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A comparison of techniques used in rainfall-runoff models : model efficiency 1982

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A COMPARISON OF TECHNIQUES USED IN RAINFALL-RUNOFF MODELS: MODEL EFFICIENCY by Keith Michael Loague B.Sc, The University of Michigan, 1978 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Geological Sciences) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November 1982 © K e i t h Michael Loague, 1982 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 for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Geological Sciences The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date 25 November 1982 DE-6 (3/81) ABSTRACT A s u i t e of three u n d e r l y i n g r a i n f a l l - r u n o f f modeling techniques i s a p p l i e d to two data s e t s and the r e s u l t s used to compare model e f f i c i e n c i e s for s e l e c t e d events. L i n e a r r e g r e s s i o n , u n i t hydrograph, and q u a s i - p h y s i c a l l y based models make up the modeling s u i t e . The two data sets come from a 7.2 KM subwatershed (MCW) near Klingerstown, Pennsylvania and a 0.096 KM2 subwatershed (R-5) near Chickasha, Oklahoma.- I n d i v i d u a l model e f f i c i e n c i e s are determined on the b a s i s of a sums of squares c r i t e r i o n . These e f f i c i e n c i e s are s u r p r i s i n g l y poor. R e s u l t s i n d i c a t e that the most i n f o r m a t i v e independent l i n e a r r e g r e s s i o n v a r i a b l e s for MCW and R-5 are volume of r a i n f a l l and average r a i n f a l l i n t e n s i t y r e s p e c t i v e l y . There i s a general improvement in c o r r e l a t i o n c o e f f i c i e n t s and r e g r e s s i o n model e f f i c i e n c i e s f o r both MCW and R-5 with i n c r e a s e s in the number of s e l e c t e d events. The u n i t hydrograph and q u a s i - p h y s i c a l l y based models e x h i b i t e d p r e d i c t i v e prowess only f o r the R-5 events. The u n i t hydrograph technique i s found to be s t r o n g l y dependent upon an accurate estimate of s p a t i a l l y - v a r i a b l e excess r a i n f a l l . The e f f i c i e n c y of the p h y s i c a l l y - b a s e d , d e t e r m i n i s t i c , d i s t r i b u t e d model was found to d e t e r i o r a t e d r a s t i c a l l y with i n c r e a s e s i n bas i n s i z e due to the lumping of s p a t i a l l y - v a r i a b l e s o i l h y d r a u l i c p r o p e r t i e s . i i i Based on t h i s work a d e f i n i t i v e l y s u p e r i o r r a i n f a l l - r u n o f f modeling technique i s not suggested. L i m i t a t i o n s of each of the three models and the e f f i c i e n c y c r i t e r i o n used f o r t h e i r e v a l u a t i o n are d i s c u s s e d . T h i s work prov i d e s the foundation f o r a subsequent i n v e s t i g a t i o n t o be c a r r i e d out by the author, to determine i f space-time t r a d e o f f s e x i s t across data sets of v a r i o u s r a i n f a l l - r u n o f f modeling techniques. Future research w i l l focus on the concept of data-worth and the q u e s t i o n of model c h o i c e . TABLE OF CONTENTS Page ABSTRACT i i i LIST OF TABLES. v i LIST OF ILLUSTRATIONS ix ACKNOWLEDGEMENTS . x i i 1. INTRODUCTION 1 1.1 Terminology and C l a s s i f i c a t i o n of Hy d r o l o g i c Models ..2 1.2 Unde r l y i n g Techniques used in Hydro l o g i c Modeling . . . 1 0 1.2.1 C o r r e l a t i o n A n a l y s i s 11 1.2.2 P a r t i a l System Syn t h e s i s with L i n e a r A n a l y s i s . . 1 2 1.2.3 System S y n t h e s i s 14 1.2.3.1 P h y s i c a l l y - B a s e d Models 14 1.2.3.2 Q u a s i - P h y s i c a l l y - B a s e d Models 15 1.3 Space-time T r a d e o f f s 17 1.4 Data-Worth and Model Choice 22 1.5 T h e s i s O b j e c t i v e 23 2. MODELS AND COMPARISON 27 2 . 1 Regression 27 2.2 Unit Hydrograph 33 2.3 Q u a s i - P h y s i c a l l y - B a s e d 47 2.4 Model E f f i c i e n c y 58 3. DATA SOURCES AND EVENT SELECTION 61 3 .1 Mahantango Creek Subwatershed 64 3.2 R-5 Subwatershed 77 3.3 Event S e l e c t i o n 81 4. RESULTS AND DISCUSSION 85 4.1 Regression Models 86 4.2 Unit Hydrograph Model 102 4.3 D i s t r i b u t e d Model 112 5. CONCLUSIONS AND FUTURE RESEARCH 125 REFERENCES • 132 APPENDIX A 146 APPENDIX B 1 50 APPENDIX C 176 APPENDIX D 185 L I S T O F T A B L E S T a b l e P a g e 1 M a j o r r a i n f a l l - r u n o f f e v e n t s i m u l a t i o n m o d e l s ( a f t e r V i e s s m a n e t a l . , 1 9 7 7 ) 19 2 H y d r o l o g i c p r o c e s s e s a n d o p t i o n s u s e d b y m a j o r e v e n t s i m u l a t i o n m o d e l s ( f r o m V i e s s m a n e t a l . , 1 9 7 7 ) 20 3 C h a r a c t e r i z a t i o n o f s e l e c t e d r a i n f a l l - r u n o f f m o d e l i n g t e c h n i q u e s ( a f t e r F r e e z e , 1 9 8 2 a ) 21 4 N o r m a l e q u a t i o n s f o r t h e e q u a l i t y - c o n s t r a i n e d l e a s t s q u a r e s t e c h n i q u e u s e d i n t h e c o m p u t e r p r o g r a m U N I T ( a f t e r M o r e l - S e y t o u x a n d K i m z e y , 1 9 8 0 ) 43 5 I n p u t r e q u i r e m e n t s f o r s e l e c t e d m o d e l i n g t e c h n i q u e s r e l a t i v e t o t h e c a l i b r a t i o n p r o c e s s 60 6 A v e r a g e s o i l d e p t h s w i t h i n t h e M a h a n t a n g o C r e e k S u b w a t e r s h e d ( a b s t r a c t e d f r o m E n g m a n , 1 9 7 4 ) 67 7 S o i l c h a r a c t e r i s t i c p a r a m e t e r s f o r t h e M a h a n t a n g o C r e e k S u b w a t e r s h e d ( a f t e r E n g m a n a n d R o g o w s k i , 1 9 7 4 a ) . 6 8 8 A n t e c e d e n t s o i l w a t e r c o n t e n t s f o r t h e M a h a n t a n g o C r e e k S u b w a t e r s h e d a n d t h e R - 5 S u b w a t e r s h e d . 72 9 C h a r a c t e r i s t i c p a r a m e t e r s a n d d e p t h s f o r R - 5 S u b w a t e r s h e d s o i l s 80 10 R a i n f a l l - r u n o f f c h a r a c t e r i s t i c s f r o m t h e M a h a n t a n g o C r e e k S u b w a t e r s h e d a n d t h e R - 5 S u b w a t e r s h e d . . . . . 8 4 v i L I S T O F T A B L E S — C O N T I N U E D i T a b l e P a g e 11 C o r r e l a t i o n m a t r i x f o r M a h a n t a n g o C r e e k S u b w a t e r s h e d r a i n f a l l - r u n o f f v a r i a b l e s b a s e d o n 15 s e l e c t e d e v e n t s w i t h o u t b a s e f l o w s e p a r a t i o n 88 12 C o r r e l a t i o n m a t r i x f o r M a h a n t a n g o C r e e k S u b w a t e r s h e d r a i n f a l l - r u n o f f v a r i a b l e s b a s e d o n 15 s e l e c t e d e v e n t s w i t h b a s e f l o w s e p a r a t i o n 89 13 C o r r e l a t i o n m a t r i x f o r M a h a n t a n g o C r e e k S u b w a t e r s h e d r a i n f a l l - r u n o f f v a r i a b l e s b a s e d o n 21 s e l e c t e d e v e n t s w i t h o u t b a s e f l o w s e p a r a t i o n 90 14 C o r r e l a t i o n m a t r i x f o r M a h a n t a n g o C r e e k S u b w a t e r s h e d r a i n f a l l - r u n o f f v a r i a b l e s b a s e d o n 21 s e l e c t e d e v e n t s w i t h b a s e f l o w s e p a r a t i o n 91 15 S u m m a r y o f c o r r e l a t i o n m a t r i x t a b l e s .' 92 16 L i n e a r r e g r e s s i o n m o d e l s a n d e f f i c i e n c i e s f o r t h e M a h a n t a n g o C r e e k S u b w a t e r s h e d 95 17 C o r r e l a t i o n m a t r i x f o r R - 5 S u b w a t e r s h e d r a i n f a l l - r u n o f f v a r i a b l e s b a s e d o n s i x s e l e c t e d e v e n t s 97 18 C o r r e l a t i o n m a t r i x f o r R - 5 S u b w a t e r s h e d r a i n f a l l - r u n o f f v a r i a b l e s b a s e d o n n i n e s e l e c t e d e v e n t s . . 9 8 19 L i n e a r r e g r e s s i o n m o d e l s a n d e f f i c i e n c i e s f o r t h e R - 5 S u b w a t e r s h e d 100 vi i L I S T O F T A B L E S — C O N T I N U E D T a b l e P a g e 20 U n i t h y d r o g r a p h m o d e l e f f i c i e n c i e s f o r t h e M a h a n t a n g o C r e e k S u b w a t e r s h e d a n d R - 5 S u b w a t e r s h e d 105 21 S u m m a r y o f t h e t r a n s f o r m e d M a h a n t a n g o C r e e k S u b w a t e r s h e d . . . 1 1 5 22 D i s t r i b u t e d m o d e l e f f i c i e n c i e s f o r t h e M a h a n t a n g o C r e e k S u b w a t e r s h e d a n d R - 5 S u b w a t e r s h e d 117 23 S u m m a r y o f t h e t r a n s f o r m e d R - 5 S u b w a t e r s h e d 120 24 E f f e c t o f a n t e c e d e n t s o i l w a t e r c o n t e n t o n s i m u l a t e d l a t e r a l i n f l o w h y d r o g r a p h v o l u m e s f o r s e l e c t e d M a h a n t a n g o C r e e k S u b w a t e r s h e d e v e n t s 122 vi i i LIST OF ILLUSTRATIONS F i g u r e Page 1 Flow c h a r t of h y d r o l o g i c model c l a s s i f i c a t i o n ( a b s t r a c t e d from C l a r k e , 1 973 ) 7 2 Flow c h a r t i l l u s t r a t i n g the pot and p i p e l i n e s t r u c t u r e of the S t a n f o r d Watershed Model IV ( a f t e r Crawford and L i n s l e y , 1966) 18 3 P o s s i b l e methodology f o r s e l e c t i n g a r a i n f a l l - r u n o f f modeling technique ( a f t e r Dooge, 1978) 24 4 Flow ch a r t of the o p e r a t i o n s i n v o l v e d in the u n i t hydrograph technique (from Amorocho and Hart, 1964) 36 5 Determination of a design storm hydrograph: (a) Excess r a i n f a l l , (b) u n i t hydrograph, and (c) s u r f a c e runoff hydrograph (from Viessman et a l . , 1977). 37 6 Instantaneous u n i t hydrograph: (a) input f u n c t i o n , (b) k e r n e l f u n c t i o n , and (c) output f u n c t i o n ( a f t e r Chow, 1964b) 39 7 Nash's model for r o u t i n g instantaneous r a i n f a l l through a s e r i e s of l i n e a r storage r e s e v o i r s ( a f t e r Chow, 1964b) 41 8 <J> index method of c a l c u l a t i n g excess r a i n f a l l 45 9 Base flow s e p a r a t i o n technique ( a f t e r Engman, 1974)...... 46 10 Systems r e p r e s e n t a t i o n of h y d r o l o g i c c y c l e (from Viessman et a l . , 1977) 48 ix LIST OF ILLUSTRATIONS- _Continued F i g u r e Page 11 Schematic diagram of a dynamic watershed (from Engman, 1974).... 49 12 Flow ch a r t f o r d i s t r i b u t e d model code ( a f t e r Engman, 1974) 51 13 Mahantango Creek Subwatershed (Gburek, pe r s o n a l communication, 1982) 65 14 S p a t i a l v a r i a t i o n of s o i l type and land slope w i t h i n the Mahantango Subwatershed (Gburek, pe r s o n a l communication, 1982) ..66 15 Example s o i l water frequency d i s t r i b u t i o n s ( a f t e r Engman and Rogowski, 1974a) 70 16 S o i l moisture f o r 1971 w i t h i n the Mahantango Creek Subwatershed (Henninger, 1972) 71 17 Depression storage as a f u n c t i o n of land slope and use ( a f t e r Hiemstra, 1968) 74 18 Open channel c r o s s s e c t i o n 75 19 Base flow s e p a r a t i o n r e l a t i o n s h i p f o r the Mahantango Creek Watershed ( a f t e r Engman, 1974).. 76 20 R-5 Subwatershed (Gander, p e r s o n a l communication, 1981) . 78 x L I S T O F I L L U S T R A T I O N S - - C o n t i n u e d F i g u r e p a g e 21 L o c a t i o n o f i n s t r u m e n t a t i o n a n d s o i l p a r a m e t e r m e a s u r e m e n t s w i t h i n t h e R - 5 S u b w a t e r s h e d ( G a n d e r , p e r s o n a l c o m m u n i c a t i o n , 1 981 ) 79 22 A v e r a g e d o n e - h o u r u n i t h y d r o g r a p h f o r t h e M a h a n t a n g o C r e e k S u b w a t e r s h e d ( C o m p o n e n t e v e n t s 1 5 , 2 4 , 2 5 , 3 2 , 4 2 , 4 7 , a n d 4 9 ) 104 2 3 L i n e a r * i n d e x r e l a t i o n s h i p f o r t h e M a h a n t a n g o C r e e k S u b w a t e r s h e d 107 24 E x a m p l e u n i t h y d r o g r a p h 108 2 5 A v e r a g e d o n e - h o u r u n i t h y d r o g r a p h f o r t h e R - 5 S u b w a t e r s h e d ( C o m p o n e n t e v e n t s 1, 5 , 1 0 , 1 2 , a n d 15) 109 26 L i n e a r * i n d e x r e l a t i o n s h i p f o r t h e R - 5 S u b w a t e r s h e d 110 27 W a t e r s h e d s e g m e n t s u s e d t o t r a n s f o r m t h e M a h a n t a n g o C r e e k S u b w a t e r s h e d i n t o o v e r l a n d f l o w p l a n e s 114 28 C h a n n e l r o u t i n g s c e n a r i o f o r t h e M a h a n t a n g o C r e e k S u b w a t e r s h e d 116 2 9 W a t e r s h e d s e g m e n t s u s e d t o t r a n s f o r m t h e R - 5 S u b w a t e r s h e d i n t o o v e r l a n d f l o w p l a n e s 119 x i A C K N O W L E D G E M E N T S A n u m b e r o f p e o p l e h a v e b e e n d i r e c t l y o r i n d i r e c t l y i n v o l v e d i n t h e r e a l i z a t i o n o f t h i s t h e s i s . T h e i r i n t e r e s t , g e n e r o s i t y a n d c o n t r i b u t i o n s a r e g r a t e f u l l y a c k n o w l e d g e d . I e x p r e s s my v e r y s i n c e r e t h a n k s t o A l l a n F r e e z e who i n i t i a t e d t h i s r e s e a r c h a n d e m p l o y e d me a s a r e s e a r c h a s s i s t a n t . A l ' s s t i m u l a t i n g a d v i s e a n d e n t h u s i a s m t h r o u g h o u t t h i s p r o j e c t h a s b e e n i n v a l u a b l e . I am g r a t e f u l t o t h e g r o u p s a t t h e N o r t h e a s t W a s t e r s h e d , R e s e a r c h C e n t e r , U n i v e r s i t y P a r k , P e n n s y l v a n i a a n d t h e S o u t h e r n G r e a t P l a i n s R e s e a r c h W a t e r s h e d , C h i c k a s h a , O k l a h o m a f o r p r o v i d i n g me w i t h p r e c i o u s d a t a s e t s . S p e c i f i c a l l y , a p p r e c i a t i o n i s e x t e n d e d t o W i l l i a m G b u r e k a n d G e n e G a n d e r o f U n i v e r s i t y P a r k a n d C h i c k a s h a r e s p e c t i v e l y f o r t h e i r a s s i s t a n c e . I am v e r y t h a n k f u l t o E d w i n E n g m a n o f t h e B e l t s v i l l e A g r i c u l t u r a l R e s e a r c h C e n t e r , B e l t s v i l l e , M a r y l a n d f o r p r o v i d i n g h i s p a r t i a l a r e a c o d e . T h e e s p r i t d e c o r p s o f f r i e n d s , G r a n t G a r v e n a n d J e n n i f e r R u l o n , h a s a l s o g r e a t l y f a c i l i t a t e d t h i s w o r k . I a p p r e c i a t e t h e i n t e r e s t a n d h e l p f u l c o m m e n t s o f c o m m i t t e e m e m b e r s J a n d e V r i e s , M i k e N o v a k a n d L e s l i e S m i t h . M a n y t h a n k s a r e e x t e n d e d t o G o r d o n H o d g e a n d M e l a n i e S u l l i v a n f o r d r a f t i n g f i g u r e s a n d t a b l e s . S u p p o r t f o r t h i s w o r k c a m e f r o m a g r a n t t o A l l a n F r e e z e f r o m t h e N a t u r a l S c i e n c e a n d E n g i n e e r i n g R e s e a r c h C o u n c i l o f C a n a d a . L a s t l y , my m o s t s i n c e r e t h a n k s t o my p a r t n e r E m i l y , f o r h e r c o n t i n u e d s u p p o r t . xi i 1 CHAPTER ONE INTRODUCTION / Dooge (1972) d e s c r i b e s the r e s e a r c h h y d r o l o g i s t as one who i s bound to be p r o l i f i c i n the p r o d u c t i o n of a l l kinds of models, but one who must recognize the hardships the a p p l i e d h y d r o l o g i s t faces attempting to choose the c o r r e c t one f o r a given s i t u a t i o n . Dooge (1978) notes that w i t h i n the l a s t two decades there has been an immense growth in the modeling - l i t e r a t u r e d e a l i n g almost e x c l u s i v e l y with d e s c r i p t i o n and recommendation, but h a r d l y ever e v a l u a t i o n . T h i s t h e s i s and the r e s e a r c h i t r e p r e s e n t s i s an attempt to evaluate, by comparison, the e f f i c i e n c i e s of s e l e c t e d r a i n f a l l - r u n o f f modeling techniques. A b r i e f h i s t o r i c a l review of the development of hydrology and the types of models c u r r e n t l y in use i s presented in L i n s l e y ' s (1981) overview of r a i n f a l l - r u n o f f models. T h i s work u n d e r l i e s a subsequent i n v e s t i g a t i o n to determine i f space-time t r a d e o f f s e x i s t a c r o s s the data s e t s of v a r i o u s r a i n f a l l - r u n o f f modeling techniques. B u i l d i n g upon t h i s f oundation, f u t u r e r e s e a r c h w i l l focus on the concept of data-worth and the q u e s t i o n of model c h o i c e . Chapter One i s i n t r o d u c t o r y . I t reviews the terminology and c l a s s i f i c a t i o n of h y d r o l o g i c models; u n d e r l y i n g modeling techniques i n hydrology; and the concepts of space-time. 2 t r a d e o f f s , data-worth and model choice as they are r e l a t e d to h y d r o l o g i c modeling. At the end of t h i s f i r s t chapter the general t h e s i s o b j e c t i v e i s d e s c r i b e d . In Chapter Two, the three r a i n f a l l - r u n o f f modeling techniques that are used in t h i s study are f u l l y d e s c r i b e d , and e f f i c i e n c y and comparison c r i t e r i a are presented. Chapter Three d e s c r i b e s the data sources and the methods used to s e l e c t events from the a v a i l a b l e r e c o r d s . The s i m u l a t i o n s and t h e i r r e s u l t s are presented in Chapter Four. Conclusions and d i s c u s s i o n s of f u t u r e research appear in Chapter F i v e . 1.1 Terminology and C l a s s i f i c a t i o n of H y d r o l o g i c Models Woolhiser (1973) d e s c r i b e s a h y d r o l o g i c model as an a b s t r a c t i o n that r e p l a c e s the o r i g i n a l h y d r o l o g i c system with a s i m i l a r but simpler s t r u c t u r e . Each of these models r e f l e c t s some but not a l l the p r o p e r t i e s of the p r o t o t y p e . A great number of h y d r o l o g i c models c u r r e n t l y e x i s t . These models are the r e s u l t of attempts by r e s e a r c h h y d r o l o g i s t s both to expand t h e o r e t i c a l understanding of h y d r o l o g i c phenomena and to provide engineers with the necessary t o o l s f o r d e c i s i o n s concerning o p e r a t i o n and d e s i g n . As noted by Dooge (1978) the methods used i n h y d r o l o g i c r e s e a r c h have not enjoyed a u n i f i e d terminology i n t h e i r 3 c l a s s i f i c a t i o n . As a r e s u l t , much of todays jargon i s undercut with a c o n f u s i n g array of shared or c o n f l i c t i n g d e f i n i t i o n s . The purpose of t h i s s e c t i o n i s to review, not i n t r o d u c e , h y d r o l o g i c model c l a s s i f i c a t i o n s and t h e i r terminology. The focus of t h i s review i s e x c l u s i v e l y on mathematical models r a t h e r than models of the sand-box or r e s i s t a n c e - c a p a c i t a n c e type. Many authors have attempted to c l a s s i f y the continuum of methods and models a p p l i e d i n hydrology. The most widely quoted c l a s s i f i c a t i o n schemes a r e : Amorocho and Hart (1964), and Cla r k e (1973). Amorocho and Hart (1964) i n t h e i r c l a s s i c paper d i v i d e d the modeling community i n t o p h y s i c a l hydrology and systems i n v e s t i g a t i o n . P h y s i c a l hydrology i s d i r e c t e d towards a f u l l understanding of mechanisms and i n t e r a c t i o n s , while systems i n v e s t i g a t i o n d e a l s with d e s i g n i n g workable r e l a t i o n s h i p s between measurable parameters. Amorocho and Hart f u r t h e r c h a r a c t e r i z e systems i n v e s t i g a t i o n as e i t h e r parametric or s t o c h a s t i c . F o l l o w i n g t h e i r d e f i n i t i o n s , parametric hydrology i s the development of r e l a t i o n s h i p s among p h y s i c a l parameters i n v o l v e d i n h y d r o l o g i c events and the use of these r e l a t i o n s h i p s to generate s y n t h e t i c sequences. S t o c h a s t i c hydrology i s the use of s t a t i s t i c a l c h a r a c t e r i s t i c s of h y d r o l o g i c v a r i a b l e s to solve problems. T h i s o f t e n i n v o l v e s the generation of sequences to which c e r t a i n l e v e l s of p r o b a b i l i t y can be a t t a c h e d . K i s i e l (1967) s t a t e s that parametric hydrology i s concerned with 4 d i s c r e t e events while s t o c h a s t i c hydrology i s concerned with the time sequences of these d e s c r e t e events. Dawdy and O'Donnell (1965) fo l l o w the d e l i n e a t i o n s of Amorocho and Hart, l a b e l i n g p h y s i c a l hydrology and system i n v e s t i g a t i o n as component and o v e r a l l catchment modeling r e s p e c t i v e l y . These two groups of models are o b v i o u s l y l i n k e d together, as the o v e r a l l c l a s s gains a d d i t i o n a l i n f o r m a t i o n from the component c l a s s while the former provides feedback in f o r m a t i o n to the l a t t e r . K i s i e l (1967,1969) d e f i n e s determinism as synonomous with c a u s a t i o n and d e s c r i b e s the s t o c h a s t i c approach as weaving u n c e r t a i n t y , by way of p r o b a b i l i t y laws, i n t o the f a b r i c of the hydrodynamic and phenomenological r e l a t i o n s of the system. C o r n e l l (1964) d e s c r i b e s a s t o c h a s t i c model as concerned not only with the c e n t r a l tendency values p r e d i c t e d by d e t e r m i n i s t i c models, but a l s o with the inherent and unexplained v a r i a t i o n observed in p h y s i c a l phenomena. (Chow, 1964a) d e f i n e s a model as d e t e r m i n i s t i c i f the chance of occurrence for the v a r i a b l e i n v o l v e d i s ignored, and as s t o c h a s t i c or p r o b a b i l i s t i c i f chance i s taken i n t o c o n s i d e r a t i o n and the concept of p r o b a b i l i t y i n t r o d u c e d . Rosenblueth and Weiner (1945) separate models i n t o two c l a s s e s : m a t e r i a l and symbolic. According t c Woohiser (1973) a symbolic model i s a mathematical d e s c r i p t i o n of an i d e a l i z e d s i t u a t i o n that shares some of the s t r u c t u r a l p r o p e r t i e s of the 5 r e a l system. Woolhiser c l a s s i f i e s mathematical models as e m p i r i c a l or t h e o r e t i c a l , lumped or d i s t r i b u t e d , and d e t e r m i n i s t i c or s t o c h a s t i c . In Woolhiser's judgement, an e m p i r i c a l model i s based upon f a c t , having no p r e d i c t i v e prowess under changing c o n d i t i o n s , while the t h e o r e t i c a l model hinges upon e x p l a n a t i o n of o b s e r v a t i o n . According to Woolhiser, a lumped model can be represented in ge n e r a l , by an or d i n a r y d i f f e r e n t i a l equation or a s e r i e s of l i n k e d o r d i n a r y d i f f e r e n t i a l equations. A d i s t r i b u t e d model a l t e r n a t i v e l y i n c l u d e s s p a t i a l v a r i a t i o n s in inpu t s , parameters and dependent v a r i a b l e s , and would c o n s i s t of a p a r t i a l d i f f e r e n t i a l equation or l i n k e d p a r t i a l d i f f e r e n t i a l equatibns. Under Woolhiser's c l a s s i f i c a t i o n , a model i s d e t e r m i n i s t i c i f , when the i n i t i a l c o n d i t i o n s , boundary c o n d i t i o n s and inputs are s p e c i f i e d , the output i s known with c e r t a i n t y . Woolhiser d e f i n e s s t o c h a s t i c models as d e s c r i b i n g processes governed by p r o b a b i l i t y laws. Dooge (1968) d e f i n e s a h y d r o l o g i c system as a set of p h y s i c a l , chemical and/or b i o l o g i c a l processes a c t i n g upon input v a r i a b l e s to convert them i n t o output v a r i a b l e s . According to Cla r k e (1973) a model i s a s i m p l i f i e d r e p r e s e n t a t i o n of a complex system. Cla r k e c a t e g o r i z e s mathematical models i n t o four major groups: S t o c h a s t i c - c o n c e p t u a l , s t o c h a s t i c - e m p i r i c a l , d e t e r m i n i s t i c - c o n c e p t u a l and d e t e r m i n i s t i c - e m p i r i c a l . A model i s regarded as s t o c h a s t i c i f any of the v a r i a b l e s i n i t s mathematical e x p r e s s i o n are d e s c r i b e d by a p r o b a b i l i t y 6 d i s t r i b u t i o n . A model i s termed d e t e r m i n i s t i c i f a l l the v a r i a b l e s are b e l i e v e d to be f r e e from random v a r i a t i o n s so that the model i n v o l v e s no d i s t r i b u t i o n s i n p r o b a b i l i t y . Models are c a l l e d c onceptual i f t h e i r mathematical expr e s s i o n s are d e r i v e d from c o n s i d e r a t i o n of the p h y s i c a l processes, and e m p i r i c a l i f they are not. In C l a r k e ' s assessment, there are s e v e r a l s u b - c a t e g o r i z a t i o n s as w e l l . A model i s l i n e a r i n the systems theory sense i f the p r i n c i p l e of s u p e r p o s i t i o n holds and l i n e a r in the s t a t i s t i c a l r e g r e s s i o n sense i f l i n e a r in the parameters to be estimated. Clarke f u r t h e r i d e n t i f i e s three s u b - c a t e g o r i e s i n v o l v i n g s p a t i a l v a r i a b i l i t y of input v a r i a b l e s . These are 1) lumped models, that do not account f o r s p a t i a l d i s t r i b u t i o n , 2) p r o b a b i l i t y - d i s t r i b u t e d models, that d e s c r i b e s p a t i a l v a r i a b i l i t y without refere n c e to geometrical c o n f i g u r a t i o n i n the measurement network and 3) g e o m e t r i c a l l y d i s t r i b u t e d models that express s p a t i a l v a r i a b i l i t y i n terms of o r i e n t a t i o n w i t h i n the measurement network. F i g u r e 1 shows C l a r k e ' s c l a s s i f i c a t i o n of h y d r o l o g i c models, and r e f e r e n c e s a few examples of each type. Machado-01ive (1975) d i s t i n g u i s h e s between s t a t i s t i c a l and s t o c h a s t i c models. A model i s s t a t i s t i c a l i f i t i n c l u d e s the concept of p r o b a b i l i t y , with h y d r o l o g i c v a r i a b l e s subject to random f l u c t u a t i o n s that are assumed to be independent f o r d i f f e r e n t o b s e r v a t i o n s . S t o c h a s t i c models i n c o r p o r a t e the HYDROLOGIC M O D E L S PHYSICAL ANALOG Chow 1967 Diskin 1967 STOCHASTIC- CONCEPTUAL I Dawdy & O'Oonnell 1965 Freeze 1980 LINEAR IN THE SYSTEMS THEORY SENSE MATHEMATICAL MODELS STOCHASTIC- EMPIRICAL r ~ Snyder 1955 DETERMINISTIC- CONCEPTUAL Wooding 1966 Eagleson 1970 Freeze 1971 NON-LINEAR IN THE SYSTEMS THEORY SENSE DETERMINISTIC- EMPIRICAL Amorocho & Ortob 1961 LINEAR IN THE STATISTICAL REGRESSION SENSE Same Sub-Classifications as Linear in the Systems Theory Sense LUMPED PROBABILITY DISTRIBUTED GEOMETRICALLY DISTRIBUTED Same Sub-Classifications as Linear in the Statistical Regression Sense Same Classification as Stochastic -Conceptual Figure 1. Flow chart of hydrologic model c l a s s i f i c a t i o n (abstracted from Clarke, 1973) 8 sequence with which h y d r o l o g i c events occur w i t h i n a time s e r i e s and presume past events may i n f l u e n c e f u t u r e events. Dooge (1972), Quimpo (1973) and Laurenson (1974) each d i s c u s s the combination of d e t e r m i n i s t i c and s t o c h a s t i c model components i n t o a u n i f i e d type of model, c l a s s i f i e d as h y b r i d by K i s i e l (1969). Klemes (1978) however, c a u t i o n s that what o f t e n happens with such combinations i s that the d e t e r m i n i s t has j u s t i n c l u d e d an e r r o r term while the s t o c h a s t i c i s t was only n o t i c i n g mathematically s i m i l a r models. Klemes adds, that u n i f i c a t i o n of s t o c h a s t i c and d e t e r m i n i s t i c models amounts to a "Don Q u i x o t i a n " task, as any model can be c l a s s i f i e d as e i t h e r depending upon whether i t s v a r i a b l e s and parameters c o n t a i n an element of randomness. O u t l i n i n g h i s own c l a s s i f i c a t i o n scheme, with the most d e c i s i v e changes in t e r m i n o l o g y - i n t e r p r e t a t i o n seen yet, Klemes (1978) d e f i n e s the term d e t e r m i n i s t i c , as a one-to-one r e l a t i o n s h i p dependent upon theory development, knowledge of i n i t i a l c o n d i t i o n s and accuracy of measurement. Klemes d e f i n e s the term random, as a completely haphazard order, and f i n a l l y , the term s t o c h a s t i c , as i n c o r p o r a t i n g both an element of determinism and randomness. Klemes argues that with these d e f i n i t i o n s i t f o l l o w s that the two c l a s s i f i c a t i o n s , d e t e r m i n i s t i c and random, are only s p e c i a l cases of the s t o c h a s t i c . Klemes f u r t h e r d e f i n e s a p r o b a b i l i s t i c model as one that i m p l i e s d e s c r i p t i o n and e x p l a n a t i o n , while a s t a t i s t i c a l 9 model only i n v o l v e s d e s c r i p t i o n . F i n a l l y , Klemes addresses the a r b i t r a r i n e s s of h i e r a r c h y i n model c l a s s i f i c a t i o n and concludes that the most fundamental l e v e l of c l a s s i f i c a t i o n should be the c o n c e p t u a l - e m p i r i c a l d i v i s i o n ( C l a r k e , 1973; K i s i e l , 1 9 6 9 ) that has a l s o been l a b e l e d s y n t h e t i c - a n a l y t i c ( O ' D o n n e l l , 1 9 6 6 ) , g e n e t i c - s t a t i s t i c a l ( K a r t v e l i s h v i l i , 1 9 6 7 ) , c o n c e p t u a l - a n a l y t i c (Wood, 1 9 7 3 ) , d e s c r i p t i v e - p r e s c r i p t i v e ( J a c k s o n , 1 9 7 5 ) , p h y s i c a l l y b a s e d - o p e r a t i o n a l (Klemes, 1 9 7 4 ) and e m p i r i c a l - t h e o r e t i c a l (Woolhiser, 1 9 7 3 ) . The f i n a l l e v e l of c l a s s i f i c a t i o n f o r h y d r o l o g i c models to be presented here d i f f e r e n t i a t e s between generic and s i t e - s p e c i f i c models. Generic models are used to f u r t h e r the understanding of h y d r o l o g i c phenomena, while s i t e - s p e c i f i c models are used for o p e r a t i o n and p r e d i c t i o n . What i s evident f o r the f o r e g o i n g c l a s s i f i c a t i o n schemes and t h e i r terminology, i s that the range and scope of the v a r i o u s h y d r o l o g i c models must be great to permit such d i v e r s i t y in model c a t e g o r i z a t i o n . To i n s u r e c o n t i n u i t y i n terminology throughout the remainder of t h i s t h e s i s , C l a r k e ' s c l a s s i f i c a t i o n , which has been adopted by many authors and which i s summarized in F i g u r e 1, w i l l be used e x c l u s i v e l y . 10 1.2 U n d e r l y i n g Techniques used i n H y d r o l o g i c Modeling C l a r k e (1973) d e s c r i b e d the general h y d r o l o g i c model as: V f ( p t - l ' p t - 2 ' " , * q t - l * q t - 2 » " " ' a r a 2 » " , ) + e t (1) where, P = input v a r i a b l e s q = output v a r i a b l e s a^ = system parameters I = r e s i d u a l e r r o r t f = f u n c t i o n a l form of the model V a r i a b l e s and parameters are c h a r a c t e r i s t i c s of the system being modeled. V a r i a b l e s change with time; parameters remain con s t a n t . The f u n c t i o n can be e i t h e r conceptual or e m p i r i c a l . The input and output v a r i a b l e s as w e l l as the system parameters and r e s i d u a l e r r o r can be e i t h e r s t o c h a s t i c or d e t e r m i n i s t i c . The purpose of t h i s s e c t i o n i s to review d i f f e r e n t techniques^ used i n h y d r o l o g i c modeling, c o n c e n t r a t i n g upon those which w i l l be employed in t h i s study. In a s s e s s i n g any model f o r i t s e f f i c i e n c y i n a given s i t u a t i o n , as compared to another model, i t i s important to f i r s t r e cognize the b a s i c s t r u c t u r e and o p e r a t i o n a l technique of the i n d i v i d u a l model with regard to the type of a v a i l a b l e or e c o n o m i c a l l y - o b t a i n a b l e data. The connection between the model c l a s s i f i c a t i o n d e s c r i b e d i n the p r e v i o u s section,' and the u n d e r l y i n g modeling techniques d i s c u s s e d here, l i e s i n the combinations of i n d i v i d u a l modeling 11 techniques, inherent in the v a r i o u s h y d r o l o g i c models, which s a t i s f y v a r i o u s c l a s s d e f i n i t i o n s . The u n d e r l y i n g modeling techniques to be b r i e f l y d e s c r i b e d here a r e : C o r r e l a t i o n a n a l y s i s , p a r t i a l system s y n t h e s i s with l i n e a r a n a l y s i s , and system s y n t h e s i s . Other techniques used in v a r i o u s h y d r o l o g i c modeling s i t u a t i o n s not p e r t i n e n t to t h i s r e s e a r c h but to be i n c l u d e d i n f u t u r e i n v e s t i g a t i o n s i n c l u d e : Non-linear a n a l y s i s (Amorocho, 1973), frequency a n a l y s i s (Chow, 1964a), t i m e - s e r i e s a n a l y s i s (Matalas, 1967; K i s i e l , 1969), Monte C a r l o s i m u l a t i o n ( F i e r i n g and Jackson, 1971; Freeze, 1980) and K r i g i n g (de M a r s i l y , 1982). D e l i n e a t i o n of modeling techniques i n t h i s manner i s l a r g e l y based upon the nomenclature of Amorocho and Hart (1964). 1.2.1 C o r r e l a t i o n A n a l y s i s C o r r e l a t i o n a n a l y s i s e x p l o r e s d i f f e r e n t combinations of dependent v a r i a b l e s to determine the combination that most c l o s e l y approximates the output f u n c t i o n i n terms of the recorded input f u n c t i o n . Along with other a r b i t r a r y parameters, the c o r r e l a t i o n - a n a l y s i s technique d e s c r i b e s the best l i n e a r p r e d i c t i o n equation. Often h y d r o l o g i c systems that are n a t u r a l l y n o n - l i n e a r can be transformed and e x p l a i n e d by l i n e a r models. Y e v d j e v i c h (1964) d i s c u s s e s when and why data 12 t r a n s f o r m a t i o n s are necessary. Haan (1977) d i s c u s s e s many aspects of c o r r e l a t i o n a n a l y s i s as r e l a t e d to i t s use i n h y d r o l o g i c modeling. Examples of c o r r e l a t i o n a n a l y s i s are simple and m u l t i p l e l i n e a r r e g r e s s i o n , m u l t i v a r i a t e s t a t i s t i c a l methods (Snyder, 1962; Wong, 1963; W a l l i s , 1965), and l i n e a r programing (Kolman and Beck, 1980). D i s k i n (1970) concludes that the r e g r e s s i o n equation can be i n t e r p r e t e d in terms of a simple three-element conceptual model fo r annual r a i n f a l l - r u n o f f r e l a t i o n s h i p s . However, many authors b e l i e v e that the use of c o r r e l a t i o n a n a l y s i s as a d i r e c t t o o l in h y d r o l o g i c modeling leads to unwarranted g e n e r a l i z a t i o n s (Haan, 1977). Amorocho and Hart (1964) note that a great d e a l of s u b j e c t i v i t y u n d e r l i e s the process of s e l e c t i n g a best model and there i s no assurance that the optimum model has been c o n s i d e r e d . C o r r e l a t i o n a n a l y s i s i s used e x t e n s i v e l y in the es t i m a t i o n of model parameters f o r other techniques. C o r r e l a t i o n a n a l y s i s i s a s t o c h a s t i c - e m p i r i c a l aproach in C l a r k e ' s c l a s s i f i c a t i o n scheme. 1.2.2 P a r t i a l System S y n t h e s i s with L i n e a r A n a l y s i s Amorocho and Hart (1964) d e s c r i b e system a n a l y s i s as a mathematical process used to d e f i n e an input-output r e l a t i o n s h i p , i n v o l v i n g the use of measured input and output 13 data only, without any attempt to d e s c r i b e the i n t e r n a l mechanisms of the system i n e x p l i c i t form. System s y n t h e s i s i s d e f i n e d by Amorocho and Hart as an attempt to d e s c r i b e the system o p e r a t i o n of components whose presence i s presumed to e x i s t and whose f u n c t i o n s are known and p r e d i c t a b l e . A n a l y s i s has the form of unique f u n c t i o n while s y n t h e s i s does not. The c l a s s i c a l u n i t hydrograph (Sherman, 1932; Dooge, 1959) combines both s y n t h e s i s and a n a l y s i s as d e f i n e d above i n t o a technique that can be d e s c r i b e d as p a r t i a l system s y n t h e s i s with l i n e a r a n a l y s i s . R a i n f a l l excess and base flow s e p a r a t i o n f u n c t i o n s combined with a l i n e a r c o n v o l u t i o n o p e r a t i o n represent the u n i t hydrograph s y n t h e s i s that i s assumed e q u i v a l e n t to the o p e r a t i o n of a watershed. U n i t hydrograph theory can be summarized in s i x words: The system i s l i n e a r and t ime-invar i a n t . The c o n s t r a i n e d l i n e a r system model proposed by Natale and T o d i n i (1977) i s another example of p a r t i a l system s y n t h e s i s with l i n e a r a n a l y s i s . It r e l a t e s e f f e c t i v e p r e c i p i t a t i o n to runoff f o r a time i n v a r i a n t l i n e a r system where c o n s t r a i n t s are p l a c e d on the parameters to be estimated. P a r t i a l system s y n t h e s i s with l i n e a r a n a l y s i s i s e i t h e r a d e t e r m i n i s t i c - e m p i r i c a l or s t o c h a s t i c - e m p i r i c a l approach in C l a r k e ' s c l a s s i f i c a t i o n scheme, depending on whether there i s a p r o b a b i l i t y d i s t r i b u t i o n a s s o c i a t e d with the parameters to be estimated. 14 1.2.3 System Syn t h e s i s Amorocho and Hart (1964) d e s c r i b e the process of system s y n t h e s i s as beginning with the p o s t u l a t i o n of a more-or-less complex model, whose s t r u c t u r e i s based upon q u a l i t a t i v e and s e m i - q u a l i t a t i v e knowledge of phenomena i n v o l v e d in the h y d r o l o g i c c y c l e . Depending upon the l e v e l of s o p h i s t i c a t i o n , systems s y n t h e s i s can vary from a black-box model to a f u l l y c onceptual model. System s y n t h e s i s can be s u b d i v i d e d i n t o two l e v e l s of a b s t r a c t i o n . These are p h y s i c a l l y - b a s e d models and q u a s i - p h y s i c a l l y - b a s e d models which are d i s c u s s e d below. C l a r k e ' s four major c l a s s i f i c a t i o n groups are represented by v a r i o u s combinations of the sytem-synthesis technique. 1 .2.3.1 P h y s i c a l l y - B a s e d Models In t h e i r blue p r i n t , Freeze and Harlan (1969a) assess the f e a s i b i l i t y of developing a r i g o r o u s p h y s i c a l l y - b a s e d mathematical model of the complete h y d r o l o g i c system. Freeze and Harlan d e s c r i b e a p h y s i c a l l y - b a s e d model of the time-dependent h y d r o l o g i c processes as being represented by a set of p a r t i a l d i f f e r e n t i a l equations i n t e r r e l a t e d by the concepts of c o n t i n u i t y of mass and momentum. These equations along with the r e s p e c t i v e boundary c o n d i t i o n s comprise the 1 5 boundary-value-problem that Freeze and Harlan c a l l the h y d r o l o g i c response model. In response models of t h i s type, the movement of water through the h y d r o l o g i c system i s governed by the Sa i n t Venant equations in the ove r l a n d and channel flow phases and the Darcian equation of groundwater flow in the subsurface flow phase (Freeze and Harla n , 1969a; Freeze, 1974; Freeze, 1978). Stehale (1966) however, has argued that while the purpose of mechanics i s to provide a complete d e s c r i p t i o n of systems o c c u r r i n g in nature, that i n hydrology t h i s has not been accomplished and may never be. To date, Stehale has been proven c o r r e c t as no p h y s i c a l l y - b a s e d model of the type d e s c r i b e d above has ever proven s u c c e s s f u l i n f i e l d a p p l i c a t i o n s on any reasonable s c a l e (Woolhiser, 1973; Klemes, 1978). Klemes (1979) a l s o d i s c u s s e s the reasons why a h y d r o l o g i c model i n the form of a component boundary value problem cannot be c o n s i d e r e d the u l t i m a t e model. 1 .2.3.2 Q u a s i - P h y s i c a l l y - B a s e d Models P h y s i c a l l y - b a s e d models are u s u a l l y made up of a set of coupled p a r t i a l d i f f e r e n t i a l e q u a t i o n s . Q u a s i - p h y s i c a l l y - b a s e d models on the other hand use s o l u t i o n s to these equations.as o p e r a t i n g a l g o r i t h i m s . Such a model i s d e s c r i b e d by Engman 16 (1974). The mathematical f u n c t i o n used to d e s c r i b e the s o i l i n f i l t r a b i l i t y i s P h i l i p ' s (1969) two-parameter s o l u t i o n to Richard's general flow equation. The kinematic approximation to the complete flow equation i s used f o r the overland-flow and channel-flow components and the Manning r e l a t i o n s h i p s are r assumed to h o l d (Brakensiek, 1966). The development of the kinematic form of the shallow-water equations i s reviewed by Eagleson (1970). The kinematic approach does not have the same r e s t r i c t i v e assumptions of l i n e a r i t y and time i n v a r i a n c e seen in the u n i t hydrograph methods (Wooding, 1965; K i l b e r and Woolhiser, 1970). Q u a s i - p h y s i c a l l y - b a s e d models o f t e n have n o n - p h y s i c a l l y based components. Components are l i n k e d and keyed by some s o r t of t r i g g e r that may or may not have p h y s i c a l b a s i s . In such models, mathematical approximations r e p r e s e n t i n g complex n a t u r a l mechanisms convert p r e c i p i t a t i o n i n t o stream flow. The i n f l u e n c e of these mathematical f u n c t i o n s , d e f i n i n g the model a l g o r i t h i m s , are dependent upon the magnitude of c a l i b r a t e d parameters w i t h i n the equations. Once the model parameters have been c a l i b r a t e d , a f i x e d budgeting framework f o r p r e d i c t i o n , e x i s t s . U n c e r t a i n t i e s i n t h i s kind of s y n t h e s i s are due t o : E r r o r s i n recorded data, s p a t i a l d i s t r i b u t i o n s of parameters, i m p e r f e c t i o n s i n model s t r u c t u r e and the non-uniqueness of the proce s s . Freeze and Harlan (1969a) d e s c r i b e n o n - p h y s i c a l l y - b a s e d model components as storage elements and 17 t r a n s m i s s i o n routes, connected i n p a r a l l e l and i n s e r i e s by a set of d e c i s i o n p o i n t s . A pot and p i p e l i n e s t r u c t u r e , i l l u s t r a t e d i n F i g u r e 2, i s a f i t t i n g d e s c r i p t i o n f o r the way these models represent the h y d r o l o g i c c y c l e . Along with u n i t hydrographs, v a r i o u s combinations of r e s e r v o i r r o u t i n g , channel r o u t i n g , i n f i l t r a t i o n , snowmelt and base flow component' techniques are used to e x p l a i n complex n a t u r a l mechanisms. Routing methods are reviewed by Chow (1959) and Henderson (1966). Table 1 l i s t s a number of the d i g i t a l system-synthesis event s i m u l a t i o n models in use. Table 2 d i f f e r e n t i a t e s between the component techniques used in these models (Viessman et a l . , 1977). Table 3 l i s t s the techniques d e s c r i b e d i n s e c t i o n 1.2, as they are used, and c l a s s i f i e s them a c c o r d i n g to input requirements, nature of v a r i a b l e s , model s t r u c t u r e , s p a t i a l and temporal response and use. 1.3 Space-time T r a d e o f f s Moss (1979) d e f i n e s the space-time' t r a d e o f f of h y d r o l o g i c data c o l l e c t i o n as the a b i l i t y t o s u b s t i t u t e s p a t i a l coverage f o r temporal extensions of r e c o r d s . Freeze (1982b) d e f i n e s a time-space t r a d e o f f as the r e l a t i v e i n c r e a s e i n e f f i c i e n c y that can be achieved through a length e n i n g of records as opposed to 18 Figure 2. Flow chart i l l u s t r a t i n g the pot and p i p e l i n e structure of the Stanford Watershed Model IV (aft e r Crawford and Lins ley, 1966) CODE NAME MODEL NAME HEC-1 HEC-1 Flood Hydrograph Package TR-20 Computer Program for Project Hydrology HYMO Hydrologic Model Computer Language SWMM Storm Water Management Model USGS USGS Rainfall - Runoff Model AGENCY/ORGANIZATION Army Corps of Engineers (1073) Soil Conservation Service (1074) Agricultural Research Service (Williams and Harm, 1073) Environmental Protection Agency (1071) Geological Survey (Carrigan. 1073) Table 1. Major r a i n f a l l - r u n o f f event simulation models (after Viessman et a l . , 1977) 20 Model Code Names Modeled Components HEC-1 TR-20 USGS HYMO SWMM (Corps) (SCS) (USGS) (ARS) (EPA) Infiltration and Losses Holtan's equation Horton's equation Phillip's equation SCS curve number method Variable loss rate Standard capacity curves Unit Hydrograph Input Clark's Snyder's 2-parameter gamma response Dimensionless unit hydrograph River Routing Hydraulic Muskingum Tatum Straddle-stagger Modified Puis Working R & D Variable storage coefficient Convex method Translation only Reservoir Routing Storage-indication Base Flow Input Constant value Recession equation Snowmelt Routine X X X X X X X X X X Yes X X X X X X No X X X X X X No No No Table 2. Hydrologic processes and options used by major event simulation models (from Viessman et a l . , 1977) 1 MODELING TECHNIQUE INPUT REQUIREMENTS NATURE OF VARIABLES MODEL STRUCTURE SPATIAL RESPONSE TEMPORAL RESPONSE USE S tr ea m fl ow  P re ci pi ta ti on  W at er sh ed  P ar am et er s S to ch a st ic  D et er m in is tic  Em pi ric al  C on ce pt ua l Lu m pe d D is tr ib ut ed  Ti m e - In va ria nt  Ti m e - Va ria nt  I - ? S t •* m * i s i 5 O pe ra tio na l Fo re ca st  RAINFALL - RUNOFF MODEL8 Regression • • • • • • • UnH Hydrograph • • • • • • • • Quasi - Physically Baaed • • • • • • • • STREAMFLOW ROUTING Hydraulic Routing Using Open Channel Flow Equations • • • • • • Table 3. Characterization of selected r a i n f a l l - r u n o f f modeling techniques (after Freeze, 1982a) 22 an i n c r e a s e i n the d e n s i t y of measuring p o i n t s . Most documented examples of the aforementioned t r a d e o f f have been f o r a s i n g l e p r e c i p i t a t i o n data set using only one model. There i s great promise f o r extending the space-time t r a d e o f f idea a c r o s s h y d r o l o g i c data s e t s . T h i s r e s e a r c h u n d e r l i e s f u t u r e work, by the author, which w i l l address the p o s s i b i l i t y of improving h y d r o l o g i c modeling e f f i c i e n c y by i n c r e a s i n g g e o m e t r i c a l l y d i s t r i b u t e d measurements of s p a t i a l l y - v a r i a b l e t i m e - i n v a r i a n t watershed parameters on a one-time c o l l e c t i o n b a s i s , and thereby, reducing the need for long continuous r a i n f a l l - r u n o f f r e c o r d s . 1.4 Data-Worth and Model Choice The concept of data worth i s married to c o s t - b e n e f i t a n a l y s i s . Hence, i n c r e a s e s i n model e f f i c i e n c y due to improvements i n the data a q u i s i t i o n network are s u b j e c t to economical j u s t i f i c a t i o n . Dooge (1972) s t a t e s that the use of i n c o r r e c t methods leads to e i t h e r economic waste due to c o n s e r v a t i v e f a c t o r s of s a f e t y , or economic l o s s r e s u l t i n g from f a u l t y p r e d i c t i o n s . Davis et a l . ( l 9 7 9 ) d e f i n e the value of a d d i t i o n a l data as the incremental i n c r e a s e in expected payoff or r e d u c t i o n i n expected l o s s . 