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Development of a research watershed system and a streamflow prediction model Kennedy, Gary Franklin 1969

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DEVELOPMENT OF A RESEARCH WATERSHED SYSTEM AND A STREAMFLOW PREDICTION MODEL by GARY FRANKLIN KENNEDY B . A . S c , U n i v e r s i t y o f B r i t i s h Co lumbia , 1965 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department o f A g r i c u l t u r a l E n g i n e e r i n g We accept t h i s t h e s i s as conforming to the r e q u i r e d s tandard THE UNIVERSITY OF BRITISH COLUMBIA May, 1969 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and S t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d b y t h e Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f A g r i c u l t u r a l E n g i n e e r i n g The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada i i ABSTRACT Two independent h y d r o l o g i c research p r o j e c t s , the development of (1 ) a research watershed system and (2) a streamflow p r e d i c t i o n model, were c a r r i e d out. The f i r s t p r o j e c t was p r i m a r i l y a f i e l d instrumen-t a t i o n task i n v o l v i n g both design and implementation of a system of research watersheds. Two small (50 acre) research watersheds which 1may become e i t h e r r e p r e s e n t a t i v e or e x p e r i -mental i n nature were i n i t i a t e d w i t h i n the U n i v e r s i t y of B r i t i s h Columbia Research Forest. A l a r g e r research water-shed system was described which could i n c l u d e the Alouette R i v e r Watershed. This system of watersheds when subjected to more rig o r o u s experimental procedures should y i e l d v a l u -able, management and conservation design c r i t e r i a f o r P a c i f i c Coast f o r e s t e d r e g i o n s . The second p r o j e c t was p r i m a r i l y a n a l y t i c i n nature, employing the use of m u l t i p l e regression.and a d i g i t a l com-puter. A computer program was developed which models the snowmelt streamflow of lar g e watersheds i n a manner which makes short term p r e d i c t i o n of the streamflow p o s s i b l e . The I i i prediction variables were temperature recorded at a single c e n t r a l l y l o c a t e d station, time and streamflow recorded at the outlet from "the watershed. The model predicted flood flow one to f i v e days i n advance of measured streamflow for the Praser River Watershed (78,000 square miles i n area) during the spring runoff period of 1955 and 1964. This model required c a l i b r a t i o n at the beginning of each s p r i n g runoff period. i v TABLE OP CONTENTS Page ABSTRACT i i LIST OF TABLES v i LIST OF FIGURES v i i LIST OF MODEL COMPONENTS x ACKNOWLEDGEMENTS xv I INTRODUCTION' 1 PART ONE RESEARCH WATERSHED SYSTEM 4 I I . REVIEW OF FUNDAMENTALS 2.1 Hydrology and Applied Hydrology. 5 Natu r a l Hydrologic Processes 5 Watershed C h a r a c t e r i s t i c s 6 .2.2 Research i n the Hydrology of Watersheds 9 Scope of Study 9 Aims of Study 10 Tools f o r A n a l y s i s 10 I I I A SYSTEM OF RESEARCH WATERSHEDS IN THE ALOUETTE RIVER WATERSHED 3.1 S i t e S e l e c t i o n 13 3.2 Description, and Instrumentation of Watershed System 15 Measurements and Surveys 22 PART TWO STREAMFLOW PREDICTION MODEL IV DEVELOPMENT OP A STATISTICAL PREDICTION MODEL 4.1 General D e s c r i p t i o n of Model Purpose 27 V Page Snowmelt Stream Plow Forecasting 31 Prediction Method 34 4.2 Variables, Parameters, Constants and the Prediction Equation 36 4.3 Computerized Model 42 V APPLICATION OP THE PREDICTION MODEL 5.1 Description of Watershed Tested ' 4 7 5.2 Significance of Variables, Parameters, Constants and the Regression Equation Significance of Variables 51 Significance of Parameters 54 C a l i b r a t i o n of Model 56 Significance of Regression Equation 57 5 . 3 Prediction Results 57 VI CONCLUSIONS AMD RECOMMENDATIONS FOR FUTURE WORK 6 3 LIST OF REFERENCES 66 APPENDIX A Tables of results (A .1 to A.7) 69 APPENDIX B Computer Program Flow diagrams 7 8 Computer Program for 3-Day Prediction Model 8 4 V I LIST OP TABLES TABLE PAGE 3.1 Area and E l e v a t i o n s o f A l o u e t t e R i v e r Watershed and sub-basins 16 A.1 Sample B a s i c Data (B1 3) 1960 69 A.2 (a) Summary of P-Ratios o f Independent V a r i a b l e s X ( l ) , 1=1,8 (B 13) 1960 70 (b) Summary o f P-Ratios o f Independent V a r i a b l e s X ( I ) , 1=9,16 (B 13) 1960 71 A.3 R e g r e s s i o n A n a l y s i s output (B 13) 1960 72 A.4 1, 2 and 3 Day Praser R i v e r Flood Plow P r e d i c t i o n at Hope, B. C. (A22) 1955 73 A.5 1 , 2 and 3 Day F r a s e r R i v e r Flood Flow P r e d i c t i o n at Hope, B. C. (B 13) 1960 74 A.6 1, 2 , ..,5 Day Praser R i v e r Flood Flow P r e d i c t i o n at Hope, B. C. (A 32) 1955 75 A.7. 1,2, ..,5 Day F r a s e r R i v e r Flood Flow P r e d i c t i o n at Hope, B. C. (B 2 3 ) 1960 76 v i i LIST OF FIGURES FIGURE PAGE 2.1 The Hydrologic Cycle 7 3 .1 Alouette R i v e r Watershed and Sub-Basins 14 3 . 2 O r i e n t a t i o n of M i l i t z a Lake and Lost Lake Research Watersheds 19 3.3 Photograph of the M i l i t z a Lake Detention Area - 1600 foot E l e v a t i o n 20 3.4 Photograph I l l u s t r a t i n g Forested and Slash Ground Covers, M i l i t z a Lake Basin - 2 1 0 0 foot E l e v a t i o n 20 3.5 M i l i t z a Lake Basin 21 3.6 Weather S t a t i o n Measuring Water Inflow ( P r e c i p i t a t i o n ) and Ambient Conditions (Humidity and Temperature) M i l i t z a Lake Ba s i n - 1600 foot E l e v a t i o n 24 3.7 Water Outflow (Evaporation) M i l i t z a Lake Basin - 2 1 0 0 foot E l e v a t i o n 2 4 3.8 Water Outflow ( D i r e c t Runoff) 120°Sharp Crested V-Motch Weir 24 4.1 (a) Hydrograph of Snowmelt Stream I l l u s t r a t i n g v i i i FIGURE PAGE Region which i s subject to Short Term P r e d i c t i o n 28 (b) Minimal Gaging of a Watershed - A Stream Flow Gage at the Outlet and a Temperature Gage C e n t r a l l y l o c a t e d 28 (c) Basic Data - Fraser R i v e r Watershed -Year 1955 30 4.2 Flow Diagram I l l u s t r a t i n g Snowmelt Runoff Methods of Analyses 33 4.3 (a) Short Term P r e d i c t i o n of Discharge i s an E x t r a p o l a t i o n of the Regression P r e d i c t i o n of Discharge 35 (b) E x t r a p o l a t i o n Adjustment Constant "CORR" 35 (c) Diagram I l l u s t r a t i n g the P r e d i c t i q n Procedure and the E x t e r n a l Model Parameters 37 4.4 S i m p l i f i e d Flpw Diagram of P r e d i c t i o n Model 44 5.1 Fraser R i v e r and Willow R i v e r Watersheds and Gaging S t a t i o n s 49 5»2 Basic Data - Fraser R i v e r Watershed -Year 1955 ' . . 50 5.3 S i g n i f i c a n c e of I n d i v i d u a l Linear Temperature Terms T ( i - n ) , n=Q,9 52 5.4 S i g n i f i c a n c e of the Independent V a r i a b l e i x FIGURE PAGE X (11) over a range of regression equations 55 5 . 5 Significance of the Independent variables X(I), 1=1, 16 for single Regression Equation No. 110 55 5 . 6 Optimization of the I n i t i a l Value for Various Transformations of the Basic Variable Time 56 5.7 Significance of Regression Equation 3 Day Prediction 1955 58 5 . 8 Significance of Regression Equation 3 Day Prediction 1960 58 5-9 Actual and Predicted Stream Discharge at Hope, B.C. 3 Day Prediction 1960 (B 13) 60 5.10 Actual and Predicted Stream Discharge at Hope, B.C. 5 Day Prediction 1960 (B 2 3 ) 61 5.11 Error of Prediction 5 Day Prediction 1960 62 B.1 Flow Diagram of I n i t i a l Transformations 78 B.2 Flow Diagram of Regression Analysis 79 B.3 (a) Flow Diagram of prediction Routine 83 B.3 (b) Flow Diagram of Z-Test Routine 83 1 X LIST OF MODEL COMPONENTS DATA INPUT Transformation and Prediction Routines I - Day " i " , used as a subscript f o r the time ordered v a r i a b l e s . The subscript I starts numbering from March-1st of each year. MA - A constant which reduces the magnitude of the sub-s c r i p t I, conserves computer storage. MIA - Day I of f i r s t observation to enter the model f o r a given year. MAIIA - F i r s t observation of the i n i t i a l set of observations to enter model for regression analysis, NNPIA - Last observation of the I n i t i a l set of observations to enter regression analysis. NNFFA - Last observation of the f i n a l set of observations tq enter regression analysis. NFA - Last day of discharge to be forecast for a given year. RI, RII - The number assigned to the day beginning the "Time" variable sequence. C - A constant used to weight d a i l y maximum and minimum temperature. D - Used, to change'the magnitude of average temperature by a constant amount.. MSSTA, SSTEMP - The day I on which summation of temperature• begins. x i DATA INPUT (cont'd) MSSQA, SSQII - The day on which summation of discharge begins, IYEAR - The year being considered. NPRED - Maximum length of f o r e c a s t . QI(I) - D a i l y discharge. TMAX(I) - Maximum d a i l y temperature. . TMIN(l) - Minimum d a i l y temperature. Regression Routine KK PLMTI FLMTO - The number of v a r i a b l e s to be considered i n the r e g r e s s i o n a n a l y s i s . - The l i m i t i n g P - r a t i o value used when c o n s i d e r i n g an independent v a r i a b l e f o r entry i n t o the r e -g r e s s i o n equation (stepwise r e g r e s s i o n ) . - The l i m i t i n g P - r a t i o value used when c o n s i d e r i n g an independent v a r i a b l e f o r e l i m i n a t i o n from .the r e g r e s s i o n equation (stepwise r e g r e s s i o n ) . DATA OUTPUT Transformation Routine T ( l ) T The weighted average d a i l y temperature defined by equation ( 4 . 1 ) . STI(I) - Cumulative temperature. SQI(I) - Cumulative discharge. R(I) - The number assigned to any day I of the "Time" : v a r i a b l e sequence. x i i LATA OUTPUT (Cont'd) X ( l , n ) n=1,17 - The seventeen r e g r e s s i o n v a r i a b l e s as used i n equation (4.4). Regression Routine MAI - The f i r s t o b servation i n a set of observations used i n r e g r e s s i o n a n a l y s i s . NNF ' - The l a s t o bservation i n a set of observations used i n r e g r e s s i o n a n a l y s i s . N - The number of observations i n a set of observations used i n r e g r e s s i o n a n a l y s i s . I I - Subscript denoting an independent v a r i a b l e . IAM, IAMS(I) - MAI transformed back to o r i g i n a l (magnitude) s c a l e . IAN, IANS(I) - NNF transformed back to o r i g i n a l (magnitude) s c a l e . Simple Regression STD.ERR CRY, SERORY(II) - Standard e r r o r of dependent v a r i a b l e Y,(X(-I ,17)) w i t h respect to independent v a r i a b l e Xj_, ( X ( I , I I ) ) ; standard e r r o r of estimate. A, AAA(II) - Int e r c e p t or i n i t i a l r e g r e s s i o n parameter i n simple r e g r e s s i o n equation. B, BBB(II) - The r e g r e s s i o n parameter corresponding to the independent v a r i a b l e X ( I , I I ) . STD.ERRORB, SERORB(lI) - Standard e r r o r of r e g r e s s i o n parameter B B B ( l l ) w i t h respect to independent v a r i a b l e Xj_, ( X ( I , I I ) ) . x i i i DATA OUTPUT (cont'd) F-RATIO, PRAT(NNF,II) - Simple r e g r e s s i o n F-Ratio. CORRELATION R, RCOR(II) - Simple r e g r e s s i o n c o r r e l a t i o n c o e f f i c i e n t . M u l t i p l e Regression NSTEP - The step number i n stepwise r e g r e s s i o n . PRATIO - M u l t i p l e r e g r e s s i o n P-Ratio. STDEVRES, STDEVR, STDEVY, STDEVY(l) - Standard d e v i a t i o n of r e s i d u a l s or standard e r r o r of estimate. RSQ, RSQS(I) - C o e f f i c i e n t of m u l t i p l e determination. BB - I n i t i a l r e g r e s s i o n parameter i n m u l t i p l e r e g r e s s i o n equation (A i n equation 4.4). B ( I I ) - The r e g r e s s i o n parameter corresponding to the independent v a r i a b l e X ( l , I I ) . STERB(II) - Standard e r r o r of r e g r e s s i o n parameter B ( I I ) w i t h respect to independent v a r i a b l e X ( I , I I ) . FPAR(II), FPAR(NNF,Il) - P a r t i a l F-Ratio i n m u l t i p l e r e g r e s s i o n a n a l y s i s , a s i g n i f i c a n c e t e s t of the a d d i t i o n a l e f f e c t of l a s t ' independent v a r i a b l e to enter the r e g r e s s i o n equation. P r e d i c t i o n Routine DATE, IDAY(I+1 ) -. The day of the month corresponding to a • one day f o r e c a s t . Q ( I + 1 ) , PQI(I+ 1,2) - The p r e d i c t e d discharge f o r a one day f o r e c a s t . x i v DATA OUTPUT (cont'd) r ERROR, ERRDS(I+1) - The percentage d i f f e r e n c e between the a c t u a l and the p r e d i c t e d discharge f o r a one day for e c a s t . . CORR, CORRS(I) - The d i f f e r e n c e between the l a s t known value of discharge and the corresponding value determined by the r e g r e s s i o n equation; a constant used to adjust p r e d i c t e d discharge. Z-Test Routine EMEAN(JL) - Mean value of e r r o r ( I , J L ) . STDEV(JL) - Standard d e v i a t i o n of e r r o r ( I , J L ) . C0NP90(JL) - Magnitude of maximum e r r o r . ( I , J L ) w i t h i n the 90 percent confidence i n t e r v a l . CON95(JL) - Magnitude of maximum e r r o r ( I , J L ) w i t h i n the 95 percent confidence i n t e r v a l . XV ACKNOWLEDGEMENTS Acknowledgement i s o f f e r e d f o r a s s i s t a n c e and adv i ce g r a t e f u l l y r e c e i v e d f rom: P r o f e s s o r T . L . Cou l t ha rd who served as chairman on the r e -sea r ch committee and d i r e c t e d the development o f the Research Watershed System, D r . R. S ingh and P r o f e s s o r P. Mu i r who served on the r e s e a r c h committee and d i r e c t e d the development o f the Stream-f low P r e d i c t i o n Mode l , D r . W. J e f f e r y , D r . V . C . B r i nk and Dr . R.E . Kucera f o r s e r v i n g on the r e s e a r c h committee and r e v i ew ing t h i s pape r , Mr . W. Gleave i n the t e c h n i c a l development o f i n s t r u m e n t a t i o n . equipment f o r the Research Watersheds . I INTRODUCTION To b e t t e r serve the immediate and futu r e use of the water resource of B r i t i s h Columbia a b e t t e r q u a l i t a t i v e and q u a n t i t a t i v e understanding of that resource through r e -search i s r e q u i r e d . To help meet t h i s requirement the f o l l o w i n g two research p r o j e c t s were undertaken. T h e . f i r s t p r o j e c t (Development of a research water-shed system) i s the p r e l i m i n a r y design and implementation of a system of research watersheds. The system proposed i s the Alouette R i v e r Watershed and i t s sub-basins: the North Alouette R i v e r , Blaney Creek, M i l i t z a Lake and Lost Lake. P r e l i m i n a r y implementation i n v o l v e d the in s t r u m e n t a t i o n of the two small ( 5 0 acre) research watersheds, the M i l i t z a Lake and Lost Lake Watersheds. These research watersheds were i n i t i a t e d so that upon completion of d e t a i l e d i n s t r u m e n t a t i o n and f i e l d surveys of watershed c h a r a c t e r i s t i c s by futu r e researchers the data 2 obtained would describe the complete h y d r o l o g i c behavior of a watershed from which "both q u a l i t a t i v e and q u a n t i t a t i v e i n -formation might be e x t r a c t e d . A d i s c u s s i o n of the parameters and processes which describe the hy d r o l o g i c balance of a watershed and the general procedures of hy d r o l o g i c research of watersheds i s presented (Chapter I I ) . This m a t e r i a l provided the basi s from which to b u i l d a p r e l i m i n a r y • d e s i g n of a research watershed system (Chapter I I I ) . The second p r o j e c t (Development of a Streamflow P r e d i c t i o n Model) i s the b u i l d i n g and t e s t i n g of a S t a t i s -t i c a l model which w i l l p r e d i c t streamflow one to f i v e days i n advance of known streamflow. The hydrol o g i c c y c l e i s i n v o l v e d p h y s i c a l l y ' i n t h i s study but the model i t s e l f i s r e s t r i c t e d to a minimal number of hydrol o g i c v a r i a b l e s , these being temper-ature, time and streamflow. The model i s f u r t h e r r e s t r i c t e d to a p a r t i c u l a r time of the year and type of watershed; that i s , a watershed which y i e l d s s p r i n g snowmelt as the major c o n t r i b u t i o n to peak streamflow. I t i s intended that t h i s model be used to give short term advance warning of dangerous high flow r a t e s and thereby serve as a f l o o d f o r e c a s t method f o r the Fraser r i v e r . Continued encroachment upon the f l o o d p l a i n r a i s e s the value of p o s s i b l e f l o o d damage should a f l o o d occur. The estimated value of f l o o d damage f o r 1965 was 100 m i l l i o n d o l l a r s ] The 3 most recent f l o o d occurred i n 194-8 with a peak flow of 536,000 cubic feet per second. The economic l o s s r e s u l t i n g from t h i s f l o o d reached 40 m i l l i o n d o l l a r s . The most recent peak flow years were 1955, 1964 and 1967 . The theory of the computerized s t a t i s t i c a l model i s discussed i n Chapter IV and i n Chapter V the a p p l i c a t i o n of t h i s model to the Fraser R i v e r f o r the years 1955 and 1964 i s presented. PART ONE RESEARCH WATERSHED SYSTEM 5 I I REVIEW pP FUNDAMENTALS An understanding of the fundamental processes making up the hy d r o l o g i c c y c l e of a watershed i s e s s e n t i a l i n the design of watershed research. Research i s necessary i n order to solve h y d r o l o g i c management problems and to expand the basic knowledge of h y d r o l o g i c a l processes. 