UBC Theses and Dissertations

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UBC Theses and Dissertations

Computer model for flow simulation of mission creek. Leith, Rory Marshall Montgomery 1972

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A COMPUTER MODEL FOR FLOW SIMULATION OF MISSION CREEK b y RORY MARSHALL MONTGOMERY L E I T H B . S c . , 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 , 1964 M . S c , 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 , 1966 A THESIS SUBMITTED I N P A R T I A L FULFILMENT i OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D SCIENCE i n t h e D e p a r t m e n t o f C i v i l E n g i n e e r i n g We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF B R I T I S H COLUMBIA F e b r u a r y , 1972 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available f o r reference and study. I further agree that permission fo r extensive copying of t h i s thesis f o r scholarly purposes may be granted by the Head of my Department or by h i s representatives. It i s understood that copying or p u b l i c a t i o n of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of C i v i l E n g i n e e r i n g The University of B r i t i s h Columbia Vancouver 8, Canada Date February 1, 1972 A B S T R A C T A d e s c r i p t i o n i s g i v e n o f t h e d e v e l o p m e n t a n d a p p l i c a t i o n o f a c o m p u t e r p r o g r a m t o s i m u l a t e t h e s t r e a m f l o w s i n M i s s i o n C r e e k . T h i s p r o g r a m p r o v i d e s a m a t h e m a t i c a l h y d r o l o g i c m o d e l o f t h e M i s s i o n C r e e k b a s i n a n d i s a p p l i e d t o 16 y e a r s o f r e c o r d b e t w e e n 1948 a n d 19 7 1 . T h e l e n g t h o f r e c o r d f o r a y e a r i s n o r m a l l y f r o m 31 M a r c h t o 30 S e p t e m b e r i n c l u s i v e . The m o d e l h a s b e e n u t i l i z e d t o s t u d y t h e m e c h a n i s m s f o r g e n e r a t i n g r u n o f f , p a r t i c u l a r l y r a i n r u n o f f , t h e r e l a t i o n s h i p b e t w e e n e v a p o t r a n s p i r a t i o n a n d e l e v a t i o n ; a n d t h e e f f e c t i v e n e s s o f c e r t a i n a r e a s o f t h e b a s i n i n g e n e r a t i n g r u n o f f . The s e n s i t i v i t y a n d r a n g e o f t h e p a r a m e t e r s u s e d i n t h e m o d e l h a v e b e e n e x a m i n e d a n d t e c h n i q u e s f o r p r e d i c t i n g t h e p a r a m e t e r s h a v e b e e n d e v e l o p e d . H y d r o l o g i c a r e a s o f c o n c e r n i n t h e m o d e l a r e : s n o w m e l t , e v a p o -t r a n s p i r a t i o n , r u n o f f f r o m r a i n f a l l a n d s o i l m o i s t u r e d e f i c i e n c y . TABLE OF CONTENTS P a g e L I S T OF TABLES v L I S T OF FIGURES v i CHAPTER I . INTRODUCTION 1 1 .1 D e s c r i p t i o n o f t h e O k a n a g a n V a l l e y 1 1 . 2 The W a t e r Q u a n t i t y P r o b l e m o f t h e O k a n a g a n 1 1 . 3 G e o l o g i c a l B a c k g r o u n d o f t h e O k a n a g a n V a l l e y 2 1 .4 D e s c r i p t i o n o f M i s s i o n C r e e k B a s i n 4 I I . COMPUTER MODELING 7 I I . 1 D e f i n i t i o n o f Terms a n d B a s i c P h i l o s o p h y 7 I I . 2 T y p e s o f S i m u l a t i o n 8 I I . 3 A p p l i c a t i o n t o H y d r o l o g y 9 I I . 4 H y d r o l o g i c M o d e l R e q u i r e m e n t s 10 I I . 5 E x a m p l e s o f H y d r o l o g i c M o d e l i n g , 1 0 I I . 5 . 1 N a s h a n d S u t c l i f f e 10 I I . 5 . 2 R o c k w o o d a n d N e l s o n 12 I I . 5 . 3 S t a n f o r d I V 16 I I I . MISSION CREEK FLOW MODEL 23 I I I . l I n p u t D a t a S o u r c e s 23 1 1 1 . 2 B a s i n S u b d i v i s i o n 26 1 1 1 . 3 T r e a t m e n t o f t h e I n p u t D a t a 26 I I I . 3 . 1 T e m p e r a t u r e 26 I I I . 3 . 2 P r e c i p i t a t i o n 27 I I I . 3 . 3 E v a p o r a t i o n 28 I I I . 4 S n o w m e l t 31 I I I . 5 Snow L i n e R e c e s s i o n 33 I I I . 6 I n t e r c e p t i o n 34 I I I . 7 E a r l y S e a s o n S t o r a g e 36 I I I . 8 I n f i l t r a t i o n 36 1 1 1 . 9 R u n o f f 37 1 1 1 . 1 0 R o u t i n g 38 1 1 1 . 1 1 O p e r a t i o n o f t h e C o m p u t e r P r o g r a m 39 i i i i v CHAPTER Page I V . RESULTS AND CONCLUSIONS 40 I V . 1 O b j e c t i v e s o f t h e M o d e l 40 I V . 2 M o d e l B e h a v i o u r 41 I V . 2 . 1 B e s t F i t P a r a m e t e r s 41 I V . 2 . 2 E f f e c t o f L a k e E v a p o r a t i o n 43 I V . 2 . 3 E f f e c t o f E a r l y S e a s o n S t o r a g e 48 I V . 3 A n a l y t i c a l R e s u l t s 48 I V . 3 . 1 P r e c i p i t a t i o n E l e v a t i o n R e l a t i o n s h i p s . . . 48 I V . 3 . 2 E v a p o t r a n s p i r a t i o n L a p s i n g 50 I V . 3 . 3 B a s i n W a t e r B u d g e t 57 I V . 3 . 4 S o i l M o i s t u r e D e f i c i e n c i e s . . . 70 I V . 4 P r e d i c t i v e R e s u l t s 70 I V . 5 C o n c l u s i o n s 75 BIBLIOGRAPHY 7 9 A P P E N D I X 1 F l o w C h a r t f o r t h e C o m p u t e r P r o g r a m 81 A P P E N D I X 2 P a r a m e t e r s U s e d i n M i s s i o n C r e e k F l o w M o d e l 8 2 A P P E N D I X 3 L i s t o f V a r i a b l e s 8 3 A P P E N D I X 4 O r d e r o f D a t a I n p u t S 5 L I S T OF TABLES T a b l e Page 1. G e o l o g i c a l T i m e S c a l e 3 2 . A r e a s a n d E l e v a t i o n s o f t h e B a n d s U s e d i n M i s s i o n C r e e k M o d e l 4 3 . I n p u t D a t a S t a t i o n f o r t h e M i s s i o n C r e e k B a s i n . . . . 25 4 . A v e r a g e M o n t h l y P a n C o e f f i c i e n t s f o r S u m m e r l a n d . . . . 29 5 . B e s t F i t V a l u e s o f P a r a m e t e r s U s e d i n M o d e l 42 6 . A v e r a g e R e s i d u a l V a r i a n c e s a n d S t a n d a r d D e v i a t i o n s f o r Y e a r s W i t h a n d Y e a r s W i t h o u t L a k e E v a p o r a t i o n D a t a 44 7 . E f f e c t o f A d d i n g E a r l y S e a s o n S t o r a g e t o M o d e l . . . . 48 8 . P o t e n t i a l E v a p o t r a n s p i r a t i o n and S l o p e o f P o t e n t i a l E v a p o t r a n s p i r a t i o n 50 9 . Summary o f W a t e r B u d g e t R e s u l t s 58 1 0 . 1970 M i s s i o n C r e e k W a t e r B u d g e t 60 1 1 . 1969 M i s s i o n C r e e k W a t e r B u d g e t 61 1 2 . 1968 M i s s i o n C r e e k W a t e r B u d g e t 62 1 3 . 1967 M i s s i o n C r e e k W a t e r B u d g e t 63 1 4 . 1965 M i s s i o n C r e e k W a t e r B u d g e t 64 1 5 . 1964 M i s s i o n C r e e k W a t e r B u d g e t 65 1 6 . 1963 M i s s i o n C r e e k W a t e r B u d g e t 66 17 . 1961 M i s s i o n C r e e k W a t e r B u d g e t 67 1 8 . 1960 M i s s i o n C r e e k W a t e r B u d g e t 68 1 9 . 1959 M i s s i o n C r e e k W a t e r B u d g e t 69 2 0 . C o m p a r i s o n o f M i s s i o n C r e e k F l o w s a n d O k a n a g a n B a s i n R u n o f f 71 2 1 . W a t e r E q u i v a l e n t s f o r t h e Snow C o u r s e s i n t h e M i s s i o n C r e e k B a s i n . 73 v L I S T OF FIGURES F i g u r e Page 1. O k a n a g a n V a l l e y a n d t h e M i s s i o n C r e e k B a s i n . 5 2 . C u m m u l a t i v e D i s t r i b u t i o n o f I n f i l t r a t i o n C a p a c i t y ( S t a n f o r d I V M o d e l ) 17 3 . P e r c e n t o f t h e I n c r e a s e i n S u r f a c e D e t e n t i o n R e t a i n e d b y t h e U p p e r S o i l Zone as a F u n c t i o n o f U p p e r S o i l Zone M o i s t u r e R a t i o ( S t a n f o r d I V ) 18 4 . A s s i g n m e n t o f I n f i l t r a t e d W a t e r t o G r o u n d W a t e r ( S t a n f o r d I V ) . 19 5 . C u m m u l a t i v e D i s t r i b u t i o n o f P o t e n t i a l E v a p o t r a n s p i r a t i o n ( S t a n f o r d I V ) 21 6. M i s s i o n C r e e k I n p u t D a t a S t a t i o n s 24 7. E x a m p l e o f L a p s i n g t h e D a i l y P r e c i p i t a t i o n 27 8 . L a k e E v a p o r a t i o n as a F u n c t i o n o f M o n t h l y D e g r e e Days . . . . 30 9 . R e g r e s s i o n o f F i t t e d LSW o n P r e d i c t e d LSW 35 1 0 . Shape o f U n i t H y d r o g r a p h 39 1 1 . R e s i d u a l V a r i a n c e a s a F u n c t i o n o f C2 f o r 1959 44 1 2 . R e s i d u a l V a r i a n c e a s a F u n c t i o n o f C2 f o r 1960 45 1 3 . R e s i d u a l V a r i a n c e as a F u n c t i o n o f C2 f o r 1970 45 1 4 . R e s i d u a l V a r i a n c e as a F u n c t i o n o f M e a s u r e d F l o w 46 1 5 . P r e c i p i t a t i o n E l e v a t i o n R e l a t i o n s h i p s f o r 1 9 6 4 , 1 9 6 5 , 1 9 6 7 , 1 9 6 8 , 1969 49 1 6 . R a t i o o f A c t u a l E v a p o t r a n s p i r a t i o n t o P o t e n t i a l E v a p o t r a n s -p i r a t i o n as a F u n c t i o n o f R a i n f a l l i n t h e F i r s t E l e v a t i o n B a n d 52 1 7 . E v a p o t r a n s p i r a t i o n E l e v a t i o n R e l a t i o n s h i p s f o r 1 9 6 6 , 1 9 6 8 , 1970 53 1 8 . E v a p o t r a n s p i r a t i c n E l e v a t i o n R e l a t i o n s h i p s f o r 1 9 4 8 , 1 9 5 4 , 1 9 5 8 , 1962 • 54 1 9 . T o t a l A c t u a l E v a p o t r a n s p i r a t i o n f o r t h e M i s s i o n C r e e k B a s i n as a F u n c t i o n o f t h e S e a s o n D e g r e e D a y s 55 v i v i i F i g u r e Page 20. T o t a l A c t u a l E v a p o t r a n s p i r a t i o n f o r a S e a s o n as a F u n c t i o n o f t h e S l o p e o f t h e R a i n f a l l i n t h e M i s s i o n C r e e k B a s i n . . . 56 2 1 . V o l u m e o f S e a s o n F l o w f r o m M i s s i o n C r e e k as a F u n c t i o n o f t h e A v e r a g e o f Maximum W a t e r E q u i v a l e n t s 73 22. A v e r a g e D a i l y F l o w s f o r 1970 76 A C K N O W L E D G E M E N T S The a u t h o r w i s h e s t o t a k e t h i s o p p o r t u n i t y t o t h a n k h i s s u p e r v i s o r , D r . M . C . Q u i c k , f o r h i s s u g g e s t i o n o f t h e p r o b l e m a n d h i s e n c o u r a g e m e n t a n d a s s i s t a n c e t h r o u g h o u t t h e c o u r s e o f t h e d e v e l o p m e n t o f t h e m o d e l ; M r . A . P i p e s f o r h i s a d v i c e a n d a i d w i t h t h e p r o g r a m m i n g ; and P r o f e s s o r S . 0. R u s s e l l f o r h i s v a l u a b l e s u g g e s t i o n s . S i n c e r e t h a n k s a r e a l s o due t o M r . R i c h a r d B r u n f o r t h e d i a g r a m s . F u n d i n g f o r t h e r e s e a r c h came f r o m two s o u r c e s , t h e B . C . P r o v i n c i a l W a t e r R e s o u r c e s G r a n t and t h e B . C . D i s a s t e r R e l i e f F u n d . The w o r k f o r m s p a r t o f a c o n t i n u i n g s t u d y on f l o w f o r e c a s t i n g a n d t h e h y d r o l o g y o f m o u n t a i n c a t c h m e n t s . v i i i CHAPTER I INTRODUCTION 1 .1 D e s c r i p t i o n o f t h e O k a n a g a n V a l l e y The O k a n a g a n V a l l e y , w h i c h c o n t a i n s t h e M i s s i o n C r e e k b a s i n , i s l o c a t e d i n t h e Thompson P l a t e a u o f B r i t i s h C o l u m b i a . E x t e n d i n g some 100 m i l e s n o r t h f r o m t h e C a n a d a - U n i t e d S t a t e s b o r d e r , t h i s v a l l e y c o n t a i n s s e v e r a l l a k e s , t h e l a r g e s t o f w h i c h i s L a k e O k a n a g a n . T h e s e l a k e s t o g e t h e r w i t h a p l e a s a n t s e m i - a r i d c l i m a t e a r e a t t r a c t i n g i n c r e a s i n g num-b e r s o f b o t h t o u r i s t s a n d p e r m a n e n t r e s i d e n t s . A s y e t , i n d u s t r i a l d e v e l o p m e n t i n t h e O k a n a g a n i s l i g h t , b u t a g r i -c u l t u r e , p r i m a r i l y f r u i t f a r m i n g , r e q u i r e s i r r i g a t i o n and summer t o u r i s m r e l i e s o n t h e w a t e r r e c r e a t i o n a f f o r d e d by t h e l a k e s . W a t e r i s t h e r e f o r e o f g r e a t i m p o r t a n c e t o t h e v a l l e y . 1 .2 The W a t e r Q u a n t i t y P r o b l e m o f t h e Okanagan T h e r e h a s b e e n r e c e n t c o n c e r n f o r t h e q u a l i t y o f t h e w a t e r i n t h e l a k e s , b u t as f a r as w a t e r q u a n t i t y i s c o n c e r n e d t h e p r i m a r y p r o b l e m o f t h e O k a n a g a n i s l a k e l e v e l r e g u l a t i o n . L a k e O k a n a g a n h a s a s u r f a c e a r e a o f 8 4 , 2 0 0 a c r e s a n d i s o p e r a t e d t h r o u g h a s u r f a c e e l e v a t i o n r a n g e o f 4 f e e t , p r o v i d i n g a l i v e s t o r a g e o f 3 3 7 , 0 0 0 a c r e - f e e t . The drawdown l i m i t i s i m p o s e d p r i m a r i l y b y e s t h e t i c c o n s i d e r a t i o n s f o r t h e t o u r i s t s a n d r e s i -d e n t s a r o u n d t h e l a k e . The a n n u a l i n f l o w i n t o t h e l a k e c a n r a n g e f r o m -8 0 , 0 0 0 a c r e - f e e t t o 6 0 0 , 0 0 0 a c r e - f e e t w i t h a n a v e r a g e o f 3 5 0 , 0 0 0 a c r e - f e e t . 1 2 T h e s e i n f l o w s , w h i c h a r e n e t o f e v a p o r a t i o n , t o g e t h e r w i t h a l i m i t e d c a p a c i t y t o d i s c h a r g e w a t e r f r o m t h e l a k e , p r o v i d e some i n d i c a t i o n o f why l a k e l e v e l r e g u l a t i o n i s a p r o b l e m . To a c h i e v e l a k e l e v e l r e g u l a t i o n i m p r o v e d p r e d i c t i o n p r o c e d u r e s a r e r e q u i r e d . To t h i s e n d t h e m e c h a n i s m s f o r r u n o f f a r e b e i n g s t u d i e d . The M i s s i o n C r e e k F l o w S i m u l a t i o n h a s as one o f i t s p r i m e o b j e c t i v e s t h e e x a m i n a t i o n o f r u n o f f g e n e r a t i o n . 1.3 G e o l o g i c a l B a c k g r o u n d o f t h e Okanagan V a l l e y The p r e s e n t f o r m o f t h e O k a n a g a n V a l l e y i s c o m p a r a t i v e l y r e c e n t , o f t h e o r d e r o f 10,000 y e a r s . B u t t h e h i s t o r y o f t h e O k a n a g a n V a l l e y b e -g a n i n t h e e a r l y T e r t i a r y , T a b l e 1, when e x t e n s i v e swamps a n d l a k e d e p o s i t s f o r m e d i n t h e l o w a r e a s o f w h a t i s now B r i t i s h C o l u m b i a ' s Thompson P l a t e a u . D u r i n g t h e m i d d l e T e r t i a r y , t h e a r e a was s u b j e c t e d t o u p l i f t and e x t e n s i v e l a v a f l o w s . A l s o d u r i n g t h i s p e r i o d a l i n e o f w e a k n e s s a p p e a r e d a l o n g t h e p r e s e n t c o u r s e o f t h e v a l l e y . To t h e n o r t h o f K e l o w n a t h e m a i n d e p r e s s i o n became a compound v a l l e y w h i l e t o t h e s o u t h i t r e m a i n e d a s i n g l e t r e n c h . 3 T A B L E 1 GEOLOGICAL TIME SCALE M I L L I O N S OF DURATION ERA PERIOD EPOCH YEARS AGO M I L L I O N S OF YEARS RECENT QUATENARY P L E I S T O C E N E 1 1 PLIOCENE 1 - 1 3 13 CENEZOIC TERTIARY MIOCENE 13 - 25 12 OLIGOCENE 25 - 36 11 EOCENE 36 - 58 22 PALEOCENE 58 - 63 5 D u r i n g t h e P l e i s t o c e n e , t h e p r e s s u r e o f a 7 , 0 0 0 f o o t i c e p a c k c a r v e d t h e v a l l e y t o i t s p r e s e n t U s h a p e , w i t h p r e - e x i s t i n g s o i l s and o t h e r l o o s e m a t e r i a l s b e i n g moved a n d m i x e d i n t h e i c e . The t i l l f r o m t h i s g l a c i a l p e r i o d s t i l l c o v e r s t h e h i g h e r e l e v a t i o n s o f t h e v a l l e y . The l a s t g l a c i a l p e r i o d was t h e W i s c o n s i n w h i c h o c c u r r e d a p p r o x i m a t e l y 25 t o 50 t h o u s a n d y e a r s a g o . The g l a c i a l r e t r e a t t o o k p l a c e some 1 0 , 0 0 0 y e a r s ago a n d a t t h i s t i m e t h e O k a n a g a n a p p e a r e d i n r o u g h l y i t s p r e s e n t f o r m . A more c o m p l e t e d e s c r i p t i o n o f t h e s u r f a c e g e o l o g y o f t h e O k a n a g a n a r e a may be f o u n d i n N a s m i t h [ 1 9 6 2 ] . 4 1 .4 D e s c r i p t i o n o f M i s s i o n C r e e k B a s i n M i s s i o n e r e e k f l o w s i n t o O k a n a g a n L a k e j u s t s o u t h o f K e l o w n a , F i g u r e 1. The b a s i n c o v e r s some 3 30 s q u a r e m i l e s , much o f w h i c h i s u p -l a n d a r e a , T a b l e 2 , S e c t i o n 3 . 2 . TABLE 2 AREAS AND ELEVATIONS OF THE BANDS USED I N THE MISSION CREEK MODEL CENTER BAND BAND FROM TO ELEVATION ARE, NO. ( f t . ) ( f t . ) ( f t . ) ( s q . l 1 1000 1500 1250 8 2 1500 2000 1750 12 3 2000 2500 2250 8 4 2500 3000 2750 15 5 3000 3500 3250 24 6 3500 4000 3750 33 7 4000 4500 4250 66 8 4500 5000 4750 68 9 5000 5500 5250 38 10 5500 6000 5750 37 11 6 0 0 0 6500 6250 26 12 6500 7000 6750 2 F i r s t L e v e l S e c o n d L e v e l T h i r d L e v e l . R o u g h l y s p e a k i n g , t h r e e l e v e l s may be d i s t i n g u i s h e d o n t h e b a s i s o f s o i l , c l i m a t e , a n d v e g e t a t i o n . The f i r s t l e v e l , e x t e n d i n g f r o m t h e v a l l e y f l o o r t o 2 , 0 0 0 f e e t i s m a r k e d b y g r a s s l a n d w i t h s h r u b v e g e t a t i o n a n d s c a t t e r e d p i n e t r e e s . The s e c o n d l e v e l , f r o m 2 , 0 0 0 f e e t t o 4 , 0 0 0 f e e t , h a s more f e r t i l e s o i l w i t h i n c r e a s i n g l y t h i c k f o r e s t c o v e r . Above 4 , 0 0 0 FIG.I OKANAGAN LAKE AND MISSION CREEK BASIN. 