Geoscience Reference
In-Depth Information
where
S
is bulk catchment storage,
t
is time,
R
t
is rainfall input at time
t
,
E
is actual evapotranspiration,
and
Q
is discharge from the catchment. Under the assumption that
Q
can be specified as an arbitrary
function of
S
, then this can also be expressed in terms of the change of discharge through time as
dQ
dt
dQ
dS
dS
dt
dQ
dS
=
=
(
R
t
−
E
t
−
Q
t
)
=
g
(
Q
) (
R
t
−
E
t
−
Q
t
)
(4.2)
dQ
dS
The function
g
(
Q
)
=
can then be defined by
dQ
dt
g
(
Q
)
=
(4.3)
(
R
t
−
E
t
−
Q
t
)
It is then clear that this function is most easily determined from discharge information alone when
R<<Q
and
E<<Q
, i.e. winter recession curves during dry periods (see also Brutsaert and Nieber,
1977; Lamb and Beven, 1997). Plots of
d
dt
against
Q
during such periods should show the regularity of
this function in a particular catchment under different conditions. Figure 4.1 shows the Kirchner example
at Plynlimon in Wales.
Figure 4.1
Plots of the function g
(
Q
)
for the Severn and Wye catchments at Plynlimon: (a) and (b) time step
values of
d
dt
against Q; (c) and (d) functions fitted to mean values for increments of Q (after Kirchner, 2009,
with kind permission of the American Geophysical Union).