2.1 Hydrology and Ap p l i e d hydrology Hydrology i s the science t r e a t i n g the water of the earth i n i t s various forms ( i n the atmosphere, on the earth's surface and below the surface of the e a r t h ) . I t i s concerned wi t h the o r i g i n , d i s t r i b u t i o n and p r o p e r t i e s of t h i s water. Using t h i s science f o r p r a c t i c a l and b e n e f i c i a l purposes con-s t i t u t e s a p p l i e d hydrology. N a t u r a l Hydrologic Processes The many processes such as evaporation and surface r u n o f f are un i t e d by forms of r e g u l a r i n t e r a c t i o n and together make up a system known as the hydrol o g i c c y c l e . This c y c l e b a s i c a l l y i n v o l v e s water l e a v i n g the atmosphere by the process of p r e c i p i t a t i o n and r e - e n t e r i n g the atmosphere by evaporation from oceans. The net change i n the amount of water contained, i n the g l o b a l c y c l e i s zero. There are many smaller water cy c l e s w i t h i n l a r g e r ones, f o r example, water evaporating from land surfaces and from the p r e c i p i t a t i o n i t s e l f . A more d e t a i l e d d i s c u s s i o n of these h y d r o l o g i c processes considered from, the point of view of a s i n g l e water-shed can be best i l l u s t r a t e d with a diagram of the hy d r o l o g i c c y c l e ( f i g u r e 2.1). Water enters the watershed as p r e c i p -i t a t i o n . E n route to the s o i l s u r f a c e , some of the p r e c i p -i t a t i o n i s i n t e r c e p t e d by v e g e t a t i o n . Some of t h i s p r e c i p -i t a t i o n , and i n t e r c e p t e d p r e c i p i t a t i o n evaporates d i r e c t l y , r e t u r n i n g the water t o the atmosphere. Water that reaches the s o i l surface may be r e t a i n e d i n depression storage, l o s t from the watershed as surface r u n o f f or i n f i l t r a t e d i n t o the s o i l . Again evaporation may take place from any of these stages. Water e n t e r i n g the s o i l e i t h e r flows by i n t e r f l o w and deep p e r c o l a t i o n or i s reta i n e d i n the s o i l above the water t a b l e i n the form of c a p i l l a r y and hygroscopic water.. C a p i l l a r y water may be taken i n by p l a n t s , although much of i t i s returned to the atmosphere by e v a p o t r a n s p i r a t i o n . The g r a v i t a t i o n a l water that reaches open channels i s u l t i m a t e l y c a r r i e d to the oceans from whence i t may evaporate. Watershed C h a r a c t e r i s t i c s The major c h a r a c t e r i s t i c s of a watershed that i n -fluence n a t u r a l h y d r o l o g i c processes are c l i m a t e , physiography, land use, cover c o n d i t i o n s , s o i l and g e o l o g i c a l formation. The main c l i m a t i c f a c t o r i s the amount, rat e and d i s t r i b u t i o n of p r e c i p i t a t i o n . Sunshine or r a d i a n t energy i s important i n determining the rate of snowmelt, e v a p o t r a n s p i r a t i o n and evaporation. Physiographic c h a r a c t e r i s t i c s i n c l u d e the shape, o r i e n t a t i o n , topography and drainage p a t t e r n of the v/atershed. U s e f u l measures of watershed shape^ inc l u d e length-width r a t i o , form f a c t o r and compactness f a c t o r . The length-width r a t i o Snowmelt I n f i l t r a t i o n — ' j i P e r c o l a t i o n ~" I n t e r f l o w .I'll!.!'-' i i ' i : n : l i ' i Radiant Energy Groundwater t a b l e •Groundwater flow ; FIGURE 2.1 The Hydro l o g i c Cycle i s measured p a r a l l e l and perpendicular to the main drainage channels, the form f a c t o r i s the r a t i o of the average width to the a x i a l l e n g t h of the basin and the compactness coe-f f i c i e n t i s the r a t i o of the length of the perimeter of a watershed to the circumference of a c i r c l e of equal area. Watershed o r i e n t a t i o n i s u s e f u l when c o n s i d e r i n g a c c e s s i b i l i t y of the snow pack to incoming rays of s u n l i g h t and when con-s i d e r i n g the d i r e c t i o n of a storm passing over the watershed. Topographical features can be measured by determining the t o t a l watershed r e l i e f , mean e l e v a t i o n , medium e l e v a t i o h , and average slope from a prepared pontour map of the watershed. The t o t a l watershed r e l i e f i s the d i f f e r e n c e i n e l e v a t i o n be-tween the gaging s t a t i o n and the highest p o i n t . The water-shed's drainage p a t t e r n a f f e c t s i t s hydrology s u b s t a n t i a l l y . A w e l l defined system of drainage reduces the amount of i n -f i l t r a t i o n to r e s u l t i n more concentrated r u n o f f . Measures of drainage patterns are drainage d e n s i t y (the r a t i o of t o t a l length of defined drainage channels to the t o t a l drainage area), the number of streams and the t o t a l stream l e n g t h . Land-use and cover c o n d i t i o n s are important f a c t o r s since they can be a l t e r e d through management. Water l o s s by e v a p o t r a n s p i r a t i o n can be increased or decreased by a l t e r i n g the plant species and numbers. I n f i l t r a t i o n c a p a c i t y of the s o i l can be a l t e r e d by changing the ground cover or compaction of the s o i l s urface. Cover conditions, such as marshes and swamps which serve as r e t e n t i o n areas to slow the rate of runoff may be r e a d i l y a l t e r e d by drainage. 9 The type of s o i l present and the geological conditions below the s o i l surface are factors which help to explain why the hydrologic behaviour of one watershed d i f f e r s from that of another. Structure, grain size and composition of the soil,determine the hydraulic conductivity of the s o i l (how ea s i l y water i n f i l t r a t e s into the s o i l p r o f i l e and percolates through i t ) . The depth of the s o i l above bedrock, ground water table depth, permeability of the strata below the s o i l , com-position of the s o i l parent material and the degree of weath-ering of the rock a l l influence drainage c h a r a c t e r i s t i c s of a watershed. 2.2 Research i n hydrology of Watersheds Once the fundamental hydrologic processes involved are understood, a research procedure can be proposed. In designing a research procedure, the scope, aims and the tools of the study must be defined and evaluated. Scope of Study Research i n the hydrology of watersheds may involve the o v e r a l l watershed, a sub-basin within a watershed, or some single hydrologic variable within a watershed or sub-basin.^" Often a hydrologic study involves a combination of these approaches. Sub-basins are often studied i n d e t a i l and resu l t s projected to the larger surrounding watershed. Once the scope of a study i s decided, objectives or aims must be defined. Aims of Study-Two underlying general objectives which are i n -herent i n any hydrologic study are:^ (1) to improve our fundamental or q u a l i t a t i v e understanding of the natural hydrologic processes and (2) to arrive at better quantitative design values for application i n watershed management. These two objectives are i n t e r r e l a t e d . An improvement i n one aids the advancement of the other. A study designed to obtain a better q u a l i t a t i v e understanding of a large region may be termed a representative study, and one designed to measure the effect of some treatment applied to a watershed termed an experimental study. Prom the point of view of applied hydro-logy* the s p e c i f i c aims of research are mainly of the quanti-t a t i v e type. Tools for Analysis The techniques for analyzing the hydrologic regimes of a watershed f a l l into two main categories; research water-sheds and models. Pield study i s a natural f i r s t step i n carrying out research although a l i m i t a t i o n of the method i s obtaining representative information as opposed to purely l o c a l or re-gional information. Due to the complexity and i n t e r r e l a t i o n of the hydrologic processes, i s o l a t i o n of a single watershed c h a r a c t e r i s t i c from a large watershed using limited measure-ments i s impossible or very approximate. A better method of 11 i s o l a t i n g a s i n g l e f a c t o r i s to consider and measure the t o t a l hydrology of a watershed. This i s p o s s i b l e i f working w i t h a s e l f contained small watershed. These instrumented water-4.5 sheds are commonly r e f e r r e d to as research watersheds ' and i n c l u d e . u n i t - s o u r c e watersheds and p l o t s . ^ These research watersheds can be r e p r e s e n t a t i v e or experimental i n nature.5 6,7 Models simulate an a c t u a l p h y s i c a l process or system w i t h i n a basin or sub-basin. The system, the hydrolo-g i c c y c l e ( t o t a l hydrology of a watershed) or a s i n g l e process such as r u n o f f could be modelled. The major types of models are p h y s i c a l and mathematical models. Mathematical models in c l u d e analog and d i g i t a l models. S t a t i s t i c a l l y there are d e t e r m i n i s t i c and s t o c h a s t i c models. I n i t i a l l y , the r e l a t i o n -ships used i n the mathematical models are h i g h l y e m p i r i c a l as i s the case with any r e l a t i v e l y new f i e l d . Computers have opened the way f o r more accurate a n a l y s i s of h y d r o l o g i c data through the use of computer mathematical models. The s t o -c h a s t i c nature of hydr o l o g i c processes can now be b e t t e r approximated by i n c o r p o r a t i n g the p r o b a b i l i t y d i s t r i b u t i o n of the parameters s t u d i e d . Models o f f e r much more f l e x i b i l i t y f o r treatment s t u d i e s since c o n t r o l over the n a t u r a l v a r i a b l e s and processes i s e a s i e r . In p a r t i c u l a r study e i t h e r or both of these methods may be used. An example of u s i n g both a research watershed and a model i s the case where a model i s developed f o r a research watershed and t h i s model i s projected to other water-sheds of v a r y i n g s i z e s i n the same general r e g i o n . Several 12 research watersheds can be combined i n a treatment study f o l l o w i n g a p e r i o d of c a l i b r a t i o n . The use of research water-sheds and models as t o o l s f o r a n a l y s i s w i l l r e s u l t i n a more exact understanding of h y d r o l o g i c processes. 13 I I I A SYSTEM OF RESEARCH WATERSHEDS I N THE ALOUETTE RIVER WATERSHED 3.1 S i t e S e l e c t i o n The s i t e chosen f o r t h i s study i s centered i n the U n i v e r s i t y of B r i t i s h Columbia research f o r e s t l o c a t e d adjacent to the south west corner of G a r i b a l d i Park, north of Haney, B r i t i s h Columbia. Two small watersheds ( M i l i t z a and Lost Lake), each c o n t a i n i n g a small l a k e , are l o c a t e d on the east and west side of Loon Lake. These two watersheds l i e w i t h i n the l a r g e r Blaney Creek V/atershed which i n t u r n i s loc a t e d w i t h i n the North Alouette Watershed. The North Alouette Watershed i s part of the Alouette V/atershed. The l o c a t i o n of the watersheds i s shown i n f i g u r e 3.1 The general research o b j e c t i v e was to develop s e v e r a l research watersheds which could serve as e i t h e r rep-r e s e n t a t i v e or experimental basins. These watersheds would have the dense ins t r u m e n t a t i o n needed to measure the t o t a l hydrology of the basins. Larger watersheds i n the same r e g i o n would be l e s s densely instrumented to serve as a check against the v a l i d i t y of the mathematical models constructed from.the research watersheds. The research watersheds are represen-t a t i v e of the neighboring l a r g e r watersheds and the e n t i r e system of watersheds i s r e p r e s e n t a t i v e of west coast c o n d i t i o n s ; that i s , the watershed c h a r a c t e r i s t i c s , s o i l , c l i m a t e , geology, v e g e t a t i o n and ground cover are r e p r e s e n t a t i v e . 14 15 Since the research watersheds are to y i e l d data which w i l l describe the t o t a l h y d r o l o g i c balance of that basin, ease i n measurement of the processes was an important d i r e c t i v e i n a d d i t i o n to r e p r e s e n t a t i v e n e s s . A main feature w i t h both Lost Lake and M i l i t z a Lake basins i s the " t i g h t n e s s " of the basins ( i e . minimal leakage from basins through bedrock). Runoff leaves the basins i n one l o c a t i o n only and i s f l o w i n g over bedrock at the e x i t from the b a s i n . A p r e l i m i n a r y i n -v e s t i g a t i o n of these basins suggests that l i t t l e water leaves the basin as p e r c o l a t i o n or groundwater flow through the bed-rock.® Also the s o i l depth above the bedrock around the p e r i -meter.of the b a s i n i s f a i r l y shallow, a l l o w i n g l i t t l e water to leave the b a s i n as i n t e r f l o w . The measurement of the r u n o f f . process i s t h e r e f o r e g r e a t l y s i m p l i f i e d . The f o l l o w i n g general reasons f u r t h e r support the s i t e s e l e c t i o n . The heart of the Alouette watershed i s l o c a t e d w i t h i n a f o r e s t research s t a t i o n and much of the remaining part of the watershed forms part of the, G a r i b a l d i P r o v i n c i a l Park; t h e r e f o r e , s e c u r i t y and a c c e s s i b i l i t y to the various gaging s t a t i o n s i s good. Another r e s u l t i s the a v a i l a b i l i t y of data from other researchers i n the area, namely the U n i v e r s i t y of B r i t i s h Columbia Faculty of F o r e s t r y , F a c u l t y of Science b i o l o g i c a l research team and the Federal Gov-ernment Inland Waters Branch. Co-operation among these v a r i o u s workers can r e s u l t i n a more economical data c o l l e c t i o n . 16 3.2 D e s c r i p t i o n and Instrumentation of the Watershed System A summary of the surface area, the maximum and the minimum e l e v a t i o n s of the Alouette R i v e r watershed and i t s sub-basins i s presented i n Table 3.1. Also included i n the t a b l e i s an o r i e n t a t i o n of the watersheds w i t h respect to each other. TABLE 3.1 Area and E l e v a t i o n s of Alouette R i v e r Watershed and Sub-basins V/atershed Surface Area (acres) E l e v a t i o n Max Min (f e e t ) Remarks Alouette R i v e r 67,000 ( 5 1 , 0 0 0 ) * 5600 10 O v e r a l l V/atershed North Alouette R i v e r 13,500 (8,500) 5600 10 Sub-basin of Alou e t t e Blaney Creek 4,500 2500 10 Sub-basin of North Alouette M i l i t z a lake 50 2100 1600 Sub-basin of Blaney Creek Lost lake 50 1700 1300 Sub-basin of Blaney Creek *Area to stream gaging s t a t i o n s on 14th Avenue Haney, B. C. The f o r e s t e d p o r t i o n of the Alouette R i v e r i s made up p r i m a r i l y of Douglas f i r , western hemlock and western red q cedar. The age of the tre e s vary, the oldest being 800 year o l d Douglas f i r . The average age of the o l d growth i s 300-350 years. The oldest of the second-growth stands i s 120 years. Logging has been p r a c t i s e d w i t h i n the watershed and f i r e s p e r i -o d i c a l l y have burned parts of the watershed v e g e t a t i o n . There 17 are numerous lakes covering the watershed. , The climate i s c h a r a c t e r i s t i c of the southern c o a s t a l r e g i o n of B r i t i s h Columbia. The watershed i s warm and dry during the summer and mild and wet during the w i n t e r . The average annual p r e c i p i t a t i o n i n the north Alouette water-shed i s 92 inches, and the average f r o s t - f r e e period i s 195 days. At lower e l e v a t i o n s the p r e c i p i t a t i o n i s p r i m a r i l y i n the form of r a i n f a l l , while at the higher e l e v a t i o n s p r e c i p i -t a t i o n i s i n the form of s n o w f a l l . For a more d e t a i l e d des-c r i p t i o n of climate r e f e r d i r e c t l y to the m e t e r o r o l o g i c a l data 1 n f o r the area. The u n d e r l y i n g bedroqk i s p r i n c i p a l l y quartz d i o r i t e and g r a n o d i o r i t e . Some v o l c a n i c rocks and g r a n i t e occur l o c a l l y . The bedrock i s o v e r l a i d by g l a c i a l t i l l , outwash, glacio-marine and l a c u s t r i n e deposits of var y i n g thickness ( s i x to f o r t y -eight i n c h e s ) . The s o i l s have developed on a complex of ab-l a t i o n , t i l l and c o l l u v i a l m a t e r i a l which i s g e n e r a l l y unsorted and of a g r a v e l l y loam t e x t u r e . The s o i l above the bedrock i s very shallow i n general throughout the watershed except i n the depression areas which c o n s i s t of peat and open water. The area i n general i s very rugged w i t h much bare rock i n the fo r e s t e d regions. The land near the o u t l e t qf the Blaney