6 f e e t , i n c r e a s e d p r e c i p i t a t i o n p r o v i d e s w i n t e r snow p a c k s o f 20 i n c h w a t e r e q u i v a l e n t a t 6 , 0 0 0 f e e t a n d d e n s e f o r e s t o c c u r s e x c e p t i n a l p i n e meadow a r e a s . M i s s i o n C r e e k p r o v i d e s some 20 t o 25 p e r c e n t o f t h e y e a r l y i n -f l o w t o L a k e O k a g a n a n [ P i p e s , 1971] a n d i s t h e m o s t i m p o r t a n t s i n g l e c o n -t r i b u t o r t o l a k e i n f l o w . T h u s i t i s a r e a s o n a b l e c a n d i d a t e f o r t h e s t u d y o f t h e m e c h a n i s m s o f r u n o f f g e n e r a t i o n i n t h e O k a n a g a n . The M i s s i o n C r e e k F l o w M o d e l d e s c r i b e d i n t h e f o l l o w i n g c h a p t e r s i s p r i m a r i l y an a t t e m p t t o s t u d y t h e g e n e r a t i o n o f r u n o f f . CHAPTER I I COMPUTER MODELING I I . 1 D e f i n i t i o n o f Terras a n d B a s i c P h i l o s o p h y As t h e c o n c e p t s o f s y s t e m , s i m u l a t i o n , a n d m o d e l a r e now em-p l o y e d i n w i d e l y d i v e r g e n t d i s c i p l i n e s , s u b t l e s h a d e s o f m e a n i n g a r e a t t a c h e d t o t h e s e t e r m s . F o r e x a m p l e , c o m p u t e r p r o g r a m s r e f e r r e d t o as s i m u l a t o r s b y some w r i t e r s a r e c o n s i d e r e d m o d e l s b y o t h e r s . I n t h e f a c e o f t h i s d i v e r g e n c e o f o p i n i o n t h i s t h e s i s h a s a d o p t e d t h e f o l l o w i n g d e f i -n i t i o n s f r o m E v a n s [ 1 9 6 7 ] . ( i ) a m o d e l i s d e f i n e d as a r e p r e s e n t a t i o n b o t h o f t h e p a r t s o f a s y s t e m a n d o f t h e i n t e r a c t i o n s o f t h e p a r t s . The m o d e l may b e a s y m b o l i c r e p r e s e n t a t i o n o r a p h y s i c a l r e p l i c a o f t h e s y s t e m ; ( i i ) a s y s t e m i s d e f i n e d as a c o l l e c t i o n o f i d e n t i -f i a b l e p a r t s c a p a b l e o f i n t e r a c t i n g i n s u c h a manner t h a t t h e e n t i r e s y s t e m f u n c t i o n s t o -g e t h e r ; ( i i i ) a t any g i v e n i n s t a n t o f t i m e t h e s y s t e m i s i n a p a r t i c u l a r c o n d i t i o n o r s t a t e . The s t a t e s o f a, s y s t e m a r e u s u a l l y c o n s i d e r e d i n a c h r o n o -l o g i c a l s u c c e s s i o n r e f e r r e d t o as a s t a t e h i s -t o r y . Two g e n e r a l t y p e s o f n u m e r i c a l q u a n t i t i e s a r e u s e d i n m o d e l s , p a r a m e t e r s a n d v a r i a b l e s . P a r a m e t e r s may be e i t h e r c o n s t a n t s o r f u n c -t i o n a l l y c h a n g i n g v a l u e s . F o r e x a m p l e , i n t h e m o d e l d e s c r i b e d i n t h i s t h e s i s , t h e a r e a s o f t h e b a n d s a r e c o n s t a n t p a r a m e t e r s f o r e a c h y e a r , w h i l e U Z , t h e u n i t h y d r p g r a p h p a r a m e t e r , i s a f u n c t i o n o f f l o w . P a r a -m e t e r s a r e u s e d as i n d i c e s o f t h e i n t e r a c t i o n s o f t h e c o m p o n e n t s o f a 7 8 s y s t e m a n d as s u c h may be c o n s i d e r e d as o p e r a t o r s o n t h e v a r i a b l e s . V a r i -a b l e s may be s u b d i v i d e d i n t o i n p u t v a r i a b l e s , s u c h as d a i l y t e m p e r a t u r e a n d v a r i a b l e s c a l c u l a t e d w i t h i n t h e m o d e l , s u c h as d a i l y a c t u a l e v a p o t r a n s p i r -a t i o n . The b a s i c p h i l o s o p h y o f m o d e l i n g may be s t a t e d i n t e r m s o f i n p u t s , o u t p u t s a n d t r a n s f o r m a t i o n s . I n p u t s a n d . o u t p u t s a r e k n o w n , w i t h some i n -p u t s o r o u t p u t s known w i t h g r e a t e r a c c u r a c y t h a n o t h e r s . Now t h e s y s t e m i s t h e s o - c a l l e d " b l a c k b o x " w h i c h t r a n s f o r m s t h e i n p u t s i n t o o u t p u t s . B e t t e r s i m u l a t i o n , t h a t i s c l o s e r r e p l i c a t i o n , o f t h e s y s t e m ' s s t a t e h i s t o r y b y t h e m o d e l ' s s t a t e h i s t o r y i s a s s u m e d t o i n d i c a t e b e t t e r r e p r e s e n t a t i o n o f t h e s y s t e m , s e e S e c t i o n I V . 1 . The b e t t e r r e p r e s e n t a t i o n o f t h e s y s t e m p r o -v i d e s a more r e l i a b l e q u a n t i t a t i v e d e s c r i p t i o n o f t h e c o m p o n e n t s a n d o f t h e i r i n t e r a c t i o n s i n t h e s y s t e m . W i t h t h i s a p p r o a c h , s i m u l a t i o n may b e r e g a r d e d a s t h e i n d i r e c t i n v e s t i g a t i o n o f t h e r e s p o n s e o r b e h a v i o u r o f t h e s y s t e m . C e r t a i n c o n s i d e r a t i o n s a r e i m p o r t a n t i n m o d e l i n g . A s u i t a b l e t y p e o f m o d e l s h o u l d be c h o s e n f o r t h e s y s t e m . The m o d e l s h o u l d h a v e a maximum p h y s i c a l o r e m p i r i c a l b a c k g r o u n d w h i l e r e m a i n i n g as s i m p l e as p o s s i b l e w i t h -i n t h e l i m i t s o f t h e i n p u t d a t a . T h e s e c o n s i d e r a t i o n s a r e e l a b o r a t e d u p o n i n t h e f o l l o w i n g s e c t i o n s . I I . 2 T y p e s o f S i m u l a t i o n T h r e e t y p e s o f m o d e l s a r e u s e d i n s i m u l a t i o n : p h y s i c a l m o d e l s , a n a l o g m o d e l s , a n d d i g i t a l m o d e l s . T h i s t h e s i s i s c o n c e r n e d w i t h t h e m o s t r e c e n t d e v e l o p m e n t i n d i g i t a l m o d e l s , d i g i t a l c o m p u t e r m o d e l s . I n d i g i t a l c o m p u t e r m o d e l i n g , t h e m o d e l i s t r a n s l a t e d i n t o a c o m p u t e r p r o g r a m . T h i s 9 p r o g r a m i s t h e n a m a t h e m a t i c a l r e p r e s e n t a t i o n o f t h e m o d e l a n d t h e s t a t e h i s t o r y o f t h e m o d e l i s g e n e r a t e d b y t h e c o m p u t e r . I n any s i m u l a t i o n p r o c e d u r e t h e m o d e l i s t e s t e d a n d i m p r o v e d b y s i m u l a t i n g s y s t e m s w i t h known i n p u t a n d o u t p u t . I n d i g i t a l c o m p u t e r m o d e l -l i n g enormous b e n e f i t s i n s p e e d and c o s t o f c o m p u t a t i o n s a r e r e a l i z e d . B e -c a u s e o f t h e h i g h c o m p u t a t i o n s p e e d , t h e m o d e l p a r a m e t e r s may be t e s t e d f o r a d e q u a c y , s e n s i t i v i t y , and o p t i m u m v a l u e s . II.3 A p p l i c a t i o n t o H y d r o l o g y T h e h y d r o l o g i c a l c y c l e i s f a i r l y e a s y t o d e s c r i b e i n q u a l i t a t i v e t e r m s . P r i n c i p a l c o m p o n e n t s o f t h e c y c l e a r e r e a s o n a b l y e a s y t o i d e n t i f y a n d t h e i n t e r a c t i o n s among m a j o r c o m p o n e n t s a r e known a t l e a s t q u a l i t a t i v e -l y . The a p p l i c a t i o n o f t h i s q u a l i t a t i v e k n o w l e d g e t o o b t a i n q u a n t i t a t i v e r e -s u l t s i s i m p e d e d b y t h e d i f f i c u l t y i n a c h i e v i n g a n a l y t i c a l d e s c r i p t i o n s o f t h e i n t e r a c t i o n s s u b j e c t t o t h e i n i t i a l a n d b o u n d a r y c o n d i t i o n s o f t h e b a s i n . D i g i t a l c o m p u t e r m o d e l i n g o f t h e h y d r o l o g i c c y c l e h a s as i t s o b -j e c t t h e d e v e l o p m e n t o f a g e n e r a l s y s t e m o f q u a n t i t a t i v e a n a l y s i s , i n o t h e r w o r d s , an a n a l y t i c a l d e s c r i p t i o n o f t h e s y s t e m . The h i g h c o m p u t a t i o n -a l s p e e d o f a d i g i t a l c o m p u t e r a l l o w s t h i s a n a l y t i c a l d e s c r i p t i o n t o t a k e t h e f o r m o f c o n t i n u o u s m a t h e m a t i c a l r e l a t i o n s among t h e e l e m e n t s o f t h e h y d r o l o g i c a l s y s t e m . I n m o d e l i n g t h e r u n o f f f r o m a b a s i n , t h e b a s i n i s c o n s i d e r e d t o be t h e s y s t e m a n d t h e s e r i e s o f o u t f l o w s a r e t h e s t a t e h i s t o r y . The i d e n t i f i a b l e p a r t s o f t h e s y s t e m may i n c l u d e : i n t e r c e p t i o n , e v a p o t r a n s p i r a t i o n , p r e c i p i -t a t i o n , s o i l m o i s t u r e , i n f i l t r a t i o n . The i n t e r a c t i o n s i n c l u d e p r e c i p i t a t i o n -i n f i l t r a t i o n - s o i l m o i s t u r e - e v a p o t r a n s p i r a t i o n , a n d t e m p e r a t u r e - s n o w m e l t r u n o f f . 10 1 1 . 4 H y d r o l o g i c M o d e l R e q u i r e m e n t s C o n t i n u o u s s i m u l a t i o n o f t h e m a j o r p r o c e s s e s a n d i n t e r a c t i o n s i n t h e s y s t e m i s t h e p r i m e r e q u i r e m e n t f o r a q u a n t i t a t i v e h y d r o l o g i c m o d e l . B u t s i m u l a t i o n o f a l l t h e c o m p o n e n t s a n d i n t e r a c t i o n s o ? t h e s y s t e m c a n -n o t b e r e a l i z e d b e c a u s e o f t h e p r o h i b i t i v e amounts o f d a t a r e q u i r e d . The p r i n c i p a l c o m p o n e n t s a n d Interactions m u s t b e s e l e c t e d t o p r o d u c e a q u a l i -t a t i v e d e s c r i p t i o n w i t h an a c c e p t a b l e l e v e l o f s i m p l i c i t y w i t h i n t h e l i m i t s i m p o s e d b y t h e a v a i l a b l e d a t a . I n s h o r t , t h e s c o p e o f t h e m o d e l i s r e s t r i c -t e d b y t h e a v a i l a b l e d a t a , a n d t h e amount known a b o u t t h e c o m p o n e n t s and i n t e r a c t i o n s o f t h e s y s t e m . A d d i t i o n a l c r i t e r i a f o r a h y d r o l o g i c m o d e l i n c l u d e : 1. The m o d e l s h o u l d r e p r e s e n t t h e h y d r o l o g i c r e g i m e s o f a w i d e v a r i e t y o f s t r e a m s w i t h a h i g h l e v e l o f a c c u r a c y . 2 . The m o d e l s h o u l d b e e a s i l y a p p l i e d t o d i f f e r e n t w a t e r s h e d s w i t h e x i s t i n g h y d r o l o g i c d a t a . 3 . The m o d e l s h o u l d b e p h y s i c a l l y r e l e v a n t s o t h a t e s t i m a t e s o f o t h e r u s e f u l q u a n t i t i e s s u c h as a c t u a l e v a p o -t r a n s p i r a t i o n a n d o v e r l a n d f l o w may b e o b t a i n e d . 1 1 . 5 E x a m p l e s o f H y d r o l o g i c M o d e l i n g I I . 5 . 1 N a s h a n d S u t c l i f f e . N a s h a n d S u t c l i f f e [1970] d i s c u s s t h e p r o b l e m o f d e t e r m i n i n g t h e r i v e r f l o w s f r o m r a i n f a l l , e v a p o r a t i o n , a n d o t h e r f a c t o r s b y means o f c o n c e p t u a l m o d e l s . By c o n c e p t u a l m o d e l s t h e y r e f e r t o a m a t h e m a t i c a l m o d e l w h i c h i s t r a n s l a t e d t o a c o m p u t e r p r o g r a m . T h e i r c o n -t e n t i o n i s t h a t t h e p r o c e s s e s l i n k i n g r a i n f a l l , s n o w m e l t a n d r i v e r f l o w a r e d e t e r m i n i s t i c a n d a r e g o v e r n e d by r e a s o n a b l y w e l l known p h y s i c a l l a w s . The d i f f i c u l t i e s a r e e s s e n t i a l l y t h o s e o u t l i n e d i n S e c t i o n I I . 3 i n v o l v i n g i n t e r -a c t i o n s a n d b o u n d a r y c o n d i t i o n s . S i m p l i f y i n g a s s u m p t i o n s a r e j u s t i f i e d , 11 t h e y c l a i m , b e c a u s e t h e b a s i n i s a g e o m o r p h o l o g i c a l s y s t e m whose c o m p o n e n t s a r e r e l a t e d t o e a c h o t h e r b y l o n g common h i s t o r y . They a l s o h o l d o u t t h e i n t e r e s t i n g t h o u g h t t h a t i f t h e r e l a t i o n b e t w e e n t h e o p e r a t i o n o f t h e b a s i n i n c o n v e r t i n g p r e c i p i t a t i o n t o r u n o f f c a n b e r e c o g n i z e d , t h e n t h e o p e r a -t i o n o f e v e n a n u n g a u g e d c a t c h m e n t m i g h t b e f o r e c a s t f r o m , f o r e x a m p l e , a e r i a l p h o t o g r a p h s . T r a d i t i o n a l m e t h o d s o f f o r e c a s t i n g d i s c h a r g e f r o m r a i n f a l l t e n d t o d i v i d e t h e p r o b l e m i n t o (a) f o r e c a s t i n g v o l u m e s o f r u n o f f ; a n d (b) f o r e -c a s t i n g t h e t i m e d i s t r i b u t i o n o f t h e r u n o f f . T h i s p r o c e d u r e f o r f o r e c a s t -i n g i s d i s t i n c t f r o m f o r e c a s t s b a s e d on r o u t i n g h y d r o g r a p h s o b s e r v e d u p -s t r e a m . C o - a x i a l g r a p h i c a l c o r r e l a t i o n was d e v e l o p e d b y L i n s l e y , K o h l e r , a n d o t h e r s t o f o r e c a s t f o l u m e s [ L i n s l e y , 1 9 4 9 ] . T h i s m e t h o d r e l i e s u p o n e s t a b l i s h i n g e m p i r i c a l r e l a t i o n s b e t w e e n t h e v o l u m e s o f r u n o f f i n s i n g l e f l o o d s a n d c o r r e s p o n d i n g v o l u m e s a n d d u r a t i o n s o f r a i n f a l l , i n d i c e s o f p r e v i o u s r a i n f a l l , a n d t i m e o f y e a r . The d i s t r i b u t i o n o f t h e r u n o f f i n t i m e i s u s u a l l y e s t i m a t e d b y t h e a p p l i c a t i o n o f a u n i t h y d r o g r a p h . N a s h a n d S u t c l i f f e c l a i m t h a t due t o i n h e r e n t i m p o s s i b i l i t y o f s e p a r a t i n g t h e two c o m p o n e n t s , s t o r m r u n o f f a n d b a s e f l o w , t h e c o - a x i a l g r a p h i c a l t e c h n i q u e a n d t h e u n i t h y d r o g r a p h t e c h n i q u e a p p e a r i n c a p a b l e o f f u r t h e r e v o l u t i o n . I f f l o w w e r e t h e o n l y v a r i a b l e - o f i n t e r e s t f o r a b a s i n , t h e n t h e o n l y m o d e l r e q u i r e m e n t s w o u l d be s p e c i f i c a t i o n o f t h e m o d e l ' s f o r m and p a r a -m e t r i c v a l u e s s u c h t h a t t h e c o m p u t e d o u t p u t o r s t a t e h i s t o r y o f t h e m o d e l was a c l o s e r e p r o d u c t i o n o f t h e m e a s u r e d o u t p u t o r s t a t e h i s t o r y o f t h e s y s t e m . 12 B u t i f t h e m o d e l i s a l s o t o e x a m i n e t h e p r o c e s s o f c o n v e r t i n g r a i n f a l l t o d i s c h a r g e , t h e n a d d i t i o n a l r e q u i r e m e n t s m u s t b e m e t . F i r s t , some g u i d e t o t h e r e l a t i v e s i g n i f i c a n c e o f m o d e l p a r t s a n d t h e a c c u r a c y a n d s t a b i l i t y o f p a r a m e t r i c v a l u e s i s r e q u i r e d . S e c o n d , t h e m o d e l s h o u l d r e f l e c t t h e p h y s i c s o f t h e s y s t e m as c l o s e l y as p o s s i b l e . T h i r d , t h e m o d e l p a r a m e t e r s s h o u l d b e as i n d e p e n d e n t as p o s s i b l e . I n s h o r t , t h e m o d e l s h o u l d b e as v e r s a t i l e as p o s s i b l e , w h i l e b e i n g as s i m p l e as p o s s i b l e . O p t i m i z a t i o n o f t h e m o d e l s h o u l d b e a c h i e v e d b y a u t o m a t i c m e a n s , t h a t i s , b y t h e u s e o f c o m p u t e r o p t i m i z a t i o n p r o g r a m s . The i n d e x o f a g r e e -ment b e t w e e n o b s e r v e d a n d c o m p u t e d v a l u e s ' i s s u g g e s t e d t o b e a sum o f 2 s q u a r e s o f t h e d i f f e r e n c e s , F , a n a l o g o u s t o t h e r e s i d u a l v a r i a n c e o f r e g r e s -s i o n a n a l y s i s . 2 ~ The s h a p e o f t h e F s u r f a c e i n t h e v i c i n i t y o f t h e o p t i m u m p o i n t may be t a k e n as a n i n d i c a t i o n o f t h e s t a b i l i t y o f t h e o p t i m u m v a l u e o f t h e p a r a m e t e r s . A d d i t i o n a l d e t a i l s i n a p p l y i n g t h i s p h i l o s o p h y t o m o d e l i n g f l o w f r o m b a s i n s i s g i v e n i n 0 1 C o n n e l [1970] a n d M a n d e v i l l e [ 1 9 7 0 ] . I I . 5 . 