UNIT HYDROGRAPHS - PRAIRIE REGION

RESEARCH REPORT

J. M. Wigham

U N I T HYDROGRAPHS - P R A I R I E REGION

RESEARCH REPORT

D I V I S I O N OF HYDROLOGY

Research Report No. 17, Div is ion of Hydrology, College of Engineering, Univers i ty of Saskatchewan, Saskatoon, Saskatchewan.

TABLE OF CONTENTS

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . EFFECTIVE: DRAINAGE AREA

General . . . . . . . . . . . . . . . . . . . . . . . . . Development and U s e of Non-Dimensional Curves . . . . . .

. . . . . . . . . . . . . . . . . Resu l t s and Discussion

. . . . . . . . . . . . . . . . . . . UNIT HYDROGRAPH DURATION

General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Durat ion from S-Hydrographs

. . . . . . . . . . . . Durat ion from Hydrograph Analysis

Durat ion Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion and Recommendations

. . . . . . . . . . . . . APPENDIX A . Durat ion Analyses

. . . . . . . . . . . . . APPENDIX B . Computer Programs

LIST OF FIGTJRES

Page

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Figure

Figure

Figure

Figure

Figure

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Flood Frequency Div is ions and Mean Annual Flood Regions on t h e Canadian P r a i r i e s . . . . . . . . . 6

Regional V a r i a t i o n of Mean Annual Flood wi th Drainage Area . . . . . . . . . . . . . . . . . . 7

R a t i o of Mean Dai ly Discharge t o Mean Annual Flood w i t h Return Per iod by Div i s ions . . . . . . 8

Dimensionless Discharge Ra t io and E f f e c t i v e Area Curves . . . . . . . . . . . . . . . . . . . 9

Dimensionless Discharge and E f f e c t i v e Area Curves f o r Middle Creek and Lodge Creek

. . . . . . . . . . . . . . . . . . . T r i b u t a r i e s 16

Dimensionless Discharge and E f f e c t i v e Area Curves f o r Lodge Creek Drainage Basin . . . . . . 17

Schematic of a Watershed System Having D i f f e r e n t . . . . . . . . . . . . Storage and Loss Elements 22

S-Curve V a r i a t i o n and Ca lcu l a t i on of Unit . . . . . . . . . . . . . . . Hydrograph Durat ion 26

D e f i n i t i o n Sketch of Components of a Runoff . . . . . . . . . . . . . . . . . . . . Hydrograph 28

LIST OF TABLES

Table 1 . Dimensionless Ef fec t ive Area Curves . . . . . . . . Table 2 . Drainage Areas Tr ibutary t o t h e Qu' Appelle

. . . . . . . . . . . . . . . . . River by Reaches

Table 3 . Average Dimensionless E f f e c t i v e Area Curves . . . . Table 4 . Maximum and Minimum Unit Hydrograph Durations

Found by S-Curve Technique . . . . . . . . . . . . Table A l . Predic ted Durations . . . . . . . . . . . . . . . . Table A2 . R a i n f a l l Duration . . . . . . . . . . . . . . . . . Table B 1 . Computer Programs . . . . . . . . . . . . . . . . .

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10

INTRODUCTION

The hydrographs of runoff f o r a s t ream i n t h e P r a i r i e Region i s

a f f e c t e d by t h e d i s t i n c t i v e topographic and c l i m a t i c cond i t i ons preva-

l e n t i n t h e a r e a . Most of t h e runoff from p r a i r i e watersheds occurs

du r ing t h e snowmelt per iod and t h e r a p i d i t y of t h e melt and t h e volume

of runoff may va ry cons iderably . P r a i r i e watersheds a l s o a r e cha rac t e r -

ized by f l a t l and s lopes and l a r g e a r e a s of p o s s i b l e water shor tage .

The r e s u l t of t h e l a t t e r i s a cons iderable v a r i a t i o n i n t h e percentage

of runoff from storms o r snowmelt events a s t h e s t o r a g e volumes a r e

dependent on antecedent catchment cond i t i ons .

The e f f e c t s of v a r i a t i o n s i n catchment water s to rage may b e taken

i n t o account through t h e use of a v a r i a b l e dra inage a r e a a s proposed

by S t i c h l i n g and Blackwell (1958). The hydrograph of runoff then may

be ca t egor i zed by r e f e r r i n g t o t h e dra inage producing i t . Genera l ly ,

t h e r e a r e t h r e e major d i v i s i o n s made i n con t r ibu t ing a r e a and t h e s e a r e

c a l l e d d r y , wet and g ros s drainage a reas , each of which may b e r e l a t e d

t o a runoff event of a given frequency.

The catchment a r e a producing runoff i s important i n any u n i t

hydrograph d e r i v a t i o n a s it is used t o determine t h e average depth of

runoff from t h e a r e a . The con t r ibu t ing a r e a t h e r e f o r e must be determined

f o r each hydrograph analyzed.

The u n i t hydrograph d u r a t i o n usua l ly i s determined from examination

of t h e t i m e v a r i a t i o n s of t h e event producing t h e runof f . Determination

of t h e e f f e c t i v e du ra t ion i s d i f f i c u l t i f t h e hydrograph r e s u l t s from

snowmelt. R a i n f a l l d a t a may be nonrep resen ta t ive o r too f a r away f o r

u se on small catchments so summer runoff events a l s o a r e d i f f i c u l t t o

analyze.

A l a r g e number of summer and s p r i n g runoff even t s from catchments

i n Saskatchewan were examined i n an at tempt t o develop a s tandard method

of u n i t hydrograph d e r i v a t i o n f o r t h e p r a i r i e r eg ion . Emphasis was

placed on ways i n which the c o n t r i b u t i n g a r e a could be considered and on

methods of determining t h e e f f e c t i v e du ra t ion f o r t h e u n i t hydrograph.

EFFECTIVE DRAINAGE ARTlA

General Concepts

The e f f e c t i v e drainage a r e a , f o r a catchment, may be def ined a s

t h a t p a r t of t h e catchment t h a t might be expected t o e n t i r e l y c o n t r i b u t e

runoff t o t h e main s t ream dur ing a runoff event . It i s t h e sum of t h e

a r e a s of a l l t h e sub-areas con t r ibu t ing t o t h e runoff r e g a r d l e s s of t h e i r

type o r p h y s i c a l l o c a t i o n on t h e watershed.

The e f f e c t i v e drainage a r e a a t a given t ime, may be considered t o

be a func t ion of t h e topography of t h e a r e a and of t h e antecedent con-

d i t i o n s of p r e c i p i t a t i o n , evapo t r ansp i r a t ion and i n f i l t r a t i o n as these

d e f i n e t h e s to rage p o t e n t i a l of each of t h e sub-areas. The p o r t i o n of

t h e p r e c i p i t a t i o n o r snowmelt a v a i l a b l e f o r runoff from a sub-area is

the g ros s amount l e s s t h a t used t o s a t i s f y t h e s to rage requirements .

The t o t a l volume of runoff and t h e peak va lue a r e r e l a t e d t o t h e average

excess and t o t h e t o t a l con t r ibu t ing a r e a o r summation of t h e sub-areas.

A given runoff volume could be produced by a l a r g e excess over a sma l l

a r e a o r by a sma l l e r excess over a l a r g e r a r e a , however, because of t h e

i n t e r r e l a t i o n s h i p of excess volume and c o n t r i b u t i n g a r e a t h e l a r g e r

runoff events a r e l i k e l y t o be produced from t h e l a r g e r con t r ibu t ing

a r e a s . The peak flows and t h e hydrograph shapes would be d i f f e r e n t i n

t h e two cases and t h e peak flow a l s o i s l i k e l y t o b e dependent on t h e

c o n t r i b u t i n g a rea . It i s perhaps poss ib l e t h e r e f o r e , t o r e l a t e a runoff

f lood peak of a given r e t u r n per iod t o t h e e f f e c t i v e a r e a of t he watershed.