Creek, North Alouette and Alouette. i s r e l a t i v e l y f l a t and about ten feet above sea l e v e l . This- area supports a g r i -c u l t u r e and urban :developments, In t h i s r e g i o n , dyking of the r i v e r s i s necessary to protect the land from f l o o d i n g during 18 spring snowmelt. There are certain features c h a r a c t e r i s t i c of. in d i v i d u a l watersheds. M i l i t z a Lake and Lost Lake basins are of the same size and general elevation. They both contain a small lake which serves as a detention area. The ground coyer conditions are si m i l a r . Both are one t h i r d slash and two-thirds timber. M i l i t z a i s oh the east side of Loon Lake on a westerly slope and Lost Lake i s on the west side of Loon Lake on an easterly slope, r e s u l t i n g i n opposite aspects. This orientation i s i l l u s t r a t e d i n figure 3.2. Figures 3.3 and 3.4- i l l u s t r a t e the lake detention, forested and slash areas of M i l i t z a Lake Basin. M i l i t z a Lake basin,, the f i r s t research watershed s i t e selected i s located between longitude 122 34' 15" W and 122° 34' 54" W, and latitude 49° 18' 19" N and 49*18' 41" N as i l l u s t r a t e d in. Figure 3.5<> The elevation of the f i f t y acre watershed ranges from 1720 feet at the south end to 1560 feet at the centre and 2100 feet at the north end. The eastern one-third of the watershed i s covered with slash while the remainder of the watershed supports old growth hemlock, red cedar and amabalis f i r with the exception of the central area which includes open water ( M i l i t z a Lake) and woody shrubs The land association^ for the area i s described as h i l l y to gently r o l l i n g , granitic-cored uplands. The central one-third of the basin consists of very wet peat. The remainder of the basin.is composed of v/ell drained ablation t i l l and c o l l u v i a l complex (gravelly sand loam texture) overlaying g l a c i a l t i l l FIGURE 3.2 20 FIGURE 3.3 Photograph of the M i l i t z a Lake Detention Area - 1600 foot elevation FIGURE 3.4 Photograph I l l u s t r a t i n g Forested and Slash Ground Covers. M i l i t z a Lake Basin - 2100 foot Elevation LATITUDE 49°18'41"N (compact and cemented) that r e s t s on bedrock, two to three feet below the s u r f a c e . The Blaney Creek system which contains M i l i t z a and Lost Lake basins, because of the lower e l e v a t i o n , has very l i t t l e snowmelt; t h e r e f o r e , r a i n f a l l i s the main incoming source\of water. The North Alouette and A l o u e t t e , however have a greater e l e v a t i o n and therefore snowmelt i s a major source of water which adds to the peak s p r i n g r u n o f f . Measurements and surveys I t i s d e s i r a b l e to measure as many of the watershed c h a r a c t e r i s t i c s as i s p o s s i b l e . The de n s i t y of s i m i l a r measurements w i t h i n a watershed depends upon the nature of study and accuracy of r e s u l t s d e s i r e d . For the research watersheds, an extensive number of measurements were d e s i r e d . A t o p o g r a p h i c a l survey of the area of M i l i t z a and Lost Lake was c a r r i e d out. S o i l r e p o r t s of the area were recorded and geology was considered to the point of s a t i s f y i n g the pre-l i m i n a r y design of the watershed system?'' That i s , " t i g h t n e s s " of bedrock and approximate depth of s o i l to bedrock was con-sidered i n order to estimate the f e a s i b i l i t y of measuring bas i n r u n o f f and i n t e r f l o w . A c l i m a t i c data c o l l e c t i n g net-work was i n s t a l l e d . Each research watershed has three weather s t a t i o n s and one hydrometric s t a t i o n . The design of the hydro-metric s t a t i o n s was based on approximate discharges obtained by the r a t i o n a l method?»^ M i l i t z a Lake watershed has a snow p l a t e s t a t i o n . The weather s t a t i o n s continuously record temperature, humidity and r a i n f a l l . Evaporation i s recorded d a i l y or weekly at each weather s t a t i o n . Sunshine, r a d i a t i o n and wind i s recorded from one s t a t i o n on each watershed. S o i l moisture and s o i l temperature are recorded p e r i o d i c a l l y and lake water l e v e l s are recorded. I n d i v i d u a l research p r o j e c t s are a l s o c a r r i e d out on these watersheds which o f f e r a d d i t i o n a l data. Such s t u d i e s as e v a p o t r a n s p i r a t i o n and stream r o u t i n g are being c a r r i e d out. Water q u a l i t y determination i s made p e r i o d i c a l l y . Figures 3.5,' 3.6, 3.7 and 3.8 i l l u s t r a t e i n -strumentation of M i l i t z a Lake Basin. On the l a r g e r North Alouette watershed, the U n i v e r s i t y of B r i t i s h Columbia f o r e s t r y f a c u l t y maintains three c l a s s A weather s t a t i o n s . Much c l i m a t i c r u n o f f and water q u a l i t y data i s c o l l e c t e d on these l a r g e r watersheds by other agencies l i s t e d e a r l i e r . At present a l l the data c o l l e c t i n g s t a t i o n s except those of the f i s h e r i e s b i o l o g i c a l research team are attended by t e c h n i c i a n s . The f i s h e r i e s research personnel introduced t e l e m e t e r i n g techniques. U l t i m a t e l y , f o r the most economical h y d r o l o g i c research of the Alouette watershed and i t s sub-basins, an o v e r a l l t e l e m e t e r i n g network may prove d e s i r a b l e . Such a scheme could t i e together a l l the data d e s i r e d by the many researchers i n the area and take i t to a common base computer. Future snow course measurements may re q u i r e t e l e -metering techniques. The hydrology researcher must, now design the s p e c i f i c FIGURE 3.6 Weather S t a t i o n Measuring Water Inflow ( P r e c i p i t a t i o n ) and Ambient Conditions (Humidity and Temperature) M i l i t z a Lake Basin - 1600 foot E l e v a t i o n FIGURE 3.7 Water Outflow (Evaporation) M i l i t z a Lake Basin - 2100 foot E l e v a t i o n FIGURE 3.8 Water Outflow ( D i r e c t Runoff) 120°Sharp Crested V-Notch Weir 25 research which w i l l f a l l w i t h i n the l i m i t s set out i n the p r e l i m i n a r y design. He w i l l c a r r y out d e t a i l e d f i e l d s u r -veys of s o i l s , geology, v e g e t a t i o n , ground cover and others; as the proposed research d i c t a t e s . Topics which were on the author's mind while c a r r y i n g out the p r e l i m i n a r y design were the e f f e c t of management and conservation p r a c t i c e s on water y i e l d / water q u a l i t y and e r o s i o n on watersheds. Other spe-c i f i c t o p i c s which have been proposed in c l u d e time of con^-c e n t r a t i o n and peak r u n o f f events as a f u n c t i o n of the i n -f l u e n c i n g c h a r a c t e r i s t i c s . 26 PART TWO STREAMFLOW PRED ICT ION MODEL 2 7 IV DEVELOPMENT OP A STATISTICAL PREDICTION MODEL The p r e d i c t i o n method, i t s assumptions and l i m i t -a t i o n s are discussed p r i o r to developing the r e g r e s s i o n equation and the computerized model. 4 . 1 General d e s c r i p t i o n of method Purpose I t i s des i r e d to study the f e a s i b i l i t y of using m u l t i p l e r e g r e s s i o n techniques f o r a short term p r e d i c t i o n model. This model i s to p r e d i c t the flow during the r i s i n g limb and peak r u n o f f region of the hydrograph i n a snowmelt stream f o r a s i n g l e watershed and s i n g l e year. The streamflow i s c a l c u l a t e d as a f u n c t i o n of l i m i t e d c l i m a t i c data. The primary use f o r t h i s model i s f o r short term f l o o d or peak flow f o r e c a s t i n g . The model was developed f o r use wit h l a r g e watersheds, ( 5 0 , 0 0 0 to 1 0 0 , 0 0 0 square m i l e s ) . The reason f o r developing a short term p r e d i c t i o n model f o r l a r g e watersheds was f o r f l o o d p r e d i c t i o n . The model was l e s s e x t e n s i v e l y t e s t e d on small watersheds ( 1 , 0 0 0 square miles i n are a ) . A d i s c u s s i o n of the pr e d i c t e d r e g i o n of the hydro-graph and the d i s t r i b u t i o n of gaging s i t e s w i l l serve as a basis f o r d i s c u s s i o n of the p r e d i c t i o n technique ( f i g u r e 4 . 1 (a)&(b)). The p r e d i c t i o n method i s r e s t r i c t e d to the highest p o r t i o n of the r i s i n g limb and peak of the snowmelt r e g i o n of the hydrograph. The reasons f o r t h i s are ( 1 ) This i s the Time (day) (a) Hydrograph of Snowmelt Stream I l l u s t r a t i n g Region which i s subject to Short Term Prediction at the Outlet and a Temperature Gage Centrally located FIGURE 4.1 region of most concern since i t determines the highest stream-flow throughout the year f o r snowmelt streams and (2) A pre-d i c t i o n technique using temperature as an index of snowmelt i s r e s t r i c t e d to the snowmelt r e g i o n (temperatures below which no snow melts and above which most snow has melted). Figure 4 .1 (c) i l l u s t r a t e s t h i s l a t t e r p o i n t . In the r e g i o n of concern, f l u c t u a t i o n s i n temperature are c o r r e l a t e d w i t h f l u c -t u a t i o n s i n streamflow. On la r g e watersheds, temperature i s the only c l i m a t i c measurement re q u i r e d by the model since snowmelt i s the major component of streamflow. R a i n f a l l i s a minor c o n t r i b u t o r . On small watersheds however, r a i n f a l l i s s i g n i f i c a n t and the measurement of i t becomes necessary. The c l i m a t i c gaging s i t e should be l o c a t e d c e n t r a l l y , both i n p l a n and e l e v a t i o n , i n the snowmelt r e g i o n of the watershed. The streamflow i s gaged at i t s o u t l e t from the watershed. Only one c l i m a t i c data gaging s i t e i s used f o r t h i s study of large watersheds because i t i s a f e a s i b i l i t y study of a p a r t i c u l a r p r e d i c t i o n technique. I f the technique works using only one weather s t a t i o n then i t should work f o r a weighted network of weather s t a t i o n s . The time increment of data re c o r d i n g i s 24 hours ( d a i l y data) which i s c h a r a c t e r i s t i c of the s p a r s e l y gaged watersheds i n B r i t i s h Columbia. The length of time that streamflow can be p r e d i c t e d depends on the ba s i n time l a g which i s i n f l u e n c e d by physio-graphic features of the watershed. The time l a g i s i l l u s t r a t e d 0£ 31 i n f i g u r e 4.1 ( c ) , i t i s the length of time between c o r r e s -ponding f l u c t u a t i o n s on the temperature and discharge p l o t s . P r e d i c t i o n time can be extended by u s i n g p r e d i c t e d temperature data. Snowmelt Stream Plow-Forecasting In regions where snowmelt i s the major c o n t r i b u t o r to peak and volume of d i r e c t r u n o f f , the e s t i m a t i o n of the snow pack volume with respect to a r e a l d i s t r i b u t i o n provides a measure of the p o t e n t i a l f o r r u n o f f . Combining t h i s i n i t i a l storage measure with other i n t e r r e l a t e d f o r e c a s t i n g v a r i a b l e s r e s u l t s i n v a r i o u s types of f o r e c a s t s . Forecasts issued by the S o i l Conservation S e r v i c e , 11 U.S. Department of A g r i c u l t u r e are of four major types: (1) seasonal volume, the t o t a l volume of water which w i l l con-t r i b u t e to r u n o f f during the snowmelt season, (2) peak, the maximum one-day flow of water, (3) r e s i d u a l , the number of days streamflow w i l l be above a s p e c i f i e d amount and the date the flow w i l l f a l l below t h i s amount, and (4) hydrograph f o r e -c a s t s , the d a i l y flow f o r the snowmelt season. The f o r e c a s t i n g v a r i a b l e s used are correspondingly (1) snow water equivalent of the snow pack, f a l l p r e c i p i t a t i o n index and an average s p r i n g p r e c i p i t a t i o n index; (2) seasonal volume, temperature ( r a d i a t i o n ) during melt season and melt season p r e c i p i t a t i o n ( r a i n ) to a l e s s e r degree; (3) seasonal volume and peak flow v a r i a b l e s and (4) a l l of the above v a r i a b l e s . 32 The complexity of a forecast procedure varies depending upon purpose and type of forecast, accuracy desired, length of forecast (long range, short range or instantaneous simulation), data available and equipment ( d i g i t a l computers) available, A forecast procedure i s further complicated i f i t i s updated as the melt season progresses, using new data as i t becomes avai l a b l e . Forecast procedures vary i n complexity from simple empirical deterministic equations (models) to highly complex p r o b a b i l i s t i c s t a t i s t i c a l models which require d i g i t a l computers. The p r i n c i p a l procedure used today'''' i s a. "least squares" multiple regression analysis which may be supplemented with multigraphical techniques i n an e f f o r t to reveal hydrolog-i c a l l y unsound rel a t i o n s contained within :the regression model. A summary of methods being presently used i n order of complexity and refinement are (1) temperature index or degree-days method, (2) degree-days plus recession analysis method (U.S. Bureau of Reclamation), (3) generalised snowmelt equations (U.S. Corp. of Engineers), (4) index plots plus regression equation (University of New Brunswick) and (5) hydrograph synthesis plus 12 streamflow routing. The flow diagram (Figure 4.2) summarizes the various hydrologic analyses of snowmelt runoff data. The heavy l i n e •joins those features which combine to form the short range forecast procedure developed i n t h i s thesis ("temperature index plus regression equation"- University of B r i t i s h Columbia). 33 This model provides a p a r t i a l hydrograph forecast which includes the peak flow. Other short term forecast studies have been con-ducted by researchers i n B r i t i s h Columbia. A model using a flood routing technique rather than a temperature index has been developed by the C i v i l Engineering department, University of B r i t i s h Columbia. This work was, as with t h i s thesis,, motivated by the increasing flood potential of the Praser River flood p l a i n . Work (on a temperature index) had been carried out prior* to t h i s thesis by the B. C. p r o v i n c i a l water r e -sources investigations branch using Praser r i v e r data. Their re s u l t s v e r i f i e d that temperature (degree-day) was highly correlated to d a i l y streamflow during the snowmelt season!3 Snowmelt Runoff a Forecast Frequency Analysis Extensive Record Limited Record r r— Seasonal Volume Peak Residual Hydrograph Forecast Forecast Forecast Forecast Long Range Short Range Instantaneous Forecast Forecast Simulation Flood Routing Climatic Parameters Figure 4.2 Flow Diagram I l l u s t r a t i n g Snowmelt runoff methods of analyses. 34 Prediction Method Multiple l i n e a r and c u r v i l i n e a r regression techniques are used to calculate discharge as a function of climatic data. The runoff process, having a skewed frequency d i s t r i b u t i o n , i s assumed to have a normal d i s t r i b u t i o n as i s required by the multiple regression technique being used. The regression c o e f f i c i e n t s are calculated for a known period of discharge. Discharge as the dependent variable i s regressed on the climatic data which are assumed to be i n -dependent variables (various transformations of temperature, storage and time). Extrapolation of the r e s u l t i n g regression equation from t h i s region of known discharge i s then used to predict discharge for a short period. The independent variables are assumed to r e f l e c t the response of the system s u f f i c i e n t l y • to allow t h i s extrapolation. Figure 4.3 (a) i l l u s t r a t e s t h i s prediction method. Each time new actual data become available the regression c o e f f i c i e n t s are recalculated and the new pre-dicted value for each time increment (24 hours for the large, watersheds) up to a maximum equal to the time lag of the basin between the temperature station and the stream gaging station (5 to 7 days for large watersheds). Figure 4.3 (b) i l l u s t r a t e s a coarse adjustment which i s used on the extrapolated values. A constant, termed " C O R R " , i s calculated for each new.prediction equation. "CORR" i s the difference between the l a s t known value of discharge and that value determined by the regression equation. Each of the •  predicted values of discharge Q . • (J=1,KPRED) i s adjusted 35 CQ O o m •rl Known P r e d i c t e d * • p PI Discharge Discharge // // /s / * / / * s / ***** // // to O o CQ • r l Time (day) (a) Known Discharge P r e d i c t e d Discharge by Regression E q u a t i o n E x t r a p o l a t e d P r e d i c t e d Discharge by R e g r e s s i o n E q u a t i o n Known P r e d i c t e d *  1 - m l | I r Discharge Discharge „ - --^ • Ad justm< snt C< 3RR" m s t a n t Time (day) (b) FIGURE 4.3 Short Term P r e d i c t i o n o f Discharge i s an E x t r a p o l a t i o n o f the Regression ; P r e d i c t i o n o f Discharge 36 by t h i s constant CORR. ^i+j i s "the discharge ' j ' days i n advance of day ' i ' (today). The maximum value o f ' i ' i s the maximum length of prediction NPRED. It was f e l t that for short term prediction the adjusted values would consistently be better than unadjusted values. This would l i k e l y not be the case for longer range predictions using predicted tem-perature values. Figure 4.3 (c) i l l u s t r a t e s the ranges o f data involved, the prediction procedure and the i n t e r n a l para-meters discussed i n the following section. 