2 R o c k w o o d a n d N e l s o n . Rockwood and N e l s o n [1966] d e s c r i b e a c o m p u t e r p r o g r a m f o r s i m u l a t i n g n a t u r a l s t r e a m f l o w a n d t h e e f f e c t s o f r e s e r v o i r r e g u l a t i o n f o r t h e C o l u m b i a R i v e r B a s i n . T h i s p r o g r a m i s c l a i m e d t o b e g e n e r a l e n o u g h t o be a p p l i e d t o any b a s i n c o n f i g u r a t i o n . S t r e a m f l o w s a r e s y n t h e s i z e d b y e v a l u a t i n g t h e e n t i r e h y d r o l o g i c p r o c e s s o f s n o w m e l t a n d r a i n f a l l r u n o f f f o r a l l i m p o r t a n t l o c a t i o n s a l o n g t h e r i v e r s y s t e m . The d a t a n e c e s s a r y f o r t h e p r o g r a m i s p r i m a r i l y p h y s i c a l a n d m e t e o r o l o g i c a l t o g e t h e r w i t h t i m e a n d r u n o f f c o e f f i c i e n t s r e p r e s e n t i n g t h e 13 hydrologic character of the individual sub-basins, channel reaches and reservoirs. Some of these coefficients are derived empirically, others from physical data. But the empirical coefficients can be derived from repetiti\e t r i a l and error approximations through the use of h i s t o r i c a l hydrometeorological data. Four requirements for developing this hydrologic model were: (1) a time increment sufficiently small to allow representation of fluc-tuations of streamflow that occur in a given drainage basin; (2) time from receipt of basic meteorological data to derivation of forecasted flows should be less than four hours; (3) the program should allow for adjustment to the computed streamflow-values in accordance with observed streamflow conditions; and (4) the method of applying forecast values of input water supply should be flex i b l e , and allow for applying more than one forecast condition. The program combines evaluation of various hydrometeorological functions to represent the entire process of streamflow simulation, from computation of the following: (1) daily snowmelt over a sub-basin for a period of study or forecast; (2) the r a i n f a l l observed or forecast to f a l l ; (3) the relative contributing area of snowmelt or r a i n f a l l effective in producing runoff; (4) the division of r a i n f a l l or snowmelt excesses i n -to surface or subsurface flow components; 15) the routing of water input through basin storage and addition of appropriate base flow values to derive streamflow from headwater or intermediate drainages; (6) the routing of out-flows derived from basin storage through successive reaches of channel stor-age; (7) the amount of intermediate tributaries inflows, and summing the 14 t o t a l r o u t e d f l o w s a t r i v e r j u n c t i o n s ; (8) t h e r o u t i n g o f t o t a l l a k e o r r e s e r v o i r i n f l o w s t h r o u g h r e s e r v o i r s t o r a g e ; (9) t h e sum o f t o t a l s t r e a m -f l o w a t d o w n s t r e a m c o n t r o l p o i n t s . The p r o g r a m i s d e s i g n e d t o s y n t h e s i z e s t r e a m f l o w f o r p e r i o d s o f one m o n t h a t a t i m e f o r e a c h b a s i n , c h a n n e l r e a c h , l a k e o r r e s e r v o i r . The h y d r o m e t e o r o l o g i c a l i n f o r m a t i o n r e q u i r e d f o r d e t e r m i n i n g i n p u t t o b a s i n s , c h a n n e l s , o r r e s e r v o i r s i s s p e c i f i e d f o r e a c h c o m p u t a t i o n p e r i o d a t a t i m e . . The i n f o r m a t i o n i n c l u d e s : ( a ) . d a i l y t e m p e r a t u r e i n d e x d a t a a n d d a i l y s n o w m e l t r a t e s f o r c o m p u t i n g s n o w m e l t e x c e s s e s ; (2) d a i l y r a i n f a l l amounts by b a s i n s ; (3) s p e c i f i e d s n o w c o v e r o r c o n t r i b u t i n g a r e a v a l u e s ; (4) i n p u t p e r i o d d i s t r i b u t i o n v a l u e s f o r b r e a k i n g down d a i l y w a t e r e x -c e s s e s t o p e r i o d amounts [3 h o u r s , 6 h o u r s , e t c . ] ; (5) s p e c i f i e d d a i l y s t r e a m f l o w v a l u e s f o r a r e a s f o r w h i c h b a s i n r o u t i n g i s n o t r e q u i r e d ; (6) s p e c i f i e d d a i l y o u t f l o w s f o r s t o r a g e r e s e r v o i r s w i t h c o n t r o l l e d o u t f l o w ; a n d (7) s p e c i f i e d d a i l y s t o r a g e v a l u e s f o r t h o s e r e s e r v o i r s o p e r a t e d w i t h p r e s c r i b e d s t o r a g e i n c r e m e n t s . S n o w m e l t i s c o m p u t e d on a maximum d a i l y t e m p e r a t u r e i n d e x , w i t h a b a s e t e m p e r a t u r e a n d a m e l t r a t e c h a r a c t e r i s t i c o f t h e b a s i n . The b a s e t e m p e r a t u r e a n d m e l t r a t e a r e d e t e r m i n e d , e x p e r i m e n t a l l y : t h e y a r e v a r i a b l e a n d may b e s p e c i f i e d f o r e a c h d a y . S n o w c o v e r d e p l e t i o n i s one o f t h e p r i m e v a r i a b l e s i n c o m p u t i n g d a i l y s n o w m e l t r u n o f f . I n t h i s p r o g r a m , s n o w c o v e r d e p l e t i o n d u r i n g a c t i v e s n o w m e l t i s e x p r e s s e d as a c u b i c f u n c t i o n o f a c c u m u l a t e d g e n e r a t e d r u n o f f , t h a t i s , 2 3 Y = A + BX + CX + DX w h e r e Y i s t h e s n o w - c o v e r e d a r e a i n p e r c e n t o f b a s i n t o t a l , X i s t h e a c c u m u -15 l a t e d g e n e r a t e d r u n o f f , i n p e r c e n t o f s e a s o n t o t a l , a n d A , B , C a n d D a r e c o e f f i c i e n t s d e r i v e d f r o m e x p e r i m e n t a l d a t a b y u s e o f c u r v e f i t t i n g p r o c e d u r e s . E a c h , d a y ' s c o m p u t e d s n o w m e l t a n d r a i n f a l l a r e c o m b i n e d t o p r o v i d e t h e t o t a l d a i l y w a t e r e x c e s s e s . As t h e r o u t i n g t i m e t h r o u g h b a s i n s t o r a g e i s g e n e r a l l y l e s s t h a n one d a y , t h e d a i l y w a t e r e x c e s s e s a r e n o r m a l l y s u b -d i v i d e d i n t o p e r i o d v a l u e s . W a t e r i n p u t t o n a t u r a l d r a i n a g e s a r e s e p a r a t e d i n t o t h r e e compo-n e n t s : (1) s u r f a c e ; (2) s u b s u r f a c e ; (3) b a s e f l o w . T h e s e c o m p o n e n t s a r e a r r a n g e d i n o r d e r o f t i m e d e l a y b e t w e e n i n f l o w a n d o u t f l o w . B a s e f l o w r e p r e s e n t s f l o w d e r i v e d f r o m d e e p p e r c o l a t i o n t h r o u g h s u b t e r r a n e a n c h a n n e l s a n d may b e d e l a y e d b y s e v e r a l m o n t h s . The s u b s u r f a c e f l o w t a k e s p l a c e w i t h -i n t h e f i r s t few f e e t b u t b e l o w t h e f i r s t few i n c h e s o f t h e s u r f a c e . The t i m e d e l a y f o r s u b s u r f a c e f l o w i s o f t h e o r d e r o f a few d a y s . The s u r f a c e f l o w o c c u r s on t h e s u r f a c e o r w i t h i n t h e f i r s t few i n c h e s o f s o i l , a n d i t s t i m e d e l a y may r a n g e f r o m a few h o u r s t o a few d a y s f o r a l a r g e b a s i n . The t o t a l w a t e r i n p u t i s d i v i d e d b e t w e e n s u r f a c e and s u b s u r f a c e f l o w o n a v a r i a b l e p e r c e n t a g e b a s i s . F o r h i g h r a t e s c f i n p u t , a l a r g e r p e r c e n t a g e o f w a t e r i s a s s i g n e d t o s u r f a c e r u n o f f . B a s e f l o w s a r e n o t r o u t e d b u t a r e s p e c i f i e d f r o m k n o w l e d g e o f r u n -o f f c h a r a c t e r i s t i c s o f a p a r t i c u l a r b a s i n . B a s e f l o w ' v a l u e s a r e s p e c i f i e d f o r t h e b e g i n n i n g a n d e n d o f t h e c o m p u t a t i o n p e r i o d , and t h e p r o g r a m i n t e r -p o l a t e s i n t e r m e d i a t e v a l u e s f o r e a c h t i m e p e r i o d . 16 B a s i n s t o r a g e r o u t i n g ( i n c r e m e n t a l s t o r a g e r o u t i n g ) : t h e c o m p u t e d p e r i o d w a t e r e x c e s s e s a r e c o n v e r t e d t o b a s i n i n f l o w amounts ( i n c f s . ) . W a t e r e x c e s s e s i n e a c h p e r i o d a r e r o u t e d t h r o u g h s u r f a c e and s u b - s u r f a c e f l o w s e p a -r a t e l y . The number o f i n c r e m e n t s , up t o 5 , o f s t o r a g e and t i m e o f s t o r a g e p e r i n c r e m e n t a r e s p e c i f i e d i n t h e b a s i n c h a r a c t e r i s t i c s f o r e a c h b a s i n . By v a r y i n g t h e number o f i n c r e m e n t s o f s t o r a g e , t h e t i m e o f s t o r a g e a n d t h e c o -e f f i c i e n t s u s e d i n s e p a r a t i n g s u r f a c e a n d s u b s u r f a c e r u n o f f , any s h a p e o f t i m e d i s t r i b u t i o n o f r u n o f f may b e g e n e r a t e d . I f t h e l a g a n d p e a k c h a r a c t e r i s t i c s h a v e b e e n f o u n d f r o m a p r e v i o u s l y d e r i v e d u n i t h y d r o g r a p h , t h e b a s i n s t o r a g e r o u t i n g c o e f f i c i e n t s r e q u i r e d t o s y n t h e s i z e t h e u n i t h y d r o g r a p h b y i n c r e m e n t a l s t o r a g e r o u t i n g method may b e f o u n d . The p a p e r c o n t i n u e s w i t h d e t a i l s o f c h a n n e l r o u t i n g , l a k e o r r e s e r -v o i r r o u t i n g , s p e c i f y i n g b a s i n o r c h a n n e l o u t f l o w s , and a d j u s t m e n t s o f s t r e a m -f l o w r o u t i n g v a l u e s t o o b s e r v e d c o n d i t i o n s . T h e s e a r e n o t o f i m m e d i a t e i n t e r -e s t t o t h i s t h e s i s . I I . 5 . 3 S t a n f o r d I V . R e s e a r c h i n d i g i t a l m o d e l s o f t h e h y d r o l o g i c c y c l e b e g a n a t S t a n f o r d i n 1 9 5 9 . The o b j e c t o f t h i s r e s e a r c h i s t h e d e v e l o p -ment o f a g e n e r a l s y s t e m o f q u a n t i t a t i v e a n a l y s i s f o r h y d r o l o g i c r e g i m e s . The m o s t r e c e n t d e v e l o p m e n t i n t h i s a n a l y s i s i s t h e S t a n f o r d I V m o d e l , d e s c r i b e d b y C r a w f o r d [ 1 9 6 6 ] . A f t e r e x p l a i n i n g c e r t a i n e l e m e n t s o f t h e h y d r o l o g i c c y c l e , C r a w f o r d g o e s o n t o d e s c r i b e t h e r e p r e s e n t a t i o n s o f t h e s e e l e m e n t s i n t h e m o d e l . The m o d e l f o r i n f i l t r a t i o n c o n s i d e r s t h e m o i s t u r e s u p p l y , t h a t i s t h e v o l u m e o f p r e c i p i t a t i o n o r s n o w m e l t p l u s t h e s u r f a c e d e t e n t i o n c a r r y -o v e r a v a i l a b l e f o r i n f i l t r a t i o n . I n f i l t r a t i o n i s made up o f two c o m -p o n e n t s , d i r e c t a n d d e l a y e d . D e l a y e d i n f i l t r a t i o n o c c u r s f r o m w a t e r w h i c h 17 f l o w s i n t o t e m p o r a r y s t o r a g e s . When h e a v y r a i n f a l l o c c u r s , t h e t e m p o r a r y s t o r a g e s f i l l and o v e r l a n d f l o w b e g i n s t o o c c u r . As a r e a l a n d t e m p o r a l v a r i a t i o n s i n i n f i l t r a t i o n c a p a c i t y i n t h e w a t e r s h e d w i l l s t r o n g l y i n f l u e n c e w a t e r s h e d b e h a v i o u r , a c u m m u l a t i v e d i s t r i b u t i o n o f i n f i l t r a t i o n c a p a c i t y i s c o n s i d e r e d , as shown i n F i g u r e 2 . M O I S T U R E 0 2 5 5 0 7 5 1 0 0 P E R C E N T O F A R E A W I T H A N I N F I L T R A T I O N C A P A C I T Y L E S S T H A N O R E Q U A L T O T H E I N D I C A T E D V A L U E FIG.2 F i g u r e 2 C u m m u l a t i v e D i s t r i b u t i o n o f I n f i l t r a t i o n C a p a c i t y R e a c t i o n o f a W a t e r s h e d t o a M o i s t u r e S u p p l y o f x I n a r e a 1 a l l i n f i l t r a t e d w a t e r i s a s s u m e d t o move i n t o t h e l o w e r z o n e a n d g r o u n d w a t e r s t o r a g e s . I n a r e a 2 , t h e i n f i l t r a t e d w a t e r c o n t r i -b u t e s t o i n t e r f l o w . F u n c t i o n a l r e l a t i o n s h i p s f o r l a n d s u r f a c e r e s p o n s e i n t e r m s o f x , c a n d b c a n be o b t a i n e d . T h e s e r e l a t i o n s l e a d t o f u n c t i o n s w h i c h p r o v i d e s m o o t h v a r i a t i o n i n t h e c o m p o n e n t s o f l a n d s u r f a c e r e s p o n s e as t h e 18 m o i s t u r e s u p p l y i s v a r i e d . The q u a n t i t y o f n e t a n d l o w e r z o n e o r g r o u n d -w a t e r i n f i l t r a t i o n i s d e t e r m i n e d by t h e c u r r e n t v a l u e o f b . The v a l u e o f c a l t e r s o u t f l o w h y d r o g r a p h s h a p e by c o n t r o l l i n g t h e s u r f a c e d e t e n t i o n . D e l a y e d i n f i l t r a t i o n i s e s t i m a t e d f r o m t h e u p p e r z o n e s t o r a g e (UZS) .and t h e u p p e r z o n e n o m i n a l c a p a c i t y ( U Z S N ) . UZSN i s an i n p u t p a r a -m e t e r . E v a p o t r a n s p i r a t i o n a n d p e r c o l a t i o n remove w a t e r f r o m t h e u p p e r z o n e s t o r a g e . Q UJ CO < < t-CE CE ( J _ ^ o o — M UJ t-X Z a. I - UJ UJ 5 ^ U) < O IL h cr tr U 3 > Q . CO C D 0-Q -U i I I 0 0 6 0 4 0 -4 . 0 U P P E R Z O N E S O I L M O I S T U R E R A T I O ( U Z S / U Z S N ) FIG. 3 F i g u r e 3 P e r c e n t a g e o f t h e I n c r e a s e i n S u r f a c e D e t e n t i o n R e t a i n e d b y t h e U p p e r Zone as a F u n c t i o n o f t h e U p p e r Zone S o i l M o i s t u r e R a t i o 19 O v e r l a n d f l o w , t h e d i s c h a r g e i n t o a s t r e a m c h a n n e l d u r i n g a g i v e n t i m e i n t e r v a l , i s a f u n c t i o n o f t h e m o i s t u r e s u p p l y r a t e and o f t h e a v e r -age d e t e n t i o n s t o r a g e d u r i n g t h a t t i m e i n t e r v a l . A r e q u i r e m e n t f o r t h i s c a l c u l a t i o n i s t h a t t h e t i m e i n t e r v a l o f c a l c u l a t i o n i s s u f f i c i e n t l y s m a l l s o t h a t t h e v a l u e o f d i s c h a r g e i n a n y t i m e i n t e r v a l r e m a i n s a s m a l l f r a c t i o n o f t h e v o l u m e s u r f a c e d e t e n t i o n . The l e n g t h , s l o p e , a n d e s t i m a t e d r o u g h n e s s o f a n o v e r l a n d f l o w p l a n e a r e u s e d as i n p u t i n t h e w a t e r s h e d m o d e l . I n t e r f l o w i s c a l c u l a t e d f r o m i n t e r f l o w d e t e n t i o n s t o r a g e a n d r e -q u i r e s ~ as a n i n p u t p a r a m e t e r a d a i l y r e c e s s i o n o r d e p l e t i o n c o n s t a n t . The i n f l o w t o g r o u n d w a t e r s t o r a g e i s a p o r t i o n o f t h e n e t i n f i l -t r a t i o n a n d a p o r t i o n o f t h e d e l a y e d i n f i l t r a t i o n f r o m u p p e r z o n e s t o r a g e . 0 1.0 2.0 3.0 SOIL MOISTURE RATIO (LZS/LZSN) FIG. 4 F i g u r e 4 A s s i g n m e n t o f I n f i l t r a t e d W a t e r t o G r o u n d w a t e r 20 The o u t f l o w f r o m g r o u n d w a t e r s t o r a g e i s m o d e l e d by a s s u m i n g a r e p r e s e n t a t i v e c r o s s - s e c t i o n a l a r e a o f f l o w a n d b y e s t i m a t i n g t h e e n e r g y g r a d i e n t a s a b a s e g r a d i e n t p l u s a v a r i a b l e g r a d i e n t w h i c h d e p e n d s o n g r o u n d w a t e r a c c r e t i o n . T h i s p a p e r c l a i m s t h e m a i n c o n t r i b u t o r s t o s n o w m e l t a r e c o n v e c -t i o n , c o n d e n s a t i o n , a n d r a i n f a l l . I n one s u b r o u t i n e i n t h e p r o g r a m , s n o w -m e l t i s c a l c u l a t e d f r o m r a d i a t i o n , w i n d v e l o c i t y , d e w p o i n t t e m p e r a t u r e a n d t e m p e r a t u r e . T h i s c a l c u l a t i o n c a n b e u s e d o n l y i n w e l l i n s t r u m e n t e d w a t e r -s h e d s . A n a l t e r n a t e s u b r o u t i n e u s i n g o n l y a i r t e m p e r a t u r e d a t a was d e v e -l o p e d f o r s p a r s e d a t a s i t u a t i o n s . F r o m c o m p a r i s o n o f t h e s e two s n o w m e l t c a l c u l a t i o n s , w i n d v e l o c i t y and d e w p o i n t t e m p e r a t u r e d a t a w o u l d p r o v i d e f o r more a c c u r a t e s n o w m e l t c a l c u l a t i o n s . F o r t h e f i r s t r o u t i n e , c a l c u l a t i o n s a r e made h o u r l y a n d i n c o m i n g p r e c i p i t a t i o n i s a d d e d t o t h e snow p a c k o r t o l i q u i d w a t e r s t o r a g e . Temp-e r a t u r e and r a d i a t i o n d a t a a r e u s e d t o f i n d t h e n e t h e a t e x c h a n g e i n t h e h o u r . I f t h e n e t h e a t e x c h a n g e i s n e g a t i v e t h e n h e a t i s b e i n g l o s t f r o m t h e snow p a c k a n d t h e r e i s a n a d d i t i o n t o t h e n e g a t i v e h e a t s t o r a g e . When t h e n e t h e a t e x c h a n g e becomes p o s i t i v e , t h e n e g a t i v e h e a t s t o r a g e i s r e d u c e d , a n d when t h i s s t o r a g e i s z e r o , s n o w m e l t b e g i n s . The m e l t e n t e r s l i q u i d w a t e r s t o r a g e u n t i l a l i m i t i n g v a l u e i s r e a c h e d a f t e r w h i c h a d d i t i o n a l m e l t o r r a i n f a l l i s d i s c h a r g e d f r o m t h e snow p a c k . Snow a l b e d o v a r i e s b e t w e e n 0 . 7 5 a n d 0 . 6 5 , w i t h t h e h i g h v o l u m e u s e d a f t e r new s n o w f a l l . H o u r l y t e m p e r a t u r e s a r e c a l c u l a t e d f o r e a c h w a t e r s h e d segment f r o m maximum a n d minimum t e m p e r a t u r e s a t b a s e s t a t i o n s . L a p s e r a t e s a r e a l t e r e d t o a l l o w f o r d i u r n a l v a r i a t i o n a n d t y p i c a l d r y w e a t h e r o r s t o r m c o n d i t i o n s . 