S t i c h l i n g and Blackwell (1958) suggested t h e use of an e f f e c t i v e

a r e a f o r hydro logic s t u d i e s . Three drainage a r e a d e f i n i t i o n s based on

t h e i r s t u d i e s a r e given below;

(1) Gross drainage a r e a

The g ros s drainage a r e a of a s t ream a t a s p e c i f i e d l o c a t i o n i s

t h a t p lane a r e a enclosed by i ts drainage d iv ide and which might be

expected t o e n t i r e l y c o n t r i b u t e runoff t o t h e s p e c i f i e d l o c a t i o n only

under extreme condi t ions .

(2) Wet dra inage a r e a

That p o r t i o n of a drainage bas in which might be expected t o

e n t i r e l y c o n t r i b u t e runoff t o t h e main s t ream dur ing per iods of much

above normal p r e c i p i t a t i o n , say t h e one i n 50 year f lood . I n gene ra l ,

i t inc ludes any p o r t i o n of t h e bas in which i s connected t o t he main

s t ream by any i n d i c a t i o n of a channel.

(3) Dry dra inage a r e a

That po r t ion of a dra inage bas in which might be expected t o

e n t i r e l y c o n t r i b u t e runoff t o t h e main s t ream dur ing per iods of low

p r e c i p i t a t i o n , say t h e one i n two-year f lood . This a r e a excludes marsh

and s lough a r e a s and o t h e r n a t u r a l o r a r t i f i c i a l s t o r a g e a r e a s which

would prevent runoff reaching t h e main s t ream i n an average year .

It i s p o s s i b l e t o r e l a t e t h e e f f e c t i v e a r e a t o f lood peaks of

s p e c i f i e d r e t u r n per iod through t h e above d e f i n i t i o n s . The g ros s dra in-

age a r e a could be assumed t o be the e f f e c t i v e a r e a f o r t h e maximum

probable f lood .

The Saskatchewan Water Resources Commission and the P r a i r i e Farm

R e h a b i l i t a t i o n Agency have determined the d ry , wet and g ros s dra inage

a r e a s f o r many watersheds i n Saskatchewan, us ing topographic maps and

f i e l d information. An ex tens ive s tudy of t h e magnitude and frequency

of f l oods on va r ious p r a i r i e watersheds was r epo r t ed by Durrant and

Blackwell (1959). These two sources of information provided t h e d a t a

necessary t o r e l a t e e f f e c t i v e a r e a and f lood peaks of a p p r o p r i a t e

r e t u r n per iod .

Develo~ment and U s e of Non-Dimensional Curves

The d ry , w e t and g ros s dra inage a r e a s were obta ined from t h e

Saskatchewan Water Resources Commission and/or P.F.R.A. f o r some 30

watersheds and f o r some 20 odd t r i b u t a r i e s o r reaches of t h e QulAppelle

River . The two-year and f i f t y -yea r r e t u r n per iod f lood peaks were

determined f o r t h e s e watersheds us ing t h e method suggested by Durrant

and Blackwell. This cons i s t ed of determining t h e l o c a t i o n of t h e water-

shed i n terms of t h e Div is ion and Region d e l i n e a t i o n s of Figure 1 and

using t h e app ropr i a t e curves on Figures 2 and 3 t o determine t h e mean

annual f lood and t h e f lood peaks of t h e des i r ed r e t u r n per iod . The

dry dra inage a r e a was used a s t h e e f f e c t i v e a r e a i n determining the

mean annual f l ood r a t i o obtained from Figure 3 then allowed c a l c u l a t i o n

of t h e f lood peak.

A method of p l o t t i n g t h e corresponding e f f e c t i v e a r ea - f l ood peak

i n a non-dimensional way was developed i n order t o determine i f some

r eg iona l s i m i l a r i t i e s e x i s t e d between watersheds. The procedure adopted

was t o d i v i d e t h e dry (A ) and wet (A ) dra inage a r e a s by t h e g ros s d w

dra inage a r e a (A ) t o provide non-dimensional a r e a r a t i o s . The two- G

year (Q ) and f i f t y - y e a r r e t u r n per iod (QS0) f loods were d iv ided by 2

t h e f i f t y - y e a r r e t u r n per iod f lood g iv ing non-dimensional flood-flow

r a t i o s . The Q2/Q50 r a t i o was p l o t t e d a g a i n s t Ad/AG and t h e 950/c)50

r a t i o was p l o t t e d aga ins t t h e %/AG p o s i t i o n . A curve then was drawn

through t h e two r a t i o p o i n t s and t h e o r i g i n . A t y p i c a l r e s u l t i s shown

i n Figure 4.

The non-dimensional e f f e c t i v e a r ea curves were drawn f o r t h e t h i r t y

s t a t i o n s l i s t e d i n Table 1 and f o r 38 t r i b u t a r i e s o r reaches of t h e

Qu'Appelle River a s l i s t e d i n Table 2.

A s e p a r a t e s tudy us ing d a t a f o r t h e Lodge Creek bas in i n south-

wes tern Saskatchewan a l s o was completed. The e f f e c t i v e dra inage a rea

Flood ~ r k u e l i c ~ Divisions and Mean A~i~iual Flood llegio~is on thc Canadian Prairies.

Figure 1

- (I) LL 0 - - l i

.1,003 - a - ri

- - - - -

n 0

- 0 -I - LL

- -I a 3 Z 5 l o o - - - Z a - W - E -

-

-

R E G I O N 7

M A F. - A'.?

k R E G I O N 3

Y . M.A.F. - A ' . ' ~

R E G I O N 5

M.A.F. - A'"

EFFECTIVE DRAINAGE AREA - SQ. M I .

Regional Variation of Mean Annual Flood with Drainage Area.

Figure 2

EFFECTIVE AREA RATIO A/AG

Figure 4. Dimensionless Discharge Ratio and Effective Area Curves

Table 1

Dimensionless E f f e c t i v e Area Curves

A r m River near Bethune

Berry Creek nea r t h e mouth

Cutarm River nea r Spy H i l l

Fahlman Creek near Davin

Frenchman River below Eastend I r r i g a t i o n P r o j e c t

Horse Creek a t I n t e r n a t i o n a l Boundary

Indian Head Creek nea r Indian Head

Jumping Deer Creek near Lipton

Kaposvar Creek nea r Esterhazy

Lodge Creek a t I n t e r n a t i o n a l Boundary

Long Creek near Noonan

Long Creek a t Western Crossing a t I n t e r n a t i o n a l Boundary

Lyons Creek a t I n t e r n a t i o n a l Boundary

Manyberries Creek a t Brodin 's Farm

Moose Jaw River nea r Rouleau

Moose Jaw River above Thunder Creek

Pheasant Creek near Abernathy

Pheasant Creek near Blackwood

Pipestone Creek above Moosomin Reservoir

East Poplar River a t I n t e r n a t i o n a l Boundary

Middle Branch of Poplar River a t I n t e r n a t i o n a l Boundary

Table 1 (Continued)

Qu'Appelle River above Buffalo Pound Lake

Russe l l Creek near Vanguard

Sour is River near Estevan

Swan River nea r Norquay

Swift Current Creek a t Swif t Current

Torch River nea r Love

Whitewater Creek a t I n t e r n a t i o n a l Boundary

Woodpile Coulee nea r I n t e r n a t i o n a l Boundary

Wood River n e a r La Fleche

Table 2

Drainage Areas Tr ibutary t o the OulAppelle River by Reaches

Reach No. Location of Downstream End of Reach

1 QulAppelle above Buffalo Pound Lake a t t he gauging s t a t i o n (05JG004)

2 Qu'Appelle j u s t below Buffalo Pound Lake

3 Moose J a w River near Rouleau a t t h e gauging s t a t i o n (05JE004)

4 Moose Jaw River above Thunder Creek a t t h e gauging s t a t i o n (05JE001)

5 Moose Jaw River above the Qu'Avpelle a t t h e gauging s t a t ion (05JG006)

6 Qu'Appelle below Moose Jaw River (05JC007)

7 Wascana Creek at Sedley a t the gauging s t a t i o n (05JF004)

8 Wascana Creek a t Richardson a t t he gauging s t a t i o n (05JF009)

9 Wascana Creek above t h e Qu'Appelle a t t he gauging s t a t i o n (05JF005)

10 Local inf low area t o the gauging s t a t i o n QulAppelle a t Lumsden (05JFOOl)

11 Boggy Creek above the QtllAppelle a t the gauging s t a t i o n (05JF006)

12 Lanigan Creek below divers ion a t the gauging s t a t i o n (0555003)

1 3 A r m River nea r Bethune a t the gauging s t a t i o n (05JH001)

