inventory of surface water resources in sahelien zones...

Y -6

I N V E N T O R Y OF SURFACE WATER RESOURCES I N S A H E L I A N ZONES

WITHOUT PERbtANENT H Y D R O L O G I C A L NETWORK

= b y Marcel F. Roche

Ingénieur en chef B Elec tr ic i té d e France

Chef du Service hydrologique de 1 ‘ORSTOM

A B S T R A C T

. Sahelian zones are generally too broad, have too low density o f inhabitants, and toopoor surface water résources, t o economically allow a dense network o f hydrological stations. The method i s then t o keep o d y a s l i g h t basic hydrological network and t o s t u d y a s deeply a s possible the mechanism of the xunoff on selected basins considered as representative. T h e optimal s i ze o f these basins, i n order t o have the best understanding o f the phenomenon, i s from 2 or 5 km2 t o about 50 km2. These basins are ope- r a t e d dur ir ìg 3 t o 5 years . A mathematical model may be f i t t e d w i t h the help of the collected information i n order t o create, b y simulation, longer ser ies , and t o allow the estimation o f a runoff frequency distribution curve. The studied catchmentsare c l a s s i f i e d according t o their physiographi- c a l characteristics and a se t o f distribution curves can be drawn f o r each class or s t a n d a r d basin and f o r d i f f e ren t values o f the median yearly pre- c ipi tat ion. So a se t o f graphes can be established, which can be used t o estimate the runoff distribution f o r unknown catchments, a f t e r a f i e l d survey o f them followed b y an analysis o f the ir physiographical conditions.

1. 1NTRODU.CTION . -

1.1. The word llSAHELIAN1l is t a k e n h e r e i n t h e g e n e r a l meaning f o r Africa

i n t h e S o u t h of S a h a r a . As f a r as h y d r o l o g y is c o n c e r n e d , i t is g e n e r a l l y ad-

m i t t e d t h a t t h e " S a h e l i a n zone" is i n c l u d e d i n t h e i n t e r t r o p i c a l zone and dé-

l imi ted by t h e i s o h y e t s 300 and 750 mm.

1.2. The main f e a t u r e o f t h e s a h e l i a n b a s i n s i s t h e phenomenon of "hydro-

g r a p h i c d e g r a d a t i o n " less r e m a r k a b l e t h a n i n d e s e r t i c or s u b d e s e r t i c z o n e s , b u t

still v e r y clear. It c o n s i s t s i n a p r o g r e s s i v e v a n i s h i n g of t h e stream b e d s from

ups t ream t o downstreamc The i n t e n s i t y of t h e phenomenon depends c h i e f l y on t h e

d r y n e s s of t h e climate, b u t a l s o on morphology ( e s p e c i a l l y s l o p e s ) and t y p e s o f

s o i l . But mean relief and s o i l d e g r a d a t i o n s are by some d e g r e e c o r r e l a t e d t o t h e

s ize of t h e ca tchment . I n t h e most p a r t of the s a h e l i a n zone , t h e h y d r o g r a p h i c

d e g r a d a t i o n g e n e r a l l y d o e s n o t a p p e a r below 400-500 kin2* Above 1000 km2, streams

are almost a l w a y s affected by t h i s d e g r a d a t i o n ,

1.3. The p r e c e d i n g remark l e a d s t o c l a s s i f y s a h e l i a n c a t c h m e n t s a c c o r d i n g

t o t h e i r size, For i n s t a n c e , i n t h e s t u d y c a r r i e d o u t by Dr. R o d i e r on t h e b a s i s

of r e s u l t s o b t a i n e d 'from ORSTON's r e p r e s e n t a t i v e b a s i n s i n A f r i c a n S a h e l , f i v e

classes have been c o n s i d e r e d :

a - a few h e c t a r e s s i z e d c a t c h m e n t s ;

b - 2 t o 40 km2 ;

c - 40 t o 500 km2, ex tended i n c e r t a i n cases t o 600 and e v e r 800 km2

f o r r e l a t i v e l y weak h y d r o g r a p h i c d e g r a d a t i o n ;

d - more t h a n 1000 km2 ;

e - more t h a n 10000 km2.

1.4. The class 2 t o 40 km2 is t h e most i m p o r t a n t f o r s u r f a c e water economy

i n Saheliàn a f r i c a n zone ( s i t e s f o r small r e s e r v o i r s ) . I n a d d i t i o n , i t c o r r e s -

ponds i n Africa t o t h e most c u r r e n t s ize of r e p r e s e n t a t i v e ca tchment : f o r t h a t

we c a n d i s p o s e o f t h e b e s t and more c o m p l e t e i n f o r m a t i o n . T h i s p a r t will be

t r e a t e d i n d e t a i l .

1.5. The aim of t h i s l e c t u r e is t o e x p l a i n h o w . t o make a n - a s s e s s m e n t of

water s u r f a c e r e s o u r c e s i n a S a h e l i a n zone. It t a k e s as a n example t h e s t u d y rea-

l i z e d by Dr. R o d i e r , w i t h t h e h e l p of Mr. Girard l , a n h y d r o l o g i s t s p e c i a l i s t

i n m a t h e m a t i c a l ’ m o d e l i n g f o r c a t c h m e n t b e h a v i o r . Such a k i n d of s t u d y n e c e s s i t s

local i n f o r m a t i o n b u t some of t h e r e s u l t s may be c a u t i o u s l y e x t r a p o l a t e d t o a n o t h e r similar r e g i o n s .

2. G e n e r a l p r i n c i p l e s f o r s u r f a c e water a s s e s s m e n t i n s a h e l i a n r e g i o n s .

[I

2.1. Among o t h e r s , t h e methodology will depend o n t h e s ize of t h e c a t c h -

ments a c c o r d i n g . t o t h e c l a s s i f i c a t i o n g i v e n i n 1.3. However, a common p l a n c a n

be d e s c r i b e d a t least f o r classes a ) t o d ) .

