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UBC Theses and Dissertations

Rainfall estimation from satellite images Ingraham, Diane Verna 1980

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RAINFALL ESTIMATION FROM SATELLITE IMAGES by DIANE VERNA INGRAHAM B.Sc. (Physics) , Dalhousie U n i v e r s i t y , H a l i f a x , 1974 S.M. ( C i v i l E n g i n e e r i n g - Water Resources), Massachusetts I n s t i t u t e o f Technology, Cambridge, U.S.A. 1976 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING We accept t h i s t h e s i s as conforming to the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA October 19 80 (c) Diane Verna Ingraham, 19 80 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I agree t h a t t h e L i b r a r y s h a l l make i t f r e e l y 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 . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be 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 u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n 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 p e r m i s s i o n . Department o f C i v i l E n g i n e e r i n g The U n i v e r s i t y o f B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 1 Date October 17, 1980 i i RAINFALL ESTIMATION FROM SATELLITE IMAGES ABSTRACT The de s i g n , management and o p e r a t i o n (as w e l l as the a s s o c i a t e d costs) o f major water resource p r o j e c t s are d i -r e c t l y r e l a t e d to the assessment of the a n t i c i p a t e d volumes o f r u n o f f to be handled by the p r o j e c t . In remote or sp a r -s e l y gauged regions i t i s o f t e n very d i f f i c u l t to determine these volumes due to a lack o f data. The m e t e o r o l o g i c a l s a -t e l l i t e s , and i n p a r t i c u l a r , the Geo s t a t i o n a r y O p e r a t i o n a l Environmental S a t e l l i t e s (GOES) can provide good a r e a l cover-age o f the E a r t h and i t s weather systems p o t e n t i a l l y every h a l f hour day and n i g h t . Since the f i r s t m e t e o r o l o g i c a l s a t e l l i t e images were t r a n s m i t t e d , many attempts have been made to estimate r a i n -f a l l u s i n g the images to i d e n t i f y s p e c i f i c c l o u d c h a r a c t e r i s -t i c s and c o r r e l a t i n g these with expected r a i n f a l l . However, these methods have been l i m i t e d to c o n v e c t i v e r a i n f a l l i n the t r o p i c s o r near t r o p i c s . A method i s pres e n t e d here f o r e s t i m a t i n g h a l f - h o u r l y r a i n f a l l which r e l a t e s the v e r t i c a l u p d r a f t v e l o c i t i e s and hence, the moisture f l u x i n t o the c l o u d , to the r a t e o f v e r t i -c a l and h o r i z o n t a l growth of the c l o u d top as r e v e a l e d i n the GOES i n f r a r e d images. The method performs w e l l i n e s t i m a t i n g r a i n f a l l from w i d e s p r e a d f r o n t a l systems common over B r i t i s h C o lumbia. 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 w hich a r o s e d u r i n g the r e s e a r c h were r e s o l v e d . One was t o a s c e r t a i n c l o u d top t e m p e r a t u r e c o n t o u r s f o r tho s e GOES i n f r a r e d images w h i c h were n o t enhanced. 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 m o n i t o r system. The second was one o f bookkeeping t o "keep t r a c k o f " the i n d i v i d u a l c l o u d c e l l s . T h i s was taken c a r e o f t h r o u g h t h e use o f computer r o u -t i n e s w h i c h d i r e c t e d the i n p u t and o u t p u t o f d a t a , a c c o u n t e d f o r t h e growth and movement o f the s t o r m c e l l s o v e r the 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 t h o s e l o c a t i o n s w h i c h f e l l 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 method was used t o e s t i m a t e r a i n f a l l f o r a number o f t e s t storms o c c u r r i n g o v e r B r i t i s h C olumbia. The r e s u l t s were re 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 were some l o c a l i n a d e q u a -c i e s . An u p d a t i n g -procedure was d e v e l o p e d i n whi 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 i n t o c o n s i d e r a t i o n the 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 o b s e r v a t i o n s . F u r t h e r m o r e , the parameters o f the u p d a t i n g model ( d e t e r m i n e d f o r gauged - l o c a t i o n s ) can be used t o update r a i n f a l l e s t i m a t e s f o r ungauged l o c a t i o n s . i v I n t h e l i g h t o f p r e s e n t r a i n g a u g e i n s t a l l a t i o n and o p e r a t i n g c o s t s and the l i m i t a t i o n s o f r a d a r i n mountainous a r e a s , t h e 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 p r o v i d e s an e c o n o m i c a l o p e r a t i o n a l supplement t o e x i s t i n g c o n v e n t i o n a l p r e c i p i t a t i o n d a t a c o l l e c t i o n . V TABLE OF CONTENTS ABSTRACT i i TABLE OF CONTENTS ,. V LIST OF TABLES i x LIST OF FIGURES x i NOTATIONS USED x v i ACKNOWLEDGEMENTS x i x CHAPTER I INTRODUCTION -; !• 1.1 Study O b j e c t i v e s 3-1.2 O u t l i n e o f the F o l l o w i n g Chapters 5. I I METEOROLOGICAL SATELLITES: BACKGROUND 7. 2.1 Some S a t e l l i t e Systems and Sensors 7. 2.2 The GOES System 1 3 . 2.3 GOES Image F o r m a t i o n and Enhancement Schemes . 1 6 . 2.4 Other Sources o f S a t e l l i t e I n f o r m a t i o n . . . . 2 6 . I I I A REVIEW OF SATELLITE IMAGE PRECIPITATION ESTIMATION 2 8 . 3.1 GOES R a i n f a l l E s t i m a t i o n Techniques 3 0 . 3.1.1 The NHEML Technique 3 0 . 3.1.2 The UW Technique 3 1 . 3.1.3 The S c o f i e l d / O l i v e r Technique 3 2 . 3.2 Summary 3 7 . v i IV THE MODEL USED TO DESCRIBE PRECIPITATING CLOUDS . . . . 39 4.1 P r e c i p i t a t i o n i n B r i t i s h Columbia 39 4.2 The Model 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 Model 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 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 4.4 The C o n t i n u i t y E q u a t i o n Used 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 the V e r t i c a l V e l o c i t y w 50 4.4.2 R e w r i t i n g t h e C o n t i n u i t y E q u a t i o n 53 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 Between Average Divergence and C o l d e s t Contour D i v e r g e n c e 55 4.5.2 One Proposed D i v e r g e n c e F u n c t i o n 56 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 59 4.6 Consequences o f the Model 60 4.7 The Other Model Parameters 61 4.7.1 The Water Content wc 61 4.7.2 The Lapse Rate y 6 5 4.7.3 Adjustment F a c t o r e . . . . . 65 4.8 Summary 66 v i i V COMPUTATIONAL PROCEDURE FOR ESTIMATING RAINFALL FROM SATELLITE IMAGES 68 5.1 C o n c e p t u a l P r o c e d u r e 68 5.1.1 Movement o f Storm C e l l s Near A S t a t i o n . . 77 5.2 Computer R o u t i n e Sequence 82 VI ESTIMATES OF PRECIPITATION USING SATELLITE IMAGES • . 86 6.1 T e s t Storms 86 6.2 The O c t o b e r 31, 19 78 R a i n f a l l E s t i m a t e s 8 9 6.2.1 Storm D e s c r i p t i o n 89 6.2.2 R e s u l t s 92 6.2.3 Comparison o f S t r e a m f l o w and R a i n f a l l Volumes 93 6.3 Th:e December 17, 19 79 R a i n f a l l E s t i m a t e s . . . . 98 6.3.1 Storm D e s c r i p t i o n 98 6.3.2 R e s u l t s 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 . . . . 109 6.4 The June 4, 19 77 R a i n f a l l E s t i m a t e s 114 6.4.1 Storm D e s c r i p t i o n 114 6.4.2 R e s u l t s 114 6.5 The N&vember 20, 1979 R a i n f a l l E s t i m a t e s . . . . 117 6.5.1 Storm D e s c r i p t i o n 117 6.5.2 R e s u l t s . . . . . . 120 v i i i 6.6 The December 5, 19 79 R a i n f a l l E s t i m a t e s 123. 6.6.1 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 Comparison 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 A l l Storms 128. V I I AN UPDATING PROCEDURE USING OBSERVED DATA 130. 7.1 The U p d a t i n g Model 130. 7.2 Comparison o f Updated and Observed R a i n f a l l . . . 133. 7.2.1 The Updated O c t o b e r 31, 19 78 R a i n f a l l E s t i m a t e s 135. 7.2.2 The Updated December 17, 19 79 R a i n f a l l E s t i m a t e s 139. 7.3 L i m i t a t i o n s on T r a n s f e r r i n g a and b 141. 7.4 Summary 145. V I I I 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. i x LIST OF TABLES T a b l e No. T i t l e Page 2.1 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 (from H o l t o n 19 72 and Knox, 1978) 8. 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 f o r Space-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. 2.3 Some P r e s e n t and P r o p o s e d S a t e l l i t e s , t h e i r Sen-s o r s , and C h a r a c t e r i s t i c s . A d d i t i o n a l i n f o r m a t i o n i s a v a i l a b l e from WMO (19 76), 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 and Water Content 62. 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 t h e Atmosphere ( R e c e i v e d by the 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, Washington, D.C.). 64. 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 the P e r i o d 00 45 GMT on O ctober 31, 19 80 t o 2245 GMT on November 1, 19 78. 94. 6.2 Comparison o f R a i n f a l l and Runoff Volumes i n m 3 x l 0 6 . 99. 6.3 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 00 00 GMT t o 0 60 0 GMT on December 17, 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 used t o c a l i b r a t e t h e adjustment parameter e. 105. 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 the 6-hour Segment 0000 GMT t o 0600 GMT on December 17, .1.9 79 . For each s t a t i o n the e m p i r i c a l a d j u s tment 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. 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 the s t o r m o f June 4, 19 77. 1 1 8 • 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 the Storm o f November 20, 1979. 122. 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 the Storm o f December 5, 19 79. 126. X 7.1 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 Each New P a i r o f Observed and 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. 7.2 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 the Storm o f December 17, 19 79. 142. x i LIST OF FIGURES F i g u r e No. C a p t i o n Page 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 O b s e r v i n g R a i n f a l l on 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 the same as on t h e S a t e l l i t e Images. (Lambert Conformal C o n i c , F a r l e y 1980). 2. 2.1 F i v 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 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 and NOAA, 1979). 14. 2.2 Assembly o f a VISSR Image. Each Scan L i n e i s composed o f 8 V i s i b l e Sensor L i n e s V^ and 1 I n f r a r e d Sensor L i n e . One Scan L i n e Represents a West t o E a s t 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 N o r t h - S o u t h Manner (Adapted from McKowan 19 7 7 ) . 17. 2.3 D i s t r i b u t i o n o f the 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 C e n t r e ( a f t e r C o r b e l l et al., 1977). 20. V i s i b l e and I n f r a r e d S e c t o r s S e c t o r Centre P o i n t R e s o l u t i o n (km) ( l a t / l o n g )  SA-1 36°N/118°w 1 SA-2 45°N/1160W 1 SB-6 42°N/1240W 2 UC-2 2 8QN/135°W 4 2.5 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 ) from GOES-West. 22. 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 ) from GOES-West. 23. 2.7 A T y p i c a l S a t e l l i t e Enhanced I n f r a r e d Image (SB6 S e c t o r , "EC" Enhancement Scheme) from GOES-West. 24. 2.8 The "EC" Enhancement Scheme wh i c h R e l a t e s Tempe-r 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. x i i Segment Temperature Reason f o r Segment No. Range °C Enhancement  1 +56.8 to +37.3 No s i g n i f i c a n t d a t a 2 +36.3 to +20.8 Land and w a t e r 3 +20.3 to -13.2 Water and low c l o u d s 4 -13.7 to -15.7 Benchmark between low and medium l e v e l c l o u d s 5 -16.2 to -50.2 Medium and h i g h c l o u d s ( c o o l season p r e c i p i -t a t i o n ) 6 -51.2 to -60.2 C o n v e c t i v e c l o u d tops 7 -61.2 to -70.2 C o n v e c t i v e c l o u d tops 8 -71.2 to-110.2 C o l d e s t c l o u d tops and space 3.1 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 from GOES Images u s i n g the S c o f i e l d / O l i v e r Tech-n i q u e ( A f t e r Ingraham, et al., 1977). 36 4.1 A Column o f A i r Between t h e L e v e l s z and z+dz a t Times t and t + d t . 44, 4.2 Schematic Diagram o f A i r C i r c u l a t i o n D u r i n g a Major Storm. 52 5.1 E x p l a n a t i o n o f the V a r i o u s Terms used t o De-scribeGOES 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 S u r r o u n d i n g Warmer C o n t o u r s . STORM- The Cloudy A r e a on the S a t e l l i t e Image whi 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 5.2 Steps 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 from GOES S a t e l l i t e Images. 70, 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 Compu-t e r T e r m i n a l 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 the T a b l e t and the Temperature Contours are T r a c e d u s i n g the S t y l u s . 72 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 Determine Temperature Contours from Un-enhanced I n f r a r e d S a t e l l i t e Images. 74 5.5 The top photo shows the s a t e l l i t e image as seen on the v i d e o m o n i t o r b e f o r e 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. The second photo shows the s a t e l l i t e image as seen on the v i d e o m o n i t o r a f t e r x i i i t he 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. Those c l o u d s warmer th a n T°C on the tempera-t u r e - g r e y s c a l e have been shown as b l a c k areas w h i l e those c o l d e r than T°C are shown as l i g h t e r a r e a s . The boundary between the two i s the T°C c o n t o u r . 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 M o n i t o r Arrangement Used t o Determine Temperature Contours from GOES Unenhanced I n f r a -r e d Images. 7 o ' 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 Con-t o u r 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 i and t 2 . The D i s p l a c e m e n t o f the 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 from c i t o C2. From These "Snap-Shot" Views, 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 8 ' 5.8 The C e l l ' s P o s i t i o n a t Time t2 i s S h i f t e d Back H a l f the 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. 79, 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 . B oth Are S h i f t e d so 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 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 re shown by the Dashed Curve 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) f o r the P e r i o d O c t o b e r 29 t o November 2, 19 7 8 ( A f t e r S c h a e f e r 1979a, b) . 90. 6.2 A r e a l E x t e n t o f the October 31, 19 7 8 Storm a t 0115 GMT as Viewed from GOES-West. 91. 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 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. 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 E s t i m a t e d I s o h y e t s f o r the October 31, 19 78 Storm. 96. 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 31, 1978 Storm Based on the G r i d P o i n t s Shown i n F i g u r e 6.4. 9 7 . 6.6 Map o f t h e Vancouver I s l a n d - Lower 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 the 7-Day P e r i o d from December 12 t o 18) 1979 . ( A f t e r S c h a e f e r , 1980). 1 0 O . x i v 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. 10 2. L o c a t i o n o f S t a t i o n s Used i n the December 17, 1979 Storm A n a l y s i s . 103. 1 B l u e R i v e r 14 P r i n c e George A i r p o r t 2 B u l l Harbour 15 P r i n c e R upert A i r p o r t 3 Burns Lake 16 Quesnel A i r p o r t 4 C a s t l e g a r A i r p o r t 17 R e v e l s t o k e A i r p o r t 5 Cranbrook A i r p o r t 18 Salmon Arm 6 Dease Lake 19 S a n d s p i t A i r p o r t 7 Hope A i r p o r t 20 T e r r a c e A i r p o r t 8 Kamloops A i r p o r t 21 T o f i n o A i r p o r t 9 Kelowna A i r p o r t 22 Vancouver I n t e r n a t i o n a l 10 L angara A i r p o r t 11 L y t t o n 23 V i c t o r i a I n t e r n a t i o n a l 12 P e n t i c t o n A i r p o r t A i r p o r t 13 P o r t Hardy A i r p o r t 24 W i l l i a m s Lake A i r p o r t 25 B a n f f 26 C a l g a r y 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 De-cember 17, 19 79 Storm. (For each s t a t i o n the e m p i r i c a l a djustment 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 . ) 108. Storm C e l l R a i n f a l l "Maps" f o r 2 Hours D u r i n g the December 17, 1979 Storm. 110. 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 the December 17, 19 79 Storm. HI. Observed 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 T o f i n o 22.6 Vancouver 10.6 V i c t o r i a 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 the December 17, 1979 Storm E s t i m a t e d f o r the 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 A n a l y s i s : 1 Duncan Lake Dam 2 R e v e l s t o k e A i r p o r t 3 M i c a Dam 4 C a s t l e g a r A i r p o r t d i n the June 4, 19 77 Storm 5 E l k o 6 Cranbrook A i r p o r t 7 B l u e R i v e r XV 6.14 A r e a l E x t e n t o f June 4, 1977 Storm a t 0245 GMT as Viewed from GOES-West. 116 6.15 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 June 4, 19 77 Storm. 119 6.16 A r e a l E x t e n t o f November 20, 1979 Storm a t 1115 GMT as Viewed from GOES-West, 121 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, 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 Storm. 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 T e s t Storms. 129 7.1 The B e h a v i o u r o f the Weights W i = W 1 ( n _ l ) f o r n=50 and 3 v a l u e s o f W]_. 134 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 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 . T y p i c a l V a l u e s o f a, b f o r Each S t a t i o n a re Gi v e n i n Table 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) where the 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 where o n l y one o f the s t a t i o n s (A) has a r a i n g a u g e . S a t e l l i t e e s t i m a t e s o f r a i n f a l l a r e a v a i l a b l e f o r a l l 4 s t a t i o n s t h r o u g h -o u t the d u r a t i o n o f t h e storm. By u p d a t i n g the e s t i m a t e d s e r i e s f o r A w i t h the o b s e r v e d d a t a measured t h e r e , v a l u e s o f a and b can 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 used t o update the 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 G o s p e l 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 case 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 Gos p e l 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 . 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 the December 17, 19 79 Storm Updated 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 the G r i d P o i n t s Shown i n F i g u r e 6.11 144 X V I NOTATIONS USED The f o l l o w i n g n o t a t i o n s a re f r e q u e n t l y used. a r a d i u s o f the e a r t h a u p d a t i n g model parameter a Q c o n s t a n t i n UW t e c h n i q u e a^ c o n s t a n t i n UW t e c h n i q u e A c l o u d a r e a A c s a t e l l i t e (cloud) a r e a i n NHEML t e c h n i q u e A e r a d a r echo 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 parameter 0 ^ 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 pressure=c^+R c v s p e c i f i c h e a t of a i r a t c o n s t a n t volume e ad j u s t m e n t f a c t o r , e f f i c i e n c y E e v a p o r a t i o n f , f 1 , f 2 c o n s t a n t s i n t h e d i v e r g e n c e f u n c t i o n s Fx,Fy, Fz e a s t w a r d , n o r t h w a r d , v e r t i c a l components o f f r i c t i o n , r e s p e c t i v e l y g g r a v i t y 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 added p e r u n i t mass o f a i r i i n d e x 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 d i v e r g e n c e o f the c o l d e s t c o n t o u r M mass o f a column o f a i r n t o t a l number i n a s e r i e s 0 " o r d e r o f magnitude o f " p p r e s s u r e x v i i P p r e c i p i t a t i o n (mm) r^ volume ra i n rate i n NHEML technique R gas constant R volume rain rate i n UW technique t time ,T temperature u eastward component of v e l o c i t y V v northward component of v e l o c i t y V Y vel o c i t y vector w v e r t i c a l component of v e l o c i t y V wc water content i - t h weight i n updating model W-j^  weighting parameter i n updating model x eastward horizontal component x estimated r a i n f a l l i n updating model y northward horizontal component y observed or "true" r a i n f a l l i n updating model z v e r t i c a l component a s p e c i f i c volume Y lapse rate v environmental lapse rate env Y saturated adiabatic lapse rate s p density <[> latitude fi angular v e l o c i t y of the Earth x v i i i Acronyms: AES A t m o s p h e r i c Environment S e r v i c e A T S - I I I A p p l i c a t i o n s Technology S a t e l l i t e - I l l 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 R a i l w a y 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 Program ESSA. E n v i r o n m e n t a l Survey S a t e l l i t e - E n v i r o n m e n t a l S c i e n c e S e r v i c e s A d m i n i s t r a t i o n GMS Geosynchronous M e t e o r o l o g i c a l S a t e l l i t e (Japan) GMT Greenwich Mean Time ( S u b t r a c t 8 hours from GMT t o g e t PST) GOES G e o s t a t i o n a r y O p e r a t i o n a l E n v i r o n m e n t a l S a t e l l i t e GOES-Tap H i g h q u a l i t y t e l e p h o n e l i n k f o r t r a n s m i s s i o n o f GOES images IR i n f r a r e d (image) METEOSAT M e t e o r o l o g i c a l S a t e l l i t e (European Space Agency) NESS N a t i o n a l E n v i r o n m e n t a l S a t e l l i t e S e r v i c e PST P a c i f i c S t a n d a r d Time PWC P a c i f i c Weather C e n t r e , Vancouver, B.C. SMS Synchronous M e t e o r o l o g i c a l S a t e l l i t e TIROS - 1 , TIROS-N T e l e v i s i o n I n f r a r e d O b s e r v a t i o n a l S a t e l l i t e - 1 , -N VISSR! 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 x i x ACKNOWLE DGEMENTS I want to thank Dr. S.O. (Denis) R u s s e l l whose a d v i c e and guidance was i n v a l u a b l e t h r o u g h o u t the co u r s e o f the stu d y and 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 has been a p l e a s u r e t o work w i t h Dr. R u s s e l l . I would a l s o thank Dr. 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 ; Dr. M. Q u i c k , Department o f C i v i l E n g i n e e r i n g ; Dr. P. Murth a , Department o f F o r e s t r y ; and Dr. J . Hay, Department o f Geography; 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 work. Thanks go t o Dr. J . Amorocho, 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 , and Dr. 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; and t o NESS, Washington, D.C. f o r p r o v i d i n g GOES s a t e l l i t e images and f i l m l o o p s . Thanks a l s o go t o Dr. P. H a e r i n g and Mr. J . Spagnol o f the 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 making GOES-West s a t e l l i t e images and 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 extended t o Mr. W. K r e u d e r , Water Survey 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 a r e a b a s i n s ; t o Mr. N. Penny o f the AES and to Mr. B. Yorke o f t h e C l i m a t o l o g i c a l Data S e r v i c e s , AES, 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 d a t a ; and t o Dr. D.G. S c h a e f e r f o r p r o v i d i n g the r e s u l t s o f h i s a n a l y s i s o f the October 31, 19 78 and December 17, 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 S c i e n c e s 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 are exten 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 the m a n u s c r i p t , t o Mr. R i c h a r d Brun f o r the d r a f t i n g a s s i s t a n c e and t o Mr. J . Bonser f o r computer programming a s s i s t a n c e . I would a l s o l i k e t o thank my f a m i l y and f r i e n d s f o r b e i n g t h e r e when I needed 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 the de-velopment o f i t s n a t u r a l r e s o u r c e s w i t h t h e q u a l i t y o f t h i s growth dependent on the s k i l l f u l e x p l o i t a t i o n and management o f the r e s o u r c e s . As a b a s i s f o r the e f f i c i e n t p l a n n i n g , de-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 de-s c r i p t i o n o f the r e s o u r c e 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 t o p r o v i d e . I n B r i t i s h Columbia w a t e r i s a major r e s o u r c e c o n t r i b u t -i n g d i r e c t l y and i n d i r e c t l y t o the economy and w e l l - b e i n g o f the p r o v i n c e . The amount o f r a i n f a l l i n g o v e r t h e r e g i o n i s an i m p o r t a n t q u a n t i t y i n the w a t e r r e s o u r c e i n v e n t o r y . The measurement o f t h e r a i n f a l l i s hampered because t h e e x i s t i n g network 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 and i n some i n -s t a n c e s n o n - e x i s t e n t . F i g u r e 1 . 1 shows the 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 on an h o u r l y b a s i s t h r o u g h o u t B r i t i s h Columbia. Most o f these s t a t i o n s a re grouped near cen-t r e s o f p o p u l a t i o n o r a l o n g t r a n s p o r t a t i o n r o u t e s , b o t h t o f a -c i l i t a t e i n s t a l l a t i o n and maintenance, and t o keep c o s t s t o a minimum. There a r e , however, l a r g e areas w h i c h remain w i t h o u t gauges o r which have gauges where d a t a are n o t a v a i l a b l e f o r use on a r e a l - t i m e b a s i s , such as i n f l o o d f o r e c a s t i n g . The l a c k o f d e t a i l e d r a i n f a l l d a t a from r i v e r b a s i n s has l o n g been 2. FIGURE 1.1 Dis t r i b u t i o n of Stations i n B r i t i s h Columbia Observing R a i n f a l l on an Hourly Basis. The Projection i s the Same as on the S a t e l l i t e Images, (Lambert Cohformal Conic, Farley 1980). 