1 4 Ungauged inflow t o Last Mountain Lake a t Valeport dam

Table 2 (Continued)

Reach No. Location of Downstream End of Reach

Local in f low t o Craven a t t h e gauging s t a t i o n (05JK003)

Loon Creek near Markinch a t t h e gauging s t a t i o n (05JK006)

Local inf low t o C?ulAppelle below Loon Creek a t t h e gauging s t a t i o n (05X007)

Jumping Deer Creek n e a r Lipton a t t h e gauging s t a t i o n (05JK004)

Ungauged inf low t o Pasqua Lake

llngauged inf low t o Echo Lake

Ungauged i n f l o t j t o Mission Lake

Ungauged inf low t o Katepwa Lake o u t l e t a t t h e gauging s t a t i o n (05JL001)

Pheasant Creek near Abernethy a t t h e gauging s t a t i o n (05JL005)

Pheasant Creek a r e a between Abernethy s t a t i o n and Blackwood gauging s t a t i o n (05JL003)

Indian Head Creek near Indian Head a t t h e gauging s t a t i o n (05JL002)

Redfox Creek a t t h e confluence w i t h t h e QulAppelle River

Adair Creek a t t h e confluence wi th t h e QulAppelle River

Local inf low t o the gauging s t a t i o n C?ulAppelle a t Hyde (05JM013)

P e a r l Creek a t t h e confluence wi th the QulAppelle River

Ungauged inf low t o Crooked Lake

Table 2 (Continued)

Reach No.

3 1

Location of Oownstream End of Reach

Ekapo Creek a t the confluence with the Qu'Appelle River

IJngauged inflow t o R-ound Lake

Kaposvar Creek near Esterhazy a t the gauging s t a t i o n (05JM012)

Kaposvar Creek a rea between Esterhazy and Tantal lon gauging s t a t i o n s (05JM005)

Local inflow t o t h e gauging s t a t i o n Qu'Appelle a t Tantal lon (05JM003)

Cutarm Creek near Spy H i l l - upper gauging s t a t i o n (05JM015)

Cutarm Creek a r e a between upper and lower Spy H i l l gauging s t a t i o n (05JM004)

Local inflow Tantal lon t o the Assiniboine River

discharge r e l a t i o n s h i p s f o r four t r i b u t a r i e s a r e shown i n Figure 5 and

t h e corresponding non-dimensional e f f e c t i v e a rea curve i s shown i n

Figure 6. The p o i n t s shown on the curves i n Figure 5 correspond t o t h e

two-year and 50-year r e t u r n period d ischarges p l o t t e d a t the e f f e c t i v e

a r e a pos i t ions f o r t h e dry drainage and wet drainage a reas r e spec t ive ly .

The dura t ion of a u n i t hydrograph proceeds by using t h e peak flow - e f f e c t i v e a r e a r e l a t i o n s h i p o r the non-dimensional e f f e c t i v e a r e a curve

t o determine t h e e f f e c t i v e a rea f o r a given runoff event . The peak

discharge f o r the event i s divided by t h e f i f ty -yea r r e t u r n per iod

f lood f o r t h e catchment. This provides a discharge r a t i o which can be

used wi th the non-dimensional e f f e c t i v e a r e a curve f o r t h e catchment t o

y i e l d a va lue f o r t h e r a t i o of the e f f e c t i v e a r e a t o t h e g ross area .

This r a t i o when mul t ip l i ed by the gross a r e a gives the e f f e c t i v e con-

t r i b u t i n g a r e a f o r t h e event .

The a n a l y s i s of the hydrograph of t h e event proceeds along f a m i l i a r

l i n e s i n t h a t a composite recess ion curve i s used t o sepa ra te complex

hydrographs i n t o sdmple components a f t e r which t h e base flow, i f any,

i s sub t rac ted from t h e hydrograph. The volume of flow under t h e r e s u l t -

i n g su r face runoff hydrograph then i s divided by t h e e f f e c t i v e con t r ibu t ing

a r e a f o r t h e event . This r e s u l t s i n t h e r a i n f a l l excess depth o r snowmelt

depth, which over t h e e f f e c t i v e con t r ibu t ing a r e a , produced t h e recorded

flows. The o rd ina tes of the hydrograph a r e divided by t h i s excess depth

value i n inches r e s u l t i n g i n a u n i t hydrograph appl icable t o the

e f f e c t i v e con t r ibu t ing area .

Figure 6. Dimensionless Discharge and Ef fec t ive Area Curves f o r Lodge Creek Drainage Basin

The u n i t hydrographs f o r a number of events may be compared and,

i f s u f f i c i e n t l y s i m i l a r i n shape and i n d u r a t i o n , may be used t o produce

an average u n i t hydrograph. This u n i t hydrograph would apply over t h e

range of c o n t r i b u t i n g a r e a s of t h e even t s used i n i t s de r iva t ion .

Resu l t s and Conclusions

The non-dimensional e f f e c t i v e a r e a curve f o r Lodge Creek a s shown

on Figure 6 i s t h e curve r ep re sen t ing t h e d a t a f o r fou r p a r t s of t h e

Lodge Creek bas in . It would appear t h a t a s i n g l e non-dimensional curve

may apply f o r a b a s i n and i t s t r i b u t a r i e s .

The non-dimensional e f f e c t i v e a r ea curves f o r t h e o t h e r watersheds

s tud ied were compared t o each o t h e r and groupings made on t h e b a s i s of

s i m i l a r i t y of curve shape. The r e s u l t s of t h e comparisons a r e shown i n

Table 3 a s a l i s t i n g of groups of watersheds wi th s i m i l a r non-dimensional

e f f e c t i v e a r e a curves. It would appear t h a t t h e r e a r e some r e g i o n a l

c h a r a c t e r i s t i c s p re sen t though some of t h e watersheds l i s t e d i n a group

a r e widely separa ted i n a c t u a l l oca t ion . The s i m i l a r i t y of shape pro-

bably r e p r e s e n t s no more than a s i m i l a r i t y of topographic c h a r a c t e r i s t i c s

a s t h e a r e a r a t i o s of dry t o gross and w e t t o gross a r e , by d e f i n i t i o n ,

determined by t h e topography. The flow r a t i o s a l s o a f f e c t t h e p o s i t i o n i n g

of t h e curves , however, only t h e two-year t o f i f t y - y e a r r a t i o is e f f e c t i v e .

