z e n i t h a n g l e a n d was a s s i g n e d a  v a l u e o f 0.076.  of t h e s o l a r following  D i r e c t beam s c a t t e r i n g  zenith angle.  i s a function  I t was c a l c u l a t e d u s i n g t h e  expression:  a = 0.0467563 + 0.0014173-0 + 0 . 0 0 0 0 5 2 5 8 • 8  2  + 0.000000651•0  3  (3.11) where 6 i s i n d e g r e e s . of s o l a r z e n i t h a n g l e s 3.4.6  T h i s e x p r e s s i o n was v a l i d  f o r a range  o f up t o 85°.  E s t i m a t i o n o f Minimum  Brightness  The minimum b r i g h t n e s s (*p)  o f  t a r g e t represents the  a  t a r g e t ' s b r i g h t n e s s under c l o u d - f r e e c o n d i t i o n s . estimated  from  an e q u a t i o n d e v e l o p e d  by T a r p l e y  I t was (1979):  2 I  = a + bcosd  + c c o s 7 s i n 0 + dcos  7sin0  (3.12)  where 8  solar  z e n i t h angle  (degrees)  7  S u n - s a t e l l i t e azimuth  a, b,  regression coefficients  angle  (degrees)  c, d  The r e g r e s s i o n c o e f f i c i e n t s were d e r i v e d u s i n g corresponding Prior  to the c l e a r  t o these  sky hours l i s t e d  calculations a quality  pixels  The mean b r i g h t n e s s o f e a c h c o n t i g u o u s was a s s e s s e d  f o r each primary  image.  i n Table  c o n t r o l check  p e r f o r m e d on t h e 60 x 120 p i x e l p r i m a r y m i s s i n g and c l o u d - c o n t a m i n a t e d  imagery 3.1. was  i m a g e s t o remove  from  this set.  5 x 5  pixel  array  A g i v e n a r r a y was n o t  46  entered  i n t o s u b s e q u e n t c a l c u l a t i o n s i f more t h a n 33%  p i x e l s were m i s s i n g  (due  to e x c l u s i o n during q u a l i t y  The  mean b r i g h t n e s s v a l u e s  and  S u n - s a t e l l i t e azimuth angles  Regression  were r e g r e s s e d  the c o e f f i c i e n t  each equation  3.4.7  standard  British  e r r o r of  computed  with  s p a t i a l v a r i a t i o n s and  are  V.  C a l c u l a t i o n of Cloud T h r e s h o l d The  c l o u d t h r e s h o l d c o n t r o l s the d e c i s i o n t o process  s a t e l l i t e data algorithms. a l b e d o was  t h r o u g h e i t h e r the c l e a r or the c l o u d y  I t was  evaluated  estimated  12 c o u n t s ;  a f t e r Raphael,  in surface albedo, tent.  The  with this greater  radiance  was  used.  sky  algorithm.  2.6.  margin of 1982)  o b s e r v e d by  The and  the  sky surface was  0.0056 ( e q u i v a l e n t  to  t o accomodate s m a l l v a r i a t i o n s  a t m o s p h e r i c w a t e r v a p o u r and  threshold value.  than the  using Equation  f r o m t h e minimum b r i g h t n e s s  i n c r e m e n t e d by a c o n f i d e n c e  3.4.8  Triangular  of d e t e r m i n a t i o n  displayed interesting  i n Chapter  The  control).  solar zenith  Package a v a i l a b l e from the U n i v e r s i t y of  and  discussed  against  u s i n g the  Columbia Computing Centre L i b r a r y . estimate  of i t s  the  I f the  aerosol  s a t e l l i t e was  compared  observed radiance  t h r e s h o l d , then the cloudy  sky  O t h e r w i s e , c a l c u l a t i o n s were b a s e d on  con-  was  algorithm the c l e a r  E s t i m a t i o n of Cloud A b s o r p t i o n Cloud  absorption  was  a p p r o x i m a t e d as a l i n e a r  c l o u d b r i g h t n e s s , v a r y i n g f r o m 0.0  f u n c t i o n of  f o r no c l o u d , t o 0.2  (20%)  47  f o r the b r i g h t e s t c l o u d s . s c a t t e r e d back t o s p a c e  The  solar  r a d i a t i o n which  by a c l o u d l a y e r was  d i f f e r e n c e between the r a d i a n c e m o n i t o r e d (KT) and  c a l c u l a t e d as  by t h e  between t h e e x t r a t e r r e s t r i a l threshold.  T h u s , $ was  Concluding  estimated 'KT  - Kt,  K'  - K1\  (K') and  the c l o u d  by:  x  0.2  (3.13)  o u t l i n e d the r e g i o n a l c o n t e x t , the  and m o d e l l i n g p r o c e d u r e s The  irradiance  difference  Remarks  T h i s c h a p t e r has  insolation.  overview  used  t o d e r i v e e s t i m a t e s of  Raphael  a n d Hay  o f t h e G a u t i e r model e m p h a s i z e d  (1984).  The  reader  i s directed to  (1982) f o r more d e t a i l e d d i s c u s s i o n s o f s p e c i f i c procedures.  data  the  m o d i f i c a t i o n s a p p l i e d t o t h e a l g o r i t h m s u s e d by R a p h a e l and  The  t  assumed t o be t h e  the  satellite  the estimated c l o u d t h r e s h o l d radiance (Kt >.  maximum p o s s i b l e s c a t t e r i n g was  3.5  was  the  (1982) Raphael  computational  48  Chapter IV SATELLITE CHARACTERIZATION OF THE MESOSCALE VARIABILITY 4.1  INSOLATION  Introduction The  s t u d y a r e a d e s c r i b e d i n S e c t i o n 3.1 d i s p l a y s .a  complex s o l a r  radiation  c l i m a t e a s s o c i a t e d w i t h mountain-  l o w l a n d , c o a s t a l - i n l a n d and u r b a n - r u r a l c o n t r a s t s (Hay, 1984). The  feasibility  over  t h e lower  initially  of using s a t e l l i t e data  t o estimate  insolation  F r a s e r V a l l e y ( v i a t h e G a u t i e r m o d e l ) was  e v a l u a t e d by  Raphael  (1982).  H i sanalyses  were  b a s e d on t i m e - s e r i e s c o m p a r i s o n s b e t w e e n t h e s a t e l l i t e and  the observed  insolation  However, t h e i n d i v i d u a l no  o b j e c t i v e of t h i s chapter  almost  of the observed  i s t o determine  whether  field. such  exists.  Method of A n a l y s i s The  the  assessments provide  the spatial characteristics  a capability 4.2  station  stations.  i n f o r m a t i o n on t h e a b i l i t y o f t h e s a t e l l i t e e s t i m a t e s t o  replicate The  a t s e l e c t e d network  estimates  insolation variability  interstation correlations,  or e s t i m a t e d correlation insolation ability  was a s s e s s e d  by d e t e r m i n i n g  u s i n g h o u r l y data measured a t ,  f o r , t h e 12 p y r a n o m e t r i c  stations.  f u n c t i o n s d e r i v e d from t h e observed were s u b s e q u e n t l y  and estimated  compared i n o r d e r t o e v a l u a t e t h e  of the s a t e l l i t e - b a s e d  variability.  The d i s t a n c e -  approach t o d e s c r i b e t h e s p a t i a l  49  The P e a r s o n p r o d u c t - m o m e n t c o r r e l a t i o n provided a quantitative of  insolation  coefficient (r)  measure o f t h e c o n c o m i t a n t  for a given station p a i r .  variation  I t was c a l c u l a t e d  as  follows: £ ( x . - x ) (y. - y ) ^ 1 No o x y  r=  where N i s t h e number o f p a i r e d are  standard deviations.  assumed t h a t related. by  observations  t h e mean i n s o l a t i o n a t s t a t i o n s  respective  the s t a t i o n  F i g u r e 4.1  (Hay,  were a l s o  (x^,y^);  insolation pairings  shows t h a t  stations. similar  method  were  this condition  known t o d i s p l a y  x and y  X and Y; a a n d a a r e t h e ' x y  The c o r r e l a t i o n  d a t a f r o m t h e UBC a n d A i r p o r t  pairings  (4.1)  was  Other  linearly approximated station  characteristics  p e r s . comm., 1 9 8 4 ) . The v a r i a t i o n  of t h e i n t e r s t a t i o n c o r r e l a t i o n  with  d i s t a n c e h a s been u s e d t o d e f i n e t h e s p a t i a l c o h e r e n c e o f numerous c l i m a t o l o g i c a l Hay,  1981).  since  fields  (e.g. Alaka,  T h i s a p p r o a c h was a d o p t e d i n t h e p r e s e n t  i t offered  a c o n c i s e and c o n v e n i e n t  However, a c o r r e s p o n d e n c e b e t w e e n t h e functions  1970; L o n g l e y ,  1974;  analysis  representation.  distance-correlation  o f t h e o b s e r v e d and e s t i m a t e d f i e l d s d i d not  constitute  a complete assessment of the s a t e l l i t e methodology as o n l y relative variations d a t a may the  were c o n s i d e r e d .  v a r y i n u n i s o n t h o u g h t h e y may n o t n e c e s s a r i l y  same s p a t i a l d i s t r i b u t i o n .  absolute  The o b s e r v e d and e s t i m a t e d  i n s o l a t i o n were a l s o  represent  Hence, comparisons of t h e undertaken t o evaluate the accuracy  50  UBC  Figure 4 . 1  INSOLATION( k J m ^ h - ) 1  Comparison between t h e i n s o l a t i o n o b s e r v e d a t A i r p o r t and a t UBC f o r t h e h o u r s l i s t e d i n T a b l e 3.1.  51  o f t h e model p r e d i c t i o n s . should  provide  modelling  r e s u l t s of b o t h t h e s e  c o n c l u s i v e evidence w i t h which to assess  c a l c u l a t i o n s were p e r f o r m e d u s i n g  the hours l i s t e d  12 s t a t i o n  i n T a b l e 3.1.  Since  74  insolation  arrays.  array dimensions assessed  the a n a l y s e s  These p a i r i n g s  Yet  pixel  array  represented  the  spatial  insensitivity  of the  s p a t i a l averaging.  4.3.1  I t s implementation  issue w i l l  be  on  the  to a reduction  in  examined i n  4.3.4.  R e s u l t s and  Discussion  Network-based C o r r e l a t i o n s Figure  4.2a  illustrates,  f o r the  network d a t a ,  the  i n t e r s t a t i o n c o r r e l a t i o n s as a f u n c t i o n of s e p a r a t i o n The  field.  accuracy  would r e l y  s a t e l l i t e estimates This  be  finest resolution  a t t a i n a b l e w i t h i n the c o n s t r a i n t s of n a v i g a t i o n a l (Sect ion 3.2.2.2).  by  s m a l l e r a r r a y s would  The  on  smallest  s c a l e dependence  f o r a more d e t a i l e d r e s o l u t i o n of t h e  4.3  between  i n i t i a l l y estimated  preferred  Section  data  involved  These comprised the  for spatial  (1982) [ S e c t i o n 2 . 2 . 2 ] .  3 x 3  insolation  separation distances  f o r e a c h s t a t i o n was  b a s i s of 5 x 5 p i x e l  Raphael  the  km.  The the  the  l o c a t i o n s , 66 p a i r i n g s were p o s s i b l e .  c o r r e s p o n d e d t o a range of s t a t i o n 4 and  analyses  procedure.  The for  The  c o r r e l a t i o n s d i s p l a y a gradual  separation, confirming  our  decrease with  expectation  distance.  station  that s t a t i o n s  hourly  52  10-  * * <%> 0-8-  10-  08-  10<j,  0  «.  ©  «  «•  0-8©©  8  0-6-|  z  o £  10© ©  ©  ©  »  ©  *  © O  0 8-  <is  0 <> !  ©  # © ©  *  ©  ©  ©  0-6-  +  0-4-  +  0:2OBSERVED + 00-  I 20  10  30 40 50 STATION SEPARATION (km)  F i g u r e 4.2a-d The d i s t a n c e - c o r r e l a t i o n hourly insolation. a. b. c. d.  a l l data c l e a r sky data p a r t l y cloudy sky data overcast sky data  Grouse Mountain pairings 60  70  80  f u n c t i o n s of the observed  53  located  in closer  variability. correlated  are  Systematically  observed for s t a t i o n p a i r i n g s This feature  i s consistent  Hay  (1981).  with  relationships  sky  data d i s p l a y  cloud,  a highly  more v a r i a b l e , as  correlations about the distinct 4.3.2  with  distance  general trend.  of  The  and The  exhibit  the  The  clear  absence  greater  of  anomalously  overcast  sky  data  more r a p i d d e c r e a s e  functions  p i x e l a r r a y s are  s p a t i a l c o h e r e n c e of  separation  distance,  variable.  