23 If time-space t r a d e o f f s e x i s t s , the demands of i n c r e a s i n g i n d i v i d u a l model e f f i c i e n c i e s can be e v a l u a t e d economically based upon the cost and delay of o b t a i n i n g the r e q u i r e d data. Depending upon the s i t u a t i o n , c e r t a i n modeling techniques and t h e i r corresponding data s e t s may be p r e f e r r e d . The worth of t h i s data w i l l be d i r e c t l y r e l a t e d to the s i z e and c o s t of a p r o j e c t . A l s o , delays in a p r o j e c t to o b t a i n a d d i t i o n a l data, fo r s p e c i f i c model e f f i c i e n c y requirements, w i l l be c h a r a c t e r i z e d by a d e c r e a s i n g marginal u t i l i t y . In t h i s r esearch,the stage i s being set for an i n i t i a l assessment of data-worth as i n d i c a t e d by the e f f i c i e n c i e s of i n d i v i d u a l r a i n f a 1 1 - r u n o f f - m o d e l i n g techniques as i t r e l a t e s to space-time t r a d e o f f s . The data-worth concept as d e s c r i b e d here, along with adequate d e f i n i t i o n of the modeling problem, may become a b a s i s for f u t u r e model c h o i c e . A p o s s i b l e methodology for s e l e c t i o n of a modeling technique that might be coupled with t h i s type of data-worth assessment i s shown in F i g u r e 3 . 1.5 T h e s i s O b j e c t i v e The c o r r e c t choice of a h y d r o l o g i c modeling technique i s o f t e n l e s s than obvious. C r i t e r i a are needed to f a c i l i t a t e such d e c i s i o n s . These c r i t e r i a must be f u n c t i o n s not only of the Define problem Choose class of model Select a particular model Calibrate the model for given data Evaluate model performance Use calibrated model for prediction Embed in general problem Figure 3. Possible methodology for s e l e c t i n g a r a i n f a l l - r u n o f f modeling technique ( a f t e r Dooge, 1978) 25 a v a i l a b l e m o d e l s , b u t a l s o t h e a v a i l a b l e d a t a . F r e e z e ( I 9 8 2 a , b ) p r o p o s e s t h a t i t may b e p o s s i b l e t o i n c r e a s e m o d e l i n g e f f i c i e n c y b y a t r a d e o f f o f l o n g e r r a i n f a l l a n d s t r e a m f l o w r e c o r d s a g a i n s t a d d i t i o n a l m e a s u r e m e n t s o f s p a t i a l l y v a r i a b l e - s o i l s i n f o r m a t i o n . T h e t e s t i n g o f t h i s h y p o t h e s i s r e q u i r e s s i m u l a t i o n s a c r o s s a s u i t e o f m o d e l i n g a p p r o a c h e s w i t h a v a r i e t y o f d a t a s e t s . T h e o b j e c t i v e o f t h e p r e s e n t r e s e a r c h i s t o c o m p a r e t h e e f f i c i e n c i e s o f v a r i o u s s e l e c t e d h y d r o l o g i c m o d e l i n g t e c h n i q u e s o n a l i m i t e d s u i t e o f s e l e c t e d d a t a s e t s . T h e s c o p e o f t h i s w o r k , i n i t s i n i t i a l p h a s e a s p r e s e n t e d h e r e , i s l i m i t e d t o e v e n t - b a s e d r a i n f a l l - r u n o f f m o d e l i n g t e c h n i q u e s . The s e l e c t e d t e c h n i q u e s a r e l i n e a r a n d m u l t i p l e r e g r e s s i o n , t h e u n i t h y d r o g r a p h , a n d q u a s i - p h y s i c a l l y - b a s e d s y s t e m s y n t h e s i s . S e l e c t e d r a i n f a l l - r u n o f f e v e n t s , a t e x p e r i m e n t a l s u b w a t e r s h e d s i n O k l a h o m a a n d P e n n s y l v a n i a a r e u s e d t o d e t e r m i n e i n d i v i d u a l m o d e l e f f i c i e n c i e s . C o m p a r i s o n o f m o d e l e f f i c i e n c i e s f o r t h e a f o r e m e n t i o n e d t e c h n i q u e s may b e u s e f u l i n f u t u r e a s s e s s m e n t o f s p a c e - t i m e - t r a d e o f f p o t e n t i a l a n d t o g a i n a n i n i t i a l i n d i c a t i o n o f d a t a w o r t h . T h e t w o s u b w a t e r s h e d s w e r e c h o s e n b e c a u s e e a c h m a i n t a i n e d i n s t r u m e n t a t i o n a n d m e a s u r e m e n t p r o g r a m s c o m p a t i b l e w i t h t h e d a t a r e q u i r e m e n t s o f t h e t h r e e s e l e c t e d m o d e l i n g t e c h n i q u e s . I f s p a c e - t i m e t r a d e o f f s a c r o s s d a t a s e t s h a v e t h e p o t e n t i a l t o i n c r e a s e p r e d i c t i o n e f f i c i e n c i e s , t h e n r a i n f a l l - r u n o f f 26 m o d e l i n g t e c h n i q u e s a n d d a t a c o l l e c t i o n n e t w o r k s c a n c o n c e i v a b l y b e s e l e c t e d f o r g i v e n d e s i g n o r o p e r a t i o n a l s p e c i f i c a t i o n s , b a s e d u p o n m o d e l e f f i c i e n c y a n d c o s t - b e n e f i t a n a l y s i s . S u c h c r i t e r i a w o u l d b e u s e f u l t o t h e a p p l i e d h y d r o l o g i s t . 27 CHAPTER TWO MODELS AND COMPARISON In t h i s chapter the three e s t a b l i s h e d u n d e r l y i n g r a i n f a l l - r u n o f f - r n o d e l i n g techniques employed i n t h i s study are f u l l y d e s c r i b e d . The e f f i c i e n c y and comparison c r i t e r i o n used for model e v a l u a t i o n are presented. 2.1 Regress i on Models based on simple l i n e a r r e g r e s s i o n (SLR) with one independent v a r i a b l e , are commonly used in hydrology. A l i n e a r r e l a t i o n s h i p of the form: Y=a+6X (2) i s assumed between two v a r i a b l e s X and Y, where X and Y are the independent and dependent v a r i a b l e s r e s p e c t i v e l y . A common example i s f o r the independent v a r i a b l e to be p r e c i p i t a t i o n and the dependent v a r i a b l e to be d i s c h a r g e . The r e g r e s s i o n l i n e : Y=a+bX (3) approximates Equation 2, where a and b are estimates of a and 3 r e s p e c t i v e l y . The c o e f f i c i e n t b and constant a are 28 c a l c u l a t e d from a set of data [ X ^ , [Y ] with means X and Y as f o l l o w s : b=£x.y./Ex? 1 1 1 (4) a=Y-bX ,_. ( b ) where, x . =X . -X 1 1 - (6) y r V Y (7) T h i s procedure of l e a s t squares i s based upon minimizing the d i f f e r e n c e between the observed and p r e d i c t e d v a l u e s : Z.e?=Z(Y.-Y.)2 1 1 1 (8) The d e v i a t i o n between an observed value Y and the value p r e d i c t e d Y from the r e g r e s s i o n model d e s c r i b e d by Equation 3, i s represented by a r e s i d u a l e r r o r term. In order to determine i f a r e g r e s s i o n l i n e i s the c o r r e c t approach f o r a given set of data, some s o r t of e v a l u a t i o n i s r e q u i r e d . One approach i s to determine how much of the v a r i a b i l i t y i n the dependent v a r i a b l e i s e x p l a i n e d by r e g r e s s i o n . The method commonly used i s a r a t i o of the sum of squares due to r e g r e s s i o n and the sum of squares c o r r e c t e d f o r the mean, expressed as: 29 r2=E(Y.-Y) 2/i:v? (9) The range of r 2 , which i s known as the c o e f f i c i e n t of de t e r m i n a t i o n , i s between zero and one as h y d r o l o g i c systems have p o s i t i v e c o r r e l a t i o n . When r2 i s equal to one, the r e g r e s s i o n equation i s p r o v i d i n g p e r f e c t p r e d i c t i o n s and Ee =0. When r2 i s equal to zero the r e g r e s s i o n l i n e i s e x p l a i n i n g none s of the v a r i a t i o n and E.e?=£y 2. A SLR r a i n f a l l - r u n o f f model c o u l d take any of the f o l l o w i n g forms: V a + b V P P T QpK=a+bPPT TQ p K=a+bPPT D where, = p r e d i c t e d volume of runoff V p p T = observed volume of r a i n f a l l Q p K = p r e d i c t e d peak d i s c h a r g e (10) (11) (12) PPT = average observed r a i n f a l l i n t e n s i t y T * Q_.. = p r e d i c t e d time t o peak d i s c h a r g e PPT p = observed d u r a t i o n of r a i n f a l l M u l t i p l e l i n e a r r e g r e s s i o n (MLR) r a i n f a l l - r u n o f f models are p o s s i b l e with combinations of independent v a r i a b l e s or when more than one r a i n gage i s a v a i l a b l e . In MLR the dependent v a r i a b l e i s a f u n c t i o n of s e v e r a l independent v a r i a b l e s and unknown 30 p a r a m e t e r s e x p r e s s e d b y : Y = B 1 X 1 + B 2 X 2 + - " + B p X p (13) w h e r e , 6 ,B2, • • •,Bp a r e t h e u n k n o w n p a r a m e t e r s . T h e S L R m o d e l i s a s p e c i a l c a s e o f t h e M L R m o d e l . I n p r a c t i c e , t h e r e w o u l d b e n o b s e r v a t i o n s o f t h e d e p e n d e n t v a r i a b l e a n d n c o r r e s p o n d i n g o b s e r v a t i o n s o f e a c h i n d e p e n d e n t v a r i a b l e . S u b s e q u e n t l y , t h e r e w i l l b e n e q u a t i o n s a n d p u n k n o w n p a r a m e t e r s , w h e r e n s h o u l d b e g r e a t e r t h a n o r e q u a l t o t h e n u m b e r o f i n d e p e n d e n t v a r i a b l e s . I n p r a c t i c e n s h o u l d be a t l e a s t t h r e e o r f o u r t i m e s a s l a r g e a s p . T h e m a t r i c e s o f t h e s e n e q u a t i o n s a r e w r i t t e n : • ~ Y f Y 2 — Y 8 n X l , l X l , 2 '"' X 1 , P X 2 , l X 2 , 2 ' " • X 2 , P n, 1 X n , 2 X n , P W r i t t e n i n m a t r i x n o t a t i o n : Y=8 X (14) S i m i l a r t o t h e c o e f f i c i e n t o f d e t e r m i n a t i o n s e e n i n S L R , t h e m u l t i p l e c o e f f i c i e n t o f d e t e r m i n a t i o n i s a n e v a l u a t i o n o f t h e u s e f u l n e s s o f M L R f o r a g i v e n d a t a s e t . W r i t t e n i n m a t r i x n o t a t i o n , t h e m u l t i p l e c o e f f i c i e n t o f d e t e r m i n a t i o n i s a s 1 f o l l o w s : 3 1 r 2=^ TX TY- nY 2 / Y_TY-nY 2 (15) "X T T where, J3 ,_X ,Y are the transpose of JL>2L>X n i s the s i z e of the Y ve c t o r ~ T x -1 T 1 =(X X) X Y The range of r f 2 i s from zero to one, the c l o s e r to one the b e t t e r the f i t . A c o r r e l a t i o n matrix should be computed before using the MLR technique to determine i f a l i n e a r model can be used and what independent v a r i a b l e s should be i n c l u d e d . A l l the v a r i a b l e s r e t a i n e d in a r e g r e s s i o n model should make a s i g n i f i c a n t c o n t r i b u t i o n . High c o r r e l a t i o n between two . v a r i a b l e s does not always mean there i s a cau s e - a n d - e f f e c t r e l a t i o n s h i p though, as e x t e r n a l f o r c e s can be i n v o l v e d . Regression c o e f f i c i e n t i n f e r e n c e s , e x t r a p o l a t i o n and confidence i n t e r v a l s f o r MLR, as we l l as SLR, are d i s c u s s e d by Hann (1977). Johnston (1963) d i s c u s s e s the u n d e r l y i n g assumptions and technique of MLR a n a l y s i s i n d e t a i l . M u l t i v a r i a t e r e g r e s s i o n a n a l y s i s i s used to p r e d i c t more than one dependent q u a n t i t y from the same set of independent v a r i a b l e s . W a l l i s (1965) d i s c u s s e s s i x m u l t i v a r i a t e s t a t i s t i c a l methods used i n hydrology i n c l u d i n g r e g r e s s i o n a n a l y s i s . A MLR r a i n f a l l - r u n o f f model has the f o l l o w i n g general form: Y = b 1 X 1 + b 2 X 2 + - - - + b M V a •32 where, Y = a p r e d i c t e d runoff v a r i a b l e Xi = an observed r a i n f a l l v a r i a b l e at gage i b± = c a l c u l a t e d c o e f f i c i e n t s a = c a l c u l a t e d constant A MLR r a i n f a l l - r u n o f f model can have any of the general forms shown i n Equations 10, 11, and 12 with more than one independent v a r i a b l e . In t h i s study, the UBC T r i a n g u l a r Regression Package (TRP) i s used f o r simple and m u l t i p l e l i n e a r r e g r e s s i o n a n a l y s i s . TRP c a l c u l a t e d means, standard d e v i a t i o n s , the c o r r e l a t i o n matrix of independent and dependent variable's, as w e l l as the c o e f f i c i e n t s of d e t e r m i n a t i o n , r e s i d u a l s , p r e d i c t e d values and confidence i n t e r v a l s f o r the d e s i r e d r e g r e s s i o n equation. I l l u s t r a t i v e examples from the implementation of the TRP a l g o r i t h m are shown in the TRP d e s c r i p t i o n (Le and T e n i s c i , 1977). In a p r e d i c t i v e mode SLR and MLR r a i n f a l l - r u n o f f models r e q u i r e p r e c i p i t a t i o n records i n order to a b s t r a c t v a r i o u s independent r a i n f a l l v a r i a b l e s . The output produced from these models i s i n the form of runoff v a r i a b l e s . 33 2.2 Unit Hydrograph The r e g r e s s i o n r a i n f a l l - r u n o f f models j u s t d e s c r i b e d only allow f o r the e s t i m a t i o n of runoff v a r i a b l e s such as volume and peak flow. Often a r a i n f a l l - r u n o f f model i s d e s i r e d that p r e d i c t s the form of the storm hydrograph. The u n i t hydrograph i s such a model. Sherman (1932) d e f i n e d the u n i t graph as f o l l o w s : If a given one-day r a i n f a l l produces a one inch depth of runoff over the given drainage area, the hydrograph showing the r a t e s at which runoff o c c u r r e d can be con s i d e r e d a u n i t graph for that watershed. Sherman's u n i t graph i s a dimensionless r o u t i n g model that i s roughly l i n e a r and of u n i t volume. The u n i t hydrograph theory having evolved from the u n i t graph method i n c o r p o r a t e s u n i t t ime. The u n i t hydrograph, d e s p i t e being an approximate technique with many t h e o r e t i c a l d i f f i c u l t i e s , has r e c e i v e d c o n s i d e r a b l e use by the h y d r o l o g i c community, u s u a l l y as a p r e d i c t o r of f l o o d peaks. A l l u n i t hydrographs are based on the f o l l o w i n g two p r i n c i p l e s (Dooge, 1959): 1) Inv a r i a n c e - t h e hydrograph of s u r f a c e r u n o f f from a catchment due to a given p a t t e r n of r a i n f a l l excess i s i n v a r i a b l e . 2 ) S u p e r p o s i t i o n - t h e hydrograph r e s u l t i n g from a given p a t t e r n of r a i n f a l l excess can be b u i l t by s u p e r i m p o s i t i n g the u n i t hydrographs due to the separate amounts of r a i n f a l l excess o c c u r r i n g i n each p e r i o d . T h i s 34 i n c l u d e s t h e p r i n c i p l e o f p r o p o r t i o n a l i t y , b y w h i c h t h e o r d i n a t e s o f t h e h y d r o g r a p h a r e p r o p o r t i o n a l t o t h e v o l u m e o f r a i n f a l l e x c e s s . D o o g e ( 1 9 7 3 ) c l e a r l y s t a t e s t h e i m p l i c a t i o n s o f t h e l i n e a r a s s u m p t i o n s i n t h e u n i t h y d r o g r a p h t h e o r y . I m p l i c i t t o i t s l i n e a r a s s u m p t i o n , t h e d e v e l o p m e n t o f a u n i t h y d r o g r a p h r e q u i r e s s i m u l t a n e o u s d a t a o f e x c e s s r a i n f a l l a n d s t o r m f l o w . E x c e s s r a i n f a l l i s d e f i n e d h e r e a s t o t a l r a i n f a l l m i n u s i n f i l t r a t i o n . S t o r m f l o w i s d e f i n e d a s t o t a l r u n o f f m i n u s b a s e f l o w . B a s e f l o w i s g e n e r a l l y a c c o u n t e d f o r b y n o r m a l d a y - t o - d a y g r o u n d w a t e r c o n t r i b u t i o n s t o s t r e a m f l o w . E x c e s s r a i n f a l l a n d s t o r m f l o w v o l u m e s f o r a s e l e c t e d e v e n t a r e e q u a l . V a r i o u s b a s e f l o w s e p a r a t i o n t e c h n i q u e s u s e d t o e s t i m a t e s t o r m f l o w v o l u m e s a r e d i s c u s s e d b y V i e s s m a n e t a l . ( 1 9 7 7 ) a n d D u n n e a n d L e o p o l d ( 1 9 7 8 ) . T h e S o i l C o n s e r v a t i o n S e r v i c e c u r v e n u m b e r m e t h o d o l o g y , w i t h e m p i r i c a l r a t i n g s b a s e d o n s o i l s a n d v e g e t a t i o n ( U . S . S o i l C o n s e r v a t i o n S e r v i c e , 1 9 7 2 ) , i s o n e m e t h o d o f e s t a b l i s h i n g e x c e s s r a i n f a l l v a l u e s . O t h e r m e t h o d s i n c l u d e t h e a n t e c e n d e n t p r e c i p i t a t i o n i n d e x ( V i e s s m a n e t a l . , 1 9 7 7 ) , t h e <j> a n d t h e W i n d i c e s ( S c h u l t z , 1 9 7 6 ) . G e n e r a l l y , t h e a s s u m p t i o n s a b o u t u n i f o r m r a i n f a l l d i s t r i b u t i o n a r e n o t m e t a n d v a r i a t i o n i n u n i t h y d r o g r a p h o r d i n a t e s f o r d i f f e r e n t s t o r m s s h o u l d b e e x p e c t e d . A v e r a g i n g i n d e p e n d e n t l y d e r i v e d u n i t h y d r o g r a p h s i s d i s c u s s e d b y L i n s l e y e t a l . d 9 7 5 ) . L i n s l e y e t a l . ( 1 9 7 5 ) , V i e s s m a n e t a l . d 9 7 7 ) , a n d 35 D u n n e a n d L e o p o l d ( 1 9 7 8 ) a l l s h o w e x a m p l e s o f u n i t h y d r o g r a p h d e r i v a t i o n s . F i g u r e 4 s h o w s a f l o w c h a r t o f t h e b a s i c o p e r a t i o n s i n v o l v e d i n t h e u n i t h y d r o g r a p h p r o c e d u r e . A n i l l u s t r a t i o n o f m a t r i x m e t h o d s u s e d t o d e f i n e t h e u n i t h y d r o g r a p h i s p r e s e n t e d i n V i e s s m a n e t a l . ( l 9 7 7 ) . C a l c u l a t i o n o f a d e s i g n s t o r m h y d r o g r a p h i s g r a p h i c a l l y d e m o n s t r a t e d f o r a t h r e e p e r i o d s t o r m i n F i g u r e 5 . I n m a t r i x n o t a t i o n t h e s t o r m h y d r o g r a p h i s g i v e n b y : ^ ( , 7 ) w h e r e , Q_ = t h e e x i s t i n g s t o r m h y d r o g r a p h v e c t o r P = k n o w n e x c e s s r a i n f a l l m a t r i x U = t h e u n i t h y d r o g r a p h v e c t o r T h e r e v e r s e o f t h e p r o c e s s s h o w n i n F i g u r e 5 i s t h e b a s i s o f t h e m a t r i x m e t h o d . S u b j e c t t o t h e r e s t r i c t i o n s o f m a t r i x a l g e b r a t h e s o l u t i o n f o r t h e u n i t h y d r o g r a p h m a t r i x b e c o m e s : T - I T u =C P P) P o - ~ ( 1 8 ) R e p r o d u c t i o n o f i n i t i a l s t o r m h y d r o g r a p h s b a s e d o n m a t r i x m e t h o d s a r e g e n e r a l l y n o t e x a c t . A d j u s t m e n t s a r e u s u a l l y m a d e b y r e d u c i n g t h e s q u a r e o f t h e e r r o r s . M a t r i x m e t h o d s a r e d i s c u s s e d b y S n y d e r ( 1 9 5 5 ) , N e w t o n a n d V i n y a r d ( 1 9 6 7 ) a n d M o r e l - S e y t o u x ( 1 9 8 2 ) . T h e i n s t a n t a n e o u s u n i t h y d r o g r a p h ( I U H ) , t r a c e d t o C l a r k ( 1 9 4 5 ) i s t h e h y d r o g r a p h o f o n e i n c h r u n o f f s p r e a d u n i f o r m l y ABBREVIATIONS R.E = RAINFALL EXCESS INF. t INFILTRATION S R « STORM RUNOFF B F . « BASE FLOW ANALYSIS T I M E Figure 4. Flow chart of the operations involved i n the unit hydrograph technique (from Amorocho and Hart, 1964) 37 Figure 5. Determination of a design storm hydrograph: (a) Excess r a i n f a l l , (b) unit hydrograph, and (c) surface runoff hydrograph (from Viessman et a l . , 1977) 38 o v e r a n a r e a g e n e r a t e d i n a n i n f i n i t e s i m a l t i m e p e r i o d . M a t h e m a t i c a l l y , t h e I U H i s t h e k e r n a l f u n c t i o n i n t h e c o n v o l u t i o n r e l a t i o n s h i p f o r a l u m p e d l i n e a r t i m e i n v a r i a n t c a u s a l s y s t e m . T h e c o n v o l u t i o n i n t e g r a l h a s t h e f o l l o w i n g f o r m : t o y ( t ) = / X ( X ) h ( t - A ) d A 0 (19) w h e r e , y ( t ) = s t o r m r u n o f f h y d r o g r a p h x ( A ) = e x c e s s r a i n f a l l h y e t o g r a p h h ( t ~ A ) = u n i t h y d r o g r a p h F i g u r e 6 s h o w s t h e i n p u t , o u t p u t a n d k e r n a l f u n c t i o n s . Q u i m p o ( 1 9 7 3 ) a n d F r e e z e ( 1 9 8 2 a ) d i s c u s s t h e l i n k a g e o f I U H a n d a u t o r e g r e s s i v e s t r e a m f l o w m o d e l s . T h e e q u a t i o n o f c o n t i n u i t y f o r a n y r e s e r v o i r c a n b e w r i t t e n a s : p - q = d s / d t ( 2 0 ) w h e r e , p = i n f l o w q = o u t f l o w s = o u t f l o w s t o r a g e A l i n e a r r e s e r v o i r i s o n e i n w h i c h t h e o u t f l o w i s a l i n e a r f u n c t i o n o f t h e s t o r a g e : q=ks (21 ) w h e r e k i s a w a t e r s h e d p a r a m e t e r . C o m b i n i n g e q u a t i o n s 20 a n d 21 l e a d s t o t h e d i f f e r e n t i a l e q u a t i o n : 39 X(A) EXCESS RAINFALL HYETOGRAPH - t h htoH i " INSTANTANEOUS UNIT HYDROGRAPH h(t -A) H Figure 6. Instantaneous unit hydrograph: (a) input function, (b) kernel function, and output function ( a f t e r Chow, 1964b) 40 (dq/dt)+kq=kp (22) The s o l u t i o n t o t h i s e q u a t i o n f o r t h e i n i t i a l c o n d i t i o n q=0 a t t=0 i s : q(t)=/ t ke" k ( t _ X )p(A)dA 0 (23) E q u a t i o n s 19 and 23 a r e e q u i v a l e n t when h(t)=(l/K)e" t / K (24) where K = 1/k. U s i n g E q u a t i o n 24 as t h e IUH and E q u a t i o n 19 as a r a i n f a l l - r u n o f f p r e d i c t o r i s e q u i v a l e n t t o c o n s i d e r i n g a w a t e r s h e d as a s i n g l e l i n e a r r e s e r v o i r . A c o n c e p t u a l model of t h e IUH d e s c r i b e d by Nash (1959) i s shown i n F i g u r e 7. "Nash p r o p o s e d r o u t i n g i n s t a n t a n e o u s r a i n f a l l t h r o u g h a s e r i e s of s u c c e s s i v e l i n e a r r e s e r v o i r s . F o r n l i n e a r r e s e v o i r s t h e IUH becomes: h ( t ) = ( l / k r ( n ) ) ( t / K ) n " 1 e " t / K , x (25) where r (n) i s t h e n t h o r d e r gamma f u n c t i o n . The a p p r o a c h h e r e i s l i n e a r as K i s a c o n s t a n t t h a t can be e v a l u a t e d by t h e method of moments. The c a l c u l a t i o n of u n i t h y d r o g r a p h s f o r e x p e r i m e n t a l s u b w a t e r s h e d s i n t h i s s t u d y was c a r r i e d out w i t h t h e computer p r o g r a m UNIT, w h i c h u s e s a m a t r i x method e m p l o y i n g o p t i m i z a t i o n t e c h n i q u e s , a u t h o r e d by M o r e l - S e y t o u x and Kimzey ( 1 9 8 0 ) . From t h e t h e o r y o f l i n e a r s y s t e m s , t h e i n s t a n t a n e o u s s t o r m f l o w r a t e Figure 7. Nash's model for routing instantaneous r a i n f a l l through a s e r i e s of l i n e a r storage resevoirs (after Chow, 1964b) 42 at the end of p e r i o d n i s g i v e n by the d i s c r e t e e q u i v a l e n t t o E q u a t i o n 19: n _ q(n)=Z 6 ( n - j + l ) r ( j ) , v j - 1 ( 2 6 ) where, ^(m) = n t h o r d i n a t e of the u n i t hydrograph r ( j ) = mean excess r a i n f a l l r a t e d u r i n g p e r i o d j F o l l o w i n g the development of M o r e l - S e y t o u x and Kimzey (1980), the normal e q u a t i o n s used i n the e q u a l i t y - c o n s t r a i n e d l e a s t square method of UNIT are summarized i n Table 4. The r e s u l t i n g system of l i n e a r e q u a t i o n s i s s o l v e d by g a u s s i o n e l i m i n a t i o n . The f i r s t M s o l u t i o n s are the d e s i r e d u n i t hydrograph. The UNIT code, or more s p e c i f i c a l l y the t e c h n i q u e i t uses, i s a p r a c t i c a l c h o i c e f o r d e t e r m i n i n g u n i t hydrographs i n t h i s s t u d y . Computer s o l u t i o n g r e a t l y reduces the c o m p u t a t i o n a l time r e l a t i v e t o hand c a l c u l a t i o n methods. The IUH method r e q u i r e s r a i n f a l l p a t t e r n s t o be known as c o n t i n u o u s f u n c t i o n s , which they r a r e l y a r e . A l i s t i n g of the UNIT code i s g i v e n i n Appendix A. I l l u s t r a t i v e examples and hand computations v e r i f y i n g the UNIT program are found i n the u s e r s manual (Morel-Seytoux and Kimzey, 1980). To employ UNIT, excess r a i n f a l l and storm f l o w must be d e t e r m i n e d f o r s e l e c t e d e v e n t s . The $ index method of c a l c u l a t i n g e x c e s s r a i n f a l l i s used i n both e x p e r i m e n t a l subwatersheds. The * index i s d e f i n e d as the amount of r a i n f a l l t h a t i s r e t a i n e d by the b a s i n d i v i d e d by the d u r a t i o n of the M+1 I a. .x. = b. i = 1 , 2 , . . . , M + 1 j=l 1 J J 1 where the a ^ and b̂  are given by the formulae: N as-i = I r(n-i+l)r(n-j+l) for i = 1,-2 M n=j and j = 1 ,2 , . . . ,M but with j > i For j < i = a^. (symmetry) i = 1,2 M a i ,M+l = \ 1 = 1 .2,--- . M a M+l,j = 1 j = 1 , 2 M aM+l,M+1 = 0 N b = ^ / 7 ( n - l + l ) q ( n ) i = 1 . 2 . . . . . M 1 n=l bM+l = 1 - The prime indicates that the indices corresponding to periods with missing runoff are skipped i n the summation. These equations guarantee that the discre t e kernels add up to one but do not guarantee nonnegativity for them. Table 4. Normal equations for the equality-constrained least squares technique used i n the computer program UNIT (aft e r Morel-Seytoux and Kimzey, 1980) 44 storm (Dunne and Leopold, 1978). The $ index p r o v i d e s a means of r e p l a c i n g the time v a r y i n g i n f i l t r a t i o n f u n c t i o n by an average v a l u e . When data are i n s u f f i c i e n t to d e r i v e an i n f i l t r a t i o n curve, the <J> index i s o f t e n used. The <t> index method i s i l l u s t r a t e d in F i g u r e 8. Storm flow i s determined by s e p a r a t i n g base flow from the t o t a l observed hydrograph.. Only one of the experimental subwatersheds considered in t h i s study experiences base flow s e p a r a t i o n . The c r i t e r i a used f o r s e p a r a t i o n in t h i s study i s the simple but o b j e c t i v e technique d e s c r i b e d by Engman (1974). The procedure i s i l l u s t r a t e d in F i g u r e 9, and in e f f e c t shows that no s u r f a c e runoff i s c o n t r i b u t i n g to the hydrograph a f t e r . the i n t e r s e c t i o n of the base flow s e p a r a t i o n l i n e and the hydrograph r e c e s s i o n . The value of the slope a i s chosen by a n a l y z i n g s e v e r a l hydrographs from a study area with a s u b j e c t i v e d e c i s i o n as to where the most r a p i d change in the r e c e s s i o n curve occurs on the average. The o index determined from a s i n g l e storm i s not g e n e r a l l y a p p l i c a b l e to other storms and t h e r e f o r e not c o n s i d e r e d a basin constant in t h i s study. The slope a used f o r base flow s e p a r a t i o n i s c o n s i d e r e d a basin constant i n t h i s study s e r v i n g as a l y n c h p i n between storm flow and c a l c u l a t e d excess r a i n f a l l . In i t s p r e d i c t i v e mode the u n i t hydrograph r e q u i r e s mean values of excess r a i n f a l l f o r u n i t p e r i o d s as input and produces output i n the form of a storm flow hydrograph. HYETOGRAPH O < cr 5 10 - 15 ~ 20 - 25 - 30 - 3 5 TIME (hours) 2 _ L 4 5 I I 6 INFILTRATION EXCESS RAINFALL (storm flow) ure 8. $ index method of calculating excess rainfa 46 Figure 9. Base flow separation technique ( a f t e r Engman, 1974) 47 2.3 Q u a s i - P h y s i c a l l y - B a s e d Q u a s i - p h y s i c a l l y - b a s e d - r a i n f a l l - r u n o f f models attempt to approximate the p h y s i c a l processes o c c u r r i n g w i t h i n the h y d r o l o g i c c y c l e i l l u s t r a t e d in F i g u r e 10. Many authors have attempted t o d e s c r i b e the component mechanisms r e s p o n s i b l e f o r r u n o f f . R a i n f a l l - r u n o f f processes are reviewed by Kirkby (1978) and Freeze (1974). A number of r a i n f a l l - r u n o f f s i m u l a t i o n models have been proposed to e x p l a i n watershed p h y s i c s . Common to a l l i s the problem of accounting f o r n a t u r a l watershed v a r i a b i l i t y in terms of necessary input data as w e l l as boundary and i n i t i a l c o n d i t i o n s . The model chosen f o r use i n t h i s study (Engman, 1974) i s based on p a r t i a l area concepts (Betson, 1964) and emphasizes t r a n s f o r m a t i o n of a n a t u r a l heterogeneous system i n t o a corresponding d i s t r i b u t e d system compatible with computer s i m u l a t i o n . H e r e a f t e r , Engman's q u a s i - p h y s i c a l l y - b a s e d r a i n f a l l runoff modeling technique w i l l be r e f e r r e d to as a d i s t r i b u t e d model. Based on a dynamic watershed approach, i l l u s t r a t e d i n F i g u r e 11, the d i s t r i b u t e d model may be d i v i d e d i n t o three p a r t s (Engman and Rogowski, 1974a). The f i r s t part d e s c r i b e s a p h y s i c a l l y based s o i l i n f i l t r a b i l i t y c a l c u l a t i o n f o r developing the p r e c i p i t a t i o n excess. The next two p a r t s d e a l with kinematic r o u t i n g phases: One f o r developing a l a t e r a l i nflow System inflow System outflow 1'recipitation Kvnporalion I R;im Sleet ll:iil Snow Inlen cplion Depression storage Snow ;Ki'inntil.ition ami melt Wale laml surl 1 • t o n I ( K e i l a i u l How aee | Dneel n m o l l Infiltration System oul flow _ _ J Root /.OI1C storaee l-vapotranspiration I ( hannel flow I . Diversions System ontllow ( hannel secpar.i Imported (iioiindwater water inflow } - f System inllow System inflow — I n t c r l l n w A i V . T u l . i h n i i — M I < iioiimtwatei storage J Kesc rvoir storage Water alloeatiims System outflow (iroumlwalcr I low System outflow Figure 10. Systems representation of hydrologic cycle (from Viessman et a l . , 1977) 00 BEPORI PRECIPITATION Figure 11. Schematic diagram of a dynamic watershed (from Engman, 1974) 50 hydrograph from the overland flow plane and one f o r r o u t i n g the channel hydrograph. The model does not address p o s s i b l e o r i g i n s of runoff other than those caused by the r a i n f a l l i n t e n s i t y exceeding the i n f i l t r a t i o n c a p a c i t y . A p p l i c a t i o n of the model i s t h e r e f o r e l i m i t e d to the p r e d i c t i o n of the storm flow hydrograph from areas c o n t r i b u t i n g o verland flow without c o n s i d e r a t i o n of. subsurface storm flow to the stream, d i r e c t groundwater discharge to the stream, or the e v a p o t r a n s p i r a t ion component mechanisms. A flow c h a r t of the s i m u l a t i o n model i s shown in Fi g u r e 12. The f i r s t computational step of the d i s t r i b u t e d model i n v o l v e s c a l c u l a t i o n of p e r t i n e n t i n f i l t r a t i o n c a p a c i t y and excess r a i n f a l l , as f u n c t i o n s of time for the d i f f e r e n t s o i l s e r i e s composing the watershed. The model sim u l a t e s a two l a y e r system. T h i s step i s based on Richard's (1931) one-dimensional i n f i l t r a t i o n equation f o r a un s a t u r a t e d - s a t u r a t e d system: (3/3z){K(i|0 (Oi|i/3z) + l ) } = C ( ^ ) 3^/9t where, t = time z = v e r t i c a l d i s t a n c e from the s o i l s u r f a c e downward ty = pressure head R(ty),C{ty) are unsaturated 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 h y d r a u l i c c o n d u c t i v i t y and s p e c i f i c moisture r e s p e c t i v e l y . A n a l y t i c and numeric s o l u t i o n s f o r one-dimensional i n f i l t r a t i o n boundary value problems are d i s c u s s e d by P h i l i p (1957a,b,c,d,e, f Read in watershed \ ( geometry and W V depression storage J Read in break point precipitation data from raingage or simulated event Calculate precii for each soil ty chosen initial s citation excess 'pe for the oil moisture Subtract depression storage until all depressions are filled and assign a depth of water for routing to each soil zone Route overland flow to calculate lateral inflow hydrograph - includes infiltration where capacity is available Route lateral inflow hydrographs in proper downstream sequence Outflow hydrograph Figure 12. Flow chart for d i s t r i b u t e d model code ( a f t e r Engman, 1974) 52 1958a,b) and Freeze (1969b) r e s p e c t i v e l y . In the model, i n f i l t r a t i o n c a p a c i t y i s d e s c r i b e d by P h i l i p ' s (1969) two-parameter i n f i l t r a t i o n e q u ation: i=%St 2+A where, i = i n f i l t r a t i o n r a t e S = S o r p t i v i t y A i s a constant that i s approximated by 1/2 the s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y S o r p t i v i t y values are computed from Parlange's (1972) approximation: S = { 2 / ( 6 - e 0)Dd c 1" 2 where, 6 = v o l u m e t r i c s o i l water content 6 i = s o i l water content of s o i l s u r f a c e So = i n i t i a l s o i l water content D = s o i l water d i f f u s i v i t y The s o i l water d i f f u s i v i t y i s d e s c r i b e d by: D=K(6) (dij>/de) (28) l 6 0 (29) ( 3 0 ) where K i s h y d r a u l i c c o n d u c t i v i t y . The unsaturated c h a r a c t e r i s t i c curves of h y d r a u l i c c o n d u c t i v i t y and s o i l water p r e s s u r e head as a f u n c t i o n of s o i l water content are computed using m o d i f i e d models proposed by Rogowski (1971, 1972a,c,d) and Parlange (1972). 53 T h e i n p u t r e q u i r e d f o r t h e f i r s t s t e p o f t h e d i s t r i b u t e d m o d e l i s : 1) a n t e c e n d e n t s o i l m o i s t u r e f o r e a c h s o i l , 2 ) t h e d e g r e e o f s a t u r a t i o n f o r e a c h s o i l , 3 ) h y d r a u l i c c o n d u c t i v i t y a t a i r e n t r y f o r e a c h s o i l , 4 ) s o r p t i v i t y v a l u e s f o r e a c h s o i l , 5 ) t h e i n i t i a l i n f i l t r a t i o n r a t e f o r e a c h s o i l . T h e i n p u t r e q u i r e d t o d e t e r m i n e s o i l c h a r a c t e r i s t i c c u r v e s w i t h t h e m e t h o d s d e s c r i b e d b y R o g o w s k i ( 1 9 7 1 , 1 9 7 2 a , c , d ) a n d P a r l a n g e ( 1 9 7 2 ) i s : 1) t h e p o r o s i t y o f e a c h s o i l , 2 ) s o i l m o i s t u r e a t 1 . 5 M P a f o r e a c h s o i l , 3 ) t h e a i r e n t r y v a l u e f o r e a c h s o i l , 4 ) t h e w a t e r e n t r y v a l u e o f e a c h s o i l , a n d 5 ) t h e h y d r a u l i c c o n d u c t i v i t y o f e a c h s o i l a t a i r e n t r y . T h e s e c o n d s t e p o f t h e d i s t r i b u t e d m o d e l r o u t e s e x c e s s s u r f a c e w a t e r f r o m c o n t r i b u t i n g a r e a s t o t h e s t r e a m t a k i n g i n t o a c c o u n t d e t e n t i o n s t o r a g e a n d r e i n f i l t r a t i o n . F l o w o f w a t e r o v e r a s u r f a c e o r i n a c h a n n e l i s d e s c r i b e d b y t w o d i f f e r e n t i a l e q u a t i o n s b a s e d o n t h e f o l l o w i n g a s s u m p t i o n s ( C h o w , 1 9 5 9 ) : 1) v e l o c i t y a t a n y s e c t i o n i s u n i f o r m a n d u n i d i r e c t i o n a l , 2 ) c h a n n e l s l o p e i s s m a l l , 3 ) s t r e a m l i n e c u r v a t u r e s a r e s m a l l , 4 ) e n e r g y l o s s e s a r e r e p r e s e n t e d b y t h e s l o p e o f t h e e n e r g y g r a d i e n t t i m e s t h e l e n g t h o f t h e c h a n n e l r e a c h . T h e c o n t i n u i t y e q u a t i o n , b a s e d o n t h e c o n s e r v a t i o n o f m a s s , i s e x p r e s s e d a s : A (3V/3X)+V (3A/3X)+3A/3t=q T h e m o m e n t u m e q u a t i o n , b a s e d o n t h e c o n c e p t t h a t t h e s u m o f 54 f o r c e s a c t i n g o n a n e l e m e n t o f w a t e r i s e q u a l , i s e x p r e s s e d a s : S . - S =(l/g){(3V/3t)+V(3V/3X) + (g/A)(3(Ay")/3X)+Vq/A} , % 0 t ( 3 2 ) w h e r e , A = c r o s s s e c t i o n a l a r e a o f w a t e r V = a v e r a g e v e l o c i t y X = h o r i z o n t a l d i s t a n c e y = d e p t h o f w a t e r t o c e n t r o i d o f v o l u m e SQ = b e d s l o p e o f c h a n n e l S f = f r i c t i o n s l o p e t = t i m e g = a c c e l e r a t i o n o f g r a v i t y cf = s o u r c e t e r m E q u a t i o n s 31 a n d 3 2 , w h i c h a r e k n o w n a s t h e , S a i n t V e n a n t o r s h a l l o w w a t e r e q u a t i o n s , m a t h e m a t i c a l l y d e s c r i b e t h e p r o p o g a t i o n o f a w a v e a n d c a n n o t b e s o l v e d i n c l o s e d f o r m f o r p r a c t i c a l s i t u a t i o n s . ( L i g g e t a n d W o o l h i s e r , 1 9 6 7 ; S t r e l k o f f , 1 9 6 9 , 1 9 7 0 ) . K i n e m a t i c a p p r o x i m a t i o n s t o t h e c o m p l e t e f l o w e q u a t i o n s a r e u s e d t o s i m u l a t e t h e o v e r l a n d f l o w h y d r o g r a p h t h a t r e s u l t s f r o m r a i n f a l l e x c e s s . T h e k i n e m a t i c e q u a t i o n s t a k e t h e f o r m o f f i r s t o r d e r d i f f e r e n t i a l e q u a t i o n s , c o m p u t a t i o n a l l y m u c h s i m p l e r t h a n t h e c o m p l e t e h y p e r b o l i c s h a l l o w w a t e r e q u a t i o n s . K i n e m a t i c r o u t i n g h a s b e e n a n a l y z e d b y K i b l e r a n d W o o l h i s e r ( 1 9 7 0 ) , O v e r t o n a n d B r a k e n s i e k ( 1 9 7 0 ) , a n d S m i t h a n d W o o l h i s e r ( 1 9 7 1 ) . K i n e m a t i c f l o w o c c u r s o n a p l a n e w h e n e v e r a b a l a n c e b e t w e e n 55 g r a v i t a t i o n a l and f r i c t i o n a l f o r c e s i s a c h i e v e d . Under these c o n d i t i o n s E q u a t i o n 32 reduces to S = S . S i s d e f i n e d by a M O f f stage d i s c h a r g e r e l a t i o n s h i p . In t h e i r k i n e m a t i c forms the e q u a t i o n s of motion and c o n t i n u i t y are g i v e n r e s p e c t i v e l y by: Q=Qn (33) (9Q/SX)+9y/at=q (34) where, Q = d i s c h a r g e Q = normal d i s c h a r g e n y = depth of water q = source term = p r e c i p i t a t i o n exces s , P E T u r b u l e n t flow i s assumed in the d i s t r i b u t e d model , t h e r e f o r e E q u a t i o n 33 i s w r i t t e n in form: Q - C l . O / i O y 1 ' 6 6 ^ ( 3 5 ) where n i s Manning ' s roughness c o e f f i c i e n t . The c o n t i n u i t y e q u a t i o n in f i n i t e d i f f e r e n c e form i s : E (36) CAQ/AX)+Ay/At=P R e w r i t i n g e q u a t i o n 36 i n terms of the change in water d e p t h : Ay=(.(AQ/AX)-PE)At . { 3 7 ) E q u a t i o n 37 i s s o l v e d n u m e r i c a l l y by e x p l i c i t f i n i t e d i f f e r e n c e methods. For a d i s c u s s i o n of the s t a b i l i t y of the e x p l i c i t 56 method, parameter f i t t i n g and component v e r i f i c a t i o n of the sur f a c e water r o u t i n g a l g o r i t h m the reader i s d i r e c t e d to Engman (1974). The input requirements f o r the second step i n c l u d e : 1) a three-dimensional s o i l d i s t r i b u t i o n of the watershed, 2) s o i l s l o p e s , 3) de p r e s s i o n storage, 4) Manning's n roughness v a l u e s fo r o v erland flow, 5) average water s u r f a c e widths, and 6) channel reach l e n g t h s . In the t h i r d and f i n a l s t e p of the d i s t r i b u t e d model su r f a c e runoff hydrographs become l a t e r a l i n flow f o r channel r o u t i n g . A kinematic f l o o d r o u t i n g program developed by Brakensiek (1966a) i s used to s y n t h e s i z e the channel hydrograph in any given reach of a stream. The method i s i d e n t i c a l to that employed i n step two, except that flow in a r e c t a n g u l a r open channel i s c o n s i d e r e d r a t h e r than flow across a plane. The f o r m u l a t i o n of kinematic f l o o d r o u t i n g i s composed of the c o n t i n u i t y equation: (8Q/3X)+3A/8t=q (38) The source term q i s now the l a t e r a l i n flow to the stream determined as output from the step-two s i m u l a t i o n of ov e r l a n d flow. The equation of motion i s now i n the form of a r a t i n g f u n c t i o n : Q=Q(A) (39) 57 U t i l i z i n g a n a l g o r i t h m d e v e l o p e d b y B r a k e n s i e k ( 1 9 6 6 b ) a r a t i n g f u n c t i o n i s d e v e l o p e d f o r e a c h c h a n n e l c r o s s s e c t i o n s o t h a t : AQ=f (AA) ( 4 0 ) N o r m a l ( t u r b u l e n t ) f l o w i s a s s u m e d s o t h a t : q n = ( 1 . 0 / „ > R ° - 6 ^ ( 4 1 ) w h e r e R i s t h e h y d r a u l i c r a d i u s o f t h e c h a n n e l ( a r e a / w e t t e d p e r i m e t e r ) . S i m u l t a n e o u s s o l u t i o n s o f E q u a t i o n 40 a n d t h e f i n i t e d i f f e r e n c e a p p r o x i m a t i o n o f E q u a t i o n 38 r e q u i r e s a n i t e r a t i v e p r o c e d u r e . T h e n u m e r i c a l t e c h n i q u e u s e d i s t h e m e t h o d o f f a l s e p o s i t i o n ( K u n z , 1 9 5 7 ) . B r a k e n s i e k ( 1 9 6 7 ) r e v i e w s t h e a p p l i c a t i o n o f t h e k i n e m a t i c t e c h n i q u e i n f l o o d r o u t i n g . A s d e s c r i b e d b y E n g m a n ( 1 9 7 4 ) B r a k e n s i e k 1 s ( 1 9 6 6 a ) f l o o d r o u t i n g p r o g r a m t a k e s t h e u p s t r e a m i n f l o w h y d r o g r a p h f o r a n y g i v e n r e a c h , a d d s t h e l a t e r a l i n f l o w h y d r o g r a p h f o r t h a t r e a c h , a n d r o u t e s t h e t w o t o g e t h e r t o f o r m t h e o u t f l o w h y d r o g r a p h f r o m t h e r e a c h . T h i s c a l c u l a t e d o u t f l o w h y d r o g r a p h b e c o m e s t h e i n f l o w h y d r o g r a p h f o r t h e n e x t r e a c h . T r i b u t a r i e s a r e t r e a t e d a s l a t e r a l i n f l o w h y d r o g r a p h s o v e r a v e r y s h o r t r e a c h . Dummy s e c t i o n s a r e u s e d a b o v e a n d b e l o w s h o r t t r i b u t a r y s e c t i o n s t o s m o o t h t h e a v e r a g i n g d o n e i n t h e n u m e r i c a l s o l u t i o n . T h e s i m u l a t i o n p h i l o s o p h y o f t h e d i s t r i b u t e d m o d e l p r o p o s e d b y E n g m a n ( 1 9 7 4 ) , a s d e s c r i b e d h e r e , i s t h a t o f a c o n c e p t u a l l y s o u n d m o d e l t h a t d o e s n o t d e p e n d u p o n t h e c a l i b r a t i o n o f 58 watershed parameters with h i s t o r i c a l r e c o r d s . The s e l e c t i o n of watershed parameters should be made on the b a s i s of simple f i e l d measurements and values a v a i l a b l e i n the l i t e r a t u r e . The input r e q u i r e d f o r the t h i r d step i s : 1) channel reach l e n g t h s , 2) Manning's n roughness values f o r open channel flow, and 3) a' normal flow r a t i n g f u n c t i o n . The i n p u t s r e q u i r e d f o r the program used to develop the channel r a t i n g f u n c t i o n s (Brakensiek, 1966b) are: 1) channel bed s l o p e s , 2) Manning's n roughness val u e s for open channel flow, and 3) channel c r o s s s e c t i o n geometry. L i s t i n g s of the four codes that d e f i n e the d i s t r i b u t e d r a i n f a l l - r u n o f f technique are found i n Appendix B. Each of these codes was v e r i f i e d with the example output c o n t a i n e d i n the source documentation. 2.4 Model Ef f i c iency The m o d e l - c a l i b r a t i o n process i s made up of c a l i b r a t i o n , v e r i f i c a t i o n , and p r e d i c t i o n time p e r i o d s (Freeze, 1982b). In the c a l i b r a t i o n p e r i o d , model parameters are estimated on the b a s i s of a v a i l a b l e r a i n f a l l - r u n o f f r e c o r d s . During the v e r i f i c a t i o n p e r i o d , the c a l i b r a t e d model i s a p p l i e d to the a v a i l a b l e r a i n f a l l records and computed runoff values are compared with the observed records i n order to assess the p r e d i c t i v e e f f i c i e n c y of the model. If the e f f i c i e n c y i s 59 adequate, the model can then be used f o r runoff p r e d i c t i o n i n the p r e d i c t i o n p e r i o d . The input data requirements f o r the techniques d e s c r i b e d i n the pr e v i o u s s e c t i o n , r e l a t i v e to the c a l i b r a t i o n process, are summarized in Table 5. The v e r i f i c a t i o n procedure, proposed by Nash and S u t c l i f f e (1970), i s used in t h i s study to compare r e l a t i v e model e f f i c i e n c i e s . The e f f i c i e n c y (analogous to the c o e f f i c i e n t of determination) of a given modeling technique i s d e f i n e d by: ? ? ? 2 R =( F0- F ) / F 0 ( 4 2 ) where the r e s i d u a l v a r i a n c e F and i n i t i a l v a r i a n c e F are 0 d e f i n e d as f o l l o w s : F 2 = X(q'-q) 2 ( 4 3 ) 2 — 2 Fj=I(q-q) Z ( 4 4 ) where, q = observed runoff v a r i a b l e q' = computed runoff v a r i a b l e q = mean of observed runoff v a r i a b l e s Based on t h i s sum of squares c r i t e r i o n , maximum model e f f i c i e n c y 2 i s achieved by maximizing R . The maximum value f o r model e f f i c i e n c y i s one. T h i s value would be reached only i f the observed and computed runoff v a r i a b l e s were i d e n t i c a l . A negative e f f i c i e n c y i n f e r s that the model's p r e d i c t e d value i s worse than simply using the observed mean. DISTRIBUTED MODEL* INPUT REQUIREMENT R EG R ES S IO N  U N IT  H YD R O G R A P H  80 IL  CH AR AC TE RI ST IC S OV ER LA ND  FL OW  R OU TI NG  CH AN NE L RA TI NG  FU NC TI ON  OP EN  C HA NN EL  RO UT IN G Rainfall CVP P Excess Rainfall CVP Runoff CV Baseflow CVP Stormflow CV Porosity P Soil Moisture 1.5 MPa P Antecedent Soil Moisture P Soil Moisture Frequency P Degree of Saturation P Pressure Air Entry P Pressure Water Entry P Hydraulic Conductivity, Air Entry P P Sorptivity P Initial Infiltration Rate P 3-D Soil Distribution P Depression Storage P Soil Slope P Manning n, Overland P Manning n, Channel • P P Average Water Surface Width P Channel Length P P Channel Bed Slope P Channel Geometry P Normal Flow Ratings P Tolerance Levels P P Time Step P P P 60 C - Calibration mode V - Verification mode P - Prediction mode • - Ungaged basin Table 5. Input requirements for selected modeling techniques relative to the calibration process / 61 CHAPTER THREE DATA SOURCES AND EVENT SELECTION In t h i s chapter, the two experimental subwatersheds chosen for t h i s study are d e s c r i b e d and the a v a i l a b l e data from each are d i s c u s s e d . The c r i t e r i a used f o r s e l e c t i n g r a i n f a l l - r u n o f f events are a l s o presented. The s e l e c t i o n of study areas f o r t h i s r e s e a r c h was r e s t r i c t e d to North American experimental subwatersheds. I t i s f e l t by the author that the e v a l u a t i o n of r a i n f a l l - r u n o f f modeling techniques must begin at the h i l l s l o p e or subwatershed s c a l e and progress to l a r g e r b a s i n s c a l e s only a f t e r understanding the smaller s c a l e . The experimental subwatershed data bases d e s c r i b e d here are used to compare the e f f i c i e n c i e s of the s e l e c t e d modeling techniques d e s c r i b e d i n Chapter Two. In order f o r an experimental subwatershed to be s e l e c t e d f o r t h i s study, a v a i l a b l e records from the basin i n s t r u m e n t a t i o n program and data c o l l e c t i o n network had to be compatible with the input requirements of each u n d e r l y i n g r a i n f a l l - r u n o f f modeling technique being e v a l u a t e d . Another l i m i t a t i o n p l a c e d upon b a s i n s e l e c t i o n i s that runoff not be generated from snowmelt. S c i e n t i s t s at three Canadian experimental subwatersheds and ten experimental subwatersheds l o c a t e d i n the U n i t e d S t a t e s were co n t a c t e d to f i n d data sets, that i n c l u d e d : 1 )' p r e c i p i t a t i o n and 62 s t r e a m f l o w r e c o r d s i n c l u s i v e e n o u g h t o a l l o w a b s t r a c t i o n o f s e l e c t e d r a i n f a l l - r u n o f f e v e n t s , 2 ) s o i l s u r v e y s , 3) s u f f i c i e n t s o i l m o i s t u r e m e a s u r e m e n t s t o a l l o w f o r t h e e s t i m a t e s o f a n t e c e d e n t s o i l w a t e r c o n d i t i o n s f o r e a c h s e l e c t e d r u n o f f e v e n t , a n d 4 ) m e a s u r e m e n t s o f s p a t i a l l y v a r i a b l e , p h y s i c a l l y b a s e d p a r a m e t e r s , i n c l u d i n g t h e c h a r a c t e r i s t i c c u r v e s o f h y d r a u l i c c o n d u c t i v i t y a n d m o i s t u r e c o n t e n t a s f u n c t i o n s o f p r e s s u r e h e a d . T h e e x p e r i m e n t a l s u b w a t e r s h e d s c o n t a c t e d r a n g e i n a r e a f r o m 2 2 8 0 , 0 0 0 M t o 1 0 . 