4.2 Variables, parameters, constants, and the Prediction equation The dependent and independent variables are derived from the basic variables (discharge, temperature and time). For small watersheds p r e c i p i t a t i o n becomes an additional basic var i a b l e . Since snowmelt i s the chief contributor to stream-flow during peak runoff conditions, temperature serves as an index of snowmelt. The effectiveness of temperature as a snowmelt predictor varies throughout i t s e f f e c t i v e range, be-coming less important as the snow pack diminishes. Storage serves as an indicator of how much snow i s l e f t to melt. Tests v e r i f i e d that accumulated discharge gave the opposite corr-e l a t i o n to that of storage but retained the same magnitude. Therefore, the sum of discharge i s used for the storage term. Time v a r i a t i o n (both d a i l y and seasonal) explains a part o f streamflow trend which temperature f a i l s to explain. From day to day the snow pack decreases i n surface area and i n 37 Diagram I l l u s t r a t i n g t h e j P r e d i c t i o n P r o c e d u r e and the E x t e r n a l MODEL Parameters Time (day) FIGURE 4.3 ( c ) 38 volume. Also as the season progresses so does the p r o b a b i l i t y that the snow, which c o n t r i b u t e s to the peak flow, w i l l soon be gone. P r e c i p i t a t i o n as a p r e d i c t o r v a r i a b l e i s not s i g n i f i c a n t f o r l a r g e watersheds, since a given storm covers only a small percentage of the watex'shed at a given time. On smaller water-sheds where p r e c i p i t a t i o n occurs over a l a r g e r percentage of the v/atershed at any given time, p r e c i p i t a t i o n i s a s i g n i f i c a n t independent v a r i a b l e . The independent v a r i a b l e s are made by transforming the basic v a r i a b l e s . Prom the p r e l i m i n a r y t e s t s c a r r i e d out to determine the s i g n i f i c a n c e of various independent v a r i a b l e s , the f o l l o w i n g transformations were s e l e c t e d to test, the f e a s i -b i l i t y of the short term p r e d i c t i o n model. Temperatures The average temperature f o r any day " i " i s T ± = (C*TMAXi + (1-C) TKINi)- -D ( 4.1) where TMAXj_ and TKINi are the maximum and minimum temper-atures r e s p e c t i v e l y . The constant ' C weights the average of the maximum and minimum temperatures and D transforms ( s h i f t s ) t h i s average by a constant amount. The temperature transformations are: Tj_ - j , j = NPRED, NPRED + 5, T i - j i s the average temp-erature j days p r i o r to day i (today), ' ( T i - j ) 2 ' J = NPRED* NPRED + 5 , the average temperature Tj__j r a i s e d to the second power and Z^i-NPRED » "the average temperature Tj_ summed to NPRED days p r i o r to day " i " (today). 39 Storage: The storage transformations i n c l u d e : "^Qi-NPRED » discharge summed to NPRED days p r i o r t o day ' i ' , and ("£Qi_]\TpKED) ' accumulative discharge r a i s e d to the second power. Time: The transformations of time are: Rj_ , the number assigned to day i , (Rj_ ) d , Rj_ r a i s e d to second power, and Ln R i , the n a t u r a l l o g a r i t h m of R-^ . Each of these transformed independent v a r i a b l e s i s r e l a t e d to model parameters and constants which define i n i t i a l c o n d i t i o n s and range of sequences used i n the p r e d i c t i o n model. The r e g r e s s i o n equation contains r e g r e s s i o n c o e f f i c i e n t s (k=o, n where n = number of independent v a r i a b l e s ) . In-cluded i n the i n t e r n a l model parameters (constants which are v a r i a b l e ) are the f o l l o w i n g : Temperature: SSTEMP, the day on which the summation of temperature T-j_ begins C and D, constants used i n weighting the average d a i l y temperature Discharge: SSQII, the day on which the summation of discharge Qj_ begins Time: SSRI, the day on which the summation of time Rj_ begins. 40 The e x t e r n a l parameters i n c l u d e : N , the number of days o f data (number o f obser-v a t i o n s ) used i n the r e g r e s s i o n a n a l y s i s MAI , the f i r s t o b s e r v a t i o n or day i n the set o f o b s e r v a t i o n s N M F , the l a s t day i n the set o f o b s e r v a t i o n s N or the day i n advance of which the p r e d i c t i o n i s made MAII , the i n t i a l value o f MAI f o r a p a r t i c u l a r year NNFI , the corresponding i n t i a l value o f NNF NNFF , the f i n a l value o f NNF f o r a p a r t i c u l a r year NPRED , the l e n g t h o f the short term p r e d i c t i o n F i g u r e 4.3 (c) i l l u s t r a t e s the meaning o f these e x t e r n a l parameters as they apply to the p r e d i c t i o n model. Ex t e n s i v e p r e l i m i n a r y t e s t i n g o f v a r i a b l e s was c a r r i e d out p r i o r t o dev e l o p i n g the p r e d i c t i o n program. These 14 t e s t s were made c o n c u r r e n t l y on the F r a s e r R i v e r Watershed and on the s m a l l e r Willow R i v e r and the Cottonwood R i v e r Watersheds. The t e s t i n g procedure i n c l u d e d c a l c u l a t i n g the c o r -r e l a t i o n c o e f f i c i e n t s , simple r e g r e s s i o n , m u l t i p l e l i n e a r r e -g r e s s i o n , and stepwise r e g r e s s i o n equations f o r a s e l e c t e d group o f independent v a r i a b l e s . B a s i c data and t r a n s f o r m a t i o n of b a s i c data (both dimensional and nondimensional) were used as independent v a r i a b l e s . An o p t i m i z a t i o n program was developed to t e s t the e f f e c t of v a r y i n g i n t e r n a l and e x t e r n a l 41 model parameters. Results from t h i s preliminary t e s t i n g along with res u l t s from the actual prediction program are discussed i n section 5.2. Prom these tests, s i m p l i f i e d regression equations (three day and f i v e day predictions) for a large .watershed were developed. Sixteen standard independent variables.were selected and constant values were assigned to many of the i n t e r n a l and external model parameters. The re-gression equations have the general form: Y = A Q + Ai X(1) + + A n X(n) (4.2) The three day prediction equation for large watersheds i s : X (17)' = A 0 '+ A-, X (1 ) + A 2 X (2) + + A 1 6 X (16) (4.3) or Q (I) = A 0 + Ai T(l-3) + A 2 T ( l - 4 ) "'+ A 3 T(I-5) + A 4 T(l-6) + A 5 T(I-7) + A 6 T ( l - 3 ) 2 + A ? T ( l - 4 ) 2 + A 8 T ( l - 5 ) 2 + A g T ( l - 6 ) 2 + A 1 0 T ( l - 7 ) 2 + A-,-, S T l ( l - 3 ) + A 1 2 SQl(l-3) + A 1 5 S Q K l - 3 ) 2 + A u R(I) + A 1 5 R ( I ) 2 + A 1 6 LnR(l) (4.4) where I = NNF + J, J=1, 3 and the fiv e day prediction equation for large watersheds i s as equation (4.4) except 42 T(I-n), n = 5,9 STI(I-n), n = 5 SQI(l-n), n = 5 and I = NN'F + J, J = 1,5 The regression c o e f f i c i e n t s (k = 0,16) are constant for a. p a r t i c u l a r prediction equation. The prediction equation (4.4) w i l l predict one, two and three days (I = NNF + 1 , 1 = NNF + 2, I = NNF + 3) i n advance of day NNF. The transformed variables T(I -3 ) , T(l - 7 ) weighted average temperature 3 to 7 days p r i o r to day I o o T(I-3) , T(l-7) the square of the average temperatures STl(l - 3 ) the accumulative temperature SQl(l - 3 ) the accumulative discharge summed to three days p r i o r to day I SQl( l - 3 ) 2 accumulative discharge squared 2 R ( l ) , R(I) and InR(l) the number assigned to day I i n lin e a r , squared and logarithm form , constitute the independent variables while Q(l) the d a i l y discharge i s the dependent variable i n equation (4.4). 4.3 Computerized Model Transformation of the basic data (independent r e-gression variables), formation of the regression equation (ca l c u l a t i o n of the regression c o e f f i c i e n t s ) and prediction of streamflow are combined to form the basic prediction model. This model, which i s used d a i l y to make short term predictions 4 3 (one to f i v e days) has an added m o d i f i c a t i o n which allows the d a i l y p r e d i c t i o n s to be made i n succession. This m o d i f i c a t i o n i s used when t e s t i n g the model against h i s t o r i c a l data. The basic model has a f u r t h e r m o d i f i c a t i o n which allows normal-i z a t i o n or c a l i b r a t i o n of the model. The modified model used on h i s t o r i c a l data a l s o tests the p r e d i c t i o n r e s u l t s of the model. The model, with i t s m o d i f i c a t i o n s , i s i l l u s t r a t e d with a s i m p l i f i e d flow diagram ( f i g u r e 4.4). The computer program i s given i n appendix B. The basic data (discharge, maximum temperature and minimum temperature) i s read. For t e s t i n g the model with h i s t o r i c a l data, a l l the data are read i n and stored by the computer; f o r using the model wi t h a new year, only the data which are known to date can be read i n t o the computer. The model constants are read i n t o the computer along with the above basic data. Further model constants are c a l c u l a t e d . Transformation of the i n i t i a l data i s conducted (figure- B.1) and a r e g r e s s i o n a n a l y s i s ( f i g u r e B.2) c a r r i e d out to compute the r e g r e s s i o n c o e f f i c i e n t s . This r e g r e s s i o n equation i s then used to ex t r a p o l a t e discharge values s e v e r a l days i n advance ( f i g u r e B.3 ( a ) ) . I f the model i s c a l i b r a t e d with a small amount of h i s t o r i c a l data, the data range of the r e g r e s s i o n a n a l y s i s i s v a r i e d and a new p r e d i c t i o n made, the be t t e r p r e d i c t i o n r e s u l t thus determining the value of MAI (the s t a r t i n g date of r e g r e s s i o n data range). I f the model-i s being run continuously on a year of h i s t o r i c a l data then ( START ) 44 \REAT) CONSTANTS BASIC DATA COMPUTE CONSTANTS COMPUTE TRANSFORMATIONS T ( I ) , S T ( I ) , SQI( I ) I = i n i t i a l , NNFT IDAY( I ) , X ( l , n ) , R( I ) I = i n i t i a l , NNFT + NPRED n=1, 17 NNF = J I I JII=NNFI,NNFF COMPUTE TRANSFORMATIONS T ( I ) , ST I ( I ) , SQ I ( l ) I=NNF ' ' " ,1) I=NNF+NPRED IDAY( I ) , X ( l , n ) , R(: MAI= C o n s t a n t o r MAI=K T = 1, F <D Reg ress i on A n a l y s i s Compute Augmented C o r r e l a t i o n Ma t r i x A ( I , J ) 1=1, 33 J = 1, 33 I Compute S imple Reg res s i on A ( I I ) , B ( I I ) , SERORY ( I I ) SERORB ( I I ) , FRATIO ( I I ) CORRELATION ( I I ) I I = 1, 16 Compute STPREG o r MULREG FRATIO, STDEVR, RSQ, B B ( I I ) , STERB( I I ) , FPAR(I I ) I I = 1, 16 ~5 FIGURE 4.4 •(MAI OPTION) MAI i s v a r i a b l e -Included i f MAI i s a cons tant S i m p l i f i e d Flow Diagram o f P r e d i c t i o n Model FIGURE 4.4 (cont . ) PRINT SIMREG and STPREG or MULREG II = 1, 16 P r e d i c t i o n Routine * L _ S t a t i s t i c a l Z-Test of P r e d i c t i o n Errors COMPUTE PREDICTION P Q I f l . J j ) JJ=2,NPRED+1 I=NNF,NNF+NPRED ERRDS(I,JL),CORR(NNF) PRINT PREDICTION RESULTS 7 K=K+ 1 1 JII=JII+1 PRINT PREDICTION TABLE 7 COMPUTE Z-TEST EMEAN(JL), STDEV(JL) C 0 N F 9 0 ( J L ) , CONF95(JL) JL = 1, NPRED \ PRINT Z-TEST VALUES / \ PRINT CONSTANTS / \ NNFI, NNFF, MAII, / \ PRINT F-Table / \ SIMREG and MULREG / PRINT TRANSFORMATION TABLE 7 ( STOP ~") 46 new basic data i s transformed, a new regression equation i s formed and new set of prediction values i s computed. After the entire desired range of the years hydrograph has been through the model a s t a t i s t i c a l z-test (figure B . 3 (b)) i s carried out on the prediction r e s u l t s . This test serves to measure the accuracy of the model. The flow diagrams of figures B . 1 , B . 2 and B . 3 explain i n d e t a i l a l l parts of the model. The regression analysis part of the model was 1 5 programmed by the author aft e r a computational method ^ and does not contain b u i l t i n safety features which would auto-matically exclude poorly chosen independent variables ( v a r i -ables which cause numbers to be divided by near zero quan-t i t i e s ) . The regression program i s very v e r s a t i l e however, as i t can be used f o r simple regression, multiple regression and stepwise multiple regression analysis and can serve as a sub-routine to a main program. Normalization of the model refers simply to est-ablishment of the i n i t i a l value of MAI. The effect of varying MAI i s discussed i n greater d e t a i l i n chapter f i v e . The model i s normalized (MAI determined) during the early stages of pre-d i c t i o n for any given year. This normalized MAI value i s re-lated to the physical s t a r t i n g date of the snowmelt season. 47 V APPLICATION OP THE PREDICTION MODEL The prediction model was tested on both a large watershed (the Eraser River) and a small watershed (the Willow River). This discussion r e s t r i c t s i t s e l f mainly to r e s u l t s of tests made on the large watershed. Since the data used was based on a 24 hour time increment the tests on the large water-shed produced clearer r e s u l t s . A discussion of the prediction results obtained from the model i s presented following a b r i e f description of the watersheds tested and a discussion of the significance of variables, parameters, constants and the r e -gression equation. 5.1 Description of Watersheds Tested The necessity of short term flood prediction on the Praser River was the reason for selecting the Eraser River Watershed. It has the highest flood damage poten t i a l of any watershed i n B r i t i s h Columbia due to the industry, communication network, agriculture and population located i n the Praser Valley flood p l a i n . The estimated flood p o t e n t i a l i n 1965 was 100 m i l l i o n d o l l a r s : The v a l l e y i s protected by a dyking system and limited detention upstream. The short term prediction of streamflow w i l l provide advance warning of an impending flood. The stream gaging l o c a t i o n chosen i s located at Hope, B r i t i s h Columbia (latitude 49°22'50",. longitude 121° 4 8 2 7'05"). The. drainage area above t h i s s t a t i o n i s 78,300 square m i l e s . The average streamflow equals 94,600 c u b i c f e e t per second (the maximum i s 536,000 cubi c f e e t per second while the minimum i s 12,000 cubi c f e e t per second). T h i s s t a t i o n has a long p e r i o d o f r e c o r d s (1912 to d a t e ) . The s i n g l e temperature measuring s t a t i o n s e l e c t e d i s at B a r k e r v i l l e , B r i t i s h Columbia. T h i s s t a t i o n was s e l e c t e d because i t i s c e n t r a l l y l o c a t e d w i t h i n snowpack area both i n p l a n and e l e -v a t i o n . Figure 5.1 i l l u s t r a t e s the a r e a l extent of the F r a s e r R i v e r Watershed and the l o c a t i o n of the gaging s t a t i o n s . A l s o i l l u s t r a t e d i n f i g u r e 5.1 i s the l o c a t i o n o f the s m a l l watershed. I t i s a sub-basin of the F r a s e r which i n c l u d e s B a r k e r v i l l e v / i t h i n i t s boundaries. The stream gaging s t a t i o n i s l o c a t e d near the town o f Willow'River ( l a t i t u d e 54^04'07", l o n g i t u d e 122° 27 »50" ). The area of t h i s watershed i s 1,200 square m i l e s with an average streamflow of 1,550 cubic f e e t per second (the maximum flow i s 9,450 cubi c f e e t per second while the minimum i s 154 c u b i c f e e t per second). The temperature measuring s t a t i o n remained at B a r k e r v i l l e . The b a s i c data c o l l e c t e d and used with the p r e d i c t i o n model i s i l l u s t r a t e d i n f i g u r e 5.2. For the l a r g e watershed temperature and streamflow are the o n l y r e q u i r e d data. For the s m a l l e r watersheds p r e c i p i t a t i o n data i s a l s o r e q u i r e d . Figure 5.2 f u r t h e r r e v e a l s that i n the snowmelt r e g i o n temper-e r a s e r R i v e r a s w m o w p F l G U R E 5 ' 1 ^ ^ - . ^ S t a t i o n . 56' 54' — PRASER RIVER WATERSHED — - E r a s e r R i v e r Watershed above j Hope -——-Bridge R i v e r Sub-Bas in S torage WILLOW RIVER WATERSHED -® Temperature Gage © Stream Plow Gage SCALE 1 i n c h = 60 m i l e s Wi l low R i v e r A l b e r t a ^ B a r k e r v i l l e Praser-R i v e r P a c i f i c Ocean •Willow R i v e r B r i t i s h Columbia Hope 120° U n i t e d S ta tes CD 40 _ 5 0 60 70 80 90 10Q 110 120 130 140 APRIL | MAY [ JUNE | JULY DRY OF 5ER50N MRR-JUL 51 ature extremes precede streamflow f l u c t u a t i o n s by a pe r i o d of seven days. This i s the b a s i n time l a g f o r the Praser R i v e r V/atershed f o r the year 1955. 