21 Snow e v a p o r a t i o n i s c a l c u l a t e d f r o m e s t i m a t e d p o t e n t i a l snow e v a p o r a t i o n i f t h e a i r t e m p e r a t u r e i s b e l o w 3 2 ° F . S t o r a g e o f l i q u i d w a t e r i n t h e snowpack i s l i m i t e d b y a n i n p u t p a r a m e t e r WC t h a t a s s i g n s t h e maximum o r l i m i t i n g l i q u i d w a t e r s t o r a g e a s a f r a c t i o n o f s t o r a g e i n t h e s n o w p a c k . - D a i l y l a k e e v a p o r a t i o n o r p o t e n t i a l e v a p o t r a n s p i r a t i o n d a t a a r e u s e d as i n p u t s . F o l l o w i n g t h e a s s u m p t i o n made f o r i n f i l t r a t i o n c a p a c i t y t h e c u m m u l a t i v e f r e q u e n c y d i s t r i b u t i o n o f e v a p o t r a n s p i r a t i o n o p p o r t u n i t y i s a s s u m e d t o b e l i n e a r . P O T E N T I A L E V A P O T R A N S P I R A T I O N r EVAPOTRANSP IRAT ION O P P O R T U N I T Y 100 P E R C E N T OF A R E A W ITH A D A I L Y E V A P O T R A N S P I R A T I O N O P P O R T U N I T Y L E S S T H A N OR E Q U A L TO THE IND ICATED V A L U E FIG. 5 " i g u r e 5 C u m m u l a t i v e D i s t r i b u t i o n o f P o t e n t i a l E v a p o t r a n s p i r a t i o n 22 i The c u a n t i t y o f w a t e r l o s t by e v a p o t r a n s p i r a t i o n f r o m t h e l o w e r E 2 z o n e when E i s l e s s t h a n r i s E = E - p w h e r e E i s t h e a c t u a l E - T . P P 2T" r i s c o m p u t e d f r o m K 3 , a n i n p u t p a r a m e t e r , and t h e r a t i o o f s t o r a g e i n t h e l o w e r z o n e , L Z S , a n d t h e n o m i n a l s t o r a g e , L Z S N . The p a p e r c o n c l u d e s w i t h some p h i l o s o p h y a n d p r e d i c t i o n s c o n -c e r n i n g d i g i t a l m o d e l i n g as a p p l i e d t o h y d r o l o g y . I n t h i s c o n t e x t t h e a u t h o r s n o t e t h a t p a r a m e t e r o p t i m i z a t i o n d o e s n o t n e c e s s a r i l y i m p l y o p t i m u m m a t h e m a t i c a l r e p r e s e n t a t i o n . CHAPTER I I I MISSION CREEK FLOW MODEL I I I . l I n p u t D a t a S o u r c e s A s was n o t e d i n S e c t i o n I I . 4 , a m o d e l i s l i m i t e d by t h e amount a n d i n a c c u r a c y o f t h e i n p u t d a t a . F o r t h e M i s s i o n C r e e k b a s i n t h e i n p u t d a t a a r e s p a r s e , b u t s t i l l more numerous t h a n f o r o t h e r c r e e k s f l o w i n g i n t o L a k e O k a n a g a n . D a i l y maximum a n d minimum t e m p e r a t u r e s a n d p r e c i p i t a t i o n s a r e a v a i l a b l e f r o m t h r e e s t a t i o n s , K e l o w n a Bowes S t r e e t (1160 f t . ) , J o e R i c h C r e e k (2870 f t . ) , a n d M c C u l l o c h (4100 f t . ) . T h i s means t h a t no d a t a i s a v a i l a b l e f o r e l e v a t i o n s above 4100 f t . , o r a b o u t 2/3 c f t h e b a s i n a r e a . The l o c a t i o n s o f t h e s e m e t e o r o l o g i c a l s t a t i o n s a r e shown i n F i g u r e 6 a n d t h e d a t a a r e l i s t e d i n Monthly Record of Meteorological Observations, Canada. M o n t h l y snow d e p t h s a n d w a t e r e q u i v a l e n t s o f t h e snowpack a r e a v a i l a b l e a t M c C u l l o c h (4200 f t . ) , A b e r d e e n (4300 f t . ) , P o s t i l l (4500 f t . ) a n d M i s s i o n C r e e k (6000 f t . ) . The d a t a f r o m t h e s e s t a t i o n s a r e p r o v i d e d i n British Columbia Snow Survey Bulletin. T h e m o n t h l y s t o r a g e f r o m A p r i l t h r o u g h J u n e f o r t h e l a k e s a n d r e s e r v o i r s G r e y s t o k e , H a y n e s , H y d r a u l i c , I d e a l , James a n d P o s t i l l a r e a l s o a v a i l a b l e i n British Colurrbio. Snow Survey Bulletin. E v a p o r a t i o n d a t a when a v a i l a b l e a r e t a k e n f r o m S u m m e r l a n d a n d a r e l i s t e d i n Monthly Record Meteorological Observations, Canada. A l t h o u g h S u m m e r l a n d i s n o t i n t h e M i s s i o n C r e e k b a s i n , i t i s o n O k a n a g a n L a k e so 23 24 / r \ v ) / O S P R E Y L A K E \ \ I \ / 3 \ i i v \ V E R N O N C O L D S T R E A M ( ) \ A b O K A N A G A N C E N T R E V ; A B E R D E E N L A K E I D E A L J O E R I C H C R E E K / S C A L E I N M I L E S : i - G R E Y S T O K E M I S S I O N C R E E K M c C U L L O C H H Y D R A U L I C H A Y N E S .5 0 10 P E N T I C T O N A l R P O R T © M E T E O R O L O G I C A L S T A T I O N S A S N O W C O U R S E S O L A K E S A N D R E S E R V O I R S FIG.6 LOCATIONS OF INPUT DATA STATIONS 25 TABLE 3 INPUT DATA STATIONS FOR THE MISSION CREEK B A S I N STATION NAME ELEVATION DATA K e l o w n a Bowes S t r e e t 1160 J o e R i c h C r e e k I d e a l M c C u l l o c h H a y n e s H y d r a u l i c A b e r d e e n James F o s t h i l l G r e y s t o k e M i s s i o n C r e e k 2870 ^ 4000 4100 4200 ^ 4200 4300 4500 4500 6000 6000 D a i l y Maximum a n d M i n i m u m T e m p e r -a t u r e D a i l y P r e c i p i t a t i o n D a i l y Maximum a n d M i n i m u m T e m p e r -a t u r e D a i l y P r e c i p i t a t i o n M o n t h l y S t o r a g e ( a c r e f t . ) D a i l y Maximum and M i n i m u m T e m p e r -a t u r e D a i l y P r e c i p i t a t i o n W a t e r E q u i v a l e n t ( i n c h e s o f w a t e r ) M o n t h l y S t o r a g e ( a c r e f t . ) M o n t h l y S t o r a g e ( a c r e f t . ) W a t e r E q u i v a l e n t ( i n c h e s ) M o n t h l y S t o r a g e ( a c r e f t . ) W a t e r E q u i v a l e n t ( i n c h e s ) M o n t h l y S t o r a g e ( a c r e f t . ) M o n t h l y S t o r a g e ( a c r e f t . ) W a t e r E q u i v a l e n t ( i n c h e s ) t h e e v a p o r a t i o n d a t a a r e assumed t o be r e p r e s e n t a t i v e o f t h e e v a p o r a t i o n a t t h e f i r s t l e v e l o f t h e M i s s i o n C r e e k b a s i n . 26 M i s s i o n C r e e k f l o w s a r e g a u g e d by a r e c o r d i n g gauge ( 8 n m l l 6 ) a t T a y l o r R o a d , 1-1/2 m i l e s s o u t h w e s t o f R u t l a n d . The gauge was moved 1-3/4 m i l e s d o w n s t r e a m i n 1 9 6 8 . The f l o w s u s e d i n t h e m o d e l a r e t h e d a i l y mean f l o w s i n c u b i c f e e t p e r s e c o n d . 1 1 1 . 2 B a s i n S u b d i v i s i o n F o r a n a l y t i c a l p u r p o s e s t h e M i s s i o n C r e e k b a s i n was d i v i d e d i n -t o 12 e l e v a t i o n b a n d s o r l e v e l s . F o r e x a m p l e , t h e f i r s t b a n d e x t e n d s f r o m a n e l e v a t i o n o f 1 , 0 0 0 f t . a b o v e s e a l e v e l t o 1 , 5 0 0 f t . w i t h a c e n t e r b a n d e l e v a t i o n o f 1 , 2 5 0 f t . a n d a n a r e a o f 8 s q . m i . , T a b l e 2 . The h e i g h t o f t h e e l e v a t i o n b a n d s was a r r i v e d a t a r b i t r a r i l y w h i l e t h e a r e a s w e r e d e t e r m i n e d f r o m a t o p o g r a p h i c a l map o f t h e r e g i o n . W i t h t h e r e l o c a t i o n o f t h e M i s s i o n C r e e k gauge i n 1 9 6 8 , t h e d r a i n a g e a r e a o f t h e b a s i n was a p p a r e n t l y i n c r e a s e d f r o m 322 t o 338 s q u a r e m i l e s . I n t h e m o d e l t h e 338 s q u a r e m i l e v a l u e was u s e d f o r a l l t h e y e a r s . 1 1 1 . 3 T r e a t m e n t o f t h e I n p u t D a t a I I I . 3 . 1 T e m p e r a t u r e . The d a i l y maximum a n d minimum t e m p e r a t u r e s a r e a v e r a g e d a t e a c h s t a t i o n . T h i s a v e r a g e s t a t i o n t e m p e r a t u r e i s l a p s e d o v e r a l l t h e e l e v a t i o n b a n d s o f t h e b a s i n u s i n g t h e l a p s e r a t e , T L A P S , u s u a l l y 3 . 5 F ° / 1 0 0 0 f t . T h i s p r o v i d e s t h r e e t e m p e r a t u r e s f o r e a c h b a n d , w h i c h a r e a v e r a g e d t o p r o v i d e t h e a v e r a g e d a i l y t e m p e r a t u r e i n a b a n d , T ( J , L ) . The d a i l y maximum t e m p e r a t u r e s w e r e h a n d l e d i n a s i m i l a r manner t o p r o v i d e a maximum d a i l y t e m p e r a t u r e f o r e a c h b a n d , T X L ( J , L ) . The v a l u e o f 3 .5F/ ' 1000 f t . was c h o s e n f r o m c o n s i d e r a t i o n o f t h e I n t e r n a t i o n a l S t a n d a r d A t m o s p h e r e . L a t e r r e s u l t s i n d i c a t e d t h a t t h i s v a l u e i s l o w f o r some y e a r s , b u t d o e s a p p e a r a r e a s o n a b l e s t a r t i n g v a l u e . 27 I I I . 3 . 2 P r e c i p i t a t i o n . An e x a m p l e o f t h e m e t h o d f o r f i n d i n g t h e d a i l y p r e c i p i t a t i o n i n e a c h b a n d i s shown i n F i g u r e 7 . F o r b a n d s 1 t o 4 p r e c i p i t a t i o n v a l u e s a r e f o u n d f r o m a s t r a i g h t l i n e c o n n e c t i n g p r e c i p i t a -t i o n s a t K e l o w n a Bowes S t r e e t a n d J o e R i c h C r e e k . F o r h i g h e r b a n d s a s t r a i g h t l i n e c o n n e c t i n g p r e c i p i t a t i o n v a l u e s a t J o e R i c h C r e e k a n d M c -C u l l o c h i s e x t r a p o l a t e d . I f t h e p r e c i p i t a t i o n s h o u l d become n e g a t i v e i t i s s e t e q u a l t o z e r o . I f t h e d a i l y a v e r a g e t e m p e r a t u r e i n a b a n d was l e s s t h a n o r e q u a l t o 3 5 ° F . , t h e n any p r e c i p i t a t i o n f a l l i n g i n t o t h a t b a n d was c o n s i d e r e d t o b e snow. 1 2 5 0 2 2 5 0 3 2 5 0 4 2 5 0 5 2 5 0 6 2 5 0 E L E V A T I O N ( F T . ) Day 52 Y e a r 1970 K e l o w n a Bowes S t r e e t J o e R i c h C r e e k M c C u l l o c h . 2 5 i n c h e s . 3 9 . 5 2 P r e c i p i t a t i o n o n Day 52 B a n d 10 i s . 7 i n c h e s F i g u r e 7 E x a m p l e o f L a p s i n g t h e P r e c i p i t a t i o n 28 T h e r e a r e a r g u m e n t s f o r u s i n g r e l a t i o n s o t h e r t h a n l i n e a r i n t h e p r e c i p i t a t i o n - e l e v a t i o n r e l a t i o n . F o r t h i s m o d e l , l a c k o f i n f o r m a t i o n r e -g a r d i n g o r i e n t a t i o n , e x p o s u r e a n d s l o p e d i c t a t e d t h e use o f t h e s i m p l e l i n e a r s e g m e n t s . I I I . 3 . 3 E v a p o r a t i o n . E v a p o r a t i o n i s a g e n e r a l t e r m f o r t h e c o m -p l e x p r o c e s s e s i n v o l v e d i n t h e n e t t r a n s f e r o f l i q u i d w a t e r f r o m s o i l a n d p l a n t s t o w a t e r v a p o u r i n t h e a i r . I n p a r t i c u l a r , a l l w a t e r l o s s e s b y b o t h t r a n s p i r a t i o n a n d e v a p o r a t i o n , w h e r e t r a n s p i r a t i o n i s t h e p r o c e s s by w h i c h p l a n s t r a n s f e r w a t e r t o t h e a t m o s p h e r e , a r e known as t o t a l e v a p o r a t i o n o r e v a p o t r a n s p i r a t i o n ( E - T ) . The maximum r a t e a t w h i c h w a t e r c a n be t r a n s -f e r r e d t o t h e a i r i s c a l l e d t h e p o t e n t i a l e v a p o t r a n s p i r a t i o n r a t e . I n c r o p - o r i e n t e d s t u d i e s , t h e t e r m c o n s u m p t i v e u s e i s f r e q u e n t l y a p p l i e d t o t h e t o t a l amount o f w a t e r t a k e n up b y v e g e t a t i o n f o r t r a n s p i r a -t i o n a n d b u i l d i n g o f p l a n t t i s s u e p l u s e v a p o r a t i o n o f s o i l m o i s t u r e , e v a p o -r a t i o n f r o m s n o w , a n d i n t e r c e p t e d p r e c i p i t a t i o n . C o n s u m p t i v e u s e i s h i g h l y d e p e n d e n t u p o n e n v i r o n m e n t a l f a c t o r s s u c h as w e a t h e r , s o i l m o i s t u r e , and g r o u n d w a t e r . I n t h i s t h e s i s t h e a c t u a l e v a p o t r a n s p i r a t i o n i s t a k e n t o b e e q u a l t o c o n s u m p t i v e u s e . E v a p o r a t i o n i s d e p e n d e n t upon v a p o u r p r e s s u r e d i f f e r e n c e b e t w e e n t h e w a t e r s u r f a c e a n d t h e a i r above t h e w a t e r s u r f a c e , t h e t e m p e r a t u r e s i n t h e a i r a n d w a t e r , w i n d , a t m o s p h e r i c p r e s s u r e , t h e q u a l i t y o f the ' w a t e r , and t h e n a t u r e o f t h e e v a p o r a t i n g s u r f a c e . ' I n t h i s m o d e l , b e c a u s e o f t h e l i m i t e d a v a i l a b l e d a t a , t h e p a r a m e t e r o f m a j o r c o n c e r n i s t e m p e r a t u r e . A s t h e t e m p e r a t u r e o f a b o d y o f w a t e r i n c r e a s e s , t h e k i n e t i c e n e r g y o f t h e m o l e c u l e s i n t h e b o d y o f w a t e r i n c r e a s e s a n d t h e r a t e o f e s c a p e o f m o l e -c u l e s a n d h e n c e e v a p o r a t i o n i n c r e a s e s . 29 Of s p e c i a l i n t e r e s t i n t h e m o d e l i s t h e b e h a v i o u r o f e v a p o r a t i o n w i t h e l e v a t i o n [ B l a n e y , 1 9 5 6 ] . The r e d u c t i o n i n p r e s s u r e w i t h i n c r e a s i n g e l e v a t i o n s h o u l d i n c r e a s e e v a p o r a t i o n , b u t t e m p e r a t u r e w i l l d e c r e a s e w i t h e l e v a t i o n . A d d i t i o n a l f e a t u r e s s u c h as t h e o r i e n t a t i o n o f t h e s l o p e f u r -t h e r c o m p l i c a t e t h e r e l a t i o n . L a k e e v a p o r a t i o n was a s s u m e d t o b e t h e p o t e n t i a l e v a p o t r a n s p i r a -t i o n f o r t h e f i r s t l e v e l o f t h e M i s s i o n C r e e k b a s i n . I f l a k e e v a p o r a t i o n d a t a were n o t a v a i l a b l e , t h e p a n e v a p o r a t i o n was c o r r e c t e d t o l a k e e v a p o r -a t i o n u s i n g t h e a v e r a g e p a n c o e f f i c i e n t s l i s t e d i n T a b l e 4 . T h e s e c o e f f i -c i e n t s w e r e c a l c u l a t e d f r o m months when b o t h p a n a n d l a k e e v a p o r a t i o n d a t a w e r e p r o v i d e d . H e r e p a n c o e f f i c i e n t s a r e d e f i n e d as t h e r a t i o o f e v a p o r a -t i o n f r o m a l a r g e b o d y o f w a t e r and e v a p o r a t i o n f r o m a p a n . TABLE 4 AVERAGE MONTHLY PAN C O E F F I C I E N T S FOR SUMMERLAND MONTH PAN C O E F F I C I E N T NUMBER OF YEARS STANDARD DEVIATION A p r i l 0 . 7 5 6 0 . 0 2 May 0 . 7 4 7 J u n e 0 . 7 2 6 0 . 0 1 J u l y 0 . 7 0 6 A u g u s t 0 . 6 8 6 S e p t e m b e r 0 . 6 9 6 30 I f n e i t h e r p a n n o r l a k e e v a p o r a t i o n w e r e a v a i l a b l e t h e m o n t h l y e v a p o r a t i o n was e s t i m a t e d f r o m t h e m o n t h l y d e g r e e d a y s , F i g u r e 8 . The m o n t h l y d e g r e e d a y s , S T E X ( M ) , i s t h e sum o v e r t h e number o f d a y s o f t h e m o n t h o f t h e d a i l y a v e r a g e t e m p e r a t u r e s m i n u s 4 0 . T h i s 40 b a s e was c h o s e n as t h e STEX(M) ' f i t t e d t h e l a k e e v a p o r a t i o n d a t a b e t t e r t h a n STEX(M) w i t h a b a s e 3 2 . The c o m p a r i s o n was made when l a k e e v a p o r a t i o n d a t a w e r e a v a i l -a b l e . A s c a n be s e e n f r o m F i g u r e 8 t h e r e i s c o n s i d e r a b l e s c a t t e r , e v i d e n c e t h a t w i n d a n d o t h e r f a c o t r s m u s t be c o n s i d e r e d i n e v a p o r a t i o n . The r e g r e s -- 3 s i o n e q u a t i o n was f o u n d t o be LKEVP = 4 . 6 x 10 x STEX(M) + 2 . 5 . F i g u r e 8 L a k e E v a p o r a t i o n as a F u n c t i o n o f D e g r e e Days 31 The d a i l y p o t e n t i a l e v a p o t r a n s p i r a t i o n f o r t h e f i r s t l e v e l was f o u n d f r o m a r a t i o o f t h e d a i l y e x c e s s t e m p e r a t u r e , T E X ( J , 1 ) , a n d t h e m o n t h l y d e g r e e d a y s , S T E X ( M ) , m u l t i p l i e d b y t h e m o n t h l y e v a p o r a t i o n . T h a t i s , DPEVP ( J , l ) = X LKEVP(M) To l a p s e t h e p o t e n t i a l e v a p o t r a n s p i r a t i o n t o t h e h i g h e r b a n d s , , t h e maximum d a i l y t e m p e r a t u r e , T X L ( J , L ) , o f e a c h b a n d was e m p l o y e d a s f o l l o w s : r n V T f T T \ DPEVP ^'^ - ^ <tl) X ^^'^ w h e r e t h e s u b s c r i p t J r e f e r s t o t h e d a y , L t o t h e l e v e l , a n d M t o t h e m o n t h . E v a p o r a t i o n f r o m t h e snowpack was a s s u m e d t o be z e r o . T h i s was d u e t o l a c k o f d a t a on w i n d s p e e d , v a p o u r p r e s s u r e , a n d o r i e n t a t i o n o f t h e s l o p e s o r s h e l t e r i n g o f t r e e s . N e l s o n [1962] i n d i c a t e s t h a t f r o m a h y d r o -l o g i c a l p o i n t o f v i e w , e v a p o r a t i o n l o s s e s f r o m a l a r g e w a t e r s h e d a r e a a r e l i k e l y t o b e l e s s t h a n t h e e r r o r s i n o b t a i n i n g t h e t o t a l w a t e r c o n t e n t o f t h e s n o w p a c k . I I I . 4 S n o w m e l t The p h y s i c s o f s n o w m e l t a r e c o m p l i c a t e d . The t h e r m a l c o n d u c t i v i t y o f snow a p p e a r s t o b e a f u n c t i o n o f d e n s i t y a n d c r y s t a l s t r u c t u r e b u t a l w a y s h a s a r e l a t i v e l y s m a l l v a l u e a n d s o h e a t t r a n s m i s s i o n t h r o u g h snow i s n o t l a r g e . 