The magnitudes of t hese flows a r e determined from reg iona l curves hence

t h e r e must be some inhe ren t tendency t o r eg iona l s i m i l a r i t i e s . The

r eg iona l n a t u r e of t h e curves might be more meaningful and apparent i f

-19-

Table 3

Average Dimensionless Ef fec t ive Area Curves

Group I

(1) Long Creek near Noonan

(2) Long Creek a t Western Crossing a t I n t e r n a t i o n a l Boundary

(3) Sour is River nea r Estevan

Group I1

(1) Moose Jaw River near Rouleau

(2) Moose Jaw River above Thunder Creek

Group 111

(1) Arm River near Bethune

(2) Indian Head Creek near Indian Head

(3) Pheasant Creek near Abernathy

(4) Pheasant Creek near Blackwood

(5) Ou'Appelle River above Buffalo Pound Lake

Group I V

(1) Cutarm River near Spy H i l l

(2) Kaposvar Creek near Esterhazy

Group V

(1) Eas t Poplar River a t I n t e r n a t i o n a l Boundary

(2) Swift Current Creek a t Swift Current

Table 3 (continued)

Group V I

(1) Frenchman River below Eastend I r r i g a t i o n Projec t

(2) Manyberries Creek a t Brodin's Farm

Group V I I

(1) Berry Creek near t h e mouth

(2) Fahlman Creek near Davin

(3) Lodge Creek a t In t e rna t iona l Boundary

( 4 ) Lyons Creek a t I n t e r n a t i o n a l Boundary

(5) Swan River nea r Norquay

(6) Russe l l Creek near Vanguard

(7) Woodpile Coulee near I n t e r n a t i o n a l Boundary

Single Grouping

- Jumping Deer Creek near Lipton

- Torch River near Love

- Pipestone Creek above Moosomin Reservoir

- Wood River near La Fleche

- Whitewater Creek a t I n t e r n a t i o n a l Boundary

t h e flow r a t i o s w e r e developed us ing some va lues of t h e maximum probable

f l ood from the g ros s dra inage a rea i n s t e a d of us ing t h e f i f t y - y e a r r e t u r n

period flow. The curves then would pass through an a r e a r a t i o of 1 .0 a t

a maximum discharge r a t i o of 1 . 0 w i th t h e dry and wet a r eas and t h e

corresponding flows provid ing two p o i n t s a t l e s s e r r a t i o va lues . E s t -

imates of maximum probable f l oods were n o t a v a i l a b l e and were d i f f i c u l t

i f n o t impossible t o develop s o were n o t used. The number of groups

shown i n Table 3 and anamalies w i t h i n them prec lude a t tempts a t t h i s time

t o de f ine curves which could be s t a t e d t o apply t o a given reg ion . This

is unfor tuna te a s r eg iona l curves could be used f o r watersheds f o r which

the dry and wet dra inage a r e a s a r e n o t ava i l ab l e .

It should be recognized t h a t t h e r e l a t i o n s h i p shown a s a l i n e on

each f i g u r e a c t u a l l y i s a band a s a given flow could r e s u l t from d i f f e r e n t

excesses of snowmelt o r r a i n f a l l over d i f f e r e n t a r eas a s p rev ious ly noted.

The width of t h e band would depend on t h e range of antecedent condi t ions

t h a t could occur and which would modify t h e s to rage and l o s s p o t e n t i a l of

t he va r ious p a r t s of t he watershed. The curves a r e intended f o r use i n

t h e development of u n i t hydrographs so t h e use of a s i n g l e l i n e represent -

i n g perhaps some average r e l a t i o n s h i p between e f f e c t i v e a r e a and peak f low

is s u f f i c i e n t . The curves drawn a r e smooth and t h i s a l s o does n o t have t o

be the case - t h e r e would be breaks i n t he curve r ep re sen t ing a d d i t i o n a l

sub-areas becoming e f f e c t i v e i n providing flow. The use of a smooth curve

does n o t seem unreasonable, however, i n view of t he o the r problems and

inaccu rac i e s of u n i t hydrograph development.

Implications for Watershed Models

The form of the non-dimensional effective area curves implies a

watershed system consisting of a series of storage and loss elements,

each of which must be filled before contributions from the element to

runoff can begin. A schematic of this type of system is shown in

Figure 7 (a). Figure 7 (b) shows a system which provides for varia-

tions in the storage and loss quantities and probably is more

representative of the physical behaviour.

V) W V) V) o EXCESS AVAILABLE J FOR RUNOFF V) 3 J Q

RAINFALL OR

w ABOVE BASE- C3 4 a 0 + V)

POSITION BASE LEVEL POSITION

Figure 7 (a)(b). Schematic of a Watershed System Having Different Storage and Loss Elements

The form of this model is similar to that of Kohler and Richards

(1962) for determining rainfall excesses from portions of catchments

having different soil characteristics in that there are a number of

s t o r a g e elements of unequal va lue . The i n c l u s i o n of l a r g e depress ion

s t o r a g e components i s necessary , however, t o conform t o t h e phys i ca l

s i t u a t i o n as c l o s e l y a s poss ib l e . The use of a l i n e on t h e non-dimensional

e f f e c t i v e a r e a curves impl ies t h a t t h e summation of s to rage and l o s s f o r

each element does not change o r i s t h e same from one event t o another .

This w i l l s u f f i c e only a s an i n i t i a l approximation though t h e presence of

l a r g e depress ion s t o r a g e components may make t h e assumption f e a s i b l e f o r

use f o r semi-arid condi t ions .

UNIT HYDROGRAPH DURATION

General

The du ra t ion of t h e p r e c i p i t a t i o n o r snowmelt excess is used t o

d e f i n e t h e du ra t ion of t h e u n i t hydrograph r e s u l t i n g from t h e excess .

The du ra t ion must be known so t h a t an average u n i t hydrograph can be

developed from u n i t hydrographs of s i m i l a r dura t ion . The de termina t ion

of du ra t ion from examination of p r e c i p i t a t i o n records i s d i f f i c u l t f o r

p r a i r i e catchments because such records f r equen t ly a r e a v a i l a b l e only

f o r s t a t i o n s remote from t h e catchment and c o n s i s t of d a i l y records .

I n a d d i t i o n , t h e e s t ima t ion of t h e e f f e c t i v e d u r a t i o n of r a i n f a l l i s

complicated by t h e d i f f i c u l t y of e s t ima t ing t h e l o s s e s , which u s u a l l y

a r e a s u b s t a n t i a l p ropor t ion of t h e g ros s r a i n f a l l amounts. Accordingly,

some method based on t h e runoff records a lone would be u s e f u l .

Duration From S-Hydrographs

It has been recognized f o r some t i m e t h a t t h e f l u c t u a t i o n of an S-

hydrograph about i t s maximum t h e o r e t i c a l o r d i n a t e may i n d i c a t e a n

i n c o r r e c t choice of t h e du ra t ion of t h e u n i t hydrograph used i n t h e

development. The f l u c t u a t i o n s a l s o may be due t o a v a r i e t y of o t h e r

causes inc luding t h e non- l inea r i t y of t h e system, e r r o r s i n s epa ra t ion

methods and non-uniformity of r a i n f a l l excess . It seemed d e s i r a b l e ,

however, t o i n v e s t i g a t e t h e S-curve a s a means of determining du ra t ion

as i t may be e a s i l y obta ined from a u n i t hydrograph wi th an assumed

dura t ion .

An a r t i f i c i a l u n i t hydrograph was developed which y ie lded an S -

curve which d id n o t f l u c t u a t e about i t s maximum ord ina t e when a

p a r t i c u l a r du ra t ion was ass igned t o t h e u n i t hydrograph. The e f f e c t s

of assuming o t h e r ( i n c o r r e c t ) du ra t ions f o r t h e u n i t hydrograph were

determined by c a l c u l a t i n g a new S-curve f o r each dura t ion . It was

noted t h a t a smooth S-curve r e s u l t e d when t h e assumed du ra t ion was a

f a c t o r of t h e c o r r e c t one b u t n o t i f t h e assumed du ra t ion was a

mul t ip l e of o r any o the r va lue than t h e c o r r e c t one. For example, i f

a u n i t hydrograph has a c o r r e c t du ra t ion of 12 hours , smooth S-curves

would be obtained f o r assumed du ra t ions of 1, 2, 3 , 4 , 6 o r 12 hours

but n o t f o r 8, 16 , 24 o r 36 hours . The c o r r e c t du ra t ion f o r a u n i t

hydrograph can be assumed, t h e r e f o r e , t o be t h e l a r g e s t du ra t ion which

produces a reasonably smooth S-curve.

