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Rainfall estimation from satellite images Ingraham, Diane Verna 1980

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RAINFALL ESTIMATION FROM S A T E L L I T E  IMAGES  by  DIANE VERNA  B.Sc. S.M.  INGRAHAM  (Physics) , Dalhousie U n i v e r s i t y , H a l i f a x , (Civil  Institute  E n g i n e e r i n g - W a t e r Resources), M a s s a c h u s e t t s  o f Technology,  C a m b r i d g e , U.S.A. 1976  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in  THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF C I V I L ENGINEERING  We  a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d  THE  UNIVERSITY OF BRITISH October  (c)  1974  Diane Verna  COLUMBIA  19 80  I n g r a h a m , 19 80  In presenting  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the  r e q u i r e m e n t s f o r an advanced d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h Columbia, I agree that the L i b r a r y freely  a v a i l a b l e f o r r e f e r e n c e and s t u d y .  agree that permission f o r extensive for  s h a l l make i t I  further  copying of t h i s  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 Head o f my  Department o r by h i s r e p r e s e n t a t i v e s .  I t i s understood  that copying or p u b l i c a t i o n of t h i s thesis f o r f i n a n c i a l gain  s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n  Department o f C i v i l  Engineering  The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 W e s b r o o k Vancouver, V6T  Place  Canada  1W5  D a t e O c t o b e r 17,  1  1980  permission.  ii RAINFALL ESTIMATION FROM S A T E L L I T E IMAGES  ABSTRACT The d e s i g n , associated rectly of  o f major water resource  t o be h a n d l e d by the p r o j e c t .  gauged r e g i o n s  these  (as w e l l as t h e  projects are d i -  r e l a t e d t o t h e a s s e s s m e n t o f t h e a n t i c i p a t e d volumes  runoff  sely  costs)  management a n d o p e r a t i o n  volumes  tellites,  i ti s o f t e n very  difficult  due t o a l a c k o f d a t a .  and i n p a r t i c u l a r ,  Environmental S a t e l l i t e s age o f t h e E a r t h  I n remote o r s p a r t o determine  The m e t e o r o l o g i c a l s a -  the Geostationary  Operational  (GOES) c a n p r o v i d e good a r e a l  and i t s weather systems p o t e n t i a l l y  coverevery  h a l f h o u r day and n i g h t .  Since  the f i r s t  meteorological  satellite  images were  t r a n s m i t t e d , many a t t e m p t s h a v e b e e n made t o e s t i m a t e fall  using  tics  and c o r r e l a t i n g  these  t h e images  methods  tropics  A method  with  limited  specific  cloud characteris-  expected r a i n f a l l . to convective  However,  rainfall  i s presented  here f o r estimating h a l f - h o u r l y  which r e l a t e s the v e r t i c a l  updraft  flux into the cloud,  v e l o c i t i e s and  to the rate of v e r t i -  and h o r i z o n t a l growth o f t h e c l o u d t o p as r e v e a l e d  GOES i n f r a r e d  i n the  tropics.  hence, the moisture cal  these  have been  o r near  rainfall  to i d e n t i f y  rain-  images.  The method  i n the  performs w e l l i n e s t i m a t i n g  rainfall  from w i d e s p r e a d f r o n t a l systems  common o v e r  British  Columbia.  A number o f c o m p u t a t i o n a l d i f f i c u l t i e s  which arose during  the  r e s e a r c h were r e s o l v e d .  top  t e m p e r a t u r e c o n t o u r s f o r t h o s e GOES i n f r a r e d i m a g e s w h i c h  were n o t enhanced.  One was t o a s c e r t a i n  cloud  T h i s i n v o l v e d t h e use o f a v i d e o camera-  s p e c i a l e f f e c t s g e n e r a t o r - v i d e o monitor system.  The s e c o n d  was o n e o f b o o k k e e p i n g t o "keep t r a c k o f " t h e i n d i v i d u a l cells.  cloud  T h i s was t a k e n c a r e o f t h r o u g h t h e u s e o f c o m p u t e r r o u -  t i n e s which d i r e c t e d t h e i n p u t and output o f d a t a , accounted for  t h e g r o w t h a n d movement o f t h e s t o r m c e l l s o v e r t h e r e g i o n  and i n t e r p o l a t e d f o r r a i n f a l l  a t those l o c a t i o n s which  fell  between a d j a c e n t p r e c i p i t a t i o n c o n t o u r s .  The m e t h o d was u s e d t o e s t i m a t e r a i n f a l l t e s t storms o c c u r r i n g over B r i t i s h  Columbia.  f o r a number o f  The r e s u l t s w e r e  r e m a r k a b l y s u c c e s s f u l a l t h o u g h t h e r e w e r e some l o c a l cies.  inadequa-  An u p d a t i n g - p r o c e d u r e was d e v e l o p e d i n w h i c h t h e s a t e l -  l i t e e s t i m a t e d v a l u e s o f r a i n f a l l were improved by t a k i n g  into  c o n s i d e r a t i o n t h e i n f o r m a t i o n p r o v i d e d by c o n c u r r e n t r a i n f a l l observations. model  Furthermore, the parameters o f the updating  ( d e t e r m i n e d f o r gauged - l o c a t i o n s ) c a n be used t o update  rainfall  e s t i m a t e s f o r ungauged  locations.  iv  In the l i g h t of present raingauge i n s t a l l a t i o n operating  c o s t s and t h e l i m i t a t i o n s  and  o f r a d a r i n mountainous  areas, the s a t e l l i t e r a i n f a l l e s t i m a t i o n procedure provides an e c o n o m i c a l o p e r a t i o n a l s u p p l e m e n t t o e x i s t i n g precipitation  data  collection.  conventional  V  TABLE OF  CONTENTS  ABSTRACT  i i  TABLE OF CONTENTS  ,.  V  L I S T OF  TABLES  ix  L I S T OF  FIGURES  xi  NOTATIONS USED  xvi  ACKNOWLEDGEMENTS  xix  CHAPTER I  II  III  INTRODUCTION  -  !•  ;  1.1  Study O b j e c t i v e s  3-  1.2  O u t l i n e of the F o l l o w i n g Chapters  5.  METEOROLOGICAL S A T E L L I T E S :  BACKGROUND  7.  2.1 Some S a t e l l i t e  and S e n s o r s  7.  Systems  2.2  The  GOES S y s t e m  13.  2.3  GOES Image F o r m a t i o n a n d E n h a n c e m e n t Schemes  2.4  Other Sources of S a t e l l i t e  Information  . . . .  .  16. 26.  A REVIEW OF S A T E L L I T E IMAGE P R E C I P I T A T I O N ESTIMATION 2 8 . 3.1  3.2  GOES R a i n f a l l  E s t i m a t i o n Techniques  30.  3.1.1  The NHEML T e c h n i q u e  30.  3.1.2  The  UW  31.  3.1.3  The  S c o f i e l d / O l i v e r Technique  Summary  Technique  32. 37.  vi  IV  THE MODEL USED TO DESCRIBE P R E C I P I T A T I N G CLOUDS . . . .  39  4.1 P r e c i p i t a t i o n  39  i n B r i t i s h Columbia  4.2 The M o d e l  41  4.2.1 R a i n - P r o d u c i n g C o n d i t i o n s  42  4.3 The M o d e l E q u a t i o n s  45  4.3.1 The A t m o s p h e r i c  4.4  Thermodynamic E q u a t i o n s  . . .  46  4.3.2 The Momentum E q u a t i o n s  47  4.3.3 The C o n t i n u i t y E q u a t i o n  48  The C o n t i n u i t y E q u a t i o n U s e d t o E s t i m a t e R a i n f a l l  .  48  4.4.1 E s t i m a t i n g t h e V e r t i c a l V e l o c i t y w  50  4.4.2  53  Rewriting the Continuity Equation  4.5 A d a p t a t i o n s f o r Use w i t h S a t e l l i t e Images  54  4.5.1 R e l a t i o n B e t w e e n A v e r a g e D i v e r g e n c e a n d C o l d e s t Contour 4.5.2 One P r o p o s e d  Divergence  Divergence  Function  4.5.3 The R a i n f a l l E s t i m a t i o n E q u a t i o n s  55 56 59  4.6 C o n s e q u e n c e s o f t h e M o d e l  60  4.7 The O t h e r M o d e l P a r a m e t e r s  61  4.7.1 The W a t e r C o n t e n t wc 4.7.2 The L a p s e R a t e y 4.7.3 A d j u s t m e n t 4.8 Summary  Factor e . . . . .  61 6  5  65 66  vii  V  COMPUTATIONAL PROCEDURE FOR S A T E L L I T E IMAGES  68  5.1  68  Conceptual Procedure 5.1.1  5.2  VI  ESTIMATING RAINFALL FROM  Movement o f S t o r m C e l l s  Near A S t a t i o n  . .  Computer R o u t i n e Sequence  ESTIMATES OF  82  P R E C I P I T A T I O N USING S A T E L L I T E IMAGES • .  6.1  T e s t Storms  6.2  The  O c t o b e r 31,  19 78  R a i n f a l l Estimates  89  6.2.1  Storm D e s c r i p t i o n  89  6.2.2  Results  92  6.2.3  C o m p a r i s o n o f S t r e a m f l o w and  Rainfall  Th:e  December 17,  93 19 79  R a i n f a l l Estimates  6.5  ....  98  6.3.1  Storm D e s c r i p t i o n  6.3.2  Results  101  6.3.2a P o i n t E s t i m a t e s  101  6.3.2b A r e a l R a i n f a l l D i s t r i b u t i o n 6.4  86 86  Volumes 6.3  77  The  J u n e 4,  19 77  98  ....  R a i n f a l l Estimates  109 114  6.4.1  Storm D e s c r i p t i o n  114  6.4.2  Results  114  The  N&vember 20,  1979  R a i n f a l l Estimates  ....  117  6.5.1  Storm D e s c r i p t i o n  117  6.5.2  Results  120  . . . . . .  viii  6.6 The December 5, 19 79 R a i n f a l l E s t i m a t e s 6.6.1  123.  Storm D e s c r i p t i o n  123.  6.6.2 R e s u l t s  123.  6.7 C o m p a r i s o n o f O b s e r v e d a n d E s t i m a t e d P r e c i p i t a t i o n f o r A l l Storms  VII  128.  AN UPDATING PROCEDURE USING OBSERVED DATA  130.  7.1 The U p d a t i n g M o d e l  130.  7.2 C o m p a r i s o n o f U p d a t e d a n d O b s e r v e d R a i n f a l l 7.2.1  The U p d a t e d O c t o b e r 3 1 , 19 78  135.  7.2.2 The U p d a t e d December 1 7 , 19 79 Estimates  7.4 Summary  VIII  133.  Rainfall  Estimates  7.3 L i m i t a t i o n s o n T r a n s f e r r i n g  . . .  Rainfall 139.  a and b  141. 145.  SUMMARY AND CONCLUSIONS  146.  8.1 F u t u r e D i r e c t i o n s  148.  BIBLIOGRAPHY  151.  APPENDIX A  159.  APPENDIX B  161.  ix L I S T OF T a b l e No. 2.1  Title  2.3  Page  S c a l e s o f A t m o s p h e r i c M o t i o n s ( f r o m H o l t o n 19 72 and  2.2  TABLES  Knox, 1978)  8.  M a j o r A t m o s p h e r i c Windows A v a i l a b l e f o r S p a c e c r a f t Remote S e n s i n g ( a f t e r L i n t z and S i m o n e t t , 1976)  9.  Some P r e s e n t a n d P r o p o s e d S a t e l l i t e s , t h e i r S e n s o r s , and C h a r a c t e r i s t i c s . Additional information i s a v a i l a b l e f r o m WMO (19 7 6 ) , NESS (19 7 6 ) , K o d a i r a and Murayama (1976) , NOAA (1979) , Spaceflight (19 80) , and D a v i s (19 80) .  11.  4.1  Average E f f i c i e n c i e s  62.  4.2  P o r t i o n o f T y p i c a l O u t p u t o f TIROS-N (TUXN) P r e c i p i t a b l e W a t e r (PCW) a n d o t h e r D a t a f o r V a r i o u s L e v e l s i n t h e A t m o s p h e r e ( R e c e i v e d by t h e P a c i f i c Weather C e n t r e from t h e S a t e l l i t e Data S e r v i c e s D i v i s i o n , NESS, W a s h i n g t o n , D.C.).  64.  Comparison o f Observed and E s t i m a t e d Storm T o t a l s f o r t h e P e r i o d 00 45 GMT on O c t o b e r 3 1 , 19 80 t o 2245 GMT on November 1, 19 78.  94.  Comparison o f R a i n f a l l m xl0 .  99.  6.1  6.2  3  6.3  6.4  and W a t e r C o n t e n t  and R u n o f f V o l u m e s i n  6  Comparison o f O b s e r v e d and E s t i m a t e d R a i n f a l l T o t a l s f o r t h e 6 - h o u r Segment 00 00 GMT t o 0 60 0 GMT on December 1 7 , 1979. Vancouver I n t e r n a t i o n a l A i r p o r t d a t a was u s e d t o c a l i b r a t e t h e a d j u s t m e n t p a r a m e t e r e.  105.  C o m p a r i s o n o f O b s e r v e d and E s t i m a t e d R a i n f a l l T o t a l s f o r t h e 6 - h o u r Segment 0000 GMT t o 0600 GMT on December 1 7 , .1.9 79 . F o r e a c h s t a t i o n t h e e m p i r i c a l a d j u s t m e n t f a c t o r e has been d e t e r m i n e d from the o b s e r v e d d a t a f o r t h a t s t a t i o n .  107.  C o m p a r i s o n o f O b s e r v e d and E s t i m a t e d R a i n f a l l T o t a l s f o r t h e s t o r m o f J u n e 4, 19 77.  1 1 8  •  C o m p a r i s o n o f O b s e r v e d and E s t i m a t e d R a i n f a l l T o t a l s f o r t h e S t o r m o f November 2 0 , 1979.  122.  C o m p a r i s o n o f O b s e r v e d and E s t i m a t e d R a i n f a l l T o t a l s f o r t h e S t o r m o f December 5, 19 79.  126.  X  7.1  7.2  V a r i a t i o n o f a a n d b f o r T e r r a c e A i r p o r t and G o s p e l P o i n t as E a c h New P a i r o f O b s e r v e d a n d E s t i m a t e d R a i n f a l l s a r e Added S e q u e n t i a l l y t o the U p d a t i n g P r o c e d u r e .  138.  Comparison o f a and b f o r Vancouver I n t e r n a t i o n a l A i r p o r t and V i c t o r i a I n t e r n a t i o n a l A i r p o r t f o r t h e S t o r m o f December 1 7 , 19 79. 142.  xi L I S T OF Figure 1.1  2.1  FIGURES  Caption  No.  Page  D i s t r i b u t i o n of S t a t i o n s i n B r i t i s h Columbia O b s e r v i n g R a i n f a l l o n an H o u r l y B a s i s . The P r o j e c t i o n i s t h e same as on t h e S a t e l l i t e Images. (Lambert C o n f o r m a l C o n i c , F a r l e y 1980).  2.  Five Geostationary Meteorological S a t e l l i t e s P r o v i d e G l o b a l Coverage o f the Weather ( a f t e r C o r b e l l et al., 1977 a n d NOAA, 1 9 7 9 ) .  14.  A s s e m b l y o f a V I S S R Image. E a c h S c a n L i n e i s composed o f 8 V i s i b l e S e n s o r L i n e s V^ and 1 I n f r a r e d S e n s o r L i n e . One S c a n L i n e R e p r e s e n t s a W e s t t o E a s t S c a n o f t h e E a r t h and E a c h i s P o s i t i o n e d S e q u e n t i a l l y i n a N o r t h - S o u t h Manner ( A d a p t e d f r o m McKowan 19 7 7 ) .  17.  2.3  D i s t r i b u t i o n o f t h e GOES s i g n a l  19.  2.4  S e c t o r s R e c e i v e d a t the P a c i f i c Weather Centre ( a f t e r C o r b e l l et al., 1977).  20.  2.2  Visible Sector SA-1 SA-2 SB-6 UC-2 2.5  and I n f r a r e d S e c t o r s Centre P o i n t (lat/long) 36°N/118°w 45°N/1160W 42°N/1240W 2 8QN/135°W  Resolution  (km)  1 1 2 4  A T y p i c a l S a t e l l i t e V i s i b l e Image (SB6 S e c t o r ) f r o m GOES-West.  22.  2.6  A Typical Satellite f r o m GOES-West.  23.  2.7  A T y p i c a l S a t e l l i t e E n h a n c e d I n f r a r e d Image (SB6 S e c t o r , "EC" E n h a n c e m e n t Scheme) f r o m GOES-West.  24.  The "EC" E n h a n c e m e n t Scheme w h i c h R e l a t e s Temper a t u r e s t o S p e c i f i c Grey Shades ( a f t e r H a e r i n g 1978) .  25.  2.8  I n f r a r e d Image (SB6 S e c t o r )  xii  Segment No. 1 2 3 4 5 6 7 8  3.1  4.1 4.2 5.1  5.2 5.3  5.4  5.5  Temperature Range °C  R e a s o n f o r Segment Enhancement  +56.8 t o +36.3 t o +20.3 t o -13.7 to  +37.3 No s i g n i f i c a n t d a t a +20.8 L a n d a n d w a t e r -13.2 W a t e r a n d l o w c l o u d s -15.7 Benchmark b e t w e e n l o w a n d medium l e v e l clouds -16.2 to -50.2 Medium a n d h i g h c l o u d s (cool season p r e c i p i tation) -51.2 t o -60.2 C o n v e c t i v e c l o u d t o p s -61.2 to -70.2 C o n v e c t i v e c l o u d t o p s -71.2 to-110.2 C o l d e s t c l o u d t o p s and s p a c e  F l o w c h a r t f o r the E s t i m a t i o n o f P o i n t R a i n f a l l f r o m GOES Images u s i n g t h e S c o f i e l d / O l i v e r T e c h n i q u e ( A f t e r I n g r a h a m , et al., 1 9 7 7 ) .  36  A Column o f A i r B e t w e e n t h e L e v e l s z a n d z+dz at Times t and t + d t .  44,  Schematic Diagram o f A i r C i r c u l a t i o n During a Major Storm.  52  E x p l a n a t i o n o f t h e V a r i o u s Terms u s e d t o DescribeGOES I n f r a r e d C l o u d Images. CELL - The C o l d e s t S e l f - C o n t a i n e d C l o u d Top Contour and i t s Immediately Surrounding Warmer C o n t o u r s . STORM- The C l o u d y A r e a o n t h e S a t e l l i t e Image w h i c h B r i n g s R a i n i n t o an A r e a . A i s U s u a l l y Made up o f One o r More C e l l s .  69  S t e p s F o l l o w e d t o Make E s t i m a t e s o f R a i n f a l l f r o m GOES S a t e l l i t e I m a g e s .  70,  The T e k t r o n i x D i g i t i z i n g T a b l e t - Remote Comput e r Terminal Arrangement. The I n f r a r e d S a t e l l i t e Image i s P l a c e d o n t h e T a b l e t a n d t h e T e m p e r a t u r e Contours are Traced u s i n g the S t y l u s .  72  The P a n a s o n i c WJ-4500 S p e c i a l E f f e c t s G e n e r a t o r U s e d t o D e t e r m i n e T e m p e r a t u r e C o n t o u r s f r o m Unenhanced I n f r a r e d S a t e l l i t e Images.  74  The t o p p h o t o shows t h e s a t e l l i t e image as s e e n on t h e v i d e o m o n i t o r b e f o r e t h e s p e c i a l e f f e c t s g e n e r a t o r i s e n g a g e d . The s e c o n d p h o t o shows t h e s a t e l l i t e image a s s e e n o n t h e v i d e o m o n i t o r a f t e r  xiii  the s p e c i a l e f f e c t s g e n e r a t o r i s engaged. T h o s e c l o u d s warmer t h a n T°C on t h e t e m p e r a t u r e - g r e y s c a l e h a v e b e e n shown as b l a c k a r e a s w h i l e t h o s e c o l d e r t h a n T°C a r e shown as l i g h t e r areas. The b o u n d a r y b e t w e e n t h e two i s t h e T°C contour. 5.6  5.7  5.8  The V i d e o Camera - S p e c i a l E f f e c t s G e n e r a t o r V i d e o M o n i t o r Arrangement Used t o Determine T e m p e r a t u r e C o n t o u r s f r o m GOES U n e n h a n c e d I n f r a r e d Images. A S c h e m a t i c R e p r e s e n t a t i o n o f One S t o r m C e l l Cont o u r as i t Moves O v e r 3 R a i n f a l l S t a t i o n s B e t w e e n Times t i a n d t 2 . The D i s p l a c e m e n t o f t h e C e n t r e o f G r a v i t y D u r i n g T h i s Time i s f r o m c i t o C2. From These "Snap-Shot" V i e w s , S t a t i o n 1 Appears Not t o Have R e c e i v e d Any R a i n f a l l .  7 o  '  7 8  '  The C e l l ' s P o s i t i o n a t Time t 2 i s S h i f t e d Back H a l f t h e D i s p l a c e m e n t s o t h a t I t s C e n t r e o f G r a v i t y i s a t P o s i t i o n c.  79,  Two C e l l s A f f e c t i n g R a i n f a l l a t a S t a t i o n . Both Are S h i f t e d so t h a t T h e i r Centres o f G r a v i t y are Now a t t h e M i d p o i n t s o f T h e i r R e s p e c t i v e T o t a l D i s p l a c e m e n t s , C]_ and C2. The S h i f t e d C e l l s a r e shown b y t h e D a s h e d C u r v e s .  81.  5.10  Sequence o f Computer R o u t i n e s Used.  83,  6.1  Map o f t h e T e r r a c e A r e a w i t h I s o h y e t s (mm) t h e P e r i o d O c t o b e r 29 t o November 2, 19 7 8 S c h a e f e r 1 9 7 9 a , b) .  5.9  6.2 6.3 6.4  6.5  6.6  for (After  A r e a l E x t e n t o f t h e O c t o b e r 3 1 , 19 7 8 S t o r m a t GMT as V i e w e d f r o m GOES-West.  90.  0115 91.  E s t i m a t e d and O b s e r v e d P r e c i p i t a t i o n a t G o s p e l P o i n t and T e r r a c e A i r p o r t .  95.  L o c a t i o n o f G r i d P o i n t s Used t o C o n s t r u c t S a t e l l i t e E s t i m a t e d I s o h y e t s f o r t h e O c t o b e r 3 1 , 19 78 Storm.  96.  I s o h y e t s o f S a t e l l i t e E s t i m a t e d R a i n f a l l (mm) f o r t h e O c t o b e r 3 1 , 1978 S t o r m B a s e d on t h e G r i d P o i n t s Shown i n F i g u r e 6.4.  97.  Map o f t h e V a n c o u v e r I s l a n d - L o w e r M a i n l a n d A r e a w i t h I s o h y e t s (mm) f o r t h e 7-Day P e r i o d f r o m December 12 t o 18) 1979 . ( A f t e r S c h a e f e r , 1 9 8 0 ) .  10O.  xiv  A r e a l E x t e n t o f December 1 7 , 19 79 S t o r m a t 0 715 GMT as V i e w e d f r o m GOES-West.  10 2.  Location of Stations 1979 S t o r m A n a l y s i s .  103.  1 2 3 4 5 6 7 8 9 10 11 12 13  U s e d i n t h e December 1 7 ,  Blue River B u l l Harbour Burns Lake Castlegar Airport Cranbrook A i r p o r t Dease L a k e Hope A i r p o r t Kamloops A i r p o r t Kelowna A i r p o r t Langara Lytton Penticton Airport P o r t Hardy A i r p o r t  14 15 16 17 18 19 20 21 22 23 24 25 26  P r i n c e George A i r p o r t Prince Rupert A i r p o r t Quesnel A i r p o r t Revelstoke A i r p o r t S a l m o n Arm Sandspit Airport Terrace A i r p o r t Tofino Airport Vancouver I n t e r n a t i o n a l Airport Victoria International Airport W i l l i a m s Lake A i r p o r t Banff Calgary  E s t i m a t e d and O b s e r v e d P r e c i p i t a t i o n f o r t h e Dec e m b e r 17, 19 79 S t o r m . (For each s t a t i o n the e m p i r i c a l a d j u s t m e n t f a c t o r e has been d e t e r m i n e d from the observed d a t a f o r t h a t s t a t i o n . )  108.  S t o r m C e l l R a i n f a l l "Maps" f o r 2 H o u r s December 17, 1979 S t o r m .  110.  During the  L o c a t i o n o f G r i d P o i n t s Used t o C o n s t r u c t S a t e l l i t e Estimated I s o h y e t s f o r t h e December 17, 19 79 Storm. O b s e r v e d r a i n f a l l s (mm) f o r : B u l l Harbour 8.9 P o r t Hardy 6.8 Tofino 22.6 Vancouver 10.6 Victoria 6.8 E v o l u t i o n o f I s o h y e t s o f R a i n f a l l (mm) f o r t h e December 17, 1979 S t o r m E s t i m a t e d f o r t h e G r i d P o i n t s Shown i n F i g u r e 6.11. L o c a t i o n o f S t a t i o n s Use d Analysis: 1 Duncan L a k e Dam 2 Revelstoke A i r p o r t 3 M i c a Dam 4 Castlegar Airport  i n t h e J u n e 4, 19 77 S t o r m 5 6 7  Elko Cranbrook A i r p o r t Blue River  HI.  XV  6.14  A r e a l E x t e n t o f J u n e 4, 1977 S t o r m a t 0245 GMT as V i e w e d f r o m GOES-West.  116  E s t i m a t e d and Observed P r e c i p i t a t i o n f o r the J u n e 4, 19 77 S t o r m .  119  A r e a l E x t e n t o f November 2 0 , 1979 S t o r m a t 1115 GMT as V i e w e d f r o m GOES-West,  121  A r e a l E x t e n t o f December 5, 19 79 S t o r m a t 1015 GMT a s V i e w e d f r o m GOES-West,  124  6.18  E s t i m a t e d and Observed P r e c i p i t a t i o n f o r the December 5, 1979 S t o r m .  127  6.19  E s t i m a t e d and Observed P r e c i p i t a t i o n f o r A l l F i v e Test Storms.  129  The B e h a v i o u r o f t h e W e i g h t s W i = W n=50 a n d 3 v a l u e s o f W]_.  134  6.15 6.16 6.17  7.1 7.2  ( n _ l ) 1  for  Comparison o f Updated S a t e l l i t e E s t i m a t e d R a i n f a l l and Observed R a i n f a l l f o r Gospel P o i n t and T e r r a c e A i r p o r t . T y p i c a l Values o f a, b f o r E a c h S t a t i o n a r e G i v e n i n T a b l e 7.1 (Wi=0.8) .  137  7.3  Schematic o f a r i v e r b a s i n w i t h 4 s t a t i o n s (A,B,C,D) w h e r e t h e a r e a l r a i n f a l l d i s t r i b u t i o n i s o f i n t e r e s t b u t w h e r e o n l y one o f t h e s t a t i o n s (A) h a s a r a i n g a u g e . S a t e l l i t e estimates of r a i n f a l l are a v a i l a b l e f o r a l l 4 s t a t i o n s throughout the d u r a t i o n o f the storm. By u p d a t i n g t h e estimated s e r i e s f o r A w i t h the observed data m e a s u r e d t h e r e , v a l u e s o f a a n d b c a n be d e t e r m i n e d f o r each time i n t e r v a l . These v a l u e s o f a and b c a n be u s e d t o u p d a t e t h e e s t i m a t e d r a i n f a l l a t the o t h e r ungauged s t a t i o n s (B,C,D). 140  7.4  Comparison o f Updated S a t e l l i t e E s t i m a t e d R a i n f a l l and Observed R a i n f a l l f o r Gospel P o i n t . T h i s i s s i m i l a r t o F i g u r e 7.2 e x c e p t t h a t i n t h i s c a s e the s a t e l l i t e e s t i m a t e d r a i n f a l l s f o r Gospel P o i n t were u p d a t e d u s i n g t h e a and b v a l u e s d e t e r m i n e d at Terrace A i r p o r t . 143  7.5  E v o l u t i o n o f I s o h y e t s (mm) C o n s t r u c t e d f o r t h e December 1 7 , 19 79 S t o r m U p d a t e d S a t e l l i t e R a i n f a l l E s t i m a t e s f o r t h e G r i d P o i n t s Shown i n F i g u r e 6.11  144  XVI  NOTATIONS USED The  f o l l o w i n g n o t a t i o n s a r e f r e q u e n t l y used.  a  radius o f the earth  a  u p d a t i n g model  parameter  c o n s t a n t i n UW  technique  a^  c o n s t a n t i n UW  technique  A  cloud area  a  Q  A  c  satellite  ( c l o u d ) a r e a i n NHEML t e c h n i q u e  A  e  r a d a r e c h o a r e a i n NHEML t e c h n i q u e  b  u p d a t i n g model  0^  s p e c i f i c heat o f a i r a t c o n s t a n t pressure=c^+R  c  s p e c i f i c h e a t o f a i r a t c o n s t a n t volume  v  e  adjustment  E  evaporation  f,f ,f 1  2  parameter  factor,  efficiency  constants i n the divergence functions  Fx,Fy, Fz e a s t w a r d , n o r t h w a r d ,  vertical  components o f f r i c t i o n ,  respectively g  gravity  o  H  r a t e a t w h i c h e x t e r n a l h e a t i s a d d e d p e r u n i t mass of a i r  i  index  I  r a i n r a t e p e r u n i t a r e a i n NHEML t e c h n i q u e  K  divergence o f the c o l d e s t contour  M  mass o f a c o l u m n o f a i r  n  t o t a l number i n a s e r i e s  0  "order o f magnitude o f "  p  pressure  xvii  P  precipitation  r^  volume r a i n r a t e i n NHEML technique  R  gas constant  R  volume r a i n r a t e i n UW  t  time  ,T  (mm)  technique  temperature  u  eastward  component o f v e l o c i t y V  v  northward component o f v e l o c i t y V  Y  velocity vector  w  v e r t i c a l component o f v e l o c i t y V  wc  water content i - t h weight i n updating model  W-j^  w e i g h t i n g parameter i n updating model  x  eastward  x  e s t i m a t e d r a i n f a l l i n updating model  y  northward h o r i z o n t a l  y  observed or " t r u e " r a i n f a l l i n updating model  z  vertical  a  s p e c i f i c volume  Y  lapse r a t e  v  environmental  Y  env s  horizontal  component  component  component  lapse r a t e  s a t u r a t e d a d i a b a t i c lapse r a t e  p  density  <[>  latitude  fi  angular v e l o c i t y o f the E a r t h  xviii  Acronyms:  AES  Atmospheric Environment  Service  ATS-III  A p p l i c a t i o n s Technology  Satellite-Ill  CDA  C e n t r a l Data A c q u i s i t i o n  CNR  Canadian N a t i o n a l Railway  DMSP  Defense M e t e o r o l o g i c a l S a t e l l i t e  ESSA.  Environmental Survey S a t e l l i t e Science  Services  Program  - Environmental  Administration  GMS  Geosynchronous  Meteorological Satellite  GMT  G r e e n w i c h Mean Time  (Subtract  (Japan)  8 h o u r s f r o m GMT  t o g e t PST) GOES  Geostationary  GOES-Tap  High q u a l i t y  Operational  Environmental S a t e l l i t e  telephone l i n k  f o r t r a n s m i s s i o n o f GOES  images IR  infrared  (image)  METEOSAT  Meteorological Satellite  NESS  National Environmental S a t e l l i t e  PST  Pacific  S t a n d a r d Time  PWC  Pacific  Weather C e n t r e ,  SMS  Synchronous  (European Space  Agency)  Service  V a n c o u v e r , B.C.  Meteorological  Satellite  TIROS-1, TIROS-N  Television Infrared Observational  VISSR!  Visible  Satellite  and I n f r a r e d S p i n - S c a n Radiometer  - 1 , -N  xix  ACKNOWLE DGEMENTS  I w a n t t o t h a n k D r . S.O. ( D e n i s ) R u s s e l l whose a d v i c e a n d g u i d a n c e was i n v a l u a b l e t h r o u g h o u t t h e c o u r s e o f t h e s t u d y a n d who s u p e r v i s e d t h i s t h e s i s w i t h i n t e r e s t and o p t i m i s m . I t c e r t a i n l y h a s b e e n a p l e a s u r e t o work w i t h D r . R u s s e l l . I w o u l d a l s o t h a n k D r . W. C a s e l t o n , Department o f C i v i l E n g i n e e r i n g ; D r . M. Q u i c k , D e p a r t m e n t of C i v i l Engineering; D r . P. M u r t h a , D e p a r t m e n t o f F o r e s t r y ; and D r . J . H a y , D e p a r t m e n t o f G e o g r a p h y ; f o r t h e i r comments and s u g g e s t i o n s c o n c e r n i n g t h i s w o r k . Thanks go t o D r . J . A m o r o c h o , U n i v e r s i t y o f C a l i f o r n i a , D a v i s , a n d D r . R. S c o f i e l d , NESS f o r i n t r o d u c i n g me t o r a i n f a l l e s t i m a t i o n from s a t e l l i t e images; a n d t o NESS, W a s h i n g t o n , D.C. f o r p r o v i d i n g GOES s a t e l l i t e i m a g e s a n d f i l m loops. T h a n k s a l s o go t o D r . P. H a e r i n g a n d Mr. J . S p a g n o l o f t h e P a c i f i c Weather C e n t r e f o r t h e i r i n t e r e s t and a d v i c e as w e l l as f o r m a k i n g GOES-West s a t e l l i t e i m a g e s a n d TIROS-N d a t a a v a i l a b l e . A p p r e c i a t i o n i s e x t e n d e d t o Mr. W. K r e u d e r , W a t e r S u r v e y o f Canada f o r p r o v i d i n g r u n o f f d a t a f o r T e r r a c e K i t i m a t area basins; t o Mr. N. Penny o f t h e AES a n d t o Mr. B. Y o r k e o f t h e C l i m a t o l o g i c a l D a t a S e r v i c e s , A E S , f o r p r o v i d i n g p r e c i p i t a t i o n data; a n d t o D r . D.G. S c h a e f e r f o r p r o v i d i n g t h e r e s u l t s o f h i s a n a l y s i s o f t h e O c t o b e r 3 1 , 19 78 and December 1 7 , 19 79 s t o r m s . F u n d i n g f o r t h i s s t u d y came from t h e N a t u r a l Sciences and E n g i n e e r i n g Research C o u n c i l , and was g r e a t l y a p p r e c i a t e d . Thanks a r e e x t e n d e d t o Mrs. T i l l y S c h r e i n d e r s f o r the e x c e l l e n t t y p i n g o f t h e m a n u s c r i p t , t o Mr. R i c h a r d Brun f o r t h e d r a f t i n g a s s i s t a n c e and t o Mr. J . B o n s e r f o r computer programming a s s i s t a n c e . being  I w o u l d a l s o l i k e t o t h a n k my f a m i l y a n d f r i e n d s f o r t h e r e when I n e e d e d them.  1.  CHAPTER I INTRODUCTION  The  growth o f a r e g i o n i s d i r e c t l y r e l a t e d t o t h e de-  velopment o f i t s n a t u r a l resources  with the quality of this  g r o w t h d e p e n d e n t o n t h e s k i l l f u l e x p l o i t a t i o n a n d management of the resources.  As a b a s i s f o r t h e e f f i c i e n t p l a n n i n g , d e -  s i g n , and o p e r a t i o n o f p r o j e c t s , a d e t a i l e d and r e l i a b l e des c r i p t i o n of the resource  i s r e q u i r e d b u t t h i s has u s u a l l y been  d i f f i c u l t to provide.  