3. a recognized problem among hydrologists but there appears to be l i t t l e prospect of i t being resolved by surface meas-urement techniques i n the near future. This i s p a r t i c u l a r l y true i n the more remote unpopulated regions where some of the largest water resource developments are now being engineered. Meteorological s a t e l l i t e s hold the promise of providing meteorologic information over large regions. The geostation-ary operational environmental s a t e l l i t e s , GOES, record atmospher-i c conditions on the Earth around the clock and provide h a l f -hourly images such as those shown on the t e l e v i s i o n weather fore-cast. GOES images have been employed to estimate r a i n f a l l from large convective c e l l s i n t r o p i c a l and sub-tropical areas by applying empirical r e l a t i o n s s p e c i f i c a l l y derived for this type of storm, (Scofield and O l i v e r , 1977a; G r i f f i t h et al. , 19 78; Stout et al., 19 79). On the whole these approaches o f f e r l i m i t e d guidance for extending r a i n f a l l estimation using s a t e l l i t e images to other types of storms or geographic regions. 1.1 Study Objectives The aims of the study described i n the following chapters were to extend the s a t e l l i t e r a i n f a l l estimation procedure which would be applicable to f r o n t a l storms and other p r e c i p i t a t i o n systems i n the higher l a t i t u d e s , to develop an applicable physi-c a l concept for the estimation procedure, and to t e s t the proce-dure by applying i t to actual storms. 4. The more s u c c e s s f u l methods f o r computing r a i n f a l l from s a t e l l i t e images a l l use the changes i n the a r e a o f the c l o u d top temperature c o n t o u r s from one image t o the n e x t as i n p u t parameters t o t h e i r c o m p u t a t i o n a l p r o c e d u r e s , as f o r example i n S c o f i e l d and O l i v e r (19 77a) . I n the c o u r s e o f the p r e s e n t s t u d y i t was r e a l i z e d t h a t the r a t e o f change i n the c l o u d top t e m p e r a t u r e c o n t o u r s p r o v i d e s 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 the a s c e n d i n g a i r i s s p r e a d i n g o u t a t the c l o u d t o p . By c o n t i n u i t y t h i s i s i n t u r n r e l a t e d t o t h e r a t e a t w h i c h a i r e n t e r i n g the c l o u d i s r i s i n g . I t has 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 from a knowledge o f t h e r a t e a t w h i c h an a i r mass was r i s i n g and i t s m o i s t u r e c o n t e n t (Byers and Braham, 1948) , b u t i t has never been p o s s i b l e t o measure the v e r t i c a l v e l o c i t y o f the a s c e n d i n g a i r . Now, as shown i n the p r e s e n t s t u d y , t h e v e r t i c a l v e l o c i t y can be e s t i m a t e d from the d i v e r -gence o f the c l o u d t o p w h i c h can be d e t e r m i n e d from s u c c e s s i v e s a t e l l i t e images. 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 s u c c e s s o f t e c h n i q u e s such as t h a t o f S c o f i e l d and O l i v e r (19 7 7 a ) , and i t a l s o p r o v i d e d a s o l i d 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 fundamental concepts t o the t y p e o f storms e n c o u n t e r e d i n B r i t i s h Columbia. To a p p l y the concept i t was n e c e s s a r y t o develop p r o c e d u r e s f o r e s t i m a t i n g 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 a method f o r u p d a t i n g t h e s e e s t i m a t e s i n the l i g h t o f a c t u a l r e c o r d e d d a t a , and t o develop computer r o u t i n e s t o h e l p w i t h the e x t e n s -5. ive c a l c u l a t i o n s . Such procedures were developed and tested on a number of major and minor storms which occurred over B r i t -i s h Columbia and for which s a t e l l i t e images were av a i l a b l e . The emphasis throughout has been on developing a p r a c t i -cal technique which can be used by hydrologists and meteorolo-g i s t s . P o t e n t i a l engineering applications of the data include providing real-time regional flood forecasts, reservoir inflows, as well as the study of previous large storms for design flood c a l c u l a t i o n s . 1.2 Outline of the Following Chapters Chapter II contains general background information on meteorological s a t e l l i t e s , i n p a r t i c u l a r GOES, which provided the images used i n this study. Chapter III reviews other inves-tigations into the application of s a t e l l i t e imagery for r a i n f a l l estimation. Chapter IV describes the model employed to relate cloud growth as observed i n s a t e l l i t e images to the actual r a i n -f a l l from the cloud. Chapter V discusses the conceptual and com-puter sequence followed to arrive at s a t e l l i t e estimates of r a i n -f a l l , while Chapter VI presents the estimates of p r e c i p i t a t i o n for a number of storms over B r i t i s h Columbia and compares them with the observed p r e c i p i t a t i o n . The f i r s t part of Chapter VII d i s -cusses the updating procedure for incorporating the information contained i n the observed r a i n f a l l series with that of the e s t i -mated s e r i e s . The second part of Chapter VII contains the updated 6. p r e c i p i t a t i o n e s t i m a t e s f o r two storms o v e r B r i t i s h Columbia and compares them t o t h e measured p r e c i p i t a t i o n . Chapter V I I I draws t o g e t h e r t h e c o n c l u s i o n s , recommendations and s u g g e s t e d d i r e c t i o n s f o r f u t u r e r e s e a r c h t h a t have become apparent d u r i n g the c o u r s e o f t h i s s t u d y . 7. CHAPTER I I METEOROLOGICAL SATELLITES: BACKGROUND With space f l i g h t came the o p p o r t u n i t y f o r t a k i n g a c l o s e r look at c o n d i t i o n s on E a r t h ( l i k e the weather) from a unique vantage p o i n t . Present m e t e o r o l o g i c a l s a t e l l i t e s scan the E a r t h r e g u l a r l y a t a l e v e l o f r e s o l u t i o n which allows 3 7 o b s e r v a t i o n o f meso and macroscale (10 to 10 m) phenomena. (Atmospheric motions o f v a r i o u s s c a l e s and types are summarized i n Table 2 .1). These s a t e l l i t e s o f f e r a p o t e n t i a l s o l u t i o n to the problem o f inadequate 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 on a s p a t i a l and temporal s c a l e v i r t u a l l y 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 ground based-networks. 2.1 Some S a t e l l i t e Systems and Sensors There are two c o n s i d e r a t i o n s which have a f f e c t e d meteor-o l o g i c a l s a t e l l i t e systems and t h e i r s e n s o r s . One i s the op-t i c a l behaviour o f the atmosphere a t d i f f e r e n t wavebands and the o t h e r i s the type o f o r b i t the s a t e l l i t e can take above the Earth' s s u r f a c e . The atmosphere has "windows" ( i . e . i s t r a n s p a r e n t to r a d i a t i o n o f c e r t a i n wavelengths) which are important f o r remote s e n s i n g , i n the v i s i b l e , near v i s i b l e , i n f r a r e d , and microwave bands. These are shown i n Table 2 . 2 . Consequently sens o r s , 8. TABLE 2.1 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 (from H o l t o n , 19 72 and Knox, 19 78) TYPE OF MOTION HORIZONTAL SCALE (m) m o l e c u l a r mean f r e e p a t h ,10"7 minute t u r b u l e n t e d d i e s 10 - 2 t o 1 0 - 1 s m a l l e d d i e s 10"1 t o 1 d u s t d e v i l s 1 t o 10 g u s t s 10 t o 102 tornadoes i o 2 cumulonimbus c l o u d s 103' f r o n t s , s q u a l l l i n e s 104 t o 105 h u r r i c a n e s 10 5 s y n o p t i c c y c l o n e s 106 p l a n e t a r y waves 10 7 9. TABLE 2.2 Major 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 , 19 76) WINDOW WAVEBAND u l t r a v i o l e t and v i s i b l e 0 .30 t o 0 .75y <-0 .77 t o 0 .91 near i n f r a r e d 1 .0 t o 1 .12 1 .19 t o 1 .34 1 .55 t o 1 .75 • 2 .05 t o 2 .4 m i d - i n f r a r e d 3 .5 t o 4 .16 4 .5 t o 5 .0 t h e r m a l i n f r a r e d 8 .0 t o 9 .2 10 .2 t o 12 .4 17 .0 t o 22 .0 mi crowave 2 .06 t o 2 .22 mm 3 .0 t o 3 .75 7 .5 t o 11 .5 20 .0 + 10. s e n s i t i v e 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 . T a b l e 2.3 l i s t s some 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 l o n g w i t h t h e i r s e n s o r s . The two most p o p u l a r wavebands f o r o p e r a t i o n a l use are the v i s i b l e and the t h e r m a l i n f r a r e d bands. I n a d d i t i o n to o b s e r v i n g the E a r t h i n s e v e r a l wavebands, the type o f o r b i t the s a t e l l i t e assumes can a l s o be c o n t r o l l e d . Weather s a t e l l i t e s g e n e r a l l y have one o f two o r b i t a l c o n f i g u r a -t i o n s : a p o l a r o r b i t - the o r b i t o f t h e s a t e l l i t e p a sses o v e r b o t h p o l e s ; o r a g e o s t a t i o n a r y o r b i t - the o r b i t o f the s a t e l l i t e has a p e r i o d o f a p p r o x i m a t e l y 24 hours so t h a t i t remains " f i x e d " o v e r one p o s i t i o n on the E a r t h ' s s u r f a c e . The advantage o f p o l a r o r b i t i n g s a t e l l i t e s l i e s i n the p r o v i s i o n o f images o v e r the e n t i r e s u r f a c e o f the E a r t h . T h i s i s e s p e c i a l l y i m p o r t a n t f o r o b t a i n i n g d a t a f o r the p o l a r r e g i o n s . The w i d t h o f t h e swath t h a t p o l a r s a t e l l i t e s sweep o u t i n t h e i r o r b i t s i s dependent i n p a r t on the t y p e o f s e n s o r and t h e a l t i t u d e o f t h e s p a c e c r a f t . The f r e q u e n c y o f r e p e a t coverage o v e r any one l o c a t i o n v a r i e s w i t h the s a t e l l i t e used. (See T a b l e 2.3). I t i s t h i s r e p e a t 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 d i s a d v a n t a g e o f p o l a r o r b i t -i n g s a t e l l i t e s - i t i s u s u a l l y t o o low t o r e v e a l r a p i d l y changing weather f e a t u r e s . G e o s t a t i o n a r y s a t e l l i t e s p r o v i d e a " g l o b a l view" o f wea-t h e r on a v e r y f r e q u e n t b a s i s : one image as o f t e n as every h a l f hour d u r i n g r e g u l a r o p e r a t i o n and more o f t e n d u r i n g s e v e r e TABLE 2.3 Some Present 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 . A d d i t i o n a l Information i s Ava i l a b l e from WMO (1976), NESS (1976), Kodaira and Murayama (1976), NOAA (1979), Spaceflight (1980), and Davis (1980). SATELLITE SENSOR WAVEBAND NOMINAL NADIR RESOLUTION (km) REMARKS Geostationary S a t e l l i t e s : SMS/GOES V i s i b l e and Infrared Spin-Scan Radiometer (VISSR) 0 .55-0 .7 10 .5-12 .5 1 8 Repeat coverage every h hr, r e s o l u t i o n double nadir value at 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 expected launch Aug. 19 80 . GMS "Sunflower" VISSR 0.5-0.75 10 .5-12.5 1.25 5 Japanese s a t e l l i t e l o c a t e d at (0°N, 140°E). METEOSAT VISSR Water Vapor (WV) 0.7 11 6 1.25 • 5 5 European Space Agency S a t e l -l i t e (ESA=Belgium, Denmark, France, Germany, I t a l y , Swe-den, Switzerland, and the United Kingdom). S a t e l l i t e l o c a t e d at (0°N, 0°W); as of Nov. 24/79 on l i m i t e d operation due to onboard overload problem. STORMSAT Advanced Atmospheric . Sounding and Imaging Radiometer (AASIR) not a v a i l a b l e not a v a i l a b l e 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 scanner; expected launch: mid 19 80's. Polar S a t e l l i t e s NIMBUS 5 E l e c t r i c a l l y Scanning Microwave Radiometer (ESMR) 0.8 cm 32 Repeat coverage every 12 m. TABLE 2.3 (continued) SATELLITE SENSOR WAVEBAND NOMINAL NADIR RESOLUTION (km) REMARKS NIMBUS 6 Temperature-Humidity-Infrared- Radiometer (THIR) 6 .5-7.1 10 .3-12 .5 22 8 Repeat coverage every 12 hr. NIMBUS G THIR (same as f o r NIMBUS 6) Scanning M u l t i f r e -quency Microwave Ra-diometer (SMMR) 4.55 cm 2.81 cm 1.67 cm 1.36 cm 0.81 cm 118 x 103 73 x 66 47 x 41 37 x 32 22 x 19 Repeat coverage every 36 hr., swath width 780 km. NOAA 5,6 Scanning Radiometer (SR) 0.5-0.7 or 0.5-0.9 10 .5-12.5 3.5 8 Repeat coverage every 12 hr, swath width 3000 km Very High Resolution Radiometer (VHRR) 0 .6-0.7 10 .5-12.5 1 1 TIROS-N Advanced VHRR (AVHRR) 0 .55-0 .9 0 .72-1.1 3.55-3.93 10 .5-11.5 1 - 4 Repeat coverage every 12 hr, swath width 2 800 km, launched Oct. 31/78. 13. weather such as h u r r i c a n e s and t o r n a d o e s . There i s , however, a drawback: away from the e q u a t o r the images become i n c r e a s i n g -l y 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 too d i s t o r t e d t o be u s e f u l beyond about 60° l a t i t u d e . F i v e g e o s t a -t i o n a r y s a t e l l i t e s f o r m i n g the Wo r l d Wide Geosynchronous S a t e l -l i t e System are 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-i m a t e l y 36,000 km, as shown i n F i g u r e 2.1. B r i t i s h Columbia r e c e i v e s s a t e l l i t e images from GOES-West w h i c h i s l o c a t e d o v e r the e q u a t o r and 145° l o n g i t u d e . 2.2 The GOES System The f r e q u e n t , 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 a t t r a c t i v e f o r o b s e r v i n g the changes i n weather 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 w i t h r a i n f a l l as r e v e a l e d by the growth and decay o f c l o u d systems. (Images from t h e GOES-West s a t e l l i t e were used i n t h i s s t u d y f o r t h i s r e a s o n , and, because t h e s e s a t e l l i t e images were r e a d i l y a v a i l a b l e l o c a l l y ) . The f o l l o w i n g b r i e f l y d e s c r i b e s the GOES system w h i c h i s g e n e r a l l y s i m i l a r t o o t h e r g e o s t a t i o n a r y s a t e l l i t e s the 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 (GMS) o f Japan and the M e t e o r o l o g i c a l S a t e l l i t e (METEOSAT) o f the European Space Agency. The GOES s a t e l l i t e s are an outgrowth o f e a r l i e r 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) r e s e a r c h and development. The p r i m a r y aims o f the SMS/GOES program a r e : Japan USA U S A Europe U S A QMS G O E S - G O E S - METEOSAT G O E S -West East Indian Ocean FIGURE 2.1 F i v 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 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., 19 77 and NOAA, 19 7 9 ) . 1 5 . a - t o i n c r e a s e the knowledge and u n d e r s t a n d i n g o f at 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 motions and l i f e c y c l e s o f storms and o t h e r phenomena, b - t o a i d i n the 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 network 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 o b s e r -v a t i o n s and e a r l y warnings i n r e a l t i m e , 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 f en-v i r o n m e n t a l parameter measurements. These aims are a c h i e v e d by c o m b i n a t i o n o f SMS/GOES s a t e l l i t e s , ground 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 GOES 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 p i n - s c a n r a d i o -meter (VISSR) senses c o n d i t i o n s on the E a r t h u s i n g two wavebands -the v i s i b l e (0.55 t o 0.7y) band which 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 hour d u r i n g the d a y l i g h t h o u r s , and the t h e r m a l i n f r a r e d (10.5 t o 12.6y) band 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 hour t w e n t y - f o u r hours a day. Under s p e c i a l stormy c o n d i t i o n s the 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 the a f f e c t e d a r e a e v e r y f i v e m i n u t e s . T h i s i s c o n t r o l l e d by the owner o f the s a t e l l i t e . The VISSR a l l o w s the mapping o f c l o u d f e a t u r e s b o t h day and n i g h t u s i n g e i g h t v i s i b l e c h a n n els t o g i v e measurements o f albedo from 0.5 t o 100 p e r c e n t , and two t h e r m a l i n f r a r e d c h a n n e ls (one o f whi c h i s redundant) which g i v e r a d i a n c e temperature measurements between -9 3 and 42°C. The European Space Agency's METEOSAT has an a d d i t i o n a l s e n s o r f o r w a t e r vapor ( i n the 6p band) ( D a v i s , 1980), and s l i g h t l y d i f f e r e n t 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 Japan's GMS, ( K o d a i r a and Murayama, 1976). F o r the s e s a t e l l i t e s t he v i s i b l e r e s o l u t i o n i s 1.25 km and the i n f r a r e d r e s o l u t i o n i s 5 km. Bo t h METEOSAT and GMS have redundant v i s i b l e s e n s o r s as w e l l . 2.3 GOES Image F o r m a t i o n and Enhancement Schemes The f o r m a t i o n o f the GOES s a t e l l i t e image i s a r e s u l t o f a c o m b i n a t i o n o f the s a t e l l i t e ' s s p i n m o t i o n (100 rpm) on 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 c o r -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 pe r f o r m e d f o r each s a t e l l i t e r o t a t i o n , w h i l e the s c a n n e r p o s i t i o n s each l i n e i n a n o r t h - s o u t h manner. (METEOSAT scans from e a s t t o west and s t e p s i n a s o u t h - n o r t h manner). Once t h e f u l l E a r t h d i s c has been sensed (a p r o c e d u r e which t a k e s a p p r o x i m a t e l y 18 minutes f o r GOES and 25 minutes f o r GMS and METEOSAT), t h e scanner o p t i c s r e t r a c e t o t h e o r i g i n a l s t a r t i n g p o s i t i o n ( i n a p p r o x i m a t e l y 2 m i n u t e s ) . See F i g u r e 2.2. F U L L E A R T H DISC I One infrared! sensor l ine FIGURE 2.2 Assembly of a VISSR Image. Each scan l i n e i s composed of 8 v i s i b l e sensor lines and 1 i n f r a r e d sensor l i n e . One scan l i n e represents a west to each scan of the earth and each i s positioned sequentially i n a north-south manner (Adapted from McKowan, 19 77). 1.8. The s i g n a l from GOES-West i s s e n t i n i t i a l l y t o t h e Na-t i o n a l E n v i r o n m e n t a l S a t e l l i t e S e r v i c e (NESS) C e n t r a l Data A c q u i s i t i o n (CDA) f a c i l i t y 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 p r o c e s s i n g o c c u r s i n c l u d i n g " s t r e t c h i n g " t h e s i g n a l . ( S i n c e the i n f o r m a t i o n on the E a r t h t a k e s up l e s s than 5 p e r c e n t o f an e n t i r e VISSR s c a n l i n e , t h a t p o r t i o n o f the s i g n a l must be expanded b e f o r e - b e i n g assembled i n t o a r e c o g -n i z a b l e image). The s i g n a l i s th e n t r a n s m i t t e d back t o the s a t e l l i t e f o r b r o a d c a s t t o the NESS C e n t r a l P r o c e s s i n g F a c i l i t y i n Washington, D.C. From he r e the i n f o r m a t i o n i s s e n t by h i g h q u a l i t y t e l e p h o n e l i n e t o s i x major 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, Mi a m i , H o n o l u l u , and Anchorage) f o r f u r t h e r d i s t r i b u t i o n t o o t h e r u s e r s under the GOES-Tap program. (For d e t a i l s on GOES-Tap see Appendix I I I o f C o r b e l l et. at., 1977). F i g u r e 2.3 shows t h i s d i s t r i b u t i o n s c h e -m a t i c a l l y . The volume o f d a t a c o l l e c t e d by the 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 c a p a b i l i t i e s f o r p r o c e s s i n g , s t o r i n g and t r a n s m i t t i n g d a t a . T h i s 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 E a r t h d i s c image f o r a n a l y s i s and subse-quent 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 subareas are known as s e c t o r s and a few o f the t y p i c a l s e c t o r s r e c e i v e d i n Vancouver, B.C., a r e shown i n F i g u r e 2.4. Of c o u r s e , w i t h a r e c e i v i n g s t a t i o n l o c a t e d i n t h e Vancouver areas (as i s pr o p o s e d 0 E S U s e r s ) ) I ) V / ) l t ) ) ) I V / / ) ) / ) / ) / / ) ) / t I'/ I f II 1 ) i > > ft t > > > > } NESS CDA N E S S NESS C E N T R A L FACILITY Wallops Is.,VA. Washington,D.C. Washington, D.C. FIGURE 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 20. Sectors Received at the P a c i f i c Weather Centre (after Corbell et al., 1977) V i s i b l e and Infrared Sectors: Sector Centre Point Resolution ( l a t ./Long.) (km) SA-1 36°N/118°W 1 SA-2 45°N/116°W 1 SB-6 42 N/124°W 2 UC-2 28°N/135°W 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 chosen, i n c l u d i n g the f u l l E a r t h d i s c f o r a g l o b a l view o f the w e a t h e r , o r " c l o s e - u p s " o f t r o u b l e a r e a s w i t h i n B r i t i s h Columbia. Popham and R i c h (1975) d e s c r i b e a GOES VISSR ground s t a t i o n . Seymour et al. (19 77) and MDA (19 77) g i v e d e t a i l s o f a l o w - c o s t r e c e i v i n g , a n a l y z i n g and d i s t r i b u t i o n system f o r v a r i o u s e n v i -r o nmental s a t e l l i t e s i n c l u d i n g GOES and METEOSAT. The o p e r a t i o n - a l p r e s e n t a t i o n o f t h e s e s a t e l l i t e d a t a i s s t i l l i n t h e form o f hardcopy photographs o f t h e h a l f - h o u r l y v i s i b l e and i n f r a r e d views o f d e v e l o p i n g weather systems. Both the v i s i b l e and i n f r a r e d s a t e l l i t e images have been used t o i d e n t i f y p r e c i p i t a t i n g c l o u d s , a l t h o u g h t h e emphasis i n t h i s s t u d y l i e s w i t h the i n f r a r e d images. F i g u r e 2.5 shows an example o f a v i s i b l e image form GOES-West, w h i l e F i g u r e 2.6 and 2.7 r e s p e c t i v e l y , show t y p i c a l unenhanced and enhanced i n f r a r e d images. The enhancement scheme, t h a t i s , the r e l a t i o n s h i p be-tween te m p e r a t u r e and the photo grey s c a l e used t o c o n t o u r F i g u r e 2.7, 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. When tempera-t u r e g r a d i e n t s d e t e c t e d by the VISSR are s m a l l i t i s d i f f i c u l t t o r e c o g n i z e s i g n i f i c a n t c l o u d and s u r f a c e f e a t u r e s ( f o r example, f o g , s t r a t u s and t h u n d e r s t o r m c l o u d tops) i n the i n f r a r e d image. E n h a n c i n g , t h e n , i n c r e a s e s the c o n t r a s t between those f e a t u r e s and t h e i r background. An 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 making th e enhanced image t o o c o n f u s i n g . There are FIGURE 2.5 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 ) from GOES-West. 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 ) f r o m GOES-West. 24. FIGURE 2 . 7 A T y p i c a l S a t e l l i t e Enhanced I n f r a r e d Image (SB6 S e c t o r , "EC" Enhancement Scheme) from GOES-West. 2.5. DIGITAL C O U N T 0 51 102 153 204 255 White r- r 1 1 ]—i 1 5 1 T E M P E R A T U R E ° C FIGURE 2.8 The "EC" Enhancement Scheme wh i c h R e l a t e s Temperature t o S p e c i f i c g r e y shades ( a f t e r H a e r i n g , 1978) Segment Number Temperature Range ( C) Reason f o r Segment Enhancement 1 +56.3 t o +37.3 No s i g n i f i c a n t d a t a 2 +36.3 t o +20.8 Land and Water 3 +20.3 t o -13.2 Water and Low Clouds 4 +13.7 t o -15.7 Benchmark between Low and Me-dium L e v e l Clouds 5 -16.2 t o -50 .2 Medium and Hi 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 ) 6 -51.2 t o -60.2 C o n v e c t i v e C l o u d Tops 7 -61.2 t o -70.2 C o n v e c t i v e C l o u d Tops 8 -71.2 t o -110.2 C o l d e s t C l o u d Tops and Space a l a r g e number o f enhancement schemes a v a i l a b l e , a l t h o u g h o n l y a few o f them a r e used o p e r a t i o n a l l y . These a r e de-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. (1977). 2.4 Ot h e r Sources o f S a t e l l i t e I n f o r m a t i o n A number o f m e t e o r o l o g i c a l s a t e l l i t e systems have e v o l v e d each w i t h a d i f f e r e n t c o m b i n a t i o n o f s e n s o r and o r b i t . I n t h e U n i t e d S t a t e s t h e r e are the NOAA, NIMBUS, TIROS, SMS/GOES, DMSP, and 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 . P a r a l l e l systems are b e i n g d e v e l o p e d i n o t h e r c o u n t r i e s , n o t a b l y the USSR, the European n a t i o n s t h rough ESA, and Japan. I n the 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 h e r e , microwave s a t e l -l i t e s have been o m i t t e d . A l t h o u g h they a re p r o m i s i n g i n the d e t e r m i n a t i o n o f p r e c i p i t a t i o n a r e a s , they a r e o f l i t t l e use i n r e a l - t i m e a n a l y s e s a t p r e s e n t because none a r e e x p e c t e d t o e x i s t i n g e o s t a t i o n a r y o r b i t s u n t i l p o s s i b l y 19 85, ( L o v e j o y , 1978) . A d d i t i o n a l i n f o r m a t i o n on the GOES system i s c o n t a i n e d i n McKowan (1977), C o r b e l l et a l . , (1977) and Fordyce et al., (1974). L i e n e s c h et a l . , (1975) d i s c u s s the a c c u r a c y and c a l i -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 . V e s e l y and Botzo n g (19 74) and S p a n g l e r (19 74) 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 S a t e l l i -t e Program (DMSP). F o r t u n a and Hambrick (1974) d i s c u s s the NOAA p o l a r - o r b i t i n g system, w h i l e Hussey (19 77) d e s c r i b e s the TIROS-N p o l a r - o r b i t i n g system. A p p l i c a t i o n s o f weather s a t e l l i t e o b s e r -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 McG i n n i s et al. , (1980), and t o weather s e n s i t i v e army o p e r a t i o n s by M i e r s (1976). Numerous a u t h o r s ( i n c l u d i n g G r i f f i t h et al., 1977; L o v e j o y and A u s t i n ; 1979; L e t h b r i d g e , 1967; Gurka 1976; Gantry et al. , 19 76 ; Purdom, 19 76 ; C l a r k et al ., 19 80; and Maddox, 19 80); have 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 geo-s t a t i o n a r y s a t e l l i t e s (GOES) f o r o b s e r v i n g v a r i o u s m e t e o r o l o g -i c a l parameters o f use 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 such as wind speeds, c l o u d c o v e r , and a l b e d o . 28. CHAPTER I I I A REVIEW OF SATELLITE IMAGE PRECIPITATION ESTIMATION Since the f i r s t p i c t u r e s r e t u r n e d by TIROS-1 i n 1960 s c i e n t i s t s have been i n t r i g u e d by the wealth of data c o n t a i n e d i n a s i n g l e image. The images showed very c l e a r l y the o r g a n i -z a t i o n and s t r u c t u r e o f c l o u d systems ranging from the l a r g e c y c l o n i c systems of a thousand k i l o m e t e r s across to i n d i v i d u a l clouds of 1 k i l o m e t e r o r so i n diameter. Other f e a t u r e s c o u l d a l s o be d i s c e r n e d such as the c l o u d f e a t u r e s a s s o c i a t e d w i t h , h u r r i c a n e s , thunderstorms, s q u a l l l i n e s , j e t streams, mountain waves, and regions of s t r o n g wind shear. A n a l y s i s of a time sequence o f these images i n d i c a t e s the development, decay and/ or movement of weather through a r e g i o n . The power o f s a t e l l i t e images l i e s i n the v a s t s p a t i a l i n f o r m a t i o n o b t a i n e d on a 24-hour a day b a s i s f o r remote, o c e a n i c or o t h e r areas where o b s e r v i n g networks may be too sparse to r e v e a l these f e a t u r e s by conven-t i o n a l means. U n t i l r e c e n t l y , much o f the i n f o r m a t i o n c o n t a i n e d i n s a t e l l i t e images has been of a q u a l i t a t i v e nature and d i f f i -c u l t to use d i r e c t l y . Anderson and V e l t i s c h c h e v (19 73) d i s c u s s and i l l u s t r a t e the p o t e n t i a l of s a t e l l i t e images i n weather anal-y s i s and f o r e c a s t i n g . In t h e i r work i s a wealth of s a t e l l i t e images, i n c l u d i n g some o f the very e a r l i e s t weather s a t e l l i t e photographs, which serve as a catalogue of v a r i o u s weather con-d i t i o n s and c l o u d types as seen from a s a t e l l i t e ' s vantage p o i n t i n space. I t i s an i d e a l r e f e r e n c e f o r a c q u i r i n g s k i l l i n c l o u d and weather i d e n t i f i c a t i o n u s i n g s a t e l l i t e images. 