In p a r t i c u l a r , the  discrepancy  not  by  partly  - d). In the  regions  scatter  of  of  points are  Correlations  distance-correlation  the  the  lowland  clear,  with  to  Grouse Mountain p a i r i n g s  the  f o r the  insolation  shown i n F i g u r e 4.3a  these f i e l d s  t h e i r network c o u n t e r p a r t s .  display  do  associated  cases.  Satellite-based  estimated using 5 x 5  4.2b  p a r t l y c l o u d y and  j u d g e d by  i n both these  The  d.  The  (Figure  coherent f i e l d .  Grouse Mountain p a i r i n g s  lower c o r r e l a t i o n s . are  classes  lower  noted p r e v i o u s l y  C o m p a r a b l e p l o t s were p r o d u c e d f o r t h e o v e r c a s t sky  well  is attributed  i n c l o u d i n e s s b e t w e e n m o u n t a i n and  and  c l o u d y and  similar  appears g e n e r a l l y  network.  Grouse Mountain s i t e .  differences  tend to e x h i b i t a  insolation field  throughout the  correlations the  The  proximity  i s s i m i l a r to  However, f o r a  that  given  s a t e l l i t e - b a s e d c o r r e l a t i o n s are  anomaly o b s e r v e d i s r e l a t e d to the  Grouse Mountain p a i r i n g s i n the  -  network s e t .  f a c t that .while the  do  less not  This network  data  54  1-0-  0-8-  10'  0 8 -  1-0-  +" °  *  +  +  ^ «, »  «,  gO-8-  rx cr O o  0 6 -  2  o I  1-0-  * 0-8-  0-6-  0  4-  0-2-  ESTIMATED ( 5 x 5 pixel arrays) -+- Grouse Mountain pairings  0  010  2 0  3 0  STATION  F i g u r e 4.3a-d  4 0  5 0  6 0  I  7 0  8 0  SEPARATION (km)  The d i s t a n c e c o r r e l a t i o n f u n c t i o n s o f t h e s a t e l l i t e - e s t i m a t e d i n s o l a t i o n ( b a s e d on 5 x 5 pixel arrays). a. b. c. d.  a l l data c l e a r sky data p a r t l y cloudy sky data overcast data  55  correspond are  to point observations, the s a t e l l i t e - b a s e d  s p a t i a l averages  (the averaging  occurs during the s a t e l l i t e  o b s e r v a t i o n and i n s o l a t i o n m o d e l l i n g p r o c e s s e s ) . satellite  estimates  estimates represent a spatially-smoothed  Since the field,  random d i f f e r e n c e s between s t a t i o n p a i r i n g s a r e r e d u c e d . 4.3.3  C o m p a r i s o n s Between t h e O b s e r v e d a n d E s t i m a t e d Insolation The  Figure 313  observed  4.4a.  and e s t i m a t e d  The p l o t  i n s o l a t i o n a r e compared i n  i n c l u d e s 3756 d a t a p a i r s d e r i v e d  h o u r l y v a l u e s a t e a c h o f t h e 12 n e t w o r k s t a t i o n s .  from The  correspondence  b e t w e e n t h e two s e t s i s s u m m a r i z e d i n T a b l e 4.1.  The  ( i . e . systematic) e r r o r inherent i n the  long-term  m o d e l i s q u a n t i f i e d by t h e m e a n - b i a s - e r r o r MBE = K| - K |  (4.2)  o  w h e r e , K| i s t h e mean h o u r l y e s t i m a t e d i t s observed  counterpart.  (MBE):  i n s o l a t i o n and  The s h o r t - t e r m a c c u r a c y  is  of the  m o d e l i s e v a l u a t e d by t h e r o o t - m e a n - s q u a r e e r r o r (RMSE):  RMSE  where K\ a n d K| and  V  :  dU -  KA  |  )2 —  (4.3)  N  a r e t h e h o u r l y e s t i m a t e d and observed  N i s t h e number o f d a t a  data,  pairs.  F i g u r e 4.4a i n d i c a t e s a g e n e r a l l y good a g r e e m e n t b e t w e e n the observed small  and e s t i m a t e d d a t a .  The m a g n i t u d e o f t h e MBE i s  (+0.4%) r e l a t i v e t o t h e p y r a n o m e t r i c  accuracy  (±2%; a f t e r L a t i m e r ,  1980).  calibration  The MBE's a s s o c i a t e d  56  OBSERVED INSOLATION ( M m  F i g u r e 4.4a  - 2  ^ ) 1  C o m p a r i s o n s between t h e o b s e r v e d and e s t i m a t e d hourly insolation. The l a t t e r a r e b a s e d on 5 x 5 pixel arrays. a.  a l l data  DATA GROUPING  1  N  a  o  "o/KJ  o  a/Kl  r  MBE  MBE%  RMSE  RMSE%  CLEAR  1212  2125 2  2187 1  719 2  748 6  30  30  0 .978  +61.9  +2 9  127 .7  6.0  PARTLY CLOUDY  1524  1023 1  978 1  888 8  774 4  90  80  0 862  -44. 9  -4 4  337 .8  33 .0  OVERCAST  1020  541 9  567 7  513 9  413 2  70  70  0 810  +25.8  +4 8  220 .4  40 .0  ALL DATA  3756  1205 7  1210 3  969 6  940 9  80  80  0 927  +4.6  +0 4  261 .8  21 .7  N  — Kl -K|  :  sample  size  :  observed mean i n s o l a t i o n  :  estimated mean i n s o l a t i o n  fj : ° CT :  standard d e v i a t i o n standard d e v i a t i o n  MBE:  Mean Bias E r r o r  r e l a t i v e e r r o r s are determined with respect to the observed mean i n s o l a t i o n  - 2h- 1 ) -2 -1 (kjm h )  (kJm  -2 -1  of the observed i n s o l a t i o n (kjm h ) -2-1 of the estimated i n s o l a t i o n (kjra h )  (kJm~ h 2  -1  or %)  -2 -1 RMSE:  Root-Mean-Square  Error  (kJm  h  T a b l e 4.1  or %)  C o m p a r i s o n s between t h e o b s e r v e d estimated based  (Kl) insolation  on 5 x 5 p i x e l  (M ) 0  and  (thel a t t e r are  arrays).  58  with  i n d i v i d u a l s t a t i o n data are,  i n most c a s e s , i n s i g n i f i c a n t  (Table 4.2).  These r e s u l t s c o n f i r m  is describing  the  The  observed  that  on  average, the  field.  RMSE ( f o r a l l d a t a ) i s w i t h i n  21.7%.  The  w h i c h e x i s t between i n d i v i d u a l d a t a p a i r s a r e since the  the  o v e r a l l b i a s of  s c a t t e r i s not  model  differences  non-systematic  the model i s n e g l i g i b l e .  statistically  random;  However,  overestimation  is  -2 —1 predominant at estimation  (Figure  irradiances  generally  -2 2750 kJm  low  occurs at higher  h  ).  4.4b  The  - m;  overestimation.  ) while  irradiances  under-  (1200  -  i n d i v i d u a l s t a t i o n data  Table 4.2),  comparisons  in addition, reveal the  that  prime c o n t r i b u t o r s  U n d e r e s t i m a t i o n a p p e a r s t o be  to  the the  a feature  of  stations. Gautier  the  h  -1  Grouse Mountain p a i r i n g s are  all  (<1200 kJm  et a l . (1980) found t h a t  o b s e r v e d i n s o l a t i o n when c l o u d  This  t e n d e n c y was  large.  Gautier  inability cloud  R a p h a e l and ization  Hay  m o d e l t o a c c o u n t f o r s h a d o w i n g by back-scattering  (1984) a l s o  s u g g e s t e d the  absorption.  by  (>0.75).  as a r e s u l t o f  over t h a t  R a p h a e l and  the  droplets.  inadequate  Presumably, the  the  to  also  uneven  water  parameter-  insolation  f o r G r o u s e M o u n t a i n i s more s u s c e p t i b l e  overestimation of c l o u d  high  e n h a n c e d when s o l a r z e n i t h a n g l e s were  anisotropic  of c l o u d  calculated  a l b e d o was  overestimated  (1982) a t t r i b u t e d t h i s t y p e of e r r o r  of the  t o p s and  the model  more f r e q u e n t  to  occurrence  station.  Hay  (1984) a t t r i b u t e d the  underestimation to cloud  threshold  errors.  t e n d e n c y f o r model The  Gautier  STATION GROUPING  N  a • < V K | O O"/KJ  GROUSE MTN  313  1174 .0  1226 .6  N.  VANCOUVER  313  1173 9  1177  3  VANCOUVER B.C. HYDRO BLDG  313  1174 0  1198  AIRPORT  313  1264  1240  TSAWWASSEN  313  1326 .6  1320 .8  PITT MEADOWS  313  1171 .3  1164  MISSION CITY  313  1169  5  ABBOTSFORD CITY  313  1185  ABBOTSFORD AIRPORT  313  1214  LANGLEY CITY  2  MBE  r  MBE%  RMSE  RMSE%  951 0  87  78  0 871  +52 6  +4 5  370 .9  31 6  965 1  927  9  82  79  0 939  +3 4  +0 3  239 9  20 4  2  964 0  915 5  82  76  0 951  +24  2  +2 1  215. 8  18 4  2  987 0  940 3  78  76  0 920  -24  7  -2 0  280 0  22 1  4  998 6  77  76  0 962  -5 8  -0 4  199 0  15 0  1  954 3  940 4  81  81  0 919  -7 2  -0 6  273  0  23 3  1180  1  933 6  925 2  80  78  0 912  +10 6  +0 9  278  6  23 .8  0  1194  3  934 6  926 1  79  78  0 915  +9 3  +0 8  274  6  23 2  7  1201  2  937 3  924 4  77  77  0 930  -13. 5  ' -1 1  249 2  20 5  313  1175 1  1195  0  938 2  932 9  80  78  0. 921  +19 9  +1 7  265 9  22 6  LANGARA  313  1144 0  1166 .2  934 4  940 3  82  81  0 940  +22  0  +1 9  231 .2  20 2  UBC  313  1290  0  970 5  80  77  0. 953  -32 8  -2 5  227  17 .6  9  4  1257  6  1019  1019  1035  9  relative errors are determined observed mean insolation  Table  4.2 I n d i v i d u a l observed (the  station  c o m p a r i s o n s between t h e  ( K J ) and e s t i m a t e d (Kj) i n s o l a t i o n Q  l a t t e r a r e b a s e d on 5 x 5 p i x e l  arrays).  1  with respect to the  60  O B S E R V E D  Figure  4.4b-e  INSOLATION(  k J m ^ r f  1  )  C o m p a r i s o n s between t h e o b s e r v e d a n d e s t i m a t e d hourly insolation. The l a t t e r a r e b a s e d on 5 x 5 pixel arrays. b. c. d. e.  Grouse Mountain data North Vancouver data V a n c o u v e r (B.C. H y d r o B l d g . ) d a t a . UBC d a t a  61  Figure  4.4f-i  C o m p a r i s o n s b e t w e e n t h e o b s e r v e d and e s t i m a t e d hourly i n s o l a t i o n . The l a t t e r a r e b a s e d on 5 x 5 pixel arrays. f. g. h. i.  A i r p o r t data Tsawwassen d a t a Langara data Abbotsford C i t y data  62  O B S E R V E D  Figure  4.4j-m  INSOLATION)  Mm"  2  IT1  )  C o m p a r i s o n s b e t w e e n t h e o b s e r v e d and e s t i m a t e d hourly i n s o l a t i o n . The l a t t e r a r e b a s e d on 5 x 5 pixel arrays. j. k. 1. m.  Abbotsford Airport Langley C i t y data P i t t Meadows d a t a Mission C i t y data  data  63  model c l a s s i f i e s each p i x e l as c l e a r  o r c l o u d y by c o m p a r i n g  the p i x e l r e f l e c t a n c e ( c o n v e r t e d t o energy in  S e c t i o n 3.2.2.3) w i t h a t h r e s h o l d v a l u e .  be m i s c l a s s i f i e d for  units,  as c l o u d y  (i.e.  Partly  statistics  variable,  The m o d e l o v e r e s t i m a t e s  insolation  h  Estimated Using  order t o determine  fields  under  under partly  o f t h e model i s  -2 -1 h ) f o r the c l e a r sky  ) f o r the o v e r c a s t sky  The RMSE's a r e p r i m a r i l y  Insolation In  ±6% (127.7 kJm -2 -1  t o ±40% (220.4 kJm  estimates. 4.3.4  The s h o r t - t e r m a c c u r a c y  r a n g i n g from  cloudy  ( T a b l e 4.1) a r e c o n s i s t e n t  and o v e r c a s t s k i e s w h i l e i t u n d e r e s t i m a t e s  cloudy c o n d i t i o n s .  inevitably,  to cloud threshold errors.  w i t h the p r e v i o u s assessments. clear  field  T h i s would l e a d t o the  to the underestimation of the i n s o l a t i o n .  The d a t a s u b s e t  may  t o account  by t h e c l o u d y s k y m o d e l a n d ,  are p a r t i c u l a r l y s e n s i t i v e  pixel  i n t h e minimum b r i g h t n e s s  the cloud threshold i s too low).  processing of p i x e l s  A clear  i f the threshold f a i l s  the inherent v a r i a b i l i t y  as d e s c r i b e d  non-systematic  3 x 3  Pixel  i n nature.  Arrays  whether s i g n i f i c a n t d i f f e r e n c e s i n  estimation occur with a reduction i n s p a t i a l averaging, the hourly  i n s o l a t i o n d e r i v e d from  with those  from  5 x 5  F i g u r e 4.5 a n d T a b l e are almost is less  identical.  than  ±1%.  