The procedure f o r determining t h e du ra t ion by the S-curve technique

c o n s i s t s of developing a number of S-curves from the u n i t hydrograph,

f o r a number of assumed dura t ions . The S-curves a r e examined and the

maximum dura t ion which produces t h e minimum f l u c t u a t i o n i s assumed t o

be c o r r e c t . The minimum f l u c t u a t i o n may be determined by comparing the

S-curve va lue (P ) a t t h e p o i n t a t which the S-curve should reach 1

equi l ibr ium t o the va lue (P ) which i s one un5t du ra t ion away ( see 2

Figure 8). The d i f f e r e n c e between t h e maximum and minimum va lues

between P and P i s determined and t abu la t ed f o r each assumed du ra t ion 1 2

( see Table 4 ) and the choice of du ra t ion made on the b a s i s of minimizing

t h i s value.

The ins tan taneous u n i t hydrograph may be developed from t h e S-

curve. I f i t is d i f f i c u l t t o choose t h e du ra t ion from the S-curve

a n a l y s i s a lone then minimizing t h e f l u c t u a t i o n s i n t h e ins tan taneous

u n i t hydrograph may a s s i s t . The average equi l ibr ium o r d i n a t e of t h e

S-curve a l s o should be reasonably co r r ec t .

I n a c t u a l p r a c t i c e t h e a p p l i c a t i o n of t he S-curve technique may

n o t g ive a very p r e c i s e i n d i c a t i o n of t he c o r r e c t dura t ion . The e f f e c t

of many incons i s t enc i e s customari ly induced i n t o t h e u n i t hydrograph

due t o such f a c t o r s a s non-uniform i n t e n s i t y and a r e a l d i s t r i b u t i o n of

t he runoff producing event a r e bound t o show a s f l u c t u a t i o n s i n t h e S-

curve. It i s seldom p o s s i b l e t o s epa ra t e t hese e f f e c t s from those

induced by us ing an i n c o r r e c t u n i t du ra t ion wi thout accu ra t e information

about t h e event which i s , of course , gene ra l ly no t a v a i l a b l e .

TIME

Figure 8 . S-Curve Variation and Calculation of Unit Hydrograph Duration

Table 4

Maximum and Minimum Unit Hydrograph Durations Found by S-Curve Technique

% I n d i c a t e s s e l e c t e d du ra t ion

e t c . C

-

2 5 3:-

400

900

B

-

250

75%

800

A

1 2 h r .

24 h r .

36 h r .

60 h r .

e tc .

-

56'

800

700

For tuna te ly t h e runoff hydrographs from a catchment a r e n o t very

a s e n s i t i v e t o t h e e f f e c t i v e d u r a t i o n of r a i n f a l l s o t h e accuracy of t h e

method probably i s s u f f i c i e n t .

Duration From Hydrograph Analysis

An a l t e r n a t e method, a s proposed by DeLaine ( ) , f o r determining

s h o r t d u r a t i o n u n i t hydrographs and t h e i n t e n s i t y and du ra t ion of r a in -

f a l l excess , was examined. It i s assumed t h a t t h e catchment a s a system

i s a l i n e a r and t ime-invariant - which is a l s o the b a s i s of u n i t hydro-

graph concepts. The system response accord ingly i s assumed t o be t h e

same f o r a l l events .

It may be assumed t h a t t h e r e a r e two unknowns - t h e r a i n f a l l excess

time d i s t r i b u t i o n and t h e u n i t hydrograph form - i n an event which

produces a runoff hydrograph. These two unknowns can be determined

t h e o r e t i c a l l y , however, i f two runoff events a r e examined and i f t h e

system response o r u n i t hydrograph is the same f o r both.

The d e f i n i t i o n ske tch (Figure 9 ) may be used t o d e f i n e t h e

components of t he system.

m PARTS n PARTS mtn- l PARTS

Figure 9. D e f i n i t i o n Sketch of Components of a Runoff Hydrograph

4

X

The fol lowing equa t ions may be der ived;

i A '* RUNOFF

EXCESS UNIT PRECIPITATION

HYDROGRAPH HYDROGRAPH

n C h e l S ince i t i s a u n i t hydrograph 1

t t t . TIME T1ME TIME

The i n p u t must equa l t h e ou tput a s t h e i n p u t is exces s p r e c i p i t a t i o n .

The summations may be set equa l t o o n e u n i t y f o r convenience by d i v i d i n g

by t h e a p p r o p r i a t e cons t an t s , then

I f t h e equations 1, 2 and 3 a r e solved t h e r e w i l l be a t least one

set of r e a l va lues t o s a t i s f y t h e equations a s t h e da ta would be from a

real event . I f another output , y , i s used t h e r e w i l l be a second s e t

of so lu t ions which w i l l have the s a m e s e t of u n i t hydrograph o rd ina te

values i f t h e system response is t h e same. Simultaneous s o l u t i o n of

t h e two s e t s of equat ions would provide the common u n i t hydrograph

response.

DeLaine sugges ts one way of so lv ing the equations by descr ib ing

t h e input and system response a s polynomial equat ions

n-1 h(k) = h + h (k) + h (k)2 * * * * * h k

1 2 3 n

then x(k) h(k) = x h + (x h + x h ) k

1 1 1 2 2 1

From equation 1

. e t c .

m+n-2 x(k) h(k) = y l + y (k) + y (k )2 + m m * * *

2 3 Y (k) (6)

mtn-1

It may be seen t h a t t h e polynomial i n equat ion 6 wi th c o e f f i c i e n t s

t h a t a r e success ive o r d i n a t e s of t h e ou tpu t y , i s equal t o t h e product

of t h e two polynomials i n 4 and 5 t h a t have c o e f f i c i e n t s which a r e t h e

success ive o r d i n a t e s of t h e inpu t x and t h e u n i t hydrograph h. The

f a c t o r s of t h e polynomial i n 6 t h e r e f o r e a r e a l s o t h e f a c t o r s of

equat ions 4 and 5.

The procedure followed i n u s ing t h i s method involves us ing two o r

more s u r f a c e runoff hydrographs obta ined from sepa ra t ion procedures

and p re fe rab ly r e s u l t i n g from storms of d i f f e r e n t c h a r a c t e r i s t i c s . The

o r d i n a t e s of t h e hydrographs a r e determined f o r t ime increments equal

t o t h e des i r ed u n i t hydrograph du ra t ion . The summation of t h e o r d i n a t e s

is "normalized" o r s e t equal t o one by d iv id ing each o r d i n a t e by t h e

a c t u a l o r d i n a t e summation. A polynomial equat ion i s developed f o r each

hydrograph us ing t h e normalized runoff o r d i n a t e s a s c o e f f i c i e n t s and

t h e r o o t s of t h e equat ions determined us ing a computer program. The

r o o t s of t h e polynomial equat ions then a r e compared t o each o t h e r and

grouped i n t o matching and non-matching r o o t s . The r o o t s which match

a r e s e l e c t e d and a polynomial expansion preformed. The normalized

o r d i n a t e s a r e t hose of a normalized u n i t hydrograph of a d u r a t i o n equal

t o t h e spacing of t h e o rd ina t e s . The unmatching r o o t s may b e used t o

determine t h e s torm c h a r a c t e r i s t i c s producing t h e runof f .

Durat ion Analyses

The runoff hydrographs from e i g h t watersheds were examined and

u n i t hydrographs developed. The S-hydrograph and/or t h e DeLaine method

w a s used t o eva lua t e t h e u n i t hydrograph du ra t ions . The runoff hydro-

graphs f o r snowmelt even t s as w e l l as f o r r a i n f a l l even t s , were used

though it was recognized t h a t t h e assumption of l i n e a r i t y might n o t be

c o r r e c t i n t h i s case . Where both methods were used, a comparison of

excess r a i n f a l l (or snowmelt excess) du ra t ion was made. The S-hydrograph

method assumes a cons tan t r a t e of r a i n f a l l excess wh i l e t h e DeLaine

method c a l c u l a t e s t h e t ime d i s t r i b u t i o n of excess supply so t h e

comparisons were made w i t h r e s p e c t t o t o t a l du ra t ion .