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 imagery has p a r a l l e l e d t h e e v o l u t i o n o f s a t e l l i t e s e n s o r s , c h i e f l y those w h i c h sense r a d i a t i o n i n two major bands ( v i s i b l e and t h e r m a l i n f r a r e d ) . E a r l y work i n e x t r a c t i n g quan-t i t a t i v e i n f o r m a t i o n from s a t e l l i t e imagery was based on f i n d i n g 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 b r i g h t -ness and such parameters as p r e c i p i t a t i o n . M a r t i n and S c h e r e r (19 73) p r o v i d e a b r i e f o v e r v i e w o f s a t e l l i t e e s t i m a t i o n t e c h n i -ques up to 1973. Some s t u d i e s , f o r example, B a r r e t t (1970), i n -v e s t i g a t e d the a r e a l s t a t i s t i c s o f c l o u d c o v e r and c l o u d type 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 and i n t e n s i t y on a monthly b a s i s , w h i l e o t h e r s 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 and/or tem-p e r a t u r e w i t h 24-hour r a i n f a l l ( G e r r i s h , 1970, and F o l l a n s b e e , 1973). F o l l a n s b e e (1973) and F o l l a n s b e e and O l i v e r (1975) a d a p t -ed 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 r a i n f a l l , c o n c e n t r a t i n g s o l e l y on r a i n - p r o d u c i n g c l o u d t y p e s (cumulonimbus, n i m b o s t r a t u s , and cumulus c o n g e s t u s ) . D a v i s and Serebreny (19 72) have used 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 p r e c i p i t a t i o n i n c l u d i n g 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 o n c e - d a i l y ESSA ( E n v i r o n m e n t a l Survey S a t e l l i t e - E n v i r o n m e n t a l S c i e n c e S e r v i c e s A d m i n i s t r a t i o n ) s a t e l l i t e images. A n o t h e r approach e v o l v e d w h i c h used c l o u d b r i g h t n e s s as a key v a r i a b l e i n e s t i m a t i n g c o n v e c t i v e p r e c i p i t a t i o n ( S i k d a r and Suomi, 1971; S i k d a r , 1972) . I n f a c t , M a r t i n and Suomi (1971, 19 72) t e s t e d b r i g h t n e s s enhancement o f A T S - I I I ( A p p l i c a t i o n s 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 a r e a s o f i n t e n s e c o n v e c t i o n . T h i s i s s i m i l a r t o an approach d e v e l o p e d by Woodley and 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 by Woodley et al., (1972) and 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 . I n o r d e r t o take advantage o f the 24-hour a v a i l a b i l i t y o f i n f r a r e d imagery, S c h e r e r and Hudlow (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 top areas i n t o prob-a b l e 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 r a i n f a l l amounts. 3.1 GOES R a i n f a l l E s t i m a t i o n Techniques These i n i t i a l s t u d i e s formed the background f o r the 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 : W o o d l e y / G r i f -f i t h ' s group a t the 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-o l o g y L a b o r a t o r y (NHEML) i n F l o r i d a , t he U n i v e r s i t y o f Wiscon-s i n (UW) group, and S c o f i e l d / O l i v e r ' s group i n Washington, D.C., 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 v i s i b l e and i n f r a r e d images from t h e GOES s a t e l l i t e s . Each group's approach i s d i s c u s s e d b r i e f l y i n the f o l l o w i n g s e c t i o n s . 3.1.1 The NHEML Technique The NHEML t e c h n i q u e i s based on the o b s e r v a t i o n t h a t areas o f a c t i v e deep c o n v e c t i o n and r a i n f a l l i n the t r o p i c s appear b r i g h t e r on v i s i b l e images and 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 a r e a s . A T S - I I I and GOES images were c a l i b r a t e d w i t h r a d a r d a t a from the so u t h o f F l o r i d a . The e m p i r i c a l r e l a t i o n NHEML d e v e l o p e d i s r v = I A e 3 ' 1 3 Where r v i s the volume r a i n r a t e (m / h ) , I i s the r a i n 3 2 r a t e p e r u n i t a r e a ((in /h)/km ) and i s a f u n c t i o n o f the r a d a r 2 echo a r e a growth t r e n d ) , and A g i s the r a d a r echo a r e a (km ) whic h i s d e f i n e d by a t h r e s h o l d r a i n r a t e o f 1 mm/h. '1' can be d e r i v e d f o r any g e o g r a p h i c a r e a p r o v i d e d a p p r o p r i a t e r a d a r d a t a a r e a v a i l a b l e (which l i m i t s i t s u s e f u l n e s s i n mountainous t e r -r a i n ) . The r a d a r echo a r e a , A e , i s de t e r m i n e d on a c l o u d by 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 a r e a A c and r a d a r echo a r e a A g . 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 storms i n F l o r i d a and Ve n e z u e l a 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 ., 1978). 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 t h a t t h e i r a c c u r a c y 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 the a r e a o f c l o u d c o v e r examined. They a n t i c i p a t e d i n c r e a s -e d a c c u r a c y w i t h d i g i t a l d a t a and, i n a pa p e r by Waters 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 d i g i t a l g e o s t a t i o n a r y d a t a t o as s e s s 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 h u r r i c a n e s . 3.1.2 The UW Technique L i k e t h e work o f t h e NHEML group, t h e UW t e c h n i q u e r e l a t e s 2 the 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 ) and r a d a r echo a r e a ( S t o u t et a l . , 19 77, 19 79) . I n a d d i t i o n , t he UW t e c h n i q u e e x p l i c i t l y i n c l u d e s the r a t e o f change o f the c l o u d a r e a dA 2 ( (m /s) ) i n the r e l a t i o n f o r the r a i n f a l l r a t e R: R = a o A + a i H 3 - 2 t h e c o n s t a n t s a Q (m/s) and a^ (m) a r e de t e r m i n e d by a l e a s t squares 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 r a i n r a t e ( d e t e r m i n e d a t v a r i o u s r e f l e c t i v i t y l e v e l s ) , and have s l i g h t l y d i f f e r e n t v a l u e s depending on whether v i s i b l e o r i n f r a -r e d images a re b e i n g 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 the NHEML t e c h n i q u e and as such was dev e l o p e d t o p r o v i d e e s t i m a t e s o f r a i n f a l l from l a r g e p r e c i p i t a t i n g cumulonimbus c e l l s o v e r the t r o p i c a l N o r t h A t l a n -t i c . The a u t h o r s s u g g e s t 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 s k i l l e d m e t e o r o l o g i s t s . They r e c o g n i z e the 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 A t l a n t i c , e s p e c i a l l y i f c o n v e c t i v e c e l l s a r e n o t the major c o n t r i b u t o r s t o the t o t a l r a i n f a l l and note t h a t t h e i r c o e f f i c i e n t s , a Q , a ^ would 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) and S c o f i e l d and O l i v e r (1977a) 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 g i v e s h a l f - h o u r l y 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 from GOES i n f r a r e d and h i g h r e s o l u -t i o n v i s i b l e images. I t i s a d e c i s i o n h i e r a r c h i c a l approach based on the 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 systems 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 (-80°C) t r o p o p a u s e s . The t e c h n i q u e was e s s e n t i a l l y d e v e l o p e d f o r the s o u t h e r n c o n t i n e n t a l U n i t e d S t a t e s and papers 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 cases ( S c o f i e l d , 1976 a,b; 1978a,b; S c o f i e l d and O l i v e r , 19 75, 1977b," S c o f i e l d and W e i s s , 1976 ; S c o f i e l d et a l . , 1980 ; and S c o f i e l d and O l i v e r , 1980) show the u s e f u l n e s s o f the p r o c e d u r e . The S c o f i e l d / O l i v e r t e c h n i q u e has been m o d i f i e d s l i g h t l y and used t o 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 f o r a number o f s t o r m s i t u a t i o n s o v e r V e n e z u e l a and Colombia (Ingraham et al., 1977). The S c o f i e l d / O l i v e r t e c h n i q u e s t a r t s w i t h the s i m p l e em-p i r i c a l 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 o f the (cumulonimbus) c l o u d , the h e a v i e r t h e r a i n f a l l , and s u b s e q u e n t l y adds f a c t o r s which improve t h i s r e l a t i o n s h i p . The two most i m p o r t a n t f a c -t o r s are t h e r a t e o f growth o f the a n v i l and the p o s i t i o n o f t h e cumulonimbus under the a n v i l . As w e l l , a number o f o t h e r 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 as the p r e s -ence o r absence o f o v e r s h o o t i n g t o p s , the i m p o r t a n c e o f merging c e l l s , and merging c o n v e c t i v e c e l l l i n e s , i n o r d e r t o improve the e s t i m a t e s o f r a i n f a l l . These f a c t o r s are a r r a n g e d i n a de-c i s i o n t r e e o r f l o w c h a r t which =allows the u s e r t o determine the a p p r o p r i a t e r a i n f a l l amount f o r a p a r t i c u l a r p o i n t . There are t h r e e major s t e p s i n the c o m p u t a t i o n p r o c e s s : 34. A - I d e n t i f i c a t i o n o f t h e c o n v e c t i v e system and the d e t e r m i n a t i o n o f the a c t i v e r a i n p r o d u c i n g p o r t i o n o f the system, B - The i n i t i a l e s t i m a t i o n o f p r e c i p i t a t i o n u s i n g the c l o u d top t e m p e r a t u r e s as g i v e n by the enhanced i n f r a -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 r e l a t i o n s , 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 e s t i m a t e s by the use o f a m p l i f i c a t i o n f a c t o r s based on the dynam-i c b e h a v i o u r o f the c o n v e c t i v e c l o u d system ( f o r example, o v e r s h o o t i n g t o p s , merging c e l l s , o r m e r g i n g c o n v e c t i v e c e l l l i n e s ) . 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 by f o l l o w i n g a s e t o f d i a g n o s t i c i n d i c e s i n c l u d i n g : 1 - I d e n t i f i c a t i o n o f c o n v e c t i o n : a) shape o f the c l o u d ( c i r c u l a r , o v a l , c a r r o t -shaped) from the i n f r a r e d and v i s i b l e images b) depth o f c o n v e c t i o n - v e r t i c a l development o f the c l o u d , from the enhanced i n f r a r e d 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 c o n v e c t i v e system. a) a r e a o f s t e e p e s t temperature g r a d i e n t , from enhanced i n f r a r e d images; b) t e x t u r e and b r i g h t n e s s o f the c l o u d t o p , from the v i s i b l e images; c) 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 , from the enhanced i n f r a r e d images; d) 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 o f the c l o u d a n v i l , from t h e v i s i b l e 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 the S c o f i e l d / O l i v e r f l o w c h a r t , (Ingraham et a l . , 1977). There 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 appa-r e n t a f t e r u s i n g the S c o f i e l d / O l i v e r t e c h n i q u e . I r r e g u l a r l y shaped c l o u d c e l l s cannot be a d e q u a t e l y i n c l u d e d . Clouds w i t h l o c a l 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 a l s o a p r o b l e m . ( I t i s t h o u g h t t h a t t h e s e " h o l e s " w i t h i n the c l o u d b o u n d a r i e s i n d i c a t e the c o l l a p s e o f s h o r t - l i v e d o v e r -s h o o t i n g t o p s ) . Some o f the f a c t o r s w h i c h produce h i g h r a i n -f a l l r a t e s depend upon ac c e s s t o the h i g h (1 km) r e s o l u t i o n v i s -i b l e images w h i c h are 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 * l e v e l ( e x c e p t i f he has a c c e s s t o h i s own r e c e i v i n g s t a t i o n ) . The i d e n t i f i c a t i o n o f the a m p l i f i c a t i o n parameters from the s a t e l l i t e images i s v e r y much dependent on the o b s e r v e r and h i s FIGURE 3.1 Flowchart and Table for the Estimation of Point R a i n f a l l from the S c o f i e l d / O l i v e r Technique (after Ingraham et al., 1977) GOES Images Using A - RECOGNITION OF ACTIVE PORTION OF DEEP CONVECTION NO I YES \ CLOUD GROWTH: 0.25 I mm ? TABLE ON RIGHT I UNCORRECTED ESTIMATE C - CORRECTIONS FINAL ESTIMATE LEGEND: REFER TO SECTION 3.1.3 GROWTH OF CLOUD IN A HALF HOUR IS SUCH THAT THE COLDEST CONTOUR DIAMETER „ expands >2/3 l a t . is >l/3° l a t . l a t . expands 1.1/3 l a t . remains the same contracts expands12/3 1 but CORRESTIONS FOR LOCAL OCCUR-RENCE OF 1 overshooting top 2 merging thunderstorms 3 convective cloud l i n e mergers FOR EACH OF THESE ADD 12.7 (mm) TO UNCORRECTED ESTIMATE TO GET FINAL ESTIMATE TABLE: PRECIPITATION ESTIMATES (mm) CONTOUR COLOR 1975 1 2 3 = DARK GREY 12.7 3.1 3.8 2.5 LIGHT GREY 15.110.2 5.1 3.8 BLACK 25.4 15.2 7 .6 5.1 WHITE 38.1 19 .1 ID. 17.6 1976 0.3 0.8 1.3 2.0 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 WHITE 38.1 22.9 12.7 10.12.5 s k i l l a t s a t e l l i t e image i n t e r p r e t a t i o n . As w e l l , t h i s t e c h n i -que l i k e t h e o t h e r s d i s c u s s e d , does not e x p l i c i t l y a l l o w f o r the movement of the s t o r m c e l l o v e r a r e g i o n . B u t , even 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 a t t h e r e would be g r e a t d i f f i c u l t y i n t r a n s f e r r i n g the use o f t h i s t e c h n i q u e 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 r a i n t - p r o d u c -i n g - c l o u d regimes 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 c o n v e c t i v e c l o u d systems i n t r o p i c a l a i r masses. N e v e r t h e l e s s , 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 does i n d i c a t e which c l o u d top p a r a -meters are c r u c i a l t o the 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 be-speaks the s k i l l o f the s e i n v e s t i g a t o r s i n o b s e r v i n g cumulonimbi and d e t e r m i n i n g a w o r k a b l e e m p i r i c a l r e l a t i o n s h i p . 3.2 Summary A l l o f t h e s e e a r l y p r e c i p i t a t i o n e s t i m a t i o n t e c h n i q u e s f o c u s on d e t e r m i n i n g t h e r a i n f a l l from deep t r o p i c a l c o n v e c t i v e  systems. T h i s i s u n d e r s t a n d a b l e because cumulonimbi are easy t o i d e n t i f y and th e y are r e a s o n a b l y s e l f - c o n t a i n e d . Cheng and Rodenhius (19 77) compare r a d a r r a i n r a t e s and s a t e l l i t e convec-t i v e r a i n f a l l e s t i m a t e s based on v i s i b l e c l o u d b r i g h t n e s s o r 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 such as tho s e p r e s e n t e d h e r e . They note t h a t a l t h o u g h r a i n f a l l r a t e s and s a t e l l i t e image b r i g h t n e s s o r c o l d n e s s a r e r e l a t e d , q u a n t i t a t i v e d i f f e r e n - ces i n r a i n f a l l cannot be e x p l a i n e d as b e i n g due t o e i t h e r b r i g h t o r c o l d c l o u d s . However, i n s u g g e s t i n g t h a t s p a t i a l and t e m p o r a l 38. a v e r a g i n g 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 -c i e n c y common t o t h e s e t e c h n i q u e s : t h e need f o r a more p h y s i -c a l b a s i s r e l a t i n g the s a t e l l i t e image c l o u d c h a r a c t e r i s t i c s ( b r i g h t n e s s , c o l d n e s s , r a t e o f growth) t o the r a i n f a l l produced. CHAPTER IV THE MODEL USED TO DESCRIBE PRECIPITATING CLOUDS P r e v i o u s 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, and NHEML) i d e n t i f i e d i n t h e i r t e c h n i q u e s the c r u c i a l c l o u d top c h a r a c t e r -i s t i c s t o be 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 and they d e v e l o p e d 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 im-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 what the 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 the dynamics o f the 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 on which t h e i r t e c h n i q u e s c o u l d be m o d i f i e d 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 C olumbia. 4.1 P r e c i p i t a t i o n i n B r i t i s h Columbia There a re t h r e e main types o f a i r mass which b r i n g r a i n t o B r i t i s h Columbia. Warm, humid and r e l a t i v e l y s t a b l e M a r i t i m e T r o p i c a l (mT) . a i r w i t h i t s o r i g i n s i n t h e t r o p i c s t o the southwest o c c a s i o n a l l y reaches B r i t i s h Columbia i n w i n t e r i n the warm s e c t o r ( o r , more o f t e n i n the upper l e v e l s o f an o c c l u d e d warm s e c t o r ) o f f r o n t a l waves and g i v e s r i s e t o major r a i n f a l l s . On the o t h e r hand, showery p r e c i p i t a t i o n i s o f t e n a s s o c i a t e d w i t h M a r i t i m e A r c t i c (mA) a i r as i t i s warmed and m o i s t e n e d d u r i n g i t s r e l a t i v e l y s h o r t t r i p o v e r the N o r t h P a c i f i c from the A r c t i c landmasses o f N o r t h A m e r i c a and A s i a t o B r i t i s h Co-l u m b i a . M a r i t i m e P o l a r (mP) a i r has the same o r i g i n s as mA a i r b u t w i t h a l o n g e r t r a j e c t o r y o v e r the ocean a f t e r w hich i t reaches t h e c o a s t from a more w e s t e r l y d i r e c t i o n . The c h a r a c -40. t e r i s t i c s 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 are i n t e r m e -d i a t e between mT and mA a i r . The mountain ranges o f B r i t i s h Columbia are a f o r m i d a b l e b a r r i e r t o the e a s t w a r d movement o f a i r from the P a c i f i c . The tendency o f t h e a i r t o produce r a i n i s i n c r e a s e d through l i f t -i n g and the windward s l o p e s r e c e i v e among the w o r l d ' s l a r g e s t a n n u a l amounts o f p r e c i p i t a t i o n . The c l i m a t e a l o n g the c o a s t i s c h a r a c t e r i z e d by m i l d , humid w i n t e r s and warm b u t not h o t summers. The i n t e r i o r o f B r i t i s h C o lumbia, w h i c h l i e s e f f e c t i v e -l y i n the r a i n shadow o f the c o a s t a l m o u n t ains, i s n o t e d f o r h o t and f a i r l y dry summers p u n c t u a t e d by the o c c a s i o n a l t h u n d e r -s t o r m , and f o r c o l d w i n t e r s w i t h snow. Weather systems a f f e c t i n g B r i t i s h C o l u m b i a , i n g e n e r a l , o r i g i n a t e t o t h e west as d e p r e s s i o n s o v e r the ocean and a r e u s u a l l y i n a mature s t a t e o f development and w e l l o c c l u d e d be-f o r e they r e a c h t h e c o a s t . P e r i o d s o f showery weather w i t h i n the mP 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 a l o n g the f r o n t s and o c c l u s i o n s . T h i s p r e v a i l s t h r o u g h o u t the y e a r , a l t h o u g h d u r i n g t h e summer months (June through August) the storms are fewer, l e s s i n t e n s e , and s m a l l e r i n s i z e . The a c t u a l c e n t r e s o f t h e s e d i s t u r b a n c e s g e n e r a l l y do not c r o s s t h e c o a s t b u t r a t h e r f i l l and s t a g n a t e o v e r t h e A l e u t i a n s o r A l a s k a w i t h o n l y t h e 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 c o a s t f u r t h e r s o u t h . The i n t e r i o r p l a t e a u r e g i o n r e c e i v e s a p p r e c i a b l e s n o w f a l l i n w i n t e r from t h e s e e a s t w a r d moving f r o n t s , w h i l e i n summer much o f the r a i n f a l l o r i g i n a t e s from t h u n d e r s t o r m s . The f r o n t s do n o t pen-e t r a t e - f a r i n t o s o u t h e r n B r i t i s h Columbia l e a v i n g t h i s r e g i o n m a i n l y c l e a r and sunny. The a n n u a l p a t t e r n o f p r e c i p i t a t i o n i n B r i t i s h 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 N o r t h 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 w h i c h m i g r a t e s s e a s o n a l l y . D u r i n g the 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 and de-f l e c t s s t o r m t r a c k s n o r t h w a r d s , w h i l e d u r i n g the w i n t e r i t s h i f t s 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 b r i n g i n g more storms i n t o the p r o v i n c e . I n summary, p r e c i p i t a t i o n i n B r i t i s h Columbia f a l l s a l -most e x c l u s i v e l y from a i r o f P a c i f i c o r i g i n and a n n u a l p r e c i p i -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 the i n t e r i o r and deep v a l l e y f l o o r s i n c r e a s i n g a g a i n a l o n g the windward s l o p e s o f the Rocky M o u n t a i n s . R a i n and snow f a l l c h i e f l y i n a s s o c i a t i o n w i t h o c c l u s i o n s and 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 con-t r i b u t i o n s i n the i n t e r i o r o f t h e p r o v i n c e . The d i s t r i b u t i o n o f 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 t o the l o c a l e f f e c t s o f r e l i e f . (Kendrew and K e r r , 19 55; Hare, 196 3; H e t h e r i n g t o n , 19 76) . 4.2 The 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 r a i n f a l l from s a t e l l i t e images was d e v e l o p e d by f i r s t c o n s i d e r i n g t h e a t -m o s p h e r i c c o n d i t i o n s r e q u i r e d f o r p r e c i p i t a t i o n , and than examin-ing'' the 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 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 d e r i v e d t o t a k e advantage o f the i n f o r m a t i o n about the motions and d e v e l -opment o f c l o u d systems p r o v i d e d by s a t e l l i t e images. 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 Mason (19 71, 19 75) i n h i s work 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 n e c e s s a r y f o r the f o r m a t i o n o f r a i n , w hich a r e : 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 a i r w h i c h f l o w s i n t o B r i t i s h C o l u m b i a ) , a mechanism f o r l i f t i n g (as p r o v i d e d by mountains o r a l o n g f r o n t s ) and hence c o o l i n g the a i r so t h a t c o n d e n s a t i o n can o c c u r , and a s o u r c e o f n u c l e i on which the moisture i n t h e a i r can condense t o form c l o u d d r o p l e t s . I f the d r o p l e t s have enough time t o r e a c h a s i z e where t h e i r t e r -m i n a l v e l o c i t i e s exceed the l i f t i n g o r u p d r a f t v e l o c i t i e s i n the c l o u d , t h e n t h e y w i l l f a l l as r a i n and w i l l r e a c h t h e ground, p r o v i d e d they are n o t e n t i r e l y e v a p o r a t e d d u r i n g t h e i r 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 l i f e t i m e o f a p r e c i p i t a t i n g c l o u d system i s c o n t r o l l e d l a r g e l y by the v e r t i -c a l a i r m o t i o n s , r a i n f a l l can be d i s t i n g u i s h e d as b e i n g one o f two t y p e s depending on w h i c h l i f t i n g mechanism i s dominant (Rogers, 19 7 6 ) . Widespread, c o n t i n u o u s r a i n f a l l , o f the type u s u a l l y found on the c o a s t o f B r i t i s h C o lumbia, i s a s s o c i a t e d w i t h l a r g e s c a l e a s c e n t produced by f r o n t s , topography, o r l a r g e s c a l e low l e v e l h o r i z o n t a l convergence. 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 t h e t y p e 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 d u r i n g the summer months, i s a s s o c i a t e d w i t h c u m u l u s - s c a l e c o n v e c t i o n i n u n s t a b l e a i r . R e g a r d l e s s o f the p a r t i c u l a r l i f t i n g mechanisms c a u s i n g v e r t i c a l m o t i o n , t h e a i r cannot c o n t i n u e t o r i s e i n d e f i n i t e l y . I n the case o f major s t o r m s , the tropopause a c t s as a l i m i t t o the upward movement o f the a i r and a t t h i s l e v e l t h e a i r must s p r e a d o u t h o r i z o n t a l l y . - The r i s i n g a i r i s r e p l a c e d by a i r c o n v e r g i n g a t lower l e v e l s . By c o n t i n u i t y the r a t e o f a i r mass convergence a t lower l e v e l s must e q u a l the r a t e o f r i s e w h ich i n t u r n must e q u a l the r a t e o f d i v e r g e n c e ( o r s p r e a d i n g ) a t upper l e v e l s ( f o r example, t h r o u g h t h e top s o f c l o u d s ) . The moti o n 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 has been g e n e r a l l y n o t e d t h a t s e v e r e weather phenomena o f t e n o c c u r w i t h areas o f upper l e v e l d i v e r g e n c e (and a s s o c i a t e d lower l e v e l c o n v e r g e n c e ) , (Beebe and B a t e s , 1955; House, 1958; McN u l t y , 1977; and S c h a e f e r , 1977). D u r i n g the e a r l y 1950's s e v e r a l i n v e s t i g a t o r s (Cressman, 1954; Byers and Braham, 1948) t r i e d t o e s t i m a t e the r a i n f a l l r a t e o f thunderstorms by d e t e r m i n -i n g the v e r t i c a l v e l o c i t y 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 ( t h a t i s , the low l e v e l convergence o f a i r i n t o the base o f the c l o u d ) . Danard (1975, 1978) used a s i m i l a r approach t o y i e l d e s t i m a t e s o f t h e 24-hour r a i n f a l l amounts f o r s o u t h e r n B r i t i s h C olumbia. A l t h o u g h t h e y were a b l e t o make r e a s o n a b l e e s t i m a t e s At time t Aw At time t +At A w + d w FIGURE 4.1 A Column o f A i r Between the L e v e l s z and z+dz a t Times t and t+dt f o r 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 f e a s i b l e 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 i n measuring o r e s t i m a t i n g n e a r - s u r f a c e w i n d s . I t was a l s o known t h a t the v e r t i c a l v e l o c i -t y c o u l d be d e t e r m i n e d i f t h e h o r i z o n t a l winds a t the top o f the r i s i n g column c o u l d be measured. But t h a t was even more d i f f i -c u l t t o do i n p r a c t i c e . Now, however, h o r i z o n t a l d i v e r g e n c e o f the a i r mass can be e s t i m a t e d from s u c c e s s i v e images o f c l o u d tops as sensed 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 such as GOES. A d l e r and Fenn (19 79a, b) have s u c c e s s f u l l y used t h e approach t o e s t i m a t e the v e r t i c a l v e l o c i t i e s o f thunderstorms a l -though not t o e s t i m a t e the r a i n f a l l s from t h e s e s t o r m s . The t h e o r y f o r d e t e r m i n i n g r a i n f a l l from the h o r i z o n t a l d i v e r g e n c e o f c l o u d tops as seen from GOES images i s g i v e n below. 