In B r i t i s h ing  Columbia water i s a major resource  d i r e c t l y and i n d i r e c t l y  the p r o v i n c e . an i m p o r t a n t  t o t h e economy a n d w e l l - b e i n g o f  The amount o f r a i n f a l l i n g  over the region i s  quantity i n the water resource  measurement o f t h e r a i n f a l l  contribut-  inventory.  The  i s hampered because t h e e x i s t i n g  n e t w o r k o f r a i n g a u g e s i s g e n e r a l l y i n a d e q u a t e a n d i n some i n stances  non-existent.  Figure  1.1  shows t h e d i s t r i b u t i o n o f  s t a t i o n s r e c o r d i n g p r e c i p i t a t i o n o n an h o u r l y b a s i s British  Columbia.  Most o f these  throughout  s t a t i o n s are grouped near  cen-  tres o f population o r along t r a n s p o r t a t i o n routes, both t o f a cilitate minimum.  installation  and maintenance, and t o keep c o s t s t o a  There a r e , however, l a r g e areas which remain  gauges o r w h i c h h a v e g a u g e s w h e r e d a t a use  are not a v a i l a b l ef o r  o n a r e a l - t i m e b a s i s , s u c h as i n f l o o d f o r e c a s t i n g .  lack of d e t a i l e d r a i n f a l l  data  without  The  from r i v e r b a s i n s has l o n g been  2.  FIGURE 1.1 D i s t r i b u t i o n o f S t a t i o n s i n B r i t i s h Columbia Observing R a i n f a l l on an Hourly B a s i s .  The P r o j e c t i o n i s the  Same as on the S a t e l l i t e Images, (Lambert Cohformal Conic, F a r l e y  1980).  3.  a r e c o g n i z e d problem among h y d r o l o g i s t s but there appears to be l i t t l e p r o s p e c t o f i t b e i n g r e s o l v e d by s u r f a c e measurement techniques  i n the near f u t u r e .  This i s p a r t i c u l a r l y  t r u e i n the more remote unpopulated regions where some o f l a r g e s t water resource  developments are now  being  the  engineered.  M e t e o r o l o g i c a l s a t e l l i t e s h o l d the promise o f p r o v i d i n g meteorologic  i n f o r m a t i o n over l a r g e r e g i o n s .  The  geostation-  ary o p e r a t i o n a l environmental s a t e l l i t e s , GOES, r e c o r d atmospheric  c o n d i t i o n s on the E a r t h around the clock and p r o v i d e  h o u r l y images such as those cast.  shown on the t e l e v i s i o n weather f o r e -  GOES images have been employed to estimate  from l a r g e convective  half-  rainfall  c e l l s i n t r o p i c a l and s u b - t r o p i c a l areas  by a p p l y i n g e m p i r i c a l r e l a t i o n s s p e c i f i c a l l y d e r i v e d f o r t h i s type o f storm, ( S c o f i e l d and O l i v e r , 1977a; S t o u t et  19 78;  al.,  19 79).  On  G r i f f i t h et  the whole these  o f f e r l i m i t e d guidance f o r extending  al.  ,  approaches  r a i n f a l l estimation  using  s a t e l l i t e images to o t h e r types of storms or geographic r e g i o n s .  1.1  Study O b j e c t i v e s T h e aims of the study  d e s c r i b e d i n the f o l l o w i n g  chapters  were to extend the s a t e l l i t e r a i n f a l l e s t i m a t i o n procedure which would be  a p p l i c a b l e to f r o n t a l storms and other  precipitation  systems i n the h i g h e r l a t i t u d e s , to develop an a p p l i c a b l e p h y s i c a l concept f o r the e s t i m a t i o n procedure, and to t e s t the dure by  a p p l y i n g i t to a c t u a l storms.  proce-  4. The more s u c c e s s f u l m e t h o d s f o r c o m p u t i n g  rainfall  f r o m s a t e l l i t e i m a g e s a l l use t h e c h a n g e s i n t h e a r e a o f the c l o u d top temperature n e x t as i n p u t p a r a m e t e r s  c o n t o u r s f r o m one  to t h e i r computational  as f o r e x a m p l e i n S c o f i e l d and O l i v e r of  image t o  t h e p r e s e n t s t u d y i t was  procedures,  (19 77a) .  In the  r e a l i z e d t h a t the r a t e  change i n t h e c l o u d t o p t e m p e r a t u r e  a i r i s s p r e a d i n g out a t the c l o u d t o p .  is  rising.  I t has  course  of  contours provides a  measure o f the d i v e r g e n c e , o r the r a t e a t w h i c h  i n t u r n r e l a t e d to the rate a t which  the  By  the  ascending  continuity this i s  a i r e n t e r i n g the c l o u d  l o n g been r e a l i z e d t h a t the r a i n f a l l r a t e  c o u l d be e s t i m a t e d f r o m a k n o w l e d g e o f t h e r a t e a t w h i c h a i r mass was  rising  1948) , b u t i t h a s  and i t s m o i s t u r e c o n t e n t  never been p o s s i b l e t o measure the  v e l o c i t y of the ascending a i r . study, the v e r t i c a l  velocity  gence o f the c l o u d t o p w h i c h s a t e l l i t e images.  ( B y e r s and  Now,  an Braham,  vertical  as shown i n t h e p r e s e n t  c a n be e s t i m a t e d f r o m t h e c a n be d e t e r m i n e d  diver-  from s u c c e s s i v e  T h i s i n s i g h t p r o v i d e d an e x p l a n a t i o n , w i t h a  sound p h y s i c a l b a s i s , f o r the success o f t e c h n i q u e s such t h a t o f S c o f i e l d and O l i v e r solid to  (19 7 7 a ) , and i t a l s o p r o v i d e d a  f o u n d a t i o n f o r e x t e n d i n g t h e s e same f u n d a m e n t a l  the type of storms  t h e c o n c e p t i t was  encountered  necessary  as  in British  Columbia.  to develop procedures  the d i v e r g e n c e from s a t e l l i t e images, t o develop  concepts To  apply  for estimating  a method f o r  u p d a t i n g these e s t i m a t e s i n the l i g h t of a c t u a l r e c o r d e d d a t a , and  to develop  computer r o u t i n e s t o h e l p w i t h the  extens-  5.  ive  calculations.  Such procedures were developed and  tested  on a number o f major and minor storms which o c c u r r e d over B r i t ish  Columbia  and f o r which s a t e l l i t e images were a v a i l a b l e .  The emphasis throughout has been on d e v e l o p i n g a p r a c t i c a l technique which gists.  can be used by h y d r o l o g i s t s and meteorolo-  P o t e n t i a l e n g i n e e r i n g a p p l i c a t i o n s o f the data i n c l u d e  providing real-time regional flood forecasts, reservoir inflows, as w e l l as the study o f p r e v i o u s l a r g e storms  f o r design f l o o d  calculations.  1.2  O u t l i n e o f the F o l l o w i n g Chapters Chapter I I c o n t a i n s g e n e r a l background  i n f o r m a t i o n on  m e t e o r o l o g i c a l s a t e l l i t e s , i n p a r t i c u l a r GOES, which p r o v i d e d the images used i n t h i s study.  Chapter I I I reviews o t h e r i n v e s -  t i g a t i o n s i n t o the a p p l i c a t i o n o f s a t e l l i t e imagery estimation.  for r a i n f a l l  Chapter IV d e s c r i b e s the model employed to r e l a t e  c l o u d growth as observed i n s a t e l l i t e images to the a c t u a l fall  from the c l o u d .  p u t e r sequence  rain-  Chapter V d i s c u s s e s the conceptual and com-  f o l l o w e d to a r r i v e at s a t e l l i t e estimates o f r a i n -  f a l l , w h i l e Chapter VI p r e s e n t s the estimates o f p r e c i p i t a t i o n f o r a number o f storms over B r i t i s h Columbia the observed p r e c i p i t a t i o n .  The  and compares them w i t h  f i r s t p a r t o f Chapter VII  dis-  cusses the updating procedure f o r i n c o r p o r a t i n g the i n f o r m a t i o n contained i n the observed r a i n f a l l s e r i e s with t h a t o f the e s t i mated s e r i e s .  The second p a r t o f Chapter VII c o n t a i n s the updated  6.  precipitation  e s t i m a t e s f o r two s t o r m s o v e r B r i t i s h  and compares them t o t h e m e a s u r e d p r e c i p i t a t i o n .  Columbia  Chapter  VIII  draws t o g e t h e r t h e c o n c l u s i o n s , r e c o m m e n d a t i o n s a n d s u g g e s t e d directions the  f o r f u t u r e r e s e a r c h t h a t h a v e become a p p a r e n t d u r i n g  course of t h i s  study.  7.  CHAPTER I I  METEOROLOGICAL S A T E L L I T E S :  With space closer  look  flight  scan  came t h e o p p o r t u n i t y  a t c o n d i t i o n s on E a r t h  a unique vantage p o i n t . the Earth  BACKGROUND  (like  t h e weather)  Present meteorological  regularly at a level  o b s e r v a t i o n o f meso a n d m a c r o s c a l e  These s a t e l l i t e s  the problem o f inadequate  2.1  (10  offer  on a s p a t i a l  u n a t t a i n a b l e by c o n v e n t i o n a l  Some S a t e l l i t e  allows  7  t o 10  m) phenomena. a r e summarized  a potential  solution to  h y d r o l o g i c i n f o r m a t i o n by p r o v i d i n g  economical and t i m e l y data virtually  satellites  motions o f v a r i o u s s c a l e s and types  2.1).  i n Table  from  o f r e s o l u t i o n which 3  (Atmospheric  f o rtaking a  and t e m p o r a l s c a l e ground based-networks.  Systems a n d S e n s o r s  T h e r e a r e two c o n s i d e r a t i o n s w h i c h h a v e a f f e c t e d m e t e o r ological tical the  satellite  behaviour  other  Earth's  systems and t h e i r s e n s o r s .  One i s t h e o p -  o f t h e a t m o s p h e r e a t d i f f e r e n t wavebands a n d  i s the type  of orbit  the s a t e l l i t e  can take  surface.  The  a t m o s p h e r e h a s "windows"  ( i . e . i s transparent to  r a d i a t i o n o f c e r t a i n wavelengths) which a r e important sensing, bands.  above t h e  i n the v i s i b l e ,  near v i s i b l e ,  These a r e shown i n T a b l e  2.2.  infrared,  f o r remote  and microwave  Consequently  sensors,  8. TABLE 2.1  Scales o f Atmospheric a n d K n o x , 19 78)  TYPE OF MOTION  ( f r o m H o l t o n , 19 72  Motions  HORIZONTAL SCALE  (m)  m o l e c u l a r mean free  ,10"  path  7  minute t u r b u l e n t eddies  10  small  10" t o 1 1 t o 10 10 t o 10  dust  eddies  to  gusts  io  tornadoes cumulonimbus  10  1  devils  lines  hurricanes cyclones  p l a n e t a r y waves  2  2  10 '  clouds  fronts, squall synoptic  -2  3  10  4  t o 10  10 106  5  10 7  5  -1  9.  TABLE 2.2  M a j o r A t m o s p h e r i c Windows A v a i l a b l e Remote S e n s i n g ( a f t e r L i n t z  a n d S i m o n e t t , 19 76)  WINDOW  ultraviolet  WAVEBAND  and v i s i b l e <-  near  infrared  •  mid-infrared  thermal  infrared  mi c r o w a v e  f o r Spacecraft  0 .30  to  0 .75y  0 .77  to  0 .91  1 .0  to  1 .12  1 .19  to  1 .34  1 .55  to  1 .75  2 .05  to  2 .4  3 .5  to  4 .16  4 .5  to  5 .0  8 .0  to  9 .2  10 .2  t o 12 .4  17 .0  to  22 .0  2 .06  to  2 .22  3 .0  to  3 .75  7 .5  to  20 .0 +  11 .5  mm  10.  sensitive  t o r a d i a t i o n i n t h e s e bands were d e v e l o p e d .  2.3  some m e t e o r o l o g i c a l  lists  sensors. are  The  two  the v i s i b l e  satellites  most p o p u l a r  and  tions:  the E a r t h  g e n e r a l l y h a v e one  p o s i t i o n on  of p o l a r o r b i t i n g s a t e l l i t e s  o b t a i n i n g data  the E a r t h ' s  sweep o u t  t h e t y p e o f s e n s o r and  frequency of repeat the s a t e l l i t e used.  satellites  weather  This  over  satellite  The  advantage  is especially width  the a l t i t u d e of the  c o v e r a g e o v e r any (See  The  important of the  swath  i n t h e i r o r b i t s i s dependent i n  Table 2.3).  - i t i s u s u a l l y too  one  spacecraft.  location varies  I t i s this  repeat  disadvantage of p o l a r low  orbit-  to r e v e a l r a p i d l y changing  features.  Geostationary t h e r on  configura-  l i e s i n the p r o v i s i o n o f images o v e r  f r e q u e n c y w h i c h forms the p r i n c i p a l ing  surface.  f o r the p o l a r r e g i o n s .  that polar s a t e l l i t e s  with  orbital  24 h o u r s s o t h a t i t r e m a i n s  the e n t i r e s u r f a c e o f the E a r t h .  The  o f two  o r b i t - the o r b i t o f the  a p e r i o d of approximately  p a r t on  a l s o be c o n t r o l l e d .  a p o l a r o r b i t - the o r b i t of the s a t e l l i t e passes  " f i x e d " o v e r one  for  i n s e v e r a l wavebands,  s a t e l l i t e assumes c a n  both poles; or a geostationary has  use  i n f r a r e d bands.  In a d d i t i o n to o b s e r v i n g  Weather s a t e l l i t e s  their  wavebands f o r o p e r a t i o n a l  the thermal  the type of o r b i t the  along with  Table  a very  hour during  satellites  frequent  basis:  provide one  r e g u l a r o p e r a t i o n and  a " g l o b a l v i e w " o f wea-  i m a g e as o f t e n as every h a l f  more o f t e n d u r i n g  severe  TABLE 2.3  Some P r e s e n t and Proposed S a t e l l i t e s , t h e i r Sensors and C h a r a c t e r i s t i c s . Additional I n f o r m a t i o n i s A v a i l a b l e from WMO (1976), NESS (1976), K o d a i r a and Murayama (1976), NOAA (1979), Spaceflight (1980), and Davis (1980).  SENSOR  SATELLITE  Geostationary  WAVEBAND  REMARKS  NOMINAL NADIR RESOLUTION (km)  Satellites: Repeat c o v e r a g e e v e r y h h r , r e s o l u t i o n double n a d i r value a t l a t i t u d e s >50°, p o l a r coverage l i m i t e d , GOES-B e x p e c t e d launch Aug. 19 80 .  V i s i b l e and I n f r a r e d S p i n - S c a n Radiometer (VISSR)  0 .55-0 .7  1  10 .5-12 .5  8  GMS "Sunflower"  VISSR  0.5-0.75 10 .5-12.5  1.25 5  Japanese s a t e l l i t e a t (0°N, 1 4 0 ° E ) .  METEOSAT  VISSR  0.7 11  1.25 • 5  European Space Agency S a t e l l i t e (ESA=Belgium, Denmark, F r a n c e , Germany, I t a l y , Sweden, S w i t z e r l a n d , and t h e U n i t e d Kingdom). S a t e l l i t e l o c a t e d a t (0°N, 0 ° W ) ; as o f Nov. 24/79 on l i m i t e d o p e r a t i o n due t o o n b o a r d o v e r l o a d problem.  SMS/GOES  Water (WV)  STORMSAT  Polar  Vapor  Advanced A t m o s p h e r i c . Sounding and Imaging Radiometer (AASIR)  6  not available  5  not available  located  Prototype s a t e l l i t e , v i s i b l e and i n f r a r e d s c a n n e r ; e x p e c t e d l a u n c h : mid 19 80's.  Satellites  NIMBUS 5  E l e c t r i c a l l y Scanning Microwave Radiometer (ESMR)  0.8 cm  32  Repeat  c o v e r a g e e v e r y 12 m.  TABLE 2.3 (continued)  SENSOR  SATELLITE  WAVEBAND  NOMINAL NADIR RESOLUTION (km) 22 8  Repeat  x 103 x 66 x 41 x 32 x 19  Repeat coverage e v e r y 36 h r . , swath w i d t h 780 km.  3.5  Repeat coverage e v e r y 12 h r , swath w i d t h 3000 km  NIMBUS 6  Temperature-HumidityI n f r a r e d - Radiometer (THIR)  6 .5-7.1 10 .3-12 .5  NIMBUS G  THIR  (same as f o r NIMBUS 6)  Scanning M u l t i f r e quency Microwave Radiometer (SMMR)  NOAA 5,6  TIROS-N  Scanning (SR)  Radiometer  4.55 2.81 1.67 1.36 0.81  cm cm cm cm cm  0.5-0.7 o r 0.5-0.9  118 73 47 37 22  10 .5-12.5  8  Very High R e s o l u t i o n Radiometer (VHRR)  0 .6-0.7 10 .5-12.5  1 1  Advanced VHRR (AVHRR)  0 .55-0 .9 0 .72-1.1 3.55-3.93 10 .5-11.5  1-4  REMARKS  c o v e r a g e e v e r y 12 h r .  Repeat coverage e v e r y 12 h r , swath w i d t h 2 800 km, l a u n c h e d O c t . 31/78.  13.  w e a t h e r s u c h as h u r r i c a n e s a drawback: ly  and tornadoes.  There i s , however,  away f r o m t h e e q u a t o r t h e i m a g e s become i n c r e a s i n g -  d i s t o r t e d due t o t h e c u r v a t u r e  o f t h e E a r t h , becoming t o o  d i s t o r t e d t o be u s e f u l b e y o n d a b o u t 60° l a t i t u d e . tionary satellites lite  Five  geosta-  f o r m i n g t h e W o r l d Wide Geosynchronous  Satel-  System a r e a r r a n g e d around t h e E a r t h a t a l t i t u d e s o f approx-  imately  36,000 km, as shown i n F i g u r e  r e c e i v e s s a t e l l i t e images  2.1. B r i t i s h  Columbia  f r o m GOES-West w h i c h i s l o c a t e d o v e r  t h e e q u a t o r a n d 145° l o n g i t u d e .  2.2  The GOES S y s t e m The  frequent,  l a r g e a r e a l coverage o f a g e o s t a t i o n a r y  m e t e o r o l o g i c a l s a t e l l i t e makes i t p a r t i c u l a r l y observing with  t h e changes i n w e a t h e r c o n d i t i o n s w h i c h a r e a s s o c i a t e d  r a i n f a l l as r e v e a l e d b y t h e g r o w t h a n d d e c a y o f c l o u d s y s t e m s .  (Images this  attractive f o r  f r o m t h e GOES-West s a t e l l i t e w e r e u s e d i n t h i s s t u d y f o r  r e a s o n , a n d , because t h e s e s a t e l l i t e images were  available  locally).  The f o l l o w i n g b r i e f l y  describes  readily t h e GOES  system which i s g e n e r a l l y s i m i l a r t o other geostationary the G e o s t a t i o n a r y  Meteorological Satellite  and t h e M e t e o r o l o g i c a l S a t e l l i t e  satellites  (GMS) o f J a p a n  (METEOSAT) o f t h e E u r o p e a n  Space  Agency.  The GOES s a t e l l i t e s meteorological s a t e l l i t e  a r e an outgrowth o f e a r l i e r  (SMS) r e s e a r c h  synchronous  and development.  p r i m a r y aims o f t h e SMS/GOES p r o g r a m a r e :  The  Japan  USA  USA  Europe  QMS  GOESWest  GOESEast  METEOSAT  USA GOESIndian O c e a n  FIGURE 2.1 Five Geostationary  Meteorological Satellites  G l o b a l Coverage o f t h e Weather, 19 77 a n d NOAA, 19 7 9 ) .  Provide  ( a f t e r C o r b e l l et al.,  15.  a - t o i n c r e a s e t h e knowledge and u n d e r s t a n d i n g o f a t m o s p h e r i c p r o c e s s e s by o b s e r v i n g t h e m o t i o n s and  l i f e c y c l e s o f storms  a n d o t h e r phenomena,  b - t o a i d i n t h e development o f a domestic  (U.S.)  and i n t e r n a t i o n a l d a t a n e t w o r k c a p a b l e o f c o l l e c t i n g , p r o c e s s i n g , and d i s t r i b u t i n g r o u t i n e observ a t i o n s and e a r l y warnings  i n real  time,  c - t o i n c r e a s e the k i n d , q u a l i t y and q u a n t i t y o fenv i r o n m e n t a l parameter  measurements.  T h e s e a i m s a r e a c h i e v e d b y c o m b i n a t i o n o f SMS/GOES ground  satellites,  s t a t i o n s and remote d a t a c o l l e c t i o n p l a t f o r m s  (DCP's).  (McKowan, 19 7 7 ) .  The meter  GOES s a t e l l i t e v i s i b l e  (VISSR) s e n s e s  the v i s i b l e  (0.55  and i n f r a r e d s p i n - s c a n r a d i o -  c o n d i t i o n s o n t h e E a r t h u s i n g two wavebands -  t o 0.7y) b a n d w h i c h  p r o v i d e s 1 km r e s o l u t i o n  images e v e r y h o u r d u r i n g t h e d a y l i g h t h o u r s , and t h e t h e r m a l infrared  ( 1 0 . 5 t o 12.6y) b a n d w h i c h p r o v i d e s 8 km r e s o l u t i o n  images e v e r y h a l f h o u r t w e n t y - f o u r hours stormy  a day. Under  special  c o n d i t i o n s t h e f r e q u e n c y o f t h e images can be i n c r e a s e d  t o p r o v i d e , f o r example, images o f t h e a f f e c t e d a r e a e v e r y minutes.  T h i s i s c o n t r o l l e d b y t h e owner o f t h e s a t e l l i t e .  five  The V I S S R a l l o w s t h e m a p p i n g o f c l o u d f e a t u r e s b o t h d a y a n d night using eight v i s i b l e  c h a n n e l s t o g i v e measurements o f  a l b e d o f r o m 0.5 t o 100 p e r c e n t , a n d two t h e r m a l i n f r a r e d channels  (one o f w h i c h i s redundant) w h i c h g i v e r a d i a n c e  t e m p e r a t u r e m e a s u r e m e n t s b e t w e e n -9 3 a n d 42°C. Space Agency's vapor  METEOSAT h a s a n a d d i t i o n a l s e n s o r f o r w a t e r  ( i n t h e 6p band)  (Davis, 1980), and s l i g h t l y  r e s o l u t i o n s p e c i f i c a t i o n s , as does J a p a n ' s Murayama, 1 9 7 6 ) . is  F o r these s a t e l l i t e s  and GMS h a v e r e d u n d a n t v i s i b l e  different  GMS, ( K o d a i r a a n d  the v i s i b l e  1.25 km a n d t h e i n f r a r e d r e s o l u t i o n i s 5 km.  2.3  The E u r o p e a n  resolution  B o t h METEOSAT  s e n s o r s as w e l l .  GOES Image F o r m a t i o n a n d E n h a n c e m e n t Schemes The  f o r m a t i o n o f t h e GOES s a t e l l i t e image i s a r e s u l t o f  a combination o f the s a t e l l i t e ' s  spin motion  (100 rpm) o n i t s  a x i s and t h e s t e p a c t i o n o f i t s s c a n n i n g o p t i c s .  One l i n e  cor-  r e s p o n d i n g t o t h e E a r t h ' s w e s t - e a s t a x i s i s performed f o r each satellite  r o t a t i o n , w h i l e t h e scanner p o s i t i o n s each l i n e  i na  n o r t h - s o u t h m a n n e r . (METEOSAT s c a n s f r o m e a s t t o w e s t a n d s t e p s i n a s o u t h - n o r t h manner). sensed  Once t h e f u l l E a r t h d i s c h a s b e e n  ( a p r o c e d u r e w h i c h t a k e s a p p r o x i m a t e l y 18 m i n u t e s f o r  GOES a n d 25 m i n u t e s  f o r GMS a n d METEOSAT), t h e s c a n n e r  retrace to the original 2 minutes).  starting position  S e e F i g u r e 2.2.  optics  ( i n approximately  FULL EARTH DISC  I  One infrared! sensor line  FIGURE 2.2  Assembly o f a VISSR Image. 8 v i s i b l e sensor l i n e s  Each scan l i n e i s composed o f and 1 i n f r a r e d  sensor l i n e .  One  scan l i n e r e p r e s e n t s a west t o each scan o f the e a r t h and each i s p o s i t i o n e d s e q u e n t i a l l y i n a north-south manner (Adapted from McKowan, 19 77).  1.8.  The  s i g n a l f r o m GOES-West i s s e n t i n i t i a l l y  t i o n a l Environmental Acquisition  S a t e l l i t e Service  (CDA) f a c i l i t y  including "stretching" the  ( S i n c e t h e i n f o r m a t i o n on t h e E a r t h  5 percent  o f an e n t i r e V I S S R s c a n l i n e ,  s i g n a l must be expanded b e f o r e - b e i n g n i z a b l e image). satellite  takes  up l e s s t h a n  that portion of the  assembled i n t o a  recog-  The s i g n a l i s t h e n t r a n s m i t t e d b a c k t o t h e  f o r broadcast  i n W a s h i n g t o n , D.C. quality  (NESS) C e n t r a l D a t a  a t W a l l o p s I s l a n d , V i r g i n i a , where  p r e l i m i n a r y processing occurs signal.  t o t h e Na-  telephone  t o t h e NESS C e n t r a l P r o c e s s i n g  Facility  From h e r e t h e i n f o r m a t i o n i s s e n t b y h i g h  l i n e t o s i x m a j o r d i s t r i b u t i o n c e n t r e s (San  F r a n c i s c o , Kansas C i t y , Washington, D.C, Anchorage) f o r f u r t h e r d i s t r i b u t i o n GOES-Tap p r o g r a m .  Miami, Honolulu,  to other  users  and  under t h e  ( F o r d e t a i l s o n GOES-Tap s e e A p p e n d i x I I I o f  C o r b e l l et. at., 1 9 7 7 ) .  Figure  2.3 shows t h i s d i s t r i b u t i o n  sche-  matically.  The  v o l u m e o f d a t a c o l l e c t e d b y t h e GOES s a t e l l i t e s f a r  exceeds t h e p r e s e n t  capabilities  transmitting data.  This has r e s u l t e d i n the s e l e c t i o n o f s m a l l  subareas o f the f u l l Earth  f o r p r o c e s s i n g , s t o r i n g and  d i s c image f o r a n a l y s i s a n d s u b s e -  q u e n t t r a n s m i s s i o n by l a n d l i n e t o t h e u s e r s .  These s u b a r e a s  a r e known as s e c t o r s a n d a few o f t h e t y p i c a l s e c t o r s i n V a n c o u v e r , B.C., a r e shown i n F i g u r e receiving station  2.4.  received  Of c o u r s e , w i t h  l o c a t e d i n t h e Vancouver areas  a  (as i s p r o p o s e d  0 ES  Users  ) ) I ) V / ) l t )  ) ) I V / / ) ) / ) / ) / / ) ) / t I'/  NESS CDA  NESS  NESS C E N T R A L  Wallops Is.,VA. Washington,D.C.  FIGURE 2.3  I f II  1 ) i > > ft  FACILITY  Washington, D . C .  Distribution  o f t h e GOES S i g n a l  t > > > >  }  20.  S e c t o r s Received a t the P a c i f i c Weather Centre ( a f t e r C o r b e l l et al.,  1977)  Visible  Sector  SA-1 SA-2 SB-6 UC-2  and  Infrared Sectors:  Centre P o i n t ( l a t ./Long.) 36°N/118°W 45°N/116°W 42 N/124°W 28°N/135°W  Resolution (km) 1 1 2 4  f o r 19 8 1 ) , o t h e r s e c t o r s o f l o c a l i n t e r e s t c o u l d be i n c l u d i n g the  f u l l Earth  or "close-ups" Popham and  Rich  Seymour et  al.  d i s c f o r a g l o b a l view of the  of t r o u b l e areas w i t h i n B r i t i s h  (19 77)  and  ronmental s a t e l l i t e s  MDA  (19 77)  give d e t a i l s of a  i n c l u d i n g GOES and satellite  METEOSAT.  data i s s t i l l  hardcopy photographs of the h a l f - h o u r l y v i s i b l e  low-cost  The  and  operation-  i n the  and  infrared  lies with  clouds, although  the i n f r a r e d images.  the emphasis i n  Figure  2.5  shows  e x a m p l e o f a v i s i b l e image f o r m GOES-West, w h i l e F i g u r e r e s p e c t i v e l y , show t y p i c a l u n e n h a n c e d and  images.  The  2.7,  the photo grey  d e t e c t e d by  and  infrared  surface  thunderstorm c l o u d tops)  Enhancing, then, increases t h e i r background.  An  contour  When t e m p e r a -  the VISSR are s m a l l i t i s  s i g n i f i c a n t c l o u d and  f o g , s t r a t u s and  and  s c a l e used to  i s g i v e n g r a p h i c a l l y i n F i g u r e 2.8.  ture gradients to recognize  enhanced  2.6  an  e n h a n c e m e n t scheme, t h a t i s , t h e r e l a t i o n s h i p b e -  t w e e n t e m p e r a t u r e and Figure  form of  i n f r a r e d s a t e l l i t e images have been  used to i d e n t i f y p r e c i p i t a t i n g  2.7  envi-  weather systems.  Both the v i s i b l e  t h i s study  station.  d i s t r i b u t i o n system f o r v a r i o u s  p r e s e n t a t i o n of these  views o f developing  weather,  Columbia.  (1975) d e s c r i b e a GOES V I S S R g r o u n d  r e c e i v i n g , a n a l y z i n g and  al  chosen,  features  difficult ( f o r example,  i n the i n f r a r e d  the c o n t r a s t between those  image.  features  i d e a l enhancement d i s t i n g u i s h e s a  l i m i t e d number o f f e a t u r e s and p r o v i d e s  as much d e t a i l as p o s s i -  b l e w i t h o u t m a k i n g t h e e n h a n c e d image t o o c o n f u s i n g .  There  are  FIGURE 2.5 A Typical Satellite Visible GOES-West.  Image (SB6 S e c t o r )  from  0045 31DC78 35E-1ZA 00622 22231 SB6  FIGURE 2.6 A T y p i c a l S a t e l l i t e I n f r a r e d Image (SB6 S e c t o r ) GOES-West.  from  24.  FIGURE  2.7  A T y p i c a l S a t e l l i t e E n h a n c e d I n f r a r e d Image (SB6 "EC"  E n h a n c e m e n t Scheme) f r o m GOES-West.  Sector,  2.5. DIGITAL  0 White  COUNT  51  102  153  r  1  1  r-  TEMPERATURE  204 ]—i  255 1  5  1  °C  FIGURE 2.8 The "EC" E n h a n c e m e n t Scheme w h i c h R e l a t e s T e m p e r a t u r e t o S p e c i f i c g r e y s h a d e s ( a f t e r H a e r i n g , 1978) Segment Number  Temperature Range ( C) to to to to  +37.3 +20.8 -13.2 -15.7  1 2 3 4  +56.3 +36.3 +20.3 +13.7  5  -16.2 t o -50 .2  6 7 8  -51.2 t o -60.2 -61.2 t o -70.2 -71.2 t o -110.2  R e a s o n f o r Segment  Enhancement  No s i g n i f i c a n t d a t a Land and Water W a t e r a n d Low C l o u d s B e n c h m a r k b e t w e e n Low a n d Medium L e v e l C l o u d s Medium a n d H i g h C l o u d C c ' o o l Season P r e c i p i t a t i o n ) C o n v e c t i v e C l o u d Tops C o n v e c t i v e C l o u d Tops C o l d e s t C l o u d Tops a n d S p a c e  a l a r g e number o f e n h a n c e m e n t schemes a v a i l a b l e , o n l y a few o f them a r e u s e d o p e r a t i o n a l l y . s c r i b e d i n d e t a i l i n C o r b e l l et al.  2.4  Other Sources o f S a t e l l i t e A number o f m e t e o r o l o g i c a l  evolved  These a r e d e -  (1977).  Information s a t e l l i t e systems have  each w i t h a d i f f e r e n t combination  In the United States there  although  o f sensor  and o r b i t .  a r e t h e NOAA, NIMBUS, TIROS, SMS/GOES,  DMSP, a n d STORMSAT e i t h e r o p e r a t i o n a l o r p r o p o s e d . systems a r e b e i n g  developed i n other  USSR, t h e E u r o p e a n n a t i o n s  countries, notably the  t h r o u g h ESA, and J a p a n .  b r i e f d i s c u s s i o n o f weather s a t e l l i t e s here, l i t e s have been o m i t t e d . determination  Although  they  of p r e c i p i t a t i o n areas,  i n real-time analyses exist i n geostationary  a t present  Parallel  I n the  microwave  are promising  sateli n the  they a r e o f l i t t l e use  b e c a u s e none a r e e x p e c t e d t o  o r b i t s u n t i l p o s s i b l y 19 85,  (Lovejoy,  1978) .  A d d i t i o n a l i n f o r m a t i o n o n t h e GOES s y s t e m i s c o n t a i n e d i n McKowan ( 1 9 7 7 ) , (1974).  Lienesch  C o r b e l l et a l . , (1977) a n d F o r d y c e et al., et a l . , (1975) d i s c u s s  b r a t i o n o f SMS i n f r a r e d o b s e r v a t i o n s . and  Spangler  t e Program  (19 74) (DMSP).  the accuracy  Vesely  and c a l i -  and Botzong  d e s c r i b e t h e Defense M e t e o r o l o g i c a l Fortuna  and Hambrick  p o l a r - o r b i t i n g system, w h i l e Hussey p o l a r - o r b i t i n g system.  (19 77)  (19 74)  Satelli-  (1974) d i s c u s s t h e NOAA describes  t h e TIROS-N  A p p l i c a t i o n s o f weather s a t e l l i t e  obser-  2:7.  v a t i o n s t o w a t e r r e s o u r c e s managers a r e d i s c u s s e d by et  al. , ( 1 9 8 0 ) ,  Miers  (1976).  1977;  Lovejoy  Gantry  McGinnis  a n d t o w e a t h e r s e n s i t i v e army o p e r a t i o n s b y Numerous a u t h o r s  (including G r i f f i t h  et  al.,  a n d A u s t i n ; 1979; L e t h b r i d g e , 1 9 6 7 ; G u r k a 1 9 7 6 ;  et al. , 19 76 ;  P u r d o m , 19 76 ;  C l a r k et al ., 19 80; a n d  Maddox, 19 80); h a v e i n d i c a t e d t h e p o t e n t i a l c a p a b i l i t i e s o f g e o stationary satellites ical such  (GOES) f o r o b s e r v i n g v a r i o u s  meteorolog-  p a r a m e t e r s o f u s e t o h y d r o l o g i s t s as w e l l as m e t e o r o l o g i s t s as w i n d s p e e d s , c l o u d c o v e r , a n d  albedo.  