4 KM . A l l t h i r t e e n s u b w a t e r s h e d s h a v e a d e q u a t e r a i n f a l l - r u n o f f d a t a . T h r e e o t h e r w i s e a c c e p t a b l e d a t a s e t s w e r e e l i m i n a t e d b e c o u s e s n o w m e l t w a s t h e p r i n c i p a l s o u r c e o f r u n o f f . T h e m o s t r e s t r i c t i v e d a t a r e q u i r e m e n t , h o w e v e r t u r n e d o u t t o b e t h e m e a s u r e m e n t o f s p a t i a l l y v a r i a b l e p h y s i c a l p a r a m e t e r s , t h e l a c k o f w h i c h e l i m i n a t e d s e v e n m o r e b a s i n s . O n e o f t h e t h r e e s e l e c t e d d a t a s e t s , f r o m a 1 3 2 , 0 0 0 M 2 s u b w a t e r s h e d l o c a t e d i n t h e H u b b a r d B r o o k E x p e r i m e n t a l F o r e s t , New H a m p s h i r e , i s n o t u s e d i n t h i s s t u d y d u e t o t h e n e c e s s i t y f o r c o n s i d e r a b l e d a t a r e d u c t i o n . T h i s p r e c i o u s d a t a s e t w a s o b t a i n e d w i t h t h e g e n e r o u s c o o p e r a t i o n o f t h e N o r t h e a s t e r n F o r e s t E x p e r i m e n t S t a t i o n , D u r h a m , N . H . , ( F e d e r e r , p e r s o n a l c o m m u n i c a t i o n , 1 9 8 2 ) a n d w i l l c e r t a i n l y b e i n c l u d e d i n f u t u r e r e s e a r c h . T h e f i r s t o f t w o s u b w a t e r s h e d s u s e d i n t h i s s t u d y i s w i t h i n 2 t h e 4 2 0 K M M a h a n t a n g o C r e e k W a t e r s h e d l o c a t e d i n e a s t - c e n t r a l P e n n s y l v a n i a . T h e A g r i c u l t u r a l R e s e a r c h S e r v i c e C A R S ) o f t h e ) 63 . U n i t e d S t a t e s D e p a r t m e n t o f A g r i c u l t u r a l ( U S D A ) h a s a n u m b e r o f W a t e r s h e d R e s e a r c h C e n t e r s t h r o u g h o u t t h e U n i t e d S t a t e s . T h e M a h a n t a n g o C r e e k W a t e r s h e d , d e s c r i b e d b y P i o n k e a n d W e a v e r ( 1 9 7 7 ) , i s t h e r e s e a r c h w a t e r s h e d f o r t h e N o r t h e a s t W a t e r s h e d R e s e a r c h C e n t e r (NWRC) o f t h e A R S . D a t a c o l l e c t i o n p r o g r a m s a t N W R C , a n d w i t h i n t h e A R S i n g e n e r a l , h a v e b e e n d e s i g n e d t o f a c i l i t a t e s p e c i f i c r e s e a r c h p r o j e c t s w i t h i n t h e g e n e r a l a r e a s o f r a i n f a l l - r u n o f f r e l a t i o n s h i p s , h y d r o l o g y - w a t e r q u a l i t y i n t e r a c t i o n s , a n d m a t h e m a t i c a l m o d e l i n g o f h y d r o l o g i c p r o c e s s e s ( E n g m a n e t a l . , 1 9 7 1 ; E n g m a n e t a l . , 1 9 7 4 ; R o g o w s k i e t a l . , 1 9 7 4 ; H e n n i n g e r e t a l . , 1 9 7 6 ; G b u r e k , 1 9 7 7 ) . T h e s u b w a t e r s h e d d a t a s e t , f r o m t h e M a h a n t a n g o C r e e k W a t e r s h e d , u s e d i n t h i s s t u d y w a s o b t a i n e d f r o m N W R C , U n i v e r s i t y P a r k , P a . ( G b u r e k , p e r s o n a l c o m m u n i c a t i o n , 1 9 8 2 ) . T h e s e c o n d s u b w a t e r s h e d u s e d i n t h i s s t u d y i s w i t h i n t h e A R S S o u t h e r n G r e a t P l a i n s R e s e a r c h W a t e r s h e d . A n u m b e r o f e x p e r i m e n t a l w a t e r s h e d s a r e l o c a t e d n e a r C h i c k a s h a , O k l a h o m a . T h e s u b w a t e r s h e d c h o s e n w a s r e c o m m e n d e d t o t h e a u t h o r , w h i l e i n q u i r i n g a b o u t a n o t h e r f a c i l i t y , a s m e e t i n g t h e d a t a r e q u i r e m e n t s o f t h i s s t u d y ( L u x m o o r e , p e r s o n a l c o m m u n i c a t i o n , 1 9 8 1 ) . T h e d a t a s e t i t s e l f was o b t a i n e d f r o m t h e A R S a t C h i c k a s h a ( G a n d e r , p e r s o n a l c o m m u n i c a t i o n , 1 9 8 1 ) . T h e t w o e x p e r i m e n t a l d a t a s e t s u s e d i n t h i s w o r k a r e d e s c r i b e d i n t h e f o l l o w i n g s e c t i o n s . 64 3 . 1 M a h a n t a n g o C r e e k S u b w a t e r s h e d 2 T h e 7 . 2 K M M a h a n t a n g o C r e e k S u b w a t e r s h e d (MCW) s h o w n i n F i g u r e 13 i s l o c a t e d i n t h e r i d g e a n d v a l l e y r e g i o n n e a r K l i n g e r s t o w n , P e n n s y l v a n i a . T h e c h a r a c t e r i s t i c p h y s i o g r a p h i c f e a t u r e s o f t h i s r e g i o n a r e l o n g m o u n t a i n r i d g e s o f f a i r l y u n i f o r m e l e v a t i o n c u t a t i n t e r v a l s b y w a t e r g a p s . T h e m a j o r l a n d u s e s a r e p e r m a n e n t p a s t u r e a n d c u l t i v a t e d f i e l d s . P r e c i p i t a t i o n a n d s t r e a m f l o w r e c o r d s i n b r e a k p o i n t f o r m , c o v e r i n g t h e s i x y e a r p e r i o d 1971 t h r o u g h 1 9 7 6 , a r e u s e d i n t h i s s t u d y . T h e l o c a t i o n s o f t w o r a i n g a g e s a n d a d u a l n o t c h w e i r w i t h w a t e r l e v e l r e c o r d e r , m a k i n g u p t h e c o n t i n u o u s r a i n f a l l - r u n o f f m o n i t o r i n g n e t w o r k , a r e s h o w n i n F i g u r e 1 3 . C a r r ( 1 9 7 3 ) d e s c r i b e s t h e g a g e s , t h e g a g e n e t w o r k a n d t h e d a t a r e d u c t i o n p r o c e d u r e u s e d . T e x t u r a l l y , t h e s o i l s a r e c l a s s i f i e d a s s h a l y s i l t l o a m s . T h e s p a t i a l d i s t r i b u t i o n o f s o i l t y p e a n d t h e v a r i a t i o n i n l a n d s l o p e s a r e s h o w n i n F i g u r e 1 4 . A v e r a g e t o p s o i l a n d s u b s o i l d e p t h a r e l i s t e d i n T a b l e 6 . M o i s t u r e c h a r a c t e r i s t i c , h y d r a u l i c c o n d u c t i v i t y , a n d s o i l w a t e r d i f f u s i v i t y c u r v e s f o r t h e m o d e l e d s o i l s s h o w n i n F i g u r e 14 w e r e c o n s t r u c t e d u s i n g i n p u t p a r a m e t e r s s i m i l a r t o t h e a v e r a g e d v a l u e s s h o w n i n T a b l e 7 . T h e s e p a r a m e t e r s w e r e e i t h e r a b s t r a c t e d o r e s t i m a t e d f r o m t h e a v a i l a b l e l i t e r a t u r e ( E n g m a n a n d R o g o w s k i , 1 9 7 4 a ) . E n g m a n a n d R o g o w s k i ( 1 9 7 4 b ) d i s c u s s t h e s e l e c t i o n o f s o i l m o i s t u r e 65 Datum It • • • toval Figure 13. Mahantango Creek Subwatershed (Gburek, personal communication, 1982) Figure 14. S p a t i a l v a r i a t i o n of s o i l type and land slope within the Mahantango Subwatershed (Gburek, personal communication, 1982) SOIL NUMBER SOIL NAME DEPTH (m) TOPSOIL SUBSOIL 149 KKnesville .23 .46 145 Berks .23 .64 166 Calvin .20 .71 66 Leek Kill .20 .71 54 Hartleton .23 .76 71 Albrights .23 .52 69 Meckensville .23 .61 57 Alvira .23 .76 Table 6. Average s o i l depths within the Mahantango Creek Subwatershed (abstracted from Engman, 19 6 8 SOIL NUMBER SOIL NAME K . n l O 4 (M/S) 01.5 (PERCENT BY VOLUME) 149 Klinesvlfle 3.0 47 38 11 145 Berks 3.0 47 38 11 166 Calvin 2.19 47 38 11 66 Leek Kid 2.19 37 30 12 54 Hartteton 1.6 42 34 12 71 Albrights .64 43 34 14 69 Meckensvllle .64 39 31 18 57 Alvira .64 38 30 15 K e - Averaged values of hydraulic conductivity at air entry (T^ 0o - Total pore space Be - Soil water content at air entry 6A 5 - Soilwater content at 1.5 MPa <Pe'- Estimated as 60 mm of water i Table 7. S o i l c h a r a c t e r i s t i c parameters f o r the Mahantango Creek Subwatershed ( a f t e r Engman and Rogowski, 1974a) 69 parameters. The l o c a t i o n s of a very l i m i t e d amount of s o i l moisture data obtained f o r t h i s study are shown in F i g u r e 13. These data were measured by the neutron s c a t t e r i n g method over a f i v e year p e r i o d . However, records of s o i l moisture proved to be inadequate f o r a f f i x i n g i n i t i a l c o n d i t i o n s f o r each s e l e c t e d r a i n f a l l - r u n o f f event. In order to estimate antecedent s o i l water contents f o r t o p s o i l and s u b s o i l l a y e r s , s o i l water frequency d i s t r i b u t i o n s s i m i l a r to the ones shown i n F i g u r e 15 were used. The general approach to the seasonal s o i l water frequency d i s t r i b u t i o n i s o u t l i n e d by Rogowski (I972bc). The employed d i s t r i b u t i o n s were developed with Henninger's (1972) s o i l moisture data, gathered i n 1971. These data are summarized i n F i g u r e 16. The general assumption made i n using these d i s t r i b u t i o n s i s that the same or very s i m i l a r s o i l moisture c o n d i t i o n s w i l l apply in any given year. Except f o r two events, no measurement of antecedent s o i l moisture was a v a i l a b l e . T h e r e f o r e , i n i t i a l c o n d i t i o n s f o r the r e s p e c t i v e s o i l s were set at t h e i r 50% p r o b a b i l i t y l e v e l . For the two events i n which measurements of s o i l moisture roughly c o i n c i d e with the s t a r t of r a i n f a l l , the frequency of measured s o i l moisture a s s o c i a t e d with the most obvious source area was used for a l l other s o i l s to estimate i n i t i a l c o n d i t i o n s . The most obvious source area i s taken as the s o i l with the lowest h y d r a u l i c c o n d u c t i v i t y : A l v i r a s i l t loam i n F i g u r e 14. Table 8 summarizes the antecedent s o i l •1.0 H H- 0-8 i Z LU Z 0.7 i o o LU .H < 0.5 O 0.4 H ( 0 LU > 0.3 H < Qj 0.2 H OC 0.1 H #57 #71 #66 #54 #145 #149 #166 JULY. "T—i 1 r 0.1 10 50 90 PROBABILITY (%) 99 99.9 Figure 15. Example s o i l water frequency d i s t r i b u t i o n s (after Engman and Rogowski, 1974a) HARTLETON KLINESVILLE LECK KILL , 1 1 1 1 -j June July August Sept. October Nov. MONTHS S o i l moisture for 1971 within the Mahantango Creek Subwatershed (a f t e r Henninger, 1972) ANTECEDENT SOIL WATER CONTENT* 80IL NO. SOIL NAME SOIL LAYER MCW R-5 149 Itijnesville T S .225 .225 145 Berks T S .225 .225 166 Calvin T S .237 .237 66 Leek Hill T S .237 .237 54 Hartleton T S .229 .229 71 Albrights T S .258 .258 69 Meckensville T S .278 .278 57 Alvira T S .278 .278 1 Kingfisher T S .218 .245 2 Grant T S .218 .245 3 Renfrow T S .218 .245 T - Topsoil ) S - Subsoil • - Initial soil moisture m 8 water/m3 soil Table 8. Antecedent s o i l water contents for the Mahantango Creek Subwatershed and the R-5 Subwatershed 73 water contents f o r MCW s o i l s , at t h e i r 50% p r o b a b i l i t y l e v e l s . Huggins and Monke (1966) and Hiemstra (1968) propose that d e p r e s s i o n storage (Viessman et a l . , 1977) i s a watershed constant f o r a given p a t t e r n of land use. F i g u r e 17 i l l u s t r a t e s the e s t i m a t i o n of depression storage as a f u n c t i o n of land slope and use as d e s c r i b e d by Hiemstra (1968). The average t o t a l d e p r ession storage f o r MCW i s taken as 4 mm of water (Engman and Rogowski, 1974a ) . Values of Manning's n of 0.35 and 0.05, f o r overland and channel flow r e s p e c t i v e l y , are assumed (Engman, 1974). Engman determined the n value for the overland flow p o r t i o n of the hydrograph by f i t t i n g I zzard's (1946) data f o r a s l o p i n g t u r f plane. The n value f o r channel flow was chosen by handbook procedures and v e r i f i e d with f i e l d measurements. Channel geometry was taken as p r i s m a t i c t r i a n g u l a r . F i g u r e 18 shows the assumed channel c r o s s s e c t i o n . The average water surface width i s taken to be 3.0 M. Channel sl o p e s were a b s t r a c t e d from topographic contour maps. The base flow s e p a r a t i o n s l o p e a , shown on F i g u r e 9, i s taken as 1 . 28* 1 0~4 M 3/Sec 2, based on the 1 . 79* 1 0~5 M 3/Sec 2-KM Z r e l a t i o n s h i p i l l u s t r a t e d i n F i g u r e 19, that was e s t a b l i s h e d by Engman (1974) f o r the Mahantango Creek Watershed. 74 Figure 17. Depression storage as a function of land slope and use ( a f t e r Hiemstra, 1968)  < 1 1 10 100 1000 X m MAHANTANGO CREEK BASIN AREAS (km2) Figure 19. Base flow separation r e l a t i o n s h i p for the Mahantango Creek Watershed (after Engman, 1974) 77 3.2 R-5 Subwatershed 2 The 96,000 M R-5 subwatershed (R-5), shown i n F i g u r e 20, i s l o c a t e d i n r o l l i n g p r a i r i e g r a s s l a n d t e r r a i n i n the Washita r i v e r v a l l e y , near Chickasha, Oklahoma. R-5 has been subjected to continuous well-managed g r a z i n g of beef c a t t l e (Sharma et a l . , 1980). P r e c i p i t a t i o n and stream flow records in break p o i n t form c o v e r i n g the e i g h t - y e a r p e r i o d 1967 through 1974, are used in t h i s study. L o c a t i o n s of the continuous r e c o r d i n g r a i n gage and weir used in t h i s study are shown in F i g u r e 21. S o i l types and s u r f a c e contours f o r R-5 are shown i n F i g u r e 20. Approximately 51% of the area i s Renfrow s i l t loam, 43% Grant s i l t loam, and 6% K i n g f i s h e r s i l t loam (Sharma et a l . , 1980). T o p s o i l and s u b s o i l depths are shown in Table 9. There i s an o v e r a l l g e n t l e land slope of about 3%. Parameters used to c o n s t r u c t s o i l c h a r a c t e r i s t i c curves are shown i n Table 9. These data are taken from the r e f e r e n c e s o i l parameters d e s c r i b e d by Luxmoore and Sharma (1980). Water r e t e n t i o n and h y d r a u l i c c o n d u c t i v i t y data are d i s c u s s e d by Sharma and Luxmoore (1979) and Luxmoore and Sharma (1980). Based on standard s t a t i s t i c a l t e s t s , no d i f f e r e n c e can be shown between the three s o i l s (Sharma and Luxmoore, 1979). The l o c a t i o n s of s o i l moisture data, f o r t o p s o i l and s u b s o i l l a y e r s , from neutron s c a t t e r i n g measurements are shown LEGEND |H Grant silt loam | | Renfrow silt loam IH Kingfisher silt loam Scale: 1cm = 12m Area: 96.000m2 Contour interval: 4 ft. Datum Is eea level Figure 20. R-5 Subwatershed (Gander, personal communication, 1981) 79 SOIL SOIL NAME LAYER K e *10 4 Oo #1.5 DEPTH NUMBER (M/S) (PERCENT BY VOLUME) (m) 1 Kingfisher Silt Loam T S 1.86 .31 44 44.3 39.6 39.9 9 14.8 .2 .8 2 Grant Silt Loam T S 1.88 .31 44 44.3 39.6 39.9 9 14.8 .2 1.30 3 Renfrow Silt Loam T S 1.86 .31 44 44.3 39.6 39.9 9 14.3 .2 1.30 T - Topsoil S - Subsoil K e - Estimated as 1/2K saturated 0e - Estimated as 0.9f?0 (Rogowski, 1972b) Table 9. C h a r a c t e r i s t i c parameters and depths for R-5 Subwatershed s o i l s 81 i n F i g u r e 21. These data represent measurements taken at 34 s i t e s over a four year p e r i o d and averaged v a l u e s from a separate four year p e r i o d . Antecedent s o i l water contents f o r R-5 were estimated as the means of a l l measured v a l u e s , taken from the two l a y e r s p r e v i o u s l y d e s c r i b e d , f o r the same s i x month p e r i o d used i n event s e l e c t i o n . Assuming s o i l water content to be normally d i s t r i b u t e d (Rogowski, 1972b), t h i s mean value i s the same as the 50% frequency u t i l i z e d at MCW. Table 8 summarizes the antecedent s o i l water contents used f o r R-5 s o i l s . Depression storage for R-5 i s estimated, from F i g u r e 17, as 10 mm. Manning n Values are taken as 0.35 f o r overland flow (Engman, 1974) and 0.2 for channel flow (Luxmoore and Sharma, 1980). Channel geometry i s taken as p r i s m a t i c t r i a n g u l a r . The average water s u r f a c e width i s assumed to be 1.5 M. The channel slope i s constant at 2%. No base flow s e p a r a t i o n i s c o n s i d e r e d as observed hydrographs e x h i b i t a f l a s h y response with l i t t l e or no base flow (Luxmoore and Sharma, 1980). 3.3 Event S e l e c t i o n In t h i s s e c t i o n the c r i t e r i a used f o r s e l e c t i n g i n d i v i d u a l r a i n f a l l - r u n o f f events from the MCW and R-5 data sets are d i s c u s s e d . These s e l e c t e d r a i n f a l l - r u n o f f events are simulated 82 i n Chapter Four, using the u n d e r l y i n g modeling techniques d e s c r i b e d i n Chapter Two. The observed events are used to compare the e f f i c i e n c i e s of the i n d i v i d u a l models i n Chapter Four. Events were s e l e c t e d on the f o l l o w i n g b a s i s : 1) Only events that show an obvious cause-and-effect r a i n f a l l - r u n o f f r e l a t i o n s h i p were chosen. 2) Only storms of simple s t r u c t u r e were c o n s i d e r e d . 3) Only events o c c u r r i n g i n the s i x month p e r i o d A p r i l through September were c o n s i d e r e d , to a v o i d runoff due to snowmelt. 4) The d u r a t i o n of an i n d i v i d u a l r a i n f a l l event was r e s t r i c t e d to a maximum of ten hours. The d u r a t i o n of a runoff event was taken from the s t a r t of the r a i n f a l l event u n t i l runoff had subsided t o the prestorm r a t e . Both base flow s e p a r a t i o n and/or another r a i n f a l l event o c c u r r i n g i n the t a i l of the hydrograph shorten t h i s p e r i o d . 5) An attempt was made to s e l e c t storms that maintained a uniform i n t e n s i t y throughout the p e r i o d of r a i n f a l l . The assumption was made that r a i n f a l l was uni f o r m l y d i s t r i b u t e d over the e n t i r e subwatershed. Simple a r i t h m e t i c averages were used when the r a i n f a l l r e c o r d f o r an event was a v a i l a b l e from two gages. 6) Only p r e c i p i t a t i o n and stream flow records showing e r r o r f r e e data were c o n s i d e r e d i n the s e l e c t i o n of an event, with no attempt to a d j u s t records based on a v a i l a b l e e r r o r codes. Nine events were s e l e c t e d from the R-5 data base. Twenty-one events, s i x of which have r a i n f a l l at two gages, were 83 s e l e c t e d f r o m t h e MCW d a t a b a s e . T h e s e l e c t e d r a i n f a l l - r u n o f f e v e n t s a n d t h e i r c h a r a c t e r i s t i c s a r e s u m m a r i z e d i n T a b l e 10. EVENT NO. VPPT PPT P P T D VQ Q PK V QPK* TQPK 1 2804. 11.43 2.58 429. .11 .51 2 6071. 7.37 8.65 1958. .58 1.56 3 4170. 7.37 5.83 1367. .48 5.19 4 7510. 18.29 4.28 1002. .26 1.65 R-5 5 7754. 32.26 2.51 408. .17 1.54 10 8778. 63.50 1.44 4378. 1.79 .51 12 3146. 17.02 1.92 1601. .51 2.03 14 4779 . 7.87 6.25 974. .22 2.95 15 2780. 2.79 10.16 626. .09 10.40 3 201865. 30.73 .91 6476. .78 2346. .77 1. 33 4 73405. 7.62 1.33 19465. .56 1631. .40 2.25 15 128460. 5.59 3.25 73895. 1.76 4519. 1.37 1.58 16 128460. 104.65 .17 17629. 1.08 • 1316. 1 .02 .92 17 146811. 35.05 .58 7034. .59 1597. .56 1.16 • •20 201865. 3.05 9.24 198326. 1.95 11799. 1.60 8.00 21 293622. 5.33 7.54 43580. 2.86 9520. 2.81 3.92 24 183514. 13.21 1.91 17479. 1.04 6082. 1.03 2.16 MCW 25 403730. 14.48 3.83 206484. 5.76 35859. 5.67 2.00 26 183514. 8. 38 3.00 93602. 1.66 37129. 1.56 1.24 32 • 238568. 10.41 3. 17 66527. 1.20 19427. 1.13 2.41 33 183514. 7.62 3. 33 8569. .46 2059. .44 . 4.17 • 42 128460. 3.56 5.08 80237. .49 4121. . 31 6.07 ••43 128460. 4.06 4.42 8290. . 17 752 . .13 3. 87 • •43b 110108. 2.82 5.50 63518. .29 3534. .22 6.11 ••44 73405. 3.30 3.17 9840. .17 94. .06 3.29 ••45 137635. 10.41 1.83 10676. .63 1395. .51 2.00 ••46 192689. 3.30 8.34 133564. .59 2344. .46 5.19 47 201865. 11.94 2.33 97750. 1.84 13154. 1.75 2.41 48 73405. 13.46 .75 6164. .52 997. .43 1.49 49 201865. 4.06 6.92 1 32825. 1.24 5676. 1.08 1.94 VpPT - Volume of rainfall, m 3 Q PK - Peak flow rate, m3/sec PPT - Average rainfall intensity, mm/hr TQPK - Time to peak flow, hrs P P T D - Duration of rainfall, hr * - With base flow separation Vr, - Volume of runoff, m 3 - Rainfall records averaged from two rain gages Table 10. R a i n f a l l - r u n o f f c h a r a c t e r i s t i c s from the Mahantango Creek Subwatershed and the R-5 Subwatershed 85 C H A P T E R F O U R R E S U L T S A N D D I S C U S S I O N I n t h i s c h a p t e r s i t e - s p e c i f i c r a i n f a l l - r u n o f f e v e n t s a r e s i m u l a t e d f o r t h e s e l e c t e d M a h a n t a n g o C r e e k a n d C h i c k a s h a s u b w a t e r s h e d s . T h e p u r p o s e o f t h i s c h a p t e r i s t h e p r e s e n t a t i o n a n d d i s c u s s i o n o f t h e s e r e s u l t s . T h e u n d e r l y i n g r a i n f a l l - r u n o f f m o d e l i n g t e c h n i q u e s d e s c r i b e d i n C h a p t e r T w o a n d t h e MCW a n d R-5 d a t a s e t s p r e s e n t e d i n C h a p t e r T h r e e m a k e u p t h e s u i t e o f m o d e l s a n d s e t s o f d a t a u s e d i n t h i s s t u d y . P r e d i c t e d r u n o f f v a r i a b l e s a r e e v a l u a t e d w i t h t h e e f f i c i e n c y c r i t e r i o n d e s c r i b e d i n C h a p t e r T w o . T h i s c r i t e r i o n i s u s e d t o s t a n d a r d i z e m o d e l e v a l u a t i o n a c r o s s t h e s u i t e o f m o d e l i n g t e c h n i q u e s u n d e r c o m p a r i s o n . L e v e l s o f e f f i c i e n c y a c c e p t a b i l i t y a r e n o t e s t a b l i s h e d i n t h e p r e s e n t s t u d y f o r d e c i s i o n s c o n c e r n i n g m o d e l u s e . I n s t e a d , c a l c u l a t e d e f f i c i e n c i e s a r e u s e d a s a n i n d e x f o r a m o r e g e n e r a l q u a l i t a t i v e m o d e l i n t e r p r e t a t i o n . E f f i c i e n c i e s o f l e s s t h a n z e r o , d o a r i s e i n t h i s s t u d y , b u t t h e i r v a l u e s a r e s e t e q u a l t o z e r o . T h e e f f i c i e n c y v a l u e s a r e t h e r e f o r e r e s t r i c t e d t o t h e r a n g e z e r o t o o n e . A l l s i m u l a t i o n s a n d m o s t c a l c u l a t i o n s i n t h i s w o r k w e r e d o n e o n t h e U B C A M D A H L V 8 - I I c o m p u t e r o p e r a t i n g u n d e r t h e M i c h i g a n T e r m i n a l S y s t e m . 86 4.1 Regression Models Independent r a i n f a l l v a r i a b l e s and dependent runoff v a r i a b l e s , from MCW and R-5, used to c o n s t r u c t simple-and m u l t i p l e - l i n e a r - r e g r e s s i o n r a i n f a l l - r u n o f f models, as d e s c r i b e d in Chapter Two, are shown in Table 10. The r e g r e s s i o n - a n a l y s i s s c e n a r i o used in t h i s study i n v o l v e d the f o l l o w i n g three steps: 1) c o n s t r u c t a number of r a i n f a l l - r u n o f f models based on l e s s than the t o t a l number of events a v a i l a b l e ; 2) use these models to p r e d i c t the remainder of the events; and 3) i n c o r p o r a t e a l l a v a i l a b l e events i n t o new r e g r e s s i o n models. The determination of the c o e f f i c i e n t s and constants in the f i r s t s tep c o n s t i t u t e s the c a l i b r a t i o n phase of the model c a l i b r a t i o n p r o c e s s , as d e s c r i b e d i n Chapter Two. The second step c o n s t i t u t e s the v e r i f i c a t i o n phase, wherein the e s t a b l i s h e d r e g r e s s i o n models are used to p r e d i c t the dependent runoff v a r i a b l e s . In the t h i r d or p r e d i c t i v e phase, not i n c l u d e d in t h i s study, the r e g r e s s i o n models are used to p r e d i c t runoff v a r i a b l e s o u t s i d e the combined set used i n the f i r s t two phases. By re p e a t i n g the f i r s t phase of model c a l i b r a t i o n , a f t e r i n c o r p o r a t i n g the a d d i t i o n a l events, subsequent improvements in the r e g r e s s i o n models can be i d e n t i f i e d . The e v a l u a t i o n of l i n e a r r e g r e s s i o n models i n t h i s work i s presented i n terms of the e f f i c i e n c i e s c a l c u l a t e d f o r p r e d i c t e d runoff v a r i a b l e s i n the v e r i f i c a t i o n phase of model c a l i b r a t i o n . 87 The n a t u r a l r a i n f a l l - r u n o f f process shows only p o s i t i v e c o r r e l a t i o n . T h e r e f o r e , only r a i n f a l l - r u n o f f v a r i a b l e s showing p o s i t i v e c o r r e l a t i o n are c o n s i d e r e d i n t h i s work. No other s i g n i f i c a n c e t e s t i n g of r a i n f a l l - r u n o f f v a r i a b l e s i s used i n t h i s study. C o r r e l a t i o n matrices f o r the s i x MCW l i n e a r r e g r e s s i o n v a r i a b l e s (Table 10) are shown i n Tables 11, 12,. 13, and 14. The c o r r e l a t i o n c o e f f i c i e n t s in Tables 11 and 13 are based upon the observed r a i n f a l l - r u n o f f v a r i a b l e s , while those i n Tables 12 and 14 r e s u l t from dependent-variable data r e d u c t i o n , in the form of base flow s e p a r a t i o n as d e s c r i b e d i n Chapter Two. The c o r r e l a t i o n c o e f f i c i e n t s i n Tables 11 and 12 are based upon v a r i a b l e s from 15 s e l e c t e d events, while those i n Tables 13 and 14 r e s u l t from the v a r i a b l e s of 21 MCW s e l e c t e d events. Table 15 d i f f e r e n t i a t e s between Tables 11, 12, 13, and 14. The heavy l i n e d boxes i n Tables 11, 12, 13, and 14 separate out the nine c o r r e l a t i o n s that represent r a i n f a l l - r u n o f f r e l a t i o n s h i p s . In Table 11 there are f i v e p o s i t i v e c o r r e l a t i o n s between r a i n f a l l - r u n o f f v a r i a b l e s : 1) Volume of r a i n f a l l and volume of r u n o f f , 2) volume of r a i n f a l l and peak flow r a t e , 3) d u r a t i o n of r a i n f a l l and volume of r u n o f f , 4) d u r a t i o n of r a i n f a l l and peak flow r a t e , and 5) d u r a t i o n of r a i n f a l l and time to peak flow. The c l o s e r these c o e f f i c i e n t s are to 1.0 the b e t t e r the suggested r a i n f a l l - r u n o f f r e l a t i o n s h i p . A l s o i n Table 11, there are four negative c o r r e l a t i o n s between r a i n f a l l - r u n o f f VPPT PPT P P T D V Q QPK TQPK VPPT 1.0 PPT -.1174 1.0 P P T D .2779 -.5730 1.0 V Q 1 .5585 -.2802 .5813 1.0 QpK .8723 -.0584 .2610 .7242 1.0 T Q p K -.0764 -.4816 .8423 .3858 -.1250 1.0 Table 11. Correlation matrix for Mahantango Creek Subwatershed r a i n f a l l - r u n o f f variables based on 15 selected events without base flow separation oo oo VRPT PPT P P T D VQ QPK TQPK VP T 1.0 PPT - . 1 1 7 4 1.0 P P T D . 2 7 7 9 - . 5 7 3 0 1.0 • VQ I . 8 6 1 0 - . 1 7 1 1 . 2 6 5 7 1.0 QPK . 8 9 4 4 - . 0 3 6 7 . 2 2 9 4 . 8 6 6 4 1.0 TQPK - . 0 7 6 4 - . 4 8 1 6 . 8 4 2 3 . 0 0 8 7 - . 1 5 3 3 1.0 Table 12. Cor r e l a t i o n matrix for Mahantango Creek Subwatershed r a i n f a l l - r u n o f f variables based on 15 selected events with base flow separation oo VPPT PPT P P T D V Q QPK TQPK VPPT 1.0 PPT - . 0 6 9 6 1.0 P P T D . 3 3 3 7 - . 5 1 5 3 1.0 V Q . 6 0 4 5 - . 2 6 5 8 . 6 5 2 5 1.0 QPK . 8 5 4 1 - . 0 0 6 9 . 1 9 6 1 . 6 5 7 7 1.0 TQPK - . 0 0 5 6 - . 4 4 1 9 . 7 7 0 2 . 3 8 4 0 - . 1 1 2 4 1.0 Table 13. Correlation matrix for Mahantango Creek Subwatershed r a i n f a l l - r u n o f f variables based on 21 selected events without base flow separation o V P P T PPT PPT D V Q Q P K T Q p K V P P T 1.0 PPT - .0696 1.0 PPT D .3337 - .5153 1.0 VQ .8408 - . 1 127 .1942 1.0 QPK .8712 .0146 .1668 .8778 1.0 T QPK - .0056 - .4419 .7702 .0109 - .1373 1.0 Table 14. Correlation matrix for Mahantango Creek Subwatershed r a i n f a l l - r u n o f f variables based on 21 selected events with base flow separation VO T A B L E S U B W A T E R S H E D N U M B E R O F S E L E C T E D E V E N T S B A S E F L O W S E P A R A T I O N 11 MCW 15 NO 12 MCW 15 YES 13 MCW 21 NO 14 MCW 21 YES 17 R-5 6 NO 18 R-5 9 NO Table 15. Summary of c o r r e l a t i o n matrix tables 93 v a r i a b l e s : 1) Volume of r a i n f a l l and time to peak flow, 2) average r a i n f a l l i n t e n s i t y and volume of r u n o f f , 3) average r a i n f a l l i n t e n s i t y and peak flow r a t e , and 4) average r a i n f a l l i n t e n s i t y and time to peak flow. • The i n d i v i d u a l c o r r e l a t i o n c o e f f i c i e n t s i n Tables 12, 13, and 14 show the same general p o s i t i v e and negative c o r r e l a t i o n s d e s c r i b e d f o r Table 11. The negative c o r r e l a t i o n s i n Tables 11, 12, 13, and 14 in c l u d e every r a i n f a l l - r u n o f f v a r i a b l e combination of average r a i n f a l l i n t e n s i t y . T h i s suggests that the average r a i n f a l l i n t e n s i t y i s not a u s e f u l r a i n f a l l - r u n o f f r e g r e s s i o n model v a r i a b l e f o r MCW with comparable events and sample s i z e s . Tables 12 and 14 (with data r e d u c t i o n ) when compared with Tables 11 and 13 (no data r e d u c t i o n ) show i n c r e a s e s i n two p o s i t i v e c o r r e l a t i o n c o e f f i c i e n t s . Both of these i n c r e a s e d c o r r e l a t i o n c o e f f i c i e n t s have the volume of r a i n f a l l as a component v a r i a b l e . T h i s suggests that using the volume of r a i n f a l l as an independent v a r i a b l e i n a r a i n f a l l - r u n o f f r e g r e s s i o n model f o r MCW w i l l be more i n f o r m a t i v e f o r storm flow p r e d i c t i o n s . Again comparing Tables 12 and 14 with Tables 11 and 13, there are decreases in two p o s i t i v e c o r r e l a t i o n c o e f f i c i e n t s with data r e d u c t i o n . Both of these decreased c o r r e l a t i o n c o e f f i c i e n t s have the d u r a t i o n of r a i n f a l l as a component v a r i a b l e . T h i s suggests that using the d u r a t i o n of r a i n f a l l as an independent v a r i a b l e i n a r a i n f a l l - r u n o f f r e g r e s s i o n model f o r MCW w i l l be more i n f o r m a t i v e f o r t o t a l flow p r e d i c t i o n s . 94 The seven MCW l i n e a r r e g r e s s i o n models i n c l u d e d i n t h i s study, with and without data r e d u c t i o n , and t h e i r r e s p e c t i v e v e r i f i c a t i o n e f f i c i e n c i e s are summarized i n Table 16. The heavy l i n e d boxes i n Table 16 separate out the model v e r i f i c a t i o n e f f i c i e n c i e s . The v e r i f i c a t i o n e f f i c i e n c i e s of models based on 15 events without data r e d u c t i o n range from 0.0 to 0.83. The v e r i f i c a t i o n e f f i c i e n c i e s of models based on 15 events with data r e d u c t i o n range from 0.0 to 0.48. Table 16 a l s o i n c l u d e s the c o e f f i c i e n t of determination f o r each r a i n f a l l - r u n o f f r e g r e s s i o n model. These r e g r e s s i o n model e v a l u a t i o n s ( c a l i b r a t i o n phase) are shown f o r both 15 event and 21 event models. The p o i n t should be made that even f o r c a l i b r a t e d data, model e f f i c i e n c i e s w i l l not be equal to one. A constant i n c r e a s e in the c o e f f i c i e n t of det e r m i n a t i o n i s seen with data r e d u c t i o n , i n a l l MCW models that i n c l u d e the r a i n f a l l volume as an independent v a r i a b l e . The c o e f f i c i e n t s of det e r m i n a t i o n based on 21 events are g r e a t e r than the c o e f f i c i e n t s of det e r m i n a t i o n based on 15 events f o r runoff volume models, without data r e d u c t i o n , i n every case suggesting stronger r e l a t i o n s h i p s f o r these models with i n c r e a s e d sample s i z e s . In Table 16, model number one (without data reduction) has a. v e r i f i c a t i o n e f f i c i e n c y (0.48) that i s g r e a t e r than e i t h e r of i t s c o e f f i c i e n t s of d e t e r m i n a t i o n (0.31 and 0.37). V e r i f i c a t i o n - e f f i c i e n c i e s higher than the c o e f f i c i e n t s of determination are NO SEPARATION WITH BASEFLOW SEPARATION MODEL V P P T PPT PPTD Q P K T Q P K R* 'I r 2 6 1 • • .31 .48 .37 .74 .48 .71 2 • • .34 .68 .43 .07 .0 .04 3 • • • .51 .83 .59 .74 .42 .72 4 • • .76 .48 .73 .80 .43 •76 5 • • .07 .0 .04 .05 .0 .03 6 • • • .76 .43 .74 .80 .48 .78 . 7 • • .71 .0 .59 .71 .0 .59 r 2 - Regression (multiple) models based on events 3, 4, 15, 16, 17, 20, 21, 24, 25, 26, 32, 33, 42, 1 , 4 43, and 43b R 2 5 - Predicting events 44, 45, 46, 47, 48, and 49 with r^r 4 ) regression (multiple) models r* - New regression (multiple) models based on all events R - Model efficiency r - Coefficient of determination Table 16. Linear regression models and e f f i c i e n c i e s for the Mahantango Creek Subwatershed 96 a l s o s e e n i n t h e o t h e r t w o MCW r u n o f f v o l u m e m o d e l s ( w i t h o u t d a t a r e d u c t i o n ) i n T a b l e 1 6 . T h e s e h i g h e r v e r i f i c a t i o n e f f i c i e n c i e s f o r m o d e l s 1 , 2 , a n d 3 a r e e x p l a i n e d b y t h e o b s e r v e d v o l u m e s o f r u n o f f b e i n g , b y c h a n c e , c l o s e t o t h e f i t t e d r e g r e s s i o n l i n e . T h e c o r r e l a t i o n c o e f f i c i e n t i n t e r p r e t a t i o n s , r e l a t i n g t o d a t a r e d u c t i o n , f o r MCW a r e a l s o i l l u s t r a t e d i n T a b l e 1 6 . W i t h d a t a r e d u c t i o n t h e c o e f f i c i e n t o f d e t e r m i n a t i o n v a l u e s a r e s h o w n t o i n c r e a s e f o r m o d e l s i n c l u d i n g t h e v o l u m e o f r a i n f a l l a n d d e c r e a s e f o r m o d e l s i n c l u d i n g t h e d u r a t i o n o f r a i n f a l l . I n g e n e r a l t h e p r e d i c t i v e p r o w e s s o f MCW r e g r e s s i o n m o d e l s , t h a t i n c l u d e t h e v o l u m e o f r a i n f a l l a s a n i n d e p e n d e n t v a r i a b l e , w o u l d a p p e a r t o b e f a i r l y g o o d w i t h i n t h e i r c a l i b r a t e d r a n g e s . T h i s s u g g e s t s t h a t t h e v o l u m e o f r a i n f a l l i s t h e m o s t u s e f u l i n d e p e n d e n t v a r i a b l e f o r MCW r a i n f a l l - r u n o f f r e g r e s s i o n m o d e l s . I t s e e m s i n t u i t i v e t h a t t h e r e s h o u l d b e a s t r o n g c o r r e l a t i o n b e t w e e n r a i n f a l l - v o l u m e s a n d s t o r m f l o w v o l u m e s . D u n n e a n d L e o p o l d ( 1 9 7 8 ) d e s c r i b e t h e s c a t t e r t h a t i s u s u a l l y f o u n d i n r e g r e s s i o n m o d e l s o f t h i s t y p e a s r e s u l t i n g f r o m d i f f e r e n c e s i n r a i n f a l l i n t e s i t y a n d d u r a t i o n a s w e l l a s t h e a n t e c e d e n t m o i s t u r e c o n d i t i o n s o f t h e b a s i n f r o m e v e n t t o e v e n t . T h e c o r r e l a t i o n m a t r i c e s f o r t h e R - 5 l i n e a r r e g r e s s i o n v a r i a b l e s ( T a b l e 10) a r e s h o w n i n T a b l e s 17 a n d 1 8 . T h e c o r r e l a t i o n c o e f f i c i e n t s i n T a b l e 17 a r e b a s e d u p o n v a r i a b l e s f r o m s i x s e l e c t e d e v e n t s , w h i l e t h o s e i n T a b l e 18 r e s u l t f r o m VPPT PPT P P T D V Q QPK TQPK VPPT 1 . 0 PPT . 7 4 1 8 1 .0 P P T D - . 2 6 1 4 - . 7 0 3 2 1 . 0 V Q . 5 2 2 3 . 7 1 6 2 - . 1 3 0 6 1 .0 QPK . 5 3 6 4 . 7 8 6 1 - . 2 4 4 2 . 9 9 1 1 1 . 0 TQPK - . 3 2 1 5 - . 4 6 9 0 . 4 5 6 6 - . 1 9 8 1 - . 2 1 0 3 1 . 0 e 17. Correlation matrix for R-5 Subwatershed r a i n f a l l - r u n o f f v a r i a b l e s based on s i x selected events VO VPPT PPT P P T D V Q QPK TQPK VPPT 1 . 0 PPT . 7 4 4 4 1 . 0 P P T D - . 3 3 6 3 - . 6 7 4 3 1.0 V Q I . 5 1 5 9 . 7 3 9 5 - . 2 8 2 8 1 . 0 QPK . 6 1 5 6 . 8 1 2 6 - . 3 7 4 1 . 9 8 9 7 1 . 0 TQPK - . 5 0 3 8 - . 4 9 7 3 . 7 3 3 6 - . 3 1 6 8 - . 3 5 2 0 1 . 0 Table 18. Correlation matrix for R-5 Subwatershed r a i n f a l l - r u n o f f variables based on nine selected events ^3 CO 99 the v a r i a b l e s of nine R-5 s e l e c t e d events. Table 15 d i f f e r e n t i a t e s between Tables 17 and 18. The heavy l i n e d boxes in Tables 17 and 18 separate out the nine c o r r e l a t i o n s that represent r a i n f a l l - r u n o f f r e l a t i o n s h i p s . There are f i v e p o s i t i v e and four negative c o r r e l a t i o n s between r a i n f a l l - r u n o f f v a r i a b l e s shown in Tables 17 and 18. The p o s i t i v e c o r r e l a t i o n s in Tables 17 and 18 are: 1) Volume of r a i n f a l l and volume of r u n o f f , 2) volume of r a i n f a l l and peak flow r a t e , 3) average r a i n f a l l i n t e n s i t y and volume of. r u n o f f , 4) average r a i n f a l l i n t e n s i t y and peak flow r a t e , and 5) d u r a t i o n of r a i n f a l l and time to peak flow. The negative c o r r e l a t i o n s i n Tables 17 and 18 a r e : 1) Volume of r a i n f a l l and time to peak flow, 2) average r a i n f a l l i n t e n s i t y and time to peak flow, 3) d u r a t i o n of r a i n f a l l and volume of r u n o f f , and 4) d u r a t i o n of r a i n f a l l and peak flow r a t e . The negative c o r r e l a t i o n s shown in Tables 17 and 18 suggest that the d u r a t i o n of r a i n f a l l i s not a u s e f u l r a i n f a l l - r u n o f f model v a r i a b l e f o r R-5. There i s a general i n c r e a s e in p o s i t i v e c o r r e l a t i o n c o e f f i c i e n t s from Table 17 to Table 18 suggesting g r e a t e r model e f f i c i e n c i e s with i n c r e a s e d sample s i z e s as would be expected. The seven R-5 l i n e a r r e g r e s s i o n models, i n c l u d e d i n t h i s study, and t h e i r r e s p e c t i v e e f f i c i e n c i e s are summarized in Table 19. The v e r i f i c a t i o n e f f i c i e n c i e s of these models, based on s i x events, range from 0.14 to 0.99. The models that v e r i f y most e f f i c i e n t l y a l l i n c l u d e the average r a i n f a l l i n t e n s i t y as an i M O D E L VpRT P P T P P T D Q P K T Q P K i 1 • • .27 .14 .27 2 • • .51 .91 .55 3 • • • .51 .92 .55 4 • • .29 .52 .31 5 • • .62 .98 .66 6 • • • .62 .99 .67 7 • • .21 .37 .54 Regression (multiple) model based on events 1, 2, 3, 4, 5, and 10 Predicting events 12. 14, and 15 with r, regression (multiple) models New regression (multiple) models based on all events '1 -"i - Table 19. Linear regression models and e f f i c i e n c i e s f o r the R-5 Subwatershed 101 independent v a r i a b l e . These same models a l s o have the highest c o e f f i c i e n t s of d e t e r m i n a t i o n , suggesting that the average r a i n f a l l i n t e n s i t y v a r i a b l e may provide the best r e g r e s s i o n a n a l y s i s i n f o r m a t i o n f o r R-5. The seven MCW (with and without data reduction) and the seven R-5 l i n e a r r e g r e s s i o n models d e s c r i b e d thus f a r , represent only 33% of the r a i n f a l l - r u n o f f l i n e a r r e g r e s s i o n r e l a t i o n s h i p s that c o u l d c o n c i e v a b l y be used as p r e d i c t i o n models. The remainder were not analyzed because the c o r r e l a t i o n a n a l y s i s on Tab l e s 11, 12, 13, 14, 17, and 18 showed negative c o r r e l a t i o n s . V e r i f i c a t i o n e f f i c i e n c i e s f o r R-5 r e g r e s s i o n models are in general much b e t t e r than v e r i f i c a t i o n e f f i c i e n c i e s f o r MCW r e g r e s s i o n models d e s p i t e the smaller R-5 sample s i z e . For MCW and R-5 the most i n f o r m a t i v e independent r e g r e s s i o n v a r i a b l e s would appear to be volume of r a i n f a l l and average r a i n f a l l i n t e n s i t y r e s p e c t i v e l y . C o r r e l a t i o n matrices f o r nine l i n e a r r e g r e s s i o n v a r i a b l e s (two r a i n gages) are presented in Appendix C f o r MCW data. These matrices are based on the s i x s e l e c t e d events f l a g g e d i n Table 10." F o l l o w i n g the p o s i t i v e c o r r e l a t i o n standard f o r r a i n f a l l - r u n o f f v a r i a b l e s , 168 MCW l i n e a r r e g r e s s i o n models are e s t a b l i s h e d and presented in Appendix C. The 168 models represent 44% of those p o s s i b l e . C o e f f i c i e n t s of dete r m i n a t i o n f o r MLR models, with and without data r e d u c t i o n , are i n general very h i g h . The a n a l y s i s of "these models i s not taken any 102 f u r t h e r , as more events with records at two r a i n gages, are needed to advance i t to a v e r i f i c a t i o n mode. The sma l l sample s i z e s used i n t h i s study without q u e s t i o n e f f e c t s c o r r e l a t i o n c o e f f i c i e n t s and i n turn must c o n t r o l , to some degree, the p r e d i c t i v e e f f i c i e n c i e s of r a i n f a l l - r u n o f f r e g r e s s i o n models. In f u t u r e work more r a i n f a l l - r u n o f f events are necessary to uncover p o t e n t i a l l i n e a r r e g r e s s i o n models and monitor the r e l a t i v e i n c r e a s e i n model e f f i c i e n c i e s f o r MCW and R-5. These a d d i t i o n a l events w i l l r e q u i r e longer p e r i o d s of r e c o r d . There appears to be some promise f o r using MLR a n a l y s i s where independent v a r i a b l e s are a b s t r a c t e d from two rain-gage data s e t s . The standard t e s t f o r the s i g n i f i c a n c e of a c o r r e l a t i o n c o e f f i c i e n t , at a s p e c i f i c c o n f i d e n c e l e v e l , c o u l d perhaps be used as a b a s i s f o r s e t t i n g standards of e f f i c i e n c y a c c e p t a b i l i t y i n f u t u r e work. 4.2 Unit Hydrograph Model In t h i s s e c t i o n one-hour d u r a t i o n u n i t hydrographs are determined f o r MCW and R-5, as d e s c r i b e d i n Chapter Two, using observed hydrographs and hyetographs from a set of r a i n f a l l - r u n o f f events. These models are then used to simulate s e l e c t e d r a i n f a l l - r u n o f f events. $ index values are c a l c u l a t e d f o r each of the MCW and R-5 s e l e c t e d events summarized i n Table 103 1 0 . The c a l i b r a t i o n p h a s e f o r u n i t h y d r o g r a p h model c a l i b r a t i o n i n t h i s s t u d y c o n s i s t e d o f t h r e e p a r t s : 1 ) C a l c u l a t i n g $ i n d e x v a l u e s f o r e a c h s e l e c t e d e v e n t b a s e d on s t o r m f l o w v o l u m e s , 2 ) a v e r a g i n g i n d i v i d u a l l y d e v e l o p e d u n i t h y d r o g r a p h s , and 3 ) m e a s u r i n g t h e e f f i c i e n c y w i t h w h i c h e v e n t s t o r m f l o w h y d r o g r a p h s can be r e c o n s t r u c t e d w i t h an a v e r a g e u n i t h y d r o g r a p h m o d e l . In o r d e r t o v e r i f y t h e form of a s t o r m h y d r o g r a p h p r e d i c t e d w i t h t h e u n i t h y d r o g r a p h model, e x c e s s p r e c i p i t a t i o n must be d e t e r m i n e d f o r a r a i n f a l l e v e n t w i t h o u t knowledge of t h e s t o r m r u n o f f . In t h i s s t u d y two methods u s e d a r e : 1 ) a mean $ i n d e x , and 2 ) a l e a s t - s q u a r e s $ i n d e x ^ e x c e s s - r a i n f a l l r e l a t i o n s h i p . The p r e d i c t i v e p hase f o r u n i t h y d r o g r a p h model c a l i b r a t i o n i s not i n c l u d e d i n t h i s s t u d y . The MCW one-hour u n i t h y d r o g r a p h d e t e r m i n e d i n t h i s s t u d y i s shown i n F i g u r e 2 2 . I t i s a v e r a g e d from one-hour u n i t h y d r o g r a p h s d e v e l o p e d f o r e a c h of s e v e n s e p a r a t e e v e n t s . The c a l i b r a t i o n e f f i c i e n c i e s f o r t h r e e r u n o f f v a r i a b l e s , b a s e d on t h e MCW e v e n t s showing e x c e s s r a i n f a l l a r e summarized i n t h e t o p l i n e of t h e upper t a b l e o f T a b l e 2 0 . The e f f i c i e n c y of t h e MCW u n i t h y d r o g r a p h f o r r e c o n s t r u c t i n g s t o r m f l o w volumes and peak s t o r m f l o w s b o t h show v e r y h i g h v a l u e s . V e r i f i c a t i o n e f f i c i e n c i e s f o r t h e MCW u n i t h y d r o g r a p h model b a s e d on e v e n t s showing e x c e s s r a i n f a l l a r e summarized i n t h e heavy l i n e d boxes of t h e upper t a b l e of T a b l e 2 0 . The mean MCW 30 H 0 1 2 3 4 5 6 7 8 TIME (hours) Figure 22. Averaged one-hour unit hydrograph for the Mahantango Creek Subwatershed (Component events 15, 24, 25, 32, 42, 47, and 49) MCW R 2 NO. OF EVENTS Q P K T Q P K INDIVIDUALLY CALCULATED 191 1.0 .70 .0 LINEAR RELATIONSHIP 10 2 .0 .0 .0 AVERAGE RELATIONSHIP 10 2 .0 .0 .0 R-5 R 2 NO. OF EVENTS Q P K T Q P K INDIVIDUALLY CALCULATED 9 .81 .23 .0 LINEAR RELATIONSHIP 8 3 .48 .19 .0 AVERAGE RELATIONSHIP 5 4 .28 .30 .0 1 - Events 3. 4, 15. 16, 17. 20, 21, 24, 25. 26. 32, 33, 42,43b. 45, 46. 47. 48. 49 2 - Events 3, 16. 17. 21. 25. 26. 32. 45, 47, 49 3 - Events 1. 2. 3. 5. 10, 12. 14, and 15 4 - Events 2, 4. 5, 10, and 12 Table 20. Unit hydrograph model e f f i c i e n c i e s for the Mahantango Creek Subwate and R-5 Subwatershed 106 $ index, based on 21 events, i s 13.0 mm/hour. The l i n e a r index r e l a t i o n s h i p for MCW i s shown i n Figure 23. The MCW u n i t hydrograph model now shows a b s o l u t e l y no p r e d i c t i v e a b i l i t i e s and d r a m a t i c a l l y i l l u s t r a t e s the importance of knowing the excess r a i n f a l l d i s t r i b u t i o n .before employing the model as a p r e d i c t o r . Example computer output from the implementation of the UNIT code for MCW event #25 i s shown in F i g u r e 24. T h i s i s one of the seven u n i t hydrographs used to get the MCW average u n i t hydrograph. The R-5 one-hour-duration u n i t hydrograph used in t h i s study, i s shown in Fig u r e 25. I t i s averaged from one-hour u n i t hydrographs from f i v e events*. The same c a l i b r a t i o n and v e r i f i c a t i o n s c e n a r i o e s t a b l i s h e d f o r the MCW u n i t hydrograph model was used f o r the R-5 u n i t hydrograph model. The bottom t a b l e i n Table 20 summarizes the c a l i b r a t i o n and v e r i f i c a t i o n e f f i c i e n c i e s of the R-5 u n i t hydrograph model. V e r i f i c a t i o n e f f i c i e n c i e s are l o c a t e d i n the heavy l i n e d boxes. The mean R-5 $ index, based on nine events, i s 21 mm/hour. The l i n e a r * index r e l a t i o n s h i p f o r R-5 i s shown i n Fig u r e 26. The R-5 u n i t hydrograph c a l i b r a t i o n e f f i c i e n c i e s f o r storm flow volumes and peak storm flows are both lower than those d e s c r i b e d f o r MCW, although the former i s s t i l l q u i t e h i gh. V e r i f i c a t i o n e f f i c i e n c i e s f o r the R-5 u n i t hydrograph model using the l i n e a r and average $ index r e l a t i o n s h i p s , show gr e a t e r promise than i n the MCW case. T h i s i s e s p e c i a l l y so 7.62 25.4 50.8 X TOTAL PRECIPITATION DEPTH (mm) Figure 23. Linear b index relationship for the Mahantango Creek Subwatershed o 108 UNIT HVDROGRAPH FDR MCW25-1HR PERIOD NUMBER OF LAST NON-ZERO EXCESS RAINFALL . PERIOD NUMBER OF LAST NON-ZERO RUNOFF . 