4.3 The Model E q u a t i o n s Three s e t s o f e q u a t i o n s a re needed t o s o l v e f o r the p r e -c i p i t a t i o n r a t e from a s t o r m : 1 - the a t m o s p h e r i c thermodynamics e q u a t i o n s 2 - t h e momentum e q u a t i o n s 3 - t h e c o n t i n u i t y e q u a t i o n . The 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 i s d i f f i c u l t g i v e n the complex n a t u r e o f a t m o s p h e r i c motions and the l i m i t e d d a t a a v a i l a b l e t o d e s c r i b e t h e s e m o t i o n s , u n l e s s v a r i o u s assump-t i o n s can be 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 A t m o s p h e r i c Thermodynamics E q u a t i o n s For an i d e a l gas the e q u a t i o n o f s t a t e pa = RT 4.1 and t h e f i r s t law o f thermodynamics o H d t = c vdT + pda 4.2 r e l a t e the 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 temperature T o f t h e a i r . H i s t h e r a t e a t which e x t e r n a l h e a t i s added pe r u n i t mass o f a i r , and c v i s the 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. The f i r s 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 the e x t e r n a l h e a t added t o the 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 and c o n d u c t i o n i s e q u a l t o the change i n i n t e r n a l energy o f t h e a i r mass (c vdT) p l u s the work done by t h e a i r mass on i t s s u r r o u n d i n g s ( p d a ) . I f no e x t e r n a l h e a t i s added, H = 0, then t h e motion o f the a i r mass i s s a i d t o 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 the system motions a r e c o n s i d e r e d t o be a p p r o x i m a t e l y a d i a b a t i c . 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, a l o n g w i t h c^ = c v + R, where Cp i s the s p e c i f i c h e a t a t con-s t a n t p r e s s u r e , can be used t o r e w r i t e the f i r s t law o f thermo-dynamics as o H d t = c dT - adp 4.3 The change i n temperature w i t h p r e s s u r e can then be g i v e n as _ H d t + J L = d T c p dp c p dp T h i s r e s u l t ' w i l l be used l a t e r t o r e l a t e t h e change i n temper-a t u r e t o the change i n a l t i t u d e . 4.3.2 The Momentum E q u a t i o n s The changes i n t h e v e l o c i t y f i e l d w i t h time a re g i v e n by the 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 H o l t o n ' s (19 72, p2 8) n o t a t i o n du = uvtanj, . uw _ 1 |£ + 2 Q v s i n ^ _ 2 n w c o S ( ( ) + F x 4 . 5 d t a a p 3 x 2 dv -u tanc}) vw 1 3p „ c -rr - - — - — - 2fiusin<b+Fy, 4.6 dt a a p ay T 1 2 2 d w U + V 1 3 p , o« ^ , A n j r = - — r*- - g + 2nucoscp + Fz 4.7 at a p 3 z: _ where u, v, w are t h e e a s t w a r d , n o r t h w a r d and v e r t i c a l components o f the v e l o c i t y , a i s t h e r a d i u s o f the E a r t h , cj> i s the l a t i t u d e , p i s the d e n s i t y , p i s the p r e s s u r e , n i s the a n g u l a r v e l o c i t y o f the E a r t h , and Fx, Fy and Fz are the e a s t w a r d (x) , n o r t h 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 . H o l t o n (1972, c h a p t e r 2, s e c t i o n 4) uses s c a l e a n a l y s i s t o reduce the above e q u a t i o n s t o tho 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 -4 -2 of magnitude l e s s than 10 m/s / 48. du d t * p 3X dv d t - 2nusin<() - - | E p 3y 1 3 P p 9 z ^ 4.8 4.9 4 .10 E q u a t i o n 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 are 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 t h a t the v e r t i c a l v e l o c i t y cannot be d e t e r m i n e d d i r e c t l y from t h e v e r t i c a l momentum e q u a t i o n . S i n c e the v e r t i c a l m o t i o n i s o f p r i m a r y i n t e r e s t i n the e s t i m a -t i o n o f r a i n f a l l , i t must be d e t e r m i n e d i n d i r e c t l y from t h e con-t i n u i t y e q u a t i o n . 4/i 3. 3 The C o n t i n u i t y E q u a t i o n The c o n t i n u i t y e q u a t i o n 1 dP ± HT. + v -V = 0 4.11 p d t 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 the motion 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 V. 4.4 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 R a i n f a l l D u r i n g t h e e x p l o r a t o r y development 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 t e c h n i q u e t h e e q u a t i o n o f c o n t i n u i t y i n a form s u g g e s t e d by M c i n t o s h and Thorn (19 73, c h a p t e r s 5 and 8 ) , and W a l l a c e and Hobbs (19 77, c h a p t e r 8) was c o n s i d e r e d t o d e s c r i b e t h e r a i n f a l l r a t e from c l o u d systems. A s i m i l a r e x p r e s s i o n was p r o p o s e d by V i e z e e et al., (1980) f o r e s t i m a t i n g the mois-t u r e budget o f c y c l o n e s u s i n g microwave d a t a . The 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 by 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 the a i r b e i n g l i f t e d , wc i s the w a t e r c o n t e n t o f t h e a i r , and E i s the e v a p o r a t i o n r a t e . Wc«w r e p r e s e n t s the r a t e a t which w a t e r e n t e r s the base o f the c l o u d and i s l i f t e d . T h i s minus l o s s e s due t o e v a p o r a t i o n y i e l d s the r a i n f a l l r a t e . E q u a t i o n 4.12 assumes t h a t a l l the w a t e r w h i c h e n t e r s a c l o u d e i t h e r f a l l s as r a i n o r i s e v a p o r a t e d . I n p r a c t i c e , not a l l o f the m o i s t u r e e n t e r i n g a c l o u d i s p r e c i p i t a t e d . Appre-c i a b l e amounts are r e t a i n e d w i t h i n the a i r mass as w a t e r v a p o r . A f a c t o r e can be i n t r o d u c e d i n t o e q u a t i o n 4.12 t o a l l o w f o r m o i s t u r e r e t e n t i o n . R e w r i t i n g e q u a t i o n 4.12 y i e l d s where e i s t h e f r a c t i o n o f wa t e r which f a l l s as r a i n . I n some l i t e r a t u r e t h i s f r a c t i o n i s t a k e n as a measure o f the e f f i c i e n -cy o f the s t o r m . I n e q u a t i o n 4.2, e r e p r e s e n t s an adjustment f a c t o r w h i c h can o n l y be de t e r m i n e d e m p i r i c a l l y on the b a s i s o f dP d t = e«wc«w-E 4.13 50. e x p e r i e n c e . The w a t e r r c o n t e n t wc (g/m ) o f the a i r mass can v a r y w i t h temperature and l o c a t i o n . On the b a s i s o f c u r r e n t s p a t i a l and t e m p o r a l o b s e r v a t i o n s (such as tho s e from TIROS-N) the 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 a p a r t i c u l a r l o c a t i o n , changes v e r y g r a d u a l l y and may be assumed 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 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 d u r i n g a r a i n f a l l and can be n e g l e c t e d . Then e q u a t i o n 4.13 becomes dP , , . -r- = e -wc-w 4 .14 dt 4.4.1 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 The f o l l o w i n g d i s c u s s i o n f o c u s s e s 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. The c o n s e r v a t i o n o f mass r e l a t e s the v e r -t i c a l and h o r i z o n t a l motion f i e l d s and can be used t o e s t i m a t e the v e r t i c a l v e l o c i t y ( H o l t o n , 19 72) . The h o r i z o n t a l d i v e r g e n c e o f the 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 images i s d i r e c t l y r e l a t e d t o the v e r t i c a l v e l o c i t y o f a i r e n t e r i n g the c l o u d . C o n s i d e r a p a r c e l o f a i r w i t h i n the c l o u d , w i t h c r o s s -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 and t i m e , i e . A = A ( z , t ) , c o n f i n e d between the l e v e l s z and z+dz, and w h i c h has a d e n s i t y p. (See F i g u r e 4.1). The mass o f t h i s a i r p a r c e l i s M = pAdz 4.15 51. A l t h o u g h the shape o f the p a r c e l changes w i t h t i m e , the mass of the p a r c e l i s c o n s e r v e d f o l l o w i n g the mo t i o n o f the p a r c e l , t h a t i s -rr- = 0. I n o t h e r words g£ (pAdz) = 0 4.16 The change i n d e n s i t y o f the a i r j ~ ( O ^ I O - 6 S - 1 ) i s g e n e r a l l y s m a l l r e l a t i v e t o the terms i Q ( O 1 0 - 5 S - 1 ) and ( o l 0 ~ 5 S _ 1 ) , A a t dz ( F l e a g l e , 1946) and may be i g n o r e d . F o r a f l o w v o l u m e ( F i g u r e 4.1) which i s h a l d c o n s t a n t i n the z d i r e c t i o n , so t h a t net i n -f l o w i s c a l c u l a t e d as a f u n c t i o n o f z, but which i s p e r m i t t e d t o expand i n the h o r i z o n t a l p l a n e , so t h a t no f l o w c r o s s e s t h e moving boundary, the e q u a t i o n o f c o n t i n u i t y can be w r i t t e n a s : 1 dA dw A . . _ A d t + d i - = ° 4 - 1 7 1 dA j£ g£ i s the 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 o f the ve-l o c i t y . V H • V. By r e a r r a n g i n g and i n t e g r a t i n g e q u a t i o n 4.17 w i t h r e s p e c t t o the a l t i t u d e z g i v e s the v e r t i c a l v e l o c i t y i n terms o f the h o r i z o n t a l d i v e r g e n c e (or s p r e a d i n g ) . I 1 dz 4.18 Z 2 Z 2 where z 2 and z^ (see F i g u r e 4.2) d e f i n e the t h i c k n e s s o f t h e d i v e r g i n g l a y e r between the l e v e l o f zero d i v e r g e n c e z 2 and .5.2. 3.T3 Cloud top at time t+At Cloud top at t ime t _ z , , T 2 * "2 Limit between upper level d ivergence and lower level c o n v e r g e n c e n • i Surface FIGURE 4.2 Schematic Diagram o f A i r C i r c u l a t i o n D u r i n g a Major Storm. \ 5 7 (The h o r i z o n t a l s c a l e s o f such storms a r e 0^10 - 10 m , 4 w h i l e the v e r t i c a l s c a l e s a r e 0^10 m.) 5 3 . the t r o p o p a u s e o r the top o f the c l o u d , z^. E q u a t i o n 4.18 g i v e s the change i n t h e v e r t i c a l v e l o c i t y o f the a i r between t h e t r o p o p a u s e o r top o f the c l o u d and t h e l e v e l o f n o n - d i v e r -gence. I f the v e r t i c a l v e l o c i t y a t the tropopause i s c o n s i d e r -ed z e r o then the v e l o c i t y i n t o the c l o u d a t the l e v e l o f non-d i v e r g e n c e i s S u b s t i t u t i n g 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 ( e q u a t i o n 4.20) 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 r a t e (equa-t i o n 4.14) y i e l d s E q u a t i o n 4.20 needs t o be m o d i f i e d s t i l l i . f u r t h e r . The enhanced i n f r a r e d s a t e l l i t e images c o n t a i n the t e m p e r a t u r e o f the c l o u d top as w e l l as t h e a r e a s o f the t e m p e r a t u r e c o n t o u r s . Compari-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 images a l s o g i v e s the change i n t h e c l o u d t o p a r e a i n t i m e . I t i s a d i f f i c u l t m a t t e r t o measure th e a l t i t u d e s o f t h e c l o u d tops and t o determine the l e v e l o f z e r o d i v e r g e n c e (the l i m i t s o f i n t e g r a t i o n i n e q u a t i o n 4.20). U s i n g the f i r s t law o f thermodynamics ( e q u a t i o n 4.4) and the a s s u m p t i o n t h a t the v e r t i c a l motions are a p p r o x i m a t e l y 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 dP d t 4.2Q h y d r o s t a t i c ( e q u a t i o n 4.10), the 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 _ d l + E a i = Y 4 21 dz Cp dz Cp _ Y * which i s d e f i n e d as the l a p s e r a t e y. U s i n g e q u a t i o n 4.21 the l i m i t s o f i n t e g r a t i o n can be changed from a l t i t u d e s z t o tempe r a t u r e s T whi c h can be imme-d i a t e l y d e t e r m i n e d from the s a t e l l i t e i magery. So the r a i n f a l l r a t e ( e q u a t i o n 4.21) can be w r i t t e n T 3 dP _ e-wc / 1 dA 4 2 2 d t " Y L A d t d T  A2 where T 3 i s the temp e r a t u r e o f the c l o u d top and T 2 i s the tempe r a t u r e o f t h e a i r a t the l e v e l o f zer o d i v e r g e n c e . 4.5 A d a p t a t i o n s f o r Use Wi 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 are made t o e q u a t i o n 4.2 2 be-f o r e e s t i m a t e s o f r a i n f a l l can be made from s a t e l l i t e images. F i r s t o f a l l , t he temp e r a t u r e a t the l e v e l o f non - d i v e r g e n c e i s assumed t o be 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 second a d a p t a t i o n i n v o l v e s t h e average d i v e r g e n c e f T 3 1 dA de t e r m i n e d from the i n t e g r a l t e n r i ^ A dt d T ' r e c a l l i n 9 t h a t t h e a r e a i s a f u n c t i o n o f b o t h temperature T and time t , A=A(T,t). I n o r d e r t o e v a l u a t e the i n t e g r a l i t i s n e c e s s a r y 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 the c l o u d changes a t each t e m p e r a t u r e 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 and l i k e l y v a r i e s from s t o r m t o s t o r m depending on the e n e r g e t i c s o f the s t o r m ; however, the s a t e l l i t e images do show from one image t o the n e x t , the change i n the c r o s s - s e c t i o n a l a r e a o f the c l o u d a t d i s c r e t e temperature l e v e l s . I d e a l l y , as the 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 the i n f r a r e d images i n c r e a s e s , the c l o s e r t h e s e d i s c r e t e areas approximate the t r u e ( c o n t i n u o u s ) v a r i a t i o n o f the c l o u d c r o s s - s e c t i o n a l a r e a w i t h t e mperature l e v e l T. P r e s e n t enhancements, however, d i s t i n g u i s h o n l y a few te m p e r a t u r e l e v e l s . F o r f r o n t a l systems i n w h i c h t h e u p l i f t i n g 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 and g r a d u a l , th e c o l d e s t c o n t o u r o f 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 a l o n g the f r o n t may be the o n l y one which i s s e p a r a b l e on the s a t e l l i t e i n f r a r e d image, t h e warmer c o n t o u r s o f the i n d i v i d u a l c e l l s h a v i n g a l l j o i n e d t o g e t h e r . The r a i n f a l l r a t e , t h e r e f o r e , u s u a l -l y can o n l y be e s t i m a t e d from the d i v e r g e n c e d e t e r m i n e d a t the c o l d e s t temperature l e v e l T 3 on the s a t e l l i t e image. 4.5.1 R e l a t i o n Between Average D i v e r g e n c e and C o l d e s t Contour  Divergence Reducing 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 the average d i v e r g e n c e i n the l a y e r between T 2 and T^ dP e-wc 1 dA / m m . d t = " — A d t ( T 3 ~ T 2 > 4 ' 2 3 where t h e o v e r b a r denotes a v e r a g i n g w i t h r e s p e c t t o temperature T, a l l o w s the r a i n f a l l r a t e t o be e s t i m a t e d from the d i v e r g e n c e o f the c o l d e s t c o n t o u r . The d i v e r g e n c e term can be ta k e n o u t s i d e the i n t e g r a l i f i t i s s i m i l a r , so t h a t the p r o c e s s i s e s s e n t i a l -l y n o n - d i m e n s i o n a l , i n whi c h case the mean, t h e maximum, o r the d i v e r g e n c e a t any p a r t i c u l a r l e v e l can be used i n p l a c e of the average 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 can now be shown to be a r e a s o n a b l e f i r s t a p p r o x i m a t i o n t o t h e average d i v e r g e n c e , 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 about the b e h a v i o u r o f the c r o s s - s e p t i o n a l a r e a are g e n e r a l l y known and they a r e : 1 - a t the l e v e l o f n o n - d i v e r g e n c e T 2 the d i v e r g e n c e i s by d e f i n i t i o n z e r o : 1 d A ( T 2 , t ) = A ( T 2 , t ) d t 2 - a t the c l o u d top l e v e l T 3 the d i v e r g e n c e i s 4.24 dA(T^,t) J • = K 4.25 A ( T 3 , t ) d t where K i s the d i v e r g e n c e measured from s a t e l l i t e i n f r a r e d images 4.5.2 One Proposed D i v e r g e n c e F u n c t i o n One s i m p l e f u n c t i o n r e l a t i n g t he b e h a v i o u r o f the d i v e r -1 dA (T t) gence ^ ^ t o the temperature l e v e l T can be shown to have an average v a l u e w h i c h i s p r o p o r t i o n a l t o the d i v e r g e n c e a t the c o l d e s t c o n t o u r l e v e l T^. F o r example, c o n s i d e r the d i v e r -1 dA(T t) G E N C E A (T ,t) d t " * — a s a ^ u n c t : " - o n °^ temperature T o f the form dA(T.t) = f T n 4.26 A (T ,t) d t L l 2 where f-^ and f 2 are c o n s t a n t s t o be d e t e r m i n e d from the two boundary c o n d i t i o n s above. T h i s f u n c t i o n can be shown t o have a mean v a l u e 1 r- dA(T,t) = A (T , t) d t K 1 1 T f 1 - t n + l ) T & + ^ ( T 3 - T 2 ) Tn+IT T n . T n 4 - 2 7 which i s d i r e c t l y p r o p o r t i o n a l t o the d i v e r g e n c e K a t l e v e l T-.. Assuming t h a t t h e b e h a v i o u r o f t h e d i v e r g e n c e w i t h tem-p e r a t u r e can be approximated by the f u n c t i o n suggested above, then t h e r a i n f a l l r a t e can be e s t i m a t e d s a t i s f a c t o r i l y u s i n g : 5 8 . dP dt 1 d A ( T 3 , t ) r "y" A ( T 3 , t ) d t J e -wc dT 4.21 o r dP _ e <wc 1 d t = ~ y A ( T 3 , t ) d A ( T 3 , t ) dt AT 4.29 where AT=T 3~T 2 i s the temperature d i f f e r e n c e from the l e v e l o f z e r o d i v e r g e n c e t o c l o u d t o p . 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 time t o g i v e the change i n r a i n f a l l dP from time t t o t + d t : t+dt dP _ e-wc J 1 d A ( T 3 , t ) t A ( T 3 , t ) e -wc In A(T 3,t+dt) ATT7~E1 d t AT AT d t 4.30 4. 31 (Appendix B c o n t a i n s a b r i e f s e n s i t i v i t y a n a l y s i s o f t h e r a i n f a l l e s t i m a t i o n r e l a t i o n . ) 59. 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 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 A t can be e s t i m a t e d from the 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 images u s i n g A P = - ! ^ £ A T l n A ( T 3 , t + A t ) A ( T 3 , t J 4.32 w i t h A ( T 3 , t ) > 0 I n 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 u n t i l t h e second s a t e l l i t e image, t h a t i s A ( T 3 , t ) = 0, the e x p r e s s i o n i n e q u a t i o n 4.31 i s u n d e f i n e d . The d i s c r e t e form of e q u a t i o n 4.29 i s used t o p r o v i d e as e s t i m a t e o f the amount of p r e c i p i t a t i o n AP f a l l i n g i n the f i r s t t i m e i n t e r v a l A t : e-wc A(T , t + A t ) - A ( T 3 , t ) i n - e *W^» J J Am 'All F " T ~ 0 . 5 ( A ( T 3 , t + A t ) + A ( T 3 , t ) ) A i 4 ' 3 3 o r AP = -^M 2 AT 4.34 f o r A ( T 3 , t ) = 0 E q u a t i o n s 4.32 and 4.34 form the b a s i s o f the computer r o u t i n e w h i c h computes the p r e c i p i t a t i o n amounts from s a t e l l i t e p i c t u r e d a t a . 6 0 . 4.6 Consequences of t h e Model There are t h r e e consequences o f 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 p o s t u l a t e d t h a t r a i n f a l l s from o n l y t h o s e c l o u d c e l l s w h i c h are a c t i v e l y growing i n time as e v i d e n c e d i n the s p r e a d i n g o f the c o l d e s t c l o u d top c o n t o u r from one s a t e l l i t e image t o t h e n e x t . T h i s i s r e a s o n a b l e a l t h o u g h some l a r g e r c e l l s w h ich are d e c a y i n g o f t e n c o n t i n u e t o d e p o s i t r e d u c i n g amounts o f r a i n . However, t h i s r a i n f a l l i s n o t c o n s i d e r e d t o be a s i g n i f i -c a n t p o r t i o n o f the o v e r a l l s t o r m t o t a l . The second consequence i s t h a t no r a i n f a l l s f o r those c l o u d s w h i c h a r e below the chosen l e v e l o f z e r o d i v e r g e n c e . T h i s means t h a t r a i n f a l l from some c l o u d s below t h i s l e v e l w i l l n o t be a c c o u n t e d f o r i n t h e a n a l y s i s o f the s a t e l l i t e images. T h i s cannot be a v o i d e d a t p r e s e n t due t o t h e l i m i t a t i o n s o f the enhancement schemes b e i n g used on the i n f r a r e d images. The model i s however, g e n e r a l enough t o be u s e f u l f o r a n a l y z i n g t h e s e lower l e v e l c l o u d s when an a p p r o p r i a t e enhancement scheme w h i c h c o n t r a s t s the s m a l l temperature g r a d i e n t s o f t h e s e c l o u d s becomes a v a i l a b l e . I t s h o u l d be p o i n t e d o u t , however, t h a t those c e l l s w h i c h r e a c h near tropopause h e i g h t s o f v e r t i c a l development are l i k e l y 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 o v e r an a r e a . The t h i r d consequence o f t h e model l i e s i n the manner i n w h i c h the s p a t i a l d i s t r i b u t i o n o f r a i n f a l l from a s t o r m c e l l i s o b t a i n e d . Because the average d i v e r g e n c e 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 o f the c o l d e s t con-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 f u n c t i o n s , then the r a i n f a l l from a p a r t i c u l a r t emperature c o n t o u r i s p r o p o r t i o n a l t o the t h i c k n e s s AT o f the d i v e r g i n g l a y e r under 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 2 i s t h e l e v e l o f n o n - d i v e r g e n c e ) . F o r con-t o u r s o t h e r than the c o l d e s t one, the r a i n f a l l i s found u s i n g AT=T^-T 2 i n the a p p r o p r i a t e model e q u a t i o n ( e i t h e r 4.32 o r 4 . 3 4 ) . 4.7 The Other Model Parameters The a r e a and temperature parameters can be o b t a i n e d from the s a t e l l i t e i n f r a r e d p i c t u r e s . That l e a v e s t h e w a t e r c o n t e n t wc, the l a p s e r a t e y, and t h e e f f i c i e n c y e t o be d e t e r m i n e d . I d e a l l y , the b e s t c h o i c e o f v a l u e s f o r t h e s e parameters would be o b s e r v e d v a l u e s . I n p r a c t i c e , however, i t may be n e c e s s a r y t o r e l y on o t h e r s o u r c e s o f d a t a . These are d i s c u s s e d below. 4.7.1 Water Co 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 i n an a i r column t h a t i s a v a i l a b l e f o r p r e c i p i t a t i o n . The l i t e r a t u r e shows a wide range o f v a l u e s o f wc v a r y i n g w i t h the c l o u d t y p e . Table 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 from p u b l i s h e d m a t e r i a l . Water c o n t e n t can be de t e r m i n e d from v a l u e s o f the p r e c i p i t a b l e w a t e r w h i c h a r e r e p o r t e d e v e r y 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 TIROS-N. Table 4.2 shows a sample p r i n t o u t o f TIROS-N d a t a . As w e l l , w a t e r c o n t e n t can be d e t e r -mined from r e l a t i v e h u m i d i t y o b s e r v a t i o n s a t nearby upper a i r weather s t a t i o n s . TABLE 4.1 Average E f f i c i e n c i e s and Water Content C l o u d Type E f f i c i e n c y e (as a f r a c t i o n ) Water C o n t e n t wc (g/m 3) Seafog S t r a t u s O r o g r a p h i c (Hawaii) S m a l l Cumulus Cumulus Congestus Cumuloniumbus 0.05 0 .05-0.10 0\.10 0 .15 0.20-0.30 0 .10 0.35 0 .35 0.5-1.4 1.0 2.0-10.0 (from MASON, 19 71, 19 75; FLETCHER, 196 2; ROGERS, 19 76) TABLE 4.2 Portion of T y p i c a l Output of TIROS-N (TUXN) P r e c i p i t a b l e Water (PCW) and Other Data f o r Various Levels i n the Atmosphere. (Received by the P a c i f i c Weather Centre from NESS S a t e l l i t e Data Services 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 LAT LONG 850 MB 700 MB 500 MB 400 MB 300 MB 250 MB CL ACT SFT TRT 0500Z 2 8N 140W 48 400 90%:THKS FM1000MB 136 294 558 724 928 052 90%:PCW FM1000MB 013 016 017 . 019 // 0500Z 34N 136W— 93 294 70%:THKS FM1000MB 135 294 560 729 935 060 70%:PCW FM1000MB 016 022 024 017 // 0500Z 35N 132N 19 300 90%:THKS FM1000MB 137 297 564 733 940 064 90%:PCW FM1000MB 017 021 022 • 018 // TABLE 4.2 (continued) DATM LAT LONG 850 MB 700 MB 500 MB 400 MB 300 MB 250 MB CL ACT SFT TRT 0500Z 42N 137W 10 441 90%:THKS FM1000MB 133 291 555 723 928 051 90%:PCW FM1000MB 008 009 010 O i l / / 0500Z 42N 130W 09 30 6 60%:THKS FM1000MB 133 290 553 719 923 047 60%:PCW FM1000MB 007 008 009 • 012 / / 0500Z 45N 142@ 18 661 70%:PCW FM1000MB O i l 014 015 005 / / 0500Z 46N 136W 29 750 90%:PCW FM1O00MB O i l 014 015 • 009 / / 42 506 0500Z 64N 144W 90%:PCW FM920MB 002 003 004 M15 / / 0422Z 62N 126W 37 432 90%:THKS FM780MB 081 326 481 673 79 4 90%:PCW FM7 80MB 001 002 003 M15 / / 65. 4.7.2. The Lapse Rate y The l a p s e r a t e y can be assumed e q u a l t o the s a t u r a t e d a d i a b a t i c l a p s e r a t e y = y - 5°C/1000m wh i c h i s a r e a s o n a b l e assumption d u r i n g a r a i n f a l l . A l t e r n a t e l y , the a c t u a l e n v i r o n -m e n t a l l a p s e r a t e y = y as r e c o r d e d from r a d i o s o n d e a s c e n t s ' env can be used. 4*7.3. Adjustment F a c t o r e The parameter e i s an e m p i r i c a l adjustment f a c t o r t h a t some i n v e s t i g a t o r s have l i n k e d t o the a c t u a l e f f i c i e n c y o f a c l o u d i n p r o d u c i n g r a i n . The l i t e r a t u r e i n d i c a t e s a wide range o f v a l u e s f o r e depending on c l o u d type and v a r y i n g s i g n i f i c a n t l y w i t h i n each c l o u d t y p e . 