5 .2 S i g n i f i c a n c e of v a r i a b l e s , parameters, constants and the r e g r e s s i o n equation. S i g n i f i c a n c e of V a r i a b l e s The v a r i a b l e s are considered i n d i v i d u a l l y and i n groups. Their r e l a t i v e s i g n i f i c a n c e i n any s i n g l e equation i s considered as w e l l as the s i g n i f i c a n c e of a s i n g l e v a r i a b l e from equation to equation. The l a t t e r shows how the s i g n i f -icance of a v a r i a b l e changes throughout the r e g i o n of the hydrograph being p r e d i c t e d . Testing of the independent v a r i a b l e s f o r the l a r g e watershed (Praser) r e s u l t e d i n the f o l l o w i n g observations. Temperature: The l i n e a r temperature v a r i a b l e s (T(l-n),n= 0 , 9) e x h i b i t e d the trend shown i n f i g u r e 5 . 3 . The optimum term v a r i e d f o r each year f o r a. p a r t i c u l a r watershed. This optimum term may be r e l a t e d to the time l a g between the area of major snowmelt and the point of gaged r u n o f f . Second order temperature terms ( T ( l - n ) ) 2 were more s i g n i f i c a n t than the l i n e a r terms. Accum-u l a t e d temperature proved h i g h l y s i g n i f i c a n t and was i n c l u d e d i n the model as a f u r t h e r independent v a r i a b l e . Accumulative discharge: 2 The second order accumulative discharge term, ( S Q I ( I - 3 ) ) » 52 was more s i g n i f i c a n t than the f i r s t order term S Q I ( l - 3 ) . Both terms were used i n the model e q u a t i o n . S i g n i f i c a n c e of I n d i v i d u a l L i n e a r Temperature Terms T (1-n) , n = 0,9 2 0 0 S 1 6 0 120 80 Pr a s e r 1 MAI = 1 9 5 5 ^ i v e r V/ate] 3 5 ,MP = rshed 121 / T ( I ) T(I-2) T ( l - 4 ) T(I-6) T ( l - 8 ) T ( I - 1 ) T ( l - 3 j T ( l - 5 ) T ( l - 7 ) T ( l - 9 ) Independent' V a r i a b l e s FIGURE 5 . 3 Time: This v a r i a b l e was q u i t e s i g n i f i c a n t : i n most o f the r e -g r e s s i o n e q u a t i o n s . I t s s i g n i f i c a n c e v a r i e d throughout the range of hydrograph being p r e d i c t e d . Depending upon the value o f i n t e r n a l model parameters c e r t a i n forms of the b a s i c v a r i -able time were more s i g n i f i c a n t than o t h e r s . Figure 5.4 i l l u s t r a t e s the manner i n which an i n -53 dependent v a r i a b l e ( X ( l l ) = S T l ( l - 3 ) ) v a r i e d i n s i g n i f i c a n c e from equation to equation. Table A-1 provides a d e t a i l e d record of P-Ratios f o r a l l the independent v a r i a b l e s f o r the e n t i r e range of days being p r e d i c t e d f o r the Praser River Watershed i n 1960 . The simple r e g r e s s i o n F-Ratio expresses the s i g n i f i c a n c e of i n d i v i d u a l independent v a r i a b l e s . The simple r e g r e s s i o n P-Ratio (P^g) i s r e l a t e d to the simple c o r -r e l a t i o n c o e f f i c i e n t ( r ) by the equations 2 FSR = ~~—o- • ^ r e s i d u a l t 5 ' 1 ) ( 1-r^) where DPresia ± s ^ e number of degrees of freedom a s s o c i a t e d with the r e s i d u a l source of v a r i a t i o n . The c o e f f i c i e n t of det e r m i n a t i o n ( r 2 ) i s the f r a c t i o n of the v a r i a t i o n of one 16 v a r i a b l e explained by v a r i a t i o n of the other v a r i a b l e . For example, a simple c o r r e l a t i o n c o e f f i c i e n t of 0 . 50 means that one-quarter of the v a r i a t i o n i n e i t h e r v a r i a b l e may be ex-plai n e d by v a r i a t i o n of the other. T h e ' p a r t i a l P-Ratio s i m i l a r i l y expresses the s i g n i f i c a n c e of the i n d i v i d u a l v a r i a b l e s i n the m u l t i p l e r e g r e s s i o n equation. The p a r t i a l P - r a t i o i s r e l a t e d to the p a r t i a l c o r r e l a t i o n c o e f f i c i e n t which, when squared, corresponds to the percentage of the r e s i d u a l v a r i a t i o n explained by the l a s t v a r i a b l e to enter the r e g r e s s i o n . Por the p a r t i c u l a r example i l l u s t r a t e d i n f i g u r e 5.4 i t i s observed that X ( l l ) (accumulated temperature) gains i n s i g n i f i c a n c e as the model approaches the peak of the streamflow hydrograph. Whether t h i s v a r i a b l e r e a l l y does 54 e x p l a i n more of the variance as the p r e d i c t i o n s progress along the r i s i n g limb of the hydrograph depends on the r e l a t i v e progress of the remaining independent v a r i a b l e s . Figure 5.5 i l l u s t r a t e s the manner i n which a l l the independent v a r i a b l e s change i n s i g n i f i c a n c e f o r any given r e g r e s s i o n equation. Table A-2 provides the numerical v a l u e s . Both the simple r e g r e s s i o n F - r a t i o and the p a r t i a l F - r a t i o are again presented. Considering the v a r i a b l e s i n d i v i d u a l l y i t i s seen that v a r i a b l e s X ( j ) , J = l l , 1 6 are more s i g n i f i c a n t than f i r s t and second order temperature terms ( X ( j ) , J=1,10). These general observations a l s o apply to smaller watersheds as v e r i f i e d by the t e s t s c a r r i e d out with the Y/illow R i v e r "watershed. P r e c i p i t a t i o n i s an added basic v a r i a b l e which becomes s i g n i f i c a n t on smaller watersheds. S i g n i f i c a n c e o f Parameters I n t e r n a l and e x t e r n a l model parameters have optimum values, but are set equal to a r b i t r a r y constants i n the b a s i c model. Figure 5.6 i l l u s t r a t e s the o p t i m i z a t i o n of SSRI, the day on which the summation oi* time R^ begins. The optimum form v a r i e s from t e s t to t e s t . The l i n e a r form of time R ( l ) has a constant F - r a t i o f o r any s t a r t i n g value of time while R ( I ) 2 and In R ( l ) (transformed v a r i a b l e s ) approach the F - r a t i o value of R ( l ) or have an optimum. S T l ( l - 3 ) , accumulated temperature, has an optimum F - r a t i o corresponding to an optimum SSTEMP, the day S i g n i f i c a n c e of Independent V a r i a b l e s B 13 55 56 Simple Regression QI(I) vs Time 700 1964 Fraser River Watershed MAI = 90 , NNF =110 Ln R(I) R ( D 30 40 50 60 70 I n i t i a l Value of Time 90 100 FIGURE 5.6 Optimization of the I n i t i a l Value for Various Transformations of the Basic Variable Time on which the summation of temperature begins. The s i g n i f i -cance of the temperature independent variables also changes with changes i n the i n t e r n a l parameters C. Likewise SQl ( l - 3 ) , accumulated discharge, has an optimum F-ratio r e s u l t i n g from a corresponding optimum SQII, the i n i t i a l discharge to enter summation. C a l i b r a t i o n of Model Prom model t e s t i n g i t was found that a v a r i a t i o n i n MAI caused a v a r i a t i o n i n the accuracy of the p r e d i c t i o n r e -s u l t s . A v a r i a t i o n i n MAI may compensate f o r the f a c t that the i n t e r n a l parameters were a r b i t r a r i l y set equal to constant values. A good value of MAI can be determined e a r l y during . the p r e d i c t i o n range and that value w i l l serve f o r the e n t i r e range. The value of MAI may be equal to a constant (as used i n the model t e s t s reported i n t h i s t h e s i s ) or may vary according to some mathematical equation. When MAI remains constant the number of observations used i n computing the r e -g r e s s i o n c o e f f i c i e n t s increases with successive r e g r e s s i o n equations. S i g n i f i c a n c e of r e g r e s s i o n equation The accuracy of i n d i v i d u a l r e g r e s s i o n equations i s i n d i c a t e d by the computed values of the m u l t i p l e r e g r e s s i o n P - r a t i o and B!~ (the c o e f f i c i e n t of m u l t i p l e d e t e r m i n a t i o n ) . These two values are r e l a t e d by the equation: R 2 D P r e s i d u a l P M R = / . p 2 , ' = " — ( 5 . 2 ) D p r e g r e s s i o n where ^ r e s i d u a l and D P r e g r e s g - j _ o n are the degrees of freedom corresponding to the v a r i a t i o n due to r e g r e s s i o n and r e s i d u a l r e s p e c t i v e l y . The s i g n i f i c a n c e of the r e g r e s s i o n equation v a r i e s throughout the range of r e g r e s s i o n equation as i l l u s -t r a t e d i n f i g u r e s 5 . 7 and 5 . 8 . S i g n i f i c a n c e o f Reg r e s s i o n Equation 58 6000 4000 o •H -P «• I 2 0 0 0 0 " — — —\ •\ N V _ - -V. — "\ \ \ / P-Ratio R 2 x 1 0 0 80 9 0 1 0 0 110 120 P r e d i c t i o n E q u a t i o n No. FIGURE 5 . 7 3 Day P r e d i c t i o n 1955 100.0 99.5 o o 99.0 CM 98.5 130 o •rl -P I 6 0 0 400 2 0 0 0 80 120 9 0 1 0 0 110 P r e d i c t i o n Equation No. FIGURE 5.8 3 Day P r e d i c t i o n 1960 % R " R 2 . I ^ r e s i d . ^ r e g r . / ^— — >— — X 1 V 1 \ 1 M y. // // // // // // t \ ' V 99.5 99.0 98.5 o o X CM rt 98.0 130 5 9 5.3 P r e d i c t i o n r e s u l t s The p r e d i c t i o n r e s u l t s are i l l u s t r a t e d n u m e r i c a l l y i n Tables A-4, A-5, A-6 and A-7 and g r a p h i c a l l y i n f i g u r e s 5.9 and 5.10. Tables A-4, A-5 and f i g u r e 5 . 9 r e p r e s e n t the 3 day p r e d i c t i o n model while t a b l e s A-6, A-7 and f i g u r e 5 . 1 0 represent the 5 day p r e d i c t i o n model. The s t a t i s t i c a l Z - t e s t c a r r i e d out on each set of p r e d i c t i o n s i s summarized at the bottom o f each o f these t a b l e s . The 5 day model Z - t e s t summary i s rep r e s e n t e d g r a p h i c a l l y i n f i g u r e 5.11. T h i s t e s t measures the o v e r a l l accuracy o f the model as a p r e d i c t o r f o r the r i s i n g limb p o r t i o n of the snowmelt hydrograph f o r a p a r t i c u l a r year. Por the year 1955 (3 day p r e d i c t i o n model) the standard d e v i a t i o n was 8.0$ while the e r r o r w i t h i n both the 90 and 95$ confidence i n t e r v a l was 13.3 and 1 5 . 8 $ r e -s p e c t i v e l y . The corresponding v a l u e s f o r the year 1960 were 8.2$, 13.5$, and 16.1$. S i m i l a r values f o r 5 day p r e d i c t i o n were 15.8$, 26.0$ and 31.0$ f o r 1 9 5 5 and 10.6$, 17.5$ and 21.9$ f o r 1960. Length of p r e d i c t i o n i s l e s s on the s m a l l watershed because o f the s h o r t e r b a s i n l a g . T e s t s on a model, with NPRED = 2 days, were c a r r i e d out on the Willow Watershed. P r e d i c t i o n r e s u l t s were poor, p r i n c i p a l l y because the time increment of 24 hours was too l a r g e f o r the s m a l l watershed.• STRFRM niSrHRRKF BT HPIPF VS riRT PIF SFRSflN 1 3 m : R7 nOY HF ^ FQSnN MDR- llll go IDO no ^_ _iao " "DRY OF SEASON MRR-JUL E r r o r o f P r e d i c t i o n u o u u +20 5.10% 0 - p £-0.89% -20 1 Day Pred, / \ A/ 1 \7-Standard D e v i a t i o n 95$ Confidence I n t e r v a l 5 Day Pred, 63 VI CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK 6.1 Part One Research Watershed Conclusions The research watershed system outlined consists of the Alouette River watershed and i t s sub-basins, the North Alouette, Blaney, M i l i t z a Lake and Lost Lake watersheds. The l a t t e r two are research watersheds which support detailed instrumentation networks. The larger watersheds are less densely instrumented and w i l l serve as a check against extrap-ola t i o n of data from the research watersheds or simulation models of the research watersheds. Recommendations for Future Work A more representative hydrologic model for West Coast conditions would include the snowmelt process; therefore, the addition of snowmelt instrumentation at higher elevations i n the North Alouette and Alouette watersheds would seem a d e s i r -able extension to the i n i t i a t e d watershed research system. 6.2 Part Two Prediction Model Conclusions The prediction model developed meets the objective of making a short term prediction of snowmelt streamflow for a unique watershed and a single year. Because the data are available at not less than d a i l y i n t e r v a l s and p r e c i p i t a t i o n on the watershed i s neglected, the use of the model i s r e s t r i c t e d 64 to r e l a t i v e l y large watersheds (50,000 to 100,000 square miles i n area). The length of one forecast period i s dependent upon the basin time lag; that i s , the time required for snowmelt to reach the outlet of the basin. Forecasts of flood flows i n the lower reaches of the Fraser River are possible for periods from one to f i v e days. For the smaller watersheds (1,000 square miles i n area) considered, the forecasts are r e s t r i c t e d to periods from 3 to 15 hours. P r e c i p i t a t i o n as an index of run-o f f should be included i n the model for these small watersheds. Data for the peak flow years 1955 and 1964 of the Fraser River were used to test the performance of the three and f i v e day forecast models. The predicted discharges are r e l a t i v e l y good estimations of the actual discharges; for example, the three day forecast (for forty-three successive days i n 1960) resulted i n a standard deviation of error equal to 8.2 percent and an error within the 95$ confidence i n t e r v a l equal to 16.1 percent. The corresponding mean value of error was -1.6 percent. The models also provided significance-test results for indepen-dent variables considered singly (e.g. the simple regression F-ratio t e s t ) and with respect to a group of variables (e.g. the multiple regression p a r t i a l F-ratio t e s t ) ; and for the entire regression equations (the o v e r a l l multiple regression F-ratio t e s t ) . Recommendations for Future Work In order to increase the precision of the forecasts i t i s recommended that the number of temperature stations be 65 i n c r e a s e d and the weighted average temperature be computed. A f u r t h e r refinement would i n v o l v e s u b d i v i s i o n of l a r g e water-sheds i n t o s e v e r a l sub-basins (sub-basins which are l a r g e enough to a l l o w the use of 24 hour d a t a ) , each with i t s own temperature and streamgaging s t a t i o n s . The r e s u l t i n g models could then be superimposed. I t i s suggested t h a t the b a s i c model developed i n t h i s t h e s i s might work on s m a l l e r watersheds i f d a i l y maximum and minimum temperatures were i n t e r p o l a t e d f o r a time increment of s i x or twelve hours. S i m i l a r l y , 24 hour streamflow data could be l i n e a r l y i n t e r p o l a t e d . T h i s procedure would a l l o w the use o f present d a i l y data. 66 LIST OF REFERENCES 1. Sewell, W.R.D., "Water Management and. Floods i n the Fraser R i v e r Basin." 2. L i n s l e y , R.K., M.A. Kohler, J.L.H. Paulhus, "Hydrology f o r Engineers." 3. Burford, J.B., J.H. L i l l a r d , " R e l a t i o n of Selected Charac-t e r i s t i c s to Hydrologic Performance of Two Small Water-sheds," P. 394 ASAE Transactions Volume 9 No. 3. •. 4. Amerman, C.R., J.L. McGuinness, " P l o t and Small Water-shed Runoff: I t s R e l a t i o n to Larger Areas," P. 464 ASAE Transactions Volume 10 No. 4. 5. N a t i o n a l Research C o u n c i l , "Proceedings of Hydrology Symposium No. 4 Research Watersheds (1964)." 6. Huggins, L.F., E.J. Monke, "The A p p l i c a b i l i t y of Sim-u l a t i o n Techniques to the Design of Hydrologic S t r u c t u r e s , " P. 460 ASAE Transactions'Vol. 10 No. 4. ' 7. Crawford, N.H., R.K. L i n s l e y , " D i g i t a l S i m u l a t i o n i n Hydrology: Stanford Watershed Model IV," 1966, Technical Report No. 39? Dept. of C i v i l Engineering, Stanford U n i v e r s i t y . 8. Halstead, E.C., "Personal Communication," Geologist w i t h Energy, Mines and Resources Dept., Federal government, Vancouver, B. C. 9. Lacate, D.S., "Forest Land C l a s s i f i c a t i o n f o r the Univ-e r s i t y of B r i t i s h Columbia Research Forest," Dept.. of Forestry P u b l i c a t i o n No. 1107, 1965. 10. U.B.C. Research Forest, Meteorologic data c o l l e c t e d from three weather s t a t i o n s l o c a t e d with i n the U.B.C. Research Forest. 11. Barton, M., ''Forecasting Stream Flow on Snowmelt Streams." A.3.A.E. Paper No. 67-207. 12. Davar, K.S., "Peak Flow-Snowmelt Events," S e c t i o n 9 -F a m i l i a r i z a t i o n Seminar on P r i n c i p l e s of Hydrology sponsored, by Canadian I.H.D. and U n i v e r s i t y of Saskatchewan,. Saskatoon 1 966 . 13. Hunter, H.,"Personal communication," h y d r o l o g i s t with Water Resources I n v e s t i g a t i o n s Branch, B.C. P r o v i n c i a l Government, V i c t o r i a , B.C. 6? 14. Kennedy, G.F., "Eraser R i v e r P r e d i c t i o n Studies, Pre-l i m i n a r y Report," 1 9 6 7 unpublished r e p o r t , C i v i l Engineering Dept. U.B.C. 15« Draper, N"., Smith, H., "Applied Regression A n a l y s i s , " John Wiley & Sons, Inc. 1 9 6 6 , Section 6 . 8 . 