5 MEMDRV TIME > 5 TIME PERIOD RAINFALL EXCESS 0 2COOO 0 0 0.0 0.0 0.0 0 02133 0 11172 0.0*905 0 02326 O 00947 DISCRETE KERNELS FOR UNIT HYDROGRAPH 0 091 BO 0 5*375 0.23040 O 10155 O 03250 I— CEo " Q or 1 4.0 TIME ~ i — 5.0 I — E.O ~ I — 1.0 0.0 • — I — 1 .0 2.0 I — 3.0 6 0 Figure 24. Example unit hydrograph i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 TIME (hours) Figure 25. Averaged one-hour unit hydrograph for the R-5 Subwatershed (Component events 1, 5, 10, 12, and 15)  I l l when one c o n s i d e r s the l i m i t e d number of events i n c l u d e d in the two $ index standards used to c a l c u l a t e excess r a i n f a l l . The f a c t t h at R-5 i s a smaller and more homogeneous basin than MCW may account f o r the f a c t that the R-5 unit-hydrograph model appears to have gr e a t e r p r e d i c t i v e prowess than the MCW unit-hydrograph model. In these models, excess r a i n f a l l i s a lumped input parameter, whereas i n r e a l i t y , i t i s s t r o n g l y v a r i a b l e over space due to d i f f e r e n c e s in i n f i l t r a t i o n c a p a c i t i e s . Smaller basins are l e s s e f f e c t e d than l a r g e r basins by t h i s v a r i a b i l i t y . L i n s l e y et a l . (1975) suggest that unit-hydrograph models are best s u i t e d to basins of l i m i t e d s p a t i a l v a r i a b i l i t y . N e i t h e r of the u n i t hydrograph models used in t h i s study show any e f f i c i e n c y f o r r e c o n s t r u c t i n g or p r e d i c t i n g the time i t takes f o r peak storm flows to occur. T h i s may be the r e s u l t of the way the models were c o n s t r u c t e d . The MCW and R-5 u n i t hydrographs are simple a r i t h m e t i c averages of concurrent c o o r d i n a t e s . L i n s l e y et a l . (1975) suggest that a more d e f e n s i b l e procedure i s to compute average peak flow and time to peak flow, then sketch the average u n i t hydrograph conforming to the general shape of the component graphs p a s s i n g through the computed p o i n t . T h i s recommendation w i l l be t e s t e d i n f u t u r e work. The r e s u l t s ' from MCW and R-5 unit-hydrograph models presented here i l l u s t r a t e that the technique may be dependent 112 u p o n t h e a v e r a g i n g c r i t e r i o n u s e d , a n d i s s t r o n g l y d e p e n d e n t u p o n t h e c a l c u l a t i o n o f e x c e s s r a i n f a l l . A t t e m p t s t o i n c r e a s e t h e s e n s i t i v i t y o f 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 b y c a l c u l a t i n g s h o r t e r d u r a t i o n m o d e l s w e r e s t y m i e d a s e x c e s s - r a i n f a l l d i s t r i b u t i o n s , d e t e r m i n e d b y t h e $ i n d e x m e t h o d , f a i l e d t o c o r r e l a t e w e l l w i t h e i t h e r MCW o r R - 5 s t o r m f l o w h y d r o g r a p h s . T h e e f f i c i e n c y c r i t e r i o n a d a p t e d f o r t h i s s t u d y i s i n s u f f i c i e n t f o r e v a l u a t i n g t h e p r e d i c t e d f o r m o f t h e s t o r m h y d r o g r a p h s i m u l a t e d w i t h 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 . 4.3 D i s t r i b u t e d M o d e l R e s u l t s f r o m s i m u l a t i o n s o f MCW a n d R - 5 r a i n f a l l - r u n o f f e v e n t s , u s i n g t h e d i s t r i b u t e d m o d e l d e s c r i b e d i n C h a p t e r T w o , a r e p r e s e n t e d a n d d i s c u s s e d i n t h i s s e c t i o n . T h e i n p u t d a t a r e q u i r e d b y t h e d i s t r i b u t e d m o d e l i s d e s c r i b e d i n C h a p t e r T w o , t h e a v a i l a b l e MCW a n d R - 5 d a t a u s e d t o f i l l t h e s e r e q u i r e m e n t s i s p r e s e n t e d i n C h a p t e r T h r e e . T h e r e i s n o c a l i b r a t i o n p h a s e r e q u i r e d f o r t h e d i s t r i b u t e d m o d e l u s e d i n t h i s s t u d y . V e r i f i c a t i o n e f f i c i e n c i e s f o r s t o r m h y d r o g r a p h s p r e d i c t e d w i t h t h e d i s t r i b u t e d m o d e l a r e c a l c u l a t e d f o r t w o t y p e s o f r a i n f a l l - r u n o f f e v e n t s : 1) E v e n t s t h a t p r o d u c e d e x c e s s r a i n f a l l ( l a t e r a l i n f l o w h y d r o g r a p h s ) , a n d 2 ) e v e n t s t h a t d i d n o t g e n e r a t e e x c e s s r a i n f a l l . T h e p r e d i c t i v e p h a s e o f m o d e l 1 1 3 c a l i b r a t i o n i s not addressed i n t h i s study f o r the d i s t r i b u t e d model. The watershed segments used to transform MCW i n t o overland flow planes compatible with the d i s t r i b u t e d model are shown in F i g u r e 27. The s i z e and o r i e n t a t i o n of the o v e r l a n d flow planes are based upon the MCW c o n t r i b u t i n g areas d e s c r i b e d by Engman (1974). Table 21 summarizes the transformed subwatershed. The 16 major segments and t h e i r s u b d i v i s i o n s were a b s t r a c t e d from F i g u r e 14 and topographic contour maps. The major watershed segment lengths d e f i n e r o u t i n g reaches of equal channel slope and h y d r a u l i c behavior. The s u b d i v i s i o n s of the major watershed segments c h a r a c t e r i z e averaged s o i l zone dimensions and s l o p e . These s o i l zones i d e n t i f y the areas over which p a r t i c u l a r i n f i l t r a t i o n curves apply i n the c a l c u l a t i o n of excess p r e c i p i t a t i o n . The reaches and t r i b u t a r i e s d e s c r i b i n g the channel r o u t i n g s c e n a r i o used f o r MCW are i l l u s t r a t e d i n F i g u r e 28. The storm runoff volumes f o r each of the 21 s e l e c t e d MCW events were simulated i n t h i s study. The top t a b l e i n Table 22 (Group A) shows that there i s no p r e d i c t i v e e f f i c i e n c y f o r the d i s t r i b u t e d model when a l l of these events are taken as a group. The dashes in Table 22 represent runoff v a r i a b l e s not evaluated in the r e s p e c t i v e group of events. I n s p e c t i o n of i n d i v i d u a l s i m u l a t i o n s revealed that i n more than one-half of a l l s e l e c t e d events no l a t e r a l inflow was being generated. T h i s was due to 114 Figure 27. Watershed segments used to transform the Mahantango Creek Subwatershed into overland flow planes Ol -tk CO O CD 00 CD CO ro SUBBASIh I ro -» _* —A to -» to -» 4k CO to -* co ro -» ro -> co ro -» to -> SEGMENT r~ m -ti - i CO o m cn 4̂ cn 4̂ CD CD a> co •A 4k cn 4k cn 0> CO" CD 0> cn 4k 4k cn cn 4k cn cn 4k 0) cn 4k CD o> +k cn co CD CD CD 4k o> CD cn co —A CD 4k CD Ol CD 4k CD CD cn co - J 4k -» cn SOIL TYPE co -j cn _& _* cn 1» b -» cn cn cn ro to -A cn cn cn ro co cn -» to cn -* -* CO -* _ » -vl cn cn cn cn cn b u b cn - J cn oi cn cn CO -» - J Ol Ol 0 co ro 01 — J oi cn cn cn SOIL SLOPE _& co CO IO co to to -» cn -» 0) CT) CD cn CO ro co co •A •A o> ro ro o co -» 4k o _» 4k O cn 4k cn to -» 0) ->l CD CO to -» -» CO to to - s i CD CO 4k -» to CO 4k CO CO to CD cn co cn -» co CO CD Ol -J WIDTH (m) _& co -t to -» ro -» ro -» ro -» co ro -» to -» ro -» co ro -» Co ro —* co ro -» to -» SEGMENT R IG H T S ID E cn O) W 0) 4k » 4k co cn CO 4k o> cn 0) 4k co cn CD CT) 4k 0") cn 0) cn 4k 0> 4k cn cn 4k 4k cn cn CD 4k CO cn cn 4k ~-l CD 4. CD CD Ol CO CD 4k CD CD cn co CD 4k -J CD cn -A CD -~1 CO —* SOIL TYPE R IG H T S ID E cn O O cn cn cn cn o -» cn -» cn cn -» to cn -» ro cn cn -* co -» - ~ i cn cn -* -» ro cn cn cn cn cn cn -» O -> cn cn cn O CO O Ul S Ol cn oi oi 0 -» o cn -» cn 01 Ol Ol o -» o cn -* cn cn cn oi -» O -k Ol Ol Ol SOIL SLOPE R IG H T S ID E _* cn to co O "s| cn co ro -» ro o O 4k cn ro -~l o CO co ro o> o o -4 4k 00 CD 4k _» CO cn -» to -» CO 4k 1̂ co o co cn cn to CD CO CO CD 4k CO cn co CO -» ro ro cn co 0) cn -» 4k O >l 4k IO CO CO 4k -> S 4» cn co co co CO 4k CD CO WIDTH (m) R IG H T S ID E 1055 -vi ro cn ro cn co co cn to CO ro CO CO co CO ro to CO CO cn 4k CO 4k o CD CD 4k CO CO cn co 4k 4k co CO CO Ol CO CO REACH LENGTH (m) b cn b 4k b 4k b --4 b to b to b to b ro b ro b O) b to b CO b ro b to b CO —1 o REACH SLOPE Figure 28. Channel routing scenario f or the Mahantango Creek Subwatershed MCW GROUP NO. OF EVENTS Q P K T Q P K A 27 1 .0 — — • B 8 2 .0 .0 .01 R-5 R 2 GROUP NO. OF EVENTS VQ Q P K T Q P K A 9 .20 — — B 5 3 .56 .81 1.0 1 - 1 5 events with 1 raingage and 6 events with 2 raingages 2 - Events 3, 16, 17, 2 1 , 24, 25, 26, and 45 3 - Events 3, 4, 5, 10, and 12 A - Including an events B - Including only events generating lateral inflow Table 22. D i s t r i b u t e d model e f f i c i e n c i e s f o r the Mahantango Creek Subwatershed and R-5 Subwatershed 118 the way break p o i n t p r e c i p i t a t i o n was d i s t r i b u t e d over the d u r a t i o n of the s e l e c t e d event. When the r a i n f a l l i n t e n s i t y was averaged over the e n t i r e events i n these cases, i t remained lower than the i n f i l t r a t i o n c a p a c i t y thus p r e v e n t i n g surface r u n o f f . The e i g h t MCW events i n which l a t e r a l i nflow was generated are taken as a subgroup of the t o t a l events. The top t a b l e i n Table 22 (Group B) summarizes the lack of p r e d i c t i v e e f f i c i e n c y the d i s t r i b u t e d model has f o r t h i s subgroup of events. These s i m u l a t i o n s draw a t t e n t i o n to a s p e c i f i c l i m i t a t i o n in the c r i t e r i o n being used to evaluate model e f f i c i e n c y i n t h i s study. Only groups of p r e d i c t e d runoff events can be evaluated, without any i n d i v i d u a l event e v a l u a t i o n . The e v a l u a t i o n of a given d i s t r i b u t e d model s i m u l a t i o n i s important f o r uncovering the type of events the model can or cannot handle e f f i c i e n t l y . The watershed segments used to transform R-5 i n t o the overland flow planes, shown in F i g u r e 29, were a b s t r a c t e d from F i g u r e 20. The e n t i r e subwatershed was taken as a c o n t r i b u t i n g a r ea. Table 23 summarizes the transformed subwatershed. The storm runoff volumes for each of the nine s e l e c t e d R-5 events were simulated i n t h i s study. The bottom t a b l e i n Table 22 (Group A) shows the r e l a t i v e l y low p r e d i c t i v e e f f i c i e n c y f o r the d i s t r i b u t e d model when a l l of these events are taken as a group. The f i v e R-5 events generating l a t e r a l i nflow are taken as a subgroup of the t o t a l events. The bottom t a b l e i n Table 22 S - Section L - Left subbasln segment R - Right subbasln segment Subbasln Figure 29. Watershed segments used to transform the Subwatershed i n t o overland flow planes 120 LEFT SIDE RIGHT SIDE X ft- R EA C H  L EN G ' (m ) SU BB AS IN  SE G M EN T SO IL  T YP E W ID TH  (m ) SE G M EN T SO IL  T YP E W ID TH  ( m ) R EA C H  L EN G ' (m ) 1 1 3 98 1 2 3 3 2 3 61 128 220 146 2 1 2 24 1 2 31 85 2 3 122 2 3 122 1 1 12 1 1 12 3 2 2 49 2 2 31 79 3 3 110 3 4 3 2 49 116 1 1 12 1 1 12 4 2 2 61 2 2 37 73 3 3 85 3 4 3 2 61 122 Table 23. Summary of the transformed R-5 Subwatershed 121 (Group B) summarizes the p r e d i c t i v e e f f i c i e n c i e s f o r t h i s subgroup of events. Taken o v e r a l l these v a l u e s , used to v e r i f y the model, are q u i t e high when compared with the MCW v a l u e s . The antecedent s o i l water contents f o r the MCW and R-5 s e l e c t e d events would appear to be the parameter of g r e a t e s t u n c e r t a i n t y . The s e n s i t i v i t y of the antecedent s o i l water contents was i n v e s t i g a t e d f o r a s u i t e of seven MCW events. Table 24 summarizes the r e s u l t s of t h i s a n a l y s i s . S o i l moisture f r e q u e n c i e s , d i s c u s s e d i n Chapter Three, of 20% and 80% are used as i n d i c a t i v e of dry and wet c o n d i t i o n s r e s p e c t i v e l y . The dashes i n Table 24 represent i n i t i a l s o i l water contents not c o n s i d e r e d f o r s p e c i f i c events. For each event s i m u l a t i o n two values are presented i n Table 24: 1) C a l c u l a t e d storm runoff volumes, and 2) percentages of measured storm runoff volumes. Although the d i s t r i b u t e d model i s s e n s i t i v e to antecedent s o i l water content, s e l e c t e d MCW events are s t i l l p o o r l y p r e d i c t e d using the s o i l moisture frequency c r i t e r i a as shown in Table 24. Using e x i s t i n g time s e r i e s of s o i l moisture to produce i n i t i a l moisture e s t i m a t e s , as a f u n c t i o n of time of year, c o u l d be u s e f u l i n f u t u r e work. T h i s author f e e l s though, that improved estimates of antecedent s o i l water content, to be used as d e t e r m i n i s t i c input parameters, w i l l not n e c e s s a r i l y i n c r e a s e the p r e d i c t i v e e f f i c i e n c y of the d i s t r i b u t e d model due to the s p a t i a l v a r i a b i l i t y of s o i l h y d r a u l i c p r o p e r t i e s . There are at l e a s t three reasons that c o u l d be advanced i n e x p l a n a t i o n of the 122 SIMULATED RUNOFF VOLUMES (m 3) (PERCENTAGE OF MEASURED VALUES*) EVENT NO. MEASURED RUNOFF VOLUME (m3) SOIL MOISTURE FREQUENCY 20% 50% 75% 80% 3 2346 462 19.7* 566 24.1* 800 34.1* 4 1631 8 0.5* 8 0.5* , 8 0.5* 15 4519 14 0.3* 14 0.3* 14 0.3* 16 1316 1568 119.0* 2127 162.0* 2242 170.0* 17 1597 573 35.9* 878 55.0* 20 11799 23 0.2* 23 0.2* 23 0.2* 25 35859 1239 3.5* 3278 9.1* 4028 11.2* Table 24. E f f e c t of antecedent s o i l water content on simulated l a t e r a l inflow hydrograph volumes for selected Mahantango Creek Subwatershed events 1 2 3 poor p r e d i c t i v e e f f i c i e n c i e s of the d i s t r i b u t e d model. The next three paragraphs d i s c u s s each i n t u r n . F i r s t , subsurface storm flow (Whipky, 1965), has been shown to be an important component of the r a i n f a l l - r u n o f f r e l a t i o n s h i p f o r R-5 events (Sharma and Luxmoore, 1979; Luxmoore, 1982). As d e s c r i b e d i n Chapter Two, the d i s t r i b u t e d model does not c o n s i d e r the subsurface storm flow component, thereby h e l p i n g to e x p l a i n why the simulated R-5 runoff volumes are too low. Second, as p r e v i o u s l y d e s c r i b e d , the way i n which a r a i n f a l l - i n t e n s i t y d i s t r i b u t i o n i s d e r i v e d i n the d i s t r i b u t e d model appears to be l i m i t e d to high i n t e n s i t y storms of short d u r a t i o n . The e f f i c i e n c y of the d i s t r i b u t e d model i s t h e r e f o r e s t r o n g l y dependent upon the type of r a i n f a l l event being simulated. T h i r d , when concurrent stream reaches or t r i b u t a r i e s are s u b s t a n t i a l l y d i f f e r e n t i n l e n g t h (MCW), the channel flow r o u t i n g component of the d i s t r i b u t e d model does not s a t i s f y c o n s e r v a t i o n of mass going from one s e c t i o n to the next. The f i n i t e d i f f e r e n c e approximation used by the d i s t r i b u t e d model simply averages the concurrent r e a c h / t r i b u t a r y l e n g t h s . I t i s suggested here that the i n c o r p o r a t i o n of a weighting f u n c t i o n may be necessary. Of course i f a l l reaches are of s i m i l a r lengths (R-5), weighting f u n c t i o n s are not necessary as c o n s e r v a t i o n of mass i s a l r e a d y achieved. If a very l a r g e number of watershed segments were used f o r a b i g b a s i n , the 124 averaging and l i n e a r approximations made with the d i s t r i b u t e d model would be l e s s s u b j e c t i v e , but the amount of s p a t i a l l y v a r i a b l e input data r e q u i r e d would be s t a g g e r i n g . Based on the r e s u l t s presented here and those of Engman (1974), the modeling e f f i c i e n c y of the d i s t r i b u t e d model, . although promising f o r smaller b a s i n s , appears to degenerate with an i n c r e a s e i n the number of o v e r l a n d flow planes necessary to simulate l a r g e r b a s i n s . It i s f e l t by the author that u n c a l i b r a t e d , p h y s i c a l l y - b a s e d , d e t e r m i n i s t i c , r a i n f a l l - r u n o f f models w i l l probably not provide s a t i s f a c t o r y r e s u l t s for l a r g e r basins due to the s p a t i a l v a r i a b i l i t y of the input data requirements. The e f f i c i e n c y of the d i s t r i b u t e d model may improve i f a c a l i b r a t i o n phase i s i n c l u d e d . Parameters that might be c a l i b r a t e d a g a i n s t i n c l u d e the s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y , d e p r e s s i o n storage and the roughness c o e f f i c i e n t s . As with the u n i t hydrograph technique, the e f f i c i e n c y c r i t e r i o n used in t h i s study i s not s u f f i c i e n t f o r a n a l y z i n g the form of the storm flow hydrograph simulated by the d i s t r i b u t e d model. I l l u s t r a t i v e examples, in the form of sample computer output, f o r each of the four codes (Appendix B) making up the d i s t r i b u t e d model are presented i n Appendix D. The simulated event used f o r these examples i s MCW #16. 125 CHAPTER FIVE CONCLUSIONS AND FUTURE RESEARCH The v i t a l i t y of a f a l s e n o t i o n i s o f t e n s u r p r i s i n g . I t i s sometimes c r u s h i n g t o our f a i t h i n the s u r v i v a l of the f i t t e s t C h a m b e r l i n , 1884 In t h i s study a s u i t e of t h r e e u n d e r l y i n g r a i n f a l l - r u n o f f modeling t e c h n i q u e s were a p p l i e d t o two data s e t s and the r e s u l t s were used t o compare model e f f i c i e n c i e s f o r s e l e c t e d e v e n t s . I n d i v i d u a l model e f f i c i e n c i e s , based on a sum of squares c r i t e r i o n , were r e f e r e n c e d t o the t h r e e phases of model c a l i b r a t i o n . A toe h o l d f o r c o n t i n u i n g r e s e a r c h , t h i s work e s t a b l i s h e s a framework f o r e v a l u a t i n g r a i n f a l l - r u n o f f models. F u t u r e work w i l l emphasize the q u a n t i t a t i v e i n v e s t i g a t i o n of space-time t r a d e o f f s and data worth c o n c e p t s . I t w i l l r e q u i r e an e x t e n s i o n of the e s t a b l i s h e d d a t a s e t s and a r e f i n e d model e f f i c i e n c y c r i t e r i o n . The e f f i c i e n c i e s of the t h r e e u n d e r l y i n g r a i n f a l l - r u n o f f m odeling t e c h n i q u e s used i n t h i s study were found t o be s u r p r i s i n g l y poor. The r e s u l t s l e a d t o the f o l l o w i n g q u a l i t a t i v e c o n c l u s i o n s : a) The most i n f o r m a t i v e independent v a r i a b l e s f o r MCW and R-5 l i n e a r r e g r e s s i o n models appear t o be volume of r a i n f a l l and average r a i n f a l l i n t e n s i t y r e s p e c t i v e l y . There i s a g e n e r a l 1 2 6 improvement'in c o r r e l a t i o n c o e f f i c i e n t s and regression-model e f f i c i e n c i e s f o r both MCW and R-5 with i n c r e a s e s in the number of s e l e c t e d events. The e f f i c i e n c i e s are s u r p r i s i n g l y high in some cases c o n s i d e r i n g the small sample s i z e s . P o s i t i v e and negative c o r r e l a t i o n c o e f f i c i e n t s f o r MCW and R-5 r a i n f a l l - r u n o f f v a r i a b l e s were presented in Tables 11, 12, 13, 14, 17, and 18. E f f i c i e n c y v a l u e s f o r MCW and R-5 r e g r e s s i o n models are shown in Tables 16 and 19. The e f f e c t of base flow s e p a r a t i o n on c o r r e l a t i o n c o e f f i c i e n t s and r e g r e s s i o n model e f f i c i e n c i e s f o r MCW were summarized in Tables 11, 12, 13, 14, and 16. b) With respect to the u n i t hydrograph model only the R-5 a n a l y s i s demonstrated any p r e d i c t i v e prowess. The u n i t hydrograph technique was found to be s t r o n g l y dependent upon an a ccurate estimate of s p a t i a l l y v a r i a b l e excess r a i n f a l l . The e f f i c i e n c i e s f o r MCW and R-5 u n i t hydrograph models were presented in Table 20. c) The d i s t r i b u t e d modeling technique only e x h i b i t e d p r e d i c t i v e prowess for the R-5 events. I t i s b e l i e v e d by the author that the e f f i c i e n c y of the p h y s i c a l l y - b a s e d , d e t e r m i n i s t i c , d i s t r i b u t e d - m o d e l d e t e r i o r a t e s d r a s t i c a l l y with i n c r e a s e s i n b a s i n s i z e due to the lumping of s p a t i a l l y - v a r i a b l e s o i l h y d r a u l i c p r o p e r t i e s . The e f f i c i e n c i e s with which the d i s t r i b u t e d model p r e d i c t e d s e l e c t e d MCW and R-5 r a i n f a l l - r u n o f f events were summarized in Table 22. 127 d) The e f f i c i e n c i e s determined f o r three r a i n f a l l - r u n o f f modeling techniques used i n t h i s study do not uncover a d e f i n i t i v e l y s u p e r i o r model. L i m i t a t i o n s i n each of the u n d e r l y i n g modeling techniques were d i s c u s s e d i n Chapter Four. Small sample s i z e s and s p a t i a l v a r i a b i l i t y i n input parameters were i d e n t i f i e d as the primary f a c t o r s c o n t r i b u t i n g to low p r e d i c t i v e e f f i c i e n c i e s . The r e g r e s s i o n model was found to be the only technique with any predict.ive e f f i c i e n c y f o r MCW. These r e g r e s s i o n model p r e d i c t i o n s are shrouded though by marginal c a l i b r a t i o n ranges and l a r g e confidence i n t e r v a l s . The u n i t hydrograph model and the d i s t r i b u t e d model were both found to be more e f f i c i e n t for the sm a l l e r R-5, but r e q u i r e improved estimates of s p a t i a l l y v a r i a b l e input parameters to reach accep t a b l e l e v e l s . e) R a i n f a l l - r u n o f f r e g r e s s i o n model e f f i c i e n c i e s can be improved by i n c r e a s i n g the number of s e l e c t e d events upon which they are based. S p a t i a l v a r i a b i l i t y of s o i l h y d r a u l i c p r o p e r t i e s i s the reason f o r low p r e d i c t i v e e f f i c i e n c i e s f o r the u n i t hydrograph model and the d i s t r i b u t e d model. For R-5, these v a r i a b i l i t i e s are smaller and the e f f i c i e n c i e s of both modeling techniques are g r e a t e r . D e t e r m i n i s t i c r e p r e s e n t a t i o n of model input parameters would appear to be the major p i t f a l l of the d i s t r i b u t e d model used in t h i s study. ^. f) The e f f i c i e n c y c r i t e r i o n i t s e l f i s inadequate f o r : 1) E v a l u a t i n g the form of a simulated storm flow hydrograph i n s t e a d 128 of s e l e c t e d runoff v a r i a b l e s , 2) uncovering small sample b i a s e s , 3) e v a l u a t i n g a s i n g l e event, and 4) e s t a b l i s h i n g a c c e p t a b l e model standards. T h i s study has set the stage for c o n t i n u i n g r e s e a r c h by the author. The f o l l o w i n g d i s c u s s i o n of f u t u r e r e s e a r c h i s centered in three a r e a s : 1) Modeling techniques, 2) model e v a l u a t i o n , and 3) a d d i t i o n a l data. The s p a t i a l v a r i a b i l i t y of input parameters i s the A c h i l l e s ' heel of the comprehensive, p h y s i c a l l y - b a s e d , r a i n f a l l - r u n o f f model at any p r a c t i c a l s p a t i a l g r i d s c a l e . Future r e s e a r c h w i l l focus upon determining e f f e c t i v e values f o r these parameters. This w i l l i n c l u d e : 1 ) a s s e s s i n g the worth of a d d i t i o n a l data p o i n t s i n e s t i m a t i n g e f f e c t i v e v a l u e s , and 2) a n a l y z i n g the i n f l u e n c e of u n c e r t a i n t i e s in the estimates of e f f e c t i v e values on runoff p r e d i c t i o n s . O p t i m i z a t i o n techniques, such as l i n e a r programming may be u s e f u l f o r c a l c u l a t i n g parameters such as depression storage, while the i n f i l t r a t i o n parameter might best be handled as a s t o c h a s t i c var i a b l e . The s p a t i a l v a r i a b i l i t y of s o i l h y d r a u l i c p r o p e r t i e s has been addressed by a number of authors. Future assessment of the d i s t r i b u t e d r a i n f a l l - r u n o f f modeling technique w i l l i n c l u d e the e v a l u a t i o n of v a r i o u s component techniques that are being used to d e s c r i b e s o i l h y d r a u l i c p r o p e r t i e s . These may i n c l u d e : K r i g i n g (de M a r s i l y , 1982), s c a l i n g methods (Warrick et a l . , 1977) and s t a t i s t i c a l a n a l y s i s (Russo and B r e s l e r , 1980). 1 2 9 Future e v a l u a t i o n of the q u a s i - p h y s i c a l l y based modeling technique w i l l not be r e s t r i c t e d to the model used i n t h i s study. A model s i m i l a r to the one used in t h i s work i s d e s c r i b e d by Smith and Woolhiser (1971). Two recent approaches used i n the d i s t r i b u t e d modeling technique are found i n Freeze (1980) and Moore and C l a r k e (1981). V a r i o u s methods of c a l c u l a t i n g excess r a i n f a l l w i l l be t e s t e d with the u n i t hydrograph technique. The l i n e a r - r e s e r v o i r model, d e s c r i b e d in Chapter Two and the c o n s t r a i n e d l i n e a r system model (Natale and T o d i n i , 1977) w i l l a l s o be added to the s u i t e of u n d e r l y i n g r a i n f a l l - r u n o f f modeling techniques being e v a l u a t e d . Regression a n a l y s i s of r a i n f a l l - r u n o f f v a r i a b l e s w i l l be f a c i l i t a t e d in f u t u r e work with i n c r e a s e d sample s i z e s . The major focus of f u t u r e r e s e a r c h w i l l be determining i f space-time t r a d e o f f s e x i s t a c r o s s the data sets of v a r i o u s r a i n f a l l - r u n o f f modeling techniques. The c r i t e r i o n used to e s t a b l i s h t r a d e o f f s w i l l be model e f f i c i e n c y . The standard a model must meet to be c o n s i d e r e d s u i t a b l y e f f i c i e n t i s the key q u e s t i o n i n model e v a l u a t i o n . Moore and C l a r k e (1981) d e s c r i b e the present s t a t e of r a i n f a l l - r u n o f f modeling as extremely fragmented with a b e w i l d e r i n g l y l a r g e array of models to choose from. With so many models a s t a n d a r d i z e d e v a l u a t i o n i s indeed an important problem. The model e v a l u a t i o n approach used i n t h i s study w i l l c ontinue to be employed i n f u t u r e r e s e a r c h , but the simple 130 c r i t e r i o n used here must be supplemented with new c r i t e r i a f o r improved assessments. Future work w i l l i n c o r p o r a t e a q u a n t i t a t i v e index, based on Pearson product-moment c o e f f i c i e n t s , f o r comparing the form of computed and measured hydrographs (McCuen and Snyder, 1975). Future research w i l l a l s o concentrate on e v a l u a t i n g model components as d e s c r i b e d by Nash and S u t c l i f f e (1970). S e n s i t i v i t y a n a l y s i s , i n the form of Monte C a r l o s i m u l a t i o n , may be u s e f u l f o r e v a l u a t i n g model components. The f u t u r e s t u d i e s w i l l employ data sets from three r a t h e r than two subwatersheds. In a d d i t i o n to R-5 and MCW, data from the Hubbard Brook Subwatershed, d e s c r i b e d in Chapter Three, w i l l a l s o be used. For the Pennsylvania watershed (MCW) a subwatershed known as Mr. Pauls' farm (Engman and Rogowski, 1974a) shown in Fi g u r e 13, w i l l be emphasized i n f u t u r e i n v e s t i g a t i o n . The author hopes to v i s i t each of the subwatersheds used in f u t u r e study, i n order to augment the r e s p e c t i v e data sets of s o i l h y d r a u l i c p r o p e r t i e s f o r s p e c i f i c needs. An extensive summary of p u b l i s h e d s o i l h y d r a u l i c p r o p e r t i e s i s a l s o now a v a i l a b l e to the author (Rawls, personal communication, 1981). In order to estimate antecedent s o i l moisture c o n d i t i o n s i n f u t u r e work a l l a v a i l a b l e s o i l moisture records need to be p l o t t e d i n t o time s e r i e s and seasonal s o i l - w a t e r frequency d i s t r i b u t i o n s . F i n a l l y , r a i n f a l l - r u n o f f records need to be put 131 i n t o as complete a form as p o s s i b l e i n order to increase the number of s e l e c t e d events and modeling o p t i o n s . 1 3 2 REFERENCES Amorocho, J . , and G. T. Orlob, Non-linear a n a l y s i s of h y d r o l o g i c systems, Univ. of C a l i f . 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Personal Communication, Gburek, W. J . , U S D A - A g r i c u l t u r a l Research S e r v i c e , U n i v e r s i t y Park, Pennsylvania, 1982. Personal Communication, Luxmoore, R. J . , Oak Ridge N a t i o n a l Laboratory, Oak Ridge, Tennessee, 1981. Personal Communication, Rawls, W. J . , U S D A - A g r i c u l t u r a l Research S e r v i c e , B e l t s v i l l e , Md., 1981. 146 o APPENDIX A Unit hydrograph code UNIT 147 C T h i s code computes t h e c o e f f i c i e n t s A ( I , J ) and B ( I ) f o r a C s y s t e m of l i n e a r e q u a t i o n s used f o r i d e n t i f y i n g . U n i t C H y d r o g r a p h o r d i n a t e s b a s e d on t h e method of l e a s t s q u a r e s . C i e . sum o v e r J ( A ( I , J ) * X ( I ) ) = B ( I ) C where , I and J = 1,2,....,M+1 C C O r i g i n a l code , M o r e l - S e y t o u x and Kimzey ( 1 9 8 0 ) . The code C as shown i n t h i s t h e i s was a d a p t e d , by Loague (1982) , f o r C use a t UBC. C C IMSL LIBRARY : s u b r o u t i n e LEQT1F C C XRAIN = a r r a y f o r e x c e s s r a i n f a l l i n p u t C XRUN = a r r a y f o r r u n o f f i n p u t C **NOTE** f o r m i s s i n g r u n o f f d a t a s e t XRUN(I)= - 1 . e C IRAIN = p e r i o d number of l a s t n o n - z e r o e x c e s s r a i n f a l l C IRUN = p e r i o d of l a s t n o n - z e r o r u n o f f C X ( J ) = u n i t h y d r o g r a p h o r d i n a t e J = 1,2,...,M C M = memory t i m e of w a t e r s h e d C T1,...,T10 = t i t l e C DIMENSION B ( 7 0 0 ) , A ( 7 0 0 , 7 0 0 ) , X R A I N ( 7 0 0 ) , XRUN(700), WKAREA(700), 1 B l ( 7 0 0 , 1 ) , X ( 7 0 0 ) , Y (700) C r e a d i n p u t d a t a and i n f o r m a t i o n READ (5,160) IRAIN, IRUN, M, T I , T2, T3, T4, T5, T6, T7, T8, T9, 1T1 0 DO 1 0 J = 1 , I RUN X R A I N ( J ) = 0.0 XRUN(J) = 0.0 10 CONTINUE DO 30 I = 1, IRUN READ (5,20) X R A I N ( I ) , XRUN(I) 2 0 FORMAT ( F i O . 2 , 1X, F10.2) 30 CONTINUE MM = M + 1 N = IRUN C c a l c u l a t e c o e f f i c i e n t s A ( I , J ) = sum o v e r N = J , J + i , . . . , C M(XRAIN(N-I+1)*XRAIN(N-J+1)) , where I and J = 1,2,...,M C and J > I C C i n i t i a l i z e A - m a t r i x DO 50 I = 1 , 20 DO 40 J = 1, 20 40 A ( I , J ) = 0. 50 CONTINUE IF ( I R A I N .GE. N) GO TO 70 KI = IRAIN + 1 DO 60 I = K I , N 60 X R A I N ( I ) = 0. 70 DO 100 I = 1, M DO 90 J = I , M SUMIJ = 0 . DO 80 J J = J , N XRU = XRUN(JJ) IF (XRU .EQ. - 1.) GO TO 8 0 I I = J J - I + 1 J J J = J J - J + 1 A I J = X R A I N ( I I ) * X R A I N ( J J J ) SUMIJ = SUMIJ + A I J . 80 CONTINUE 148 A ( I , J ) = SUMIJ C completed 1 loop of J , now increase J by 1 and repeat 90 CONTINUE C completed J loops for one I , now increase I by 1 and repeat 100 CONTINUE C completed A ( I , J ) matrix for J > I , now complete res t of matrix A (MM, MM) = 0. DO 110 I = 1 , M A(I,MM) = .5 A(MM,I) = 1 . 110 CONTINUE DO 130 I = 2, M 1 1 = 1 - 1 DO 120 J = 1, I I 120 A ( I , J ) = A ( J , I ) 130 CONTINUE C c a l c u l a t e c o e f f i c i e n t B ( I ) = sum over N = 1,1*1,...,N (XRAIN C (N-I+l)*XRUN(N)) , where I = l,2,...,M DO 150 I = 1 , M SUMRQ = 0. DO 14 0 K = I , N IF (XRUN(K) .EQ. - 1.) GO TO 140 RQ = XRAIN(K - I + 1) * XRUN(K) SUMRQ = SUMRQ + RQ 140 CONTINUE B ( I ) = SUMRQ C completed loop for B ( I ) with K = I ,N 150 CONTINUE B ( MM ) = 1 . C completed for a l l B ( I ) I = i,M C C p r i n t r e s u l t s WRITE (6,170) T l , T2, T3, T4, T5, T6, T7, TE, TS, T l O , IRAIN, II RUN, M 160 FORMAT (315, A4, A4, A4, A4, A4, A4, A4, A4, A4, A4) 170 FORMAT ('1', 5X, A4, A4, A4, A4, A4, A4, A4, A4, A4, A4, /////, 1 5X, 'PERIOD NUMBER OF LAST NON-ZERO EXCESS RAINFALL = ', 2 115, //, EX, 'PERIOD NUMBER OF LAST NON-ZERO RUNOFF = ', 3 115, //, 5X, 'MEMORY TIME = ', 115, ////) WRITE (6,180) WRITE (6,190) (I ,XRAIN(I) ,XRUN(I ) ,1 = 1 ,I RUN) 180 FORMAT (5X, 'TIME PERIOD', 10X, 'RAINFALL EXCESS', 14X, 'RUNOFF', 1 /, 5X, ' ' , 1 OX, ' ' , 1 4X, 2 ' ' , ///) 190 FORMAT (8X, 115, 17X, F l O . 5 , 14X, F10.5) DO 200 1 = 1 , MM 200 B l ( I , 1 ) = B ( I ) CALL LEQT1F(A, 1, MM, 700, B l , 0, WKAREA, IER) WRITE (6,220) WRITE (6,210) (I,B1(I,1),1=1,M) 210 FORMAT (1X, 16, 5X, 1F9.5) 220_FORMAT ('0', //, 1 OX, 'DISCRETE KERNELS FOR UNIT HYDROGRAPH' , //, 1 10X, ' ', //, 5X, ' I ' , 2 ) C compute maximum d i s c r e t e kernel AMAXB = 0. DO 230 I = 1 , M IF ( B 1 (I , 1 > .GT. AMAXB) AMAXB = B1(I,1 ) 230 CONTINUE C p l o t r e s u l t i n g d i s c r e t e kerne ls 149 XMAX = FLOAT(M + 3) YMAX = AMAXB + (0.1*AMAXB) DO 240 I = 1, M X(I) = I Y(I) = B1(I , 1 ) 24 0 CONTINUE CALL ALSI2E(8.0, 5.0) CALL ALAXIS('TIME', 4, 'UNIT ORDINATE', 13) CALL ALSCAL(0.0, XMAX, 0.0, YMAX) CALL ALGRAF(X, Y, M, -3) CALL PLOTND STOP END 150 APPENDIX B D i s t r i b u t e d model component codes: B.1 Code used to determine s o i l c h a r a c t e r i s t i c c u r v e s . B.2 Code used to s y n t h e s i z e storm hydrographs from p a r t i a l source areas. B.3 Code used to c a l c u l a t e normal d i s c h a r g e r a t i n g f u n c t i o n s . B.4 Code used f o r open channel flow r o u t i n g . appendix b.1 151 C The f i r s t p a r t of t h e code p e r f o r m s c o m p u t a t i o n s of s o i l C h y d r a u l i c c o n d u c t i v i t y and d i f u s s i v i t y as a f u n c t i o n of C w a t e r c o n t e n t and/or p r e s s u r e . The second p a r t of t h e code C u t i l i z e s P a r l a n g e s ' a p p r o x i m a t i o n t o P h i l i p ' s e q u a t i o n s t o C compute a b s o r p t i o n r a t e , c u m u l a t i v e s o i l a b s o r p t i o n , C i n f i l t r a t i o n r a t e s and d e p t h of t h e w e t t i n g f r o n t p e n e t r a t i o n . C C O r g i n a l c o d e , Rogowski (197 1 > . The code as shown i n C t h i s t h e s i s was a d a p t e d , by Loague ( 1 9 8 2 ) , f o r use a t UBC. C C ID = sample i d e n t i f i c a t i o n C I END = t e r m i n a t i o n c a r d (80 columns punched w i t h 9's) C NC = number of i n c r e m e n t e d p o r e c l a s s e s chosen f o r C c a l c u l a t i n g d a t a (NC i s l i m i t e d t o 99, d i m e n s i o n s C can be changed) C N = number of p o r e c l a s s e s between THETA1 and THETAE C M = N+1 C THETAE = w a t e r c o n t e n t a t a i r e n t r y p r e s s u r e , (CM**3/CM**3) C CONE = e x p e r i m e n t a l l y o b t a i n e d or e s t i m a t e d c o n d u c t i v i t y C (CM/DAY) C TF = f i e l d t e m p e r a t u r e i n d e g r e e s c e n t i g r a d e C TM = t e m p e a t u r e a t m a t c h i n g i n d e g r e e s c e n t i g r a d e C PSI 1 = i n i t i a l p r e s s u r e (CM of w a t e r ) , a b s o l u t e v a l u e C P S I E = a b s o l u t e v a l u e of a i r e n t r y p r e s s u r e , (CM) C PSI2 = w a t e r e n t r y p r e s s u r e =(1/2) PSIE C PSI15 = a b s o l u t e v a l u e of 15-bar p r e s s u r e , (CM) C T H E T 1 5 = m o i s t u r e c o n t e n t a t 15-bar C STDINC = s t a n d a r d water c o n t e n t i n c r e m e n t f o r c a l c u l a t e d C v a l u e s (CM**3/CM**3) C TINC = i n c r e m e n t e d THETA (CM**3/CM**3) C PSI = i n c r e m e n t e d PSI f o r r e s p e c t i v e TINC (CM OF WATER) C PCH = i n t e r m e d i a t e sum of p r o d u c t s of c o e f f i c i e n t s and C heads i n c o n d u c t i v i t y e q u a t i o n C SPCH = f i n a l sum of p r o d u c t s C TAU = c o n v e r s i o n f a c t o r t h a t t a k e s i n t o a c c o u n t t e m p e r a t u r e C and g r a v i t y i n f l u e n c e s C = (325.4*TF+9671.7)/(325.4*TM+9671.7) C A = t h e exponent a l p h a i n t h e PSI,THETA f u n c t i o n C B = t h e exponent b e t a i n t h e P S I , THETA f u n c t i o n C PRESSURE = m a t r i c s u c t i o n (CM of w a t e r ) , a b s o l u t e v a l u e C THETA = w a t e r c o n t e n t (CM**3/CM**3) C upper l i m i t = h i g h e r m o i s t u r e , l o w e r a b s o l u t e p r e s s u r e C CCAL = r e l a t i v e p e r m a b i l i t y , of r e s i s t i v i t y ratio(W/WE) C CMAT = matched c o n d u c t i v i t y (CM/DAY), c a l l e d 'CONDUCTIVITY' C DPSI = i s t h e p a r t i a l of PRESSURE ( P S I ) w i t h r e s p e c t t o . C THETA a t a g i v e n v a l u e of THETA, (CM) C DIF = t h e d i f f u s i v i t y g i v e n as t h e p r o d u c t of K(THETA) and C t h e p a r t i a l of PRESSURE ( P S I ) w i t h r e s p e c t t o THETA a t C a g i v e n v a l u e of THETA, (CM**2/DAY) C SORP = s o r p t i v i t y (CM/HRS**0.5) C FS = s o r p t i v i t y (FT/HRS**0.5) C PROS = i n i t i a l i n f . c a p . a f t e r one s e c . (CM/HRS) C F l = i n i t i a l i n f . c a p . a f t e r one s e c . (FT/HRS) C ETA = THETA/THETA2 C KE = c o n d u c t i v i t y i n FT/HRS C PHI = s o l u t i o n of one d i m e n s i o n a l a b s o r p t i o n e q u a t i o n C SS = s o r p t i v i t y , P h i 1 i p , 1 9 6 9 , A d v a n c e s i n H y d r o s c i e n c e C 5(237),CM/SEC**0.5 C S = s o r p t i v i t y , C M / D A Y * * 0 . 5 C SINC = n o r m a l i z e d v a l u e of STDINC 152 C CONE = c o n d u c t i v i t y at a i r entry = 1/2 Ksat C HETA(I) = normalized value of* THETA(I) C IDATE = date on which event occured C TSRT = s t a r t i n g time (HRS) C TEND = ending time (HRS) C MSOL = s o i l i d e n t i f i c a t i o n number C NM = denates i n i t i a l s o i l water c l a s s in the C moisture c h a r a c t e r i s t C NT = number of i n t e r v a l s a given time period C of r a i n i s divi d e d into C DIMENSION ID(10), TINC(99), PSI(99), SPCH(99), CCAL(99), CMAT(99), 1 DPS1(99), DIF(99), TIN(99), C(99), THETA(99), CP(99), 2 D(99), F(99), G(99), H(99), PHI(99), SUM1(99), SUM2(99), 3 S(99), T(99), TIME(99), CABS(99), ABSRT(99), VO(99), 4 Z(99,99), SUM4(99,99), HETA(99), CPP(99), SUM11(99), 5 SORP(99), PROS(99), ETA(99), HDF(99), FS(99) , F1(99) C read input parameters and v a r i a b l e s 10 READ (5,20) IDI, ID2, ID3, ID4, ID5, ID6, ID7, ID8, ID9, ID10, 11 END 20 FORMAT (10A4, 30X, 12) IF (I END - 99) 30, 680, 30 30 READ (5,40) NC, T H E T 1 5 , THETAE,' THETA2, PSI 15, PSI 1 , PSIE, PSI2, 1 CONE, TF, TM 40 FORMAT (13, 3(1X,F6.0), 2(1X,F7.0), 2(1X,F5.0), 2X, F8.0, 1 2(1X,F4.0)) C c a l c u l a t e exponent alpha A = (THET15 - TKETAE) / AL0G ( P S I 1 5.- PSIE + 1) C c a l c u l a t e exponent beta B = (THETA2 - THETAE) / ALOG(PSIE - PSI2 + 1) C c a l c u l a t e i n i t i l moisture content corresponding to PSI1 THETA1 = (ALOG(PSIl - PSIE + 1 ) ) * A + THETAE C c a l c u l a t e conversion factor TAU = (325.4*TF + 9 6 7 1 . 7 ) / (325.4*TM + 9671.7) C c a l c u l a t e increment size RNC = NC STDINC = (THETA2 - THETA1) / RNC C i n i t i a l i z e TINC array TINC(1) = THETA1 TIN(1) = THETA1 NCP1 = NC + 2 DO 50 I = 2, NCP1 50 TIN(I) = TIN(I - 1) + STDINC C c a l c u l a t e midpoint values of each increment for TINC DO 60 I = 2, NCP1 60 TINC(I) = (TIN(I) + TIN(I - 1)) * 0.5 C c a l c u l a t e adjusted PSI(I) values at midpoint of each C increment N = ((THETAE - THETA1)/STDINC) + 0.5 DO 110 I I I I I = 1, NCP1 C (11111 ) = TINC(IIIII) - THETAE IF ( C d l l l l ) ) 70, 70, 90 7 0 CONTINUE DO 80 I = 1, N PSI(I) = PSIE - 1 + EXP((TINC(I) - THETAE)/A) C c a l c u l a t e p a r t i a l of PRESSURE with respect to THETA DPSI(I) = (l./A) * EXP((TINC(I) - THETAE)/A) DPSI(I) = ABS(DPSI(I)) 80 CONTINUE GO TO 110 153 90 CONTINUE M = N + 1 DO 100 I = M, NCP1 PSI(I) = PSIE + 1 - EXP((TINC(I) - THETAE)/B) C c a l c u l a t e p a r t i a l of PRESSURE with respect to THETA DPSI(I) = (1./B) * EXP((TINC(I) - THETAE)/B) 100 CONTINUE 1 10 CONTINUE C c a l c u l a t e product of c o e f f i c i e n t and 'HEAD' terms for C each pore c l a s s NCI = NC + 1 KL = NC1 DO 130 J = 1, NC1 NL = NCP1 - J PCH = 0.0 DO 120 I = J, NC1 PCH = PCH + (2*1 + 1 - 2*J) * (1./PSI(NL)) ** 2 120 NL = NL - 1 SPCH(KL) = PCH C c a l c u l a t e W for a given water content and pressure CCAL(KL) = SPCH(KL) 130 KL = KL - 1 DO 140 I = 1, NCI C c a l c u l a t e r e l a t i v e c o n d u c t i v i t y CCAL(I) = CCAL(l) / CCAL(NCI) * ((THETAE/TINC(I ) ) * * 2 ) * 2 C c a l c u l a t e matched c o n d u c t i v i t y at each water content CMAT(I) = TAU * CONE * CCAL(I ) C c a l c u l a t e d i f f u s i v i t y DIF(I) = CKAT(I) * DPS!(I) DIF(I) = ABS(DIF(I)) 140 CONTINUE WRITE (6,150) IDI, ID2, ID3, ID4, ID5, ID6, ID7, ID8, ID9, ID1 0 150 FORMAT ( ' 1 ' , 20X, 10A4i WRITE (6,160) 160 FORMAT ('0', ' NC T H E T 1 5 THETAE T H E T A 2 P P S I 1 5 PSI 1 PSIE P S I 2 1 CONE TF TM ' ) WRITE (6,170) 170 FORMAT (' ', ' (CM3/CM3) (CM OF WATER) (CM 1/DAY) DEG.C '/) WRITE (6,180) NC, T H E T 1 5 , THETAE, T H E T A 2 , PSI15, P S I 1 , PSIE, P S I 2 , 1 CONE, TF, TM 180 FORMAT (' ', 13, 3(1X,F6.4), 2(1X,F7.1), 2(1X,F5.1), 1X, F8.4, 1 2(1X,F4.1)) WRITE (6,190) 190 FORMAT CO', ' CLASS PRESSURE THETA PERMEABILITY CONDUCTIVITY DIFF 1 U S S I V I T Y DPSI/DTHETA') . WRITE (6,200) 200 FORMAT (' ', ' (CM) (CM3/CM3) (CM/DAY) (CM 12/DAY '/) DO 220 I = 1, NCI WRITE (6,210) I, PSI(I), TINC(I), CCAL(l), CMAT(I), DIF(I), 1 DPSI(I) 210 FORMAT (' ', 13, 2X, F9.1, IX, F6.4, 2X, 1PE9.2, 4X, 1PE9.2, 6X, 1 1PE9.2, 6X, 1PE9.2) 220 CONTINUE C computation of s o r p t i v i t y as a function of THETA/THETAE C Parlange, Guelph.Symp equation 10 WRITE (6,230) 230 FORMAT ('1', ' SORPTIVITY AS A FUNCTION OF WATER CONTENT '//) FE = CONE / (24.0*2.54*12.0) 154 i 240 1 250 1 260 270 280 290 300 310 320 330 340 350 360 370 380 390 WRITE (6,240) THETAE, ID1, ID2, ID3, ID4 IDI0, FE FORMAT C O ' , ' THETAE = ', F6.4, 5X, 10A4, 1PE13.4, //) WRITE (6,250) FORMAT C ', ' CLASS INITIAL FLUX (CM./HRS) 0.5) Fl(FT/HRS) FS(FT/HRS**.5) THETA/THETA2 DO 260 I = 1, NC1 ETA(I) = TIN(I) / THETA2 CONTINUE NM = 1 MN = NM + 1 DO 280 I = NM, NC1 HDF(I) = DIF(1) / 24.0 DO 2 90 I = MN, NCI CPP(I) = (TINC(I) - TINC(NM)) * HDF(I) * STDINC SUM 11(NM) = 0.0 DO 300 I = MN, NC1 SUM11(I) = SUM11(I - 1) + CPP(I) SORP(NM) =• (2.0*SUM11(NCI)) ** 0.5 FS(NM) = SORP(NM) / (2.54*12.0) PROS(NM) = (0.5*SORP(NM)/(1.0/60.0)) + (CONE/24.0) F1(NM) = PROS(NM) NM = NM + 1 IF (NM - NC1) 270, SORP(NC1) = 0.0 DO 330 I = 1, NC1 WRITE (6,320) I, FORMAT (' ', 2X, I 6X, 0PE6.4 CONTINUE computation of PHI 111(2)134,1971 READ (5,340) NM, FORMAT (213, MN = NM + 1 HETA(NM) = 0 IF (NC - MN) ID5, ID6, ID7, ID8, ID9,  ' KE(FT/HRS) = ' , SORPTIVITY(CM/HRS * * THETA MID.INT.', //) / (2.54*12.0) 310, 310 PROS(I), SORP(I) 13, 10X, 1PES.2, , 9X, F6.4) Fl (I ), FS(I ) , ETA(I ), TINC(I ) 15X, E9.2, 10X, 2(3X,E9.2), AND s o r p t i v i t y from Parlange S o i l Science 2F5, .0 10, NT, 2, TSTRT, 16, 3X, TEND, 13) I DATE, MSOL 1 0 , and 350 STDINC normalize THETA DO 360 I = MN, NC1 HETA(I) = (TINC(MN - 1) - SINC = STDINC / (THETA2 - DO 370 I = MN, NC1 CP(I) = SINC * (DIF(I)) TINC( I ) ) • TI NC(MN - / (TIN C(MN 1 ) ) 1) - THETA2! D(I ) = CONTINUE SUM 1 (NM) SUM2(NM) DO 380 I SUM1(I) SUM2(I) CONTINUE compute (HETA(I)) * (CP(I)) = 0.0 = 0.0 = MN, NCI = SUM1(I - = SUM2(I - f i r s t term 1 ) 1 ) CP (I ) D(I ) Of * * equatlon E = (2.0*SUM2(NC1)) ** 0.5 compute second term of equation DO 3 90 I = MN, NC1 F(I) = (HETA(I)) * SUM 1(NCI) G(I) = CP(I) / F(I) CONTINUE H(NCP1) = 0.0 1 4 (Parlange,71) 14 (Parlange,71 MNN = NCP1 - MN DO 400 L = 1, MNN I = NCP1 - L H ( I ) = H ( I + 1) + G ( I ) 400 CONTINUE C compute PHI as a p r o d u c t of t h e f i r s t and second terms C of e q u a t i o n 14 DO 410 I = MN, NC1 P H I ( I ) = H ( I ) * E 410 CONTINUE C i n t e g r a t e PHI t o o b t a i n s o r p t i v i t y S on per day b a s i s S(NM) = 0.0 DO 420 I = MN, NC 1 420 S ( I ) = S ( I - 1) + ( S T D I N C * P H I ( I ) ) C compute s o r p t i v i t y of per second b a s i s SS = S(NC1 ) / 293.9388 SSS = S(NC1) * 10.0 / 24.0 ** 0.5 WRITE (6,430) 430 FORMAT ('1', WRITE (6,440) 4 40 FORMAT (' 1 / ) " DO 4 60 I = MN 4 50 FORMAT (' 4 60 CONTINUE WRITE (6,470) 4 70 FORMAT ('0', VALUES OF PHI AND SORPTIVITY ', //) PSI(CM) THETA(CM3/CM3) THETA* PHI NC 1 WRITE (6,450) I , P S I ( I ) , T I N C ( I ) , H E T A ( I ) , P H I ( I ) 13, 2X, F9.1, 5X, F6.4, 7X, F6.4, 7X, 1PE9.2) S(NC1), SS, SSS SORPTIVITY(CM/DAY**0.5) = ', 1PE9.2, 1 ' (CM/SEC**0.5)= ', 1PE9.2, 2 ' (MM/HRS**0.5)=', 1PE9.2, //) WRITE (6,480) A, 3, SINC, STDINC 480 FORMAT ( 4 ( 4 X , F 7 . 4 ) ) C c o m p u t a t i o n of i n f i l t r a t i o n c a p a c i t y C u s i n g v a l u e s of s o r p t i v i t y SS(CM/HRS**0.5),and c o n d u c t i v i t y C a t a i r e n t r y , cone,and P h i l i p ' s e q u a t i o n . TINT = (TEND - TSTRT) / 50.0 TIME(1) = 0.0 C s o r p t i v i t y i n CM/HRS**0.5 and h y d r a u l i c c o n d u c t i v i t y C i n CM/HRS SS = S(NC1) / 24.0 ** 0.5 CONE = CONE / 24.0 DO 490 K = 2, 51 TIME(K) = TIME(K - 1) + TINT T(K) = (TIME(K)) ** 0.5 VO(K) = ( 0 . 5 * S S / T ( K ) ) + CONE 4 90 CONTINUE C P a r l a n g e c o n s i d e r s t h i s VO n e g a t i v e and l e s s t h a n C cone,(Guelph,Symp.) WRITE (6,500) 500 FORMAT ( ' 1 ' , ' INFILTRATION CAPACITY (CM/HRS) '//) WRITE (6,510) 510 FORMAT (' ', ' K TIME(HRS) INF.CAPP.(CM/HRS) '//) DO 530 K = 2, 51 L = K - 1 WRITE (6,520) L, T I M E ( K ) , VO(K) 520 FORMAT (' ', 1 3 , 2(6X,1PE9.2)) 530 CONTINUE WRITE (6,540) IDATE, TSTRT, TEND, TINC(NM) 540 FORMAT C O ' , ' DATE ', 1 6 , 'START TIME(HRS)=', F6.2, 1 'END TIME(HRS) = ' , F6.2, 'THETA INITIAL(CM**3/CM**3) = ' 156 2 F6.4) C c o m p u t a t i o n of m o i s t u r e p r o f i l e s , P a r l a n g e EQ.24 DO 590 K = 2, 11 MN = NM + 1 DO 570 I = NM, NC Z ( I , K ) = ( D I F ( I ) * S T D I N C ) / ( ( C M A T ( N C 1 ) * T I N C ( I ) ) - CMAT(I)) I F ( Z ( I , K ) ) 550, 560, 560 550 Z ( I , K ) = ( D I F ( I ) * S T D I N C ) / ( ( C M A T ( N C l ) ) - CMAT(I)) 560 CONTINUE 570 CONTINUE TINT = (TEND - TSTRT) / 10.0 TIME(1) = 0.0 TIME(K) = TIME(K - 1) + TINT Z(NC1,K) = CONE * (TIME(K)) SUM4(NCP1,K) = 0.0 NMM = NCP1 - NM DO 58 0 I = 1, NMM NL. = NCP1 - 'I 580 SUM4(NL,K) = SUM4(NL + 1,K) + Z(NL,K) 590 CONTINUE WRITE (6,600) 600 FORMAT ( T , ' MOISTURE PROFILES , Z(CM) '//) WRITE (6,610) 610 FORMAT ('0', ' I THETA* K=1 K=2 K=3 K=4 1 K=5 THETA(CM**3/CM**3) '//) DO 630 I = NM, NC1 WRITE (6,620) I , H E T A ( I ) , (SUM4(I,K),K=2,6), T I N C ( I ) 620 FORMAT (' ', 13, 2X, F6.4, 5 ( 2 X , 1 P E 9 . 2 ) , 5X, 0PF6.4) 630 CONTINUE WRITE (6,640) 64 0 FORMAT ('0', ' MOISTURE ROFILES CONTINUED ,Z(CM) '//) WRITE (6,650) ' 650 FORMAT ('0', ' I THETA* K=6 K=7 K=8 K=9 1 K=10 THETA(CM**3/CM**3) '//) WRITE (6,660) I , H E T A ( I ) , CSUM4(I,K),K=7, 1 1), T I N C ( I ) 660 FORMAT C ', 13, 2X, F6.4, 5 ( 2 X , 1 P E 9 . 