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UBC Theses and Dissertations

Storm flows of the Lower Fraser Valley Taylor, John W. 1975

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STORM FLOWS 0? THE LOWER FBASER VALLEY by JOHN W. TAYLOR B A S c , U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B. C , 1973 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department o f C i v i 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 standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1975 In presenting th i s thesis in pa r t i a l fu l f i lment of the requirements for the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th i s thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes is for f inanc ia l gain sha l l not be allowed without my writ ten permission. Department of Cn/i( £nam€P/^/^q The Univers i ty of B r i t i s h Columbia Vancouver 8, Canada an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that ABSTRACT Un i t hydrographs are d e r i v e d f o r f o u r watersheds i n the Lower F r a s e r V a l l e y using a computerized l e a s t squares technique. These u n i t hydrographs are then r e l a t e d to s p e c i f i c b asin c h a r a c t e r i s t i c s so t h a t s y n t h e t i c u n i t hydrographs can be c o n s t r u c t e d f o r the ungauged b a s i n s i n the area. A f t e r attempting s e v e r a l techniques t o r e l a t e the u n i t hydrographs to basi n c h a r a c t e r i s t i c s both the time-to-peak and the peak flow were r e l a t e d t o the b a s i n s l o p e , shape, channel length and degree of u r b a n i z a t i o n . To more f u l l y d e f i n e the s y n t h e t i c u n i t hydrograph shape, the u n i t hydrograph widths at 50 per cent and 75 per cent of the peak flow were r e l a t e d to the peak flow. In t h i s way f i v e p o i n t s can be used to e s t a b l i s h the u n i t hydrograph shape (one f o r the peak and f o u r f o r the widths). Other r e s u l t s i n c l u d e d e s t i m a t e s of average i n f i l t r a t i o n r a t e s f o r each b a s i n c a l c u l a t e d from r a i n f a l l and r u n o f f data. i i i TABLE OF CONTENTS Page L i s t of Tables ........................................ i v L i s t of Figures v 1. INTRODUCTION 1 2. DESCRIPTION OF STUDY AREA 2.1 Introduction 7 2.2 Climate 7 2.3 S o i l s 9 2.4 Cover 12 2.5 Basin C h a r a c t e r i s t i c s 13 3. BACKGROUND 3.1 Introduction 15 3.2 The Rational Method 16 3.3 The Unit Hydrograph 19 3.4 Synthetic Unit Hydrographs 22 3.5 Urbanization 26 3.6 The Least Squares Technique 40 4. METHOD.... 44 5. RESULTS 5.1 The Derived Unit Hydrographs ..................... 48 5.2 Generalization of the Results .................... 53 5.3 The Width Relationships .......................... 60 5.4 The I n f i l t r a t i o n Rates 60 6. SUMMARY AND RECOMMENDATIONS 65 REFERENCES 69 APPENDIX - Least Squares Computer Program i v LIST OF TABLES TABLE Page 1 Basin C h a r a c t e r i s t i c s ............................... 8 2 Van Sickle's Development C l a s s i f i c a t i o n s ............ 31 3 Summary of Results ..................................48 4 I n f i l t r a t i o n Rates 62 V LIST OF FIGURES FIGURE Page 1 Study Area .......................................... 2 2 Surrey Kwantlen Park - P r e c i p i t a t i o n Data ........... 10 3 R a i n f a l l Contours for Study Area 11 4 Effect of Development on the Unit Hydrograph ........ 27 5 Time to Peak vs. Basin Factor (Van Sickle) .......... 32 6 Peak Discharge vs. Basin Factor (Van Sickle) ........ 33 7 Unit hydrograph - Hahood Creek ...................... 49 8 Unit hydrograph - Murray Creek 50 9 Unit hydrograph - Barker Creek ...................... 51 10 Unit hydrograph - Salmon River ...................... 52 11 Lag Time vs. Basin Parameter LLc ................... 54 12 Lag Time vs. Basin Parameter LLca/>/s" ............... 56 13 Lag Time vs. Basin Factor, K ....................... 58 14 Unit Hydrograph Peak vs. Basin Factor, K ........... 59 15 Unit Hydrograph Peaks vs. Widths ................... 61 ACKNOWLEDGEWENTS The w r i t e r i s indebted t o P r o f e s s o r S. 0. B u s s e l l f o r h i s encouragement and guidance i n the p r e p a r a t i o n of t h i s t h e s i s . He would a l s o l i k e t o thank h i s f r i e n d s and f a m i l y f o r t h e i r p a t i e n c e and understanding. The work was supported by a f e l l o w s h i p from the Department of C i v i l E n g i n e e r i n g which was g r e a t l y a p p r e c i a t e d . 1 CHAPTER ONE INTRODUCTION The Lower Fr a s e r V a l l e y i s e x p e r i e n c i n g c o n s i d e r a b l e change at t h i s time due mainly t o housing p r e s s u r e s from the Vancouver M e t r o p o l i t a n area. As the c i t y c o n t i n u e s to grow more c i t y d w e l l e r s are l o o k i n g f o r land and homes i n the c o u n t r y . At the same time t h e r e i s pressure f o r p r e s e r v a t i o n of the land i n i t s n a t u r a l s t a t e . The P r o v i n c i a l Government has been e s t a b l i s h i n g "green b e l t " areas and encouraging farming i n t e r e s t s to remain i n p r o d u c t i o n . The net r e s u l t of a l l these c o n f l i c t i n g i n f l u e n c e s i s t h a t land w i l l become more i n t e n s i v e l y used i n the f u t u r e , although a completely urban environment i s u n l i k e l y . Comprehensive p l a n n i n g w i l l help t o f o r e s t a l l c o n f l i c t s and ensure o r d e r l y development. A v i t a l p a r t of such planning i s the r a t i o n a l o r g a n i z a t i o n and l a y o u t of s e r v i c e s which should be p r o v i d e d at l e v e l s a p p r o p r i a t e to the v a r i o u s types of land use. One of the more important s e r v i c e s and o f t e n the most expensive i s d r a i n a g e . L i n s l e y and F r a n z i n i (1) estimate t h a t drainage accounts f o r a major p a r t of the c o s t of d e s i g n i n g and c o n s t r u c t i n g s e r v i c e s i n urban ar e a s . The most d i f f i c u l t p a r t of drainage i s f i n d i n g design f l o w s , l a r g e l y because of l a c k of data. The b a s i n s of i n t e r e s t Fig.I STUDY AREA BRITISH COLUMBIA - C A N A D A I WASHINGTON - U.S.A. 3 Are u s u a l l y not gauged and i f they are , the r e c o r d i s u s u a l l y not of s u f f i c i e n t l e n g t h . Storm p r e c i p i t a t i o n data however, are g e n e r a l l y a v a i l a b l e f o r a given area and from these, r a i n f a l l - r f r e g u e n c y curves can be obtained and used with some form of r a i n f a l l - r u n o f f r e l a t i o n s h i p s t o c a l c u l a t e design flows. Although a v a r i e t y of r a i n f a l l r u n o f f techniques e x i s t , the most widely used i s the R a t i o n a l Method. I t w i l l be d e s c r i b e d i n d e t a i l i n Chapter 3. Most a u t h o r i t i e s agree t h a t the method i s a good one f o r s m a l l areas but t h a t i t becomes u n r e l i a b l e with l a r g e r b a s i n s . The s i z e a t which i t becomes u n r e l i a b l e i s not w e l l e s t a b l i s h e d . Dalrymple (2) reccomends an upper l i m i t of 200 acres while L i n s l e y and F r a n z i n i { 1 ) suggest c a u t i o n a f t e r 10 a c r e s . In p r a c t i c e however, the R a t i o n a l Method i s used f o r l a r g e areas because th e r e i s u s u a l l y not enough data to support more ac c u r a t e methods. Another method f o r e s t a b l i s h i n g r a i n f a l l - r u n o f f r e l a t i o n s i s the u n i t hydrograph which i s a l s o d i s c u s s e d i n d e t a i l i n Chapter 3. While t h i s method can be used more c o n f i d e n t l y f o r l a r g e b a s i n s , a l a c k of data from gauged streams prevents i t s widespread use. T h i s t h e s i s d e a l s with the d e r i v a t i o n and g e n e r a l i z a t i o n of u n i t hydrograph data f o r the Lower F r a s e r V a l l e y . Four ba s i n s are analysed and the r e s u l t s are g e n e r a l i z e d to a l l the b a s i n s i n the area. To render the r e s u l t s more u s e f u l i n a d e v e l o p i n g r e g i o n such as the Lower F r a s e r V a l l e y the e f f e c t s of u r b a n i z a t i o n on u n i t hydrographs are a l s o d i s c u s s e d . Chapter 2 d e s c r i b e s the c h a r a c t e r i s t i c s of the study area 4 r e l e v a n t t o drainage i n c l u d i n g topography, s o i l s , v e g e t a t i o n , and c l i m a t e . The study area, which i s shown i n f i g u r e 1, c o n s i s t s of 360 square miles o f r o l l i n g h i l l s v a r y i n g i n e l e v a t i o n from sea l e v e l to 400 f e e t above sea l e v e l . The fou r b a s i n s analysed are the Salmon R i v e r , Mahood Creek, Murray Creek, and Barker Creek i n Whalley. The Hater Survey of Canada r e c o r d i n g s t a t i o n s are r e s p e c t i v e l y 8MH090, 8MH018, 8MH129 and, 8NHT34. Barker creek i s l i s t e d as Unnamed Creek by the Water Survey of Canada. These basins are f a i r l y r e p r e s e n t a t i v e of the area, having mainly a r u r a l c h a r a c t e r and c o n s i s t i n g of scrub f o r e s t and open pasture areas. The channels d r a i n i n g from them have r e l a t i v e l y g r a d u a l s l o p e s and c o n t a i n grass and d e b r i s . Because of the e f f e c t s of the surrounding mountains, p r e c i p i t a t i o n i n c r e a s e s i n a n o r t h e a s t e r l y d i r e c t i o n . The most severe p r e c i p i t a t i o n occurs i n the winter due to P a c i f i c storms moving i n l a n d . , The s o i l s of the area c o n s i s t p r i m a r i l y of t i l l m a t e r i a l u n d e r l a i n by a c l a y l a y e r . Pockets of peat occur i n the low l y i n g , p o o r l y d r a i n e d areas under t i d a l i n f l u e n c e s . Chapter 3 g i v e s the background t o the techniques used i n t h i s study. The R a t i o n a l Method i s f i r s t d e s c r i b e d . Then, by using t h i s method f o r comparison, the b a s i c concepts of the u n i t hydrograph are presented. An e v a l u a t i o n i s made on how w e l l the bas i n s i n the Lower F r a s e r V a l l e y conform t o the assumptions of the U n i t Hydrograph technique. A l s o o u t l i n e d i s the l e a s t squares technique f o r a n a l y s i n g the storm hydrographs. As a way of g e n e r a l i z i n g the r u n o f f i n f o r m a t i o n from each b a s i n , the concept of " s y n t h e t i c " u n i t hydrographs i s d e s c r i b e d . F i n a l l y , the e f f e c t of u r b a n i z a t i o n on r a i n f a l l — r u n o f f r e l a t i o n s and 5 p a r t i c u l a r l y the e f f e c t of u r b a n i z a t i o n on the u n i t hydrograph are d i s c u s s e d . Chapter 4 c o n t a i n s a d e t a i l e d d e s c r i p t i o n of the procedure used t o d e r i v e the u n i t hydrographs and to g e n e r a l i z e them. The c h o i c e of b a s i n s i s based on a v a i l a b i l i t y of r e c o r d i n g s t a t i o n s . The p r e c i p i t a t i o n r e c o r d s are then examined f o r s u i t a b l e storms f o r the a n a l y s i s . Next, u n i t hydrographs are obtained by computer c a l c u l a t i o n s f o r each storm. From these u n i t hydrographs, one r e p r e s e n t a t i v e u n i t hydrograph f o r each b a s i n i s determined. F i n a l l y , the b a s i n u n i t hydrographs are g e n e r a l i z e d u s i n g the s y n t h e t i c u n i t hydrograph concept. Chapter 5 p r e s e n t s the r e s u l t s of the a n a l y s i s . The b a s i n u n i t hydrographs are f i r s t presented. From these, parameters d e f i n i n g e q u i