16. S t e e l , R.G.D., T o r r i e , J.H., " P r i n c i p l e s and Procedures of S t a t i s t i c s , " 1 9 6 0 , McGraw-Hill. 68 APPENDIX A SAMPLE BASIC DATA Bl 3 13 15 17 O. 5 19 31.0 52.0 9.0 33.0 28.5 38.7 30 40.0 40.0 40.0 18.0 26.0 26.0 67.4 106.0 22 83125123 0 0.0 1.0 0.5 20.0 19 19 1960 29.0 30.0 37.0 39.0 45.0 56.0 59.0 53.0 49.0 50.0 44.0B03602T+ 40.0 44.0 40.0 37.0 36.0 37.0 B03603T+ 20.0 23.0 16.0 30.0 30.0 30.0 26.0 29.0 27.0 29.0 25.0 21.0 28.7 30.0 28.8 29.4 29.6 26.9 25.0 29.0 20.0 22.0 32.0B03602T-B03603T-27.6 30.4 33.4 35.3 36.71803602Q 47.2 50.4 53.3 60.1 62.2 67.1 1803603Q 40.0 48.0 56.0 43.0 49.0 59.0 60.0 41.0 45.0 43.0 36.0B046CM T+ 37.0 39.0 40.0 40.0 39.0 41.0 41.0 40.0 46.0 44.0 42.0 50.0 58.0 61.0 59.0 33.0 31.0 29.0 20.0 20.0 25.0 32.0 29.0 22.0 24.0 41.0B04602T+ B04603T+ 19.0B04601T-24.0 12.0 25.0 27.0 12.0 29.0 30.0 28.0 30.0 27.0 20.0 24.0 25.0 26.0 29.0 68.5 71.7 73.5 79.4 82.2 84.4 89.3 95.3 94.8 25.0B04602T-B04603T-95.4 102.01804601Q 85.6 112.0 107.0 88.0 38.1 101.0 98.3 95.9 86.8 88.2 89.9 94.2 91.4 88.4 85.2 84.5 84.81804602Q 18046030 31 47.0B05601T+ 55.0B05602T+ B05603T+ 52.0 48.0 55.0 30.0 32.0 27.0 50.0 51.0 44.0 47.0 51.0 49.0 50.0 56.0 50.0 38.0 49.0 50.0 48.0 47.0 46.0 46.0 34.0 48.0 45.0 37.0 52.0 35.0 52.0 41.0 44.0 50.0 92.9 152.0 188.0 30 47.0 54.0 59.0 35.0 39-0 39.0 186.0 262.0 6 61 -0 41.0 27.0 26.0 30.0 30.0 33.0 27.0 23.0 22.0 34.0 33.0 30.0 30.0 98.5 106.0 158.0 171.0 183.0 177.0 113.0 118.0 180.0 184.0 171.0 169.0 32.0 32.0 33.0 29.0 31.0 31.0 124.0 129.0 179.0 174.0 177.0 188.0 26.0 30.0 24.0 32.0 35.0 29.0 32.0 29.0 32.0B05601T-27.0B05602T-B05603T-125.0 124.0 131.0 146.0 152.0 1805601Q 177.0 177.0 176.0 184.0 187.0 1805602Q 1805603Q 47.0 52.0 43.0 _5_5_.0_ 64.0 64.0 29.0 36.0 38.0 40.0 39.0 45.0 203.0 216.0 240.0 251.0_ 273.0 291.0 54.0 54.0 46.0 47.0 44.0 _52_._Q_ 51.0 49.0 57.0 44.0 62.0 55.0 64.0 70.0 59.0 61.0 68.0 68.0 66.0 35.0 33.0 34.0 32.0 35.0 37.0 37.0 41.0 34.0 32.0 35.0 35.0 37.0 36.0 39.0 45.0 60.0B06601T+ 56.0B06602T+ B06603T+ 30.0B06601T-40.0R06607T-41.0 45.0 47.0 219.0 216.0 211.0 202.0 263.0 264.0 266.0 274.0 310.0 321.0 321.0 B06603T-199.0 208.0 218.0 224.0 227.018066010 276.0 266.0 251.0 247.0 2 52.018066020 18066030 61.0 38.0 60.0 39.0 72.0 74.0 79.0 69.0 58.0 61 .0 62.0 71 .0 81tOB0760lT + 325.0 329.0 330.0 38.0 43.0 44.0 47.0 327.0 318.0 308.0 297.0 28.0 36.0 37.0 43.0 45.0B07601T-292.0 287.0 288.0 285.0 273.01807601Q T A B L E A . I 70 SUMMARY QF F-RATIOS IND VARS 1 T o n B.1-J! XI X2 X3 X4 X5 X6 X7 X8 NNFF-•SIMREG F -SIMREG • F -SIMREG F-•SIMREG F-•SIMREG F -SIMREG F -SIMREG F -SIMREG F-STPREG F--STPREG F -STPREG F-•STPREG F- STPREG F- STPREG F -STPREG F -STPREG 83 9.26 13.46 12.89 15.61 13.41 7.65 , 11.79 . 11.-.22. 0.00 0723" 0.44 1.02"~ 0. 11 ""o'.bz"" 07l9 _ ) ^ a 84 7.49 13.26 13.70 14.00 15. 51 5.98 11.36 11.87 0.00 0.17 0.78 1.17 0.44 0.07 0.09 1.87 eS 6.07 10.89 13.43 14.81 13.95 4.65 9.08 11.39 . 0.01 O.U 0.76 1.39 0.56 0.05 • 0.03 1.52 86 5.40 9.04 11.12 14.55 __14..8p 3.96 _7.32 9.18 0.01 0.20 1.06 "" 1.57" 0.70 ""O.oTT 6.04 ' 1.66 87 6.06 8.27 9.48 12.41 14.72 . 4.49 6.50 7.63 0.01 0.20 1.14 1.74 0.74 0.09 0.03 1.73 88 7.03 9.04 8.83 10.89 12.92 5. 36 7.13 6.91 . 0.00 , .0.22 1.12 1.67 0.67 0. 10 6.63 1.76 89 7.94 10.11 9.53 10.30 11.62 6.1 8 8.11 7.48 ~6To6". 0.16 0.B7 1.46 0.50 "0. 15 0.02 1.44 " 90 9.02 11.17 10.55 11.04 11.07 7.21 9.08 18.40 — O.Ofl 0.08 0.54 1.26 0.40' 0.35 6.00 1.00 91 9.28 . 12.61 11.68 12.23 11.87 ' 7.33 10.47 9.44 0.09 0.08 0.57 1. 32 0.41 0.37 0.00 1.03 92 9.97 12.83 13.27 13.56 _13.23_ 7.88 10.52 1 10.?9_ 0. 10 0.04 0.89 1.64 ' . 0". 74 0.42 0.02" "" 1.46 " 93 10.79 13. 62 13.48 15.19 14.57 8.59 11.17 11.03 0.12 0.03 0.83 1.93 0.91 0.53 0.03 1.26 94 8.54 14.61 14.21 15.18 16.50 6.64 12.65, 11.62 0.13 0.01 0.90 1.38 1.60 0.94 0.16 1.07 95 9. 19 11.32 15.13 15.85 16.29 7_._17._ ""6'. 98" •> 9.16 12.43 0.20 0.03 0.43 ~ 1.25" 6792' 0.48 96 10.41 12.03 11.77 16.79 16.99 8.33 ?-74 9.50 0.17 0.08 0.51 1.14 0.97 0.99 0.66 0.27 97 9.65 13.37 12.46 13.42 17.99 7.50 11.03 16.05 0.37 0.10 0.46 1.41 0.97 1.59 0.72 0.23 98 10.94 12.59 13.72 J *_•!'*.. 14.79 8.73 . . .J. _lJ9li*_ 0.40 0.09 0.48 1.45 6.97 1.661 "o773~ 6724 " 99 12.67 13.93 ' 13.il 15.39 15.56 10.77 \ 11.43 10.52 0.57 0.13 0.50 1.49 1.04 2.64 - 0.64 0.29 16o 14.56 . 15\97 14.38 14.79 16.82 12.51 13.56 11.73 0.59 0.32 0.37 1.48 1.69 2.06 1.28 0.20 101 14.99 18.04 16.63 _16.22 16.02 12.78 iAi.7.?_-. 14.09 0.50 0.33 0.29 1.33 1.10 1.83 1 .32 0.14 102 16.36 18.44 18.85 18.83 17.59 14.13 15.94 16.44 0.51 0.33 0.29 1.38 1.13 1.66 1.36 0.14 103 19.38 .' .19.99 19.17 21.26 20.41 17.SI 17.48 16.58 0.36 0.36 0>27 1.40 1.48 1.59 1.45 0.11 104 23. 48^  *' 23.34 20.70 21 .55 . 2.2-95 22.01 ._ _21._2.1., 16.09 0.04 ""75717"' 0.40 1.05" .' 1.49 0".78 " 1.06 0.19 105 28.12 . 27.92 24.12 23.17 23.21 27.06 26.18 .21.92 0.00 0.02 0.71 1. 12 1.28 0.44 0.63 0.41 106 33.19 : 33.30 29.03 26.96 24.90 32.74 32.00 27.35 . 0.00 0.02 0.85 1.24 1.30 0.45 0.70 0.49 107 16.47 39.29 34.95 32.59 ._??_. 10 3^6. M _ 38.77_ 33.97 0.05 6.04 0.70. ""1.02 1.14 ""0729" 6787~ 0.38 108 40.86 ,, '42.94'' '.41,48 39 .37 35.40 41.39 42.79 41.56 0.06 1 '. • •. 0.01 0.63 0.93 1.01. 0.27 - 0.74 0.33 109 45.28 47.68 45.13 46 .10 42.21 46.54 48.26 45.63 0.11 0.00 0.96 0.90 0.93 0. 19 0.68 0.61 110 49.40 52.48 , 49.89 49.96 49.04 51.29 53.82 51.16 47.72' • 0.15 p. 00 . 1.03 1.16 0.95 0.16 0.65 56.95 0.66 111 57.'(jbJ 54.80 55.07 53.07 46.64 59.07 0.05 ' 0;oo 0.82 • 1.15 0.67 0.49 0.78. 0.48 112 45.-77 55.08' . ,59.34 60.23 58.33 45.80 56.06 62.26 0.04 o.bi 0.83 1-16 Q',68^  .0._51._ 0.90 0.48 113 47.93 53.48 58.05 "64786 " 63.39" "47.9T 53.56 59.93 0.04 , 0.00 1.29 1.23 0.63 0.53 0.74 0.92 114 49.18 55.91: 57.16 .64.30 67.76 48.87 55.95 58.21 0.12 \. 0.00 1.72 1.96 1.21 0. J2.; 0.84 1.41 115 49.46 57.35' .59.64 63.53 67.46 48.68 57.08 60.68 0.12 0.00 1.73 2.24 1.89 0.29 0.69 1.38 116 52.68 57.50 61.02 66.17 66.50 52". 13 56767 61.73 0.15 0.00 1.71 2.28 1.87 0.26 0.75 1.36 117 58.13 61.20 60.80 67.41 69. 19 1 55.97 60.66 60.84 2.09 0.03, 1.50 1.53 1.84 0.33 1.20 1.12 118 64.54 67.86 .-, 64.70 66.69 70.23 62.26 65.56 65. 15 1.86 1.20 0.90 1.31. 0.80 0.23 0.05 0.49 119 69.71 . 76.08 73.09 "70.90 68.69 67.92 74.01 72.43 1.51 1.46 3.65 1.06 0.47 0. 09 0.11 3.05 120 75.96 81.96 82.78 81.23 72.94 75.08 80.64 83.10 .1.64 1.16 3.99 4.22 . 0.23 0. 14 0.03 3.34 121 84.50 88.93 88.90 91 .98 83.95 85.17 88.79 1 90.24 2.24 1.03 3.37 _4.83_. A-61.. 0.38 0.02 2.56 122 94.89 98. 15 96.11 ~98751 " 94r46 " 96.60 " 98.79 3.62 0.80 4.27 3.30 4.99 1. 14 6.66 3.48 123 105.60 109.45 105.69 106.20 101.12 108:54 111.69 110.15 3.92 1.34 4.26 3.31 4.36 1.34 6.68 3.38 124 .117.51 121.10 117.36 116.38 108.95 120.71 124.40 122.63 4.20 . _ i » 2 5 _ 4_.53_ 3.35 4.41 1.48 0.08 . 3.64 125 129.52 133.59 ~i29.~14~~ 128.37 119.08 133.09 136.38 '" 'i'ii'.'iiT 4.22 0.96 4.74 2.71 4.55 1.51 6.60 3.98 TABLE A.2(a) -71 SUMMARV OF F-RATIOS 1N0 VARS 9 TO .16 "' '• X9 X 1 0 X U X 1 2 X 1 3 X14 X 1 5 X 1 6 NNFF-•SIMREG F -SIMREG F-SIMREG F-SIMREG F -SIMREG F-SIHREG F-SIHREG F -SIHREG F-STPREG F-STPREG • r -STPREG F-STPREG F-STPREG F -STPREG F-STPREG F-STPREG 8 3 1 4 . 3 6 1 2 . 0 9 2 4 1 . 6 9 2 1 7 . 7 2 3 4 5 . 0 1 1 6 5 . 9 1 2 8 1 . 9 5 8 7 . 2 5 2 . 5 2 0 . 6 2 1 5 . 4 3 1 4 . 1 3 2 2 . 2 3 4 1 . 8 1 3 2 . 7 6 3 9 . 0 7 8 4 1 2 . 5 0 1 4 . 2 8 2 6 5 . 6 8 , 2 4 3 . 0 2 367-. 85 1 8 1 . 6 1 3 1 4 . 2 0 9 2 . 7 2 2 . 2 8 1 . 2 6 1 6 . 8 9 1 0 . 7 6 1 8 . 9 3 3 8 . 9 9 2 9 . 2 3 35 . 1 1 8 5 1 3 . 1 5 1 2 . 4 8 2 9 0 . 7 9 2 7 0 . 3 2 3 8 9 . 1 8 1 9 8 . 2 4 3 4 8 . 8 7 9 8 . 3 1 2 . 4 8 1 9 . 9 8 5 . 8 5 1 2 . 8 5 3 1 . 9 3 2 2 . 3 0 2 7 . 6 5 8 6 12 .66 13:17 3 1 7 . 2 4 2 9 8 . 6 9 4 0 3 . 7 1 2 1 5 . 9 1 *__V5__ _l.0_.i2.2__ 1 2 . 51 1 . 1 6 2 1 . 2 4 3 . 2 5 9 . 2 1 2 7 . 6 1 1 8 . 1 3 " "_3 .~21'" ' 8 7 1 0 . 5 5 1 2 . 8 7 3 4 3 . 7 6 3 2 2 . 8 5 3 9 3 . 2 9 2 3 4 . 0 2 4 1 2 . 5 3 1 1 0 . 8 1 2 . 6 3 1 . 1 8 2 3 . 4 2 3. 14 1 0 . 1 6 3 1 . 6 1 1 9 . 9 6 2 5 . 1 7 88 9 . 6 7 , 1 1 . 08 3 6 5 . 9 6 3 3 7 . 6 5 3 6 0 . 0 1 2 5 0 . 6 3 4 2 5 . 5 8 1 1 7 . 7 5 2 . 5 9 ' 1 . 1 6 . 2 3 . 7 5 4 . 8 7 1 5 . 3 3 4 2 . 7 7 2 6 . 9 2 3 2 . 13 8 9 8 . 3 9 9 . 7 9 / ' 3 7 9 . 3 0 3 3 9 . 8 4 3 1 4 . 6 6 2 6 3 . 6 9 _ 4 1 9^8 5_ _ 1 2 4 . 6 1 . . _ 2 .3 .9 - '• • • 1 .01 2 0 . 9 7 B . 16 ~ _ T . 6 1 " 5 6 . 1 2 35~J 5 9 3 9 7 7 5 " 9 0 9 . 0 0 .'. 9 . 1 4 • 3 8 7 . 1 8 3 3 6 . 4 2 2 7 5 . 9 3 2 7 4 . 6 3 4 0 6 . 8 7 1 3 1 . 4 3 2.00 0 . 9 2 1 8 . 9 1 1 1 . 4 8 3 1 . 8 6 68. 11 4 2 . 9 3 4 5 . 7 8 91 1 0 . 1 0 9 . 8 1 4 0 5 . 3 7 .345 . 1 1 2 6 0 . 7 4 2 9 0 . 5 8 4 1 1 . 6 0 1 3 8 . 9 2 2.10 0 . 9 4 1 9 . 4 4 1 2 . 8 1 3 6 . 6 6 7 7 . 14 4 6 . 5 6 4 8 . 9 4 9 2 1 1 . 36 1 1 . 09 4 3 3 . 9 3 3 6 6 . 7 1 2 6 3 . 3 2 3 1 1 . 5 6 . . . 4 3 4 . 0 5 . 1 4 6 . 5 4 . _ 2 . 3 4 1.44 2 0 . 7 3 9 . 5 1 32~ .29 H.i\ 4 1 . 4 9 ~ 4 3 . 79 7 9 3 1 2 . 9 7 1 2 . 3 5 - 4 5 9 . 9 1 3 8 3 . 9 1 2 6 1 . 0 6 3 3 1 . 9 4 4 4 9 . 5 1 1 5 4 . 5 0 2 . 6 7 1 . 6 0 2 3 . 4 0 8 . 4 2 3 3 . 2 6 7 6 . 6 5 4 1 . 2 0 4 3 . 2 8 9 4 1 2 . 7 8 1 4 . 3 2 4 9 5 . 3 8 4 1 7 . 3 8 2 7 8 . 3 2 3 5 6 . 2 4 4 8 7 . 6 6 1 6 1 . 1 6 1 . 5 0 2 . 2 0 2 3 . 4 6 1 . 3 9 1 6 . 3 3 4 8 . 4 9 2 4 . 7 1 2 6 . 4 5 9 5 1 3 . 3 2 1 3 . 9 2 5 2 8 . 8 2 4 5 7 . 3 9 3 0 6 . 1 7 3 7 8 . 4 9 - 5 3 5 . 3 1 1 6 5 . 6 3 1 . 0 4 0 . 9 1 2 7 . 4 0 " 0 7 6 5 " 3.99 2 4 . 1 8 1 0 . 8 9 - T 2 " . 4 5 ~ 9 6 1 4 . 1 6 1 4 . 4 8 5 6 4 . 6 6 5 0 0 . 0 2 4 . 7 2 3 3 4 . 4 6 4 0 1 . 9 0 5 8 6 . 1 2 1 7 0 . 3 0 6 . 9 3 0 . 7 2 3 2 . 2 9 0 . 5 4 1 4 . 6 2 5 . 6 0 6 . 8 4 9 ? 1 1 . 14 1 5 . 3 8 6 0 5 . 0 4 5 4 2 ; . 5 6 3 5 5 . 1 4 o . b 9 4 2 8 . 8 1 6 3 5 . 1 4 1 7 6 . 4 8 0 . 9 7 0 . 7 0 3 6 . 8 9 8 . 5 9 1 3 . 6 5 4 . 6 3 5 . 8 5 9 8 1 1 . 7 4 1 2 . 4 9 6 4 7 . 2 5 3 6 2 . 8 7 4 5 7 . 7 3 . _ 6 7 3 . 9 7 _184. . J )7 1.00 "67 7 1 " 4 0 . 6 9 " 1 0 . 5 8 0 . 1 6 17.61" ______ ""67 78 " 9 9 1 2 . 9 1 1 3 . 1 3 . 6 7 9 . 5 3 5 9 4 . 8 6 3 5 0 . 0 7 4 8 3 . 8 3 6 8 4 . 0 3 1 9 2 . 7 9 1 .01 0 . 7 9 4 1 . 1 3 1 0 . 3 1 0.55 2 2 . 2 5 7 . 3 7 8 . 7 7 1 0 0 1 2 . 1 9 1 4 . 3 3 782.82 5 9 8 . 6 6 3 3 1 . 0 4 5 0 7 . 0 4 6 7 8 . 6 6 2 0 1 . 8 1 1 . 12 0 . 7 9 3 9 . 5 8 9 . 0 5 1 . 6 7 3 0 . 0 1 1 0 . 5 8 1 2 . 0 6 101 1 3 . 5 8 1 3 . 3 9 7 4 0 . 1 9 6 1 9 . 6 1 3 2 6 . 6 2 _ 5 . 36 .52 6 9 6 . 2 5 2 1 0 . 7 6 0.99 . 0 . 8 6 4 0 . 2 7 " ~ 8 . 8 l " 3 . 1 2 38". 44 " I T . " 2 7 " 7 4 7 8 7 102 1 6 . 3 9 1 4 . 9 4 7 8 8 . 0 2 6 5 5 . 6 7 3 3 3 . 8 9 5 7 0 . 0 3 7 3 3 . 0 6 2 1 8 . 9 0 1 . 02 , 0 . 8 8 4 2 . 4 6 9 . 7 3 3 . 7 8 4 3 . 65 1 4 . 4 8 1 6 . 1 4 103 1 9 . 0 1 1 4 . 0 6 8 4 0 . 5 3 6 9 8 . 3 4 3 4 5 . 6 8 6 0 5 . 0 8 . 7 7 7 . 7 7 2 2 6 . 4 6 1 . 0 5 1 . 1 9 4 6 . 3 4 11 .51 3 . 2 3 4 4 . 9 2 1 4 . 0 2 1 5 . 7 1 1 0 4 19 . 1 1 2.SX76 8 9 6 . 1 9 7 4 3 . 1 2 • 3 5 7 . 6 5 6 4 1 . 5 8 8 2 4 . 3 9 2 3 3 . 9 8 0 . 7 3 1722 " 4 9 3 5 " T - . 5 1 2 . 4 9 4 3 . 5 9 1 2 . 8 0 1 4 . 4 3 1 0 5 , 2 0 . 7 3 0 . , 8 l 2 0 . 8 2 9 5 6 . 3 8 7 9 2 . 8 8 3 7 2 . 0 0 6 7 9 . 0 8 8 7 6 . 8 8 2 4 1 . 0 1 1 .01 5 1 . 0 4 1 2 . 9 0 2 . 2 9 4 3 . 2 5 1 2 . 4 0 1 3 . 9 2 106 25.04 2 2 . 5 4 1 0 2 1 . 8 1 8 5 1 . 0 5 3 9 1 . 9 7 7 1 5 . 4 9 9 4 0 . 0 4 2 4 6 . 6 9 0 . 9 1 1 . 0 3 5 1 . 9 2 1 3 . 14 2.33 4 4 . 3 9 1 2 . 6 3 1 4 . 3 1 107 3 1 . 4 3 2 7 . 4 1 1 0 8 6 . 9 4 9 1 7 . 7 3 4 2 0 . 4 1 J 7 4 5 . 5 4 1 0 1 4 . J 7 2 _ 2 4 9 . 8 7 0 . 7 0 0 . 8 7 5 2 . 6 6 " 1 3 " . 0 9 ' 2 . 7 9 " 4 8 7 4 6 " 1 3 . 5 9 1 5 . 8 1 108 3 9 . 1 9 3 4 . 7 2 1 1 4 2 . 6 6 9 8 7 . 8 5 4 5 7 . 7 5 7 6 3 . 9 1 1 0 9 5 . 0 5 2 5 0 . 0 6 -0 . 6 3 0 . 7 3 5 5 . 4 2 1 3 . 2 7 i' _ . 3 . 4 8 5 3 . 3 1 1 5 . 1 2 1 7 . 7 6 1 0 9 46_»'5 4 2 . 3 7 1 2 0 8 . 6 0 1 0 6 3 . 6 5 4 9 2 . 3 7 7 8 8 . 5 3 1 1 8 0 . 9 7 2 5 1 . 7 9 0 . 6 1 0 . 6 B 6 4 . 2 8 1 3 . 6 6 5 . 4 9 6 3 . 8 6 1 9 . 4 3 2 2 . 1 0 110 5 1 . 2 8 5 0 . 1 5 1 2 8 1 . 5 7 1 1 4 4 . 2 5 5 2 4 . 2 5 8 1 6 . 9 3 1 2 7 1 . 5 3 2 5 4 . 4 0 0 . 9 0 0 . 7 0 8 1 . 0 1 1 4 . 5 2 9 . 1 4 7 6 . 6 3 2 5 . 6 3 2 7 . 1 1 HI 5 7 . 3 2 5 4 . 6 9 1 3 4 8 . 7 7 1 2 3 0 . 2 6 5 6 0 . 8 7 8 3 9 . 9 3 1 3 6 8 . 2 4 2 5 5 . 7 9 0 . 8 5 0 . 4 2 1 0 9 . 6 5 1 7 . 6 3 1 2 . 9 9 8 5 . 3 4 2 8 . 8 6 2 8 . 7 6 1 1 2 6 3 . 4 5 6 0 . 9 0 1 4 2 1 . 4 3 1 3 2 1 . 8 6 5 9 3 . 5 8 8 6 7 . 2 0 1 4 7 0 . 5 0 2 5 8 . 1 0 0 . 8 6 0 . 4 3 1 2 0 . 0 7 1 8 . 6 8 1 8 . 0 1 3 1 . 3 2 3 0 . 3 3 1 1 3 6 8 . 8 3 - 6 6 . 7 7 1 5 0 8 . 7 2 1 3 9 9 . 0 5 5 9 9 . 7 0 9 1 0 " ; 18" 1 5 5 3 . 9 4 2 6 4 . 2 4 0 . 9 1 0 . 6 6 1 2 3 . 6 4 1 8 . 3 3 2 7 . 6 0 9 9 . 5 7 3 6 . 1 5 3 3 . 6 1 1 1 4 6 7 . 3 2 7 1 . 7 0 1 5 6 1 . 8 3 1 4 0 4 . 0 2 5 6 6 . 1 0 9 5 4 . 7 6 1 5 5 0 . 9 5 2 7 3 . 3 3 1 . 7 5 0 . 9 7 1 1 6 . 9 9 - 1 7 . 2 2 4 1 . 5 5 1 0 7 . 2 8 4 1 . 4 2 3 7 . 1 2 115 6 5 . 6 5 7 0 . 5 2 1 5 8 9 . 9 5 1 3 7 3 . 3 4 5 2 4 . 9 5 9 9 5 . 2 7 1 5 0 8 . 3 9 2 8 3 . 0 5 2 . 1 3 1 . 7 8 1 1 7 . 3 4 1 6 - ' | 9 . 5 6 . 0 8 . H 3 . 4 0 . 4 4 . 7 5 3 9 . 3 6 1 1 6 6 8 . 3 0 6 8 . 5 9 1 6 3 1 . 0 8 1 3 6 2 . 2 2 4 9 7 . 3 8 1 0 4 0 . 0 3 T 4 9 0 7 3 6 2 9 2 . 6 6 2 . 1 9 1 . 7 7 121.00 1 6 . 8 4 6 3 . 5 0 1 1 7 . 2 9 4 6 . 1 8 4 0 . 3 6 1 1 7 6 9 . 1 4 7 1 . 2 9 1 6 9 8 . 8 8 1 3 8 9 . 4 6 4 8 7 . 4 7 1 0 9 1 . 2 9 1 5 1 6 . 4 4 3 0 1 . 4 8 1 .51 1 . 6 0 1 2 4 . 6 0 1 6 . 3 6 5 9 . 12 1 1 1 .03 4 1 . 8 9 3 6 . 2 9 118 6 7 . 5 7 7 1 . 8 6 1 7 8 9 . 5 5 1 4 4 8 . 3 3 4 9 1 . 3 6 1 1 4 4 . 2 0 1 5 7 8 . 2 6 3 0 8 . 7 4 1 . 2 6 0 . 6 3 121 . 57 " 1542 .12 " 1 5 . 5 9 5 0 . 15 9 8 . 8 9 3 5 . 13 2 9 . 8 6 119 7 2 . 3 9 6 9 . 3 3 1 8 9 2 . 8 1 5 1 3 . 7 9 1 1 8 3 . 2 2 1 6 8 0 . 6 ? 111 .97 0 . 8 9 0 . 3 1 1 1 9 . 6 0 1 6 . 7 1 4 5 . 7 6 9 2 . 9 4 3 2 . 3 0 2 6 . 7 8 1 2 0 8 2 . 2 4 7 4 . 3 0 : 1 9 6 4 . 1 2 1 6 4 5 . 3 2 5 5 1 . 7 3 1 1 8 8 . 9 5 1 7 9 1 . 8 9 3 0 9 . 9 0 4 . 4 2 0 . 0 6 1 1 7 . 7 8 1 7 . 9 3 4 1 . 15 8 6 . 81 2 9 . 5 0 2 3 . 5 5 121 9 4 . 3 0 • 8 5 . 0 9 2 0 1 4 . 7 5 1 7 4 5 . 4 4 5 9 6 . 2 8 1 1 7 9 . 1 4 1 8 9 9 . 3 8 3 0 5 . 9 0 5 . 2 3 2 . 2 3 1 0 9 . 8 4 ..IB.62 _ .7.5'.?_9 2 4 . 6 3 1 8 . 0 2 122 VOl. 98 9 6 . 5 1 2 0 9 7 . 6 1 1 8 5 9 . 1 0 "636 . 4 4 1186 .~82 2 0 2 1 . 5 7 3 0 4 . 5 0 3.44 5 . 0 5 1 0 9 . 3 7 1 8 . 4 8 2 8 . 8 3 6 9 . 9 5 2 2 . 0 2 1 5 . 4 1 1 2 3 111.2* 1 0 4 . 3 1 2 1 9 2 . 0 5 : 1 9 8 0 . 9 1 6 7 5 . 2 1 1 1 9 8 . 3 2 2 1 5 1 . 4 1 3 0 3 . 7 8 3 . 4 8 4 . 3 4 1 1 2 . 9 5 1 7 . 7 6 2 6 . 0 2 6 6 . 2 0 1 9 . 6 6 1 3 . 3 2 1 2 4 V 2 3 . 3 5 1 1 3 : 6 5 2 2 9 8 . 7 0 2 1 1 1 . 0 7 7 1 1 . 8 5 1 2 1 3 . 1 3 2 2 8 9 . 0 5 3 0 3 . 6 4 3 . 5 3 4 . 3 8 1 1 6 . 7 9 . 1 8 . 0 1 . _ 2 6 _ . 6 8 _ 68..1.0 _ 2 0 . _ 5 6 _ . 1 4 . 01 125 1 3 5 . 6 7 1 2 5 . 4 9 2 4 2 3 . 8 6 2 2 4 8 . 6 3 7 4 1 . 5 1 1 2 3 6 7 8 8 - 2 4 3 5 . " 4 2 ~ " " 3 0 4 . 8 " - " " 2 . 8 0 4 . 5 7 1 1 5 . 4 1 1 8 . 9 4 2 8 . 4 8 7 2 . 7 5 2 3 . 9 6 1 7 . 1 5 .• TABLE A.2(b) I AM = 30 I AN = 83 B1 3 SIMPLE REGRESSION DEP.VAR XII, 17) INDEP. VAR. X(I ,11) STD. ERROR Y A B STD. ERROR 8 F-RATIO CORRELATION R 1 32.738 63.568 2.9378 0.96565 9.2556 0.38871 2 31 .669 56.126 3.4160 0.93094 13.464 0.45352 3 31.808 57.561 3.3153 0.92340 12.890 0.44569 4 31.161 53.288 3.5700 0.90348 15.613 0.48054 5 31.681 56. 187 3.4142 0.93218 13.415 0.45285 6 33.176 87.041 0.84983E-01 0.30726E-01 7.6496 0.35811 7 32.082 82.635 0.10150 0.29562E-01 11.789 0.42989 8 32.226 83.446 0.97785E-01 0.29192E-01 11.221 0.42129 9 31.454 80.401 0.10798 0.28494E-01 14.361 0.46520 10 32.007 82.385 0.10252 0.29488E-01 12.087 0.43428 11 14.952 39.923 0.12621 0.81186E-02 241.69 0.90716 12 15.607 57.866 0.19745E-01 0.13382E-02 217.72 0.89845 13 12.860 77.850 0.33973E-05 0.18290E-06 345.01 0.93221 14 17.358 41.735 1.9521 0.15155 165.91 0.87256 15 14.021 68.329 0.284UE-01 0.16920E-02 281.95 0.91885 16 21.714 -70.648 52.673 5.6391 87.245 0.79155 MULREG.OR.STPREG DEP.VAR XII, 17) ""STEP NO; 16 DEPENDENT VAR. Y(I) FRATIO 234.9 STDEVRES 4. 