2 ) , 5X, 0PF6.4) 67 0 CONTINUE GO TO 10 680 STOP END APPENDIX B.2 157 C T h i s code i s f o r t h e s y n t h e s i s of s t o r m h y d r o g r a p h s from C p a r t i a l a r e a s C C O r g i n a l code ,Engman ( 1 9 7 4 ) . The code as shown i n C t h i s t h e s i s was a d a p t e d , by Loague ( 1 9 8 2 ) , f o r use a t UBC. C C MHR = h o u r s from r a i n g a g e c h a r t C MIN = m i n u t e s from r a i n g a g e c h a r t C PACCUM = a c c u m u l a t e d p r e c i p i n i n c h e s from r a i n g a g e c h a r t C W = c h a n n e l w i d t h i n f e e t C SECLEN = d e l t a x, i n c r e m e n t a l l e n g t h of f l o w p l a n e f o r r o u t i n g C SECLEN2 = d e l t a x f o r o v e r l a n d f l o w r o u t i n g i f changed C RCHLEN = l e n g t h of main c h a n n e l r e a c h between x s e c t s i n f e e t C S L O P L l ( ) , S L O P R ( ) = a v e r a g e s l o p e v a l u e s f o r o v e r l a n d f l o w C p l a n e i n each s o i l zone f r o m SCS maps C DEPL(),DEPR() = t o t a l d e p t h of d e p r e s s i o n s t o r a g e C f o r t h a t s o i l zone i n f e e t C WDTH() = p e r p e n d i c u l a r d i s t a n c e from s t r e a m t o s o i l boundary C w = a c t u a l w i d t h of c h a n n e l water s u r f a c e i n f e e t C XLLL = l e n g t h of f l o w p l a n e (maximum p o s s i b l e ) C NEND = number of i n c r e m e n t s a v a i l a b l e f o r r o u t i n g C i e . number of i n c r e m e n t s XLLL can be d e v i d e d i n t o C XEND = number of o v e r l a n d f l o w r o u t i n g s e c t i o n s C X R ( ) , X L ( ) = t h e d i m e n s i o n of t h e s o i l z o n e s on e i t h e r C s i d e of t h e c h a n n e l measured i n f e e t from t h e C c h a n n e l t o t h e f a r t h e s t edge ( s h o u l d be even C m u l t i p l e s of SECLEN) C TIMINC = c o m p u t a t i o n a l t i m e i n t e r v a l i n seconds C XMANNN = mannings "N" f o r o v e r l a n d f l o w C SLPRNT = 0.0 i n f i l t r a t i o n and s o i l s i n f o r m a t i o n not p r i n t e d C DPPRNT = 0.0 the d e p t h s a r e not p r i n t e d C PRPRN'T = 0.0 the v a l u e s of PRE() a r e not p r i n t e d C XPUNCH = 0 . 0 QI c a r d s a r e not punched C SOILNH = s o i l i d e n t i f i c a t i o n number C SOILDP = d e p t h of t o p s o i l l a y e r i n f e e t C SOLDP2 = d e p t h of second s o i l l a y e r i n f e e t C THETA2 = s o i l water c o n t e n t C THETAE = s o i l water c o n t e n t a t a i r e n t r y C DEGSAT = de g r e e of s a t u r a t i o n , T H E T A 2 / T H E T A ( s a t u r a t i o n ) C FRQDEG = f r e q u e n c y of s o i l m o i s t u r e from a p r o b a b i l i t y C d i s t r i b u t i o n C FS = s o r p t i v i t y i n f t / s e c * * . 5 C FK = c o n d u c t i v i t y a t a i r e n t r y i n f t / s e c C F l = i n i t i a l i n f i l t r a t i o n v a l u e i n f t / s e c C NTINT = l e n g t h of a r r a y ( i e . 1.5 t i m e s t h e l e n g t h of C t h e s t o r m so t h e h y d r o g r a p h w i l l have a f u l l C r e c e s s i o n and not be c u t s h o r t ) C * n o t e * NTINT w i l l a l w a y s be 40 f o r s h o r t s t o r m s C PREX = t h e p r e c i p i t a t i o n e x c e s s a f t e r d e p r e s s i o n s t o r a g e C i s s u b t r a c t e d C PRCP = r a i n f a l l i n t e n s i t y i n i n c h e s / h o u r C DUR = d u r a t i o n of r a i n f a l l DIMENSION MHR(50), M I N ( 5 0 ) , PACCUM(50), PTOT(50), ITTOT(50) DIMENSION THETA2(10), THETAE(10), DEGSAT(10), FRQDEG(10) DIMENSION X L ( 1 0 ) , X R ( 1 0 ) , P I N F ( 5 0 0 ) , WFRNT(500) DIMENSION P E X ( 1 0 , 5 0 0 ) , Q L L L ( 5 0 0 ) , Q L L R ( 5 0 0 ) , Q L ( 5 0 0 ) , PREX(10,500) DIMENSION X L L L ( 5 0 0 ) , XLLR(500) DIMENSION F S ( 1 0 ) , F K ( 1 0 ) , F 1 ( 1 0 ) , THETAI(10) DIMENSION LI S T L ( 1 0 ) , L I S T R ( 1 0 ) 158 10 20 30 40 50 60 70 80 DIMENSION S O I L D P O 0 ) , T H E T I 2 O 0 ) , THET22(10), THETE2 ( 1 0 ) , 1 DEGST2(10), FRQDG2(10), F S 2 O 0 ) , F K 2 ( 1 0 ) , F 1 2 ( 1 0 ) , 2 SOLDP2(10) DIMENSION S L O P L O 0 ) , S L O P R O 0 ) , D E P L ( l O ) , DEPR(lO) INTEGER S O I L N ( I O ) , SOIL2(10) COMMON PR E ( 5 0 0 , 5 0 0 ) , F L O ( 5 0 0 , 5 0 0 ) , DPTK(500,500), V01(10,500) 1 FTLONG(500), P ( 5 0 0 ) , SLOP(500) LOGICAL*1 DATE(70) LOGICAL*1 GAGE(70) LOGICAL*1 SECTON(70) FORMAT (70A1) (212, F14.7, 11) (8F10.0) (13 ( ' 1 (' ( ' FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT '//> 90 100 FORMAT FORMAT 1 110 FORMAT ION AND 2 120 FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT ( ' 08X ' FK ( ' ( ' 08X ( ' 1 EXCESS //) 2X, 7F10.0, F4.0, 11) 45X, '<<< SOIL PARAMETERS >>: IX, 13, 8 ( 2 X , F 1 2 . 5 ) / / / ) 1X, 13, 6X, 13, 5 ( 2 X , F 1 2 . 5 ) ) 'SOIL*', 06X, 'THETA2 1, 08X, 'DEGSAT', 08X, 'FRQDEG', 07X, (FT/HR)', 0 5X, 'F1(FT/HR)'/) 'SECONDS PER TIMI NT = ', F5.0////) 'SOIL*', 03X, 'TIMI NT' , 06X, ' V O l ( F T ) ' , 08X, P E X ( F T ) ' , 07X, ' P I N F ( F T ) ' , 7X, 'WFINC(FT)'/) 5X, ' DIVISION OF TOTAL PRECIPITATION INTO INF1LTRATI COMPONENTS USING SOIL PARAMETERS AND RAINGAGE DATA'/ 'THETAE', 08X, 'THETAI 'FS(FT/HR)', 05X, 1 P(F1 1 3 0 1 4 0 1 5 0 1 6 0 1 7 0 (' ', 10X, 'DATE OF EVENT: ', 70A1//////) (' ', 'ORIGINAL RAINFALL DATA FROM ', 70A1//) (' ', 30X, 'TIME', 06X, 'INCHES'/) (' ', 30X, 212, IX, F10.2) ( ' I ' , 'CALCULATION OF LATERAL INFLOW HYDROGRAPHS' (' ', 'TC? LAYER SOIL DEPTH=', F5.3, 5X, 'SECOND LAYER SOIL DEPTH=', F7.3) i n i t i a l i z e a i l a r r a y s used i n ' t h e p r e c i p breakdown DO 180 J = 1, 500 1 8 0 1 90 200 210 220 SLOP (J ', DO 200 = 0.0 J = 1 , 500 1 , 500 = 0.0 = 0.0 = 0.0 230 DO 190 K = DPTH(K,J) FLO(K,J) P R E ( K , J ) CONTINUE CONTINUE DO 220 J = 1 , DO 210 K = PREX(K,J) P E X ( K , J ) CONTINUE CONTINUE DO 230 J = 1 , X L L L ( J ) = 0 P I N F ( J ) = .0 X L L R ( J ) = 0 FTLONG(J) = P ( J ) = 0.0 QLL R ( J ) = 0.0 Q L L L ( J ) = 0.0 Q L ( J ) = 0.0 CONTINUE DO 240 J = 1, 50 500 1 , 10 = 0.0 = 0.0 500 0 0 0 0.0 159 MIN(J) = 0 . 0 MHR(J) = 0 M I N ( J ) = 0 PACCUM(J) = 0 . 0 PTOT(J) = 0 . 0 ITTOT(J) = 0 . 0 240 CONTINUE C r e a d t h e e v e n t d a t e and r a i n g a g e used READ ( 5 , 1 0 ) DATE READ ( 5 , 1 0 ) GAGE C r e a d b r e a k p o i n t r a i n g a g e d a t a ; a f t e r l a s t c a r d , i n s e r t a c a r d , C of a l l 1's I = 1 250 READ (5,20) M H R ( I ) , M I N ( I ) , PACCUM(I), NSTOP IF (NSTOP .NE. 0) GO TO 260 1 = 1 + 1 GO TO 250 260 NPINTS = I - - 2 C r e a d t i m e i n t e r v a l of c a l c u l a t i o n s i n seconds READ (5,30) TIMINC, SECLEN, TOLR, XEND, SLPRNT, DPPRNT, PRPRNT, 1 X P U N C H NEND = XEND INCTIM = TIMINC X E N D 3 = XEND DELTX = SECLEN C. c o n v e r t b r e a k p o i n t d a t a t o p r e c i p d e p t h v e c t o r NTSUM = 0 DO 260 1 = 1 , NPINTS PTOT ( I ) = (PACCUM ( I •+ 1) - PACCUM(U) / 1 2 . INCHR = M H R ( I + 1) - MHR(I) INCMIN = M I N ( I + 1) - M I N ( I ) I F (INCMIN .GE. 0 ) GO TO 27 0 INCMIN = INCMIN + 60 INCHR = INCHR - 1 270 ITTOT(I) = (INCHR*3600) * (INCMIN*60) + NTSUM 280 NTSUM = I T T O T ( I ) PSUM = 0 . 0 PCUM = 0 . 0 NSECSS = 0 ITIME = 0 ITSUM = 0 1 = 1 290 NSECSS = NSECSS + INCTIM ITIME = ITIME + 1 IF (NSECSS .GE. ITTOT(NPINTS)) GO TO 320 300 IF (NSECSS .LE. I T T O T ( I ) ) GO TO 3 1 0 ITSUM = I T T O T ( I ) PSUM = PTOT(I) 1 = 1 + 1 GO TO 300 310 SECS = NSECSS TTOT = IT T O T ( I ) TSUM = ITSUM P ( I T I M E ) = ((SECS - TSUM)/(TTOT - TSUM)) * (PTOT(I) - PSUM) + 1PSUM - PCUM PCUM = PCUM + P ( I T I M E ) GO TO 290 320 P ( I T I M E ) = PTOT(NPINTS) - PCUM C w r i t e h e a d i n g , d a t e , g a g e , a n d o r g i n a l p r e c i p d a t a WRITE (6,110) 160 WRITE ( 6 , 120) DATE, .WRITE ( 6 , 130) GAGE WRITE (6,90) TIMINC WRITE (6,140) NPREC = NPINTS + 1 DO 330 K = 1, NPREC 330 WRITE (6,150) MHR(K), M I N ( K ) , PACCUM(K) C r e a d s o i l i n p u t d a t a C C t o p s o i l l a y e r C a f t e r l a s t c a r d i n s e r t c a r d w i t h a l l 3's I = 1 340 READ (5,40) S O I L N ( I ) , T H E T A 2 ( I ) , T H E T A E ( I ) , DEGSAT(I), FRQDEG(I), 1 F S ( I ) , F K ( I ) , F 1 ( I ) , S O I L D P ( I ) , MSTOP IF (MSTOP .GT. 2) GO TO 350 1 = 1 + 1 GO TO 340 350 I = 1 . 360 CONTINUE C second s o i l l a y e r r e a d i n d a t a C a f t e r l a s t c a r d i n s e r t c a r d w i t h a l l 6's READ (5,40) S O I L 2 U ) , T H E T 2 2 ( I ) , THETE2 (I ) , D E G S T 2 ( I ) , FRQDG2 (I ) , 1 F S 2 ( I ) , F K 2 ( I ) , F 1 2 ( I ) , S O L D P 2 U ) , MSTOP IF (MSTOP .GT. 5) GO TO 370 1 = 1 + 1 GO TO 360 370 1 = 1 - 1 C c a l c u l a t e s o i l - t i m e a r r a y of V O l , e x c e s s , and i n f i l t r a t i o n C p r i n t i n i t i a l s o i l p a r a m e t e r s and c a l c u l a t e d o u t p u t NTI NT = 1.5 * I TIME + 1 IF (NTI NT .LT. 40) NTI NT = 4 0 DO 500 NSOIL = 1, I IF ( F S ( N S O I L ) ) 360, 380, 400 380 DO 390 INP = 1, NT I NT 390 PEX(NSOIL,INP) = P(INP) GO TO 440 400 CONTINUE THETAI (NSOIL) = DEGSAT(NSOI L) * THETA2(NSOIL) V 0 1 ( N S O I L , l ) = F l ( N S O I L ) * TIMINC / 3600. P E X ( N S O I L , l ) = P ( l ) - VOl(NSOIL,1) I F (PEX(NSOIL,1) .GT. 0.0) P I N F ( 1 ) V = VOl(NSOIL,1) IF (PEX(NSOIL,1) .LE. 0.0) P I N F ( 1 ) = P ( 1 ) WETFRT = P I N F ( 1 ) / (THETAE(NSOIL) - THETAI(NSOIL)) WFRNT(1) = WETFRT DO 410 INP = 2, NT I NT RLTIME = INP * TIMINC / 3600. V O l ( N S O I L , I N P ) = ((0.5*FS(NSOIL)/RLTIME**0.5) + F K ( N S O I L ) ) * 1 TIMINC / 3600. PEX(NSOIL,INP) = P ( I N P ) - VOl(NSOIL,INP) I F (PEX(NSOIL,INP) .GT. 0.0) P I N F ( I N P ) = VO1(NSOIL,INP) I F (PEX(NSOIL,INP) .LE. 0.0) P I N F ( I N P ) = P ( I N P ) WETFRT = WETFRT + P I N F ( I N P ) / (THETAE(NSOIL) - THETAI(NSOIL)) WFRNT(INP) = WETFRT II N P = INP C c h e c k i n g t o see i f w e t t i n g f r o n t has p r o c e e d e d below C t h e t o p s o i l . i f i t has go t o second l a y e r w h i c h now C c o n t r o l s VOl I F (WETFRT .GT. SOI LDP(NSOIL)) GO TO 420 410 CONTINUE 420 XWET = 1.0 1 6 1 THETI2(NS0IL) = DEGST2(NS0IL) * THET22(NSOIL) DO 430 INP = I I N P , NTINT RLTIME = INP * TIMINC / 3600. V O l ( N S O I L , I N P ) = ((0.5*FS2(NSOIL)/RLTIME**0.5) + FK 2 ( N S O I L ) ) * 1 TIMINC / 3600. PEX(NSOIL,INP) = P ( I N P ) - V O l ( N S O I L , I N P ) IF (PEX(NSOIL,INP) .GT. 0.0) P I N F ( I N P ) = VO l ( N S O I L , I N P ) IF (PEX(NSOIL,INP) .LE. 0.0) P I N F ( I N P ) = P ( I N P ) WETFRT = WETFRT + P I N F ( I N P ) / (THETAE(NSOIL) - THETAI(NSOIL)) WFRNT(INP) = WETFRT 4 30 CONTINUE • IF (SLPRNT .LE. 0.0) GO TO 490 440 CONTINUE IF ( F S ( N S O I L ) ) 450, 450, 470 450 WRITE (6,460) 460 FORMAT (' ', 'LATERAL INFLOW FROM IMPERVIOUS AREA ,.PEX=PRECI P' ) GO TO 470 470 CONTINUE w r i t e o r g i n a l s o i l s d a t a •WRITE (6,50) WRITE (6,80) WRITE (6,60) SOILN(NSOIL), THETA2(NSOIL), THETAE(NSOIL), 1 THETAI(NSOIL), DEGSAT(NSOIL), FRQDEG(NSOIL), F S ( N S O I L ) , 2 F K ( N S O I L ) , F l ( N S O I L ) WRITE (6,60) S O I L 2 ( N S O I L ) , THET22(NSOIL), THETE2(NSOIL), 1 THETI2(NSOIL), DEGST2(NSOIL), FRQDG2(NSOIL), F S 2 ( N S 0 1 L ) , 2 F K 2 ( N S O I L ) , F12(NSOIL) WRITE (6,170.) SOILDP(NSOIL) , SOLDP2 (NSOI L ) w r i t e out i n f i 1 t r a t i o n , p r e c i p i t a t i o n e x c e s s and d e p t h of t h e w e t t i n g f r o n t . WRITE (6,100) DO 480 INP = 1, NTINT 480 WRITE (6,70) SOILN(NSOIL), INP, VO1(NSOIL,INP), P ( I N P ) , 1 P E X ( N S O I L , I N P ) , P I N F ( I N P ) , WFRNT(INP) 4 90 CONTINUE 50 0 CONTINUE NNSOIL = I 510 CONTINUE s e t a r r a y s t o z e r o DO 520 1 = 1 , 500 DO 520 J = 1, 500 P R E ( I , J ) = 0.0 520 CONTINUE DO 530 L = 1, 10 X L ( L ) = 0.0 XR(L) = 0.0 SLOPL(L) = 0 . 0 SLOPR(L) = 0 . 0 DEPL(L) = 0.0 DEPR(L) = 0.0 LI S T L ( L ) = 0 530 L I S T R ( L ) = 0 I = NNSOIL r e a d i n w a t e r s h e d geometry READ (5,540) SECTON, IZSTOP 540 FORMAT (70A1, 9X, I I ) IF (IZSTOP - 9) 550, 1040, 550 550 READ (5,560) ( L I S T L ( L ) , L = 1 , 1 0 ) , ( L I S T R ( L ) , L = 1 , 1 0 ) , LISTNL, LISTNR 560 FORMAT (1012, 1012, 12, 12) READ (5,570) ( X L ( L ) , L = 1 , L I S T N L ) , (XR(L),L=1,LISTNR) 570 FORMAT (16F5.0) READ (5,570) ( S L O P L ( L ) , L = 1 , L I S T N L ) , (SLOPR(L),L=1,LISTNR) READ (5,570) ( D E P L ( L ) , L = 1 , L I S T N L ) , (DEPR(L),L=1,LISTNR) READ (5,30) RCHLEN, W, XMANNN, SECLN2, XEND2 IF (SECLN2 .GT. 0.0) GO TO 580 XEND = XEND3 NEND = XEND SECLEN = DELTX GO TO 590 580 SECLEN = SECLN2 XEND = XEND2 NEND = XEND 590 CONTINUE C s u b t r a c t i n g d e t e n t i o n s t o r a g e o n l y when i n f i l t r a t i o n C i s e x c e e d e d L = 1 600 L I S T = L NSOIL = LI S T L ( L ) DETENT = D E P L ( L I S T ) DO 630 INP = 1, NTINT DELDEP = 0.1 * DEPL(LI ST) IF (PEX(NSOIL,INP) .LE. 0.0) GO TO 620 IF (DETENT .LE. 0.0) GO TO 620 IF (DELDEP .LE. PEX(NSOIL,INP)) GO TO 610 DETENT = DETENT - PEX(NSOIL,INP) PREX(NSOIL,INP) = 0.0 GO TO 630 610 PREX(NSOIL,INP) '= PEX(NSOIL,INP) - DELDEP DETENT = DETENT - DELDEP GO TO 630 620 PREX(NSOIL,INP) = PEX(NSOIL,INP) 6 30 CONTINUE L = L + 1 IF (L .LE. LISTNL) GO TO 600 XN2 = XEND LN2 = NEND C d i s t r i b u t i n g SLOPE and PREX t o each r o u t i n g segment C i n t h e f l o w p l a n e DO 660 L I S T = 1, LISTNL DO 650 I TINT = 1 , NTINT XN1 = XN2 - X L ( L I ST) / SECLEN LN1 = XN1 JOK = L I S T L ( L I S T ) DO 640 L = LN1, LN2 SLOP(L) = SLOPL(LI ST) 640 P R E ( L , I T I N T ) = PREX(JOK,ITINT) 650 CONTINUE LN2 = LN1 - 1 660 CONTINUE CALL SUROUT(TIMINC, NEND, SECLEN, XMANNN, I TIME, TOLR) DO 67 0 I TINT = 1, NTINT X L L L ( I T I N T ) = FTLONGfI TINT) 670 Q L L L ( I T I N T ) = FLO(NEND,ITINT) 680 CONTINUE C e x a c t d u p l i c a t e of l e f t s i d e c a l c u l a t i o n s C r i g h t s i d e p a r t i a l a r e a DO 700 J = 1, 500 DO 690 K = 1, 500 P R E ( K , J ) = 0 . 0 690 CONTINUE 700 CONTINUE DO 710 K = 1, 500 710 SLOP(K) = 0.0 L = 1 720 L I S T = L NSOIL = L I S T R ( L ) DETENT = DEPR(LIST) DO 750 INP = 1 , NTINT DELDEP = 0.1 * DEPR(LIST) I F (PEX(NSOIL,INP) .LE. 0.0) GO TO 740 I F (DETENT .LE. 0.0) GO TO 740 I F (DELDEP .LE. PEX(NSOIL,INP)) GO TO 730 DETENT = DETENT - PEX(NSOIL,INP) PREX(NSOIL,INP) = 0.0 GO TO 750 730 PREX(NSOIL,INP) = PEX(NSOIL,INP) - DELDEP DETENT = DETENT - DELDEP GO TO 7 50 740 PREX(NSOIL,INP) = PEX(NSOIL,INP) 750 CONTINUE L = L + 1 I F (L .LE. LISTNR) GO TO 720 XN2 = XEND LN2 = NEND DO 780 L I S T = 1, LISTNR DO 77 0 I TINT = 1 , NTINT XN1 = XN2 - X R ( L I S T ) / SECLEN LN1 = XN 1 JOK = L I S T R ( L I S T ) DO 760 L = LN1, LN2 SLOP(L) = SLOPR(LIST) 760 P R E ( L , I T I N T ) = PREX(JOK,ITINT) 770 CONTINUE LN2 = LN1 - 1 780 CONTINUE CALL SUROUT(TIMINC, NEND, SECLEN, XMANNN, I TIME, TOLR) DO 790 I TINT = 1 , NTINT X L L R ( I T I N T ) = FTLONG(ITINT) 790 QLLR(ITINT) = FLO(NEND,ITINT) C t o t a l l a t e r a l i n f l o w C sums l e f t + r i g h t s i d e s + c h a n n e l p r e c i p i t a t i o n 800 CONTINUE DO 810 INQQ = 1, NTINT QL(INQQ) = QLLL(INQQ) + QLLR(INQQ) + W * P(INQQ) / 3600 810 CONTINUE QLT = 0.0 C volume of p r e c i p e x c e s s DO 820 ITQL = 1, NTINT QLT = QLT + QL(ITQL) * TIMINC 820 CONTINUE C t o t a l volume of r u n o f f from r e a c h QLTT = QLT * RCHLEN C f o r m a t f o r o u t p u t C p r i n t out and punched C a r d o u t p u t WRITE (6,160) WRITE (6,10) SECTON WRITE (6,830) (DEPL(L),L=1,LISTNL) 830 FORMAT (' ', 'LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE' 1 1 0 ( F 6 . 4 , 3 X ) ) WRITE (6,840) (DEPR(L),L=1,LISTNR) 164 840 FORMAT (' ', 'RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE', 5X, 1 10(F6.4,3X)) WRITE (6,850) (SLOPL(L),L=1,LISTNL) 850 FORMAT (' ', 'LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE', 5X, 1 10(F6.4,3X)) WRITE (6,860) (SLOPR(L),L=1,LISTNR) 860 FORMAT (' ', 'RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE', 5X, 1 10(F6.4,3X)) WRITE (6,870) ( X L ( L ) , L = 1 . L I S T N L ) 870 FORMAT (' ', 'LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM', 5X, 1 10 ( F 6 . 1 , 3 X ) ) WRITE (6,880) (XR(L),L=1,LISTNR) 880 FORMAT (' ', 'RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM', 5X, 1 10 ( F 6 . 1 , 3 X ) ) WRITE (6,890) RCHLEN, W, XMANNN, SECLEN 890 FORMAT (' ', 'REACH LENGTH=', 5X, F7.2, 5X, 'STREAM WIDTH=', 5X, 1 F5.2, 5X, 'MANNINGS N=', 5X, F8.6, 5X, 'DELTAX=', F7.2) WRITE (6,900) QLT 900 FORMAT (' ', 'VOLUME OF PRECIPITATION EXCESS=', F20.10, 5X, 1 'CU FT') WRITE (6,910) QLTT 910 FORMAT (' ', 'TOTAL RUNOFF VOLUME FROM REACH=', F20.10) WRITE (6,920) 920 FORMAT ('-', 30X, 'PRECIP EXCESS VALUES FOR EACH DELT') WRITE (6,930) 930 FORMAT (' ', ' QL CFS/FT PRECIP DEPTH LEFT SIDE 1QL WIDTH OF CONTRIB AREA RIGHT SIDE QL WIDTH OF RIGHT SIDE') DO 940 I = 1, NTINT 94 0 WRITE (6,950) Q L ( I ) , P ( I ) , Q L L L ( I ), X L L L ( I ), QLLR(I ), X L L R ( I ) 950 FORMAT (' ', 6(F14.7,5X)) IF (XPUNCH .LE. 0.0) GO TO 990 DO 960 1= 1 , NTINT 960 PUNCH 970, Q L ( I ) 970 FORMAT (20X, F12.7, 48X) DUMMY = 1111111. PUNCH 980, DUMMY ' 98 0 FORMAT (F10.0) 990 CONTINUE DO 1010 I = 1, NTINT WRITE (8,1000) Q L ( I ) 1000 FORMAT (' ', 19X, F12.7, 48X) 1010 CONTINUE DUMMY = 1111111. WRITE (8,1020) DUMMY 1020 FORMAT (' ', F10.0) 1030 CONTINUE DPCT = 0.0 GO TO 510 1040 STOP END SUBROUTINE SUROUT(TIMINC, NEND, SECLEN, XMANNN, I TIME, TOLR) C s u b r o u t i n e r o u t e s d e p t h of p r e c i p e x c e s s o v e r p a r t i a l C a r e a l e n g t h u s i n g s s i m p l e k i n e m a t i c f o r m u l a t i o n COMMON P R E ( 5 0 0 , 5 0 0 ) , F L O ( 5 0 0 , 5 0 0 ) , DPTH(500,500), V O 1 ( l 0 , 5 0 0 ) , 1 FTLONG(500), P ( 5 0 0 ) , SLOP(500) DUR = I TIME TINT = TIMINC / 60. NTINT = 1.5 * ITIME I F (NTINT .LT. 40) NTINT = 40 NSECS = TIMINC * I TIME 1 6 5 NTPL1 = NTINT + 1 NTIMEP = NSECS / TIMJNC INTER = NTIMEP + 1 NTPLS = NTINT + 1 DO 10 I TINT = 1, NTINT 10 FTLONG(I TINT) = 0.0 DO 30 I TINT = 1 NTPLS DO 20 I SECT = 1, NEND 2 0 DPTH(I SECT,ITINT) = 0.0 30 CONTINUE DO 50 I TINT = 1, NTINT DO 4 0 I SECT = 1 , NEND 40 FLO(ISECT,ITINT) = 0.0 50 CONTINUE C s e t i n i t i a l d e p t h = p r e c i p i t a t i o n e x c e s s DO 60 ISECT = 1, NEND 60 DPTH(I SECT,1) = PRE(I SECT,1 ) DO 210 ITINT = 1, NTINT C c a l c u l a t e s f l o w r a t e from manning's e q u a t i o n NTT = 0 DO 80 ISECT = 1, NEND IF (DPTH(I SECT,I TINT) .LE. 0.0) GO TO 70 FLO(I SECT,ITINT) = 1.486 * (DPTH(I SE C T , I T I N T ) * * 1.67) * (SLOP( 1 ISECT)**0.5) / XMANNN GO TO 80 7 0 FLO(I SECT,I TINT) = 0.0 8 0 CONTINUE ITPL1 = ITINT + 1 DO 200 ISECT = 2, NEND I SMI 1 = I SECT - 1 QIN = FLO(I SMI 1 ,I TINT) QOUT = FLO(I SECT,I TINT) C r o u t i n g w i t h c o n t i n u i t y e q u a t i o n IF ( PRE(ISECT,ITPL1) .LT. 0.0) GO TO 90 PRP = PRE(ISECT,ITPL1) GO TO 100 90 PRP = 0.0 100 YDELT = ((QIN - QOUT)*60.*TINT/SECLEN) + PRP C c a l c u l a t i n g new d e p t h DPTH(ISECT,ITPL1) = DPTH(I SECT,ITINT) + YDELT A IF (PRE(ISECT,ITPL1) .GT. 0.0) GO TO 120 DIF = PRE(I SECT,ITPL1 ) + DPTH(I SECT,ITPL1 ) C PRE i s s u b t r a c t e d i f PRE i s n e g a t i v e C t h i s amount t o be r e - i n f i 1 t r a t e d f o r t h i s DELTAX IF (DIF .LT. 0.0) GO TO 110 PRE'(ISECT,ITPL1 ) = 0.0 DPTH(I SECT,ITPL1 ) = DIF GO TO 120 110 PRE(ISECT,ITPL1) = DIF DPTH(ISECT,ITPL1) = 0.0 120 CONTINUE IF (DPTH(I SECT,ITPL1)) 130, 1 40, 140 130 DPTH(I SECT,ITPL1 ) = 0.0 140 IF (DPTH(I SMI 1,ITPL1 )) 150, 160, 160 150 DPTH(I SMI 1,ITPL1) = 0.0 160 CONTINUE C check t o see i f DEPTH i s not t o o l a r g e A = (DPTH(I SECT,ITPL1) - DPTH(I SECT,ITINT) + DPTH(I SMI 1 ,1TPL1) 1 -DPTH(I SMI 1,ITINT)) * 0.5 / TIMINC B = ( 1 .486*(SLOP(ISECT)**.5)/XMANNN) * (DPTH(I S E C T , I T P L 1 ) * * 1 . r 166 1 33 - DPTH(ISMI1,ITPL1)**1.33) C = (P R E ( I S E C T , I T P L 1 ) + PRE(I SECT,ITINT)) / 2. FH = A + B - C IF (FH .LT. TOLR) GO TO 180 DFH = 0.5 / TIMINC + ( 1 .486*5.*(SLOP(I SECT)**.5)/XMANNN* 3.) * 1 DPTH(I SECT,ITPL1) ** 0.67 DPTH(I SECT,ITPL1) = DPTH(I SECT,ITPL1) - FH / DFH IF (DPTH(I SECT,ITPL1)) 1 70, 160, 1 60 170 DPTH(I SECT,ITPL1) = 0.0 GO TO 160 180 CONTINUE IF (NTT .GT. 0) GO TO 200 IF (DPTH(I SECT,ITPL1) .GT. 0.0) GO TO 190 GO TO 200 190 FTLONG(1TPL1) = (NEND - I SECT) * SECLEN NTT = 1 200 CONTINUE 210 CONTINUE RETURN END APPENDIX B.3 167 C C C C C C C C c c c c c c c c c c c c c c c c 10 20 30 40 50 60 70 80 90 100 1 10 1 20 T h i s code p e r f o r m s d a t a r e d u c t i o n f o r c h a n n e l h y d r a u l i c s t u d i e s . The o r g i n a l code , B r a k e n s i e l ( 1 9 6 6 ) , was m o d i f i e d Engman ( 1 9 7 4 ) . The code as shown i n t h i s t h e s i s was a d a p t e d , by Loague ( 1 9 8 2 ) , f o r use a t UBC. by SLOPC = bed s l o p e of c h a n n e l SLOPR = ground s l o p e i n d i r e c t i o n of f l o w , r i g h t bank SLOPL = ground s l o p e i n d i r e c t i o n of f l o w , l e f t bank ZU1 = d i s t a n c e below zmax (zmax i s maximum d e p t h ) DELN = d i v i s o r f o r c a l c u l a t i o n an e l e v a t i o n i n c r e m e n t XR = c h a n n e l manning's N d i v i d e d by r i g h t bank N XL = c h a n n e l manning's N d i v i d e d by l e f t bank N ZZ = c a r d punch t r i g g e r ( i f .GT. 1.0 p u n c h i n g c a r d s ) XID1 = w a t e r s h e d l o c a t i o n XID2 = i d e n t i f i c a t i o n of s e c t i o n KODE = d i g i t h a v i n g v a l u e of 1 f o r l a s t c a r d KODEi = d i g i t h a v i n g v a l u e of 1 f o r l e f t bank c o o r d i n a t e = d i g i t h a v i n g v a l u e of 2 f o r r i g h t bank c o o r d i n a t e YCOR(I) = h o r i z o n t a l d i s t a n c e of e a c h s u r v e y p o i n t ( r e f e r e n c e d t o an o r g i n a t c e n t e r l i n e of c h a n n e l ) ZCOR(I) = v e r t i c a l e l e v a t i o n of each s u r v e y p o i n t DIMENSION DIMENSION DIMENSION DIMENSION DIMENSION DIMENSION DIMENSION DIMENSION DIMENSION XINT(C,D,E YCOR(500), Y C O R l d ) , AREA( 500,1), ZCOR( 50 0 ) , Z C O R l ( l ) WP( 500,1), X L A ( 1 ) , X L W P d ) , X C A ( l ) , X C W P d ) , XRA ( 1 ) XRWRd), A H Z d ) , W P H Z d ) , AMODd), WPMOD ( 1 ) , TW(l) RH(1), R V R ( 1 ) , R V C ( 1 ) , R V L ( 1 ) , RMOD(1) XKNVR(1), X K N V C ( l ) , XKNVL(1), XKNVT(I) XQNMOd), XQNVT(I), XHYD ( 1 ) XQNHZ(1), XQNVR(1), XQNVC(1), XQNVL(1) YCOR3 ( 5 0 0 ) , ZCOR3(500), XRWPd) DEPTH(1 ) F,G) = C + ((G - E ) / ( F XKNHZ(1 ) XKNMO(1) E) ) (D • * (D - E) / C) 2. (C D) ) XAREA(A,B,C,D,E) = (2.*A - B - C) XWP(A,B,C,D) = SQRT((A - B ) * ( A - B) + (C - D)' XKN(A,B) = 1.486 * (A**0.67) * B XQN(A,B,C) = XKN(A,B) * SQRT(C) LL = 1 IC1 = 0 LS = 0 IC = 0 I = 0 READ (5,30,END=630) SLOPC, SLOPR, SLOPL, ZU1, DELN, XR, XL, ZZ FORMAT (8F8.4) READ IN SECTION DATA CARDS AND SET INDEXS FOR LEFT,RIGHT BANKS, c h a n n e l bottom and max l e f t Y-CORRDINATE 1 = 1 + 1 READ (5,50) XID1, XID2, KODE, KODE1, Y C O R ( I ) , ZCOR(I) FORMAT (2A4, 212, 2F8.2) IF ( Y C OR(I)) 90, 60, 70 LS = LS + 1 GO TO 90 GO TO (80, 9 0 ) , LS YCOR(I) = -YCOR(I) IF ( Y C OR(I)) 100, 110, 120 YCOR2 = YCOR(I) GO TO 120 I LOW = I IF (KODE1 - 1) 150, 130, 140 168 130 I LOB = I GO TO 150 140 I ROB = I 150 IF (KODE) 40, 40, 160 160 NO = I C Y-CORRDINATE r e f e r e n c e d t o l e f t most p o i n t of s e c t i o n N01 = NO - 1 YCOR3(1) = YCOR(1) ZCOR3(1) = ZCOR(1) N02 = 1 DO 190 I = 1, N01 J = I + 1 YCOR3(J) = YCOR(J) ZCOR3(J) = ZCOR(J) IF (YCOR(J)) 170, 180, 170 170 N02 = N02 + 1 GO TO 190 180 I ZERO = N02 + 1 190 CONTINUE I ZER01 = I ZERO - 1 DO 200 K = 1, IZER01 J = 1ZERO - K YCOR(K) = YCOR3(J) 200 ZCOR(K) = ZCOR3(J) K = I ZERO DO 210 L = K, N01 M = L + 1 YCOR(L) = YCOR(M) 210 ZCOR(L) = ZCOR(M) I LOW = I ZER01 I LOB = I ZERO - I LOB I ROB = I ROB - 1 NO = NOI • DO 220 I = 1, NO 220 YCOR(I) = YCOR(I) - YCOR2 C Y-CORRDINATES of out.-of-bank p o i n t s , e l e v d i f f e r n c e i n s e c t i o n , a n d C e l e v c o m p u t a t i o n p o i n t s YL = YCOR(ILOB) YR = YCOR(IROB) IF (ZCOR(ILOB) - ZCOR(IROB)) 230, 230, 240 230 ZL = ZCOR(ILOB) GO TO 250 240 ZL = ZCOR(IROB) 250 IF ( Z C O R d ) - ZCOR(NO)) 260, 260, 270 260 ZMAX = ZCOR(1) GO TO 280 270 ZMAX = ZCOR(NO) 280 ZLOW = ZCOR(ILOW) ZU = ZMAX - ZU1 DELZ1 = (ZMAX - ZLOW) / DELN DELZ = DELZ1 290 GO TO ( 300, 10) , LL 300 I = 1 IC1 = 0 ZCOR1(I) = ZLOW + DELZ IF ( Z C O R l ( I ) - ZMAX) 310, 320, 320 310 DELZ = DELZ + DELZ1 GO TO 330 320 ZCOR1(I) = ZMAX LL = 2 169 C i n i t i a l i z e f o r s e c t i o n c o m p u t a t i o n s 330 K = 1 XRA(K) = 0 . 0 XRWP(K) = 0.0 XCA(K) = 0.0 XCWP(K) = 0.0 XLA(K) = 0 . 0 XLWP(K) = 0.0 TW(K) = 0.0 TW1 = 0.0 TW2 = 0.0 TW3 = 0.0 TW4 = 0.0 C s e c t i o n c o m p u t a t i o n s f o r a r e a , w e t t e d p e r i m e t e r , a n d t o p w i d t h N2 = NO N22 = N2 - 1 DO 48 0 J = 1, N22 IF (ZCOR.(J) - ZCORI(K)) 340, 350, 360 340 IF (ZCOR(J + 1) - ZCOR1(K)) 370, 370, 380. 350 IF (ZCOR(J + 1) - ZCORI(K)) 370, 400, 400 360 I F (ZCOR(J + 1) - ZCOR1(K)) 390, 400, 400 370 AREA(J,K) = XAREA(ZCOR1(K),ZCOR(J),ZCOR(J + 1),YC0R(J + 1),YC0R( 1 J ) ) WP(J.K) = XWP(YCOR(J + 1),YCOR(J),ZCOR(J + 1 ) , Z C 0 R ( J ) ) TW1 = YCOR(J + 1) - YCOR(J) GO TO 4 10 360 YCORl(K) = XINT(YCOR(J),YCOR(J + 1),ZCOR(J),ZCOR(J + l),ZCOR1(K) 1 ) AREA(J,K) = XAREA(ZCOR1(K),ZCORl(K),ZCOR(J),YCOR1(K),YCOR(J)) WP(J,K) = XWP(YCOR1(K),YCOR(J),ZCOR1(K),ZCOR(J)) TW2 = YCOR1(K) - YCOR(J) GO TO 4 10 390 YCORl(K) = XI NT(YCOR(J),YCOR(J + 1 ) , Z C O R ( J ) , Z C O R ( J + l ) , Z C O R l ( K ) 1 ) AREA(J,K) = XAREA(ZCOR1(K),ZCOR1(K),ZCOR(J + l ) , Y C O R ( J + 1 ) , 1 Y C O R l ( K ) ) WP(J,K) = XWP(YCOR(J * 1),YCOR1(K),ZCOR1(K),ZCOR(J + 1)) TW3 = YCOR(J + 1) - YCORl(K) GO TO 4 10 400 AREA(J , K ) = 0.0 WP(J,K) = 0.0 TW4 = 0.0 410 IF (YCOR(J) - YL) 420, 440, 440 420 I F (YCOR(J + 1) - YL) 430, 430, 440 4 30 XLA(K) = XLA(K) + AREA(J,K) XLWP(K) = XLWP(K) + WP(J,K) GO TO 470 440 IF (YCOR(J + 1) - YR) 450, 450, 460 4 50 XCA(K) = XCA(K) + AREA(J,K) XCWP(K) = XCWP(K) + WP(J,K) GO TO 470 460 XRA(K) = XRA(K) + AREA(J,K) XRWP(K) = XRWP(K) + WP(J,K) 4 70 CONTINUE TW(K) = TW(K) + TW1 + TW2 + TW3 + TW4 TW1 = 0.0 TW2 = 0.0 TW3 = 0 . 0 TW4 = 0.0 480 CONTINUE 170 C s e c t i o n c o m p u t a t i o n s f o r t o t a l a r e a . h y d r a u l i c radius,CVY*N,Q*N, C and h y d r a u l i c d e p t h s AHZ(K) = XLA(K) + XCA(K) + XRA(K) WPHZ(K) = XLWP(K) + XCWP(K) + XRWP(K) IF (ZCORl(K) - ZU) 490, 510, 510 490 I F (ZCORI(K) - ZL) 510, 510, 500 500 D = ZU - ZL D1 = ZCOR1(K) - ZL AD = AHZ(K) - XCA(K) WPD = WPHZ(K) - XCWP(K) AMOD(K) = XCA(K) + (Dl/D) * AD WPMOD(K) = XCWP(K) + (Dl/D) * (WPD) GO TO 520 510 AMOD(K) = AHZ(K) WPMOD(K) = WPHZ(K) 520 CONTINUE RH(K) = AHZ(K) / WPHZ(K) IF (XRWP(K)) 530, 530, 540 530 RVR(K) = 0.0 GO TO 550 54 0 RVR(K) = XRA(K) / XRWP(K) 550 I F (XLWP(K)) 560, 560, 570 560 RVL(K) = 0.0 GO TO 58 0 570 RVL(K) = XLA(K) / XLWP(K) 58 0 RVC(K) = XCA(K) / XCWP(K) RMOD(K) = AMOD(K) / WPMOD(K) XKNHZ(K) = XKN(RH(K) ,AH Z(K) ) XKNVR(K) = XKN(RVR(K),XRA(K)) XKNVC(K) = XKN(RVC(K) , XCA(K)) XKNVL(K) = X K N ( R V L ( K ) , X L A ( K ) ) XKNVT(K) = XR * XKNVR(K) + XKNVC(K) + XL * XKNVL(K) XKNKO(K) = XKN(RMOD(K),AMOD(K)) XQNHZ(K) = XQN(RH(K),AHZ(K),SLOPC) XQNVR(K) = XQN(RVR(K),XRA(K),SLOPR) XQNVC(K) = XQN(RVC(K),XCA(K),SLOPC) XQNVL(K) = XQN(RVL(K),XLA(K),SLOPL) XQNVT(K) = XR * XQNVR(K) + XQNVC(K) + XL * XQNVL(K) XQNMO(K) = XQN(RMOD(K),AMOD(K),SLOPC) DEPTH (K) = ZCORI'(K) - ZLOW 590 XHYD(K) = AHZ(K) / TW(K) IC = IC + 1 IC1 = IC1 + 1 IF (ZZ .LE. 1.0) GO TO 610 PUNCH 600, A H Z ( I ) , XQNHZ(I) 600 FORMAT (20X, 2F10.5, 50X) 610 WRITE (6,620) Z C O R 1 ( I ) , D E P T H ( I ) , A H Z ( I ) , XQNHZ(I), WPHZ(I), 1TW(I), XID1, XID2, I C 1 , IC 620 FORMAT (' ', F9.4, 5F10.5, 2X, A4, 2X, A4, 2X, 13, 13) GO TO 290 630 STOP END APPENDIX B.4 1 7 1 C T h i s code p e r f o r m s s t o r a g e f l o o d r o u t i n g w i t h o u t c o e f f i c i e n t s C C The o r g i n a l code . B r a k e n s i e k ( 1 9 6 6 ) , was m o d i f i e d by C Engman (1974). The code as shown i n t h i s t h e s i s C was a d a p t e d , by Loague ( 1 9 8 2 ) , f o r use a t UBC. C C C - l o w e r bound f o r wanted t a b l e C D = upper bound f o r wanted t a b l e C E = l o w e r bound f o r argument t a b l e C F = upper bound f o r argument t a b l e C G = argument C DELT = t i m e i n c r e m e n t used i n r o u t i n g c o m p u t a t i o n s C ( c o n s t a n t ) i n se c o n d s C DELT1 = same as DELT , s a v e d f o r i n i t i a l i z a t i o n C DELA = a r e a i n c r e m e n t i n r a t i n g t a b l e , used t o C e s t a b l i s h an upper of l o w e r bound C DELA = same as DELA , s a v e d f o r i n i t i a l i z a t i o n C TOLR = t o l e r a n c e , i t e r a t i o n c u t o f f C N1 = number of i n f l o w h y d r o g r a p h e n t r i e s C N2 = number of t a b u l a t e d r a t i n g f u n c t i o n e n t r i e s C N5 = 0 r e a d a l l l a t e r a l i n f l o w c a r d s C = 1 no i n p u t - l a t e r a l i n f l o w s a l l z e r o C = 2 l a t e r l a i n f l o w s a l l e q u a l t o one v a l u e ( r e a d ) C ZZ = c a r d punch t r i g g e r ( i f .GT. 1.0 p u n c h i n g c a r d s ) C DIMENSION AREA1(2000), DISCH1(2000), Q 1 ( 2 0 0 0 ) , A 1 ( 2 0 0 0 ) , 1 AREA2(2000) DIMENSION DISCH2(2000), Q 2 ( 2 0 0 0 ) , A 2 ( 2 0 0 0 ) , Q L 1 ( 2 0 0 0 ) , QL2(2000) DIMENSION QN1(2000), QN2(2000) COMMON AREA 1 , NI, I , J , K, M, XI, DELT, DELT1 COMMON N2, X4, X2, DELA, DELA 1 , ANEW", TOLR, X3 : COMMON A l , DELX, QL1, QL2 COMMON QN1, QN2 10 FORMAT ( F 5 . 0 , F8.4) 20 FORMAT (20X, F12.7, 48X) 30 FORMAT (F5.3) 40 FORMAT (20X, 2F10.5, 40X) 5 0 FORMAT (20X, F12.7, 48X) 60 FORMAT (4F5 . 0 , F7.0, 313, F5.0) XINT(C,D,E,F,G) = C + ((G - E ) / ( F - E ) ) * (D - C) READ (5,60) DELT, DELT1, DELA, DELA1, TOLR, N I , N2, N5, ZZ C r e a d f i r s t s e c t i o n r a t i n g and i n f l o w DO 7 0 I = 1, N1 70 READ (5,50) Q 1 ( I ) DO 80 I = 1, N2 80 READ (5,40) AREA 1 ( I ) , QN1(I) IF (N5 - 1) 90, 140, 160 90 DO 130 I = 1, N1 READ (5,20) Q L 1 ( I ) IF ( Q L 1 ( I ) - 100.) 120, 100, 100 100 IKE = I DO 110 IMP = IKE, N1 110 QL1(IMP) = 0.0 GO TO 180 120 CONTINUE 130 CONTINUE GO TO 180 140 DO 150 I = 1, N1 150 Q L 1 ( I ) = 0.0 GO TO 180 160 READ (5,20) QL1(1) N7 = N1 - 1 DO 170 I = 2, N7 17 0 Q L 1 ( I ) = QL1(1) QL1(N 1 ) = 0 . 0 C c a l c u l a t e f i r s t s e c t i o n a r e a s 180 READ (5,30) XN1 WRITE (6,1,90) XN1 190 FORMAT ('1', 15X, 'XN1=', F8.4) DO 200 I = 1, N2 2 00 D I S C H 1 ( I ) = QN1(I) / XN1 210 DO 220 I = 1, NI CALL TBLLP(DISCH1, Q l ) 220 A1(I) = XI NT(AREA 1 (K),AREA 1 ( J ) ,DISCH1 (K),DISCH1 ( J ) , Q 1 ( I )) C r e a d s e c ond s e c t i o n r a t i n g and l a t e r a l i n f l o w LL 1 = 0 ' LL2 = 0 N i l = NI 230 M = NI 240 1 = 1 DELT = DELT1 N 1 = N 1 1 J 1 = N1 + 1 IF (M - NI) 270, 270, 250 250 DO 260 J = J1 , M 260 Q L 2 ( J ) = 0.0 270 CONTINUE DO 280 I = 1, N2 280 READ (5,40,END=670) A R E A 2 ( I ) , QN2(I) IF (N5 - 1) 310, 360, 290 290 READ (5,20) QL2(1) N7 = Ni - 1 DO 300 I = 2, N7 300 Q L 2 ( I ) = QL2(1) QL2(N1) = 0.0 GO TO 380 310 DO 350 I = 1, N1 READ (5,20) Q L 2 ( I ) I F ( Q L 2 ( I ) - 100.) 340, 320, 320 320 IPE = I DO 330 IMP = I P E , NI 330 QL2(IMP) = 0.0 GO TO 380 340 CONTINUE 3 50 CONTINUE GO TO 380 360 DO 370' I = 1 , NI 370 Q L 2 ( I ) = 0.0 C r e a d s e c o n d s e c t i o n i n i t i a l v a l u e ane d e l x 380 I = 1 . READ (5,10) DELX, Q 2 ( I ) READ (5,30) XN2 DO 390 I = 1, N2 390 D I S C H 2 ( I ) = QN2(I) / XN2 I = 1 CALL TBLLP(DISCH2, Q2) A 2 ( I ) = XI N T ( A R E A 2 ( K ) , A R E A 2 ( J ) , D I S C H 2 ( K ) , D I S C H 2 ( J ) , Q 2 ( I ) ) J = 1 N1 = M C r o u t i n g d u r i n g i n f l o w 173 400 ALPHA = ( A 1(I) + A 2 ( I ) ) / 2. I = J + 1 BETA = (DELT/DELX) * Q 1 ( I ) + ( - A I ( I ) + ( D E L T ) * ( Q L 1 ( I ) + Q L 2 ( I ) ) ) / 1 2. XI = ALPHA + BETA IF (XI - TOLR) 410, 410, 430 410 Q 2 ( I ) = Q2(1) A 2 ( I ) = A 2 ( 1 ) DELT = DELT + DELT1 I = I - J J = J + 1 IF ( J - N1) 400, 420, 420 420 I = J GO TO 470 430 CALL SOLVE(DISCHl, DISCH2, Q I , Q2, AREA2, A2) IF ( Q 2 ( I ) - Q2(1) - TOLR) 440, 440, 450 440 Q 2 ( I ) = Q2(1) A 2 ( I ) = A2(1) 450 CONTINUE DELT = DELT1 IF (I - N1) 460, 470, 470 460 J = I GO TO 400 C r o u t i n g a f t e r i n f l o w 470 N3 = 0 480 J = I N3 = N3 + 1 IF ( J - 1 9 9 S ) 510, 490, 490 490 WRITE (6,500) 500 FORMAT (' LATERAL INFLOW TOO LARGE,SUBSCRIPT I > 2000') 510 ALPHA = ( A 1 ( N l ) + A 2 ( I ) ) / 2 . I = J + 1 BETA = (DELT/DELX) * Q1(N1) + ( - A l ( N l ) + DELT*(QL1(N 1) + Q L 2 ( N 1 ) ) ) 1 / 2 . X I = ALPHA + BETA IF ( X I - TOLR) 520, 520, 530 520 Q 2 ( I ) = Q I ( N I ) A 2 ( I ) = Al(N1) GO TO 550 530 CALL SOLVE(DISCH1,DISCH2, Q1, Q2, AREA2, A2) IF ( Q 2 ( I ) - Q1(N1) - TOLR) 520, 520, 540 540 GO TO 480 550 M = M + N3 12 = N I + 1 DO 560 I = 12, M Q L 1 ( I ) = 0.0 Q L 2 ( I ) = 0.0 A 1 (I ) = A l (N1 ) 560 Q I ( I ) = Q I ( N 1 ) LL1 = LL1 + 1 .LL2 = LL1 + 1 C p r i n t out and i n t e r c h a n g e IF (LL1 .GT. 1) GO TO 580 WRITE (6,570) TOLR, XN2, DELT1, DELA, DELX 570 FORMAT (' ', 15X, 'TOLR=' , F8.7, 5X, 'XN2=', F8.4, 5X, 'DELT=' , 1 F10.5, 5X, 'DELA=' , F10.5, 5X, 'DELX=' , F8.0, 5X///) GO TO 600 580 WRITE (6,590) TOLR, XN2, DELT1, DELA, DELX 590 FORMAT ('1', 15X, 'TOLR=' , F8.7, 5X, 'XN2=', F8.4, 5X, 'DELT=' , 1 F10.5, 5X, 'DELA-' ,' F l 0.5, 5X, 'DELX=' , F8.0, 5X///) 174 600 WRITE (6,610) L L 1 , LL2 610 FORMAT (20X, 'IN SECTION NO =', 13, 14X, ' OUT SECTION NO =', 13) WRITE (6,620) 620 FORMAT (24X, ' IN AREA', 6X, ' IN DISCH', 10X, ' OUT AREA', 5X,_ 1 ' OUT DISCH', 10X, 'TOTAL TIME , SECONDS') 630 FORMAT (20X, 2F13.5, 5X, 2F13.5, 15X, F10.0) DO 650 I = 1, M CUMT = DELT1 * FLOAT(I) - DELT1 WRITE ( 6 , 630) A 1 ( I ) , Q 1 ( I ) , A 2 ( I ) , Q 2 ( I ) , CUMT 640 Q L 1 ( I ) = Q L 2 ( I ) , A 1 ( I ) = A 2 ( I ) 650 Q I ( I ) = , Q 2(I) C i n t e r c h a n g e r a t i n g t a b l e s DO 660 I = 1, N2 AREA 1 ( I ) = AREA2(I) 660 D I SCH1(I) = D I S C H 2 ( I ) GO TO 240 670 CONTINUE DO 690 I = 1, M WRITE (8,680) Q1(I) 680 FORMAT (' ', 19X, F l O . 5 , 50X) 690 CONTINUE DO 710 I = 1, M IF (ZZ .LE. 1.0) GO TO 7 20 PUNCH 700, Q 1 ( I ) 700 FORMAT (20X, F10.5, 50X) 710 CONTINUE 720 STOP END SUBROUTINE SOLVE(DISCH1, DISCH2, Q I , Q2, AREA2, A2) . DIMENSION AREA1(2000), DI SCH 1(2000), Q U 2 0 0 0 ) , A 1 ( 2 0 0 0 ) , 1 AREA2(2000) DIMENSION DISCH2(2000) , Q 2 ( 2 0 0 0 ) , A 2 ( 2 0 0 0 ) , Q L 1 ( 2 0 0 0 ) , QL212000 ) DIMENSION QN1(2000), QN2(2000) COMMON AREA 1 , N1 , I , J , K, M, X I , DELT, DELT1 COMMON N2, X4, X2, DELA, DELA1, ANEW, TOLR, X3 COMMON A l , DELX, QL1, QL2 COMMON QN1, QN2 XINT(C,D,E,F,G) = C + ((G - E ) / ( F - E ) ) * (D - C) AU = 0. FAU = 0. AL = 0. FAL = 0. DELA = DELA1 10 A 2 ( I ) = A 2 ( I - 1) 20 CALL TBLLP(AREA2, A2) Q 2 ( I ) = XI NT(DISCH2(K) ,DISCH2(J),AREA2(K) ,AREA2(J) ,A2(I ) ) X2 = (DELT/DELX) * Q 2 ( I ) + ( A 2 ( I ) ) / 2. X2 = X2 - XI IF (X2) 70, 130, 30 30 DELA = DELA1 AU = A 2 ( I ) FAU = X2 I F (AL) 110, 40, 110 40 A 2 ( I ) = A 2 ( I ) - DELA 50 IF ( A 2 ( I ) ) 60, 60, 20 60 DELA = DELA * .5 A 2 ( I ) = A 2 ( l ) + DELA GO TO 50 7 0 DELA = DELA1 175 AL = A 2 ( I ) FAL = -X2 IF (AU) 110, 80, 110 80 A 2 ( I ) = A 2 ( I ) + DELA 90 IF ( A 2 ( I ) - AREA2(N2) ) 20, 20, 100 100 DELA = DELA * .5 A 2 ( I ) = A 2 ( I ) - DELA GO TO 90 110 ANEW = AU - (FAU/(FAU + F A L ) ) * (AU - AL) X3 = ANEW - A 2 ( I ) X3 = ABS(X3) I F (X3 - TOLR) 130, 130, 120 120 A 2 ( I ) = ANEW GO TO 20 130 A 2 ( I ) = ANEW CALL TBLLP(AREA2, A2 ) Q2 ( I ) = XI N T ( D I S C H 2 ( K ) , D I S C H 2 ( J ) , A R E A 2 ( K ) , A R E A 2 ( J ) , A 2 ( I ) ) RETURN END SUBROUTINE TBLLP(A, B) C A=argument t a b l e C B=argument DIMENSION A ( 2 0 0 0 ) , B(2000) DIMENSION AREA1(2000), DI SCH 1 ( 2000 ) , Q1.(2000), A l ( 2 0 0 0 ) , 1 AREA2(2000) DIMENSION DIS C H 2 ( 2 0 0 0 ) , Q 2 ( 2 0 0 0 ) , A 2 ( 2 0 0 0 ) , Q L K 2 0 0 0 ) , QL2(2000) DIMENSION QN1(2000), QN2(2000) COMMON AREA 1 , N1, I , J , K, M, X I , DELT, DELT1 COMMON N2, X4 , X2, DELA, DELA1, ANEW, TOLR, X3 COMMON A l , DELX, QL1, QL2 COMMON QN1, QN2 X4 = B ( I ) IF (X4) 20, 10, 20 10 J = 2 K = J - 1 RETURN 20 DO 40 J = 2, N2 IF ( A ( J ) - X4) 40, 30, 30 30 K = J - 1 RETURN 4 0 CONTINUE WRITE (6,50) 50 FORMAT (' WHOOPS!') RETURN END APPENDIX C R e s u l t s from r a i n f a l l - r u n o f f r e g r e s s i o n a n a l y s i s of s i x Mahantango Creek Subwatershed events (two r a i n gages): C.1 C o r r e l a t i o n m a t rices of nine Mahantango Creek Subwatershed r e g r e s s i o n v a r i a b l e s , with and without data r e d u c t i o n . C.2 Summary of 168 Mahantango Creek Subwatershed l i n e a r r e g r e s s i o n models and t h e i r r e s p e c t i v e v e r i f i c a t i o n e f f i c i e n c i e s . APPENDIX C l Without base flow separation V PPT Y P P T p p T ( B ) P P T , U PPTf," PPT ( D E ) Q p K TQP K V P P T 1.0 w <E ) V P P T .0708 1.0 PPT ( B ) .0138 .1626 1.0 PPT ( E ) .1614 .2876 .0705 1.0 PPTlDB) .7364 .6124 - . 5 0 2 6 - . 4 0 2 2 1.0 PPT ( D E ) .7066 .6401 - . 5 0 5 1 - . 4 5 1 7 .0427 1.0 VQ .3768 .3283 - . 3 8 7 6 - . 4 1 8 0 .7467 .8553 1.0 QPK .8863 .0434 .1466 .2760 .4641 .5023 .0792 1.0 TQP K .1071 .0160 - . 7 7 3 4 - . 7 7 5 3 .6855 .6764 .6902 - . 0 8 1 8 1.0 With base flow separation VPPT V PPT pp T (B) PPT ( B ) PPT(oB) PPT ( D E ) VQ QpK T Q P K V PPT 1.0 w <E> V PPT .9708 1.0 PPT ( B ) .0138 .1626 1.0 WT ( E ) .1614 .2876 .9795 1.0 PPJ (D B) .7364 .6124 - .5926 -.4922 1.0 PPTCDE) .7066 .6491 -.5051 -.4517 .9427 1.0 .8270 .8793 -.0616 .0576 .5639 .6121 1.0 .8864 .9388 .1347 .2687 .4667 .4966 .9507 1.0 .1071 .0160 -.7734 -.7753 .6855 .6764 .1992 -.0750 1.0 APPENDIX C.2 V P P T W (E) V P P T pp T CB) PPT t k ) PPTD B > P P T D E ) Q P K T Q P K 'I • • • • • . 8 8 .93 • • • • . 7 6 . 8 0 • • • • . 8 4 . 8 0 • • • • . 8 4 . 7 3 • • • • . 7 8 . 8 5 • • • . 1 8 . 7 9 • • • . 6 2 . 6 9 • • • . 6 0 . 8 4 • • • . 7 7 . 6 8 • • • . 8 2 . 7 8 • • • . 7 6 . 3 8 • • . 6 8 . 1 4 • • . 7 7 . 1 1 • • . 3 2 . 6 6 • • . 3 8 . 7 3 180 Oi. CM CD CD as CS o n 09 o CO a CO OS OS o 01 OS o o o o as o OS CM CD q o CO o CD CO o o o o o CM as OS a O t- a O >° i ° Q. Q. • • • • • • • • !Q r-a. a. • • • • • • • • • i r— 0. a. • • D >-QL a. • • • • • • • • • Ul a. a, > • • • • • • • • • • • • CD — h- a. >°- • • CM CM k- o CO CO o 00 IO CO eo 00 CO CO CM 00 CM CO CO 00 q CO 00 CO CO -00 CO CO CM «- CD CM CO o CO IO CD CO CO CO CO CN 00 CM CO o CD CO CO CD CO CO o CO co 09 Q. o t - Q. o >° So 1- 0. CL • • • • • • • ta \- 0. Q . • • • • • • • • <*• I J 0. Q . • • • • • • • 1 0 r - Q . a. • • • • • • • +s — a. a. • • * a o. >°- 182 o o • CM 01 CO o 0 CO CM »- • • o o • CM • • o o> T -09 o a> i n O 0. O >° =p 0. • • • • • • w O H OL Q. • • • • • UJ 1 • • • • • c 0 I - Q. QL • • • • • • • UJ - K 0. a > • • • • • CD a. 1 183 W (B) V P P T V P P T P P T ( B ) P P t l t ) PPT D B ) PPT D E ) Q P K T Q P K 2 R 1 'I • • • .82 .82 • • • .73 .73 • • • .73 .73 • • • .77 .77 • • • .48 .48 • • .01 .01 • • .0 .0 • • .47 .47 • • .46 .46 r - Coefficient of extermination r1 - Regression (multiple) models lor •vents 20, 43,43b. 44, 4ft, and 4 « with no baaeflow separation r 2 - Regression (multiple) models for events 20, 43. 43b, 44, 46, and 46 with baaeflow aeparatlon B f - Rain gages 185 APPENDIX D Example implementation of the d i s t r i b u t e d model: D.1 Computer generated s o i l c h a r a c t e r i s t i c curved f o r the Mahantango Creek Subwatershed. D.2 Computer generated l a t e r a l i n f l o w hydrographs f o r D.3 Computer generated normal discharge r a t i n g f u n c t i o n f o r a 1:1.5 p r i s m a t i c t r i a n g u l a r open channel of 2% s l o p e . D. 4 Computer generated open channel flow routin.g f o r Mahantango Creek Subwatershed s e l e c t e d event #16. APPENDIX D.l #2 BERKS (145) SILT LOAM NC THET15 T.HETAE THETA2 PPSI15 PSI1 PSIE PSI2 CONE TF (CM3/CM3) (CM OF WATER) (CM/DAY) DEG.C 48 0.1100 0,3800 0.4700 15306.0 15306.0 6.0 3.0 108.0000 20.0 20.0 CLASS PRESSURE THETA PERMEABILITY CONDUCTIVITY DIFFUSSIVITY DPSI/DTHETA (CM) (CM3/CM3) (CM/DAY) (CM2/DAY .1 15306. 0 0. 1 100 1 . 03E-08 1 . 11E-06 6 . 09E-01 5 . 46E+05 2 13389 . 4 0. 1 1 38 4 . 16E-08 4 . 49E-06 2 . 14E+00 4 . 78E+05 3 10246. 3 0 12 13 9 . 47E-08 1 . 02E-05 3 . 74E+00 3 . 65E+05 4 784 1 . 4 0 . 1288 1 . 81E-07 1 . 96E-05 5 . 47E+00 2 . 80E+05 5 6001 . 1 0. 1363 3 . 18E-07 3 . 43E-05 7 . 34E.+ 00 2 . 14E+05 6 4593 . 1 0. 1438 5 . 32E-07 5 . 75E-05 9 41E+00 1 . 64E+05 7 3515 . 7 0. t5 13 8 . 67E-07 9 . 37E-05 1 . 17E+01 1 . 25E+05 8 2691 . 2 0. 1587 1 . 39E-06 1 . 50E-04 1 . 44E+01 9 . 59E+04 9 2060. 4 0. 1662 2 . 22E-06 2 . 39E-04 1 . 76E+01 7 . 34E+04 10 1577 . 8 0. 1737 3 . 5 1E-06 3 . 80E-04 2 13E+01 5 . 61E+04 1 1 1208 . 4 0. 18 12 5 . 56E-06 6 . 01E-04 2 . 58E+01 4 . 29E+04 12 925 . 8 0. 1887 8 . 80E-06 9 . 50E-04 3 . 12E+01 3 . 29E+04 13 709 . 6 0. 1962 1 . 39E-05 1 . 50E-03 3 . 78E+01 2 . 51E+04 14 544 . 1 0. 2037 2 . 21E-05 2 . 38E-03 4 . 59E->01 1 . 92E+04 15 4 17. 5 0. 2 112 3 . 50E-05 3 . 78E-03 5 . 57E+01 1 . 47E+04 16 320. 7 0. 2 187 5 . 56E-05 6 01E-03 6 . 77E+01 1 . 13E+04 1 7 246 . 5 0. 2262 8 84E-05 9 . 55E-03 8 . 23E+01 8 . 62E+03 18 189 . 8 0. 2337 1 41E-04 1 . 52E-02 1 . 00E+02 6 . 60E+03 19 146 . 4 0. 24 12 2 .24E-04 2 42E-02 1 . 22E+02 5 . 05E+C3 20 113. 2 0. 2487' 3 56E-04 3 .84E-02 1 . 48E+02 3 . 86E+03 2 1 B7 . 8 0 . 2562 5 .64E-04 6 .10E-02 1 . 80E+02 2 95E+03 22 68 , 4 0. 2637 8 .94E-04 9 .65E-02 2 18E+02 2 . 26E + 03 23 53 . 5 0. 27 12 .1 .41E-03 1 .52E-01 2 64E+02 1 73E+03 24 42 . 1 0. 2787 2 .22E-03 2 .39E-01 3 .17E+02 1 . 32E + 03 25 33 . 4 0. 2862 3 .46E-03 3 .73E-01 3 .78E+02 1 .01E+03 26 26 . 7 0. 2937 5 .35E-03 5 .78E-01 4 . 48E+02 7 . 75E+02 27 2 1 6 0. 3012 8 .19E-03 8 .85E-01 5 .25E+02 5 .93E+02 28 17 . 7 0. 3087 1 .24E-02 1 .34E+00 6 .07E+02 4 .54E+02 29 14 . 7 0. 3 162 1 .85E-02 1 .99E+00 6 .93E+02 3 .47E+02 30 12 . 4 0. 3237 2 .71E-02 2 .92E+00 7 .77E+02 2 .66E+02 31 10 . 7 0. 3312 3 .89E-02 4 .20E+00 8 .55E+02 2 .03E+02 32 9 . 4 0. 3387 5 .49E-02 5 .92E+00 9 .22E+02 1 .56E+02 33 8 . 3 0. 3462 7 .57E-02 8 .17E+00 9 .73E+02 1 .19E+02 34 7 . 6 0 . 3537 1 .02E-01 1 .10E+01 1 .OOE+03 9 .11E+01 35 7 .0 0. . 3612 1 .35E-01 1 .46E+01 1 .02E+03 6 .97E+01 36 6 . 5 0. . 3687 1 .75E-01 1 .89E+01 1 .01E+03 5 .33E+01 37 6 . 1 0 . 3762 2 .22E-01 2 .39E+01 3 .48E+02 1 .45E+01 38 5 .9 0. .3837 2 .76E-01 2 .98E+01 4 .86E+02 1 .63E+01 39 5 . 8 0 .3912 3 .37E-01 3 .64E+01 6 .66E+02 1 .83E+01 40 5 . 7 0. . 3987 4 .04E-01 4 .37E+01 8 .98E+02 2 .06E+01 4 1 5 . 5 0 .4062 4 .78E-01 5 .16E+01 1 .19E+03 2' '. 3 1 E +01 42 5 . 3 0 .4137 5 .58E-01 6 .02E+01 1 .56E+03 2 .59E+01 43 5 . 1 0 .4212 6 .44E -01 6 .95E+01 2 .02E+03 2 .91E+01 44 4 .9 0 .4287 7 .36E -01 7 .95E+01 2 .60E+03 3 . 26E+01 45 4 .6 0 . 4362 8 .36E -01 9 .02E+01 3 .31E+03 3 .66E+01 46 4 . 3 0 .4437 9 .43E -01 1 .02E+02 4 .19E+03 4 . 1 1E+01 47 4 .0 0 .4512 1 .06E+00 1 . 14E+02 5 .28E+03 4 .62E+01 48 3 .6 0 .4587 1 . 19E+00 1 .28E+02 6 .64E+03 5 .18E+01 49 3 . 2 0 . 4662 1 . 33E+00 1 .43E+02 8 .34E+03 5 .82E+01 T H E T A E = 0 . 3 8 0 0 Ii2 K I R K S ( 1 4 b ) SI I. I LOAM C L A S S I N I T I A L F LUX ( C M / H R S I ' SORP T I V I I Y ( CM/HRS ' ' 0 . '."> ) 1 9 58E+01 3 04 E ' ()D 2 9 53E+0I 3 03 fc OO 3 9 4 2E '01 2 99 E OO 4 9 30E tOI 2 95 E oo 5 9 18Ft01 2 91E 0 0 6 9 07E+01 2 87E 100 7 8 95E+01 2 83E • OO 8 8 83E+01 2 79E >00 9 8 70E*01 2 75E OO 10 8 58E+OI 2 7 IF ' 0 0 1 1 8 45E+01 2 67E 'OO 12 8 32E+01 2 62F 0 0 13 8 19E *01 2 58E • oo 14 8 ORE tQ1 2 54E ' 0 0 15 7 92E'01 2 4 9 F • OO 16 7 79E+01 2 45E 0 0 17 7 65E+01 2 40E •OO 18 7 50E+01 2 35 E OO 19 7 36E ' 0 1 2 30E • 0 0 20 7 2 1E + 01 2 25E • no 2 1 7 06E +01 2 20E • 0 0 22 6 9 IE «01 2 15E ' 0 0 23 6 75E+01 2 10E • 0 0 24 6 59E+01 2 05 E • 0 0 25 6 43E+01 1 99 E • 0 0 26 6 2GE KM 1 9 IE 0 0 27 6 09E » 0 1 1 HHF • OO 28 5 92E+01 1 82F • Ot) 29 5 75E »G1 1 77F (10 30 5 57EiQI 1 7 1 F o o 3 1 5 39E +01 1 6b F 'OO 32 5 2UE H)1 1 581 l o o 33 5 0 1 F. • 0 1 1 521 t 1 « ) 34 4 82F'Ol 1 4(.l. Mill 35 4 03E<01 1 3'M > o o 36 4 43F*01 1 3 31' I ( lO 37 4 22FMM 1 261 1 o o 38 4 OIOOI 1 I9L 'OO 39 3 7HF K) 1 1 1 1 F M">0 40 :> 55F ' 0 1 1 03F ' IJO 4 1 3 30E ' O 1 9 5 (.)f • 111 4 2 3 04 F • 0 1 8 b'.M -O 1 43 2 761 KM / ('.;)( I) 1 4 4 2 4GF •(.) 1 /Ol (> 1 4 b 2 1 IF t i l l 5 65 f" O 1 Kt(FI/HRS) = 1 4764E-01 F 1 I M / H R S ) FS( F T/HRS • ' 5 ) THETA/THETA2 THE T A M I D I NT . 3 14F *00 9 99E -02 0 2340 O 1 100 3 13F'OO 9 93E -02 0 2500 0 1 138 3 09F'00 9 ROE 02 0 2660 0 12 13 3 05E+00 9 6RE -02 0 28 19 0 1288 3 OIE'OO 9 55E 02 0 2979 0 1363 2 97E+00 9 42E -02 0 3138 0 1438 2 94E'00 9 29E -02 0 3298 0 1513 2 90F <-00 9 16E -02 0 3457 0 1587 2 86E'OO 9 02E -02 0 3617 0 1662 2 8 IE *00 . 8 89 F -02 0 3777 0 1737 2 77E+00 8 7 5F. -02 0 3936 O 18 12 2 73E+00 8 6 1E -02 0 4096 O 1887 2 69E *00 8 47E -02 O 4255 o 1962 2 64F tOO 8 32E -02 0 44 15 0 2037 2 GOEKJO 8 17E -02 0 4574 o 2 112 2 55F *00 8 02E -02 0 4734 o 2 187 2 51F +00 7 87E -02 0 4894 0 2262 2 46F tOO 7 7 IE -02 O 5053 0 2337 2 41E tOO 7 56E -02 0 52 13 0 24 12 2 37F tOO 7 39E -02 0 5372 0 2487 2 32t tOO 7 23E 02 0 5532 0 2562 2 2 7 E t OO 7 06E -02 0 569 1 0 2637 2 21E * OO 6 89E -02 0 5851 0 27 12 2 16EtOO 6 72E -02 0 601 1 0 2787 2 1 IE tOO 6 '54E -02 0 6 170 0 2862 2 05EtOO 6 36E 02 0 6330 0 2937 2 OOF tOO 6 17F -02 o 64 89 0 3012 1 9 IEtOO 5 9RE -02 0 6649 0 3087 1 89ftOO 5 79E 02 o 6809 0 3162 1 R3F.tOO 5 60E -02 o 6968 0 3237 1 7 7 E•OO 5 40E -02 0 7 128 0 3312 1 7 IEtOO 5 20E -02 0 7287 0 3387 1 64E tOO 4 99E -02 0 7447 0 3462 1 58E tOO 4 78E -02 0 7606 0 3537 1 52FtOO 4 57E -02 0 7766 o 36 12 1 45FtOO 4 35E -02 0 7926 0 3687 1 39EtOO 4 13E -02 0 8085 0 3762 t 32F.tOO 3 89E -02 0 8245 0 3837 1 2 4 E'OO 3 G5E -02 o 8404 o 3912 1 16E tOO 3 39E -02 0 8564 0 3987 1 ORE *00 3 12E •02 0 8723 0 4062 ;i 96E-01 2 83E -02 0 8883 o 4137 9 05E-01 2 52E -02 0 9043 0 42 12 R 07E-01 2 20E -02 0 9202 0 4287 7 03E 01 1 85E -02 0 9362 0 4362 188 *4 L E C K K I L L ( 6 6 ) S I L T LOAM NC T H E T 1 5 THETAE T H E T A 2 P P S I 1 5 P S I 1 P S I E P S I 2 CONE TF TM ( C M 3 / C M 3 ) (CM OF WATER) ( C M / D A Y ) D E G . C 48 0 . 1 2 0 0 0 . 3 0 0 0 0 . 3 7 0 0 1 5 3 0 6 . 0 1 5 3 0 6 . 0 6 . 0 3 . 0 7 9 . 0 0 0 0 2 0 . 0 2 0 . 0 C L A S S P R E S S U R E THETA P E R M E A B I L I T Y C O N D U C T I V I T Y D I F F U S S I V I T Y D P S I / D T H E T A ( C M ) ( C M 3 / C M 3 ) ( C M / D A Y ) (CM2/DAY 1 1 5 3 0 5 . 9 0 . 1 2 0 0 4 . 6 8 E - 0 9 3 . 7 0 E - 0 7 3 . 0 3 E - 0 1 8 . 1 9 E + 0 5 2 1 3 3 1 5 . 0 0 . 1 2 2 6 1 . 9 4 E - 0 8 1 . 5 3 E - 0 6 1 . 0 9 E + 0 0 7 . 1 3 E + 0 5 3 1 0 0 7 6 . 4 0 . 1 2 7 8 4 . 6 5 E - 0 8 3 . 6 8 E - 0 6 1 .98E+00 5 . 3 9 E + 0 5 4 7 6 2 5 . 9 0 . 1 3 3 0 9 . 3 6 E - 0 8 7 . 3 9 E - 0 6 3 . 0 2 E + 0 0 4 . 0 8 E + 0 5 5 5 7 7 1 . 6 0 . 1 3 8 2 1 . 7 3 E - 0 7 1 . 3 6 E - 0 5 4 . 2 1 E + 0 0 3 . 0 9 E + 0 5 6 4 3 6 8 . 5 0 . 1 4 3 4 3 . 0 3 E - 0 7 2 . 4 0 E - 0 5 5 . 6 0 E + 0 0 2 . 3 4 E + 0 5 7 3 3 0 6 . 8 0 . 1 4 8 6 5 . 1 9 E - 0 7 4 . 1 0 E - 0 5 7 . 24E + 0 0 1 . 7 7 E + 0 5 8 2 5 0 3 . 4 0 . 1 5 3 9 8 . 7 2 E - 0 7 6 . 8 9 E - 0 5 9 . 21E + 0 0 1 . 3 4 E + 0 5 9 1 8 9 5 . 5 0 . 159 1 1 . 4 5 E - 0 6 1 . 1 5 E - 0 4 1 . 16E + 01 1 . 0 1 E + C 5 10 1 4 3 5 . 5 0 . 1 6 4 3 2 . 4 1 E - 0 6 1 . 9 0 E - 0 4 1 . 4 6 E + 0 1 7 . 6 6 E + 0 4 1 1 1087 . 5 0 . 1 6 9 5 3 . 9 7 E - 0 6 • 3 . 1 4 E - 0 4 1 . 8 2 E + 0 1 5 . 7 9 E + 0 4 12 8 2 4 . 1 0 . . 1 7 4 7 6 . 5 5 E - 0 6 5 . 1 8 E - 0 4 2 . 2 7 E + 0 1 4 . 3 8 E + 0 4 13 6 2 4 . 8 0 . 1 7 9 9 1 . 0 8 E - 0 5 8 . 5 3 E - 0 4 2 . 8 3 E + 0 1 3 . 3 2 E + 0 4 14 4 7 4 . 0 0 . 1 8 5 1 1 . 7 8 E - 0 5 1 . 4 1 E - 0 3 3 . 5 3 E + 0 1 2 . 5 1 E + 0 4 15 3 5 9 . 9 0 . 1 9 0 3 2 . 9 3 E - 0 5 2 . 3 2 E - 0 3 4 . 4 0 E + 0 1 1 . 9 0 E + 0 4 16 2 7 3 . 5 0 1 9 5 5 4 . 8 4 E - 0 5 3 . 8 2 E - 0 3 5 . 4 9 E + 0 1 1 . 4 4 E + 0 4 17 2 0 8 . 2 0 . 2 0 0 7 7 . 9 7 E - 0 5 6 . 2 9 E - 0 3 6 . 8 5 E + 0 1 1 . 0 9 E + 0 4 18 158 , 7 0 . 2 0 5 9 1 . 3 1 E - 0 4 1 . 0 4 E - 0 2 8 . 5 3 E + 0 1 8 . 2 3 E + 0 3 19 12 1 . 