arrays.  3 x 3  The c o m p a r i s o n s  4.3 i n d i c a t e The MBE  The a c c u r a c y  p i x e l a r r a y s a r e compared shown i n  t h a t t h e two s e t s o f e s t i m a t e s  i s 0% i n a l l c a s e s a n d t h e RMSE o f t h e model i s a p p a r e n t l y  u n a f f e c t e d by t h e s e c h a n g e s i n s p a t i a l As m i g h t t h e r e f o r e be a n t i c i p a t e d ,  averaging. t h e network data and  64  ESTIMATED  INSOLATION ( k J m ^ r r  (5x5  Figure  4.5  1  )  pixel arrays)  Comparison between t h e h o u r l y i n s o l a t i o n e s t i m a t e d on t h e b a s i s o f 5 x 5 a n d 3 x 3 p i x e l a r r a y s .  DATA GROUPING  CLEAR  N  1212  2187  1  2192  0-/KJ  a  Kl  *o  r  2  MBE  MBE%  RMSE  RMSE%  2  748. 6  753 9  30  30  0 .995  +5 .1  0 0  52 .2  0. 0  1524  978. 1  991. 7  774. 4  773. 9  80  80  0 .960  +13 .6  0. 0  156 . 0  0. 2  OVERCAST  1020  567. 7  578. 7  413. 2  435 3  70  70  0 .947  +11 . 0  0. 0  99 . 6  0. 2  ALL  3756  1210. 3  1221. 9  940. 9  942  80  80  0 .984  +11 .6  0. 0  119 .3  0. 1  PARTLY CLOUDY  DATA  7  r e l a t i v e estimated  T a b l e 4.3  C o m p a r i s o n s between t h e e s t i m a t e d  e r r o r s mean  insolation  b a s e d on 5 x 5 a r r a y s a n d 3 x 3 p i x e l  arrays.  are  determined  i n s o l a t i o n  based  w i t h on  respect 5  x  5  to  p i x e l  the a r r a y s  66  the  3 x 3  array estimates  agreement s i m i l a r (Figure 4.4a). magnitudes of data.  4.3.5  the  e r r o r s f o r a l l but  latter  p i x e l arrays are  corresponding the  reduction  illustrated  increase  i n both  pixel  changes i n the insolation  in Figures  f o r e a c h s e t of e s t i m a t e s  5 x 5  array  results.  insolation field  in  the  sky the  arrays)  differ spatial  The  w i t h i n the  from  - d.  The  i s comparable  implied  and  unaltered  3 x 3  to induce  by that  pixel  significant  c h a r a c t e r i s t i c s of the  derived  fields.  Summary and  Conclusions  issues are  investigated in t h i s chapter.  concerned the a b i l i t y  of the  satellite  the mesoscale i n s o l a t i o n v a r i a b i l i t y pyranometric network.  The  estimates  over the  The to  first  resolve  12 s t a t i o n  c o r r e l a t i o n analyses  and  the  s c a t t e r p l o t c o m p a r i s o n s i n d i c a t e a good a g r e e m e n t b e t w e e n network data analyses  to  spatial  T h i s would suggest  5 x 5  sufficiently  derived  4.7a  is relatively  in s p a t i a l averaging.  a r r a y s does not  Two  an  array  the p a r t l y c l o u d y  situation,, a reduction  the average v a r i a b i l i t y  4.4  5 x 5  i n t e r s t a t i o n c o r r e l a t i o n s for estimates  c o h e r e n c e of this  the  display  long-term e r r o r s i s noted.  correlation pattern the  using  Satellite-based Correlations ( 3 x 3 The  3 x 3  to that obtained  T a b l e 4.4)  Comparisons i n d i c a t e a s l i g h t  In t h i s  s h o r t - and  ( F i g u r e 4.6;  and  the  satellite  a l s o r e v e a l that the  estimates.  the  The c o r r e l a t i o n  satellite-based fields  (notably  67  OBSERVED, INSOLATION( W i n ^ h - 1 )  Figure  4.6  Comparison between t h e o b s e r v e d and e s t i m a t e d hourly insolation ( a l l data). The l a t t e r a r e b a s e d on 3 x 3 p i x e l a r r a y s .  DATA GROUPING  N  0  KJ  CLEAR  1212  2125  PARTLY CLOUDY  1524  1023. 1  OVERCAST  1020  ALL DATA  3756  2  2192 .2  c  WKl  o  r  z  MBE  MBE%  RMSE  RMSE%  6 .5  719 .2  753 .9  30  30  0 .976  +67 .0  +3 2  137 .2  7  888. 8  773. 9  90  90  0 875  -31 .4  -3. 1  321  8  31 0  541. 9  578. 7  513. 1  432. 3  90  70  0 794  +36 .8  +6.8  228. 4  42 0  1205. 7  1221. 9  969. 6  942. 7  80  80  0. 931  +16 .2  +1.3  255. 7  21  991  relative errors are determined observed mean insolation  T a b l e 4.4 C o m p a r i s o n s between estimated  the observed  (Kl) insolation  b a s e d on 3 x 3 p i x e l  and  (the l a t t e r a r e  arrays).  0  with respect to the  69  10-  *»7 0-8'  10-  0 8 -  10-  08-  06-  cc  1-0' A  © T  4  +  ©  ©  © ©  ©  0-8-  +  © S©  ©  «  0 6 -  0-4-  0 2-  ESTIMATED (3x3 +  OO-I  I 20  10  I 30 STATION  F i g u r e 4.7a-d  I 40  Grouse  I 50  60  pixel  arrays)  Mountain pairings  170  —f 80  SEPARATION (km)  The d i s t a n c e - c o r r e l a t i o n functions of the s a t e l l i t e - e s t i m a t e d i n s o l a t i o n ( b a s e d on 3 x 3 pixel arrays). a. b. c. d.  a l l data c l e a r sky data p a r t l y cloudy sky data overcast sky data  70  those  r e p r e s e n t i n g c l o u d y c o n d i t i o n s ) a r e more homogeneous.  This effect  i s a t t r i b u t e d t o the  the s a t e l l i t e methodology. and  the  satellite-based  s p a t i a l averaging  Comparisons between the  insolation  p r o v i d i n g an a c c u r a t e c h a r a c t e r i z a t i o n  observed  field.  by  a/  K|;  of  However, t h e s h o r t - t e r m a c c u r a c y  l a r g e , the v a r i a b i l i t y Table  4.4)  observed  show t h a t t h e m o d e l i s , on  average,  i s comparatively poor.  inherent in  the of the  model  Though t h e h o u r l y m o d e l l i n g e r r o r s a r e of the e s t i m a t e d  is larger.  The  insolation  estimates are  (as d e f i n e d therefore  meaningful. The  second i s s u e c o n s i d e r e d the  p i x e l a r r a y s to r e s o l v e the s p a t i a l between the 5 x 5  and  3 x 3  network data not  have l i t t l e in  shown by  on t h e e s t i m a t e d  the coherence of the observed  and  field.  finer  pixel array.  this variability  the is  appears to  i t i s assumed  o r i g i n a t e s at s p a t i a l  G a u t i e r model c a l c u l a t e s  with  satellite-estimated  as a r e s u l t of s p a t i a l a v e r a g i n g ,  t h a t of t h e 3 x 3  3 x 3  Since d i f f e r e n c e s  t h a t most o f t h e v a r i a b i l i t y than  While  a r r a y e s t i m a t e s , such  This reduction in s p a t i a l averaging  impact  f i e l d s occur  would imply t h a t the  the 5 x 5  3 x 3  The d i f f e r e n c e s  should d i s p l a y a greater s i m i l a r i t y  than  the case.  field.  of u s i n g  array estimates are minor.  the e f f e c t s of s p a t i a l a v e r a g i n g array estimates  feasibility  Although  scales the  i n s o l a t i o n on a p i x e l - b y - p i x e l b a s i s ,  c a n n o t be a s s e s s e d  by t h e n a v i g a t i o n a l e r r o r s .  due  to l i m i t a t i o n s  imposed  71  Chapter  V  S A T E L L I T E MAPPING OF 5.1  Introduction The  preceding  satellite-based mesoscale.  confirm  Although  the c a p a b i l i t y insolation  this potential  efforts  had  (1982),  In t h i s c h a p t e r , lower  estimates and  G a u t i e r model was  Minimum b r i g h t n e s s was  estimated  to reduce c a l c u l a t i o n s ,  regression equation  are  i n f l u e n c e on  s i n c e the c l e a r  sky  region. over  x 120  been shown t o d i f f e r  on  not  derived by  certain  pixel  pixel  3.12. of  In  field. an  the  t h e b a s i s of 5 x 5 p i x e l insolation  e x p e c t e d t o have a  t h e minimum b r i g h t n e s s  insolation  the  t o t h e Mode  3 x 3  a r r a y s used i n the  significant  by  Procedure  the c o e f f i c i e n t s  Such m o d i f i c a t i o n s a r e  1978),  discussed.  by E q u a t i o n  modelling.  in  produced  insolation  o v e r a 60  were e v a l u a t e d  i n s t e a d of t h e 3 x 3  a r r a y s has  beyond those  ( S e c t i o n 3.4.1), u s i n g contiguous insolation  arrays  Ellis,  implemented a c c o r d i n g  a r r a y s t o r e s o l v e the  effort  the  i t s e n v i r o n s , a r e mapped and  I m p l e m e n t a t i o n of the Mapping  II procedure  the  been r e c o g n i z e d  of the h o u r l y  of the m e s o s c a l e v a r i a b i l i t y  The  of  f o r the S t . Lawrence - Lake O n t a r i o  Fraser Valley,  aspects  at  ( e . g . V o n d e r H a a r and  e x a m p l e s o f m e s o s c a l e maps e x i s t  Gautier  5.2  analyses  m e t h o d o l o g y t o map  e a r l i e r modelling few  INSOLATION  from 3 x 3  estimates and  5 x 5  i n s i g n i f i c a n t amounts  72  (Table 4.3).  The r e g r e s s i o n c o e f f i c i e n t s were s t o r e d by  the c o o r d i n a t e s of t h e c e n t r a l p i x e l Minimum b r i g h t n e s s was e s t i m a t e d subsequently 3 x 3  at these  grid  arrays.  l o c a t i o n s and  e x t r a p o l a t e d t o the c e n t r a l p i x e l c o o r d i n a t e s of  arrays using the nearest-neighbour  Kiefer, 5.2.1  of t h e 5 x 5  method  (Lillesand  and  1979). Minimum B r i g h t n e s s P r e d i c t i o n s  The s t a n d a r d coefficient equation  e r r o r of the e s t i m a t e 2  of d e t e r m i n a t i o n  to assess  predictions.  (SE) a n d t h e  ( r ) were c o m p u t e d f o r e a c h  t h e p e r f o r m a n c e o f t h e minimum b r i g h t n e s s  These measures d i s p l a y e d a h i g h v a r i a b i l i t y  with  2  r a n g e s o f SE and r  between  1.61  - 7.37  0.975, r e s p e c t i v e l y ( A p p e n d i x B ) . apparently  p r o v i d e s an i n f e r i o r  counts  a n d 0.229 -  The r e g r e s s i o n m o d e l  o f t h e minimum 2 brightness i n certain cases. A histogram of r v a l u e s r e v e a l s t h a t the d i s t r i b u t i o n i s bimodal ( F i g u r e 5.1a). The l o w e r 2 coefficients  (i.e. r  approximation  < 0.650, t h e m i d p o i n t  0.699 c l a s s i n t e r v a l ) t e n d  o f t h e 0.600 -  t o be a s s o c i a t e d w i t h l a r g e w a t e r  dominated s u r f a c e s , i n c l u d i n g p o o r l y d r a i n e d t e r r a i n i n southeastern  p a r t s of the lowland  ( F i g u r e 5.1b).  E r r o r s of  p r e d i c t i o n a r e a l s o h i g h e r over these s u r f a c e s (note t h a t 2 2 SE i s r e l a t e d t o r by t h e e x p r e s s i o n , SE = a^/[1 - r ] , where i s the standard The g e n e r a l  d e v i a t i o n o f t h e minimum b r i g h t n e s s ) .  form of t h e r e g r e s s i o n model  i s b a s e d on t h r e e g e o m e t r i c  functions:  ( S e c t i o n 3.4.6)  cos0 accounts  e f f e c t s o f a c h a n g i n g sun a n g l e ; c o s 0 s i n 7  accounts  f o r the  for surface  74  2  s h a d i n g and c o s 7 S i n 0 s i m u l a t e s p r o p e r t i e s of t h e s u r f a c e . term i s q u e s t i o n a b l e negligible (Wanless,  of the l a s t  surfaces  term t o account  surfaces exhibit  (Brennan and Bandeen,  t e r m was shown t o be an  d e s c r i p t o r o f t h e minimum b r i g h t n e s s  issue  f o r the surface  Land and water  1970). While t h e c o s 7 s i n 0  by t h e r e g r e s s i o n  i s r e l a t e d to the  scattering characteristics 2  ineffectual  the r e g r e s s i o n  The p o o r e r f i t p r o v i d e d  scattering anisotropy. different  The s i g n i f i c a n c e o f t h e s e c o n d  i m p a c t on t h e p e r f o r m a n c e . o f 1983).  