v a l e n t . s y n t h e t i c u n i t hydrographs are computed (two parameters are used to c h a r a c t e r i z e a s y n t h e t i c u n i t hydrograph) arid an attempt i s made t o f i n d a g e n e r a l r e l a t i o n s h i p between these and drainage b a s i n c h a r a c t e r i s t i c s such as s l o p e , shape arid l e n g t h of channel. Ho g e n e r a l r e l a t i o n s h i p c o u l d be found. However, when the degree of u r b a n i z a t i o n was taken i n t o account i t became apparent that the r e s u l t s f o l l o w e d a p a t t e r n s i m i l a r to t h a t found i n other s t u d i e s (Van S i c k l e , Ref. 17). I t was then p o s s i b l e to express the r e s u l t s i n terms of b a s i n s l o p e , shape, l e n g t h of channel and degree of u r b a n i z a t i o n . Thus, by measurement of these b a s i n c h a r a c t e r i s t i c s , s y n t h e t i c u n i t hydrographs can be d e r i v e d f o r ungauged b a s i n s i n the Lower Fr a s e r V a l l e y . To more f u l l y d e f i n e the s y n t h e t i c u n i t hydrograph shape, data were analysed to determine the 6 relationship of the width of the unit hydrographs in the Lower Fraser Valley to the unit hydrograph peaks. Using these r e s u l t s , four more points are available to define the shape. Other important r e s u l t s are the c a l c u l a t i o n of average i n f i l t r a t i o n rates i n the basins studied. These data would be used i n the estimation of losses to the r a i n f a l l when ca l c u l a t i n g excess p r e c i p i t a t i o n . F i n a l l y , the experience gained i n manipulating the least squares routine i s outlined since i t may be useful to other potential users. Chapter 6 summarizes the r e s u l t s and b r i e f l y discusses the recommendations for further work i n the hydrology of the Lower Fraser valley. 7 CHAPTER TWO DESCRIPTION OF THE STUDY AREA 2.J Introduction The study area, shown i n figure 1, i s roughly 12x30 miles containing a t o t a l area of 360 square miles. The land consists of r o l l i n g h i l l s varying i n elevation from sea l e v e l to 400 feet above sea l e v e l . The various basins drain i n t o either the Fraser River to the north or Boundary Bay to the south. Three recording p r e c i p i t a t i o n stations are used i n t h i s study and are shown i n figure 1. The Surrey Kwantlen Park station has 12 years of record and i s used with runoff data for Barker Creek. Surrey Municipal H a l l to the south has 11 years of record. Its r a i n f a l l data were averaged with Surrey Kwantlen Park data for use with Mahood Creek. To the east, Langley Lochiel provides data for the Murray and Salmon basins and has a record of three years. The four basins are shown i n figure 1 and t h e i r main physical c h a r a c t e r i s t i c s are summarized i n Table 1. 2.2 Climate The climate of the Lower Fraser Valley i s a modified Mediterranean type, influenced by, the surrounding mountain ranges and by the presence of the ocean. The Olympic Mountains 8 to the south, the Vancouver Island range to the west and the P a c i f i c Range of the Coast Mountains a l l a f f e c t the c i r c u l a t i o n patterns of the atmosphere above. These patterns show marked seasonal variations. The winter storms are f r o n t a l storms generally coming from the P a c i f i c from a southwesterly direction although a secondary storm path p a r a l l e l s the coast from the northwest bringing storms from the Gulf of Alaska, Generally the storms are widespread and accompanied by high winds and abundant, long duration p r e c i p i t a t i o n . In summer most of the large P a c i f i c storms are kept at sea by a high pressure area located offshore,, The wind from the coast i s d r i e r and i s directed from the west and northwest. Summer storms are generally convective and more l o c a l i n nature. (3) Table j[ BASIN CHARACTERISTICS 1 ., — |Drainage | Basin | area jSlope I(sg mi) | , + _ - j — . Mahood Cr | 7.4 1.032 Barker Cr | 0.92 |.099 Salmon R | 19.8 |.007 Murray Cr | 9.0 8 |.014 Length of Longest channel (miles) 2.3 1.55 12.4 5.2 Length to Centroid of area (miles) + 1.4 0.45 7.0 3.6 The seasonal differences i n the types of storms are r e f l e c t e d i n the p r e c i p i t a t i o n records. J . B . Wright (4) found that winter storms produce about four times as much r a i n f a l l as 9 summer storms but that the s p a t i a l d i s t r i b u t i o n i n the two seasons i s sim i l a r . The summer storms tend to be of shorter duration and higher i n t e n s i t y than winter storms. This i s i l l u s t r a t e d i n figure 2 which shows winter and summer data for Surrey Kwantlen Park, The winter storms are usually considered for design since they are larger and the antecedent p r e c i p i t a t i o n i s greater, Sporns (5) found that 93% of the largest annual one day storms analysed between 1925 and 1961 occurred between the months of October and February. Because there are few recording stations i n the area the s p a t i a l d i s t r i b u t i o n for i n d i v i d u a l storms cannot be adequately determined. Therefore, the storms recorded at each p r e c i p i t a t i o n station are assumed to be uniform over the corresponding basin. On a broader basis however, the records of daily p r e c i p i t a t i o n stations reveal that the annual p r e c i p i t a t i o n increases i n a northeasterly d i r e c t i o n as shown i n figure 3, 2.3 S o i l s The s o i l s of the area f a l l into two broad categories: peat and p o s t - g l a c i a l t i l l . T i l l i s found on the uplands of the region and covers most of the study area including the four basins analysed. I t consists of sandy or clay loam with a medium permeability. Much of the area contains a layer of cemented material or boulder clay at a depth of three feet. This subsurface layer i s usually semi-permeable and i s sometimes completely impermeable.(6) F i g . 2 SURREY KWANTLEN PARK - PRECIPITATION DATA I i i i i i 60 2hl20 Duration - minutes 6h 360 I2h720 24h 1440 Fig.3 RAINFALL CONTOURS FOR STUDY AREA 12 The major peat areas in the study area are shown i n figure 1. In these low lying areas periodic flooding has deposited fi n e material on the land, A combination of t h i s and dead organic matter has caused the formation of peat. Since the runoff from these peat areas i s believed to be quite d i f f e r e n t than the rest of the area they are not included i n the study. 2.4 Cover The runoff from an area i s greatly affected by the type of cover i n the basin and hence by the land use. The study area has mainly a r u r a l character with the amount of development decreasing with the distance from Vancouver. The most r u r a l of the basins are the Hurray and Salmon which d i f f e r i n s i z e and shape but have similar drainage conditions. Most of the area in these basins consists of scrub forest with f i r and alder. The forest f l o o r i s covered with a carpet of r o t t i n g leaves and twigs.. These wooded areas are broken by pasture and cu l t i v a t e d land for the few commercial farms i n the region. Dotted throughout are small hobby farms and houses b u i l t on large l o t s . The natural channels i n these r u r a l areas meander through shallow gorges and are f i l l e d with debris such as broken branches, leaves and moss. Ditches p a r a l l e l the roads and eventually empty t h e i r contents into the natural channels. The ditches are up to four feet deep and generally are no more e f f i c i e n t than the natural channels. 1 3 2.5 Basin Characterstics The Mahood basin i s situated closer to Vancouver and so i s s l i g h t l y more developed than the Salmon and Murray basins. The character of the Mahood watershed remains generally as described above but with more single family dwellings. Although there are several groups of r e s i d e n t i a l areas i n the watershed, no large impervious area e x i s t s . The Mahood basin i s also characterized by two major branches which flow from nearly opposite d i r e c t i o n s . The southern branch has a drainage area about twice as large as the northern branch., From examination of many storm hydrographs, i t seems that the times to peak of the two branches are about the same. The southern branch contributes more flow because of i t s greater area. To determine the c h a r a c t e r i s t i c lengths f o r r e l a t i n g basin parameters to the unit hydrograph data, a weighted average based on r e l a t i v e basin s i z e was used. The area closest to Vancouver has experienced considerable development which has an e f f e c t on the runoff from the area. Along Highway 99 just south of the Fraser River are many commercial establishments and adjacent to the highway on both sides are single family dwellings and appartment buildings. The area i s drained by roadside ditches or by storm sewers depending on the building density. This urbanized area i s located almost completely within the watershed of Barker Creek and has caused about H0% of the watershed to be impervious. Because of thi s development three changes i n flow can be expected: higher peaks, greater runoff volume and e a r l i e r peaking. The channel however. 14 i s c l u t tered with debris which causes ponding in some sections alternating with sections of rapid flow. Under these conditions the e f f e c t s of overland flow from the developed areas upstream are somewhat subdued and i t i s f e l t that i n e f f e c t , the flow regime approaches that of the more r u r a l basins studied. From the discussion above i t i s evident that each of the four basins has c h a r a c t e r i s t i c s which are unlike the other basins. The conditions for generalizing the data to other basins are not i d e a l . , However, while the d e t a i l s of runoff from each basin may d i f f e r , i t i s f e l t that i n general, the mechanisms of runoff are the same. 15 CHAPTER THREE BACKGROUND 3,1 introduction The c a l c u l a t i o n of runoff from a drainage basin i s a necessary step i n the design of many water resource projects. Although a dire c t r e l a t i o n s h i p between storm flows and t h e i r respective frequencies i s needed, so few basins are gauged that, as a r u l e , t h i s information i s not available. Designers have been forced to use techniques which make up for t h i s lack of data. / Since p r e c i p i t a t i o n data i s often more readi l y available than flow data, c l i m a t i c information i s usually analysed to establish frequency of occurrence. The hydrologist i s then l e f t to establish the relationship between r a i n f a l l and runoff from a basin. There are two widely used methods for establishing t h i s r e l a t i o n s h i p : the so c a l l e d Rational Method and the Unit Hydrograph Method. Although they have t h e i r shortcomings both have the advantage of being simple and r e l a t i v e l y s traight forward to apply. Neither require excessive amounts of data as would more sophisticated and perhaps more accurate methods. The Rational Method can be considered a s i m p l i f i e d version of the Unit Hydrograph Method. I t i s discussed in the following 16 section. Next, the Unit Hydrograph Method and i t s l i m i t a t i o n s are discussed. As a way of generalizing unit hydrograph information to other basins, synthetic unit hydrographs are used and these are described i n d e t a i l . The e f f e c t s of urbanization on runoff are considered including how the r e s u l t s of t h i s study may have to be modified to account for i t . F i n a l l y , the storm hydrographs i n t h i s study were analysed using a least squares technique i n a computer program and since i t i s a r e l a t i v e l y new technique the mathematical basis and biases inherent i n i t are discussed. 