2.2. Data c o l l e c t i o n .

The first s t e p is t o assess t h e . a v a i l a b l e i n f o r m a t i o n e s p e c i a l l y i n

c l i m a t o l o g y ( o v e r a l l r a i n f a l l d a t a ) and i n hydrometry.

2.2.1. R a i n f a l l d a t a .

2.2.1.1. The p r o c e s s i n g is t h e same whatever is t h e s ize of t h e c a t c h -

ment. I n A f r i c a n S a h e l , f o r i n s ’ t a n c e , more t h a n 70 s t a t i o n s w i t h good r e c o r d s

c a n b e s e l e c t e d , some of them h a v i n g l o n g p e r i o d s of r e c o r d i n g . The p r o c e s s i n g

c o n s i s t s , f o r e a c h s t a t i o n , i n computing t h e mean and t h e median y e a r l y t o t a l

( i s o h y e t a l maps) and i n s t u d y i n g t h e f r e q u e n c y d i s t r i b u t i o n of y e a r l y t o t a l s .

2.2.1.2. F i g u r e 1 g i v e s t h e i s o h y e t a l maps (medians)- f o r West and

[ll) C e n t r a l Africa from S a h e l i a n t o d e s e r t i c z o n e s ( e x t r a c t e d from r e f e r e n c e

The f r e q u e n c y d i s t r i b u t i o n of y e a r l y t o t a l s depends on t h e v a l u e of t h e median

and a s t u d y c a r r i e d o u t by a method of y e a r s - s t a t i o n s showed t h a t t h e d i s t r i b u -

t i o n c a n b e e x p r e s s e d by a g e n e r a l i z e d e x p o n e n t i a l law as 1/0.4

F (excedence p r o b a b i l i t y ) = 1 - e x p [- xo ] w i t h xo = 7.6 x loe4 Pm2 - 52.4

S = 1.1579 (Pm - x0)

n Pm b e i n g t h e median v a l u e of t h e a n n u a l r a i n f a l l s . The r e p r e s e n t a t i v e c u r v e s of

1

6

>*

x

*

t h i s fo rmula are g i v e n on F i g u r e 2.

2.2.2. H y d r o l o g i c a l d a t a .

2.2 -2.1. They come f rom s e v e r a l o r i , g i n s . c o r r e s p o n d i n g t o t h e v a r i o u s

gaug ing and s u r v e y o p e r a t i o n s , from r e g u l a r h y d r o m e t r i c ne twork t o s p e c i f i c ( o r

l o c a l ) measurements c a r r i e d o u t d u r i n g s h o r t p e r i o d s . I n s a h e l i a n r e g i o n s r e g u l a r

s t a t i o n s ve ry r a r e l y o p e r a t e d for ca t chmen t areas below 500. t o 1000 km2 . O n t h e o t h e r

hand, s a h e l i a n b a s i n s w i t h areas e q u a l o r g r e a t e r t h a n 10000 km2 are a l s o v e r y

seldom. I n A f r i c a n S a h e l , for i n s t a n c e , o n l y 7 o r 8 b a s i n s of t h i s t y p e e x i s t

f rom S e n e g a l t o Sudan.

2.2.2.2. For t h e most p a r t o f t h e ca t chmen t s , b a s i c h y d r o l o g i c a l d a t a

are p r o v i d e d by r e p r e s e n t a t i v e b a s i n s y t o g e t h e r w i t h a n a n a l y s i s o f t h e r a i n -

f a l l - d i s c h a r g e r e l a t i o n s h i p l e a d i n g among o t h e r s t o estimate t h e r u n o f f c o e f -

f i c i e n t and its v a r i a t i o n s . I n t h e example of ORSTOM s t u d i e s i n A f r i c a n Sahel,

a l o t o f r e p r e s e n t a t i v e b a s i n s have been worked o u t from 1955 t o 1971. They can

p r o v i d e p r e c i s e v a l u e s on y e a r l y r a i n f a l l and r u n o f f , t h e d u r a t i o n o f o b s e r v a -

t i o n s n o t e x c e e d i n g 3 o r 4 y e a r s ; it is i n s u f f i c i e n t t o p r o v i d e a s t a t i s t i c a l

r

1 L

series, b u t it is s u f f i c i e n t i n t h e most p a r t o f t h e cases t o a l l o w t h e f i t t i n g

of a m a t h e m a t i c a l ca tchment b e h a v i o u r model ; t h e n a s t a t i s t i c a l series of a n n u a l

r u n o f f may b e d e r i v e d from a l o n g r a i n f a l l series which is o f t e n a v a i l a b l e .

2.2.2.3. Another s o u r c e s o f i n f o r m a t i o n comes f rom r e g i o n a l s t u d i e s

c a r r i e d d u r i n g 1 t o 4 y e a r s and a l so g i v i n g d a t a i n t h e f i e l d s o f r a i n f a l l and

r u n o f f . The t y p e o f i n f o r m a t i o n is close t o t h i s o n e o f r e p r e s e n t a t i v e b a s i n s

b u t t h e size of t h e c a t c h m e n t s is g e n e r a l l y g r e a t e r i n a n a v e r a g e , and t h e ob-

s e r v a t i o n s n o t s o i n t e n s i v e and d e n s e i n t h e s p a c e .

2.2.2.4. The case of g r e a t t r o p i c a l r i v e r s c r o s s i n g t h e s a h e l i a n

zone must b e t a k e n a p a r t . T h i s r i v e r s , l i k e Nile, C h a r i , N i g e r , S e n e g a l , a re

f e d by humid t r o p i c a l zones and do n o t p r e s e n t any c h a r a c t e r i s t i c of s a h e l i a n

stream. On a n o t h e r hand, t h e i r reg imen are p r e t t y well known from c l a s s i ca l

b a s i c ne tworks .