reflectance  a s i t s i n c l u s i o n was f o u n d t o h a v e a  model over water dominated inability  the b i d i r e c t i o n a l  i n the case of water  i s exemplified i n Figure  appropriate  o v e r l a n d , i t was  (Wanless,  1983).  This  5.2a - d, w h i c h d i s p l a y s t h e  a c t u a l a n d p r e d i c t e d minimum b r i g h t n e s s v a r i a t i o n s o v e r and w a t e r t a r g e t s d u r i n g J u l i a n d a y 196/79.  land  I t i s evident  that a b e t t e r a p p r o x i m a t i o n of b r i g h t n e s s v a r i a t i o n s i s obtained  over l a n d .  The d i u r n a l a s y m m e t r y e x h i b i t e d by w a t e r  i s n o t r e p r o d u c e d by t h e m o d e l . of w a t e r d o m i n a t e d  The r e f l e c t a n c e c h a r a c t e r i s t i c s  s u r f a c e s moreover e x h i b i t day-to-day  v a r i a t i o n s w h i c h a r e n o t a c c o u n t e d f o r by t h e p a r a m e t e r s of t h e r e g r e s s i o n . tidal  These i n c l u d e changes a s s o c i a t e d  c y c l e s , seasonal  into the S t r a i t and o t h e r  v a r i a t i o n s of the sediment  with  discharge  o f G e o r g i a a n d o f t h e m o i s t u r e c o n t e n t o f bogs  poorly drained  land areas.  Although the regression  m o d e l i s shown t o be an i n a p p r o p r i a t e p r e d i c t o r o f t h e minimum b r i g h t n e s s o f w a t e r d o m i n a t e d  surfaces, the confidence  m a r g i n o f 12 c o u n t s a d d e d t o t h e c l o u d t h r e s h o l d  ( S e c t i o n 3.4.7)  LAND  TARGETS  WATER  100  TARGETS  100  80  \ \  60 •  2 c  60  40  40-  3  o o  3: ( 5 x 5  array central pixel coordinate: 38,28)  0 ^ ( 5 x 5  array central pixel coordinate :  3,33)  w CO UJ  f.  CO CO  100  UJ  I  z  m  o  100  1-  o  I  rx m  80  * ss  60-  is  \ V \  40  t>* ( 5 x 5 8  80  \  \  \ \  \  60  \  \  40C h ( 5 x 5 array central pixel coordinate; 48,53)  array central pixel coordinate: 68, 3 ) 10  12 TIME  14  16  (LAT)  F i g u r e 5.2a-d  18  predicted  10  -actual  A c t u a l and p r e d i c t e d d i u r n a l v a r i a t i o n b r i g h t n e s s f o r J u l i a n d a y 196/79  12 TIME  14 (LAT)  o f minimum  —r— 16  -T*  18  76  is  sufficiently  l a r g e t o accomodate t h e e r r o r s of p r e d i c t i o n .  A d j u s t m e n t s t o t h e model a r e t h e r e f o r e judged 5.3  S a t e l l i t e - b a s e d Mean H o u r l y The  t o be  unnecessary.  I n s o l a t i o n Maps  mean h o u r l y i n s o l a t i o n e s t i m a t e s  forclear,  partly  c l o u d y , o v e r c a s t and a l l c o n d i t i o n s a r e mapped i n F i g u r e 5.3a - d. 5.4a  T h e i r n e t w o r k - b a s e d c o u n t e r p a r t s a r e shown i n F i g u r e - d.  The l o c a t i o n s o f t h e d a t a p o i n t s u s e d t o c o n t o u r  the e s t i m a t e d and  field  a r e d i s p l a y e d i n F i g u r e 5.5.  extent of the s p a t i a l  sampling  The d e n s i t y  contrasts with that  p r o v i d e d by t h e 12 s t a t i o n n e t w o r k a n d h i g h l i g h t s t h e u t i l i t y of t h e s a t e l l i t e a p p r o a c h , p a r t i c u l a r l y  over  mountainous  t e r r a i n where m e a s u r e m e n t s a r e l a r g e l y n o n - e x i s t e n t .  For -2 -1  c o n s i s t e n c y b e t w e e n maps, a c o n t o u r i s a p p l i e d i n a l l cases. with the p o s i t i o n the accuracy  error  ( o r m a g n i t u d e ) o f an i s o l i n e w i l l field  of a g i v e n  (Table 4.4).  e r r o r s cancel out i n the averaging  i n h e r e n t i n e a c h map c o r r e s p o n d s  distribution.  o f 100 kJm  depend on Since the  process, the  t o t h e MBE o f t h e  The c o n f i d e n c e m a r g i n a s s i g n e d t o t h e c o n t o u r s  field  i s determined  by: (5. 1 )  e(%)  where ±2% i s t h e p y r a n o m e t r i c  calibration  v a l u e s o f e a r e w i t h i n 100 kJm The  clear  h  The c o n f i d e n c e m a r g i n a s s o c i a t e d  of the represented  non-systematic  interval  h  (see c o r r e s p o n d i n g  sky e s t i m a t e d and observed  comparable ranges over  those  uncertainty. A l l maps).  insolation display  regions monitored  by b o t h t h e  Figure  5.3a  S p a t i a l d i s t r i b u t i o n of t h e mean h o u r l y i n s o l a t i o n ( c l e a r sky d a t a ) .  estimated  Figure  5.3b  S p a t i a l d i s t r i b u t i o n of t h e mean h o u r l y i n s o l a t i o n ( p a r t l y c l o u d y sky d a t a ) .  estimated  Figure  5.3c  S p a t i a l d i s t r i b u t i o n of t h e mean h o u r l y i n s o l a t i o n ( o v e r c a s t sky d a t a ) .  estimated  Figure  5.3d  S p a t i a l d i s t r i b u t i o n of t h e mean h o u r l y insolation ( a l l data).  estimated  Figure  5.4a  S p a t i a l d i s t r i b u t i o n o f t h e mean h o u r l y i n s o l a t i o n ( c l e a r sky d a t a ) .  observed  00  contour interval  100  KJm"2h  km  - 1  0  5  10  20  + Network Station  Figure  5.4b  S p a t i a l d i s t r i b u t i o n of t h e mean h o u r l y i n s o l a t i o n ( p a r t l y c l o u d y sky d a t a ) .  observed  Figure  5.4c  S p a t i a l d i s t r i b u t i o n of t h e mean h o u r l y i n s o l a t i o n ( o v e r c a s t sky d a t a ) .  observed  OO  Network Station  Figure  5.4d  S p a t i a l d i s t r i b u t i o n o f t h e mean h o u r l y insolation ( a l l data).  observed  CD  •  location of the central pixel of 3x3 pixel array 0  Figure  5.5  5  10  L o c a t i o n s of t h e c e n t r a l p i x e l of 3 x 3 p i x e l a r r a y s u s e d t o map t h e s a t e l l i t e - e s t i m a t e d insolation.  86  satellite  and  insolation northerly  the network.  i s small.  The  The  r e l a t i v e v a r i a n c e of  lowest  r e g i o n s where snow has  the G a u t i e r model.  insolation  occurs  in  been i n t e r p r e t e d a s c l o u d  This erroneous  artifact  o f t h e snow c o v e r .  southward  Larger  i n t e n s i t i e s w o u l d have been a n t i c i p a t e d a t h i g h e r due  t o a s m a l l e r o p t i c a l a i r mass.  discernable  i n t h e n e t w o r k map,  satellite-based distribution. the e s t i m a t e d  insolation  contamination  i n these  While  Presumably, the  regions.  The  w i t h t h e g e n e r a l a x i s of r i d g e s and  insolation  shading.  i s less structured.  coast  i s p r i m a r i l y an a r t i f a c t  (i.e.  noise)  induced  wider  insolation  tidal  The  s k i e s due features. may  towards the Coast  insolation  detail  of snow  coincident  are p o s s i b l y the  observed  of the m o d e l l i n g  lowland along  the  procedure  flats.  distribution  o r o g r a p h i c e f f e c t s , a s shown by  The  i n the  intensity  alignment  v a l l e y s and  under p a r t l y c l o u d y  range of v a l u e s .  insolation  trend i s  by t h e h i g h l y v a r i a b l e b r i g h t n e s s o f  s u r f a c e s s u c h a s b o g s and The  altitudes  spatial patterns in  By c o m p a r i s o n , The  with  radiative  by t h e e f f e c t s o f  mountainous areas d i s p l a y a n o r t h - s o u t h  related to topographic  this  i t i s not e v i d e n t  i s suppressed  by  i s enhanced i n  r e g i o n s of p e r s i s t e n t s n o w f i e l d s , but d e c r e a s e s t h e more s e a s o n a l n a t u r e  the  field  skies exhibits  a  is controlled  the gradual decrease  by  of  Mountains.  i s r e l a t i v e l y u n i f o r m under  overcast  t o the e x t e n s i v e n a t u r e of the s y n o p t i c - s c a l e c l o u d The  p a t t e r n s which occur along the mountain  be a t t r i b u t e d  to a d d i t i o n a l orographic e f f e c t s .  front  Comparisons  87  w i t h the c o r r e s p o n d i n g general  tendency  n e t w o r k - b a s e d map  for overestimation  is especially significant The  spatial  persists  in this  gradient  under o v e r c a s t  region  4.3.3).  lowland  for a l l conditions.  A  i s r e c e i v e d o v e r m o u n t a i n o u s t e r r a i n due  a t t e n u a t i o n by  o r o g r a p h i c a l l y enhanced c l o u d .  o f snow may  incorporated  be  coastal-inland gradient  i n these  i s also evident.  regions  lower to  The  patterns.  the  conditions  (Section  b e t w e e n m o u n t a i n and  i n the d i s t r i b u t i o n  insolation  indicates that  influence  A weak  Higher i r r a d i a n c e s  occur  at the coast  while the g e n e r a l l y patchy d i s t r i b u t i o n  lower  i r r a d i a n c e s found i n l a n d a r e a t t r i b u t e d t o the e f f e c t s  of e n h a n c e d c o n v e c t i v e 5.4  activity  Spatial Variability  5.4.1  at those  of the H o u r l y  l o c a t i o n s (Hay,  Estimated  of  1984).  Insolation  Spatial Correlations The  provide  c o r r e l a t i o n analyses an  undertaken i n Section  a s s e s s m e n t o f t h e c o v a r i a t i o n of t h e  i n s o l a t i o n a b o u t t h e mean.  However, they  do  4.3  hourly  not  emphasize  the  c  anisotropy topographic  i n the c o r r e l a t i o n  f i e l d which r e s u l t s  v a r i a t i o n s w i t h i n the  t h i s a n i s o t r o p y can  be  study  a p p r o a c h e m p l o y e d by Hay  arbitrarily area.  The  3 x 3  The  extent  f u r t h e r i n v e s t i g a t e d by m a p p i n g  c o r r e l a t i o n s over two-dimensional space.  contiguous  area.  from  (1981),  Following  selected array  the  an  insolation estimates  a r r a y s were c o r r e l a t e d w i t h t h o s e  from  from  l o c a t e d at the c e n t r e of the  r e s u l t s of t h i s a n a l y s i s were mapped, a s  of  an study  shown i n  88  Figure  5.6a  The the  -  d.  c l e a r sky  study area.  northern parts a r t i f a c t s of  The of  the  p a r t l y c l o u d y and The  field  displays a high  s t u d y a r e a but  snow c o v e r . overcast  The  this  f i e l d s provide  generally  high  p a r t l y cloudy f i e l d  The  mountainous  the  patterns  configuration  the  lower Fraser  of  c o m p a r a t i v e l y c o m p l e x and terrain.  conditions.  The  Especially the  5.4.2  and  along  c o r r e l a t i o n s over  map  also  noteworthy are  are  the  Valley.  field  The  displayed  reveals the  the  the  However, i t  m o d u l a t e d by  physical is  mountainous between  under a l l  some i n t e r e s t i n g d e t a i l .  higher  correlations  associated  deeper mountain v a l l e y s .  S p a t i a l Sampling Requirements f o r Hourly Estimated Insolation E s t i m a t e s of  g r i d of  contrast.  S i m i l a r , though l e s s pronounced d i f f e r e n c e s lowland regions  the  orographic  h i g h l y a n i s o t r o p i c over  m o u n t a i n and  with  are  to  regions.  gradient  lowland approximate i s o t r o p i c c h a r a c t e r i s t i c s . i s apparent that  of  about the c e n t e r  i m p o r t a n c e of  c o n t r o l s under these c o n d i t i o n s .  due  a marked  e x h i b i t s a strong  mountain f r o n t , r e f l e c t i n g the  in  is likely  s p a t i a l patterns  d e c r e a s e r a p i d l y t o w a r d s c o a s t a l and The  throughout  c o r r e l a t i o n s decrease s l i g h t l y  the  c o r r e l a t i o n s are  coherence  800  the h o u r l y  sample p o i n t s .  