3.2 Rational Method The Rational Method i s the most widely used technique in drainage design. Although treated with skepticism by some, i t i s generally considered accurate enough for small basins, Schaake, Geyer, and Knapp (7), i n t h e i r experimental investigation of the method found that i t s inherent assumptions were reasonably good for small basins and low return periods. This limited accuracy coupled with i t s s i m p l i c i t y have been the main reasons for i t s widespread use. Over the l a s t f i f t y years i t has been used to design b i l l i o n s of d o l l a r s worth of drainage f a c i l i t i e s and, while t h i s t r a d i t i o n of use does not j u s t i f y i t s existence i t does i l l u s t r a t e that the method i s at least reasonably successful. This section discusses the Rational Method and i t s l i m i t a t i o n s and assumptions. The Rational Method was o r i g i n a l l y proposed by Kuichling{8) i n 1889, Although variations on the technique have been 1 7 developed i t has remained as o r i g i n a l l y proposed. The basic formula i s Q = CIA (1) Q = peak discharge i n c f s , C = runoff c o e f f i c i e n t dependent on basin char-a c t e r i s t i c s , I = average r a i n f a l l i n t e n s i t y for a duration egual to the concentration time and for a s p e c i f i c return period. A = area of drainage basin in acres. One of the underlying assumptions of the Rational Method i s that af t e r a c e r t a i n length of time, referred, to as the time of concentration, the runoff from the most remote area of the drainage basin begins contributing to the storm flow. The i n t e n s i t y of r a i n f a l l corresponding to t h i s length of time and to a s p e c i f i c return period i s chosen as the design i n t e n s i t y , I i n equation ( 1 ) . As the size of basin increases the time of concentration becomes greater. A point i s reached i n size at which the steady state condition i s r a r e l y , i f ever achieved. The runoff from a basin of t h i s size would be i n c o r r e c t l y estimated by the Rational Method., In contrast, the Dnit Hydrograph technique described i n the next section assumes that the steady state condition i s not reached. Instead of a constant rate of outflow t h i s technique considers a storm hydrograph to be constructed of a series of hydrographs added together. One r e s u l t of the difference i n assumptions of the 18 two techniques i s that the unit hydrograph can be used for large basins. One of the problems of the Rational Method i s choosing an appropriate time of concentration for the s i z e and drainage conditions i n the basin. I t cannot be calculated accurately because the d e t a i l s of the drainage phenomenon are usually not well enough known. Designers have been forced to use handbook methods or rough formulas based on assumed hydraulic c h a r a c t e r i s t i c s . This continues to be a weakness of the method. Another assumption basic to the Rational Method i s that the losses from r a i n f a l l represented by the runoff c o e f f i c i e n t , C, are a fr a c t i o n of the r a i n f a l l and that t h i s f r a c t i o n i s constant throughout the storm. The c o e f f i c i e n t must account f o r such losses as i n f i l t r a t i o n , depression and detention storage and channel storage. These losses tend to be higher at the st a r t of a storm. It can be seen that the choice of the runoff c o e f f i c i e n t requires considerable judgement of the c l i m a t i c and physiographic conditions of the basin. Unless the choice i s tempered with experience t h i s step i n the design process can be weak. , It i s assumed that the p r e c i p i t a t i o n i s uniform over the drainage basin. Since the pro b a b i l i t y of uniform p r e c i p i t a t i o n decreases for larger basins t h i s assumption further l i m i t s the size of basins suitable for the Rational Method.„ F i n a l l y , the method assumes that r a i n f a l l has a constant i n t e n s i t y over the time of concentration. Since t h i s time i s at 19 least ten minutes even for small basins, and i t i s unlikely that the i n t e n s i t y w i l l remain uniform for even t h i s duration, t h i s assumption represents another approximation. In summary, although the Rational Method i s reasonably accurate for small basins i t becomes unreliable for larger basins. The Unit Hydrograph technique, described i n the next chapter, retains much of the s i m p l i c i t y of the Rational Method and i s more accurate for larger basins. 3.3 The Unit Hydrograph The basic concept of the unit hydrograph i s that i f s i m i l a r storms could occur over a drainage basin under i d e n t i c a l i n i t i a l conditions, the runoff hydrographs of these storms would be the same. This concept has led to the use of a c h a r a c t e r i s t i c hydrograph c a l l e d a unit hydrograph to represent a l l of the basin parameters a f f e c t i n g runoff. Sherman (9) was the f i r s t to propose the unit hydrograph p r i n c i p l e i n 1932. although developments have been made from i t such as the instantaneous unit hydrograph and the nonlinear unit hydrograph the basic concept has remained as o r i g i n a l l y proposed. A more precise d e f i n i t i o n of the unit hydrograph i s that i t i s the amount of d i r e c t runoff from an e f f e c t i v e r a i n f a l l of constant i n t e n s i t y fo r a unit duration. E f f e c t i v e r a i n f a l l i s that portion of the r a i n f a l l which enters the stream channel. Direct runoff was defined by Sherman to be the sum of the surface flow and interflow. However, i t i s f e l t that for the small basins in the Lower Fraser Valley the interflow component does not contribute 20 to the storm peak. Direct runoff then, refers only to surface flows i n t h i s study. The volume of runoff from a unit hydrograph i s usually adjusted to contain one inch of r a i n f a l l over the drainage basin.. A storm hydrograph f o r a basin can be synthesized by multiplying each ordinate of the unit hydrograph by the t o t a l r a i n f a l l volume i n inches. For storms of more than one unit duration the unit hydrographs are multiplied by the volume of e f f e c t i v e r a i n f a l l and superimposed upon one another with each successive hydrograph lagged by one unit duration. In t h i s study a unit duration of one hour was chosen since the r a i n f a l l and stage records are published for these durations. For Barker Creek a one hour duration may be too long to adequately represent the runoff i n the basin. The U.S. Bureau of Reclamation(10) i n i t s handbook "Dnit Graph Pro-ceedures", states that the "unit duration should not exceed about one fourth or at most one t h i r d of the concentration time of the basin". The concentration time for Barker Creek i s two hours. One of the underlying assumptions of unit hydrograph theory i s that unit hydrographs can be added l i n e a r l y to synthesize a storm hydrograph.. Researchers (11) have found that t h i s assumption of l i n e a r i t y i s a ctually violated by such influences as time of year and magnitude of the storm. Although attempts have been made to incorporate these e f f e c t s into unit hydrograph theory, nonlinearity remains primarily a research concern. For each additional parameter being considered, the data 21 requirements increase many times. In p r a c t i c a l hydrology i t seems that finding even the most basic data i s d i f f i c u l t enough and t h i s i s no less true i n the Lower Fraser Valley. It i s f e l t that to assume l i n e a r i t y i n t h i s study does not decrease the value of the r e s u l t s . Another assumption of the unit hydrograph i s that the hydrologic response of a basin which depends on c h a r a c t e r i s t i c s such as slope, shape, and channel geometry can i n fact be represented by a unit hydrograph. This i s not s t r i c t l y true since some basin c h a r a c t e r i s t i c s such as i n f i l t r a t i o n rate and condition of the channel do change from storm to storm. Also, each storm upon which the analysis i s based i s unique in i t s d i s t r i b u t i o n over the basin and i n i t s time-intensity r e l a t i o n . The d i f f e r e n t combinations of i n t e n s i t i e s and durations of the r a i n f a l l earmark each storm unit hydrograph. Therefore, in practice each storm produces a d i f f e r e n t unit hydrograph. The differences however, are usually small enough that a representative unit hydrograph can be e a s i l y defined. Unit hydrograph theory assumes that storms are uniform s p a t i a l l y throughout the entire basin. This i s not s t r i c t l y true as pointed out above but i f the basins are small enough, fo r p r a c t i c a l purposes i t i s reasonably true. The r a i n f a l l i s also assumed to be uniform f o r the length of time of the unit duration, which i n t h i s study i s one hour. Again, i t i s unlikely that a storm would be uniform for such a length of time even for the long duration, low i n t e n s i t y storms which occur in the Lower Fraser Valley. An average i n t e n s i t y i s assumed in the 22 analysis and t h i s i s usually accurate enough for p r a c t i c a l purposes. From the discussion of the unit hydrograph above some of the advantages of the technique become apparent. The unit hydrograph i s a single curve which describes the complex runoff process occurring i n a basin. It can be used on large basins with reasonable accuracy and i s only s l i g h t l y more complex than the Rational Method. Unlike other simple methods, the technique produces an entire storm hydrograph so that routing i s possible i n design. The data requirements consist of the r a i n f a l l and corresponding runoff of only a few major storms. These advantages make i t an a t t r a c t i v e technique. The derivation of unit hydrographs for gauged streams i s reasonably simple. However, since the majority of streams are not gauged, techniques have been developed to generalize unit hydrograph data to these ungauged streams. One such technigue, the synthetic unit hydrograph, i s used i n t h i s study and i t i s discussed i n the next section.. 3.4 Synthetic Unit Hydrographs In 1938 F. F. Snyder (12) related unit hydrograph character-i s t i c s to watershed parameters based on data collected i n the Appalachians. Since then his relationships have been widely used for deriving unit hydrographs, c a l l e d synthetic unit hydrographs, for ungauged basins. The o r i g i n a l r elationships that he defined are given below. 