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2 . 3 . Methodology fo r water r e s c u r c e s a s s e s s m e n t

2.3.1. Class e) : area g r e a t e r t h a n 10000 km

These b a s i n s are g e n e r a l l y u s e l e s s f o r s u r f a c e water management ; t h e

2

median a n n u a l s u r f a c e f l o w is n u l l f o r t h e most of them. I n a d d i t i o n , t h e y u a n t i -

t a t i v e i n f o r m a t i o n a b o u t t h e i r f l o w is v e r y scarse and t h e knowledge o f r a i n f a l l ,

i f any , is n o t v e r y h e l p f u l . However, t h e knowledge of t h e s u r f a c e r u n o f f may

o n l y come from t h e d i r e c t o b s e r v a t i o n of t h e d i s c h a r g e s ( c l a s s i c a l ne twork) and

t h e most p a r t of t h e time one c a n o n l y g i v e some o r d e r s of magnitude. An example

is g i v e n on f i g u r e 3 : r u n o f f d e p t h s a g a i n s t p r o b a b i l i t i e s of exceedence . The

g e o g r a p h i c a l t r a n s p o s i t i o n is i m p o s s i b l e .

2.3.2. Class d ) : area between 1 O00 and 10 O00 kmL

2.3.2.1. The h e t e r o g e n e i t y of t h e s e c a t c h m e n t s is st i l l too h i g h f o r

e s t a b l i s h i n g a r e l i a b l e lumped 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 . It is p o s s i b l e , and

i t h a s been made by G, ) f o r t h e c a t c h m e n t o f Oued Ghorfa

( M a u r i t a n i a ) , t o .fit a complex model t o t h e r e s u l t s o b t a i n e d by a r e g i o n a l s t u d y ,

a n d e v e n t u a l l y t o produce a l o n g a n n u a l r u n o f f series by s i m u l a t i o n , b u t t h i s

r e m a i n s f o r t h e s t u d i e d ca tchment i tself and c a n n o t be t r a n s p o s e d t o a n o t h e r one .

2.3.2.2. However, some g r e a t l i n e s may b e e s t a b l i s h e d f o r a r a t h e r qua-

[Il ' l i t a t i v e e s t i m a t i o n o f a n n u a l r u n o f f i n t h i s c lass of b a s i n s . I n h i s s t u d y

Dr. R o d i e r d i s t i n g u i s h e s 2 s e p a r a t e g r o u p s :

2.3.2.2.1. B a s i n s on g r a n i t e o r g r a n i t o - g n e i s s - They have been s t u d i e d , i n A f r i c a n S a h e l , c h i e f l y i n Ouaddaï (Chad) ,

i n t h e n o r t h o f Upper-Volta (Djibo, Lake of Bam), t h e V o l t a ï a n t r i b u t a r i e s of

Niger R i v e r ( D a r g o l , Gorouol) , t h e E a s t e r n Upper-Volta ( G o u l b i of Haradi)

r u n o f f c o e f f i c i e n t f o r median y e a r v a r i e s from 1 t o . 5 % and t h e f r e q u e n c y i s shown

on f i g u r e 4. Of c o u r s e , i t is p o s s i b l e t o d e s c r i b e t h e g e n e r a l c h a r a c t e r i s t i c s

of t h e p l o t t e d c a t c h m e n t s , b u t t h e s e c h a r a c t e r i s t i c s are too complex t o p r o v i d e

The

a n u s e f u l t o o l f o r a r e a l e x t r a p o l a t i o n o f t h e r e s u l t s t o a n o t h e r c a t c h m e n t s .

However, a s i m p l e comparison between t h e c h a r a c t e r i s t i c s ( i n c l u d i n g mean a n n u a l -

- 5 - I

r a i n f a l l ) of any ca tchment t o b e deve lopped and t h o s e o f one o f t h e c a t c h m e n t s

p l o t t e d on f i g u r e 4,may p r o v i d e a n o r d e r of magni tude o f t h e s u r f a c e water deve-

lopment p o s s i b i l i t i e s .

2.3.2.2.2. Clayey b a s i n s on s c h i s t , m a r l y - l i m e s t o n e , etc.

The e f f i c i e n c y o f t h e s e b a s i n s i s b e t t e r t h a n t h i s o n e o f t h e p r e -

c e d i n g group. The r u n o f f c o e f f i c i e n t f o r median y e a r v a r i e s f rom 3 t o 14 %. I n

t h e ORSTOM s t u d i e s , t h e conce rned r e g i o n s are e s p e c i a l l y t h e Gorgo1 Noir, t h e

Brakna and t h e Ghorfa i n M a u r i t a n i a , t h e Ader Dou tch i and t h e Waggia i n Nige r .

Same remarks as f o r item 2.3.2.2.1. T h e f r e q u e n c y d i s t r i b u t i o n of a n n u a l - r u n o f f

d e p t h s is p l o t t e d on f i g u r e 5.

2.3.5. Class c) : area between 40 and 1 O00 kmL

2.3.3.1. The i n f o r m a t i o n comes c h i e f l y from r e p r e s e n t a t i v e b a s i n s and

f rom r e g i o n a l s t u d i e s . However, c e r t a i n r e s u l t s coming from r e g u l a r ne tworks may

still b e used . For Afr i can S a h e l a b o u t 42 r e p r e s e n t a t i v e c a t c h m e n t s are a v a i l a b l e .

The r e l a t i o n s h i p s between r a i n f a l l and r u n o f f are s t i l l d i f f i c u l t t o b e e s t a b -

l i s h e d . However, t h e runof f c o e f f i c i e n t computed for t h e median y e a r l y p r e c i p i -

t a t i o n s a l l o w s t o a p p r e c i a t e t h e r e l a t i v e i m p o r t a n c e o f r u n o f f from one b a s i n t o

a n o t h e r . .