28.  CHAPTER I I I  A REVIEW OF  Since scientists in  the  S A T E L L I T E IMAGE PRECIPITATION ESTIMATION  first  h a v e b e e n i n t r i g u e d by  a s i n g l e image.  zation  and  The  of  a l s o be  d i s c e r n e d such  hurricanes, waves, and  as  the  cloud  sequence o f  these  images a day  lies  i n the  basis  f o r remote, o c e a n i c  n e t w o r k s may  be  t i o n a l means. in  satellite  cult and  t o use  and  sparse  Until  directly. the  i m a g e s , i n c l u d i n g some o f photographs, which serve ditions in and  and  space.  cloud  to r e v e a l these  types  I t i s an  ideal  weather i d e n t i f i c a t i o n  a time  the  satellite  on  where  and/  a  24-hour  observing conven-  information  contained  nature  Veltischchev  and  (19 73)  diffidiscuss  images i n w e a t h e r  anal-  t h e i r work i s a w e a l t h o f  satellite  the  satellite  as as  with,  f e a t u r e s by  been o f a q u a l i t a t i v e  In  could  mountain  power o f  obtained  areas  p o t e n t i a l of s a t e l l i t e  forecasting.  associated  The  or other  A n d e r s o n and  individual  development, decay  information  r e c e n t l y , much o f  images has  illustrate  ysis  too  to  large  Analysis of  a region.  vast s p a t i a l  organi-  j e t streams,  of s t r o n g wind shear.  o r movement o f w e a t h e r t h r o u g h  the  Other features  features  images i n d i c a t e s t h e  contained  from the  across  i n diameter.  thunderstorms, s q u a l l l i n e s , regions  clearly  c l o u d systems r a n g i n g  o r so  1960  the wealth of data  a thousand kilometers  1 kilometer  TIROS-1 i n  images showed v e r y  structure of  c y c l o n i c systems of clouds  p i c t u r e s r e t u r n e d by  very  e a r l i e s t weather  a catalogue  of v a r i o u s weather  seen from a s a t e l l i t e ' s reference using  vantage  for acquiring s k i l l  satellite  images.  in  conpoint cloud  Development of r a i n f a l l e s t i m a t i o n p r o c e d u r e s i n v o l v i n g s a t e l l i t e i m a g e r y has  p a r a l l e l e d the e v o l u t i o n of  sensors,  chiefly  (visible  and  titative  i n f o r m a t i o n f r o m s a t e l l i t e i m a g e r y was  satellite  t h o s e w h i c h s e n s e r a d i a t i o n i n two  thermal  infrared).  major bands  E a r l y work i n e x t r a c t i n g q u a n b a s e d on  finding  r e l a t i o n s h i p s between i n f r a r e d t e m p e r a t u r e and/or v i s i b l e n e s s and (19 73)  s u c h p a r a m e t e r s as p r e c i p i t a t i o n .  provide  q u e s up  Some s t u d i e s , f o r e x a m p l e , B a r r e t t ( 1 9 7 0 ) , i n -  areal statistics  of cloud cover  w i t h r e s p e c t to r a i n f a l l p r o b a b i l i t y b a s i s , while others perature with 1973). ed  Scherer  a b r i e f overview of s a t e l l i t e estimation t e c h n i -  t o 1973.  v e s t i g a t e d the  M a r t i n and  bright-  (1973) and  ( G e r r i s h , 1970, Follansbee  and  B a r r e t t ' s method f o r e s t i m a t i n g d a i l y  s o l e l y on r a i n - p r o d u c i n g  cloud types  and  Davis  cumulus c o n g e s t u s ) .  and  and  satellite  Follansbee,  (cumulonimbus,  nimbostratus,  (19 72)  have used  precipitation including  - Environmental  once-daily Science  images.  Another approach evolved which used c l o u d b r i g h t n e s s key  variable i n estimating convective  S u o m i , 1971; 19 72)  S i k d a r , 1972) .  tested brightness  adapt-  concentrating  s n o w f a l l o v e r mountainous r e g i o n s o f Montana u s i n g  Services Administration)  a n d / o r tem-  O l i v e r (1975)  Serebreny  Survey S a t e l l i t e  type  rainfall,  a s i m i l a r approach f o r e s t i m a t i n g t o t a l  ESSA ( E n v i r o n m e n t a l  cloud  i n t e n s i t y on a m o n t h l y  c o r r e l a t e d c l o u d top b r i g h t n e s s  24-hour r a i n f a l l  Follansbee  and  and  precipitation  I n f a c t , M a r t i n and  enhancement o f A T S - I I I  as  (Sikdar  Suomi  a and  (1971,  (Applications  30.  Technology S a t e l l i t e  - I I I ) images w i t h r a d a r images t o  i s o l a t e areas o f intense convection.  T h i s i s s i m i l a r t o an  a p p r o a c h d e v e l o p e d by Woodley a n d Sancho  (19 71) w h i c h was  f u r t h e r d e v e l o p e d b y W o o d l e y et al., (1972) a n d G r i f f i t h et al.,  (1976) f o r e s t i m a t i n g r a i n f a l l i n F l o r i d a .  In of  o r d e r t o t a k e advantage o f t h e 24-hour  i n f r a r e d i m a g e r y , S c h e r e r a n d Hudlow  availability  (19 71) d e v e l o p e d a  t e c h n i q u e f o r t r a n s f o r m i n g minimum c l o u d t o p a r e a s i n t o p r o b able  r a d a r echo areas and hence, by a s t a t i s t i c a l model, t o  rainfall  3.1  amounts.  GOES R a i n f a l l E s t i m a t i o n These i n i t i a l  Techniques  s t u d i e s formed t h e background f o r t h e  emergence o f t h r e e groups i n t h e U n i t e d S t a t e s :  Woodley/Grif-  fith's  group a t t h e N a t i o n a l H u r r i c a n e and E x p e r i m e n t a l Meteor-  ology  Laboratory  (NHEML) i n F l o r i d a , t h e U n i v e r s i t y o f W i s c o n -  sin  (UW) g r o u p , a n d S c o f i e l d / O l i v e r ' s g r o u p i n W a s h i n g t o n ,  who  have worked towards a r a i n f a l l e s t i m a t i o n p r o c e d u r e u s i n g  visible  and i n f r a r e d images  f r o m t h e GOES s a t e l l i t e s .  group's approach i s d i s c u s s e d b r i e f l y  3.1.1  i n the following  D.C.,  Each sections.  The NHEML T e c h n i q u e The NHEML t e c h n i q u e i s b a s e d o n t h e o b s e r v a t i o n t h a t a r e a s  of  a c t i v e deep c o n v e c t i o n a n d r a i n f a l l i n t h e t r o p i c s  b r i g h t e r on v i s i b l e  images  appear  a n d c o l d e r on i n f r a r e d images  than  i n a c t i v e areas.  A T S - I I I a n d GOES i m a g e s w e r e c a l i b r a t e d w i t h  r a d a r d a t a from t h e south o f F l o r i d a .  The e m p i r i c a l  relation  NHEML d e v e l o p e d i s  r  Where r  v  =  I  A  e  3  '  1  3  i s t h e v o l u m e r a i n r a t e (m / h ) , I i s t h e r a i n 3 2 r a t e p e r u n i t a r e a ((in /h)/km ) a n d i s a f u n c t i o n o f t h e r a d a r 2 v  echo a r e a growth t r e n d ) , and A which  g  i s t h e r a d a r echo area  i s d e f i n e d b y a t h r e s h o l d r a i n r a t e o f 1 mm/h.  d e r i v e d f o r any g e o g r a p h i c are a v a i l a b l e rain) .  '1' c a n be  area provided appropriate radar  (which l i m i t s i t s u s e f u l n e s s i n mountainous  The r a d a r e c h o a r e a , A , i s d e t e r m i n e d e  r a d a r echo a r e a A . g  A  c  i n F l o r i d a and  R e s u l t s were g e n e r a l l y good a l t h o u g h t h e a u t h o r s n o t e d  1978).  that  v a r i e d w i t h the t o t a l p e r i o d o f c a l c u l a t i o n and  w i t h t h e area o f c l o u d cover examined. ed  area  as w e l l as f o r s i x h u r r i c a n e s ( G r i f f i t h et al .,  t h e i r accuracy  ter-  T e s t i n g o f t h i s t e c h n i q u e has been  c a r r i e d o u t f o r a number o f c o n v e c t i v e s t o r m s Venezuela  data  on a c l o u d b y  c l o u d b a s i s from e m p i r i c a l r e l a t i o n s between s a t e l l i t e and  (km )  accuracy w i t h d i g i t a l  d a t a and,  They a n t i c i p a t e d  increas-  i n a p a p e r b y W a t e r s et al.,  (1977), p r e s e n t t h e i r f i r s t e x p e r i m e n t a l r e s u l t s u s i n g  digital  geostationary data t o assess t h e r a i n f a l l p o t e n t i a l o f s e l e c t e d hurricanes. 3.1.2  The UW T e c h n i q u e  L i k e t h e w o r k o f t h e NHEML g r o u p , t h e UW t e c h n i q u e r e l a t e s 2 t h e v o l u m e t r i c r a i n r a t e t o c l o u d a r e a , A(m ) a n d r a d a r e c h o  area  ( S t o u t et a l . , 19 77,  explicitly dA (  I n a d d i t i o n , t h e UW  2 (m / s ) ) i n t h e r e l a t i o n f o r t h e r a i n f a l l  the constants a squares  Q  o  a  =  A  +  a  r a t e R:  i H  3  -  2  (m/s) a n d a ^ (m) a r e d e t e r m i n e d b y a l e a s t  f i t from p a i r s o f s a t e l l i t e  a r e a and r a d a r echo  (determined a t v a r i o u s r e f l e c t i v i t y  slightly  technique  i n c l u d e s t h e r a t e o f change o f t h e c l o u d a r e a  R  rate  19 79) .  d i f f e r e n t values depending  r e d images a r e b e i n g  rain  l e v e l s ) , and have  on w h e t h e r v i s i b l e o r i n f r a -  used.  T h i s t e c h n i q u e i s a v a r i a n t o f t h e NHEML t e c h n i q u e a n d as s u c h was d e v e l o p e d  t o provide estimates o f r a i n f a l l  from  p r e c i p i t a t i n g cumulonimbus c e l l s o v e r t h e t r o p i c a l N o r t h tic.  The a u t h o r s s u g g e s t  s k i l l e d meteorologists.  Atlan-  t h a t t h e s e c e l l s be i d e n t i f i e d by They r e c o g n i z e t h e p o t e n t i a l f o r e r r o r s  i n t h e i r t e c h n i q u e i f used o u t s i d e t h e t r o p i c a l N o r t h especially i f convective cells the t o t a l r a i n f a l l  large  and n o t e  Atlantic,  a r e n o t the major c o n t r i b u t o r s t o  that their  coefficients, a , a ^ Q  w o u l d need t o be r e d e f i n e d .  3.1.3  The S c o f i e l d / O l i v e r  Technique  O l i v e r and S c o f i e l d  (1976) a n d S c o f i e l d a n d O l i v e r  have d e v e l o p e d  an o p e r a t i o n a l t e c h n i q u e w h i c h  gives half-hourly  o r h o u r l y r a i n f a l l e s t i m a t e s f r o m GOES i n f r a r e d a n d h i g h tion visible  images.  (1977a)  I ti s a decision hierarchical  resolu-  approach  b a s e d on t h e i d e n t i f i c a t i o n o f c e r t a i n c l o u d p r o p e r t i e s f o r deep c o n v e c t i v e p r e c i p i t a t i o n s y s t e m s o c c u r r i n g i n t r o p i c a l a i r masses w i t h h i g h e s s e n t i a l l y developed and  papers  cases  (-80°C) t r o p o p a u s e s . f o r the southern  technique  ( S c o f i e l d , 1976  S c o f i e l d and O l i v e r ,  a,b;  1978a,b;  continental United  1980)  a l . , 1980 ;  show t h e u s e f u l n e s s o f t h e  been m o d i f i e d s l i g h t l y f o r a number o f  s i t u a t i o n s over Venezuela  ( I n g r a h a m et  and  Colombia  S c o f i e l d / O l i v e r technique  The  subsequently two  cells,  the estimates of r a i n f a l l .  factors fac-  the p o s i t i o n  As w e l l , a number o f  other pres-  of merging  l i n e s , i n order to improve  These f a c t o r s a r e a r r a n g e d  in a  c i s i o n t r e e or f l o w c h a r t which =allows the user to determine appropriate r a i n f a l l  of  as t h e  o r absence o f o v e r s h o o t i n g t o p s , the importance and m e r g i n g c o n v e c t i v e c e l l  em-  (cumulonimbus)  adds  c h a r a c t e r i s t i c s o f cumulonimbi are c o n s i d e r e d , such ence  1977).  most i m p o r t a n t  t o r s a r e t h e r a t e o f g r o w t h o f t h e a n v i l and the cumulonimbus under the a n v i l .  storm  s t a r t s w i t h the s i m p l e  and  which improve t h i s r e l a t i o n s h i p .  and  al.,  r e l a t i o n s h i p t h a t the h i g h e r the top of the  c l o u d , the h e a v i e r the r a i n f a l l ,  and  procedure.  used to s u c c e s s f u l l y e s t i m a t e r a i n f a l l  pirical  States  S c o f i e l d and O l i v e r , 19 7 5 ,  S c o f i e l d et  S c o f i e l d / O l i v e r t e c h n i q u e has  The  was  d e s c r i b i n g i t s a p p l i c a t i o n i n a number o f v a r i e d  1977b," S c o f i e l d and W e i s s , 1976 ;  The  The  amount f o r a p a r t i c u l a r p o i n t .  three major steps i n the computation  process:  There  dethe are  34.  A - I d e n t i f i c a t i o n of the convective  system and  determination o f the a c t i v e r a i n producing of the  the  portion  system,  B - The  initial  estimation of p r e c i p i t a t i o n using  c l o u d t o p t e m p e r a t u r e s as g i v e n by t h e e n h a n c e d  the  infra-  r e d imagery and e m p i r i c a l r a i n f a l l - t e m p e r a t u r e - c l o u d growth  relations,  C - C o r r e c t i o n o f the i n i t i a l p r e c i p i t a t i o n b y t h e use o f a m p l i f i c a t i o n ic  behaviour  example,  convective  f a c t o r s b a s e d on t h e dynam-  of the convective  overshooting cell  estimates  c l o u d system ( f o r  tops, merging  c e l l s , or  merging  lines).  The i d e n t i f i c a t i o n s t e p i s a c c o m p l i s h e d b y f o l l o w i n g a set  of diagnostic indices i n c l u d i n g :  1 - Identification of a)  convection:  shape o f the c l o u d  (circular, oval, carrot-  shaped) f r o m t h e i n f r a r e d and v i s i b l e  b)  depth of c o n v e c t i o n - v e r t i c a l o f the c l o u d , from the enhanced  images  development infrared  images  2 - I d e n t i f i c a t i o n o f the a c t i v e p o r t i o n o f the system.  convective  a)  area of s t e e p e s t temperature g r a d i e n t , enhanced  b)  infrared  images;  a r e a o f l e a s t downwind e x p a n s i o n a l o f t , the enhanced  d)  images;  t e x t u r e and b r i g h t n e s s o f t h e c l o u d t o p , f r o m the v i s i b l e  c)  from  infrared  from  images;  l o c a t i o n w i t h r e s p e c t t o the upwind p o r t i o n the c l o u d a n v i l ,  from the v i s i b l e  of  images.  F i g u r e 3.1  shows a s t r e a m l i n e d v e r s i o n o f t h e S c o f i e l d / O l i v e r  flowchart,  (Ingraham  et a l . , 1 9 7 7 ) .  T h e r e a r e a number o f d i f f i c u l t i e s w h i c h become r e n t a f t e r using the S c o f i e l d / O l i v e r technique. shaped local  cloud c e l l s  appa-  Irregularly  c a n n o t be a d e q u a t e l y i n c l u d e d .  Clouds w i t h  areas o f s u b s i d e n c e ("holes") w i t h i n t h e i r b o u n d a r i e s are  also a problem.  ( I t i s thought that these "holes" w i t h i n  the  cloud boundaries i n d i c a t e the c o l l a p s e of s h o r t - l i v e d overshooting tops). fall  Some o f t h e f a c t o r s w h i c h p r o d u c e h i g h  r a t e s d e p e n d upon a c c e s s t o t h e h i g h (1 km)  rain-  resolution  vis-  ible  images w h i c h a r e r a r e l y a v a i l a b l e a t the o p e r a t i o n a l u s e r *  level  ( e x c e p t i f he h a s a c c e s s t o h i s own  The  receiving  i d e n t i f i c a t i o n of the a m p l i f i c a t i o n parameters  satellite  i m a g e s i s v e r y much d e p e n d e n t  station). from the  on t h e o b s e r v e r a n d h i s  FIGURE 3.1 F l o w c h a r t and T a b l e f o r t h e E s t i m a t i o n o f P o i n t R a i n f a l l the  Scofield/Oliver  Technique  ( a f t e r Ingraham et al.,  from GOES Images  Using  1977)  LEGEND: A - RECOGNITION OF ACTIVE PORTION OF DEEP CONVECTION  REFER TO SECTION 3.1.3  PRECIPITATION ESTIMATES (mm) CONTOUR COLOR  I  NO  YES  \ CLOUD GROWTH:  GROWTH OF CLOUD IN A HALF HOUR IS SUCH THAT THE COLDEST CONTOUR DIAMETER „ expands 2/3 lat. is >l/3° l a t . but expands 12/3 1l a t . expands 1.1/3 lat. remains t h e same contracts >  0.25 mm  I ? TABLE ON RIGHT  I UNCORRECTED ESTIMATE C - CORRECTIONS  FINAL ESTIMATE  TABLE:  1975  1  2  3  =  DARK GREY 12.7 3.1 3.8 2.5 0.3 LIGHT GREY 15.110.2 5.1 3.8 0.8 BLACK  25.4 15.2 7 .6 5.1 1.3  WHITE  38.1 19 .1 ID. 17.6 2.0  1976 LIGHT GREY 10.1 5.1 3.82.5 0.3 DARK GREY  22.9 12.7 6.45.1 1.3  BLACK  27.9 17 .8 10.2 7.6 2.0  CORRESTIONS FOR LOCAL OCCURRENCE OF WHITE 1 overshooting top 2 merging t h u n d e r s t o r m s 3 convective cloud l i n e mergers FOR EACH OF THESE ADD 12.7 (mm) TO UNCORRECTED ESTIMATE TO GET FINAL ESTIMATE  38.1 22.9 12.7 10.12.5  skill que  at satellite  like  image i n t e r p r e t a t i o n .  the others  As w e l l , t h i s t e c h n i -  d i s c u s s e d , does n o t e x p l i c i t l y  allow f o r  t h e movement o f t h e s t o r m c e l l o v e r a r e g i o n .  But,  e v e n more i m p o r t a n t l y , i t i s r e c o g n i z e d  t h e r e w o u l d be g r e a t technique ing-  difficulty  that  i n t r a n s f e r r i n g t h e use o f t h i s  t o more n o r t h e r l y l a t i t u d e s w i t h d i f f e r e n t  raint-produc-  c l o u d r e g i m e s s i n c e i t was d e r i v e d e m p i r i c a l l y f o r deep  convective  c l o u d systems i n t r o p i c a l a i r masses.  the S c o f i e l d / O l i v e r technique  Nevertheless,  does i n d i c a t e w h i c h c l o u d t o p p a r a -  meters a r e c r u c i a l t o t h e e s t i m a t i o n o f r a i n f a l l , and t h i s bespeaks the s k i l l and  determining  3.2  investigators i n observing  cumulonimbi  a workable e m p i r i c a l r e l a t i o n s h i p .  Summary All  focus  o f these  on d e t e r m i n i n g  systems. to  o f these  the r a i n f a l l  This i s understandable  identify  Rodenhius  early precipitation estimation  and they  (19 77)  f r o m deep t r o p i c a l  t i v e r a i n f a l l estimates  self-contained.  b a s e d on v i s i b l e  They n o t e t h a t a l t h o u g h  image b r i g h t n e s s ces i n r a i n f a l l or cold clouds.  o r coldness  Cheng a n d  r a i n r a t e s and s a t e l l i t e  convec-  cloud brightness or  i n f r a r e d t e m p e r a t u r e u s i n g r e l a t i o n s s u c h as t h o s e here.  convective  because cumulonimbi are easy  are reasonably  compare r a d a r  techniques  presented  r a i n f a l l r a t e s and s a t e l l i t e  are related, quantitative differen-  c a n n o t b e e x p l a i n e d as b e i n g However, i n s u g g e s t i n g  due t o e i t h e r b r i g h t  t h a t s p a t i a l and t e m p o r a l  38.  averaging ciency  would a l l e v i a t e t h i s , t h e y m i s s e d the o b v i o u s d e f i -  common t o t h e s e t e c h n i q u e s :  cal basis  r e l a t i n g the  (brightness, coldness,  satellite  t h e n e e d f o r a more p h y s i image c l o u d  r a t e o f growth) t o the  characteristics rainfall  produced.  CHAPTER I V  THE MODEL USED TO DESCRIBE P R E C I P I T A T I N G CLOUDS  Previous  i n v e s t i g a t o r s ( S c o f i e l d / O l i v e r , UW, a n d NHEML)  identified i n their istics  techniques  the c r u c i a l  cloud top character-  t o b e c o n s i d e r e d when e s t i m a t i n g p r e c i p i t a t i o n a n d t h e y  developed q u a n t i t a t i v e r e l a t i o n s h i p s f o r use w i t h s a t e l l i t e i m ages b u t t h e i r s t u d i e s d i d n o t e x t e n d t o w h a t t h e s e c h a r a c t e r i s t i c s were r e v e a l i n g about t h e dynamics o f t h e c l o u d .  Hence,  t h e r e was no t h e o r e t i c a l b a s i s o n w h i c h t h e i r t e c h n i q u e s be m o d i f i e d  4.1  t o encompass s t o r m c o n d i t i o n s o v e r B r i t i s h  Precipitation i nBritish  Tropical  Columbia. (mT)  o f a i r mass w h i c h b r i n g  Warm, h u m i d a n d r e l a t i v e l y s t a b l e  Columbia i n w i n t e r i n the  o f f r o n t a l waves and g i v e s r i s e t o m a j o r  On t h e o t h e r h a n d , s h o w e r y p r e c i p i t a t i o n i s o f t e n with Maritime  Arctic  landmasses o f North  Maritime  rainfalls.  associated  (mA) a i r as i t i s warmed a n d m o i s t e n e d  during i t s r e l a t i v e l y s h o r t t r i p over the North  lumbia.  Maritime  ( o r , more o f t e n i n t h e u p p e r l e v e l s o f an o c c l u d e d  warm s e c t o r )  the A r c t i c  rain  .a i r with i t s o r i g i n s i n the tropics t o the  southwest o c c a s i o n a l l y reaches B r i t i s h warm s e c t o r  Columbia.  Columbia  There a r e t h r e e main types to B r i t i s h  could  Polar  America  Pacific  from  a n d A s i a t o B r i t i s h Co-  (mP) a i r h a s t h e same o r i g i n s as mA a i r  but w i t h a longer  t r a j e c t o r y over t h e ocean a f t e r which i t  reaches t h e coast  f r o m a more w e s t e r l y  direction.  The  charac-  40.  teristics  o f p r e c i p i t a t i o n w i t h i n t h i s a i r mass a r e  d i a t e b e t w e e n mT  The  interme-  and mA a i r .  mountain ranges of B r i t i s h  b a r r i e r to the eastward  Columbia are a  formidable  movement o f a i r f r o m t h e P a c i f i c .  The  tendency of the a i r to produce r a i n i s i n c r e a s e d through i n g and annual is  t h e w i n d w a r d s l o p e s r e c e i v e among t h e w o r l d ' s amounts o f p r e c i p i t a t i o n .  hot  The  i n t e r i o r of B r i t i s h  largest  c l i m a t e along the  c h a r a c t e r i z e d b y m i l d , h u m i d w i n t e r s a n d warm b u t  summers. ly  The  lift-  coast  not  Columbia, which l i e s  hot  effective-  i n t h e r a i n shadow o f t h e c o a s t a l m o u n t a i n s , i s n o t e d and  storm,  fairly and  d r y summers p u n c t u a t e d  for cold winters with  by  the o c c a s i o n a l  for  thunder-  snow.  Weather systems a f f e c t i n g B r i t i s h Columbia, i n g e n e r a l , o r i g i n a t e t o t h e w e s t as d e p r e s s i o n s  over  t h e o c e a n and  are  u s u a l l y i n a m a t u r e s t a t e o f d e v e l o p m e n t and w e l l o c c l u d e d f o r e they reach t h e mP  the coast.  P e r i o d s o f showery weather w i t h i n  a i r mass a l t e r n a t e w i t h r a i n y s p e l l s  and o c c l u s i o n s .  d u r i n g t h e summer months  (June t h r o u g h  fewer,  smaller i n size.  of these  disturbances  rather f i l l the  and  along the f r o n t s  This p r e v a i l s throughout the y e a r ,  l e s s i n t e n s e , and  g e n e r a l l y do n o t  stagnate  be-  over  although  August) the storms The  are  a c t u a l centres  cross the coast  but  the A l e u t i a n s or A l a s k a w i t h  a s s o c i a t e d f r o n t s c r o s s i n g the coast f u r t h e r south.  only The  i n t e r i o r plateau region receives appreciable snowfall i n winter  f r o m t h e s e e a s t w a r d m o v i n g f r o n t s , w h i l e i n summer much o f t h e rainfall  originates  from t h u n d e r s t o r m s .  etrate- f a r into southern B r i t i s h m a i n l y c l e a r and s u n n y . British  The  The  Columbia  f r o n t s do n o t  leaving this  pen-  region  annual p a t t e r n of p r e c i p i t a t i o n i n  Columbia i s c o n t r o l l e d c h i e f l y by the p o s i t i o n o f the  North P a c i f i c s u b - t r o p i c a l a n t i c y c l o n e which migrates  seasonally.  D u r i n g t h e summer months i t i s c e n t e r e d o f f t h e c o a s t a n d  de-  flects  storm t r a c k s northwards, w h i l e d u r i n g the w i n t e r i t  shifts  f u r t h e r s o u t h w i t h t h e r e s u l t t h a t t h e s t o r m t r a c k s move  southwards  In  b r i n g i n g more s t o r m s i n t o t h e p r o v i n c e .  summary, p r e c i p i t a t i o n i n B r i t i s h  most e x c l u s i v e l y  from a i r of P a c i f i c  origin  Columbia  and a n n u a l  t a t i o n i s h i g h a l o n g the c o a s t d i m i n i s h i n g towards and deep v a l l e y of  falls a l -  the  precipiinterior  f l o o r s i n c r e a s i n g again along the windward slopes  t h e Rocky M o u n t a i n s .  R a i n and snow f a l l  chiefly i n association  w i t h o c c l u s i o n s a n d f r o n t s , e x c e p t f o r summer t h u n d e r s t o r m t r i b u t i o n s i n the i n t e r i o r of the p r o v i n c e . of  The  con-  distribution  t h i s p r e c i p i t a t i o n i s h i g h l y s u b j e c t to the l o c a l e f f e c t s  relief.  4.2  (Kendrew and K e r r , 19 55; H a r e ,  The  196 3;  H e t h e r i n g t o n , 19 76) .  Model  A p h y s i c a l c o n c e p t u a l model used t o e s t i m a t e such f r o m s a t e l l i t e i m a g e s was mospheric ing''  of  conditions  d e v e l o p e d by  first  rainfall  c o n s i d e r i n g the a t -  required for precipitation,  and t h a n  t h e f l u x o f w a t e r t h r o u g h a column o f a i r i n the  examin-  atmosphere.  The  e x p r e s s i o n f o r e s t i m a t i n g t h e r a i n f a l l was  derived to  take advantage o f the i n f o r m a t i o n about the motions opment  4.2.1  o f c l o u d s y s t e m s p r o v i d e d by s a t e l l i t e  images.  Rain-Producing Conditions Mason (19 7 1 , 19 75)  i n h i s w o r k on c l o u d p h y s i c s , d i s c u s -  ses the c o n d i t i o n s necessary are:  and d e v e l -  f o r the f o r m a t i o n o f r a i n ,  a s o u r c e o f m o i s t a i r ( l i k e t h e mP  British  Columbia),  a i r which  a mechanism f o r l i f t i n g  mountains or along f r o n t s )  which  flows  into  (as p r o v i d e d b y  and h e n c e c o o l i n g t h e a i r s o t h a t  c o n d e n s a t i o n c a n o c c u r , a n d a s o u r c e o f n u c l e i on w h i c h  the  moisture i n t h e a i r c a n c o n d e n s e t o f o r m c l o u d d r o p l e t s .  If  t h e d r o p l e t s h a v e enough t i m e t o r e a c h a s i z e w h e r e t h e i r  ter-  minal velocities  in  exceed  the l i f t i n g or u p d r a f t v e l o c i t i e s  the c l o u d , then they w i l l f a l l ground,  as r a i n and w i l l r e a c h  p r o v i d e d they are not e n t i r e l y evaporated  the  during  their  des c e n t .  S i n c e t h e a r e a l e x t e n t , i n t e n s i t y , and p r e c i p i t a t i n g c l o u d system cal  a i r motions,  two  types depending  ( R o g e r s , 19 7 6 ) .  i s c o n t r o l l e d l a r g e l y by  r a i n f a l l c a n be on w h i c h  Widespread,  the  verti-  d i s t i n g u i s h e d as b e i n g one  of  l i f t i n g mechanism i s dominant continuous  u s u a l l y f o u n d on t h e c o a s t o f B r i t i s h with  l i f e t i m e of a  l a r g e s c a l e ascent produced  by  r a i n f a l l , of the  Columbia,  i s associated  f r o n t s , topography,  s c a l e low l e v e l h o r i z o n t a l convergence.  type  or  large  L o c a l i z e d showery p r e -  c i p i t a t i o n , o f the type u s u a l l y o c c u r r i n g i n the i n t e r i o r o f B r i t i s h Columbia cumulus-scale  d u r i n g t h e summer m o n t h s , i s a s s o c i a t e d w i t h  convection i n unstable a i r .  Regardless o f the p a r t i c u l a r v e r t i c a l motion,  t h e a i r cannot  l i f t i n g mechanisms c a u s i n g  continue to r i s e  In t h e case o f major storms, t h e tropopause t h e u p w a r d movement o f t h e a i r a n d a t t h i s spread out horizontally.-  which  a c t s as a l i m i t t o l e v e l t h e a i r must  The r i s i n g a i r i s r e p l a c e d by a i r  converging a t lower l e v e l s . mass c o n v e r g e n c e  By c o n t i n u i t y t h e r a t e o f a i r  a t lower l e v e l s must e q u a l t h e r a t e o f r i s e  i n t u r n must e q u a l t h e r a t e o f d i v e r g e n c e  at upper l e v e l s motion  indefinitely.  ( f o r example, through  (or spreading)  the tops o f c l o u d s ) .  The  o f a i r w i t h i n a t y p i c a l s t o r m i s shown s c h e m a t i c a l l y i n  F i g u r e 4.1.  I t h a s b e e n g e n e r a l l y n o t e d t h a t s e v e r e w e a t h e r phenomena o f t e n occur w i t h areas o f upper l e v e l d i v e r g e n c e lower l e v e l convergence), McNulty,  (Beebe a n d B a t e s , 1 9 5 5 ; H o u s e , 1 9 5 8 ;  1977; and S c h a e f e r , 1977).  several investigators  the v e r t i c a l v e l o c i t y  ( t h a t i s , t h e low l e v e l cloud).  Danard  During the e a r l y  (Cressman, 1954;  t r i e d t o estimate the r a i n f a l l ing  (and a s s o c i a t e d  Byers  1950's  a n d B r a h a m , 1948)  r a t e o f thunderstorms  by d e t e r m i n -  from t h e h o r i z o n t a l n e a r - s u r f a c e winds  convergence  o f a i r i n t o the base o f the  ( 1 9 7 5 , 1978) u s e d a s i m i l a r a p p r o a c h  to yield  e s t i m a t e s o f t h e 2 4 - h o u r r a i n f a l l amounts f o r s o u t h e r n Columbia.  A l t h o u g h t h e y w e r e a b l e t o make r e a s o n a b l e  British estimates  At  FIGURE  time Aw  t  At time t +At A w +dw  4.1  A Column o f A i r B e t w e e n t h e L e v e l s z a n d z+dz a t Times t a n d t + d t  for a  few s t o r m s ,  t h e t e c h n i q u e was n o t c o n s i d e r e d  o p e r a t i o n a l l y due t o t h e d i f f i c u l t y near-surface winds.  i n measuring o r e s t i m a t i n g  I t was a l s o known t h a t t h e v e r t i c a l  t y c o u l d be determined rising  feasible  veloci-  i f t h e h o r i z o n t a l winds a t the top o f the  column c o u l d be measured.  c u l t t o do i n p r a c t i c e .  B u t t h a t was e v e n more  diffi-  Now, h o w e v e r , h o r i z o n t a l d i v e r g e n c e o f  t h e a i r mass c a n b e e s t i m a t e d f r o m s u c c e s s i v e i m a g e s o f c l o u d tops  as s e n s e d  as GOES.  by g e o s t a t i o n a r y m e t e o r o l o g i c a l s a t e l l i t e s  A d l e r a n d Fenn  such  (19 7 9 a , b) h a v e s u c c e s s f u l l y u s e d t h e  approach t o estimate t h e v e r t i c a l v e l o c i t i e s o f thunderstorms though n o t t o e s t i m a t e t h e r a i n f a l l s theory f o r determining of c l o u d tops  4.3  The M o d e l  rainfall  from t h e h o r i z o n t a l  divergence  Equations  c i p i t a t i o n r a t e from a  2 - t h e momentum  a r e needed t o s o l v e f o r t h e p r e -  storm:  1 - the atmospheric  thermodynamics  equations  equations  3 - the continuity  equation.  