23 .3 tp = (Ct) (Lc«L) (2) Qp = (Cp) (640) (A)/tp (3) t r = tp/5.5 (4) T = 3+3(tp/24) (5) tp = Lag i n hours defined as the difference in t i n e between the center of gravity of the r a i n f a l l and the peak discharge. Lc = Distance along the r i v e r from the station to the center of the drainage area. L = Length of the basin measured along the r i v e r . Qp = Discharge at design point i n c f s . T = Time base of the unit hydrograph i n days. t r = The unit duration of r a i n f a l l excess in hours. Ct •= The c o e f f i c i e n t r e l a t i n g to slope and storage and hence to the time of peak, Cp = A c o e f f i c i e n t related to the s i z e of the peak. As a further aid i n constructing unit hydrographs the U, S, Army Corps of Engineers (13) related the width of the unit hydrograph to the peak flow according to equations (6) and (7), W{50) =770/q*.oa ( 6 ) »(75) =U40/g».O8 (7) W(50) and W(75) are the widths in hours of the unit hydrographs at 50 per cent and 75 per cent respectively of the peak flow. g i s the peak runoff i n cfs per square mile. For the purposes of t h i s study two changes are made in Snyder's equations so that the synthetic relationships w i l l be more suitable for the Lower Fraser Valley. These changes are discussed below. Equation (5) i s not suitable for determining the time base of the unit hydrograph because i t was developed to account f o r subsurface flow. As discussed e a r l i e r i t i s f e l t that the subsurface flow does not contribute appreciably to the storm peaks i n the Lower Fraser Valley. For these basins, equation (5) would overestimate the length of the recession part of the curve. In order to determine the lengths of synthetic unit hydrographs an area proceedure i s reccomended. The proceedure involves adjusting the area under the unit hydrograph by changing the length of the recession. Five points for the synthetic unit hydrograph are known from basin parameters(four width points and one for the peak). A smooth curve through these points plus a guess for the recession curve w i l l determine a unit hydrograph. If the volume of runoff i s not one inch, the recession curve i s lengthened or shortened u n t i l the volume does contain one inch. The corresponding unit hydrograph length i s 25 the synthetic length. The d e f i n i t i o n of the lag time tp, must be altered s l i g h t l y to conform to the type of analysis carried out in t h i s study. The d e f i n i t i o n proposed by Snyder was designed to be used f o r storms of constant i n t e n s i t y and for the technique of simply dividing each ordinate of the storm hydrograph by the t o t a l volume of runoff to produce the unit hydrograph. The larger, more complex storms used i n t h i s study have secondary peaks and the r a i n f a l l i s far from uniform. The use of the least squares technique described l a t e r further complicates the cal c u l a t i o n of the lag by Snyder's method because i t divides the storm hydrograph into a se r i e s of unit hydrographs. For t h i s study the l ag i s defined as the time difference between the derived unit hydrograph peak and the middle of the unit duration. In 1959 Lin s e l y , Kohler and Paulhus{14) introduced an expression for basin lag much l i k e Snyder's but based on studies i n C a l i f o r n i a watersheds. I t takes the form of equation <8). .5 n tp = Ct(L*Lc/S ) (8) The symbols appearing before have the same d e f i n i t i o n s and S i s the average basin slope. The authors found Ct to be dependent on the type of basin and c l a s s i f i e d t h e i r r e s u l t s into valley, f o o t h i l l , and mountain drainages. The corresponding values of Ct vary between 0.35 and 1.2 and n was found to be 0.38 for C a l i f o r n i a watersheds. Since 1959 the form of equation(8) has come into common usage for 26 description of basin c h a r a c t e r i s t i c s . It i s often used instead of Snyder's equation ( 2 ) although with a d i f f e r e n t c o e f f i c i e n t , Ct. In Chapter 5 , Snyder's c o e f f i c i e n t s are calculated from the data analysed in t h i s study. These can be used in conjunction with equations ( 2 ) to (7) to c a l c u l a t e the synthetic unit hydro-graph for an ungauged basin. I t i s well known that the runoff from a basin i s affected by urbanization within the basin. Often t h i s change in runoff must be estimated before the development of the basin occurs. The following section considers how t h i s might be done. 3 . 5 Urbanization As mentioned e a r l i e r , development i s creating a need for more and better drainage f a c i l i t i e s i n the Lower Fraser Valley. Coupled with t h i s need however, i s a lack of knowledge of how to design for the e f f e c t s of urbanization. The problem i s that while r a i n f a l l - r u n o f f r e lationships are reasonably well established for r u r a l watersheds, no general relationships e x i s t f o r urban development i n a basin. This thesis was not intended to e s t a b l i s h such a r e l a t i o n s h i p from experimental r e s u l t s . However, the usefulness of the r e s u l t s of t h i s thesis i s at least partly dependent on how they can be used to account for the future urbanization of the area.. This section f i r s t describes the e f f e c t s on the storm hydrograph due to urbanization of a basin. next, the problem of how to design for urban development i s considered and the approaches used by other 27 researchers i s reviewed. F i n a l l y , the problem of design in the Lower Fraser Valley i s discussed. I t i s generally accepted that urbanization of a watershed changes two physical c h a r a c t e r i s t i c s of a basin which a f f e c t the runoff. The f i r s t i s an increase in the amount of impervious area due to pavement, parking l o t s , roofs etc. The second i s the establishment of smoother and more e f f i c i e n t channels. The net r e s u l t of these two changes i s a higher storm runoff peak due to less i n f i l t r a t i o n and a decrease i n the time to peak because the time of concentration i s l e s s . The increase i n the t o t a l runoff i s not as s i g n i f i c a n t as i s the greatly accentuated rate at which the runoff occurs. The e f f e c t s of urbanization on runoff are i l l u s t r a t e d i n figure 4. Fig.4 E F F E C T OF D E V E L O P M E N T ON UH Time 28 Some researchers have found that the magnitude of the increase becomes less s i g n i f i c a n t f or floods of increasing magnitude. These r e s u l t s are summarized by Espey and Winslow (15)., Martens found that.for the L i t t l e Sugar watershed i n Horth Carolina the increase i n peaks due to urbanization were as follows: 1) for the mean annual flood a 58% increase, 2) for a ten year flood a 30% increase, and 3) for a twenty year flood a M% increase. Anderson further states that his study of a northern V i r g i n i a watershed indicated that urbanization had an i n s i g n i f i c a n t e f f e c t on the flood of a hundred year recurrence i n t e r v a l . I t was pointed out by Espey and Winslow that these e f f e c t s from larger floods are caused by loss of e f f i c i e n c y in the channels due to ponding and overflow. While the q u a l i t a t i v e e f f e c t s of urbanization are r e l a t i v e l y s t r a i g h t forward, predicting the magnitude of the changes represents the most d i f f i c u l t problem. Researchers have found that a broad range of changes are possible from no increase i n peak flow at a l l to peaks f i v e times that of the same basin without development. To i l l u s t r a t e the variety of magnitudes which can occur the re s u l t s of three research studies are summarized below. Ramey(16) found that floods in the Chicago area had increased two and a half times because of urban development. Van Sickle(17) found increases i n peak discharge rates of two to f i v e times while Espey and Winslow (15) reported increases of three times i n the Houston area. I t can be seen that i t i s very d i f f i c u l t to predict the magnitude of the change due to urbanization. The Lower Fraser 29 Valley i s no exception because there i s no data on urbanization. For r u r a l areas, techniques such as synthetic unit hydrographs are available for t r a n s f e r r i n g data from one region to another. The methodology for generalizing urban runoff information has not advanced yet to the same l e v e l as for r u r a l watersheds. As a step towards solving t h i s problem a review w i l l be made of the methods that have been used i n the past and occur in the l i t e r a t u r e . It w i l l lead to a discussion of the options available i n the Lower Fraser Valley for consideration of urbanization. Several approaches to urban design are i d e n t i f i e d i n the l i t e r a t u r e . The most common approach has been to r e l a t e several basin parameters, including some for urbanization, to the peak flow hydrograph., Examples of t h i s approach are the Rational Method, Unit Hydrograph method and multiple regression methods. Techniques such as these tend to be easy to use but are limited by t h e i r simplifying assumptions. Another approach, sometimes c a l l e d a hydrograph method, i s to simulate by mathematical equations the runoff process from the time the rain touches the ground u n t i l i t reaches the main drainage l i n e . In practice t h i s has to be done by computer. Examples are the Chicago Hydrograph Method, the Los Angeles Hydrograph Method and the Stormwater Management Model. This approach i s expensive because of the amount of detailed work but i t i s also l i k e l y to be more accurate. Between the two approaches described above i s a range of techniques which eliminate the d e t a i l of the hydrograph approach but also r e t a i n a simulation of the runoff phenomenon. Examples of t h i s approach are the Inlet Method and the Road 30 Research Laboratory Method. A l l three approaches are described in more d e t a i l below. The simplest and most widely used approach i s to choose certa i n basin parameters and r e l a t e them to peak runoff. The Rational method i s the most common example because the runoff c o e f f i c i e n t can be conveniently related to the degree of urbanization., As mentioned e a r l i e r however, the Rational method i s l i m i t e d to small basins. The unit hydrograph approach lumps the e f f e c t s of urbanization into the shape and peak of the unit hydrograph. Eagleson(18) was the f i r s t to use t h i s technique to analyse urban runoff.. Based on limited data from L o u i s v i l l e , Kentucky, his study found that the time to peak of an urbanized area could be related to the basin parameters developed by Linsley, Kohler and Paulhus and expressed i n equation (8)., Van Sickle (17) t r i e d to e s t a b l i s h a relationship between Snyder's synthetic unit hydrograph c o e f f i c i e n t s and the degree of urbanization but found that although the c o e f f i c i e n t s change with urbanization no s i g n i f i c a n t r e l a t i o n s h i p could be found. However, urbanization was related to a combination of basin parameters c a l l e d a basin factor, K, shown i n equation (9). . 5 K = (Lt) (L)/(S) (9) Lt = t o t a l length of drainage channel i n the basin i n miles L = mean basin length i n miles 31 S = mean slope of basin Four l e v e l s of urban development were then defined by the descriptions shown i n Table 2. For each Texas watershed in his study, the basin factor and the l e v e l of urbanization were determined. Then, using unit hydrographs the peak flow and time to peak were related to the basin factors f o r each l e v e l of urbanization. The r e s u l t s of Van Sickle's study are shown in figures 5 and 6. From these curves synthetic unit hydrographs can be calculated f o r ungauged basins which w i l l experience some sort of development i n the future. Table 2 VAN SICKLE'S DEVELOPMENT CLASSIFICATIONS A. Fully urbanized, well developed drainage system including storm sewers. B. F u l l y urbanized, poorly developed drainage system,mostly open channels. C. P a r t i a l l y urbanized, few drainage f a c i l i t i e s of any type. . D. Undeveloped, with natural drainage system only. The approach of Denver, Colorado (19) i s to use three d i f f e r e n t methods for three l e v e l s of basin s i z e . For areas le s s than 200 acres the Rational Method i s used, for areas between 200 acres and 10 square miles a unit hydrograph approach i s used and for areas greater than 10 square miles a peak flow versus drainage area r e l a t i o n was used. The advantage of t h i s Fig.5 TIME TO PEAK VS. BASIN FACTOR from Von Sickle (17) DEVELOPMENT CLASSIFICATION T y p e A • Fu l ly D e v e l o p e d T y p e B A T y p e C O T y p e D X U n d e v e l o p e d 4 0 0 . 