The watersheds examined were;

1. Lodge Creek a t I n t e r n a t i o n a l Boundary

2 . Middle Creek a t Wright 's Ranch

3 . Indian Head Creek a t Indian Head

4. Pheasant Creek a t Abernathy

5 . Horse Creek a t I n t e r n a t i o n a l Boundary

6 . Middle Branch - Poplar River a t I n t e r n a t i o n a l Boundary

7. Eas t Poplar at I n t e r n a t i o n a l Boundary

8. Experimental Watershed - Lacrosse Wisconsin

The f i r s t seven b a s i n s l i s t e d a r e i n southern Saskatchewan and have

g ros s dra inage a r e a s ranging from 73.5 t o 797 square mi l e s . These b a s i n s

were chosen on t h e a v a i l a b i l i t y of d a t a and l e n g t h and q u a l i t y of record .

I n a l l c a ses t h e a v a i l a b l e p r e c i p i t a t i o n d a t a i s f o r s t a t i o n s r a t h e r

. remote from t h e catchments.

The experimental watershed a t Lacrosse was chosen because i t i s

small (2.71 a c r e s ) and because t h e r e a r e good r eco rds of r a i n f a l l and

runoff . Groundwater flow con t r ibu t ions were non-exis tent f o r t h e even t s

s tud ied so t h e runoff hydrographs were easy t o analyze.

Some of t h e d e t a i l s of t he s t u d i e s a r e shown i n Appendix A. The

d a t a and hydrographs a r e maintained i n f i l e s mentioned the re in .

Discussion and Recommendations

The du ra t ions obta ined f o r t h e u n i t hydrographs us ing t h e S-curve

method appear t o be reasonable f o r the Saskatchewan watersheds considered.

The du ra t ions a r e c o n s i s t e n t w i th e s t i m a t e s based on watershed a r e a and

wi th t h e r a i n f a l l type and du ra t ion l i k e l y t o be e f f e c t i v e i n producing

runoff . A s p rev ious ly noted, t h e method i s s u b j e c t t o a number of

i n f l u e n c e s which a r e l i k e l y t o produce e r r o r s , inc luding a somewhat

s u b j e c t i v e way of desc r ib ing f l u c t u a t i o n s i n t h e curve. The i n s e n s i t i v i t y

of t h e hydrographs t o du ra t ion (wi th in l i m i t s ) a l lows t h e method t o be

used, i n a p r a c t i c a l way, f o r r a i n f a l l events .

The du ra t ions obta ined by t h e S-curve method f o r snowmelt events

were much more v a r i a b l e a s might be expected. The du ra t ions a l s o appear

t o be too smal l i n some cases . The unit-hydrographs o f t e n were n o t

c o n s i s t e n t i n shape i n d i c a t i n g t h e runoff process was d i f f e r e n t f o r

d i f f e r e n t events . It appears t h a t t h e development of a s i n g l e u n i t

hydrograph f o r t h e complete snowmelt event i s n o t p r a c t i c a b l e - t h e

d i u r n a l n a t u r e of t h e snowmelt process i s such a s t o prec lude t h i s .

This was expected, however, i t was considered t h a t t h e n a t u r a l s t o r a g e

and perhaps some cons is tency i n snow accumulations might make t h e

development of a s i n g l e u n i t hydrograph f e a s i b l e .

The DeLaine method of determining t h e u n i t hydrograph and t h e

r a i n f a l l excess producing i t is ve ry a t t r a c t i v e a s only runoff d a t a a r e

requi red . It is much more s e n s i t i v e t o e r r o r s i n hydrograph sepa ra t ion

and d e l i n e a t i o n , however. The t o t a l du ra t ion obtained f o r t h e Lodge

Creek a t t h e I n t e r n a t i o n a l Boundary was reasonable and compared ve ry

we l l w i th t h e du ra t ion obta ined us ing t h e S-curve method. The comparison

was n o t good on t h e small Wisconsin watershed w i t h the DeLaine method

g iv ing r a t h e r h igh d u r a t i o n s and t h e S-hydrograph method r a t h e r low ones.

The matching of r o o t s proved d i f f i c u l t i n most ca ses and r equ i r ed

a s u b j e c t i v e dec i s ion a s t o matching and non-matching groupings. Seve ra l

t r i a l s u s u a l l y were necessary t o develop a grouping which gave reasonable

r e s u l t s . The o r d i n a t e spacing t o use a l s o posed a problem a s a sma l l e r

spac ing increased t h e number of r o o t s t o be determined and a l a r g e

spac ing r e s u l t e d i n l e s s p r e c i s e d e l i n e a t i o n of t h e hydrograph. The

power of t h e method is such t h a t a d d i t i o n a l t ime should be spen t

i n v e s t i g a t i n g t h e a p p l i c a t i o n of i t . The method does n o t r e l y on any

e s t ima t ion of c o n t r i b u t i n g a r e a a s t h i s i s i m p l i c i t i n t h e system of

equat ions .

I n summary, t h e S-curve method provides a rough e s t ima te of t h e

u n i t hydrograph du ra t ion and probably has some p r a c t i c a l va lue i n

hydrograph ana lys i s . The use of t h i s , o r any o t h e r d u r a t i o n technique,

f o r hydrographs of snowmelt runoff w i l l r e l y on a much f i n e r s epa ra t ion

of t h e hydrograph i n t o c o n t r i b u t i o n s from snowmelt on a day t o day

b a s i s a s s i n g l e sp r ing u n i t hydrographs can n o t be obta ined i n c e r t a i n

cases .

The DeLaine method of determining t h e u n i t hydrograph should be

inves t iga t ed f u r t h e r - perhaps some opt imiza t ion technique would a s s i s t

i n t h e d e l i n e a t i o n of t h e u n i t hydrograph and r a i n f a l l excess .

A P P E N D I X A

DURATION ANALYSES

A. Basin S tud ie s

1. Lodge Creek Drainage Basin Study (Ref. F i l e 1/11)

A s tudy on t h e Lodge Creek Basin was cont inued ( see F i l e i/08-5).

The dra inage bas in is loca t ed i n t h e southern p a r t of Alber ta and

Saskatchewan by t h e United S t a t e s border . It i s a t y p i c a l p r a i r i e

watershed and t h e r a i n f a l l r eco rds a r e r a t h e r spa r se .

Two s t a t i o n s were examined i n d e t a i l .

(1) Lodge Creek nea r I n t e r n a t i o n a l Boundary (gross a r e a =

797 sq . mi les ) .

(2) Middle Creek a t Wright 's Ranch (gross a r e a = 151 sq. m i l e s ) .

Lodge Creek a t I n t e r n a t i o n a l Boundary - Moving Averages (Ref. F i l e #11-1)

1. (a) The same records t h a t were previous ly used f o r t h i s s tudy of

Lodge Creek a t I n t e r n a t i o n a l Boundary were aga in examined. This t ime

t h e "moving averages" method which smooths o u t d i u r n a l e f f e c t s w a s no t

used.

The average u n i t hydrographs and ins tan taneous hydrographs compared

very c l o s e l y t o those which were previous ly obta ined . See Graph A i n

F i l e #11-2 f o r a c t u a l comparison of graphs.

It is concluded t h a t i f minor f l u c t u a t i o n s of t h e hydrograph occur

i t is no t necessary t o use t h e moving averages method.

Lodge Creek a t I n t e r n a t i o n a l Boundary - Ear ly Years Record ( ~ e f . F i l e ]Ill-3)

1. (b) I n o rde r t o s e e whether changing land uses over t h e yea r s

caused any v a r i a t i o n s i n t he average u n i t hydrograph, t h e e a r l y yea r s

of record f o r t h e s t a t i o n were examined.

Seven d i f f e r e n t hydrographs were looked a t . A d e t a i l e d S-Curve

a n a l y s i s was done and t h r e e u n i t hydrographs wi th a du ra t ion of 24 hours

were used t o determine an average u n i t hydrograph. This average u n i t

hydrograph was compared wi th t h a t ob ta ined p rev ious ly ( s e e Graph B i n

F i l e - 3 The two u n i t hydrographs compared very c lose ly .