2.3.3.2. The median v a l u e o f t h e r u n o f f c o e f f i c i e n t c h i e f l y depends ,

i n a d d i t i o n t o t h e mean a n n u a l r a i n f a l l , on t h e s o i l s characterist ics g e n e r a l l y

d e r i v e d f rom t h e g e o l o g i c a l s t r u c t u r e of t h e ca t chmen t . I n A f r i c a n S a h e l , f o r

i n s t a n c e , Dr. R o d i e r h a s c o n s i d e r e d two g e o l o g i c a l classes of c a t c h m e n t s f o r

area class c.

2.3.3.2.1. Bas ins on g r a n i t e and g r a n i t o - g n e i s s - I n these b a s i n s , t h e h y d r o g r a p h i c a l d e g r a d a t i o n is v e r y f r e q u e n t ,

o v e r a l l i n t h e n o r t h and i f t h e s l o p e s i n t h e b a s i n are n o t t o o h igh . As a r u l e ,

t h e p e r m e a b i l i t y is g r e a t and t h e r u n o f f c o e f f i c i e n t s are low t o v e r y low. T h e i r

median v a l u e s v a r y from less t h a n 1 % t o 6-7 %.

2.3.3.2.2. Basins on o t h e r s o i l s (marls, sandy s o i l s , l a t e r i t i c

c u i r a s s e s , s a n d s t o n e , s c h i s t s and c l a y s ) . The d e g r a d a t i o n is less marked t h a n

fo r b a s i n s on g r a n i t e , and c a n be shown o n l y f o r

g e n e r a l l y less p e r v i o u s and t h e s l o p e s are s h a r p e r . Except f o r s p e c i a l c o n d i -

t i o n s , v e r y seldom i n t h a t case, a s a g r e a t i m p o r t a n c e of wind s a n d d e p o s i t , t h e

median r u n o f f c o e f f i c i e n t g o e s from 5 t o 19 %.

g r e a t e r areas. The s o i l s are

O f c o u r s e , t h e v a r i a t i o n s of t h e r u n o f f c o e f f i c i e n t i n s i d e o f e a c h g e o l o -

g i c a l class are due e s p e c i a l l y t o

- t h e v a r i a t i o n o f t h e size of t h e c a t c h m e n t (40 t o 1 O00 km2), t h e ' coeffi-

c i e n t d i m i n i s h i n g when t h e size i n c r e a s e s ,

- t h e v a r i a t i o n o f t h e median a n n u a l r a i n f a l l (300 t o 750 mm).

2.3.3.3. Frequency d i s t r i b u t i o n of a n n u a l r u n o f f

The most e f f i c i e n t t o o l i n o r d e r t o e v a l u a t e t h e s u r f a c e water r e s c u r -

ces i n s a h e l i a n zone is t h e g r a p h of t h e a n n u a l runoff a g a i n s t i ts f r e q u e n c y ,

d e r i v e d f o r e a c h t y p e of c a t c h m e n t , from t h e p r e c e d i n g i n f o r m a t i o n and s t u d i e s . Y

F o r S a h e l i a n Africa, t h e f r e q u e n c y c u r v e s e s t a b l i s h e d f o r b a s i n s on 7 ri g r a n i t e o r g r a n i t o - g n e i s s , are g i v e n on f i g u r e 6 . The same c u r v e s b u t f o r t h e

s e c o n d g e o l o g i c a l class are g i v e n on f i g u r e 7.

Each c u r v e c o r r e s p o n d s t o t h e e s t i m a t i o n s macle f o r a g i v e n s t u d i e d

b a s i n , d e s c r i p t i o n of which is g i v e n i n t h e t e x t of r e f e r e n c e 1 (3.A. R o d i e r ) .

F o r a n unknown c a t c h m e n t , it is n e c e s s a r y t o examine c a r e f u l l y t h e v a r i o u s cha- [I

racteristics of it and t o c h o o s e t h e closest b a s i n t y p e b e f o r e e n t e r i n g i n t o

t h e g r a p h s 6 o r 7.

2 2.3.4. Class b : area between 2 and 40 km

It will e x p l a i n e d i n d e t a i l l a t e r on i n a s p e c i a l c h a p t e r .

2.3.5. Class a : area : a f e w . h e c t a r e s

2.3.5.1. T h i s is t h e f i e l d of impluviums fo r c i s t e r n s w h i c h c a n a l so

be i n t e r e s t i n g f o r v e r y small r e s e r v o i r s . I n A f r i c a n S a h e l , some i n f o r m a t i o n i s

a v a i l a b l e f o r 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 i n v a r i o u s c o n d i t i o n s . The r u n o f f -

c o e f f i c i e n t s are as follow ( i s o h y e t of a b o u t 600 m m ) :

I - 7 -

I

I n median y e a r

- Clayey s o i l s w i t h medium s l o p e 40 t o 50 % ( t y p e A )

- Soi l s c o v e r e d by a t h i c k l a y e r of l a te r i t i c

g r a v e l s w i t h non n e g l e c t a b l e v e g e t a b l e c o v e r 4 t o 8 % ( t y p e C)

( t y p e A )

( t y p e C)

- C l a y s d e r i v e d from s c h i s t s

- G r a n i t e s wea the r i n b l o c k s

40 t o 50 %

less t h a n t o 10 S

- G r a n i t i c g l a c i s w i t h modera t e s l o p e s 30 % ( t y p e 8)

I n v e r y r a i n y y e a r s ( a b o u t 100 y e a r s - f r e q u e n c y )

- Type A : 60-70 %

- Type B : 40-50 %

- Type C : 20-30 %

I n v e r y d r y y e a r ( a b o u t 100 y e a r s - f r e q u e n c y )

- Type A : 25-30 X

- Type 6 : 5-10 %

- Type C : O- 5 %

2.3.5.2. P r a c t i c a l d e t e r m i n a t i o n of t h e r u n o f f

- Deduce f rom f i g . 1 t h e y e a r l y p r e c i p i t a t i o n f o r t h e ca t chmen t i n evo lu -

t i o n (median v a l u e ) .

- I n t r o d u c i n g t h i s median v a l u e i n t o f i g . 2 , choose t h e n e a r e s t y e a r l y

r a i n f a l l f r e q u e n c y d i s t r i b u t i o n c u r v e (by i n t e r p o l a t i n g i f n e c e s s a r y ) .