the  i n s o l a t i o n were o b t a i n e d These d a t a p r o v i d e  i n t e n s i v e s p a t i a l coverage p o s s i b l e w i t h i n image n a v i g a t i o n . evaluation  of  The  derived  spatial patterns,  field  the  p e r m i t s an  the  over a  most  accuracy  of  initial  h i t h e r t o unknown o v e r  large  Figure  5.6a  V a r i a t i o n o f t h e c o r r e l a t i o n of t h e s a t e l l i t e based e s t i m a t e s w i t h d i s t a n c e from the c e n t r e of t h e s t u d y a r e a ( c l e a r s k y d a t a ) .  F i g u r e 5.6b  V a r i a t i o n of t h e c o r r e l a t i o n of t h e s a t e l l i t e based e s t i m a t e s w i t h d i s t a n c e from the c e n t r e of t h e s t u d y a r e a ( p a r t l y c l o u d y s k y d a t a ) .  Figure  5.6c  V a r i a t i o n o f t h e c o r r e l a t i o n of t h e s a t e l l i t e based e s t i m a t e s w i t h d i s t a n c e from the c e n t r e of t h e s t u d y a r e a ( o v e r c a s t sky d a t a ) .  48 45 51'  121°  contour interval +  005  central 3 x 3 array ( central pixel coordinate  Figure  5.6d  62,32)  V a r i a t i o n of t h e c o r r e l a t i o n of the s a t e l l i t e based e s t i m a t e s w i t h d i s t a n c e from t h e c e n t r e of t h e study a r e a ( a l l d a t a ) .  93  parts  of  the  processing spatial can  be  study area.  required  a s s e s s e d by  differences  the  the  could  l a r g e amount o f  field,  data  a reduction  in  the  have a b e n e f i c i a l e f f e c t .  examining the  e r r o r and  c a l c u l a t i o n of  to the  to define  sampling density  extrapolation  and  Due  This  r e l a t i o n s h i p between  distance.  The  standard deviation  between the  estimate  a l l other estimates  (K-^,..):  approach involves of  the h o u r l y  f o r the  the  insolation  central array  (K|  6 2  ,32)  (5.2)  where, D  i.j M  If  the  field  "  K  J  A  i s assumed t o be  independent of  * i . : " I  K  '"'  J  3 2  (5.2a)  3 2  (5.2b)  homogeneous ( i . e . v a r i a n c e s  l o c a t i o n ) , XID.  • = 0,  1  1  becomes:  and  Equation  are  5.1  J  (5.2c)  The  spatial differences  over the 1984). The and  the  lower Fraser The  i n the  V a l l e y h a v e been shown t o be  a s s u m p t i o n of  a n a l y s i s was r e s u l t s are  t o W i l s o n and  long-term average i n s o l a t i o n  homogeneity i s hence a v a l i d  p e r f o r m e d on illustrated  Petzold  small  each of  in Figure  (1972), d i f f e r e n c e s  the 5.7a  data - d.  b e t w e e n two  (Hay, one.  groupings According sample  94  estimates  are not s i g n i f i c a n t  a (%) = y t  The r e l e v a n t  threshold  study area.  they exceed a 2"  (5.3)  |V'(RMSE%)  display small  differences  The l a r g e r e r r o r s w h i c h o c c u r  regions  incorporate  cover.  The map i n d i c a t e s t h a t  from t h e c e n t e r  value:  i s shown on e a c h map.  The c l e a r s k y e s t i m a t e s the  unless  modelling  t o any o t h e r  i n mountainous  a r t i f a c t s associated  with  t h e i n s o l a t i o n c a n be  l o c a t i o n , with errors  one  fc  = 9.2% o f t h e mean e s t i m a t e  sample would a d e q u a t e l y d e f i n e  remaining  occur  i n the p a r t l y cloudy  field.  -1  o f t h e mean ( i . e . 448 k j m  i n s o l a t i o n at the center lowland,  excluding  characterized estimate  errors. _ 2  (i.e.  322 kJm  Larger  h  Thus  variations  ) a r e not s i g n i f i c a n t .  The  throughout the  c o a s t a l l o c a t i o n s . The o v e r c a s t  Since  ).  H o w e v e r , d i f f e r e n c e s o f up t o  c a n be e x t r a p o l a t e d  by b o t h s m a l l  h  —i  _ 2  43.8%  ( i . e . 196 k j m  the f i e l d .  snow  extrapolated  —2  below o  over  field i s  i n s o l a t i o n d i f f e r e n c e s and l a r g e  d i f f e r e n c e s o f up t o 5 9 . 4 % o f t h e mean  -1  h  ) are i n s i g n i f i c a n t ,  over t h e e n t i r e s t u d y a r e a and o n l y  extrapolation  i s possible  one s a m p l e i s r e q u i r e d .  U n d e r a l l c o n d i t i o n s , t h e i n s o l a t i o n c a n be e x t r a p o l a t e d t o -2-1 w i t h i n 2 9 . 7 % o f t h e mean ( i . e . 358 kJm l o s s of i n f o r m a t i o n .  h  This corresponds t o a region  encompasses t h e l o w l a n d  and p a r t  of t h e mountain  The a n a l y s i s s u g g e s t s t h a t t h e i n i t i a l can  ) w i t h no s i g n i f i c a n t  front.  sampling  density  be s u b s t a n t i a l l y r e d u c e d . The c l e a r s k y i n s o l a t i o n i s  homogeneous o v e r t h e s t u d y a r e a a n d i s a d e q u a t e l y by  which  the estimate  f o r the c e n t r a l array.  characterized  In contrast, the  Figure  5.7a  V a r i a t i o n o f t h e s t a n d a r d d e v i a t i o n of t h e i n s o l a t i o n d i f f e r e n c e s w i t h d i s t a n c e from the c e n t r e o f t h e s t u d y a r e a ( c l e a r sky d a t a ) .  F i g u r e 5.7b  V a r i a t i o n of the s t a n d a r d d e v i a t i o n of the i n s o l a t i o n d i f f e r e n c e s w i t h d i s t a n c e from the c e n t r e o f t h e s t u d y a r e a ( p a r t l y c l o u d y sky d a t a ) .  - f central 3x3 array ( central pixel coordinate 62,32^ o = 322 k J r r r r f ( ± 59.4% of the observed mean insolation ) 2  1  i  F i g u r e 5.7c  V a r i a t i o n of the standard d e v i a t i o n ofthe i n s o l a t i o n d i f f e r e n c e s w i t h d i s t a n c e from t h e c e n t r e of t h e study area (overcast sky d a t a ) .  Figure  5.7d  V a r i a t i o n o f t h e s t a n d a r d d e v i a t i o n of t h e i n s o l a t i o n d i f f e r e n c e s w i t h d i s t a n c e from the c e n t r e of the study area ( a l l d a t a ) .  99  the  i n s o l a t i o n p a t t e r n s under cloudy  v a r i a b l e but the l a r g e m o d e l l i n g of t h e s p a t i a l d i s t r i b u t i o n . of t h e model p r e c l u d e s sampling 5.5  conditions are highly  e r r o r s prevent  The p o o r s h o r t - t e r m  accuracy  any c o n s i d e r a t i o n of t h e p r e c i s e  requirements.  Summary a n d C o n c l u s i o n s Geostationary  s a t e l l i t e d a t a were u s e d t o map t h e  mesoscale i n s o l a t i o n adjacent  over  Coast Mountains.  t h e lower  F r a s e r V a l l e y and t h e  The m a p p i n g p r o c e d u r e r e q u i r e d  estimates  o f minimum  Tarpley's  (1979) r e g r e s s i o n e q u a t i o n .  provided over  an a s s e s s m e n t  brightness.  The  v a r i a t i o n s over  It failed  using  relationship  a g o o d c h a r a c t e r i z a t i o n o f t h e minimum  land surfaces.  "modelling  T h e s e were d e r i v e d  brightness  t o reproduce the brightness  w a t e r d o m i n a t e d s u r f a c e s due t o t h e  of the b i d i r e c t i o n a l  inadequate  reflectance properties.  The mean h o u r l y s a t e l l i t e - b a s e d maps d i s p l a y e d t h e m o u n t a i n - l o w l a n d d i f f e r e n c e s w h i c h had been p r e v i o u s l y inferred  from the network d a t a .  coverage provided patterns.  by t h e s a t e l l i t e c l e a r l y  The maps c o m p i l e d  that the d i s t r i b u t i o n i n f l u e n c e d by l o c a l larger  time  However, t h e g r e a t e r  by G a u t i e r  defines  spatial  these  ( 1 9 8 2 ) l i k e w i s e showed  of t h e mesoscale i n s o l a t i o n  was  t o p o g r a p h y t h o u g h h e r d a t a were b a s e d on  and space s c a l e s .  S p a t i a l c o r r e l a t i o n s were mapped t o a s s e s s of t h e h o u r l y  insolation  field.  were i s o t r o p i c and homogeneous  The c l e a r  the coherence  sky c o r r e l a t i o n s  throughout the study  area  100  (excluding cover).  r e g i o n s a s s o c i a t e d w i t h a r t i f a c t s o f t h e snow  The p a r t l y c l o u d y a n d o v e r c a s t  variable. lowland  Both d i s p l a y e d d i s t i n c t  regions.  i s o t r o p y over  The c o r r e l a t i o n s  f i e l d s were more  p a t t e r n s over  m o u n t a i n and  r e v e a l e d some d e g r e e o f  t h e l o w l a n d b u t were h i g h l y a n i s o t r o p i c i n  mountainous r e g i o n s . Certain artifacts in this chapter.  of t h e m o d e l l i n g procedure  The i n a b i l i t y  of t h e p r e s e n t  were  noted  insolation  model t o d i s t i n g u i s h b e t w e e n snow a n d c l o u d d i s t o r t e d t h e clear  sky p a t t e r n s .  E r r o r s due t o snow were n o t a p p a r e n t  p r e v i o u s assessments i n v o l v i n g the Grouse Mountain (Chapter northerly  station  I V ) s i n c e t h e s e e r r o r s a r e a s s o c i a t e d w i t h more l o c a t i o n s where snow c o v e r  tends  The s t a n d a r d d e v i a t i o n o f t h e h o u r l y d i f f e r e n c e s was d e t e r m i n e d  i n an a t t e m p t  feasibility  of r e d u c i n g t h e s p a t i a l  clear  was a d e q u a t e l y  field  represented  was hampered by t h e l o w a c c u r a c y  t o be  to evaluate the density.  The  by one s a m p l e .  Any  of t h e c l o u d y  of the model.  the average h o u r l y i n s o l a t i o n are m e a n i n g f u l , p o s s i b l e t o account fields until  f o r the v a r i a b i l i t y  the short-term accuracy  persistent.  insolation  sampling  assessment of the mesoscale v a r i a b i l i t y  improved.  in  fields  Though maps o f i twill  n o t be  of i n d i v i d u a l  hourly  of t h e G a u t i e r model i s  101  Chapter SUMMARY AND  The  aim of t h i s  the  insolation  over  t h e l o w e r F r a s e r V a l l e y and  had  demonstrated  alternative The  u s e d t o map  f o r the study area  the s u p e r i o r i t y  the  developed  insolation.  (Raphael  network-based f i e l d s . o f c l o u d y s k i e s and  T h i s was  over  was  a t t r i b u t e d t o the  ( S e c t i o n 4.3.3) c o n f i r m e d  than  corresponding  e s p e c i a l l y e v i d e n t i n the i n f l u e n c e of  and  estimated  spatial  the p o t e n t i a l c a p a b i l i t y  insolation f o r the  s a t e l l i t e - b a s e d mapping of the m e s o s c a l e f i e l d .  Though  RMSE of t h e h o u r l y e s t i m a t e s were l a r g e , t h e MBE  was  t h a t t h e e s t i m a t e s w e r e , on a v e r a g e ,  a c c u r a t e r e p r e s e n t a t i o n of the observed d i s p l a y e d a tendency  case  procedure.  Comparisons between the o b s e r v e d  the  small,  p r o v i d i n g an  insolation.  towards o v e r e s t i m a t i o n under  The  model  overcast  T h e s e d i s c r e p a n c i e s were most f r e q u e n t l y a s s o c i a t e d  w i t h e s t i m a t e s f o r t h e G r o u s e M o u n t a i n l o c a t i o n due higher  1984)  ( S e c t i o n 4.3.2) h a v e shown t h a t  i n the s a t e l l i t e - b a s e d  conditions.  