Therefore, i t was assumed t h a t changing land uses and water

development i n t h e Lodge Creek Basin d id no t change t h e average u n i t

hydrograph s i g n i f i c a n t l y .

The S-Curve a n a l y s i s which was done l e d t o s a t i s f a c t o r y r e s u l t s .

(See F i l e {Ill-3 f o r f u l l d e t a i l s ) .

The DeLaine method was a l s o used. Only two o u t of t h e seven

hydrographs could be analyzed because of d i f f i c u l t y encountered w i t h

t h e Rooter program. (An excess ive amount of time w a s r equ i r ed t o s o l v e

f o r t h e r o o t s ) .

However, t h e r e s u l t s t h a t were obtained were i n very c l o s e agreement

t o t h e r e s u l t s of t h e S-Curve. Both methods p red ic t ed t h e same approxi-

mate d u r a t i o n s ( a s shown i n the t a b l e below) and normalized u n i t

hydrographs .

-38-

Table A l . P red ic t ed Dura t ions

Lodge Creek a t I n t e r n a t i o n a l Boundary (Ear ly Years)

Middle Creek a t Wright 's Ranch (Ref. F i l e /Ill-4)

1. (c) S i x d i f f e r e n t hydrographs were examined f o r t h e Middle Creek

s tudy u s i n g only t h e S-Curve technique.

1925

12 h r .

12 h r .

1922

An average dimensionless u n i t hydrograph was c a l c u l a t e d and

compared t o t h a t of Lodge Creek a t I n t e r n a t i o n a l Boundary (See Graph E

i n F i l e # l l -4) . The comparison was very c lose .

S-Curve Method

DeLaine Method

The S-Curve r e s u l t s seemed t o be c o r r e c t , a f t e r examining t h e u n i t

hydrographs and comparing t h e shape and o t h e r f e a t u r e s w i t h t h e d i f f e r e n t

du ra t ions t h a t were determined.

24 - 36 h r .

36 h r .

A DeLaine a n a l y s i s should be done so a comparison between t h e two

methods can be made.

2. Qu'Appelle Drainage Basin Study (Ref. F i l e #12-1)

. The two s t a t i o n s examined were:

(1) Indian Head Creek a t Indian Head (gross a r e a = 149 sq. mi les )

(2) Pheasant Creek a t Abernathy (gross a r e a = 510 sq. mi l e s )

Both s t a t i o n s were examined f o r s p r i n g hydrographs and, a s w e l l ,

s u m e r hydrographs were a l s o examined f o r Indian Head Creek.

A d e t a i l e d S-Curve a n a l y s i s was done f o r each s t a t i o n . The r e s u l t s

y i e lded were q u i t e s a t i s f a c t o r y . See f l u c t u a t i o n t a b l e s i n F i l e #12-1.

A p r e c i p i t a t i o n ( snowfa l l accumulation) and temperature a n a l y s i s

was done f o r t h e sp r ing hydrographs of Indian Head and Pheasant Creek.

The maximum and minimum temperatures were p l o t t e d on t h e hydrographs

corresponding t o t h e days of runof f . As w e l l , t h e t o t a l snowfa l l from

mid-November t o t h e hydrograph peak was ca l cu la t ed f o r each one.

For t h e sp r ing hydrographs of Indian Head t h e du ra t ions were found

t o vary from 12 t o 48 hours. The summer hydrograph du ra t ions were found

t o be 12 hours o r l e s s . For t h e Pheasant Creek s p r i n g hydrographs the

du ra t ions v a r i e d from 12 t o 60 hours .

It was ev ident from t h e S-Curve a n a l y s i s t h a t t h e du ra t ions of

summer r u n o f f s were gene ra l ly of a s h o r t e r time i n t e r v a l than s p r i n g

runoff hydrographs. A s w e l l , t h e shape of t h e summer u n i t hydrographs

were s l i g h t l y d i f f e r e n t from t h e 12-hour s p r i n g u n i t hydrographs.

I f t h e average summer u n i t hydrograph was analyzed f o r du ra t ions

l e s s than 12 hours , t h e c o r r e c t du ra t ion would i n a l l l i ke l ihood be l e s s

than 12 hours. I f t h i s were c o r r e c t and t h e average summer u n i t hydro-

graph f o r a 12-hour d u r a t i o n was c a l c u l a t e d and compared t o t h e 12-hour

s p r i n g u n i t hydrograph, t h e comparison might be q u i t e c lose .

It is recommended t h a t more work be done on comparing s p r i n g and

summer hydrographs of t h e same du ra t ion .

It was obvious t h a t t h e d i f f e r e n t v a r i a t i o n s i n temperature and

snow accumulation a f f e c t e d t h e runoff hydrographs, causing d i f f e r e n t l y

shaped hydrographs. However, i t was a l s o ev ident t h a t t h e sp r ing u n i t

hydrographs f o r bo th s t a t i o n s f e l l i n t o approximately t h r e e u n i t hydro-

graph groups r ep re sen t ing :

Group I - an average moderate snowfal l accumulation and sp r ing

melt temperature ( s h o r t t ime base w i t h f a s t r i s i n g

peak and s h o r t time t o base) .

Group I1 - a l a r g e accumulated snowfa l l accompanied by a s u f f i c i e n t

number of melt days t o cause most of t he snowfal l t o

become runoff (longer time base wi th very broad peak and

l a r g e time t o peak).

Group I11 - a moderate t o l a r g e accumulated snowfal l accompanied by

a number of s u f f i c i e n t melt days and some r a i n f a l l dur ing

t h e mel t per iod ( longes t time base wi th very broad peak

and l a r g e s t time t o peak).

The average u n i t hydrographs i n t h e t h r e e groups do not compare

wi th one another even when t h e c o r r e c t du ra t ion i s allowed f o r . Th i s i s

f u r t h e r evidence t h a t a more complete s tudy should be done on c l a s s i f y -

i n g s p r i n g runoff hydrographs i n t o d i f f e r e n t groups, i f t h e p r e d i c t i o n s

of hydrographs i n t h e s p r i n g a r e t o be reasonably accu ra t e .

All work which was done on t h i s bas in , i nc lud ing computer r e s u l t s ,

and va r ious graphs a r e i n F i l e #12-1.

3. Poplar and Horse Creek Study (Ref. F i l e #12-2)

The fol lowing s t a t i o n s were examined:

(1) Horse Creek a t I n t e r n a t i o n a l Boundary (gross a r ea 73.5 sq . mi les )

(2) Middle Branch of Poplar River a t I n t e r n a t i o n a l Boundary (gross

a r ea 353 sq. mi les )

(3) Eas t Poplar a t I n t e r n a t i o n a l Boundary (gross a r e a 542 sq. mi les )

An S-Curve a n a l y s i s was performed f o r each of t h e s t a t i o n s . The

r e s u l t s y ie lded were n o t completely s a t i s f a c t o r y .

For both Horse Creek and Middle Poplar t h e dry , wet and g ros s dra inage

a r e a s were equal . Thereby, i t was thought t h a t a s a t i s f a c t o r y u n i t hydro-

graph and dura t ion a n a l y s i s could be e a s i l y obta ined . However, a s i t

turned o u t , t h e cons tan t e f f e c t i v e a r e a c r ea t ed problems. For example,

a s t h e depth of snow inc reases over a cons tan t a rea t h e r e l a t i o n of

length and i n t e n s i t y of t h e melt per iod upon runoff becomes more compli-

ca ted . The e f f e c t i v e a r e a i n r e a l i t y i s q u i t e l i k e l y n o t a t a l l cons tan t .

This problem was not examined i n d e t a i l because of l i m i t i n g time.

However, i t can l i k e l y b e concluded t h a t when t h e gross , wet and dry

a r e a s a r e equal , i t i s ve ry d i f f i c u l t t o c a l c u l a t e an average u n i t

hydrograph s i n c e i n t e n s i t y a s w e l l a s l e n g t h of t h e melt per iod can

cause numerous v a r i a t i o n s i n t h e a c t u a l shape of t h e runoff hydrograph.