5 50 100 1000 B a s i n F a c t o r , K 10000 500C Fig.6 PEAK DISCHARGE VS. BASIN FACTOR from Van Sickle (17) DEVELOPMENT CLASSIFICATION T y p e A • Ful ly D e v e l o p e d T y p e B A T y p e C O T y p e D X Undeve loped 4 0 0 5 0 100 1000 B a s i n F a c t o r , K 10000 50 0 0 0 34 approach i s that various s i z e s of basins can be accomodated by using the most powerful technique for the size. Extensive data c o l l e c t i o n was undertaken to c a l i b r a t e each of the three methods to the Denver area. For the Rational Method, the data were used to c a l i b r a t e the runoff c o e f f i c i e n t , the time of concentration and the frequency i n t e n s i t y duration r e l a t i o n s h i p . The c a l i b r a t i o n of the unit hydrograph method involved constructing synthetic unit hydrographs based on Snyder's approach. The c o e f f i c i e n t s were ca l i b r a t e d for urban conditions but could be varied up to ten per cent depending on the channel conditions. A more d i r e c t approach to the basin parameter methods i s to r e l a t e flows of various frequencies to basin parameters by regression methods., Espey and Winslow (15) summarized the research with regression techniques which appears below. In 1961 Carter established a r e l a t i o n s h i p for eastern watersheds between the mean annual flood, the drainage area, the lag time and an adjustment factor for the amount of impervious area. I t was applied with some success to other eastern watersheds and to a basin i n Texas, In 1962 Benson related flows to basin c h a r a c t e r i s t i c s i n New Mexico and Texas, The form of his relationships was: Q = f (A,P,S,L,St) (10) Q = flood of a given frequency from frequency analysis A drainage basin area P r a i n f a l l i n t e n s i t y for a given duration and 35 frequency S = main channel slope L = basin length St = surface area of lakes and ponds Espey and Winslow, i n the paper referred to above, described relationships developed for Texas and east coast watersheds based on the form of Q = f (A,I,S,R,Th) (11) I = impervious cover as a percentage R = r a i n f a l l i n inches for a six hour duration Th = channel urbanization factor dependent on the amount of channel improvement and vegetation i n the channel Other parameters same as above Applying t h e i r r e s u l t s to watersheds i n the same area they found differences between measured and calculated flows to be between 10 and ii0 per cent. The basin parameter approach to urban design i l l u s t r a t e d by the techniques just described has the advantage of s i m p l i c i t y over other approaches. It i s r e l a t i v e l y inexpensive and easy to apply., However, the assumptions necessary to simplify the runoff process into these techniques l i m i t s t h e i r f l e x i b i l i t y to accurately calculate runoff e s p e c i a l l y for basins with sp e c i a l conditions such as unusual shape or a r t i f i c i a l channel 36 improvements. Transferring these techniques to other areas can be ris k y unless they are calib r a t e d well. The hydrograph approach involves considering separately each factor which a f f e c t s the urban runoff and then combining each one i n various ways to compute the outflow hydrograph. Horner and Flynt (20) were the f i r s t to attempt t h i s approach to an urban area. They calculated r a t i o s between runoff and r a i n f a l l for three small, heavily urbanized areas. The r a t i o s were found to vary widely so that th e i r r e s u l t s could not be used elsewhere. Later, Horner and Jens (21) used experimental data to suggest a design proceedure aimed at c a l c u l a t i n g more accurately parts of the runoff phenomenon such as overland flow, i n f i l t r a t i o n losses and gutter storage. The f i r s t actual design by the hydrograph method was done by Hicks (22) i n 1939 for Los Angeles., For the design, data were collected on r a i n f a l l - r u n o f f r e l a t i o n s h i p s , overland flow r e l a t i o n s and conduit detention r e l a t i o n s . The Chicago Hydrograph Method (23) u t i l i z e d the most com-prehensive approach ever attempted at that time for the study of urban runoff. Considerable e f f o r t was spent c a l c u l a t i n g each step of the runoff process i n d e t a i l . In spite of t h i s comprehensive approach, i t was c r i t i c i z e d for using r e l a t i o n -ships which were not well enough established i n practice. Lately, with. the development of d i g i t a l computer techniques, mathematical models have become popular. Their approach i s the same as the hydrograph approach except that the d e t a i l s are more neatly handled i n a computer. The models 37 d i f f e r from one another mainly i n t h e i r l e v e l of d e t a i l and their assumptions. It seems that although several models have been developed none have been applied to many si t u a t i o n s . Some of the better known models as summarized by the Australian Water Resources Council(24) are the Stanford Watershed Model, the U.S. Geological Survey Model, the U.S. Environmental Protection Agency's Stormwater Management Model, and the Water Resources Engineers Model. In summary, the hydrograph approach i s l i k e l y to be the most accurate of the three approaches because i t considers far more basin parameters making i t more sensitive to special basin c h a r a c t e r i s t i c s . However, for the same reasons i t i s also an expensive approach and r e a l l y can be j u s t i f i e d only for very large urban projects. The hydrograph approach i s d i f f i c u l t to transfer to other areas not only because of the data required to c a l i b r a t e i t but also because the runoff structure within the basic units of the model may change. For example the Chicago Hydrograph Method i s d i f f i c u l t to transfer elsewhere because i t was set up only for the type of housing arrangements in the Chicago area. The hydrograph method of f e r s an advantage from an academic viewpoint of furthering the knowledge of runoff processes by v e r i f y i n g t h e o r e t i c a l r e s u l t s , In time, the relationships may become well enough established that an accurate yet s i m p l i f i e d approach to runoff w i l l be possible. The t h i r d group of approaches to urban runoff design i s a combination of the hydrograph methods and the simple methods. This approach usually consists of a s i m p l i f i e d overland flow 38 c a l c u l a t i o n followed by a routing technique. The advantage of these methods i s that they are more accurate than the basin parameter methods but reguire less e f f o r t then the hydrograph methods. The simplest of these hybrid techniques i s the I n l e t Method (25) i n which the peak runoff from an area i s calculated from three terms: the f i v e minute r a i n f a l l i n t e n s i t y , a factor related to the amount of impervious area and the basin area. A simple i n l e t hydrograph i s constructed from t h i s peak and i s then routed downstream to the design point. This method i s more sophisticated than the Rational Method because i t involves routing. I t i s based on actual data for the Baltimore area but i t s authors report that i t i s more accurate for many situations than the Rational Method. Chien and Saigal (26) developed a more general version much l i k e the Inlet Method c a l l e d the Linearized Subhydrographs Method. In t h i s , the Rational Method i s b a s i c a l l y used to define peaks of triangular hydrographs. These hydrographs are then routed i n simple steps through the basin. Terstriep and Stahl (27) tested a method developed by the B r i t i s h Road Research Laboratory which i s used extensively in the United Kingdom. I t follows the hydrograph approach but assumes that only r a i n f a l l from impervious surfaces d i r e c t l y connected to the drainage system contributes to the storm peaks. The design proceedure involves f i r s t c a l c u l a t i n g a time-area diagram from a detailed plan of the area. , Then, from a design r a i n f a l l pattern, i n l e t hydrographs are synthesized and routed i n one step through the basin. Terstriep and Stahl claim the 39 method i s as accurate as the unit hydrograph method and that i t has a further advantage of being able to calculate design flows from detailed plans of the area. . The hybrid methods discussed above have a combination of the advantages and disadvantages of the other two approaches. They are more complicated than the simple methods and generally are more a c c u r a t e . B u t , they reguire more data for c a l i b r a t i o n and hence are more expensive. The Hoad Research Laboratory Method i s expensive to use because of the detailed calculations required. The Inlet Method was developed for the Baltimore area arid to apply i t to the Lower Fraser Valley would require more data c o l l e c t i o n . The Linearized Subhydrographs method i s l i k e l y to be more accurate then the Rational Method but again, with a corresponding increase i n cost. The choice of technique for urban design i n the Lower Fraser Valley i s li m i t e d by the type of development expected there. Development w i l l l i k e l y occur slowly and sporadically throughout the area. Since a master plan has not been drawn up f o r the area the d e t a i l s of future urbanization are unknown. The problem i s that drainage for an entire basin may need to be designed without knowledge of the future changes i n the watershed. This l i m i t s the choice of techniques to those not requiring d e t a i l s of the basins. Another l i m i t a t i o n to the basin design i s cost. Since the area i s unlikely to become an intense commercial area a large expenditure for drainage f a c i l i t i e s cannot be j u s t i f i e d . This further l i m i t s the techniques to simple methods which have been 40 successful elsewhere. Van Sickle's approach to urbanization as i l l u s t r a t e d in figures 5 and 6 i s perhaps the most suitable for the needs of the Lower Fraser Valley. However, since his data were collected f o r Texas watersheds they must be calibrated for t h i s area. To do t h i s the basin parameters of the four watersheds studied are calculated i n Chapter 5 and graphs corresponding to Van Sickle's are drawn. 3.6 Least Squares Technique The unit hydrographs were determined from r a i n f a l l and runoff data with a technique described by Newton and Vinyard(28). This technique uses a least squares method to solve for the unit hydrograph vector 0 i n equation (11). (12)2 = 2 (11) RO i s an (nxj) matrix of excess p r e c i p i t a t i o n values 0 i s an (jx1) vector of unit hydroqraph ordinates 2 i s an (nx1) vector of storm flow ordinates n i s the number of storm ordinates j i s the number of unit hydrograph ordinates 1 i s the number of excess p r e c i p i t a t i o n values The number of storm periods, r a i n f a l l excess periods and unit hydrograph ordinates are related by equation (12). 