32 H e a t may be t r a n s f e r r e d t o t h e s n o w p a c k f r o m t h e s u r r o u n d i n g a i r , t h e g r o u n d b e l o w , r a i n f a l l i n g i n t o t h e snow and d i r e c t s o l a r r a d i a t i o n . A c c o r d i n g t o L i n s l e y [ ] 9 4 9 ] , t h e h e a t t r a n s f e r r e d b y c o n d u c t i o n f r o m s t i l l a i r i s s m a l l a n d c o n v e c t i v e t r a n s f e r i s more e f f i c i e n t . H e a t f l o w t o t h e snowpack f r o m t h e u n d e r l y i n g s o i l p r o b a b l y d o e s n o t c o n t r i b u t e t o t h e s n o w m e l t a f t e r t h e p a c k h a s b e e n o n t h e g r o u n d f o r s e v e r a l w e e k s , b u t i t may m e l t s u f f i c i e n t snow t o f i l l t h e s o i l m o i s t u r e d e f i c i t . T h i s p r i m -i n g o f t h e s o i l may b e a n i m p o r t a n t a n t e c e d e n t c o n d i t i o n . H e a t f r o m r a i n -f a l l i s b y i t s e l f n o t i m p o r t a n t i n m e l t i n g snow [ L i n s l e y , 1 9 4 9 ] . D i r e c t s o l a r r a d i a t i o n i s a n i m p o r t a n t a n d u n d e r some c o n d i t i o n s may b e t h e m o s t i m p o r t a n t f a c t o r i n m e l t i n g s n o w . S o l a r r a d i a t i o n p e n e -t r a t e s o n l y some 18 i n c h e s o f p a c k . I f t h e p a c k i s t h i n enough f o r r a d i -a t i o n t o r e a c h t h e g r o u n d t h e n a g r e a t e r p o r t i o n o f t h e r a d i a t i o n i s a b -s o r b e d a n d t h e snowpack i s warmed f r o m b e n e a t h . The amount o f i n c o m i n g r a d i a t i o n i s a f u n c t i o n o f t i m e o f y e a r a n d c l o u d c o v e r . The amount o f r a d i a t i o n p r o d u c i n g s n o w m e l t i s d e t e r m i n e d by t h e s n o w ' s a l b e d o , t h a t i s , r e f l e c t i o n c o e f f i c i e n t , w h i c h i s d e p e n d e n t on t h e s n o w ' s c o n d i t i o n . D r y f r e s h l y f a l l e n snow may h a v e a n a l b e d o o f 0 . 9 0 w h i l e a n o l d w e t snow s u r -f a c e may h a v e a n a l b e d o o f 0 . 4 0 . The w a t e r e q u i v a l e n t o f t h e s n o w , t h a t i s , t h e d e p t h o f w a t e r w h i w o u l d r e s u l t f r o m m e l t i n g i s d e p e n d e n t on snow d e n s i t y as w e l l as d e p t h . W a t e r c o n t e n t r e f e r s t o t h e l i q u i d w a t e r i n t h e snow, w i t h snow b e i n g a b l e t o h o l d l a r g e v o l u m e s o f w a t e r w h i c h c a n b e r e l e a s e d s u d d e n l y . I n t h i s m o d e l , r a i n f a l l i n g i n t o snow c o n t r i b u t e d t o r u n o f f t h r o u g h s n o w m e l t by t h e q u a n t i t y B M R F ( J , L ) . 33 As no o t h e r d a t a w e r e a v a i l a b l e , s n o w m e l t i n t h i s m o d e l was e s t i -o m a t e d f r o m t h e number o f d e g r e e s t h e d a i l y b a n d t e m p e r a t u r e was above 32 F . a n d a p o i n t m e l t f a c t o r P T M . The p o i n t m e l t f a c t o r was 0 . 5 5 c u b i c f e e t p e r s e c o n d p e r s q u a r e m i l e p e r F a h r e n h e i t d e g r e e p e r d a y , i n a l l y e a r s b u t 1 9 6 9 . I I I . 5 Snow L i n e R e c e s s i o n Snow l i n e r e c e s s i o n was e s t a b l i s h e d t h r o u g h a b a n d s w i t c h p a r a -m e t e r L S W ( L ) . The b a n d s w i t c h t i m e f o r a b a n d i s t h e d a y o n w h i c h t h e snow l i n e p a s s e s t h e u p p e r b o u n d a r y o f t h a t b a n d . The r a t i o n a l e f o r u s i n g b a n d s w i t c h t i m e s f o r snow l i n e r e c e s s i o n i s p r o v i d e d i n G e i g e r [ 1 9 6 5 ] , S e c t i o n 4 6 . E v e n i f t h e snow m e l t s a t d i f f e r e n t t i m e s i n d i f f e r e n t y e a r s , t h e m e l t i n g p a t t e r n i s t h e same. The a c t u a l manner i n w h i c h snow m e l t s i n u p l a n d a r e a s i s c l o s e l y r e l a t e d t o t o p o g r a p h y w i t h s t e e p s o u t h e r n f a c i n g s l o p e s m e l t i n g f i r s t , f o l l o w e d b y t h e more g e n t l e s l o p e s a n d n o r t h e r n s l o p e s . F o r 1 9 6 0 , 1 9 6 3 , 1 9 6 4 , 1 9 6 5 , 1 9 6 7 , 1968 a n d 1969 t h e b a n d s w i t c h d a y s (LSW) w e r e o b t a i n e d by f i n d i n g t h e b e s t f i t s i m u l a t i o n o f t h e d a i l y f l o w s . H e r e , b e s t f i t was e s t a b l i s h e d on t h e b a s i s o f m i n i m i z i n g t h e r e s i -d u a l v a r i a n c e . F r o m t h e s e b e s t f i t v a l u e s , a r o u t i n e was e s t a b l i s h e d by w h i c h a c e r t a i n p e r c e n t a g e o f t h e v/ater e q u i v a l e n t i n e a c h b a n d was m e l t e d . The w a t e r e q u i v a l e n t was f o u n d b y c o n s t r u c t i n g a l i n e a r r e l a t i o n , o n a s e m i - l o g g r a p h , b e t w e e n t h e w a t e r e q u i v a l e n t s , o n a l o g a r i t h m i c s c a l e , a n d t h e e l e v a t i o n s o n a l i n e a r s c a l e , a t M c C u l l o c h (4200 f t . ) , A b e r d e e n (4300 f t . ) , P o s t i l l (4500 f t . ) a n d M i s s i o n C r e e k (6000 f t . ) . 34 The r a t e a t w h i c h t h e snow m e l t e d was f o u n d f r o m t h e d a i l y a v e r a g e b a n d t e m p e r a t u r e s , T ( J , L ) a n d t h e p o i n t m e l t f a c t o r , P T M . The number o f d a y s r e q u i r e d t o m e l t t h e d e t e r m i n e d p e r c e n t a g e o f snow i n a b a n d p r o v i d e d t h e b a n d s w i t c h d a y f o r t h a t b a n d . As t h e c o m p u t e r p r e d i c t e d b a n d s w i t c h d a y s a n d t h e b e s t f i t b a n d s w i t c h d a y s f o r t h e v a r i o u s y e a r s d i d now show c o m p l e t e c o r r e l a -t i o n , F i g u r e 9 , a n e q u a t i o n r e l a t i n g t h e f i t t e d L S W ' s a n d t h e p r e d i c t e d L S W ' s was d e v e l o p e d . LSW(L) T m m T ^ = 6 . 1 + 0 . 9 5 x LSW(L) n „ n ^ „ , ^ F I T T E D PREDICTED I I I . 6 I n t e r c e p t i o n I n t e r c e p t i o n i s t h e e f f e c t o f v e g e t a l c o v e r i n r e d u c i n g t h e amount o f p r e c i p i t a t i o n r e a c h i n g t h e g r o u n d . I n t e r c e p t i o n i s m o s t e f f e c -t i v e o n t h e e a r l y p r e c i p i t a t i o n f r o m a s t o r m . As m o s t s t o r m s y i e l d s m a l l amounts o f p r e c i p i t a t i o n , i n t e r c e p t i o n b y d e n s e c o v e r o r f o r e s t s may amount t o 25 p e r c e n t o f t h e a n n u a l p r e c i p i t a t i o n . W i n d e f f e c t s i n t e r c e p t i o n i n two o p p o s e d w a y s , o n one h a n d r e d u c i n g t h e maximum s t o r a g e b y s h a k i n g t h e b r a n c h e s a n d l e a v e s a n d o n t h e o t h e r i n c r e a s i n g t h e e v a p o r a t i o n f r o m s t o r a g e . F o r m u l a e f o r i n t e r c e p t i o n h a v e b e e n d e v e l o p e d [ L i n s l e y , 1949] b u t t h e s e r e q u i r e k n o w l e d g e o f p a r a m e t e r s n o t m e a s u r e d o r known i n t h e M i s s i o n C r e e k b a s i n . I n t e r c e p t i o n o f p r e c i p i t a t i o n was m o d e l e d s i m p l y b y a s s u m i n g t h a t t h e i n t e r c e p t i o n was a f r a c t i o n o f t h e r a i n f a l l , t h e f r a c t i o n i n -c r e a s i n g w i t h e l e v a t i o n . The f r a c t i o n v a r i e d f r o m 10 f o r t h e l o w e s t b a n d s t o 20 p e r c e n t f o r t h e h i g h e s t b a n d s . FIG.9 THE REGRESSION OF FITTED BAND SWITCH TIMES (LSW) ON PREDICTED BAND SWITCH TIMES. 36 111.7 Early Season Storage The e a r l y season storage i s estimated i n two p a r t s , the f i r s t f or A p r i l , the second for May. A f t e r June 1st the assumption of no basin storage i s made. A p r i l storage i s found by consideration of the change i n t o t a l storage of the r e s e r v o i r s , Haynes, Hydraulic, James, Greystoke. Ideal and P o s t i l l between A p r i l 1st and May 1st. May storage i s the change i n these r e s e r v o i r s between May 1st and June 1st. T h i r t y per cent of the d a i l y flow from each of the bands 7 through 12 i s subtracted f o r storage, u n t i l e i t h e r the storage r e q u i r e -ment f o r the month has been f i l l e d or the month i s over. 111.8 I n f i l t r a t i o n I n f i l t r a t i o n i s defined as the passage of water through the s o i l surface i n t o the s o i l . I n f i l t r a t i o n capacity i s the maximum rate at which a given s o i l i n a given condition can absorb r a i n as i t f a l l s . I n f i l t r a t i o n capacity v a r i e s with the p o r o s i t y of the s o i l , the i n i t i a l moisture content of the s o i l , the r a i n f a l l i n t e n s i t y , and the season. For f i n e dry sandy s o i l s , the i n f i l t r a t i o n capacity may be low when the s o i l i s dry and increase as the s o i l i s wetted. The rate of i n f i l t r a t i o n u s ually v a r i e s d i r e c t l y with r a i n f a l l i n t e n s i t y provided i n t e n s i t y i s less than i n f i l t r a t i o n capacity. . But when the i n t e n s i t y ex-ceeds the i n f i l t r a t i o n capacity then i n t e n s i t y has l i t t l e e f f e c t on the rate of i n f i l t r a t i o n . F i n a l l y , the i n f i l t r a t i o n rate i s a function of season [Horton, 1940], with i n f i l t r a t i o n capacity increasing i n May and decreasing i n September. 37 I n f i l t r a t i o n i s n o t d i r e c t l y m o d e l l e d ; i n s t e a d a f e e d b a c k l o o p i n v o l v i n g s o i l m o i s t u r e d e f i c i t , a c t u a l e v a p o t r a n s p i r a t i o n , p r e c i p i t a t i o n , a n d r u n o f f i s e m p l o y e d . The a c t u a l d a i l y e v a p o t r a n s p i r a t i o n [ D E V P ( J , L ) ] e q u a l s t h e p o t e n t i a l d a i l y E . T . [DPEVP ( J / L ) ] t i m e s a f a c t o r [FACTOR ( J , L ) ] . T h i s f a c t o r i s d e p e n d e n t o f t h e s o i l m o i s t u r e d e f i c i t [MDEF ( J , L ) ] a n d a d e c a y p a r a m e t e r C 2 . FACTOR ( J , L ) = E X P [ - 1 X C2 x M D E F ( J , L ) ] The s o i l m o i s t u r e d e f i c i t i s s e t t o 0. o n t h e d a y t h e snow l i n e p a s s e s o u t o f a b a n d . T h i s i s a r e a s o n a b l e a s s u m p t i o n f o r t h e u p p e r b a n d s , a l t h o u g h t h e l o w e r b a n d s may h a v e a p e r m a n e n t d e f i c i e n c y . T h e r e a f t e r t h e s o i l m o i s t u r e d e f i c i t i s d e t e r m i n e d b y t h e g a i n o f m o i s t u r e , p r e c i p i t a t i o n , a n d t h e l o s s o f m o i s t u r e , a c t u a l e v a p o - t r a n s p i r a t i o n , a n d r u n o f f . An a s s u m p -t i o n i s made t h a t i f t h e p r e c i p i t a t i o n i s g r e a t e r t h a n o r e q u a l t o . 2 5 o f a n i n c h o f r a i n i n a d a y , t h e E - T w o u l d t a k e p l a c e a t t h e p o t e n t i a l r a t e . N e x t a d d i t i o n a l a s s u m p t i o n s i n t h e f o r m o f a n e t w o r k o f I F - s t a t e -m e n t s i n v o l v i n g t h e p r e c i p i t a t i o n a n d s o i l m o i s t u r e d e f i c i t w e r e f i t t e d f o r s e v e r a l y e a r s . T h e s e s h o u l d a p p r o x i m a t e t h e i n f i l t r a t i o n c a p a c i t i e s o f t h e s o i l s i n t h e b a s i n . As o n l y d a i l y r e c o r d s a r e a v a i l a b l e , i n t e n s i -t i e s a r e o v e r a 2 4 - h o u r p e r i o d a n d t h i s makes m o d e l l i n g d i f f i c u l t . A l s o r a i n araounts o n t h e b a n d s a b o v e 4 , 0 0 0 f e e t a r e q u i t e u n c e r t a i n . D e t a i l s o f t h e n e t w o r k a r e g i v e n i n A p p e n d i x 2 . I I I . 9 R u n o f f R u n o f f i s p r o v i d e d t h r o u g h s n o w m e l t a n d r a i n f a l l . The snow i s m e l t e d i n d a i l y amounts f r o m a b a n d u s i n g PTM a n d t h e d a i l y t e m p e r a t u r e 38 above 32°F., up to that band's band switch time on which day the snow i s assumed to have gone from that band. The band melts above each band are summed for each day and then t h i s sum of band melts i s routed by the previously derived unit hydrogradi to provide an estimated band runoff EBRO(J,L) f o r a given band on a given day. A s i m i l a r procedure i s followed f o r r a i n f a l l which i s e f f e c t i v e i n producing runoff,PRO(J,L), that i s r a i n f a l l over and above that needed to supply s o i l moisture d e f i c i t and evapotranspiration requirements. The estimated band runoff f o r l e v e l L on day J i s EBRORF( J' L^-III.10 Routing The runoff from both snow and r a i n i s routed by means of a u n i t hydrograph. Two parameters c o n t r o l the u n i t hydrograph, NUH, the number of days covered by the u n i t hydrograph, and UZ, which controls the shape of the u n i t hydrograph. The value of the u n i t hydrograph on day K i s UH(K) = (K/UZ) * EXP(-K/UZ). The sum of the UH(K)'s over NUH i s normalized. The general shape of the u n i t hydrographs f o r UZ = 1.0, 2.0 and 3.0 i s shown i n Figure 10. 39 U J FIG. 10 F i g u r e 10 Shape o f U n i t H y d r o g r a p h I I I . 1 1 O p e r a t i o n o f t h e C o m p u t e r P r o g r a m The p r o g r a m , MICKFLMO, w r i t t e n i n F o r t r a n I V was r u n o n t h e IBM 360 c o m p u t e r a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . A f l o w c h a r t o f t h e m o d e l , a l i s t o f p a r a m e t e r s a n d a l i s t o f v a r i a b l e s a r e p r o v i d e d i n A p p e n d i c e s 1 t o 3 r e s p e c t i v e l y . The i n p u t d a t a f o r a y e a r o f r e c o r d was s t o r e d i n a f i l e , t h e f o r m o f w h i c h i s shown, i n A p p e n d i x 4 . The a v e r a g e CPU t i m e t o e x e c u t e t h e p r o g r a m f o r a y e a r o f r e c o r d was a p p r o x i m a t e l y 16 s e c o n d s , t h e t i m e d e p e n d i n g u p o n t h e amount o f i n f o r m a t i o n r e q u i r e d a b o u t t h e b a s i n . The a v e r a g e c o m p i l e t i m e was 30 s e c o n d s , 10 f o r t h e m a i n p r o -g r a m , a n d 20 f o r t h e r u n o f f g e n e r a t i o n s u b r o u t i n e , ROGEN. CHAPTER I V RESULTS AND CONCLUSIONS I V . 1 O b j e c t i v e s o f t h e M o d e l The M i s s i o n C r e e k F l o w M o d e l (MICKFLMO) was n o t p r i m a r i l y i n -t e n d e d t o b e p r e d i c t i v e , b u t as was n o t e d i n t h e I n t r o d u c t i o n , was d e s i g n e d t o s t u d y c e r t a i n h y d r o l o g i c p r o c e s s e s . T h e s e p r o c e s s e s i n c l u d e : v a r i a t i o n o f e v a p o t r a n s p i r a t i o n w i t h e l e v a t i o n ; how much r a i n f a l l a n d s n o w m e l t r u n s o f f ; a n d t h e a r e a s o f t h e b a s i n w h i c h p r o d u c e t h e m o s t r u n o f f . I n o r d e r t o o b t a i n a m o d e l w h i c h b e s t e x p l a i n e d t h e a b o v e m e n t i o n e d p r o c e s s e s , t h e s i m u l a t e d f l o w f r o m t h e b a s i n was made t o f i t t h e m e a s u r e d f l o w as c l o s e l y as p o s s i b l e b y v a r y i n g t h e m o d e l p a r a m e t e r s . A t f i r s t t h e b e s t f i t was j u d g e d by i n s p e c t i o n t h e n l a t e r by u s e o f t h e r e s i -d u a l v a r i a n c e b e t w e e n s y n t h e s i z e d a n d m e a s u r e d f l o w s . A s was p o i n t e d o u t i n s e c t i o n I I . 5 . 3 , c a r e m u s t be e x e r c i s e d w i t h t h e a s s u m p t i o n t h a t t h e b e s t f i t m o d e l i s i n d e e d t h e b e s t m o d e l f o r e x p l a n a t i o n . The r e s i d u a l v a r i a n c e i s c o m p u t e d b y ND £ [BRO(J) - F T ( J ) ] J = l w h e r e B R O ( J ) i s t h e m e a s u r e d f l o w o n day J , F T ( J ) I s t h e s y n t h e z i e d f l o w o n day J , a n d ND i s t h e number o f d a y s o f r e c o r d . The r e s i d u a l v a r i a n c e p r o v i d e s a m e a s u r e o f t h e s p r e a d o f t h e s y n t h e s i z e d a n d m e a s u r e d f l o w s w i t h l a r g e d i f f e r e n c e s g i v e n l a r g e w e i g h t i n g . The s q u a r e r o o t o f t h e r e s i d u a l v a r i a n c e d i v i d e d b y t h e number o f d a y s o f r e c o r d p r o v i d e s a n e s t i m a t e o f 40 41 t h e a v e r a g e d a i l y d i s c r e p a n c y b e t w e e n t h e m e a s u r e d a n d s y n t h e t i c f l o w s . Some p r e d i c t i v e w o r k was a l s o a t t e m p t e d w i t h t h e m o d e l . As f l o w r e c o r d s a r e e n t i r e l y m i s s i n g f o r M i s s i o n C r e e k i n 1948 a n d 1966 a n d o n l y p a r t i a l f l o w r e c o r d s a r e a v a i l a b l e i n 1961 a n d 1 9 6 2 , t h e m o d e l was e m p l o y e d t o s i m u l a t e t h e m i s s i n g d a t a . E x i s t i n g r e c o r d s i n 1961 a n d 1962 p r o v i d e d p a r t i a l c h e c k s o n t h e s i m u l a t e d d a t a b u t i n 1948 a n d 1966 t h e o n l y c h e c k o n t h e s i m u l a t i o n was t h e e s t i m a t e d t o t a l f l o w f o r M i s s i o n C r e e k , S e c t i o n I V . 