159 RSQ 99.03 EB -467.4 "" INDEP. VAR. "Xll.i'i) B(Il) STERBII I) FPARI II1 13 -0.2469E-04 0.5238E-05 22.23 IC 0.1831E-01 0.2333E-01 0.6156 8 O.2818E-01 0.2400E-01 1.378 -3 -0.5194 0.7859 0.4367 5 -0.2666 0.7890 0.1142 9 0.3611E-01 0.2275E-01 2.521 4 -0.7761 0.7697 1.017 7 0.1092E-01 0.2537E-01 0.1853 2 -0.3924 0.8102 0.2346 12 0.2105 0.5600E-01 14.13 1 1 0.4392 0.1118 15.43 1 0.2142E-01 0.8153 0.6903E-03 15 0.4529 0.7912E-01 32.76 14 -57.67 8.918 41.81 16 405.2 64.83 39.07 6 -0.3977E-02 0.2531E-01 0.2468E-01 TABLE A.3 1121AND 3 DAY FRASER RIVER FLOOD FLOW PREDICTION AT HOPE 1955 A 22 ACTUAL 1 DAY PREDICTION 2 DAY PREDICTION 3 DAY PREDICTION ADJUST PREDICTION EQUATION DATE QUI DATE 0(1 + 1) ERROR DATE Q1I+2) ERROR DATE QII+3) ERROR CORR RSQ STDEVY MAI NNF 22 209.00 23 197.59 -3.14 24 173.66 -9.55 25 151.28 -16.42 -0.09 99.972 1.37847 60 83 23 204.00 24 187.34 -2.43 25 176.12 -2.69 26 166.07 -5.11 0.05 99.977 1.30209 60 84 24 192.00 25 184.70 2.04 26 181.51 3.72 27 184.77 6.80 0.07 99.978 1.26130 60 85 25 181.00 26 174.26 -0.42 27 172.09 -0.52 28 174.76 -0.70 -0.16 99.980 1.19393 60 86 26 175.00 27 173.37 0.22 28 176.60 0.34 29 181.40 -1.42 0.04 99.980 1.17314 60 87 27 173.00 28 175.82 -0.10 29 179.87 -2.25 30 175.31 -6.25 -0.04 99.980 1.14750 60 88 28 176.00 29 180.12 -2.11 30 175.64 -6.07 31 166.91 -5.70 0.03 99.981 1.10447 60 89 29 184.00 30 183.20 -2.03 31 178.58 0.89 1 177.51 -1.93 0.39 99.981 1.10858 60 90 30 187.00 31 184.87 4.45 1 186.15 2.85 2 191.66 0.87 0.51 99.980 1.11595 60 91 31 177.00 1 175.32 -3.14 2 177.98 -6.33 3 179.60 -8.37 -1.27 99.969 1.36715 60 92 1 181.00 2 184.95 -2.66 3 187.78 -4.20 4 191.13 -5.38 0.93 99.967 1.40214 60 93 2 190.00 3 193.83 -1.11 4 198.78 -1.59 5 201.39 -6.33 1.28 99.961 1.50617 60 94 3 196.00 4 200.55 -0.72 5 203.99 -5.12 6 213.78 -3.26 1.03 99.960 1.53154 60 95 4 202.00 5 204.86 -4.72 6 215.74 -2.38 7 219.06 -2.64 0.98 99.959 1.53674 60 96 5 215.00 6 225.18 1.89 7 232.78 3.46 8 235.40 3.70 4.67 99.919 2.17802 60 97 6 221.00 7 228.62 1.61 8 231.42 1.95 9 230.38 -2.79 0.23 99.924 2.13360 60 98 7 225.00 8 227.17 0.07 9 224.95 -5.08 10 217.60 -12.61 -1.43 99.926 2.11497 60 99 8 227.00 9 224.54 -5.26 10 216.63 -13.00 11 218.38 -16.97 -0.65 99.929 2.09656 60 TOO" 9 237.00 10 230.40 -7.47 11 235.45 -10.48 12 253.35 -8.54 4.88 99.896 2.56019 60 101 10 249.00 11 259.52 -1.32 12 283.06 2.19 13 312.90 6.43 8.24 99.789 3.70061 60 102 11 263.00 12 291.93 5.39 13 327.81 11.50 14 360.53 16.30 3.23 99.784 3.82935 60 103 12 277.00 13 306.57 4.28 14 339.56 9.53 15 357.91 11.85 -2.63 99.787 3.90701 60 104 13 294.00 14 322.16 3.92 15 341.52 6.72 16 360.55 10.60 -3.24 99.785 4.05246 60 105 14 310.00 15 328.24 2.57 16 340.75 4.52 17 361.51 10.22 -1.87 99.796 4.09355 60 106 15 320.00 16 331.22 1.60 17 347.46 5.93 18 343.76 6.10 -1.49 99.811 4.07527 60 107 16 326.00 17 341.18 4.02 18 334.27 3.17 19 327.79 5.06 -0.89 99.825 4.05087 60 108 17 328.00 18 318.27 -1.77 19 305.07 -2.22 20 288.12 -4.28 -1.60 99.834 4.06800 60 109 18 324.00 19 312.04 0.01 20 296.89 -1.36 21 277.00 -6.10 0.72 99.844 4.02862 60 110 19 312.00 20 296.97 -1.34 21 277.16 -6.05 22 257.69 -10.84 0.25 99.853 3.96066 60 111 20 301.00 21 281.58 -4.55 22 263.03 -8.99 2~3 250.51 -12.41 IT69 99.858 3.92658 60 TIT 21 295.00 22 276.99 -4.16 23 264.66 -7.46 24 269.66 -4.04 6.28 99.840 4.18199 60 113 22 289.00 23 277.18 -3.08 24 282.17 0.42 25 300.56 6.96 7.89 99.810 4.57277 60 114 23 286.00 24 291.80 3.84 25 311.46 10.84 26 326.33 10.25 7.94 99.785 4.86767 60 115 24 281.00 25 300.51 6.94 26 315.74 6.67 27 336.77 3.62 -1.40 99.788 4.82267 60 116 25 281.00 26 299.41 1.15 27 319.35 -1.74 28 338.23 -11.46 -10.86 99.742 5.31314 60 117 26 296.00 TT 320.29 -1.45 28 338.35 -11.43 29 353.64 -11.59 -6.29 99.730 5.45179 60 TTW 27 325.00 28 343.57 -10.06 29" 358.76 -10.31 30 373.60 -5.89 -0.71 99.740 5.39641 60 119 28 382.00 29 384.96 -3.76 30 405.26 2.08 1 385.24 -1.98 17.80 99.629 6.60850 60 120 29 400.00 30 413.37 4.12 1 398.19 1.32 2 370.75 -1.92 14.88 99.571 7.31701 60 121 30 397.00 1 382.00 -2.80 2 354.57 -6.20 3 330.00 -7.82 -0.85 99.600 7.23451 60 122 MEAN VALUE OF ERROR!I•JL) -0.54 PERCENT -1.17 PERCENT -2.10 PERCENT STD DEV OF ERRORII.JL) 3.64 PERCENT 6.1? PERCENT 8.08 PERCENT "~ 90 PERCENT CONF INTERVAL 5.99 PERCENT 10.15 PERCENT 13.30 PERCENT 95 PERCENT CONF INTERVAL 7.13 PERCENT 12.10 PERCENT 15.84 PERCENT MA MIA MAIIA NNFIA NNFFA NFA NPRED RII C D MSSTA MSSQA KK FLMTI FLMTO 44 47 54 83 122 125 3 2.00 0.50 20.00 51 51 17 0.OOO 0.000 TABLE A.4 —j v > ) 1,2,AND 3 DAY FRASER RIVER FLOOD FLOW PREDICTION AT HOPE 1960 B 13 ACTUAL 1 DAY PREDICTION 2 DAY PREDICTION 3 DAY PREDICTION ADJUST PREDICTION EQUATION DATE Q (I ) DATE 0(1+1) ERROR DATE 011+2) ERROR DATE 011+3) ERROR CORR RSQ STDEVY MAI NNF 22 176.00 • 23 172.37 -6.32 24 166.22 -11.11 25 160.54 -14.61 -1.55 • 99.025 4.15939 30 83 23 184.00 24 178.54 -4.52 25 174.55 -7.15 26 169.23 -7.53 4.78 99.028 4.25904 .' 30 84 24 187.00 25 184.09 -2.08 26 .80.63 -~1. 30 27 178.72 0.97 6.62 98.983 4.46254" 30 85 25 188.00 26 185.75 1.50 27 185.01 4.53 28 186.92 9.31 5.87 98.973 4.58244 30 86 26 183.00 27 182.58 3.15 28 184.78 B.06 29 18e.34 11.44 1 .75 99.021 4.53940 30 87 27 177.00 28 178.89 4.61 29 182.12 7.76 30 184.88 4.45 -2.20 99.050 4.51165 30 88 28 171.00 29 173.40 2.60 30 175.43 -0.89 31 176.73 -6.00 -6.05 99.013 4.61547 30 89 29 169.00 30 170.44 -3.71 31 170.93 -9.08 I 168.43 -9.44 -6. 35 98.972 4.71913 30 90 \ 30 177.00 31 177.50 -5.58 1 '175.03" -5.90" 2 170.31 -16.10 0.12 99.006 4.66 795 '•' 30" " '91 " " 31 188.00 1 185.98 -0.01 2 182.38 -10.16 3 178.18 -17.51 6.48 98.984 4.77506 30 92 1 186.00 2 182.86 -9.92 3 179.20 - 17.04 4 173.88 -20.60 4.05 99.000 4.77992 30 93 2 203.00 3 199.17 -7.79 4 196.11 -10.45 5 195.11 -9.67 13.86 98.763 5.41754 30 94 3 216.00 4 212.77 -2.84 5 214.57 -0.66 6 213.95 1.40 17.55 98.407 6.30662 30 95 4 219.00 5 220.94 2.29 6 222.78 5.58 7 218.77 8.30 14.28 98.256 6.76343 30 96 5 216.00 6 217.42 3.04 7 213.59 5.74 8 217.15 9.12 5.37 98.319 6.77016 30~ ' 97 " 6 211.00 7 207.21 2.58 8 210.76 5.91 9 219.89 5.71 -0.60 98.398 6.70699 30 98 7 202.00 8 205.45 3.24 9 214.47 3.11 10 221.31 1.52 -3.49 98.441 6.67150 30 99 8 199.00 9 208.02 0.01 10 214.83 -1.45 11 213.88 -4.52 -5.96 98.451 6.69166 30 100 9 208.00 10 214.84 -1.45 11 214.13 -4.41 12 210.17 -7.41 -3.58 98.493 6.66135 30 101 10 218.00 11 217.28 -3.00 12 213.35 -6.01 13 214.65 -7.48 -0.27 98.558 6.60199 30 102 11 224.00 12 220.51 -2.86 13 2 2"l.85 -4.37 14 2 32.21 -3.25 3.96 98.611 " 6.57805 30 103 12 227.00 13 229.73 ' -0.98 14 240.32 0.13 15 257.24 2.49 5.48 98.644 6.59595 30 104 13 232.00 14 243.46 1.44 15 259.40 3.35 16 273.24 3.89 3.64 98.694 6.57458 30 105 14 240.00 15 255.96 1.98 16 269.78 2.58 17 272.59 3.25 0.08 98.761 6.51903 30 106 15 251.00 16 264.68 0.64 17 267.52 1.33 18 270.09 1.54 -2.03 98.628 6.47837 30 107 16 263.00 17 265.87 0.71 18 268.34 0.88 19 270.42 -1.31 -1.63 98.901 6.43408 30 108 17 264.00 18 266.24 0.09 19 "267.74 -2.28 "20 271.35 -i.69 -1.65 98.965" '." 6.38836 30 109 18 266.00 19 267.19 -2.48 20 270.48 -2.00 21 266.24 0.09 -0.86 99.024 6.33932 30 110 19 274.00 20 277.78 0.64 ' 21 274.32 3.13 22 268.98 7.17 2.21 99.078 6.30471 30 111 20 276.00 21 272.57 2.47 22 267.27 6.48 23 266.44 7.87 0.22 99.130 6.25608 30 112 21 266.00 22 260.41 3.75 23 259.04 4.88 24 257.01 1.99 -3.40 99.162 6.23508 30 113 22 251.00 23 249.00 0.81 24 247.03 -1.97 25 241.23 -7.93 -7.22 99.161 6.29612 30 114 23 247.00 24 244.87 -2.83 25" 239.36 " -8.64 " "26" 238.20 -12.75 -5.32" 99.170 6.30782 30 115 24 252.00 25 246.67 -5.85 26 245.30 -10.15 27 263.95 -9.30 1.11 99.194 6.26501 30 116 25 262.00 26 257.87 -5.54 27 273.00 -6. 19 28 290.94 - 6 . 15 7.35 99.186 6.35852 30 117 26 273.00 27 284.31 -2.30 28 297.27 -4.11 29 301.14 -6.19 10.30 99.155 6.56243 30 118 27 291.00 28 ,300.77 -2.98 29 300.54 -6.37 30 300.90 -6.26 8.18 99.159 6.66079 30 119 28 310.00 29 306.15 -4.63 30 303.85 -5.34 1 309.56 -4.75 8.58 99.171 6.76709 30 120 29 321.00 30 317.21 -1.18 . _. 319.55 -1.68 2 330.68 " " 6.51 12.31 "" 99. 155 7.00097 30 121 30 321.00 I 321.43 -1.10 2 333.83 1.47 3 343.95 4.23 10.01 99.167 7.10595 30 122 1 325.00 2 337.91 2.71 3 348.84 5.71 4 355.37 8.68 . 9.65 99.186 7.17899 30 123 2 329.00 3 339.93 3.01 4 346.42 5.94 5 351.34 10.48 0.50 99.229 7.13318 30 124 3 330.00 4 336.54 2.92 5 341.81 7.49 6 336.84 9.36 -6.23 99.256 7.14073 30 125 MEAN VALUE OF ERROR(I.JL) -0.83 PERCENT -1.27 PERCENT -1.55 PERCENT STD OEV OF ERROR(I , JL) 3.48 PERCENT 6.17 PERCENT '8.23 PERCENT 90 PERCENT CONF INTERVAL 5.73 PERCENT 10.15 PERCENT 13.53 PERCENT 95 PERCENT CONF INTERVAL 6.83 PERCENT 12.09 PERCENT 16.12 PERCENT MA MIA MA I IA NNFIA NNFFA NFA NPRED RII C D MSSTA MSSOA KK FLMTI FLMTO 13 15 22 83 125 128 _ 3 1.013 0.50 .20.00 19 19 17 0,000..0.000 . TABLE A.5 1,2,...,5 CAY FRASER RIVER FLOOD FLOW PREDICTION AT HOPE 1955 A3 2 TABLE A.6 ACTUAL 1 DAY PREDICTION 2 DAY PREDICTION 3 DAY PREDICTION 4 DAY PREDICTION 5 DAY PREDICTION ADJUST PREDICTION EQUATION DAY 011;) DAY o( m i r ERROR DAY Q(1+2) ERROR DAY Q( 1+3) ERROR DAY Q(1+4) ERROR DAY Q(1+5) ERROR CORR RSQ STDEVY MAI NNF 30 1875. 31 183.10 3.45 1 177.49 -1.94 2 189.80 -0. 11 3 210.18 7.23 4 208.33 3.13 -5.03 99.416 5. 776 57 91 31 1.77. " \ i 165.14 -8.76 2 170.06 -10.50 ' 3 181.87 -7.21 4 171.22 -15.24 5 180.09 116."?4 -1.91 99.417 5.721 57 92 1 181. 2 191.58 0.83 3 210.14 7.21 4 205.27 1.62 5 222.07 3.29 6 230.94 4.50 3.12 99.400 5.768 57 93 2 190. 3 209.14 6.70 4 204.61 1.29 5 222.07 3.29 6 231.62 4.80 7 260.35 15.71 0.35 99.427 5.630 57 94 202. 215. 221. 225. 227. 9 237. 10 2A<i. U 263 . 12 277s. 13 254. 1-4 ,31C. 189.06 5 217.98 6 222.72 7 246.06 8 228.77 9 234.88 10 231.02 11 235.97 12 274.48 13" 314.54 14 335.22 15 331.60 -6.41 I. 39 Oi.78 9.36 0.78 -0.90 -7.22 -10.28 -0.91 6.9 8" 8. 14 3.63 5 203.99 6 225.72 7 247.59 8 248.25 9 236.70 10 229.09 11 217.09 12 246.02 13 306.40 14 360.46 15 367.55 16 311.63 •5.12 2.13 10.04 9.36 -0.13 -8.00 209.49 7 250.53 8 250.31 9 262.48 10 233.78 11 215.95 11.35 10.27 10.75 -6.11 -17.89 7 233.27 8 253.22 9 264.47 10 260.25 11 221.60 12 223.00 11.55 11.59 4.52 -15.74 -19.49 8 232.67 9 267.33 10 262.69 11 252.71 12 231.07 13 243.51 2.50 12.80 5.50 -3.91 -16.58 -17.17 -3. 10 3.25 0.10 -0.74 -10.19 -6.12 99.421 99.425 99.460 99.492 99.379 99.370 5.664 5.663 5. 543 5.436 6.080 6. 190 -19.39 -8. 13 11^36 24.21 ' 7.26 -8. 17 -17.52 -3.67 16.79 16.29 4.66 -12.50 57 57 57 5 7 57 57 95 96 97 98 99 100 -17.46 -11.18 4.22 16.28 14.86 -4.41 12 223.30 13 270.10 14 345.21 15 397.46 16 349.67 17 301.20 13 242.50 14 298.63 15 373.71 16 379.12 17 343.28 18 283.49 14 265.61 15 315.43 16 353.21 17 377.18 18 329.83 19 250.20 -14.32 -1.43 8.35 14.99 1.80 -19.81 -2.08 8.27 18.52 8.68 -3.62 -8.29 99.404 99.375 99.101 99.094 99.160 99.154 6. 103 6.363 7.806 8.054' 8.012 8.336 57 57 57 57 57 57 101 102 103 104 105 106 15 320. 16 294. 97 -9. 52 17 282.09 -14. 00 18 264 .13 -18.48 19 229.44 -26.46 20 191.35 -36.43 -5. 69 99.197 8.413 57 107 16 326. 17 311. 76 -4; 95 18 300.14 -7. 37 19 266 .90 -14.45 20 234.40 -22.13 21 207.28 -29.74 5. 58 99.226 8.532 57 108 17 328. 18 312. 37 -3. .59 19 283.50 -9. 14 20 250 .07 -16.92 21 227.11 -23.01 2? 209.89 -27.37 4. 47 99.262 8.572 57 109 18 324. 19 293. 17 -6i. 03 20 2-65.28 -11. 87 21 241 .93 -17.99 22 228.58 -20.91 23 191.81 -32.93 3. 24 99.300 8.539 57 110 19 312. 20 285. 46 -5. 16 21 270.44 -8. 32 22 258 .33 -10.61 23 228.84 -19.99 24 217.93 -22.45 3. 67 99.318 8.550 57 111 20 301. 21 290. 90 -1; 39 22 286.35 -0. 92 23 261 .67 -8.51 24 256.17 -3.84 25 268.61 -4.41 4. 16 99.329 8.560 57 112 22 289. 23 286. 24 281. 25 281. 26 296. 23 265.82 24 282.55 25 292.39 26 301.59 27 32C.64 28 330.64 29 376.11 30 401.65 1 400.39 OF ERROR ERROR CONF INT -7.06 0;55 4.05 1.89 -1.34 -13.44 -5.97 1.17 1.88 -1.26 5.65 24 262.18 25 294.13 26 312.81 27 326.85 28 326.13 29 339.64 30 393.31 1 410.64 2 414.56 PERCENT PERCENT -6.70 4.67 5.68 0.57 -14.63 -15.09 -0.93 4.49 9.67 -1.98 9.01 25 274. 26 314. 27 338. 28 331. 29 335. 76 91 73 05 17 -2.22 6.39 4.22 -13.34 -16.21 -10.69 1.76 11.57 12.84 -2.82 11.53 26 293.87 27 339.97 28 342.01 29 340.19 30 350.07 1 355.33 2 404.15 3 410.15 4 395.48 PERCENT PERCENT -0.72 4.60 -10.47 -14.95 -11.82 -9.58 6.92 14.57 18.05 -3.93 13.45 26 296.83. 27 317.60 28 343.32 29 351.97 30 355.13 1 350.73 0.28 -2.28 -10.13 -12.01 -10.55 -10. 76 2.98 0.02 9.14 3.52 -4.30 -5.69 99.348 99.369 99.346 99.357 99.364 99.371 8.489 8. 382 8.544 8^480 8.478 8.408 57 57 57 57 57 57 113 114 115 116 117 118 27 325 28 ,382 29 400. '30 397. MEAN VALUE STD DEV OF 90 PERCENT 95 PBRCENT CONF INT 30 354.56 1 399.91 2 421.75 3 403.98 PERCENT PERCENT 2 366.83 3 400.77 4 404.11 5 384.67 PERCENT PERCENT -2.95 11.95 20.63 26.53 -5.09 15.78 -0.74 23.71 21.69 8.29 PERCENT PERCENT 99.396 99.227 99.116 99.153 8. 316 9.654 10.620 10.648" PERCENT PERCENT 18.96 22.59 22.13 26.36 57 119 57 120 57 121 57 122 9. 30 11.C8 14.82 17.65 PERCENT PERCENT PERCENT PERCENT PERCENT PERCENT 25.97 30.94 PERCENT PERCENT MA 44 MIA 45 MA.l IA 54 NNF I A 91 NNFFA 122 NFA 127 NPRED 5 RI I 1.00 C 0.50 D 20.00 MSSTA 49 MSSQA 49 KK 17 FLMTI 0.000 FLMTO 0.000 -0 1,2,...,5 DAY FRASER RIVER RLOOO FLOW PREDICTION AT HDPE 1960 B2 3 TABLE A.7 ACTUAL 1 DAY PREDICTION 2 DAY PREDICTION 3 DAY PREDICTION 4 DAY PREDICTION 5 DAY PREDICTION ADJUST PREDICTION EQUATION DAY Q U I DAY Q(1*1) ERROR DAY 0(1 + 2): ERROR DAY Q(1+3) ERROR DAY Q(1+4) ERROR DAY Q( 1 + 5) ERROR CORR RSQ STDEVY MAI' NNF 77 176. 73 174.24 -5.31 74 168.68 -9.80 75 161.4? -14.14 76 155.20 -15_._1.9_ 27 147.89 -16.44 0.86 99.152 3.828 34 83 23 184. 24 178.66 -4. 35 25 174.15 -7.37 26 170.52 -6.62 27 165.24 -6.65 28 164.13 -4.02 4.37 99.134 3.964 34 84 24 187. 25 182.56 - 2 i 8 9 26 181.88 -0.61 27 178.57 0.89 28 179.69 5.08 29 180.80 6.98 5.69 99.094 4.153 34 85 25 188. 26 187.90 '7.68 27 186.47 5.35 28 189.40 10.76 29 197.20 13.73 30 194.11 9.67 5.25 99.077' 4.284 34 BS 26 183. 27 177. 78 171. 27 181.60 28 179.54 -29 172^31 2.60 28 184.59 4 i 9 9 29 182.00 11% 3_0_122_,_7_8_ 7.95 29 187.47 10.93 30 189.45 7.69 30 183.52 3.68 31 184.94 _ r 2 _ J f l 31 173.112 -l.*2 1 169.88-7.03 31 191.39 -1.63 1 182.83 -8.67 2 168.72 29 169. 30 177. 31 198. 30 168.62 31 176.73 1 184.90 -4.73 31 168.08 -6.00 1 172.99 -0.59 2 183.97 -10.60 1 164.13 -11.76 2 161.96 -7.00 2 171.10 -15.71 3 169.82 -9.37 3 183.55 -15.02 4 178.97 -20.21 3 160.41 -21.38 4 164.52 -18.78 5 177.70 1.81 -1.70 -16.88 -25. 74 -24.88 17.73 0.15 -7.5? -6.18 -5.31 1.81 - 7.97 99.124 4.230 99.142 4.217 99.085 4.366 99.055 4.441 99.080 4.403 90.010 4.618 34 34 _3_4_ 34 34 34 87 88 _H9_ 90 91 97 1 186. 2 203'. 3 216. 2 185.43 3 204.21 4 716.89 -8.66 3 185.79 -5.46 4 203.18 _j__.0_._l6 5 220.^6--13.98 4 182.24 -7.22 5 204.68 _2_22 _6_2_22_^23_ 4 219. 5 216. 6 211. 5 222.12 6 220.16 7 214.98 2 i 8 3 6 226.32 4.34 7 224.11 6.43 8 215.93 7.27 7 229.88 10.95 8 225.75 8.51 9 216.01 98.996 4.690 98.736 5.361 9_B.A_ti. &...UL7_ 98.395 6.360 98.483 6.308 9H.535 6.287 34 34 _2_4_ 34 34 34 93 94 _93_ 96 97 98 7 202. 8 199. 10 218 11 224 11 218.41 12 224.10 9 2-03.64 10 201.51 u_2ia.. 12 218.50 13 227.85 -2.10 10 206.44 -7.57 11 201.72 0 12. 2X0_..5_. -3.75 13 222.64 -1.79 14 237.93 -5.30 -9.95 98.461 90.425 6.495 6.606 -4.03 -0.86 _9Jl.Aa2__6_._54.A_ 98.520 6.546 98.554 6.567 34 34 _3ii_ 34 34 99 100 _1D.I__ 102 103 13 232. 14 242.24 0 i 9 3 15 255.34 1.73 16 266.44 1.31 17 270.49 2.46 18 269.65 1.37 • 4.01 98.646 6.551 34 105 14 240. 15 253.34 0.93 16 264.49 0.57 17 268.20 1.59 18 267.39 0.52 19 264.89 -3.33 0.92 98.718 6.493 34 106 15 25:1.. _16_ -2.6JL._98_ _-^ QV.3_9__ _J_7 -265_._88 0.71 18 265.29 -0.27 _1_9_ 262.88 -4.06 20 261.36 -5.31 -0.66 9S.-794 _6_.A3.8_ 34 __L07_. 16 263. 17 266.93 1. 11 18 266.32 0.12 19 263.86 -3.70 20 262.31 -4.96 21 257.42 -3.22 0.17 98.874 6. 384 34 108 17 264. 18 263.28 -1.02 19 260.81 -4.81 20 259.45 -6.00 21 254.32 -4.39 22 245.74 -2. 10 -1.13 98.943 6. 334 34 109 18 266. 19 263.54 -3.82 20 262.25 -4.98 ?\ 257.10 -3-35 22 248.86 -0.85 ?3 241.36 -7.7S 0.6H 99.006 6.7R1 34 1 1 n 19 274. 20 273.41 -0.94 21 270.35 20 276. 21 274.24 3.10 22 269.04 _21_Z66_. 22_260..3_9 _1._7_V Z3_255..86_ 22 251. 23 245.53 -0.60 24 240.87 -4.42 23 247. 24 242.16 -3.91 25 235.55 -10.10 1.63 22 263.77 5.09 23 258.79 7.19 23 265.19 7.36 24 262.26 3.59 74 757.08 0.03 75 747.76 4.77 24 253.84 0.73 5.14 4.07 25 259.14 -1.09 3.43 ^ 5 ^ 4 3 26 246.18 _l9_^8_3 - L . 74 99.045 6.305 99.092 6.284 _9_9._l.3_. 6.._2_4_6_ 34 34 34 111 112 _1X3__ 25 234.62 26 232.71 -10.45 -14.76 26 232.25 27 241.86 -14.93 -16.89 27 241.59 28 257.16 -16.98 -17.05 -5.55 -2.15 99.137 99.159 274 236 34 34 114 115 25 262. 26 259.61 -4.91 27 268.37 -7.78 28 2 84. 94 1 ' • j1 -8.08 ' -29 — 293.65 -8.52 __ 30 290.02 . _ — -9.65 11.73 99. 126 . , _ ^ _ — 6.471 -L—— 34 —_____—_ 117 26 273. 27 284.32 -2.29 28 298.01 -3.87 29 305.39 -4.86 30 304.91 -5.01 1 299.70 -7.78 15.23 99.046 6.846 34 118 27 291. 28 301.11 - 2 i 8 7 79 303.96 -5.31 30 304.51 -5.14 1 301.85 -7.12 ? 313.44 -4.73 9.65 99.033 7.01R 34 119 28 310. 29 309.80 -3149 30 306.38 -4.55 1 304.13 -6.42 2 318.46 -3.20 3 330.97 0.29 8.41 99.049 7.126 34 120 29 321. 30 313.99 -2118 1 307.02 -5.53 2 323.61 -1.64 3 339.54 2.89 4 348.39 6.54 9.25 99.063 7.253 34 121 30 321. 1 310.75 - 4 i 3 8 2 324.83 -1.27 3 342.82 3.88 4 353.96 8.24 5 358.51 1 7.74 7.R7 99.086 7.376 34 1 i»? 1 325. 2 337.68 2 i 6 4 3 352.64 6.86 4 365.28 11.71 5 372.86 17.25 6 363.53 18.03 11.42 99.081 7.510 34 123 2 329. 3 343.64 4; 13 4 356.51 9.03 5 364.08 14..49 6 354.87 15.22 7 346.66 16.72 1.70 99.131 7.461 34 124 3 330. 4 347.32 4.68 5 349.06 9.77 ft 340.03 lOi.40 7 332.45 11 .94 8 321.J.3 10.00 -8.36 99. 1 55 7.500 34 1 75 MEAN VALUE OF ERROR -0.89 PERCENT -1.44 PERCENT -I.H3 PERCENT -2.29 PERCENT -3.09 PERCENT STD DEV OF ERROR 3; 64 PERCBNT 6.58 PERCENT 8*77 PERCENT 10.10 PERCENT 10.64 PERCENT 90 PERCENT CONF INT 5.99 PERCENT 10.83 PERCENT 14.42 PERCENT 16.61 PERCENT 17.50 PERCENT 95 PERCENT CONF LNT 7i14 PERCBNT 12.91 PERCENT 17.19 PERCBNT 19.79 PERCENT 20.85 PERCENT MA MIA HAfr IA NNFIA NNFFA NFA NPRFD RT I- C I) HSSTA MSSOA KK FIMT1 FI MTD 13 13 22 83 125 130 5 I.00 0.50 20.00 17 17 17 0.000 0.000 77 APPENDIX B N N F T = N N F X - 1 N M P I Q - N N F T • N P R E D S T = O . O Sc\- O - O I - M I - i YES I D A Y ; , = I A YES I O A Y l = IA - 31 YES I D A Y i c I A - 61 YES I D A Y i. = I A- 92 YES I DAY; . : 1 f t - 1 2 2 Y E S S T I ; = S T + T i S T = S T I ; SQXi - SQ * QT-L SQ - S Q l j . KU = MS ST * 3 Yes X i , , , = S T t ; . K L = MSSQ+-3 X k 3 ( C - T M M i + C l . O - O - T M I N j ) - D FIGURE B.1 Plow Diagram o f I n i t i a l T r ans fo rma t i ons X i , , t = S Q I i . , = [ S Q I ; . * ] 8 YES K i . = R I R I * R u • L O = T i - » X i , Z = **.» « T i - S * i . 4 = T l - T cn. 4 i 2 x i , S = : X k , io -* t , 1.4 = x i , IS ' * i , 1 4 = X i . n e 7 9 M = M A I R N : N N - M • i HI = KK - I KF = KK + KI KKH = KK*I sxi=oo * I =M SXj. = SXJ + Xi.j SX. r SX: 1 = T+l Sxx = o o S XXKT : SXX + X.„ • V,-j K = K-v 1 1 krti = K-l T-K SClRT<CSXXk K • CSXX.j") YES cr- i * K , j r J^.*1 K+ 1 K= KKK FIGURE B.2 Flow Diagram o f R e g r e s s i o n A n a l y s i s FIGURE B .2 (cont.) IT K = I T a KKK yes T=T+i K= K+l I I = I BBBu= CSXX.. ) (. K/CSXX. i >vi. A.AAu"".S*k„ /RN)-BBB , i ' . SX^ /nw SEROR.yti = SO«T« c s x x k k k K -l c s x , < a , k K ) a / c s x x u , u ) / < B N - 2 ^ S r « O R B _ i = S O W (f SERORV L l) 2 / C 3 X X U ) F R R T U - (( C S * X U > k k . Z / c s x x i i . U > / < S E B O R y i £ > 2 RCOR.;^  _ CSXX__ k h / SQRT u= i r + i L L - 1 1 B i a v t = o . o I - I yes T = I LL = L I_ yes BISVI t x = I r= L L LI-.