- F i e l d e x a m i n a t i o n o r , i f i m p o s s i b l e , e x a m i n a t i o n of aer ia l p h o t o g r a p h s ,

i n o r d e r t o r e d u c e t h e a c t u a l unknown b a s i n t o a s t u d i e d case.

- Determine t h e f r e q u e n c y d i s t r i b u t i o n c u r v e of y e a r l y r u n o f f , f rom t h r e e

p o i n t s ( c o r r e s p o n d i n g t o v e r y d r y , medium and v e r y r a i n y y e a r s , computed

f rom t h e r a i n f a l l s w i t h t h e h e l p o f c o e f f i c i e n t s g i v e n above.

3. D e t a i l e d s t a t e m e n t on t h e methodology f o r b a s i n s w i t h areas between 2 an 40 km2

3.1. T h i s area i n t e r v a l i s v e r y i n t e r e s t i n g because it c o r r e s p o n d s t o t h e

e most f r e q u e n t need f o r water development i n s a h e l i a n r e g i o n s and c o n s e q u e n t l y i

h a s been p r e t t y well s t u d i e d . I n a d d i t i o n , c a t c h m e n t s o f s u c h s izes may be c o n s i -

d e r e d as p h y s i c a l c l n i t s a s well from t h e p o i n t o f view o f phys iog raphy a s from

I - 8 - ~~ ~

f

t h i s one o f meteoro logy . T h i s is t h e r e a s o n why t h i s p o i n t merits a s p e c i a l

s t a t e m e n t i n o u r pape r .

3.2. The i n f o r m a t i o n g e n e r a l l y comes from r e p r e s e n t a t i v e ca t chmen t s . For

t h e s t u d y of Dr. R o d i e r i n A f r i c a n S a h e 1 , t h e r e s u l t s of 41 r e p r e s e n t a t i v e b a s i n s

have been used. These b a s i n s have been c l a s s i f i e d a c c o r d i n g t o t h e i r g e o l o g i c a l

c o m p o s i t i o n and its i n c i d e n c e on t h e p e r m e a b i l i t y , i n o r d e r t o f a c i l i t a t e t h e

a n a l y s i s of t h e v a r i o u s f a c t o r s . T a b l e I shows t h i s c l a s s i f i c a t i o n , It c o v e r s

o n l y t h e cases for which f i e l d s t u d i e s have been c a r r i e d o u t .

As a matter o f fac t , e v e r y c a t c h m e n t is p h y s i c a l l y complex and b a s i -

c a l l y non homogeneous. So i t would be u n r e a l l i s t i c t o c l a s s i f y a l l t h e p o s s i b i -

l i t i es i n c l u d i n g c o m b i n a t i o n s o f a l l p o s s i b l e components and t o t r y t o e x p l i c i t

t h e s p e c i f i c i n f l u e n c e o f them on t h e 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 . It a p p e a r e d

i t would be b e t t e r t o choose some c h a r a c t e r i s t i c c a t c h m e n t s b e h a v i o u r o f which

b e r e p r e s e n t a t i v e o f a set o f s t u d i e d

i s c a l l e d " s t a n d a r d b a s i n " f o r g i v e n c o n d i t i o n s . The list o f " s t a n d a r d b a s i n s "

is g i v e n i n T a b l e II.

or u n s t u d i e d ca t chmen t s . Such a ca t chmen t Y

I 6,

3.3. Frequency d i s t r i b u t i o n o f r u n o f f ( s t a n d a r d area : 25 I") 3.3.1. A r e p r e s e n t a t i v e b a s i n i s o p e r a t e d , on a a v e r a g e , d u r i n g 3 y e a r s .

It is v e r y a r b i t r a r y , under t h o s e c o n d i t i o n s , t o d e t e r m i n e t h e mean v a l u e o r t h e

median of t h e r u n o f f d e p t h o r of t h e r u n o f f c o e f f i c i e n t . On t h e o t h e r hand, t h i s

i n f o r m a t i o n is s u f f i c i e n t t o f i t a m a t h e m a t i c a l model s i m u l a t i n g t h e r u n o f f

b e h a v i o u r o f t h e ca tchment . I n t h e s t u d y of Dr. R o d i e r , t h e " s i m p l i f i e d model" of

G. G i r a r d h a s been used .

3.3.1.1. T h i s model (see r e f e r e n c e 3 ) is o p e r a t i n g w i t h d a i l y p r e - [I c i p i t a t i o n s , b u t t h e r e s u l t s are v a l i d o n l y mon th ly or b e t t e r y e a r l y .

The p r i n c i p l e s are f o l l o w i n g :

t h e " e f f i c i e n t p r e c i p i t a t i o n " HU ( a b l e t o g i v e r u n o f f ) is related t o t h e

"-

i

t o t a l d e p t h HT o f t h e s t o r m by t h e mean r e l a t i o n s h i p :

HU = a ( H t - '5)

- 9 -

TABLE I

B A S I N S WITH A R E A BETWEEN 2 A N D 4 0 K M 2

Classif ication according t o geological consti tution

1. Sandy s o i l s . - Dunes (dead o r a c t i v e )

2. G r a n i t e and - G r a n i t i c a r e n a s (more o r - Wind d e p o s i t c o v e r

g r a n i t o - g n e i s s less deep)

3. Sands tone "I

- Glacis o r ped imen t s s a n d y - c l a y s o i l s r e g s - o u t c r o p s - Smal l streams beds ( u p p e r p a r t o f ca t chmen t s )

_. Coarse sand on t h e bot tom, sandy c l a y banks - Downstream, v a l l e y s bot tom w i t h hydromorphic soils - Later i t ic g r a v e l s f rom d e s t r u c t i o n of c u i r a s s e s