4 . I V .2 M o d e l B e h a v i o u r I V . 2 . 1 B e s t F i t P a r a m e t e r s . The b e s t f i t p a r a m e t e r s y e a r b y y e a r a r e shown i n T a b l e 5 , b u t n o t a l l p a r a m e t e r s w e r e f i t t e d i n e v e r y y e a r . T h e r e i s i n d i c a t i o n t h a t t h e l a p s e r a t e o f 3 . 5 F ° / 1 0 0 0 f t . i s t o o l o w i n some y e a r s , b u t s t i l l a p p e a r s a r e a s o n a b l e s t a r t i n g v a l u e . The l a p s e r a t e w o u l d n o r m a l l y b e e x p e c t e d t o r a n g e b e t w e e n 3 . 0 a n d 5 . 0 F ° / 1 0 0 0 f t . C 2 , t h e e v a p o r a t i o n d e c a y c o n s t a n t , was p u z z l i n g a s no s i m p l e r e l a t i o n s h i p a p p e a r s t o e x i s t b e t w e e n C2 a n d f l o w o r a n y o t h e r v a r i a b l e . T h i s may b e due t o t h e c o m p l i c a t e d n a t u r e o f t h e h y d r o l o g i c i n t e r a c t i o n s m o d e l l e d by r e l a t i o n s i n v o l v i n g C 2 . B o t h e v a p o r a t i o n a n d t r a n s p i r a t i o n a r e c o n s i d e r e d i n t h e d e c a y o f a c t u a l e v a p o t r a n s p i r a t i o n . S o i l e v a p o r a -t i o n s h o u l d , m o s t e x p e r t s a g r e e , d e c r e a s e q u a s i - e x p o n e n t i a l l y w i t h s o i l m o i s t u r e , b u t t r a n s p i r a t i o n may, a c c o r d i n g t o some w r i t e r s , be i n d e p e n d e n t o f a v a i l a b l e s o i l m o i s t u r e u n t i l t h e w i l t i n g p o i n t i s r e a c h e d . T h i s i n d e p e n d -e n c e o f s o i l m o i s t u r e may be t h e r e a s o n f o r C 2 ' s a p p a r e n t l y c o m p l i c a t e d b e -h a v i o u r . TABLE 5 BEST F I T PARAMETERS AND FLOWS FOR THE MISSION CREEK MODEL , ^ T „ . . r , r , , ^ T r , „ „ T BEST F I T PARAMETERS VOLUME RESIDUAL YEAR MEAS. S I M . VARIANCE C l C2 UZ TLAPS LSW * * * 1948 6. 70 7+ 0 . 9 3 . 3 . 5* 1 2 3 17 22 26 39 59 69 85 98 121 1954 6 . 26 6 . 73 1. 09 X 1 0 6 + 1. 0 0 . 7 3 . 3 . 5 * 1 2 3 10 14 23 39 61 74 98 115 140 1958 3 . 88 4 . 47 5 . 40 x 1 0 7 1. 0 1. 2 3 . 0 3 . 5 1 2 3 4 7 12 19 45 52 66 . : 73 95 1959 7. 54 8. 50 1. 13 X 1 0 6 + 1. 0 1. 1 3 . 5 3 . 5 * 1 2 3 14 20 32 57 71 86 99 106 124 1960 4 . 30 3. 95 7. 40 X 1 0 +2 1. 0 0 . 2 2 . o* 3 . 5* 1 2 3 6 14 21 29 40 61 83 92. 108 1961 7. 20 T / . 4-9 1. 0 0 . 6 3 . 3 . 5* 1 2 3 4 5 12 30 51 62 70 81 97 1962 5 . 75 1. 0 0 . 7 3 . 3 . 5* 1 2 3 10 14 18 27 63 69 88 95 105 1963 4 . 10 3 . 88 5 . 97 X 1 0 7 1. 0 0 . 8 3 . 3 . 5* 1 2 3 4 6 14 21 28 45 53 70 100 1964 7. 55 7. 80 2. 45 X 1 0 7 1. 0 °-3 3 . o* 3 . 5* 1 2 3 4 5 6 30 62 .67 77 92 110 1965 6 . 35 7. 30 6 . 71 X 1 0 2 1. 0 0 . 5 * 3 . 3 . 5 * 1 2 3 4 5 6 32 64 76 81 90 105 1966 4 . 80 1. 0 0 . 7 * 3 . o* 3 . 5* 1 2 3 9 11 14 22 43 60 81 95 112 1967 4 . 08 4 . 85 4 . 68 X 1 0 6 1. 0 0 . 7 3 . o* 3 . 5* 1 2 3 4 .5 6 32 61 75 78 90 107 1968 6 . 45 5 . 68 6 . 02 X 1 0 7 1. 0 0 . 7 3 . o* 3 . 5* 1 2 3 4 5 6 24 45 64 81 92 110 1969 7. 10 6 . 70 1. 07 X 1 0 6 1. 0 0 . 3 3 . 0 3 . 5 1 2 3 4 10 24 45 55 60 66 72 115 1970 2 . 82 3. 78 4 . 06 X i o 6 1. 0 0 . 9 3 . 0 3 . 8 1 2 3 8 12 21 32 53 63 77 86 97 B e s t f i t on t h e b a s i s o f l o w e s t r e s i d u a l v a r i a n c e ; 1 9 4 8 , 1 9 6 1 , 1 9 6 2 , 1966 h a v e n o n -e x i s t i n g d a t a o r i n c o m p l e t e f l o w d a t a . * No t r i a l s w i t h o t h e r v a l u e s . + N o e a r l y s e a s o n s t o r a g e i n m o d e l . 2 I n c o m p l e t e f l o w d a t a , y e a r c a n n o t be f i t t e d . NUM = 10 f o r a l l t e s t s . The a r e a s a n d number o f bands w e r e k e p t c o n s t a n t . Volumes i n t h e u n i t s o f 10 c u b i c f e e t . 43 The b a n d s w i t c h t i m e s , L S W ( L ) , a r e v e r y s e n s i t i v e . I n y e a r s when a s u b s t a n t i a l r a i n e v e n t o c c u r s n e a r a b a n d s w i t c h d a y a- c h a n g e o f one d a y i n s w i t c h t i m e s w i l l c h a n g e t h e f l o w s f o r s e v e r a l d a y s b y h u n d r e d s o f c u b i c f e e t p e r s e c o n d . The p r e d i c t i o n o f b a n d s w i t c h t i m e f r o n s n o w -p a c k a n d t e m p e r a t u r e d a t a i s g o o d o n l y t o a few d a y s , as e v i d e n t f r o m t h e s c a t t e r o f d a t a p o i n t s i n F i g u r e 9 . F i g u r e s 1 1 , 1 2 , a n d 13 show i n d i c a t i o n s t h a t U Z , t h e u n i t h y d r o g r a p h p a r a m e t e r i s h i g h e r i n h i g h f l o w y e a r s , 1 9 5 9 , t h a n i n l o w f l o w y e a r s , 1 9 6 0 . I f t r u e , t h i s i s a s u r p r i s i n g r e s u l t m e a n i n g t h a t t h e b a s i n t e n d s t o s m o o t h t h e f l o w . I n 1960 t h e l a r g e s t s i n g l e c o n t r i b u t i o n t o t h e f l o w comes f r o m b a n d 1 0 , i n 1959 t h e l a r g e s t s i n g l e c o n t r i b u t i o n i s f r o m b a n d 8 . B a n d 8 i s l a r g e r a n d f l a t t e r t h a n b a n d 10 so t h e f l o w may t a k e l o n g e r t o d e v e l o p i n b a n d 8 . I n l o w f l o w y e a r s t h e v a l u e s o f C 2 , TLAPS a n d UZ a r e n o t as c r i t i c a l as i n h i g h f l o w y e a r s . T h i s r e s u l t c a n be s e e n by c o m p a r i n g t h e s h a r p minimum i n F i g u r e 11 w i t h t h e b r o a d m i n i m a i n F i g u r e s 12 a n d 1 3 . T h i s r e s u l t i s i n a g r e e m e n t w i t h t h e i n d i c a t i o n i n F i g u r e 1 4 , w h e r e t h e r e s i d u a l v a r i a n c e o f t h e m o d e l i s shown t o be d i r e c t l y p r o p o r t i o n a l t o t h e t o t a l y e a r l y f l o w . So t h e m o d e l f i t s l o w f l o w o r n o n - c r i t i c a l y e a r s more c l o s e l y t h a n h i g h f l o w y e a r s when t h e v a l u e s o f t h e p a r a m e t e r s a r e more s e n s i t i v e . I V . 2 . 2 E f f e c t o f L a k e E v a p o r a t i o n D a t a . I n o r d e r t o a s c e r -t a i n i f t h e S u m m e r l a n d l a k e e v a p o r a t i o n d a t a p r o v i d e d a s i g n i f i c a n t i m p r o v e -m e n t i n t h e m o d e l ' s p e r f o r m a n c e o v e r p a n e v a p o r a t i o n and e s t i m a t e d e v a p o r a -t i o n d a t a , a t - t e s t was o n c u d c t e d w i t h t h e n u l l h y p o t h e s i s t h a t t h e a v e r a g e 44 1-5 •— I X 10 A UZ = 2.0 TLAPS = 3. 0 UZ = 2.0 Q O UZ = 3.0 Ixicfh • UZ = 3.5 TLAPS = 3.5 O UZ = 2.0 TLAPS = 4.0 9 8 7 UJ 6 U < 4 > < 3 => I A UJ or 2 9 .9 I.I FIG. II RESIDUAL VARIANCE AS A FUNCTION OF C 2 FOR 1959 l . 5 r ~ or < > < O to UJ or IxlO' 9 8 7 A o o 45 UZ = o uz = A UZ = TLAPS = 2.0 3.0 3.5 3.5 .5 1.3 FIG.12 RESIDUAL VARIANCE AS A FUNCTION 0FC 2 F0R I960. • UZ = 2.0 O UZ = 3.2 • UZ = 3.0 TLAPS = 3.2 TLAPS = 4.0 o UZ = 2.0 IXIOV O UZ = 3.0 A UZ = 3.5 TLAPS = 3.8 < Q CO UJ or 9 -8 UJ 7 - O UZ = 2.0 U • UZ = 3.0 X UZ = 3.5 0- • 03 TLAPS= 3.5 £ T o O o 6 • I.I c A 2 FIG. 13 RESIDUAL VARIANCE AS A FUNCTION OF C 2 FOR 1970. 25xl0 6 20x10* U J (_> z < * I5xl06 < > < o to I0xl0€ U J tr. 5 x l O b -2 3 4 5 6 MEASURED VOLUME IN UNITS I09 CUBIC FEET 8 FIG. 14 RESIDUAL VARIANCE AS A FUNCTION OF MEASURED FLOW. 47 r e s i d u a l variance f o r years with lake evaporation data was equal to the r e s i d u a l variance f o r years without lake evaporation data. Unfortunately there are only three years with complete sets of lake evaporation data, 1967, 1968 and 1969. Table 6 presents the r e s u l t s of the t - t e s t which i n d i c a t e that lake evaporation data does not s i g n i f i c a n t l y improve the model. TABLS 6 t-TEST DATA NUMBER AVG. RES. VAR. STAND. DEV. Years with lake evaporation data 3 A = 7.17 x 10 6 2.28 Years without lake evaporation data 8 A, = 9.57 x 10 6 2 2.50 Value of t s t a t i s t i c with 9 degrees of freedom: 0.23 At a 1% l e v e l of s i g n i f i c a n c e t Q ^ (9) = 2.821 N u l l hypothesis A^ = A 2 i s accepted as t tabulated > t ca l c u l a t e d 48 IV.2.3 E f f e c t of Adding Early Season Storage. The e f f e c t on the r e s i d u a l variance including early season storage i n the model i s in d i c a t e d i n Table 7. The procedure for estimating the e f f e c t of ea r l y season storage on flow i s described i n Section III.7. In general the f i t was improved, that i s , the r e s i d u a l variance decreased, except i n 1969 where the increase i n r e s i d u a l variance was small. Apparently early season storage i s a s i g n i -f i c a n t element i n the system. TABLE 7 EFFECT OF ADDING EARLY SEASON STORAGE TO THE MODEL SIM FLOW SIM FLOW RES. VAR. RES. VAR. WITHOUT WITH WITHOUT WITH YEAR MES. FLOW E.S.S. E.S.S. E.S.S. E.S.S 1964 7.55 x 10 7.80 x 10 7.71 x 10 2.56 x 10 2.45 x 10 1965 6.35 x 10 7.30 x 10 7.20 x 10 6.85 x 10^ 6.71 x 10^ 1967 4.06 x 10 r 4.85 x 10^ 4.67 x 10^ 6.18 x 10^ 4.68 x 10°. 1968 6.47 x 10^ 5.88 x 10 5.69 x 10^ 6.74 x lot 6.02 x 10^ 1969 7.10 x 10 6.77 x 10^ 6.70 x 10^ 1.03 x l o ' 1.08 x 10^ 1970 2.82 x 10 3.92 x 10 3.76 x 10 6.96 x 10 5.40 x 10 IV.3 A n a l y t i c a l Results IV.3.1 P r e c i p i t a t i o n E l e v a t i o n Relationships. To a rough approxi-mation, the p r e c i p i t a t i o n e l e v a t i o n r e l a t i o n s generated by the model appear l i n e a r , Figure 15, with the deviations from l i n e a r i t y due to high r a i n f a l l at Joe Rich Creek. However, i f the curves are taken as l i n e a r then an i n t e r e s t i n g r e s u l t unfolds, namely, the rate of change of r a i n f a l l r 1968(D) 2 . 8 7 I OOOFT § 1964(0) 2 . 8 V I OOOFT 1965 2.8"/I OOOFT 1969 1.1 / I OOOFT 1967 l.l"/ I OOOFT o O o o O o in m m in m in O J rvj O J — O J O J ro ro o in O J o m o in O J in o o o m in m O J m (0 ELEVATION IN FEET ••s> 15 PRECIPITATION-ELEVATION RELATIONSHIPS FOR 1964,65,67, 68 AND 69. 50 with e l e v a t i o n i s proportional to the r a i n f a l l i n the f i r s t l e v e l . Apparent-l y i n warm years, i . e . , years with high STEX, the r a i n f a l l i s low and conse-quently the r a i n f a l l gradient i s low, which has d e f i n i t e repercussions i n evaporation considerations. These r e s u l t s are, of course, a consequence of the model chosen f or lapsing the d a i l y p r e c i p i t a t i o n . Had a model such that the d a i l y average p r e c i p i t a t i o n been applied throughout the basin been adopted, then the p r e c i p i t a t i o n e l e v a t i o n r e l a t i o n would have been a h o r i z o n t a l s t r a i g h t l i n e . IV.3.2 Evapotranspiration Lapsing. According to the r e s u l t s of the model, the t o t a l seasonal p o t e n t i a l evapotranspiration declines l i n e a r -l y with increasing e l e v a t i o n . The slope of t h i s r e l a t i o n s h i p bears no apparent c o r r e l a t i o n with evapotranspiration at the f i r s t l e v e l , the sum of the degree days, or the slope of the r a i n f a l l curve. Unfortunately there are too few lapse r a t e values to attempt a c o r r e l a t i o n study. TABLE 8 POTENTIAL EVAPOTRANSPIRATION AND SLOPE OF POTENTIAL EVAPOTRANSPIRATION AMOUNT SLOPE SLOPE OF POT E-T ACTUAL E-T OF RAIN OF YEAR POT E-T 1st LEVEL 1st LEVEL STEX 1st LEVEL RAIN 1948 1.67"/1000 F t . 28.77 11.67 12.8 4.45 1954 1.40"/1000 Ft . 28.13 9.05 • 2867 7.9 4.85 1958 1.25"/1000 Ft . 27 .95 5.60 3779 4.4 2.8 1959 1.62"/1000 Ft. 24.14 5 .82 3105 6.0 3.6 1960 1.68"/1000 F t . 24.95 11.1 3366 .'4.3 0.98 1961 1.46"/1000 Ft . 32.05 4.25 3691 11.8 2.9 1962 1.43"/1000 Ft . 30.30 7 .32 3157 4.8 1.7 1963 l . i r y i o o o F t . 28.90 7.12 — 5 .4 1.5 1964 0.00"/1000 F t . 26.23 9.27 2942 7.8 2.8 1965 1.30"/1000 F t . 27.65 7 .18 3348 5.5 2.8 1966 1.40"/1000 F t . 29.49 7.66 — 5.2 0.80 1967 1 . 5 3 V 1 0 0 0 F t . 34.23 6.82 3752 3 .3 1.1 1968 1.43"/1000 Ft . 30.11 9.05 3255 7.8 2.8 1969 1.46"/1000 F t . 32.05 11.24 3536 6.1 1.1 1970 2.00"/1000 F t . 35.01 6.25 3404 4.0 l . i ' y i o o o 51 The t o t a l s e a s o n a l a c t u a l e v a p o t r a n s p i r a t i o n b e h a v e s i n a much more c o m p l i c a t e d f a s h i o n . I n t h e f i r s t e l e v a t i o n b a n d t h e a c t u a l E - T i s f r o m 20 t o 40 p e r c e n t o f t h e p o t e n t i a l E - T , w i t h t h e p e r c e n t a g e d i r e c t l y p r o p o r t i o n a l t o t h e amount o f r a i n , F i g u r e 1 6 . I n o t h e r w o r d s , as p o i n t e d o u t i n S e c t i o n I V . 3 . 1 , i n h o t d r y y e a r s t h e r a t i o o f a c t u a l e v a p o t r a n s p i r a -t i o n t o p o t e n t i a l e v a p o t r a n s p i r a t i o n i s l o w , w h i c h i s a common s e n s e r e s u l t . The s h a p e o f t h e a c t u a l E - T e l e v a t i o n c u r v e c h a n g e s f r o m y e a r t o y e a r w i t h t h e maximum a p p a r e n t l y p r o p o r t i o n a l t o r a i n f a l l . F i g u r e s 17 a n d 18 show t h a t u s u a l l y a s t h e maximum v a l u e o f t h e E - T i n c r e a s e s t h e r e i s a t e n d e n c y f o r t h e maximum t o o c c u r i n h i g h e r b a n d s . I n warm y e a r s , t h e t a i l o f t h e c u r v e t e n d s t o f l a t t e n , as t h e u p p e r l e v e l s a r e warmer a n d t e n d t o l o s e more w a t e r . The t o t a l a c t u a l E - T f o r t h e b a s i n i s i n v e r s e l y p r o p o r t i o n a l t o t h e e x c e s s t e m p e r a t u r e , t h a t i s , t h e sum o f t h e d e g r e e d a y s , F i g u r e 1 9 . Or as t h e sum o f t h e d e g r e e d a y s a n d t h e r a i n f a l l g r a d i e n t a r e i n v e r s e l y r e -l a t e d , t h e t o t a l a c t u a l E - T f o r t h e b a s i n i s d i r e c t l y p r o p o r t i o n a l t o t h e r a i n f a l l g r a d i e n t f o r t h e b a s i n , F i g u r e 2 0 . I I I I I I I I I L _ I i i I I 0 1 2 3 4 5 6 7 8 9 10 II 12 13 14 AMOUNT OF RAINFALL IN THE FIRST BAND IN INCHES FIG. 16 RATIO OF ACTUAL EVAPOTRANSPIRATION TO POTENTIAL EVAPOTRANSPIRATION IN THE FIRST ELEVATION BAND AS A FUNCTION OF RAINFALL IN THE FIRST ELEVATION BAND. o o O o in in in in CM N CM h -_ O J CVJ o in O J to o O O O O O o in in in m in m in h- O J N O J O J r-ro in m 10 ELEVATION IN FEET FIG. 17 EVAPOTRANSPIRATION ELEVATION RELATIONSHIPS FOR 1966,1968,1970. U l FIG. 18 EVAPOTRANSPIRATION ELEVATION RELATIONSHIPS. 100 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 SEASON DEGREE DAYS FIG. 19 TOTAL ACTUAL EVAPOTRANSPIRATION FOR THE MISSION CREEK BASIN ASA FUNCTION OF THE SEASON DEGREE DAYS. 100 r < U J > oc o U L 90 h co U J 5 80 70 60 50 o o I U J < o < 40 30 < 20 o i -I 0 ± ± SLOPE 1.0 2.0 3.0 4.0 OF RAINFALL IN INCHES PER 1000 5.0 FEET FIG. 20 TOTAL ACTUAL EVAPOTRANSPIRATION FOR A SEASON AS A FUNCTION OF THE SLOPE OF THE RAINFALL IN THE MISSION CREEK BASIN . 5 7 I V . 3 . 3 W a t e r B u d g e t i n t h e B a s i n . T a b l e 9 c o n t a i n s a summary o f r e s u l t s f r o m a w a t e r b u d g e t a n a l y s i s o n a b a n d by b a n d b a s i s f o r t h e M i s s i o n C r e e k B a s i n . By way o f e x p l a n a t i o n o f t e r m s i n t h e t a b l e , t h e snow e f f i c i e n c y i s t h e p e r c e n t a g e o f t h e t o t a l s n o w p a c k t h a t p r o d u c e s r u n o f f , t h e r a i n e f f i c i e n c y i s t h e p e r c e n t a g e o f r a i n t h a t p r o d u c e s r u n -o f f , w h e r e t h e r a i n i s t h e t o t a l p r e c i p i t a t i o n b u t t h e r a i n r u n o f f i s m e a s u r e d f r o m t h e d a t e o f snow l i n e r e c e s s i o n , t h e o v e r a l l e f f i c i e n c y i s t h e p e r c e n t a g e o f t h e t o t a l w a t e r i n p u t t o b a s i n t h a t p r o d u c e s r u n o f f . A s t h e r e a r e p o s s i b l e e r r o r s i n t h e e s t i m a t i o n o f b o t h t h e snowpack and r a i n f a l l , t h e e f f i c i e n c i e s m u s t be r e g a r d e d o n l y as r o u g h i n d i c a t o r s . O b -v i o u s l y t h e r a i n f a l l i n g i n t o snow c o n t r i b u t e s t o r u n o f f a n d h e n c e t h e t o t a l r a i n e f f i c i e n c y w o u l d b e h i g h e r a n d t h e t o t a l snow e f f i c i e n c y l o w e r . The v o l u m e o f r a i n r u n o f f f r o m e a c h b a n d i s v e r y s t r o n g l y i n f l u e n c e d b y t h e v a l u e s o f C 2 , L S W ' s . T a b l e s 10 t h r o u g h 19 p r o v i d e d e t a i l s f o r t h e v a r i o u s y e a r s . I n g t h e s e t a b l e s , v o l u m e s a r e s t a t e d i n 10 c u b i c f e e t , s n o w p a c k i s b a s e d o n t h e w a t e r e q u i v a l e n t s f o r 1 A p r i l , r a i n f a l l i s m e a s u r e d f o r 31 M a r c h o n , a n d t h e r a i n f a l l r u n o f f i s t h e r u n o f f a f t e r t h e snow l i n e h a s r e c e e d e d . 