3 0 2 111 2 . 1 6 E - 0 4 1 . 7 0 E - 0 2 1 . 0 6 E + 0 2 6 . 2 3 E + 0 3 2 0 9 3 . 0 0 . 2 164 3 . 5 4 E - 0 4 2 . 8 0 E - 0 2 1 . 3 2 E + 0 2 4 . 7 1 E + 0 3 2 1 7 1 . 6 0 . 22 16 5 . 7 9 E - 0 4 4 . 5 7 E - 0 2 1 . 6 3 E + 0 2 3 . 5 7 E + 0 3 22 5 5 . 4 0 . 2 2 6 8 9 . 4 3 E - 0 4 7 . 4 5 E - 0 2 2 . 0 1 E + 0 2 2 . 7 0 E + 0 3 2 3 4 3 . 1 0 . 2 3 2 0 1 . 5 3 E - 0 3 1 . 2 1 E - 0 1 2 . 4 6 E + 0 2 2 . 0 4 E + 0 3 24 3 3 . 9 0 . 2 3 7 2 2 . 4 6 E - 0 3 1 . 9 4 E - 0 1 3 . 0 0 E + 0 2 1 . 5 4 E + 0 3 2 5 2 6 . 8 0 . 2 4 2 4 3 . 9 1 E - 0 3 3 . 0 9 E - 0 1 3 . 6 1 E + 0 2 1 . 1 7 E + 0 3 2 6 2 1 . 5 0 . 2 4 7 6 6 . 1 6 E - 0 3 4 . 8 7 E - 0 1 4 . 3 1 E + 0 2 8 . 8 5 E + 0 2 27 17 . 5 0 . 2 5 2 8 9 . 5 6 E - 0 3 7 . 5 5 E - 0 1 - 5 . 0 6 E + 0 2 6 . 6 9 E + 0 2 2 8 14 . 5 0 . 2 5 8 0 1 . 4 6 E - 0 2 1 . 1 5 E + 0 0 5 . 8 4 E + 0 2 5 . 0 6 E + 0 2 2 9 12 . 2 0 . 2 6 3 2 2 . 1 9 E - 0 2 1 . 7 3 E + 0 0 6 6 2 E + 0 2 3 . 8 3 E + 0 2 3 0 10 . 4 0 . 2 6 8 4 3 . 2 1 E - 0 2 2 . 5 3 E + 0 0 7 . 3 4 E + 0 2 2 . 9 0 E + 0 2 31 9 . 1 0' . 2 7 3 6 . 4 . 6 0 E - 0 2 3 . 6 3 E + 0 0 7 . 9 7 E + 0 2 2 . 1 9 E + 0 2 3 2 8 . 1 0 . 2 7 8 9 6 . 4 4 E - 0 2 5 . 0 9 E + 0 0 ' 8 4 4 E + 0 2 1 . 6 6 E + 0 2 3 3 7 . 3 0 . 2 8 4 1 8 . 8 0 E - 0 2 6 . 9 5 E + 0 0 8 . 7 4 E + 0 2 1 . 2 6 E + 0 2 34 6 8 0 . 2 8 9 3 1 . 1 8 E - 0 1 9 . 2 9 E + 0 0 8 . 8 3 E + 0 2 9 . 5 1 E + 0 1 3 5 6 . 3 0 . 2 9 4 5 1 . 5 3 E - 0 1 1 . . 2 1E + 0 1 8 . 7 2 E + 0 2 7 . 1 9 E + 0 1 3 6 6 . 0 0 . 2 9 9 7 1 . 9 6 E - 0 1 1 . . 5 5 E + 0 1 3 0 5 E + 0 2 1 . 9 7 E + 0 1 37 5 . 9 0 . 3 0 4 9 2 . 4 5 E - 0 1 1 . . 9 4 E + 0 1 4 . . 2 3 E + 0 2 2 . 1 8 E + 0 1 3 8 5 8 0 . 3 1 0 1 3 0 1 E - 0 1 2 . 3 8 E + 0 1 5 . 7 5 E + 0 2 2 4 2 E + 0 1 3 9 5 . . 6 0 . 3 1 5 3 3 . 6 2 E - 0 1 2 . 8 6 E + 0 1 7 6 7 E + 0 2 2 . 6 8 E + 0 1 4 0 5 . 5 0 . 3 2 0 5 4 • 2 9 E - 0 1 3 . . 3 9 E + 0 1 1 . 0 1 E + 0 3 2 9 7 E + 0 1 4 1 5 . . 3 0 . 3 2 5 7 5 0 2 E - 0 1 3 . 9 7 E + 0 1 1 . . 3 1 E + 0 3 3 . 3 0 E + 0 1 4 2 5 . 2 0 . 3 3 0 9 5 8 1 E - 0 1 4 . . 5 9 E + 0 1 1 . 6 8 E + 0 3 3 . G 5 E + 0 1 4 3 5 . . 0 0 . 3 3 6 1 6 6 6 E - 0 1 5 . . 2 6 E + 0 1 2 . . 1 3 E + 0 3 4 . 0 5 E + 0 1 4 4 4 . . 7 0 . 3 4 1 4 7 . 5 6 E - 0 1 5 . . gsE '+oi 2 . 6 8 E + 0 3 4 . 4 9 E + 0 1 4 5 4 . 5 0 . 3 4 6 6 8 . . 5 4 E - 0 1 6 . 7 5 E + 0 1 3 . . 3 6 E + 0 3 4 . 9 8 E + 0 1 4 6 4 . . 2 0 . 3 5 1 8 9 . 5 9 E - 0 1 7 , 5 7 E + 0 1 4 . . 1 8 E + 0 3 5 . 5 2 E + 0 1 4 7 3 . 9 0 . 3 5 7 0 1 0 7 E + 0 0 8 . 4 7 E + 0 1 5 . . 1 9 E + 0 3 6 . 12E + 01 4 8 3 . 6 0 . 3 6 2 2 1 . . 2 0 E + 0 0 9 . 4 5 E + 0 1 6 . 4 1 E + 0 3 6 . 79E + 01 4 9 3 . 2 0 . 3 6 7 4 1 . . 3 3 E + 0 0 1 . 0 5 E + 0 2 7 . . 9 3 E + 0 3 7 . 5 2 E + 0 1 C J x. ai cn - J cc I O C - M C J i- Ln cn - J co to to O - ro oo x. £ 'J uj u i U i r j i > i > i » o t s > i < 5 i u i * . u i o - i D O i c n i . r o o O > o i a m m r r m m m m m m r r r r m r r m m r r m r n m r n m r n r n r r , n rr + +. + + 4.*4.* + r+- + f + + + + * + + + + + i * X o o o o o o o o o c o o c o c o o o o o o o c c o o t > i f f l - u i . m ' > i i i O M u i . w < ! i a - r o u t u i ' a i ^ B o o - r o u t i j ^ c x o — o o o m r o c r c o - J — ' » O " " 3 1 O i m m rr. rr m m r i + . » • * + + • + • + + • * * - + ' + • * • + c o o o o o c o o o o o o o c o o o . C C J I C J V C X I - O - O C O C E C O C O — — - * - » - » — — — - - u u ro w ro o o o i N i t f l t n O c n — ffi — t D C O C • 'o ro u - i m O - O i . ^ - J U ' C O u ' O u ^ y 'O c o u t ^ u i L" j i j i c ^ 3 i < - J < c o 3 ) i a ] C D C o c o O O X ' j c J i x - i - J O - O C r j - ^ C ' J T ci ffl c. n c o o o o m rr, rr rr m rr m m m m rr O O O Ĉ  O Z- O C O O C C C- ~ C O C O O O O C O n —< r— X ro —• m > m Z . II O > I- CJ C -n o on o- r- o O CD C X «. •—- o o n ' \ ~ r — X3 L E  * 30 r - r— < — ro ro Ci •5) o c -< —- ! -r -r (—i * r — ', "~ — 7Z c > — — ro ro fO ro ro N J ro C O C O O O C - - -o >Z ro o- — i O co ui ul i . C J l f f l J l ^ C C X C C L C - - - - ' - - * - - ' - 1 - ' - ' " ' " ' " ' " ' " ' " ' - " ' ' ' " ' " - - " * - £ * £ m m £ 8 m m m S m rr rr, m rr rr, m rr rr m m r r m rr. m m rr. m rr m m rr rr rr .̂ . + . ; i c o o o o o o c o o c g o g - ^ - ^ . o u u r o u u u c o u u u u u t t i - t i i i t . J i u i o i u i a r m t n i o i ^ o 5 i o i e i o < T > _ m c n < r i < J i a i r o ' c J l ^ C C - U U l f f l C O C - C J J C . U l ^ C O ^ s s s s s s s s s s s s s s s s s s s s s ^ O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O S g s S 5 S s s = i s s S § s a s S s s § = CO CD o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o > o 68T \ 190 <»5 HARTLETON (54) SILT LOAM NC THE T15 THETAE THETA2 PPSI15 PSI1 PSIE PSI2 CONE TF TM (CM3/CM3) (CM OF WATER) (CM/DAY) DEG.C 48 0.1200 0.3400 0.4200 15306.0 15306.0 6.0 3.0 58.0000 20.0 20.0 CLASS PRESSURE THETA PERMEABILITY CONDUCTIVITY DIFFUSSIVITY DPSI/DTHETA (CM) (CM3/CM3) (CM/DAY) (CM2/DAY 1 15306 . 0 0 . 1200 6 .39E-09 3 .71E-07 2 .48E -01 6 .70E+05 2 1 3348 . 7 0 .1231 2 .62E-08 1 .52E-06 8 .88E-01 5 . 84E + 05 3 10153 . 3 0 . 1294 6 .17E-08 3 .58E-06 1 .59E+00 4 .44E+05 4 7723 . 1 0 . 1356 1 .22E-07 7 .06E-06 2 .39E+00 3 .38E+05 5 5874 . 9 0 .14 19 2 .20E-07 1 .28E-05 t 3 .28E+00 2 .57E+05 6 4469 . 2 0 .148 1 3 .80E-07 2 .20E-05 ' 4 .30E+00 1 .96E+05 7 3400 . 2 0 . 1544 6 .37E-07 3 .69E-05 5 .49E+00 1 .49E+05 8 2587 . 1 0 . 1606 1 .05E-06 . 6 .09E-05 6 .89E+00 1 .13E+05 9 1968 . 8 0 . 1669 1 .72E-06 9 .96E-05 8 .56E+00 8 .60E+04 •10 1498 . 5 0 .1731 2 .79E-06 1 .62E-04 1 .06E+01 6 . 54E + 04 1 1 1 140 . 9 0 . 1794 4 .53E-06 2 .63E-04 1 .31E+01 4 .97E+04 12 868 . 9 0 . 1856 7 .34E-06 4 . 26E-04 1 .61E+01 3 .78E+04 13 662 .0 0 .19 19 1 .19E-05 6 .90E-04 1 .98E+01 2 .88E+04 14 504 . 7 0 . 198 1 1 .93E-05 1 .12E-03 2 . 45E + 01 2 .19E+04 15 385 .0 0 . 2044 3 .13E-05 1 .81E-03 3 .02E+01 1 .66E+04 16 294 .0 0 . 2 106 5 .07E-05 2 .94E-03 3 .72E+01 1 .27E+04 1 7 224 . 8 0 . 2 169 8 .23E-05 4 .77E-03 4 .59E+01 9 .63E+03 18 172 . 2 0 . 223 1 1 .33E-04 7 .74E-03 5 .67E+01 7 .32E+03 19 132 . 1 0 . 2294 2 .16E-04 1 .25E -02 6 .99E+01 C .57E+03 20 101 . 7 0 . 2356 3 .50E-04 2 .03E-02 8 .60E+01 4 .23E+03 2 1 78 . 5 0 .24 19 5 .65E-04 3 .28E-02 1 .06E+02 3 .22E+03 22 60 . 9 0 . 248 1 9 .10E-04 5 .28E-02 1 .29E+02 2 . 45E+03 23 47 . 5 0 . 2544 1 .46E-03 8 45E-02 1 .57E+02 1 . 86E + 03 24 37 . 3 0. . 2606 2 .32E-03 1 .35E-01 1 .91E+02 1 . 42E + 03 25 29 6 0. 2669 3 66E-03 2 .13E-01 2 .29E+02 1 . .08E+03 26 23 . 7 0. 2731 5 .73E-03 3 .32E-01 2 .72E+02 8 . 19E+02 27 19 . 2 0. 2794 8 .84E-03 5 . 13E-01 3 .20E+02 . 6. 23E+02 28 15 . 8 0. 2856 1 .35E-02 7 . 80E-01 3 .70E+02 4 . 74E+02 29 13 . 2 0. 29 19 2 . 01E-02 1 . 17E+00 4 .21E+02 3 . 60E+02 30 1 1 . . 3 0. 2981 2 . 95E-02 1 . 71E+00 4 , .70E+02 2 . 74E+02 3 1 9 . 8 0. 3044 4 . 24E-02 2 . 46E+00 5 . 13E+02 2 . 09E+02 32 8 . 6 0. 3106 5 . 96E-02 3 . 46E+00 5 . 48E+02 1 . 59E+02 33 7 . 8 0. 3169 8 . 19E-02 4 . 75E+00 5. 73E+02 1 . 21E+02 34 7 . 1 0. 3231 1 . 10E-01 6 . 38E+00 5 . 85E+02 9 . 17E+01 35 6 . 6 0. 3294 1 . 44E-01 8 . 38E+00 5 . 84E+02 6 . 98E+01 36 6 . 1 0. 3356 1 . 86E-01 1 . 08E+01 1 . 73E+02 1 . 61E+01 37 6 . 0 0. 34 19 2 . 34E-01 1 . 36E+01 2 . 43E+02 1 . 79E+01 38 5 . 8 0. 3481 2 . 89E-01 1 . 68E+01 3 . 35E+02 1 . 99E+01 39 5 . 7 0. 3544 3 . 51E-01 2 . 03E+01 4 . 52E+02 2 . 22E+01 40 5 . 6 0. 3606 4 . 18E-01 2 . 43E+01- 6 . 01E+02 2 . 48E+01 4 1 5 . 4 0. 3669 4 . 92E-01 2 . 85E+01 7 . 87E+02 2 . 76E+01 42 5 . 2 0. 3731 5 . 71E-01 3. 31E+01 1 . 02E+03 3 . 08E+01 43 5. 0 0. 3794 6 . 56E-01 3 . 80E+01 1 . 30E+03 3. 43E+01 44 4 . 8 0. 3856 7 . 47E-01 4 . 33E+01 1 . 66E+03 3 . 82E+01 45 4 . 5 0. 3919 8 . 46E-01 4 . 90E+01 2 . 09E+03 4 . 26E+01 46 4 . 3 0. 3981 9. 51E-01 5 . 52E+01 2 . 62E+03 4 . 74E+01 47 3 . 9 0. 4044 1 . 07E+00 6 . 18E+01 3 . 27E+03 5 . 29E+01 48 3 . 6 0. 4 106 1 . 19E+00 6 . 91E+01 4 . 07E+03 5 . 89E+01 49 3 . 2 0. 4 169 1 . 33E+00 7 . 72E+01 5 . 07E+03 6 . 57E+01 191 O — T c c o ) — Ticcn — 91c 01 • • T 10 o — t » rji - ^ c a c i — ^ I O C I O — rrioo">"-'rioo)"-'Tioo)"-'Tcooi Ococnin — c o r r o i o n c n i n — co-TOioocnin — co^Oiococnin — o ^ O i o o c N C N C N C O ' T T i n i o t o r ^ o c o o i o i O — r < N n ^ T ^ l n B ^ o ^ ^ o r J 1 ( 7 ) 0 ' - • - ( N ( ^ l n ^ J ' I l n l I l U l ^ ^ • o ( I l " ' " " " ' " ' " ' ' ' ' ' n n n n i N n N n n n i c N N N n r i i n n n n n n n n o n n n n n n o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o ID in CN — O o CO 10 in m CN O 01 CO r- to in c i CN — o CT) co m r> .- O 01 co r- in *T Cl CN ,_ 0) CO co in in O LO O LO O in cn 01 0) T 01 T CO n co to CO n CO Cl CO CN r- CN r- CN CN r- 10 CO 10 CO o in O in c CO O n ID r~ CO o *~ to T ID r~ 01 O CN r> in 10 CO 01 CN *r cn r- co O co CO r- 0) o CN co LO CO CO m CN CN n o n r> c-> co *T in in in in in in in u> LO CO 10 10 CO r~ r- r- r- CO CO CO CO co co co 0) 01 01 o O O O o O O O o o o o o O O O O O O O O O o o O O O O O O O O O O O O O O O o O O O O O CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN O O O O G o O o O O O O O o O O O o O o O cu LU LU UJ UJ UJ UJ UJ UJ UJ UJ UJ LU UJ Lu LU UJ UJ LU Lu UJ LU CN cc C CN n LO 10 cc O ~- CN co CO T T ~- T ro ro CN in to CN — O 0) i 00 r- ID cn Cl CN *~ O 01 CO to 10 10 10 10 10 CO CO in m in LO in in in LO in in in T T CN CN CN CN CN CN CN CN CN CN CN CN CN CN C N C N C N CN C N C N C N C N C N c o o C o o O O o O O o C O Q p O O o o o 0 o LU UJ UJ UJ UJ UJ UJ LU UJ LU UJ UJ LU U J U J U J U J U J U J U J U J U J '— 01 00 O r ? CN 0) r- T — r~ T O — LO O <N LP LP Cl — co CN o 01 r ~ to LO CN O CO L T n CN c X LD rr C N T rt T T co ro co co Cl co co C N CN c\ C N C N C N — —• — O o O C O O O o O C O O O o O O o o o O O 0 O c O o o o O O o o o O O o o o o Q 0 + » * •r •*• * » * * •*• + + + 4- * -» 4. UJ U_ UJ UJ UJ - J UJ UJ UJ U-' UJ UJ UJ u- UJ L U L U L U UJ UJ CN o r- CN o !-- LP CN c- — cc LO CN 01 CO n , ^ O O C cn at Cl •31 CO x . X r- '•0 to to LO L O IT. CN CN O 0 O 0 0 O O O 0 O O 0 O c O 0 0 O O c 0 c C 0 O O O O O 0 O c O O O •* — •* •* + •*• 4- * 1 1 • 1 1 UJ UJ UJ u-- UJ UJ L U UJ UJ UJ LL,' 'jJ UJ UJ UJ UJ U J U J UJ :aJ n O J) ui C N X T '«£ C N to C N LP C »- Q C N *T n C N C N C N — 0 n J) n T r; '- — o o o o c o o o o o o o o o c o o o ^ * ^ * * » * * + U U j U U ' U L J U J t U U o i r ^ i n c N O r ^ L O r N O o i o i o i o i o i c o c o c o x •0 o c c e o c c c o x to Co O r-r-r-iotOtOcOLOLOLOT O O O C O O ^ — *r rr rt n n O C C C C O C r- 71 01 c C N x <N O . - - - O 01 LO — r» r~ CN O l W O l c O C O r - r - l C ' J J O O O O O O O O O O O O O O O O O O O O O O C O O C O O O O O O O C O O O O O O C- c~ ̂  " G + + + + + + + + + + + + + + + + + + + + + U J U J L U U J L U m u J U J U J l u L U U J L u L U l U U J l x J W W U J U J L U U J U J U J L ^ O t o o i C N ^ r t o o i ^ n i n t o c c O ^ C N c o r T L O c o c O ' ^ c o t o t O i n * T c o c N - - c r c c - o p c o ' - c c ' o r , c c ~ ^ ^ - * , - . ^ -CN — 0 0 0 ) c o r ~ r - c O L O T C O n c N — O O i o o r - t o j i ' d n c N — o c j ! f l o ^ i r ) i n n r o i > i n r ^ ' j i ! » ^ ! ; ; l O i c i f l t s i n L T i n i n i n i n i n i n i n i f i i f i i r i ^ ' r ' j ' i ' r ^ ^ ' r ' i ' j p i n c i r , n n n n r < M r < n c i « r ( - - - - r c ^ l n ^ t q l s ^ o f f l O r c ^ l ^ 7 l n l C ^ o o l O - c N n 7 l D c B ^ c o ^ O ' c \ n T l ^ l t ^ c c a l O • • c ^ n ' t l . • ! ^ r r r ^ ^ ^ ^ ^ ^ ^ N M n ( N C N n n c N n n n n r i n n n n n n , 7 r r , : i i : ^ 1 9 2 *7 ALBRIGHTS (71) SILT LOAM NC THET15 THETAE THETA2 PPSI15 PSI1 PSIE PSI2 CONE TF TM (CM3/CM3) (CM OF WATER) (CM/DAY) DEG.C 48 0.1400 0.3400 0.4300 15306.0 15306.0 6.0 3.0 23.0000 20.0 20.0 CLASS PRESSURE THETA PERMEABILITY CONDUCTIVITY DIFFUSSIVITY DPSI/DTHETA 1 2 3 4 5 6 7 8 9 10 1 1 1 2 13 14 15 16 17 18 19 20 2 1 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 4 1 42 43 44 45 46 47 48 49 (CM) 15306.0 13233 . 6 9892 . 8 7395 . 7 5529 . 2 4134 . 1 309 1 . 4 2311.9 1729 . 3 1293 . 9 96S 725 543 407 305 229 . 8 173.0 1 30 95 75 57 44 34 26 2 1 17 14 11.8 10. 1 8 . 8 9 1 6 1 0 9 8 6 5 3 2 0 8 6 4 1 (CM3/CM3) 1400 1430 149 1 155 1 16 1-1 1672 1732 1793 1853 0. 1914 0.1974 O.2034 0.2095 0.2155 0. 2216 0. 2276 0. 2336 O.2397 0.2457 0.2518 0.2578 O.2639 0.2699 0.2759 0 . 2820 0. 2880 . 294 1 3001 306 1 3122 3 182 3243 3303 3364 3424 3484 3545 3605 3666 3726 3786 3847 3907 3968 4028 4089 8 0.4149 5 0.4209 2 0.4270 1  ) (CM/DAY ) (CM2/DAY 3.84E-09 8.84E-08 6.52E -02 7.37E+05 1.60E-08 3.67E-07 2.34E-01 6.37E+05 3.87E-08 8.90E-07 4.24E-01 4.76E+05 7.88E-08 1.81E-06 6.45E-01 3.56E+05 1.48E-07 3.39E-06 9.03E-01 2.66E+05 2.64E-07 6.07E-06 1.2 1E+00 1 .99E + 05 4.60E-07 1.06E-05 1.57E+00 \,49E+05 7.90E-07 1.82E-05 2.02E+00 l'. 1 1E + 05 1.34E-06 3.09E-05 2.57E+00 8.31E+04 2.28E-06 5.24E-05 3.25E+00 6.21 E + 04 3.85E-06 8.85E-05 4.11E+00 4.64E+04 6.50E-06 1.49E-04 5.19E+00 3.47E+04 1.10E-05 2.52E-04 6.54E+00 2.59E+04 1.85E-05 4.26E-04 8.25E+00 1.94E+04 3.12E-05 7.19E-04 1.04E+01 1.45E+04 5.27E-05 1.21E-03 1.31 E + 01 1.08E+04 8.89E-05 2.04E-03 1.65E+01 8.09E+03 1.50E-04 3.44E-03 2.08E+01 6.05E+03 2.51E-04 5.78E-03 2.62E+01 4.52E+03 4 , 2 1 E-04 9.69E-03 3 27E+01 3.38E+03 7.03E-04 1.62E-02 4.08E+01 2.53E+03 1.16E-03 2.68E-02 5.06E+01 1.89E+03 1.91E-03 4.40E-02 6.22E+01 1.41E+03 3.12E-03 7.17E-02 7.56E+01 1.06E+03 5 . 0 1E-03 1.15E-01 9.08E+01 7.89E+02 7.92E-03 1.82E-01 1.07E+02 5.89E+02 1.23E-02 2.83E-01 1.25E+02 4.41E+02 1.87E-02 4.30E-01 1.42E+02 3.29E+02 2.78E-02 6.39E-01 1.57E+02 2.46E+02 4.03E-02 9.26E-01 1.70E+02 1.84E+02 5.68E-02 1.31E+00 1.80E+02 1.38E+02 7.82E-02 1.80E+00 1.85E+02 •1 .03E+02 1.05E -01 2.41E+00 1.85E+02 7 .68E + 01 1.37E-01 3.16E+00 4.60E+01 - 1 .46E+01 1.76E-01 4.05E+00 6.47E+01 1.60E+01 2.20E-01 5.06E+00 8.88E+01 1.75E+01 2.69E-01 6.20E+00 1.19E+02 1.93E+01 3.24E-01 7.45E+00 1.57E+02 2.11E+01 3.83E-01 8.81E+00 2.04E+02 2.32E+01 4.47E-01 • . 1.03E+01 2.62E+02 2.55E+01 5.15E-01 1.19E+01 3.31E+02 2.79E+01 5.89E-01 1.35E+01 4.15E+02 3.07E+01 6.67E-01 1.53E+01 5.16E+02 3.36E+01 7.50E-01 1.72E+01 6.37E+02 3.69E+01 8.39E-01 1.93E+01 7.82E+02 4.05E+01 9.34E-01 2.15E+01 9.55E+02 4.45E+01 1.04E+00 2.38E+01 1.16E+03 4.88E+01 1.15E+00 2.64E+01 1.41E+03 5.36E+01 1.27E+00 2.92E+01 1.72E+03 5.88E+01 THETAE = 0.3400 "7 CLASS INITIAL FLUX(CM/HRS) 1 3 54E»0 1 2 3 52E*01 3 3 18E+01 4 3 44E+01 5 3 39E*01 6 3 35E+01 7 3 30E*01 8 3 26E+01 9 3 21E+01 IO 3 17E+01 1 1 3 12E+01 12 3 07E+01 13 3 02E+01 14 2 97E+01 15 2 92E+01 16 2' 87E+01 17 2 82E+01 18 2 76E+01 19 2 7 1E+01 20 2 65E+01 2 1 2 60E+01 22 2 54E+01 23 2 48E+01 24 2 42E+01 25 2 36E+01 26 2 30E «01 27 2 23E+01 28 2 17E+01 29 2 10E+01 30 2 04E+01 3 1 1 97E+01 32 1 90E+01 33 1 83E »01 34 1 76E *01 35 1 69E »01 36 1 .6-1001 37 1 .53E»01 38 1 •» -1E • 0 1 39 1 . JGE-K) 1 40 1 . 26E+01 4 1 1 . 1 7 O 0 1 42 1 . 0CiO01 4 3 9 .57E*00 44 8 . 4 31: K.K.) 4 5 7 . 2JOOO ALHKlCMrS (7 1) SILI LOAM SORPTI VIT Y(CM/HRj••0.5) 1 1'JEUJO 1 ME-tOO 1 13E tOO 1 1 1E 10 0 1 10E t()(j 1 08E+00 1 07E tOO 1 05Et00 1 04 Ft 00 1 02E+0G 1 01E*00 9 9 1F-01 9 7GE-01 9 5HE 01 9 4 11: 0 1 9 24E-0 1 9 07E-01 8 89E-01 8 7 1 E 01 8 52E-01 8 33E-01 8 ME -01 7 95E-01 7 75E-01 7 54 E Ol 7 34E-01 7 13E-01 6 9 1E-01 6 C.9E-01 6 47E-01 6 25E-U1 6 02 E - 01 5 79E- 01 5 55F. -0 1 5 3 0 E 0 1 5 O l L - 01 4 77E-01 4 I9F -Ol 4 I'OL - 0 1 3 H9E-01 3 571 - 0 1 3 ? 3 E - 0 1 2 . 87E-01 2 .49E -U1 2 .09E - o 1 KLM FT/MRS) = 3 FKFI/HHS) FS( FT/HRS' *. 5 ) 16E tOO 3 77E -02 KiE-tOO 3 75E -02 ME tOO 3 70E -02 13E+00 3 65E -02 1 I E 10 0 3 6 IE -02 101tOO 3 56E -02 08EtOO 3 5 1E -02 07 F * 00 3 46E -02 05E+00 3 4 IE -02 OIF tOO 3 36E -02 02f. tOO 3 3 1E -02 01E t OO 3 25E -02 9 IE-01 3 20E -02 75E 01 3 ME -02 5HE-01 3 09E -02 11F.-01 3 03E -02 2 IE -O 1 2 97E -02 9 06E-01 2 92E -02 8 8RE-01 2 86E -02 8 70E-01 2 80E -02 8 52E-01 2 73E -02 8 33E-01 2 67E -02 8 14 F - 01 2 6 IE -02 7 94E-01 2 5 IE -02 7 7 4 F - 0 1 2 48E -02 7 54E-01 2 4 IF. -02 7 33E-01 2 34 E -02 7 12E-01 2 2 7E -02 6 90E-01 2 20E -02 6 69E-01 2 12E -02 6 46E-01 2 05E -02 6 24E-01 1 97E -02 6 OIF.-01 1 90E -02 5 77E-01 1 82E -02 53E-01 1 74E -02 5 2HE-01 1 6SE -02 5 01E-01 1 57E -02 4 74E-01 1 47E -02 4 .45E 01 1 . 3BE -02 4 ME -Ol 1 . 28E -02 3 . B3I -01 1 . 1 7E -02 ;i . 491- -Ol 1 . OGE -02 j . ME -01 9 . 4 2E -03 2 77E-01 8 . 1 7 E -03 o 37E-01 6 . 86E -03 1441E-02 T HE TA/THE TA 2 THETA MID. INT. 0. 3256 0. MOO 0. 3396 0. 14 30 0. 3537 0. 149 1 0. 3677 0. 1551 o. 38 18 0. 161 1 0. 3958 0. 1672 0. 4099 0. 1732 0. 4239 0. 1793 0 4380 0. 1853 o 4520 0. 19 14 0 4661 0. 1974 0 4801 0. 2034 0 4942 0. 2095 0 5082 0. 2 155 o 5223 0. 22 16 o 5363 0. 2276 0 5504 0. 2336 0 5644 0 2397 0 5785 0. 2457 0 5925 0. 2518 0 6066 0 2578 0 6206 o 2639 0 6347 0 2699 0 6487 0 2759 0 6628 0 2820 o 6768 0 2880 o 6909 0 294 1 0 7049 0 3001 0 7 190 o 306 1 0 7330 0 3122 o 747 1 0 3182 o 76 1 1 0 3243 0 7752 0 3303 0 7892 0 3364 0 8033 0 3424 0 8 173 0 3484 0 8314 0 3545 o 8454 o 3605 0 8595 0 3666 0 8735 0 3726 0 8876 0 3786 0 9016 0 3847 0 . 9 157 0 3907 0 .9297 0 3968 0 . 9438 o .4028 194 »8 MECKENSVILLE (G9 ) SILT LOAM NC THET15 THETAE THETA2 (CM3/CM3 ) P P S I 1 5 . P S I 1 PSIE PSI2 CONE TE (CM OF WATER) (CM/DAY) DEG.C TM 48 0.1800 0.3100 0.3900 15306.0 15306.0 6.0 3.0 23.0000 20.0 20.0 CLASS PRESSURE THETA PERMEABILITY CONDUCTIVITY DIFFUSSIVITY DPSI/DTHETA 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 1 7 18 19 20 2 1 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 4 1 42 43 44 45 46 47 48 49 (CM) 15305 13015 94 12 6807 4923 356 1 2576 1864 1 349 977 707 5 1 3 372 270 197 143 105 77 57 43 32 24 19 15 12 10 8 7 7 6 . 6 5 . 5 . 5 . 5 . 5 . 5 . 5 . 5 . 5 . 4 . 4 . 4 . 4 . 4 . 3 . 3 . 3 . 3 . (CM3/CM3) . 9 0 . 1 8 0 0 .8 0.1822 .4 0.1866 .10.19C9 .2 0.1953 0. 1997 0 . 204 1 0. 2084 O. 2 128 0.2 172 22 16 2259 2303 2347 239 1 243J 2J78 2522 2566 2609 0 . 2653 0 . 2697 0.274 1 2784 2828 2872 29 16 2959 1 0.3003 5 0.304 7 309 1 3 1 34 3178 3222 3266 3 309 3353 3397 3441 3484 3528 3572 36 16 3659 3703 3747 3791 3834 3878 !3 (CM/DAY ) (CM2/DAY 1 .45E-09 3 .33E-08 3 .78E-02 1 .13E+06 6 .20E-09 1 .43E-07 1 .37E-01 9 . 64E+05 1 .59E-08 3 .66E-07 2 .55E-01 6 .97E*05 3 .46E-08 7 .97E-07 4 .02E-01 5 .04E+05 6 .98E-08 1 . 6 1 E - 0 6 5 .85E-01 3 .65E+05 1 .35E-07 3 .11E-06 8 .19E-01 2 .64E+05 2 .55E-07 5 .87E-06 1 .12E+00 1 .91E+05 4 .76E-07 1 .10E-05 1 . 51E+00 1 .38E+05 8 .83E-07 2 .03E-05 2 .02E+00 9 .96E+04 1 .63E-06 3 .75E-05 2 . 70E+00 7 . 20E-"-04 3 .OOE-06 6 .89E-05 3 . 59E + 00 5 .21E*04 5 .51E-06 1 .27E-04 4 . 77E->00 3 .77E+04 1 .01E-05 2 .33E-04 6 . 33E+00 2 .72E+04 1 .85E-05 4 .26E-04 8 . 39E + 00 1 .97E+04 3 .39E-05 7 .80E-04 1 . 1 1E+01 1 .42E+04 6 .19E-05 1 .42E-03 1 .47E+01 1 .03E+04 1 .13E-0J 2 .59E-03 1 . 93E+01 7 .44E+03 2 .C4E-C4 4 .70E-03 2 . 53E+01 5 . 38E + 03 3 .6BE-04 8 .46E-03 3 . 29E + 01 3 .89E+03 6 .57E-04 1 .51E-02 4 . 25E + 01 2 .81E*03 1 .16E-03 2 .67E-02 5 . 43E + 01 2 .03E+03 2 .02E-03 4 .64E-02 6 . 83E+01 1 .47E+03 3 .45E-03 7 .94E-02 8 . 4 4 E * 0 1 1 .06E+03 5 .77E-03 ' l .33E-01 1 .02E+02 7 .69E+02 9 .41E-03 2 .16E-01 1 .20E+02 5 .56E+02 1 .49E-02 3 .43E-01 1 .38E+02 4 .02E+02 2 .29E-02 5 . 26E-01 1 .53E+02 2 .91E+02 3 40E-02 7 .82E-01 1 , 64E+02 2 . 10E+02 4 . 89E-02 1 , 13E+00 1 . 71E+02 1 . 52E+02 6 . 82E-02 1 . 57E+00 1 . 72E+02 1 . 10E*02 9 . 22E-02 2 . 12E+00 3 . 62E+01 1 . 70E+01 1 . 21E-01 2 . 79E+00 5 . 13E+01 1 . 84E+01 1 . 55E-01 3 . 56E+00 7 . 07E+01 1 . 98E+01 1 . 93E-01 4 . 4 4 E+00 9 . 50E+01 2 . 14E+01 2 . 35E-01 5 . 4 1E + 00 1 . 25E+02 2 . 31E+01 2 . 82E-01 6 . 47E+00 1 . 61E+02 2 . 49E+01 3 . 32E-01 7 . 63E+00 2 . 05E+02 2 . 69E+01 3 . 86E-01 8 . 8 8 E+00 2 . 57E+02 2 . 90E+01 4 . 44E-01 1 . 02E+01 3 . 19E+02 3 . 13E+01 5 . 06E-01 1 . 16E+01 3 . 93E+02 3 . 37E+01 5 . 72E-01 1 . 32E+01 4 . 79E+02 3 . 64E+01 6 . 42E-01 1 . 48E+01 5 . 80E+02 3 . 93E+01 7 . 16E-01 1 . 65E+01 6 . 98E+02 4 . 23E+01 7 . 95E-01 1 . 83E+01 8 . 35E+02 4 . 57E+01 8 . 79E-01 2 . 02E+01 9 . 96E+02 4 . 93E+01 9. 68E-01 2 . 23E+01 1 . 18E+03 5 . 32E+01 1 . 06E+00 2 . 45E+01 1 . 40E+03 5 . 73E+01 1 . 17E+00 2 . 68E+01 1 . G6E+03 6 . 19E+01 1 . 28E+00 2 . 94E+01 1 . 96E+03 G . 67E+01 THETAE = 0.3100 #8 CLASS INITIAL FLUX(CM/HRS) 1 2 86E+01 2 2 84E+01 3 2 81E+01 4 2 77E+01 5 2 74E+01 6 2 70E+01 7 2 67E+01 8 2 63E+01 9 2 59E+01 10 2 56E+01 1 1 2 52E+01 12 2 48E+01 13 2 44E+01 14 2 .'40E+01 15 2 36E+01 16 2 32E+01 17 2 28E+01 18 2 24E+01 19 2 19E+01 20 2 15E+01 2 1 2 10E+01 22 2 06E+01 23 2 01E+01 24 1 96E+01 25 1 9 1E+01 26 1 87E+01 27 1 82E +01 28 1 76E +01 29 1 7 1E+01 30 1 G6E+01 3 1 1 6 1E+01 32 1 55E+01 33 1 49E+01 34 1 43E+01 35 1 37E+01 36 1 . 3 1E + 01 37 1 .24E+01 38 1 . 17E+01 39 1 . 10E+01 40 1 02E+01 4 1 9 .44E+00 42 8 .6 IE+ 00 43 7 .74E+00 44 6 .83E+00 45 5 .87E+00 MECKENSVILLE (69) S1L I LOAM SORPT[VI1Y(CM/HRS•'O.5) 9 2 IE •01 9 15E -01 9 04E -0 1 8 93E -01 8 8 1E •O 1 8 69E - 0 1 8 57E - 0 1 8 4 5E -O 1 8 33E -Ol 8 2 1E - 0 1 8 0 8 E O 1 7 95 E -01 7 82E -O 1 7 69E 0 1 7 55E • o i 7 42E •01 7 28E -01 7 13E -01 6 99E -01 6 84E - 0 1 6 69E - 0 1 6 54E -Ol 6 38E -01 6 22E -01 6 061 -0 1 5 90E - 0 1 5 73E • 0 1 5 56F. - 0 1 5 39E -C) 1 5 2 1E - 0 1 5 04E -(.11 4 B5E - 0 1 4 66E - 0 1 4 46E -01 4 25E - o i 4 04 E -0 1 3 82E - 0 1 3 59E - o i 3 . 34E - 0 1 3 09E - 0 1 2 . 83E - 0 1 2 55E - o i 2 . 26E - 0 1 1 . 96E - 0 1 1 . 64E -01 KEIFT/HRS) = 3 F 1 (F 1/HRS) FS(FT/HRS*' . 5 ) 9 . 38E 01 3 02E -02 9 33E 01 3 00 E 02 9 2 IE 01 2 97 E 02 9 10E -01 2 93E 02 8 99E -01 2 89E 02 8 87 F -01 2 85E 02 8 75F -01 2 8 1E -02 8 63E 01 2 77E 02 8 5 IE -01 2 73E -02 8 39 E -01 2 69 E -02 a 27E -01 2 65E -02 8 14E -01 2 6 1E -02 8 01E 01 2 57 E 02 7 88E -01 2 52E -02 7 75E 01 2 48E -02 7 61E -01 2 43E -02 7 4RE -01 2 39E -02 7 34E -01 2 34E -02 7 19E -01 2 29E -02 7 05 E -01 2 24E -02 6 90E -01 2 20E -02 6 75E -01 2 15E -02 6 60E -01 2 09 E -02 6 44E -01 2 04 E -02 6 28E -01 1 99E -02 6 12E -01 1 94E -02 5 96 E -01 1 88E -02 5 79E -01 1 83€ -02 5 62E -01 1 77E -02 5 45E -01 1 7 1E -02 5 27E -01 1 65E -02 5 09 E -01 1 59E -02 4 90E -01 1 53E -02 4 70E -01 1 46E -02 4 50E -01 1 . 40E -02 4 29E - o i 1 33E -02 4 07E -01 1 . 25E -02 3 84E -01 1 .18E-02 3 6 1E -01 1 . 10E -02 3 36E -01 1 .01E -02 3 . 10E -01 9 . 28E -03 2 . 83E -01 8 . 37E -03 2 .54E -01 7 42E -03 2 24E -01 6 . 42E -03 1 93E -01 5 . 37E -03 1441E-02 THETA/THETA2 THETA MID.INT. 0. 46 15 O. 1800 0. 4728 0. 1822 0. 4840 0. 1866 0. 4952 O. 1909 0. 5064 O. 1953 0. 5176 O. 1997 0. 5288 0. 204 1 0 5401 0. 2084 0 5513 0. 2 128 0 5625 0. 2 172 0 5737 0. 22 16 0 5849 0. 2259 0 5962 0. 2303 0 6074 0. 2347 0 6 186 0 2391 o 6298 O 2434 0 64 10 0 2478 0 6522 0 2522 0 6635 0 2566 0 6747 0 2609 0 6859 0 2653 0 697 1 O 2697 0 7083 0 274 1 0 7 196 0 2784 0 7308 0 2828 0 7420 0 2872 0 7532 0 2916 0 7644 0 2959 0 7756 o 3003 0 7869 0 304 7 0 7981 0 309 1« 0 8093 o 3134 0 8205 0 3178 0 83 17 0 3222 0 8429 0 3266 0 8542 o 3309 0 8654 0 3353 0 8766 0 3397 0 .8878 0 344 1 0 .8990 0 . 3484 0 .9103 0 . 3528 0 .9215 o . 3572 0 .9327 0 .3616 0 . 9439 0 . 3659 0 .9551 0 .3703 VO Ln *9 ALVIRA (57) SILT LOAM NC THET15 THETAE THETA2 PPSI15 PSI1 PSIE PSI2 CONE TF TM (CM3/CM3) (CM OF WATER) (CM/DAY) DEG.C 48 0.1500 0.3000 0.3800 15306.0 15306.0 6.0 3.0 23.0000 20.0 20.0 CLASS PRESSURE THETA PERMEABILITY CONDUCTIVITY DIFFUSSIVITY DPSI/DTHETA (CM) (CM3/CM3) (CM/DAY) (CM2/DAY 1 15306. 0 0. 1500 2 . 22E-09 5 . 11E-08 5 . 02E-02 9 .83E+05 2 13123. 4 0. 1524 9 . 38E-09 2 . 16E-07 1 . 82E-01 8 . 43E + 05 3 9647 . 8 0. 1572 2 . 35E-08 5 . 40E-07 3 34E-01 6 .19E+05 4 7093 . 0 0. 16 20 4 . 95E-08 1 . 14E-06 5 . 19E-01 4 .55E+05 5 52 15 . 1 0. 1668 9 . 65E-08 2 . 22E-06 7 , 43E-01 3 .35E+05 6 3834 , 8 0. 17 16 1 . 80E-07 4 . 14E-06 1 . 02E+00 2 .46E+05 7 2820. 1 0. 1764 3 . 27E-07 7 . 52E-06 1 . 36E+00 1 .8 1E+05 8 2074 . 3 0. 18 11 5 . 86E-07 1 . 35E-05 1 . 79E+00 1 .33E+05 9 1526 . 0 0. 1859 1 . 04E-06 2 . 40E-05 2 34E+00 9 . 77E + 04 10 1123. 1 0. 1907 1 . 85E-06 4 . 25E-05 3 . 05E+00 7 .18E+04 1 1 826 . 8 0. 1955 3 . 26E-06 7 . 50E-05 3 96E+00 5 .28E+04 12 609 . 1 0. 2003 5 . 76E-06 1 . 32E-04 5 14E+00 3 .88E+04 13 . 449 . 0 c. 205 1 1 . 01E-05 2 . 33E-04 6 66E+00 2 .85E+04 14' 33 1 . 4 0. 2099 1 . 79E-05 4 . 11E-04 8 . 62E+00 2 .10E+04 15 2 4 4 , 9 0. 2 147 3 . 14E-05 7 . 23E-04 1 11E+01 1 54E+04 16 18 1. 4 0 . 2 195 5 . 53E-05 1 . 27E-03 1 .44E+01 1 .13E+04 17 134 , 6 0. 2243 Q 70E-05 2 . 23E-03 1 86E+01 8 33E+03 18 100 3 0. 229 1 1 .70E-04 3 . 90E-03 2 . 39E + 01 6 12E+03 19 75 0 0 . 2339 2 96E-04 6 . 80E-03 3 .06E+01 4 .50E+03 20 56 . 5 0. 2386 5 12E-04 1 .18E-02 3 90E+01 3 . 31E + 03 2 1 42 . 8 0. 2434 8 . 82E-04 2 . 03E-02 4 . 93E + 01 2 . 43E + 03 22 32 . 8 0. 2482 1 , 50E-03 3 . 46E-02 6 . 17E+01 1 .79E+03 23 25 . 4 0. 2530 2 .53E-03 5 .81E-02 7 .64E+01 1 .31E+03 24 20 .0 0. 2578 4 .19E-03 9 63E-02 9 .30E+01 9 . 66E + 02 25 16 .0 0. 2626 6 81E-03 1 .57E-01 1 .11E+C2 7 .10E+02 26 13 . 1 0. 2674 1 08E-02 2 . 49E-01 1 .30E+02 5 . 22E + 02 27 1 1 .0 0. 2722 1 68E-02 3 . 86E-01 1 .48E+02 ' 3. 83E+02 28 9 . 4 0. 2770 2 .53E-02 5 . 83E-01 1 .64E+02 2 .82E+02 29 8 . 2 0. 2818 3 .72E-02 8 . 55E-01 1 .77E+02 2 .07E+02 30 7 . 4 0. 2866 5 .29E-02 1 .22E+00 1 .85E+02 1 .52E+02 31 6 . 7 0. 2914 7 .32E-02 1 .68E+00 1 .88E+02 1 .12E+02 32 6 . 1 0. 2961 9 .87E-02 2 .27E+00 3 .68E+01 1 .62E+01 33 6 .0 0. 3009 1 .30E-01 2 .98E+00 5 .25E+01 1 .76E+01 34 . 5 . 9 0. 3057 1 .66E-01 3 .8 1E+00 7 .30E+01 1 .91E+01 35 5 . 8 0. 3105 2 07E-01 4 .75E+00 9 .89E+01 2 .08E+01 36 5 . 7 0. 3153 2 .52E-01 5 .80E+00 " 1 . 31E+02 2 .26E+01 37 5 . 6 0. 3201 3 02E-01 6 .95E+00 1 .71E+02 2 .45E+01 38 5 . 5 0. 3249 3 .56E-01 8 .20E+00 2 .19E+02 2 .67E+01 39 5 . 3 0. 3297 4 .15E-01 9 .54E+00 2 .76E+02 2 .90E+01 40 5 . 2 0. 3345 4 .77E-01 1 .10E+01 3 .46E+02 3 .15E+01 4 1 5 .0 0. 3393 5 .44E-01 1 .25E+01 4 .28E+02 3 .42E+01 42 4 . 9 0. 344 1 6 .14E-01 1 .41E+01 5 .26E+02 3 .72E+01 43 4 . 7 0. 3489 6 .90E-01 1 .59E+01 6 .41E+02 4 .04E+01 44 4 . 5 0. 3536 7 .70E-01 1 .77E+01 7 .77E+02 4 .39E+01 45 4 .2 0. . 3584 8 .55E-01 1 .97E+01 9 .38E+02 4 . 77E + 01 46 4 .0 o. . 3632 9 .46E-01 2 . 17E+01 1 .13E+03 5 .18E+01 47 3 .7 0, 3680 1 .04E+00 2 .40E+01 1 .35E+03 5 .63E+01 48 3 . 5 0. . 3728 1 .15E+00 2 .64E+01 1 .62E+03 6 .12E+01 49 3 . 2 0. . 3776 1 .26E+00 2 .90E+01 1 .93E+03 6 .65E+01 THETAE = 0.3000 #9 ALVIRA (57) SILT LOAM KF. ( F F/HRS ) 3 . 144 IE-02 CLASS INITIAL FLUX(CM/HRS) SORPTI V ITY(CM/MRS 4 * 0 . 5 ) FKFT/HRS) F S(F T/MRS'* .5 ) THE TA/THETA2 THETA M I D I NT 1 3 05E+01 9 84E-01 1 OOF•OO 3 23E-02 0 3947 0 1500 2 3 03E+01 9 78E-0I 9 94L -O 1 3 2 IE-02 0 4073 0 1524 3 2 99E+01 9 66E-01 9 82F-01 3 17E-02 0 4 200 0 1572 4 2 96E+01 9 51E-01 9 70F-oi 3 13E-02 0 4326 0 1620 5 2 92E+01 9 41E-01 9 58E-01 3 09E-02 0 4452 0 1668 6 2 88E+01 9 29E-01 9 I'.'.F -O 1 3 05F. -02 0 4578 O 17 16 7 2 84E+01 9 16F-01 9 33E-01 3 OOF -02 0 4704 0 1764 8 2 80E+01 9 03E-01 9 20F-Ol ? 96E 02 0 4830 0 18 11 9 2 77E+01 8 90E-01 9 07F-01 2 92E-02 0 4956 0 1859 10 2 73E+01 8 7GF-01 fl 9 IE-01 2 8RE-C2 0 5082 0 1907 1 1 2 6RE+01 8 63E-01 R 8 IF-Ol 7 R3E-02 o 5208 0 1955 12 2 64E+01 8 49E-01 8 G7E-01 2 79E-02 0 5334 0 2003 13 2 60E+01 8 35E-01 8 5 IE -Ol 2 74E-02 o 546 1 0 205 1 14 2 56E+01 8 21E-01 8 40F-01 2 69E-02 0 5587 0 2099 15 2 52E+01 8 07E-01 8 25F-01 2 G5E-02 0 57 13 0 2 147 16 2 47E+01 7 92E-01 8 1 1E-01 2 60E-02 0 5839 0 2 195 17 2 43E+01 7 77E-01 7 96F. -Ol 2 55E-02 0 5965 0 2243 18 2 38E+01 7 62E-01 7 R 1 E - 0 1 2 50E-02 0 609 1 0 2291 19 2 34E+01 7 47E-01 7 66F-01 2 4 5E-02 0 62 17 0 2339 20 2 29E+01 7 31E-01 7 5 IF. Ol 1 40E-02 0 6343 0 2386 2 1 2 24E+01 7 15E-01 7 35E-01 2 34E 02 0 6469 0 2434 22 2 19E+01 6 98F-01 7 19E-01 2 29E-02 0 6595 0 2482 23 2 14E+01 6 82E-01 7 02E-01 2 24E-02 0 672 1 0 2530 24 2 09E+01 6 65E-01 6 B6E-01 2 18E-02 0 6848 0 2578 25 2 04E+01 6 47E-01 6 69E-01 2 12E-02 0 6974 o 2626 26 1 99E+01 6 30E-01 6 51E-01 2 07E-02 0 7 100 0 2674 27 1 93E+01 6 12E01 6 3 IE-01 2 OIE-02 0 7226 0 2722 28 1 88E*01 5 9 4 E 0 1 G 16E-01 1 95E-02 0 7352 0 2770 29 1 82E+01 5 75E-01 5 9RE-01 1 R9E-02 0 7478 0 2818 30 1 77E+01 5 57E-01 5 79E-01 1 R3E-02 0 7604 0 2866 3 1 1 71E+01 5 38E-01 5 6 IE-01 1 76E-02 0 7 7 30 0 2914 32 1 65E+01 5 18E-01 5 4 lE-OI 1 70E-02 0 7856 0 2961 33 1 59E+01 4 98E-01 5 22E-01 1 63E-02 0 7982 0 3009 34 1 53E+01 4 77F-01 5 01E-01 1 57E-02 0 8 109 0 3057 35 1 46E+01 4 55E-01 4 80E-01 1 49E-02 0 8235 0 3105 36 1 39E+01 4 33E-01 4 57E-01 1 4?E-0'2 0 8361 0 3153 37 1 32E+01 4 3 09E-01 4 34E-01 1 34E-02 0 8487 0 3201 38 1 25E+01 85E-01 4 10E-01 1 26E-02 0 8613 0 3249 39 1 17E+01 3 59F-01 3 85E-Ol 1 18E-02 0 8739 0 3297 40 1 09E+01 3 32F-U1 3 59E-01 1 09E-02 0 8865 0 3345 4 f 1 OIE'01 3 04 E-0 1 3 3 IE-01 9 9RE-03 0 899 1 0 3393 42 9 20E+0O 2 75E-01 3 02E-O1 9 02E-03 0 9117 0 344 1 4 3 8 28E+00 2 44F-0 1 2 72E-01 8 OOE-03 0 924 3 0 3489 44 7 30E-»00 2 11E-01 2 40E-Ol G 94E-03 0 9369 0 3536 45 6 27E+00 1 77E-01 2 06E-01 5 8 IE-03 0 9496 0 3584 APPENDIX D.2 198 DATE OF EVENT: ORIGINAL RAINFALL DATA FROM SECONDS PER TIMINT = 120. 21 JULY 72 2.77 SQUARE MILE MAHANTANGO SUB-WATERSHED TIME INCHES 1750 1755 18 0 3 . 20 3.40 3.90 SOIL/C 145 THETA2 O. 26300 THFTAE 0. 37600 THETAI O. 149 1? DECSA I O . 56 700 F RUDEG O.7 5000 FSIFT/HR) FMFT/HR) FKFT/HR) 0.06940 0.14720 2.O90OO 145 O. 26300 0. 37GOO O. 14912 0. 56700 O. 7 5000 O . 06940 O. 14720 2 . 33000 TOP LAYER SOIL DEPTH=0.750 SOIL* TIMINT VOKFT) SECOND LAYER P(FT) SOIL D E P T H = PEX(FT ) 1 . 500 PINF(FT) WFINC(FT) 145 1 0. 06967 0. 00667 - 0 . 06300 0. 00667 0. 02938 145 2 0. 00939 0. 00667 -o. 002 7 2 O. O06G7 0. 05877 145 3 0. 00856 0. 01 167 0. 003 10 0. 00856 0. 09652 145 4 0. 00807 0. 01667 0. 00859 0. 00807 0. 132 1 1 145 5 0. 007 7 4 O 01667 0 00893 0. 007 7 4 0. 16622 145 6 0. 0074 9 0 0 -o. 007 4 9 0. 0 0. 16622 145 7 0. 007 30 0 0 -o. 007 30 0. 0 0. 16622 145 8 0. 007 15 0 0 - 0 . 0O7 15 0. 0 0. 16622 145 9 o. 00702 0 0 - 0 . 00702 O. 0 0. 16G22 145 10 0. 00691 0 0 -o. 0069 1 0. 0 0. 16622 145 1 1 0. 00682 0 0 - 0 . 0068 2 0. 0 0. 16622 145 12 0. 00674 0 0 - 0 . 0067 4 0. 0 0. 16622 145 13 0. 00666 0 0 - 0 . 00666 0. 0 0. 16622 145 14 0. 00660 O 0 -o. 0O66O O. O 0 16622 145 15 0. 00654 0 0 -o. 006 54 0. .0 0. 16622 145 16 0. .00649 0 0 -o. 0064 9 0. .0 0. 16622 145 17 0. 0064 4 0 0 - 0 . 0064 4 0. o 0. 16622 145 18 0 00640 0 0 -0 006 4 O 0. .0 0. 16622 145 19 0 00636 0 0 - 0 . 006 36 0 .0 0 16622 145 20 0. .00632 0 .0 - 0 . .00632 0. .0 0 16622 145 2 1 o .00629 0 .0 -o 00629 o o 0. 16622 145 22 0 .00626 0 .0 - 0 00626 0 o 0 16622 145 23 0 .00623 0 .0 -o .00623 0 .0 0 16622 145 24 0 .00620 0 .0 -0 00620 0 .0 0 16622 145 25 0 .00617 0 .0 -o .00617 o .0 o 16622 145 26 0 .00615 0 .0 - 0 .00615 0 .0 0 . 16622 145 27 0 .006 13 0 .0 - 0 .00613 0 .0 0 16622 145 28 0 .00610 0 .0 -o .006 10 0 .0 0 . 16622 145 29 0 .00608 0 .0 -o .00608 0 .0 0 .16622 145 30 0 .00606 o .0 - 0 .00606 0 .0 0 16622 145 31 0 .00604 0 .0 -0 .00604 0 .0 0 . 16622 145 32 0 .00603 0 .0 - 0 .00603 0 .0 0 . 16622 145 33 0 .00601 0 .0 - 0 .00601 0 .0 0 .16622 145 34 0 .00599 0 .0 - 0 .00599 0 .0 0 . 16622 145 35 0 .00598 0 .0 -0 .00598 0 0 0 . 16622 VO VO < r i r - - C D T i o O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 0 * - c N C N n r o n c 7 C o n ( ^ n r o r o n n n n n n r o n o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o t » CO O f - CN C - e c c n > j CP in TT TJ rr O O O O O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o CNOO — " - O O C O O O O O O O C O O O O C O C O O O O O O O O O O O O o o o o o o o o o c o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o c o o o o o o o o o o o o o o o o o o o o o o o o c o o r~ r-- r-- r-- CO CD c p CD CD ID CD — CD CD O O — — — o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o ^ c o 0 ^ c ^ O - T c o ^ D L n M c J l ^ B T l f ^ o t o ^ J l n n n O C ! c o ^ l X l l n T t n r ^ O l - 0 * - - - c o i r T T r o c N * - o o o j C O C T ) a > c o c o o D c o r ^ r ^ r ~ r ^ r ^ r ^ c D c c o r N i n ^ T T T T f T f T T ^ T i n n n n n n n n o o n n n n o n n c o c o c o n n n c o c o C O O O O O O C O O O O Q O O O O O O O O O O O O O O O O O O O O O O O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o ^ c \ n T ^ L n l l ^ ^ s l O ) 0 ' " « n T t l n ^ l ^ ^ o O ) 0 ' w n T l L n l J 5 ^ c o a l O ' • c N n T J l n T - ^ T - T - T - T - T - T - T - ^ C N C N C S C N C N C N C N C N C N C N n n n C O C O C O CDlj?CD<j3CDCD(jOCDCDlj?(jPCDCDCDlDCjOircDCO CDCj?CPCDCDCDCDCDCDCPCC(j7cpcjOCDCDCDCj?CDCDtj7a^ - ^ M s n n n n n n n n n n n n n n n n n n n n n r , n n n n n n n n n C N O ' T ^ a O O O C D C C C C C O C D ( 2 t X C C K ' X C C C O C C C O C O C D e D C D C C C Q C O C O ( D C O [ C C C C C O a ^ — cc. — r T r ^ r ~ r ^ r ^ r ^ r ^ r ~ r ^ t ^ r ^ r ~ > r ^ r ^ r ~ r ^ r ^ r ^ r ^ r ^ r ^ r ~ r ~ r ~ r ^ r - r ^ i ^ r ~ r ^ r ^ ° ° ~~ " " ' " " " ' . " *~ "~ "". ~ o o o c o o o o o o o o o o o o o o o o o o o o o o o o o o o c o o o I- Cl CN — 0) is 01 T — cc C- IT. i n IT. TT c c o o o o o o o o o o o o o o o o o o o o o o o o o o o o c o o o o o o c o o c o o o o o o o o o o c o o o o o o o c o o c o o o o o o o ci ci IT r-•r CN CN TT r- _ CO CN CC' — cc i n CN O co CO TT CN — 01 c L l T CN — C 01 CO n CN i n r - IT IT. "J n n CN CN — — - o c O O cn 01' 01 01- C l c CO CO X X X c X r~ r~ b c  — TT TT TT T TT -7 T? TT TT T? TT •» T CO n r> n o r> r> n n c i r, ci C l n n n «- G o o c C O c o o o o o o c o  O O O O O O O C c O D r-, o O C O O O b o O O o o o O o o o o c c o o o O C O O O O C O O O o o o c o o o o o o o o o o o o c o o o o o o o o o o o o o o o o c o o r» r- r» r» r- c p c p c o CD CD CD CD — CD CD S o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o c o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 r> CN O TT CN CN TT r- CO CN CO TT — eo in CN 0 on ID TT CN — 0) co CD in TT CN O 0) 0 0 0) TT — CO t - CD in TT C1 D CN CN - O 0 O 0 0) 01 CD 01 0) CO CO co CO CO X X X r~ r~ TT in in in TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT ci CO r> n ci r> r> n O n rs r> r> TT O O O O 0 O O 0 0 0 O O O 0 0 0 0 0 0 O O O O O O O O O O O O O O Q O O O O O 0 O O 0 0 0 O O O 0 0 0 0 0 0 O O O O O O O O O O O O O O O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 " - c N r > T T i n i j 5 r ~ x a > O " - c > i r 5 T j i n i j 5 t ^ x 0 j O ' - c N C 0 T T ) n i ^ T T T T T T T T T T T T T T T T T f T T ' T T T T T f T I T T T T T f T T T l ' T T T T T f T T T T T T T T T T T T T T T T T T T T T T T T T i n u i i n i n i n i n i n i n i n i n u i i n i n i n i n i n i n i A i n i n u ^ SOIL* THETA2 THETAE , THETAI DEGSAT FROOEG FSIFT/HR) FK(F T/HR) F1 ( F T/HR) 7 1 0.29400 0.34200 0.20374 O.G9300 0.75000 0.03250 0.05900 O.97700 7 1 0. 29400 O. 34 200 0. 20374 0.69300 O. 75000 O.02370 0.03 130 O. 74200 TOP LAYER SOIL 0EPTH=0.75O SOIL* TIMINT VOKFT) SECOND LAYER SOIL OFPTH= P(FT) PEX(F r ) 1 . 670 PINFIFT) WFINC(FT) 7 1 1 0 .03257 0 .00667 - 0 .02590 0 .00667 0. 04822 7 1 2 0 .00406 0 .00667 0 .00260 o .00406 0. 077G2 7 1 3 0 .00368 0 .01167 0 .007 99 O .00368 0. 10423 71 4 0 .00345 0 .01667 0 .01322 0 .00315 o. 1 29 18 7 1 5 0 .00329 0 .01667 0 .01337 O .00329 o. 1 5 30 1 7 1 6 0 .00318 0 .0 -o .00318 0 0 0. 15301 71 7 0 .00309 0 0 -0 .OO309 0 0 0 15301 71 8 0 .00302 0 .0 -0 .00302 0 .0 o. 15301 71 9 0 .00296 0 .0 -o .002 96 O O 0. 15301 7 1 10 0 .00290 0 0 -0 .00290 o O 0 15301 71 1 1 0 .00286 0 .0 -o .002A6 0 .0 0. 15301 7 1 12 0 .00282 0 .0 -o .002n2 o .0 0. 1530 1 71 13 0 .00279 0 .0 -0 .00279 0. 0 0. 15301 71 14 0 .00276 0 .0 -0 .00276 o 0 0. 15301 7 1 15 0 .00273 0 0 -0 0027 3 0. .0 0. 15301 71 16 0 .00271 0 .0 -0 .002 71 0 0 0. 15301 7 1 17 0 .00269 0 .0 -o .002G9 0 O o. 15301 7 1 18 0 .00267 O 0 - 0 . 00267 0 0 0 15301 7 1 19 0 .00265 0 0 - 0 . .00265 0. 0 o. 15301 7 1 20 0 00263 0 0 -o 00263 0 0 o. 15301 7 1 2 1 0 0026 1 0 0 -0 .007G1 o. 0 0. 15301 7 1 22 0 00260 0 0 - 0 . .00260 0 0 0. 15301 7 1 23 0 .00259 0 0 -0 00259 0. 0 o. 15301 7 1 24 0 00257 0. 0 - 0 . 002T.7 o. 0 o. 15301 7 1 25 0. 00256 0. 0 -o. 00256 0 . 0 0. 15301 7 1 26 0. 00255 0 0 •0 00255 0 . 0 0. 1530 1 7 1 27 0 00254 0 0 -o 00254 0. 0 0. 15301 7 1 28 0. 00253 0. 0 -o. 00253 0. 0 0 15301 7 1 29 0. 00252 0. 0 - 0 . 00252 0. 0 0 15301 7 1 30 ' 0. 00251 0 0 - 0 . 0025 1 0. 0 0 15301 71 31 0. O0250 0. 0 -0 00250 0 0 0. 15301 7 1 32 0. 00249 0. 0 -0 . 00249 o. 0 0. 15301 7 1 33 0. 00248 o. 0 -o. O02JH o. 0 0 15301 7 1 34 0 00248 0. o - 0 . 00248 0. 0 0. 1530 1 7 1 35 0 0024 7 0 0 -0 . 002 4 7 0. 0 0 1530 1 O r-O SOIL* THETA2 THETAE THE TAI DFGSAI FRODF.C, FS(FT/HR) FK(FT/HR) F1(FT/HR) 69 0.33700 O.3150O 0.29016 0.86100 0.75000 0.01790 0.05900 0.53900 69 O. 33700 0. 31500 0. 29016 0. 86 100 O. 7 5000 0.01280 0.03130 0. 4 1400 TOP LAYER SOIL DEPTH=0.750 SOIL* TIMINT VOKFT) SECOND LAYER SOIL DEPTH- P(FT) PEX(FT) 2 . OOO PINF(F T ) WFINC(FT ) 69 1 0 .01797 0 .00667 - 0 . 01 130 0 . 00667 0. 26835 69 2 0 .00312 0 .00667 0 00354 0 003 12 0. 39402 69 3 0 .00291 0 .01167 0 00876 0 00291 0. 51116 69 4 0 .00278 0 .01667 0 01388 0 .00278 0. 6232 1 69 5 0 .00270 O .01667 0 .01397 O 00270 0. 73 179 69 6 0 .00263 0 .0 - 0 . 00263 0 .0 0. 73179 69 7 0 .00258 0 .0 -o 00258 0 .0 0. 73 179 69 8 0 .00254 O .0 o 00254 0 0 0. 73 179 69 9 0 .00251 O .0 - 0 . 0025 1 0 O 0. 73 179 69 10 0 .00248 O .0 - 0 . 00248 O 0 0. 73 179 69 1 1 0 .00246 0 .0 -o 0024 6 o .0 0. 73 179 69 12 0 .00244 O .0 -o .00244 0 0 0. 73 179 69 13 0 .00242 O .0 -0 00242 0 .0 0. 73 179 69 14 0 .00240 O O - 0 . .00240 0 0 0. 73 179 69 15 - 0 .00239 0 0 - 0 . 00239 0 0 0. 73 179 69 16 0 .00238 O O -0 00238 0 0 o. 73 179 69 17 0 .00236 0 .0 - 0 . 002 36 0 0 0. 73 179 69 18 0 .002 35 0 0 - 0 00235 0. 0 0. 73 179 69 19 0 00234 0 .0 -o. 00234 0 0 0. 73 179 69 20 0 .00233 0 0 -o 00233 0 0 0. 73179 69 21 0 .002 32 0 0 -o. 00232 0 .0 0. 73 179 69 22 0 .00232 0 O -o. 00232 0 0 0. 73 179 69 23 0 .00231 0 .0 - 0 . 002 31 0 0 0. 73 179 69 24 0. .00230 0 0 - 0 00230 0 0 0. 73 179 69 25 0 .00229 0 0 - 0 00229 0 0 0. 73 179 69 26 0 .00229 0 0 -0 00229 0 0 0. 73 179 69 27 0 .00228 0 .0 - 0 . 00228 0 0 0. 73 179 69 28 0 .00228 o 0 - 0 . 00228 0 .0 0. 73 179 69 29 0 O0227 o .0 -0 00227 0 .0 0. 73179 69 30 0 .00226 o .0 -o 00226 0 0 0. 73 179 69 31 0 .00226 0 .0 -0 00226 0 0 0. 73179 69 32 0 .00226 0 .0 - 0 . 00226 0 0 0. 73 179 69 33 0 .002 25 o .0 - 0 . 00225 0 0 0. 73179 69 34 0 O02 25 o .0 -0 00225 0 0 0. 73179 69 35 0 .00224 0 .0 - 0 . 00224 0 0 0. 73179 NJ O LO SOIL* THETA2 THETAE THE TAI DEGSAT FRODEG FS(FT/HR) F M F T / H R ) F K F T / H R ) 57 0 . 2 8 7 0 0 0 . 3 0 4 0 0 0 . 2 1 8 1 2 0 . 7 6 0 0 0 0 . 7 5 0 0 0 0 . 0 2 5 7 0 O 05890 0 . 7 7 1 0 0 57 0 . 2 8 7 0 0 0 . 3 0 4 0 0 0 . 2 1 8 1 2 0 76000 0 . 7 5 0 0 0 0 . 0 1 8 7 0 0 . 0 3 1 3 0 0 . 5 9 2 0 0 TOP LAYER SOIL DEPTH=0.750 SECOND LAYER SOIL DEPTH= 2 . 5 0 0 SOIL* TIMINT V01(FT ) P ( F T ) PEX(FT) P INF (FT ) WFINC(FT) 57 1 0 . 0 2 5 7 0 0 .00667 - 0 .01903 0 .00667 0 .07763 57 2 0 .00362 0 .00667 0 . 00304 0 00362 0 . 1 138 1 57 3 0 .00332 0 .01167 0 .008 35 0 .00332 o , 15844 57 4 0 .00314 0 .01667 o .0135 3 o .003 14 0 19496 57 5 0 .00301 0 .01667 0 013G5 0 .00301 0 2 3004 57 6 0 .00292 0 . 6 - 0 .00292 0 . 0 o 2 3004 57 7 0 .00285 0 . 0 - o .00285 0 . 0 0 2 3004 57 8 0 .00279 0 0. - o .00279 0 . 0 0 2 3004 57 9 0 .00275 0 . 0 - 0 . 002 75 o . 0 0 23004 57 10 0 .00271 0 . 0 - 0 . .002 7 1 o 0 o 23004 57 1 1 0 .00267 0 . 0 - 0 .00267 0 o 0 2 3004 57 12 0 .00264 0 . 0 - 0 . 00264 0 0 0 . 2 3004 57 13 0 0026 1 0 . 0 - 0 . 0026 1 0 0 0 . 2 3004 57 14 0 00259 0 O - 0 . 00259 0 . 0 0 . 2 3004 57 15 0 00257 0 O - o 00257 0 0 0 . 23004 57 16 0. .00255 0 . 0 - o 00255 0 0 0 . 23004 57 17 O 00253 0 . 0 - 0 . 00253 0 o 0 23004 57 18 O. .00252 0 0 - 0 . 00252 0 0 0 . 23004 57 19 0. 00250 0 0 - 0 . 00250 0 0 0 23004 57 20 0 . 00249 0 0 - o 002 4 9 o 0 o 2 3004 57 21 0 00248 0 0 - 0 0024 8 0 . 0 0 . 23004 57 22 O 00246 O 0 - o 0024 6 0 0 o 23004 57 23 0 . 00245 0 0 - 0 0024 5 0 0 0 . 23004 57 24 0 . 00244 0 0 - o . 00244 0 0 0 . 23004 57 25 0 00243 0 0 - 0 . 00243 0 . 0 0 . 23004 57 26 0 . 00242 0 0 - 0 . 00242 0 . 0 0 . 2 3004 57 27 0 . 0024 1 0 . 0 - o . 002 4 1 0 0 0 . 23004 57 28 0 . 0024 1 0 0 - 0 0024 1 0 0 0 . 23004 57 29 0 . 00240 0 . 0 - 0 . 00240 0 . 0 0 . 2 3004 57 30 0 . 00239 0 0 - 0 . 00239 0 . 0 0 . 2 3004 57 3 1 0 00238 0 0 - o 00238 0 0 0 . 2 3004 57 32 0 . 00238 o 0 -o. 00238 0 0 0 . 2 3004 57 33 0 00237 0 0 - o . 00237 0 0 0 . 2 3004 57 34 0 00237 0 0 - 0 . 00237 0 0 0 . 23004 57 35 0 00236 0 0 - 0 . 00236 0 0 0 . 2 3004 f ho o CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 1 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0 0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.0550 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 220.0 1100.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 140.0 1300.0 REACH LENGTH= 1750.OO STREAM WIDTH= 10.00 MANNINGS N= 0.350000 DE LTAX = 20.00 VOLUME OF PRECIPITATION EXCESS= 2.3111543655 CU FT TOTAL RUNOFF VOLUME FROM REACH^ 4044.52001953 13 PRECIP EXCESS VALUES FOR EACH DELT OL CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT SIDE 0 .0000185 0 .0066667 0 .0 0 .0 0 .0 0 .0 O .OOOO185 0 .0066667 0 .0 0 .0 0 .0 0 .0 0 .0003071 0 .0116667 0 .0000394 1 100 .OOOOOOO 0 .0002353 1300 .OOOOOOO 0 .0019133 0 .0166667 0 .00057 20 1 100 .OOOOOOO o .0012949 1300 .OOOOOOO o .0046056 0 .0166667 o .0015763 1 100 .OOOOOOO o 0029829 1300 .OOOOOOO 0 .0030786 0 .0 0 .00059 12 1 100 .OOOOOOO o 0024874 1300 .OOOOOOO 0 .0020887 0 .0 0 .00004 7 7 1 100 OOOOOOO o .0020410 ' 1300 .OOOOOOO 0 .OO16400 0. .0 0 .0 1080. OOOOOOO o .0016400 1280 .OOOOOOO 0 .0012818 0. .0 0 .0 1060. OOOOOOO 0 0012818 1260. .OOOOOOO 0 .0009651 0. .0 0 .0 1040. .OOOOOOO 0. 0009651 1240 .OOOOOOO 0 .0007058 0. .0 0 .0 1020. OOOOOOO 0 0007058 1220. . OOOOOOO 0 .0005586 0. 0 0 .0 1000. OOOOOOO 0 0005586 1200. . OOOOOOO 0 .0005656 0. 0 0 .0 980. OOOOOOO 0 0005656 1 180. OOOOOOO 0 .0005399 0. O 0 .0 940. OOOOOOO 0. 0005399 1 140. OOOOOOO 0 .0004394 o. 0 0 .0 920. OOOOOOO 0. 0004394 1 120. OOOOOOO 0 .00O3021 0. 0 0 .0 900. OOOOOOO 0. 0003021 1 100. OOOOOOO 0 .0001677 0. 0 0 .0 880. OOOOOOO 0. 0001677 1080. .OOOOOOO 0 .0000611 0. 0 0. .0 840. OOOOOOO 0. 000061 1 1040. . OOOOOOO 0 .0000024 0. 0 0. .0 0. 0 0 0000024 80. .OOOOOOO 0. 0 0. 0 0. 0 0. 0 0. 0 0. .0 N3 O Ln INFLOW HYDROGRAPHS CALCULATION OF LATERAL SECTION 2 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0 .0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0 .2000 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0 .0550 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 100.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 140 0 REACH LENGTH= 1290.00 STREAM WIDTH= 10.00 VOLUME OF PRECIPITATION EXCESS^ 4.6148881912 TOTAL RUNOFF VOLUME FROM REACH= 5953.2031250000 0.0125 0.0125 O.3750 0 .1150 180.0 260 .0 MANNINGS N CU FT 0 .0125 0 .0125 0 .0550 0 .0550 9 4 0 . 0 1360.0 0 .350000 DELTAX= 20. OO OL CFS/FT 0 .0000185 0 .0000185 .0008053 .004 1353 .0093574 .0079914 .0067818 .0056747 0 .0013448 0 .0009992 0 .0006796 O.0004050 0 .0001926 0 .0000534 O.O O. O. O. O. O. O. PRECIP PRECIP DEPTH 0.0066667 0066667 0116667 0166667 0166667 O O 0 0 O O 0 0 0 O EXCESS VALUES FOR LEFT SIDE OL 0 . 0 0 .0 0.0005376 0 .0027940 0.0063281 0.0055040 0.0047408 0.0040348 0.0000630 0.0000341 0.0000062 0 . 0 0 . 0 0 . 0 0 . 0 EACH DELT WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT SIDE 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 940 .0000000 0 .0002353 1360 .OOOOOOO 940 .0000000 0 .0012949 1360 .OOOOOOO 940 0000000 0 .0029829 1360 .OOOOOOO 940 .ooooooo 0 .0024874 1360 .OOOOOOO 940. 0000000 0 .0020410 1360. .OOOOOOO 920. ooooooo 0. 0016400 1340. .OOOOOOO 900. ooooooo o. 0012818 1320. OOOOOOO 880. ooooooo 0. 0009651 1300. OOOOOOO 840. ooooooo 0. 0006734 1260. OOOOOOO 0. 0 0. 0004050 80 . OOOOOOO 0. 0 0 . 0001926 60 . OOOOOOO 0. 0 0. 0000534 20 . OOOOOOO 0. 0 0. 0 0. 0 NJ O CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 3 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.3750 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.0550 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 140.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 140.0 REACH LENGTH= 1130.00 STREAM WIDTH= 10.00 VOLUME OF PRECIPITATION EXCESS^ TOTAL RUNOFF VOLUME FROM REACH= 2 .8512601852 322 1 .9238281250 0.0125 0.0125 0.1150 0.1150 980.0 260.0 MANNINGS CU FT 0.0125 0.0550 1320. N = 0.350000 DELTAX= 20.00 OL CFS/FT 0.0000185 .0000185 .0003855 .0025444 .0062 1 13 0.0039540 0.0025722 0.0021158 0.0017742 .OO14606 .0011294 .0007709 .0004668 0.0002397 0.0000888 O.0000098 0 . 0 0. 0. O. 0. O. O. O. O. PRECIP EXCESS VALUES FOR EACH DELT SIDE OL WIDTH OF CONTRIB AREA O.O 0 .0 980.OOOOOOO 980.0000000 980.OOOOOOO PRECIP DEPTH 0.0066667 0.0066667 0.0116667 0.0166667 0.0166667 0 0 0 0 0 0 O 0 O 0 0 0 LEFT 0 .0 O 0 O O 0 0 0000711 0010329 0028465 0010676 0000861 O 0 O 0 O 0 O O 0 0 980.OOOOOOO 960.OOOOOOO 940.0000000 920.0000000 880.0000000 860.OOOOOOO .0 .0 .0 .0 0. O. O. 0. O . O 0 .0 RIGHT 0.0 0 O O O 0 O 0 O 0 0 O 0 o o o 0 SIDE OL O 0002819 0014652 0033185 0028863 002486 1 0021158 0017742 0014606 OOI1294 0007709 0004668 0002397 0000888 00O0098 O WIDTH OF RIGHT SIDE 0 .0 O.O 1320.0000000 1320.0000000 1320.0000000 1320.0000000 1320.0000000 1300.OOOOOOO 1280.0000000 1260.0000000 1220.0000000 100.OOOOOOO 80.OOOOOOO 60.OOOOOOO 20.OOOOOOO 0.0 0 .0 o CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 4 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM REACH LENGTH= 1170.00 STREAM WIDTH* VOLUME OF PRECIPITATION EXCESS^ TOTAL RUNOFF VOLUME FROM REACH= 0.0125 0.0125 0.0550 0.0550 100.0 100.0 10.00 4.2111063004 4926.9921875000 0.0125 0.0125 O.3750 0.3750 220.0 180.0 MANNINGS CU FT 0.0125 0.0125 0.0550 0.0550 900.0 740.0 N = O.350000 DELTAX= 20.00 PRECIP EXCESS VALUES FOR EACH DELT . CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIFJ AREA RIGHT SIDE OL WIDTH OF RIGI 0 .0000185 0 .0066667 0 .0 0 .0 0 . 0 o .0 0 .0000185 0 .0066667 0 .0 0 .0 0 .0 O .0 O .0005962 0 .0116667 0 .0002819 900 .OOOOOOO 0 .00028 19 740 .OOOOOOO 0 .0029767 0 .0166667 0 .0014652 900 .OOOOOOO 0 .0014652 740 .ooooooo 0 .0066833 0 .0166667 0 .0033185 900 .OOOOOOO 0 .0033185 740 .ooooooo 0 .0057727 O 0 0 .0028863 900 .OOOOOOO 0 .0028863 740 .ooooooo 0 .0049722 0 .0 0. 0024861 900 .OOOOOOO 0 .0024861 740 .ooooooo 0 .0042317 0. .0 0 002 1158 880 ooooooo 0 0021158 720 .ooooooo 0 .0033824 0. 0 0 0016912 860. ooooooo 0 0016912 700 .ooooooo 0. .0025036 0. 0 0. 0012518 840. ooooooo. 0. 0012518 680. ooooooo 0. .0018534 0. 0 0. 0009267 800. ooooooo 0. 0009267 640. ooooooo 0. .0011660 0. 0 0. 0005830 60. ooooooo 0. 0005830 60. ooooooo 0. 0006190 0. 0 0. 0003092 40. ooooooo 0. 0003099 40. ooooooo 0. 0002511 0. 0 0. 000125 1 20. ooooooo 0. 0001260 20. ooooooo 0. 0000473 0. 0 0. 00002 34 0. 0 0. 0000239 0. 0 0. O 0. 0 0. 0 0. 0 0. 0 0. o o 00 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 5 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.0550 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 1220.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 300.0 520.0 REACH LENGTH= 2130.00 STREAM WIDTH= 10.00 MANNINGS N= 0.35OO0O DELTAX= 20.00 VOLUME OF PRECIPITATION EXCESS^ 3.4995746613 CU FT TOTAL RUNOFF VOLUME FROM REACH= 7454.0937500000 OL CFS/FT 0.0000185 0.0000185 O.0005405 0.0029334 O.0067417 0.0053478 0.0041594' 0.0031252 0.0022451 0.0015246 0.0009793 0.0006569 0.0004433 0.0002662 O.OOO1282 0.0000345 0.0 PRECIP PRECIP DEPTH 0.0066667 0.0066667 0.0116667 O.0166667 0.0166667 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 EXCESS VALUES FOR LEFT SIDE OL 0.0 0.0 0.00025 13 0.001513 1 0.0035563 0.0026755 0.001913 1 0.0012670 0.0007 391 0.0003360 0.00007 37 0.0 0.0 0.0 O.O 0.0 0.0 EACH DELT WIDTH OF O 0 CONTRIB AREA O 0 12 20.0000000 12 20.0000000 ' 12 20.OOOOOOO 1220.0000000 1200.0000000 1180.OOOOOOO 1 160.OOOOOOO 1120.OOOOOOO 1 10O.OOOOOOO 0.0 0.0 0.0 0.0 0.0 0.0 RIGHT SIDE OL 0.0 O.O 0.0002568 0.0013740 0.0031391 0.0026723 0.0022463 0.0018582 0.0015060 0.0011887 0.0009056 0.0006569 0.0004433 O.0002662 0.0001282 0.000034 5 0.0 WIDTH OF RIGHT SIDE 0.0 0.0 520.0000000 520.0000000 520.0000000 520.0000000 500.OOOOOOO 480.0000000 440.OOOOOOO 4 20.0000000 300.OOOOOOO 300.OOOOOOO 280.0000000 260.0000000 220.0000000 180.OOOOOOO 0.0 N J O VO CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 6 "LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 100.