- S u b h o r i z o n t a l l a y e r s

- Sandy s o i l s on s a n d s t o n e g e n e r a l l y s h a l l o w - Sandy-c lay a l l u v i u m i n v a l l e y bot tom - Laterit ic c u i r a s s e s c o v e r i n g s a n d s t o n e - washed f e r r u g i n o u s t r o p i c a l s o i l s unde r c u i r a s s e s

- Black c l a y s on marls or mar ly l i m e s t o n e s o r s andy c l a y e y c o l l u - vium and f e r r u g i n o u s s o i l s

4. Marly s a n d s

5. S c h i s t s - Clay and sandy c l a y f rom w e a t h e r i n g o f s c h i s t s

6. C o n t i n e n t a l - H o r i z o n t a l t a b l e s o r r i d g e s t e r m i n a l from f e r r u g i n o u s s a n d s t o n e

more o r less wea the red

- 10 -

very p e r v i o u s

p e r v i o u s b u t r a p i d l y s a t u r a t e d when s h a l l o w

i m p e r v i o u s

v e r y p e r v i o u s

i m p e r v i o u s when w e t t e d

p e r v i o u s if t h e l a y e r i s t h i c k e r t h a n 15-20 cm - impervi0u.s when compact - p e r v i o u s screes o r

i m p e r v i o u s when s a t u r a t e d d i a c l a s e s

r a t h e r i m p e r v i o u s

g e n e r a l l y i m p e r v i o u s

r a t h e r i m p e r v i o u s

r a t h e r i m p e r v i o u s

p e r v i o u s

TABLE I ( su i t e )

C l a s s i f i c a t i o n . C o m p o n e n t s P e r m e a b i li t y --------------------------- ...................................... ...................... i

6 . C o n t i n e n t a l t e r m i n a l ( su i t e l - On t h e s l o p e s : marly lime

s t o n e s and more o r less c l a y e y c o l l u v i u m

- Brown-red s o i l s on material from s a n d s t o n e - c u l t i v a t e d areas - Sands i n t h e bed of t h e streams ( u p p e r p a r t of t h e c a t c h m e n t s )

- Downstream : hydromorphic s o i l s .

i m p e r v i o u s

r a t h e r p e r v i o u s

p e r v i o u s

i m p e r v i o u s

- 11 -

I-

>

T A B L E I I

EASIN .AREA.5 . BETWEEN 2 AND 4 0 K M 2

S t a n d a r d basins

Desi g n a t i on Areas Median annual Median r u n o f f r a i n f a l l . C o e f f i c i e n t C l a s s i f i cation

% ( s e e T a b l e I )

No V I 1 of Niamey Abou Goulem

Barlo Barlo II Cagara-Ouest Koubaka II Sebikotane II Sebikotane III Kadiel Pô

Kountkouzout

20 12.3 17.8 36.6 28

30 43

2.6 39.5 2.7 16.6

600 410

790-800 790-800 400-420

570 620

620 450-475 . 450 390-400

0.5 4.2

10-12 6-10 12

17 6-7

10-12 10

30 15

1 2 2

2 : 2

3

4

4 5 5 6

- 12 -

The r u n o f d e p t h LR g e n e r a t e d by a storm is related t o HU by

LR = K (HU - SU)

. Mixing b o t h e q u a t i o n s ? .one c a n write

LR = KO ( H t - HO)

. Ho c h i e f l y depends o n . s o i l m o i s t u r e i n t h e c a t c h m e n t and v a r i e s f rom

O t o Ho max. I n t h e model, it; is computed from a n i n d e x

= (H3 + H t j ) C "3 + 1 H j b e i n g a p r e c i p i t a t i o ' n i n d e x fo r t h e day 3 .and

H t j t h e t o t a l p r e c i p i t a t i o n on t h e same day

C is a f i t t i n g coefficient o f t e n n e a r 0.7

If H j > Ho max. Ho = O

I f O C H ~ C H ~ max HO = HO max - ~j I n t h e p r a c t i c e , KO and Ho max are f i t t i n g p a r a m e t e r s .

3.3.1.2. Such model was f i t t e d on t h e r e s u l t s of two r e p r e s e n t a t i v e

c a t c h m e n t s i n A f r i c a n S a h e l , q u i t e d i f f e r e n t by t h e i r r u n o f f b e h a v i o u r .

The c a t c h m e n t of K a d i e l , l i t t l e p e r v i o u s , has a n area o f 39 km2 and

a mean p r e c i p i t a t i o n of 475 mm. One found f o r t h e model Ho max = 27, KO = 0.60.

42 y e a r s c o u l d be s i m u l a t e d from r a i n f a l l d a t a of t h e t h r e e s t a t i o n s . The ana-

l y s i s of t h i s sample a l l o w e d t o draw t h e f r e q u e n c y d i s t r i b u t i o n c u r v e f o r a

K a d i e l s t a n d a r d b a s i n , c o r r e s p o n d i n g t o a mean y e a r l y r a i n f a l l of 450 .rom. T h i s

c u r v e is a l s o c o n s i d e r e d a s v a l u a b l e f o r 25 km 2 . The c a t c h m e n t of Abou Goulem is v e r y p e r v i o u s and h a s a n area of

12.3 km2 and a mean p r e c i p i t a t i o n of 400 mm. The v a l u e s of t h e p a r a m e t e r s of

t h e model are Ho max = 24 mm and KO = 0.22. The r e s u l t s of t h e s i m u l a t i o n g i v e ,

after r e d u c t i o n t o 25 km2, a f r e q u e n c y c u r v e d e f i n e d by t h e f o l l o w i n g v a l u e s of

r u n o f f :

985 f r e q u e n c y of exceedence : O

. 965 : 1 mm

. median : 12 mm

II

. O 1 f r e q u e n c y . o f exceedence : 104 mm

- 13 - 1

c..

c

Y

From t h e s e c u r v e s e s t a b l i s h e d f o r 400 mm (Abou-Goulem) and 450 mm

( K a d i e l ) , o n e d e r i v e d s imi la r c u r v e s for median r a i n f a l l s between 300 and 750 mm.