s o l u t i o n o f t h e above t h r e e t y p e s o f e q u a t i o n s  g i v e n t h e complex nature o f atmospheric  i s difficult  motions and t h e l i m i t e d  data a v a i l a b l e t o describe these motions, tions  The  as s e e n f r o m GOES i m a g e s i s g i v e n b e l o w .  Three s e t s o f equations  The  from these storms.  al-  u n l e s s v a r i o u s assump-  c a n b e made t o s i m p l i f y t h e e q u a t i o n s .  46.  4.3.1  The For  A t m o s p h e r i c Thermodynamics E q u a t i o n s an i d e a l g a s t h e e q u a t i o n o f s t a t e  4.1  pa = RT and t h e f i r s t  law o f  thermodynamics o  4.2  H d t = c d T + pda v  r e l a t e t h e p r e s s u r e p and s p e c i f i c volume a t o t h e t e m p e r a t u r e T of the a i r . per  o  H i s t h e r a t e a t w h i c h e x t e r n a l h e a t i s added  u n i t mass o f a i r ,  c o n s t a n t volume.  and c  The f i r s t  v  i s the s p e c i f i c heat of a i r a t law o f thermodynamics,  e q u a t i o n 4.2,  s t a t e s t h a t t h e e x t e r n a l h e a t added t o t h e a i r from such p r o c e s ses  as c o n d e n s a t i o n , r a d i a t i o n a n d c o n d u c t i o n i s e q u a l t o t h e  c h a n g e i n i n t e r n a l e n e r g y o f t h e a i r mass  (c dT) p l u s v  done by t h e a i r mass o n i t s s u r r o u n d i n g s ( p d a ) .  t h e work  I f no e x t e r n a l  h e a t i s a d d e d , H = 0, t h e n t h e m o t i o n o f t h e a i r mass i s s a i d to  be a d i a b a t i c .  F o r m i d l a t i t u d e s y n o p t i c s c a l e systems the  e x t e r n a l h e a t i n g term H d t i s s m a l l i n comparison w i t h t h e o t h e r terms and hence t h e system motions a r e c o n s i d e r e d t o be approximately adiabatic. a l o n g w i t h c^ = c  v  The e q u a t i o n o f s t a t e , e q u a t i o n 4.1,  + R, w h e r e Cp i s t h e s p e c i f i c h e a t a t c o n -  s t a n t p r e s s u r e , c a n be u s e d t o r e w r i t e t h e f i r s t dynamics  law o f thermo-  as H d t = c dT - adp  4.3  The  c h a n g e i n t e m p e r a t u r e w i t h p r e s s u r e c a n t h e n be g i v e n as  _ H d t c dp  +  J  c  p  T h i s r e s u l t ' w i l l be u s e d  L p  l a t e r t o r e l a t e t h e change i n t e m p e r -  ature  t o t h e change i n a l t i t u d e .  4.3.2  The Momentum The  d T dp  =  Equations  changes i n t h e v e l o c i t y  f i e l d w i t h t i m e a r e g i v e n by  t h e momentum e q u a t i o n s w r i t t e n i n s p h e r i c a l c o o r d i n a t e s u s i n g Holton's  du dt  (19 7 2 , p2 8)  =  notation  u v t a n j , . uw _ 1 | £ a a p 3x  +  2  Q  v  s  i  n  ^  _  2 n w c o S ( ( )  +  F  x  4  .  5  2 dv - u tanc}) vw 1 3p -rr - — - — - 2fiusin<b+Fy, dt a a p ay T  2  d w U + V jr = at a  2  c  A n 4.7  13p , o« ^ , - — r*- - g + 2nucoscp + F z p 3 z: _  where u, v , w a r e t h e e a s t w a r d , n o r t h w a r d of  „ 4.6  1  and v e r t i c a l  t h e v e l o c i t y , a i s t h e r a d i u s o f t h e E a r t h , cj> i s t h e l a t i t u d e ,  p i s the density, p i s the pressure, n i s the angular of  components  t h e E a r t h , and F x , Fy and Fz a r e t h e e a s t w a r d  (y),  and v e r t i c a l  ( z ) components o f f r i c t i o n .  velocity  (x) , n o r t h w a r d  Holton  c h a p t e r 2, s e c t i o n 4) u s e s s c a l e a n a l y s i s t o r e d u c e  (1972,  t h e above  e q u a t i o n s t o t h o s e below by n e g l e c t i n g t h o s e terms w i t h o r d e r s of  m a g n i t u d e l e s s t h a n 10  -4  m/s  -2  48.  /  du dt  *  dv dt 1  p  - 2nusin<() - -  |E  4.9  3y  p  P 9z  4.8  3X  3  p  Equation  4.10  4 .10  ^  i m p l i e s t h a t motions i n s y n o p t i c s c a l e systems  a p p r o x i m a t e l y h y d r o s t a t i c and be  determined  directly  tinuity  4/i 3. 3  cannot  f r o m t h e v e r t i c a l momentum e q u a t i o n .  Since the v e r t i c a l motion t i o n of r a i n f a l l ,  t h a t the v e r t i c a l v e l o c i t y  are  i s of primary  i t m u s t be  determined  i n t e r e s t i n the indirectly  estima-  from the  con-  equation.  The  Continuity Equation  The  continuity  equation 1 ±  dP HT. + v -V = 0  4.11  dt  p  s t a t e s t h a t the f r a c t i o n a l i n c r e a s e i n the d e n s i t y p f o l l o w i n g motion  4.4  i s e q u a l t o minus the d i v e r g e n c e o f the v e l o c i t y  The  C o n t i n u i t y E q u a t i o n Used to E s t i m a t e  V.  Rainfall  During the e x p l o r a t o r y development of the s a t e l l i t e fall  estimation technique  suggested Wallace  by M c i n t o s h  a n d Hobbs  the equation of c o n t i n u i t y i n a  and Thorn (19 7 3 , c h a p t e r s 5 and  (19 77,  chapter  8) was  the  8),  rainform and  considered to describe  the r a i n f a l l  r a t e from c l o u d systems.  A similar  expression  was p r o p o s e d b y V i e z e e et al., (1980) f o r e s t i m a t i n g t h e m o i s t u r e budget o f c y c l o n e s u s i n g microwave  The  data.  r a t e o f p r e c i p i a t i o n dP i s g i v e n b y dt dP 3t = WC'W-E  4.12  where w i s t h e v e r t i c a l v e l o c i t y o f t h e a i r b e i n g is  lifted,  wc  t h e w a t e r c o n t e n t o f t h e a i r , and E i s t h e e v a p o r a t i o n  rate.  Wc«w r e p r e s e n t s t h e r a t e a t w h i c h w a t e r e n t e r s t h e b a s e o f t h e c l o u d and i s l i f t e d . the r a i n f a l l  rate.  T h i s m i n u s l o s s e s due t o e v a p o r a t i o n Equation  enters a cloud either f a l l s not a l l o f the moisture  4.12 assumes t h a t a l l t h e w a t e r w h i c h as r a i n o r i s e v a p o r a t e d .  In practice,  entering a cloud i s precipitated.  c i a b l e amounts a r e r e t a i n e d w i t h i n t h e a i r mass a s w a t e r A f a c t o r e c a n be i n t r o d u c e d i n t o e q u a t i o n moisture  retention.  Rewriting equation  vapor.  4.12 y i e l d s  4.13  where e i s t h e f r a c t i o n o f w a t e r w h i c h f a l l s  cy o f t h e s t o r m .  Appre-  4.12 t o a l l o w f o r  dP = e«wc«w-E dt  literature this  yields  as r a i n .  I n some  f r a c t i o n i s t a k e n as a m e a s u r e o f t h e e f f i c i e n In equation  4.2, e r e p r e s e n t s a n a d j u s t m e n t  f a c t o r w h i c h c a n o n l y be d e t e r m i n e d  e m p i r i c a l l y on t h e b a s i s o f  50.  experience.  The w a t e r r c o n t e n t wc  vary w i t h temperature spatial  and t e m p o r a l  (g/m ) o f t h e a i r mass c a n  and l o c a t i o n . observations  On t h e b a s i s o f c u r r e n t  ( s u c h as t h o s e  t h e w a t e r c o n t e n t , f o r a g i v e n a i r mass o v e r  f r o m TIROS-N)  a particular  l o c a t i o n , c h a n g e s v e r y g r a d u a l l y a n d may be assumed throughout  a storm.  during a r a i n f a l l  constant  The r a t e o f e v a p o r a t i o n E i s n e g l i g i b l e  a n d c a n be n e g l e c t e d .  Then e q u a t i o n  4.13  becomes dP = e -wc-w -r-  , . 4, .14  dt  4.4.1  Estimating the V e r t i c a l Velocity w The  f o l l o w i n g d i s c u s s i o n focusses on e s t i m a t i n g the  v e r t i c a l v e l o c i t y w. tical  The c o n s e r v a t i o n o f mass r e l a t e s t h e v e r -  and h o r i z o n t a l m o t i o n f i e l d s  the v e r t i c a l  velocity  a n d c a n be u s e d t o e s t i m a t e  ( H o l t o n , 19 72) .  The h o r i z o n t a l  o f t h e c l o u d t o p as r e v e a l e d by s a t e l l i t e  divergence  images i s d i r e c t l y  related to the v e r t i c a l v e l o c i t y of a i r entering the cloud.  Consider  a p a r c e l of a i r w i t h i n the cloud, with cross-  s e c t i o n a l a r e a w h i c h may be a f u n c t i o n o f a l t i t u d e a n d t i m e , i e . A=A(z,t), a density  c o n f i n e d between t h e l e v e l s z and z+dz, and w h i c h has p . (See F i g u r e 4 . 1 ) . The mass o f t h i s  M = pAdz  a i r parcel i s  4.15  51.  Although  t h e shape o f t h e p a r c e l changes w i t h  time,  t h e mass  of the p a r c e l i s conserved f o l l o w i n g the motion o f the p a r c e l , t h a t i s -rr- = 0.  In other  g£  words  (pAdz) = 0  4.16  The change i n d e n s i t y o f t h e a i r j ~  (O^IO  small relative  - 5  (Fleagle, 4.1)  - 6  S  - 1  )  i s generally  t o the terms i Q (O10 S ) and ( A at dz 1946) a n d may be i g n o r e d . For a flow volume  which i s hald constant  - 1  i n the z d i r e c t i o n ,  o l 0 ~  5  S  _ 1  ),  (Figure  so t h a t n e t i n -  f l o w i s c a l c u l a t e d a s a f u n c t i o n o f z, b u t w h i c h i s p e r m i t t e d t o expand i n t h e h o r i z o n t a l p l a n e , moving boundary, t h e e q u a t i o n  1 dA A d t  +  dw d i -  s o t h a t no f l o w c r o s s e s t h e  o f c o n t i n u i t y c a n be w r i t t e n a s :  . ._ -  A =  °  4  1 7  1 dA j£ g £ i s t h e d e f i n i t i o n o f t h e h o r i z o n t a l d i v e r g e n c e locity. V  H  • V.  with respect  of the ve-  By r e a r r a n g i n g a n d i n t e g r a t i n g e q u a t i o n  to the a l t i t u d e  z gives  terms o f t h e h o r i z o n t a l d i v e r g e n c e I  the v e r t i c a l  4.17  velocity i n  (or spreading). 1 dz  Z  where z  2  2  a n d z^ ( s e e F i g u r e  Z  4.18  2  4.2) d e f i n e  the thickness o f the  d i v e r g i n g l a y e r between t h e l e v e l o f zero  divergence  z  2  and  .5.2.  3. 3 Cloud top at time t + A t T  C l o u d top at time t  _  z,,T 2 * "2 Limit between upper level d i v e r g e n c e and lower l e v e l convergence  n •i Surface  FIGURE 4.2  S c h e m a t i c Diagram  o f A i r C i r c u l a t i o n During a Major  Storm.  \ 5 7 (The h o r i z o n t a l s c a l e s o f s u c h s t o r m s a r e 0^10 - 10 m , while the v e r t i c a l  4  s c a l e s a r e 0^10 m.)  53.  the tropopause  o r t h e t o p o f t h e c l o u d , z^.  g i v e s t h e change i n t h e v e r t i c a l v e l o c i t y the tropopause gence. ed  Equation  of the a i r between  o r t o p o f t h e c l o u d and t h e l e v e l o f  I f the v e r t i c a l v e l o c i t y  zero then the v e l o c i t y  into  4.18  a t the tropopause  non-diveri s consider-  the c l o u d a t the l e v e l of  non-  divergence i s  4.19  2  4.4.2  R e w r i t i n g the C o n t i n u i t y E q u a t i o n Substituting  ( e q u a t i o n 4.20) tion  4.14)  the e x p r e s s i o n f o r the v e r t i c a l v e l o c i t y  i n t o the e q u a t i o n f o r the r a i n f a l l  rate  (equa-  yields  dP dt  Equation  4.20  infrared  satellite  t o p as w e l l  4.2Q  n e e d s t o be m o d i f i e d s t i l l i . f u r t h e r . images c o n t a i n the t e m p e r a t u r e  as t h e a r e a s o f t h e t e m p e r a t u r e  son o f a s u c c e s s i o n o f s a t e l l i t e i n the cloud top area i n time. measure t h e a l t i t u d e s  4.20).  Using the f i r s t  the assumption  enhanced  o f the  contours.  change  I t i s a d i f f i c u l t matter to determine  (the l i m i t s of i n t e g r a t i o n law o f thermodynamics  t h a t the v e r t i c a l motions are  cloud  Compari-  images a l s o g i v e s the  o f t h e c l o u d t o p s and  l e v e l of zero divergence  The  to the  i n equation  ( e q u a t i o n 4.4) approximately  and  hydrostatic  (equation 4.10), t h e decrease i n temperature T w i t h  i n c r e a s i n g h e i g h t z can be w r i t t e n  _  d  T = _ i _ l dz Cp dz d  +  E a i = Cp _  Y  4 21 *  Y  y.  w h i c h i s d e f i n e d as t h e l a p s e r a t e  U s i n g e q u a t i o n 4.21 t h e l i m i t s o f i n t e g r a t i o n c a n b e changed from a l t i t u d e s  z t o temperatures T which  d i a t e l y determined from t h e s a t e l l i t e rate  imagery.  c a n be immeSo t h e r a i n f a l l  ( e q u a t i o n 4.21) c a n b e w r i t t e n T  dP _ e-wc / dt " L 2 Y  3  1 dA A dt  4 d  2  2  T  A  where T  3  i s t h e temperature o f t h e c l o u d t o p and T  i s the  2  temperature o f t h e a i r a t the l e v e l o f zero divergence.  4.5  A d a p t a t i o n s f o r Use W i t h S a t e l l i t e  Images  A number o f m o d i f i c a t i o n s a r e made t o e q u a t i o n 4.2 2 b e fore estimates of r a i n f a l l First of a l l , is  c a n b e made f r o m s a t e l l i t e  images.  the temperature a t the l e v e l o f non-divergence  assumed t o b e r e a s o n a b l y c o n s t a n t t h r o u g h o u t a s t o r m .  The s e c o n d a d a p t a t i o n i n v o l v e s t h e a v e r a g e f 3 T  determined from t h e i n t e g r a l  tenri^  divergence  1 dA A dt  d T  '  r  e  c  a  l  l  i  n  9  that  t h e a r e a i s a f u n c t i o n o f b o t h t e m p e r a t u r e T and time t , A=A(T,t).  I n order to evaluate the i n t e g r a l i t i s necessary t o  .55.  know how t h e c r o s s - s e c t i o n a l a r e a o f t h e c l o u d c h a n g e s a t e a c h temperature  l e v e l T.  I n p r a c t i c e t h i s i s n o t known a n d l i k e l y  varies  from s t o r m t o s t o r m depending on t h e e n e r g e t i c s o f t h e  storm;  h o w e v e r , t h e s a t e l l i t e i m a g e s do show f r o m o n e image  to  t h e n e x t , t h e change i n t h e c r o s s - s e c t i o n a l a r e a o f t h e c l o u d  at  d i s c r e t e temperature  levels.  I d e a l l y , as t h e number o f tem-  p e r a t u r e l e v e l s c o n t r a s t e d by enhancement o f t h e i n f r a r e d i n c r e a s e s , the c l o s e r these d i s c r e t e areas approximate  images  the true  (continuous) v a r i a t i o n o f the cloud c r o s s - s e c t i o n a l area with t e m p e r a t u r e l e v e l T.  P r e s e n t enhancements, however,  o n l y a few t e m p e r a t u r e uplifting the  levels.  F o r f r o n t a l systems  distinguish i n which the  o f one a i r mass o v e r a n o t h e r i s w i d e s p r e a d a n d g r a d u a l ,  coldest contour of the i n d i v i d u a l p r e c i p i t a t i n g c e l l s  along  the f r o n t may be t h e o n l y one w h i c h i s s e p a r a b l e on t h e s a t e l l i t e i n f r a r e d i m a g e , t h e warmer c o n t o u r s o f t h e i n d i v i d u a l having a l l joined together.  cells  The r a i n f a l l r a t e , t h e r e f o r e ,  usual-  l y c a n o n l y be e s t i m a t e d f r o m t h e d i v e r g e n c e d e t e r m i n e d a t t h e c o l d e s t temperature  4.5.1  level T  3  on t h e s a t e l l i t e  R e l a t i o n Between Average  image.  Divergence and C o l d e s t Contour  Divergence R e d u c i n g e q u a t i o n 4.2 2 t o an e x p r e s s i o n f o r r a i n f a l l i n terms o f t h e average  d i v e r g e n c e i n the l a y e r between T  dP dt  e-wc =  " —  where t h e o v e r b a r denotes  1 dA A  dt  / m ( T  m  a n d T^  .  3~ 2> T  2  4  '  2  3  averaging w i t h r e s p e c t to temperature  T, a l l o w s t h e r a i n f a l l of  r a t e t o be e s t i m a t e d from t h e d i v e r g e n c e  the c o l d e s t contour.  the i n t e g r a l  The d i v e r g e n c e t e r m c a n be t a k e n o u t s i d e  i fi ti s similar,  ly non-dimensional,  i n which  i s essential-  c a s e t h e mean, t h e maximum, o r t h e  d i v e r g e n c e a t any p a r t i c u l a r average  so t h a t t h e p r o c e s s  level  c a n be u s e d  i n place of the  d i v e r g e n c e i n e q a u t i o n 4.23.  The c o l d e s t c o n t o u r d i v e r g e n c e c a n now be shown t o be a reasonable f i r s t a p p r o x i m a t i o n t o t h e average  divergence,  g i v e n t h a t o n l y two p i e c e s o f i n f o r m a t i o n a b o u t t h e b e h a v i o u r of  t h e c r o s s - s e p t i o n a l a r e a a r e g e n e r a l l y known a n d t h e y a r e :  1 - a t the l e v e l o f non-divergence definition  T  2  t h e d i v e r g e n c e i s by  zero:  1 A(T ,t)  dA(T ,t) dt 2  2  2 - a t the cloud top l e v e l T  3  4.24  =  the divergence i s  dA(T^,t) J  A(T ,t)  dt  3  •= K  4.25  where K i s t h e d i v e r g e n c e measured from s a t e l l i t e  4.5.2  One P r o p o s e d  Divergence  One s i m p l e f u n c t i o n 1 gence  infrared  images  Function  relating  the behaviour of the d i v e r -  dA (T t ) ^  h a v e an a v e r a g e  ^  t o the temperature  value which  the c o l d e s t contour l e v e l  l e v e l T c a n be shown t o  i s p r o p o r t i o n a l to the divergence a t  T^.  F o r example, c o n s i d e r the d i v e r -  G E N C E  1 A (T ,t)  dA(T t ) dt"*—  a s  a  ^  u n c t :  "-  o n  °^ t e m p e r a t u r e T o f t h e  L  l  form  A (T ,t)  w h e r e f-^ a n d f boundary  dA(T.t) dt  =  f  T  2  n  4.26  a r e c o n s t a n t s t o b e d e t e r m i n e d f r o m t h e two  2  conditions  above.  T h i s f u n c t i o n c a n be shown t o h a v e  a mean v a l u e  1 r- d A ( T , t ) A (T , t ) dt  K  1 1 T f ( T - T ) Tn+IT 3  2  which i s d i r e c t l y  Assuming  1  =  - tn+l)T& n . n T  +  ^ 4  T  proportional to the divergence K a t l e v e l  that the behaviour of the divergence with  -  2 7  T-..  tem-  p e r a t u r e c a n be a p p r o x i m a t e d b y t h e f u n c t i o n s u g g e s t e d  above,  then the r a i n f a l l  using:  r a t e c a n be e s t i m a t e d s a t i s f a c t o r i l y  58.  dP dt  e -wc "y" A(T ,t) 1  3  dA(T ,t) dt  r  3  J  dT  4.21  or dA(T ,t)  dP _ e <wc 1 dt ~ y A(T ,t)  3  dt  =  3  where AT=T ~T 3  i s the temperature  2  AT  4.29  d i f f e r e n c e from the l e v e l  of  zero divergence to cloud top.  For ease i n programming, e q u a t i o n 4.29 i s i n t e g r a t e d w i t h r e s p e c t t o t i m e t o g i v e t h e change i n r a i n f a l l  dP  from  time t to t+dt: t+dt dP  _  e-wc  t  e -wc In  (Appendix B c o n t a i n s a b r i e f r a i n f a l l estimation  dA(T ,t)  1  J  3  A(T ,t) 3  A(T ,t+dt) 3  ATT7~E1  sensitivity  relation.)  dt  AT  dt  AT  a n a l y s i s of the  4.30  4.  31  59.  4.5.3  The  R a i n f a l l Estimation Equations  The  amount o f r a i n AP  f a l l i n g i n the time i n t e r v a l  c a n be e s t i m a t e d f r o m t h e d i s c r e t e s e r i e s o f s a t e l l i t e  At  images  using  A  =  P  - ! ^ £  A(T ,t+At) A(T ,tJ  ln  AT  3  4.32  3  with  In  A(T ,t) > 0 3  the case where the c o l d e s t c l o u d top c o n t o u r i s n o t p r e s e n t  until  the second s a t e l l i t e  i m a g e , t h a t i s A ( T , t ) = 0, 3  e x p r e s s i o n i n e q u a t i o n 4.31 of  e q u a t i o n 4.29  of  p r e c i p i t a t i o n AP  The  discrete  form  i s u s e d t o p r o v i d e as e s t i m a t e o f t h e amount f a l l i n g i n the f i r s t time i n t e r v a l e-wc  i n F  i s undefined.  the  "  e  A(T  T ~  ,t+At)-A(T ,t) 3  J  *W^»  At:  0.5(A(T ,t+At)+A(T ,t) 3  'All  Am  J  3  )  A i  4  '  3 3  or  AP  = -^M for  E q u a t i o n s 4.32 which data.  2  AT  4.34  A(T ,t) = 0  a n d 4.34  3  form the b a s i s o f the computer  computes t h e p r e c i p i t a t i o n  amounts f r o m s a t e l l i t e  routine picture  60.  4.6  Consequences of the  Model  There are t h r e e consequences of the r a i n f a l l e s t i m a t i o n model.  F i r s t , i t i s postulated that rain f a l l s  c l o u d c e l l s which are a c t i v e l y  growing  This i s reasonable  which are decaying o f t e n continue rain.  However, t h i s r a i n f a l l  cant p o r t i o n of the o v e r a l l  The  a l t h o u g h some l a r g e r  accounted  T h i s c a n n o t be  for  those  divergence. will  f o r i n the a n a l y s i s of the s a t e l l i t e images.  a v o i d e d a t p r e s e n t due  to the l i m i t a t i o n s  the i n f r a r e d  m o d e l i s h o w e v e r , g e n e r a l e n o u g h t o be  of  images.  the  The  u s e f u l f o r a n a l y z i n g these  l e v e l c l o u d s when an a p p r o p r i a t e e n h a n c e m e n t scheme w h i c h  c o n t r a s t s the s m a l l temperature available.  gradients of these  t h i r d consequence o f the model l i e s  which the s p a t i a l d i s t r i b u t i o n of r a i n f a l l obtained.  cells  h e i g h t s of v e r t i c a l development  t o r e s u l t i n the h e a v i e s t r a i n f a l l s over  The  c l o u d s becomes  I t s h o u l d be p o i n t e d o u t , h o w e v e r , t h a t t h o s e  which reach near tropopause likely  signifi-  f r o m some c l o u d s b e l o w t h i s l e v e l  e n h a n c e m e n t schemes b e i n g u s e d on  lower  a  total.  clouds which are below the chosen l e v e l o f zero  n o t be  cells  t o d e p o s i t r e d u c i n g amounts o f  s e c o n d c o n s e q u e n c e i s t h a t no r a i n f a l l s  T h i s means t h a t r a i n f a l l  in  f r o m one s a t e l l i t e  i s n o t c o n s i d e r e d t o be  storm  those  i n t i m e as e v i d e n c e d  the spreading of the c o l d e s t c l o u d top contour image t o t h e n e x t .  from o n l y  Because the average divergence  an  are  area.  i n t h e manner i n  from a storm  cell is  o f t h e c e l l has  been  shown t o be p r o p o r t i o n a l t o t h e d i v e r g e n c e t o u r f o r two g e n e r a l d i v e r g e n c e from a p a r t i c u l a r temperature  of the coldest  f u n c t i o n s , then  contour  con-  the r a i n f a l l  i s p r o p o r t i o n a l to the  t h i c k n e s s AT o f t h e d i v e r g i n g l a y e r u n d e r t h a t c o n t o u r T^ w h i c h i s AT=T^-T  2  (where T  tours other than AT=T^-T  4.7  2  2  i s the l e v e l of non-divergence).  the c o l d e s t one, the r a i n f a l l i s found  i n the a p p r o p r i a t e model e q u a t i o n  (either  4.32  using or  4.34).  The O t h e r M o d e l P a r a m e t e r s The a r e a a n d t e m p e r a t u r e  the s a t e l l i t e  p a r a m e t e r s c a n be o b t a i n e d  infrared pictures.  wc, t h e l a p s e r a t e y,  be o b s e r v e d  values.  of data.  content  f o r these parameters would necessary  These a r e d i s c u s s e d b e l o w .  W a t e r C o n t e n t wc The w a t e r c o n t e n t i s t h e t o t a l amount o f m o i s t u r e  a i r column t h a t i s a v a i l a b l e  forprecipitation.  The  i n an  literature  shows a w i d e r a n g e o f v a l u e s o f wc v a r y i n g w i t h t h e c l o u d Table  from  determined.  I n p r a c t i c e , h o w e v e r , i t may be  r e l y on o t h e r s o u r c e s  4.7.1  That leaves the water  a n d t h e e f f i c i e n c y e t o be  I d e a l l y , the best choice of values  to  F o r con-  4.1 shows a summary o f w a t e r c o n t e n t v a l u e s o b t a i n e d  published material.  W a t e r c o n t e n t c a n be d e t e r m i n e d  from  type. from values  of the p r e c i p i t a b l e water which a r e r e p o r t e d every s i x hours by the p o l a r - o r b i t i n g s a t e l l i t e p r i n t o u t o f TIROS-N d a t a .  stations.  Table  4.2 shows a s a m p l e  As w e l l , w a t e r c o n t e n t c a n be d e t e r -  mined from r e l a t i v e humidity weather  TIROS-N.  o b s e r v a t i o n s a t nearby upper a i r  TABLE  4.1  Average E f f i c i e n c i e s  Cloud Type  Efficiency  e  (as a f r a c t i o n )  W a t e r C o n t e n t wc (g/m ) 3  0 .10  Seafog Stratus  0.05  Orographic (Hawaii) Small  and Water Content  Cumulus  Cumulus  Congestus  Cumuloniumbus  0 .05-0.10  0.35 0 .35  0\.10  0.5-1.4  0 .15  1.0  0.20-0.30  2.0-10.0  ( f r o m MASON, 19 7 1 , 19 75; FLETCHER, 196 2; ROGERS, 19 76)  TABLE 4.2  P o r t i o n o f T y p i c a l Output o f TIROS-N (TUXN) P r e c i p i t a b l e Water (PCW) and O t h e r Data f o r V a r i o u s L e v e l s i n the Atmosphere. (Received by t h e P a c i f i c Weather C e n t r e from NESS S a t e l l i t e Data S e r v i c e s D i v i s i o n , Washington, D.C.)  RETRIEVAL OF TUXN DATA 3 HRS BFR AND AFT OOZ 0 5 DECEMBER (19 79) NOTE: % IS CONFIDENCE VALUE IN READINGS AMOUNT OF CLOUD (CL) IN %, AVG CLOUD TOP (ACT) IN MB THICKNESS (THKS) IN DECAMETERS PRECIPITABLE WATER (PCW) IN MILLIMETERS SURFACE TEMP(SFT) , TROPOPAUSE TEMP (TRT)  DATM 0500Z 90%:THKS 90%:PCW  .  LAT 2 8N FM1000MB FM1000MB  LONG  700 MB  500  MB  400  MB  300  MB  250  MB  140W 136  0500Z 70%:THKS 70%:PCW  34N FM1000MB FM1000MB  136W—  0500Z 90%:THKS 90%:PCW  35N FM1000MB FM1000MB  132N  •  850 MB  135  137  294 013  294 016 297 017  558 016  560 022 564 021  724  729 024 733  928 017  935  940 022  CL  ACT  48  400  SFT  TRT  019  //  017  //  018  //  052  93  294  19  300  060  064  TABLE 4.2  (continued)  DATM  LAT  0500Z 90%:THKS 90%:PCW  42N FM1000MB FM1000MB  LONG  850 MB  700 MB  500 MB  400 MB  300 MB  250 MB  137W 133  0500Z 60%:THKS 60%:PCW •  42N FM1000MB FM1000MB  0500Z 70%:PCW  45N FM1000MB  142@  0500Z 90%:PCW •  46N FM1O00MB  136W  0500Z 90%:PCW  64N FM920MB  144W  0422Z 90%:THKS 90%:PCW  62N FM780MB FM7 80MB  126W  291 008  555 009  723 010  928  051  130W 133  290 007  Oil Oil  002 081 001  CL  ACT  10  441  09 553 008  719  014  TRT  Oil  //  012  //  005  //  009  //  M15  //  M15  //  30 6  047  18  661  29  750  015  014  015  003 326 002  923 009  SFT  42  506  37  432  004 481  673 003  79 4  65.  4.7.2. The L a p s e R a t e y The  l a p s e r a t e y c a n be assumed e q u a l t o t h e s a t u r a t e d  adiabatic lapse rate y = y  - 5°C/1000m w h i c h i s a  assumption during a r a i n f a l l .  reasonable  A l t e r n a t e l y , the actual environ-  mental lapse rate y = y as r e c o r d e d ' env c a n be u s e d .  from radiosonde  ascents  4*7.3. A d j u s t m e n t F a c t o r e The  p a r a m e t e r e i s an e m p i r i c a l a d j u s t m e n t f a c t o r  that  some i n v e s t i g a t o r s h a v e l i n k e d t o t h e a c t u a l e f f i c i e n c y o f a cloud i n producing of values  rain.  The l i t e r a t u r e i n d i c a t e s a w i d e r a n g e  f o r e d e p e n d i n g on c l o u d t y p e  w i t h i n each c l o u d type.  significantly  S i n c e v a r i o u s i n v e s t i g a t o r s have  t o d e f i n e e a n d wc d i f f e r e n t l y , v a l u e s ten occur i n p a i r s  and v a r y i n g  f o r these parameters o f -  c o n s i s t e n t w i t h the d e f i n i t i o n  employed.  B e c a u s e i n t h i s m o d e l e i s an e m p i r i c a l a d j u s t m e n t it  can be used t o t a k e i n t o account  parameters.  Consider  tended  factor  uncertainties i n the other  the s i t u a t i o n o f a storm  r a i n i n g over  a  r e g i o n w h i c h h a s a number o f s t a t i o n s o n l y o n e o f w h i c h i s a b l e to provide values  f o r t h e w a t e r c o n t e n t and t h e l a p s e  along with the observed  rate,  p r e c i p i t a t i o n A P ^ g from the raingauge o r  radar located at this s t a t i o n .  A c a l c u l a t i o n o f the r a t i o  wc , "A(T ,t+ At)~ — In Y A(T ,t) 3  3  yields  a value f o r e which contains both  determine  the d i f f i c u l t to  " e f f i c i e n c y " o f t h e c l o u d , and t h e u n c e r t a i n t y i n  the other parameters. w e l l serve  This value of the e f f i c i e n c y e could  as t h e b e s t i n i t i a l  estimate of e f o r a l l o f the  stations i n the region.  Once t h e e f f i c i e n c y e , w a t e r c o n t e n t wc a n d l a p s e r a t e y have been chosen f o r each s t a t i o n constant  throughout  reasonable  is  4.8  a r e assumed t o r e m a i n  T h i s i s c o n s i d e r e d t o be a  assumption s i n c e the c h a r a c t e r i s t i c s  over the s t a t i o n certainty  the storm.  they  o f the airmass  change v e r y s l o w l y d u r i n g t h e s t o r m .  (The u n -  i n the p r e c i p i t a t i o n t h a t t h i s assumption introduces  accounted  f o r i n the updating r o u t i n e d i s c u s s e d i n Chapter  7) ;.  Summary A b r i e f d i s c u s s i o n o f the conditions necessary  for preci-  p i t a t i o n t o o c c u r p o i n t e d towards a p h y s i c a l - c o n c e p t u a l model which considers the p r e c i p i t a t i o n process of water through determined  an a i r c o l u m n .  from the lower  i n terms o f t h e f l u x  The v e r t i c a l v e l o c i t y  l e v e l convergence o f a i r i n t o  c o u l d be the c o l -  umn. - an a p p r o a c h t h a t was u s e d b y s e v e r a l r e s e a r c h e r s t o e s t i mate r a i n f a l l b u t was n e v e r e x p l o i t e d o p e r a t i o n a l l y due t o t h e difficulties  involved i n determining  the lower  l e v e l winds.  S a t e l l i t e i m a g e s , h o w e v e r , p r o v i d e t h e means f o r d e t e r m i n i n g t h e u p p e r l e v e l d i v e r g e n c e w h i c h c a n be u s e d as a b a s i s f o r e s t i m a t i n g the v e r t i c a l v e l o c i t y .  The c l o u d i t s e l f i s t r e a t e d as a t r a c e r o f  67.  the motions o f the atmosphere o f w h i c h i t i s a p a r t . (equations formation  4.32  and 4.34) was  satellite  images  The  model  developed k e e p i n g i n mind the i n -  provide.  68. CHAPTER V COMPUTATIONAL PROCEDURE FOR ESTIMATING RAINFALL FROM SATELLITE IMAGES  The a n a l y s i s o f r a i n f a l l events u s i n g GOES images  involve  a d i f f i c u l t e x e r c i s e i n bookkeeping t o keep t r a c k o f the e s s e n t i a l image parameters d e s c r i b i n g the storm, e s p e c i a l l y i f the  storms are major ones c o n t a i n i n g many i n d i v i d u a l  cells,  which appear, grow and decay as they move over an a r e a . 