A  and Hay,  of t h i s approach  t h e e s t i m a t e d d i s t r i b u t i o n s were more c o h e r e n t  indicating  of  methods.  correlation analyses  averaging  of a  adjacent  A s i m p l e p h y s i c a l l y - b a s e d model  by G a u t i e r e t a l . ( 1 9 8 0 ) was verification  t o assess the a b i l i t y  to r e s o l v e the mesoscale v a r i a b i l i t y  mountainous r e g i o n .  prior  CONCLUSIONS  t h e s i s was  GOES-based p r o c e d u r e  VI  to  the  i n c i d e n c e of o r o g r a p h i c c l o u d over mountainous r e g i o n s .  Underestimation  o c c u r r e d under p a r t l y c l o u d y c o n d i t i o n s ,  102  i r r e s p e c t i v e of s t a t i o n  location.  Insolation estimates not  differ  significantly  derived  from those  ( S e c t i o n s 4.3.4 a n d 4 . 3 . 5 ) . feasibility spatial not  of applying  field.  result  using  scales. was of  arrays  These r e s u l t s d e m o n s t r a t e d t h e  similarity  t o resolve the  w i t h t h e network  a s i t u a t i o n w h i c h m i g h t be a n t i c i p a t e d a s a i n s p a t i a l averaging.  t h a t most o f t h e i n s o l a t i o n v a r i a b i l i t y  occurs  The e f f e c t s o f s p a t i a l a v e r a g i n g  experienced  arrays d i d  I n t e r e s t i n g l y , the 3 x 3 array estimates d i d  of the r e d u c t i o n  scales.  5 x 5  the 3 x 3 p i x e l arrays  e x h i b i t any i n c r e a s e d  observations,  from 3 x 3 p i x e l  This  implies  at smaller  are therefore  p r i m a r i l y between t h e p o i n t and t h e 3 x 3  A more s p e c i f i c  i n v e s t i g a t i o n of s p a t i a l  pixel  averaging  not undertaken since n a v i g a t i o n a l e r r o r s r e s t r i c t smaller  t h e use  arrays.  A r e g r e s s i o n d e v e l o p e d by T a r p l e y t h e minimum b r i g h t n e s s  field  (1979) was u s e d t o map  ( S e c t i o n 5.2.1).  The p e r f o r m a n c e  2 o f t h e m o d e l , a s d e t e r m i n e d by r dominated s u r f a c e s .  a n d SE, was p o o r e r  Assessments i n d i c a t e d that the b i d i r e c t i o n a l  r e f l e c t a n c e c h a r a c t e r i s t i c s o f s u c h s u r f a c e s were portrayed The  s p a t i a l p a t t e r n s o f t h e mean h o u r l y  estimated  ( S e c t i o n 5.3) were d o m i n a t e d by m o u n t a i n - l o w l a n d  differences.  of  inadequately  by t h e m o d e l .  insolation  modelling  f o r water  The maps d i s p l a y e d c e r t a i n a r t i f a c t s  procedure.  In p a r t i c u l a r ,  they  of t h e  showed t h e i n a b i l i t y  t h e s a t e l l i t e - b a s e d i n s o l a t i o n model t o d i f f e r e n t i a t e  b e t w e e n snow a n d c l o u d a n d t h e s e n s i t i v i t y  of the modelled  103  insolation  to v a r i a t i o n s i n surface  Maps o f t h e c o r r e l a t i o n 5.4.1) showed t h a t t h e c l e a r lower  c o r r e l a t i o n s obtained  albedo.  of t h e h o u r l y field  insolation  (Section  was h i g h l y c o h e r e n t .  The  i n n o r t h e r l y l o c a t i o n s were due t o  modelling  a r t i f a c t s c a u s e d by t h e o c c u r e n c e o f snow i n t h e s e  regions.  The p a t t e r n s d i s p l a y e d by t h e c l o u d y  w e r e c o n t r o l l e d by t o p o g r a p h y .  The c o r r e l a t i o n s e x h i b i t e d  a c e r t a i n degree of i s o t r o p y over rapidly  sky d i s t r i b u t i o n s  the lowland,  but  t o w a r d t h e m o u n t a i n s where p a t t e r n s were  decreased  relatively  complex. The s t a n d a r d  d e v i a t i o n of the h o u r l y  insolation differences  ( S e c t i o n 5.4.2) i n d i c a t e d t h a t t h e m e s o s c a l e v a r i a b i l i t y o f i n d i v i d u a l h o u r l y f i e l d s c a n n o t be r e s o l v e d u s i n g t h e s a t e l l i t e based approach.  The h o u r l y m o d e l l i n g  associated with cloudy variability  errors (particularly  those  f i e l d s ) were s o l a r g e a s t o o b s c u r e t h e  of the e s t i m a t e d  field.  The u s e f u l n e s s o f t h e  m a p p i n g p r o c e d u r e a p p e a r s t o be l i m i t e d  to assessments of the  average i n s o l a t i o n ,  errors are small.  f o r which modelling  However, i t i s a l s o n o t e d under c l o u d y  that estimates  of the h o u r l y  c o n d i t i o n s h a v e l i k e w i s e been d e r i v e d w i t h  a c c u r a c i e s u s i n g m e t h o d s b a s e d on s u r f a c e d a t a The l a c k o f d i s t i n c t i o n p o s e s an a d d i t i o n a l  resolved  (Davies,  b e t w e e n snow a n d c l o u d  limitation  1980).  surfaces  snow c o v e r i s  F o r s u c h r e g i o n s , t h i s p r o b l e m n e e d s t o be  i f s a t e l l i t e - b a s e d mapping i s expected  r e l i a b l e estimates  poor  i n mountainous and temperate  e n v i r o n m e n t s where p e r s i s t e n t o r s e a s o n a l experienced.  insolation  of the i n s o l a t i o n  to y i e l d  availability.  1 04  FOOTNOTES CHAPTER I 7  The t e r m s " i n s o l a t i o n " a n d " s o l a r i r r a d i a n c e " a r e u s e d interchangeably throughout t h i s t h e s i s . They a r e b o t h d e f i n e d a s , " t h e r a d i a n t f l u x p e r u n i t a r e a i n c i d e n t upon a s u r f a c e " (Hay, 1980). CHAPTER I I 1  SR i s t h e r a t i o o f t h e r a d i a n t e n e r g y r e f l e c t e d by a s u r f a c e t o t h a t i n c i d e n t upon i t , n o r m a l i z e d f o r an o v e r h e a d s u n , a s d e s c r i b e d i n S e c t i o n 3.2.2.3. 2  Refer t o L i s t of a c r o n y m s .  of Symbols and A b b r e v i a t i o n s  f o r the expansion  3  A p i x e l ( p i c t u r e element) corresponds t o the p r o j e c t i o n the ground of the i n s t a n t a n e o u s f i e l d - o f - v i e w of t h e satellite.  on  4  The t e r m " b r i g h t n e s s " i s a r e l a t i v e measure o f t h e i n t e n s i t y of t h e r a d i a t i o n e m e r g i n g f r o m an image p l a n e .  105  BIBLIOGRAPHY A l a k a , M.A., 1970: T h e o r e t i c a l a n d P r a c t i c a l C o n s i d e r a t i o n s f o r Network D e s i g n . 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C l i m a t o l o g i c a l B u l l e t i n , 11, M c G i l l U n i v e r s i t y , 15-22.  i  11 2  APPENDIX A PROGRAM TO IMPLEMENT GAUTIER'S MODEL Modified  A . l Main Unit  by M.D.R. 7/8 3  Program  assignments: S a t e l l i t e d a t a w i n d o w s r e a d f r o m UNIT 8 E l e v a t i o n m a t r i x r e a d f r o m UNIT 4 R e g r e s s i o n c o e f f i c i e n t s r e a d f r o m UNIT 3 L i m i t s r e a d f r o m UNIT 2 C o n t r o l i n f o r m a t i o n r e a d f r o m UNIT 5 P r e d i c t e d f l u x e s , e t c p r i n t e d on UNIT 7 P r e d i c t e d h o u r l y i n s o l a t i o n v a l u e s p r i n t e d on UNIT 10 If par=reg s p e c i f i e d , data f o r b r i g h t n e s s r e g r e s s i o n o u t p u t on UNIT 9 COMMON /REG/ R D A T A ( 5 0 , 5 0 ) , R F L A G LOGICAL RFLAG  D e t e r m i n e secondary  image s i z e , e t c  CALL INIT(NRS,NCS,JR,JC,MODE,RFLAG) R e a d i n a primary 5  image a n d d e t e r m i n e  angles, e t c ,  CALL INPUT(NAVTIM,XLAPT,NRP,NCP,X1,X2,X3,MODE,&5,&99) CALL GETLIM(NAVTIM,&5)  F o r e a c h secondary image: 1) p e r f o r m d a t a q u a l i t y c o n t r o l c h e c k 2) c a l c u l a t e a t m o s p h e r i c a b s o r p t i o n 3) c a l c u l a t e minimum b r i g h t n e s s 4) d e t e r m i n e n o r m a l i z e d r e f l e c t a n c e 5) d e t e r m i n e minimum r e f l e c t a n c e 6) c a l c u l a t e t h e s o l a r f l u x e s 7) s t o r e t h e d a t a by s e c o n d a r y image p o s i t i o n IF(MODE.EQ.2) GOTO 20 MODE I p r o c e s s i n g : 12 s t a t i o n  network  DO 10 ISTN=1,12 CALL GETPOS(ISTN,NR,NC,IR,IC,MODE) CALL QCHECK(NAVTIM,NR,NC,ISTN,ISTN,&10) CALL A B S 1 ( X 1 , I R , I C , A L T ) CALL B 1 ( X 1 , X 2 , X 3 , I S T N , B M I N ) RMIN=RNORM(BMIN,X1)*1353.0*X1 CALL THRESH(X1,X2,X3,RMIN,ALBS,THR)  11 3  10  CALL CALC(X1,X2,X3,THR,ALBS,XKD,NCLDY,XKDO,XKDC) I F ( R F L A G ) CALL RSTORE(ISTN,ISTN) CALL STORE(ISTN,ISTN,XKD) CONTINUE CALL PRINT1 I F ( R F L A G ) CALL RPR1(X1,X2,X3) GOTO 5  MODE II p r o c e s s i n g -- m o v i n g 20  C C C C C C C  25 30  99  DO  grid  30 NR=1,NRP,JR ISR=(NR-1)/JR+1 DO 25 NC=1,NCP,JC ISC=(NC-1)/JC+1 CALL GETPOS(0,NR+NRS/2,NC+NCS/2,IR,IC,MODE) CALL QCHECK(NAVTIM,NR,NC,ISR,ISC,& 2 5) CALL A B S 1 ( X 1 , I R , I C , A L T ) CALL B2(X1,X2,X3,NR+NRS/2,NC+NCS/2,ALT,BMIN) CALL STORE(ISR,ISC,BMIN) RMIN=RNORM(BMIN,X1)* 1353.0*X1 CALL THRESH(X1,X2,X3,RMIN,ALBS,THR) CALL CALC(X1,X2,X3,THR,ALBS,XKD,NCLDY,XKDO,XKDC) I F ( R F L A G ) CALL R S T O R E ( I S R , I S C ) CALL STORE(ISR,ISC,XKD) CONTINUE CONTINUE CALL PRINT2(JR,JC,NRP,NCP) I F ( R F L A G ) CALL RPR2(JR,JC,NRP,NCP,X1,X2,X3) GO TO 5 CALL SPAN CALL M E R G E ( ( N R P - 1 ) / J R + 1 , ( N C P - 1 ) / J C + 1 ) IF(MODE.EQ.2) CALL F P R I N T ( J R , J C , N R P , N C P ) STOP END  11 4  A. 2 S u b r o u t i n e s SUBROUTINE  ABS1(COSZZ,IR,IC,ALT)  Input p r e c i p i t a b l e water atmospheric absorption.  ( i f n e c e s s a r y ) and c a l c u l a t e  INTEGER L I S T ( 1 ) / ' * ' / REAL E L E V ( 1 2 0 , 6 0 ) / 7 2 0 0 * 0 . 0 / COMMON/ATTEN/ABSUN,ABSAT,ABSUNT,ABSUNB,BREFL,ABSATT, *ABSATB,DENOM LOGICAL FIRST/.TRUE./,WARN/.TRUE./ If  first  20 23 C C661  25 C  pass - read  i nprecip.  water and e l e v a t i o n  matrix  I F ( . N O T . F I R S T ) GOTO 23 FIRST=.FALSE. WRITE(6,20) FORMATC INPUT PRECIP.WATER I N MM.') READ(5,LI ST) W READ(4) ELEV ALT=ELEV(60+IC,30+IR) WRITE(6,661) I R , I C , A L T FORMATC *** ' , 21 5 ,F9. 1 ) IF(ALT.GE.O.O) GOTO 25 IF(WARN) WRITE(6,100) WARN=.FALSE. ALT=0.0 COSZ=COSZZ IF(COSZZ.LT.O.O) COSZZ= 0.009 ZED=ARCOS(COSZZ)*180.0/3.14159 I F ( Z E D . G T . 9 0 . 0 ) ZED=90.0  K a s t e n ' s a i r mass  algorithm  A M S U N = E X P ( - A L T / 8 2 4 3 . 0 ) / ( C O S Z Z + 0 . 1 5 / ( ( 9 3 . 8 8 5 - Z E D ) * * 1.253)) U1 = W I F ( A L T . G T . 5 0 0 . 0 ) U1=U1*0.8 ABSUN=YAM(U1,AMSUN) ( N o t e : 56.4 i s t h e s a t e l l i t e *  z e n i t h angle f o r Vancouver  latitude)  AMSAT=EXP(-ALT/8 2 4 3 . 0 ) / ( C O S ( 5 6 . 4 * 3 . 1 4 1 5 9 / 1 8 0 . 0 ) + 0 . 1 5 / ((93.885-56.4)**1.253)) ABSAT=YAM(U1,AMSAT) U2=U1*0.3 ABSUNT=YAM(U2,AMSUN) ABSATT=YAM(U2,AMSAT)  1 15  U2=U1*0.7 ABSUNB=YAM(U2,AMSUN) BREFL=COUL(COSZ) ABSATB=YAM(U2,AMSAT) RETURN 100 FORMATC0*** WARNING <ABS 001> *** NO ELEVATION DATA', 1 ' A V A I L A B L E FOR ONE',/,' ' , 3 1 X, ' OR MORE LOCATIONS', 2 ' - 0 ASSUMED.') END  11 6  SUBROUTINE  Bl(XI,X2,X3,NS,B)  R e t u r n s t h e p r e d i c t e d t a r g e t c l e a r b r i g h t n e s s . The minimum b r i g h t n e s s c o e f f i c i e n t s a r e b a s e d on a n a l y s i s o f c l e a r images i n a l l s e a s o n s (no s n o w ) . REAL A ( 1 2 ) / 3 7 . 6 9 8 , 3 9 . 3 4 5 , 4 1 . 4 9 4 , 4 0 . 5 3 4 , 4 0 . 5 4 0 , 4 1 . 8 7 7 , 4 0 . *529,39.763,40.389,40.716,39.636,40.132/ REAL B A B ( 1 2 ) / 3 9 . 8 4 2 , 4 2 . 9 5 2 , 4 2 . 0 4 3 , 4 9 . 9 6 9 , 5 2 . 1 0 2 , 3 0 . 