The S-Curve f l u c t u a t i o n t a b l e s f o r t h e t h r e e s t a t i o n s a long wi th

u n i t hydrograph graphs and o the r information a r e i n F i l e #12-2.

The u n i t hydrographs f o r a l l t h r e e s t a t i o n s v a r i e d cons iderably ,

a l though f o r each s t a t i o n t h e r e was a s h o r t du ra t ion , h igh peaked u n i t

hydrograph (max.), a broad shaped, h igh du ra t ion (min.) and a n average

u n i t hydrograph which was shaped somewhere between t h e two extremes

r ~ p r e s e n t i n g t h e ma jo r i t y of u n i t hydrographs. The S-Curve du ra t ions

were somewhat i n d i c a t i v e of t h e genera l c h a r a c t e r i s t i c s of t h e hydro-

graphs, b u t d id n o t y i e l d a s s a t i s f a c t o r y r e s u l t s a s i n o t h e r bas in

s t u d i e s .

4. La Crosse, Wisconsin Basin Study (Ref. F i l e #13-1)

The bas in examined a t La Crosse, Wisconsin i s one of t h e United

S t a t e s Experimental Watershed Basins. It is a very small bas in , (2.71

ac res ) but the runoff hydrographs a r e accompanied by r a i n f a l l da ta

taken a t c lose ly spaced time i n t e r v a l s , thus providing s u f f i c i e n t ra in-

f a l l records . Because of the small s i z e of the bas in the re was no

ground water f low before o r a f t e r r a i n f a l l events .

A d e t a i l e d DeLaine a n a l y s i s was done on the bas in . A s w e l l , an

S-Curve a n a l y s i s was done a s a check. The DeLaine method yielded what

seemed f a i r l y accura te dura t ion r e s u l t s . However, the S-Curve did no t

y i e l d dura t ion r e s u l t s corresponding t o the DeLaine method.

Four hydrographs were examined by each method. Three t r i a l s were

done by t h e DeLaine technique before s a t i s f a c t o r y r e s u l t s were obtained.

The dura t ion r e s u l t s a r e l i s t e d i n the following t ab le :

Table A2. Ra in fa l l Duration

( ) ' - a c t u a l r a i n f a l l dura t ion accounting f o r major por t ion of runoff

Hydrograph

1940 Aug. 16

1941 June 29

1941 Sept . 15

1952 June 23

Actual Duration (Minutes)

22 - 24 (10) '

12 - 14 (10) '

21 - 22 (12) '

22 (6) '

Predic ted Duration (Minutes)

DeLaine

2 2

14

20

26

S-Curve

4

4

2

2

From t h e above t a b l e i t is ev iden t t h a t t h e r e is a l a r g e

d iscrepancy between t h e DeLaine and S-Curve p r e d i c t i o n s . The DeLaine

a n a l y s i s produced a c l o s e comparison of t h e p red ic t ed and a c t u a l r a in -

f a l l dura t ions . The S-Curve p red ic t ed r a t h e r low d u r a t i o n s ; however,

=he r e s u l t s a r e no t a s poor a s i t seems. The a c t u a l r a i n f a l l runoff

du ra t ions l i s t e d i n t h e t a b l e , i nc lude small i n t e n s i t y runof f s , a s

we l l a s l a r g e i n t e n s i t y runoffs . Therefore , t h e a c t u a l d u r a t i o n of

t h e storm is somewhat sma l l e r i f j u s t t h e major p o r t i o n of t h e s torm

is considered ( s e e v a l u e s i n b racke t s i n t a b l e ) . The DeLaine method

shows t h e complete du ra t ion f o r which runoff occurs ; however, t h e S-

Curve which assumes a cons t an t i n t e n s i t y throughout t h e d u r a t i o n i s

l i k e l y t o show only t h e major du ra t ion of t h e storm.

When t h i s i s taken account f o r , t h e S-Curve a n a l y s i s i s somewhat

c l o s e r t o t h e a c t u a l du ra t ion . However, it s t i l l gave a low va lue f o r

t h e du ra t ions of t h e hydrographs examined i n t h i s bas in .

For a complete s tudy of r e s u l t s and graphs s e e F i l e #13-1.

5. Other Basin S tud ie s

There were s e v e r a l b a s i n s examined by t h e DeLaine method i n

which no conclus ive r e s u l t s were obtained. These bas ins a r e l i s t e d

a s fol lows:

(1) Fennimore, Wisconsin (Ref. F i l e #13-2), 52 a c r e s

(2) Albuquerque, New Mexico (Ref. F i l e 1113-3), 97 a c r e s

(3) Cochocton, Ohio (Ref. F i l e #13-4), 1 .6 a c r e s

(4) Indian Head Creek ( ~ e f . F i l e #12-I), 149 sq. mi les

(5) Horse Creek (Ref. F i l e #12-2), 73.5 sq. mi l e s

The f i r s t t h r e e of t h e above l i s t e d a r e "United S t a t e s Experimental

Drainage Basins". A s we l l , an S-Curve a n a l y s i s was done f o r each, b u t

no s a t i s f a c t o r y r e s u l t s were obta ined . The l a s t two l i s t e d a r e p r a i r i e

dra inage b a s i n s i n Saskatchewan i n which a d e t a i l e d S-Curve a n a l y s i s

was done. However, t h e DeLaine method d id n o t y i e l d any s i g n i f i c a n t

r e s u l t s .

I t is recommended t h a t continued work be done on the above dra inage

bas ins . The r e s u l t s need t o be re-examined and perhaps some c o r r e l a t i o n s

between r e s u l t s may be obtained.

A P P E N D I X B

COMPUTER PROGRAMS

Computer Use

The Hewlett Packard computer was used extens ive ly f o r t h e

c a l c u l a t i o n s involved wi th the analyses.

The programs which were used a r e l i s t e d i n Table B 1 , along wi th a

b r i e f desc r ip t ion a s t o what each program does. For a l i s t i n g of each

program see F i l e #lo-1.

Two of t h e programs, "Unit Hydrograph" and "S-Curve" were

previously s e t up. Kinor modif icat ions were made and, a s w e l l , these

two programs were t r a n s l a t e d i n t o Fortran. The " R ~ o t e r ' ~ program was

obtained from l i b r a r y s torage . Af te r some modif icat ions were made t o

decrease t h e time taken t o determine the r o o t s , the "Modified Rooter"

program was s e t up. The o the r programs were s e t up and used according

t o remaining ca lcu la t ions t o be done.

The major i ty of computer work done w a s i n Basic, mainly because of

t h e convenience of access. However, f o r f u t u r e use i n the s tudy of the

two methods, t he For t ran should be used because of i t s speed.

Table B1. Computer Programs

S-Curve

u - ~ r a ~ h

E-Area

Vol . Norm.

Rooter

Modified - Rooter

Poly - Exp.

R a i n f a l l - D i s t r i b u t i o n

Basic

J

J

Program - Function

For t r an

J

J

S-Curve + determines S-Curve and ins tan taneous u n i t

hydrograph.

U-Graph + c a l c u l a t e s t h e u n i t hydrograph i f e f f e c t i v e

a r e a and runoff hydrograph a r e known.

E-Area + t h e e f f e c t i v e a r e a i s determined when t h e u n i t

hydrograph i s known.

Vol . + determines volume of runoff hydrograph i n inches .

Norm. + normalizes a s e t of numbers.

Rooter + c a l c u l a t e s t he r o o t s of a polynomial equat ion

( r e a l and imaginary numbers).

Modified - + a s i m i l a r program t o "Rooter", w i th some changes Rooter

made i n o rde r t o determine r e s u l t s qu icker .

Program - Function (Continued)

8. Poly - Exp. -+ performs the polynomial expansions of roots

which may be both real and imaginary.

9. &in - -+ modified form of normalization program; Distribution

multiplies a normalized set of numbers by a

constant.