PUB in practice: case studies - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 329

a) b)

Burkina Faso

5

6
7

2

4

1

3

8
Togo

Upper East Region of Ghana

c)

Burkina Faso

Kilometers

0 5 10 20 30 40

Benin

Togo

Ghana

Cote d'lvory

Reservoir 1 234 5 67 8

8.8 11.2 8.9 14.8 17.6 15.1 29.5 8.8

SR size (ha)
WS (ha)

822 518 144 403 357 1549 1829 194

Gulf of Guinea

Figure 11.61. (a) Map showing location of study area and the eight catchments used in the case study. SR and WS relate to reservoir and
catchment area, respectively. From Liebe et al.( 2009b ). (b) Typical small-scale irrigation (onions) and dry season landscape; and (c) very small
reservoir (2 ha surface area) at the end of the dry season. Photos: J. Liebe.

should have the properties that the contributing area is zero
when rainfall just wets up the soil to field capacity and
should be equal to 1 when rainfall approaches infinity. One
such expression that satisfies these boundary conditions is

P e 1 Q f ¼ − exp ð− aP e Þ

250 m

where a is a constant with dimension (T/L) expressed
in (days/mm), which is an indicator of a catchment s

sensitivity to runoff generation. Noting that P e is equiva-
lent to the effective rainfall as defined in Steenhuis et al.
( 1995 ), we can differentiate with P e to obtain the contrib-
uting area, A f :

'

Figure 11.62. Small reservoir and outline (white) on Envisat ASAR.

runoff model was developed to predict the
catchment outflow to the reservoir. It

A rainfall -

is based on the

Thornthwaite Mather procedure (Thornthwaite and

Mather, 1955 ). In this procedure a water balance of the
root zone is maintained. The actual evaporation is a linear
function of the plant available water. At field capacity the
evaporation is equal to the potential evaporation and at
wilting point it is negligible. Any rainfall in excess of the
maximum storage in the root zone, S max (i.e., when the soil
moisture exceeds field capacity), is released to the subsoil
as percolation. The portion of the percolation (P e )
that recharges the reservoir as quickflow, Q f , becomes
generally greater the greater the rainfall amount. This rela-
tionship between contributing area and effective rainfall
amounts is not known. In developing such a relationship it

-

A f ¼ 1 −ð aP e Þ exp ð− aP e Þ

We can see this has the required property that A f is 0 when
the P e ¼ 0 and that it is equal to 1 when P e goes to infinity.

Results
The catchments extracted from the SRTM DEM, includ-
ing the reservoirs, range from 144 to 1829 ha ( Figure
11.61 ). The results of the reservoir surface area classifi-
cation obtained from the radar image analysis are listed
in Table 11.12 . On the basis of these remotely sensed