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 100.0 REACH LENGTH= 1340.00 STREAM WIDTH* 10.00 VOLUME OF PRECIPITATION EXCESS* 5.2303237915 TOTAL RUNOFF VOLUME FROM REACH* 7008.6328 125000 0.0125 0.012' 0.3750 0.1150 220.0 1260.0 MANNINGS CU FT 0.0125 560.0 0.0125 0.1150 0.1150 860.0 O.350000 DELTAX* • 20.00 PRECIP EXCESS VALUES FOR EACH DELT OL CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT 0 ,0000185 0 .0066667 0 .0 0 .0 0 .0 0 .0 0. ,0000185 0 .0066667 0 .0 0 .0 0 .0 0 .0 0 ,0008477 0 .0116667 0 .0004077 860 .OOOOOOO 0 .0004077 1260 .OOOOOOO 0. .0042836 0. .0166667 0 .0021187 860 .OOOOOOO 0 0021187 1260 .OOOOOOO 0 .0096434 O .0166667 0 .0047985 860 .OOOOOOO 0 0047985 1260 .OOOOOOO 0. .0083473 0 .0 0 .0041736 860 .OOOOOOO 0 0041736 1260. .OOOOOOO 0. .007 1898 0 .0 0. .0035949 840 .ooooooo 0 0035949 1240. .OOOOOOO 0. .0061190 O .0 0 .0030595 820 .ooooooo 0 0030595 1220. .OOOOOOO 0. .0035175 0 .0 0 .0015988 800 .ooooooo 0 .0019 187 1 180 .OOOOOOO 0 .0017627 0 .0 0 .0008016 760 .ooooooo 0. 0009610 1 160. OOOOOOO O. .0011186 0. .0 0. .0004886 740. .ooooooo 0. 0006300 100. .OOOOOOO 0 .0005359 0. O 0. .0001920 40. .ooooooo 0 0003439 80. .OOOOOOO 0. .0001665 0. .0 0 0000322 0. 0 0 0001343 60. OOOOOOO 0. .0000170 0 .0 0. 0 0. .0 0. 0000170 20. OOOOOOO 0. .0 0 .0 0. 0 0. .0 0. 0 0 0 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 7 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM REACH LENGTH= 1800.00 STREAM WIDTHS VOLUME OF PRECIPITATION EXCESS= TOTAL RUNOFF VOLUME FROM REACH= 0.0125 0.0125 0.0125 0.2000 0. 1 150 O. 1 150 180.0 340.0 4 20.0 10.00 MANNINGS 3.9879989624 CU FT 7178.3945312500 N = O. 350000 DELTAX= 20.00 OL CFS/FT PRECIP PRECIP DEPTH EXCESS VALUES FOR LEFT SIDE OL EACH DELT WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT SIDE 0 OOOO185 0 .0066667 0 .0 0 .0 0 .0 0 .0 0. .0000185 0 .0066667 0 .0 0 .0 0 .0 0 .O 0. .0005615 0 .0116667 0 .0004897 340 .OOOOOOO 0 .O000394 420 .OOOOOOO 0. .0032384 0 .0166667 0 .0026201 340 .OOOOOOO 0 .0005720 420 .OOOOOOO 0. .0076086 0 .0166667 0 .0059860 340 OOOOOOO 0 .0015763 420 .OOOOOOO 0. .0056870 0 .0 0 .0050958 340 .OOOOOOO 0 .0005912 400 .OOOOOOO 0. .0043313 0 .0 0 .0042836 320 .OOOOOOO 0 .00004 7 7 380 .OOOOOOO 0. .0035435 0 .0 0 0035435 300 .OOOOOOO 0 O 0 .0 0. .0028719 0 .0 0. 0028719 260 .OOOOOOO 0 .0 0 .0 0. .0022667 0. .0 0. 0022667 240. OOOOOOO 0 0 0 .0 0 .0017269 0. .0 0. .0017269 180. OOOOOOO 0 .0 0 .0 o. .0012527 0. .0 0. 0012527 120. .OOOOOOO 0 0 0. o 0. .0001078 0. .0 0. 0001078 0. 0 0 0 0 .0 0. .0 0. 0 0. 0 0. 0 o. 0 0. .0 CALCULATION OF LATERAL INFLOW HYOROGRAPHS SECTION 8 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.3750 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 340.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 180.O REACH LENGTH* 960•OO STREAM WIDTH* 10.00 VOLUME OF PRECIPITATION EXCESS* TOTAL RUNOFF VOLUME FROM REACH* 3 . 37 10384369 3236.1967773438 0.0125 O.2000 1 120.0 MANNINGS CU FT O.350000 DELTAX* 20.00 PRECIP EXCESS VALUES FOR EACH DELT . CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT 0.0000185 0 .0066667 0 .0 0 .0 O.O 0 .0 0.OOOO185 0 .0066667 0 .0 O .0 0.0 0 .0 0.0006130 0 .0116667 0 .0003737 1 120 .ooooooo 0.0002069 180 .OOOOOOO 0.0038079 0 .0166667 0 .0024210 1 120 .ooooooo 0.0013407 . 180 .OOOOOOO 0.0090562 0 0166667 0 .0057987 1120 .ooooooo 0.0032112 180. .OOOOOOO 0.0064231 0 .0 0 004 1339 1 100. OOOOOOO 0.0022892 180, .OOOOOOO 0.0042516 0 .0 0 0027363 1060. OOOOOOO 0.0015153 160. .OOOOOOO 0.0024888 0 0 0 0016018 240. ooooooo 0.0008870 140. OOOOOOO 0.0011466 0. 0 0. 0007379 220. ooooooo 0.0004086 100. OOOOOOO 0.0002G78 0. 0 0. 0001723 200. ooooooo 0.0000954 80. OOOOOOO 0.0 0. 0 0. 0 0. 0 0.0 0. 0 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 9 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.2000 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 720.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 260.0 REACH LENGTH= 1090.00 STREAM WIDTH= 10.00 VOLUME OF PRECIPITATION EXCESS^ TOTAL RUNOFF VOLUME FROM REACH= 1.66129016RR 1810.0061523438 0.0125 0.0125 0. 1 150 0. 1 150 460.0 MANNINGS CU FT 960. N = 0.350000 DELTAX= 20.00 PRECIP EXCESS VALUES FOR EACH DELT OL CFS/FT PRECIP DEPTH LEFT SIDE QL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT 0. .0000185 0 .0066667 0. .0 0 .0 0 .0 0 .0 0. .0000185 0. .0066667 0 .0 0 O 0 .0 0 .0 0 .0002913 0. .0116667 0 00020G9 720 .OOOOOOO 0 .0000519 960 .OOOOOOO 0. .00214 13 0 .0166667 0. .0013407 720 .OOOOOOO 0 000754 3 960 .OOOOOOO 0. ,0053363 0, .0166667 0 0032112 720 OOOOOOO 0 0020788 960 .OOOOOOO 0. .0030689 0. .0 0 0022892 720. OOOOOOO 0 0007797 960 .OOOOOOO 0. 0015782 0. .0 0. 0015153 700 OOOOOOO 0. 0000629 940 .OOOOOOO 0. .0008870 0. .0 0. 0008870 680. OOOOOOO 0 0 920. OOOOOOO 0. .0004086 0. 0 0. 0004086 640. OOOOOOO 0. 0 900 OOOOOOO 0. .0000954 0. 0 0. 0000954 620 OOOOOOO 0. 0 860. .OOOOOOO 0. 0 0. 0 0. 0 0. 0 0. 0 840. OOOOOOO CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 10 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.017.5 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.3750 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 380.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 300.0 1360.0 REACH LENGTH* 960.00 STREAM WIDTH* 10.00 MANNINGS N= 0.350OO0 DELTAX* 20.00 VOLUME OF PRECIPITATION EXCESS* 2.1109523773 CU FT TOTAL RUNOFF VOLUME FROM REACH* 2026.514 1601563 OL CFS/FT PRECIP DEPTH 0 .0000185 0 .0066667 0 .0000185 0 .0066667 0 .0003548 0 .0116667 0 .0025923 O .0166667 0 .0064491 0 .0166667 o .0037431 0 .0 0 .0019992 0 .0 o. .0012670 0 .0 0 .0007 391 0. 0 0. .0003360 0. 0 0. 0000737 0. 0 0. 0 0. 0 XCESS VALUES FOR EACH DELT LEFT SIDE QL WIDTH OF CONTRIB AREA 0 .0 0 .0 0 .0 0 .0 0 .0002513 380 .OOOOOOO 0 .001513 1 380 .OOOOOOO 0 .0035563 380 .OOOOOOO 0 .0026755 380 .OOOOOOO 0. 0019131 360 OOOOOOO 0. 0012670 340. ooooooo 0. 0007391 320. ooooooo 0. 0003360 280. ooooooo 0. 00007 37 260. ooooooo o. 0 0. 0 RIGHT SIDE OL WIDTH OF RIGHT SIDE 0 .0 0 .0 0 .0 0 0 0 .0000711 1360 .ooooooo 0 .0010329 1360 .ooooooo 0 .0028465 1360 .ooooooo o .0010676 1360 .ooooooo 0. 000086 1 1340. .ooooooo 0. 0 1320. ooooooo 0. 0 1300. ooooooo 0. 0 1260. ooooooo 0 . 0 1240. ooooooo 0. o 0. 0 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 11 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 120.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 1600.0 REACH LENGTH= 420.00 STREAM WIDTH= 10.00 MANNINGS N= 0.350000 DELTAX= 20.00 VOLUME OF PRECIPITATION EXCESS= 4.1731872559 CU FT TOTAL RUNOFF VOLUME FROM REACH= 1752.7 385253906 PRECIP EXCESS VALUES FOR FACH DELT OL CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT SIDE o .0000185 0 .0066667 0 .0 0 .0 0 0 0 .0 O .OOO0185 0 .0066667 0 .0 0 .0 0 .0 0 .0 o .0006913 0 .0116667 0 .0004077 120 .OOOOOOO 0 .00025 13 1600 .OOOOOOO o, .0036781 0 .0166667 0 .0021187 120 .OOOOOOO 0 .OO15131 1600 .OOOOOOO o. .0084011 0 .0166667 0 .0047985 120 .OOOOOOO 0 0035563 1600 .OOOOOOO o. .0068491 0 .0 0 .00417 36 120 .OOOOOOO 0. 0026755 1600. .OOOOOOO 0. 0O55080 0 .0 0 0035949 120 .OOOOOOO 0. 0019131 1580. .OOOOOOO 0. .0043265 0 .0 0 .0030595 100. .OOOOOOO 0 0012670 1560. OOOOOOO o. .0033046 0. .0 0 0025656 80 OOOOOOO 0. 0007 391 1540. OOOOOOO 0. .0014180 0 .0 0 0010820 60. .OOOOOOO 0. 0003360 1500. OOOOOOO o. .0004582 o. .0 0. .0003845 40. OOOOOOO 0. 0000737 1480. OOOOOOO 0. .0001028 0. .0 0 0001028 20. OOOOOOO 0. 0 0. 0 0. OOOOO18 0. 0 0 OOOOO18 0. 0 0. 0 0. 0 o. o 0. .0 0. 0 0. 0 0. 0 0. .0 ho U l CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 12 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.2000 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.2000 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 1O6O.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 680.0 REACH LENGTH= 1170.00 STREAM WIDTH= 10.00 VOLUME OF PRECIPITATION EXCESS= TOTAL RUNOFF VOLUME FROM REACH= 0.9140815735 1069.4753417969 0.0125 0. 1 150 1180.0 MANNINGS CU FT N^ O.350000 DELTAX= 20.OO OL CFS/FT 0.0000185 0.0000185 O.OOO1363 O.OO15550 0.0042039 O.OO15594 0.0001258 0.0 PRECIP EXCESS VALUES FOR EACH DELT PRECIP DEPTH 0.00666G7 0.0066667 0.0116667 0.0166667 0.0166667 O.O 0.0 O.O LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL 0.0 0.0 0000519 0007543 0020788 0007797 0000629 0 0.0 0.0 1060.0000000 1060.0000000 1060.0000000 1040.0000000 1000.OOOOOOO 0.0 o 0 0000519 000754 3 0020788 0007 797 0000629 O WIDTH OF RIGHT SIDE 0.0 0.0 1180.OOOOOOO 1180.OOOOOOO 1180.0000000 1180.OOOOOOO 1 180.0000000 1 160.0000000 i—1 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 13 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.2000 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.2000 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 640.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 680.0 REACH LENGTH* 2680.00 STREAM WIDTH* 10:00 VOLUME OF PRECIPITATION EXCESS* TOTAL RUNOFF VOLUME FROM REACH* 0.9140815735 2449.7385253906 0.0125 O. 1 150 1880.0 MANNINGS CU FT 0 . 3500OO DELTAX= 20.00 PRECIP EXCESS VALUES FOR EACH DFLT OL CFS/FT 0.0000185 0.0000185 0.0001363 0.0015550 0.0042039 0.0015594 0.0001258 0.0 PRECIP DEPTH 0.0066667 0.0066667 0.0116667 0.0166667 0.0166667 0.0 0.0 0.0 LEFT SIDE OL WIDTH OF CONTRIB AREA 0 0 0000519 000754 3 0020788 0007797 0000629 0 0.0 0.0 640 OOOOOOO 640.OOOOOOO 640.0000000 620.0000000 580.0000000 0.0 RIGHT SIDE OL 0.00005 19 0.0007543 .0020788 .0007797 .0000629 .0 O. O. 0. O. WIDTH OF RIGHT SIDE 0.0 0.0 1880.0000000 1880.0000000 1880.0000000 1880.0000000 1860.0000000 1840.0000000 N5 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 14 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.0550 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 0.0550 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 380.0 840.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 340.0 720.0 REACH LENGTH* 2380.00 STREAM WIDTH* 10.00 MANNINGS N= 0.350000 DELTAX* 20.00 VOLUME OF PRECIPITATION EXCESS* 2.7123842239 CU FT TOTAL RUNOFF VOLUME FROM REACH* G455.4726562500 PRECIP EXCESS VALUES FOR EACH DELT OL CFS/FT PRECIP DEPTH ' . LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT 0 .OOOO185 0 .0066667 0 .0 0 .0 0 .0 0 .0 0 .0000185 0 .0066667 0 .0 0 .0 0 .0 0 .0 0 .0003537 0 .0116667 0 .0002819 840 .OOOOOOO o .0000394 720 .OOOOOOO 0 .0020835 0 0166667 0 .0014652 840 .OOOOOOO 0 .0005720 720 .OOOOOOO 0 .00494 1 1 0 .0166667 0 .0033185 840 .OOOOOOO 0 .0015763 720 .OOOOOOO 0 .0034776 0. .0 0. 0028863 840 .OOOOOOO o .0005912 720 .OOOOOOO 0 .0025338 0 0 0. 0024861 820 .ooooooo 0 .00004 7 7 720 .OOOOOOO 0 .0021158 0 .0 0. 0021158 800 .ooooooo o .0 720 .ooooooo 0 .0017742 0. .0 0. 0017742 780 .ooooooo 0 .0 700 .ooooooo 0 OOI4606 0. 0 0. 0014606 740 .ooooooo 0 .0 680 .ooooooo 0, .0011746 0. 0 0. 0011746 720 .ooooooo 0 .0 680. .ooooooo 0. .0009162 0. 0 0. 0009 162 380 ooooooo 0 .0 "660 .ooooooo 0. .0006859 0. 0 0. 0006859 380. .ooooooo 0 0 640. .ooooooo 0. .0004844 0. 0 0. 0004844 360 ooooooo 0 0 620. ooooooo 0. .0003130 O. 0 0. 0003 130 340 ooooooo 0. 0 600 ooooooo 0. .0001737 0. 0 0. 0001737 300 ooooooo 0. 0 580. ooooooo 0. .0000698 0. 0 0. 0000698 280. ooooooo o. 0 540. ooooooo 0. .0000082 0. 0 0. 0000082 240. ooooooo 0. o 500. ooooooo 0. O 0. 0 0. 0 . 0. 0 0. 0 0. 0 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 15 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.0550 0.0550 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 760.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 260.0 1000.0 REACH LENGTH= 2380.00 STREAM WIDTH= 10.00 MANNINGS N= 0.350000 DELTAX= 20.00 VOLUME OF PRECIPITATION EXCESS^ 2.0400657654 CU FT TOTAL RUNOFF VOLUME FROM REACH= 4855.3554687500 PRECIP EXCESS VALUES FOR EACH DELT OL CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT 0. .0000185 0 .0066667 0 .0 0 .0 0 0 0. .0 0 .0000185 0 0066667 0 .0 0 0 0. 0 0. .0 o .0003824 0 .0116667 0 .0002069 760 .OOOOOOO 0 0001431 1000. .OOOOOOO 0. 002314 1 0 .0166667 0 .0013407 760 OOOOOOO 0. 0009272 10OO. OOOOOOO o. 0054782 0 0166667 0 .0032112 760 OOOOOOO o 0022208 1000. OOOOOOO 0. .0038724 0 0 0 .0022892 760 .OOOOOOO 0. 0015831 1000. .OOOOOOO 0. 0025632 0 0 0 .0015 153 740 OOOOOOO o 0010479 1000. OOOOOOO 0. .0015004 0 0 0 .0008870 720 .OOOOOOO 0. 0006134 980. OOOOOOO 0. 00069 1 3 0 .0 0 .0004086 680 .OOOOOOO 0 0002826 960. OOOOOOO 0. .0001614 0. .0 0 .0000954 660 .OOOOOOO 0 0000660 940 . OOOOOOO o. 0 0. 0 0 .0 0 .0 0. 0 900. .OOOOOOO CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 16 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.3750 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 600.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 500.0 REACH LENGTH= 3460.00 STREAM WIDTH= 10.00 MANNINGS N= 0.350000 DELTAX= 20.00 VOLUME OF PRECIPITATION EXCESS= 3.3710384369 CU FT TOTAL RUNOFF VOLUME FROM REACH= 11663.7929687500 PRECIP EXCESS VALUES FOR EACH DELT OL CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT SIDE o OOOO185 0 .0066667 0 .0 0 .0 0 .0 0 .0 o OOOO185 0 .0066667 0 .0 0 .0 0 o 0 .0 o .0006130 0 .0116667 0 .0003737 600 .OOOOOOO 0 .0002069 500 .OOOOOOO 0. .0038079 0 .0166667 0 .0024210 600 .OOOOOOO 0 .0013407 500 .OOOOOOO 0. .0090562 0 .0166667 0 .0057987 600 .OOOOOOO 0 .0032112 500 .OOOOOOO o. .0064231 0 .0 0 .0041339 580 .OOOOOOO 0. 0022892 500 .OOOOOOO 0. .0042516 0 .0 0. 0027363 540 .OOOOOOO 0 0015153 480 .OOOOOOO o. .0024888 0 0 0 0016018 500 OOOOOOO 0. 0008870 460 .OOOOOOO 0. 0011466 0 .0 0. 0007379 480 OOOOOOO 0. 0004086 4 20 .OOOOOOO 0. 0002678 0. .0 0. 0001723 460. .OOOOOOO 0. 0000954 400. ,OOOOOOO 0. 0 0 0 0. 0 0. 0 0. 0 0. .0 NJ NJ O 221 APPENDIX D.3 a b C d e f 0 . 0 8 3 5 0 . 0 8 3 5 0 0 . 0 0 9 9 6 0 . 0 0 0 2 2 0 . 2 9 1 2 1 0 . 2 3 8 5 7 0 . 1 6 7 0 0 . 1 6 7 0 0 0 . 0 3 9 8 4 0 . 0 0 1 3 9 0 . 5 8 2 4 4 0 . 4 7 7 16 0 . 2 5 0 5 0 . 2 5 0 5 0 0 . 0 8 9 6 4 0 . 0 0 4 1 0 0 . 8 7 3 6 4 0 . 7 1 5 7 1 0 . 3 3 4 0 0 . 3 3 4 0 0 0 . 1 5 9 3 7 0 . 0 0 8 8 3 1 . 1 6 4 8 7 0 . 9 5 4 3 0 0 4 175 0 . 4 1 7 5 0 0 . 2 4 9 0 1 0 . 0 1 6 0 3 1 . 4 5 6 0 7 1 . 1 9 2 8 6 0 . 5 0 1 0 0 . 5 0 1 0 0 0 . 3 5 8 5 8 0 . 0 2 6 0 8 1 . 7 4 7 2 9 1 . 4 3 1 4 4 0 . 5 8 4 5 0 . 5 8 4 5 0 0 . 4 8 8 0 6 0 . 0 3 9 3 6 ' 2 . 0 3 8 4 9 1 . 6 7 0 0 0 0 . 6 6 8 0 0 . 6 6 8 0 0 0 . 6 3 7 4 7 0 . 0 5 6 2 2 2 . 3 2 9 7 2 1 . 9 0 8 5 8 0 . 7 5 15 0 . 7 5 1 5 0 0 . 8 0 7 4 2 0 . 0 7 6 6 9 2 . 6 4 1 5 1 2 . 17 168 0 . 8 3 5 0 0 . 8 3 5 0 0 1 . 0 0 0 3 7 0 . 1 0 1 4 9 2 . 9 6 6 0 9 2 . 4 5 0 0 0 0 . 9 1 8 5 0 . 9 1 8 5 0 1 . 2 1 6 5 7 0 . 1 3 1 2 6 3 . 2 9 0 6 7 2 . 7 2 8 3 2 1 . 0 0 2 0 1 . 0 0 2 0 0 1 . 4 5 6 0 0 0 . 1 6 6 3 6 3 . 6 1527 3 . 0 0 6 6 7 1 . 0 8 5 5 1 . 0 8 5 5 0 1 . 7 1 8 6 8 0 . 2 0 7 1 7 3 . 9 3 9 8 5 3 . 2 8 4 9 9 1 . 1 6 9 0 1 . 1 6 9 0 0 2 . 0 0 4 6 0 0 . 2 5 4 0 4 4 . 2 6 4 4 6 3 . 55334 1 . 2 5 2 5 1 . 2 5 2 5 0 2 . 3 1 3 7 5 0 . 3 0 7 3 2 4 . 5 8 9 0 4 3 . 8 4 166 1 . 3 3 6 0 1 . 3 3 6 0 0 2 . 6 4 5 8 4 0 . 3 6 7 9 8 4 . 8 9 9 2 4 4 . 1 0 2 8 6 1 . 4 195 1 . 4 1 9 5 0 2 . 9 9 8 3 9 0 . 4 3 6 2 6 5 . 1 9 0 4 4 4 . 3 4 142 1 . 5 0 3 0 1 . 5 0 3 0 0 3 . 3 7 0 8 6 0 . 5 1 1 4 3 5 . 4 8 167 4 . 5 8 0 0 0 1 . 5 8 6 5 1 . 5 8 6 5 0 3 7 6 3 2 5 0 . 5 9 3 7 3 5 . 7 7 2 8 7 4 . 8 1 8 5 6 1 . 6 7 0 0 1 . 6 7 0 0 0 4 . 1 7 5 5 6 0 . 6 8 3 4 0 6 . 0 6 4 1 0 5 . 0 5 7 1 4 1 . 7 5 3 5 1 . 7 5 3 5 0 4 . 6 0 7 7 9 0 . 7 8 0 6 7 6 . 3 5 5 3 0 5 2 9 5 7 0 1 . 8 3 7 0 1 . 8 3 7 0 0 5 . 0 5 9 9 4 0 . 8 8 5 7 6 6 . 6 4 6 5 2 5 5 3 4 2 9 1 . 9 2 0 5 1 . 9 2 0 5 0 5 . 5 3 2 0 1 0 9 9 8 9 2 6 . 9 3 7 7 2 5 . 7 7 2 8 4 2 0 0 4 0 2 . 0 0 4 0 0 6 . 0 2 4 0 0 1 1 2 0 3 7 7 . 2 2 8 9 5 6 0 1 1 4 3 2 . 0 8 7 5 2 0 8 7 5 0 6 . 5 3 5 9 2 1 . 2 5 0 3 3 7 . 5 2 0 1 5 6 . 2 4 9 9 8 2 . 1 7 10 2 . 17 1 0 0 7 . 0 6 7 7 5 1 . 3 8 9 0 1 7 . 8 1 138 6 . . 4 8 8 5 7 2 . 2 5 4 5 2 . 2 5 4 5 0 7 . 6 195 1 1 . 5 3 6 6 5 8 . 1 0 2 5 8 6 . 7 2 7 13 2 . 3 3 8 0 2 . 3 3 8 0 0 8 . 19 118 1 , . 6 9 3 4 4 8 . 3 9 3 8 0 6 9 6 5 7 1 2 . 4 2 1 5 2 42 1 5 0 8 7 8 2 7 8 1 , 8 5 9 6 1 8 . 6 8 5 0 0 7 , . 2 0 4 2 7 2 . 5 0 5 0 2 . 5 0 5 0 0 9 . 3 9 4 3 0 2 . 0 3 5 3 7 8 . 9 7 6 2 3 7 . 4 4 2 8 6 2 5 8 8 5 2 . 5 8 8 5 0 1 0 . 0 2 5 7 3 ' 2 . 2 2 0 9 3 9 . 2 6 7 4 3 7 , 6 8 1 4 1 2 . 6 7 2 0 2 . 6 7 2 0 0 1 0 . 6 7 7 0 9 2 . 4 1 6 4 8 9 5 5 8 6 6 7 . 9 2 0 0 0 2 7 5 5 5 2 . 7 5 5 5 0 1 1 . 3 4 9 1 0 2 . 6 1 8 5 8 9 . 8 7 2 0 4 8 . 1 8 4 9 8 2 . 8 3 9 0 2 . 8 3 9 0 0 12 . 0 4 4 17 2 8 2 9 8 6 1 0 . 1 9 6 6 4 8 . 4 6 3 3 3 2 . 9 2 2 5 2 . 9 2 2 5 0 12 . 7 6 2 4 8 3 . 0 5 2 5 3 1 0 . 5 2 1 2 2 8 . 74 165 3 . 0 0 6 0 3 . 0 0 6 0 0 1 3 . 5 0 4 0 2 3 . 2 8 6 8 6 1 0 . 8 4 5 8 0 9 . 0 1 9 9 7 3 . 0 8 9 5 3 . 0 8 9 5 0 14 . 2 6 8 8 1 3 . 5 3 3 0 9 1 1 . 1 7 0 4 0 9 . 2 9 8 3 2 3 . 1 7 3 0 3 . 17 3 0 0 15 . 0 5 6 8 4 3 . 7 9 147 1 1 . 4 9 4 9 8 9 . 5 7 6 6 4 3 . 2 5 6 5 3 . 2 5 6 5 0 15 . 8 6 8 1 2 4 . 0 6 2 2 5 1 1 . 8 1 9 5 9 9 . 8 5 5 0 0 3 . 3 4 0 0 3 . 3 4 0 0 0 16 . 7 0 2 2 2 4 . 3 4 9 3 4 12 . 1 2 8 1 8 1 0 . 1 1427 3 . 4 2 3 5 3 . 4 2 3 5 0 17 . 5 5 6 7 2 4 . 6 5 2 7 1 12 . 4 194 1 1 0 . 3 5 2 8 6 3 . 5 0 7 0 3 . 5 0 7 0 0 18 . 4 3 1 1 2 4 . 9 6 8 3 6 12 . 7 1061 1 0 . 5 9 1 4 2 3 . 5 9 0 5 3 . 5 9 0 5 0 19 . 3 2 5 4 9 5 . 2 9 6 4 9 13 . 0 0 1 8 3 1 0 . 8 3 0 0 0 3 . 6 7 4 0 3 . 6 7 4 0 0 2 0 . 2 3 9 7 5 5 . 6 3 7 2 5 13 . 2 9 3 0 3 1 1 . 0 6 8 5 6 3 . 7 5 7 5 3 . 7 5 7 5 0 2 1 . 1 7 3 9 2 5 . 9 9 0 8 3 13 . 5 8 4 2 6 1 1 . 3 0 7 14 3 . 8 4 10 3 . 84 1 0 0 22 . 1 2 8 0 2 6 . 3 5 7 4 3 13 . 8 7 5 4 6 1 1 . 5 4 5 7 0 3 . 9 2 4 5 3 . 9 2 4 5 0 '23 . 1 0 2 0 7 6 . 7 3 7 2 2 14 . 1 6 6 6 9 1 1 . 7 8 4 2 9 4 . 0 0 8 0 4 . 0 0 8 0 0 24 . 0 9 5 9 9 7 . 1301 1 14 . 4 5 8 6 2 12 . 0 2 3 7 3 4 . 0 9 1 5 4 . 0 9 1 5 0 2 5 . 1 1 0 2 9 7 . 5 3 4 4 0 14 . 7 5 7 4 4 12 . 2 7 1 4 7 4 . 1 7 5 0 4 . 1 7 5 0 0 2 6 . 1 4 5 3 2 7 . 9 5 2 6 4 15 . 0 5 6 2 5 12 . 5 1 9 2 1 4 . 2 5 8 5 4 . 2 5 8 5 0 2 7 . 2 0 1 0 2 8 . 3 8 4 9 7 15 . 3 5 5 0 8 12 . 7 6 6 9 7 4 . 3 4 2 0 4 . 3 4 2 0 0 2 8 . 2 7 7 4 0 8 . 8 3 1 6 2 15 . 6 5 3 9 0 13 . 0 1 4 7 1 4 . 4 2 5 5 4 . 4 2 5 5 0 2 9 . 3 7 4 4 8 9 . 2 9 2 7 5 15 . 9 5 2 7 3 13 . 2 6 2 4 7 4 . 5 0 9 0 4 . 5 0 9 0 0 3 0 . 4 9 2 2 3 9 . 7 6 8 5 5 16 . 2 5 1 5 4 13 . 5 1 0 2 1 4 . 5 9 2 5 4 . 5 9 2 4 9 31 . 6 3 0 6 8 1 0 . 2 5 9 2 0 16 . 5 5 0 3 7 13 . 7 5 7 9 7 4 . 6 7 6 0 4 . 6 7 5 9 9 3 2 . 7 8 9 7 9 1 0 . 7 6 4 8 9 16 . 8 4 9 1 7 14 . 0 0 5 6 9 4 . 7 5 9 5 4 . 7 5 9 4 9 3 3 . 9 7 0 0 2 1 1 . 2 8 0 7 7 17 . 1 5 9 8 8 14 . 2 6 7 6 1 4 . 8 4 3 0 4 . 8 4 2 9 9 3 5 . 1 7 2 5 3 1 1 . 8 1 0 4 8 17 . 4 7 5 3 7 14 . 5 3 5 2 3 4 . 9 2 6 5 4 . 9 2 6 4 9 3 6 . 3 9 7 4 3 12 . 3 5 6 3 2 17 . 7 9 0 8 9 14 . 8 0 2 8 7 5 . 0 1 0 0 5 . 0 0 9 9 9 37 . 6 4 4 6 4 12 . 9 1 8 4 5 18 . 1 0 6 4 0 15 . 0 7 0 5 0 222 5 . 0 9 3 5 5 . 0 9 3 4 9 38 .91418 5 . 1770 5 .17699 40 .20607 5 . 2605 5 . 2 6 0 4 9 4 1 .52034 5 . 3440 ' 5 . 3 4 3 9 9 42 . 85660 5 . 4275 5 . 4 2 7 4 9 44 . 2 1 3 0 3 5 . 5 1 1 0 5 . 5 1 0 9 9 45 . 5 8 9 4 0 5 . 5945 5 . 59449 46 .98572 5 . 6 7 8 0 5 . 6 7 7 9 9 48 . 4 0 1 9 5 5 . 76 15 5 .76 149 49 .83806 5 . 8450 5 . 8 4 4 9 9 51 .294 10 5 . 9285 5 . 9 2 8 4 9 52 .77011 6 . 0 1 2 0 6 . 0 1 1 9 9 54 .26599 e . 0 9 5 5 6 . 0 9 5 4 9 55 . 78 178 6 . 1790 6 . 1 7 8 9 9 57 .31754 6 . 2625 6 . 2 6 2 4 9 58 .8732 1 e . 3460 6 . 3 4 5 9 9 60 .44879 G . 4 2 9 5 6 .42949 62 .04428 6 . 5 130 6 . 5 1 2 9 9 63 . 6 5 9 7 0 6 . 5965 6 . 5 9 6 4 9 65 .29507 6 . 6800 6 . 6 7 9 9 9 66 . 9 5 0 3 0 6 . 7635 6 . 76349 68 . 6 2 6 4 5 6 . 8470 6 . 8 4 6 9 9 70 . 3 2 5 7 3 6 . 9305 6 . 9 3 0 4 9 72 .04829 7 . 0 1 4 0 7 . 0 1 3 9 9 73 . 7 9 4 0 5 7 . 0 9 7 5 7 . 0 9 7 4 9 75 . 5 6 3 0 3 7 .18 10 7 .18099 77 . 35530 7 2645 7 . 2 6 4 4 9 79 :17082 7 . 3480 7 . 3 4 7 9 9 8 1 .00899 7 . 4 3 15 7 .43 149 82 .86737 7 . 5 1 5 0 7 .51499 84 . 7 4 5 7 0 7 . 5985 7 .59849 86 .64398 7 . 6 8 2 0 7 .68199 88 562 15 7 . 7655 7 . 76549 9 0 . .50021 7 . 8490 7 .84899 92 . . 45822 7 . 9325 7 . 93249 94 .43619 e . 0 1 6 0 8 .01599 96 43404 e . 0 9 9 5 8 .09949 98 . 45172 8 . 1830 8 .18299 100. 48947 8 2665 8 26649 102 . 54700 8 3500 8 . 34999 104 . 62466 8 . 4335 8 . .43349 106 . 72200 8 . 5170 • 8 . 51699 108 . 83945 8 . 6005 8 . 60049 1 10. 97665 8 . 6840 8 . 68399 113. 13397 8 . 7675 8 . 76749 115. 31209 8 . 85 10 8 . 85099 117. 51358 8 . 9345 8 . 93449 119. 738 1 1 9 . 0 1 8 0 9 . 01799 121 . 98613 9 . 1015 9 . 10149 124 . 257 16 9 . 1850 9 . 18499 126 . 55159 9 . 2685 9. 26849 128 . 86909 9 . 3520 9 . 35199 131 . 2094 1 9 . 4355 9 . 43549 133 . 56967 9 . 5190 9 . 51899 135 . 95003 9 . 6025 9 . 60249 138 . 35013 9. 6 8 6 0 9 . 68599 140. 77037 9. 7695 9 . 76949 143 . 21028 9 . 8 5 3 0 9 . 85299 145 . 67036 9 . 9365 9 . 93649 148 . 15013 10. 0 2 0 0 10. 01999 150. 65005 13 .49707 18 .42 19 1 15 .33813 14 .09241 18 . 73740 15 .60574 14 .70467 19 . 0 5 2 9 0 15 . 87337 15 . 3 4 0 6 0 19 .3556 1 16 . 12569 15 .99913 19 .64684 16 .36427 16 .67435 19 .93803 16 .60283 17 .36639 20 . 22925 16 . 84 142 18 . 0 7 5 4 5 20 .52045 17 .07997 18 .80159 20 .81 168 17 .31856 19 .54504 2 1 .10287 17 . 557 1 1 20 . 3 0 6 0 0 2 1 .394 10 17 . 7 9 5 7 0 2 1 .08453 2 1 .68529 18 .03424 2 1 . 8 8 0 8 0 2 1 . 9 7 6 5 0 18 .27283 22 .69502 22 .26772 18 .51138 23 . 52733 22 .55893 18 . 74997 24 . 37784 22 .85013 18 .98853 25 . 24670 23 .14136 19 . 227 1 1 26 . 134 12 23 .43256 19 .46567 27 .04022 23 . 72379 19 .70425 27 . 9 6 5 1 3 24 .01498 19 .9428 1 28 .88951 24 .33157 20 .21164 29 . 8 2 8 0 0 24 .65616 20 .48996 30 . 787 14 24 .98073 20 .76828 3 1 .76706 25 .30533 2 1 .04663 32 .76794 25 .62991 2 1 .32495 33 .79007 25 .95451 2 1 .60330 34 .83359 26 .27908 2 1 .88 162 35 .91554 26 . 58450 22 .13712 37 .03075 26 . 87570 22 .37567 38 .16650 27 .16693 22 .61426 39 32301 27 . 458 1 1 22 8528 1 40 .50031 27 .74934 23 . 09 140 4 1 69858 28 . 04054 23 . 32996 42 9 1792 28 33 177 23 . 56854 44 . 15862 28 . 62297 23 . 807 10 45 . .42067 28 . 914 18 24 , 04568 46 . . 70419 29 . 20538 24 . 28424 48 . 00951 29 . 49660 24 . 52283 49 . 3 3 6 5 5 . 29 . 7878 1 24 . 76 1 38 5 0 . 68567 3 0 . 07903 24 . 99997 52 . 05676 3 0 . 37022 25 . 23853 53 . 45016 3 0 . 66 145 25 . 477 1 1 54 . 86589 3 0 . 95265 25 . 7 1567 56 . 30424 31 . 24388 25 . 95425 5 7 . 73293 3 1 . 56204 26 . 22495 59 . 17831 3 1 . 88663 26 . 50330 6 0 . 64801 32 . 2 112 1 26 . 78162 62 . 14261 32 . 53580 27 . 05995 63 . 66185 32 . 86040 27 . 33829 •65 . 20627 33 . 18497 27 . 61661 66 . 7757 1 33 . 50957 27 . 89496 68 . 39833 33 . 81337 28 . 14853 7 0 . 06175 34 . 10458 28 . 38708 71 . 74939 34 . 39580 28 . 62567 7 3 . 46107 34 . 68700 28 . 86423 7 5 . 19739 34 . 97820 29 . 10281 76 . 95795 35 . 26942 29 . 34137 78 . 743-32 35 . 56062 29 . 57996 8 0 . 55324 3 5 . 85185 29 . 81851 82 . 38828 36 . 14 305 3 0 . 057 10 10. 1035 10.1870 10.2705 10.3540 10.4375 10.5210 10.6045 10.6880 10.7715 10 . 8550 10.9385 1 1 .0220 1 1 . 1055 11.1890 1 1.2725 11.3560 11.4395 1 1 . 5230 11.6065 11.6900 11.7735 11.8570 11 9405 12.0240 12.1075 12.1910 12.2745 12.3580 12.44 15 12.5250 12.6085 12.6920 12.7755 12.8590 12.9425 13.0260 13.1095 13.19 30 13.2765 13.3600 13.4435 13 . 5270 13.6105 13 .6940 13 . 7775 13.8610 13.9445 14.0280 14.1115 14.1950 14.2785 14.3620 14.4455 14.5290 14.6125 14.6960 14.7795 14.8630 14.9465 15.0300 10.10349 10.18699 10.27049 10.35399 10.43749 10.52099 10.60449 10.68799 10.77149 10.85499 10.93849 11.02199 11.10549 11.18899 11.27249 11.35599 11.43949 11.52299 11.60549 11.68999 11.77349 11.85699 11.94049 12.02399 12.10749 12.19099 12.27449 12.35799 12 .44 149 12.52499 12.60849 12.69199 12.77549 12.85899 12.94249 13.02599 13.10949 13.19299 13.27649 13.35999 13.44349 13.52699 13.61049 13.69398 13.77748 13.86098 13.94448 14.02798 14. 11 148 14.19498 14.27848 14.36198 14.44548 14.52898 14 .61248 14.69598 14 . 77948 14.86298 14.94648 15.02998 153.16966 155.70943 158.26888 160.84846 163.44775 166.06721 168.70634 17 1. 36563 174.0458 1 176.74945 179.47609 182.22618 184.99930 187.79593 190.61551 193.4578 1 196.31999 199.20238 202.10442 205.02660 207.96846 210.93053 2 13.91223 2 16.91408 2 19.93562 222.9774C 226.03877 229.12030 232.22 15 1 235.34300 238.48405 241.64526 244.8275 1 248.03334 251.26207 254.51427 257.78906 261.08765 264.40918 267.75342 271.11743 274.50171 277 . 90576. 281.32959 284.77344 288.23706 291.72095 295.22534 298.74854 302.29248 305.85547 309.43896 313.04224 316.66553 320.30859 323.97168 327.65576 331 .36353 335.09448 338 .84839 84.24808 86.13332 88.04356 89.97939 91.94057 93.92764 95.94028 97.97905 99.99544 102.03175 104.09601 106.18860 108.30954 110.45930 1 12. 63742 1 1 4 . 88608 117.182 17 119.50606 12 1.857 16 124.2361 1 126.64270 129.07738 13 1 .53972 134.03058 136.5494 1 139.09597 14 1.67259 144.27728 146.91025 149.57257 152.26369 154.98398 157.66539 160.37 128 163.10846 165.87732 168.67723 17 1 .50981 174.37421 177.32918 180.33717 183.37622 186.44565 189.54576 192.67664 195.83870 199.03201 202.25725 205.51256 208.80020 2 12.11862 215.46930 218.85155 222.26593 225.7 1220 229.19063 232.60960 236.05896 239.54309 243.06177 36.43427 36.72546 37.01668 37.30789 37.59909 37.89032 38.18152 38.47275 38.79253 39. 1 17 1 1 39 . 44 170 39 . 76627 40.09087 40.41545 40.74005 41.04224 41.33347 41.62466 41 .91588 42.20708 42.49831 42.78951 43.08073 43.37 192 43.66315 43 . 95435 44 . 24556 44 . 53677 44.82799 45.11920 45.41042 45 . 70163 46.02301 46.34760 46.672 15 46.99675 47.32133 47.64594 47.97052 48.27112 48 . 56235 48.85355 49. 14478 49.43597 49.72720 50.01840 50.30963 50.60083 50.89204 5 1 . 18326 5 1 . 47446 5 1 . 76567 52.05688 52.34808 52.63931 52.93051 53 . 25348 53.57808 53.90265 54.22723 30.29565 30.53424 30.77280 31.01138 31.24995 31.48853 31.72710 31.96567 32.23828 32.51660 32.79495 33.07327 33.35162 33.62994 33.90826 34.15994 34.39853 34.63708 34.87567 35.11423 35.3528 1 35.59137 35.82996 36.06851 36.307 10 36.54565 36.78424 37.02280 37.26138 37.49994 37.73853 37.97708 38.25162 38.52994 38.80826 39.08661 39.36493 39.64328 39.92160 40.17137 40.40994 40.64851 40.88708 4 1 . 12566 4 1 .36423 4 1 .60280 41.84137 42.07996 42.31851 42 . 557 10 42.79565 43.03424 43.27280 43.51138 43.74994 43.98853 44.26492 44 . 54327 44.82159 45.09993 15 . 1 135 15 .11348 342 .62573 246 .61557 54 .55182 45 . 37827 15 . 1970 15 .19698 346 .42676 250 .20500 54 .87640 45 .65659 15 . 2805 15 .28048 350 .25049 253 '. 82886 55 .20102 45 .93494 15 . 3640 15 .36398 354 .09619 257 .5664 1 55 .50002 46 . 18280 15 . 4475 15 .44748 357 .96240 26 1 .36206 55 .79121 46 .42 136 15 . 53 10 15 .53098 361 .84863 265 .19 116 56 .08244 46 .65994 15 .6 145 15 .61448 365 .75464. 269 .05396 56 .37363 46 .89850 15 . 6980 15 .69798 369 .68042 272 .94995 56 .66486 47 .13708 15 78 15 15 . 78 148 373 .62622 276 88013 56 .95605 47 .37564 15 . 8650 15 .86498 377 , 59180 280 . 84399 57 . 24728 47 .61423 15 . 9485 15 .94848 38 1 . 57764 284 , .84229 57 . 53848 47 , .85278 16 . 0320 16 .03198 385 . 58301 288 . 87402 57 , .82970 48 09 1 37 16 . 1 155 16 .11548 389 . 60864 292 . •94 1 16 58 . 12090 48 32993 16 . 1990 16 . 19897 393 . 65356 297 . 04 126 58 . 4 1 209 48 . 56848 16 . 2825 16 . 28247 397 . 7 1875 301 . 17676 58 . 70328 48 . 80704 16 . 3660 16 . 36597 401 . 80396 305 . 34668 58 . 99449 49 . 04562 16 . 4495 16 . 44946 405 . 909 18 309 . 55151 59 . 28569 49 . 284 18 16 . 5330 16 . 53296 4 10. 034 18 313. 79077 59 . 57690 49 . 52274 16 . 6 165 16 . 6 1646 4 14. 17896 318 . 06494 59 . 868 10 49 . 76129 16 . 7000 16 . 69995 4 18. 34375 322 . 37476 60. 15929 49 . 99985 16 . 7000 16 . 70000 4 18. 34668 322 . 37744 60. 15945 50. 00000 a Water Surface Elevation b Water Depth c Area of Section d Normal Discharge e Wetted Perimeter f Top Width of Water Surface XNI= O.O5O0 TRIBUTARY A ™ T T 0 L R = . OOOO010 XN2 = 0.0500 DE L T = 120 OOOOO DE L A = 10.00000 DELX= 2390. APPENDIX D.4 IN SECTION NO = 1 OUT SECT I ON NO IN AREA IN DISCH OUT AREA OUT OISCH TOTAL TIME 0 .0 0.0 0 .0 0 0 0 0 .0 0.0 0 00-12 1 0 00227 120 0 .0 0.0 0 . oon i •) 0 005 1 3 240 0 .0 0.0 0 .08836 0 .11506 360 0 .0 0.0 0 .52 15 1 1 2 17 2 3 480 0 .0 0.0 1 .39103 4 . 43395 • ' 600 0 .0 0.0 1 72748 5 90.4 4 6 720 0 0 0.0 1 . 7 4 276 5 973^4 840 0 .0 0.0 1 . 57720 5 23466 960 o .0 O.O 1 . 32530 4 16066 1080 o .0 0.0 1 .05482 3 07925 1200 0 .0 0.0 0 . 82809 2 24890 1320 0 .0 0.0 0 66 12 1 1 67086 1440 0 0 0.0 0 . 53472 1 25964 1560 0 0 0 0 o 4 3 7 7 7 O 96546 1680 0 0 0.0 0 36237 0 75087 1800 0 .0 0.0 0 303 1 1 o 59013 1920 0 0 O.O 0 2557 1 0 47204 2040 o 0 0 0 0 2 175H o 37966 2 160 0 0 0 o 0 1BG4 3 0 3 1026 2280 0 .0 0.0 0 16097 0 25354 2400 0 0 0.0 0 13974 0 2 1 134 2520 0 .0 0.0 0 12 199 0 17675 2640 0 0 0.0 0 107 15 0 14783 2760 o .0 0.0 0 09457 0 12528 2880 0 0 0.0 0 OR37 7 0 1075 1 3000 0 0 0.0 0 07 4 5 1 0 09226 3120 0 0 0.0 0 06G56 0 07917 3240 o 0 0.0 0 059 7 4 0 06794 3360 0. .0 0.0 0 05380 0 05915 3480 0 0 0.0 0 04855 0 0522 1 3600 0 0 0.0 0 04393 0 04609 3720 0 0 0 0 0 03984 0 04068 3840 o 0 O.O 0 .0362 4 0 03591 3960 0 0 0.0 0 03305 0 03 170 4080 0 0 0.0 0 0302 4 o 02798 4 200 0 0 0.0 0 02776 0 02470 4320 0. 0 0.0 o .02557 0 02 180 4440 0 0 0 0 0. 02359 0 01980 4560 0. 0 0.0 0 02 177 0. 01808 4680 0 .0 0.0 0 0201 1 0 01650 4800 0 0 0.0 0. .01860 0 0 1506 4920 o. o O.O 0 O 1 7 2 2 0 01375 5040 0. 0 0.0 0 01596 0 01256 5 160 SECONDS NJ NJ Ln XNI= 0.0500 TRIBUTARY B TOLR=.0000010 XN2 = 0.0500 DE L T = 120 00000 DE LA = 10.00000 DELX = 3460. IN SECTION NO OUT SECTION NO = IN AREA IN DISCH OUT AREA 0U1 DISCH TOTAL TIME 0 0 0 .0 • 0 0 0 0 0 0 0 0 0 0 004 26 0 00256 120 0 .0 0 .0 0 .000 29 0 .00588 240 0 .0 0 .0 0 139 1 1 0 . 2 3501 360 0 .0 0 .0 0 .06791 2 .66855 480 0 .0 0 .0 2 3523 1 9 .93426 600 0 .0 0 .0 2 95526 13 53142 7 20 0 0 0 0 3 01222 13 B8944 B40 0 .0 0 0 2 .75582 12 . 30760 - 960 0 .0 0 .0 2 3 44BO 9 .89285 1080 0 .0 0 0 1 . B925B 7 .4459B 1200 0 .0 0 0 1 .50950 5 5228 1 1320 0 .0 0 0 1 22023 4 17019 1440 0 .0 0 0 0 . 9979R 3 .20417 1560 0 .0 0 0 0 82475 2 49745 1680 0 0 0 0 0 6RR 1 2 1 .96976 IBOO 0 .0 0 0 0 .57932 1 .56843 1920 0 .0 0 0 0 4 9 19 3 1 .259R8 2040 0 .0 0 0 0 4 2095 1 .02 339 2 160 0 .0 0 0 0 362G5 O .R4040 2280 0 .0 0 0 0 3 1457 0 . 693 15 2400 0 0 0 0 0 . 27436 0 57974 2520 0. 0 0 0 0 . 24066 0 48585 2640 0 0 0 0 0 2 12 15 0 .41097 2760 0 0 0. 0 0 1R7B4 0 35045 2880 0. 0 0. 0 0 16 7 12 0 298B4 3000 0. 0 0. 0 0 14928 0 257 14 3120 0 0 0. 0 0 13378 0 22340 3240 0. 0 0. 0 0 12032 0 19409 3360 0. 0 0. 0 0 10R62 0 16862 3480 0. 0 0 0 0 09R4 1 O 14727 3600 0. 0 0 0 0 OR 9 35 0 13056 3720 0. 0 0 0 0 OR 1 32 0 1 1574 3840 0. 0 0 0 0 .07421 O 1026 1 3960 0. 0 0 0 0. 06790 0 09097 4080 0. 0 0. 0 0 OC2 30 0 08064 • 4200 0. 0 0. 0 0 05734 0. 07 149 4320 0. 0 0. 0 0 052R6 0 06467 4440 0. 0 0 0 0 04879 0 05864 4560 0 0 0. 0 0. 045 10 0. 053 18 4680 0. 0 0. 0 0 04 176 0. 04822 4800 0 0 0. 0 0 . 03R72 0 04373 4920 0. 0 0. 0 0 03597 0. 03966 5040 0. 0 0. 0 0 . 033 18 0 03596 5160 SECONDS K3 XN1= 0.0500 TRIBUTARY C T0LR=.0000010 XN2 = 0.0500 DEl_T = 120 0 0 0 0 0 DELA = 10.00000 DELX= 2 130. IN SECTION NO IN AREA 0.0 0.0 O 0 0.0 O.O 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 0 0.0 0 0 0.0 0.0 0.0 0.0 O.O 0.0 0.0 0.0 0.0 0.0 . 0.0 O.O 0.0 0.0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 O.O 0.0 IN DISCH 0.0 0. o. o. o. 0. o. o. o. 0. 0. o. o. o. o. o. 0. 0. o 0 o o o. o 0 0 o 0 o 0 o o 0 o o 0 o o 0 o o 0 0.0 0.0 OUT SECTION NO OUT AREA O.O 0 00«17 t o oon 15 0. 1 2083 0 . 66 1f>7 1 71O80 2.7003R 2.33831 2 26385 2.07050 1.8 1913 1 .553G7 1.31110 1.09998 0.91-172 O.7 52 36 0.61316 0 50O65 O 4 t350 O.34490 0 29040 O 24656 0.21095 0 18170 0.15766 0 13747 O 12O50 0.10624 0 094 10 0 08363 0.07462 0.06686 0.OGO17 0 054 3 1 0.04918 O . 04.160 0.04054 0 03G95 0.03376 O 03091 O.0284 4 0.0262? 0 02422 O.02239 OUT DISCH 0.0 O 00200 0 004 50 O. 15 115 1 44825 5.04797 7 04662 7.63535 7.31753 6.49802 5.475G5 4.4445 1 3 55204 2.81791 2 2 1119 1.71399 1 30892 O.99844 O 77349 O.60884 O.48367 O 38908 O.31603 0 25962 O. 2 1333 O. 17924 O.15059 0. 12652 0.10782 0.09286 O 07998 O 06889 0 05933 O.05173 0.04585 0.04063 0.03601 0.03191 '0.02828 0.02506 0.02221 0.01968 0.01774 0.01623 TOTAL TIME . 0. 120. 240. 360. 480. 600. 720 . 840. 960 . 10BO. 1200. 1320. 1440 . 1560. 1680. 1800. 1920. 2040. 2 160. 2280. 2400. 2520. 2640. 2760. 2880. 3000. 3120. 3240. 3360. 3480. 3600. 3720. 3840. 3960. 4080. 4200. 4320. 4440. 4560. 4680 . 4 800. 4920. 5040. 5160. SECONDS Ni- ls? XNi* O.O500 TRIBUTARY D TOLR= .0000010 XN2= 0 0500 OEI.T = 120. 0 O 0 0 0 D F L A = 10 OOOOO DE LX = 2380. IN SECTION NO = OUT SEC1 I ON NO = IN AREA IN DISCH OUT AREA OUT DISCH TOTAL TIME 0 0 0 0 0.0 0 .0 0 0 .0 0.0 0.004 21 0 .002 2 7 120 O .0 0.0 0 ..00H1:) 0 .005 1 2 240 0 .0 0.0 O.OB24 1 0 .10526 360 0 .0 0.0 0 . 4 7 4 1 r, 1 073B8 480 0 .0 0.0 1.26552 3 9 1 208 600 0 .0 0.0 1 57378 5 2 1978 720 0 .0 0.0 1 .63058 5 . 467 16 840 0 .0 0.0 1.60034 5 . 33546 960 0 .0 0.0 1 .52237 4 .99585 1080 0 .0 0.0 1 .4 1552 4 .53580 1200 0 .0 0.0 1 .29 188 4 .02166 1320 0 0 0.0 1 . 15977 3 .49063 1440 0 .0 0.0 1.02512 2 .96774 1560 0 .0 0.0 0 B9205 2 .47244 1680 0 .0 0.0 0.7637 1 2 Ol 762 1800 0 .0 0.0 O.64309 1 .60956 1920 0 .0 0.0 0.53328 1 .25504 2040 0 .0 0.0 0 43787 0 96575 2 160 0 .0 0.0 0 36220 0 .75040 2280 0 0 0.0 O.302 7 7 0 58929 2400 0 0 0.0 0 25528 0 47097 2520 0 .0 0.0 0 2 17 10 0 .37B59 2640 0 0 0.0 0 18593 0 .30915 2760 0 .0 0.0 0 1604 7 0 25244 2880 0 .0 0.0 0.13926 0 .21039 3000 0 0 0.0 O. 12 152 0 175B4 3120 0 0 0.0 0.106 70 0 14696 3240 0 0 0.0 0.09414 0 12458 3360 0. 0 0 0 0.OB337 0 10684 3480 0. 0' 0.0 0.07413 0 .09163 3600 0. 0 0.0 0.06620 0 .07858 3720 0. 0 0.0 0.0594 1 0 .06739 3840 0. 0 0.0 0.05348 0 05873 3960 0. 0 0.0 0 04826 0 05 182 4080 0. 0 0.0 0 04 365 0 04572 4200 0. 0 0.0 0.03958 0 .04034 4320 0. 0 0.0 0 03599 0 .03559 4440 0. 0 0 0 0.03283 0 03 140 4560 0. 0 0.0 0.03003 0 .02770 4680 0. 0 0.0 0 02757 0 .02444 4800 0. 0 0.0 0.02539 0 02 156 4920 0. 0 0.0 0.02341 0 01964 5040 0. 0 0.0 0.02161 0 01792 5160 SECONDS NJ 00 XIMI= . 0.0500 TRIBUTARY E TOLR-.0000100 XN2 = 0.0500 DEL T = 1?0 OOOOO DE I A = 10.00000 DE L X = 1750. IN SECTION NO Oil T S F C T I O N ND = IN AREA IN DISCH Our AREA OUT DISCH TOTAL TIME 0 .0 o .0 o 0 0 0 0 0 .0 0 .0 0 .0030 7 0 .00340 120 0 .0 o .0 0 .007JJ 0 00708 240 0 .0 0 .0 0 06 J66 O 12015 3GO 0 .0 0 .0 0 36 153 1 1B358 480 0 .0 0 .0 0 9 1 3R9 4 032 15 600 0 .0 0 .0 1 .01636 4 .64032 720 0 .0 0 .0 0 94 1 RR 4 19R30 840 0 .0 o . 0 o R39G5 3 6 1518 960 0 .0 0 0 0 732GO 3 .02372 1080 0 .0 0 .0 0 62G90 2 .4 5960 1200 0 .0 0 .0 0 527B9 t .95709 1320 0 .0 o 0 0 . 4 4 6 7 R 1 5G903 1440 0 .0 0 .0 0 39R33 1 .34 305 1560 0 .0 0 .0 o .3640R 1 19162 1680 0 .0 0 0 0 3274G 1 .03595 1800 0 .0 0 0 o 2829 1 O 85348 1920 0 .0 o 0 0 .2 3304 0 657 1 1 2040 0 .0 0 .0 0 1H237 0 . 4 7640 2 160 0 .0 0 0 0 .137R8 0 .32860 22BO 0 .0 0 0 0 10620 0 .23099 2400 0 .0 0 0 0 083 12 0 .16833 2520 0 .0 0 0 0 066 1 2 0 12396 2640 0 .0 0 0 o 05342 0 .09261 2760 0 .0 0 0 0 04 355 0 07 198 2880 0 0 o. 0 0 0358 7 o .05595 3000 0 0 0 0 0 0299 1 0 0 1349 3120 0 0 0. 0 0 02527 0 03380 3240 0 0 0 0 0 02 1 43 0 02804 3360 0 0 0. 0 0 01R2J o 02326 3480 0. 0 o . 0 o. 0 1559 0 01929 3600 0 0 o . o 0 013 IO 0 . 0 1600 3720 0 0 0. 0 0 01 15R 0 01328 3840 0 0 0 0 0. 01006 0 01 101 3960 0. 0 0. o 0 OORfl 1 0. 009 1 3 4080 0. 0 0. 0 o 007 7 7 0 007 58 4 200 0. 0 o . 0 0 0069 1 o. 00629 4320 0. 0 0. 0 o. OOG 1 9 o. 00529 4440 0. 0 o . o 0 005 5-1 0. 00J73 4560 0. 0 0. o 0 . 00-19G 0 OOJ2 3 4680 0. 0 0. 0 0. OO 14 1 0. 0037 9 4 800 0. 0 0 0 0 0039 7 0. 00339 4920 o. 0 0 0 0 0035 5 0. 00304 5040 0. 0 0. o 0 003 18 0 . 002 7 2 5 160 SECONDS VD TOLR= .0000100 XN2 = O 0500 DF L T - 1 20 . O O O O O DF I. A - 10.OOOOO DE I X = 1290 IN SECTION NO 0U1 S E C T I D N N O IN AREA IN DISCH OUT ARFA OUT DISCH TOTAL TIME 0 0 O 0 O.O 0 . 0 0 0. 00397 0. 00340 0.00101 0. 0004 8 120 0. 00744 0 0O70R O.O03O3 0 O O 1 4 4 240 0 06466 O. 12015 0 OR 4 7 1 0 09 369 360 0. 36 153 1 . 18358 0 53 188 1 08302 480 0. 91389 4 . 032 15 1 568 18 4 49923 600 1 01636 4 . 64032 2.28178 7 39407 720 0 94 188 4 . 19830 2.5802 4 8 7 158R 840 O 83965 3 . 6 1548 2 597 I'l 8 79 187 960 0 7 3260 3 02372 2 . 2397.1 7 2 1460 1080 0 62690 2 . 4 5960 1.93403 5 93 7 80 1200 0 52789 1 . 95709 1 .66089 4 8509 7 1320 "0 .44678 1 56903 1.41746 3 93502 1440 0 39833 1 . 34305 1.21142 3 19994 1560 0 .36 408 1 . 1946 2 1 04 7 4 7 2 64265 16BO 0 .32746 1 . 03595 0 91686 2 2 18 18 1BOO 0 28291 O. 85348 0 806 7 9 1 87938 1920 0 23304 O 657 1 1 O. 7056 3 1 57 707 2040 0 18237 0. 47640 0 61025 1 30084 2 160 0 13788 0 32860 O 5 2053 1 05 1 50 2280 0 . 10620 O. 2 3099 0.4 3903 0 83938 2400 0 083 12 O. 16833 O . 36 9 36 O 66686 • 2520 0 .06612 O. 1239G O . 3 1 108 0 52 860 2640 o 05342 O 0926 1 O 26 2:iO 0 4 2 304 2760 0 04 355 O 07 198 0.2 2 260 0 33848 2880 0 03587 O. 05595 0. 18956 0 27477 3000 0 .02991 O. 04 349 O. 16228 0 222 17 3 120 0 02527 O 03380 0 13929 0 1823 1 3240 0 .02143 O O2 804 O 1203/ 0 15037 3360 0 01B24 O 02326 O 104RO 0 12409 3480 o 01559 O. 01929 0.OH 163 0 10430 3600 0 .01340 0 01600 0.08039 0 .08823 3720 0 .01158 0 01328 0 07081 0 07454 3840 0 01006 0 01101 0 06267 0 06 290 3960 0 .00881 0 009 1 3 O 05571 0 .05329 4080 0 .00777 0. 00758 0.04 955 0 04627 4 200 0 0069 1 0 006 29 O.04 4 1 7 0 04 008 4320 0 006 19 0 00529 0.03938 0 03168 4440 0 00554 0 004 7 3 0 03532 0 03005 4560 0 00496 0 004 2 3 0 031R3 0 .02608 4680 0 00444 0 0037 9 O 02884 0 .02 26 7 4 800 0 00397 0 00339 0.02627 0 0 1974 4920 0 00355 0 00304 O 02 3<iR 0 01754 5040 o 003 18 0 002 7 2 0 . 02 19.' 0 .Ol584 5 160 0 00285 0 0024 3 0 02004 0 0 1 4 30 5280 SECONDS ho O TOLR = OOOO100 XN2 = O.0500 IN SECTION NO = 3 IN AREA IN DISCH 0. 0 0. 0 O. 00101 0. 0004 8 0. 00303 0. 00144 0. 0842 1 0. 09369 0. 53188 1 08302 1 5G8 18 4 . 49923 2 . 28 178 7 . 39407 2 58024 8 : 7 1588 2 . 597 19 8 . 79 187 2 . 23973 7 . 2 1460 1 . 93403 5 . 93780 1 . 66089 4 85097 1 4 1746 3 . 93502 1 . 21 142 3 19994 1 . 04747 2 . 64265 O. 91686 2 . 2 18 18 O 80679 1 . 8793B 0 70563 1 . 57707 0 6 1025 1 . 30084 0 .52053 1 . 05 150 o 43903 0. 83938 0 36936 0. 66686 O .31108 0. 52860 0 .26230 0. 42304 o . 22260 0 33848 o . 18956 0 27477 0 . 16228 0. 222 17 O . 13929 0 1823 1 0 .12037 0 . 15037 o .10480 0 .12409 0 .09163 0 .104 30 0 .08039 0 .08823 0 .0708 1 0 07454 o .06267 0 06290 0 .05571 0 .05329 0 .04955 0 .04627 0 044 12 0 .04008 0 .03938 0 .03468 0 .03532 0 03005 0 .03183 0 .02G0R 0 .02884 0 022G7 0 .02627 0 .01974 o .02398 0 .01754 0 .02192 0 .01584 0 .02004 0 01430 D E I. T = ISO 00(100 DEI. A- 1 0 . 0 0 0 O 0 DEl.X = 1 1 3 0 . OUT SECT ION NO = 4 OUT AREA OUT DISCH TOTAL TIME , SECONDS 0.0 0 . 0 0 0.003 2 7 0 0 0 1 7 4 120 0 00551 0 . 002 1 1 240. 0 07 35 4 0 . 0G407 360 . 0 48936 0 79 146 480. 1 .52493 3 54047 600 . 2 . 4 24 66 G . 54 7 12 720. 3 13253 9 . 7627H 840 3.5G932 1 1 . 057 12 960. 3 52487 10. R69 1 7 1080. 3 . 28G73 9 RR8 1 3 1200. 2 973RR fl G32 1 1 1320. 2 63757 7 . 32927 1440. 2.303 79 6 1 1397 1560. 1 .992 70 5 0149 1 1680. 1.72704 4 15759 1800. 1.4 9807 3 45773 1920 . 1.3154G 2 9 13 12 2040. 1 1G 17 4 2 . 47372 2 160. 1 027G7 2 105 16 2280. 0.90778 1 787G0 2400. 0.79791 1 5 12 18 2520. 0.G9R5G 1 27077 2640. 0 6 1115 1 OG4 25 2760 0 53393 0 RR901 2880 . 0.4G7 17 0 74468 3000 0.40935 0 .62281 3120. O.3594 9 0 52534 3240 0.3164 7 0 .44199 3360 0 77885 0 .37453 3480 0.2466G 0 3 1786 3600 O 21911 0 2 7090 3720 O. 19503 0 23299 3840 0 17 40G 0 19998 3960 0 155B7 0 .17174 4080 0 14002 0 .14989 4 200 0 126 18 0 13080 4320 0. 1 1405 0 1 1409 4440 0.10339 0 09938 4560 0 09379 0 08769 4680 0.OH512 0 07757 4800 0.0/734 0 .06850 4920 0.07019 0 0605 1 5040 0.0G455 0 .05357 5 160 0.0593G 0 04752 5280 TOLR =.OOOO100 XN2 = 0.0500 IN SECTION NO = 4 IN AREA IN DI SCH 0. 0 0. 0 0. 00327 0. 00124 0. 00554 0. 002 1 1 0. 07354 0. 06407 0. 4B936 0. 79146 1 . 52493 3 54047 2 . 42466 6 . 547 12 3 . 13253 9. 26278 3 56932 1 1 . 057 12 3 52487 10 86917 3 2B673 9 . 8BB 13 . 2 973B8 8 632 1 1 2 63752 7 32927 2 30379 6 1 1392 1 99270 5 0449 1 1 72204 4 15759 1 49807 3 45773 1 31546 2 91312 1 16 174 2 47372 1 02767 2 105 16 0 90778 1 78760 0 7979 1 1 5 12 18 0 69856 1 27077 0 61115 1 06425 0 53393 0 88901 0 467 17 0 74468 0 40935 0 6228 1 0 35949 O 52534 0 31647 0 44 199 0 27885 0 37453 0 24666 0 3 1786 0 219 11 0 27090 0 19503 0 23299 0 17 406 0 19998 0 15587 0 17 17 4 0 14002 0 14989 0 12618 0 .130BO 0 1 1405 0 .11409 0 .10339 0 .09938 0 .09379 0 .08769 0 .085 12 0 .07757 0 .07 7 34 0 .06B50 0 .07049 0 .06051 0 .06455 0 .05357 0 .05936 0 04752 DELT- 120.00000 OE L A - 10 OOOOO DELX = OUT SECT ION NO = 5 OUT AREA OUT DISCH TOTAL TIME . SECONDS 0.0 0.0 0. O.OO132 0 00050 120. 0.00363 0.00138 240. 0.05732 0.045 13 360. 0.3588 7 0.524 13 4BO. 1.11582 2 34520 60O. 1 8 13 26 4 4 5 106 720. 2.50640 6 8463 3 840. 3 16935 9 409 16 960. 3.68966 11.56597 1080. 3 B8658 1? 408 12 1200. 3.831 75 12.16952 1320. 3 G0495 11 207 7 7 1440. 3 29 110 9 90605 1560. 2.94 709 B.525G3 16BO. 2.60700 7.21458 1800. 2 29-1 17 6.08041 1920. 2.O204 2 5. 13785 2040 1.78632 4.36 4 39 2 160 1 586B5 3 73 1 16 2280 1 41552 3.20728 2400 1 .267 15 2.77108 2520 1.13506 2.39904 2640 1.01555 2.07 2 99 2760 0.908 2 2 1 .7B869 2880 0 B1088 1.54468 3000 O 72353 1.3304 7 3 120 0 64618 1 . 14 550 3240 0.577 31 0 98745 3360 0.5 17 19 0.85102 3480 0 46314 0.73682 3600 0.41595 0 63672 3720 O.3742 1 0 55386 3840 0.33727 0.48229 3960 0 30458 0 . 4 1982 4080 0 2 7 554 0 36870 4 200 0 -24986 0. 32348 4320 O. 22720 0.28364 4440 0.20669 O.25135 4560 0. 1885 7 0.22283 4680 0. 17260 0 19768 4 800 0 . 158-15 0. 1754 1 4920 0. 1454.) 0 157 3 5 5040 0 13347 0 14086 5 160 0.1225" O 12585 5280 TOLR*.OO0O100 XN2* 0.0500 DELM 120 O O O O DELA- 10.00000 DELX* IN SECTION NO = 5 OUT SECTION IN AREA IN 1 DISCH OUT ARE 0. 0 0. 0 O 0 0. 00132 0. 00050 0. OO 1 3 2 0. 00363 0. OO 138 0. 003 15 0. 05732 0. 045 13 0. 057 15 0. 35887 0. 524 13 0 35837 1. 1 1582 2 . 34520 1 . 1 14 76 1. 81326 4 . 45 106 1 R1234 2 . 50640 6 . 84633 2 . 50549 3. 16935 9 . 409 16 3 . 16849 3 . 68966 1 1 . 56597 3 68903 3 8865B 12 . 408 12 3 . 88649 3 83 175 12 . 16952 3 R3 706 3 . 60495 1 1 . 20777 3 6055 3 3 29 1 10 9 90605 3 79 18 1 2 . 94709 8 52563 2 . 94785 2 60700 7 . 2 1458 2 . 607 7 8 2 . 294 17 6 . 0804 1 2 . 2949? 2 . 02042 5 . 13785 2 . 0? 1 10 1 78632 4 . 36439 1 . 78693 1 . 58685 3 . 73116 1 . 58 7 39 1 4 1552 3 . 20728 1 4 1 COO 1 . 267 15 2 . 77 10B 1 . 767 57 1 .13506 2 39904 1 . 1 354 5 1 .01555 2 07299 1 . 0159? 0 .90822 1 78869 0 9085 7 0 .81088 1 5446H O. 8 1 1 70 0 . 72353 1 .33047 O 7 7 3B3 0 . 646 18 1 .14 550 0 64645 0 .57731 0 .98745 0 57756 0 .517 19 0 .85102 0 .51741 0 . 46344 0 . 73682 0 46365 0 . 4 1595 0 . 63672 0 .41614 0 .3742 1 0 .55386 0 . 37439 0 .33727 0 .48229 0 3 37-13 0 .30458 0 .4 1982 0 .304 7 3 0 .27554 0 .36870 0 .7 7 56B 0 .24986 0 .32348 0 .7 4998 0 . 22720 0 .28364 0 .7773? 0 .20669 0 .25135 0 .706BO 0 . 18857 0 .22283 0 . 1BH67 0 .17260 0 . 19768 0 . 17 269 0 .15845 0 .17541 0 . 15B53 0 . 14543 0 .15735 0 . 14551 0 . 13347 0 .14086 0 13354 0 .12259 0 .12585 0 .17265 6 OUT DISCH TOTAL TIME . SECONDS . 0 . 0 0. 0.OOO50 120. 0.0013 1 240. 0 0-1493 360. 0.57308 480. 2 3 17 2 2 600. 4.-148 11 6 8-1 300 720. 840. 9 405/4 960. 1 1 56330 1080 . 1 2'. 407 7 2 1 200 . 12 1709 1 1320. 11.21073 \ 1440. 9 90B97 1560. B 57867 1680. 7 7 17-13 1800. 6 08 301 1920. 5 14013 2040. 4 . 36634 2 160. 3 .73782 2280. 3 70870 2400. 7 . 7773? 2520. 2.40013 2640. 2 07399 2760. 1.7B958 2B80. 1 54550 3000. 1 33 170 3 120. 1 . 146 15 3240. 0.9BB03 3360 0.85152 3480 0 73727 3600 0.6371 1 3720 0 55420 3840 0 48 259 3960 0 42010 4080 O.36894 4 200 0.32370 4320 0 28382 4440 0 25 152 4560 0.22298 4680 0 197B2 4 800 0 17553 4920 0 15746 5040 0.14096. 5160 0.12594 5280 TOLR=.0000100 XN2 = 0.0500 IN SECTION NO = G IN AREA IN DISCH 0. 0 0. 0 0. 00132 O. 00050 0. 00345 0. 0013 1 0. 057 15 0. 04493 0. 35832 0. 52308 1 . 1 1476 2 . 34222 1 . 8 1234 4 . 448 1 1 2 50549 6 . 84 300 3 . 16849 9 . 40574 3 . 68903 1 1 . 56330 3 . 88649 12 . 40772 3. 83206 12 . 17091 3 60553 1 1 . 2 1023 3 . 29 18 1 9 . 90897 2 . 94785 8 52862 2 . 60778 7 . 2 1743 2 29492 6 . 08301 2 02 1 IO 5 14013 1 78693 4 36634 1 58739 3 73282 1 .41600 3 20870 1 . 26757 2 77232 1 13545 2 40013 1 .01592 2 07399 0 .90857 1 78958 0 .81 120 1 54550 0 . 723B3 1 33 120 0 .64645 1 . 14615 0 .57756 0 98803 0 .5 174 1 0 .85 152 0 .46365 0 .73727 0 .41614 O .6371 1 0 .37439 0 .55420 0 .33743 O .48259 0 .304 7 3 0 .420IO 0 . 27568 0 .36894 0 . 24998 0 .32370 0 .22732 0 .28382 0 .20680 O .25152 0 . 18867 O .22298 0 17269 0 .19782 0 .15853 0 .17553 0 . 14 55 1 0 .15746 0 .13354 0 .14096 0 .12265 0 .12594 Dl'Ll^ 1 2 0 . 0 0 0 O 0 DE L A = 1 0 . 0 0 0 0 0 DE L X = 0U1 SECTION NO = 7 OUT AREA OUT DISCH TOTAL TIME . SECONDS 0.0 0. 0 0. 0.0O389 0 . 0014B 120. 0.007 93 0. 00348 240. O 118 19 0. 1 1979 360. 0 687 18 1 . 24 354 480. 1.93688 4 8578 1 GOO. 2 80286 7 . 96488 720 . 3 47363 IO. 65497 840 4.036 2 5 13 059 3 7 960. 4.43015 14 . 80848 1080. 4.504 60 15 . 14 140 1200, 4.33748 14 . 39408 1320. 4.0199 7 12 . 98852 1440 3 63169 1 1 . 32086 1560 3.2256 1 9 . 63734 1680 2 832 15 8 . 07748 1800 2 4 774 2 6 . 74025 1920 2 16H29 5 64 178 2040 1.906 2 5 4 . 755 15 2 160 1 .685 1 a 4 . 03899 2280 1 4 9622 3 4 5 204 2400 1 .334 18 2 968 15 2520 1.19230 2 55929 2640 1.0652 2 2 20482 2760 0 94930 1 897 17 2880 0.84728 1 63595 3000 0 7 556 3 1 407 24 3 1 20 0 673 18 1 2 1008 3240 0.60158 1 04252 3360 0.538 10 O . 89846 3480 0 48284 0 .77771 3600 0 43267 O .67196 3720 0 38988 0 .58422 3840 0 35094 0 .508 7 7 3960 O 3 1 7 1 5 0 .44 330 4080 0.28735 0 .38950 4 200 0.26033 0 .34 192 4320 0 2 3650 0 .29997 4440 0.21 589 0 26583 4560 0 19673 0 .2 3566 4680 0 . 17983 0 .20906 4 800 O 16486 0 18549 4920 0.15202 0 . 16644 5040 0 . 1 3950 0 . 149 18 5 160 0 128 IO 0 13346 5280 TOLR=.0000100 XN2 = 0.0500 IN SECTION NO = 7 IN AREA IN 1 DISCH 0. 0 0. 0 0. 00389 O. 00148 0. 00793 0. 00348 0. 118 19 0. 1 1979 0. 687 18 1 . 24354 1 . 93688 4 . 8578 1 2 . 80286 7 . 96488 3 . 47363 10. 65497 4 . 03625 13 . 05937 4 . 43015 14 . 80848 4 . 50460 15 . 14440 4 . 33748 14 . 39408 4 . 01997 12 . 98852 3 . 63169 1 1 . 32086 3 . 2256 1 9 . 63734 2 . 832 15 8 . 07748 2 . 47742 6 . 74025 2 . 16829 5 . 64 17B 1 . 90625 4 . 755 15 1 . 68518 4 . 03899 1 49622 3 . 45204 1 . 334 18 2 . 968 15 1 19230 2 . 55929 1 06522 2 . 20482 0 94930 1 . 897 17 0 . 84728 1 63595 0 . 75563 1 40724 0 .673 18 1 .21008 0 .60158 1 .04252 0 .538 10 0 .89846 0 .48284 0 .7777 1 0 .43267 0 .67196 0 .38988 0 .58422 0 .35094 0 .50877 0 .31715 0 .4 4 330 0 .28735 0 .38950 0 .26033 0 .34192 0 .23650 0 .29997 0 .21589 0 .26583 0 . 19673 0 .2 3566 0 .17983 0 .20906 0 .16486 0 .18549 O 15202 0 .16644 0 .13950 0 .14918 0 . 128 10 0 .13346 DELT- 120.OOOOO DELA- 10.00000 DELX= OUT SEClION NO = 8 OUT AREA OUT DISCH TOTAL TIME . SECONDS 0.0 O.O 0 0.00637 0 00244 120. 0.01112 0.00564 240 . 0 17039 0. 19420 360. 0.97 370 1 96 192 480 . 2.648O0 7 36957 600. 3 66940 1 1 .48031 720 . 4.35378 14 . 46697 840 . 4 846 13 16 7137 1 960. 5.13096 18 05464 1080. 5.094 3 1 17 88206 1200. 4 82565 16 6 18 15 1320. 4.42100 14.76755 1440. 3.96132 12 73334 1560 . 3.49587 IO.74656 1680. 