41 n ~ i+j-1 ( 1 2 ) To solve the overdetermined system of equations expressed in Equation<11) above, a computer program was written which used a packaged least squares system c a l l e d SVD(29). This program i s l i s t e d i n the Appendix. After equation (11) i s solved, the calculated unit hydrograph ordinates are used with the runoff values to calculate an estimate of the storm runoff, £c. The difference, 2d, between p. and gc i s a measure of how c l o s e l y the calculated unit hydrograph f i t s the actual storm. The error i n each excess p r e c i p i t a t i o n term, named E, i s computed by solving Equation (14) for E. The r e s u l t i n g E vector i s added to the o r i g i n a l runoff values to obtain better estimates of the runoff. Then, using the new runoff values and the o r i g i n a l 2 values new unit hydrograph ordinates are calculated. This process i s repeated several times. The more i t e r a t i o n s the more closely the storm i s reconstructed. A point i s reached however, at which the changes in excess p r e c i p i t a t i o n become i l l o g i c a l from a hydrologic viewpoint. I t i s assumed at t h i s point that the best balance has been reached between simulating the runoff phenomenon and f i t t i n g the storm. The corresponding unit hydrograph ordinates 2d=gc-2 (13) Qd=E (RO) (14) 42 are used. As with any a n a l y t i c a l technique, the least squares technique for finding unit hydrograph ordinates contains biases and weaknesses. The most important point to r e a l i z e i s that the solution i s a mathematical one, dependent only on the numbers fed i n t o the program. This can be quite d i f f e r e n t from a hydrologic s o l u t i o n . For example, negative hydrograph ordinates cannot be tolerated from a hydrologic viewpoint whereas mathematically they can be. It i s important to review each c a l c u l a t i o n to confirm that the solution i s h y d r c l o g i c a l l y sound. The nature of SVD i s such that the large unit hydrograph ordinates are better determined than the smaller unit hydrograph ordinates of the recession part of the curve. This i s demonstrated by the r e s u l t s of the computer program which shows that the unit hydrograph peaks are well defined while the recession points seem unstable. These unstable recession points o s c i l l a t e between high and low values about a curve which i s the actual recession curve. Furthermore, from equation (12), there are only (i-1) more equations than unknowns. A t y p i c a l example i s 39 equations for 30 unknowns. With only 9 more equations than unknowns i t can be seen that some points i n the solution w i l l not be well defined, Hewton and Vinyard suggest a method of adjusting the runoff matrix to decrease the number of unknowns. Parts of the recession curve are assumed to be l i n e a r so that some points can be expressed i n terms of others. By choosing several l i n e a r 43 sections on the recession many ordinates are eliminated. If too many ordinates are eliminated the unit hydrograph w i l l lack d e f i n i t i o n . If too few ordinates are eliminated, the i n s t a b i l i t y i n the recession occurs. These factors must be adjusted by t r i a l to f i n d a reasonable compromise. If the wrong ordinates are chosen for the transformed runoff matrix an incorrect unit hydrograph w i l l r e s u l t . Care must be taken to l i n e a r i z e only the near-linear portions of the curve. Transforming the runoff matrix has a further advantage of greatly reducing the number of calc u l a t i o n s thereby reducing the computing time. CHAPTER FOUR METHOD The method consisted of three major steps: 1) Choosing the basins to study 2) Deriving the unit hydrographs 3) Generalizing the res u l t s Each of these steps i s described i n d e t a i l below. The choice of basins to analyse was limited by the location of p r e c i p i t a t i o n and discharge recording stations. Since hourly data were necessary, only automatic recording stations could be used. ; Another l i m i t a t i o n was that the pr e c i p i t a t i o n gauges had to be located near the test basins. These c r i t e r i a quickly narrowed the choice to the four basins mentioned e a r l i e r . The derivation of the unit hydrographs for the four basins represented the most work of a l l the steps i n the study. As mentioned e a r l i e r , a method of lea s t squares was used instead of the more common approach of dividing each storm hydrograph ordinate by the t o t a l runoff volume. This technique provided the advantage of being able to analyse storms with multiple peaks or varying p r e c i p i t a t i o n i n t e n s i t i e s . I t seems that i n nature, the complexity of storms increases rapidly with storm si z e . By using the least squares technique these large storms 45 could be analysed i n spite of t h e i r complexity. Storms were chosen f i r s t for t h e i r magnitude then for t h e i r s i m p l i c i t y . The base flow was separated from the t o t a l runoff using a technique described i n Linsely, Kohler and Paulhus (14). A point on the recession was chosen as the time at which storm flow ceased to contribute to the hydrograph. From t h i s point a l i n e was drawn back i n time gradually increasing the distance between i t s e l f and the t o t a l hydrograph l i n e . This l i n e was continued u n t i l i t was situated under the peak. Another l i n e was then drawn forward i n time as an extension of the flow before the storm. The two l i n e s were then joined under the peak flow by a smooth curve. This method of separating base flow may not have accurately represented the physical s i t u a t i o n i n a l l cases. However, since i t was applied consistently to a l l storms and since the base flow was only a small f r a c t i o n of the t o t a l flow, i t was considered to be adequate. Detention and depression storage losses varied between 0.10 and 0.20 inches. The exact value taken for each storm depended on a subjective assessment of the antecedent r a i n f a l l conditions. If other storms had occurred recently, less was subtracted. Also, two factors related to the compatibility of the unit hydrograph theory were considered i n determining the losses. One factor was that the beginning of the excess rainf11 had to coincide with the beginning of the runoff. The other factor was that the number of periods of r a i n f a l l excess had to conform to equation (12). A rough estimate of the i n f i l t r a t i o n rates was obtained by 46 ca l c u l a t i n g the difference i n volume between the runoff and the r a i n f a l l . After subtracting the volume of surface losses estimated as above, t h i s volume difference was divided by the storm duration to obtain an average i n f i l t r a t i o n rate. This average rate was adjusted by increasing the rate at the beginning and decreasing i t at the end so that the change in rate with time was approximately exponential. Since the computer program adjusted the i n f i l t r a t i o n rates at each i t e r a t i o n , these estimates were used as i n i t i a l values only. The unit hydrographs for each storm were calculated using the computer program described e a r l i e r . , The best storm unit hydrographs were taken and averaged to produce the single r e s u l t i n g unit hydrograph f o r each basin. Care was taken to average the peak flows regardless of the time of occurrence of the peak and then to average the time of occurrence of the peak separately from the magnitude. The generalization of the r e s u l t s consisted of r e l a t i n g the peak unit hydrograph flow and the time to peak to certain basin c h a r a c t e r i s t i c s . Several techniques were attempted i n the search for a re l a t i o n s h i p which adequately represented the data. F i r s t , Snyder's synthetic c o e f f i c i e n t s were calculated, then the rel a t i o n s h i p introduced by Linsely, Kohler and Paulhus and expressed i n equation (8) was attempted. Neither relationship f i t the data well. However, by considering urbanization of the basins i t was found that Van Sickle's r e l a t i o n s h i p as discussed e a r l i e r could be applied to the data i n t h i s study. These r e s u l t s were expressed i n graphical form and are shown in 47 figures 13 and 14. The width relationships expressed i n equations (6) and (7) were calculated from the data and compared with the 0. S. army Corps of Engineer's r e s u l t s i n figure 15. F i n a l l y , estimates of i n f i l t r a t i o n losses i n the various basins were made based on volumes of r a i n f a l l and runoff. 48 CHAPTER FIVE RESULTS 5.1 Derived Unit Hydrographs The derived unit hydrographs for the four basins are shown i n figures 7, 8, 9 and 10. Snyder's synthetic c o e f f i c i e n t s were derived from these r e s u l t s and are summarized i n Table 3 below. Table 3 SUMMARY OF RESULTS Basin Mahood Salmon Murray Barker Basin area (sg mi) 7.4 19.4. 9,04 0.92 Peak Unitgraph Discharge (cfs) 620 810 610 200 Time to peak (hrs.) 4 7 5 2 Ct 2.50 2. 11 1.84 1.53 Cp .52 .48 .53 .68 -j Average 2.00 .55 j In 1973 the Water Resources Service of the B.C. Government derived a 24 hour unit hydrograph for Barker Creek based on 24 6 0 0 r «/> 6 I (/> ° 4 0 0 •6 \_ o .c Q. O i_ cn o k_ T3 >> X r 2 0 0 c Z> F i g . 7 UNIT HYDROGRAPH Mahood C r e e k 10 20 30 T i me - hours F i g . 9 2S 53 hour storms. From their analysis a design unit hydrograph with a peak of 55 c f s was chosen. In contrast, the 24 hour unit hydrograph derived from the one hour unit hydrograph found i n t h i s analysis has a peak of 31 c f s . While these two re s u l t s seem at f i r s t contradictory, a closer inspection reveals that they may not be e n t i r e l y d i s s i m i l a r . A 24 hour unit hydrograph w i l l tend to overestimate the peak flow because the variations i n i n t e n s i t y over the 24 hours are not accounted f o r . These variations may s i g n i f i c a n t l y a f f e c t the time to peak and the magnitude of the peak. 5.2 Generalization When Snyder o r i g i n a l l y published his paper he suggested a range for Ct of 1.8 to 2.2 and for Cp of 0.56 to 0.69 from his studies i n the Appalachians. , Later, i n 1943 (30) he confirmed these values from studies i n many watersheds a l l across the United States. The c i t y of Denver, Colorado(19) found values to range between 0.25 and 0.35 for Ct and between 0.45 and 0.55 for Cp. These were design values for urban or suburban areas up to 10 square miles i n siz e and for an area quite different hydrologically from the Lower Fraser Valley. Figure 11 i l l u s t r a t e s Snyder's relationship between the lag time and the basin parameter LLc. Line A i n the figure i s the best l i n e through the points which has a slope of 0.3 corresponding to equation (2). The greatest error i n the time to peak i s one and a half hours. This variation suggests that Snyder's relationships are not appropriate for describing the F i g . l l L A G T I M E V S . B A S I N P A R A M E T E R L L C 40 1 1 0 4> E 5 < i 1—i—i i i i i i r——i—i—i i i i i i 1 1 — i — l i M l j ' i i i i i i i i i i i—i I i l I J I i l i l l 5 10 50 100 Basin Parameter LL c-sq.miles 500 1000 55 runoff of the Lower Fraser Valley. In order to explore other p o s s i b i l i t i e s for r e l a t i n g the synthetic unit hydrograph c o e f f i c i e n t s to the basin data, the rela t i o n s h i p derived by L i n s e l y , Kohler and Paulhus and expressed i n equation (8) was plotted as shown i n figure 12. Line A represents the best f i t l i n e and has a slope of 0.24 and a Ct value of 1.45. These c o e f f i c i e n t s contrast with the authors* slope of 0.38 and Ct values ranging between 0.35 and 1.2 for C a l i f o r n i a watersheds. It i s evident that a relationship of t h i s form i s no more s a t i s f a c t o r y than the previous one. Linsely, Kohler, and Paulhus accounted for the variation in basin types by grouping th e i r data into valley, f o o t h i l l and mountain drainages. It seemed worth trying to apply t h i s approach to the data i n t h i s study. However, a l l the drainage basins occur in roughly the same type of t e r r a i n and the major differences are found i n the amount of development rather than topography. As mentioned i n Chapter Two, Barker Creek possesses more c h a r a c t e r i s t i c s of urbanization than the other three basins. By grouping the data i n figure 12 according to the amount of urbanization, l i n e s B and C can be drawn. Conceptually, this grouping agrees with the fact that the lag time for more urbanized areas i s les s than for the same basin when undeveloped. Reconsidering figure 11 and regrouping the data points i n the same way, corresponding l i n e s , B and C can be drawn as i n figure 12. Proceeding further with this idea of including the e f f e c t s of urbanization. Van Sickle's approach as Fig.12 LAG TIME VS. L L C A A / s . 