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 tended t o d e f i n e e and wc d i f f e r e n t l y , v a l u e s f o r t h e s e parameters o f -t e n o c c u r i n p a i r s 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. Because i n t h i s model e i s an e m p i r i c a l a d j u stment f a c t o r i t can be used t o t a k e i n t o account u n c e r t a i n t i e s i n t h e o t h e r p a r a m e t e r s . C o n s i d e r the s i t u a t i o n o f a sto r m r a i n i n g o v e r a r e g i o n w h i c h has a number o f s t a t i o n s o n l y one o f w h i c h i s a b l e t o p r o v i d e v a l u e s f o r the w a t e r c o n t e n t and the l a p s e r a t e , a l o n g w i t h t h e o b s e r v e d p r e c i p i t a t i o n A P ^ g from the r a i n g a u g e o r r a d a r l o c a t e d a t t h i s 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 , — I n "A(T 3,t+ A t ) ~ Y A ( T 3 , t ) y i e l d s a v a l u e f o r e which c o n t a i n s b o t h t h e d i f f i c u l t t o determine " e f f i c i e n c y " o f the c l o u d , and the u n c e r t a i n t y i n the o t h e r p a r a m e t e r s . T h i s v a l u e o f the e f f i c i e n c y e c o u l d w e l l s e r v e as the b e s t i n i t i a l e s t i m a t e o f e f o r a l l o f the s t a t i o n s i n the r e g i o n . Once the e f f i c i e n c y e, w a t e r c o n t e n t wc and l a p s e r a t e y have been chosen f o r each s t a t i o n they are assumed t o remain c o n s t a n t t h r o u g h o u t the s t o r m . T h i s i s c o n s i d e r e d t o be a r e a s o n a b l e assumption s i n c e the c h a r a c t e r i s t i c s o f the airmass o v e r the s t a t i o n change v e r y s l o w l y d u r i n g the storm. (The un-c e r t a i n t y 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 i n t r o d u c e s i s a c c o u n t e d f o r i n the u p d a t i n g r o u t i n e d i s c u s s e d i n Chapter 7) ;. 4.8 Summary A b r i e f d i s c u s s i o n o f the c o n d i t i o n s n e c e s s a r y f o r p r e c i -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 c o n s i d e r s the p r e c i p i t a t i o n p r o c e s s i n terms o f the f l u x o f w a t e r through an a i r column. The v e r t i c a l v e l o c i t y c o u l d be de t e r m i n e d from the lo w e r l e v e l convergence o f a i r i n t o the c o l -umn. - an approach t h a t was used by 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 never 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 the d i f f i c u l t i e s i n v o l v e d i n d e t e r m i n i n g the lo w e r l e v e l w i n d s . S a t e l l i t e images, however, p r o v i d e the means f o r d e t e r m i n i n g the upper l e v e l d i v e r g e n c e w h i c h can be used as a b a s i s f o r 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 . 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 . The model ( e q u a t i o n s 4.32 and 4.34) was d e v e l o p e d k e e p i n g i n mind the i n -f o r m a t i o n s a t e l l i t e images p r o v i d e . CHAPTER V 68. COMPUTATIONAL PROCEDURE FOR ESTIMATING RAINFALL FROM SATELLITE IMAGES The analysis of r a i n f a l l events using GOES images involve a d i f f i c u l t exercise i n bookkeeping to keep track of the ess e n t i a l image parameters describing the storm, esp e c i a l l y i f the storms are major ones containing many i n d i v i d u a l c e l l s , which appear, grow and decay as they move over an area. Figure 5.1 defines the image terms used i n this study. Computer rou-tines to f a c i l i t a t e the calculations of the r a i n f a l l estimates were developed during the course of the analysis of 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-plished through a computer-user i n t e r a c t i v e process which i s flowcharted i n Figure 5.2, with each of the steps discussed b r i e f l y below. The f i r s t step i n the process was to obtain the half-hour ly GOES s a t e l l i t e images. These can be obtained either through loan arrangement with the Atmospheric Environment Service, the P a c i f i c Weather Centre (or l o c a l weather centre), v i a a GOES-Tap l i n k , or through d i r e c t reception of the s a t e l l i t e s i g n a l . The FIGURE 5.1 E x p l a n a t i o n o f the Va r i o u s Terms used t o D e s c r i b e GOES I n f r a r e d Cloud Images: CELL - The C o l d e s t S e l f - C o n t a i n e d Cloud Top Contour and I t s Immediately Surrounding Warmer Contours. STORM - The Cloudy Area on the S a t e l l i t e Image Which B r i n g s Rain i n t o an Area. I t i s u s u a l l y made up of one or more c e l l s . 70. FIGURE 5.2 Step 1: Step 2: Step 3: Ste p 4: Step 5 : Step 6 : Steps 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 from GOES s a t e l l i t e images. 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 s a t e l l i t e images O b t a i n v a l u e s f o r the model parameters e, wc and y i e n t e r t h e s e a l o n g w i t h the s a t e l l i t e image d a t a . D i g i t i z e t e mperature c o n t o u r 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 t h e v i d o c a m e r a - 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 system) C a l c u l a t e c l o u d t o p temperature c o n t o u r 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 use w i t h moving s y s t e m s ) . C a l c u l a t e r a i n f a l l f o r each c o n t o u r . D i g i t i z e s t a t i o n ^ c o o r d i n a t e s . 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 where n e c e s s a r y when a ; s t a t i o n i s between two c o n t o u r s . s a t e l l i t e images used i n t h i s s t u d y were p r o v i d e d by t h e P a c i f i c Weather Centre i n Vancouver, B r i t i s h Columbia. The second s t e p i n v o l v e d the c h o i c e o f the r a i n f a l l e s t i -m a t ion model p a r a m e t e r s , the w a t e r c o n t e n t wc, t h e l a p s e r a t e y / and the adjustment 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 4.7. The n e x t major s t e p and the f i r s t i n v o l v i n g the use o f a computer r o u t i n e , was to.'input the s t o r m i n f o r m a t i o n i n c l u d i n g a s t o r m c e l l i d e n t i f i c a t i o n number, the time the s a t e l l i t e image was t a k e n , t h e enhancement scheme used, the s e c t o r used, and t h e tempe r a t u r e c o n t o u r l e v e l , and th e n t o d i g i t i z e the i n d i v i d u a l c e l l c l o u d t o p temp e r a t u r e c o n t o u r s . A 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 , F i g u r e 5.3, l i n k e d by a t i m e - s h a r i n g computer t e r m i n a l t o the U n i v e r s i t y o f B r i t i s h Columbia's Amdahl 470 V/6 model I I com-p u t e r system ( L e i g h and Duke, 19 78) was used t o d i g i t i z e t h e p e r i m e t e r o f the c l o u d top temperature c o n t o u r s and s t o r e the c o o r d i n a t e s f o r use i n the subsequent s t e p s . 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 the i n f r a r e d image had been enhanced.,, t h a t i s , i f the tempe r a t u r e s had been s c a l e d 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 t emperature c o n t o u r s . However, the 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 o r unenhanced images are b e i n g r e -c e i v e d i n s t e a d . There 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 times when more than one enhancement scheme i s i n use d u r i n g the day. D i r e c t r e c e p t i o n and enhancement o f the s a t e l l i t e image e l i m i n a t e s t h e s e p r o b l e m s , a l t h o u g h , f o r most u s e r s t h i s i s not p o s s i b l e . 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 the T a b l e t and the Temperature Contours are Traced u s i n g the S t y l u s . T h e r e f o r e , t o supplement th e enhanced images and t o f i l l i n the gaps, 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 t h e U n i v e r s i t y o f B r i t i s h Columbia w h i c h i n c l u d e d a v i d e o camera, a s p e c i a l e f f e c t s g e n e r a t o r and a v i d e o m o n i t o r . The s p e c i a l e f f e c t s g e n e r a t o r , F i g u r e 5 . 4 , a l l o w e d b l a c k i n g o u t 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) below any p a r t i c u l a r l e v e l o f b r i g h t n e s s . By s u c c e s s i v e l y b l a c k i n g o u t d a r k e r shades o f g r e y , temperature c o n t o u r s c o u l d be shown on the v i d e o m o n i t o r s c r e e n , F i g u r e 5 . 5 . These were t r a c e d and d i g i t i z e d . F i g u r e 5.6 shows the v i d e o c a m e r a - 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. The d i g i t i z e d c o n t o u r s were used as i n p u t t o the 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 o f g r a v i t y 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 t h a t f a l l s a t a p o i n t from a moving c l o u d system. The c e n t r e o f g r a -v i t y o f t h e c o l d e s t c o n t o u r was a l s o computed and used as an i n -d i c a t o r o f the movement o f the c l o u d c e l l between s u c c e s s i v e s a -t e l l i t e images. A l l o f t h i s i n f o r m a t i o n was w r i t t e n onto the computer f i l e s t h a t s e r v e d as i n p u t f i l e s f o r the n e x t s t e p i n w h i c h the r a i n f a l l was e s t i m a t e d f o r each c o n t o u r u s i n g the model e q u a t i o n s 4.32 and 4.34. T h i s a l l o w e d c o n t o u r s o f r a i n f a l l from i n d i v i d u a l c e l l s 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 . In 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 mapped by the u s e r onto a s a t e l l i t e image g r i d and then t h e i r FIGURE 5.4 The Panasonic WJ-4500 S p e c i a l E f f e c t s Generator Used to Determine Temperature Contours from 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 top photo shows the s a t e l l i t e image as seen on the 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 engaged. The second photo shows the s a t e l l i t e image as seen on the v i d e o m o n i t o r a f t e r 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. Those c l o u d s warmer th a n T°C on the t e m p e r a t u r e - g r e y s c a l e have been shown as b l a c k areas w h i l e t h o s e c o l d e r t h a n T°C are shown as l i g h t e r a r e a s . The boundary between the 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 M o n i t o r Arrangement used t o Determine Temperature Contours from GOES Unenhanced I n f r a r e d Images. 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 t a b l e t as b e f o r e . T h i s was a one 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 -c u l a t i n g t h e r a i n f a l l a t t h e s e s t a t i o n s . The c o o r d i n a t e s were used by t h e computer r o u t i n e w h i c h d e t e r m i n e d the movement o f the s t o r m c e l l o r c e l l s p a s t the s t a t 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 s h o u l d 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-t o u r s . 5.1.1 Movement o f Storm C e l l s Near A S t a t i o n S i n c e the s a t e l l i t e images form a s e r i e s o f " s n a p - s h o t s " o f a c o n t i n u o u s l y changing p r o c e s s the e f f e c t on the r a i n f a l l due t o the movement o f s t o r m c e l l s n ear a s t a t i o n was h a n d l e d i n the f o l l o w i n g manner. F i g u r e 5.7 shows a s i t u a t i o n w h i c h r e p r e s e n t s t h e p o s i t i o n s o f a 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 as seen i n two s u c c e s s i v e s a t e l l i t e images, s e p a r a t e d by a time i n t e r v a l A>t. From t h i s i t would 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 s i n c e i t l i e s o u t s i d e the c l o u d c o n t o u r i n b o t h s a t e l l i t e images. However, i t i s c l e a r t h a t 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 . To a c c o u n t f o r t h i s e f f e c t caused by the movement of the c e l l , the c e n t r e o f g r a v i t y o f the c e l l a t the second time i s s h i f t e d back t o t h e m i d - p o i n t o f the l i n e w h i c h i n d i -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 so t h a t the c e l l appears i n t h e p o s i t i o n shown i n F i g u r e 5.8. I f more th a n one c e l l p a s s e d n e a r the s t a t i o n the p r o c e -dure was e s s e n t i a l l y the same. The computer r o u t i n e C e l l at t, FIGURE 5 . 7 A Schematic Representation of One Storm C e l l Contour as i t Moves over 3 R a i n f a l l Stations Between Times t, and t 2 . The Displacement of the Centre of Gravity during t h i s Time i s from C^ to C 2. From these "Snap-Shot" views, Station 1 appears not to have received any R a i n f a l l . 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 Back H a l f the 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. s e a r c h e d 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 were c l o s e s t t o the s t a t i o n and y e t not t o t h e e a s t o f the s t a t i o n on the f i r s t s a t e l l i t e image. Because o f the g e n e r a l l y e a s t -ward movement o f t h e s t o r m s , those c e l l s t o the e a s t o f t h e s t a t i o n had a l r e a d y c o n t r i b u t e d t o t h e s t a t i o n ' s r a i n f a l l i n p r e v i o u s time i n t e r v a l s . A g a i n the c e l l s ' c e n t r e s o f 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 o f t h e l i n e j o i n i n g t h e i r p o s i t i o n s a t the b e g i n n i n g and end o f the time i n t e r v a l . T h i s i s i l l u s t r a t e d s c h e m a t i c a l l y i n F i g u r e 5.9. S h o u l d the s t a t i o n i n i t s new p o s i t i o n l i e between con-t o u r s , the i n t e r p o l a t i o n f o r r a i n f a l l was p e r f o r m e d by t h e U n i -v e r s i t y o f B r i t i s h Columbia Computing Ce n t r e l i b r a r y r o u t i n e XPAND.S (UBC Computing C e n t r e , 1979) w h i c h was m o d i f i e d somewhat t o s u i t the purpose a t hand. T h i s r o u t i n e uses a h e u r i s t i c a l g o r i t h m t o i n t e r p o l a t e f o r i n t e r m e d i a t e v a l u e s from an a r r a y o f known v a l u e s . D e t a i l s o f t h i s a l g o r i t h m are g i v e n i n the UBC Computing C e n t r e document: UBC S u r f a c e , ( M a i r , 1978b). The h a l f -h o u r l y e s t i m a t e s o f the r a i n f a l l a t each o f the s t a t i o n s a r e t h e n summed t o y i e l d c u m u l a t i v e r a i n f a l l e s t i m a t e s . 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 n e x t s e c t i o n . 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 . B o t h a re s h i f t e d so 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 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 C 2« The s h i f t e d c e l l s a r e shown by the dashed c u r v e s . 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 the sequence o f computer r o u t i n e s d e v e l o p e d d u r i n g t h i s s t u d y and used t o make e s t i m a t e s o f the r a i n f a l l from c l o u d top temperature c o n t o u r s t a k e n from GOES i n f r a r e d images. There a r e f i v e major r o u t i n e s (DOG, STATION, RF, IN, UP) which 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 y i e l d i n g a 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 . A l l o f t h e s e r o u t i n e s were programmed i n F o r t r a n f o r use on the UBC computer t e r m i n a l system. r o u t i n e s e n a b l i n g the u s e r t o i n p u t e i t h e r s a t e l l i t e image parameters and te m p e r a t u r e c o n t o u r s - DOG, o r s t a t i o n names and l o c a t i o n s - STATION, v i a the d i g i t i z i n g t a b l e t . B oth o f t h e s e r o u t i n e s make use o f the UBC Computing Centre L i b r a r y program IG ( M a i r , 19 78a) t o c o n t r o l the a c t u a l i n p u t o f the d a t a p o i n t s a l o n g w i t h s t a n d a r d i z e d x-y axes. The r o u t i n e DOG a l s o c a l c u l a t e s the a r e a (A) o f each c o n t o u r t r a c e d u s i n g The f i r s t two r o u t i n e s , DOG and STATION, are d i g i t i z i n g A - E r(x. i + i 5.1 i where x^, y^ are the c o o r d i n a t e s o f the i - t h p o i n t d i g i t i z e d . The c e n t r e o f g r a v i t y o f each c o n t o u r ( x c , yc) i s de t e r m i n e d by the r o u t i n e DOG u s i n g FIGURE 5.10 Sequence of Computer Routines Used: GOES SATELLITE PICTURES & OBSERVED DATA DIGITIZING ROUTINES RAINFALL ESTIMATION ROUTINES for contours and a g r i d of s t a t i o n s UODATING ROUTINE GOES SATELLITE INFRARED PICTURES, e, wc, y E OBSERVED RAINFALL DATA "DOG" - read i n contour p e r i -meter coor-dinates - c a l c u l a t e contour area and center o f g r a v i t y  RF' "STATION" - read i n s t a t i o n coordinates and name - accounts f o r various 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 - accounts f o r various o p e r a t i o n a l enhance-ment 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 temperature contour (up to 6) f o r each storm c e l l at each time using model equations 4.32 and 4.34. z j"IN" - accounts f o r movement of storm c e l l ( s ) over s t a t i o n _ - i n t e r p o l a t e s f o r s t a t i o n 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 contours I"UP" -updates r a i n f a l l estimates at 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 equations 7.1 (and 7.4 and 7.5). OUTPUT OUTPUT=UPDATED SATELLITE ESTIMATE OF RAINFALL; values of a, b f o r use i n updating ungauged s t a t i o n estimates; Jj hourly r a i n f a l l contours 8 . 4 . n x c 1 n y c 5.2 5.3 w h i c h e s s e n t i a l l y d e s c r i b e d t h e c e n t r e o f g r a v i t y . T h e s e c o n d two r o u t i n e s , RF a n d I N , a r e t h e r a i n f a l l e s t i m a t i o n r o u t i n e s . T h e f i r s t o f t h e s e , R F , p r o v i d e s e s t i -m a t e s o f t h e r a i n f a l l f o r e a c h t e m p e r a t u r e c o n t o u r u s i n g t h e r a i n f a l l m o d e l e q u a t i o n s 4.32 a n d 4.34. T h i s i s done a f t e r t h e r o u t i n e s c a l e s a l l t h e s a t e l l i t e i m a g e s t o t h e s i z e o f t h e SB6 i m a g e s e c t o r . T h i s i s n e c e s s a r y b e c a u s e s e v e r a l s e c t o r s c a l e s a r e r e c e i v e d o p e r a t i o n a l l y . T h e r o u t i n e t h e n m u s t d e t e r m i n e w h i c h o f t h e v a r i o u s o p e r a t i o n a l e n h a n c e m e n t s chemes i s b e i n g u s e d b e f o r e p r o c e e d i n g t o c o m p u t e t h e r a i n f a l l f o r e a c h o f t h e t e m p e r a t u r e c o n t o u r s , up t o a maximum o f 6, f o r e a c h s t o r m c e l l s i n c e e a c h o f t h e v a r i o u s c e l l s may b e e v o l v i n g a t d i f f e -r e n t r a t e s , f o r t h e d u r a t i o n o f t h e s t o r m e v e n t . T h e s e c o n d o f t h e r a i n f a l l e s t i m a t i o n r o u t i n e s , I N , p r o -v i d e s e s t i m a t e s o f r a i n f a l l f o r t h o s e s t a t i o n s whose c o o r d i n a t e s w e r e s t o r e d u s i n g t h e r o u t i n e S T A T I O N a n d t h e c e l l c o n t o u r r a i n e s t i m a t e s o b t a i n e d f r o m t h e r o u t i n e R F . The r o u t i n e I N a c c o u n t s f o r t h e movement o f t h e s t o r m a n d i t s c e l l s o v e r t h e s t a t i o n (as d e s c r i b e d i n t h e p r e v i o u s s e c t i o n ) . The s e c o n d p a r t o f t h e r o u -8.5. t i n e IN i s t o i n t e r p o l a t e , u s i n g the m o d i f i e d XPAND.S, f o r the r a i n f a l l a t the s t a t i o n a f t e r the movement o f the s t o r m has been t a k e n c a r e o f . I f the i s o h y e t s o f the r a i n f a l l a r e r e q u i r e d they are de t e r m i n e d 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 the UBC Computing C e n t r e l i b r a r y g r i d c o n t o u r i n g r o u t i n e CNTOUR (Mair, 1978b) . The f i n a l major 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 based 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 7. T h i s r o u t i n e i n c o r p o r a t e s t h e o b s e r v e d r a i n f a l l f o r each s t a t i o n w i t h the s a t e l l i t e e s t i m a t e s u s i n g the u p d a t i n g model, equa-t i o n s 7.1, 7.4 arid 7.5, i n a d d i t i o n t o the u p d a t i n g model p a r a -m e t e r s , 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 e s t i m a t e s f o r ungauged l o c a t i o n s . The o u t p u t from t h e s e 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 o f r a i n f a l l f o r v a r i o u s s t a t i o n s , c o n t o u r s o f the e s t i m a t e d r a i n f a l l p roduced by each c e l l , and i s o h y e t s o f e s t i m a t e d r a i n f a l l f o r a g r i d o f p o i n t s . 8 6 . CHAPTER VI ESTIMATES OF PRECIPITATION USING SATELLITE IMAGES 6.1 The T e s t Storms As a t e s t o f the model under a c t u a l c o n d i t i o n s , a number o f storms w h i c h o c c u r r e d o v e r 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 the a v a i l a b l e i n f r a r e d GOES-West images r e c e i v e d a t the P a c i f i c Weather C e n t r e i n Vancouver. E x c e p t f o r one o f the t e s t s t o r m dates (June 4, 19 77) s a t e l l i t e images were chosen f o r t h o s e dates and times d u r i n g w h i c h r a i n f a l l was known (from news media o r P a c i f i c Weather 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 f a l l i n g o v e r B r i t i s h C olumbia. F o r the June 4, 19 77 case i t was assumed t h a t r a i n was f a l l i n g from those c e l l s w h i c h had r e l a t i v e l y c o l d c l o u d top t e m p e r a t u r e s (<-40°C). The a c t u a l o c c u r r e n c e o f r a i n f a l l f o r the June 4, 19 77 s t o r m was c o n f i r m e d on e x a m i n a t i o n o f the h o u r l y r a i n f a l l r e c o r d s f o r the a f f e c t e d s t a t i o n . The f o l l o w i n g c r i t e r i a i n f l u e n c e d t h e c h o i c e o f t e s t s t o r m s : 1 - The s t o r m had t o be s u f f i c i e n t l y w e l l - d e v e l o p e d i n th e v e r t i c a l t o have c l o u d top t e m p e r a t u r e s w h i c h were w i t h i n the s t e p w i s e range o f the enhancement scheme used so t h a t d e f i n i t e c l o u d top temperature c o n t o u r s 'were formed on t h e s a t e l l i t e i n f r a r e d images. 87. 2 - The sto r m had t o be l o a a t e d o v e r an a r e a w h i c h had a t l e a s t one r a i n g a u g e t o a l l o w v e r i f i c a t i o n and/or c a l i b r a t i o n o f the r a i n f a l l e s t i m a t i o n 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 st o r m had 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 s a t e l l i t e 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 r a i n f a l l e s t i m a t e . Over r e g i o n s w i t h o n l y 6-hour o r 12-hour r e c o r d s o f r a i n f a l l , t he storm had t o e x i s t f o r the e n t i r e 6-hour o r 12-hour p e r i o d . D u r i n g 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 a r o s e 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 b e f o r e t h e e s t i m a t i o n p r o c e -dure c o u l d be used o p e r a t i o n a l l y . The development o f the computer r o u t i n e s , d i s c u s s e d i n the p r e v i o u s c h a p t e r , t o f a c i l i t a t e the a n a l y s i s p r oceeded a l o n g w i t h t h e e x a m i n a t i o n o f t h e 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 October 31, 19 78. The t e s t storms i n c l u d e d two examples 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 systems o c c u r r i n g on October 31, 19 7 8 and December 17, 1979, b o t h o f which were not e w o r t h y . The f i r s t , w h i ch swept a c r o s s the Queen C h a r l o t t e I s l a n d s and o v e r the T e r r a c e a r e a was dubbed t h e Halloween Deluge by l o c a l meteoro-l o g i s t s (Hammond, 19 78 ) . The second was a s t o r m w h i c h f o l l o w e d an e a r l i e r e v e n t t h a t caused e x t e n s i v e p r o p e r t y damage from f l o o d i n g and l a n d s l i d e s i n P o r t Moody on the o u t s k i r t s o f Van-c o u v e r , B r i t i s h Columbia. The o t h e r storms i n v e s t i g a t e d were 88. storms f:.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 , o c c u r r i n g on June 4, 19 77, and two w i n t e r storms w h i c h o c c u r r e d on November 20, 19 79 and December 5, 19 79. F o r each o f the t e s t storms the temperature o f the l e v e l o f n o n - d i v e r g e n c e was chosen as a c o n s t a n t 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 the l e v e l o f non-divergence when the c o r r e c t tempera-t u r e i s T m can be r e a d i l y a c c o u n t e d f o r i n the e x p r e s s i o n f o r r a i n f a l l by t h e a d d i t i o n o f an adjustment AT"'" t o t h e temperature t h i c k n e s s o f t h e d i v e r g i n g . l a y e r AT i n 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 ( 4 . 3 2 and 4.34) 6.1 where AT i s the t e m p e r a t u r e t h i c k n e s s between the t r u e tempe-r a t u r e l e v e l o f non-divergence (T m) and the t e m p e r a t u r e l e v e l a c t u a l l y chosen (T 2) . F o l l o w i n g t h e s t e p s o u t l i n e d i n the p r e v i o u s c h a p t e r , the r a i n f a l l was e s t i m a t e d from the 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 each o f the t e s t storms as w e l l as the r e s u l t s o f t h e e s t i m a t i o n p r o c e d u r e a r e d i s c u s s e d below. 6.2 The October 31, 19 7 8 R a i n f a l l E s t i m a t e s 6.2.1 Storm D e s c r i p t i o n Between October 29 and November 2, 19 78 a major s t o r m o c c u r r e d o v e r the N o r t h Coast o f B r i t i s h Columbia. D u r i n g the s t o r m , winds g u s t i n g t o 125 kph and 5-day r a i n f a l l t o t a l s ex-c e e d i n g 400mm i n some areas c o i n c i d e d w i t h heavy snowmelt t o cause f l o o d i n g and damages w e l l i n excess o f $10 m i l l i o n . Two CNR crew members were k i l l e d and two m o t o r i s t s were i n j u r e d as a r e s u l t o f roadbed damage {Chinook, 1979). S c h a e f e r (1979a, b) and Hammond (1978) d e s c r i b e the s t o r m from 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 from the r e c o r d e d r a i n f a l l amounts (from S c h a e f e r , 19 79a, 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 and the 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. The t e r -r a i n i n the a r e a i s e x t r e m e l y rugged w i t h mountains r i s i n g t o ov e r 2000 m. 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 are few and f a r between. F i g u r e 6.2 shows the 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 vie w e d from GOES-West. The aim o f the a n a l y s i s was t o check the pr o c e d u r e f o r e s t i m a t i n g r a i n f a l l w i t h a major s t o r m . S i n c e the October 31, 19 78 s t o r m was t h e f i r s t r a i n f a l l e v e n t examined, most o f the c a l c u l a t i o n s a p a r t from the d i g i t i z i n g o f the c l o u d top tempe-r a t u r e c o n t o u r s and t h e co m p u t a t i o n o f the areas w i t h i n t h e s e FIGURE 6.1 Map o f the 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 the 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 1979a, b ) . 0115 31DC78 35E-1EC 00634 22232 SB6 FIGURE 6.2 A r e a l E x t e n t o f the October 31, 19 78 Storm a t 0115 GMT as Viewed from GOES-West. 92. c o n t o u r s were c a r r i e d o u t by hand. T h i s e x p l o r a t o r y e x e r c i s e was 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 were used i n t h e 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 subsequent t e s t s t o r m a n a l y s e s . 