5.1 d e f i n e s the image terms used i n t h i s study. t i n e s to f a c i l i t a t e  Figure  Computer rou-  the c a l c u l a t i o n s o f the r a i n f a l l estimates  were developed during the course o f the a n a l y s i s o f the f i r s t major storm.  5.1  Conceptual Procedure Estimating r a i n f a l l  from GOES i n f r a r e d images was accom-  p l i s h e d through a computer-user i n t e r a c t i v e process which i s f l o w c h a r t e d i n F i g u r e 5.2, w i t h each o f the s t e p s d i s c u s s e d briefly  below.  The f i r s t step i n the process was t o o b t a i n the h a l f - h o u r l y GOES s a t e l l i t e  images.  These can be o b t a i n e d e i t h e r through  loan arrangement w i t h the Atmospheric Environment S e r v i c e , the P a c i f i c Weather Centre (or l o c a l weather link,  c e n t r e ) , v i a a GOES-Tap  o r through d i r e c t r e c e p t i o n o f the s a t e l l i t e  signal.  The  FIGURE  5.1  E x p l a n a t i o n o f t h e V a r i o u s Terms u s e d GOES I n f r a r e d C l o u d Images:  to Describe  CELL - The C o l d e s t S e l f - C o n t a i n e d C l o u d T o p C o n t o u r and I t s I m m e d i a t e l y S u r r o u n d i n g Warmer C o n t o u r s . STORM - The C l o u d y A r e a on t h e S a t e l l i t e Image W h i c h B r i n g s R a i n i n t o an A r e a . I t i s u s u a l l y made up o f one o r more c e l l s .  70.  FIGURE 5.2  S t e p s f o l l o w e d t o make e s t i m a t e s o f r a i n f a l l f r o m GOES s a t e l l i t e i m a g e s .  S t e p 1: O b t a i n h o u r l y o r h a l f - h o u r l y GOES images Step  2:  Step  3:  satellite  O b t a i n v a l u e s f o r t h e m o d e l p a r a m e t e r s e , wc and y i e n t e r t h e s e a l o n g w i t h t h e s a t e l l i t e image d a t a . D i g i t i z e temperature contour c o o r d i n a t e s from i n f r a r e d images ( g e t e q u i v a l e n t temperature c o n t o u r from unenhanced i n f r a r e d image u s i n g the vido camera-special e f f e c t s generatorv i d e o m o n i t o r system)  Step  4:  Step  5:  Step  6:  C a l c u l a t e c l o u d t o p temperature contour areas and c e n t e r o f g r a v i t y c o - o r d i n a t e s ( f o r u s e w i t h moving systems). Calculate r a i n f a l l f o r each contour. Digitize station^coordinates. C a l c u l a t e r a i n f a l l f o r each s t a t i o n i n t e r p o l a t i n g w h e r e n e c e s s a r y when a s t a t i o n i s b e t w e e n two contours. ;  s a t e l l i t e images used i n t h i s Weather Centre i n Vancouver,  The  s t u d y w e r e p r o v i d e d by t h e P a c i f i c British  second step i n v o l v e d the choice of the r a i n f a l l e s t i -  mation model p a r a m e t e r s , t h e w a t e r and t h e a d j u s t m e n t  The  Columbia.  c o n t e n t wc, t h e l a p s e r a t e y /  f a c t o r e , as d i s c u s s e d i n s e c t i o n  next major  4.7.  s t e p and t h e f i r s t i n v o l v i n g t h e u s e o f a  c o m p u t e r r o u t i n e , was t o . ' i n p u t t h e s t o r m i n f o r m a t i o n a storm c e l l i d e n t i f i c a t i o n  including  number, t h e t i m e t h e s a t e l l i t e  image  was t a k e n , t h e e n h a n c e m e n t scheme u s e d , t h e s e c t o r u s e d , a n d t h e temperature cell let, the  contour l e v e l ,  cloud top temperature  and t h e n t o d i g i t i z e contours.  the i n d i v i d u a l  A Tektronix digitizing  tab-  F i g u r e 5.3, l i n k e d b y a t i m e - s h a r i n g c o m p u t e r t e r m i n a l t o University of British  p u t e r system  C o l u m b i a ' s A m d a h l 470 V/6 m o d e l I I com-  ( L e i g h a n d Duke, 19 78) was u s e d t o d i g i t i z e t h e  p e r i m e t e r o f t h e c l o u d t o p t e m p e r a t u r e c o n t o u r s and s t o r e t h e c o o r d i n a t e s f o r use i n t h e subsequent  steps .  T h i s was a s t r a i g h t -  f o r w a r d p r o c e d u r e i n those i n s t a n c e s where t h e i n f r a r e d h a d b e e n enhanced.,, t h a t i s , i f t h e t e m p e r a t u r e s h a d b e e n i n d i s c r e t e grey s c a l e s making i d e n t i f i a b l e  image scaled  temperature contours.  However, t h e a v a i l a b i l i t y o f t h e s e enhanced images i s i n t e r m i t t e n t e s p e c i a l l y when v i s i b l e ceived instead.  There  o r unenhanced images a r e b e i n g r e -  i s an a d d i t i o n a l d i f f i c u l t y a t t i m e s when  more t h a n one e n h a n c e m e n t scheme i s i n u s e d u r i n g t h e d a y . D i r e c t r e c e p t i o n a n d e n h a n c e m e n t o f t h e s a t e l l i t e image e l i m i n a t e s these problems,  a l t h o u g h , f o r most u s e r s t h i s  i s not possible.  72.  FIGURE  5.3  The T e k t r o n i x D i g i t i z i n g T a b l e t - Remote Computer Terminal Arrangement. The I n f r a r e d S a t e l l i t e Image i s P l a c e d on t h e T a b l e t and t h e T e m p e r a t u r e C o n t o u r s are T r a c e d u s i n g the S t y l u s .  T h e r e f o r e , t o s u p p l e m e n t t h e e n h a n c e d i m a g e s and  to f i l l  i n the  g a p s , unenhanced images were f i r s t a n a l y z e d u s i n g equipment w i t h i n the C i v i l E n g i n e e r i n g Department a t the U n i v e r s i t y  of  British  effects  Columbia which i n c l u d e d a v i d e o camera, a s p e c i a l  generator  and  F i g u r e 5.4,  a video monitor.  special effects  generator,  a l l o w e d b l a c k i n g out the grey shades ( r e p r e s e n t i n g  d i f f e r e n t temperatures) By  The  b e l o w any  particular  l e v e l of brightness.  s u c c e s s i v e l y b l a c k i n g out d a r k e r shades o f g r e y ,  contours  c o u l d be  shown on t h e v i d e o m o n i t o r  T h e s e w e r e t r a c e d and camera-special  The  digitized.  F i g u r e 5.6  temperature 5.5.  screen, Figure shows t h e  e f f e c t s generator-video monitor  video  arrangement.  d i g i t i z e d c o n t o u r s w e r e u s e d as i n p u t t o t h e  computer  r o u t i n e w h i c h c a l c u l a t e d t h e i r a r e a s , as w e l l as t h e i r c e n t r e gravity falls  c o o r d i n a t e s f o r use  i n e s t i m a t i n g the p r e c i p i t a t i o n  a t a p o i n t from a moving c l o u d system.  v i t y o f t h e c o l d e s t c o n t o u r was  The  a l s o c o m p u t e d and  centre of  of  that gra-  u s e d as an i n -  d i c a t o r o f t h e movement o f t h e c l o u d c e l l b e t w e e n s u c c e s s i v e s a tellite  images.  computer f i l e s  A l l o f t h i s i n f o r m a t i o n was t h a t s e r v e d as i n p u t f i l e s  which the r a i n f a l l model e q u a t i o n s  was  4.32  from i n d i v i d u a l c e l l s  In mapped b y  w r i t t e n onto  f o r the next step i n  e s t i m a t e d f o r each contour  and  4.34.  the  using  This allowed contours  of  the rainfall  t o be p r e s e n t e d e v e r y h a l f - h o u r i f r e q u i r e d .  the n e x t s t e p the s t a t i o n l o c a t i o n s o f i n t e r e s t were the user onto a s a t e l l i t e  image g r i d and  then  their  FIGURE  5.4  The P a n a s o n i c WJ-4500 S p e c i a l E f f e c t s G e n e r a t o r Used t o D e t e r m i n e T e m p e r a t u r e C o n t o u r s f r o m Unenhanced I n f r a r e d S a t e l l i t e Images.  s  75.  FIGURE  5.5  The t o p p h o t o shows t h e s a t e l l i t e i m a g e as s e e n on t h e videomonitor before the s p e c i a l e f f e c t s generator i s e n g a g e d . The s e c o n d p h o t o shows t h e s a t e l l i t e image as s e e n on t h e v i d e o m o n i t o r a f t e r t h e s p e c i a l e f f e c t s g e n e r a t o r i s e n g a g e d . Those c l o u d s w a r m e r t h a n T°C on t h e t e m p e r a t u r e - g r e y s c a l e h a v e b e e n shown as b l a c k a r e a s w h i l e t h o s e c o l d e r t h a n T°C a r e shown as l i g h t e r a r e a s . The b o u n d a r y b e t w e e n t h e two i s t h e T°C c o n t o u r .  76.  FIGURE  5.6  The V i d e o Camera - S p e c i a l E f f e c t s G e n e r a t o r - V i d e o Monitor Arrangement used t o Determine Temperature Contours f r o m GOES U n e n h a n c e d I n f r a r e d I m a g e s .  c o o r d i n a t e s were d i g i t i z e d u s i n g the d i g i t i z i n g before.  T h i s was  a one  c u l a t i n g the r a i n f a l l  tablet  as  time o p e r a t i o n i n p r e p a r a t i o n f o r c a l -  at these s t a t i o n s .  The  c o o r d i n a t e s were  u s e d by t h e c o m p u t e r r o u t i n e w h i c h d e t e r m i n e d t h e movement o f the  storm c e l l or c e l l s  rainfall  p a s t t h e s t a t i o n and i n t e r p o l a t e d f o r  should the s t a t i o n l o c a t i o n  l i e between r a i n f a l l  con-  tours .  5.1.1  Movement o f S t o r m C e l l s N e a r A Since the s a t e l l i t e  of due in  Station  images form a s e r i e s o f " s n a p - s h o t s "  a c o n t i n u o u s l y c h a n g i n g p r o c e s s t h e e f f e c t on t h e t o t h e movement o f s t o r m c e l l s t h e f o l l o w i n g manner.  n e a r a s t a t i o n was  F i g u r e 5.7  i n t e r v a l A>t.  handled  shows a s i t u a t i o n  represents the p o s i t i o n s of a cloud top temperature s e e n i n two s u c c e s s i v e s a t e l l i t e  rainfall  images,  which  c o n t o u r as  s e p a r a t e d by a t i m e  From t h i s i t w o u l d seem t h a t S t a t i o n 1 a p p a r e n t l y  does n o t r e c e i v e any r a i n f a l l contour i n both s a t e l l i t e  since i t lies  images.  o u t s i d e the  However, i t i s c l e a r  cloud that  p a r t o f t h e s t o r m c e l l p a s s e d o v e r S t a t i o n 1 l e a v i n g some r a i n as i t d i d . of  the c e l l ,  To  a c c o u n t f o r t h i s e f f e c t c a u s e d by t h e movement  the centre of g r a v i t y o f the c e l l at the  t i m e i s s h i f t e d back  to the mid-point of the l i n e  second  which  indi-  cates the d i s p l a c e m e n t o f t h e c e n t r e o f g r a v i t y s o t h a t t h e a p p e a r s i n t h e p o s i t i o n shown i n F i g u r e  I f more t h a n one d u r e was  essentially  cell  5.8.  c e l l passed near the s t a t i o n the proce-  t h e same.  The  computer  routine  Cell  at  t,  FIGURE 5 . 7 A Schematic R e p r e s e n t a t i o n o f One Storm C e l l Contour as i t Moves over 3 R a i n f a l l S t a t i o n s Between Times t , and t . The Displacement o f the Centre o f G r a v i t y d u r i n g t h i s Time i s from C^ t o C . From these "SnapShot" views, S t a t i o n 1 appears n o t to have r e c e i v e d any Rainfall. 2  2  79.  FIGURE  5.8  The C e l l ' s P o s i t i o n a t Time t„ i s S h i f t e d B a c k H a l f t h e D i s p l a c e m e n t so t h a t i t s C e n t r e o f G r a v i t y i s a t P o s i t i o n  C.  80.  searched  f o r those  two  c e l l s whose c e n t r e s o f g r a v i t y w e r e  c l o s e s t t o t h e s t a t i o n and y e t n o t on  the  first satellite  image.  w a r d movement o f t h e s t o r m s , s t a t i o n had previous  to the e a s t of the  station  Because o f the g e n e r a l l y e a s t those  cells  to the e a s t o f  already c o n t r i b u t e d to the s t a t i o n ' s r a i n f a l l  time  intervals.  Again  the c e l l s '  of the l i n e j o i n i n g  p o s i t i o n s a t the b e g i n n i n g  of the time  and  end  i s i l l u s t r a t e d schematically i n Figure  Should  t h e s t a t i o n i n i t s new  t o u r s , the i n t e r p o l a t i o n v e r s i t y of B r i t i s h  t o s u i t the purpose a t hand.  interval.  p e r f o r m e d by library  w h i c h was  T h i s r o u t i n e uses a  Details of this  Computing Centre  document:  UBC  hourly estimates  of the r a i n f a l l  t h e n summed t o y i e l d c u m u l a t i v e  the  Uni-  routine  modified  algorithm to i n t e r p o l a t e f o r intermediate values o f known v a l u e s .  This  p o s i t i o n l i e between con-  Columbia Computing Centre 1979)  their  5.9.  f o r r a i n f a l l was  Computing C e n t r e ,  in  centres of g r a v i t y  were s h i f t e d back t o the m i d - p o i n t  XPAND.S (UBC  the  somewhat  heuristic f r o m an  array  a l g o r i t h m are g i v e n i n the  Surface,  ( M a i r , 1978b).  The  a t each of the s t a t i o n s are rainfall  estimates.  D e t a i l s o f the computer r o u t i n e sequence are g i v e n i n the next s e c t i o n .  UBC half-  FIGURE 5 . 9 Two C e l l s A f f e c t i n g R a i n f a l l a t a S t a t i o n . Both are s h i f t e d s o t h a t t h e i r C e n t r e s o f G r a v i t y a r e now a t the Midpoints o f t h e i r r e s p e c t i v e t o t a l Displacements, c-^ a n d C « The s h i f t e d c e l l s a r e shown b y t h e d a s h e d curves. 2  82.  5.2  Computer R o u t i n e  Sequence  F i g u r e 5.10 g r a p h i c a l l y c h a r t s t h e s e q u e n c e o f c o m p u t e r routines developed during t h i s study of the r a i n f a l l  a n d u s e d t o make  from c l o u d top temperature contours  GOES i n f r a r e d i m a g e s .  estimates  taken  There a r e f i v e major r o u t i n e s  from  (DOG,  STATION, RF, I N , UP) w h i c h p e r f o r m v a r i o u s o p e r a t i o n s  towards  yielding a satellite  routines  rainfall  estimate.  A l l of these  w e r e programmed i n F o r t r a n f o r u s e o n t h e UBC c o m p u t e r  terminal  system.  The  first  two r o u t i n e s , DOG a n d STATION, a r e d i g i t i z i n g  routines enabling the user  to input either s a t e l l i t e  parameters and temperature contours locations  image  - DOG, o r s t a t i o n names a n d  - STATION, v i a t h e d i g i t i z i n g t a b l e t .  Both o f these  r o u t i n e s make u s e o f t h e UBC C o m p u t i n g C e n t r e L i b r a r y p r o g r a m I G ( M a i r , 19 78a)  t o c o n t r o l the a c t u a l input o f the data  along with standardized the area  x-y a x e s .  (A) o f e a c h c o n t o u r  A  - E i  The r o u t i n e DOG a l s o c a l c u l a t e s  traced  5.1  o f the i - t h point  The  c e n t r e o f g r a v i t y o f each contour  the  r o u t i n e DOG  using  using  r ( x .i + i  w h e r e x ^ , y^ a r e t h e c o o r d i n a t e s  points  digitized.  ( x c , yc) i s determined by  FIGURE  5.10  Sequence o f Computer R o u t i n e s  GOES SATELLITE PICTURES & OBSERVED DATA  OBSERVED RAINFALL DATA  GOES SATELLITE INFRARED PICTURES, e, wc, y "DOG"  DIGITIZING ROUTINES  RF'  RAINFALL ESTIMATION ROUTINES for contours and a g r i d of s t a t i o n s  UODATING ROUTINE  Used:  E  - read i n contour p e r i meter c o o r dinates - calculate contour area and c e n t e r o f gravity  "STATION" - r e a d i n station coordinates and name  - accounts f o r v a r i o u s s a t e l l i t e p i c t u r e s c a l e s ( i e . sectors) a v a i l a b l e - a c c o u n t s f o r v a r i o u s o p e r a t i o n a l enhancement schemes a v a i l a b l e - c a l c u l a t e s r a i n f a l l f o r each t e m p e r a t u r e c o n t o u r (up t o 6) f o r each s t o r m c e l l a t each time u s i n g model e q u a t i o n s 4.32 and 4.34.  z  j"IN"  - a c c o u n t s f o r movement o f s t o r m c e l l ( s ) over s t a t i o n _ - interpolates f o r station r a i n f a l l i t s t a t i o n l i e s between r a i n f a l l c o n t o u r s  I"UP"  -updates r a i n f a l l estimates a t a g r i d of s t a t i o n s using a v a i l a b l e observed data i n model e q u a t i o n s 7.1 (and 7.4 and 7 . 5 ) .  OUTPUT OUTPUT=UPDATED SATELLITE ESTIMATE OF RAINFALL; v a l u e s o f a, b f o r use i n u p d a t i n g ungauged station estimates; Jj h o u r l y r a i n f a l l contours  8.4.  n  5.2  xc  1 n  5.3  yc  which  essentially  The  second  estimation mates  of  routine image are  scales  sector.  of  the  used before the  since  rent  rates,  vides  because  operational  the  of  the  the  the  rainfall  of  for  routine  from the  the  the  routine  section).  SB6  scales  is  being  each  for  of  each at  storm diffe-  event.  routines,  stations and the  RF.  the  determine  evolving  estimation  STATION  the  sector  for  the  after  of  schemes  6,  esti-  using  done  must  rainfall  storm  storm and i t s  previous  then  may b e  those  rainfall  size  several  a maximum o f cells  duration of  rainfall  obtained  in  various  the  is  the  enhancement  compute up t o  contour  to  The r o u t i n e  the  RF, provides  This  4.34.  necessary  to  are  temperature  is  of  using  movement  described  each  these,  4.32 a n d  contours,  second  stored  the  for  proceeding  estimates  estimates  of  images  the  gravity.  The f i r s t  satellite  various  for  of  RF a n d I N ,  operationally.  of  centre  the  This  each  The  for  a l l  the  routines,  equations  temperature  cell  were  rainfall  model  received  which  two  routines.  the  rainfall  described  whose cell  over  The s e c o n d  the  pro-  coordinates  contour  The r o u t i n e  cells  IN,  IN  rain  accounts  station  part of  the  (as rou-  8.5.  t i n e I N i s t o i n t e r p o l a t e , u s i n g t h e m o d i f i e d XPAND.S, f o r the r a i n f a l l  a t t h e s t a t i o n a f t e r t h e movement o f t h e s t o r m  has b e e n t a k e n c a r e o f .  I f the isohyets of the r a i n f a l l are  r e q u i r e d they are determined t h e UBC C o m p u t i n g C e n t r e  and p l o t t e d a u t o m a t i c a l l y u s i n g  library  g r i d c o n t o u r i n g r o u t i n e CNTOUR  ( M a i r , 1978b) .  The  f i n a l m a j o r r o u t i n e , t h e u p d a t i n g r o u t i n e , UP i s  b a s e d on t h e u p d a t i n g p r o c e d u r e  d e s c r i b e d i n Chapter  routine incorporates the observed with the tions  satellite  f o r each  This  station  e s t i m a t e s u s i n g t h e u p d a t i n g model, equa-  7.1, 7.4 arid 7.5, i n a d d i t i o n t o t h e u p d a t i n g m o d e l p a r a -  meters,  a and b, f o r use i n u p d a t i n g r a i n f a l l  ungauged  rainfall  output  from these r o u t i n e s i n c l u d e s p o i n t e s t i m a t e s  f o rvarious stations,  r a i n f a l l produced rainfall  estimates f o r  locations.  The of  rainfall  7.  by each c e l l ,  f o ra grid of points.  contours o f the estimated  and i s o h y e t s o f e s t i m a t e d  86.  CHAPTER V I  ESTIMATES OF P R E C I P I T A T I O N USING S A T E L L I T E IMAGES  6.1  The  Test  As of  Storms  a t e s t o f t h e m o d e l u n d e r a c t u a l c o n d i t i o n s , a number  storms which o c c u r r e d over B r i t i s h  Columbia were chosen f o r  a n a l y s i s u s i n g t h e a v a i l a b l e i n f r a r e d GOES-West i m a g e s at  the P a c i f i c Weather Centre i n Vancouver. ( J u n e 4, 19 77)  received  E x c e p t f o r one  the  t e s t storm dates  satellite  images were  for  t h o s e d a t e s a n d t i m e s d u r i n g w h i c h r a i n f a l l was  known  of  chosen (from  news m e d i a o r P a c i f i c W e a t h e r C e n t r e r e p o r t s , o r d i r e c t e x p e r i e n ce) t o be  falling  c a s e i t was  over B r i t i s h  Columbia.  a s s u m e d t h a t r a i n was  had r e l a t i v e l y  falling  (<-40°C).  f o r t h e J u n e 4, 19 77 s t o r m was  on e x a m i n a t i o n o f t h e h o u r l y r a i n f a l l The  from those c e l l s  c o l d c l o u d top temperatures  occurrence of r a i n f a l l  station.  F o r t h e J u n e 4, 19 77  following criteria  records f o r the  The  which actual  confirmed affected  i n f l u e n c e d the choice of  test  storms:  1 -  The  s t o r m h a d t o be s u f f i c i e n t l y  the  vertical  well-developed i n  t o have c l o u d top temperatures  which  were w i t h i n t h e s t e p w i s e range o f the enhancement scheme u s e d s o t h a t d e f i n i t e  c l o u d top  c o n t o u r s 'were f o r m e d on t h e s a t e l l i t e images.  temperature infrared  87.  2 - The s t o r m h a d t o be l o a a t e d o v e r an a r e a w h i c h h a d a t l e a s t one r a i n g a u g e t o a l l o w and/or c a l i b r a t i o n o f t h e r a i n f a l l  verification estimation  model.  3 - Over r e g i o n s w i t h h o u r l y r e c o r d s o f r a i n f a l l , t h e s t o r m h a d t o e x i s t on a t l e a s t two s u c c e s s i v e satellite rainfall or  images t o p e r m i t a c a l c u l a t i o n o f t h e estimate.  12-hour  Over r e g i o n s w i t h o n l y  6-hour  records o f r a i n f a l l , the storm had to  e x i s t f o r t h e e n t i r e 6-hour o r 12-hour  period.  During t h e a n a l y s i s o f the t e s t storms s e v e r a l problems  arose  which r e q u i r e d i n n o v a t i v e s o l u t i o n s before the e s t i m a t i o n proced u r e c o u l d be u s e d o p e r a t i o n a l l y .  The d e v e l o p m e n t  o f t h e computer  routines, discussed i n the previous chapter, t o f a c i l i t a t e the a n a l y s i s proceeded along w i t h the examination of the i n i t i a l s t o r m w h i c h o c c u r r e d on O c t o b e r  The  3 1 , 19 7 8 .  t e s t s t o r m s i n c l u d e d two e x a m p l e s  o f w i d e s p r e a d and  s e v e r e c y c l o n i c s y s t e m s o c c u r r i n g on O c t o b e r 3 1 , 19 7 8 a n d December 1 7 , 1 9 7 9 , b o t h o f w h i c h w e r e n o t e w o r t h y .  The  first,  w h i c h s w e p t a c r o s s t h e Queen C h a r l o t t e I s l a n d s a n d o v e r t h e T e r r a c e a r e a was d u b b e d t h e H a l l o w e e n D e l u g e by l o c a l logists  (Hammond, 19 7 8 ) .  The s e c o n d was a s t o r m w h i c h  meteorofollowed  an e a r l i e r e v e n t t h a t c a u s e d e x t e n s i v e p r o p e r t y damage f r o m f l o o d i n g a n d l a n d s l i d e s i n P o r t Moody o n t h e o u t s k i r t s o f V a n couver, B r i t i s h  Columbia.  The o t h e r s t o r m s i n v e s t i g a t e d w e r e  88.  storms :.of a more t y p i c a l n a t u r e , i n c l u d i n g a summer s t o r m , f  o c c u r r i n g on J u n e 4, 19 77, a n d two w i n t e r s t o r m s w h i c h  occurred  on November 2 0 , 19 79 a n d December 5, 19 79.  For each of the t e s t storms the temperature of the o f n o n - d i v e r g e n c e was  c h o s e n as a c o n s t a n t  level  T . 2  The e f f e c t o f c h o s i n g an i n c o r r e c t v a l u e T  2  f o r the  tem-  p e r a t u r e a t t h e l e v e l o f n o n - d i v e r g e n c e when t h e c o r r e c t t e m p e r a ture i s T  m  c a n be r e a d i l y a c c o u n t e d f o r i n t h e e x p r e s s i o n f o r  r a i n f a l l b y t h e a d d i t i o n o f an a d j u s t m e n t AT"'" t o t h e t e m p e r a t u r e thickness of the diverging. equations  l a y e r AT i n t h e r a i n f a l l e s t i m a t i o n  ( 4 . 3 2 and 4 . 3 4 )  6.1  w h e r e AT  i s t h e t e m p e r a t u r e t h i c k n e s s b e t w e e n t h e t r u e tempe-  rature l e v e l of non-divergence actually  chosen  (T ) and t h e t e m p e r a t u r e m  (T ) . 2  F o l l o w i n g the steps o u t l i n e d i n the previous r a i n f a l l was  level  chapter,  the  e s t i m a t e d f r o m t h e a v a i l a b l e GOES i n f r a r e d  images.  A d e s c r i p t i o n o f e a c h o f t h e t e s t s t o r m s as w e l l as t h e  results  of the e s t i m a t i o n procedure are d i s c u s s e d below.  6.2  6.2.1  The O c t o b e r  Storm  3 1 , 19 7 8 R a i n f a l l  Estimates  Description  Between October  29 a n d November 2, 19 78 a m a j o r  occurred over the North Coast o f B r i t i s h Columbia. s t o r m , w i n d s g u s t i n g t o 125 k p h a n d 5-day r a i n f a l l  storm  During the t o t a l s ex-  c e e d i n g 400mm i n some a r e a s c o i n c i d e d w i t h h e a v y s n o w m e l t t o cause  f l o o d i n g a n d damages w e l l i n e x c e s s o f $10 m i l l i o n .  CNR c r e w members w e r e k i l l e d a r e s u l t o f roadbed  Two  a n d two m o t o r i s t s w e r e i n j u r e d as  damage {Chinook,  1979).  Schaefer  ( 1 9 7 9 a , b)  and Hammond (1978) d e s c r i b e t h e s t o r m f r o m a m e t e o r o l o g i c a l p o i n t ' of; v i e w .  F i g u r e 6.1 shows t h e i s o h y e t s e s t i m a t e d f r o m  the r e c o r d e d r a i n f a l l  amounts  ( f r o m S c h a e f e r , 19 7 9 a , b ) .  I t  a l s o shows t h e p r e c i p i t a t i o n gauges a n d t h e l o c a t i o n o f s e v e r a l s m a l l b a s i n s where r u n o f f volumes were a l s o measured. r a i n i n t h e a r e a i s extremely rugged w i t h mountains o v e r 2000 m.  The t e r -  rising to  I t i s s p a r s e l y i n h a b i t e d and p r e c i p i t a t i o n and  d i s c h a r g e gauges a r e few and f a r between.  F i g u r e 6.2 shows t h e  a r e a l e x t e n t o f t h i s s t o r m a t 0115 GMT as v i e w e d f r o m GOES-West.  The  a i m o f t h e a n a l y s i s was t o c h e c k  e s t i m a t i n g r a i n f a l l w i t h a major 19 78 s t o r m was t h e f i r s t  rainfall  storm.  the procedure f o r  Since the October 31,  e v e n t e x a m i n e d , most o f t h e  c a l c u l a t i o n s a p a r t f r o m t h e d i g i t i z i n g o f t h e c l o u d t o p temper a t u r e contours and t h e computation o f t h e areas w i t h i n  these  FIGURE 6.1 Map o f t h e T e r r a c e A r e a w i t h I s o h y e t s (mm) f o r t h e P e r i o d O c t o b e r 29 t o November 2, 19 78 ( A f t e r S c h a e f e r 1 9 7 9 a , b ) .  0115 31DC78 35E-1EC 00634 22232 SB6  FIGURE 6.2 A r e a l Extent o f t h e October V i e w e d f r o m GOES-West.  3 1 , 19 78 S t o r m a t  0115 GMT as  92.  c o n t o u r s w e r e c a r r i e d o u t by h a n d . was  This exploratory  exercise  n e c e s s a r y b e f o r e d e v e l o p i n g the computer r o u t i n e s w h i c h  used i n the r a i n f a l l e s t i m a t i o n c a l c u l a t i o n s i n the  were  subsequent  t e s t storm analyses.  6.2.2  Results The  a n a l y s i s was  l i m i t e d t o two  s t a t i o n s f o r which  the  c u m u l a t i v e o b s e r v e d r a i n f a l l s were a v a i l a b l e - T e r r a c e A i r p o r t , and G o s p e l P o i n t on t h e Queen C h a r l o t t e I s l a n d s .  The  series  of  GOES-West i m a g e s e x a m i n e d c o v e r e d t h e t i m e i n t e r v a l b e t w e e n 0045 GMT  on O c t o b e r  3 1 , 19 7 8 and 22 45 GMT  the 9 3 p o s s i b l e images, rectly,  on November 1, 19 78.  Of  29 w e r e e n h a n c e d a n d c o u l d be u s e d d i -  31 w e r e u n e n h a n c e d a n d h a d  t o f i r s t be p r o c e s s e d t h r o u g h  the v i d e o camera-special e f f e c t s generator-video monitor  system  t o e x t r a c t t h e a p p r o p r i a t e c l o u d t o p t e m p e r a t u r e c o n t o u r s , 16 were m i s s i n g c l o u d i n f o r m a t i o n f o r B r i t i s h  Columbia  ( f o r such  r e a s o n s as p o o r s i g n a l q u a l i t y , no t r a n s m i t t e d s i g n a l , and  the  use o f t h e s a t e l l i t e V I S S R t o s c a n a n o t h e r s e r i o u s s t o r m  situa-  t i o n o v e r t h e U n i t e d S t a t e s ) , and 17 w e r e v i s i b l e i m a g e s .  Al-  though  t h e v i s i b l e i m a g e s c o u l d n o t be u s e d d i r e c t l y  f o r the  r a i n f a l l e s t i m a t i o n , t h e y were u s e f u l f o r d e t e r m i n i n g t h e t y p e s of clouds present.  There were a l s o 4 images f o r w h i c h the g e o g r a p h i c t h a t i s a u t o m a t i c a l l y superimposed  on t h e i m a g e , was  signifi-  c a n t l y d i s p l a c e d w i t h r e s p e c t t o the a c t u a l geography. t h e s e i m a g e s t h e g e o g r a p h i c g r i d was  grid,  r e - n a v i g a t e d by e y e  In to  c o i n c i d e w i t h i n 20 km  The  o f the observed  r a i n f a l l was  land-ocean  c a l c u l a t e d f o r both  boundaries.  Terrace  and  Gospel  P o i n t w i t h the model parameters chosen from the l i t e r a t u r e the b a s i s o f c l o u d i d e n t i f i c a t i o n The  from the s a t e l l i t e images.  c o l d e s t c l o u d s were t e n t a t i v e l y i d e n t i f i e d  cumulonimbus w i t h i n l a y e r c l o u d s . m o d e l o f f r o n t s ( B j e r k n e s , 1918; and  as b a n d s  of  Both the c l a s s i c a l Norwegian Bjerknes  and S o l b e r g ,  1922)  t h e more r e c e n t m e s o s c a l e r a i n b a n d m o d e l s ( B r o w n i n g et  1973;  H a r r o l d , 1973;  1978;  and  clouds  a l o n g an a c t i v e f r o n t a l  system.  totals  f o r Terrace  Gospel P o i n t are given i n  6.1  on  and  Matejka  et  House et a l . , 1980)  A i r p o r t and  estimated  the observed  combination  of  estimated r a i n f a l l  rainfall totals.  r a i n f a l l s i n F i g u r e 6.3.  estimated  r a i n f a l l curve  same manner as t h e o b s e r v e d  records  The  LocateHi,  Table The  r a i n f a l l s a r e compared g r a p h i c a l l y w i t h  cumulative  the cumulative  Hobbs and  anticipate this  l i e w i t h i n 12% o f t h e o b s e r v e d  cumulative  6.2.3  a l . , 1976;  al.,  cumulative  seen  r a i n f a l l curve.  Rainfall  In  measurements,  raingauge  can be  g e n e r a l l y behaves i n the  C o m p a r i s o n o f S t r e a m f l o w And a d d i t i o n to the  As  Volumes streamflow  f o r f o u r s m a l l b a s i n s i n the T e r r a c e - K i t i m a t  area,  i n c l u d i n g the Exchamsiks R i v e r b a s i n , the H i r s c h Creek b a s i n , t h e Zymoetz R i v e r b a s i n , and available.  