57 discussed i n Chapter 3, was next attempted using Lower Fraser Valley data. Each basin was c l a s s i f i e d by l e v e l of urbanization and the basin factors K, were calculated. Barker Creek was c l a s s i f i e d at a B l e v e l from Table 2 while the other three were assumed to be at a C l e v e l . The peak flow and the time-to-peak were both plotted against the basin factor and the re s u l t i n g plots are shown in figures 13 and 14. Line C was drawn through the three points and l i n e B was drawn p a r a l l e l to i t and located by i t s single data point. Line B i s necessarily weak due to lack of data but i t does indicate the order of magnitude of the increase from urbanization. For comparison, Van S i c k l e ' s r e s u l t s are drawn i n with dashed l i n e s on the same plo t . It can be seen that for Texas watersheds, both the times tc peak and the unit hydrograph peak flows are s l i g h t l y higher than for the Lower Fraser Valley. An examination of figure 13 indicates that peak flows are l i k e l y to increase by about 80 per cent when the drainage f a c i l i t i e s are improved from a C l e v e l i n Table 2 to a B l e v e l . For Texas watersheds, Van Sickle found an increase of about 75 per cent for the same change. The changes i n peak flow r e s u l t i n g from complete urbanization could not be determined experimentally i n the Lower Fraser Valley because there are no such watersheds present at t h i s time. However, i f i t i s assumed that Van Sickle's r e s u l t s continue to indicate l i k e l y increases f o r the Lower Fraser Valley, a design engineer could expect the Lower Fraser Valley peaks to increase by 160 per cent for an improvement from the C to the A l e v e l . Fig.13 L A G T I M E V S . B A S I N F A C T O R , K T — i — i i i i 11 r — i — i — i M i n Basin Factor, K Fig.14 U N I T H Y D R O G R A P H P E A K V S . B A S I N F A C T O R , K . 800 i i i i i i I I 1 1 — l l I l l I I 1 1—I—I l I l I I 500 20 1 VanSickles results Lower Fraser Valley i i i i i i i i i I I I L • I I I I I I l l 10 50 100 Basin Factor, K 500 1000 2000 60 Although figures 13 and 14 are not as well defined as they should be to conclusively establish the relationships for the Lower Fraser Valley, i t i s f e l t that they do provide a r a t i o n a l explanation for the variation i n unit hydrograph parameters found i n t h i s study. In the absence of other information the re l a t i o n s h i p s can be used to estimate the parameters for unit hydrographs for other ungauged basins thus providing a basis for r a t i o n a l and consistent design of drainage f a c i l i t i e s i n the Lower Fraser Valley. Further data i s obviously required to substantiate the r e s u l t s but Van Sickle's basin factor approach does seem to i d e n t i f y a pattern i n the variations. With more recording stations, the data gaps can be f i l l e d and the relationships better established. 5.3 Width Relationships Figure 15 i l l u s t r a t e s the width relationships expressed in equations 6 and 7. The derived unit hydrograph widths seem to c l o s e l y follow the published relationships and would thereby seem adequate for use i n constructing unit hydrographs for ungauged basins. 5.4 I n f i l t r a t i o n Rates The i n f i l t r a t i o n losses were estimated by the computer program as previously described. The r e s u l t s averaged over a l l the storms are shown i n Table 4. 61 F ig .15 U H P E A K S V S . W I D T H S . 62 Table 4 INFILTRATION RATES I | Basin I h I n f i l t r a t i o n Rate i n , per hr. Ranges i n . per hr. IHahood Cr I |Murray Cr I |Salmon R I |Barker Cr h + |Average | t L .03 .05 .06 .06 .05 .02 -.03 -.03 -.03 -I .04 -.04 .07 .09 .10 .07 | .—j These estimates of i n f i l t r a t i o n are averages of d i f f e r e n t i n f i l t r a t i o n rates occuring throughout each basin. A wide va r i a t i o n i s to be expected within each basin because of d i f f e r e n t slopes, cover and s u p e r f i c i a l s o i l . The values can be considered only as rough estimates since the computer program cannot make hydrologic judgements on the values i t calculates. Other combinations of detention and depression storage and i n f i l t r a t i o n losses could have possibly been used with equal success. Nevertheless, they do indicate i n f i l t r a t i o n rates of the order of 0.05 inches per hour. F a i l i n g other data these values could be used i n preliminary design analysis for ungauged basins. 5.5 Least Squares Technique The least squares approach i s well established for analysis of the unit hydrographs for complex storms. However, the 63 computer application of the technique i s r e l a t i v e l y new and requires some f a m i l i a r i z a t i o n before i t can be used with ease, Since the experience gained may be of use to others, some of the problems encountered are discussed below., Complex storms longer than 24 hours proved d i f f i c u l t to analyse with the least squares technique because the greater complexity quickly made the cal c u l a t i o n s unmanageable. The derived unit hydrographs could not reproduce these large storms well and i t e r a t i o n s did not quickly improve the o r i g i n a l values. Also, during these large storms, the wide variations i n the r a i n f a l l cast doubts on the assumed i n f i l t r a t i o n rate. Choosing the number of ordinates i n the transform was an area of judgement l e f t open to manipulation by Newton and Vinyard. Experience soon revealed that the number in the transform should be about one t h i r d of the t o t a l number of ordinates. The f i r s t few ordinates including the peak must always be included while the rest should be spread out at increasingly greater i n t e r v a l s . The assumption of l i n e a r i t y between the points i n the transform must never be violated. One r e s u l t of the program was that the l a s t ordinate i n the computer-produced unit hydrograph often did not continue to decrease along the recession. Instead i t had a value two to three times larger than i t should have been. This i s obviously an error introduced by the l e a s t squares solution and made no sense hydrologically. Since no cause for the error could be found the curve was smoothed to f i t the recession curve defined by the other ordinates and the area under the unit hydrograph adjusted accordingly. ft composite program was made up i n which the excess r a i n f a l l and corresponding flows for several storms were analysed at the same time. Invariably, the res u l t i n g unit hydrograph had a lower peak than a l l of the peaks for storms calculated i n d i v i d u a l l y . The location of the calculated peak was usually midway between those of the i n d i v i d u a l storms. It was concluded that t h i s program computed the arithmetic average unit hydrograph of the storms instead of the "hydrologic average". This composite program was not used to average the storm unit hydrographs. 65 CHAPTER SIX SUMMARY AND RECOMMENDATIONS From the study of the storm hydrology of the Lower F r a s e r V a l l e y d e s c r i b e d i n pr e v i o u s c h a p t e r s r e l a t i o n s h i p s were developed which allow c o e f f i c i e n t s of s y n t h e t i c u n i t hydrographs to be estimated f o r ungauged b a s i n s . A l s o , the width r e l a t i o n s h i p s c l o s e l y f o l l o w e d the U. S. Army Corps of Engineers r e l a t i o n s h i p s as shown i n f i g u r e 15. The average i n f i l t r a t i o n was found t o be about 0.05 i n . per hour. While i t was o r i g i n a l l y hoped to r e l a t e the u n i t hydrograph peaks and times to peak to Snyder»s c o e f f i c i e n t s , h i s method was found inadequate to e x p l a i n the v a r i a t i o n s between b a s i n s . An a l t e r n a t i v e approach developed by Van S i c k l e , and d e s c r i b e d i n Chapter 3, proved t o be more s a t i s f a c t o r y . The r e s u l t s are shown i n f i g u r e s 13 and 14. The l a c k of data i n the Lower F r a s e r V a l l e y prevented e s t a b l i s h i n g more e x a c t l y the r e s u l t s expressed i n these diagrams. However, i t i s f e l t that they are the best g e n e r a l i z a t i o n of the a v a i l a b l e data and th a t f o r l a c k of b e t t e r data they are acc u r a t e enough f o r p r e l i m i n a r y design purposes. T h i s i n f o r m a t i o n can be used t o g e t h e r with r e a d i l y a v a i l a b l e p r e c i p i t a t i o n data t o compile design f l o o d s f o r the prelimimary design of drainage f a c i l i t i e s i n the Lower F r a s e r V a l l e y . 66 As mentioned e a r l i e r , a considerable amount w i l l almost c e r t a i n l y be spent on drainage in the Lower Fraser Valley due to the development expected in the future. In view of the s i m i l a r i t y of the basins and the types of storms i n t h i s area i t seems r a t i o n a l to consider the design of drainage f a c i l i t i e s for the e n t i r e area rather than by i n d i v i d u a l projects. By using a comprehensive approach more e f f o r t can be invested i n finding suitable design techniques than would be possible on a piecemeal basis. In the Lower Fraser Valley such a comprehensive approach would f i r s t involve deciding on the type of design techniques most suitable for the area. a design manual should then be prepared so that the drainage system for any basin i n the area could be designed. Furthermore, a data c o l l e c t i o n scheme should be started and continued over the years so that the manual could be upgraded as more data becomes av a i l a b l e . Two types of techniques can be i d e n t i f i e d for the drainage design requirements of the area: one for large basins for channel improvement and flood protection and one for detailed design of drainage i n the more urbanized areas. The requirements for the larger basins would be larg e l y s a t i s f i e d by the r e s u l t s of t h i s study i f they could be confirmed with further data, since unit hydrographs can now be derived from figures 13 and 14. However, hourly stage data from more basins would be desireable not only to confirm the r e l a t i o n s established i n t h i s study but also to compute the unit hydrograph parameters for the two l e v e l s of development not considered i n t h i s study: for areas completely developed and for 67 areas completely undeveloped. The second type of technique, for smaller, more urbanized areas has t r a d i t i o n a l l y been handled by the Rational Method. While t h i s method can be accurate, a more suitable approach would be to use a technique designed s p e c i f i c a l l y for the Lower Fraser Valley i n the same manner as the Inlet Method was developed for the Baltimore area. By gauging runoff from areas of up to several hundred acres i t i s possible that i n l e t hydrographs could be keyed to some s p e c i f i c r a i n f a l l duration or i n t e n s i t y thereby establishing a r a i n f a l l - r u n o f f r e l a t i o n . The implementation of such a technique i s dependent on the c o l l e c t i o n of l o c a l data f o r these small areas and none of t h i s has yet been done. More recording p r e c i p i t a t i o n stations are also needed in the Lower Fraser Valley to more accurately determine the s p a t i a l d i s t r i b u t i o n of r a i n f a l l . There i s no shortage of d a i l y f a c i l i t i e s but the hourly stations are too widely spaced. Another need i n the Lower Fraser Valley i s for the analysis of storm patterns. Synthetic storms can be constructed from r a i n f a l l records and various techniques have been used elsewhere to do t h i s . The weakness of t h i s approach i s that a synthetic storm may not r e f l e c t the predominant pattern of r a i n f a l l for the area. A research program i s needed to analyse r e a l storms s t a t i s t i c a l l y to determine th e i r c h a r a c t e r i s t i c s i n t h i s area. It i s possible that a certain pattern of r a i n f a l l i n t e n s i t i e s predominates i n t h i s area._ If t h i s research were pursued, design could be based on a t y p i c a l storm instead of on a r t i f i c i a l storms. 