1 9 5 , 5 *0.239,51.981,53.205,50.7 55,50.7 0 8 , 3 7 . 7 1 3 / REAL C ( 1 2 ) / 6 . 9 2 1 , 8 . 2 5 6 , 9 . 5 3 3 , 8 . 3 3 7,9.061,3.004,7.483,5.3 *95,5.352,5.119,7.560,7.488/ REAL D ( 1 2 ) / 1 5 . 4 3 8 , 1 3 . 0 4 6 , 1 0 . 8 9 6 , 1 0 . 5 6 4 , 9 . 1 69,2.457,9.334 , *13.134,11.348,12.853,10.586,7.207/ B=A(NS)+BAB(NS)*X1+C(NS)*X2+D(NS)*X3 C WRITE(6,100) B C100 FORMAT(' BMIN : ',F8.2) RETURN END  1  17  SUBROUTINE B 2 ( X l , X 2 , X 3 , I R , I C , A L T , B 3 ) Computes t a r g e t c l e a r b r i g h t n e s s g i v e n r e l a t i v e g r i d l o c a t i o n , u s i n g r e g r e s s i o n f o r n e a r e s t c e n t r a l p i x e l o f 5x5 a r r a y INTEGER ISROW(12)/-12,-8,-5,1,14,0,6,12,14,7,-1,-5/,NW */288/ INTEGER I S C O L ( 1 2 ) / - 3 8 , - 3 5 , - 3 9 , - 4 1 , - 3 3 , 0 , 3 8 , 4 1 , 3 5 , 8 , - 3 6 , *-50/ REAL C 1 ( 3 0 0 ) , C 2 ( 3 0 0 ) , C 3 ( 3 0 0 ) , C 4 ( 3 0 0 ) LOGICAL FIRST/.TRUE./ I F ( . N O T . F I R S T ) GOTO 5 READ(3,100) ( C 1 ( I ) , C 2 ( I ) , C 3 ( I ) , C 4 ( I ) , 1 = 1 , N W ) FIRST=.FALSE. 5 IR5=(IR-1)/5+1 IC5=(IC-1)/5+1 I=(IR5-1)*24+IC5 B3=C1(I)+C2(I)*X1+C3(I)*X2+C4(I)*X3 C WRITE(6,88) I R , I C 88 FORMAT(' ',215) C I S= 1 C I F ( A L T . G T . 5 0 0 . 0 ) GOTO 15 C DMIN=9999.9 C DO 10 I = 1 , 12 C D=(IR-ISR0W(I))**2+(lC-ISCOL(l))**2 C IF(D.GE.DMIN) GOTO 10 C DMIN=D C IS=I C10 CONTINUE C15 CALL B 1 ( X 1 , X 2 , X 3 , I S , B V A L ) C B3=BVAL RETURN 100 FORMAT(4E13.6) END  118  SUBROUTINE CALC(XI,X2,X3,THR,ALBS,KDOWN,NCLDY,KDOWNO, KDOWNC) Calculate  thepredicted solar fluxes: (1) c l e a r ("KDOWNO") (2) c l o u d y ("KDOWNC") (3) a v e r a g e ("KDOWN")  INTEGER V A L S ( 5 0 , 5 0 ) COMMON /ATTEN/ ABSUN,ABSAT,ABSUNT,ABSUNB,BREFL,ABSATT, * ABSATB,DENOM COMMON /SEC/ VALS,NR,NC REAL KDOWN 0,KDOWNC,KDOWNT,KDOWN LOGICAL CLR/.FALSE./ Initialize. NCLEAR=0 NCLDY=0 KDOWNC=0.0 NVALS=NR*NC AVALBS=0.0 RKO = 1353.0 * XI KDOWN0=0.0 KDOWNT=0.0 I F ( R K O . L T . 0 . 0 ) GOTO 50 KDOWN0=RK0*(1.0-BREFL)*(1.0-ABSUN)*(1.0+ALBS*0.076)*3.60 DO 25 I=1,NR DO 20 J=1,NC Convert counts t o normalized r e f l e c t a n c e threshold.  and compare  with  RVAL = V A L S ( I , J ) REFL=RNORM(RVAL,X1)*RK0 IF(REFL.GE.THR) GO TO 10 C o u n t number  of clear  pixels  NCLEAR=NCLEAR+1 GO TO 20 Cloudy p i x e l c a l c u l a t i o n s : (1) c a l c u l a t e c l o u d a b s o r p t i v i t y ("CLABS") (2) c a l c u l a t e c l o u d a l b e d o ("CLREFL") (3) d e t e r m i n e f l u x i n c l o u d y p i x e l a n d a d d t o "KDOWNC" 10  1  NCLDY=NCLDY+1 STEP=(RKO-THR)/2 0.0 C L A B S = ( ( R E F L - T H R ) / S T E P ) * 0.01 PHI=RK0*(1.0-BREFL)*(1.0-ABSUNT)*(1.0-ABSUNB)*ALBS* (1.0-ABSATT)*((1.0-CLABS)**2)*(1.0-ABSATB)*(1.0  119  2  20 25  -0.076) BETA=RK0*(1.0-BREFL)*(1.0-ABSUNT)*(1.0-0.076)*(1.0 1 -ABSATT) GAMMA=RKO*BREFL SW=REFL GEE=BETA-2.0*PHI EFF=(GAMMA+PHI-SW)*PHI ROOT=SQRT(GEE*GEE-4.0*EFF) GEE=GEE*(-1.0) ALBCL1=(GEE+ROOT)/(2.0*PHI) ALBCL2=(GEE-ROOT)/(2.0*PHI) CLREFL=ALBCL1 I F ( C L R E F L . G T . 0 . 8 5 ) CLREFL=0.85 KDOWNT=RK0*(1.0~BREFL)*(1.0-ABSUNT)*(1.0-CLREFL) 1 *(1.0-CLABS)*(1.0-ABSUNB)*3.60 KDOWNC=KDOWNC+KDOWNT CONTINUE CONTINUE IF(NCLDY.GT.O) GO TO 40  I f no c l o u d a c t u a l s o l a r  flux = clear  sky value  KDOWN=KDOWN0 GO TO 50 I f c l o u d i n image t h e n cloudy p i x e l s 40 50  weight  f o r c l e a r and cloudy  KDOWN=(KDOWN0*NCLEAR+KDOWNC)/(NCLEAR+NCLDY) RETURN END  pixels,  120  SUBROUTINE F P R I N T ( J R , J C , N R P , N C P ) Prints  out a g r i d of p r e d i c t e d  f l u x e s on UNIT  10.  COMMON /MDATA/ T I M 1 ( 4 0 ) , T I M 2 ( 4 0 ) , F L G ( 4 0 ) , H F L U X ( 5 0 , 5 0 , 2 0 ) *,IH1,IH2 COMMON /SEC/ SIM(50,50),NRS,NCS COMMON /PDATA/ F L U X ( 5 0 , 5 0 , 4 0 ) , N T I M S ( 4 0 ) NR=NRP/JR NC=NCP/JC KC1=1+NCS/2 KC2=NCP-NCS/2 KR1=1+NRS/2 KR2=NRP-NRS/2 IDATE=NTIMS(1)/l0000 I F ( M O D ( N T I M S ( 1 ) , 1 0 0 0 0 ) . L T . 8 0 0 ) IDATE=IDATE-1 I F ( M O D ( I D A T E , 1 0 0 0 ) . N E . 9 9 9 ) GOTO 2 IDATE=IDATE/1000*1000+365 I F ( M 0 D ( I D A T E / 1 0 0 0 , 4 ) . E Q . 0 ) IDATE=IDATE+1 2 DO 20 IH=IH1,IH2 WRITE(10,100) I D A T E , I H , N R S , N C S , ( I , I = K C 1 , K C 2 , J C ) 1=0 DO 5 IR=KR1,KR2,JR 1=1+1 WRITE(10,101) I R , ( H F L U X ( I , J , I H ) , J = 1 , N C ) 5 CONTINUE 20 CONTINUE RETURN 100 F O R M A T C - PREDICTED INSOLATION FOR ',15,' HOUR ENDING ', 1 I 2 , ' : 0 0 GAUTIER''S MODEL (FLUX AVERAGING) - K J / ' 2 ,'M2/HR',/,' SECONDARY WINDOW S I Z E : ',13,' BY' 3 ,13,/,' ',5016) 101 FORMATC ' , I 3 , 5 0 F 6 . 0 ) END  121  SUBROUTINE GETLIM(NAVTIM, ) Reads i n b r i g h t n e s s  88 99 100  thresholds  for this  COMMON / L I M / LIM1,LIM2 COMMON /REG/ RDATA(50,50),RFLAG LOGICAL RFLAG IF(.NOT.RFLAG) GOTO 88 ILINE=M0D(NAVTIM/10,10000000) FIND(2'ILINE) READ(2,100,END= 99) NT,LIM1,LIM2 IF(NT.NE.NAVTIM) GOTO 99 RETURN LIM1=-1 LIM2=256 RETURN RETURN 1 FORMAT(110,215) END  image f r o m UNIT 2.  122  SUBROUTINE GETPOS(ISTN,NR,NC,IR,IC,MODE) D e t e r m i n e s image p o s i t i o n stat ion.  10  and storage l o c a t i o n  f o r next  COMMON / P R I / V A L S ( 2 5 0 , 2 5 0 ) , N R P , N C P , I C S T N COMMON /SEC/ SIM(50,50),NRS,NCS INTEGER I S R O W ( l 2 ) / - 1 2 , - 8 , - 5 , 1 , 1 4 , 0 , 6 , 1 2 , 1 4 , 7 , - 1 , - 5 / INTEGER I S C O L ( 1 2 ) / - 3 8 , - 3 5 , - 3 9 , - 4 1 , - 3 3 , 0 , 3 8 , 4 1 , 3 5 , 8 , - 3 6 , - 5 0 / IF(MODE.EQ.2) GOTO 10 IR=ISR0W(ISTN) IC=ISC0L(ISTN) NR=ISROW(ISTN)-ISROW(ICSTN)+NRP/2-NRS/2+1 NC=ISCOL(ISTN)-ISCOL(ICSTN)+NCP/2-NCS/2+1 RETURN IR=NR-NRP/2+ISROW(lCSTN) IC=NC-NCP/2+ISCOL(lCSTN) RETURN END  1 23  SUBROUTINE  INIT(NR,NC,JR,JC,MODE,RFLAG)  Reads i n s i z e o f s e c o n d a r y UNIT 5)  100 101  images & d e t e r m i n e s  MODE.(from  COMMON /SEC/ I V A L S ( 5 0 , 5 0 ) , N R S , N C S INTEGER L I S T ( 1 ) / ' * ' / LOGICAL RFLAG LOGICAL* 1 PRSTROOO) MODE=1 RFLAG=.FALSE. CALL PAR(PRSTR, I P L , 1 0 0 ) CALL FINDST(PRSTR,I PL,'MODE2',5,1,1POS) I F ( I P O S . N E . O ) MODE=2 CALL FINDST(PRSTR,I PL,'REG' ,3,1,IPOS) I F ( I P O S . N E . O ) RFLAG=.TRUE. WRITE(6,100) R E A D ( 5 , L I ST) NRS,NCS NR=NRS NC=NCS IF(MODE.NE.2) RETURN WRITE(6,101) R E A D ( 5 , L I ST) J R , J C RETURN FORMATC ENTER S I Z E OF SECONDARY WINDOWS (NROWS, NCOLS)') FORMATC ENTER ROW AND COLUMN WINDOW SPACING') END  124  SUBROUTINE INPUT(NAVTIM,XLAPT,NRP,NCP,XI,X2,X3,MODE, Reads i n a p r i m a r y  image a n d c o m p u t e s s o l a r  , )  angles.  INTEGER V A L S ( 2 5 0 , 2 5 0 ) , N T I M / 0 / REAL*8 STAT,FSTAT,FNAV COMMON /PDATA/ F L U X ( 5 0 , 5 0 , 4 0 ) , N T I M S ( 4 0 ) , X L A T S ( 4 0 ) , N I M S COMMON / P R I / VALS,NR,NC,ICSTN COMMON / S E C / I V A L S ( 5 0 , 5 0 ) , N R S , N C S LOGICAL FIRST/.TRUE./ I F ( . N O T . F I R S T ) GOTO 5 FIRST=.FALSE. NIMS=0 Input 5  image s i z e , t i m e a n d s t a t i o n  name  READ(8,100,END= 44) NR,NC,NAVTIM,STAT IF(NAVTIM.EQ.NTIM) GO TO 15 NTIM=NAVTIM  D e t e r m i n e LAT a n d a n g l e s CALL SGEOM(NAVTIM,0.0,XLPT,Y1,Y2,Y3) XLAPT=XLPT X1=Y1 X2=Y2 X3=Y3 Input b r i g h t n e s s counts 15  DO 20 1=1,NR READ(8,101) ( V A L S ( I , J ) , J = 1 , N C ) 20 CONTINUE NRP=NR NCP=NC ICSTN=ISTNUM(STAT) I F ( ( N R . L T . N R S ) . O R . ( N C . L T . N C S ) ) GOTO 30 I F ( X 1 . L E . 0 . 0 ) GOTO 55 WRITE(7,102) NAVTIM,XLAPT,NR,NC,STAT,NRS,NCS IF(((MOD(NR,NRS).NE.0).OR.(MOD(NC,NCS).NE.0)).AND.(MODE 1.EQ.2)) WRITE(6,103) NR,NC,NAVTIM NIMS=NIMS+1 NTIMS(NIMS)=NAVTIM XLATS(NIMS)=XLAPT RETURN 30 WRITE(6,104) NR,NC,NAVTIM RETURN 1 44 RETURN 2 55 WRITE(6,105) NAVTIM,XLAPT RETURN 1 100 F 0 R M A T ( I 4 , 4 X , I 3 , I 1 0 , 1 4 X , A 8 ) 101 F O R M A T ( 4 ( 6 4 I 3 ) )  125  102  FORMAT('-NAVTIM : ',110,' L.A.T. : ' , F 6 . 2 , / , 1 ' PRIMARY IMAGE : ',14,' BY' ,14, 2 ' CENTERED ON *,A8,' SECONDARY IMAGE S I Z E : ' , 1 3 , 3 ' BY',13) 103 FORMATC0*** WARNING <INPUT 001> *** PRIMARY IMAGE ', 1 'SIZE', ' (',14,' B Y ' , 1 4 , ' ) ' , 2 /,' I S NOT AN INTEGRAL MULTIPLE OF SECONDARY IMAGE' 3 ,' S I Z E . ' , / , ' PERIPHERAL DATA WILL BE IGNORED.' 4 ,'NAVTIM : ',110) 104 FORMAT('0**** ERROR <INPUT 001> **** PRIMARY IMAGE ' 1 ,'SIZE (',14,' B Y ' , 1 4 , ' ) ' , 2 A ' I S LESS THAN SECONDARY IMAGE S I Z E . ' , 3 /,' IMAGE IGNORED. NAVTIM : ',110) 105 FORMATC0*** NOTE <INPUT 001> *** NAVTIM = ',110, 1 * L.A.T. = ',F6.2,/,* 2 ,'SUN BELOW HORIZON - IMAGE IGNORED') END  126  SUBROUTINE  MERGE(NR,NC)  Merges t h e i n s t a n t a n e o u s f l u x p r e d i c t i o n s t o form h o u r l y insolation predictions. COMMON /PDATA/ F L U X ( 5 0 , 5 0 , 4 0 ) , N T I M S ( 4 0 ) , X L A T S ( 4 0 ) , N I M S COMMON /MDATA/ T I M 1 ( 4 0 ) , T I M 2 ( 4 0 ) , S F L G ( 4 0 ) , H F L U X ( 5 0 , 5 0 , 2 0 ) , 1 IH1,IH2 LOGICAL SFLG Determine e a r l i e s t  possible  s t a r t i n g hour  IH1=TIM1(1)+2.0 IH2=TIM2(NIMS) Now compute  10 15  20  C 90  hourly v a l u e s f o r each l o c a t i o n  DO 70 IR=1,NR DO 60 IC=1,NC DO 50 IH=IH1,IH2 TST=IH-1.0 DO 10 IM=1,NIMS IM1=IM IF(TIM2(IM).GT.TST+0.001 ) GO TO 15 CONTINUE IF((.NOT.SFLG(IM1)).OR.(FLUX(IR,IC,IM1).EQ.-9.999) 1 .OR.'(TIM2 (IM1 ) . L E . TST) ) GOTO 25 TFRAC=0.0 XDBAR=0.0 IF((IM1.GT.NIMS).OR.(FLUX(IR,IC,IM1).EQ.-9.999)) 1GO TO 25 I F ( . N O T . S F L G ( I M 1 ) ) GOTO 25 T1=TIM1(IM1) T2=TIM2(IM1) WRITE(6,90) T1,T2 FORMAT( 'T1=',F9.3,2X,'T2=*,F9.3)  D e t e r m i n e w e i g h t s f o r e a c h image i n h o u r TIME=AMIN1(T2,FLOAT(IH))-AMAX1(T1,TST) FRAC=TIME/(T2-T1) TFRAC=TFRAC+FRAC Weight t h e i n s t a n t a n e o u s  predictions  XDBAR=XDBAR+FRAC * F L U X ( I R , I C , I M 1 ) IM1=IM1+1 I F ( T 2 . L T . F L O A T ( I H ) ) GO TO 20  127  Convert t o k j m  h  XDBAR=XDBAR/TFRAC Store calculated  25 50 60 70 99  v a l u e s f o r hour and l o c a t i o n  IF(XDBAR.LT.O.O) XDBAR=0.0 H F L U X ( I R , IC , IH )=XDBAR GO TO 50 HFLUX(lR,IC,IH)=-9.999 CONTINUE CONTINUE CONTINUE RETURN END  1 28  SUBROUTINE  PRINT1  P r i n t s out p r e d i c t e d  fluxes  f o r 12 s t a t i o n s on UNIT 7.  COMMON /PDATA/ F L U X ( 5 0 , 5 0 , 4 0 ) , N T I M S ( 4 0 ) , X L A T S ( 4 0 ) , N I M S REAL*8 NAMES(12)/'GRSMT ' , 'NRTHMT ' ,'BCHYDRO ' , * 'VANAIR ','FERRY ','PITMED ','MISSHAB * 'ABBLIB ','ABBAIR ','LANGLEY ','LANGA ','CLISTN '/ WRITE(7,100) (NAMES(I),1=1,12) WRITE(7,101) ( F L U X ( I , I , N I M S ) , I = 1 , 1 2 ) RETURN 100 FORMAT('0 ',12A8) 101 FORMAT(' ' ,12F8. 1) END  129  SUBROUTINE PRINT2(JR,JC,NRP,NCP) P r i n t s out a g r i d  5 100 101  of p r e d i c t e d  f l u x e s on UNIT 7.  COMMON /PDATA/ F L U X ( 5 0 , 5 0 , 4 0 ) , N T I M S ( 4 0 ) , X L A T S ( 4 0 ) , N I M S COMMON / S E C / SIM(50,50),NRS,NCS NR=NRP/JR NC=NCP/JC K1=1+NCS/2 K2=NCP-NCS/2 WRITE(7,100) ( I , I = K 1 , K 2 , J C ) K1=1+NRS/2 K2=NRP-NRS/2 1=0 DO 5 IR=K1,K2,JR 1=1 + 1 WRITE(7,101) I R , ( F L U X ( I , J , N I M S ) , J = 1 , N C ) CONTINUE RETURN FORMAT(' *,5016) FORMAT(' ' , I 3 , 5 0 F 6 . 0 ) END  1 30  SUBROUTINE QCHECK(NAVTIM,NR,NC,ISR,ISC, ) E x t r a c t s s e c o n d a r y image s t a r t i n g a t (NR,NC) f r o m p r i m a r y image a n d p e r f o r m s q u a l i t y c o n t r o l c h e c k . INTEGER PIM,SIM COMMON / S E C / SIM(50,50),NRS,NCS COMMON / P R I / PIM(250,250),NRP,NCP I F ( ( N R . L T . 