T h i s e x t r a p o l a t i o n is based

- o n t h e fact t h a t t h e r u n o f f c o e f f i c i e n t is i n c r e a s i n g w i t h t h e r a i n f a l l ,

- t h e c o n s i d e r a t i o n of o t h e r c a t c h m e n t s h a v i n g similar c h a r a c t e r i s t i c s and

d i f f e r e n t median a n n u a l r a i n f a l l .

The c o r r e s p o n d i n g sets of c u r v e s are drawn i n f i g u r e s 8 and 9.

3.3.2. For e a c h s t a n d a r d b a s i n c a t a l o g u e d i n T a b l e II, t h e f r e q u e n c y

d i s t r i b u t i o n c u r v e s of r u n o f f have been drawn w i t h t h e h e l p o f t h e r e s u l t s ob-

t a i n e d on r e p r e s e n t a t i v e b a s i n ( e s p e c i a l l y : r u n o f f d e p t h and r u n o f f c o e f f i c i e n t

fo r median y e a r l y p r e c i p i t a t i o n ) , and u s i n g a s a g u i d e t h e c u r v e s of g r a p h 8 o r

9 a c c o r d i n g t o t h e t y p e a d o p t e d for t h e c o n c e r n e d s t a n d a r d b a s i n . The r e s u l t s are

g i v e n on f i g u r e 10.

2 3.4. Frequency d i s t r i b u t i o n of r u n o f f ( s t a n d a r d area 5 km )

The methodology and t h e g e n e r a l p r i n c i p l e s are e x a c t l y t h e same a s

above, b u t i n numerous cases, t h e r u n o f f c o n d i t i o n s are too d i f f e r e n t fo r u s i n g

t h e same c u r v e s . F o r p e r v i o u s areas, t h e key b a s i n is still t h i s o n e of Abou-

Goulem (12.5 km2, between 5 and 251, b u t t h e i m p e r v i o u s areas are r e p r e s e n t e d

by t h e Po b a s i n (2.7 km2). The d i s t r i b u t i o n c u r v e s f o r b o t h key b a s i n s are drawn

o n f i g u r e 11 a f t e r b e i n g r e d u c e d t o 5 km 2 . The f i n a l network for a l l t h e s t a n d a r d b a s i n s is g i v e n on f i g u r e 12.

3.5. P r a c t i c a l r u l e s f o r water r e s o u r c e s a s s e s s m e n t

. Measuring t h e s u r f a c e of t h e ca tchment .

. E v a l u a t e t h e median y e a r l y p r e c i p i t a t t o n d e p t h w i t h t h e h e l p of f i g . 1 (P,)

. Deduce from P, t h e d i s t r i b u t i o n c u r v e ( f i g u r e 2)(may b e used i n case of

d e l i c a t e i n t e r p o l a t i o n la ter o n ) .

. S t u d y on t h e f i e l d , o r if i m p o s s i b l e , on aer ia l photographs , of t h e morpho-

log ica l factors of r u n o f f .

. I f t h e b a s i n on s t u d y , w i t h a n area c l o s e t o 5 o r 2 5 km', p r e s e n t s s i m i -

l a r c h a r a c t e r i s t i c s a s one o f t h e s t a n d a r d b a s i n , one can i n t e r p o l a t e a

d i s t r i b u t i o n c u r v e c o r r e s p o n d i n g t o t h e median y e a r l y p r e c i p i t a t i o n e v a l u a -

t e d a s above.

. I f its c h a r a c t e r i s t i c s are i n t e r m e d i a t e between t h o s e o f two s t a n d a r d

b a s i n s of t h e same g e o l o g i c a l class, o n e c a n first draw t h e two d i s t r i b u t i o n

c u r v e s c o r r e s p o n d i n g t o both of t h e s e b a s i n s f o r t h e e s t i m a t e d median y e a r -

l y p r e c i p i t a t i o n s . The . f i n a l c u r v e w i l l b e i n t e r m e d i a t e between t h e s e two

c u r v e s

. I f t h e b a s i n d o e s n o t be long a s t u d i e d class, o n e s h a l l endeavour t o i n -

t e r p r e t a t e its p e r m e a b i l i t y p o s s i b i l i t i e s d u r i n g t h e f i e l d s u r v e y and t o

a d o p t t h e r e f e r e n c e class and s t a n d a r d b a s i n whichseem t o be t h e closest

from t h i s p o i n t of view.

. I f t h e s u r f a c e of t h e ca tchment is v e r y d i f f e r e n t from 5 o r 25 km2, t h e

p r e c e d i n g o p e r a t i o n s must b e made fo r b o t h of t h e s e s u r f a c e s , t h e n t h e

f i n a l c u r v e will b e o b t a i n e d by i n t e r p o l a t i o n .

2 If i n s i d e a v e r y p e r v i o u s c a t c h m e n t , e x i s t s a n i m p e r v i o u s area o f n km , t h e c a t c h m e n t must b e t r e a t e d a s a n i m p e r v i o u s c a t c h m e n t o f n km', i n

n e g l e c t i n g t h e r e m a i n i n g .

4. CONCLUSION

T h i s p a p e r shows t h a t i t is p o s s i b l e t o assess t h e s u r f a c e water re-

s o u r c e s i n a r i d z o n e s even when t h e i n f o r m a t i o n is v e r y r e s t r i c t e d i n t h e s p a c e

and i n t h e time. I n t h e case of A f r i c a n S a h e l , s t u d i e d by Dr. R o d i e r , a l l t h e

i n f o r m a t i o n is c o l l e c t e d i n t h e r e g i o n . With t h e k i n d of a n a l y s i s which h a s been

u s e d , it would be p o s s i b l e t o a p p l y t h e t a b l e s and t h e g r a p h s i n a n o t h e r r e g i o n

b u t under t h e c o n d i t i o n t h a t a l l b a s i c h y p o t h e s e s b e r e s p e c t e d :

- o n e must be s u r e t h a t t h e r e i s a real a n a l o g y between t h e p h y s i o g r a p h i c a l

c h a r a c t e r i s t i c s o f t h e unknown c a t c h m e n t s and t h e s e of t h e s t a n d a r d s

b a s i n s u s e d f o r e s t a b l i s h i n g t h e g r a p h s ;

- t h e climate must b e t h e same i n b o t h r e g i o n s , e s p e c i a l l y f o r t h e t y p e

of p r e c i p i t a t i o n s ( t r o p i c a l storms) s h a p e o f which is v e r y i m p o r t a n t f o r

I 1 5

runoff g e n e r a t i o n .