3.0508 ? 8 93797 1800. 2.65536 7 . 3978.) 1920 . 2 31234 6 14 37 1 2040. 2.02231 5 144 19 2 160 . 1.7804O 4 34534 2280. 1 57528 3.6955 1 2400. 1.40083 3.16409 2520. 1.249 19 2 7 1852 2640. 1 1 1244 2.3357 3 2760 0 . 98987. 2.00483 2880. 0 88338 1 7 264 3 3000 O.706IO 1.48332 3 120. O.69993 1.2 7 404 3240 0.6 2560 1 09704 3360 0 55880 0.94543 3480 0 50203 0.81817 3600 0.44921 0.70684 3720 0.405 29 O.6 1425 3840 0.36446 0.53497 3960 0.32913 0 4665 1 4080 0.29903 0 41007 4 200 0.2 7069 0 36016 4320 0 24568 0.31613 4440 0 22498 0 28014 4560 0.204 7 9 0 24836 4680 0.18697 0.22031 4800 0 17 119 0 19546 4920 0.15846 O. 1754 2 5040 0.14 547 0.15740 5 160 0.13356 O 14098 5280 LO TOLR =.OOOO100 XN2 = 0.0500 IN SECTION NO = 8 IN AREA IN I DISCH 0. 0 0. 0 0. 00637 0. 0024 4 0. 01112 0. 0056 1 0. 17039 0. 19420 0. 97370 1 . 96 192 2 64800 7 . 36957 3 . 66940 1 1 . 4803 1 4 . 35378 14 . 46697 4 . 846 13 16 . 7 137 1 5 . 13096 18 . 05464 5 . 094 31 17 . 88206 <J 82565 16 . 6 18 15 4 . 42 lOO 14 76755 3. 96132 12 . 73334 3 49587 IO. 74656 3 . 05082 8 . 93797 2 65536 7 39783 2 . 3 1234 6 . 1437 1 2 . 02231 5. 144 19 1 78040 4 . 34534 1 57528 3 6955 1 1 . 40083 3 16409 1 24919 2 7 1852 1 .11244 2 . 33573 0 .98987 2 00483 0 .88338 1 .72643 o .78640 1 48332 0 .69993 1 .27404 0 .62560 1 .09704 0 .55880 0 .94543 0 .50203 O .8 1817 0 . 4492 1 0 .70684 0 .40529 0 .61425 0 . 36446 0 .53497 0 .32913 0 .46651 0 .29903 o .41007 0 .27069 o .36016 0 .24568 0 .31613 0 .22498 0 2 8014 0 .20479 0 . 24H36 0 .18697 0 .2 2031 0 .17 119 0 19546 0 . 15846 o . 17542 0 .14547 o . 15740 0 .13356 0 .14098 DELT" 120.00000 DE L A = 1O.0OO00 DELX = 1340. OUT SECT ION NO - 9 OUT AREA OUT DISCH TOTAL TIME . SECONDS 0.0 0. 0 0. 0.0 0 . 0 120. 0.0 0. 0 240. 0.15O09 0 . 164 GO 360. 0.17634 0 . 2035G 480 . O.73567 1 . 35950 600 . 1.91512 4 . 78489 720. 3 07008 9 01454 840. 3.99706 12 88885 960. 4.5R745 15 . 52472 1080. 4 95397 17 . 22 1 39 1200. 5.11393 17 . 97444 1320. 5 05674 17 70522 1440 . 4 83385 16 . 65590 1560. 4 5095R 15 . 16726 1680. 4.13753 13 . 50007 18O0. 3 74475 1 1 . 79889 1920. 3 36189 10. 1965 1 2040. 3.00503 8 . 75595 2 160. 2.68193 7 50000 2280. 2 39546 6' 44024 2400. 2 14 234 5 55136 2520. 1.92060 4 80324 2640. 1 72775 4 17595 2760. 1 557 39 3 64042 2880. 1 40446 3 . 17478 3000. 1 26954 2 778 12 3 120. 1.14R0? 2 43532 3240. 1.03724 2 13057 3360. 0 93R65 1 86890 3480. 0.B4R43 1 . 63882 3600. 0 7696R 1 .44141 3720 0 . 6967(1 1 26650 3840 O. 63363 1 1 155 1 3960 0 576 14 0 984RO 4080 0.524 35 0 . 8G776 4 200 O 17926 0 7 7018 4320 0 4 38 3H 0 . 68400 4440 0 400H? 0 . 6054 2 4560 0.3GR33 0 , 54248 4680 0.3 3872 0 .485 10 4800 0.3 1193 0 .43319 4920 O 28G56 0 388 1 1 5040 0.26 503 o .35019 5 160 0 2-! 559 0 .31597 5280 XN1= 0.0500 T0LR=.0000010 XN2 = 0.0500 IN SECTION NO = 1 IN AREA IN 1 O .0 0.0 0 .0 0 0 0 .0 0.0 0 .0 0.0 0 .0 0.0 0 .0 O.O 0 .0 0.0 0 .0 O.O 0 .0 0.0 0 .0 0.0 0 0 0.0 0 .0 0.0 0 .0 0 0 0 .0 0.0 0 .0 O.O 0 .0 O.O 0 .0 0.0 0 .0 0.0 0 0 0.0 0 .0 O 0 0 0 0.0 0 0 0.0 0 .0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0. 0 0.0 0 0 0.0 0 0 0 0 0 o 0.0 0 0 0.0 0 0 0.0 0. 0 O.O 0 0 0 0 0 0 0.0 0 0 0.0 0. 0 0.0 0. 0 0.0 0. 0 O 0 0. 0 0.0 0. 0 0.0 0. 0 0.0 TRIBUTARY F DELT* 170 0 0 0 0 0 DELA* 10.00000 OUT SECT ION NO * 2 OUT AREA OUT DISCH 0 .0 0 .0 0 .001OB 0 .002 71 0 .007 7.1 0 .00585 0 . 1 1565 0 20139 0 . 63468 1 .93635 1 .59399 6 .50O69 1 .88059 8 .08706 1 85B5 1 7 . 9G 1 70 1 .7374 1 7 28679 1 .57 407 6 .39446 1 .397B1 5 43953 1 .20683 4 .50323 1 .02372 3 .62B22 0 .73563 2 3547 1 0 53 157 1 .53042 0 .39455 1 .02762 0 2996 1 0 .71207 o 232 1 1 0 50627 0 18276 o .37012 0 146 IB 0 . 27432 0 1 1844 0 . 20807 0 09726 0 . 158B7 0 OB057 0 . 125 14 0. 06743 0 .09857 0 05708 0 07764 0 04857 0 063B2 0 04 157 0 0525 1 0 035B 1 0 .04321 0. 03 107 0 03556 o. 027 16 0 02926 0 02389 0 02459 0 07 105 o 0? 130 0 0 1859 0 01844 0 . 01646 0 01597 0 01461 0 01383 0. 0 1 30? 0 01 198 0 01163 0 01037 0 01O-14 0 00898 0 . O0940 0 007 7 8 0 008 50 0 0067 3 0. 007 7 3 0 0058 3 0 00705 0 00505 0 . OOG 1 7 o 004 3 7 0. 00594 0 00395 DELX* 1800. TOTAL TIME . SECONDS O. 120. 240. 360. 480. 600. 720. 840. 960. 1080. 1200. 1320 1440. 1560. 1680. 1800. 1920 . 2040. 2 160. 2280. 2400. 2520. 2640. 2760. 2880. 3000. 3 120. 3240. 3360. 3480. 3600. 3720. 3840. 3960. 4080. 4200. 4320. 4440. 4560. 4680. 4 800 . 4920. 5040. 5 160. XN1 = 0.0500 T0LR=.0000100 XN2 = 0.0500 MAIN CHANNEL DELT = 120 OOOOO D F. L A = 10.00000 DELX = 2680 IN SECTION NO = 1 OUT SECTION NO = 2 IN AREA IN DISCH our ARFA OUT DISCH TOTAL TIME 0. 0 0. 0 0. o 0. 0 O. 0 0 0. 0 0. 00-1 1 8 0 . 0029 1 120. 0 0 0. 0 0 00803 0. 00655 240. 0. 0 0. 0 0. 036.16 0. 04775 360. 0. o 0. 0 0 3309 1 0. R7937 480 0. 0 0. 0 0 99902 3 . 799 IB 600. 0. 0 0. 0 1 023 1 7 3 . 9 16 14 720. 0. 0 o. 0 0 799:19 2 . B3609 840. 0 0 0 0 0 6 1835 2 . 02 153 960. 0. 0 o. 0 0. 4B670 1 . 47016 1080. 0. o o. 0 0. 3 a n o 7 1 . 09O15 1200. 0 0 o o 0 3 1537 O. 8 2 305 1320. 0. o o o 0. 2 58 5 9 O 63405 1440. 0. o 0 0 0. 2 14.13 0. •19309 1560. 0 0 0 0 0. 17 949 o 390 1 2 1680. 0 o 0 0 0. 15 169 0 3 104B 1800. o 0 0 o o 1 2 9 10 0 . 25224 1920. 0 0 0 0 0 1 1075 0 20493 2040 0 0 0 0 0. 09568 o 1682 1 2 160 0 .0 0 0 o 08 3(19 0 . 14069 22RO 0 0 0 0 0 07 2 55 o 1 176 7 2400 0 0 0 0 0 06 3 7 3 0 09842 2520 0 .0 0 0 0 056 35 0 08 250 2640. 0 0 0 o 0. 04 996 0 07 134 2760. 0 0 0 0 0 04 4 4 3 o 06 169 2B80 0 0 o .0 0 03966 o 05334 3000 0 o 0 0 o 0355 3 0 04612 3 120 0 .0 0 0 0 ,03195 0 039RB 3240 0 .0 0 0 0 028B7 0 03448 3360 0 0 0 .0 0 02620 0 .02982 3480 0 0 0 .0 0 02 38 3 o 02639 3600 0 .0 0 .0 0 .0217 1 0 02373 3720 0 .0 0 .0 0 .01980 0 .02133 3840 0 o 0 .0 o .0IBOB 0 019 17 3960 0 o 0 0 0 O 1 6 5 4 0 .01723 4080 0 .0 o .0 0 015 1 5 o 01549 4 200 0 .0 o .0 o 0 1390 0 01392 4320 0 .0 0 .0 0 0 12 78 o .01252 4440 0 o 0 .0 o .01178 0 .01125 4560 0 .0 0 .0 0 O 108 7 0 01011 4680 0 0 0 .0 0 .01006 o .00909 4800 0 .0 0 .0 o .009 3 2 0 .008 1 7 4920 0 o 0 .0 o . 0 O 8 6 7 0 .007 35 5040 0 0 o .0 0 .00807 0 .00660 5160 TOLR=.0000100 XN2 = 0.0500 IN SECT ION NO = 2 IN AREA IN DISCH 0. 0 0. 0 0. 004 18 0. 00291 O. 00803 0. 00655 0. 03646 0 04775 0. 3309 1 0. 87937 0. 99962 3 . 799 18 1 . 023 17 3 . 91614 0. 79939 2 . 83609 0. 61835 2 . 02 153 0. 48670 1 . 47016 0. 38907 1 . 09015 0. 3 1537 0. 82305 • 0. 25859 0. 63405 o. 2 1443 0. 49309 o. 17949 0. 39012 0. 15169 0 3 1048 0. 12910 o. 25224 0. 1 1075 o. 20493 0. 09568 o. 1682 1 0 08309 0. 14069 0. 07255 o. 1 1767 0. 06373 0. 09842 0. 05635 0. 08250 0. 04996 0. 07 134 0. .04443 o 06 169 0. .03966 o. 05334 0 .03553 o. 046 12 0 .03195 o. 03988 0 .02887 0. 03448 0 02620 0. 02982 0 02383 0 02639 0 .02171 0 02373 0 01980 0 02133 0 0 1 BOB o 01917 0 .01654 0 01723 0 .01515 0 01549 0 .01390 0 01392 0 .01278 0 01252 0 .01178 0 .01125 0 .01087 0 .01011 0 .01006 0 .00909 0 .00932 0 .00817 0 .00867 0 O0735 0 .00807 0 .00660 0 .00754 0 .00594 DELT= 120.00000 DEL*"- 10 OOOOO D E L X = 1 170 our sFcnoN N O = 3 our AREA OUT DISCH TOTAL TIME 0.0 0 0 O 0.00080 0. 00030 120 0.00253 0. 00096 240 0.01492 0. 0082 1 360 0.21863 O . 270 15 480 0.94912 1 . 89668 600 1.43405 3 26 175 720 1.53633 3 5755B 840 1 .45 191 3 . 3 1559 960 1.29807 2 86 198 1080 1.13007 2 . 3B507 1200 0.97 14 1 1 95584 1320 0.83103 1 59520 1440 0.71003 1 . 29820 1560 O 60811 1 057 34 16BO 0 52254 O 863 16 1800 0.45108 0. 7 1076 1920 O.39 1 13 0 58664 2040 0 34049 o 48852 2 160 O 298 15 0 408 5 1 2280 O.26206 0. 34497 2400 0.23138 o 29095 2520 0.20476 0 24831 2640 0. 182 15 0 2 127 1 2760 0.16290 0 18242 2880 0. 146 14 0. 15B34 3000 0. 13 14 2 0 13803 3 1 20 0.11851 0 12023 3240 0. 1072 1 0 10465 3360 0 09719 0 .09166 3480 0.0BB29 0 OB 128 3600 0 OBOlfl 0 072 1 7 3720 0 0736 1 0 064 15 3840 O.06 7 55 0 .05708 3960 0.06220 0 0508 3 40B0 0.057 17 0 .04 531 4 200 0.05314 0 .041 14 4320 0.049 15 0 .03742 4440 0.04519 0 .03102 4560 0.04213 0 .03089 46BO 0.03906 0 .02803 4 800 0 036 2 5 0 .02542 4920 0.03 369 0 02304 5040 0 03136 0 .02007 5 160 0 02923 0 .01889 5280 TOLR=.0000100 XN2 = O.0500 IN SECTION NO - 3 IN AREA IN I DISCH O. 0 0. 0 0. 00080 0 00030 0. 00253 0. 00096 O. 01492 0. 00821 0. 2 1863 0. 27015 0. 94912 1. 89668 1 . 43405 3 . 26 175 1 . 53633 3 57558 1 . 45191 3 . 3 1559 1 . 29807 2 . 86 198 1 . 13007 2 38507 0. 97 14 1 1 . 95584 0. 83 103 1 . 59520 0. 7 1003 1 . 29820 0. 608 1 1 1 . 05734 0 52254 0. 863 16 o 45 108 O. 7 1G76 0. 39 1 13 0. 58664 0. 34049 o. 48852 0. .29815 o. 4085 1 0 26206 0. 34 497 0 23138 0 29095 0 . 20476 0. 2483 1 0 . 182 15 o. 2 127 1 0 .16290 o 18242 0 146 14 o 15834 0 . 13 142 o 13803 0 . 1 1851 0 12023 0 .107 21 o .10465 0 .09719 0 .09166 0 .08829 0 .08128 0 .08048 o .07 2 1 7 0 .0736 1 o .06415 0 .06755 o 05708 0 .06220 0 .O5083 0 .05747 0 04 53 1 o .053 14 0 .04 1 14 0 049 15 0 03742 0 .04549 0 .03402 0 .04213 o .03089 0 .03906 0 .02803 0 .03625 0 02542 0 .03369 0 .02 304 0 03 136 0 .02087 D E L T ='1 2 0 . 0 0 0 0 0 DEI. A = 1 0 . 0 0 0 0 0 D E L X = (JUT SECT I ON NO - 4 OUT AREA OUT DISCH TOTAL TIME 0 O 0 0 0. 0 000RO O.0OO30 120. 0 002 36 0 00090 240. 0,014/R 0.OOR 1 1 360. O.21R03 O 269 19 480 . 0 94761 1 89767 600. 1 43293 3 2584 7 720. 1 53607 3.57478 840. 1 .45? 14 3.3 1679 960. 1.29R50 2.R6376 1080. 1 13057 7 38646 1200. 0 97190 1 .957 16 1320. 0.8 3 150 1 59637 1440. 0.71046 1 799? 1 1560. O.60H4R 1 05R19 1680 . 0.52286 O.B63R7 1800 0 45136 O. > 1136 1920. 0 39 1 39 0 587 14 2040. O.3407O 0.4 8R94 2 160. 0 2MH35 0.40BH6 2280. 0.26773 0 34577 2400. 0.23 15? 0 29 12 1 2520. 0.204 90 0.24853 2640. 0 18727 0 2 1290 2760 O 16301 0 18258 2880 0. 14674 0. 15847 3000 0 13 15 1 O 138 16 3 120 0 1 1R59 0 17034 3240 0.10727 0.10474 3360 O.09776 0.0917 4 3480 0.08R36 O OS 136 3600 0.08054 0 07223 3720 0.07366 0.064 20 3840 0 067 59 0.057 13 3960 0.06224 0.0508 8 4080 0.057 5 1 0.04535 4 200 0.0531H 0.04117 4320 0 04918 0.03746 44 40 0 04 55? 0.03405 4560 0.04?16 0.03092 4680 0.03909 0.0?806 4 800 O.03678 0.02544 4920 0.0337 1 0.02306 5040 0 03138 0 02088 5 160 TOLR* OOOO100 XN2 = 0 . 0 0 0 0 DELT = 120.00000 nn A= 1 0 . 0 0 0 0 0 DELX* IN SECTION NO OUT SECTION NO IN AREA IN DISCH OUT ARE A our DISCH TOTAL TIME 0 0 0. 0 0 .0 0 0 0 0 00080 0 00030 0 .003 7 4 0 OO 1 4 2 120 O 00236 0 00090 0 .007 7 7 0 00338 240 0 O 1-178 0 008 1 1 0 07038 0 06038 360 O 2 1803 0 269 19 0 .49507 O 803-19 480 0 9-176 1 1 . 89267 1 6225 1 3 84096 600 1 43293 3 25847 2 23200 5 8637R 720 1 53607 3 57478 2 359 17 6 30738 840 1 452 14 3 . 3 1629 2 766 7 2 5 9R476 960 1 . . 29850 2 86326 2 08746 5 36257 1080 1 .13057 2 . 38646 1 87665 4 65594 1200 O 97 190 1 95716 1 66 360 3 96954 1320 '0 83 150 1 59637 1 46085 3 343 1 1 1440 0 7 1046 1 2992 1 1 27 167 2 7 84 37 1560 0 60848 1 058 19 1 09809 2 29556 1680 0 52286 0 86307 0 940-16 1 87370 1ROO 0 45136 0 7 1 136 0 79984 1 51702 1920 0 39 139 0 587 14 0 6 7 5 12 1 2 154 3 2040 0 34070 0. . 48894 0 5707 1 0 97247 2 160 0 29835 0. 40886 0 486 IO O 78459 2280 0 26223 0 34527 0 4 1 768 O 64035 2400 0 23 152 0 29 12 1 0 36038 0. 52706 2520 0 . 20490 0. 24853 0 3 1448 0 4 3812 2640 0 18227 0 2 1290 0 2 7 4 99 0 36773 2760 0 16301 0 18258 0 24 16-1 0 30902 2880 0 14624 0 15847 0 2 14 6 3 0. 26385 3000 0 13 15 1 0; .13816 0 1907 4 0 2 7674 3 120 0 1 1859 0 12034 0 17024 0 19396 3240 0. 10727 0 10474 0 15254 0 167 15 3360 0 09726 0 09 174 0 1366 7 0 14527 3480 0 08836 0. 08 136 0 1 2 36 1 0 12776 360O 0 08054 0 07 223 0 1 1275 0 1 1 160 3720 0 07366 0 06420 0 IO? 36 0. 09797 3840 0 067 59 0 057 13 0 097B2 0 08656 3960 0 06224 0 05088 0 Ofl-149 0 07685 4080 0 0575 1 0 04535 0 07 7 14 0 06876 4 200 0 053 18 0 04117 0 07 124 0 06 138 4320 0 049 18 0 03746 •0 0660? 0 . 05579 4440 0 04 552 0 03405 0. 06 1 30 0 04978 4560 0 04216 0 .03092 0. 05703 0 O4 4R0 4680 0 03909 0 02806 0 052 75 0 0403 1 4 800 0 036 28 0 02514 0. 0-1789 0 036 25 4920 0 0337 1 0 023O6 0 .04 429 0 03290 5040 0 03138 0 02088 0 04 103 0. 02987 5 160 0 02925 0 0189 1 0 038O6 0 027 10 5280 SECONDS T0LR=.0000100 XN2- 0.0500 DELT = 120.00000 DF.LA- 10.00000 DELX = 1 IN SECTION NO = OUT SECTION NO IN AREA IN DISCH OUT AREA OUT DISCH TOTAL TIME 0.0 0.0 0.0 0.0 0 0.00374 0.00142 . 0.00649 0.0025 1 120 0.00777 0.00338 O . 0 114 3 0.00585 240 0.07038 0.06038 0. 1 1275 0. 1 1229 360 0.49507 0 80349 0.72588 1.33608 480 1.62251 3.84096 2.20971 5.7 8609 600 2.23200 5.86378 2.93262 8.46809 720 2.359 17 6.30738 3.07644 9.03980 840 2.26672 5.98476 2.97920 8.65327 960 2.08746 5.36257 2.776 12 7.86208 1080 1.87665 4.65594 2.528 10 6 . 92575 1200 1.66360 3 96954 2 26603 5 . 98234 1320 1.46085 3 343 t1 2.00625 5.09035 1440 1 .27167 2.78437 1 7570C) 4.2 7006 1560 1.09809 2.29556 1 .52206 3 53347 1680 0.94046 1.87370 1.30558 2.88407 1800 0.79984 1 .5.1702 1.10797 2.3232 1 1920 0.67542 1 .2 1543 0.92935 1.8442 1 2040. 0.57071 0.97247 0.77507 1 45642 2 160. 0.486 10 O.78459 0.65252 1 . 16066 22BO. 0.41768 0 64035 0 55450 0.93569 2400. 0.36038 0 52706 0 4 7591 0.7631 1 2520. 0 31448 0.4 38 12 0.41 176 O.62788 2640. 0.27499 0.36773 0.35812 0 52269 2760. 0.24164 0.30902 0.3 13 15 0.43556 2880. 0.21463 0.26385 0 27589 0.36931 3000. 0.19074 0.22624 0.24469 0.31439 3120. 0.17024 0.19396 0 24 704 0.26764 3240. 0.15254 0. 167 15 0 19289 0.22961 3360. 0.13667 0.14527 0.17334 0.19884 34B0. 0.12361 0. 12726 0.15692 0.17320 3600. 0. 1 1225 0.11 160 0.14083 O 15101 3720. 0.10236 0.09797 0.1268 7 0. 13176 3840. 0.09282 OOB656 O 11545 0 11601 3960. 0.08449 0.07685 0.10589 O.10283 4080. 0.07714 0.06826 0.09679 O.09119 4 200. 0.07124 0.06138 0.08858 O.OB 16 1 4320. 0.06602 0.05529 0.08 132 O 073 14 4440. 0.06130 0.0497B 0.07479 0.06553 4560. 0 05703 0.04480 0.06894 0.05869 4680. 0.05225 0 0403 1 0.06369 0.05257 4800 . 0.04789 0.03625 0.05898 0.04707 4920. 0.04 4 29 0.03290 0 05488 0.04276 5040. 0.04103 0.02987 O 05069 0.03886 5160. 0.03806 0.02710 O 04687 0.03530 5280. SECONDS ho TOLR=.0000100 XN2 = 0.0500 IN SECTION NO = G IN AREA IN DISCH 0. 0 0. 0 0. 00649 0. 0025 1 0. 01143 O. 00585 0. 1 1275 0. 1 1229 0. 7258R 1 . 33608 2 . 2097 1 5. 78609 2 . 93262 8 46809 3 . 07644 9 03980 2 . 97920 8 65327 2 77612 7 . 86208 2 52810 6. 92575 2 . 26603 5. 98234 2 . 00625 5 . 09035 1 . 75700 4 . 2 7006 1 52266 3 . 53347 1 30558 2 88407 1 10797 . 2 . 3232 1 0 92935 1 . 8442 1 0. 77567 1 . 45642 0. 65252 1 . 16066 0 55450 0. 93569 0 .47591 0. 763 1 1 0. .41 176 0 62788 0 .358 12 0 52269 0 .31315 0. 43556 0 .27589 0. 3693 1 0 .24469 0 3 1439 0 .21704 0 26764 0 .19289 0 2296 1 0 .17334 0 19884 0 .15692 O 17320 0 .14083 0 15 101 0 .12687 0 13176 0 .11545 0 .11601 0 .10589 0 10283 0 .09679 0 .09119 0 08858 0 .08 161 0 OS 132 0 .07314 0 .07479 0 06553 0 .06894 0 .05869 0 .06369 0 .05257 0 .05898 0 .04707 0 .054 88 0 .04276 0 .05069 0 .03886 0 .04687 0 .03530 DE L T = 120.OOOOO DE L A = 10.00000 DELX = 420. OUT SECTION NO = 7 OUT AREA OUT DISCH TOTAL TIME . SECONDS 0.0 0. 0 0. 0 o 0. 0 120. 0 0 0. 0 240. 0 1 1970 0. 12 187 360. 0 38402 0. 57288 480. 1 40297 3 . 17039 600. 2 48 1 25 6 75427 720 . 3 05258 8 . 94494 840. 3 19004 9 . 49 14 1 960. 3.08874 9 OR872 1080. 2 83735 8 09749 1200. 2.556 31 7 02901 1320. 2 28364 6 . 0437 1 1440. 2 02619 5 157 17 1560. 1 786 1 1 4 . 36370 1680. 1 56232 3 . 65559 1800. 1 35553 3 0309 1 1920. 1 . 1666 2 2 . 48739 2040. O 99664 2 0228 1 2 160. 0 84766 1 . 63689 2280. O 7 2 207 1 32699 2400. 0 6 1874 1 . 08 148 2520. 0 53382 0 88876 2640. 0 . 464 19 0 7384 1 2760 O 40609 0 6 1593 2880 O 35698 0 52048 3000 0 3 1590 0 44088 3120 0.28065 o 3777 1 3240 0.25051 0 32463 3360 0.22425 0 .2 7 900 3480 0 20 107 0 24 250 3600 0.18202 0 . 2 1251 3720 0 16508 0 . 18583 3840 0.14 960 0 16309 3960 0 13568 0 . 14391 4080 0.12392 0 . 12769 4 200 0 11378 0 . 1 1372 4320 0 10488 0 10144 4440 0 096 7 6 0 09 1 15 4560 0 089 14 0 08227 4680 0 08211 0 .07 406 4 800 0 07 568 0 .06656 4920 0.06998 0 0599 1 5040 0 06528 0 .05442 5 160 O.06101 0 .04945 5280 T O L R = . 0 0 0 0 1 0 0 XN2 = 0 . 0 5 0 0 I N S E C T I O N NO = 7 I N AREA IN D I S C H O 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 1 1 9 7 0 0 . 12 187 0 . 3 8 4 0 2 • 0 . 5 7 2 8 8 t. 4 0 2 9 7 3 1 7 0 3 9 2 48 125 6 7 5 4 2 7 3 0 5 2 5 8 8 9 4 4 9 4 3 . 19004 9 4 9 14 1 3 0 8 8 7 4 9 . 0 8 8 7 2 2 R 3 7 3 5 8 0 9 7 4 9 2 . 5 5 6 3 1 7 . 0 2 9 0 1 2 . 2 8 3 6 4 6 . 0 4 3 7 1 2 . 0 2 6 1 9 5 . 157 17 1 7 8 6 1 1 4 . 3 6 3 7 0 1 . 5 6 2 3 2 3 . 6 5 5 5 9 1 . 3 5 5 5 3 3 0 3 0 9 1 1 . 1 6 6 6 2 2 . 4 8 7 3 9 0 9 9 6 6 4 2 0 2 2 8 1 0 . 8 4 7 6 6 1 . 6 3 6 8 9 0 . 7 2 2 0 7 1 . 3 2 6 9 9 0 6 1 8 7 4 1 OB 148 0 . 5 3 3 8 2 0 . 8 8 8 7 6 0 . 4 6 4 19 0 7 3 B 4 1 0 4 0 6 0 9 0 6 1593 0 3 5 6 9 8 0 5 2 0 4 8 0 . 3 1 5 9 0 0 4 4 0 8 8 0 2 8 0 6 5 0 3 7 7 7 1 0 2 5 0 5 1 o: : 3 2 4 6 3 0 . 2 2 4 2 5 0 2 7 9 0 0 0 2 0 1 0 7 0 2 4 2 5 0 o. 1 8 2 0 2 o 2 1251 0 1 6 5 0 8 0 1 8 5 8 3 0 . 1 4 9 6 0 0 . 1 6 3 0 9 0 1 3 5 6 8 0 1439 1 0 1 2 3 9 2 0 1 2 7 6 9 0 1 1378 0 1 1 37 2 0 . 1 0 4 8 8 0 10144 0 . 0 9 6 7 6 0 0 9 1 1 5 0 0 8 9 14 0 0 8 2 2 7 0 (182 1 1 0 0 7 4 0 6 0 0 7 5 6 8 0 0 6 6 5 6 0 0 6 9 9 8 0 0 5 9 9 1 0 0 6 5 2 8 0 0 5 4 4 2 0 0 6 101 0 0 4 94 5 D E L T = 1 2 0 . 0 0 0 0 0 D E L A - 1 0 . 0 0 0 0 0 D E L X = 1 . OUT SECT ION NO = 8 o u r ARFA o u r D I S C H TOTAL T IME O . O 0 . 0 O 0 . 0 0 0 120 0 . 0 0 0 2 4 0 0 . 1 1 9 2 3 0 12 122 3 6 0 0 3 8 3 8 2 0 5 7 2 4 9 4 8 0 1 4 0 1 5 0 3 16607 6 0 0 2 4 7 9 7 2 6 . 7 4 8 6 8 7 2 0 3 0 5 2 0 6 8 94 2 8 9 8 4 0 3 . 1 9 0 2 B 9 4 9 2 3 9 9 6 0 3 0 8 9 3 7 9 0 9 1 2 1 1 0 8 0 2 B 3 8 0 8 8 . 1 0 0 2 9 1 2 0 0 2 . 5 5 7 0 1 7 0 3 158 1 3 2 0 2 . 2 8 4 3 1 6 0 4 6 0 3 1 4 4 0 2 0 2 6 8 3 5 . 1 5 9 3 2 1 5 6 0 1 . 7 8 6 7 3 4 3 6 5 7 0 1 6 B 0 1 . 5 6 2 9 2 3 . 6 5 7 4 6 1BOO 1 3 5 6 1 1 3 0 3 2 6 2 1 9 2 0 1 . 1 6 7 18 2 , 4 B B 9 6 2 0 4 0 0 9 9 7 1 7 2 . 0 2 4 2 3 2 1 6 0 0 8 4 8 16 1 6 3 8 13 2 2 8 0 0 7 2 251 1 3 2 8 0 4 2 4 0 0 0 . 6 19 12 1 0 8 2 3 4 2 5 2 0 0 . 5 3 4 13 0 . 8 B 9 4 6 2 6 4 0 O . 4 6 4 4 7 0 7 3 8 9 9 2 7 6 0 O 4 0 6 3 ? 0 6 1642 2 8 B O 0 . 3 5 7 19 0 . 5 2 0 8 9 3 OOO 0 . 3 1 6 0 7 0 . 4 4 122 3 120 0 . ? 8 0 8 2 0 . 3 7 8 0 0 3 2 4 0 0 2 5 0 6 5 0 3 2 4 8 8 3 3 6 0 O 2 2 4 3 9 0 . 2 7 9 2 2 3 4 8 0 0 . 2 0 1 1 9 0 . 2 4 2 6 9 3 6 0 0 0 1 82 1 2 0 . 2 1 2 6 7 3 7 2 0 0 . 1 6 5 1 7 0 . 1 8 5 9 8 3 8 4 0 0 1 4 9 6 9 b . 1 6 3 2 2 3 9 6 0 0 1 3 5 7 6 0 . 1 4 4 0 2 4 0 B O 0 1 2 3 9 9 0 . 1 2 7 7 9 4 2 0 0 0 . 1 1 3 8 5 0 . 1 1 3 8 0 4 3 2 0 0 . 1 0 4 9 3 0 . 1 0 1 5 1 4 4 4 0 0 0 9 6 B 1 0 0 9 1 22 4 5 6 0 0 O 8 9 2 0 0 . 0 8 2 3 3 4 6 8 0 0 0 8 ? 16 0 0 7 4 1 2 4 BOO 0 0 7 5 7 3 0 . 0 6 6 6 2 4 9 2 0 0 0 7 0 0 2 0 , 0 5 9 9 6 5 0 4 0 0 . 0 6 5 31 0 . 0 5 4 4 6 5 1 6 0 0 . 0 6 104 0 . 0 4 9 4 8 5 2 8 0 TOLR=.0000100 XN2 = 0.0500 DF I. I= 120.00000 DELA = 10.00000 DELX = IN SECTION NO = fl OUT SECTION IN AREA IN DISCH OUT ARE 0. 0 0. 0 0 0 0. 0 0. 0 0.00796 O. 0 0. 0 0.0064 7 O. 1 1923 0. 12 122 0.15983 O 38382 0 57249 0 65972 1 . 40150 3 . 16607 2.09052 2 . 47972 6 . 74868 3 23884 3 . 0520G 8 . 94289 3.77463 3 . 19028 9 . 49239 3 81782 3 . 08937 9 . 09 1 2 1 3 59669 2 . 83808 8 . 10029 3.226H7 2 . 55701 7 . 03 158 2 . 85329 2 . 2843 1 6 . 04603 2.5 1669 2 . 02683 5 . 15932 2 2 1175 1 . 78673 4 . 36570 1 93 17? 1 . 56292 3 65746 1 68390 1 . 356 1 1 3 . 03262 1 .4564 3 1 . 167 18 2 . 48896 1.7520? 0. 997 17 2 . 07423 1 06975 0. 848 16 1 . 638 13 0 9 1055 o. 72251 1 32804 0 77546 0 61912 1 . 08234 O 664 3 3 0 .53413 0 88946 0.57 340 0 . 46447 0 73R99 O.499H1 0 .40632 0 6 1642 O 43678 0 .357 19 0 .52089 0 385 1 5 0 .31607 0 44 122 0.3 4007 0 .28082 O .37 800 O 303 4 7 0 .25065 0 .32488 0 2 7010 0 .22439 0 27977 (). 24 16 4 0 .20119 0 . 24269 0.2 1790 0 . 182 12 0 2 1267 0.19080 0 .16517 0 18598 0. 1 78 18 0 .14969 0 . 16327 0. 1627.0 0 .13576 O .1140? 0. 1 17 35 o .12399 0 .17779 0 13 4 2 1 0 .11385 O .11380 O. 17 287 0 .10493 0 .1015 1 O.11789 0 .09681 0 .09 172 0.10470 0 .08920 0 08733 0 O97O0 0 .08216 0 .07 412 0.089 7 8 0 .07573 0 .0666 2 0 . (18773 0 07002 0 05996 O.07 590 0 .06531 0 054 46 0 0707 3 0 06 104 0 .04948 0 00 599 OUT DISCH TOTAL TIME . SECONDS 0.0 0. 0.00 1 1 7 170. 0.00750 240 . 0 17758 360. 1 . 17787 480 5.37782 600. 9.69 162 720. 11.97573 840. 1?.10894 960. 11.17787 lOBO. 9.64 750 1200. 8 15875 1320. 6.BS400 1440. 5 7 9 14 8 1560. 4.85058 1680 . 4.03487 1800. 3 3 79 50 1920. 7.7760? 2040. 7.21 '.'.53 2 160. 1 .79454 2280. 1 . 45589 2400 . 1 18890 2520. 0 97857 2640. 0 8 1350 2760 . 0 67956 2880. 0.5 7 506 3 OOO . O 4877 1 3 120. 0 4 1788 3240. 0.35912 3360. 0.3090? 3480 . 0.76899 3600. 0.73588 37 20. 0.70646 3840 . 0 18 13 1 3960 0.15999 4080 0 14 189 4 200 0. 17674 4320 O. 1 1 249 4440 0.10119 4560 0.09143 4680 0.08 24 3 4800 0.07 4 70 4920 0.06688 5040 0.0607 8 5 160 0.05575 5280 T O L R ^ . 0 0 0 0 ) 0 0 XN2- 0.0500 IN SECTION NO = 9 IN AREA IN DISCH 0. 0 0. 0 0. 00296 0 001 12 0. 0064 7 0. 00250 O. 15983 0 . 17758 0. 65972 1 . 17787 2 09052 5 . 37282 3 . 23R84 9 . 69 162 3 . 77463 1 1 . 92523 3 . 8 17B2 12 . 10894 3 . 59669 1 1 . 17287 3 . 22687 9. 64250 2 85329 8 . 15875 2 . 5 1669 6 . 88400 2 . 21 125 5 . 79 148 1 . 93472 4 . 85058 1 . 68390 4 . 03487 1 . 45643 3 . 32950 1 . 25202 2 . 72662 1 . 06925 2 2 1553 O 9 1055 1 . 79454 O. 77546 1 . 45589 0. 66433 1 . 18890 o 57340 - 0. 97857 0 .49981 0 8 1350 0 .43628 0 67956 0 .38515 0 57506 0 .34007 0 4877 1 0 .30347 0 . 4 1788 0 .27010 0 .35912 0 .24164 0 .30902 o .21790 0 26899 0 .19686 0 .23588 0 .17818 0 .20646 0 .16220 o .18131 0 14735 0 .15999 0 . 13421 0 .14189 0 . 12287 o .12624 0 .11289 0 .11249 0 .10470 0 .10119 o .09700 0 .09143 0 .08928 0 .08243 0 .08223 0 .07420 0 .07596 o .06688 0 .0707 3 0 .06078 0 .06599 0 .05525 D E L T = 120. OOOOO D E L A - 10.00000 DELX = OUT AREA OUT DISCH TOTAL TIME 0.0 0 0 0. 0.00585 0.002 2? 1 20 . 0.01014 0.004 98 240. 0 195 16 0 23366 360. 0.90531 1.78141 480. 2 70179 7.57633 600. 3.93847 12.63388 720 . 4 . 45237 14.9078 1 840. 4.41177 14 726.16 960. 4.08133 13.25550 1080. 3.5997 2 1 1 . 18567 1200. 3.13854 9.28668 1320. 2 7 3981 7 72249 1440. 2.39103 6 42403 1560. 2.07946 5.33576 1680. 1 80128 4.41250 1800. 1.55288 3.62654 1920. 1 33291 2 96440 2040 . 1.13788 2.40693 2 160. 0.96959 1.95103 2280. 0.82649 1 .5R382 2400. 0.70892 1.29553 2520. 0.6 1268 1 067 7 3 2640. 0.53351 0.88805 2760. 0.46625 0 74275 2880. 0 4 1241 O.62925 3000. 0.36408 0.53423 3120. 0.32462 0 . 45778 3240. 0.28955 0.39337 3360. 0 25858 0 33884 3480. 0.23385 0.29530 3600. 0.2116? O.25910 3720. 0. 19 t 20 0 22697 3840 0.17 369 0.19940 3960 0. 1588 1 O 17597 4080 0.14444 0.15599 4 200 0.13190 0 13869 4320 0.1?0B6 0 12348 4440 0.1119 3 0.11116 4560 0.10423 0 . 10054 4680 O.096 4 1 0.09075 4800 0.088 7 4 0 08180 4920 0.08189 0.07381 5040 O.0"6 15 0.06 7 1 1 5 160 0.07093 0.06102 5280 , SECONDS TOLR*.0000100 XN2* 0.0500 Df. L I - 1 2 0 . 0 0 0 0 0 DTLA- 10.00000 DELX* 960. IN SECTION NO 10 OUT SECTION NO 1 1 IN AREA IN DISCH OUT ARE A OUT DISCH TOTAL TIME 0. 0 O.O 0 0 0 0 0 0. 00585 0.00222 0 0 0 0 120 0. 01014 0.OO49B O.0557 3 O. 04355 240 0. 19546 0.23366 0. 1854 3 0. 2 1 7H8 360 0 9053 1 1.78141 0 494 33 0. 80 195 4 80 2 . 70179 7.57633 O . 7 1 4 1 2 1 . 307 97 600 3 93847 12.63388 1 7854 4 4 36 154 720 4 . 45237 14.90781 2.9837? 8 . 6697 3 840 4 . 4 1177 14 72626 3 793 17 12 00364 960 4 . 08 133 13.25550 4.17089 13 . 4 7 766 1080 3 . 59972 1 1 . 18567 4.08734 13 . 78 168 1200 3 . 13854 9.28668 3 82986 12 16 132 1320 2 . 7398 1 7.72249 3 4841 1 10 6997? 1440 2 . 39103 6.42403 3.17800 9 . 74.178 1560 2 . 07946 5.33576 7.797 3 7 7 . 974 5G 1680 1'. 80128 4.41250 2.48377 6 76 166 1800 1 . 55288 3.62654 7.70017 5 75270 1920 1 . 3329 1 2.96440 1.94725 4 87580 2040 1 . 13788 2.40693 1.7O901 4 . 1 1 759 2 160 0. 96959 1.95103 1 .499H5 3 . 46322 2280 0. 82649 1.58382 1 31768 2 . 90493 2400 0. 70892 1.29553 1 . 1464? 2 . 4 308 4 2520 0. 6 1268 1.06773 1.00099 2 . 03437 2640 0. 53351 0.88805 0 8755 1 1 70669 2760 0. . 46625 0.74275 0 7687 1 1 43897 2880 0 4 124 1 0.62925 0.67579 1 2 1630 3000 0 36408 O 53423 0 59868 1 . 03590 3 120 0 32462 0 45778 0 53 16.1 0 883BO 3240 0 . 28955 0.39337 0 47484 0 76085 3360 0 25858 0.33884 0 4 7603 0 65797 3480 0 23385 0.29530 0.38773 .o 5694 1 3600 0 2 1162 0.25910 0 34 4 95 0 497 1 7 3720 0 .19120 0.22697 0.3 13 19 0 43564 3840 0 .17369 0.19940 0 78 145 O . 384 40 3960 0 . 1588 1 0. 17597 0 2580 1 0 33889 4080 0 .14444 0.15599 0 . 73683 0 30055 4 20O 0 .13190 0.13869 0.21711 0 . 26776 4320 0 .12086 0. 12348 0. 199 15 0 .7 394 7 4440 0 .11193 O. 11116 0. 18 7 5 4 o ? 1333 4560 0 .10423 0.10054 0 16783 ~ o 19017 4680 0 .09641 O.0907 5 0.1555? 0 . 17 177 4 800 0 .08874 0.08 180 0 14-159 0 . 156 20 4920 0 08 189 0.07381 0 13-130 0 .14 209 5040 0 076 15 0.06711 0. 17470 0 . 17876 5 160 0 .07093 0 06 102 0 11598 • 0 1 1674 5280 SECONDS NJ T O L R = . 0 0 0 0 1 0 0 X N 2 - 0 . 0 5 0 0 DFLT = 1 2 0 onooo IN SECTION NO * IN AREA 0 . 0 0 . 0 0 . 0 5 5 7 3 0 . 185 13 0 . 4 9 4 3 3 0 . 7 1 4 1 2 1 . 7 8 5 4 4 2 . 9 8 3 2 2 3 . 7 9 3 1 7 4 . 1 2 0 8 9 4 . 0 8 7 3 4 3 . 8 2 9 8 6 3 . 4 8 4 4 1 3 . 1 2 8 0 0 2 7 9 2 3 7 2 . 4 8 3 2 7 2 . 2 0 0 1 2 1 9 4 2 2 5 1 . 7 0 9 6 1 1 . 4 9 9 8 5 1 . 3 1 2 6 8 1 . 1 4 6 4 2 1 . 0 0 0 9 9 . 0 . 8 7 5 5 1 0 . 7 6 8 7 1 0 . 6 7 5 7 9 0 . 5 9 8 6 8 0 . 5 3 1 6 4 0 . 4 7 4 8 4 0 . 4 2 6 0 3 0 . 3 8 2 2 3 0 . 3 4 4 9 5 0 . 3 1 3 1 9 0 . 2 8 4 4 5 0 . 25861 O . 2 3 6 8 3 0 . 2 1 7 1 1 0 . 199 15 0 . 1 8 2 5 4 O . 1 6 7 8 3 O . 1 5 5 5 2 O . 1 4 4 5 9 O . 1 3 4 3 6 O . 1 2 4 7 0 0 1 1598 IN DISCH 0 . 0 0 . 0 0 . 0 4 3 5 5 0 . 2 1 7 8 8 O . 8 0 1 9 5 1 . 3 0 7 9 7 4 3 6 1 5 4 8 . 6 6 9 2 3 1 2 . 0 0 3 6 4 1 3 . 4 2 7 6 6 1 3 . 2 8 1 6 8 1 2 . 1 6 1 3 2 1 0 . 6 9 9 2 2 9 . 2 4 4 7 8 7 . 9 2 4 5 6 6 . 7 6 1 6 6 5 . 7 5 2 7 0 4 . 8 7 5 8 0 4 . 1 1 7 5 9 3 . 4 6 3 2 2 2 . 9 0 4 9 3 2 . 4 3 0 8 4 2 . 0 3 4 3 7 1 . 7 0 6 6 9 1 . 4 3 8 9 7 1 . 2 1 6 3 0 1 . 0 3 5 9 6 O . 8 8 3 8 0 0 . 7 6 0 8 5 0 . 6 5 7 9 7 0 . 5 6 9 4 1 0 . 4 9 7 17 O . 4 3 5 6 4 O . 3 8 4 4 0 0 . 3 3 8 8 9 O . 3 0 0 5 5 0 . 2 6 7 7 6 0 . 2 3 9 4 7 0 . 2 1 3 3 3 O . 1 9 0 1 7 O . 1 7 127 0 1 5 6 2 0 O . 1 4 209 0 . 12876 O . 1 1674 OUT S E C T I O N NO OUT AREA 0 0 0 . 0 0 4 I O 0 . 0 0 2 5 4 0 . 2 1 0 2 6 0 7 8 3 6 8 1 3 0 6 0 7 1 .2 2 166 1 . 5 0 6 8 4 2 . 2 3 8 7 4 3 . 0 1 7 8 2 3 . 5 6 5 2 6 3 . 8 2 6 2 2 3 . 8 4 0 0 1 3 6 8 7 4 2 3 4 4 6 4 3 3 . 1 7 1 0 8 2 89 183 2 . 6 2 2 3 4 2 . 3 6 6 7 3 2 . 12784 1 9 0 7 0 4 1 . 705 10 1 . 5 2 1 3 4 1 . 3 5 5 3 6 1 . 2 0 6 6 4 1 .07 57 2 O . 9 5 8 0 7 0 . 8 5 5 16 O 7 6 4 H 0 0 6 8 5 5 4 O . 6 1730 O 5 5 6 H 6 O 5 0 3 6 4 0 4 5 7 5 3 0 . 4 1 7 7 1 0 . 3 8 0 5 2 O 3 4 8 3 0 0 32012 0 . 2 9 4 9 8 0 . 2 7 1 8 ? 0 . 2 5 0 4 0 0 . ? 3 1 5 8 O . ? 1 4 9 1 0 19993 0 18 6 13 DEI A * 1 0 . 0 0 0 0 0 DE L X = 1 0 9 0 12 OUT DISCH TOTAL TIME . SECONDS 0 . 0 0 . 0 . 0 0 1 5 6 120 . 0 . 0 0 0 9 7 2 4 0 . 0 . 2 5 6 9 7 3 6 0 . 1 4 7 6 5 0 4 8 0 . 2 . 8 8 5 5 0 6 0 0 . 2 64 M 6 7 2 0 . 3 . 4 8 4 7 4 8 4 0 . 5 . 8 8 7 2 7 9 6 0 . 8 . 8 0 6 7 8 1 0 8 0 . 1 1 . 0 3 9 9 4 1 2 0 0 . 12. 14548 1 3 2 0 . 1 2 . 2 0 5 4 9 - 14 4 0 . 1 1 . 5 5 6 5 0 1 5 6 0 . 1 0 . 5 4 3 3 9 1 6 8 0 . 9 . 4 1 6 0 4 1 8 0 0 . 8 . 3 0 6 9 2 1 9 2 0 . 7 . 2 7 0 9 2 2 0 4 0 . 6 . 3 3 5 0 5 2 1 6 0 . 5 . 5 0 0 8 4 2 2 8 0 . 4 . 7 5 7 7 9 2 4 0 0 . 4 . 1 0 3 0 7 2 5 2 0 3 . 5 2 9 4 0 2 6 4 0 . 3 . 0 3 0 4 2 2 7 6 0 . 2 . 5 9 9 4 3 2 8 8 0 . 2 . 2 3 2 9 3 3 0 0 0 1 . 9 2 0 4 5 3 120 1 . 6 5 5 6 9 3 2 4 0 1 4 2 9 18 3 3 6 0 1 . 2 3 9 6 2 3 4 8 0 1 . 0 7 8 2 1 3 6 0 0 O . 9 4 1 0 3 3 7 2 0 0 . 8 2 1 5 6 3 8 4 0 0 . 7 2 4 3 6 3 9 6 0 0 . 6 3 9 3 7 4 0 8 0 0 . 5 6 6 0 9 4 2 0 0 0 . 5 0 3 6 6 4 3 2 0 0 . 4 4 9 0 6 4 4 4 0 0 . 4 0 2 9 3 4 5 6 0 0 . 362 15 4 6 8 0 0 . 3 ? 4 4 4 4 8 0 0 0 . 2 9 1 3 1 4 9 2 0 0 . 2 6 4 2 8 5 0 4 0 0 . 2 4 0 7 0 5 1 6 0 0 . 2 1 8 9 8 5 2 8 0 TOLR=.0000100 XN2* 0 0500 DELI = 120.0OO00 IN SECTION NO = IN AREA 0.0 0.00410 0.00254 0.2102G 0.78368 1.30G07 1 .22166 1 .50684 2 . 23874 3.01782 . 3.56526 3.82622 3.84001 3.68742 3 .44643 3 . 17108 2.89183 2.62234 2.36673 2.12784 1.90704 1.70510 1 .52134 1 .35536 1 .20664 1 .07572 0.95807 0. 855 16 O. 76480 0.68554 0.61730 O. 55686 0.50364 O.45753 0.4 172 1 O. 38052 O. 34830 0. 32012 O. 29498 O 27182 0 25040 O 23158 0 2 149 1 0 19993 0 186 13 IN DISCH 0 0 0.00156 0.00097 O. 25697 1 . 47650 2 . R8550 2.64146 3.48474 5.88727 8.80678 1 1 .03994 12.14548 12.20549 1 1 . 55650 10.54339 9.41604 8.30692 7 27092 6.33505 5.5008 4 4.75779 4.10307 3.52940 3.0304 2 2 . 59943 2.23293 1.92045 1.65569 1.42918 1.23962 1.07821 0.94103 0.82156 0.72436 0.63937 0 56609 0.50366 O.41906 0 40293 0.362 15 0.32444 0.2913 1 0 26428 0.24070 O.21898 OUT SEC1ION NO OUT AREA 0 0 0.00403 0.00260 0.20922 O. 782 19 1 30548 1 22246 1 .506 3 1 2 237 1 1 3.01623 3.56 4 1 8 3.82572 3 . 83998 3 . 68772 3.44G92 3 . 17166 2.89244 2.62293 2.36731 2 1284 1 1.907 59 1 70562 1 . 52184 1 .35583 1 .20708 1 .076 1 1 O. 95044 O.85550 O . 765 10 0 68582 0.6 1755 O 55708 0 50385 0 . 4577 1 0.41737 O.380GS O 34844 O 32024 0.795 10 O 77193 O . 75050 0.7 3 16 7 0 7 1499 O 7OOOI 0.186 70 DELA- 10.00000 DE L X = 1 13 OUT DISCH TOTAL TIME . SECONDS 0.0 O. 0.00153 120. 0.00099 240. 0.75534 360. 1 .47777 480 . 2.88378 600. 2.64369 720. 3 . 48312 840. 5 88159 960. 8.80046 1080. 1 1 .03540 1200. 12. 14329 1320. 12.20535 1440. 1 1 .55777 1560. 10.54539 1680 . 9 . 4 1833 1800. 8.30925 1920. 7 . 273 16 2040. 6.33718 2 160. 5.5O203 2280. 4.75963 2400. 4 10475 2520. 3.53093 2640. 3.03181 2760. 2.60066 2880. 2.23402 3000. 1 .92 143 3120. 1 .65655 3240. 1 .42994 3360 1.24028 3480 1.07878 3600 0.94154 3720 0.82201 3840 0.72474 3960 0.63971 4080 0 56639 4200 0.50393 4320 0 44929 4440 0.40314 4560 0.36235 4680 0 374G7 4800 0.79147 4920 0. 76442 5040 0.24083 5 160 0.21910 5280 TOLR =.0000100 XN2 = 0 . 0 5 0 0 DELT- 120.OOOOO DELA- 10 OOOOO DE L X = IN S E C T I O N NO = 13 OUT S E C T I O N NO = 14 IN AREA IN D I S C H OUT ARFA OUT D I S C H TOTAL TIME 0 .0 0.0 0 0 0 .0 0 0 .00403 0 . 0 0 1 5 3 0 006 86 0 OO? 7 7 120 0 0 0 2 6 0 0.00099 0 0 0 8 5 0 0 .00387 240 0 . 20922 0.25534 0.27674 0 3 IOH 1 360 0 .78219 1.47277 1.27714 2 .8004 5 4 8 0 1 . 30548 2.88378 2 77102 7 . 84248 6 0 0 1 . 22246 2.64369 3 16908 9 408O8 7 2 0 1 .50631 3.48312 3.41772 10 4 2559 8 4 0 2 .2371 1 5 . 8 8 1 5 9 3.79958 12 0307 2 "960 3 .01623 8.8004 6 4 . 19164 13 74 199 1080 3 . 564 18 11.03540 4 41822 14 755 14 1200 3 82572 12.14329 4 45139 14 9 0 3 4 3 1 320 3 . 8 3 9 9 8 12.20535 4.31411 14 29095 1440 3 68772 1 1 .55777 4 0597 3 13 16 155 1560 3 44692 10.54539 3.744 17 1 1 79643 1680 3 17 166 9.41833 3 4 1?R8i 10 4057 3 1800 2 89244 8 . 3 0 9 2 5 3.0905 7 9 0959 7 1920 2 6 2 2 9 3 7.273 16 2.7874 1 7 . 9 0 5 4 9 2 0 4 0 2 36731 6.337 18 2.507 71 6 85 111 2 160 2 1284 1 5 . 5 0 2 8 3 2.24 9 6 0 5 9 2 5 0 9 2 2 8 0 1 9 0 7 5 9 4.75963 2 . 0 1 1 5 5 5 108 12 24 0 0 1 70562 4.10475 1 79626 4 39636 2 5 2 0 1 52 184 3 . 5 3 0 9 3 1 6 0 1 2 3 3 77543 2 6 4 0 1 35583 3.03 181 1 .4 2621 3 2387 1 2 7 6 0 1 20708 2 6O066 1 26922 2 777 16 2 8 8 0 1 . 076 1 1 2.23402 1 . 12989 2 38457 3 0 0 0 0 95844 1.92 143 1 007 26 2 05 100 3 120 0. 8 5 5 5 0 1.65655 0 90041 1 , 76912 3 2 4 0 0. 765 10 1.42994 0.80413 1 . 5 2 7 7 6 3 3 6 0 0. 6 8 5 8 2 1.24028 0 72135 1 32527 3 4 8 0 0 6 1 7 5 5 1 0 7 8 7 8 0.64931 1 . 15300 3 6 0 0 0. 55708 0.94154 0.58607 1 , 0O733 3 7 2 0 0. 5 0 3 8 5 0.82201 0 . 5 3 0 I 1 0 88033 3 8 4 0 0 4577 1 0 .72474 O 48223 0 77644 3 9 6 0 0. 4 1737 0.6397 1 0 43911 0. 68554 4 0 8 0 0. 38068 0 . 5 6 6 3 9 0.40165 0. 60702 4 2 0 0 0. 34844 0.50393 0 36 703 0 539 9 5 4 3 2 0 0. 32024 O . 4 4 9 2 9 O.33705 0. 48 187 4 4 4 0 0. 295 10 0.40314 0 3 1 166 0. 43267 4 5 6 0 0. 27 193 . 0 . 3 6 2 3 5 0 287 14 0. 389 13 4 6 8 0 0. 2 5 0 5 0 0.32462 0.264 30 0 34892 4 8 0 0 0. 23 167 0.29147 0 244 18 0 3 1349 4 9 2 0 0. 2 1499 O.26442 0 22765 0. 28439 5 0 4 0 0. 2000 1 0.24083 0 2 115 1 0 25894 5 1 6 0 0. 18620 0 2 19 10 0 19664 0 23552 5 2 8 0 SECONDS Ln O TOLR=.0000100 XN2 = 0.0500 DE L T = 120.00000 DE IA = 10.00000 DE L X = IN SECTION NO = 14 OUT SECTION NO 15 IN AREA IN DISCH OUT AREA OUT DISCH TOTAL TIME 0. 0 0.0 0.0 0 . 0 0 0. 00686 0.00277 0.00866 0 00398 120 0. 00850 0.00387 0 01273 0 . 006 ; 3 240 0. 27674 0.37081 0.339O9 0 . •1858 1 360 1 . 277 14 2.8004 5 1.71185 4 1248 1 4 80 2 77 102 7.84248 3.97525 12 79394 600 3 . 16908 9.40808 4 72780 16 . 16896 720 3 4 1772 10.42559 4.985 15 1 7 368 16 840 3 79958 12.03072 5.15806 18 187 19 960 4 19164 13.74199 5.26358 18 686 33 1080 4 4 1822 14.75514 5.22024 18 4 7 736 1200 4 45139 14.90343 5.04829 17 . 66542 - 1320 4 3 144 1 14.29095 4 77329 16 37776 1440 4 .05973 13.16155 4 4 2069 14 7 66 16 1560 3 744 17 11.79643 4.03366 1 3 04 808 1680 3 4 1288 10.40573 3.64890 1 1 . 39360 1800 3 09057 9.09597 3 28549 9 88 304 1920 2 7874 1 7.90549 2.95023 a 53809 2040 2 5077 1 6.85111 2 64687 7 . 36523 2 160 2 24960 5.92509 2.37013 6 34752 2280 2 . 01155 5 . 10812 2.115 18 5 4 5675 2400 1 . 79626 4.39636 1 .88624 4 68808 2520 1 .60123 3 . 77543 1.67929 4 02003 2640 1 .42621 3.2387 1 1 .494 16 3 44569 2760 1 26922 2.777 16 1.32927 2 95372 2880 1 . 12989 2.38457 1.1R369 2 53517 3000 1 00726 2.05100 1 05609 - 2 1806 1 3120 0. 9004 1 1 .769 12 0 94319 1 . 88 174 3240 O 804 13 1 52776 0 843 17 1 62562 3360 0 72135 1.32527 0.75691 1 4 1028 3480 0 6493 1 1.15300 0 68037 1 22725 3600 0 58607 1.00733 O 6 1507 1 07315 3720 0 . 53011 0.88033 0.55582 0 93868 3840 0 . 48223 0.77644 0.5067 6 o 82815 3960 o .4391 1 0.68554 0.46086 0 73 140 4080 0 .40165 0.60702 0.421 14 o 64 766 4 200 0 36703 0.53995 0.38563 o 57599 4320 0 . 33705 0.48187 0 35387 0 5 1446 4440 0 .31166 0.43267 0.3 7690 0 4677 1 4560 0 .287 14 0.389 13 0.302 36 0 4 1593 4680 0 .26430 0.34B92 0.778 1 1 0 .37372 4 800 0 .244 18 0.3 1349 0 25670 0 33553 4920 0 22765 0.28439 0 2 3900 0 .30436 5040 o .21151 0.25894 0.22301 o .27705 5 160 0 . 19664 0.23552 0.20708 0 .25196 5280 SECONDS NJ Ln T O L R =.0000100 XN2 = 0.0500 DELT- 120.00000 DELA- 10.00000 0ELX = 960. IN SECTION NO = 15 OUT SECTION NO - 16 IN AREA IN DISCH OUT A R I A OUT DISCH TOTAL TIME 0. 0 0.0 O.O 0 0 0. 0. 00866 0.00398 O 0 O 0 120. 0. 01273 0.00673 0.0 0 . 0 240. 0. 33909 0.4858 1 0 . 1 368 3 0. 14549 360 . 1 . 7 1 185 4. 1248 1 0. 194 2 6 0. 23 178 480. 3 . 97525 12.79394 1 .4 1480 3 . 205 1 7 600. 4 . 72780 16.16896 3. 146 10 9 3 1670 720. 4 . 98515 17.36816 4.24540 13 98235 840 . 5 . 15806 18. 182 19 4.79608 16 . 4824 1 960. 5. 26358 18.68633 5 06-14 1 1 7 . 74 132 10BO 5 . 22024 18.47736 5. 18 36 1 18 . 302 4 7 1200. 5 . 04829 17 66542 5 18944 18 32993 1320 4 . 77329 16.37776 5 09 157 17 . 86920 1440 4 . 4 2069 14 766 16 4 8 9 7 19 16 . 95409 1560 4 . 03366 13.04808 4 62359 15 . 6906 1 16BO 3. 64890 11.39360 4.30006 14 . 22676 1800 3 . 28549 9.88304 3.956 3 2 12 . 7 1 159 1920 2 . 95023 8.53809 3 6 1429 1 1 24727 2040 2 . 64687 7.36523 3 2868? 9 . 8885 1 2 160 2 37013 6.34752 2 98318 8 66907 2280 2 11518 5.45675 2.70507 7 . 58896 2400 1 88624 4 68808 2 44 794 6 63235 2520 1 . 67929 4 02003 2.21167 5 79294 2640 1 494 16 3 .44569 1 . 9950-1 5 05275 2760 1 . . 32927 2.95372 1.79792 4 40172 2880 1 18369 2.53517 1 6 1943 3 83 149 3000 1 .05609 2. 1806 1 1 45833 3 33537 3 120 0 . 94349 1 . 88 174 1 3 14 10 2 909 1 1 3240 0 843 17 1 62562 1 . 18 565 2 . 54067 3360 0 7569 1 1.41028 1 0/006 2 2 1768 3480 0 68037 1 .22725 0 96723 1 94475 3600 0 6 1507 1 . O / 3 15 0 . 8 7 466 1 7045B 3720 0 .55582 O 93868 0 79338 1 5008 2 3840 0 50676 0 828 15 0.719 36 1 32049 3960 0 .46086 0.73140 0.65591 1 . 16877 4080 0 .42114 ' 0.64766 0.59860 1 .03577 4 200 0 .38563 0.57599 0.54792 ,0 .92076 4320 0 .35387 0 51446 0 503 16 'o .82055 4 4 40 0 .32690 0.4622 1 0 . 462 15 0 7 34 1 1 4560 0 .30236 0 41593 0 . 426 13 0 . 658 18 4680 0 . 278 1 1 0.37322 0.395 1 1 O .594 35 4800 0 .25670 0.33553 0 36594 0 . 53783 4920 0 .2 3900 O.304 36 0.33854 0 48476 .5040 0 .22301 0.27705 0.31433 0 . 43784 5 160 0 20708 0.25196 0 29327 0 . 39993 5280 TOLR =.0000100 XN2 = OOOOO DE L T = 120 OOOOO DELA = IO.OOOOO DELX' 1 I N SECTION NO = 16 OUT SECTION NO = 17 IN AREA IN DISCH OUT A R E A OUT DISCH TOTAL TIME 0 .0 0.0 0.0 0 .0 0 0 .0 0.0 0 0 0 .0 120 0 .0 0.0 0.0 O .0 240 0 . 136B3 0. 14549 0. 13623 0 . 14466 360 0 . 19426 0.23 178 0. 195 14 0 . 233 16 480 1 . 4 1480 3.20517 1.41288 3 .19952 600 3 . 146 10 9.3 1670 3 14327 9 .30549 720 4 . 24540 13.98235 4.24382 13 . 97529 840 4 .79608 16.4824 1 4.79535 16 47905 960 5 .06441 17.74 132 5.06405 1 7 .73964 1080 5 .18361 18.30247 5 18342 18 .30159 1200 5 .18944 18.32993 5. 1894 3 18 32986 1320 5 09157 17 .86920 5.09175 1 7 .87003 1440 4 89719 16.95409 4 89753 16 95570 1560 4 62359 15.69061 4 62 409 15 69289 1680 4 30006 14.22676 4 30066 14 22945 1800 3 95632 12.71159 3.95698 12 7 14 4 5 1920 3 61429 11.24727 3.61496 1 1 25012 2040 3 28682 9.88851 3.28749 9 89 124 2 160 2 . 983 18 8.66907 2 98381 8 67 160 2280 2 . 70507 7.58896 2.70568 7 59128 2400 2 . 44794 6.63235 2 4 4 853 6 63449 2520 2 2 1 167 5.79294 2 2 1223 5 79490 2640 1 99504 5.05275 1 99557 5 05456 2760 1 79792 4.40172 1 . 79843 4 40336 2B80 1 . 6 1943 3.83 149 1 61991 3 83297 3000 1 . 45833 3.33537 1.45877 3 3367 1 3120 1 314 10 2.90911 1 3 145 1 2 . 9 103 1 3240 1 . 18565 2.54067 1 18604 2 54 174 3360 1 . 07006 ' 2.21768 1.0704 3 2 2 1865 3480 0. 96723 1.94475 O 96755 1 . 9456 1 3600 0. 87466 1.70458 0 87497 1 70535 3720 0. 79338 1.5008 2 O.79365 1 50150 3840 0. 7 1936 1.32049 0 7 196 1 1 . 32 1 10 3960 0. 6559 1 1 . 16877 0 656 13 1 . 169 30 4080 0 59860 1.03577 O 5988 1 1 . 03625 4 200 0. 54792 0.92076 0.548 1 1 0. 92 118 4320 0. 503 16 0.82055 0 50333 0 82092 4440 0. 462 15 0.73411 0 40231 0. 73445 4 560 0. 426 13 0.65818 0.42627 0 658 18 4680 0. 395 1 1 0.59435 0 39524 0 59460 4800 0. 36594 0.53783 0.366O0 O. 5 3808 4920 0 33854 0.48476 0.33866 0 . 48498 5040 0 3 1433 0.43784 0 3 14 4 3 0. 4 3804 5 160 0. 29327 0.39993 0 29337 0 '40010 5280 . SECONDS LO T 0 L R r.OOOO10O XN2= 0.0500 IN SFCTION NO = 17 IN AREA IN DISCH 0 0 o 0 0 0 0 0 0 O O 0 0 13623 0 14 466 0 195 14 0 233 16 1 4 1288 3 19952 3 14327 9 30549 4 24382 13 97529 4 79535 16 47905 5 06405 17 73964 5 18342 18 30159 5 18943 18 32986 5 09 175 17 87003 4 89753 16 95570 4 62409 15 69289 4 30066 14 22945 3 95698 12 7 1445 3 6 1496 1 1 25012 3 28749 9 89 124 2 9838 1 8 67 160 2 70568 7 59128 2 44853 6 63449 2 2 1223 5 79490 1 99557 5 05456 1 79843 4 40336 1 6 1991 3 83297 1 45877 3 3367 1 1 31451 2 9 103 1 1 18604 2 54 174 1 07043 2 2 1865 0 96755 1 94 56 1 0 87497 1 70535 0 79365 1 50150 0 7 196 1 1 32 1 10 0 65613 1 16930 0 5988 1 1 03625 0 548 1 1 0 92 118 0 50333 O 82092 0 46231 0 7 34.15 0 42627 0 65848 0 39524 0 59460 0 36606 0 53808 0 33866 0 .18498 0 3 14 4 3 0 4 380 1 0 29337 0 40010 DELT" 120 OOOPO DTLA- 10.00000 DE1.X= 1. OUT SECTION NO - 18 OUT AREA OUT DISCH TOTAL TIME 0 O O 0 O 0 0 0 0 120 O O 0 0 2 40 0.19091 0 2 265 1 360 0 25604 0 3 3 4 3 7 480 1 . 6 3 1 4 3 3 8684 3 600 3.717 IO 1 1 6R201 720 5.21907 18 47 169 840 6 12452 22 9 1737 960 6.63031 25 49876 10BO 6.90167 26 9 1064 1200 6 97876 27 3 1673 1320 6 866 15 26 7235 1 1440 6 58898 25 2856 1 1560 6 t967? 23 27930 1680 5.7 3608 20 98276 1800 5.24928 18 6 1736 1920 4 76 763 16 35 179 2040 4 31028 1 4 27248 2 160 3 89037 1? 4246 1 2280 3 51185 IO 8 14 13 2400 3 1702 3 9 4 1266 2520 2.86370 8 19879 2640 2 58788 7 14458 2760 2 3 3580 6 27544 2880 2 105 7 1 5 4 7 706 3000 1 89791 4 77730 3 120 1 713 26 4 17934 3240 1.54694 3 60825 3360 1 39746 3 15420 3480 1 2654 2 2 76600 3600 1.14 503 2 42694 3720 1 03911 2 13553 3840 0 9-1267 1 87957 3960 0 . 85780 1 6623 1 4080 0 . 78 1 26 1 4 704 4 4 200 O.7 1 36? 1 30676 4320 O 65364 1 16335 4440 0 . 5993! 1 1 03755 4560 O.55 702 0 93006 4680 O 5 1 11 8 0 83745 4 800 0 4 7 701 0 75496 4920 0 . 4 36 15 0 67930 5040 0.404 8 7 0 6 1337 5 160 0.37650 0 55829 5280 Ln TOLR =.0000100 XN2 = 0.0500 DE L T = 120 OOOOO DELA- 10.OOOOO DELX = IN SECTION NO = 18 OUT SECTION NO" 19 IN AREA IN DISCH 0U1 AREA OUT DISCH TOTAL TIME 0. 0 0.0 0 0 0. 0 0. 0. 0 0.0 0.0 0. 0 120. 0. 0 0.0 0.0 0. 0 240. 0. 19091 0. 22651 0.24118 0. 3082 1 360. 0. 25604 0 . 33437 0.31314 0 43554 480. 1 63143 3 . 86843 1.83968 4 53606 600. 3. 7 17 10 11.68201 4.26179 14 05564 720. 5 2 1907 18.47169 6.13393 22 . 96487 840. 6 . 12452 22.91737 7 36240 29 . 35287 960. 6 . 63031 25.49876 8.08020 33 . 25601 1080. G . 90167 26.9 1064 8 48583 35 5 1849 1200. 6. 97876 27.31673 8 62549 36 30301 1320. 6 8G6 15 26.72351 8 . 49632 35 577 12 1440. 6 58898 25.28561 8 . 14537 33 6 16 18 1560. 6 19622 23.27930 7.64401 30 86664 1680. 5 .73608 20.98276 7 05857 27 737 14 1800. 5 24928 18.61736 6.44083 2 4 . 52 1 39 1920. 4 76763 16.35 179 5 83167 2 1 45457 2040. 4 . 31028 14.27248 5.25703 18 65475 2 160. 3. .89037 12.42461 4.72989 16 17856 2280. 3 5 1 185 10.81413 4.25780 14 03779 2400. 3 17023 9.4126G 3 83680 12 19152 2520. 2 B6370 8.19879 3.46102 10 60325 2640. 2 58788 7.14458 3.12557 9 23510 2760. 2 . 33580 G.22544 2 8 2 4 4 6 8 04795 2880 . 2 1052 1 5.42 206 2 55154 7 01 155 3000. 1 89794 4.72730 2.30503 6 1 1825 3120. 1 7 1326 4.12934 2.OH 33? 5 34869 3240. 1 54694 3.60825 1.88?36 4 67506 3360. 1 39746 3.154 20 1 70104 4 09002 3480. 1 26542 2.76600 1 53992 3 58662 3600. 1 . 14503 2.42694 1.39561 3 . 14875 3720 1 039 1 1 2. 13553 1.26670 2 76975 3840. 0 94267 1.87957 1.14 905 2 4382 1 3960. 0 .85780 1.66231 1.04663 2 15549 4080 0 .78126 1.47044 0 952 17 1 90478 4200 0. .71362 1.30676 0.86984 1 69248 4320 0 65364 1.16335 0 7 9541 1 5059 1 4440 0 59939 1.03755 0 72784 1 . 34077 4560 0 55202 0.93006 0 66970 1 .20174 4680- 0 51118 0.83745 0 . 6 1826 1 .08039 4 800 0 47204 0.75496 0.5704 6 0 .97191 4920 0 436 15 0.67930 0 527 18 0 87369 5040 0 40487 O.61337 0. 4 8807 O .78875 5 160 0 37650 0.55829 0 45382 0 .7 1654 5280 NJ Ln Ln = .0000100 XN2 = 0.0500 DE L T = 120.O0O0 IN SECTION NO = 19 OUT SECTION NO IN AREA IN 1 DISCH OUI ARE O. 0 0. 0 0 0 O 0 0 0 0 o O. 0 0. 0 0. 0 0. 24 1 18 0 3082 1 0. 24080 0. 3 13 14 0. 43554 0 3 128.2 1 . 83968 4 . 53606 1 83572 4 . 26179 14 . 05564 4 . 25727 6 . 13393 22 . 96487 6 . 1 308 4 7 . 36240 29 . 35287 7 . 36050 8 . 08020 33 . 25601 8 . 079 10 8 48583 35 . 5 1849 8 48522 8 62549 36 . 30301 8 62528 8 . 49632 35 . 577 12 8 4965? 8 . 14537 33 6 1618 8 . 1 4 590 7 . 64401 30. 86664 7 644 78 7 . 05857 27 737 14 7 . 05949 6 . 44083 24 . 52 139 6 44 18? 5. 83167 2 1 45457 5 . 83?70 5. 25703 18 . 65475 5 . 25R03 4 72989 16 17856 4 7 308 5 4 25780 14 03779 4 25868 3 83680 12 19 152 3 8376 1 3 .46102 10 60325 3 46 178 3 12557 9 23510 3 1262 7 2 .82446 8 .04795 2 B25 12 2 .55154 7 .01 155 2 552 16 2 .30503 6 . 1 1825 2 3056 2 2 .08332 5 .34869 2 08387 1 .88236 4 .67506 1 88286 1 70104 4 .09002 1 .70151 1 . 53992 3 .58662 1 54036 1 .39561 3 . 14875 1 .39602 1 . 26670 2 76975 1 .267(16 1 .14905 2 .43821 1 1 .194(1 1 .04663 2 .1554 9 1 .04 695 O .952 17 1 .904 7 8 O 95216 0 .86984 1 .69248 O .87011 0 .79541 1 .50591 o .79566 0 .72784 1 .34077 0 .72807 0 .66970 1 20174 0 66990 0 . 6 1826 1 .08039 0 .61845 0 .57046 0 .97 19 1 0 .57064 0 .527 18 O .87 369 o .527 34 0 .48807 0 .78875 0 488? 3 0 .45382 0 .71654 0 . 45395 [1ELA= 10.00000 D E L X = = 20 OUT DISCH TOTAL TIME . SECONDS O.O O . O 0 1 20 . 0.0 240 . O.307 54 360 . 0.43 192 480. 4 52332 600. 14.0354 2 720 . 2?.94926 840. 29.3 1264 960 . 33 25000 1080 . 35.51509 1200. 36 30185 1320. 35.57822 1440. 33 61909 1560. 30.870BO 1680 . 2 7.7 4 200 1800. 24.52654 1920 . 21.4 5966 2040. 18.65955 2 160. 16 18295 2280. 14.0417 3 2400. 12.19502 2520. 10 60638 2640. 9 23790 2760. 8.05045 2880. 7.01382 3000. 6.12030 3 120. 5.35054 3240. 4.67673 3360 4 09153 3480 3 58797 3600 3.14995 3720 2.7 708 3 3840 2.4 39 19 3960 2 15634 4080 1.9055 7 4 200 1 .69316 4320 1.50653 4440 1.34133 4560 1.202 2 3 4680 1.08OR2 4800 0.9723 1 4920 0.87 405 5040 0.78908 5 160 0.71682 5280 TOLR- OOOO100 XN2 = O 0500 D F L T - 120.OOOOO nri.A= 10 .00000 DEI.X = 1. IN SECT IN 0 O 0 O O 1 4 6 7 8 8 . 8 8 8 7 7 6 5 5 4 4 3 3 3. 2 . 2 2 2 . 0. 0. o. 0 o. 0. 0. 0. o. 0. I ON NO AREA .0 .0 .0 .24080 .31282 .83572 .25727 .13084 .3G050 .07910 .48522 .62528 .49652 .14590 .64478 .05949 .44182 . 83270 .25803 .7 3085 .25868 .83761 . 46 178 . 12627 825 12 552 16 30562 08387 88286 70151 54036 39602 26706 14940 04695 95246 8701 1 79566 72007 66990 6 184 5 57064 52734 48823 45395 20 IN DISCH 0.0 0 0 0.0 0 . 30754 O. 43492 4 . 52332 14.03542 22.94926 29.34264 33.25000 35.51509 36.30185 35.57822 33.61909 30.87080 27.74200 24.52654 21.45966 18.65955 16.18295 14.04173 12.19502 10.60638 9.23790 8 .0504 5 7.01382 6 . 1 2030 5.35054 4 . 67673 4.09153 3.58797 3.14995 2 77083 2.43919 2.15634 1.90557 1 .693 16 1.50653 1.34 133 1 20223 1.08082 O.97 23 1 0.8 7 405 O 78908 O.7 1682 SFCTI ON NO = 2 1 OUT AREA OUT DISCH TOTAL TIME O.O 0.0 0 . 0 00353 0.00134 120. 0.OO700 0 00286 240 . O.29672 0 40599 360 . 0.75296 1.40086 480. 2 74930 7 75898 600 . 5 . 1.1 187 1B.05893 720. 6 90249 26.914 9 3 840. 8 029 16 32.97620 960 B 64984 36 44162 1080. B.964 36 38.231B4 1200 9.02071 38.55263 1320. 8 B17 10 37 39368 1440. 8.35722 34.79987 1560. 7.7B553 31.64049 1680. 7 15799 28.26088 1BOO. G 5 1 187 24 B87B3 1920. 5 8B503 2 1 7 1794 2040. 5 2974 1 (fl B4944 2 160. 4 76 169 16 32454 2280. 4 28283 14 14972 2400. 3 85667 12 27798 2520. 3 47780 10.672O9 2640. 3 13937 9.28998 2760. 2.83587 8.09179 28BO. 2.56150 7 04B01 3000. 2 3 1375 6.14B61 3120 2.09O8 7 5 37399 3240 1 88866 4.696 19 3360 1.70653 4.10768 3480 1.54 4 79 3.60161 3600 1.4 0O05 3. 16 ISO 3720 1.2 7056 2 78 1 12 3840 1 15260 2.448 16 3960 1 04988 2 164 11 40BO 0.95502 1 91234 4200 0.87245 1.69904 4320 0 797 70 1 5 1165 4440 O.72994 1 . 34579 4560 0.67151 1.20608 4680 0 6 199? 1.OB416 4 800 0.57193 0 97524 4920 0 52846 0 87659 504 0 O 48932 0.79138 5 160 0 4 54 95 0. 7 1892 5280 SECONDS Ln -̂ 1 TOLR=.0000100 XN2 = 0.0500 DE L T = 120 OOOOO DEI.A= 10 OOOOO DE L X = IN SECTION NO 2 1 OUT SECTION NO = 22 IN AREA IN DISCH OUT AREA OUT DISCH TOTAL TIME 0. 0 0. 0 0.0 0. 0 0 0. 00353 0. 00134 O 00669 0. 00265 120 0. 00700 0. 00286 0.01120 0. 00570 240 0. 29G72 0. 40599 0.34850 0 50404 360 0. 75296 1 . 40086 1.12250 2 . 36388 480 2 . 74930 7 . 75898 3.55365 10 99086 600 5 13187 18 . 05893 5.95888 22 08249 720 6 . 90249 26 . 9 1493 7.64674 30 . 88 1 35 840 8 02916 32 . 97620 8.67954 36 . 6 1066 960 8 . 64984 36 . 44 162 9.20812 39 63403 1080 8 96436 38 . 23 184 9.43507 40. 94933 1200 9 0207 1 38 . 55263 9.4 lOOl 40. 80409 1320 8 817 10 37 . 39368 9.13491 39 20976 1440 8 35722 34 . 79987 8.56869 35 98 148 1560 7 . 78553 3 1 . 64049 7.92603 32 . 41075 1680 7 . 15799 28 . 26088 7.25585 28 7801 1 1800 6. 51 187 24 . 88783 6.58196 25 24936 1920 5. 88503 2 1 . 7 1794 5 93738 2 1 97636 2040 5. 2974 1 18 84944 5.33681 19 . 03944 2 160 4 76 169 16 . 32454 4.79255 16 466 19 2280 4 . 28283 14 . 14972 4 30699 14 . 25778 2400 3 . 85667 12 27798 3 .87575 12 36098 2520 3 47780 10. 67209 3.49380 10. 73782 2640 3 13937 9 28998 3.152 18 9 34 2 10 2760 2 83587 8 09 179 2.84663 8 133 15 2880 2 56 150 7 . 04801 2.57084 7 08220 3000 2 31375 6 1486 1 2.32188 6 17694 3 120 2 09087 5 37399 2 09787 5 397 46 3240 1 88866 4 69619 1 89447 4 7 1566 3360 1 .70653 4 10768 1.7 1155 4 . 12383 3480 1 . 54479 3 . 60161 1 54922 3 6 1525 3600 1 .40005 3 . 16180 1 40408 3 17366 3720 1 . 27056 2 78 1 12 1.27407 2 79 142 3840 1 . 15260 2 448 16 1 . 1558 1 2 . 457 12 3960 1 .04988 2 164 1 1 1.05280 2 .17188 4080 O .95502 1 .91234 0.95757 1 .91913 4 200 0 .87245 1 .69904 0 87480 1 .70491 4320 0 . 79770 1 5 1 165 0 79974 1 5 1676 4440 0 .72994 1 . 34579 0 73 180 1 35024 4560 O 67 15 1 1 20608 0 673 12 1 20993 4680 0 .61992 1 .08416 0 62 140 1 .0875 1 4800 0 57 193 0 .97524 0 57322 0 97816 4920 0 .52846 0 .87659 0.52958 0 879 14 5040 0 48932 0 .79138 0. 1901 1 0 . 79368 5160 0 45495 0 .71892 0.4 5595 0 72 103 5280 SECONDS NJ Ln 00

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