the  R i v e r b a s i n , were  I s o h y e t s w e r e c o n s t r u c t e d f r o m t h e GOES i m a g e s f o r  t h e p o i n t s shown i n F i g u r e 6.4. F i g u r e 6.5  Zymagotitz  From t h e i s o h y e t s shown i n  the r a i n f a l l volume o v e r  each of the f o u r b a s i n s  was  TABLE 6.1  Comparison o f Observed and E s t i m a t e d Storm T o t a l s f o r t h e P e r i o d 0045 GMT o n O c t o b e r 3 1 , 1978 t o 2245 GMT o n November 1, 1978.  OBSERVED RAINFALL (mm)  ESTIMATED RAINFALL (mm)  port  200  Point  250  STATION  Terrace  Gospel  DIFFERENCE  e  wc g/mc  Y °C/1000m  (mm)  (%)  180  20  10  0.2  10  5  220  30  12  0.2  10  5  3  Air-  T  1  1  1  :  1  1  r  250 G O S P E L POINT E s t i m a t e d rainfall  - 2 0 0 E c o o  r  Q. U  ,o O O  GOSPEL POINT Observed rainfall  O  150  CD  "D <D  o ^  a 'OO  ,A  <  50  J__TERRACE QOO ° Observed  A  E 3 O o  CD  A  V  0  -A  /O  AIRPORT rainfall  OCD  TERRACE  AIRPORT  Estimated  rainfall  L  0600 1200 Oct. 3 1 / 7 8  1800 0 0 0 0 0 6 0 0 Nov. 1/78 Time (GMT)  1200  1800  FIGURE 6 . 3 E s t i m a t e d and Observed P r e c i p i t a t i o n Airport.  a t Gospel P o i n t and T e r r a c e  FIGURE  6.4  L o c a t i o n o f G r i d P o i n t s Used t o C o n s t r u c t S a t e l l i t e I s o h y e t s f o r t h e O c t o b e r 3 1 , 19 78 S t o r m .  Estimated  FIGURE  6.5  I s o h y e t s o f S a t e l l i t e E s t i m a t e d R a i n f a l l (mm) f o r the October 3 1 , 19 78 S t o r m B a s e d on t h e G r i d P o i n t s Shown i n F i g u r e 6.4.  98.  e s t i m a t e d and compared i n T a b l e determined off  from Schaefer's  volume r e c o r d e d  lumes e s t i m a t e d  6.2 w i t h t h e r a i n f a l l  isohyets  ( F i g u r e 6 . 1 ) , and t h e r u n -  a t t h e d i s c h a r g e gauges.  from t h e s a t e l l i t e  volume  The r a i n f a l l v o -  i m a g e s compare w e l l w i t h t h e  c o n v e n t i o n a l v o l u m e c a l c u l a t i o n s a n d a r e w i t h i n 20% o f t h e o b served r u n o f f volumes.  6.3  ( B a s e f l o w was  The December 17,19 79 R a i n f a l l The  subtracted.)  Estimates  December 1 7 , 1979 s t o r m was t h e s e c o n d m a j o r  analyzed.  Since the storm  of B r i t i s h  C o l u m b i a a n d A l b e r t a , an a r e a i n w h i c h t h e m a j o r i t y  of the people raingauges ty  occurred over  event  i n these p r o v i n c e s  the southern p o r t i o n s  r e s i d e s a n d h e n c e , w h e r e many  a r e l o c a t e d , i t was a n a p p r o p r i a t e t e s t o f t h e a b i l i -  o f the procedure  t o make r a i n f a l l e s t i m a t e s  a t a number o f  stations.  6.3.1  Storm D e s c r i p t i o n  The  s t o r m was t h e l a s t o f two e v e n t s  r e g i o n w i t h i n a 4-day p e r i o d . British  Columbia, the f i r s t  t o move i n t o t h e  I n t h e Lower M a i n l a n d  storm s a t u r a t e d s o i l s  area o f  leading to  e x t e n s i v e p r o p e r t y damage f r o m f l o o d i n g a n d m u d s l i d e s in 17,  P o r t Moody n e a r V a n c o u v e r . 19 79,  The s e c o n d s t o r m ,  especially  t h a t o f December  added t o t h e a l r e a d y h i g h w a t e r t a b l e l e v e l s  and t h e r e  w e r e many r e p o r t s o f f l o o d e d b a s e m e n t s a n d w a s h e d o u t r o a d s i n and  a r o u n d V a n c o u v e r and V i c t o r i a .  19 80)  shows t h e c o m b i n e d o b s e r v e d  F i g u r e 6.6  (from  Schaefer,  i s o h y e t s f o r t h e 7-day p e r i o d  TABLE 6.2  Comparison  of Rainfall  and R u n o f f Volumes i n m  ( B a s e f l o w has been s u b t r a c t e d  Basin:  Exchamsiks 2 ):  480  Observed  Runoff  116  Rainfall Isohyets  from  Area  (km  R a i n f a l l from s a t e l l i t e images  from the  Zymoetz  2950 (%)  281*  ( % )  x  10  streamflow.)  Zymagotitz  H i r s ch  350  330  58*  W  88  ( % )  121  (4)  388  (38)  65  (12)  81  (8)  107  (8)  328  (17)  69  (19)  73  (17)  Key: % = % Difference * I n c l u d e d some e s t i m a t e d v a l u e s  100  FIGURE  6.6  Map o f t h e V a n c o u v e r I s l a n d - L o w e r M a i n l a n d A r e a w i t h I s o h y e t s (mm) f o r t h e 7-Day P e r i o d f r o m December 12 t o 1 8 , 19 79 ( A f t e r S c h a e f e r , 1980) .  1.01.  f r o m December 12 t o December 1 8 , 1 9 7 9 , w h i l e F i g u r e 6.7 t h e a r e a l e x t e n t o f t h e s t o r m a t 0 715 GMT as v i e w e d  shows  o n December 1 7 , 19 79  f r o m GOES-West.  6.3.2. R e s u l t s The s a t e l l i t e  i m a g e s f o r December:. 1 7 , 1979 w e r e  and r a i n f a l l was e s t i m a t e d f o r 24 s t a t i o n s i n B r i t i s h and  2 stations i n Alberta.  shown i n F i g u r e 6.8.  analyzed  Columbia  The l o c a t i o n s o f t h e s t a t i o n s a r e  Since the a n a l y s i s proceeded  i n real  time  as t h e s t o r m p r o g r e s s e d , a l l o f t h e s t a t i o n s w e r e a s s u m e d t o be r e c e i v i n g p r e c i p i t a t i o n i n t h e f o r m o f r a i n . rainfall  d a t a was  a v a i l a b l e immediately  Observed h o u r l y  f o r only three s t a t i o n s :  Vancouver I n t e r n a t i o n a l A i r p o r t , V i c t o r i a I n t e r n a t i o n a l and Hope A i r p o r t .  The a c t u a l t y p e a n d amount o f p r e c i p i t a t i o n  r e c e i v e d a t t h e o t h e r s t a t i o n s was n o t known later  Airport,  ( a l m o s t 4 months) when t h e o b s e r v e d  Those o t h e r s t a t i o n s w h i c h  until  some t i m e  d a t a became a v a i l a b l e .  normally report hourly r a i n f a l l  w e r e , i n g e n e r a l , r e c e i v i n g snow a n d h e n c e o n l y 6-hour snow were a v a i l a b l e . a 6- o r 1 2 - h o u r l y  The r e m a i n i n g s t a t i o n s  amounts amounts  r e p o r t e d p r e c i p i t a t i o n on  basis.  6.3.2a P o i n t E s t i m a t e s The s e r i e s o f GOES-West i m a g e s e x a m i n e d c o v e r e d t h e 6 - h o u r interval  f r o m 00 45 t o 06 45 GMT  s e g m e n t was  on December 1 7 , 19 79 .  c h o s e n f o r a number o f r e a s o n s .  December 17, 1 9 7 9 , t h e o b s e r v e d  rainfall  and t h i s was e v i d e n t on t h e s a t e l l i t e  T h i s 6^-hour  P r i o r t o 0045 GMT  on  amounts w e r e n e g l i g i b l e  images which  r e c o r d e d low  FIGURE 6.7 A r e a l E x t e n t o f December 17, 19 79 Storm a t 0 715 GMT as Viewed from GOES-West.  103.  FIGURE  6.8  L o c a t i o n o f S t a t i o n s U s e d i n t h e December 1 7 , 1979 S t o r m A n a l y s i s . 1 2 3 4 5 6 7 8 9 10 11 12 13  Blue River B u l l Harbour Burns Lake Castlegar Airport Cranbrook A i r p o r t Dease L a k e Hope A i r p o r t Kamloops A i r p o r t Kelowna A i r p o r t Langara Lytton Pehticton Airport P o r t Hardy A i r p o r t  14 15 16 17 18 19 20 21 22 23 24 25 26  P r i n c e George A i r p o r t P r i n c e RupertAiitrport Quesnel A i r p o r t Revelstoke A i r p o r t S a l m o n Arm Sandspit Airport Terrace A i r p o r t Tofino Airport Vancouver I n t e r n a t i o n a l Airport Victoria International Airport W i l l i a m s Lake A i r p o r t Banff Calgary  104.  cloud  b u t no e x p a n d i n g deep c o l d c l o u d  6-hour p e r i o d  the  be u s e d d i r e c t l y i n t h e  procedure, thus e l i m i n a t i n g  the uncertainties  i n f r a r e d images were enhanced.  In addition,  roughly corresponded to the f i r s t day  and a l l o f t h e s t a t i o n s  (as  r a i n f a l l equivalent)  many o f t h e  t h i s 6-hour  period  6 hours o f the c l i m a t o l o g i c a l  r e p o r t e d 6-hour r a i n f a l l o r  amounts w h i c h c o u l d  the 6-hour c u m u l a t i v e r a i n f a l l  inferred  estimation  i n t r o d u c e d by  A f t e r 0 6 45 GMT  u s i n g unenhanced i n f r a r e d images.  For  During  a l l o f t h e i n f r a r e d images a v a i l a b l e were en-  h a n c e d arid as s u c h c o u l d  with  over the region.  snowfall  b e u s e d t o compare  estimates.  t h i s s e g m e n t o f t h e s t o r m t h e w a t e r c o n t e n t wc  f r o m t h e TIROS-N d a t a s i n c e  i t was r e a d i l y  a t t h e t i m e o f t h e s t o r m a n d t h e l a p s e r a t e y was to the saturated  adiabatic  lapse rate y  was  available  assumed e q u a l  = 5°C/1000m.  For  s Vancouver I n t e r n a t i o n a l and  Hope A i r p o r t t h e e f f i c i e n c y e was  4.35.  I t was assumed t h a t  n a t i o n a l A i r p o r t was the ly  Airport, Victoria International  other stations available.  determined using  representative  Inter-  of the e f f i c i e n c i e s at a l l  f o r w h i c h t h e o b s e r v e d d a t a was n o t i m m e d i a t e -  W i t h these v a l u e s o f t h e p a r a m e t e r s , the 6-hour  the 6-hour c u m u l a t i v e o b s e r v e d r a i n f a l l s  percent difference the  equation  the e f f i c i e n c y e f o r Vancouver  c u m u l a t i v e e s t i m a t e d r a i n f a l l s were c a l c u l a t e d with  Airport,  and then compared i n Table 6.3.  between t h e o b s e r v e d 6-hour r a i n f a l l  e s t i m a t e d 6-hour r a i n f a l l  the w o r s t d i f f e r e n c e s  total  total  r a n g e s f r o m 0 t o 2500%  found f o r those s t a t i o n s  The and  with  t h a t were l a t e r  105.  TABLE 6.3  Comparison o f O b s e r v e d and E s t i m a t e d R a i n f a l l T o t a l s f o r t h e 6-hour Segment 0000 GMT t o 0600 GMT on December 17, 19 79. Vancouver I n t e r n a t i o n a l A i r p o r t d a t a was used t o c a l i b r a t e the a d j u s t m e n t p a r a m e t e r e .  STATION  OBSERVED RAINFALL (mm)  ESTIMATED RAINFALL (mm)  DIFFERENCE  e  wc (g/m ) 3  (mm)  (%)  O b s e r v e d Data P r e c i p i t a t i o n Immediately A v a i l a b l e ; CALIBRATION STATIONVANCOUVER I.A. VICTORIA I.A. HOPE A.  10.6 6.8 0.0  9.5 6.4 2.5  1.1 0.4 2.5  10 6  O b s e r v e d P r e c i p i t a t i o n Data Not Immediately  Available;  Blue River B a l l Harbour Burns Lake C a s t l e g a r A. Cranbrook A. Dease Lake Kamloops A. Kelowna A. Langara Lytton P e n t i c t o n A. P o r t Hardy A. P r i n c e George A. P r i n c e R u p e r t A. Quesnel A. R e v e l s t o k e A. Salmon Arml  2 .9 0 .3  47 3  1 .2 1 .4 0 .7'7  50 88 96  S a n d s p i t A. T e r r a c e A. T o f i n o A. W i l l i a m s Lake A. Banff Calgary  6.2 S 8.9 M S 2.4 S 1.6 S 0.8 S T S T S 0.8 RS 1.6 S 0 .0 6.8 2.0 S 8.8 RS 1.3 S 6 .6 S 1.0 S 5.1 S 5.0 1.6 S 22.6 0 .2 S 0 .3 S 0.0  9.1 9.2 5.2 3.6 3.0 0.03 3.2 2.2 0.2 7.8 1.7 7.4 1.5 1.0 5.2 7.7 7.3 7.3 0.3 0.7 15.6 5.2 2.6 0 .0  10 10 5  0 .2  5 10 5 5 5 5 2 2 13 2 2 10 10 13 2 5 5 5 13 13 13 2 2 2  _  0 .6 75 6 .2 388 1 .7 0 .6 9 0 .5 25 7 .8 89 3 .9 300 1 .1 17 6 .3 6 30 2 .2 43 4 .7 94 0 .9 56 7 .0 31 5 .0 2500 2 .3 767 0 0  Key: A I.A. M RS  0.2 0.2 0.2  Airport International Airport Missing mixed r a i n and snow i n mm r a i n e q u i v a l e n t s n o w f a l l i n mm o f r a i n e q u i v a l e n t two s e p a r a t e observers  0 2  Y (°C/1000m  106.  d e t e r m i n e d t o be r e c e i v i n g snow o r m i x e d r a i n and snow. difficulty  i n estimating snowfall lies  The  i n the behaviour o f the  s n o w f l a k e s as t h e y f a l l , w i t h t h e i r t e n d e n c y  to d r i f t with the  w i n d some d i s t a n c e f r o m t h e c l o u d l o c a t i o n , as w e l l a s , i n t h e p r o b l e m o f m e a s u r i n g p o i n t snow a c c u m u l a t i o n . the  stations  Estimates f o r  r e c e i v i n g o n l y r a i n w e r e w i t h i n 10% o f t h e o b s e r v e d  6-hour r a i n f a l l  t o t a l except f o r Sandspit A i r p o r t which had a  94% o r 4.7  d i f f e r e n c e b e t w e e n o b s e r v e d a n d e s t i m a t e d 6-hour  rainfall  (mm)  totals.  nificant rainfall  S a n d s p i t A i r p o r t may h a v e b e e n r e c e i v i n g  sig-  f r o m "warm" o r l o w l e v e l c l o u d s w h i c h h a d  c l o u d t o p t e m p e r a t u r e s warmer t h a n t h e c o l d e r , s t e p w i s e e n h a n c e d , t e m p e r a t u r e r a n g e o f t h e e n h a n c e m e n t scheme u s e d on t h e i n f r a r e d images.  A f t e r the o b s e r v e d p r e c i p i t a t i o n d a t a were r e c e i v e d , the actual efficiencies the  f o r each s t a t i o n were t h e n d e t e r m i n e d  o b s e r v e d d a t a u s i n g e q u a t i o n 4.35.  from  The e s t i m a t e d 6-hour t o -  t a l p r e c i p i t a t i o n w e r e r e c a l c u l a t e d a n d a r e shown i n T a b l e  6.4.  The e s t i m a t e s a r e p l o t t e d w i t h t h e o b s e r v e d d a t a i n F i g u r e 6.9.  The e s t i m a t e s w e r e d e t e r m i n e d u s i n g t h e c o m p u t e r r o u t i n e s developed d u r i n g the course o f the a n a l y s i s o f the f i r s t ( t h a t o f O c t o b e r 3 1 , 19 78) .  The r o u t i n e s  storm  considerably eased the  c o m p u t a t i o n s s i n c e f o r t h e 6-hour p e r i o d a n a l y z e d t h e r e were 12 h a l f - h o u r l y i n f r a r e d i m a g e s w i t h up t o 41 c e l l s p e r image a n d on t h e a v e r a g e o f 2 t e m p e r a t u r e  contours per c e l l to d i g i t i z e , a l l  107 .  TABLE 6.4  Comparison o f Observed and E s t i m a t e d R a i n f a l l T o t a l s f o r t h e 6-hour Segment 0000GMT t o 0600GMT on December 1 7 , 1 9 7 9 . For each s t a t i o n t h e e m p i r i c a l a d j u s t m e n t e has been d e t e r m i n e d u s i n g the observed data f o r t h a t s t a t i o n .  STATION  Vancouver I.A Victoria I.A. Hope A. Blue River Bull Harbour Burns Lake Castlegar A. Cranbrook A. Dease Lake Kamloops A. Kelowna A. Langara Lytton Penticton A. Port Hardy A. Prince George A. Prince Rupert A. Quesnel A. Revelstoke A. Salmon Arm''" Sandspit A. Terrace A. Tofino A. Williams Lake A. Banff Calgary Key: A I .A. M RS S 1  OBSERVED RAINFALL (mm) 10 .6 6.8 0 .0 6.2 S 8.9 M S 2.4 S 1.6 S 0.8 s T S T S 0 . 8 RS 1.6 S 0 .0 6.8 2.0 S 8.8 RS 1.3 s 6.6 s 1.0 S 5.1 S 5 .0 1.6 S 22.6 0.2 S 0.3 S 0 .0  ESTIMATED RAINFALL (mm) 9.5 6.4 2 .5 9.1 9.2 5.2 3.6 3.0 0.03 3.2 2.2 0.3 7. 8 1.7 7.4 1.5 1.5 5.2 7.7 7.3 7.3 0.4 1.0 23.4 5.2 1.3 0.0  Airport International Airport Missing Mixed rain and snow in mm rain equivalent Snowfall in mm rain equivalent two separate observers  DIFFERENCE (mm) 1.1 0.4 2.5 2.9 0.3  -  1.2 1.4 0.77  -  0 .5 6.2 1.7 0.6 0.5 7.3 3.9 1.1 6.3 2.2 4.6 0 .6 0. 8 5.0 1.0 0  (%)  (9/m  10 6  10 10 10 5 10 5 5 5 5 2 2 13 2 2 10 10 13 2 5 5 5 13 13 13 2 2 2  0.2 0.2 - 0.2 47 0.2 3 0 .2 - 0 .2 50 0 .2 88 0.2 96 0 .2 - 0.2 - 0.2 63 0 . 3 388 0.2 - 0.2 9 0.2 25 0 .2 83 0.3 300 0.2 17 0.2 6 30 0 .2 43 0 .2 92 0.3 38 0.3 4 0.3 2500 0.2 333 0.1 0 0 .1  108.  T  24 1-  1  1  1  LEGEND « •  1  1  1  1  1  1  1  1  1  r  I  i  l_  rain  0  mixed rain and snow  O  snow  y  ^  /  / 20r-  /  /  /  12  / e  ©  / /  /  I 4  o.  » 8  •  i 12  Estimated Storm Total  .  L  x  16 Precipitation  I 20  i  24  28  ( mm )  FIGURE 6.9 E s t i m a t e d a n d O b s e r v e d P r e c i p i t a t i o n f o r t h e December 1 7 , 19 79 Storm. ( F o r each s t a t i o n t h e e m p i r i c a l a d j u s t m e n t e has been determined from t h e observed d a t a f o r t h a t s t a t i o n . )  109.  o f which had rainfall  t o be m a n i p u l a t e d and  estimates  " a c c o u n t e d f o r " t o make  f o r each o f the  have been a tremendous t a s k  26  t o do by  stations.  This  would  hand.  6.3.2b A r e a l R a i n f a l l D i s t r i b u t i o n As w e l l as p r o v i d i n g p o i n t e s t i m a t e s  f o r the s p e c i f i e d  s t a t i o n s , the computer r o u t i n e s a l s o o u t p u t r a i n f a l l for  each c e l l .  I n t h i s way  a series of s a t e l l i t e  amounts  pictures  be-  comes a s e q u e n c e o f c e l l r a i n f a l l  "maps", f o r e x a m p l e F i g u r e  showing the e v o l u t i o n o f r a i n f a l l  i n time r e l a t i v e to the  Some c e l l s while  can be  others  are  s e e n t o i n c r e a s e i n s i z e and decreasing  sequences of c e l l r a i n f a l l  and  not  release  o f l a r g e s c a l e c l o u d s y s t e m d e v e l o p m e n t and  is  the  accompanying  areal d i s t r i b u t i o n of r a i n f a l l  rainfall.  developing  over a smaller  area  needed.  T h i s i s a c c o m p l i s h e d by of p o i n t s  and  g r i d o f 150 I s l a n d and satellite  e s t i m a t i n g the r a i n f a l l  then c o n s t r u c t i n g the  points  estimated  isohyets.  isohyets.  as shown i n F i g u r e  t h e L o w e r M a i n l a n d was  b e t w e e n 0045 and the  Such  observation  H o w e v e r , i n p r a c t i c e , a more d e t a i l e d a n a l y s i s o f t h e s t o r m and  storm.  rainfall  releasing rainfall.  "maps" a r e u s e f u l f o r t h e  6.10,  F i g u r e 6.12  area  grid  an e x a m p l e ,  covering  chosen i n o r d e r  isohyets over t h i s  0645 GMT.  6.11  As  for a  to  a  Vancouver construct  f o r the 6-hour p e r i o d  shows t h e e v o l u t i o n  of  FIGURE  6.10  Storm C e l l  Rainfall  "Maps" f o r 2 H o u r s  D u r i n g t h e December 1 7 , 19 79 S t o r m  111.  FIGURE  6.11  L o c a t i o n o f G r i d P o i n t s Used t o C o n s t r u c t S a t e l l i t e I s o h y e t s f o r t h e December 1 7 , 19 79 S t o r m . Observed r a i n f a l l s B u l l Harbour P o r t Hardy Tofino Vancouver Victoria  (mm) f o r : 8.9 6.8 22.6 10.6 6.8  Estimated  FIGURE  6.12  E v o l u t i o n o f I s o h y e t s o f R a i n f a l l (mm) f o r t h e December 17, 19 79 S t o r m f o r t h e G r i d P o i n t s Shown i n F i g u r e 6.11.  Estimated hM  1  The  i s o h y e t s shown i n F i g u r e 6.5  w e r e b a s e d on p r e c i p i t a t i o n gauge d a t a  by and  Schaefer Schaefer's  o f t h e t e r r a i n , w h i l e t h e i s o h y e t s i n F i g u r e 6.12 entirely  from s a t e l l i t e  images.  satellite  knowledge  are  derived  A v i s u a l comparison r e v e a l s  s u b t l e d i f f e r e n c e s i n the r a i n f a l l d e r i v e d from the  (1980)  patterns.  i m a g e s show t h e  i n the s p a t i a l d i s t r i b u t i o n of the r a i n f a l l  The  isohyets  short time due  variation  t o changes i n  t h e v e r t i c a l m o t i o n s i n t h e a i r mass t h a t a r e r e f l e c t e d changes i n the tops of the c l o u d s . rainfall  d i s t r i b u t i o n are i m p l i c i t l y  determined from s u r f a c e data of the ly  s t o r m , h a v e had  incorporated  The  The  o f t e n as e v e r y  northeast  half-hour  satellite  period explicit-  o v e r ungauged the s p a r s e l y  i f necessary, less  estiareas,  populated  o f V a n c o u v e r I s l a n d can  e v o l u t i o n o f t h e i s o h y e t s can be  gauge i n f o r m a t i o n i s a v a i l a b l e and  isohyets,  images f o r r a i n f a l l  d i s t r i b u t i o n of r a i n f a l l  to the  the  pattern.  e x m p l e , t h e o c e a n a r e a t o t h e w e s t and  determined.  The  the e f f e c t s of the topography  advantage o f u s i n g s a t e l l i t e  mountainous r e g i o n s  data  included.  e f f e c t s on  f o r t h e e n t i r e s e v e n day  i n t o the r a i n f a l l  mation i s t h a t the for  Orographic  by  whereas the  frequently.  information should  examined  be  be  as  precipitation  Ideally  combined - the  gauge gauge  data  114.  p r o v i d i n g i n f o r m a t i o n on t h e s m a l l s c a l e  (<15 km) l o c a l  tions i n the r a i n f a l l ,  images p r o v i d i n g t h e  and t h e s a t e l l i t e  varia-  meso- a n d m a c r o s c a l e s p a t i a l d i s t r i b u t i o n o f t h e r a i n f a l l .  6.4  6.4.1  The J u n e  Storm  4, 19 77 R a i n f a l l E s t i m a t e s  Description  The J u n e  4, 1977 s t o r m was t h e f i r s t o f t h r e e l e s s e r  storms a n a l y z e d t o t e s t the procedure f o r e s t i m a t i n g  rainfall  f r o m more t y p i c a l e v e n t s .  The  s t o r m was i n c l u d e d t o a l s o t e s t t h e p r o c e d u r e o n  a summer r a i n f a l l e v e n t f o r 7 s t a t i o n s i n t h e i n t e r i o r o f B r i tish  Columbia.  The s t a t i o n l o c a t i o n s a r e shown i n F i g u r e 6 . 1 3 .  R a i n f a l l came f r o m a number o f a c t i v e  cells  along a weakening  e a s t w a r d m o v i n g f r o n t a l s y s t e m a n d o b s e r v e d amounts w e r e ally  l e s s t h a n 10 mm, w i t h  a c e l l r e m a i n i n g o v e r any one s t a t i o n  f o r u s u a l l y l e s s than 2 hours.  Figure  6 . 1 4 shows t h e c l o u d  c o v e r a g e f o r 0245 GMT as v i e w e d f r o m GOES-West. l o o p s c o n t a i n i n g t h e 24-hour were a v a i l a b l e  6.4.2  As w e l l ,  s e r i e s o f GOES i n f r a r e d  film  images  a l l o w i n g f o r a c l o s e r i n v e s t i g a t i o n o f t h e deve-  lopment o f t h e s t o r m . i n Washington,  gener-  The l o o p s w e r e p r o v i d e d o n l o a n f r o m NESS  D.C.  Results Of t h e 2 7 a v a i l a b l e GOES i m a g e s b e t w e e n 0115 a n d 22 45. GMT,  10 w e r e e n h a n c e d  i n f r a r e d images, 6 were unenhanced  i m a g e s a n d 11 w e r e v i s i b l e i m a g e s .  infrared  The s t o r m p o s e d a s p e c i a l  115.  FIGURE Location 1 2 3 4  6.13 of S t a t i o n s  U s e d i n t h e J u n e 4,  Duncan L a k e Dam Revelstoke A i r p o r t Mica Dam Castlegar Airport  5 6 7  1977  Storm  Analysis  Elko Cranbrook A i r p o r t Blue River  FIGURE 6.14 A r e a l E x t e n t o f June 4, 19 77 Storm a t 0 245 GMT as Viewed from GOES-West.  117.  problem  i n t h a t two d i f f e r e n t e n h a n c e m e n t schemes w e r e e m p l o y e d :  7 o f t h e e n h a n c e d i n f r a r e d i m a g e s h a d t h e "CA" e n h a n c e m e n t scheme w h i l e t h e o t h e r 3 h a d t h e "EC" e n h a n c e m e n t scheme. the  3 "EC" e n h a n c e d i m a g e s a l o n g w i t h t h e 6 u n e n h a n c e d i m a g e s  were f i r s t  analyzed with the video camera-special e f f e c t s  a t o r -video^ monitor  system  t o t h e "CA" t e m p e r a t u r e be  Consequently  t o f i n d those  contours  that  gener-  corresponded  contours, before r a i n f a l l estimates  could  made.  For t h i s storm, water  a n d e s t i m a t e d r a i n f a l l s m a t c h e d f o r Duncan L a k e  s  = 5°C/1000m.  the o t h e r s t a t i o n s which  The v a l u e s w e r e assumed c o n s t a n t f o r  i s reasonable  area i n v o l v e d .  Table  storm r a i n f a l l s  f o r t h e seven s t a t i o n s .  served rain  6.5.1  given the small geographical  6.5 compares t h e o b s e r v e d  a r e a l l w i t h i n 40% o r a p p r o x i m a t e l y  rain totals.  6.5  that the  The l a p s e r a t e y was s e t e q u a l t o t h e s a t u r a t e d a d i a b a t i c  lapse rate y  tals  e f f i c i e n c y e and  c o n t e n t wc w e r e c h o s e n f r o m t h e l i t e r a t u r e s u c h  t o t a l observed Dam.  t h e model parameters  and e s t i m a t e d  The e s t i m a t e d r a i n t o 3 mm o f t h e  observed  F i g u r e 6.IS shows a p l o t o f t h e e s t i m a t e d a n d o b totals.  The November 2 0 , 1979 R a i n f a l l  Estimates  Storm D e s c r i p t i o n The  November 2 0 , 1979 s t o r m was a n e v e n t s u g g e s t e d f o r  a n a l y s i s b y t h e P a c i f i c W e a t h e r C e n t r e s i n c e i t r e p r e s e n t e d one of the usual widespread  f r o n t a l r a i n f a l l events which  occur  over  TABLE 6.5  C o m p a r i s o n o f O b s e r v e d and E s t i m a t e d R a i n f a l l t h e S t o r m o f June 4, 19 77.  STATION  Calibration Station; Duncan L a k e Dam R e v e l s t o k e A. M i c a Dam C a s t l e g a r A. Elko C r a n b r o o k A. Blue River  Key: A. M  OBSERVED RAINFALL (mm)  ESTIMATED RAINFALL (mm)  DIFFERENCE (mm)  (%)  Totals f o r  e  wc  Y 3 ,o„ _^ (g/m ) ( C/1000m) / i n n n  8.5  8.4  0.1  1  0 .1  5  3.3 >1.7M 8.0 2.1 2.1 3.1  2 .2 2.3 11.2 2.8 2.8 2.5  1.1 ^0 .6 3.2 0.7 0.7 0.5  33 ^35 40 33 33 19  0.1 0.1 0.1 0.1 0.1 0.1  5 5 5 5 5 5  Airport Some d a t a m i s s i n g from o b s e r v e d  record  5 5 5 5 5 5  T  24 U  1  1  1  1  1  i  1  i  1  1  1  T  LEGEND rain  C - calibration  station  20  /  4*  16  12  c/  6  /  /•  •  /  /  /  /*  \L .  I  i  4  I  i  8  Estimated Storm  I  i  I  i  12  16  Total  Precipitation  I 20  .  I 24  .  I 28  (mm)  FIGURE 6 . 1 5 E s t i m a t e d and Observed P r e c i p i t a t i o n Storm.  f o r t h e J u n e 4, 19 77  120.  the  P r i n c e Rupert area of B r i t i s h  W e a t h e r C e n t r e was the  The  Pacific  i n t e r e s t e d i n determining whether or not  estimation procedure could d i s t i n g u i s h differences i n r a i n -  fall  f r o m t h i s s y s t e m a t two  and T e r r a c e . at  Columbia.  1115  GMT  Figure  adjacent stations:  Prince  Rupert  6>-16 shows t h e a r e a l c o v e r a g e o f t h e s t o r m  as v i e w e d f r o m GOES-West.  The  s t o r m p r o v i d e d an  a d d i t i o n a l check o f the p r o c e d u r e f o r the T e r r a c e - P r i n c e Rupert a r e a u n d e r more n o r m a l  6.5.2  conditions.  Results Of t h e 26 p o s s i b l e GOES i m a g e s i n t h e r a i n f a l l p e r i o d  0145  t o 1415  GMT,  12 w e r e e n h a n c e d i n f r a r e d i m a g e s ,  8 were  from  un-  e n h a n c e d i n f r a r e d i m a g e s w h i c h h a d t o f i r s t be p r o c e s s e d t h r o u g h the  video camera-special e f f e c t s generator-video monitor system  p r i o r t o a n a l y s i s , and 6 w e r e n o t  The w a t e r c o n t e n t was  available.  i n f e r r e d f r o m TIROS-N d a t a and  l a p s e r a t e y was  s e t equal to the saturated a d i a b a t i c lapse  Y  The  s  = 5°C/1000m.  u s i n g the f i r s t  e f f i c i e n c y e was  determined from e q u a t i o n  T h i s v a l u e o f e was  apply to Terrace f o r the e n t i r e storm. e s t i m a t e d and o b s e r v e d r a i n f a l l w i t h i n 1 1 % o r 4 mm  rainfall 130 km  totals.  T a b l e 6.6 The  assumed t o  compares t h e  estimated r a i n f a l l  of the observed r a i n f a l l .  The  estimation  a b l e t o d i s t i n g u i s h the d i f f e r e n c e between the  r e c e i v e d a t P r i n c e R u p e r t on t h e c o a s t and T e r r a c e some  inland.  4.35  assumed c o n s t a n t a t  P r i n c e R u p e r t f o r t h e r e m a i n d e r o f t h e s t o r m , and was  p r o c e d u r e was  rate  6-hour o b s e r v e d t o t a l p r e c i p i t a t i o n a t P r i n c e  R u p e r t as t h e c a l i b r a t i o n .  was  the  FIGURE 6.16 A r e a l Extent o f November 20, 1979 Storm a t 1115 GMT as Viewed from GOES-West.  TABLE 6.6  C o m p a r i s o n o f O b s e r v e d and E s t i m a t e d t h e S t o r m o f November 20, 1979  OBSERVED RAINFALL (mm)  ESTIMATED RAINFALL (mm)  Calibration Station: P r i n c e R u p e r t A.  64.0  T e r r a c e A.  36 .4  STATION  Key: A  Airport  R a i n f a l l Totals f o r  DIFFERENCE (mm)  (%)  59 .0  5 .0  8  40 .2  3.8  10  e  wc  Y  (g/m )  (°C/1000m)  0.1  7  5  0.1  7  5  3  123.  6.6  6.6.1  The  December 5, 1979  Storm The  R a i n f a l l Estimates  Description  a n a l y s i s o f t h e December 5, 1979  s t o r m was  also  s u g g e s t e d by t h e P a c i f i c W e a t h e r C e n t r e s i n c e t h e y e x p e r i e n c e d l e s s than normal  a c c u r a c y i n t h e i r f o r e c a s t due  to poor  ization"  of the n u m e r i c a l analyses they r e c e i v e d .  sunshine  f o r t h e Lower M a i n l a n d of B r i t i s h  by r a i n f r o m a n a r r o w lite  images.  The  initial-  The  forecast  C o l u m b i a was  replaced  b a n d o f c l o u d c l e a r l y v i s i b l e on t h e  observed p r e c i p i t a t i o n ranged  V i c t o r i a I n t e r n a t i o n a l A i r p o r t t o some 16 mm F i g u r e -6.17 shows t h e GOES-West s a t e l l i t e  satel-  from a t r a c e  a t New  at  Westminster.  image f o r 1015  GMT  on  December 5, 19 79.  The  a n a l y s i s p r o v i d e d an a d d i t i o n a l c h e c k o f t h e  procedure  o v e r a w e l l - g a u g e d a r e a ( s u c h as V a n c o u v e r ) .  6.6.2  Results Of t h e 46 p o s s i b l e GOES i m a g e s f o r t h e p e r i o d 0015  GMT, red  14 w e r e e n h a n c e d i n f r a r e d i m a g e s , images w h i c h had  t o be  14 w e r e u n e n h a n c e d  infra-  f i r s t p r o c e s s e d through the video  camera-special e f f e c t s generator-video monitor system, v i s i b l e i m a g e s and  t o 2 315  4 were  14 w e r e m i s s i n g .  The w a t e r c o n t e n t wc was a n d t h e l a p s e r a t e y was  i n f e r r e d f r o m t h e TIROS-N d a t a  s e t equal to the s a t u r a t e d a d i a b a t i c  124.  FIGURE  6.17  A r e a l E x t e n t o f December 5, 19 79 Storm a t 1015 GMT as Viewed from GOES-West.  lapse rate y  s  = 5°C/1000m.  The  e f f i c i e n c y e was  from e q u a t i o n 4.35 u s i n g the f i r s t  determined  6-hour o b s e r v e d  total  preci-  p i t a t i o n a t V a n c o u v e r I n t e r n a t i o n a l A i r p o r t as c a l i b r a t i o n . v a l u e f o r e was  assumed c o n s t a n t a t V a n c o u v e r I n t e r n a t i o n a l  p o r t f o r the remainder at  the o t h e r s t a t i o n s  o f t h e s t o r m , and was f o r the e n t i r e storm.  t h e o b s e r v e d and e s t i m a t e d r a i n f a l l yzed"  Except  totals  totals.  (9.5 mm)  F o r West Vancouver,  assumed t o a p p l y T a b l e 6.7  compares  f o r the s t a t i o n s  local orographic l i f t i n g  I n t e r n a t i o n a l A i r p o r t gauge. served r a i n f a l l  totals  T h i s may  and s u g g e s t s  u n d e r e s t i m a t e d by  shows t h e e s t i m a t e d  the estimated r a i n f a l l  below the observed r a i n f a l l .  c o u v e r was  Air-  anal-  f o r the West V a n c o u v e r gauge, the c o m p a r i s o n  tween o b s e r v e d and e s t i m a t e d r a i n f a l l s fall  This  be  due  the e f f i c i e n c y  using e determined Figure  rain-  i s 73%  to the  a t West Van-  from the Vancouver  6.18 i s a p l o t o f t h e  a g a i n s t the s a t e l l i t e  be-  estimated  ob-  rainfall  totals.  The  a n a l y s i s o f the^iDecember 5, 19 79 s t o r m r e v e a l e d  another important aspect:  satellite  rainfall  a r e not s u g g e s t e d by  occurrences which  images o f t e n c l e a r l y  :  analyses e i t h e r because o f the n e c e s s a r i l y the n u m e r i c a l models o r because o f problems a c c u r a t e l y i n i t i a l i z i n g the models. cal  the n u m e r i c a l  coarse g r i d used i n adequately  I t i s true that the  models were d e s i g n e d f o r f o r e c a s t i n g purposes  c a s t i n g from s a t e l l i t e since the s a t e l l i t e  images i s s t i l l  define  a difficult  and  and numeri-  that fore-  task;  i m a g e s do r e c o r d w h a t c l o u d s y s t e m s  however, are  l y p r e s e n t o v e r an a r e a , t h e y a r e i m p o r t a n t f o r " n o w c a s t i n g " rainfall  from these c l o u d s .  by  actualthe  TABLE 6.7  C o m p a r i s o n o f O b s e r v e d and E s t i m a t e d t h e S t o r m o f December 5 , 19 79 .  Rainfall  DIFFERENCE  Totals f o r  OBSERVED RAINFALL (mm)  ESTIMATED RAINFALL (mm)  3.6  3.5  0.1  3  0.1  10  5  Vancouver City  M  3.5  -  -  0.1  10  5  Vancouver Harbour  M  3.5  -  -  0.1  10  5  West Vancouver (Mathers Ave.)  13.0  3.5  9.5  73  0.1  10  5  New Westminster  16.4  12.2  4.2  26  0.1  10  5  Walley Forest Nursery  12.3  12.2  0.1  1  0.1  10  5  T  0  —  —  0.1  10  5  STATION  Calibration Station: Vancouver I.A.  V i c t o r i a I.A.  Key: I.A. M T  International Airport observation missing trace  (mm)  e  wc  Y  (9 /m3 )(°C/1000m)  (%)  127.  24 L  LEGEND rain C - calibration station  20  °  4  16 s °  I2  8  c  /  / /  /  j L  L  _1_  4 8 12 16 Estimated Storm Total Precipitation  FIGURE  20 (mm  24  28  )  6.18  E s t i m a t e d and O b s e r v e d Storm.  P r e c i p i t a t i o n f o r t h e December 5, 19 79  128.  6.7  Comparison All  o f Observed  and E s t i m a t e d P r e c i p i t a t i o n f o r  Storms  Figure  6.19  i s a comparison  storm t o t a l p r e c i p i t a t i o n s  o f the o b s e r v e d and e s t i m a t e d  f o r a l l f i v e t e s t storms.  The  dashed  curve r e p r e s e n t s a p e r f e c t match o f the e s t i m a t e d storm t o t a l p r e c i p i t a t i o n w i t h the observed storm t o t a l p r e c i p i t a t i o n . A l t h o u g h t h e r e i s some s c a t t e r  of the p o i n t s about  this line, i t  i s e v i d e n t from the r e s u l t s o f the f i v e t e s t cases a n a l y z e d t h a t t h e GOES s a t e l l i t e performs w e l l as w e l l  image r a i n f a l l e s t i m a t i o n p r o c e d u r e  f o r b o t h t h e low i n t e n s i t y t y p i c a l r a i n f a l l  as t h e h i g h i n t e n s i t y s e v e r e r a i n f a l l  Columbia.  generally events  events over B r i t i s h  24 I—  LEGEND  !  •  rain  /  (D  mixed rain and snow  O  snow  y  C - calibration stations  /  S - values s c a l e d by * 4*S  20  /  / 16  12  c ©  c  /  V  /  8  •  9  0  /  f y  t  '  o •  4  o  I 8  »  i 12  Estimated Storm T o t a l  FIGURE  i  I  i  16 Precipitation  I 20  i  I 24  '  l 28  ( mm )  6.19  E s t i m a t e d and Observed P r e c i p i t a t i o n Storms.  f o r A l l Five Test  l  1-30.  CHAPTER V I I  AN  The for  UPDATING PROCEDURE USING OBSERVED DATA  comparisons of observed  and e s t i m a t e d  the t e s t storms d i s c u s s e d i n Chapter  although lite  rainfalls  V I show g o o d a g r e e m e n t ,  t h e r e i s some u n c e r t a i n t y a n d i n a c c u r a c y i n t h e  rainfall  e s t i m a t e s w h i c h may  ical-conceptual  be  due  satel-  t o the form o f the  model used t o d e s c r i b e the r a i n f a l l  process,  to  the d e t e r m i n a t i o n o f the parameters used i n the model,  to  t h e i n h e r e n t l y random n a t u r e  To  a g r e a t e x t e n t t h i s u n c e r t a i n t y has  accounted  of the r a i n f a l l process  the s a t e l l i t e  rainfall  e s t i m a t e c a n be  f u r t h e r i m p r o v e d by i n -  t h e use o f an u p d a t i n g p r o c e d u r e .  means t r e a t i n g t h e s e r i e s o f s a t e l l i t e T h e r e a r e many u p d a t i n g p r o c e d u r e s of sophistication. such  and  However,  c o r p o r a t i n g the i n f o r m a t i o n contained i n the observed data through  and  itself.  been acknowledged  f o r i n t h e e m p i r i c a l a d j u s t m e n t f a c t o r e.  phys-  rainfall  In e f f e c t  e s t i m a t e s as a  this  "signal".  available at various  levels  H o w e v e r , t h e more s o p h i s t i c a t e d m e t h o d s ,  as K a l m a n f i l t e r i n g  (Kalman, I 9 6 0 . ) , t e n d t o have  restric-  t i v e a s s u m p t i o n s o r r e q u i r e d e t a i l e d i n f o r m a t i o n on e r r o r c h a r acteristics.  For the p r e s e n t e x p l o r a t o r y phase o f the  very simple procedures  7.1  The On  Updating  seemed m o s t a p p r o p r i a t e .  Model  the assumption t h a t the s a t e l l i t e  are reasonably  study,  rainfall  r e p r e s e n t a t i v e o f the t r u e r a i n f a l l  estimates  amounts ( i n -  131.  spite  of  the  uncertainties  straightforward  procedures  in  observed  the  light  of  noted for  data  above)  updating is  to  use  then  one  such  an e s t i m a t e d  a  of  the  regression  most  of  series the  form  y=a+bx  where by  the  that a by  y  is  the  "true"  observed  rain  and b , the  rainfall,  fall.  At  can be  least  rainfall,  any  and x  point  computed  assumed is  in  from  squared method,  7.1  the  time  the  to  be  satellite the  date  represented  estimate  unknown  available  that  exactly  of  parameters, up  to  that  time  is,  a=y-bx  7.2  n .y.  -  n x  y  b=  7.3  jSc,  where  x  i  _ x.,(x = V rainfall  the  s  average  x./n), values  2  -  n<5)  2  of  the  estimated  _ and y i s  the  average  y^,  (y  =  ^^y.j_/n) .  rainfall  of  the  Values  for  values  observed a  and b  (or can  "true") be  I  recalculated (y^) a  with  the  and e s t i m a t e d  and b  mates values  acquisition of  (x^)  rainfalls.  can  t h e n be  used  until  another  observed  is  available.  to  update  each The  the  new p a i r  of  observed  redetermined values satellite  and e s t i m a t e d  rainfall  rainfall  pair  of esti-  of  For example, c o n s i d e r t h e f o l l o w i n g : rainfall  every 6 hours,  and s a t e l l i t e  estimates of the r a i n f a l l  at this  Station A reports  i m a g e s a r e u s e d t o make  s t a t i o n a s w e l l as f o r a  number o f o t h e r u n g a u g e d l o c a t i o n s w i t h i n t h e b a s i n . equation  7.1 t h e s a t e l l i t e  estimates  r e c t e d " o r a d j u s t e d as t h e observed  a t S t a t i o n A c a n be " c o r data i s r e c e i v e d .  the p a r a m e t e r s a and b a r e r e c a l c u l a t e d once e v e r y do n o t change i n v a l u e u n t i l rated. far  That i s ,  6 h o u r s and  t h e new o b s e r v a t i o n s a r e i n c o r p o -  I n t h i s way t h e e s t i m a t e s o f p r e c i p i t a t i o n  from t h e " t r u e " , observed  With  do n o t d r i f t  p r e c i p i t a t i o n because o f the uncer-  t a i n t i e s i n the e s t i m a t i o n model.  The to  u p d a t i n g model i n e q u a t i o n  each p a i r o f observed  t h e p a r a m e t e r s a and b. tions  7.1 g i v e s e q u a l  and e s t i m a t e d data used t o T h i s means t h a t e s t i m a t e s  emphasis determine  and o b s e r v a -  f r o m t h e e a r l y p a r t o f t h e s t o r m h a v e as much e f f e c t o n a  and b as t h e l a t e s t o n e s .  I n p r a c t i c e , however, t h e most r e c e n t  p a i r s s h o u l d have the g r e a t e s t i n f l u e n c e .  By w e i g h t i n g t h e p a i r s by W^,  t h e emphasis o f t h e u p d a t i n g  m o d e l i s s h i f t e d t o w a r d s t h e l a t e s t p a i r s , w i t h a a n d b now by  given  133.  a = Wy - bWx  7.4  n ^ ] ^ x ^ y ^ ~ nWxWy w  b = ^  2  7.5  n .x.) (W.x.  2  -  n(Wx)  2  The weights must s a t i s f y the c o n d i t i o n :  W > W. , i i - l  7.6  There are a number o f ways t o choose filled.  For example, weights o f the form  W. = W x 1  1  satisfy  so that t h i s i s f u l -  7.6, where  (n  '  7.7  i)  i s a user s p e c i f i e d parameter  chosen  u s u a l l y t o r e f l e c t the a c t u a l interdependence o f p r e v i o u s r a i n falls  on the p r e s e n t r a i n f a l l , n i s the t o t a l number o f observed-  e s t i m a t e d r a i n f a l l p a i r s i n t h i s r a i n f a l l event up t o the p r e s e n t , and i i s the i - t h consecutive one o f these p a i r s . are p l o t t e d f o r n=50 and v a r i o u s v a l u e s o f  7.2  Comparison o f Updated and Observed  These weights  i n F i g u r e 7.1.  Rainfall  As a sample of what the updating can do, two o f the f i v e t e s t storms analyzed i n Chapter VI were chosen to be updated.  FIGURE  7.1 (n—i)  The B e h a v i o u r o f t h e W e i g h t s W^ n=50 and 3 v a l u e s  of  W,.  = W^  for  135.  T h e s e w e r e t h e two ber of  17, 19 79.  major storms o f October  The  first,  3 1 , 19 78 and Decem-  O c t o b e r 3 1 , 1978, was  chosen  because  t h e l a r g e number o f o b s e r v e d - e s t i m a t e d p a i r s a v a i l a b l e  and  as s u c h c o u l d s e r v e as a t e s t o f t h e u p d a t i n g p r o c e d u r e on long s e r i e s .  The  s e c o n d s t o r m , December 1 7 , 1 9 7 9 , was  a t e s t of the procedure f o r updating r a i n f a l l s t a t i o n s w i t h i n a c e r t a i n geographic area. storms were n o t t e s t e d because too  a  chosen  as  a t a number o f  The  three lesser  their duration, i n general,  was  s h o r t t o p e r m i t any m e a n i n g f u l d e t e r m i n a t i o n o f t h e u p d a t i n g  m o d e l p a r a m e t e r s , a and  7.2.1  Updated The  b.  O c t o b e r 3 1 , 19 78 R a i n f a l l E s t i m a t e s  satellite  estimated r a i n f a l l  v a l u e s f o r T e r r a c e and  Gospel P o i n t were updated u s i n g the w e i g h t e d r e g r e s s i o n model with the  a and b d e f i n e d b y e q u a t i o n s 7.4 w e i g h t s was  v a l u e f o r W^  and 7.5.  The  form o f  as g i v e n b y e q u a t i o n 7.7, w i t h W^=0.8.  was  chosen because  the  w e i g h t s W.  the  storms examined  This  as c a n be s e e n i n F i g u r e  d r o p o f f r a p i d l y p r e v i o u s t o W.  „.  7.1,  I n most o f  the i n d i v i d u a l r a i n p r o d u c i n g c e l l s  rarely  l a s t e d l o n g e r t h a n 2 h o u r s , e x c e p t f o r t h e v e r y l a r g e s t ones and h e n c e any e f f e c t o f r a i n f a l l more t h a n two h o u r s p r e v i o u s on p r e s e n t r a i n f a l l  is likely  quite  insignificant.  S i n c e t h e GOES-West s a t e l l i t e 15 m i n u t e s 0015, is  images a r e r e c e i v e d a t  t o t h e h o u r a n d 15 m i n u t e s a f t e r t h e h o u r  0045, 0115,  0145  GMT,  etc.),  r e p o r t e d o n t h e h o u r , i t was  and t h e o b s e r v e d  (that i s , rainfall  assumed t h a t t h e r a i n f a l l  esti-  136.  m a t e d f o r t h e one w h i c h was  rainfall  r e p o r t e d f o r the hour ending  i s not a problem  discre-  and i s t h e o n l y means o f  f o r m i n g t h e u p d a t i n g u s i n g t h e GOES-West i m a g e s .  to  15 m i n u t e s  T h i s i s not b e l i e v e d t o cause a s i g n i f i c a n t  pency i n the u p d a t i n g p r o c e d u r e ,  shift  image  r e c e i v e d a t 15 m i n u t e s p a s t t h e h o u r c o r r e s p o n d e d  the observed earlier.  hour p e r i o d ending w i t h the s a t e l l i t e  This  per-  time  w i t h t h e G O E S - E a s t i m a g e s r e c e i v e d on  t h e e a s t c o a s t o f t h e c o n t i n e n t , s i n c e t h e y a r e r e c e i v e d on t h e h o u r and h a l f - h o u r ( t h a t i s , 0000 , 0030 , 0100  The  estimated r a i n f a l l s  the f i t of the s a t e l l i t e fall.  The  Table  7.1.  of  The  content w c ,  and  The improving  t o be  does i m p r o v e rain-  a and b i s g i v e n i n i n d i c a t e t h a t some o r a l l , ( e f f i c i e n c y e,  t h e l a p s e r a t e y) v a r y i n t i m e as t h e Whether o r n o t t h i s i s so  water  cloud  remains  investigated.  ability  t o u p d a t e s e q u e n c e s has  the f i t o f e s t i m a t e d r a i n f a l l  served data.  esti-  t o the observed  e s t i m a t i o n model parameters  e v o l v e s and moves.  a problem  estimated r a i n f a l l  change i n a and b may  and  updated r a i n f a l l  updating procedure  v a r i a t i o n of the parameters  the r a i n f a l l  system  The  etc.) .  were u p d a t e d s e q u e n t i a l l y  t h e n summed t o a r r i v e a t t h e a c c u m u l a t e d m a t e s shown i n F i g u r e 7.2.  GMT,  Since the s a t e l l i t e  another  use  besides  for stations with  images a l l o w r a i n f a l l  estimated f o r a g r i d of p o s i t i o n s throughout  to  obbe  a b a s i n , then i t  137.  250 h G O S P E L POINT Observed rainfall  -  200  r  150  5  100  GOSPEL POINT Estimated rainfall  f  O  o'oo O  T E R R A C E AIRPORT O b s e r v e d r a i n f a II  50 A  TERRACE  X  ^  0  Estimated  ^  AIRPORT rainfall  a / 0600  1200  Oct. 3 1 / 7 8  1800  0000  0600  1200  800  Nov. 1/78 Time (GMT)  FIGURE 7 . 2 Comparison o f Updated S a t e l l i t e E s t i m a t e d R a i n f a l l and Observed R a i n f a l l f o r Gospel P o i n t and T e r r a c e A i r p o r t , T y p i c a l V a l u e s f o r a,b f o r E a c h S t a t i o n a r e G i v e n i n T a b l e 7 . 1 . (W^ = 0 .8) .  TABLE 7.1  Number o f Pairs i • • •  26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50  V a r i a t i o n o f a and b f o r T e r r a c e A i r p o r t and Gospel P o i n t as the l a s t 25 P a i r s o f Observed and E s t i m a t e d R a i n f a l l s are Added S e q u e n t i a l l y to the Updating Procedure  Gospel a  Point b  Terrace a  Airport b  • • •  • • •  • • •  • • •  0 .29 0.28 0 .16 0.04 -0 .02 0 .01 -0 .01 0 .10 0.03 0 .15 0 .12 0 .07 -0 .001 0 .05 -0.05 -0 .11 -0.01 0.03 -0.10' -0 .09 -0 .15 -0.15 -0 .09 -0.10 -0.17  1.07 1.02 1.02 1.03 1.04 1.04 1.04 1.00 1.01 0.96 0.94 0.94 0.95 0.94 0.96 0 .99 0 .98 0.96 1.01 1.02 1.06 1.09 1.10 1.12 1.17  0 .00 -0 .01 -0 .01 0 .001 0.002 0 .00 -0 .001 -0 .002 -0 .001 -0 .01 -0.03 -0 .02 -0.01 -0 .01 -0 .004 -0 .001 -0 .004 -0 .002 -0 .003 -0 .002 -0 .003 -0 .004 -0.01 -0 .02 -0 .01  1.27 1.23 1.19 1.15 1.15 1.14 1.14 1.15 1.15 1.13 1.08 1.02 0 .97 0 .94 0.92 0.91 0.91 0.90 0 .89 0 .89 0 .89 0.91 0.94 1.03 1.03  139.  is  r e a s o n a b l e t h a t t h e e s t i m a t e s a t t h e s e p o i n t s can be u p d a t e d  by u s i n g t h e v a l u e s o f t h e u p d a t i n g m o d e l p a r a m e t e r s determined  from t h e observed  i c a l . case. for  data.  The same a p p r o a c h  a a n d b as  F i g u r e 7.3 shows a  hypothet-  was u s e d t o u p d a t e t h e r a i n f a l l  Gospel P o i n t during the October  3 1 , 1979 s t o r m ,  and f o r t h e  V a n c o u v e r a r e a d u r i n g t h e December 1 7 , 1979 s t o r m d i s c u s s e d i n the next s e c t i o n . given i n Table lite  The v a l u e s o f a a n d b f o r T e r r a c e  7.1, w e r e u s e d t o u p d a t e t h e G o s p e l  e s t i m a t e s shown p l o t t e d a l o n g w i t h t h e " t r u e "  rainfall  i n F i g u r e 7.4.  storm,  data.  satel-  (observed)  This suggests  t h a t f o r the October  Terrace A i r p o r t t o Gospel P o i n t i s both  Gospel 3 1 , 19 79  a and b  from  f e a s i b l e and w o r t h w h i l e .  7.2.2. The U p d a t e d December 1 7 , 1979 R a i n f a l l estimated r a i n f a l l  satis-  estimates with  the t r a n s f e r r i n g o f the updating parameters  The s a t e l l i t e  Point  The e f f e c t o f t h e u p d a t i n g i s as  f a c t o r y as u p d a t i n g G o s p e l P o i n t s a t e l l i t e P o i n t observed  Airport,  Estimates  values f o r Vancouver I n -  t e r n a t i o n a l A i r p o r t a n d V i c t o r i a I n t e r n a t i o n a l A i r p o r t w e r e upd a t e d u s i n g t h e m o d e l ( e q u a t i o n 7.1) w i t h a a n d b d e f i n e d b y equations  7.4 a n d 7.5.  Again  t h e f o r m o f t h e w e i g h t s was  g i v e n b y e q u a t i o n 7.7 w i t h W^O.8. storm,  the estimated r a i n f a l l s  summed t o y i e l d  As f o r t h e O c t o b e r  3 1 / 19 78  were u p d a t e d s e q u e n t i a l l y and then  cumulative updated s a t e l l i t e  rainfall  estimates.  S i n c e t h e p u r p o s e o f u s i n g t h e December 17, 1979 was t o t e s t t h e p r o c e d u r e  that  storm  f o r updating estimated r a i n f a l l  at a  140.  FIGURE  7.3  S c h e m a t i c o f a r i v e r b a s i n w i t h 4 s t a t i o n s (A,B,C,D) where t h e a r e a l r a i n f a l l d i s t r i b u t i o n i s o f i n t e r e s t b u t w h e r e o n l y one o f t h e s t a t i o n s (A) h a s a r a i n g a u g e . S a t e l l i t e estimates of r a i n f a l l are available f o r a l l 4 s t a t i o n s throughout the d u r a t i o n of the storm. By updating the estimated s e r i e s f o r A w i t h the observed d a t a m e a s u r e d t h e r e , v a l u e s o f a and b c a n be d e t e r m i n e d f o r each time i n t e r v a l . These v a l u e s o f a and b can be u s e d t o u p d a t e t h e e s t i m a t e d r a i n f a l l a t t h e o t h e r u n g a u g e d s t a t i o n s ( B , C, D ) .  number o f s t a t i o n s  and  of which lack hourly  g r i d points  observations but  6-hour p r e c i p i t a t i o n t o t a l s , the two  stations with  hourly  therefore,  the  p a r a m e t e r s a and  t h e r e was  little  I n t e r n a t i o n a l A i r p o r t w e r e a s s u m e d t o be e n t i r e a r e a and  were used t o update the  the  a r e a as w e l l as  the  i n Figure  6.12.  is  shown i n F i g u r e  7.5.  7.3  Limitations The  on  on  g r i d points  The  a And  beyond the  of  scope of  this variability,  a g a u g e d l o c a t i o n t o an mentioned.  The  the  within  the  same m e t e o r o l o g i c a l  from p r o f e s s i o n a l are b e l i e v e d  e x p e r i e n c e , the  to behave s i m i l a r l y  t h o u g h t h e y may  be  b may  be  systems.  very  depending  Although i t i s the  transferred  nature b  of  from are  i f the  same c l o u d  un-  system  ungauged s t a t i o n s l i e  topographical g a u g e d and  region,  ungauged  or i f  stations  given identical conditions  i n d i f f e r e n t r e g i o n s o r be  from d i f f e r e n t cloud  the  f o r updating purposes  b can  and  in  isohyets  f o r t r a n s f e r r i n g a and  u n g a u g e d one  p a r a m e t e r s a and  over  updated  type of storm.  g a u g e d s t a t i o n , i f b o t h g a u g e d and the  f o r Vancouver  other stations  gauged s t a t i o n i s r e c e i v i n g r a i n f a l l from the as  difference;  t h i s research to investigate  some g u i d e l i n e s  Victoria)  b  u p d a t i n g m o d e l p a r a m e t e r s a and  s t a t i o n l o c a t i o n , t e r r a i n , and  the  used to c o n s t r u c t  evolution  Transferring  for  representative  the  isohyets  have  to what e x t e n t they  u p d a t i n g m o d e l p a r a m e t e r s a,b,  150  b  ( V a n c o u v e r and  to a s c e r t a i n  Subjectively  6.8'.', m o s t  some o f w h i c h do  observations  w e r e c o m p a r e d i n T a b l e 7.2 were d i f f e r e n t .  shown i n F i g u r e  receiving  even  rainfall  I f i t i s found from i n v e s t i g a t i n g  TABLE  No of pairs i  7.2  C o m p a r i s o n o f a and b f o r V a n c o u v e r I n t e r n a t i o n a l A i r p o and V i c t o r i a I n t e r n a t i o n a l A i r p o r t f o r t h e S t o r m o f December 17, 19 79  b  a Vancouver  I.A.  Victoria  I.A.  Vancouver  I.A.  Victoria  1  0 .00  -0 .03  1.06  1.11  2  0 .00  -0 .03  1.07  1.08  3  0 .05  -0 .01  1.12  1.13  4  0 .16  0 .09  1.37  1.24  5  0 .09  0 .06  1.36  1.27  6  -0.03  -0 .01  1.28  1.27  I.A.  .ft.  143.  0600 1200 Oct. 3 1 / 7 8  FIGURE  1800  0000 0600 Nov.1/78 Ti me (GMT )  1200  1800  7.4  Comparison o f Updated S a t e l l i t e E s t i m a t e d R a i n f a l l and Observed R a i n f a l l f o r Gospel P o i n t . This i s similar t o F i g u r e 7.2 e x c e p t t h a t i n t h i s c a s e t h e s a t e l l i t e e s t i m a t e d r a i n f a l l s f o r Gospel P o i n t were updated u s i n g the a and b v a l u e s d e t e r m i n e d a t T e r r a c e A i r p o r t .  FIGURE 7.5 E v o l u t i o n o f I s o h y e t s (mm) C o n s t r u c t e d f o r t h e December 1 7 , 19 79 S t o r m S a t e l l i t e R a i n f a l l E s t i m a t e s f o r t h e G r i d P o i n t Shown i n F i g u r e 6.11.  Updated  a and b t h a t they are f a i r l y constant from storm to storm f o r a p a r t i c u l a r r e g i o n then updating s h o r t d u r a t i o n (0.5 to 2 hour) r a i n f a l l events over t h a t r e g i o n would be g r e a t l y  facilitated,  as w e l l as updating h a l f - h o u r l y r a i n f a l l estimates f o r gauged l o c a t i o n s i n t h a t .region which r e p o r t on a l e s s f r e q u e n t b a s i s , say once every 6 or 12  7.4  hours.  Summary The need f o r a method f o r i n c o r p o r a t i n g observed  i n t o the s a t e l l i t e estimate of r a i n f a l l was simple weighted meter was  d i s c u s s e d and a very  r e g r e s s i o n type model, r e q u i r i n g o n l y one  t o be p r o v i d e d by the user, was  presented.  31, 19 78 and December 17, 19 79  storms.  para-  The model  used to s u c c e s s f u l l y update the e s t i m a t e d r a i n f a l l s  October  data  f o r the  146.  CHAPTER V I I I  SUMMARY AND  The  CONCLUSIONS  d e v e l o p m e n t a n d managementof w a t e r r e s o u r c e s  r e q u i r e s t h e e x p l o i t a t i o n o f modern t e c h n o l o g i c a l  achievements,  s u c h as t h e g e o s t a t i o n a r y m e t e o r o l o g i c a l s a t e l l i t e s ,  GOES,  w h i c h p r o m i s e t o p r o v i d e m o r e , i n e x p e n s i v e d a t a on an  areal  s c a l e a n d f r e q u e n c y o f c o v e r a g e w h i c h c a n n e v e r be a c h i e v e d by g r o u n d b a s e d of  data c o l l e c t i o n systems.  previous investigators  G r i f f i t h et  The  s u c c e s s f u l work  ( S c o f i e l d and O l i v e r ,  a l . , 1 9 7 8 ; a n d S t o u t et  al.,  19 77a;  1979), r e l a t i n g  the  g r o w t h o f c o n v e c t i v e c l o u d t o p s as s e e n i n t h e GOES s a t e l l i t e i m a g e s t o t h e r a i n f a l l i n t r o p i c a l and s e m i - t r o p i c a l a r e a s , suggested a s i m i l a r approach t o e s t i m a t i n g r a i n f a l l from o t h e r types of storms i n n o r t h e r n l a t i t u d e s . to  develop  a  H o w e v e r , i t was  necessary  p h y s i c a l e x p l a n a t i o n f o r the r e l a t i o n s h i p  be-  tween t h e r a t e o f growth o f the c l o u d top t o the r a t e o f p r e c i p i t a t i o n from the c l o u d . to  B e f o r e t h e c o n c e p t c o u l d be  the e s t i m a t i o n o f r a i n f a l l from the types of storms  extended commonly  o c c u r r i n g i n t h e h i g h e r l a t i t u d e s *, s o m e t h i n g w h i c h h a d  not  p r e v i o u s l y been a t t e m p t e d .  A model f o r e s t i m a t i n g p r e c i p i t a t i o n i m a g e s was  d e v e l o p e d and t e s t e d on a number o f m a j o r and  f r o n t a l storms which passed over B r i t i s h the  quality  f r o m GOES s a t e l l i t e  Columbia.  minor  Considering  a n d c o n s i s t e n c y o f t h e GOES-West i m a g e s r e c e i v e d  by  the P a c i f i c Weather Centre,  t h e r e s u l t s were remarkable and  i n d i c a t e d t h e f e a s i b i l i t y o f t h e a p p r o a c h as an o p e r a t i o n a l tool/  Further  t i o n estimates  t e s t s showed t h a t t h e a c c u r a c y  of the p r e c i p i t a -  c o u l d be i m p r o v e d t h r o u g h t h e use o f an  procedure which incorporated the information obtained measurements.  To f a c i l i t a t e  updating  from ground  t h e a p p l i c a t i o n o f t h e m o d e l , com-  puter  r o u t i n e s w e r e d e v e l o p e d t o p e r f o r m t h e numerous  steps  and c a l c u l a t i o n s i n v o l v e d i n e s t i m a t i n g and u p d a t i n g  fall  from s a t e l l i t e  The  rain-  images.  q u a l i t y o f s a t e l l i t e p r e c i p i t a t i o n estimates  be much b e t t e r i f t h e u s e r h a d a c c e s s lite  accounting  receiving station  to a dedicated  could  GOES s a t e l -  ( s u c h as t h e one p r o p o s e d f o r t h e V a n c o u v e r  a r e a i n 19 8 1 ) , w i t h t h e a p p r o p r i a t e  computer s o f t w a r e  t o choose  h i s own e n h a n c e m e n t scheme, o n e w h i c h d i s t i n g u i s h e s t h e t e m p e r ature ity  gradients  a t t h e t o p s o f warmer c l o u d t o p s .  w o u l d be p a r t i c u l a r l y  This capabil-  u s e f u l i n a n a l y z i n g those  weather  systems over B r i t i s h  Columbia which a r e n o t s u f f i c i e n t l y  developed v e r t i c a l l y  t o be a p p a r e n t on t h e enhanced  well  infrared  images p r e s e n t l y r e c e i v e d and y e t w h i c h r e s u l t i n s t e a d y , l o w intensity  precipitation.  F u r t h e r use o f t h i s technique both h y d r o l o g i s t s and m e t e o r o l o g i s t s  on an o p e r a t i o n a l b a s i s b y i s needed t o f u l l y / a s s e s s  i t s b e n e f i t s and l i m i t a t i o n s , however, t h i s  study  revealed  that  GOES s a t e l l i t e  i m a g e s a r e w e l l - s u i t e d as a n a l t e r n a t e o r s u p p l e -  mentary source  o f i n f o r m a t i o n , p a r t i c u l a r l y on t h e s p a t i a l d i s -  148.  tribution of r a i n f a l l .  I t s a d v a n t a g e s o v e r more c o n v e n t i o n a l  d a t a s o u r c e s , f o r example r a d a r o r r a i n g a u g e s , of coverage  (day and n i g h t ) , i t s l a r g e a r e a l c o v e r a g e ,  cost i n comparison w i t h ground networks. few: in  are i t s frequency  t h e r e s o l u t i o n o f t h e VISSR  the infrared a t the s a t e l l i t e  and i t s  I t s l i m i t a t i o n s are  (1 km i n t h e v i s i b l e sub-point)  means t h a t  a n d 8 km individual  cloud elements s m a l l e r than the r e s o l u t i o n o f the sensor be  d i s t i n g u i s h e d . B u t i t i s worth n o t i n g t h a t c l o u d systems o f  this  s m a l l a s c a l e r a r e l y produce major r a i n s over a b a s i n , and  t h a t even  estimates of r a i n f a l l  systems i n remote areas about the r a i n f a l l  f r o m o n l y t h e l a r g e (>8 km)  i s b e t t e r t h a n no i n f o r m a t i o n a t a l l  distribution  there.  T h i s s t u d y h a s shown t h a t t h e GOES s a t e l l i t e  infrared  i m a g e s , when u s e d w i t h a s o u n d p h y s i c a l l y b a s e d r a i n f a l l mation procedure,  non-tropical nature.  a c a p a b i l i t y i s i n v a l u a b l e f o r p r o v i d i n g economical estimates of r a i n f a l l  i n higher latitudes.  conventional raingauge depth-duration  esti-  can p r o v i d e acceptable estimates o f t h e s p a t i a l  p r e c i p i t a t i o n from c l o u d systems o f a  Such  and f r e q u e n t  I n areas where t h e  networks are sparse i t provides  i n f o r m a t i o n v i t a l t o water resources  management a c t i v i t i e s  8.1  cannot  w h i c h w o u l d be o t h e r w i s e  area-  design and  unobtainable.  Future D i r e c t i o n s In  theory, the t r a n s i t i o n from using t h i s procedure  h a r d c o p y images t o u s i n g i t w i t h d i g i t a l  i m a g e s o u g h t t o be  with  149.  s t r a i g h t f o r w a r d and r e s u l t i n a f u l l y - a u t o m a t e d r a i n f a l l estimation procedure.  The m a j o r  d i f f i c u l t y w o u l d be t h e p r o -  b l e m o f r e c o g n i t i o n , i d e n t i f i c a t i o n a n d t r a c k i n g o f t h e many i n d i v i d u a l c e l l s w h i c h make up a p a r t i c u l a r s t o r m . likely  I t i s more  t h a t a s e m i - a u t o m a t i c p r o c e d u r e w i l l be used i n p r a c t i c e ,  w i t h t h e r e c o g n i t i o n and i d e n t i f i c a t i o n o f i n d i v i d u a l  cells  p e r f o r m e d by t h e u s e r , u n t i l s u i t a b l e p a t t e r n r e c o g n i t i o n p r o c e d u r e s become  available.  For t h e development  and i n i t i a l  t e s t i n g of the s a t e l l i t e  r a i n f a l l e s t i m a t i o n p r o c e d u r e , i t was n e c e s s a r y t o u s e t h e h a r d copy i m a g e s b e c a u s e  of their availability  and f o r t h e i r  i m p a c t as a s e r i e s o f " s n a p - s h o t s " o f w e a t h e r was an a c c e p t a b l e a p p r o a c h  visual  conditions.  