It s h o u l d be s t r o n g l y recommended t h a t a l l t r o p i c a l c o u n t r i e s pay s p e -

c i a l a t t e n t i o n f o r i n i t i a t i n g o r p u r s u i n g i n v e s t i g a t i o n s i n t h a t f i e ld These

s t u d i e s are e x p e n s i v e b u t n e c e s s a r y f o r a good a s s e s s m e n t of s u r f a c e water re-

s o u r c e s i n a r i d zones . Each new i n f o r m a t i o n c o l l e c t e d anywhere will v a l o r i z e t h e

r e s u l t s a l r e a d y a v a i l a b l e .

- 1 6 - L -

RODIER J . A . - " E v a l u a t i o n d e I ' é c o u l e m e n t annuel d a n s l e

S a h e l T r o p i c a l a f r i c a i n " .

In "Travaux e t d o c u m e n t s d e I'ORSTOM" - no 46

ORSTCM, Paris 1975.

[ 2 ] GIRARD G. - " L e s m o d è l e s h y d r o l o g i q u e s p o u r l ' é v a l u a t i o n

d e l a l a m e é c o u l é e en zone sahe'lienne e t

l e u r s contraintes".

' In " C a h i e r s d e It0RSTOM - S é r i e Hydrologie ' '

Vol . XII-no3 -1975 - p p . 189-221.

[ 3 ] GIRARD G. - " A p p l i c a t i o n d u m o d è l e 2 d i s c x d t i s a t i o n

s p a t i a l e a u bassin d e l ' o u e d Ghorfa ( M a u r i t a -

n ie)" .

In "Cahiers d e 1 'ORSTOM - Série H y d r o l o g i e "

Vol. XII-no 3 -1975 - pp . 167-188.

- 17 -

YEARLY RAINFALL IN AFRICAN SAHEL fig- 1

200c

10oc 9 0 C 80C ?O( 60C

500

40C

300

v zoa

toa

40

20

Frequency distr ibut ion of yearly ra in fa l ls in a f r ican Sahel

(Isohyets 300 to 750mm)

Fig- 2

b

Frequency of excmedwa 0 I

I 0.02 0.05 o1 0.2 0.3 0 4 C

2000

1000 900 800 700 600

500

400

300

zoo

1 0 0

40

20 0.6 0.7 0.8 0.9 o 95 o 98 0.99 0,995

Yearly runof f for b a s h a reas greater t h a n 10000 km’ i n a f r i can Sahel

F i g - 3

2ooc Frequency distribution curves

5 0 . \ \

I -- - - - i%.‘-wL y! u-u, .- c 20.

5 3

2 10,

œ

\ U

c - c

--- ------

5 .

-- - - - - _

2 .

I l l Frequency of arccedence

0.01 0.02 0.05 0.1 0.2 0.3 0.4 O. 1

1 1

c

2

c

-F

I

20 o

100

50

!O

I C

œ .-

5 a U

0 .= C

a

. c

L

t

T

Yearly runof f for basin areas between 1000 and 10000km2 Fig- 4 in a f r i can Sahel

4 Basins on granite and granito-gneiss. tency. distribution curves

tt

+- I I I I I I

2 0.05 0.1 0.2 0.3 0.4 O

I 2 0 0

100

50

. I

!e*

2

c I

.-

O U - P

o

!

9

I

b-

B

Ø

c

9

* ,

.. b

c.

Yearly runoff for basin areas between 1000 and 10000 km* i n a f r i can Sahel

A Basins on various soils (sandstones. schists. marly limestones-.)

Frequency of exceedence 1 I I 0.01 , 0.02 0.05 0.1 0.2 c 0.4 0.5 O

- a

fig- 5

A

c

I 3

,

Yearly runoff for basin a reas between 40 and 1000 km* F i g - 6 t in a f r i c a n Sahel I

200

100

50

20

IO

5

1

I '9

n

I

4 Yearly r u n o f f for b a s i n areas between 40 and 1000km' F ig - 7 300

200

100

50

10

O

I

!

8

. 1

c

4 .

500

400

300

200

100

50

20

10

5

Yearly runoff for bas in area i n a f r i c a n Sahel Fig- 8

Kadiel standard basins

Frequency distribution curves

0.01 0.02 0.05 0.1 0.2 0.3 0.4 O 5 0.6 O.? 0.8 0.9 0.95 0.98 0.99

500

400

300

200

100

50

20

10

5

200

100

50

20

: 10

5

2

1

Yearly runoff for basin area o f 2 5 km2 i n afr ican Sahel Fig- 9 Abougoulem standard basins

Frequency distribution curves

0.01 0.02 0.05 o 1 O 2 0 3 0 4 O 5 0 6 O

II- \

O. o a

200 .

100

50

20

10

5

2

1

500

400

300

200

100

50

40

30

20

I c .' t 10 U - 1 2

i : 5

., -

2

1 O

500

400

JO0

200

100

50

40

30

E 20

c . E . U

E 10 - D 2 5 . 4

5

2

500

400

300

200

100

50

20

10

5

1

1

500

400

300

200

100

50

20

10

5

f for basin area of 5 km' in a f r i c a n Sahe l . Fig- 12 I Froquoncy distribution curvoa I

I I I

I I I

500

400

300

200

100

50

20

,