6.2.2 R e s u l t s 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 the Queen C h a r l o t t e I s l a n d s . The s e r i e s o f GOES-West images examined c o v e r e d t h e time i n t e r v a l between 0045 GMT on October 31, 19 7 8 and 22 45 GMT on November 1, 19 78. Of t h e 9 3 p o s s i b l e images, 29 were enhanced and c o u l d be used d i -r e c t l y , 31 were unenhanced and had t o f i r s t be p r o c e s s e d through t h e v i d e o c a m e r a - 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 system t o e x t r a c t the a p p r o p r i a t e c l o u d top temperature 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 reasons as poor 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 the s a t e l l i t e VISSR t o scan a n o t h e r s e r i o u s s t o r m s i t u a -t i o n o v e r the U n i t e d S t a t e s ) , and 17 were v i s i b l e images. A l -though the v i s i b l e images c o u l d n o t be used 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 types o f c l o u d s p r e s e n t . 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 g r i d , t h a t i s a u t o m a t i c a l l y superimposed on the image, was s i g n i f i -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 t h e a c t u a l geography. I n t h e s e images the g e o g r a p h i c g r i d was r e - n a v i g a t e d by eye t o c o i n c i d e w i t h i n 20 km o f the o b s e r v e d land-ocean b o u n d a r i e s . The r a i n f a l l was c a l c u l a t e d f o r b o t h T e r r a c e and G o s p e l 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 on 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 from the s a t e l l i t e images. The 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 as bands o f cumulonimbus w i t h i n l a y e r c l o u d s . Both the c l a s s i c a l Norwegian model o f f r o n t s ( B j e r k n e s , 1918; B j e r k n e s and S o l b e r g , 1922) and t h e more r e c e n t mesoscale r a i n b a n d models (Browning et a l . , 1973; H a r r o l d , 1973; House et a l . , 1976; Hobbs and L o c a t e H i , 1978; and M a t e j k a et a l . , 1980) a n t i c i p a t e t h i s c o m b i n a t i o n o f c l o u d s a l o n g an a c t i v e f r o n t a l system. The 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 e r r a c e A i r p o r t and Gospel P o i n t are g i v e n i n T a b l e 6.1 and l i e w i t h i n 12% o f the o b s e r v e d r a i n f a l l t o t a l s . The 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 a r e compared g r a p h i c a l l y w i t h t h e o b s e r v e d c u m u l a t i v e r a i n f a l l s i n F i g u r e 6.3. As can be seen the 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 c u r v e g e n e r a l l y behaves i n the same manner as t h e o b s e r v e d c u m u l a t i v e r a i n f a l l c u r v e . 6.2.3 Comparison o f S t r e a m f l o w And R a i n f a l l Volumes I n a d d i t i o n t o t h e r a i n g a u g e measurements, s t r e a m f l o w r e c o r d s 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 a r e a , i n c l u d i n g the Exchamsiks R i v e r b a s i n , t h e H i r s c h Creek b a s i n , the Zymoetz R i v e r b a s i n , and the Z y m a g o t i t z R i v e r b a s i n , were a v a i l a b l e . I s o h y e t s were c o n s t r u c t e d from the GOES images f o r the p o i n t s shown i n F i g u r e 6.4. From the i s o h y e t s shown i n F i g u r e 6.5 the r a i n f a l l volume o v e r each o f t h e 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 the P e r i o d 0045 GMT on October 31, 1978 t o 2245 GMT on November 1, 1978. STATION OBSERVED RAINFALL (mm) ESTIMATED RAINFALL (mm) DIFFERENCE (mm) (%) e wc g/mc 3 Y °C/1000m T e r r a c e A i r -p o r t 200 180 20 10 0.2 10 5 Gospel P o i n t 250 220 30 12 0.2 10 5 T 1 1 1 : 1 1 r 2 5 0 - 2 0 0 E c o o r 1 5 0 Q. U CD "D <D a 'OO E 3 O o < 5 0 V GOSPEL POINT Est imated rainfall G O S P E L POINT Observed rainfall ,o O O O o ^ A CD A J _ _ T E R R A C E AIRPORT QOO ° Observed r a i n f a l l ,A /O OCD T E R R A C E A I R P O R T Est imated r a i n f a l l 0 -A L 0 6 0 0 1200 1800 0 0 0 0 0 6 0 0 1200 1800 Oct . 3 1 / 7 8 Nov. 1/78 T i m e ( G M T ) 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 a t Gospel P o i n t and T e r r a c e A i r p o r t . 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 E s t i m a t e d I s o h y e t s f o r the October 31, 19 78 Storm. 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 31, 19 78 Storm Based on the 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 Table 6.2 w i t h the r a i n f a l l volume de t e r m i n e d from S c h a e f e r ' s i s o h y e t s ( F i g u r e 6.1), and the r u n -o f f volume r e c o r d e d a t the d i s c h a r g e gauges. The r a i n f a l l vo-lumes e s t i m a t e d from the s a t e l l i t e images compare w e l l w i t h the c o n v e n t i o n a l volume c a l c u l a t i o n s and a r e w i t h i n 20% o f t h e ob-s e r v e d r u n o f f volumes. ( B a s e f l o w was s u b t r a c t e d . ) 6.3 The December 17,19 79 R a i n f a l l E s t i m a t e s The December 17, 1979 stor m was the second major event a n a l y z e d . S i n c e the stor m o c c u r r e d o v e r the southern p o r t i o n s o f B r i t i s h Columbia and A l b e r t a , an a r e a i n which the m a j o r i t y o f the p e o p l e i n these p r o v i n c e s r e s i d e s and hence, where many rai n g a u g e s are l o c a t e d , i t was an a p p r o p r i a t e t e s t o f the a b i l i -t y o f the p r o c e d u r e 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 s t a t i o n s . 6.3.1 Storm D e s c r i p t i o n The s t o r m was the l a s t o f two events t o move i n t o the r e g i o n w i t h i n a 4-day p e r i o d . I n the Lower M a i n l a n d area o f B r i t i s h Columbia, t h e f i r s t s t o r m s a t u r a t e d s o i l s l e a d i n g t o e x t e n s i v e p r o p e r t y damage from f l o o d i n g and m u d s l i d e s e s p e c i a l l y i n P o r t Moody nea r Vancouver. The second s t o r m , t h a t o f December 17, 19 79, added t o the 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 were many r e p o r t s o f f l o o d e d basements and washed o u t roads i n and around Vancouver and V i c t o r i a . F i g u r e 6.6 (from S c h a e f e r , 19 80) shows the combined o b s e r v e d i s o h y e t s f o r the 7-day p e r i o d TABLE 6.2 Comparison of R a i n f a l l and Runoff Volumes i n m x 10 (Baseflow has been subtracted from the streamflow.) B a s i n : Exchamsiks Zymoetz Zymagotitz H i r s ch 2 Area (km ) : 480 2950 350 330 Observed Runoff (%) 116 281* ( % ) 58* W 88 ( % ) R a i n f a l l from Isohyets 121 (4) 388 (38) 65 (12) 81 (8) R a i n f a l l from s a t e l l i t e images 107 (8) 328 (17) 69 (19) 73 (17) Key: % = % D i f f e r e n c e * Included some estimated values 100 FIGURE 6.6 Map o f the Vancouver I s l a n d - Lower 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 the 7-Day P e r i o d from December 12 t o 18, 19 79 ( A f t e r S c h a e f e r , 1980) . 1.01. from December 12 t o December 18, 1979, w h i l e F i g u r e 6.7 shows the a r e a l e x t e n t o f the s t o r m a t 0 715 GMT on December 17, 19 79 as viewed from GOES-West. 6.3.2. R e s u l t s The s a t e l l i t e images f o r December:. 17, 1979 were a n a l y z e d 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 Columbia and 2 s t a t i o n s i n A l b e r t a . The l o c a t i o n s o f t h e s t a t i o n s are shown i n F i g u r e 6.8. S i n c e t h e a n a l y s i s p roceeded i n r e a l t ime as the s t o r m p r o g r e s s e d , a l l o f the s t a t i o n s were assumed 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 the form o f r a i n . Observed h o u r l y r a i n f a l l d a t a was a v a i l a b l e i m m e d i a t e l y f o r o n l y t h r e e 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 A i r p o r t , and Hope A i r p o r t . The a c t u a l t y p e and 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 not known u n t i l some time l a t e r ( a l m o s t 4 months) when the o b s e r v e d d a t a became a v a i l a b l e . Those o t h e r s t a t i o n s w h i c h n o r m a l l y r e p o r t h o u r l y r a i n f a l l amounts were, i n g e n e r a l , r e c e i v i n g snow and hence o n l y 6-hour snow amounts were a v a i l a b l e . The r e m a i n i n g s t a t i o n s r e p o r t e d p r e c i p i t a t i o n on a 6- o r 1 2 - h o u r l y b a s i s . 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 images examined c o v e r e d the 6-hour i n t e r v a l from 00 45 t o 06 45 GMT on December 17, 19 79 . T h i s 6^-hour segment was chosen f o r a number o f r e a s o n s . P r i o r t o 0045 GMT on December 17, 1979, t h e o b s e r v e d r a i n f a l l amounts were n e g l i g i b l e and t h i s was e v i d e n t on the s a t e l l i t e images which r e c o r d e d low FIGURE 6.7 Areal Extent of December 17, 19 79 Storm at 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 Used i n t h e December 17, 1979 Storm A n a l y s i s . 1 B l u e R i v e r 14 P r i n c e George A i r p o r t 2 B u l l Harbour 15 P r i n c e RupertAiitrport 3 Burns Lake 16 Quesnel A i r p o r t 4 C a s t l e g a r A i r p o r t 17 R e v e l s t o k e A i r p o r t 5 Cranbrook A i r p o r t 18 Salmon Arm 6 Dease Lake 19 S a n d s p i t A i r p o r t 7 Hope A i r p o r t 20 T e r r a c e A i r p o r t 8 Kamloops A i r p o r t 21 T o f i n o A i r p o r t 9 Kelowna A i r p o r t 22 Vancouver I n t e r n a t i o n a l 10 Langara A i r p o r t 11 L y t t o n 23 V i c t o r i a I n t e r n a t i o n a l 12 P e h t i c t o n A i r p o r t A i r p o r t 13 P o r t Hardy A i r p o r t 24 W i l l i a m s Lake A i r p o r t 25 B a n f f 26 C a l g a r y 104. c l o u d b u t no ex p a n d i n g deep c o l d c l o u d o v e r t h e r e g i o n . D u r i n g the 6-hour p e r i o d 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-hanced arid as such c o u l d be used d i r e c t l y i n the e s t i m a t i o n p r o c e d u r e , thus e l i m i n a t i n g the u n c e r t a i n t i e s i n t r o d u c e d by u s i n g unenhanced i n f r a r e d images. A f t e r 0 6 45 GMT many o f the i n f r a r e d images were enhanced. I n a d d i t i o n , t h i s 6-hour p e r i o d r o u g h l y c o r r e s p o n d e d t o t h e f i r s t 6 hours o f the c l i m a t o l o g i c a l day and a l l o f t h e s t a t i o n s r e p o r t e d 6-hour r a i n f a l l o r s n o w f a l l (as r a i n f a l l e q u i v a l e n t ) amounts w h i c h c o u l d be used t o compare w i t h the 6-hour c u m u l a t i v e r a i n f a l l e s t i m a t e s . For t h i s segment o f the storm the w a t e r c o n t e n t wc was i n f e r r e d from the TIROS-N d a t a s i n c e i t was r e a d i l y a v a i l a b l e a t the time o f the st o r m and the l a p s e r a t e y was assumed 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 l a p s e r a t e y = 5°C/1000m. F o r 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 A i r p o r t , and Hope A i r p o r t the e f f i c i e n c y e was d e t e r m i n e d u s i n g e q u a t i o n 4.35. I t was assumed t h a t the e f f i c i e n c y e f o r Vancouver I n t e r -n a t i o n a l A i r p o r t was r e p r e s e n t a t i v e o f the e f f i c i e n c i e s a t a l l the o t h e r s t a t i o n s f o r which the o b s e r v e d d a t a was n o t immediate-l y a v a i l a b l e . W i t h these v a l u e s o f the p a r a m e t e r s , the 6-hour 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 and then compared w i t h 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 i n Table 6 . 3 . The p e r c e n t d i f f e r e n c e between the o b s e r v e d 6-hour r a i n f a l l t o t a l and the e s t i m a t e d 6-hour r a i n f a l l t o t a l ranges from 0 t o 2500% w i t h the w o r s t d i f f e r e n c e s found f o r th o s e s t a t i o n s t h a t were l a t e r 105. TABLE 6.3 Comparison o f Observed and Estimated R a i n f a l l T o t a l s f o r the 6-hour Segment 0000 GMT to 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 data was used to c a l i b r a t e the adjustment parameter e. STATION OBSERVED RAINFALL (mm) ESTIMATED RAINFALL (mm) DIFFERENCE (mm) (%) e wc Y (g/m3) (°C/1000m Observed 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 STATION-VANCOUVER I.A. 10.6 VICTORIA I.A. 6.8 HOPE A. 0.0 9.5 6.4 2.5 1.1 0.4 2.5 10 6 0.2 10 0.2 10 0.2 5 Observed P r e c i p i t a t i o n Data Not Immediately A v a i l a b l e ; Blue River 6.2 S 9.1 2 .9 47 0 .2 5 B a l l Harbour 8.9 9.2 0 .3 3 10 Burns Lake M S 5.2 5 Castlegar A. 2.4 S 3.6 1 .2 50 5 Cranbrook A. 1.6 S 3.0 1 .4 88 5 Dease Lake 0.8 S 0.03 0 .7' 7 96 5 Kamloops A. T S 3.2 2 Kelowna A. T S 2.2 _ 2 Langara 0.8 RS 0.2 0 .6 75 13 Lytton 1.6 S 7.8 6 .2 388 2 Penticton A. 0 .0 1.7 1 .7 2 Port Hardy A. 6.8 7.4 0 .6 9 10 Prince George A. 2.0 S 1.5 0 .5 25 10 Prince Rupert A. 8.8 RS 1.0 7 .8 89 13 Quesnel A. 1.3 S 5.2 3 .9 300 2 Revelstoke A. 6 .6 S 7.7 1 .1 17 5 Salmon Arml 1.0 S 7.3 6 .3 6 30 5 Sandspit A. 5.1 S 7.3 2 .2 43 5 5.0 0.3 4 .7 94 13 Terrace A. 1.6 S 0.7 0 .9 56 13 Tofino A. 22.6 15.6 7 .0 31 13 Williams Lake A. 0 .2 S 5.2 5 .0 2500 2 Banff 0 .3 S 2.6 2 .3 767 2 Calgary 0.0 0 .0 0 0 0 2 2 Key: A I.A. M RS A i r p o r t I n t e r n a t i o n a l A i r p o r t Missing mixed r a i n and snow i n mm r a i n equivalent snowfall i n mm of r a i n e q u i v a l e n t two separate observers 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 mixed r a i n and snow. The d i f f i c u l t y i n e s t i m a t i n g s n o w f a l l l i e s i n the b e h a v i o u r o f the s n o w f l a k e s as they f a l l , w i t h t h e i r tendency to d r i f t w i t h the wi n d some d i s t a n c e from 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 the problem o f measuring p o i n t snow a c c u m u l a t i o n . E s t i m a t e s f o r the s t a t i o n s r e c e i v i n g o n l y r a i n were w i t h i n 10% o f the o b s e r v e d 6-hour r a i n f a l l t o t a l e x c e p t f o r S a n d s p i t A i r p o r t w h i c h had a 94% o r 4.7 (mm) d i f f e r e n c e between o b s e r v e d and e s t i m a t e d 6-hour r a i n f a l l t o t a l s . S a n d s p i t A i r p o r t may have been r e c e i v i n g s i g -n i f i c a n t r a i n f a l l from "warm" o r low l e v e l c l o u d s w h i c h had c l o u d t o p t e m p e r a t u r e s warmer than the c o l d e r , s t e p w i s e enhanced, temperature range o f the enhancement scheme used on the 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 a c t u a l e f f i c i e n c i e s f o r each s t a t i o n were then d e t e r m i n e d from the 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. 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 were r e c a l c u l a t e d and are shown i n T a b l e 6.4. The e s t i m a t e s are p l o t t e d w i t h the 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 were de t e r m i n e d u s i n g the computer r o u t i n e s d e v e l o p e d d u r i n g the cou r s e o f the a n a l y s i s o f the f i r s t storm ( t h a t o f O c t o b e r 31, 19 78) . The r o u t i n e s c o n s i d e r a b l y eased the computations s i n c e f o r the 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 images w i t h up t o 41 c e l l s p e r image and on the average o f 2 temperature c o n t o u r s p e r c e l l t o 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 17,1979. F or each s t a t i o n t h e e m p i r i c a l adjustment e has been d e t e r m i n e d u s i n g t h e 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 . STATION OBSERVED RAINFALL ESTIMATED RAINFALL DIFFERENCE (mm) (mm) (mm) (%) (9/m Vancouver I.A 10 .6 9.5 1.1 10 0.2 10 Victoria I.A. 6.8 6.4 0.4 6 0.2 10 Hope A. 0 .0 2 .5 2.5 - 0.2 10 Blue River 6.2 S 9.1 2.9 47 0.2 5 Bull Harbour 8.9 9.2 0.3 3 0 .2 10 Burns Lake M S 5.2 - - 0 .2 5 Castlegar A. 2.4 S 3.6 1.2 50 0 .2 5 Cranbrook A. 1.6 S 3.0 1.4 88 0.2 5 Dease Lake 0.8 s 0.03 0.77 96 0 .2 5 Kamloops A. T S 3.2 - - 0.2 2 Kelowna A. T S 2.2 - - 0.2 2 Langara 0 . 8 RS 0.3 0 .5 63 0 . 3 13 Lytton 1.6 S 7 . 8 6.2 388 0.2 2 Penticton A. 0 .0 1.7 1.7 - 0.2 2 Port Hardy A. 6.8 7.4 0.6 9 0.2 10 Prince George A. 2.0 S 1.5 0.5 25 0 .2 10 Prince Rupert A. 8.8 RS 1.5 7.3 83 0.3 13 Quesnel A. 1.3 s 5.2 3.9 300 0.2 2 Revelstoke A. 6.6 s 7.7 1.1 17 0.2 5 Salmon Arm''" 1.0 S 7.3 6.3 6 30 0 .2 5 5.1 S 7.3 2.2 43 0 .2 5 Sandspit A. 5 .0 0.4 4.6 92 0.3 13 Terrace A. 1.6 S 1.0 0 .6 38 0.3 13 Tofino A. 22.6 23.4 0 . 8 4 0.3 13 Williams Lake A. 0.2 S 5.2 5.0 2500 0.2 2 Banff 0.3 S 1.3 1.0 333 0.1 2 Calgary 0 .0 0.0 0 0 0 .1 2 Key: A I .A. M RS S 1 Airport International Airport Missing Mixed rain and snow in mm rain equivalent Snowfall in mm rain equivalent two separate observers 1 0 8 . 24 T 1 1 1 1 1 1 1 1 1 1 1 1 r 1- L E G E N D « • rain 0 mixed rain and snow y ^ O snow / / 12 e 2 0 r - / / / © / / / / I o . » • i . L x I i I i l_ 4 8 12 16 20 24 28 Estimated Storm Total Precipitation ( mm ) FIGURE 6.9 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 17, 19 79 Storm. (For each s t a t i o n t h e e m p i r i c a l a djustment e has been d e t e r m i n e d from the obser v e d d a t a f o r t h a t s t a t i o n . ) 109. o f w h i c h had t o be m a n i p u l a t e d and "accounted f o r " t o make r a i n f a l l e s t i m a t e s f o r each o f the 26 s t a t i o n s . T h i s w o u l d have been a tremendous t a s k t o do by 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 t h e s p e c i f i e d s t a t i o n s , t h e 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 amounts f o r each c e l l . I n t h i s way a s e r i e s o f s a t e l l i t e p i c t u r e s be-comes a sequence o f c e l l r a i n f a l l "maps", f o r example F i g u r e 6.10, 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 t o the s t o r m . Some c e l l s can be seen t o i n c r e a s e i n s i z e and r e l e a s e r a i n f a l l w h i l e o t h e r s are d e c r e a s i n g and n o t r e l e a s i n g r a i n f a l l . Such sequences o f c e l l r a i n f a l l "maps" ar e u s e f u l f o r t h e o b s e r v a t i o n o f l a r g e s c a l e c l o u d system development and accompanying r a i n f a l l . However, 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 the d e v e l o p i n g s t o r m and the a r e a l d i s t r i b u t i o n o f r a i n f a l l o v e r a s m a l l e r a r e a i s needed. T h i s i s a c c o m p l i s h e d by e s t i m a t i n g t h e r a i n f a l l f o r a g r i d o f p o i n t s and then c o n s t r u c t i n g the i s o h y e t s . As an example, a g r i d o f 150 p o i n t s as shown i n F i g u r e 6.11 c o v e r i n g Vancouver I s l a n d and t h e Lower M a i n l a n d was chosen i n o r d e r 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 o v e r t h i s a r e a f o r the 6-hour p e r i o d between 0045 and 0645 GMT. F i g u r e 6.12 shows t h e e v o l u t i o n o f the i s o h y e t s . FIGURE 6.10 Storm C e l l R a i n f a l l "Maps" f o r 2 Hours D u r i n g the December 17, 19 79 Storm 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 E s t i m a t e d I s o h y e t s f o r t h e December 17, 19 79 Storm. Observed 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 T o f i n o 22.6 Vancouver 10.6 V i c t o r i a 6.8 FIGURE 6.12 E v o l u t i o n of Isohyets o f R a i n f a l l (mm) f o r the December 17, 19 79 Storm Estimated f o r the G r i d P o i n t s Shown i n F i g u r e 6.11. h-1 M The i s o h y e t s shown i n F i g u r e 6.5 by S c h a e f e r (1980) were based on p r e c i p i t a t i o n gauge d a t a and S c h a e f e r ' s knowledge 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 a r e d e r i v e d e n t i r e l y from s a t e l l i t e images. 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 p a t t e r n s . The i s o h y e t s d e r i v e d from th e s a t e l l i t e images show the s h o r t t i m e v a r i a t i o n i n t h 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 due t o changes i n the v e r t i c a l m otions 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 by changes i n t h e t o p s o f the c l o u d s . O r o g r a p h i c e f f e c t s on t h e r a i n f a l l d i s t r i b u t i o n a r e i m p l i c i t l y i n c l u d e d . The i s o h y e t s , d e t e r m i n e d from s u r f a c e d a t a f o r the e n t i r e seven day p e r i o d o f the storm, have had the e f f e c t s o f the topography e x p l i c i t -l y i n c o r p o r a t e d i n t o the r a i n f a l l p a t t e r n . The advantage o f u s i n g s a t e l l i t e images f o r r a i n f a l l e s t i -m a t ion i s t h a t the d i s t r i b u t i o n o f r a i n f a l l o v e r ungauged a r e a s , f o r exmple, the ocean a r e a t o t h e west and the s p a r s e l y p o p u l a t e d mountainous r e g i o n s t o t h e n o r t h e a s t o f Vancouver I s l a n d can be d e t e r m i n e d . The e v o l u t i o n o f the i s o h y e t s can be examined as o f t e n as e v e r y h a l f - h o u r i f n e c e s s a r y , whereas the p r e c i p i t a t i o n gauge i n f o r m a t i o n i s a v a i l a b l e l e s s f r e q u e n t l y . I d e a l l y gauge d a t a and s a t e l l i t e i n f o r m a t i o n s h o u l d be combined - the gauge d a t a 114. p r o v i d i n g i n f o r m a t i o n on the s m a l l s c a l e (<15 km) l o c a l v a r i a -t i o n s i n the r a i n f a l l , and the s a t e l l i t e images p r o v i d i n g the meso- and 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 the r a i n f a l l . 6.4 The June 4, 19 77 R a i n f a l l E s t i m a t e s 6.4.1 Storm D e s c r i p t i o n The June 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 p r o c e d u r e f o r e s t i m a t i n g r a i n f a l l from 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 he p r o c e d u r e on 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 the i n t e r i o r o f B r i -t i s h C olumbia. 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 6.13. R a i n f a l l came from a number o f a c t i v e c e l l s a l o n g a weakening e a s t w a r d moving f r o n t a l system and o b s e r v e d amounts were gener-a l l y 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 h o u r s . F i g u r e 6.14 shows t h e c l o u d coverage f o r 0245 GMT as viewed from GOES-West. As w e l l , f i l m l o o p s c o n t a i n i n g t h e 24-hour s e r i e s o f GOES i n f r a r e d images were a v a i l a b l e 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 the deve-lopment o f the s t o r m . The l o o p s were p r o v i d e d on l o a n from NESS i n Washington, D.C. 6.4.2 R e s u l t s Of the 2 7 a v a i l a b l e GOES images between 0115 and 22 45. GMT, 10 were enhanced i n f r a r e d images, 6 were unenhanced i n f r a r e d images and 11 were v i s i b l e images. The storm posed a s p e c i a l 115. FIGURE 6.13 L o c a t i o n o f S t a t i o n s Used i n the June 4, 1977 Storm A n a l y s i s 1 Duncan Lake Dam 2 R e v e l s t o k e A i r p o r t 3 M i c a Dam 4 C a s t l e g a r A i r p o r t 5 E l k o 6 Cranbrook A i r p o r t 7 B l u e R i v e r FIGURE 6.14 Areal Extent of June 4, 19 77 Storm at 0 245 GMT as Viewed from GOES-West. 117. p r o b l e m i n t h a t two d i f f e r e n t enhancement schemes were employed: 7 o f the enhanced i n f r a r e d images had the "CA" enhancement scheme w h i l e the o t h e r 3 had t h e "EC" enhancement scheme. Co n s e q u e n t l y the 3 "EC" enhanced images a l o n g w i t h the 6 unenhanced images were f i r s t a n a l y z e d w i t h the v i d e o c a m e r a - s p e c i a l e f f e c t s gener-a t o r -video^ m o n i t o r system t o f i n d t h o s e c o n t o u r s t h a t c o r r e s p o n d e d t o t h e "CA" temperature c o n t o u r s , b e f o r e r a i n f a l l e s t i m a t e s c o u l d be made. For t h i s s t o r m , the model parameters e f f i c i e n c y e and w a t e r c o n t e n t wc were chosen from t h e l i t e r a t u r e such t h a t the t o t a l 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 matched f o r Duncan Lake Dam. The l a p s e r a t e y was s e t e q u a l t o the s a t u r a t e d a d i a b a t i c l a p s e r a t e y = 5°C/1000m. The v a l u e s were assumed c o n s t a n t f o r s the o t h e r s t a t i o n s w h i c h i s r e a s o n a b l e g i v e n the s m a l l g e o g r a p h i c a l a r e a i n v o l v e d . Table 6.5 compares the o b s e r v e d and e s t i m a t e d s t o r m r a i n f a l l s f o r t h e seven s t a t i o n s . The e s t i m a t e d r a i n t o -t a l s 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 3 mm o f the o b s e r v e d r a i n t o t a l s . F i g u r e 6.IS shows a p l o t o f the e s t i m a t e d and ob-s e r v e d r a i n t o t a l s . 6.5 The November 20, 1979 R a i n f a l l E s t i m a t e s 6.5.1 Storm D e s c r i p t i o n The November 20, 1979 s t o r m was an ev e n t s u g g e s t e d f o r a n a l y s i s by the P a c i f i c Weather Ce n t r e s i n c e i t r e p r e s e n t e d one o f the u s u a l w i d e s p r e a d f r o n t a l r a i n f a l l e v e n t s w h i c h o c c u r o v e r TABLE 6.5 Comparison of Observed and Estimated R a i n f a l l T o t a l s f o r the Storm of June 4, 19 77. STATION OBSERVED ESTIMATED DIFFERENCE e wc Y RAINFALL RAINFALL 3 , o „ / i n n n _ ^ (mm) (mm) (mm) (%) (g/m ) ( C/1000m) C a l i b r a t i o n S t a t i o n ; Duncan Lake Dam Revelstoke A. Mica Dam C a s t l e g a r A. Elko Cranbrook A. Blue River 8.5 8.4 0.1 1 0 .1 5 3.3 2 .2 1.1 33 0.1 5 >1.7M 2.3 ^0 .6 ^35 0.1 5 8.0 11.2 3.2 40 0.1 5 2.1 2.8 0.7 33 0.1 5 2.1 2.8 0.7 33 0.1 5 3.1 2.5 0.5 19 0.1 5 5 5 5 5 5 5 Key: A. A i r p o r t M Some data m i s s i n g from observed r e c o r d 24 20 16 12 6 U L E G E N D T 1 1 1 1 1 1 i 1 i 1 1 T r a i n C - calibration station / 4* c/ / • • / / / / /* \L . I i I i I i I i I . I . I 4 8 12 16 20 24 28 Estimated Storm Total Precipitation ( m m ) FIGURE 6 . 15 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 t h e June 4, 19 77 Storm. 120. the P r i n c e R u p e r t a r e a o f B r i t i s h Columbia. The P a c i f i c Weather C e n t r e was i n t e r e s t e d i n d e t e r m i n i n g whether o r not the e s t i m a t i o n p r o c e d u r e c o u l d d i s t i n g u i s h d i f f e r e n c e s i n r a i n -f a l l from t h i s system a t two a d j a c e n t s t a t i o n s : P r i n c e R u p e r t and T e r r a c e . F i g u r e 6>-16 shows the a r e a l coverage o f t h e s t o r m a t 1115 GMT as viewed from GOES-West. The storm p r o v i d e d an a d d i t i o n a l check o f t h e 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 under more normal c o n d i t i o n s . 