d u r i n g the r e s e a r c h phase.  This  However,  c u r r e n t c o m p u t e r d i g i t a l i m a g e d i s p l a y s y s t e m s , s u c h as t h e Comtal V i s i o n I system, i n o p e r a t i o n a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , a l r e a d y a r e c a p a b l e o f d i s p l a y i n g t h e image o n a s c r e e n , e n h a n c i n g t h e i n f r a r e d i m a g e s i n c o l o u r , as w e l l a s , a u t o m a t i c a l l y e x t r a c t i n g t h e area i n f o r m a t i o n f o r each temperature contour d i rectly  f r o m t h e d i g i t a l image d a t a a f t e r t h e s t o r m c e l l o f i n t e -  r e s t has been v i s u a l l y  i d e n t i f i e d and l o c a t e d by t h e u s e r .  i n f o r m a t i o n c o u l d t h e n be f e d d i r e c t l y  t o the r a i n f a l l  estimation  r o u t i n e s developed d u r i n g t h e course o f t h i s study thus the time r e q u i r e d f o r t h e u s e r t o d i g i t i z e each  I n t h e immediate  This  eliminating  contour.  f u t u r e the procedure developed here holds  the promise o f improving short-term f o r e c a s t s o f severe  weather  150.  events over the p r o v i n c e .  S i n c e s a t e l l i t e images r e c o r d the  movement o f a s t o r m as w e l l as i t s r a t e a n d s t a g e o f ment, t i m i n g t h e a p p r o x i m a t e  develop-  a r r i v a l of the storm over a p a r -  t i c u l a r r e g i o n c a n be i m m e d i a t e l y e s t i m a t e d f r o m s u c c e s s i v e images.  W i t h e x p e r i e n c e i n t h e b e h a v i o u r and l i f e  of storm c e l l s , fall,  expectancy  g a i n e d by a n a l y z i n g s a t e l l i t e i m a g e s f o r r a i n -  i t s h o u l d be p o s s i b l e t o p r e d i c t i n t h e s h o r t - t e r m (on  t h e o r d e r o f a few h o u r s )  the probable r a i n f a l l  r e c e i v e d from a p a r t i c u l a r system.  Proposed  t h a t might  be  use o f a v e r s i o n o f  t h i s p r o c e d u r e by t h e P a c i f i c W e a t h e r C e n t r e t o a i d i n t h e tification  and d e l i n e a t i o n o f r a i n f a l l  s e e n as t h e f i r s t s t e p t o w a r d s  areas over the ocean i s  t h i s e n d , and a n e c e s s a r y  one  g i v e n t h e i n e v i t a b l e p h a s i n g o u t o f Ocean S t a t i o n P a p a and i n c r e a s i n g r e l i a n c e on w e a t h e r  iden-  s a t e l l i t e observations.  portance of t h i s i s r e f l e c t e d i n the Atmospheric f i v e y e a r $10 m i l l i o n p r o p o s a l t o c o n d u c t  the  The  im-  Environment's  f u r t h e r r e s e a r c h and  d e v e l o p m e n t i n t o t h e o p e r a t i o n a l use and d i s s e m i n a t i o n o f m e t e o rological satellite  d a t a (Department  of Communications,  F u r t h e r s t u d y and m o d e l l i n g o f t h e i n t e r n a l s t r u c t u r e o f systems, i n c o n j u n c t i o n w i t h s a t e l l i t e images, predictive  capability.  would  1980). cyclonic  improve  this  1.51.  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B e l l 1980 " S a t e l l i t e Observed Cloud P a t t e r n s A s s o c i a t e d With E x c e s s i v e P r e c i p i t a t i o n Outbreaks", P r e p r i n t s 8-th AMS Conf. on Weather F o r e c a s t i n g and A n a l y s i s , Denver, 463-473 C o r b e l l , R.P., C.J. C a l l a h a n and W.J. Kotsch (eds.) 1977 "The GOES/SMS User's Guide, NCAA, NESS, NASA Cressman, G.P. 1954 "An Approximate Method Of Divergence Measurement", J . o f Meteorology V o l . 11, No. 2, 83-90  152.  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R o d g e r s , W.E. Shenk and V. O l i v e r 19 76 " D e r i v i n g Winds F o r H u r r i c a n e s U s i n g S h o r t I n t e r v a l S a t e l l i t e Imagery", 7-th Conf. on A e r o s p a c e and A e r o n a u t i c a l M e t e o r o l o g y and Symp. on Remote S e n s i n g f r o m S a t e l l i t e s , 115-118 G e r r i s h , H.O. 19 70 " S a t e l l i t e And R a d a r A n a l y s i s Of M e s o s c l e F e a t u r e s I n The T r o p i c s " , S e m i a n n u a l R e p o r t , R e s e a r c h and D e v e l o p m e n t T e c h . Rep. ECOM-0 20 5-20, U.S. Army E l e c t r o n i c s Command, F t . Monmouth, N . J . , 39p.  15.3. G r i f f i t h , C.G., W.L. Woodley, S. Browner, J . T e i j e i r o , M. Maier, D.W. M a r t i n , J . Stout, and D.N. S i k d a r 1976 " R a i n f a l l E s t i m a t i o n From Geisynchronous S a t e l l i t e s Imagery During D a y l i g h t Hours", NOAA Tech. Rep. ERL-356-WMPQ-7, 106p. , , P.G. Grube, D.W. M a r t i n , J . S t o u t , and D.N. S i k d a r 19 78 "Rain E s t i m a t i o n From S a t e l l i t e Imagery V i s i b l e and I n f r a r e d S t u d i e s " , Mon, Wea. Rev. V o l . 106, Aug., 1153-1171 Gurka, J . J . 1976 " S a t e l l i t e And Surface Observations Of Strong Wind Zones Accompanying Thunderstorms", 6-th AMS Conf. on Weather F o r e c a s t i n g and A n a l y s i s , 252-256 Haering, P. 19 78 "A G l o s s a r y Of Terms And Concepts Used In S a t e l l i t e Imagery I n t e r p r e t a t i o n " , P a c i f i c Weather Centre (Personal Communication) Hammond, B. 1978 "The Halloween Deluge - Terrace 1978", P a c i f i c Region Tech. Notes No. 78-041, P a c i f i c Weather Centre, Vancouver, B.C. Hare, F.K. 1963 The R e s t l e s s Atmosphere, An I n t r o d u c t i o n To C l i m a t o l o g y , Addison Wesley Pub. Co. H a r r o l d , T.W. 19 73 " Me onanisms/, I nf l u e n c i n g The D i s t r i b u t i o n Of P r e c i p i t a t i o n W i t h i n B a r o c l i n i c Disturbances," Quart. J . Roy. Met. Soc. 99, 232-251 H e t h e r i n g t o n , E.D. 1976 " I n v e s t i g a t i o n o f Orographic R a i n f a l l In South C e n t r a l Mountains Of B r i t i s h Columbia", Ph.D. T h e s i s Univ. Of B r i t i s h Columbia, F o r e s t r y Department Hobbs, P.V., and J.D. L o c a t e l l i 1978 "Rainbands, P r e c i p i t a t i o n Cores And Generating C e l l s I n A C y c l o n i c Storm", J . Atmos. S c i V o l . 35, 230-241 H o l t o n , J.R. 1972 Academic Press  An I n t r o d u c t i o n To Dynamic  Meteorology,  House, D.C. 1968 " A i r Mass M o d i f i c a t i o n And Upper B u l l . Amer. Met. Soc. 39, 137-143  Divergence",  Houze, R.A., P.V. Hobbs, K.R. Biswas, andW.M. Davis 1976 "Mesoscale S t r u c t u r e Of R a i n f a l l In Occluded Cyclones", 6-th AMS Conf. o f Weather F o r e c a s t i n g and A n a l y s i s , Albany, 310-317' Hussey, W.J. 1977 "TIROS-N P o l a r - O r b i t t i n g Environmental Satellite", 10th S e s s i o n ESCAP/WMO Typhoon Committee, Tokyo; NESS, NOAA, Washington, D . C , 29p. Ingraham, D.V., J . Amorocho, M. G u i l a r t e and M. E s c a l o n a 1977 " P r e l i m i n a r y R a i n f a l l Estimates In Venezuela And Columbia From GOES S a t e l l i t e Images", 2-nd AMS Conf. on Hydrometeorologyy Toronto, 316-323  154. Kalman, R.E. 1960 "A New Approach To L i n e a r F i l t e r i n g And P r e d i c t i o n Theory", T r a n s . ASME J . Of B a s i c E n g i n e e r i n g S e r i e s D, V o l . 82, March, 35-45 Kendrew, W.G., and D. K e r r 1955 The Climate Of B r i t i s h Columbia And The Yukon T e r r i t o r y , Queen's P r i n t e r , Ottawa (}  i >  Knox, J . 1978 Geography 312 L e c t u r e Notes - F a l l Term, U n i v e r s i t y o f B r i t i s h Columbia K o d a i r a , N., and N. Murayama 1976 "Development o f G e o s t a t i o n a r y M e t e o r o l o g i c a l S a t e l l i t e Systems", 7-th AMS Conf. on Aerospace and A e r o n a u t i c a l Meteorology and Symp. on Remote Sensing from" S a t e l l i t e s , 249-252 L e i g h , J . L . , and T. Duke 1978 Centre, U n i v e r s i t y o f B r i t i s h  "UBC F a c i l i t i e s " , Columbia  Computing  L e t h b r i d g e , M. 1967 " P r e c i p i t a t i o n P r o b a b i l i t y And R a d i a t i o n Data", Mon. Wea. Rev. 95, 487-490  Satellite  L i e n e s c h , J.H., B.P. Bauer and B.B. Goddard 1965 "SMS I n f r a r e d O b s e r v a t i o n s : T h e i r Accuracy And C a l i b r a t i o n " . P r o c . 10-th I n t e r n a t i o n a l Symp. on Remote Sensing o f the Envxronment, V o l . 1, 149-158 L i n t z , J . and D.S. Simonett 19 76 Remote Sensing o f Addison Wesley Pub. Co. (See Chapter 2)  Environment,  Lovejoy, S. 19 78 "The R e l a t i o n s h i p Between Coarse R e s o l u t i o n S a t e l l i t e Data And Area Of R a i n " , 4-th AMS Symp. on Meteorologi c a l Observations and I n s t r u m e n t a t i o n , 239-242 , and G.L. A u s t i n 1979 " The D e l i n e a t i o n Of Rain Areas From V i s i b l e And I n f r a r e d Data F o r Gate And M i d - L a t i t u d e s " , Atmosphere-Ocean 17(1), 77-92 Maddox, R.A. 19 80 "A S a t e l l i t e - B a s e d Study Of M i d - L a t i t u d e , Mesoscale Convective Complexes", P r e p r i n t s 8-th AMS Conf. on Weather F o r e c a s t i n g and A n a l y s i s , Denver, June, 329-338 M a i r , S. 1978a "UBC IG - The I n t e g r a t e d Graphics System", Computing C e n t r e , U n i v e r s i t y o f B r i t i s h Columbia , 1978b "UBC S u r f a c e - S u r f a c e V i s u a l i z a t i o n Computing Centre, U n i v e r s i t y of B r i t i s h Columbia  Routines",  M a r t i n , D. W., and W.D. Scherer 1973 "Review of S a t e l l i t e Rainf a l l E s t i m a t i o n Methods", B u l l . Amer. Met S o c , No. 29, J u l . 661-674 , and V.E. Suomi 19 71 "A S a t e l l i t e Study Of Cloud C l u s t e r s Over The T r o p i c a l North A t l a n t i c Ocean", F i n a l Report Of T r o p i c a l Cloud O r g a n i z a t i o n S t u d i e s , Task Order No. 3 To STAG, C o n t r a c t E-127-69-(N) Space Science And E n g i n e e r i n g Center, Madison, Wisconsin, 80p.  , and 19 72 "A S a t e l l i t e Study Of Cloud C l u s t e r s Over The T r o p i c a l North A t l a n t i c Ocean", B u l l . Amer. Met. Soc., No. 53, 135-156 Mason, B . J . 19 71 The P h y s i c s Of Clouds, P r e s s , Oxford, 6 71p.  2-nd E d i t i o n , Clarendon  1975 Clouds, Rain, and Rainmaking, 2-nd E d i t i o n , Cambridge U n i v e r s i t y Press Matejka, T . J . , R.A. Houze, and P.V. Hobbs 19 80 "Microphysics And Dynamics Of Clouds A s s o c i a t e d With Mesoscale Rainbands In E x t r a t r o p i c a l Cyclones", Quart. J . Roy. Met. Soc. 106, 29-56 McGinnis, D.F., R.A. S c o f i e l d , S.R. Schneider, and C P . Berg 1980 " S a t e l l i t e s As A i d To Water Resource Managers", J . Of Water Resources And Management Div., ASCE, V o l . 106, NoWRI, 1-20 Mcintosh, D.H., and A.S. Thorn 1973 Wykeham Pub.,(London) L t d .  E s s e n t i a l s o f Meteorology, . v  McKowan, P.L. 1977 "VISSR Data P r o c e s s i n g P l a n F o r Synchronous M e t e o r o l o g i c a l And Geostationary O p e r a t i o n a l Environmental S a t e l l i t e s (SMS/GOES)", Goddard Space F l i g h t Center, Maryland. McNulty, R.P. 1977 "On The R e l a t i o n s h i p Of Wind Maxima To Severe Weather And I t s O p e r a t i o n a l A p p l i c a t i o n " , 10-th AMS Conf., On Severe L o c a l Storms MDA 1977 "Remote Sensing Data Systems", r e p o r t by MacDonald, D e t t w e i l e r , And A s s o c i a t e s , C o n s u l t a n t s , Vancouver, B.C. M i e r s , B.T. 19 76 " A p p l i c a t i o n Of M e t e o r o l o g i c a l S a t e l l i t e Observations To Weather S e n s i t i v e Army Operations", 7-th AMS Conf. On Aerospace And A e r o n a u t i c a l Meteorology And Symp. On Remote Sensing From S a t e l l i t e s , 125-230 NOAA 1979  "The View From Space",  NESS 19 76 April  " S a t e l l i t e A c t i v i t i e s o f NOAA 19 75",  NOAA Magazine October, P56-57 NOAA S/T 76-2185,  O l i v e r , V . J . , and R.A. S c o f i e l d 1976 " E s t i m a t i o n Of R a i n f a l l From S a t e l l i t e Imagery", P r o c . 6-th AMS Conf. on Weather F o r e c a s t i n g and A n a l y s i s , May, 242-245 Popham, R. , and E . Rich 1975 "A D i r e c t Readout SMS/GOES VISSR Ground S t a t i o n C o n f i g u r a t i o n " , NESS, P r e l i m i n a r y Note, Washington D.C. Purdom, J.F.W. 1976 "Some Uses Of High R e s o l u t i o n GOES Imagery In Mesoscale F o r e c a s t i n g Of Convection And I t s Behaviour", Proc. 6-th AMS Conf. on Weather F o r e c a s t i n g and A n a l y s i s , May, 260-267  156. Rogers, R.R. Press  19 76  A Short Course In C l o u d P h y s i c s Pergammon  Schaefer, D.G. 19 79a " M e t e o r o l o g i c a l Development C o n t r i b u t i n g To The T e r r a c e Area F l o o d Of E a r l y November 1978", Scientific S e r v i c e s Unpublished Report, AES, Vancouver 19 79b "The Multi-Day Rainstorm Of October-November 1978, On The Queen C h a r l o t t e I s l a n d s " , S c i e n t i f i c S e r v i c e s Unpublished Report, AES, Vancouver 19 80 "The Rainstorm Of December 13-18, 19 79 Over Southwestern B r i t i s h Columbia", Report To I n l a n d Waters D i r e c t o r a t e Of Environment Canada, May. :  Schaefer, J.T. 19 77 "On The A p p l i c a b i l i t y Of The Divergence E q u a t i o n To Severe Storm F o r e c a s t i n g " , 10-th AMS c o n f . On Severe L o c a l Storms, Omaha, Oct. 18-21, 358-363 S c h e r e r , W.D., and M.D. Hudlow 1971 "A Technique For A s s e s s i n g Probable D i s t r i b u t i o n s Of T r o p i c a l P r e c i p i t a t i o n Echo Lengths For X-Band Radar From NIMBUS 3 HRIR Data", BOMEX B u l l . No. 10 BOMA.P o f f i c e , NOAA, R o c k v i l l e , Maryland, 63-68 S c o f i e l d , R.A. 1976a "Nowcasting: F i n e Tuning The L o c a l F o r e c a s t " , P r o c . 6-th AMS Conf. on Weather F o r e c a s t i n g and A n a l y s i s , May, 268-272 19 76b " S a t e l l i t e P i c t u r e s Used For L o c a t i n g The R a i n f a l l A s s o c i a t e d With A Convective Storm Over Texas", SAIN-: 76/18 19 7 8a "Using S a t e l l i t e Imagery To Estimate R a i n f a l l During The Johnstown Rainstorm", P r o c . AMS Conf. on F l a s h F l o o d s ; H y d r o m e t e o r o l o g i c a l A s p e c t s , May, 181-189 19 78b "Using S a t e l l i t e Imagery To Detect And E s t i m a t e R a i n f a l l From F l a s h - F l o o d Producing Thunderstorms", P r o c . AMS Conf. on Weather F o r e c a s t i n g and A n a l y s i s and A v i a t i o n Meteorology, Oct., 132-141 and V . J . O l i v e r 19 75 "The Synchronous M e t e o r o l o g i c a l S a t e l l i t e (SMS): I t s Advantages And A p p l i c a t i o n s " , Proc. 10- th I n t e r n a t i o n a l Symp. on Remote Sensing of the Environment, V o l . 1, 159-162 and 1977a "A Scheme For E s t i m a t i n g Convective R a i n f a l l From S a t e l l i t e Imagery", NOAA Tech. Memo, NESS 86, A p r i l , 47p. and 1977b "Using S a t e l l i t e Imagery To Estimate R a i n f a l l From Two Types Of Convective Systems", 11- th AMS Tech. Conf. on Hurricanes and T r o p i c a l Meteorology, Dec. 13-16, 204-211  157 . and 19 80 "Some Improvements To The S c o f i e l d / O l i v e r Technique", 2-nd AMS Conf. on F l a s h F l o o d s , A t l a n t a , Mar. 18-20, 115-122 and , and L. Spayd 19 80 " E s t i m a t i n g R a i n f a l l From Thunderstorms With Warm Tops I n The I n f r a r e d Imagery", P r e p r i n t s 8-th AMS Oohf. on Weather F o r e c a s t i n g and A n a l y s i s , Denver, June, 85-92 , and C.E. Weiss 19 76 " A p p l i c a t i o n s Of Synchronous M e t e o r o l o g i c a l S a t e l l i t e (SMS) Products And Other Data F o r S h o r t Range F o r e c a s t i n g In The Chesapeake Bay Region", P r o c . 6-th AMS Conf. on Weather F o r e c a s t i n g and A n a l y s i s , May, 67-73 Seymour, D.W., D.S. S l o a n , and N.W. Bowker 19 77 "A Low-Cost System F o r Reception, P r o c e s s i n g And D i s t r i b u t i o n Of L i n e Scan Data From Environmental S a t e l l i t e s " , The American I n s t i t u t e Of A e r o n a u t i c s And A s t r o n a u t i c s S a t e l l i t e A p p l i c a t i o n To Marine Operations Conf., L o u i s i a n a , Nov. S i k d a r , D.N. 19 72 "ATS-3 Observed Cloud B r i g h t n e s s F i e l d R e l a t e d To A Meso- To Sub-synoptic S c a l e R a i n f a l l P a t t e r n s " , TELLUS, 24,5 400-413 —: , and V.E. Suomi 19 71 "Time V a r i a t i o n Of T r o p i c a l E n e r g e t i c s As Viewed From A G e o s t a t i o n a r y A l t i t u d e " , J . o f Atmos. S c i . 2 8, 170-180 Spaceflight  1980 P222  1980  "Space A f f a i r s " ,  S p a c e f l i g h t , Vol.22 (5), May  Spangler, M.J. 1974 "The DMSP primary Data Sensor", 6-th AMS Conf. on Aerospace and A e r o n a u t i c a l Meteorology, 150-157 S t o u t , J . , D.W. M a r t i n , and D.N. S i k d a r 1977 " R a i n f a l l E s t i m a t i o n From G e o s t a t i o n a r y S a t e l l i t e Images Over The GATE Area", 11-th AMS Conf. on H u r r i c a n e s and T r o p i c a l Meteorology, Miami Beach, Dec. 13-16, 212-215 , and 19 79 R a i n f a l l From Geosynchrous S a t e l l i t e Images", V o l . 10 7, May, 585-598  " E s t i m a t i n g GATE Mon. Wea. Rev.  UBC Computing Centre 19 79 "XPAND.S" P r e l i m i n a r y note, Computing Centre, U n i v e r s i t y o f B r i t i s h Columbia V e s e l y , C.J., andW.B. Botzong 1974 "Defense M e t e o r o l o g i c a l S a t e l l i t e Program", P r o c . 6-th AMS Conf. on Aerospace and A e r o n a u t i c a l Meteorology, 146-149 V i d z e e , W., P.A. Davis and D.E. Wolf 19 78 "Technique To Use S a t e l l i t e Microwave Spectrometer Data In Moisture Budget S t u d i e s Of C y c l o n e s " , Mon. Wea. Rev. V o l . 106, Nov., 1627-1633  158.  W a l l a c e , J.M. and P.O. Academic Press  Hobbs 1977  Atmospheric S c i e n c e ,  Waters I I I , M.P., C.G. G r i f f i t h and W.L. Woodley 1977 "Use Of D i g i t a l G e o s t a t i o n a r y Imagery For Real-time E s t i m a t i o n Of H u r r i c a n e Rain P o t e n t i a l In L a n d f a i l i n g Storms", 11-th AMS Tech. Conf. on H u r r i c a n e s and T r o p i c a l Meteorology, Miami Beach, Dec. 13-16, 198-203 Woodley, W., and B. Sancho 1971 "A F i r s t Step Towards R a i n f a l l E s t i m a t i o n From S a t e l l i t e Cloud Photographs", Weather, 26, 279-289 , , and A.H. M i l l e r 19 72 " R a i n f a l l Estimati o n From S a t e l l i t e Cloud Photographs", Noaa Tech. Memo., ERL OD-11, 43p. WMO 19 76 "Informal P l a n n i n g Meeting On The S a t e l l i t e A p p l i c a t i o n s In Hydrology", F i n a l Report, Geneva, Oct.  159.  APPENDIX A  For  a d i v e r g e n c e f u n c t i o n o f t h e form  1 A(T,t)  the  dA(T,t) dt  + f 1 2  f  T  a v e r a g e d i v e r g e n c e between t h e l e v e l  T„ and t h e c o l d e s t  contour l e v e l  •2  T  dA(T,t)  1 A (T, t )  A.l  n  =  of non-divergence  c a n be d e t e r m i n e d  3  f  =  ""St  £  + f i 2 +  T  T  as  follows  A.2  n l  .T f  3  •3^2'  + f T  dT  n  7  A.3  1 l  2 n+1  (  T T ^ r T  jfl  ( T  3- 2 T  }  +  f  The  v a l u e s o f t h e two c o n s t a n t s f ^ and  two  boundary c o n d i t i o n s .  l  f  so  2  3  ,  2  , A  -  4  c a n be f o u n d f r o m t h e  (the l e v e l  o f non-divergence)  2 2  that 4T f  For  r  F o r T=T  2  n+1  T=T  3  l  = -f T 2 2  ( the coldest  11  t  i  contour l e v e l )  A  -  6  160. where K i s t h e d i v e r g e n c e substitute  of the coldest  contour.  U s i n g A.6 t o  f o r f, gives  f„ = — - — 2  n T l  Substituting  l  A.4  yields  A.10  n  T  i n the e x p r e s s i o n f o r the average  results i n  1 A(T,t)  dA(T,t) dt  3  (  3- 2» T  2  K  T^-T^  w h i c h c a n be r e w r i t t e n  T^-T^  +1  T  n+1  +1  )  A.11  as  „n+l  -  (n+l)T T 2  ( T - T ) Tn+TT" 3  < S -; ' \ T  (-KT;(T -T )  i  K  2  -KT? ± _  n T  U s i n g A.9 and A.10  ( T  l  A. 9  n  A.9 b a c k i n t o A.6  f  divergence  3  - T  2  x  3  2  L  3  n+1 .+ n T 2  A.12  161.  APPENDIX B  S e n s i t i v i t y a n a l y s i s u s i n g a t y p i c a l c e l l and the express i o n f o r the amount o f r a i n f a l l  given by equation  4.32):  B.l  B.l  The C o n t r o l The v a l u e s of the parameters used i n the c o n t r o l a r e : e = 0.2 wc = 10 gm  HI  y = 5°C/1000m A ( T , t + A t ) = 65.0113 area u n i t s 3  A ( T , t ) = 25.8830 area u n i t s 3  AT = T - T 3  2  T  3  = -60°C  T  2  = -30°C  = -3Q°C  which g i v e a r a i n f a l l of 3 AP = 11.05x10  -2 gm m  = 11.05 mm  B.2 V a r i a t i o n o f AP w i t h e A  ±10% v a r i a t i o n i n the e m p i r i c a l adjustment f a c t o r e,  h o l d i n g the other parameters a t t h e i r c o n t r o l v a l u e s g i v e s 1) f o r a +10% change i n e, e=0.22 AP = 12.16 mm which i s a 1.11 mm o r 10% i n c r e a s e i n the estimated rainfall.  2)  f o r a -10%  change i n e, e=0.18  = 9.95  AP  mm  which i s a 1.11  mm  or 10% decrease i n the estimated  rainfall. B.3  V a r i a t i o n of A P w i t h A ±10% v a r i a t i o n  wc i n the water content wc,  h o l d i n g the  other parameters a t t h e i r c o n t r o l values g i v e s : _3 1) f o r a +10%  change i n wc,  - 12.16  AP  which i s a 1.11  wc=ll gm  m  mm mm  or 10% i n c r e a s e i n the estimated  rainfall. _3 2) f o r a -1Q% change i n wc, AP = 9.95 mm which i s a 1.11  mm  wc=9 gm  m  or 10% decrease  i n the estimated  rainfall. B.4  V a r i a t i o n of A P w i t h y A  ±10% v a r i a t i o n i n the l a p s e r a t e y, h o l d i n g the o t h e r  paramters a t t h e i r c o n t r o l v a l u e s g i v e s : 1) f o r a +10% AP  change i n  = 10.05  which i s a 1 mm  Y  , Y=5.5°C/1000m  mm or 9.1%  decrease  i n the estimated  rainfall. 2) f o r a -10% AP  change i n y ,  = 12.28  which i s a 1.23 mated  rainfall.  y=4.5°C/1000m  mm mm  or 11.1%  i n c r e a s e i n the  esti-  163. B.5 V a r i a t i o n o f AP w i t h A +10% v a r i a t i o n (T ) contour a t time 3  A(T^,t+At) i n the area of the coldest  temperature  (t+At), A(T^,t+At), holding the other  parameters a t t h e i r c o n t r o l v a l u e s g i v e s : 1)  f o r a +10%  c h a n g e i n A ( T ^ , t + A t ) , A(T ,t+At)=71.5124 3  AP = 12.20  mm  w h i c h i s a 1.15 mated 2)  mm o r 10.4%  increase i n the e s t i -  rainfall.  f o r a -10% c h a n g e i n A ( T , t + A t ) , 3  AP = 9.79  3  mm  w h i c h i s a 1.26 mated  A(T ,t+At)=58.5102  mm o r 11.4%  decrease i n the e s t i -  rainfall.  B.6 V a r i a t i o n o f Ap w i t h  A(T ,t) 3  A ±10% c h a n g e i n t h e a r e a o f t h e c o l d e s t (T ) 3  at  contour a t time  temperature  ( t ) , A ( T , t ) , h o l d i n g the other parameters 3  their control values gives: 1)  f o r a +10%  change i n A ( T , t ) , 3  AP = 9.91 w h i c h i s a 1.14 mated 2)  A(T ,t)=28.47 3  mm mm o r 10.4%  decrease i n the e s t i -  rainfall.  f o r a -10% c h a n g e i n A ( T , t ) , A ( T , t ) = 2 3 . 2 9 3  AP = 12.32  mm  w h i c h i s a 1.26  mm  mated  o r 11.4%  3  increase i n the e s t i -  rainfall.  B.7: V a r i a t i o n o f AP w i t h  AT  A ±10% c h a n g e i n t h e t e m p e r a t u r e t h i c k n e s s , the  other parameters a t t h e i r c o n t r o l values g i v e s :  AT, h o l d i n g  164. 1)  f o r a +10%  change i n the temperature t h i c k n e s s  AT,  AT=-33°C AP = 12.16  mm  which i s a 1.11 mm  or 10% i n c r e a s e i n the estimated  rainfall. 2)  f o r a -10% change i n the temperature t h i c k n e s s  AT,  ~ -O  AT=-27 C AP = 9.95  mm  which i s a 1.11 mm  or 10% decrease i n the estimated  rainfall.  B.8  V a r i a t i o n of AP w i t h T  3  and T,,  The r a d i a n c e temperatures recorded on the s a t e l l i t e red  infra-  images are based on the assumption t h a t c l o u d s r a d i a t e as '..  black bodies.  In other words the e m i s s i v i t y e i s assumed to 4 equal u n i t y m the Stefan-Boltzman r e l a t i o n E=eaT , i n which E i s —2 ' —8 —2—4 the energy r a d i a t e d (W m ), a = 5.669x10 W m K , and T i s the temperature the  (K).  development  Cloud e m i s s i v i t i e s , however, change throughout  o f the c l o u d .  Suppose t h a t the e m i s s i v i t y were i n r e a l i t y l e s s than 1, say  10% l e s s , e=0.9, then the a c t u a l temperature  (T., ) o f the oa c o l d e s t contour on the s a t e l l i t e image i s g i v e n by  E = aT e  4 3 a  = cT  or _ , ,-.25  4 3  165.  For  T, = -60°C =  (273.15-60)K = 213.15K, T  temperature t h i c k n e s s  Q  = -54.31°C.  The  AT would then be  AT = -54.31-(-30) =  -24.31°C  Keeping the other parameters a t t h e i r c o n t r o l v a l u e s , then AP = 8.96 which i s a 2.14  mm  mm  or 19% decrease in. the e s t i m a t e d r a i n f a l l .  A s i m i l a r c a l c u l a t i o n can be performed f o r the temperature at  the l e v e l of non-divergence T.,. A 10% decrease i n the e m i s s i v -  i t y a t t h i s l e v e l would r e s u l t i n the a c t u a l temperature T„ being T  2a = 2 "' ' = T (0.9) * T  ( e )  2  2  For  T  0  = -30°C = (273.15-30)K = 243.15K, T  temperature t h i c k n e s s  0  = -23.51°C.  The  AT would then be  AT = -60-(-23.41) =  -36.49°C  Keeping the o t h e r parameters a t t h e i r c o n t r o l v a l u e s , then AP = 13.44  which i s a 2.39 mm  B.9  mm  or 21.6%  i n c r e a s e i n the estimated r a i n f a l l .  Summary A ±10% v a r i a t i o n i n the i n d i v i d u a l v a l u e s of the parameters  i n the e x p r e s s i o n f o r r a i n f a l l  (equation B.l) g e n e r a l l y  i n a ±10% v a r i a t i o n i n the estimated r a i n f a l l .  results  A 10% decrease  i n the e m i s s i v i t y assumed a t a p a r t i c u l a r c l o u d l e v e l r e s u l t s i n a 20% change i n the e s t i m a t e d r a i n f a l l ; however, t h i s i s cons i d e r e d as a "worst case" example of the a c t u a l v a r i a t i o n s i n cloud  emissivity.  . 166.  One  i n t e r e s t i n g f a c e t of t h i s a n a l y s i s i s t h a t  uncertainties  i n the parameters may  i n the e s t i m a t i o n procedure.  the  a c t t o c a n c e l each other out  For example, i f areas of the  c o l d e s t contours at. both times were each 10% l a r g e r than they a c t u a l l y were, then the net e f f e c t y i e l d s  P = 11.05  mm  which i s the same r a i n f a l l estimate as u s i n g the c o n t r o l v a l u e s of the areas.  PUBLICATIONS: Loucks, R.H., D.J. Lawrence, D. Ingraham and B. F l e m i n g , "A Technique f o r E s t i m a t i n g Extreme Ocean C u r r e n t V e c t o r s " , B e d f o r d I n s t i t u t e o f Oceanography Rep. S e r i e s BI-R-73-5, 1973. Ingraham, D., B. F l e m i n g , D.J. Lawrence and R.H. Loucks, " S t a t i s t i c s and Extremes o f C u r r e n t s on the S c o t i a n S h e l f " , B e d f o r d I n s t i t u t e o f Oceanography Rep. S e r i e s BI-R-73-10, 1973. Loucks, R.H., D.J. Lawrence, and D.V. Ingraham, "Summary of P h y s i c a l , B i o l o g i c a l , Socio-Economic and Other F a c t o r s R e l e v a n t t o P o t e n t i a l O i l S p i l l s i n the Passamaquoddy Region o f the Bay o f Fundy, S e c t i o n 2. D i s p e r s i o n o f S p i l l e d O i l " , F i s h e r i e s Research Board o f Canada, T e c h n i c a l Report No. 428, pp. 215-228, 1973. Loucks, R.H., and D.V. Ingraham, "Summary o f P h y s i c a l , B i o l o g i c a l , S o c i o Economic and Other F a c t o r s R e l e v a n t t o P o t e n t i a l O i l S p i l l s i n the Passamaquoddy Region o f the Bay o f Fundy, S e c t i o n 9. The I n f l u e n c e o f E n v i r o n m e n t a l C o n d i t i o n s on the O p e r a t i o n s o f O i l T e r m i n a l s " , F i s h e r i e s Research Board o f Canada, T e c h n i c a l Report No. 428, PP. 215-228, 1973. McGonigal, D., R.H. Loucks and D.V. Ingraham, " H a l i f a x Narrow Sample C u r r e n t Meter Data", B e d f o r d I n s t i t u t e o f Oceanography Data S e r i e s BI-D-14-5, 1974. Loucks, R.H., D.J. Lawrence and D.V. Ingraham, "Note on the E s t i m a t i o n o f Plume and P a t c h D i s p e r s i o n S c a l e s " , P r o c e e d i n g s o f the I n t e r n a t i o n a l Conference o f A p p l i e d S t a t i s t i c s as D a l h o u s i e U n i v e r s i t y , H a l i f a x , May 2-4, 1974. Adams, E.E., C.W. A l m q u i s t , D.V. Ingraham and K.D. S t o l z e n b a c h , "Waste Heat D i s p o s a l from O f f s h o r e N u c l e a r Power P l a n t s " , P r o c e e d i n g s o f A.S.C.E. S p e c i a l t y Conference Ocean E n g i n e e r i n g I I I , U n i v e r s i t y of Delaware, Newark, 1975. Ingraham, D.V., K.D. S t o l z e n b a c h and E.E. Adams, "Phase I I F i n a l Report - F o r e c a s t i n g Power P l a n t E f f e c t s on the C o a s t a l Zone, S e c t i o n 6.5" f o r E.G. & G. E n v i r o n m e n t a l C o n s u l t a n t s o f Waltham, Mass. 1975. Ingraham, D.V., "The S t o c h a s t i c S i m u l a t i o n o f Ocean C u r r e n t s " , T h e s i s o f C i v i l E n g i n e e r i n g a t the Massachusetts I n s t i t u t e o f Technology, 1976.  S.M.  Ingraham, D.V., J . Amorocho, M. G u i l a r t e and M. E s c a l o n a , " P r e l i m i n a r y R a i n f a l l E s t i m a t e s i n Venezuela and Colombia from GOES S a t e l l i t e Images", Second Conference on Hydrometeorology, Atmospheric Environment S e r v i c e , T o r o n t o , Oct. 1977. Ingraham, D.V., " S a t e l l i t e Image and A i r p h o t o I n t e r p r e t a t i o n Casamance R i v e r " Report t o R.H. Loucks Oceanology, J u l y , 1978. Ingraham, D.V., and S.0. R u s s e l l " E s t i m a t i n g P r e c i p i t a t i o n from S a t e l l i t e Photographs" Submitted f o r p u b l i c a t i o n i n Water Resources Research 1980.  

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