69 REFERENCES I . , Linsely, R. . K., and Franzini, J . B., " l a t e r Resources ££2i£§§li!!2" t McGraw-Hill Book Co., New YorkT T972. 2. Dalrytnple, Tate, "Hydrology of Flow Control - Part 1 Flood Charac t e r i s t i c s and Flow Determination", Section 25-1 of Handbook of Applied Hydrology , ven Te Chow (ed.), McGraw-Hill Book~Co.7~New~¥or k"7~1964. 3. Schaeffer, D..G., "Climate of the Fraser Delta", part of a Summary. Rejaort on the Fraser Delta and Estuary^ S c i e n t i f i c Support Unit of the Atmospheric Environment Service, Department of the Environment., 4. Wright, J. B., " P r e c i p i t a t i o n Patterns over Vancouver City and the Lower Fraser Valley", Department of Trans£ort^ Meteorological Branch, Toronto, Ont.7 Cir7 44747 "~T"ic~" 623, August, 1966. 5. Sporns, U., "Frequency and Severity of Storms i n the Lower Fraser Valley", Meteorological Branch, Department of Transport x Toronto, Ont., Cir.3848, TEC 469, T963. 6. Kelly, C. C , and Spilsbury, R. H., " S o i l Survey of the Lower Fraser Valley", Canada Department of Agriculture, Ottawa, Technical B u l l e t i n No._ 20^ 1939. 7 . , Schaake,John C., J r . , Geyer, John C., and Knapp, John W., "Experimental Examinatcn of the Rational Method", Journal of the Hydraulics Division , ASCE, Volume 93, ~ NO7H Y6, Proceedings~Paper~56077 November, 1967, pp.353-370. 8. Kuichling, E., "The Relation Between R a i n f a l l and the Discharge of Sewers i n Populous D i s t r i c t s " , Transactions , ASCE, Volume 20, 1889, p. 1.. 9. Sherman, L, K.,"Streamflow from R a i n f a l l by the Unit-graph Method", Engineering; flews-Record ,Volume 108, pp. 501-505, A p r i l 7, 19327 10., Barnes, B. S., "Unit-graph Proceedures", U. S. Department of the I n t e r i o r , Bureau of Reclamation , Division of Project Planning, Hydrology Branch, ~Denver7 Colorado, November, 1952, revised August,1965. I I . Summarized by Ven Te Chow i n Section 14 of Handbook of Applied Hydrology, Ven Te Chow (ed.), Mcgraw-Hill Book Company, 1964. , 12. Snyder, F. F. , "Synthetic Unit-graphs", Transactions , American Geophysical Union, Volume 19, pp.447-454, "19387" 13. U. S. Army Corps of Engineers, " Flood Hydrograph Analysis and Computations", Engineering and Design Manuals , EM 1110-70 2-1405, U. S. Government P r i n t i n g O f f i c e , Washington, D. C. , Aug. 31,1959. 14. L inse ly , R. K., Kohler, M. A,, and Paulhus, J. L., HAjrplied Hydrology^*. McGraw-Hill Book Co., New York, 1949, 15. Espey, W. H. and D. E. Wislow, "Urban Flood Frequency C h a r a c t e r i s t i c s " , Journal of the Hydraulics Divi s i o n ^ ASCE, Volume 100, No. HY27~ProceedIngs~Paper 10352,~Feb7 1974, pp. 279 - 293. 16. Ramey, H. P., "Storm Water Drainage i n the Chicago Area", Journal of the Hydraulics D i v i s i o n , ASCE, Volume 85, No. HY4,"Proceedings Paper 19957 Aprll7"~1959, pp. 11-37. 17. Van Sickle, Donald, "Experience with the Evaluation of Urban Effects for Drainage Design", paper i n Effects of Watershed Changes on Streamflow , Moore, W. L. and ~C.~w7~ Morgan, (eds.). University of Texas Press, Austin. Texas, 18. Eagleson, P. E,, "Unit Hydrograph Characteristics for Sewered Areas", Proceedings paper. Journal of the Hydraulics Divi s i o n , ASCE, Volume 88, No, HY27"March, 19627 19., Wright-McLaughlin Engineers Ltd., "Urban Storm Drainage C r i t e r i a Manual", prepared for The Denver Regional Council of Governments , March, 1969. , ~ 20. Horner, W. W. and Flynt, F. L., "Relation Between R a i n f a l l and Runoff for small Urban Areas", Transactions , ASCE, 101, 140,. (1936) . 21. Horner, w. w., And Jens, S. w., "Surface Runoff Deter-mination from R a i n f a l l Without using C o e f f i c i e n t s " , 2£ansactions , ASCE, 107, 1039, 1942. 22. Hicks, W. I . , "A Method of Computing Urban Runoff", Transactions , ASCE, 109, 1217, 1944. 23. Tholin, A. L., and C, J, Keefer, "Hydrology of Urban Runoff", Transactions , ASCE, 125, 1308, 1960, Proc, Paper 3061. 24. Australian Water Resources Council, "Hydrologic Investigation and Design i n Urban Areas - A Review", Technical Pajser No t 5 X Australian Government Publications Service,"Canberra,"1973. 25. Jens, S. W.,and M. B. McPherson, Section 20 of Handbook of A££lied Hydrology., Chow, V. T., (ed.), McGraw-Hill~Book Co.7 New York, "19647. 26. Chien,J. S., and K. K. Saigal, "Urban Runoff by Linearized Subhydrographs Method", Journal of the Hydraulics Division , ASCE, Volume 100, No. HY97 August 19747 71 27. Terstriep, M. L. , and J. B. S t a l l , "Urban Runoff by Road Research Laboratory Method", Journal of the Hydraulics Divi s i o n , Volume 95, N0.HY6, Proceedings paper 6878, NovT 19697"PP. 1809 - 1864. 28. Newton, D. W., and J. W. Vinyard, "Computer Determined Unit Hydrographs from Floods", Journal of the Hydraulics Division ASCE, Volume 93, No. HY5~7~ ""proceedings paper ~ 5449, September, 1967, pp., 219 - 235. 29., Computing Center, University of B. C., "Singular Value Decomposition of a Matrix", June, 1973. 3 0 . , Snyder, F* ,F., Discussion on paper by R. K. Linsely, Transactions^ American Geophysical Union, Volume 24, Part 2, pp.580~-~587, 1943. 72 APPENDIX LEAST SQUARES COMPUTER PROGRAM DIMENSION Y ( 8 0 ) , R ( 6 5 ) , R O ( 8 0 , 6 5 ) , I X ( 6 5 ) , O C ( 8 0 ) , Q D ( 8 0 ) DIMENSION S S S ( 8 0 ) , V D D ( 8 0 , 6 5 ) DIMENSION U 0 ( 8 0 , 6 5 ) , E ( 8 0 ) , V D ( 8 0 , 6 5 ) , S S ( 8 0 ) , R O T ( 8 0 , 6 5 ) DIMENSION B ( 8 0 ) , F ( 6 5 ),RAW(65) DIMENSION G ( 8 0 ) , F R ( 8 0 ) , X I X ( 8 0 ) , X P L ( 8 0 ) L0GICAL*1 F M T ( 8 0 ) , T I T ( 8 0 ) READ(5,902) N , I , J , I T , D R B S 902 F 0 R M A T ( 4 I 3 , F 6 . 2 ) ITP=IT+1 JP=J IP = I JWT=1 NL=N IPP=IP+1 SUMY=0 READ(5,1000) ( F M T ( I ) , 1 = 1 , 8 0 ) 1000 FORMAT(80A1) READ(5,FMT) (Y( I Q ) , IQ = 1,N ) DO 306 1=1, NL 306 SUMY=SUMY+Y(I) SUMB=(1.55E-3/DRBS)*SUMY READ(5,1000) FMT C C SET UP RUN OFF MATRIX C READ (5,FMT) ( R ( 1 1 ) , I 1=1,1P) READ(5,FMT) ( R A W ( I ) , 1 = 1 , I P ) DO 801 1=1,IP 801 F ( I ) = R ( I ) DO 304 IST=1,5 DO 303 M=1,IP DO 303 LW=1,N 303 UO(LW,M)=0 DO 450 M=1,JP C C CALCULATE STORM FLOWS C DO 500 LW=1,N RO(LW,M)=0. 500 CONTINUE 450 CONTINUE DO 700 M=1,JP LA=M LAF=LA+IP-1 MC = 1 DO 600 LW=LA,LAF RO(LW,M)=R(MC) MC=MC+1 600 CONTINUE 700 CONTINUE C C ADJUST RUN OFF MATRIX FOR ORDINATES IN TRANSFORM C I F ( J W T - l ) 8 30,830,811 830 R E A D ( 5 , 8 1 0 ) ( I X ( I ) , 1 = 1 , IT) 810 F0RMAT(40I2) 811 DO 63 1=1, IT 11X=I X ( I ) X I X ( I ) = I I X IP2=I+1 IM2=I-1 I F ( I M 2 . E Q . O ) GO TO 63 IF ( I P 2 . G T . I T ) GO TO 64 I P 3 = I X ( I P 2 ) - I I X - 1 I F ( I P 3 . L T . 1 ) GO TO 64 65 IDNNIP3 RIR=I DM IPX=IIX+1 DO 61 IA=1,IDM RIDMP=IDM+1 DO 66 IB=1,N 66 RO( IB , I I X )=RO( IB, I IX )+R IR/R IDMP*RO( IB , IPX) RIR=RIR-1 61 IPX=IPX+1 64 IM3= I IX - IX I IM2J -1 IF( I M 3 . L T . 1 ) GO TO 6 3 68 IDM=IM3 IMX=IIX-1 RIR=IDM DO 62 IC=1,IDM RIDMP=IDM+1 DO 67 101=1,N 67 R 0 ( I D l , 1 1 X )=R0 ( ID1 , I IX)+RIR/RIDMP*RO(ID 1,I MX) RIR=RIR-1 62 IMX=IMX-1 63 CONTINUE C C LEAST SQUARES TO CALCULATE UNIT GRAPH ORDINATES C DO 5000 IPC=1, IT I PT= IX ( IPC ) DO 4999 17=1,NL R 0 ( I 7 , I P C ) = R 0 ( I 7 , I P T ) 4999 ROT( 17, I P C ) = R 0 U 7 , IPT) 5000 CONTINUE DO 5001 IZ=1,NL R 0 ( I Z , I T P ) = Y ( I Z ) 5001 CONTINUE CALL S O L S V D ( R O , S S S , V O D , 8 0 , 8 0 , N L , I T , 1) S P P = S S S ( 1 ) * l E - 7 DO 209 J=1 , I T S J = S S S (J) I F ( S J . L T . S P P ) G 0 T 0 2 0 8 DO 205 1=1,IT 205 V D D ( I , J ) = V D O ( I , J ) / S J G0T0209 208 P R I N T 2 1 0 , { V D D ( I , J ) , I = 1 , N L ) 210 FORMAT( ' > ,1X ,5E12 .5 ) DO 211 1=1,IT 211 V D D ( I , J ) = 0 . 209 CONTINUE DO 207 1=1,IT 207 G ( I ) = R0 ( I » I TP ) CALL GMATV(VDD,G,B»IT,IT,80) I F ( J W T . G T . l ) GO TO 56 READ(5,814) ( T I T ( I ) , 1 = 1 , 8 0 ) 814 FORMAT(80A1) 56 WRITE(6,815) TIT 815 FORMAT(1H0»80A1) KD=1 SUMU=.5*8(1) DO 403 1=2,IT X P = I X ( I ) - I X ( K D ) A P = ( B ( I ) + B ( K D ) ) * ( X P / 2 ) SUMU=SUMU+AP KD=I 403 CONTINUE C C CALCULATE VOLUME IN UNIT GRAPH C XNCH=(SUMU*43200/5280**2)/DRBS PRINT401,XNCH 401 FORMAT(1H0,'CORRECTION TO UGRAPH I S ' , 3 X , F 7 . 4 ) DO 402 1 = 1, IT 402 B( I )=B( I )/XNCH WRITE ( 6 , 3 7 ) 37 FORMAT(1H0,28X,• HYDROGRAPH*/50X, 1'ORDINATES' ) DO 38 1 = 1, IT 11X= IX ( I ) XI X ( I )=IX( I ) WRITE ( 6 , 4 0 ) I I X , B ( I ) 40 F0RMAT(39X,'U',I2,8X,F7.1) 38 CONTINUE CALL GMATVI ROT,B»QC,NL,IT f80) WRITE(6,189 ) SUMQ=0 DO 55 1=1,NL X P L ( I ) = 1 QD(I) = Y ( I ) - Q C ( I) SUMQ=SUMQ+QD(I)**2 55 WRITE(6,188) I , Q C ( I ) , Y ( I ) , Q D ( I ) 188 FORMAT(IX,•Q' ,12,4X,F5.0,4X,F5.0,4X,F5.1) 189 FORMAT?IX,7X,'CALC Q',3X,•STORM Q•,4X,•DIFFERENCE•) WRITE(6,187) SUMQ 187 FORMAT(lHOt'VARIANCE=',F7.1) IF(SUMQ.LT.5) GO TO 186 C C CALCULATE NEW RUNOFF VALUES C DO 301 M0=1,IP ILA=MO ILA F = I L A + I P - 1 IMC = 1 K7=l DO 302 ILW=ILA,ILAF I F I K 7 . G T . I T ) GO TO 302 I F ( I M C . N E . I X I K 7 ) ) GO TO 317 76 I S X = I X ( K 7 ) UOULWf MO)=B( K7) K7=K7+1 317 IMC=IMC + 1 302 CONTINUE 301 CONTINUE DO 318 I = l t N L U 0 ( I , I P P ) = Q D ( I ) 318 CONTINUE CALL SOLSVD(UO,SS,VD,80,80,NL,IP,1) SP=SS(1 ) * l E - 7 DO 709 J=1,IP S J = S S ( J ) I F ( S J . L T . S P ) G 0 T 0 7 0 8 DO 705 1 = 1, IP 705 V D ( I , J ) = V D ( I , J ) / S J G0T0709 708 P R I N T 7 1 0 , ( V D ( I , J ) , I = 1 , N L ) 710 FORMAT{' ',1X,5E12.5) DO 711 I=1,NL 711 V D ( I , J ) = 0 . 709 CONTINUE DO 712 1=1, IP 712 F R ( I ) = U 0 ( I , I P P ) CALL GMATV(VD,FR,E,IP,IP,80) SUMR=0 DO 305 1 = 1, IP R ( I ) = R ( I ) + E ( I ) RI = R( I ) FI P = RAW(I ) IF (RI .LT.O.O) R U ) = 0 . I F ( R I . G T . F I P ) R ( I ) = F I P 305 SUMR=SUMR+R(I) DSUM=SUMB-SUMR FUDG=DSUM/IP WRITE(6,510) SUMB,SUMR,DSUM,FUDG 510 FORMAT(/,•SUM8=«,F6.4,10X,•SUMR=•,F6.4,10X,•DSUM=»,F6.4, 110X,«FUDG=',F6.4) PRINT718 718 FORMAT(1H0,10X,* NEW RUNOFF VALUES') DO 304 1=1,IP R ( I ) = R(I)+FUDG R I N F I L = RAWU)-R( I ) I F t R I N F I L . L T . 0 . ) R I N F I L = 0 . 0 PRINT717,I,E< I ) , I , R ( I ) , I , F ( I ) , I , R I N F I L 717 FORMAT!IX,'£( • , I 2,') = »,F7.4,7X,•R(»,12,•)=• tF7.4,7X, 1 ' O R I G ( ' , 1 2 , ' ) = ' , F 7 . 4 , 7 X , ' I N F I L T ( • , 1 2 , • ) = • , F 7 . 4 ) JWT=JWT+1 304 CONTINUE 186 STOP END 

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