6.5.2 R e s u l t s Of the 26 p o s s i b l e GOES images i n the r a i n f a l l p e r i o d from 0145 t o 1415 GMT, 12 were enhanced i n f r a r e d images, 8 were un-enhanced i n f r a r e d images w h i c h had 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 c a m e r a - 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 system p r i o r t o a n a l y s i s , and 6 were n o t a v a i l a b l e . The w a t e r c o n t e n t was i n f e r r e d from TIROS-N d a t a and t h e 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 l a p s e r a t e Y = 5°C/1000m. The e f f i c i e n c y e was d e t e r m i n e d from e q u a t i o n 4.35 s u s i n g the f i r s t 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 Rupert as the c a l i b r a t i o n . T h i s v a l u e o f e was assumed c o n s t a n t a t P r i n c e Rupert f o r the remainder o f the s t o r m , and was assumed t o a p p l y t o T e r r a c e f o r the e n t i r e s t o r m . T a b l e 6.6 compares the 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 t o t a l s . The e s t i m a t e d r a i n f a l l was w i t h i n 11% o r 4 mm o f the o b s e r v e d r a i n f a l l . The e s t i m a t i o n p r o c e d u r e was a b l e t o d i s t i n g u i s h t h e d i f f e r e n c e between the r a i n f a l l r e c e i v e d a t P r i n c e Rupert on the c o a s t and T e r r a c e some 130 km i n l a n d . FIGURE 6.16 Areal Extent of November 20, 1979 Storm at 1115 GMT as Viewed from GOES-West. TABLE 6.6 Comparison of Observed and Estimated R a i n f a l l T o t a l s f o r the Storm of November 20, 1979 STATION OBSERVED RAINFALL (mm) ESTIMATED RAINFALL (mm) DIFFERENCE (mm) (%) e wc (g/m3) Y (°C/1000m) C a l i b r a t i o n S t a t i o n : P r i n c e Rupert A. 64.0 59 .0 5 .0 8 0.1 7 5 Terrace A. 36 .4 40 .2 3.8 10 0.1 7 5 Key: A A i r p o r t 123. 6.6 The December 5, 1979 R a i n f a l l E s t i m a t e s 6.6.1 Storm D e s c r i p t i o n The a n a l y s i s o f the December 5, 1979 s t o r m was a l s o s u g g e s t e d by t h e P a c i f i c Weather Centre s i n c e they e x p e r i e n c e d l e s s t h a n 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 t o p o o r i n i t i a l -i z a t i o n " o f the n u m e r i c a l a n a l y s e s they r e c e i v e d . The f o r e c a s t s u n s h i n e f o r t h e Lower M a i n l a n d o f B r i t i s h Columbia was r e p l a c e d by r a i n from a narrow band o f c l o u d c l e a r l y v i s i b l e on the s a t e l -l i t e images. The o b s e r v e d p r e c i p i t a t i o n ranged from a t r a c e a t 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 a t New W e s t m i n s t e r . F i g u r e -6.17 shows the GOES-West s a t e l l i t e 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 check o f the p r o c e d u r e o v e r a w e l l - g a u g e d a r e a (such as Vancouver) . 6.6.2 R e s u l t s Of the 46 p o s s i b l e GOES images f o r the p e r i o d 0015 t o 2 315 GMT, 14 were enhanced i n f r a r e d images, 14 were unenhanced i n f r a -r e d images wh i c h had t o be f i r s t p r o c e s s e d t h r o u g h the v i d e o c a m e r a - 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 system, 4 were v i s i b l e images and 14 were m i s s i n g . The w a t e r c o n t e n t wc was i n f e r r e d from the TIROS-N d a t a and the l a p s e r a t e y was s e t e q u a l t o the s a t u r a t e d a d i a b a t i c 124. FIGURE 6.17 Areal Extent of December 5, 19 79 Storm at 1015 GMT as Viewed from GOES-West. l a p s e r a t e y = 5°C/1000m. The e f f i c i e n c y e was d e t e r m i n e d s from e q u a t i o n 4.35 u s i n g t h e f i r s t 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 Vancouver 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 . T h i s v a l u e f o r e was assumed c o n s t a n t a t Vancouver I n t e r n a t i o n a l A i r -p o r t f o r the remainder o f t h e s t o r m , and was assumed t o a p p l y a t the o t h e r s t a t i o n s f o r the e n t i r e s t o r m . T a b l e 6.7 compares the 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 the s t a t i o n s a n a l -yzed" E x c e p t f o r the West Vancouver gauge, the comparison be-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 shows the 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 West Vancouver, t h e e s t i m a t e d r a i n f a l l i s 73% (9.5 mm) below the o b s e r v e d r a i n f a l l . T h i s may be due t o the l o c a l o r o g r a p h i c l i f t i n g and s u g g e s t s the e f f i c i e n c y a t West Van-couver was u n d e r e s t i m a t e d by u s i n g e d e t e r m i n e d from the Vancouver I n t e r n a t i o n a l A i r p o r t gauge. F i g u r e 6.18 i s a p l o t o f the ob-s e r v e d r a i n f a l l t o t a l s a g a i n s t 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 t o t a l s . 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 a n o t h e r i m p o r t a n t a s p e c t : s a t e l l i t e images o f t e n c l e a r l y d e f i n e r a i n f a l l o c c u r r e n c e s which are not : s u g g e s t e d by the n u m e r i c a l a n a l y s e s e i t h e r because o f the n e c e s s a r i l y c o a r s e g r i d used by the n u m e r i c a l models o r because o f problems i n a d e q u a t e l y and a c c u r a t e l y i n i t i a l i z i n g the models. I t i s t r u e t h a t t h e numeri-c a l 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 and t h a t f o r e -c a s t i n g from s a t e l l i t e images i s s t i l l a d i f f i c u l t t a s k ; however, s i n c e t h e s a t e l l i t e images do r e c o r d what c l o u d systems are a c t u a l -l y p r e s e n t o v e r an a r e a , they 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 " the r a i n f a l l from t h e s e c l o u d s . TABLE 6.7 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 the Storm o f December 5 , 19 79 . STATION OBSERVED RAINFALL (mm) ESTIMATED RAINFALL (mm) DIFFERENCE (mm) (%) e wc (9 /m3 Y )(°C/1000m) Calibration Station: Vancouver I.A. 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 Victoria I.A. T 0 — — 0.1 10 5 Key: I.A. International Airport M observation missing T trace 127. 24 20 ° 16 I 2 8 L LEGEND rain C - calibration station 4 s ° c / / / / L j L _1_ 4 8 12 16 20 Estimated Storm Total Precipitation (mm ) 24 28 FIGURE 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 t h e December 5, 19 79 Storm. 128. 6 . 7 Comparison 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  A l l Storms F i g u r e 6.19 i s a comparison o f the o b s e r v e d and e s t i m a t e d s t o r m t o t a l p r e c i p i t a t i o n s f o r a l l f i v e t e s t s t o r m s . The dashed c u r v e 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 s t o r m t o t a l p r e c i p i t a t i o n w i t h t h e o b s e r v e d s t o r m 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 o f the p o i n t s about t h i s l i n e , 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 the GOES s a t e l l i t e 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 g e n e r a l l y p e r forms w e l l 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 e v e n ts as w e l l as the 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 e v e n ts over B r i t i s h C olumbia. 24 20 16 12 8 I— L E G E N D ! • rain / (D mixed rain and snow O snow y C - calibration stations / S - values scaled by * 4*S / / c / V / © c • / o 9 0 f y t ' o • I » i i I i I i I ' l l 4 8 12 16 20 24 28 Estimated Storm Total Precipitat ion ( mm ) FIGURE 6.19 Estimated and Observed P r e c i p i t a t i o n for A l l Five Test Storms. 1-30. CHAPTER V I I AN UPDATING PROCEDURE USING OBSERVED DATA The comparisons 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 s f o r the t e s t storms d i s c u s s e d i n Chapter VI show good agreement, a l t h o u g h t h e r e i s some u n c e r t a i n t y and i n a c c u r a c y i n 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 e s w h i c h may be due t o the form o f the phys-i c a l - c o n c e p t u a l model used t o d e s c r i b e the r a i n f a l l p r o c e s s , t o t h e d e t e r m i n a t i o n o f t h e parameters used i n the model, and t o the i n h e r e n t l y random n a t u r e o f t h e r a i n f a l l p r o c e s s i t s e l f . 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 been acknowledged and a c c o u n t e d f o r i n the e m p i r i c a l a d j u stment f a c t o r e. However, 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 e can be f u r t h e r improved by 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 c o n t a i n e d i n the o b s e r v e d r a i n f a l l d a t a t h r o u g h the use o f an u p d a t i n g p r o c e d u r e . I n e f f e c t t h i s means t r e a t i n g the s e r i e s o f s a t e l l i t e e s t i m a t e s as a " s i g n a l " . There a r e many u p d a t i n g p r o c e d u r e s a v a i l a b l e a t v a r i o u s l e v e l s o f s o p h i s t i c a t i o n . However, the more s o p h i s t i c a t e d methods, such as Kalman f i l t e r i n g (Kalman, I 9 6 0 . ) , t e n d t o have r e s t r i c -t i v e assumptions 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 char-a c t e r i s t i c s . F o r the p r e s e n t e x p l o r a t o r y phase o f the s t u d y , v e r y s i m p l e p r o c e d u r e s seemed most a p p r o p r i a t e . 7.1 The U p d a t i n g Model On the assumption t h a t 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 e s are r e a s o n a b l y 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 amounts ( i n -131. s p i t e o f t h e u n c e r t a i n t i e s n o t e d a b o v e ) t h e n o n e o f t h e m o s t s t r a i g h t f o r w a r d p r o c e d u r e s f o r u p d a t i n g s u c h an e s t i m a t e d s e r i e s i n t h e l i g h t o f o b s e r v e d d a t a i s t o u s e a r e g r e s s i o n o f t h e f o r m y=a+bx 7 . 1 w h e r e y i s t h e " t r u e " r a i n f a l l , a s s u m e d t o b e e x a c t l y r e p r e s e n t e d b y t h e o b s e r v e d r a i n f a l l , a n d x i s t h e s a t e l l i t e e s t i m a t e o f t h a t r a i n f a l l . A t a n y p o i n t i n t i m e t h e u n k n o w n p a r a m e t e r s , a a n d b , c a n b e c o m p u t e d f r o m t h e a v a i l a b l e d a t e up t o t h a t t i m e b y t h e l e a s t s q u a r e d m e t h o d , t h a t i s , a = y - b x 7 . 2 n . y . - n x y b= 7 . 3 j S c , 2 - n<5)2 w h e r e x i s t h e a v e r a g e o f t h e e s t i m a t e d r a i n f a l l v a l u e s _ _ x . , ( x = V x . / n ) , a n d y i s t h e a v e r a g e o f t h e o b s e r v e d ( o r " t r u e " ) r a i n f a l l v a l u e s y ^ , (y = ^^y.j_/n) . V a l u e s f o r a a n d b c a n b e I r e c a l c u l a t e d w i t h t h e a c q u i s i t i o n o f e a c h new p a i r o f o b s e r v e d (y^) a n d e s t i m a t e d (x^) r a i n f a l l s . T h e r e d e t e r m i n e d v a l u e s o f a a n d b c a n t h e n b e u s e d t o u p d a t e t h e 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 u n t i l a n o t h e r 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 p a i r o f v a l u e s i s a v a i l a b l e . F o r example, c o n s i d e r the f o l l o w i n g : S t a t i o n A r e p o r t s r a i n f a l l e v e r y 6 h o u r s , and s a t e l l i t e images are used t o make e s t i m a t e s o f the r a i n f a l l a t t h i s s t a t i o n as w e l l as f o r a number of o t h e r ungauged l o c a t i o n s w i t h i n the b a s i n . W i t h e q u a t i o n 7.1 t h e s a t e l l i t e e s t i m a t e s a t S t a t i o n A can be " c o r -r e c t e d " o r a d j u s t e d as the o b s e r v e d d a t a i s r e c e i v e d . That i s , the parameters a and b are r e c a l c u l a t e d once e v e r y 6 hours and do n o t change i n v a l u e u n t i l t he new o b s e r v a t i o n s are i n c o r p o -r a t e d . I n t h i s way the e s t i m a t e s o f p r e c i p i t a t i o n do n o t d r i f t f a r from t h e " t r u e " , o b s e r v e d p r e c i p i t a t i o n because o f the u n c e r -t a i n t i e s i n the e s t i m a t i o n model. The u p d a t i n g model i n e q u a t i o n 7.1 g i v e s e q u a l emphasis t o each p a i r o f o b s e r v e d and e s t i m a t e d d a t a used t o determine t h e parameters a and b. T h i s means t h a t e s t i m a t e s and o b s e r v a -t i o n s from the e a r l y p a r t o f t h e s t o r m have as much e f f e c t on a and b as the l a t e s t ones. I n p r a c t i c e , however, the 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 the p a i r s by W^ , t h e emphasis o f t h e u p d a t i n g model i s s h i f t e d towards the l a t e s t p a i r s , w i t h a and b now g i v e n by 133. a = Wy - bWx 7.4 n ^ ] w^ 2x^y^ ~ nWxWy b = 7.5 n . x . ) 2 - n ( W x ) 2 ^ (W  The weights must s a t i s f y the condition: W > W. , 7.6 i i - l There are a number of ways to choose so that t h i s i s f u l -f i l l e d . For example, weights of the form W. = W 1 ( n' i ) 7.7 x 1 s a t i s f y 7.6, where i s a user s p e c i f i e d parameter chosen usually to r e f l e c t the actual interdependence of previous r a i n -f a l l s on the present r a i n f a l l , n i s the t o t a l number of observed-estimated r a i n f a l l pairs i n t h i s r a i n f a l l event up to the present, and i i s the i - t h consecutive one of these p a i r s . These weights are plotted for n=50 and various values of i n Figure 7.1. 7.2 Comparison of Updated and Observed R a i n f a l l As a sample of what the updating can do, two of the f i v e test storms analyzed i n Chapter VI were chosen to be updated. FIGURE 7.1 (n—i) The Behaviour of the Weights W^  = W^  f o r n=50 and 3 values of W,. 135. These were the two major storms o f October 31, 19 78 and Decem-b e r 17, 19 79. The f i r s t , O c t o b e r 31, 1978, was chosen because o f the 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 such c o u l d s e r v e as a t e s t o f the u p d a t i n g p r o c e d u r e on a l o n g s e r i e s . The second s t o r m , December 17, 1979, was chosen as a t e s t o f the p r o c e d u r e f o r u p d a t i n g r a i n f a l l a t a number o f s t a t i o n s w i t h i n a c e r t a i n g e o g r a p h i c a r e a . The t h r e e l e s s e r storms were n o t t e s t e d because t h e i r d u r a t i o n , i n g e n e r a l , was too 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 the u p d a t i n g model p a r a m e t e r s , a and b. 7.2.1 Updated October 31, 19 78 R a i n f a l l E s t i m a t e s 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 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 w i t h a and b d e f i n e d by e q u a t i o n s 7.4 and 7.5. The form o f the w e i g h t s was as g i v e n by e q u a t i o n 7.7, w i t h W^=0.8. T h i s v a l u e f o r W^  was chosen because as can be seen i n F i g u r e 7.1, the w e i g h t s W. drop o f f r a p i d l y p r e v i o u s t o W. „. I n most o f the storms examined 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 r a r e l y l a s t e d l o n g e r than 2 h o u r s , e x c e p t f o r the v e r y l a r g e s t ones and hence any e f f e c t o f r a i n f a l l more th a n two hours p r e v i o u s on p r e s e n t r a i n f a l l i s l i k e l y q u i t e i n s i g n i f i c a n t . S i n c e t h e GOES-West s a t e l l i t e images are r e c e i v e d a t 15 minutes t o t h e hour and 15 minutes a f t e r the hour ( t h a t i s , 0015, 0045, 0115, 0145 GMT, e t c . ) , and t h e o b s e r v e d r a i n f a l l i s r e p o r t e d on t h e h o u r , i t was assumed t h a t the r a i n f a l l e s t i -136. mated f o r the one hour p e r i o d e n d i n g w i t h the s a t e l l i t e image which was r e c e i v e d a t 15 minutes p a s t the hour c o r r e s p o n d e d t o the o b s e r v e d r a i n f a l l r e p o r t e d f o r t h e hour e n d i n g 15 minutes e a r l i e r . 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 d i s c r e -pency i n the u p d a t i n g p r o c e d u r e , and i s the o n l y means o f p e r -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 images. T h i s time s h i f t i s n o t a problem w i t h the GOES-East images r e c e i v e d on the e a s t c o a s t o f the c o n t i n e n t , s i n c e they a r e r e c e i v e d on t h e hour and h a l f - h o u r ( t h a t i s , 0000 , 0030 , 0100 GMT, e t c . ) . The e s t i m a t e d r a i n f a l l s were updated s e q u e n t i a l l y and t h e n summed t o a r r i v e a t t h e accumulated updated r a i n f a l l e s t i -mates shown i n F i g u r e 7.2. The u p d a t i n g p r o c e d u r e does improve the f i t o f 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 t o the o b s e r v e d r a i n -f a l l . The v a r i a t i o n o f t h e parameters a and b i s g i v e n i n T a b l e 7.1. The change i n a and b may i n d i c a t e t h a t some o r a l l , o f the r a i n f a l l e s t i m a t i o n model parameters ( e f f i c i e n c y e, w a t e r c o n t e n t w c , and the l a p s e r a t e y) v a r y i n time as t h e c l o u d system e v o l v e s and moves. Whether o r n o t t h i s i s so remains a problem t o be i n v e s t i g a t e d . The a b i l i t y t o update sequences has a n o t h e r use b e s i d e s i m p r o v i n g the f i t o f e s t i m a t e d r a i n f a l l f o r s t a t i o n s w i t h ob-s e r v e d d a t a . S i n c e t h e s a t e l l i t e images a l l o w r a i n f a l l t o be e s t i m a t e d f o r a g r i d o f p o s i t i o n s t h r o u g h o u t a b a s i n , t h e n i t 137. 2 5 0 h - 2 0 0 r 1 5 0 5 1 0 0 5 0 0 G O S P E L P O I N T -O b s e r v e d r a i n f a l l G O S P E L P O I N T E s t i m a t e d ra in fa l l f O o'oo T E R R A C E A I R P O R T O O b s e r v e d ra i n f a II A T E R R A C E A I R P O R T X ^ E s t i m a t e d r a i n f a l l ^ a / 0 6 0 0 1200 1800 0 0 0 0 0 6 0 0 1200 Oct. 3 1 / 7 8 Nov. 1/78 T i m e ( G M T ) 8 0 0 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 Go s p e l 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 Each S t a t i o n a r e Giv e n i n Tabl e 7.1. (W^ = 0 .8) . TABLE 7.1 Variation of a and b for Terrace Airport and Gospel Point as the l a s t 25 Pairs of Observed and Estimated R a i n f a l l s are Added Sequentially to the Updating Procedure Number of Terrace Airport Gospel Point Pairs i a b a b • • • 26 • • • 0 .29 • • • 1.07 • • • 0 .00 • • • 1.27 27 0.28 1.02 -0 .01 1.23 28 0 .16 1.02 -0 .01 1.19 29 0.04 1.03 0 .001 1.15 30 -0 .02 1.04 0.002 1.15 31 0 .01 1.04 0 .00 1.14 32 -0 .01 1.04 -0 .001 1.14 33 0 .10 1.00 -0 .002 1.15 34 0.03 1.01 -0 .001 1.15 35 0 .15 0.96 -0 .01 1.13 36 0 .12 0.94 -0.03 1.08 37 0 .07 0.94 -0 .02 1.02 38 -0 .001 0.95 -0.01 0 .97 39 0 .05 0.94 -0 .01 0 .94 40 -0.05 0.96 -0 .004 0.92 41 -0 .11 0 .99 -0 .001 0.91 42 -0.01 0 .98 -0 .004 0.91 43 0.03 0.96 -0 .002 0.90 44 -0.10' 1.01 -0 .003 0 .89 45 -0 .09 1.02 -0 .002 0 .89 46 -0 .15 1.06 -0 .003 0 .89 47 -0.15 1.09 -0 .004 0.91 48 -0 .09 1.10 -0.01 0.94 49 -0.10 1.12 -0 .02 1.03 50 -0.17 1.17 -0 .01 1.03 139. i s r e a s o n a b l e t h a t the e s t i m a t e s a t the s e p o i n t s can be updated by u s i n g t h e v a l u e s o f the u p d a t i n g model parameters a and b as de t e r m i n e d from the o b s e r v e d d a t a . F i g u r e 7.3 shows a h y p o t h e t -i c a l . c a s e . The same approach was used t o update the r a i n f a l l f o r G o s p e l P o i n t d u r i n g t h e October 31, 1979 s t o r m , and f o r the Vancouver a r e a d u r i n g the December 17, 1979 s t o r m d i s c u s s e d i n the n e x t s e c t i o n . The v a l u e s o f a and b f o r T e r r a c e A i r p o r t , g i v e n i n Table 7.1, were used t o update t h e G o s p e l P o i n t s a t e l -l i t e 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 the " t r u e " (observed) r a i n f a l l i n F i g u r e 7.4. The e f f e c t o f the u p d a t i n g i s as s a t i s -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 e s t i m a t e s w i t h Gospel P o i n t o b s e r v e d d a t a . T h i s s u g g e s t s t h a t f o r t h e October 31, 19 79 st o r m , the t r a n s f e r r i n g o f the u p d a t i n g parameters a and b from T e r r a c e A i r p o r t t o Go s p e l P o i n t i s b o t h f e a s i b l e and w o r t h w h i l e . 7.2.2. The Updated December 17, 1979 R a i n f a l l E s t i m a t e s 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 v a l u e s 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 were up-d a t e d u s i n g the model ( e q u a t i o n 7.1) w i t h a and b d e f i n e d by e q u a t i o n s 7.4 and 7.5. A g a i n the form o f the w e i g h t s was t h a t g i v e n by e q u a t i o n 7.7 w i t h W^O.8. As f o r the October 31/ 19 78 st o r m , the e s t i m a t e d r a i n f a l l s were updated s e q u e n t i a l l y and then summed t o y i e l d c u m u l a t i v e updated 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 . S i n c e the purpose o f u s i n g the December 17, 1979 s t o r m was t o t e s t the p r o c e d u r e f o r u p d a t i n g e s t i m a t e d r a i n f a l l a t a 140. FIGURE 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) where the 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 where o n l y one o f the s t a t i o n s (A) has a r a i n g a u g e . S a t e l l i t e e s t i m a t e s o f r a i n f a l l a r e a v a i l a b l e f o r a l l 4 s t a t i o n s t h r o u g h o u t the d u r a t i o n o f t h e s t o r m . By u p d a t i n g the e s t i m a t e d s e r i e s f o r A w i t h t h e o b s e r v e d d a t a measured t h e r e , v a l u e s o f a and b can 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 used t o update 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). number o f s t a t i o n s and g r i d p o i n t s shown i n F i g u r e 6.8'.', most o f which l a c k h o u r l y o b s e r v a t i o n s b u t some o f which do have 6-hour p r e c i p i t a t i o n t o t a l s , the parameters a and b f o r t h e two s t a t i o n s w i t h h o u r l y o b s e r v a t i o n s (Vancouver and V i c t o r i a ) were compared i n T a b l e 7.2 t o a s c e r t a i n t o what e x t e n t they were d i f f e r e n t . S u b j e c t i v e l y t h e r e was l i t t l e d i f f e r e n c e ; t h e r e f o r e , the u p d a t i n g model parameters a,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 were assumed t o be r e p r e s e n t a t i v e o v e r the e n t i r e a r e a and were used t o update the o t h e r s t a t i o n s i n the a r e a as w e l l as t h e 150 g r i d p o i n t s used t o c o n s t r u c t the i s o h y e t s i n F i g u r e 6.12. The e v o l u t i o n o f the updated i s o h y e t s i s shown i n F i g u r e 7.5. 7.3 L i m i t a t i o n s on T r a n s f e r r i n g a And b The u p d a t i n g model parameters a and b may v e r y depending on s t a t i o n l o c a t i o n , t e r r a i n , and t y pe o f s torm. A l t h o u g h i t i s beyond the scope o f t h i s r e s e a r c h t o i n v e s t i g a t e the n a t u r e o f t h i s v a r i a b i l i t y , some guidelines f o r t r a n s f e r r i n g a and b from a gauged l o c a t i o n t o an ungauged one f o r u p d a t i n g purposes are mentioned. The parameters a and b can be t r a n s f e r r e d i f the un-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 t h e same c l o u d system as t h e gauged s t a t i o n , i f b o t h gauged and ungauged s t a t i o n s l i e w i t h i n the same m e t e o r o l o g i c a l and t o p o g r a p h i c a l r e g i o n , o r i f from p r o f e s s i o n a l e x p e r i e n c e , th e gauged and ungauged s t a t i o n s are b e l i e v e d t o behave s i m i l a r l y g i v e n i d e n t i c a l c o n d i t i o n s even though they may be i n d i f f e r e n t r e g i o n s o r be r e c e i v i n g r a i n f a l l from d i f f e r e n t c l o u d systems. I f i t i s found from i n v e s t i g a t i n g TABLE 7.2 Comparison of 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 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 the Storm of December 17, 19 79 No of p a i r s i a Vancouver I.A. V i c t o r i a I.A. b Vancouver I.A. V i c t o r i a I.A. 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 .ft. 143. 0 6 0 0 1200 1800 0 0 0 0 0 6 0 0 1200 1800 Oc t . 3 1 / 7 8 N o v . 1 / 7 8 T i m e ( G M T ) FIGURE 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 G o s p e l 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 case 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 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 17, 19 79 Storm Updated 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 the G r i d P o i n t Shown i n F i g u r e 6.11. a and b that they are f a i r l y constant from storm to storm for a p a r t i c u l a r region then updating short duration (0.5 to 2 hour) r a i n f a l l events over that region would be greatly f a c i l i t a t e d , as well as updating half-hourly r a i n f a l l estimates for gauged locations i n that .region which report on a less frequent basis, say once every 6 or 12 hours. 7.4 Summary The need f o r a method for incorporating observed data into the s a t e l l i t e estimate of r a i n f a l l was discussed and a very simple weighted regression type model, requiring only one para-meter to be provided by the user, was presented. The model was used to successfully update the estimated r a i n f a l l s for the October 31, 19 78 and December 17, 19 79 storms. 