-" 1 1 HR= RR 4- I.e. RMT :RN- IO P H I ' RNI-RR 80 7-3+i I = I + i F H M T - ( P H I - - U S U I . / < A k K , k „ ' * ' a V I > I Include For STPREG T K o 81 FIGURE B.2 (cont.) T = I I > O T - T + l I I B - I I - I T I A • I I + I Include For STPREG i 1 ! L - X K ; 1 I ' N S T E P : N S T E 7 . . 1 I i <o j - i i = 11 IIB = I I -\ XtA = 1 1+1 K = I I i * i E S 1 =  Ai,> - A'»' " A k » i r = _.+< I •» I I A. T =X+» T - t T + l k = x i I>I+ i T - I I A yes r=x+1 FIGURE B.2 (cont.) 1 T-( T = I 1 «I + I T=3"+| SQXQAR = O.o SMALL F = FLMTO • 6 . 0 N D F 1 - RNt S S C O L I = l . O s s o n o i = 5 S C O L I • c s _ x h k H H N D F 3 = KMT -RR PHiRES = " O F 3 S S C O U 3 = A K | T > | I K SSOR«3 = S S C O L 3 • C S X < K H k K SMCOLJ t _JSC6__/CRWt - R R > - / S M O R 5 3 - S S O W - 3 / ( R » J 1 - R R ) * V N D F Z - RR S S C O L 2 = , 1 . 0 - A H K , K K S S O R S 2 _ 5 S C O L 2 • C S * * „ K , K K SMCO-R •• S S C O L _ / R R S M O M Z t 5 - O R . 2 / R R F R A T I O = S « O R _ . / S M O R « 3 VBfVR = S K K K / R N I* It I J . Include Fo r STPREG I t » X X S T O R I K = t t 4-KK LX i i ; = O i X - I 11 r L l ; I K - X T + K K V 6 3 FPftR M W- u= T>W_R_S • / csxx STeRBfi a SQPX < SMoRS. 1 • A I K > L K /CSKX^-.i ) S»xDAR. = S_*B*R+*&AA '&„ B B = V B f l n - S » » B R R Rsq= (i-o-A k K >_ k ) - 160.0 PELtf1= SMAU.F I u- -RR. = R R • NCALC = NPRCO + I J T = I TL= JJ-I PQII * B 8 I 11 = L I . ves P Q X I = P O I . ^ i PC*.,,, = P « X t ^ +COIW I X = T . * I l A H S - , - 1 NVtF+MA -I RWM r N N F F - N H P I • | TT - 8 T L = TT -\ X L I = NN F I + T L X L F - N N P F +TL S E R R Q R = O.O X c X L t S.RROR = SERROR + EP.ROSi,;_ X - I + l E ME AN j j = SeRROR/RMM SUMS<5 = -5.0 T T= X L I I S U M S Q - SuM-Q +-( E R R O S ; ^ , - -MEANj,)* STDEV__ « SqWT (-UPLSQ/nMM-W)' CONFSOj. ~ L_4S • STOT_VJ( COMPSSjj E l - 6 0 • STBEV I (a) P r e d i c t i o n Routine FIGURE B.3 Flow Diagram (b) •Z-TEST ROUTINE 84 Computer Program f o r 3-Day P r e d i c t i o n Model SIRFTC MAIN C P 6 8 0 1 2 5 B l 3 "C" DATA l. A N G E 0 1 9 6 0 H , B 15 TO 128 C PROG QUICK RUNTHRO C LARGE WATERSHED, NPRED = 3 DAYS C MAI = CONST. C P . G . SI MR EG »MULREG OR S T P R E G , P R E D . AND ERROR STAT PI HENS ION X ( 150 , 2 0 ) ,G T( 1 50 ) ,TMAX ( 150 ) , TMLNC 150) , T[ 1*50) , ST I ( 150) , 1SGI ( 150 ) ,R I 1 5 0 ) , SX ( 20 ) ,CSX*,( 20 , 2 0 ) , A ( 41 ,41 ) , E( 41 ,41 ) , V< 20) , FPAR ( 15 2 0 , 2 0 ) , S T E R B ( 2 0 ) , L I ( 2 0 ) , B ( 2 0 ) , E R R O R ( 1 5 0 ) , I D A Y ( 1 5 0 ) , E M E AN{10) , 3 STDEV (10 ) , C O N F 9 0 ( 1 0 ) , C G N F 9 5 ( 1 0 ) ,ERRDS( 1 5 0 , 1 0 ) , P Q I ( 1 5 0 , 1 0 ) , C O R R S ( 15 4 0 ) , I A M S ( 1 5 0 ) , 1 A N S ( 1 5 0 ) , S T D E V Y ( 150) ,RSQS( 150 ) , AA A ( 20 ) , BBB ( 2 0 ) , 5 S E R 0 R Y I 2 0 ) , 3ER0RB (20 ) , F R A T ( 1 5 0 , 2 0 ) , R C O R ( 2 0 ) _C READ IN BASIC DATA  C ACTUAL PRED RUN WOULD STORE ONLY DATA TO NNFI C HERE WE ARE STORING DATA TO NNFF C DATA FOR TRANS AND PRED READ (5 ,9 ) MA , MI A ,MA I I A, NNF I A , N N F F A , N F A , NPRED, R I , C , D, M S STA , M S SQ A , I I YEAR 9 F O R M A T ( 7 1 3 , 3 F 6 . 2 , 2 I 3 , 1 5 ) C DATA FOR STPREG-GFK R E A D ( 5 , 7 8 ) K K , F- L MT I , F 1. MT 0 78 FORMAT ( 1 3 , 2 F 6 . 3 ) RE A D ( 5 , 1 0 ) K 10 FORMAT!12 ) C MA.EQ.CONST USED TO SAVE STORAGE SPACE C MI . L E . M A I I - N P R E D C MSST .GE .M I C MSSG.GE .MI H = MA-MA+1 MI = MI A-MA+1 MAI 5 = MAI 1A-MA+1 NNF I = NNFI A-MA +I NNFF = NNFF A-MA + 1 NF = NFA-MA+1 MSST = MSSTA-MA+1 MSSQ = MSSQA-MA+1 R I I = UI D O 1000 J = 1 , K R E A D ( 5 , 1 ) N N N = N + M - 1 R E A D ( 5 , 2) ( f '•'AX ( I ) , I = M - N N ) R E A ! ) ( 5 ,2 ) ( T H I N ( I ) , I = M , N N ) R E A D ( 5 , 3 ) (01 ( I ) T I = V , N N ) 1 FORMAT(12) 2 F O R M A T ( 1 2 F 6 . 1 ) 3 F 0 R M A T Q 2 F 6 . 2 ) M = ?. + N 1000 CONTINUE _C CALCULATE CONSTANTS TO BE USED IN STEPREG  K I = K K -1 KF = KK+KI C T l I NT IAL TRANSFORMATIONS C WILL BE USING 0 1 ( 1 ) TO NNF + 3 FOR COMPARISON C DEPENDENT V A R . E Q . X ( I , K K ) 85 c TRANSFORM T ( I ) , ST I {I ) , S O U I) FROM MI,MSSTfMSSQ TO NNF T c i n a V ( I ) , X ( I , N ) N = l - 1 0 AND 14-17 FROM MI ,MA I I TO NNFIQ c X ( I , 1 I ) , X ( I , N) N=12tl3 FROM MSST+NPRED, MSSQ+NPRED TO NNFI NNF T = NNFI-1 NNFIQ = NNFT+NPRED ST = 0 . 0 SO = 0.0 I = MI-1 6 5 I = 1 + 1 IA = I + MA-1 I F ( I A . G E . 1 . A N D . I A . L E . 3 1 ) I D A Y ( I ) = IA IF (I A . G E . .32. AND. I A . 1. F. 61 ) I D A Y ( I ) = I A - 31 I F ( I A . G E . 6 2 . A N D . I A . L F . 92) I D A Y ( I ) = I A - 6 1 I F d A . G F . 9 3 . AND. I A . L F . 122) I D A Y ( I ) = IA - 92 I F ( I A . G E . 1 2 3) I D A Y ( I ) = IA - 122 IF< I . G T . N N F T ) GO TO 66 H I ) = ( O T M A X U ) + (1,0-C ) *TP IN ( I ) ) - D IF ( I . L T . M S S T ) GO TO 6* 6 662 STI ( I ) = SI+T( I ) ST = ST I ( I ) 6 8 I F ( I . L T . M S S Q ) GO TO 66 - . 6663 S G I ( I ) = SC+GI (1) SQ = SG1 (I ) 66 KL = MSST+3 I F ( I . L T . K L ) GO TO 688 6664 X( 1,11.) = STI ( 1-3) 6 88 KL = MSSQ+3 I F ( I . L T . K L ) GO TO 69 6665 X ( I , 12 ) = S O U 1-3) X ( I , 1 3 ) = S G I ( 1 - 3 ) * S Q I ( 1 - 3 ) 69 IF ( I . L T . M A I I ) GO TO 7C 6667 R ( I ) = R I X ( I , KK) = 01 ( I ) X < I , 14 ) = R ( I ) X ( I , 1 5 ) = R ( I ) * R( I ) X ( I , 1 6 ) = ALOG(R ( I ) ) • R I = R ( I ) + 1. 0 X ( I , 1 ) = T ( 1 - 3 ) X( I , 2 ) = T( 1-4) X ( I , 3) = T ( 1 - 5 ) X I I , A) - T l l - f c l X( I , 5 ) = T ( 1 - 7 ) XJ I f 6 ) = T( I -3 ) *T ( 1-3) X ( I , 7 ) = T ( 1 - 4 ) * T ( 1 - 4 ) X( I , 8) •= T( 1-5 )*T ( X ( I , 9 ) = T( 1-6)*T( 1-6) X ( I , 1 0 ) = T t 1 - 7 ) * T ( 1 - 7 ) 7 0 I F ( I . L T . N N F I G ) GO TO 65 C DA ILY DO DO 9 0 0 0 J I I = NNF I ,NNF F  NNF = J 11 I = J I I C T2 DAILY TRANSFORMATIONS T ( I ) - ( C * T M A X ( I ) + (1,0-C ) *TM IN ( I ) ) - D STI (I ) = ST + T{I ) 86 ST = STI (I ) SQI ( I ) = SCJ + O K I ) SG .= S G I ( I ) 1 = 1 + NPRED IA = I + MA-]. IF ( I A . G E . L A N D . I A . L E . 31) I D A Y ( I ) = I A I F ( I A . G E . 3 2 . A N O . I A . L E . 61 ) I D A Y ( I ) = I A - 3 1 I F ( I A . G E . 6 2 . A N D . I A . L F . 92 ) I D A Y ( I ) = IA - 61 I F 1 I A . G E . 9 3 . A N D . I A . L F . 1 2 2 ) I D A Y ( I ) = IA - 92 IF ( I A . G E . 123) I D A Y ( I ) = I A - 122 R ( I ) = R I RI = R ( I ) + 1.0 X ( I , 1 ) = T ( I - 3 ) X( I , 2) = T( 1-4 ) X ( I , 3 ) = T t 1-5 ) X (I , 4 ) = T (1-6) X ( I , 5) = T U - 7 ) X ( I , 6 ) = T ( 1 - 3 ) * T ( 1 - 3 ) X ( I , 7) = T( 1-4 ) *T ( 1-4) X ( I , 8 ) = T ( 1 - 5 ) * T ( 1 - 5 ) X ( I , 9 ) = T( I-6.)*T ( 1-6) X ( I , 1 0 ) = T ( I - 7 ) * T ( 1 - 7 ) X( I ,11 ) = ST I (1-3) X ( I , 12 ) = SC I (1-3 ) X( I ,13 ) = SQI( 1-3) * SQI (1-3) X { I , 1 4 ) = R ( I ) X ( I , 15) = R I D * R ( I ) X( I , 16) = A L C G ( R ( I ) ) X ( 1 , 1 7 ) = 0 1 ( 1 ) I = J I I G REGRESS IO N ANALYS IS e c u MAI = 30 - MA + 1 801 0 M • = MA I NN = NNF RN = NN-M+l KI = KK- 1 KF=KK+KI KKK=KK+1 c STPREG -GFK c STEPWISE REGRESSION SUBROUTINE G I . SET UP AUGMENTED CORRELATION MATRIX A ( I , J ) DO 5 0 J= 1. , K K S X J = 0. 0 DO 60 1= M,NN S X ( J ) = S X J + X( I , J ) SXJ =SX ( J ) 60 CONTINUE 50 CONTINUE DO 100 K = 1 , K K DO 110 J = K ,KK • . SXX =0.0 DO 120 I=M,NN SXXKJ =SXX +X( I , K ) * X ( T, J ) SXX =SXXKJ 120 CONTINUE 87 C S X X ( K F J ) = S X X K J - ( S Y ( K ) * S X ( J ) / R N ) 1 1 0 C O N T I N U E 1 0 0 C O N T I N U E 0 0 2 0 0 K = 1 , K K K M 1 = K - 1 D O 2 1 0 J = K T K K . A ( K , J ) = C S X X ( K , J ) / S O R T (CS XX ( K , K ) *CSXX ( J , J ) ) _21 0 C O N T I N U E  I F ( K . E Q . l ) G O T O 2 0 0 D O 2 2 0 J = 1 , K M 1 A ( K , J ) = A ( J , K ) 2 2 0 C O N T I N U E 2 0 0 C O N T I N U E D O 2 3 0 K = K K K T K F L = K - K K D O 2 4 0 J = 1 , X F I F ( L . E C . J ) G C T O 2 4 1 A ( K , J ) = 0 . 0 G O T O 2 4 0 241 A ( K , J ) = - 1 . 0 2 4 0 C O N T I N U E 2 3 0 C O N T I N U E D O 2 5 0 K = 1 , K K D O 2 6 0 J = K K K , K F L = J - K K I F ( L . E Q . K ) G O T O 2 6 1 . A ( l< , J ) = 0 . 0 G O T O 2 6 0 2 6 1 A ( K , J ) = 1 . 0 2 6 0 C O N T I N U E 2 5 0 C O N T I N U E 0 0 6 6 6 6 I I = 1 , K M J B B B ( I I ) = C S X X ( T F . K K ) / C . S X X ( I I , I I ) A A A ( I I ) = { S X ( K K ' ) / R N ) - 8 P B ( I I )*SX{ I I ) / R N S E R O R Y ( I I ) = S C . R T ( (CSXX (KK-KK)-CSXX( I I»KK)**2/CSXX( I I , I I ) ) / ( R N - 2 . ) ) S E R O R B ( I I ) = S O R T ( ( S E R O R Y ( I I ) * * 2 ) / C S X X ( I I , I I ) ) F R A T ( N N F , I I ) = ( ( C S X X ( I I , K K ) * * 2 )/C S X X( I I , I I ) ) / S E R O R Y ( I I )**2 R C 0 1 U I 1 )=CSXX( I I ,KK ) / SORT(CSXX( I I , I I ) * C S X X 1 K K . K K ) )  6 6 6 6 C O N T I N U E C I I . S T E P W I S E P R O C ED U R E R R = 0 . 0 N L = 0 M I \ / = K K - 1 N S T E P = 0 D O 9 0 0 L L = 1 , N I V M S T E P = N S T E P + 1 B I G V I = C . 0 D O 3 0 0 1 = 1 j K I I F ( N L . L T . l ) G O T O 3 0 1 D O _ J 9 0 _ _ J f l j J l L \ 1 L L = L I (" J ) I F ( I . E C . I L L ) G O T O 3 0 0 3 9 0 C O N T I N U E 3 0 1 V ( I ) = A ( I , K K ) * A ( K K , I ) / A ( I , I ) I F ( V ( I ) . 1 . T . B 1 G V I ) G O T O 3 0 0 88 B IGVI =V ( I ) _ II =1  "3 00 CONTINUE J = LL 313 L H J ) = I I C TEST FOR ENTRY O F INDF PENT ANT VAR IABLE , X ( I , I I ) RR=RR+1.0 RNI =RN-1 .0  PHI = R N I - R R FENT = { PH I * 3 I G V I ) / ( A ( K K , K K ) - B I G V I ) C ENTER ALL VAR IABLES F O R MULREG C FOR STPREG INCLUDE I F ( F E N T . L T . F L M T I ) GO TO PRINT OUT OF REGR DATA N L = N L + 1 _C ADJUST CORRELATION MATRIX FOR ENTRANCE OR EL IM INAT ION OF X ( I , I I ) L = I I K = I. IK = I I + K K GO TO A13 411 L=IK i< = L ; NSTEP = NSTEP + 1 4 13 I F ( ( - 1 ) * * N S T F P ) 4 1 4 , 4 1 5 , 4 1 6 415 PRINT 417 417 FORMAT(1 OH HELP ) 4 14 DO 400 J=1,K.F 1 = H E (" I t J ) = A ( I , J ) / A ( L , L ) 400 CONTINUE I I B =11-1 I IA =11+1 00 410 J =1,K F IF_( J __ EC . I I_. AND ._L . E G . I K ) K = II ___ "I F (71 . EOT ! j " GO" TO T o i DO 420 1 = 1 , 1 IB C I I » J ) = A ( I , J ) - A( I , L ) * A ( K , J ) / A ( L t L ) 420 CONTINUE 401 DO 4 30 1=I I A , K F EJ I , J ) = A ( I , J ) - A ( I , L ) * A ( K , J ) / A ( L _ _ J 4 30 CONTINUE K = L 410 CONTINUE 00 491 J = 1 , K F DO 492 I = 1 , K F A ( I , J ) = E d , J J 492 CONTINUE 4 ° 1 CONTINUE GO TO 501 416 DO 450 J = l , K F 1= I I i j H _ J _ = JLLi * J > / G (J:_!_L_L 4 5 0 'CONTINUE " ."" ~ 113=11—1 I IA =11+1 DO 460 J = 1 , K F I F ( J . E G . I I . A N D . L . E G . I K ) K = I I 8 9 I F ( I I.EQ.1) GO TO 451 DO 470 1 = 1, I IB M I t J ) = E ( I , J ) - E ( I , L ) * E ( K , J ) / E ( L , L ) 4 70 CONTINUE 451 00 480 I =I I A , K F A ( I t J ) = E ( I , J ) - E ( I » U * E ( K , J ) / E ( L , L ) 480 CONTINUE K = L ; 460 CONTINUE C SUMMARY OF CALCULATIONS AFTER A STEP ALSO TEST FOR ELIMINATION 501 N0F1 =RN1 SSC0L1 =1.0 SS0RG1 = S S C 0 L1 * C S X X( K K , K K ) NPF3 = R NI-RR PHI RES = N D F 3 SSC0L3 = A(KK t KK) SS0RG3 = SSCGL3*CSXX. ( YKt KK ) SMC0L3 = SSCQL3/(RNI-3R) SMURG3 = SS0RG3/(RNI-PR) NDF2 = RR : . ; SSC0L2" =1.0 - A ( K K » K~K ) SS0RG2 =SSC0'L2 * C S X X ( K K , K K ) • SMC0L2 =SSCGL2/RR . S M ORG? =SSORG?/RR FRATIG =SMORG2/SMORG3 YBAR =SX(KK)/RN ; SBXBAR =0.0 SMALLF = FLMTO*2.0 DO 7 00 J=l , -ML I I = L I ( J ) I K = I I + K K. LELII^tL;JJ_G_Q_ IQ_ 7_Q0 \ P A ( K NT ,11) = ~PHIRES*A( I I , K K ) * A { I I,KK)/(A(KK,KK ) *A( IK, IK) ) IF(FPAR(NNF , I I ).GE.SMALLF) GO TO 711 SMALLF = FPAR(NNF,II) IISTOR = 11-J J J = J 711 P ( I I ) = A ( I I , KK ) *SQRT (CSXX(KK,KK)/CSXX( I 1 , I I ) ) ' STEKB ( 11 ) = S~3RT ( SM0K"G3*~A ( IK, IK ) / C S X X ( 11,111) XB A R =SX(I I)/RN SBXBAR = S B X R A R + XBAR*B(II) 700 CONTINUE 712 RB = YBAR - SBXBAR RSC = ( 1. 0 - A ( K K , K K ) ) * 10 0 . 0 . "STDFVR = SORT(SM0RG3) FELIM = SMALLF TEST FOR ELIMINATION CF VARIABLE X ( I , I I ) WITH SMALLEST F ELIM MO VARIABLES GO TO 900 II = IISTOR  IK = II + K K L I ( J J J ) = 0 RR=RR-1.0 GO TO 41 1 900 CONTINUE 90 C PRINT SIMREG AND STpREG OR MULREG 502 I AM = MAI + MA - 1 I A r\ = N H E + MA-1. PRINT 6 6 7 , I AM, I AN 667 FORMAT { OH 1 I AM. = , I 4 , 7 H I AN = , 1 4 ) PRINT 668 , KK 668 F0RMAT(36H S IMPLE REGRESSION DEP .VAR X( I,, I 3 ,1H ) ) PRINT 669 ; ; 669 FORMAT ( T l l H I~NDEP. VAR . X ( I , I I ) STD~. ERROR Y A 1 B STD. ERROR B F-RATIO CORRELATION P.) KM1 = KK - ! DO 6 70 1 1 = 1 , K M l PR I NT 6 7 1 , 1 1 , S E R O R Y ( I I ) , A A A ( I I ) ,RBB{ II ) ,SERORB( I I ) , F R A T ( N N F , 1 1 ) , 1RC0R ( I I ) . "6 7 1 F 0 R M A I ( 11* X , I 3 , 9 x , 6 (" 2 X , G1 2 . 5 ) ) 670 CONTINUE PRINT 1.9,KK 19 FORMAT(36H MULREG.OR.STPREG DEP .VAR X ( I , , I 3 , 1 H ) ) PRINT 18 .NSTEP IS F O R M A T ( i S H STEP N O . , 1 3 ) PRINT 51 51 FORMAT(? 7 H DEPENDENT VAR . Y ( I ) ) PRINT 52,FRATIO 52 FORMAT(17H FRATTO , G 1 2 . 4 ) PRIM?' 5 3 , ST OF VR STDEVRES , G 1 2 . 4 ) PRINT 14 ,RSQ 14 FORMAT(17H RSQ , G 1 2 . 4 ) PRINT 15 ,BB 1.5 FORMAT (17H BB , G 1 2 . 4 ) PRINT 16 16 F0 RMA T (6 2 H INDEP . VAR. X ( I , I I ) B{ I 1) S T E R B ( I I ) FPA 1 R ( I I ) ) DO 800 J=1 ,NL 11= L 1 ( J ) I F ( I I . L T . 1 ) GO TO BOO PRINT 17 , I I , B ( I I ) ,S T E RB( I I ) , F P AR(NN F, I I ) 17 FORMAT! 1 5 X , 1 2 , 9 Y , 3 G 1 2 . 4 ) 800 CONTINUE C PREDICT ION ROUTINE 513 NCA LC = NPREC+l I = NNF DO 2CG0 ..IJ = 1,NCALC JL = JJ-1 P O I I = BB DO 2100 J = 1. ,NL i r = L i ( J ) IF ( I I . LT. 1. ) GO TO 2 1 0 0 P Q I ( I , J J ) = P O I I + (B (I I )*X( I , I I ) ) PQI I = PQI ( I , J J ) 2100 CONTINUE CORR = 01 (NNF) - P Q U K M F , 1 ) IF ( I . E C . N N F ) GC TO 20r\ PQ I ( I , J J ) = P Q I ( I , J J ) + CORR E R R O S f l . J L ) = ( P QI ( I , J J ) / 0 I ( I ) - 1 . . 0 ) * 1 0 0 . 0 91 2001 1 = 1 + 1 2000 CONTINUE  CORKS(NNF)=CQKR IAMS(NNF)=HAI+MA-1 IANS(NNF)=NNF+MA-1 STDEVY(NNF)=STDEVR RSQS(NNF)=RSG 9000 CONTINUE  C PRINT PRED ICT ION TABLE W R I T E ( 6 , 1 1 ) IYEAR 1 1 FORMAT (1H1 , 1 0 X »60H 1 , 2 , A N D 3 DAY FRASER RIVER FLOOD FLOW PRED ICT10 IN AT HOPE ,15,/) PRINT 12 12 FORMAT ( 113H ACTUAL 1 DAY PREDICT ION 2 DAY PREDICT ION 1 3 DAY PRED ICT ION ADJUST PREDICT ION EQUAT ION ,/ ) PRINT 13 13 FORMAT (116H DATE 0 ( 1 ) DATE 0 (1 + 1 ) ERROR DATE QU+2) ERRO IK DATE Q U + 3) ERROR CORR RSQ STDEVY MAI N N F , / ) DO 9200 I= NNF I ,NNFF PRINT 2 0 1 1 , 1 CAY ( I ) ,QI ( I ) , I D A Y ( 1 + 1 ) , P Q I ( 1 + 1 , 2 ) , E RRD S ( 1 + 1 , 1 ) ,  1 I D A Y ( I + 2 ) , P Q I ( 1 + 2 , 3 ) , E R R D S ( 1 + 2 , 2 ) , 1 DAY( 1 + 3 ) , P Q I ( I + 3 » 4 ) » E R R D S ( 1 + 3 ,3 2 ) , C O R R S ( I ) ,RSQS( I ) , STDEVY ( I ) , I AMS ( I ) , I A N S ( I) 2011 FOR MAT ( 1X , I 4 , f: 7 . 2 , 3 ( I 6 , 2 F8 . 2 ) , F 1 0 . 2 , F8 . 3, F 1 0 . 5 , 2 I 5 ) 9200 CONTINUE C COMPUTE Z-TEST ON PREDICT ION ERRORS RNN = NNFF - NNFI + 1  C TESTING DIFFERENT PPED ERRORS DO 400C J J = 2 ,NCALC JL = JJ-1 I L I = NNF I+JL ILF = NNF F +JL C CALL IM /-TEST ROUTINE ; SERROR = 0 . 0 DO 3C00 I = I L I , I L F 3000 SERROR = SERROR + E R R D S ( I , J L ) EMEAN( J L ) = SERROR/RN N SUMSQ = 0 . 0 DO 3100 I = I L I , I L F  3100 SUM SO = SUMSQ +" ( E R R O S ( I , J L ) - EME A,M( JL ) ) * * 2 STDEV ( J L ) = S O R T ( S U M S C / ( R N N - 1 . 0 ) ) C 0 N F 9 0 U L ) = 1 . 6 4 5 * S T r C V ( J L ) C 0 N F 9 5 ( J L ) = 1 . 9 6 0 * S T n E V ( J L ) 4000 CONTINUE C PRINT Z-TEST VALUES  WRITE ( 6 , 311" ' ) ( E M E A N ( J L ) , J L = 1 ,NPRED) W R I T E ( 6 , 3 1 1 1 ) ( S T D E V l J L ) , J L = 1 ,NPRED) WR I T E ( 6 » 3 1 1 2 ) (C 0 NF 9 0 ( J L ) ,J L = 1 ,NPRED) W R I T E ( 6 , 3 1 1 3 ) ( C 0 N F 9 5 ( J L ) , J L = 1 ,NPRED) 3110 FORMAT(26H MEAN VALUE OF E R R O R ( I , J L ) , 3 ( F 8 . 2 , 8 H P E R C E N T , 6 X ) ) 3111 FORMAT(26H STD DEV OF E R R O R ( I , J L ) , 3 ( F 8 . 2 , 8 H PERCENT ,6X ) )  3112 FORMAT(26H 90 PERCENT CONF INTERVAL , 3 ( F 8 . 2 , 8 H PERCENT,6X)) 3113 F0RMAT(26H 9 5 PERCENT CONF INTERVAL , 3 ( F 8 . 2 , 8 H PERCENT ,6X)/) C PRINT CONSTANTS PR I NT 2021 , MA,MI A , M A I I A , N N F I A , N N F F A , N F A , N P R E D , R I I , C , D , M S S T A , 1 M S S Q A , K K , F L M T I , F L M T O 9 2 2021 F 0 R M A T ( 10 6 H MA MIA MAI I A NNF I A NNFFA NFA NPRED RI U C D MSS TA MSSQA KK FLMTI F L MTO t / 1X , 71 7 , 2 3 F 7 . 2 , 3 I 7 , 2 F 7 . 3) C PRINT F-TABLE PRINT 3025 3025 FOR MAT (A 3 F.I 1 SUM NARY OF F-RATTOS IND VARS 1 TO 8/) PRINT 302A 3024 FORMAT ( 1321! XI X2 X3 1 XA X5 X6 X7 2 Xfi /) PR INT 302 6 3026 F 0 R M A T ( 1 X , 3 H N N F , 8 ( 0 H F - S I M R E G , R X ) / A X , 8 ( 8 X , 8 H F - S T P R E G ) / ) DO 5AO I = N N F I , N N F F PRINT 5 4 1 , 1 A M S ( I ) , (FRAT( I , J ) ,J = l , 8 ) , (FPAR< I,J ) ,J = l , 8 ) 541 F O R M A T ! I X , I 3 , G ( F 8 • 2 , 8 X ) / 4 X , 8 ( 8 X , F 8 . 2 ) ) 540 CONTINUE PRINT 3035 3035 FORMAT(44H1 PRINT 3034 SUMMARY OF F-RATIOS IND VARS 9 TO 16/ ) 3 034 FORMAT(132H X9 X10 X l l 1 X I2 X1 3 X 14 X15 2 X16 /) PRINT 3026 DO 543 I = N N F I , N N F F PRINT 5 4 1 , I ANSI I) , {FR AT{ I , J ) , J = 9 , 1 6 ) , ( F P A R ( I , J ) t J = 9 , 1 6 ) 543 CONTINUE C PRINT TRANSFORMATION TABLE PRINT 2024 2024 FORMAT(23H1 TRANSFORMED DATA/) WR I TE (6 , 2 0 2 ? ) ( (X( I , J ) ,J = 1 , 1 7 ) , I = MA I I ,NF ) 202 2 FOR M A T ( 1 X , 5 F 7 . 2 , 7 F 9 . 2 , E 1 5 . 8 , F 7 . 2 , F 9 . 2 , / 1 X , F 1 2 . 8 , F 7 . 2 ) ST_OP _ END 

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