1 ) . O R . ( N C . L T . 1 ) ) GOTO 33 ITOT=0 NVAL=0 DO 10 1=1,NRS DO 5 J=1,NCS NI=NR+I-1 NJ=NC+J-1 I F ( ( N I . G T . N R P ) . O R . ( N J . G T . N C P ) ) GOTO 33 IVAL=PIM(NR+I-1,NC+J-1) ITOT=ITOT+IVAL I F ( ( I V A L . G T . 2 5 5 ) . O R . ( I V A L . L T . 1 2 ) ) GOTO 22 NVAL=NVAL+1 SIM(I,J)=IVAL 5 CONTINUE 10 CONTINUE CALL S T O R E ( I S R , I S C , F L O A T ( I T O T / N V A L ) ) RETURN 22 WRITE(6,100) NAVTIM,NR,NC CALL S T O R E ( I S R , I S C , - 9 . 9 9 9 ) CALL R S T O R E ( - I S R , - I S C ) RETURN 1 33 WRITE(6,101) NAVTIM,NR,NC,ISR CALL S T O R E ( l S R , I S C , - 9 . 9 9 9 ) CALL R S T O R E ( - I S R , - I S C ) RETURN 1 100 FORMATC 0*** WARNING <QCHECK 001> *** QUALITY CONTROL' 1 ,' F A I L U R E ' , / , ' NAVTIM ' , n o , ' PRIMARY IMAGE ' 2 ,'REFERENCE : ',214) FORMATC0*** WARNING <QCHECK 002> *** 101 SECONDARY IMAGE 1 ,'OUTSIDE PRIMARY IMAGE BOUNDS',/,' NAVTIM 2 110,' PRIMARY IMAGE REFERENCE : ',214,' STAT' 3 ,'ION : ',12) END  131  SUBROUTINE R P R 1 ( X l , X 2 , X 3 ) P r i n t s o u t d a t a f o r c l e a r b r i g h t n e s s r e g r e s s i o n on UNIT 9. (MODE I )  100  COMMON /REG/ RDATA(50,50) WRITE(9,100) X 1 , X 2 , X 3 , ( R D A T A ( I , 1 ) , 1 = 1 , 1 2 ) RETURN FORMAT(3F7.4,/,12F6.1) END  1 32  SUBROUTINE  RPR2(JR,JC,NRP,NCP,XI,X2,X3)  P r i n t s out data f o r c l e a r UNIT 9. (MODE II.)  100  brightness  r e g r e s s i o n on  COMMON /REG/ RDATA(50,50) NR=NRP/JR NC=NCP/JC WRITE(9,100) X 1 , X 2 , X 3 , ( ( R D A T A ( I , J ) , J = 1 , N C ) , I = 1 , N R ) RETURN FORMAT(3F7.4,/,10(12F6.1,/)) END  133  SUBROUTINE Stores  regression  RSTORE(NR,NC) information.  INTEGER S I M , I T A L L Y ( 2 5 6 ) COMMON / S E C / SIM(50,50),NRS,NCS COMMON /REG/ RDATA(50,50) COMMON / L I M / LIM1,LIM2 First  check  f o r missing  data  indication  I F ( N R . L T . O ) GOTO 20 Compute m e d i a n a n d mode o f s e c o n d a r y window d a t a a n d s t o r e t h e l e s s e r o f t h e two  2  5 10  15  17 20  DO 2 1=1,256 ' ITALLY(I)=0 CONTINUE NP=0 DO 10 IR=1,NRS DO 5 IC=1,NCS IV=SIM(IR,IC)+1 I F ( ( I V . L T . L I M 1 ) . O R . ( I V . G E . L I M 2 ) ) GOTO 5 ITALLY(IV)=ITALLY(IV)+1 NP=NP+1 CONTINUE CONTINUE PP=NRS*NCS I F ( N P / P P . L T . 0 . 6 7 ) GOTO 17 IC = 0 XMED=-1.0 IMODE=0 IH=NP/2 DO 15 1=1,256,4 IT=ITALLY(I) IC=IC+IT I F ( I T . G T . I T A L L Y ( I M O D E + 1 ) ) IMODE=I"1 I F ( ( I C . L T . I H ) . O R . ( X M E D . G E . 0 . 0 ) ) GOTO 15 XMED=FLOAT(I-1) IF(MOD(NP,2).NE.0) XMED=XMED+2.0 CONTINUE XREG=FLOAT(IMODE) IF(XMED.LT.XREG) XREG=XMED RDATA(NR,NC)=XREG RETURN RDATA(NR,NC)=-9.9 RETURN RDATA(-NR,-NC)=-9.9 RETURN END  134  SUBROUTINE SGEOM(NAVTIM,XPT,XLAPT,XI,X2,X3) Computes  local  REAL  apparent  time and v a r i o u s geometric  CLAT/49.217/,SATAZ/15.0/  F i r s t compute d e c l i n a t i o n , azimuth f o r t h i s time.  solar  zenith  angle, and s o l a r  RADDEG=3.14159/180.0 C1=279.457*RADDEG C2=0.985647*RADDEG YR=NAVTIM/10000000 JD=MOD(NAVTIM,10000000)/l0000 I F ( X P T . E Q . 0 . 0 ) GOTO 5 XLAPT=XPT GOTO 10 TI=FTM(NAVTIM) X=AINT((YR-65)*365.251)+JD+Tl/24.0 G=C1+C2*X X=X/365.2422  5  'EQ'  values  i s equation of time  value  EQ=(-102.5-0.142*X)*SIN(G)+(-429.8+.033*X)*COS(G)+596 1*SIN(2*G)-2.0*COS(2*G)+4.2*SIN(3*G)+19.3*COS(3*G)-12.8 2*SIN(4*G) EQ=EQ/3600 'XLAPT' i s l o c a l a p p a r e n t with central location)  time  i n hours  (constants vary  XLAPT=TI-8.0+EQ-10.8/60.0 I F ( X L A P T . L T . 0 . 0 ) XLAPT=XLAPT+ 24.0 HA=15.0*(XLAPT-12.0)*RADDEG PSI=2*3.14159*(JD-1)/365.0  10 'DEC  i ssolar * *  declination  DEC=0.006918-0.399912*COS(PSI)+0.070257*SIN(PSI) -0.006758*COS(2*PSI)+0.000907*SIN(2*PSI)-0.002697*COS (3*PSI)+0.00l480*SIN(3*PSI)  'COSZ' a n d 'SINZ' a r e s i n a n d c o s o f s o l a r z e n i t h 'CA' i s c o s o f s o l a r a z i m u t h  angle and  COS Z = S I N ( C L A T * RADDEG)*SIN(DEC)+COS(CLAT* RADDEG)* COS( DEC)*COS(HA) SINZ=SIN(ARCOS(COSZ)) CA=(SIN(CLAT*RADDEG)*COS Z~SIN(DEC))/(COS(CLAT*RADDEG) *SINZ)  *  135  Now compute t h e 3 p a r a m e t e r s o f i n t e r e s t SIGN=1 IF(XLAPT.LT.12.0)  SIGN=-i  SSA=ABS(SATAZ*RADDEG-SIGN*ARCOS(CA)) X1=COSZ X2=SINZ*COS(SSA) X3=X2*COS(SSA) RETURN END  136  SUBROUTINE SPAN Computes  30  35 40  t h e t i m e span f o r w h i c h t h e i m a g e s a r e v a l i d .  COMMON /PDATA/ F L U X ( 5 0 , 5 0 , 4 0 ) , N T I M S ( 4 0 ) , X L A T S ( 4 0 ) , N I M S COMMON /MDATA/ T I M 1 ( 4 0 ) , T I M 2 ( 4 0 ) , S F L G ( 4 0 ) LOGICAL SFLG TIM1(1)=XLATS(1)-0.25 TIM2(NIMS)=XLATS(NIMS)+0.2 5 DO 30 IM=2,NIMS TIM1(IM)=(XLATS(IM-1)+XLATS(lM))/2.0 TIM2(IM-1)=TIM1(IM) CONTINUE DO 40 IM=1,NIMS I F ( ( T I M 2 ( I M ) - T I M 1 ( I M ) ) . L E . 1 . 0 ) GOTO 35 SFLG(IM)=.FALSE. GOTO 40 SFLG(IM)=.TRUE. CONTINUE RETURN END  1 37  SUBROUTINE STORE(NR,NC,VAL) Stores  the predicted f l u x  i n the printout  array.  COMMON /PDATA/ F L U X ( 5 0 , 5 0 , 4 0 ) , N T I M S ( 4 0 ) , X L A T S ( 4 0 ) , N I M S FLUX(NR,NC,NIMS)=VAL RETURN END  138  SUBROUTINE THRESH(X1,X2,X3,RMIN,ALBS,THR) D e t e r m i n e s t h e minimum b r i g h t n e s s  C C66  threshold.  COMMON/ATTEN/ABSUN,ABSAT,ABSUNT,ABSUNB,BREFL,ABSATT, *ABSATB,DENOM RK0=1353.0*X1 DENOM=(1.0-BREFL)*(1.0-ABSUN)*(1.0-ABSAT)*(1.0-0.076) ALBS=(RMIN-RKO*BREFL)/(DENOM*RKO) ALBP=ALBS+0.00566/X1 THR=RK0*(BREFL+ALBP*DENOM) I F ( A L B S . L T . 0 . 0 ) XX=XY~X2 WRITE(6,66) THR FORMAT(' THRESH : ',F8.3) RETURN END  1 39  A.3  Functions FUNCTION COUL(COSZ)  C a l c u l a t e s C o u l s o n ' s beam  scattering.  ZEDD=ARCOS(COSZ)*l80.0/3.14159 COUL=0.0467563+0.0014173*ZEDD-0.00005258*(ZEDD**2)+ *0.000000651*(ZEDD**3) I F ( C O U L . L T . 0 . 0 4 6 ) COUL=0.046 RETURN END  FUNCTION FTM(NVTIM) Returns f l o a t i n g p o i n t time i n h r s . IT=MOD(NVTIM,10000) FTM=IT/100+MOD(IT,100)/60.0 RETURN END  FUNCTION ISTNUM(STAT) R e t u r n s t h e number o f a p a r t i c u l a r  100  'STAT'.  REAL* 8 STAT,NAMES(12)/'GRSMT ' ,'NRTHMT ' ,'BCHYDRO ' , 'VANAIR ','FERRY ','PITMED ','MISSHAB ', 'ABBLIB ','ABBAIR ','LANGLEY *,'LANGA ','CLISTN LOGICAL EQCMP DO 10 1=1,12 J=I I F ( E Q C M P ( 8 , S T A T , N A M E S ( I ) ) ) GOTO 15 I F ( I . E Q . 1 2 ) WRITE(6,100) CONTINUE ISTNUM=J RETURN FORMATC H E L L L P ! . . . THERE I S AN UNKNOWN STATION SOMEWH 1 ERE' ) END  * *  10 15  station  1 40  FUNCTION  RNORM(BMIN,Xl)  Converts counts to normalized reflectance order polynomial.  using  second  RIR=0.00154+BMIN*0.000166+BMIN*BMIN*0.0000137 RNORM=RIR/X1 RETURN END  FUNCTION YAM(UT,AM) Calculates  Yamamoto's a b s o r p t i v i t i e s f o r w a t e r  ( N o t e : C o n v e r s i o n f r o m mm t o c o r r e c t u n i t s e . g : i f r e l a t i o n s h i p f o r U i n cm t h e n u s e U=UT/10.0) U=(UT/10.0) * AM I F ( U . G T . 0 . 5 ) YAM=0.099*U**0.34 I F ( U . L E . 0 . 5 ) YAM= 0.14*U**0.44 RETURN END  vapour.  APPENDIX B C o e f f i c i e n t of of the minimum coordinates of SE i n u n i t s o f  r  13  0.617 4.49  0.802 3.76  0.797 3.81  8  0.456 5.28  0.723 4.62  13  0.486 4.38  18  18  23  0.839 3.54  0.797 3.88  0.809 3.92  0.773 4.U  0.619 5.30  0.846 3.38  0.423 4.61  0.763 3.87  23  0.403 5.06  28  28  d e t e r m i n a t i o n ( r ) and the standard e r r o r of estimate (SE) b r i g h t n e s s r e g r e s s i o n model, indexed a c c o r d i n g to the the c e n t r a l p i x e l of contiguous 5 x 5 p i x e l a r r a y s . counts.  33  38  43  48  767 24  0..781 3.,87  0..907 2..64  0..906 2.,82  0..740 4.,35  0.756 4.30  784 83  0..791 4..19  0..760 4,.18  0.,809 3..95  0.833 3.37  0.785 3.84  849 50  0.,749 3..32  0..804 3,.78  0.820 3.41  0.811 3.23  0.807 3.55  863 91  0.,825 3..27  0.354 5.42  0.393 4.98  0.499 5.67  0.723 4.07  0.856 2.88  0.347 5.33  0.423 5.55  0.565 5.11  0.865 2.81  0.901 2.34  33  0.311 6.05  0.397 5.71  0.585 4.89  0.661 4.15  38  0.421 5.54  0.616 4.79  0.690 4.38  43  0. 508 4..41  0. 596 4..20  48  0. 484 4. 38  53  58  53  0..800 3.82  58  63  68  73  78  83  88  93  98  103  108  113  1  18  0..748 4..05  0..902 2.64  0..940 2.65  0.,902 2. 78  0,.847 3.45  0..920 2. 57  0..934 2..85  0..934 2.57  0,,950 2. 33  0..889 3..24  0..904 2. 87  0..737 3.20  0..734 4. 15  0..772 0..942 4..01 2. 26  0..834 3. 55  0..819 3..68  0..813 3..74  0..949 2.02  0..866 3..38  0..935 2..50  0..874 3..30  0..915 2..88  0 .796 3..90  0..828 3..62  0..948 2. 42  0..866 3. 30  0..789 3. 76  0..820 3..74  0..791 3.,85  0.,751 4. 20  0..859 3.30  0..826 3..55  0.,734 3..60  0.,799 3. 79  0..856 3.41  0..840 3.,45  0..857 3.47  0..863 3.25  0..797 3.,75  0..975 1..61  • 0. .947 2. 19  0..855 3..54  0. 853 3. 30  0..830 3..03  0..783 3..73  0..758 3.,75  0.,805 3.64  0. 860 3. 39  0..821 3.46  0.,563 3.99  0. 785 4.03  0.,842 3.23  0. 787 3.95  0..786 3.,84  0. 572 4.68  0.,813 3..51  0. 856 3.27  0. 873 3.20  0. 804 3. 92  0. 801 3.,71  0.712 3.97  0.630 4.49  0.828 3.19  0.838 0.838 3.20 3.20  0.811 3.40  0.758 3.50  0.834 3.24  0.863 3.15  0.861 2.98  0.828 3.34  0.801 3.63  0.555 4.55  0.792 3.67  0.829 3.55  0.846 3.40  0.857 3.26  0.939 2.22  0.870 2.58  0.839 3.04  0.869 2.89  0.851 3.18  0.908 0.895 2.37 2.44  0.861 2.66  0.778 3.40  0.866 2.86  0.854 2.89  0.850 2.87  0.872 2.71  0.814 3.07  0.820 3.97  0.870 2.64  0.816 3.36  0.862 3.22  0.802 3.79  0.869 3.14  0.828 3.01  0.803 3.40  0.810 3.04  0.815 3.12  0.870 2.82  0.856 0.860 2.94 .2.98  0.796 3.23  0.883 2.63  0.834 2.93  0.828 3.16  0.900 2.42  0.858 2.83  0.828 2.83  0.870 2.62  0.876 2.70  0.772 3.64  0.770 3.64  0.757 3.78  0.790 3.48  0.752 3.82  0.530 5.18  0.649 4.60  0.652 4.22  0.511 5.97  0.374 7.37  0.725 0.772 4.04 3.54  0.711 3.62  0.859 2.83  0.781 3.49  0.808 3.28  0.823 3.16  0.836 3.05  0.804 3.32  0.786 3.19  0.852 2.65  0.734 3.74  0.811 3.31  0.703 4.11  0.660 4.4G  0..611 4..56  0. 559 5,.04  0..579 4..69  0..552 4..28  0. 619 5..41  0. 450 4..60  0.,549 3..82  0. 512 0. 385 3,.86 6..32  0. 454 6..35  0.,824 3..09  0.,860 2..80  0. 831 2..93  0..777 3.,52  0. 837 3..05  0. 713 3..62  0. 794 3..27  0.,830 2,.98  0.,729 3,.40  0..566 3..92  0. 491 4..84  0. 735 3..78  0..424 5.. 16  0..511 4..27  0..483 4..55  0. 509 4..45  0..546 4..17  0..501 4..11  0..450 3..71  0.,464 3..93  0. 401 4. 55  0..467 4.,07  0..406 5..50  0..646 5..51  0..755 3..66  0..804 3..23  0..776 3.,16  0. 753 4. 40  0..759 4..19  0.,577 4.,27  0..563 4.,94  0.,663 4..72  0..718 4..13  0.,872 2.,85  0..844 3..14  0. 503 4. 34  0. 516 4..51  0.,572 4.,62  0. 529 4.,75  0..534 3.,95  0.,423 4,.56  0. 525 4..03  0..476 4..35  0.,465 4..29  0..419 4. 20  0. 437 4., 14  0..442 4. 34  0. 229 6.,65  0.,691 4.,26  0. 858 2..67  0..824 3..09  0. 811 3.,48  0.655 4.,19  0..638 4..55  0..822 3..29  0..771 3..43  0..833 3.,31  0.,883 2.,76  0..880 2.,71  0. 844 3..09  0..565 4..91  0. .456 3..92  0. 516 6..31  0. 559 4..03  0. .599 4..59  0. 491 4..84  0. ,503 4..03  0. .450 4.. 17  0. 501 4..08  0. 510 3..58  0..547 3..38  0..481 3..60  0..464 4.. 16  0. 358 6..96  0..709 4,.15  0. 684 4..40  0. 835 3.. 18  0..863 2..81  0..860 2 .95  0..841 2..96  0..853 3..02  0..936 2..10  0..860 2..97  ,  -*  

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