1 4 6 . CHAPTER V I I I SUMMARY AND CONCLUSIONS The development and 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 a c h ievements, such as the 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, whic h p r o m i s e t o p r o v i d e more, i n e x p e n s i v e d a t a on an a r e a l s c a l e and f r e q u e n c y o f coverage w h i c h can n e v e r be a c h i e v e d by groundbased d a t a c o l l e c t i o n s ystems. The s u c c e s s f u l work of p r e v i o u s i n v e s t i g a t o r s ( S c o f i e l d and O l i v e r , 19 77a; G r i f f i t h et a l . , 1978; and S t o u t et al., 1 9 7 9 ) , r e l a t i n g the growth o f c o n v e c t i v e c l o u d tops as seen i n the GOES s a t e l l i t e images t o the 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 , s u g g e s t e d 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 t y p e s o f storms i n n o r t h e r n l a t i t u d e s . However, i t was n e c e s s a r y t o d e v e l o p a 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 the 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 t h e c l o u d . B e f o r e t h e concept c o u l d be e x t e n d e d t o the e s t i m a t i o n o f r a i n f a l l from the t y p e s o f storms commonly o c c u r r i n g i n the h i g h e r l a t i t u d e s *, something w h i c h had n o t 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 from GOES s a t e l l i t e images was d e v e l o p e d and t e s t e d on a number o f major and minor f r o n t a l storms w h i c h p a s s e d o v e r B r i t i s h C olumbia. C o n s i d e r i n g the q u a l i t y and c o n s i s t e n c y o f the GOES-West images r e c e i v e d by the P a c i f i c Weather C e n t r e , t h e r e s u l t s were rem a r k a b l e and i n d i c a t e d the f e a s i b i l i t y o f the approach as an o p e r a t i o n a l t o o l / F u r t h e r t e s t s showed t h a t t h e a c c u r a c y o f the p r e c i p i t a -t i o n e s t i m a t e s c o u l d be improved through the use o f an u p d a t i n g p r o c e d u r e w h i c h i n c o r p o r a t e d the i n f o r m a t i o n o b t a i n e d from ground measurements. To f a c i l i t a t e t h e a p p l i c a t i o n o f the model, com-p u t e r r o u t i n e s were d e v e l o p e d t o p e r f o r m the numerous a c c o u n t i n g s t e p s 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 r a i n -f a l l f rom s a t e l l i t e images. The 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 e s t i m a t e s c o u l d be much b e t t e r i f the u s e r had a c c e s s t o a d e d i c a t e d GOES s a t e l -l i t e r e c e i v i n g s t a t i o n (such as the one pr o p o s e d f o r the Vancouver 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 enhancement scheme, one whi c h d i s t i n g u i s h e s the temper-a t u r e g r a d i e n t s a t t h e to p s o f warmer c l o u d t o p s . T h i s c a p a b i l -i t y w o u l d be p a r t i c u l a r l y u s e f u l i n a n a l y z i n g t h o s e weather systems o v e r B r i t i s h Columbia w h i c h a r e n o t s u f f i c i e n t l y w e l l d e v e l o p e d v e r t i c a l l y t o be app a r e n t on the enhanced i n f r a r e d 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 , low i n t e n s i t y p r e c i p i t a t i o n . F u r t h e r use o f t h i s t e c h n i q u e on an o p e r a t i o n a l b a s i s by bot h 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 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 s t u d y r e v e a l e d t h a t GOES s a t e l l i t e images a r e w e l l - s u i t e d as an a l t e r n a t e o r s u p p l e -mentary s o u r c e 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 the s p a t i a l d i s -1 4 8 . t r i b u t i o n o f r a i n f a l l . I t s advantages 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 , a re i t s f r e q u e n c y o f coverage (day and n i g h t ) , i t s l a r g e a r e a l c overage, and i t s c o s t i n comparison w i t h ground n e t w o r k s . I t s l i m i t a t i o n s are few: t h e r e s o l u t i o n o f the VISSR (1 km i n the v i s i b l e and 8 km i n t h e i n f r a r e d a t t h e s a t e l l i t e s u b - p o i n t ) means t h a t i n d i v i d u a l c l o u d elements s m a l l e r t h a n the r e s o l u t i o n o f the s e n s o r cannot be d i s t i n g u i s h e d . B u t i t i s w o r t h n o t i n g t h a t c l o u d systems o f t h i s s m a l l a s c a l e r a r e l y produce major r a i n s o v e r a b a s i n , and t h a t even e s t i m a t e s o f r a i n f a l l from o n l y the l a r g e (>8 km) systems i n remote areas 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 about the r a i n f a l l d i s t r i b u t i o n t h e r e . T h i s s t u d y has shown t h a t the GOES s a t e l l i t e i n f r a r e d images, when used w i t h a sound p h y s i c a l l y b a sed 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 , can p r o v i d e a c c e p t a b l e e s t i m a t e s 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 n o n - t r o p i c a l n a t u r e . Such 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 e c o n o m i c a l and f r e q u e n t e s t i m a t e s o f r a i n f a l l i n h i g h e r l a t i t u d e s . I n areas where t h e c o n v e n t i o n a l r a i n g a u g e networks are s p a r s e i t p r o v i d e s a r e a -d e p t h - d u r a t i o n i n f o r m a t i o n v i t a l t o water r e s o u r c e s d e s i g n and management a c t i v i t i e s w h i c h would be o t h e r w i s e u n o b t a i n a b l e . 8.1 F u t u r e D i r e c t i o n s I n t h e o r y , t h e t r a n s i t i o n from u s i n g t h i s p r o c e d u r e w i t h hardcopy images t o u s i n g i t w i t h d i g i t a l images ought t o be 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 e s t i m a t i o n p r o c e d u r e . The major d i f f i c u l t y w o u l d be the p r o -blem 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 and t r a c k i n g o f the many i n d i v i d u a l c e l l s w hich make up a p a r t i c u l a r s t o r m . I t i s more l i k e l y 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 the 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 c e l l s 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 -cedures become a v a i l a b l e . F o r the development and i n i t i a l t e s t i n g o f 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 use the h a r d -copy images because o f t h e i r a v a i l a b i l i t y and f o r t h e i r v i s u a l 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 weather c o n d i t i o n s . T h i s was an a c c e p t a b l e approach d u r i n g the r e s e a r c h phase. However, c u r r e n t computer d i g i t a l image d i s p l a y systems, such 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 umbia, a l r e a d y are c a p a b l e o f d i s p l a y i n g the image on a s c r e e n , e n h a n c i n g the i n f r a r e d images 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 a r e a i n f o r m a t i o n f o r each t e m p e r a t u r e c o n t o u r d i -r e c t l y from the d i g i t a l image d a t a a f t e r t h e sto 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 . T h i s i n f o r m a t i o n c o u l d then be f e d d i r e c t l y t o the r a i n f a l l e s t i m a t i o n r o u t i n e s d e v e l o p e d d u r i n g t h e course o f t h i s s t u d y thus e l i m i n a t i n g 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 c o n t o u r . I n the immediate f u t u r e the p r o c e d u r e d e v e l o p e d here h o l d s t h e promise o f i m p r o v i n g s h o r t - t e r m f o r e c a s t s o f s e v e r e weather 150. e v e n t s o v e r 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 of a s t o r m as w e l l as i t s r a t e and s t a g e o f d e v e l o p -ment, t i m i n g the approximate a r r i v a l o f the s t o r m o v e r a p a r -t i c u l a r r e g i o n can be i m m e d i a t e l y e s t i m a t e d from 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 the b e h a v i o u r and l i f e e x p e ctancy o f s t o r m c e l l s , 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 images f o r r a i n -f a l l , 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 the o r d e r o f a few hours) t h e p r o b a b l e r a i n f a l l t h a t might be r e c e i v e d from a p a r t i c u l a r s y s t e m . P r o p o s e d 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 the P a c i f i c Weather C e n t r e t o a i d i n t h e i d e n -t i f i c a t i o n and d e l i n e a t i o n o f r a i n f a l l a reas o v e r t h e ocean i s seen as t h e f i r s t s t e p towards t h i s end, and a n e c e s s a r y one g i v e n the 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 Papa and the i n c r e a s i n g r e l i a n c e on weather s a t e l l i t e o b s e r v a t i o n s . The im-p o r t a n c e o f t h i s i s r e f l e c t e d i n the A t m o s p h e r i c Environment's 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 conduct f u r t h e r r e s e a r c h and development 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 meteo-r o l o g i c a l s a t e l l i t e d a t a (Department o f Communications, 1980). 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Of B r i t i s h Columbia, Forestry 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 Cells In A Cyclonic Storm", J . Atmos. Sci  Vol . 35, 230-241 Holton, J.R. 1972 An Introduction To Dynamic Meteorology, Academic Press House, D.C. 1968 "Air Mass Modification And Upper Divergence", B u l l . Amer. Met. Soc. 39, 137-143 Houze, R.A., P.V. Hobbs, K.R. Biswas, andW.M. Davis 1976 "Mesoscale Structure Of R a i n f a l l In Occluded Cyclones", 6-th  AMS Conf. of Weather Forecasting and Analysis, Albany, 310-317' Hussey, W.J. 1977 "TIROS-N Polar-Orbitting Environmental S a t e l l i t e " , 10th Session ESCAP/WMO Typhoon Committee, Tokyo; NESS, NOAA, Washington, D.C, 29p. Ingraham, D.V., J . Amorocho, M. Guilarte and M. Escalona 1977 "Preliminary 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 Linear F i l t e r i n g And Prediction Theory", Trans. ASME J . Of Basic Engineering Series  D, Vol. 82, March, 35-45 Kendrew, W.G., and D. Kerr 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 Pr i n t e r , Ottawa (} i > Knox, J . 1978 Geography 312 Lecture Notes - F a l l Term, Univer-s i t y of B r i t i s h Columbia Kodaira, N., and N. Murayama 1976 "Development of Geostationary Meteorological S a t e l l i t e Systems", 7-th AMS Conf. on Aerospace  and Aeronautical Meteorology and Symp. on Remote Sensing from" S a t e l l i t e s , 249-252 Leigh, J.L., and T. Duke 1978 "UBC F a c i l i t i e s " , Computing Centre, University of B r i t i s h Columbia Lethbridge, 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 S a t e l l i t e Radiation Data", Mon. Wea. Rev. 95, 487-490 Lienesch, J.H., B.P. Bauer and B.B. Goddard 1965 "SMS Infrared Observations: Their Accuracy And C a l i b r a t i o n " . Proc. 10-th International Symp. on Remote Sensing of the  Envxronment, Vol. 1, 149-158 L i n t z , J . and D.S. Simonett 19 76 Remote Sensing of Environment, Addison Wesley Pub. Co. (See Chapter 2) Lovejoy, S. 19 78 "The Relationship Between Coarse Resolution S a t e l l i t e Data And Area Of Rain", 4-th AMS Symp. on Meteorolog- i c a l Observations and Instrumentation, 239-242 , and G.L. Austin 1979 " The Delineation Of Rain Areas From V i s i b l e And Infrared Data For Gate And Mid-Latitudes", Atmosphere-Ocean 17(1), 77-92 Maddox, R.A. 19 80 "A Satellite-Based Study Of Mid-Latitude, Mesoscale Convective Complexes", Preprints 8-th AMS Conf. on  Weather Forecasting and Analysis, Denver, June, 329-338 Mair, S. 1978a "UBC IG - The Integrated Graphics System", Computing Centre, University of B r i t i s h Columbia , 1978b "UBC Surface-Surface V i s u a l i z a t i o n Routines", Computing Centre, University of B r i t i s h Columbia Martin, D. W., and W.D. Scherer 1973 "Review of S a t e l l i t e Rain-f a l l Estimation 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 Clusters Over The Tropical North A t l a n t i c Ocean", F i n a l Report Of Tr o p i c a l Cloud Organization Studies, Task Order No. 3 To STAG, Contract E-127-69-(N) Space Science And Engineering Center, Madison, Wisconsin, 80p. , and 19 72 "A S a t e l l i t e Study Of Cloud Clusters Over The Tropical 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 Physics Of Clouds, 2-nd E d i t i o n , Clarendon Press, Oxford, 6 71p. 1975 Clouds, Rain, and Rainmaking, 2-nd E d i t i o n , Cambridge University Press Matejka, T.J., R.A. Houze, and P.V. Hobbs 19 80 "Microphysics And Dynamics Of Clouds Associated With Mesoscale Rainbands In Extra-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 Aid To Water Resource Managers", J . Of  Water Resources And Management Div., ASCE, Vol. 106, NoWRI, 1-20 Mcintosh, D.H., and A.S. Thorn 1973 Essentials of Meteorology, . v Wykeham Pub.,(London) Ltd. McKowan, P.L. 1977 "VISSR Data Processing Plan For Synchronous Meteorological And Geostationary Operational 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 Relationship Of Wind Maxima To Severe Weather And Its Operational Application", 10-th AMS Conf., On  Severe Local Storms MDA 1977 "Remote Sensing Data Systems", report by MacDonald, Dettweiler, And Associates, Consultants, Vancouver, B.C. Miers, B.T. 19 76 "Application Of Meteorological S a t e l l i t e Observations To Weather Sensitive Army Operations", 7-th AMS  Conf. On Aerospace And Aeronautical 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", NOAA Magazine October, P56-57 NESS 19 76 " S a t e l l i t e A c t i v i t i e s of NOAA 19 75", NOAA S/T 76-2185, A p r i l O l i v er, V.J., and R.A. S c o f i e l d 1976 "Estimation Of R a i n f a l l From S a t e l l i t e Imagery", Proc. 6-th AMS Conf. on Weather  Forecasting and Analysis, May, 242-245 Popham, R. , and E. Rich 1975 "A Direct Readout SMS/GOES VISSR Ground Station Configuration", NESS, Preliminary Note, Washington D.C. Purdom, J.F.W. 1976 "Some Uses Of High Resolution GOES Imagery In Mesoscale Forecasting Of Convection And Its Behaviour", Proc.  6-th AMS Conf. on Weather Forecasting and Analysis, May, 260-267 156. Rogers, R.R. 19 76 A Short Course In C l o u d Physics Pergammon Press Schaefer, D.G. 19 79a "Meteorological Development Contributing To The Terrace Area Flood Of Early November 1978", S c i e n t i f i c Services Unpublished Report, AES, Vancouver 19 79b "The Multi-Day Rainstorm Of October-November 1978, On The Queen Charlotte Islands", S c i e n t i f i c Services 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 Inland Waters Direct-orate 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 Equation To Severe Storm Forecasting", 10-th AMS conf. On Severe  Local Storms, Omaha, Oct. 18-21, 358-363 Scherer, W.D., and M.D. Hudlow 1971 "A Technique For Assessing Probable Distributions Of Tropical 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, Rockville, Maryland, 63-68 S c o f i e l d , R.A. 1976a "Nowcasting: Fine Tuning The Local Forecast", Proc. 6-th AMS Conf. on Weather Forecasting and  Analysis, May, 268-272 19 76b " S a t e l l i t e Pictures Used For Locating The R a i n f a l l Associated 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", Proc. AMS Conf. on  Flash Floods; Hydrometeorological Aspects, May, 181-189 19 78b "Using S a t e l l i t e Imagery To Detect And Estimate R a i n f a l l From Flash-Flood Producing Thunderstorms", Proc. AMS Conf. on Weather Forecasting and Analysis and Aviation  Meteorology, Oct., 132-141 and V.J. O l i v e r 19 75 "The Synchronous Meteorologi-c a l S a t e l l i t e (SMS): Its Advantages And Applications", Proc. 10- th International Symp. on Remote Sensing of the Environment, Vol. 1, 159-162 and 1977a "A Scheme For Estimating 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 Tr o p i c a l Meteorology, Dec. 13-16, 204-211 157 . and 19 80 "Some Improvements To The Sco f i e l d / O l i v e r Technique", 2-nd AMS Conf. on Flash Floods, Atlanta, Mar. 18-20, 115-122 and , and L. Spayd 19 80 "Estimating R a i n f a l l From Thunderstorms With Warm Tops In The Infrared Imagery", Preprints 8-th AMS Oohf. on Weather Forecasting and  Analysis, Denver, June, 85-92 , and C.E. Weiss 19 76 "Applications Of Synchronous Meteorological S a t e l l i t e (SMS) Products And Other Data For Short-Range Forecasting In The Chesapeake Bay Region", Proc. 6-th AMS  Conf. on Weather Forecasting and Analysis, May, 67-73 Seymour, D.W., D.S. Sloan, and N.W. Bowker 19 77 "A Low-Cost System For Reception, Processing And Di s t r i b u t i o n Of Line Scan Data From Environmental S a t e l l i t e s " , The American In s t i t u t e Of  Aeronautics And Astronautics S a t e l l i t e Application To Marine  Operations Conf., Louisiana, Nov. Sikdar, D.N. 19 72 "ATS-3 Observed Cloud Brightness F i e l d Related To A Meso- To Sub-synoptic Scale R a i n f a l l Patterns", TELLUS, 24,5 400-413 — : , and V.E. Suomi 19 71 "Time Vari a t i o n Of Trop i c a l Energetics As Viewed From A Geostationary A l t i t u d e " , J . of  Atmos. S c i . 2 8, 170-180 Spaceflight 1980 "Space A f f a i r s " , Spaceflight, Vol.22 (5), May 1980 P222 Spangler, M.J. 1974 "The DMSP primary Data Sensor", 6-th AMS  Conf. on Aerospace and Aeronautical Meteorology, 150-157 Stout, J . , D.W. Martin, and D.N. Sikdar 1977 " R a i n f a l l Estimat-ion From Geostationary S a t e l l i t e Images Over The GATE Area", 11-th AMS Conf. on Hurricanes and Trop i c a l Meteorology, Miami Beach, Dec. 13-16, 212-215 , and 19 79 "Estimating GATE R a i n f a l l From Geosynchrous S a t e l l i t e Images", Mon. Wea. Rev.  Vol. 10 7, May, 585-598 UBC Computing Centre 19 79 "XPAND.S" Preliminary note, Computing Centre, University of B r i t i s h Columbia Vesely, C.J., andW.B. Botzong 1974 "Defense Meteorological S a t e l l i t e Program", Proc. 6-th AMS Conf. on Aerospace and  Aeronautical Meteorology, 146-149 Vidzee, 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 Studies Of Cyclones", Mon. Wea. Rev. Vol. 106, Nov., 1627-1633 1 5 8 . Wallace, J.M. and P.O. Hobbs 1977 Atmospheric Science, Academic Press 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 Geostationary Imagery For Real-time Estimation Of Hurricane Rain Potential In Landfailing Storms", 11-th AMS  Tech. Conf. on Hurricanes and Tropical 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 Estimation 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 Estimat-ion From S a t e l l i t e Cloud Photographs", Noaa Tech. Memo., ERL OD-11, 43p. WMO 19 76 "Informal Planning Meeting On The S a t e l l i t e Applications In Hydrology", F i n a l Report, Geneva, Oct. 159. APPENDIX A For a divergence f u n c t i o n of the form 1 dA(T,t) = f + f T n A . l A(T,t) dt 1 2 the average divergence between the l e v e l of non-divergence •2 T„ and the c o l d e s t contour l e v e l T 3 can be determined as f o l l o w s 1 dA(T , t ) = f + f T n A.2 A (T , t ) " " S t £ i + T 2 l .T 3 f + f 7 T n dT A.3 •3^2' 1  l 2 ( n+1 n+1 , T T ^ r T j f l ( T 3 - T 2 } + f2 3 , 2 A - 4 The v a l u e s of the two constants f ^ and can be found from the two boundary c o n d i t i o n s . For T=T 2 (the l e v e l o f non-divergence) f l r2 2 so t h a t 4T = - f T 1 1 A - 6 f l t 2 i 2 For T=T 3 ( the c o l d e s t contour l e v e l ) 160. where K i s the divergence of the c o l d e s t contour. Using A.6 to s u b s t i t u t e f o r f, g i v e s f„ = — - — A. 9 2 Tn - T n  l 3 l 2 S u b s t i t u t i n g A.9 back i n t o A.6 y i e l d s -KT? ± A.10 f l T n _ T n Using A.9 and A.10 i n the e x p r e s s i o n f o r the average divergence A.4 r e s u l t s i n 1 dA(T,t) A(T,t) dt i ( - K T ; ( T 3 - T 2 ) K < TS + 1 - T;+1' \ ( T3- T2» ( T^-T^ T^-T^ n+1 ) A.11 which can be r e w r i t t e n as „n+l K ( T 3 - T 2 ) Tn+TT" - ( n + l ) T 2 T 3 .+ n T 2 n+1 A.12 x 3 L2 161. APPENDIX B S e n s i t i v i t y analysis using a t y p i c a l c e l l and the expres-sion for the amount of r a i n f a l l given by equation 4.32): B.l The Control The values of the parameters used i n the control are: e = 0.2 wc = 10 gm HI y = 5°C/1000m A(T 3,t+At) = 65.0113 area units A(T 3,t) = 25.8830 area units AT = T 3-T 2 = -3Q°C T 3 = -60°C T 2 = -30°C which give a r a i n f a l l of 3 -2 AP = 11.05x10 gm m = 11.05 mm B.2 Variation of AP with e A ±10% v a r i a t i o n i n the empirical adjustment factor e, holding the other parameters at t h e i r control values gives 1) for a +10% change i n e, e=0.22 AP = 12.16 mm which i s a 1.11 mm or 10% increase i n the estimated r a i n f a l l . B . l 2) for a -10% change i n e, e=0.18 A P = 9.95 mm which i s a 1.11 mm or 10% decrease i n the estimated r a i n f a l l . B.3 Variation of A P with wc A ±10% v a r i a t i o n i n the water content wc, holding the other parameters at t h e i r control values gives: _3 1) for a +10% change i n wc, wc=ll gm m A P - 12.16 mm which i s a 1.11 mm or 10% increase i n the estimated r a i n f a l l . _3 2) for a -1Q% change i n wc, wc=9 gm m A P = 9.95 mm which i s a 1.11 mm or 10% decrease i n the estimated r a i n f a l l . B.4 Variation of A P with y A ±10% v a r i a t i o n i n the lapse rate y, holding the other paramters at t h e i r control values gives: 1) for a +10% change i n Y , Y=5.5°C/1000m A P = 10.05 mm which i s a 1 mm or 9.1% decrease i n the estimated r a i n f a l l . 2) for a -10% change i n y , y=4.5°C/1000m A P = 12.28 mm which i s a 1.23 mm or 11.1% increase i n the e s t i -mated r a i n f a l l . 163. B.5 V a r i a t i o n o f AP w i t h A(T^,t+At) A +10% v a r i a t i o n i n t h e a r e a o f the c o l d e s t t e m p e r a t u r e (T 3) c o n t o u r a t time ( t + A t ) , A ( T ^ , t + A t ) , h o l d i n g t h e 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 g i v e s : 1) f o r a +10% change i n A ( T ^ , t + A t ) , A(T 3,t+At)=71.5124 AP = 12.20 mm whi c h i s a 1.15 mm o r 10.4% i n c r e a s e i n the e s t i -mated r a i n f a l l . 2) f o r a -10% change i n A ( T 3 , t + A t ) , A(T 3,t+At)=58.5102 AP = 9.79 mm whi c h i s a 1.26 mm o r 11.4% d e c r e a s e i n t h e e s t i -mated r a i n f a l l . B.6 V a r i a t i o n o f Ap w i t h A ( T 3 , t ) A ±10% change i n the a r e a o f the c o l d e s t t e m p e r a t u r e (T 3) c o n t o u r a t t i m e ( t ) , A ( T 3 , t ) , h o l d i n g t h e 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 g i v e s : 1) f o r a +10% change i n A ( T 3 , t ) , A(T 3,t)=28.47 AP = 9.91 mm whi c h i s a 1.14 mm o r 10.4% d e c r e a s e i n the e s t i -mated r a i n f a l l . 2) f o r a -10% change i n A ( T 3 , t ) , A(T 3,t)=23.29 AP = 12.32 mm whi c h i s a 1.26 mm or 11.4% i n c r e a s e i n the e s t i -mated r a i n f a l l . B.7: V a r i a t i o n o f AP w i t h AT A ±10% change 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 , AT, h o l d i n g 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 g i v e s : 164. 1) for a +10% change i n the temperature thickness AT, AT=-33°C AP = 12.16 mm which i s a 1.11 mm or 10% increase i n the estimated r a i n f a l l . 2) for a -10% change i n the temperature thickness AT, ~ - O AT=-27 C AP = 9.95 mm which i s a 1.11 mm or 10% decrease i n the estimated r a i n f a l l . B.8 Variation of AP with T 3 and T,, The radiance temperatures recorded on the s a t e l l i t e i n f r a -red images are based on the assumption that clouds radiate as '.. black bodies. In other words the emissivity e i s assumed to 4 equal unity 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 radiated (W m ), a = 5.669x10 W m K , and T i s the temperature (K). Cloud e m i s s i v i t i e s , however, change throughout the development of the cloud. Suppose that the emissivity were i n r e a l i t y less than 1, say 10% l e s s , e=0.9, then the actual temperature (T., ) of the o a coldest contour on the s a t e l l i t e image i s given by 4 4 E = e a T 3 a = cT 3 or _ , ,-.25 165. For T, = -60°C = (273.15-60)K = 213.15K, T Q = -54.31°C. The temperature thickness AT would then be AT = -54.31-(-30) = -24.31°C Keeping the other parameters at t h e i r control values, then AP = 8.96 mm which i s a 2.14 mm or 19% decrease in. the estimated 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 for the temperature at the l e v e l of non-divergence T.,. A 10% decrease i n the emissiv-i t y at t h i s l e v e l would r e s u l t i n the actual temperature T„ being T2a = T 2 ( e ) " ' 2 ' = T 2(0.9) * For T 0 = -30°C = (273.15-30)K = 243.15K, T 0 = -23.51°C. The temperature thickness AT would then be AT = -60-(-23.41) = -36.49°C Keeping the other parameters at t h e i r control values, then AP = 13.44 mm which i s a 2.39 mm or 21.6% increase i n the estimated r a i n f a l l . B.9 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 values of the parameters i n the expression for r a i n f a l l (equation B.l) generally r e s u l t s 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 . A 10% decrease i n the emissivity assumed at a p a r t i c u l a r cloud l e v e l results i n a 20% change i n the estimated r a i n f a l l ; however, t h i s i s con-sidered as a "worst case" example of the actual variations i n cloud emissivity. . 166. One i n t e r e s t i n g facet of t h i s analysis i s that the uncertainties i n the parameters may act to cancel each other out i n the estimation procedure. For example, i f areas of the coldest contours at. both times were each 10% larger 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 using the control values of the areas. PUBLICATIONS: Loucks, R.H., D.J. Lawrence, D. Ingraham and B. Fleming, "A Technique f o r Estimating Extreme Ocean Current Vectors", Bedford I n s t i t u t e of Oceanography Rep. Series BI-R-73-5, 1973. Ingraham, D., B. Fleming, D.J. Lawrence and R.H. Loucks, " S t a t i s t i c s and Extremes of Currents on the Scotian Shelf", Bedford I n s t i t u t e of Oceanography Rep. Series BI-R-73-10, 1973. Loucks, R.H., D.J. Lawrence, and D.V. Ingraham, "Summary of Physical, B i o l o g i c a l , Socio-Economic and Other Factors Relevant to P o t e n t i a l O i l S p i l l s i n the Passamaquoddy Region of the Bay of Fundy, Section 2. Dispersion of S p i l l e d O i l " , F i s h e r i e s Research Board of Canada, Technical Report No. 428, pp. 215-228, 1973. Loucks, R.H., 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 Factors Relevant to P o t e n t i a l O i l S p i l l s i n the Passamaquoddy Region of the Bay of Fundy, Section 9. The Influence of Environmental Conditions on the Operations of O i l Terminals", F i s h e r i e s Research Board of Canada, Technical Report No. 428, PP. 215-228, 1973. McGonigal, D., R.H. Loucks and D.V. Ingraham, "Halifax Narrow Sample Current Meter Data", Bedford I n s t i t u t e of Oceanography Data Series BI-D-14-5, 1974. Loucks, R.H., D.J. Lawrence and D.V. Ingraham, "Note on the Estimation of Plume and Patch Dispersion Scales", Proceedings of the International Conference of Applied S t a t i s t i c s as Dalhousie Un i v e r s i t y , Halifax, May 2-4, 1974. Adams, E.E., C.W. Almquist, D.V. Ingraham and K.D. Stolzenbach, "Waste Heat Disposal from Offshore Nuclear Power Plants", Proceedings of A.S.C.E. Specialty Conference Ocean Engineering I I I , University of Delaware, Newark, 1975. Ingraham, D.V., K.D. Stolzenbach and E.E. Adams, "Phase II F i n a l Report - Forecasting Power Plant E f f e c t s on the Coastal Zone, Section 6.5" for E.G. & G. Environmental Consultants of Waltham, Mass. 1975. Ingraham, D.V., "The Stochastic Simulation of Ocean Currents", S.M. Thesis of C i v i l Engineering at the Massachusetts I n s t i t u t e of Technology, 1976. Ingraham, D.V., J . Amorocho, M. G u i l a r t e and M. Escalona, "Preliminary R a i n f a l l Estimates i n Venezuela and Colombia from GOES S a t e l l i t e Images", Second Conference on Hydrometeorology, Atmospheric Environment Service, Toronto, Oct. 1977. Ingraham, D.V., " S a t e l l i t e Image and Airphoto Interpretation -Casamance River" Report to R.H. Loucks Oceanology, July, 1978. Ingraham, D.V., and S.0. Russell "Estimating 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 for p u b l i c a t i o n i n Water Resources Research 1980. 

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