1 9 6 0 , T a b l e 1 8 , was i n t e r e s t i n g a s t h e v o l u m e o f w a t e r l e a v i n g t h e b a s i n was g r e a t e r t h a n t h e v o l u m e o f w a t e r e n t e r i n g t h e b a s i n . B u t t h i s was a y e a r when E - T e x c e e d e d t h e r a i n f a l l a n d s o r a i n f a l l may h a v e b e e n u n d e r e s t i m a t e d . I n g e n e r a l t h e r e i s a n e t w a t e r s u r p l u s o f b e t w e e n Q 10 a n d 70 x 10 c u b i c f e e t o f w a t e r . T h i s p r o b a b l y goes t o g r o u n d w a t e r a n d s l o w r u n o f f . The s l o w r u n o f f , o r b a s e f l o w f o r M i s s i o n C r e e k a p p e a r s t o g r a n g e f r o m 20 t o 60 CFS p e r d a y o r seme 10 c u b i c f e e t o v e r t h e s e a s o n . T h i s w o u l d i n d i c a t e c o n s i d e r a b l e a n d v a r y i n g amounts o f w a t e r g o i n g t o g r o u n d w a t e r . TABLE 9 SUMMARY OF WATER BUDGET RESULTS BASIN BASIN OVERALL SNOW RAIN B A S I N LARGEST RAIN RUNOFF LARGEST SNOW RUNOFF YEAR E F F I C I E N C Y E F F I C I E N C Y E F F I C I E N C Y BAND VOLUME E F F BAND VOLUME E F F 1959 75% 1.7% 40% 11 0 . 4 7 3 % 8 1 8 . 0 90% 1960 69 0 . 6 38 4 0 . 0 8 2 . 5 10 8 . 0 7 73 1963 73 - 0 . 5 31 5 0 . 0 4 1 10. 6 . 7 7 67 1964 73 1.5 36 6 0 . 4 4 4 8 1 8 . 0 105 1965 73 2 40 5 0 . 4 1 7 8 1 6 . 1 103 1967 52 0 . 5 36 6 0 . 1 1 2 8 1 2 . 0 73 1968 63 2 30 9 0 . 8 5 6 10 1 1 . 9 81 1969 67 0 . 6 40 6 0 . 3 6 5 8 1 5 . 4 92 1970 62 1.7 34 6 0 . 1 9 4 10 9 . 0 80 UI CO The o v e r a l l basin e f f i c i e n c y i s r e l a t i v e l y constant com-pared with basin snow e f f i c i e n c y i n d i c a t i n g why i t i s d i f f i c u l t to e s t i mate the runoff from snow data alone. There i s an i n d i c a t i o n that r a i n f a l l a f t e r the snow l i n e recession i s an order of magnitude less e f f e c -t i v e than snowmelt i n producing runoff. Bands 8 and 10 are the most e f f i c i e n t and also the l a r g e s t contributors to snowmelt runoff, while the most e f f i c i e n t band f o r r a i n f a l l runoff i s much more v a r i a b l e . TABLE 10 1970 MISSION CREEK WATER BUDGET WATER I N WATER OUT SNOW AND SNOWPACK P R E C I P . E - T STORAGE RAIN RAIN I N SNOW SNOW ONLY 1 2 3 4 5 6 7 8 9 10 11 12 0 . 0 0 0 . 4 8 0 . 4 1 0 . 9 8 2 . 0 2 3 . 5 5 9 . 0 8 1 2 . 0 0 8 . 5 5 1 0 . 6 0 9 . 5 6 0 . 9 4 0 . 7 4 1 .34 04 24 62 82 60 1 0 . 9 0 6 . 8 4 7 . 4 0 5 . 7 2 0 . 4 8 18 97 42 74 17 57 72 96 47 3 . 6 9 2 . 7 4 0 . 1 9 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 96 14 0 . 5 0 0 . 2 3 0 . 0 7 0 . 0 0 0 . 1 3 0 . 1 3 0 . 0 1 0 . 1 7 0 . 2 5 0 . 2 3 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 3 0 . 0 9 0 . 0 7 0 . 5 5 0 . 7 8 1 .31 4 . 5 5 8 . 7 1 6 . 3 5 9 . 0 0 7 . 0 4 0 . 6 1 0 . 0 3 0 . 0 9 0 . 0 6 0 . 4 7 0 . 6 7 1 . 0 0 4 . 1 4 7 . 8 7 5 . 9 7 8 . 4 2 6 . 8 0 0 . 5 7 5 8 . 4 2 5 4 . 7 4 4 5 . 8 2 3 . 9 0 0 . 9 2 3 7 . 0 9 3 4 . 8 9 V o l u m e s i n 10 c u b i c f e e t . TABLE 11 1969 MISSION CREEK WATER BUDGET WATER I N WATER OUT y RUNOFF SNOW AND BAND SNOWPACK P R E C I P . E - T STORAGE RAIN RAIN I N SNOW SNOW ONLY 1 2 3 4 5 6 7 8 9 10 11 12 0 . 0 0 . 4 7 0 . 4 2 1 .09 2 . 3 6 4 . 3 9 11.19 1 6 . 6 0 1 2 . 6 0 1 6 . 6 0 1 5 . 8 0 1.65 1. 2. 1. 3. 5 . 6 . 18 02 52 17 00 54 1 2 . 7 0 1 3 . 6 0 8 . 1 2 8 . 6 2 6 . 6 2 0 . 5 6 10 24 27 32 89 8 . 4 6 1 4 . 9 0 1 4 . 8 0 8 .14 8 . 0 1 5 . 2 9 0 . 2 4 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 1 .51 0 . 8 1 0 . 2 6 0 . 1 8 0 . 0 3 0 . 0 0 . 1 2 0 . 1 6 0 . 1 3 0 . 1 8 0 . 2 1 0 . 3 6 0 . 0 0 . 0 5 0 . 1 4 0 . 0 5 0 . 0 7 0 . 0 0 . 0 8 0 . 2 0 0 . 1 5 0 . 3 2 0 . 9 5 3 . 1 0 1 3 . 0 0 1 6 . 3 7 8 . 3 7 8 . 6 0 6 . 9 4 1 .14 0 . 0 8 0 . 2 0 0 . 1 5 0 . 3 0 0 . 8 6 2 , 8 9 1 1 . 9 8 1 5 . 3 6 8 . 1 2 8 . 2 3 6 . 4 2 1 . 0 4 S3.17 6 9 . 6 5 7 8 . 6 6 2.79 1 . 4 7 5 9 . 2 2 5 5 . 6 3 O v e r a l l B a s i n Snow E f f . = 67% O j . z 1 5 . 4 M a x . bar id c o n t r i b u t i n g 8 snow e f f . __ _ = 92% 1 6 . 6 16 4 o v e r a l l b a n d e f f . 3 Q * 2 ~ ^ % 6 0 . 7 O v e r a l l b a s i n e f f i c i e n c y 1 = 40% TABLE 12 MISSION CREEK WATER BUDGET WATER I N WATER OUT P R E C I P . RUNOFF BAND SNOWPACK RAIN E - T STORAGE RAIN RAIN I N SNOW SNOW ONLY 1 2 3 4 5 6 7 8 9 10 11 12 0 . 0 0 . 2 8 0 . 2 6 0 . 7 0 1 .60 3 .15 8 . 9 8 1 3 . 2 0 1 0 . 5 0 1 4 . 6 0 1 4 . 6 0 1 .61 1 .45 2 .62 2 . 0 4 4 . 3 9 7 . 4 8 1 0 . 7 0 2 2 . 5 0 2 5 . 0 0 1 5 . 4 0 1 6 . 4 0 1 2 . 6 0 1 .05 1 .67 2 . 8 7 2 .04 3 . 9 4 6 . 4 9 9 . 1 0 1 7 . 6 0 1 6 . 0 0 6 . 9 5 5 . 6 2 3 . 6 3 0 . 2 7 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 3 . 0 1 . 8 1 0 . 8 2 0 . 4 2 0 . 1 3 0 . 0 0 . 0 4 0 . 0 6 0 . 0 4 0 . 1 0 0 . 2 3 0 . 0 0 0 . 2 9 0 . 6 3 0 . 8 5 0 . 6 0 0 . 0 0 . 0 ,06 ,18 ,06 .17 0 . 1 6 0 . 3 0 0 . 5 6 0 . 7 5 .60 .40 11 . 10 1 4 . 0 4 1 2 . 6 0 1 . 3 0 0 . 1 6 0 . 2 9 0 . 4 9 0 . 5 9 2 . 5 0 8 . 6 5 9 . 3 0 1 1 . 9 0 8 . 9 5 0 . 9 5 6 9 . 4 8 1 2 1 . 6 3 7 6 . 1 8 6 . 1 8 2 . 8 2 5 4 . 0 0 4 4 . 0 1 O v e r a l l b a s i n e f f . 5 6 . 8 1 9 1 . 0 = 30% TABLE 13 1967 MISSION CREEK WATER BUDGET WATER I N WATER OUT P R E C I P . RUNOFF SNOW BAND SNOWPACK RAIN E - T STORAGE RAIN RAIN I N SNOW SNOW ONLY 1 2 3 4 5 6 7 8 9 10 11 12 0 . 0 0 0 . 3 7 0 . 3 5 0 . 9 2 2 . 0 7 4 . 0 1 1 1 . 3 0 16 . 30 1 2 . 8 0 1 7 . 5 0 1 7 . 3 0 1 .87 0 . 6 1 1 .06 0 . 8 0 1 .66 2 . 8 4 4 . 0 9 8 . 7 1 9 . 9 7 6 . 1 8 6 . 6 7 5 .14 0 . 4 3 1.27 1 .97 1 .42 2 . 8 3 4 . 5 7 6 . 3 6 1 0 . 9 0 9 . 7 3 4 . 8 5 4 . 7 6 2 . 8 1 2 . 0 5 0 . 0 0 . 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 2 . 0 6 1 .24 0 . 5 3 0 . 2 5 0 . 0 7 0 . 0 0 0 . 0 1 0 . 0 0 0 . 0 1 0 . 0 7 0 . 0 7 0 . 1 1 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 4 0 . 0 5 0 . 1 6 0..39 0 . 4 3 2 . 8 0 1 3 . 0 0 1 0 . 7 0 1 0 . 1 0 9 . 5 2 0 . 9 2 0 . 0 0 0 . 0 4 0 . 0 5 0 . 1 6 0 . 2 9 0 . 3 9 2 . 4 6 1 2 . 0 0 9 . 9 0 9 . 2 0 8 . 5 0 0 . 8 3 8 4 . 7 9 4 8 . 1 6 5 3 . 5 2 4 . 1 5 0 . 2 6 4 8 . 2 0 4 3 . 8 2 1 3 2 . 9 5 9 7 . 1 3 TABLE 14 1965 MISSION CREEK WATER BUDGET WATER IN WATER OUT P R E C I P . RUNOFF SNOW BAND SNOWPACK RAIN E - T STORAGE RAIN RAIN I N SNOW SNOW ONLY 1 2 3 4 5 6 7 8 9 10 11 12 0 . 0 0 0 . 3 8 0 . 35 0 . 9 1 03 90 1 0 . 9 0 1 5 . 6 0 1 2 . 2 2 1 6 . 5 0 1 6 . 2 0 1.74 1 . 0 3 1 . 9 8 1 .61 3 . 5 7 6 . 1 3 8 . 8 2 1 8 . 6 0 2 0 . 7 0 1 2 . 6 0 1 3 . 4 0 1 0 . 2 0 0 . 8 5 1 .03 2 . 2 4 1 .66 3 . 3 0 5 . 5 7 7 . 8 4 1 5 . 6 0 1 4 . 2 0 6 . 9 9 6 . 8 9 4 . 33 0 . 2 7 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 2 . 0 5 1 . 0 8 0 . 4 1 0 . 1 8 0 . 0 6 0 . 0 0 0 . 0 4 0 . 2 2 0 . 0 9 0 . 2 0 0 . 4 1 0 . 2 6 0 . 1 7 0 . 0 0 0 . 1 4 0 . 1 4 0 . 2 8 0 . 0 4 0 . 0 4 0 . 1 2 0 . 1 5 0 . 2 5 0 . 3 2 0 . 2 5 7 . 5 1 1 8 . 9 4 1 5 . 0 2 1 4 . 8 7 1 0 . 8 4 1 .18 0 . 0 3 0 . 1 0 0 . 1 2 0 . 1 9 0 . 2 7 0 . 2 7 6 . 8 2 1 6 . 1 0 1 4 . 1 0 1 2 . 2 3 8 . 0 2 0 . 9 6 8 0 . 7 3 9 9 . 4 9 7 0 . 1 9 3 . 7 8 2 . 0 0 6 9 . 7 0 5 9 . 1 8 1 8 0 . 2 1 3 0 . 7 TABLE 15 1964 MISSION CREEK WATER BUDGET WATER I N WATER OUT BAND SNOWPACK P R E C I P . ' RAIN E - T STORAGE RAIN SNOW AND RAIN I N SNOW SNOW ONLY 1 2 3 4 5 6 7 8 9 10 11 12 0 . 0 0 0 . 5 1.19 1.19 2 .55 4 . 6 9 1 2 . 6 0 1 7 . 3 0 1 2 . 9 0 1 6 . 9 0 1 5 . 9 0 1 .63 1 .27 2 . 7 0 5 . 3 9 5 . 3 9 8 . 9 9 1 2 . 3 0 2 4 . 8 0 2 6 . 8 0 1 5 . 9 0 1 6 . 6 0 1 2 . 9 0 1 .04 1 .73 3 . 1 0 4 . 7 7 4 . 7 7 7 .94 11 .10 2 1 . 2 0 1 7 . 2 0 8 . 9 4 8 . 3 1 5 . 2 1 0 . 3 3 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 1.16 0 . 8 7 0 . 5 4 0 . 3 4 0 . 1 5 0 . 0 1 0 . 0 4 0 . 1 2 0 . 2 0 0 . 2 0 0 . 3 1 0 . 4 4 0 . 2 4 0 . 3 5 0 . 0 7 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 2 0 . 0 7 0 . 1 9 0 . 1 9 0 . 4 1 0 . 6 6 6 . 3 6 2 1 . 0 0 1 3 . 1 0 1 6 . 7 0 1 5 . 1 1 1 .54 0 . 0 2 0 . 0 7 0 . 1 7 0 . 1 7 0 . 3 6 0 . 5 6 5 . 4 0 1 0 . 0 0 1 1 . 6 0 1 3 . 6 0 1 2 . 6 0 1 . 2 8 8 6 . 6 6 1 3 1 . 0 3 9 2 . 2 5 3 . 0 7 1 .90 7 6 . 0 0 6 3 . 7 3 TABLE 16 1963 MISSION CREEK WATER BUDGET WATER I N WATER OUT BAND SNOWPACK P R E C I P . RAIN E - T STORAGE RAIN RUNOFF SNOW RAIN I N SNOW SNOW ONLY 1 2 3 4 5 6 7 8 9 10 11 12 0 . 0 0 0 . 1 0 0 . 1 0 0 . 3 0 0 . 7 3 1.56 4 . 8 4 7 .74 6 .71 1 0 . 1 0 11 .10 1.38 1 .01 1 .73 1. 2. 4. 6. 33 81 70 62 1 3 . 8 0 1 6 . 2 0 9 . 38 9 . 9 3 7 .59 0 . 6 4 1 .32 2 . 1 0 1 .49 2 .77 4 . 3 7 5 . 4 6 1 0 . 6 0 1 0 . 9 0 6 . 3 4 6 . 0 1 4 . 0 6 0 . 2 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 4 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 6 0 . 1 4 0 . 1 4 0 . 3 8 0 . 6 5 2 . 2 7 5 . 1 5 6 . 30 6 . 7 5 7 . 2 8 6 . 9 7 0 . 8 6 0 . 0 6 0 . 1 4 0 . 1 4 0 . 3 8 0 . 6 5 1 .73 3 . 8 7 4 . 7 9 6 . 4 9 6 . 7 7 6 . 6 9 0 . 7 8 4 4 . 6 6 7 5 . 7 6 5 5 . 6 2 0 . 0 4 3 6 . 9 5 3 2 . 5 1 <7l cn TABLE 17 1961 MISSION CREEK WATER BUDGET WATER IN WATER OUT FLOW BAND SNOWPACK P R E C I P . E - T STORAGE RAIN SNOW 1 0 . 0 0 1 .52 0 . 8 2 — 0 . 0 1 0 . 0 7 2 0 . 3 0 2 . 9 6 1 .32 — 0 . 0 7 0 . 1 9 3 0 . 2 8 2 . 4 2 . 0 . 8 6 — 0 . 0 7 0 . 1 8 4 0 . 7 3 5 . 3 7 1 .59 — 0 . 1 7 0 . 3 8 5 1 .64 8 . 8 2 2 . 5 7 — 0 . 4 9 0 . 5 5 6 3 .16 1 2 . 0 0 3 . 3 0 — 0 . 4 9 1 .11 7 8 . 8 5 2 4 . 4 4 5 . 8 7 — 1 .01 4 . 0 3 8 1 2 . 8 0 2 7 . 8 0 5 . 2 7 — 0 . 6 9 6 . 5 5 9 9 . 9 7 1 7 . 1 0 2 .59 — 0 . 3 4 7 . 2 4 10 1 3 . 6 0 1 8 . 1 0 2 . 3 4 — 0 . 3 6 8 . 8 1 11 1 3 . 4 0 1 3 . 9 0 1.47 — 0 . 3 3 8 . 0 1 12 1 .44 1.15 0 . 1 0 — 0 . 0 5 0 . 7 5 6 6 . 1 7 1 3 5 . 5 8 2 8 . 1 0 4 . 0 8 3 7 . 8 7 2 0 1 . 7 5 7 0 . 0 5 4 1 . 9 5 TABLE 18 1960 MISSION CREEK WATER BALANCE WATER I N WATER OUT P R E C I P . RUNOFF SNOW BAND SNOWPACK RAIN E - T STORAGE RAIN RAIN I N SNOW SNOW ONLY 1 0 . 0 0 0 . 8 1 2 . 0 5 2 0 . 1 4 1 .66 3 . 3 4 3 0 . 1 4 1 .41 2 . 3 5 4 0 . 3 9 3 . 2 0 4 . 4 1 5 0 . 9 3 4 . 9 9 6 . 4 9 6 1 .93 6 . 2 4 8 . 4 1 7 5 . 7 9 11 .50 1 5 . 7 0 8 8 . 9 6 1 2 . 0 0 1 4 . 5 0 9 7 . 5 3 6 . 9 7 7 . 2 6 10 1 1 . 0 0 7 . 2 4 6 . 2 1 11 11 .60 5 . 4 7 3 . 8 4 12 1.34 0 . 4 5 0 . 2 6 4 9 . 7 5 6 1 . 9 4 7 4 . 8 2 0 . 0 7 0 . 0 5 0 . 0 5 0 . 0 7 0 . 1 6 0 . 1 6 0 . 0 2 0 . 1 7 0 . 1 7 0 . 0 8 0 . 6 7 0 . 6 7 0 . 0 8 1 .69 1 .56 0 . 0 4 2 . 3 7 2 . 0 8 0 . 0 0 4 . 8 1 4 . 2 7 0 . 0 0 6 . 7 4 6 . 4 3 0 . 0 0 5 . 5 3 4 . 7 5 0 . 0 0 9 . 0 9 8 . 0 7 0 . 0 0 6 . 9 7 6 . 1 8 0 . 0 0 0 . 7 1 0 . 6 5 0 . 3 6 3 8 . 9 6 3 4 . 6 4 1 0 1 . 6 9 114 .14 TABLE 19 1959 MISSION CREEK WATER BUDGET WATER IN WATER OUT BAND SNOWPACK P R E C I P . RAIN E - T STORAGE RAIN SNOW PLUS RAIN I N SNOW SNOW ONLY 1 2 3 4 5 6 7 8 9 10 11 12 0 . 0 0 0 . 6 6 0 . 5 8 1 .43 3 .02 5 . 5 0 1 4 . 6 0 1 9 . 9 0 1 4 . 7 0 1 8 . 9 0 17 .60 1.79 1 .08 2 .16 1 .08 4 . 0 5 6 . 7 4 9 . 2 9 1 9 . 5 0 2 3 . 7 0 1 5 . 4 0 1 7 . 3 0 1 3 . 8 0 1.19 1 . 0 8 2 . 0 8 1 . 6 0 3 . 1 5 4 . 9 5 6 . 25 1 0 . 0 7 1 0 . 0 3 4 . 8 9 4 . 0 9 2 . 9 1 0 . 1 9 0 . 0 0 0 . 0 3 0 . 0 1 0 . 1 1 0 . 0 6 0 . 0 0 0 . 1 0 0 . 26 0 . 3 7 0 . 3 4 0 . 4 7 0 . 0 4 0 . 0 3 0 . 1 0 0 . 0 9 0 . 8 8 1 .67 2 . 6 8 1 5 . 2 8 1 9 . 4 0 1 4 . 6 8 1 6 . 8 3 1 1 . 0 0 1 .10 0 . 0 3 0 . 1 0 0 . 0 9 0 . 8 8 1 .57 2 . 3 1 1 3 . 7 0 1 8 . 0 0 1 3 . 0 0 1 3 . 9 0 9 . 7 0 0 . 9 5 9 8 . 6 8 115 .29 5 1 . 2 9 1.79 8 2 . 6 0 7 5 . 2 3 2 1 3 . 9 7 1 3 6 . 2 9 70 I V . 3 . 4 S o i l M o i s t u r e D e f i c i e n c i e s . S o i l m o i s t u r e d e f i c i e n c i e s a r e t h e m o s t d i f f i c u l t r e s u l t s o f t h e m o d e l t o s u m m a r i z e a n d p r e s e n t . The s o i l m o i s t u r e s v a r i e d f r o m b a n d t o b a n d f r o m d a y t o day a n d y e a r t o y e a r . They w e r e a s s i g n e d a z e r o v a l u e o n t h e b a n d s w i t c h d a y f o r a b a n d a n d d e v e -l o p e d on t e m p e r a t u r e , r a i n f a l l , ' and e v a p o t r a n s p i r a t i o n f r o m t h a t d a y o n . U s u a l l y f o r w e t y e a r s , 1 9 6 5 , t h e s o i l m o i s t u r e d e f i c i e n c i e s n e v e r r o s e a b o v e 3 . 0 i n c h e s e v e n f o r t h e f i r s t b a n d , s e l d o m above 2 . 0 i n c h e s f o r t h e m i d d l e b a n d s , a n d s e l d o m a b o v e 1 . 5 i n c h e s f o r t h e u p p e r b a n d s . I n d r y y e a r s , 1 9 7 0 , t h e s o i l m o i s t u r e d e f i c i e n c i e s r o s e t o 4 . 0 i n c h e s i n t h e l o w e r b a n d s , 3 . 0 i n c h e s i n t h e m i d d l e b a n d s , a n d o c c a s i o n a l l y 3 . 0 i n t h e u p p e r b a n d s . A c o m p l e t e l i s t o f d e f i c i e n c i e s b a n d b y b a n d day b y d a y c a n b e g e n e r a t e d b y t h e p r o g r a m . The a s s i g n m e n t o f z e r o v a l u e t o s o i l m o i s t u r e d e f i c i e n c y o n t h e b a n d s w i t c h day i s p r o b a b l y r e a s o n a b l e f o r t h e u p p e r b a n d s b u t t h e r e a r e i n d i c a t i o n s [ P i p e s , 1971] t h a t i n t h e l o w e r b a n d s t h e r e may be a p e r m a n e n t s o i l m o i s t u r e d e f i c i e n c y . I n 1967 a h i g h e r p o i n t m e l t f a c t o r h a d t o b e u s e d t o o b t a i n r e a s o n a b l e f i t . T h i s may have b e e n due t o t h e b a s i n ' s s o i l s b e i n g q u i t e f u l l y c h a r g e d w i t h m o i s t u r e f r o m e a r l y s e a s o n m e l t . H o w e v e r 1967 d i d show a l o w o v e r a l l b a s i n e f f i c i e n c y . I V . 4 P r e d i c t i v e R e s u l t s The r e a s o n a b l e n e s s o f v o l u m e s p r e d i c t e d f o r 1 9 4 8 , 1 9 6 1 , 1962 a n d 1966 was t e s t e d b y c o m p a r i n g t h e t o t a l p r e d i c t e d v o l u m e t o 20 - 25% o f t h e O k a n a g a n B a s i n R u n o f f , T a b l e 2 0 . A l l v a l u e s e x c e p t 1961 f a l l r e a s o n a b l y c l o s e t o t h e 20-25% f i g u r e , w h i c h was e s t a b l i s h e d f r o m t h e r e s u l t s o f o t h e r 71 TABLE 20 COMPARISON OF MISSION CREEK FLOWS AND OKANAGAN B A S I N RUNOFF OKANAGAN B A S I N YEAR RUNOFF ( A c r e F t . x ' l 0 0 0 ) H 20% OF B A S I N RUNOFF ( i n c u b i c f t . ) MEASURED M I S S I O N CREEK FLOW ( e f t . ) SIMULATED MISSION CREEK FLOW ( e f t . ) 1948 1954 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 783 626 540 713 521 508 454 360 594 434 377 506 563 6 . 9 6 x 10" 5 . 5 6 x 1 0 ' 4 . 8 0 x 10" 6 . 3 4 x 1 0 ' 4 . 6 4 x 10" 4 . 5 2 x 1 0 ' 4 . 0 4 x 10" 3 . 2 0 x 10" 5 . 2 8 x 1 0 ' 3 . 8 6 x 10" 3 . 3 3 x 10" 4 . 5 0 x 10" 5 . 0 0 x 10" 6 . 2 6 x 1 0 ' 3 . 8 8 x 1 0 ' 7 . 5 4 x 1 0 ' 4 . 3 x 1 0 ' 4 . 1 0 x 1 0 ' 7 . 5 5 x 1 0 ' 6 . 3 5 x 1 0 ' 4 . 0 8 x 1 0 ' 6 . 4 5 x 1 0 ' 7 . 1 0 x 10 ' 2 . 8 2 x 1 0 ' 6 . 7 9 x 1 0 ' 6 . 7 3 x 10" 4 . 4 7 x 10" 8 . 5 0 x 1 0 ' 3 . 9 5 x 1 0 ' 7 . 2 0 x 1 0 ' 5 . 7 5 x 1 0 ' 3 . 8 8 x 1 0 ' 7 . 8 0 x 1 0 ' 7 . 3 0 x 10" 4 . 8 0 x 10" 4 . 8 5 x 10" 5 . 6 8 x 10" 6 . 7 0 x 1 0 ' 3 . 7 9 x 10" F o r A p r i l - J u l y s e a s o n ( v a l u e s f r o m P i p e s ) F o r A p r i l - S e p t e m b e r s e a s o n . 72 y e a r s . I n h i g h e r t h a n a v e r a g e f l o w y e a r s , M i s s i o n C r e e k a p p e a r s t o c o n t r i -b u t e h i g h e r p e r c e n t a g e t h a n i n l o w e r f l o w y e a r s . H o w e v e r , t h e Okanagan b a s i n r u n o f f i s f o r a s e a s o n o f A p r i l t o J u l y , w h i l e t h e f l o w s g e n e r a t e d b y t h e m o d e l a r e f o r A p r i l t o S e p t e m b e r . As s n o w m e l t h a s b e e n shown t o be o v e r w h e l m i n g l y i m p o r t a n t i n M i s s i o n C r e e k , f l o w , F i g u r e 21 c o u l d be u s e d t o make r o u g h e s t i m a t e s o f t h e y e a r l y v o l u m e o f f l o w . The a b s c i s s a i s t h e a v e r a g e v a l u e o f t h e m a x i -mum w a t e r e q u i v a l e n t s a t e a c h o f t h e f o u r snow c o u r s e s t a t i o n s f o r 1 A p r i l a n d 1 M a y . T h e . v a l u e s u s e d t o d e t e r m i n e t h e a v e r a g e w a t e r e q u i v a l e n t a r e l i s t e d i n T a b l e 2 1 . I n o r d e r t o c h e c k t h e s n o w m e l t r o u t i n e , t h e w a t e r e q u i v a l e n t s f o r t h e l e v e l s c o n t a i n i n g snow c o u r s e s t a t i o n s w e r e c a l c u l a t e d f o r May 1, May 15 a n d J u n e 1. T h e s e w a t e r e q u i v a l e n t s w e r e c o m p a r e d w i t h m e a s u r e d v a l u e s . A g r e e m e n t a t t h e M i s s i o n C r e e k s t a t i o n was w i t h i n 4 i n c h e s , t h a t i s a b o u t 2 0 % , f o r May 1 a n d May 1 5 , a n d w i t h i n 7 i n c h e s , o r a p p r o x i m a t e l y 50% f o r J u n e 1. U J U J LL. y 8 CD !D U cn 7 O 7 li. O b 6 z Z - 5 o z o < ° U J CO U J 5 =5 I _ J O > 7 8 9 10 II 12 AVERAGE OF MAXIMUM WATER EQUIVALENTS IN INCHES 13 14 FIG. 21 VOLUME OF SEASON FLOW FROM MISSION CREEK AS A FUNCTION OF AVERAGE OF MAXIMUM WATER EQUIVALENTS . 74 T A B L E 21 WATER EQUIVALENTS FOR THE SNOW COURSES I N THE MISSION CREEK B A S I N ( u n i t s a r e i n c h e s o f w a t e r ) M I S S I O N AVG. OF YEAR ABERDEEN P O S T I L L MCCULLOCH CREEK MAXIMUMS A M A M 1948 5 . 6 0 . 0 - - 6 . 6 4 . 5 2 1 . 9 - 1 1 . 3 -1954 7 . 6 1 . 0 8 . 1 7 . 8 6 . 2 3 . 9 2 1 . 7 2 4 . 5 1 1 . 6 6 . 3 1958 4 . 8 0 . 0 6 . 7 7 . 0 5 . 2 2 . 0 1 8 . 0 2 1 . 2 9 . 6 3 . 9 1959 8 . 8 2 . 0 1 1 . 5 8 . 9 9 . 0 4 . 5 2 5 . 3 2 4 . 9 1 3 . 7 7 . 5 1960 3 . 8 0 . 0 4 . 9 4 . 4 3 . 1 0 . 0 1 5 . 7 1 7 . 3 7 . 3 4 . 3 1961 5 . 8 1 .0 7 . 7 6 . 8 4 . 4 1 .5 1 8 . 7 2 2 . 3 1 0 . 1 -1962 9 . 1 0 . 0 1 0 . 2 4 . 4 9 . 3 2 . 8 2 0 . 9 1 7 . 8 1 2 . 4 -1963 2 . 2 0 . 0 4 . 3 3 . 4 3 . 4 0 . 8 1 4 . 7 1 8 . 4 7 . 1 4 . 1 1964 7 . 2 4 . 1 9 . 2 7 . 8 8 . 9 4 . 7 2 2 . 7 2 3 . 9 1 2 . 3 7 . 6 1965 5 . 0 0 . 0 9 . 6 4 . 1 7 . 4 2 . 8 2 2 . 7 2 1 . 1 1 1 . 2 6 . 4 1966 5 . 0 0 . 7 7 . 2 6 . 1 5 . 0 0 . 9 1 7 . 5 1 8 . 9 9 . 0 -1967 5 . 4 4 . 8 9 . 2 8 . 6 8 . 2 0 . 0 2 4 . 2 2 6 . 1 1 2 . 2 4 . 1 1968 4 . 8 2 . 5 8 . 4 7 . 8 5 . 0 1 .5 2 0 . 3 2 3 . 6 1 0 . 4 6 . 5 1969 7 . 2 0 . 0 8 . 6 5 . 9 8 . 2 1 .1 2 2 . 5 2 1 . 1 1 2 . 1 7 . 1 1970 4 . 7 3 . 7 7 . 7 7 . 9 5 . 8 4 . 6 1 4 . 0 1 8 . 2 9 . 2 2 . 8 75 I V . 5 C o n c l u s i o n s A m o d e l i s no b e t t e r t h a n t h e a s s u m p t i o n s t h a t go i n t o i t . The s t r e n g t h s o r v/eaknesses o f a m o d e l w i l l f o l l o w f r o m t h e l i m i t s i m p o s e d b y t h e a s s u m p t i o n s . F o r e x a m p l e , i n t h e M i s s i o n C r e e k F l o w M o d e l , t h e d a i l y p r e c i p i t a t i o n was l a p s e d i n two l i n e a r s e g m e n t s . T h i s p r o c e d u r e may h a v e p r e d i c t e d t o o l a r g e p r e c i p i t a t i o n s i n t h e h i g h e r e l e v a t i o n s o f t h e b a s i n , w h i c h i n t u r n e f f e c t s t h e e v a p o r a t i o n a n d r u n o f f f r o m t h e b a s i n . I n d e e d t h e r u n o f f f r o m t h e r a i n i n snow was f o u n d t o b e t o o l a r g e s o t h e p r e c i p i t a t i o n h a d t o b e d e c r e a s e d b y a f a c t o r o f 1/2 w i t h t h e a s s u m p t i o n t h a t a n y e x c e s s w e n t t o s o i l m o i s t u r e . A l s o t h e l a t e s e a s o n u p l a n d s t o r a g e r e l e a s e s a n d t h e d i v e r -s i o n s f o r i r r i g a t i o n w e r e assumed t o b e m u t u a l l y c a n c e l l i n g . T h i s was a f o r c e d a s s u m p t i o n a s no d a t a i s a v a i l a b l e o n t h e s t o r a g e r e l e a s e s a n d d i v e r s i o n . . The a s s u m p t i o n o f a z e r o s o i l m o i s t u r e d e f i c i e n c y i n a b a n d on t h e d a y a f t e r t h e snow l i n e r e c e s s i o n i s p r o b a b l y r e a s o n a b l e f o r t h e u p p e r b a n d s o f t h e b a s i n , b u t t h e l o w e r b a n d s may h a v e p e r m a n e n t s o i l m o i s t u r e d e f i c i e n c i e s . The u p p e r b a n d s a r e t h o s e w h i c h p r o d u c e m o s t o f t h e r u n -o f f , b u t i f t h e r a i n r u n o f f i s t o b e s t u d i e d t h e c o r r e c t i n i t i a l s o i l m o i s t u r e c o n d i t i o n s a r e e s s e n t i a l t o t h e m o d e l . On t h e w h o l e t h e M i s s i o n C r e e k F l o w M o d e l d i d f i t t h e f l o w s f o r t h e y e a r s when d a t a was a v a i l a b l e a n d t h e r e s u l t s a p p e a r q u a l i t a t i v e -l y r e a s o n a b l e . As c h e c k s on t h e q u a l i t a t i v e r e l i a b i l i t y o f t h e r e s u l t s , t h e l a t e r s e a s o n w a t e r e q u i v a l e n t s w e r e c h e c k e d a g a i n s t m e a s u r e d v a l u e s a n d t h e 1970 y e a r o f r e c o r d was r u n w i t h no p r e v i o u s f i t t i n g a n d t h e n c o m -p a r e d w i t h t h e m e a s u r e d f l o w s ( F i g u r e 2 2 ) . The r e s u l t s c o m p a r e d c l o s e l y 77 l e n d i n g a s s u r a n c e t o t h e r e p r e s e n t a t i v e n e s s o f m o d e l s . The 1970 s i m u l a t i o n i s shown f r o m 30 A p r i l t o 29 J u n e a s o n o t h e r d a y s t h e f l o w i n t a k e s i m u l a t e d a n d m e a s u r e d i s g e n e r a l l y l e s s t h a n 100 c u b i c f e e t p e r s e c o n d . I n r e v i e w i n g t h e o b j e c t i v e s o f t h e m o d e l , t h e f o l l o w i n g , c o n -c l u s i o n s may be d r a w n . The p o t e n t i a l e v a p o t r a n s p i r a t i o n i n t h e b a s i n d e -c l i n e s l i n e a r l y w i t h an a v e r a g e s l o p e o f 1 . 4 7 i n c h e s / 1 0 0 0 f t . , w h i l e t h e a c t u a l e v a p o t r a n s p i r a t i o n shows a hump b a c k b e h a v i o u r w i t h t h e maximum a n d t h e e l e v a t i o n o f t h e maximum v a r y i n g f r o m y e a r t o y e a r . A s t o r u n o f f f r o m r a i n f a l l a n d s n o w m e l t , f r o m 50 t o 75 p e r c e n t o f t h e w a t e r e q u i v a l e n t i n t h e snowpack c o n t r i b u t e s t o r u n o f f , w h i l e o n l y 1 t o 6 p e r c e n t o f t h e r a i n f a l l a f t e r snow c o n t r i b u t e s t o r u n o f f . Bands 8 a n d 10 p r o d u c e t h e l a r g e s t v o l u m e o f snow r u n o f f and h e n c e a r e t h e m a j o r c o n t r i b u t o r s t o r u n -o f f . A c c o r d i n g t o t h e m o d e l , s n o w m e l t i s t h e m o s t i m p o r t a n t f a c t o r i n r u n o f f a n d t h e m o s t i m p o r t a n t b a n d s a r e t h o s e l y i n g b e t w e e n 4500 a n d 6 0 0 0 f e e t . I t i s t h e r e f o r e i m p o r t a n t t h a t i f t h e h y d r o l o g i c p r o c e s s e s o f t h e M i s s i o n C r e e k B a s i n a r e t o be f u r t h e r s t u d i e d a n d b e t t e r n u m e r i c a l v a l u e s g i v e n f o r r u n o f f t h a t snow c o u r s e a n d m e t e o r o l o g i c a l d a t a f r o m t h e s e e l e v a t i o n s b e o b t a i n e d . So t h e m o d e l h a s t h u s p r o v i d e d a n i n d i c a -t i o n o f t h e a r e a s o f t h e b a s i n w h e r e a d d i t i o n a l d a t a i s r e q u i r e d . L a t e s e a s o n r a i n s c a n p r o v i d e r u n o f f s o f t h e o r d e r o f 500 CFS f o r a s h o r t t e r m , s o a d d i t i o n a l i n f o r m a t i o n o n r a i n f a l l i n t h e m i d d l e a n d u p p e r b a n d s w o u l d be r e q u i r e d f o r a more d e t a i l e d i n v e s t i g a t i o n o f r a i n r u n o f f . R a i n f a l l does a p p e a r t o b e b i a s e d by J o e R i c h C r e e k w h i c h r e c e i v e s h e a v y p r e c i p i t a t i o n c o m p a r e d w i t h M c C u l l o c h , S e c t i o n I V . 3 . 1 . 78 The m o d e l h a s shown t h a t t e m p e r a t u r e d a t a a l o n e i s n o t a d e q u a t e t o a c c u r a t e l y p r e d i c t t h e e v a p o t r a n s p i r a t i o n f r o m t h e b a s i n , b u t c a n be u s e d i n e s t i m a t i n g e v a p o t r a n s p i r a t i o n t r e n d s . A s E - T p r o c e s s a r e c o m p l i -c a t e d t h e d a t a r e q u i r e d f o r any i m p r o v e m e n t i n p r e d i c t i o n s c o u l d be p r o -h i b i t i v e . The u s e i n t h e m o d e l o f a c h a i n o f I F s t a t e m e n t s i n v o l v i n g s o i l m o i s t u r e and p r e c i p i t a t i o n v a l u e s h a s a b u i l t - i n b i a s w h i c h l i m i t e d t h e m o d e l ' s a p p l i c a t i o n t o t h e M i s s i o n C r e e k a r e a f o r l a t e s e a s o n r a i n r u n o f f . S t r i c t l y s p e a k i n g a more g e n e r a l m o d e l i s r e q u i r e d f o r o t h e r c r e e k s i n t h e O k a n a g a n , a l t h o u g h C r a w f o r d n o t e s t h a t s t o r a g e a n d i n f i l t r a t i o n p a r a -m e t e r s a r e q u i t e s t a b l e a n d u s u a l l y v a r y o n l y s l i g h t l y f o r a d j a c e n t w a t e r -s h e d s . The b i a s b u i l t i n t o t h e m o d e l a g a i n s t t h e r a i n r u n o f f i s due t o t h e l a c k o f i n f o r m a t i o n o n r a i n a t t h e h i g h e r e l e v a t i o n s . On t h e b a s i s o f t h e p r e s e n t m o d e l , t h e m i d d l e e l e v a t i o n b a n d s do h a v e some " f l a s h y " r e s p o n s e t o r a i n . I n summary, t h e w e a k n e s s e s o f t h e m o d e l h a v e b e e n d i s c u s s e d b u t t h e m o d e l d o e s h a v e s t r e n g t h s . T h e s e s t r e n g t h s a r e p r i m a r i l y s i m p l i - : c i t y , t h e r e l a t i v e l y s m a l l amount o f d a t a r e q u i r e d a n d t h e f a c t t h a t t h e m o d e l does f i t t h e m e a s u r e d f l o w s . A l s o t h e m o d e l a p p e a r s c a p a b l e o f g r o w t h ; t h e " I F s t a t e m e n t c h a i n " may b e r e p l a c e d b y a n a l g e b r a i c f u n c -t i o n ; a c o m p u t e r r o u t i n e f o r t h e o p t i m i z a t i o n o f v a r i a b l e s may be b u i l t i n ; a n d f i n a l l y i f d a t a does become a v a i l a b l e f r o m t h e 4000 t o 6 0 0 0 e l e -v a t i o n r a n g e t h e m o d e l s h o u l d be v a l u a b l e i n f u r t h e r s t u d y o f r u n o f f g e n e r a t i o n . R E F E R E N C E S Blaney, H. F. Evaporation from Free Water Surfaces at High Eleva-t i o n s . Proceedings ASCE, J. Irrigation Drainage Division, V o l . 82, No. IR3, Paper 1104 (1956). B r i t i s h Columbia Snow Survey B u l l e t i n , Water Investigations Branch, Water Resources Service, Department of Lands, Forests and Water Resources, V i c t o r i a , B.C. Crawford, N. H. and R. K. L i n s l e y . D i g i t a l Simulation i n Hydrology: Stanford Watershed Model IV, Technical Report #39, Department of C i v i l Engineering, Stanford U n i v e r s i t y , J u l y 1966. Evans, G. W. I I , G. F. Wallace, G. L. Sutherland. Simulation Using Digital Computers. Englewood C l i f f s , N.J.: P r e n t i c e - H a l l Inc., 1967. Geiger, R. The Climate Near the Ground. Cambridge, Mass.: Harvard U n i v e r s i t y Press, 1965. Horton, R. E. An Approach Toward A P h y s i c a l I n t e r p r e t a t i o n of I n f i l -t r a t i o n Capacity. Proa. Soil Sci. Soa. Am., V o l . 5 (1940), pp. 399-417. L i n s l e y , R. K., M. A. Kohler and J . H. L. Paulus. Applied Hydrology. New York: McGraw-Hill, 1949. Mandeville, A. N., P. E. O'Connell, J . V. S u t c l i f f e and J . E. Nash. River Flow Forecasting Through Conceptual Models, Part I I I : The Rye Catchment at Grendon Underwood. Journal of Hydrology, 11, (1970), pp. 109-128. Monthly Record Meteorological Observations — Canada. Nash, J . E. and J . V. S u t c l i f f e . River Flow Forecasting Through Con-ceptual Models, Part I: A Discussion of P r i n c i p l e s . Journal of Hydrology, 10, (1970), pp. 282-290. Nasmith, H. Late G l a c i a l History and S u r f i c i a l Deposits of the Okanagan V a l l e y , B r i t i s h Columbia. E u l l . No. 46, Department of Mines and Petroleum Resources, V i c t o r i a , B.C. (1962). 79 80 1 2 . N e l s o n , J . G . a n d M . J . C h a m b e r s . Weather and Climate. M e t h u e n , 1 9 6 2 . 1 3 . O ' C o n n e l l , P . E . , J . E . N a s h a n d J . P . F a r r e l l . R i v e r F l o w F o r e c a s t i n g T h r o u g h C o n c e p t u a l M e t h o d s , P a r t I I : The E r o s n a C a t c h m e n t a t F e r b a n e . Journal cf Hydrology, 1 0 , ( 1 9 7 0 ) , p p . 3 1 7 - 3 2 9 . 1 4 . P i p e s , A . An A n a l y s i s o f t h e C a r r s L a n d i n g W a t e r s h e d , IHD P r o j e c t I W B - R B - 3 7 B C 8 , J u n e 1 9 7 1 , W a t e r I n v e s t i g a t i o n s B r a n c h , W a t e r R e s o u r c e s S e r v i c e , D e p a r t m e n t o f L a n d s , F o r e s t s a n d W a t e r R e s o u r c e s , V i c t o r i a , B . C . 1 5 . R o c k w o o d , P . M . a n d M . L . N e l s o n . C o m p u t e r A p p l i c a t i o n t o S t r e a m f l o w S y n t h e s i s a n d R e s e r v o i r R e g u l a t i o n . I n t e r n a t i o n a l C o m m i s s i o n on I r r i g a t i o n a n d D r a i n a g e . S i x t h C o n g r e s s , R. 4 , Q u e s t i o n 2 2 . R E A D \ / R E A D \ E V A P . D A T A J I S N O W DATA W . E . J EV P « 0 YES MONTHLY EVAP FROM STEX YES NO FIND DAILY POT E-T SOIL MOIST. DEFICIT DAILY ACTUAL ET P R E C I P R. 0. P R E C I P . R O . P R E C I P . R O . FIND BAND MELT ESTIMATED BAND RUNOFFS EFFECT OF STORAGE YES YES I F . P, M D E F > NO I F P, M D E F r 1 NO YES FINO LSW FROM W.E. AND T R E A D P A R A M E T E R S NO , N S , N B , N U M U Z , P T , T L A P S C I , C 2 L S W R E A D T M I N T M A X P P - * — F I N D D A I L Y T , T M A X P E F F O F S T O R A G E B A N D R U N O F F ROUTING THROUG H UNIT HYDROGRAPH SNOW FLOW RAIN FLOW T O T A L F L O W R E A D \ f S T O R A G E ) ( F I N D T O T A L S T O R A G E F O R E A C H M O N T H R E A D M E A S U R E D F L O W S ) R E S I D U A L V A R I A N C E APPENDIX 2 PARAMETERS USED I N MISSION CREEK FLOW MODEL A ( L ) - A r e a o f t h e b a n d s s q u a r e m i l e s C l - P a n e v a p o r a t i o n c o e f f i c i e n t d i m e n s i o n l e s s C2 - E v a p o t r a n s p i r a t i o n d e c a y f a c t o r ( i n c h e s ) 1 E L ( I ) - E l e v a t i o n s o f t h e m e t e o r o l o g i c a l s t a t i o n s f e e t E L L ( L ) - C e n t e r e l e v a t i o n s o f t h e b a n d s f e e t LSW(L) - B a n d s w i t c h t i m e s d a y s NB - Number o f b a n d s d i m e n s i o n l e s s ND - Number o f d a y s d i m e n s i o n l e s s NS - Number o f m e t e o r o l o g i c a l s t a t i o n s d i m e n s i o n l e s s NUH - Number o f d a y s i n t h e u n i t h y d r o -g r a p h d i m e n s i o n l e s s PTM - P o i n t m e l t f a c t o r f o r snow CFS/SQ.MI,/F°/DAY TLAPS - L a p s e r a t e f o r t e m p e r a t u r e F ° / 1 0 0 0 F T . 82 APPENDIX 3 L I S T OF V A R I A B L E S INPUT T ( J , L ) T B ( I , J , L ) T X ( I , J ) T N ( I , J ) T M ( I , J ) P ( J , L ) P B ( I , J , L ) P P ( I , J ) WE (L) OUTPUT B M ( J , L ) B M R F ( J , L ) B R O ( J ) D P E V P ( J , L ) D E V P ( J , L ) E B R O ( J , L ) E B R O R F ( J , L ) T e m p e r a t u r e i n day J b a n d L ° F . T e m p e r a t u r e f r o m s t a t i o n I d a t a f o r day J l e v e l L ° F . Maximum t e m p , a t s t a t i o n I on d a y J ° F . M i n i m u m t e m p , a t s t a t i o n I o n day J ° F . A v e r a g e t e m p , a t s t a t i o n I o n d a y J ° F . P r e c i p i t a t i o n o n d a y J b a n d L i n c h e s P r e c i p i t a t i o n f r o m s t a t i o n I , d a t a f o r d a y J b a n d L i n c h x 10 P r e c i p i t a t i o n a t s t a t i o n I o n day J i n c h x 10 W a t e r e q u i v a l e n t o f snow i n b a n d L i n c h e s B a n d m e l t f o r day J , l e v e l L CFS The c o n t r i b u t i o n t o r u n o f f o f r a i n on d a y J i n l e v e l L i n c h e s M e a s u r e d d a i l y f l o w CFS D a i l y p o t e n t i a l e v a p o t r a n s p i r a t i o n f o r day J l e v e l L i n c h e s A c t u a l e v a p o t r a n s p i r a t i o n f o r day J l e v e l L i n c h e s E s t i m a t e d b a n d r u n o f f CFS E s t i m a t e d b a n d r u n o f f f r o m r a i n f a l l CFS 83 84 E T ( L ) i s t h e t o t a l a c t u a l e v a p o t r a n s p i r a t i o n f o r b a n d L f o r t h e s e a s o n i n c h e s E V P ( M , L ) i s t h e m o n t h l y e v a p o t r a n s p i r a t i o n f o r m o n t h M a n d l e v e l L i n c h e s F ( J ) F l o w due t o s n o w m e l t CFS F L S T ( L ) F l o w i n t o e a r l y s e a s o n s t o r a g e f o r b a n d L CFS F R F ( J ) D a i l y f l o w t o r a i n f a l l r u n o f f CFS F T ( J ) D a i l y t o t a l s y n t h e s i z e d f l o w CFS M D E F F ( J , L ) i s t h e s o i l m o i s t u r e d e f i c i t on d a y J a n d l e v e l L i n c h e s PANEVP(M) A m i s n o m e r , r e a l l y t h e l a k e e v a p o r a t i o n i n c h e s P I ( L ) T o t a l p r e c i p i t a t i o n i n t o b a n d L o v e r t h e s e a s o n CFS P R O ( J , L ) P r e c i p i t a t i o n r u n o f f CFS S I ( L ) T o t a l w a t e r e q u i v a l e n t o f snow b a n d L a t b e g i n n i n g o f s e a s o n i n c h e s STA(R) S t o r a g e i n r e s e r v o i r / l a k e R a t b e g i n n i n g o f A p r i l A c r e - f t . STM(R) S t o r a g e i n r e s e r v o i r / l a k e R a t b e g i n n i n g o f May A c r e - f t . S T J ( R ) S t o r a g e i n r e s e r v o i r / l a k e R a t b e g i n n i n g o f J u n e A c r e - f t . S T E X ( M , L ) The sum o f t h e e x c e s s t e m p e r a t u r e s f o r one month f o r b a n d L F ° . T E X ( J , L ) The d a i l y e x c e s s t e m p e r a t u r e f o r b a n d L (above 40°F) F ° . T P E V P ( L ) T o t a l p o t e n t i a l E - T f o r b a n d L f o r s e a s o n i n c h e s WL (L) w i n t e r l o s t t h r u g h E - T f o r s e a s o n f o r b a n d L f t . APPENDIX 4 DATA INPUT FOR MISSION CREEK FLOW MODEL CARD NO. Q U A N T I T I E S FORMAT 1 ND NS NB NUH 1017 2 6 EVAPS FOR A P R I L - S E P T 1 0 F 7 . 0 3 C l C2 1 0 F 7 . 0 4 UZ PTM TLAPS 1 0 F 7 . 0 5 ELEVATIONS OF MET STATIONS 1 0 F 7 . 0 6 CENTER BAND ELEVATIONS OF THE L E V E L S 1 0 F 7 . 0 7 CENTER BAND ELEVATIONS OF THE L E V E L S 1 0 F 7 . 0 8 AREAS OF THE L E V E L S 1 0 F 7 . 0 9 - AREAS OF THE L E V E L S 1 0 F 7 . 0 10 L S W ' S BAND SWITCH TIMES FOR THE L E V E L S 1 0 F 7 . 0 11 L S W ' S BAND SWITCH TIMES FOR THE L E V E L S 1 0 F 7 . 0 12 WATER EQUIVALENTS A P R I L 1 1 0 F 7 . 0 13 WATER EQUIVALENTS MAY 1 1 0 F 7 . 0 14 TMAX STATION 1 FOR A L L ND 1 0 F 7 . 0 85 

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