Geoscience Reference
In-Depth Information
by considering unconfined flow under the hydraulic assumption. Under drainage condi-
tions (i.e. without inflow), the outflow rate from a Dupuit-Boussinesq aquifer is given by
Equations (10.85) with (10.86). These can be converted to outflow from a catchment area
A
with a stream channel length
L
by putting
Q
=
2
Lq
and
B
=
A
/
2
L
. With
y
=
Q
/
A
as the outflow rate per unit area and
x
0, the lumped equation of continuity (12.26) (or
(1.10) or (7.11)) produces the storage expressed as a layer of water of average thickness
as follows
=
∞
S
=
y
(
t
)
dt
(12.54)
t
Upon integration of (12.54) with (10.85) and (10.86), one obtains readily
0
.
416
n
e
A
Lk
1
/
2
0
y
1
/
2
S
=
(12.55)
=
/
which is in the form of (12.48) with
m
2. In this result
n
e
is the effective drainable
porosity,
k
0
the effective hydraulic conductivity,
A
the drainage area of the catchment,
and
L
the length of all the stream channels into which aquifer drainage takes place. If
the system can be linearized, the solution is given by (10.113) and after longer times by
(10.116). Integration of Equation (12.54) with the latter produces in the same way
1
n
e
A
2
S
=
2
k
0
L
2
pD
y
(12.56)
π
=
Again, this is in the form of (12.48), but now
m
1, in accordance with (12.25), as
expected for a linear system.
In summary, most of the
m
values from field data reviewed here not only conform
with the values expected for open channels, but they appear to be intermediate between
the values for nonlinear and linear groundwater aquifers as well.
12.4
NON-STATIONARY LINEAR RESPONSE
In the definition of the unit hydrograph the two stipulated assumptions are linearity and
time invariance. Until now, these two assumptions have mainly been studied separately,
and their combined effect has not yet been fully explored. The incorporation of nonlinear
effects into stationary systems, which is treated in Section 12.3, seems to have received
more attention in the literature and relatively few studies have been devoted to nonsta-
tionary effects on linear catchment response. Yet, several experimental investigations
reviewed in Chapter 11 have indicated that, for instance, the ratio of old and new water
in the catchment outflow is affected not only by the intensity of the rain, but also by such
factors as seasonal moisture status and the time since the start of the rain. Hence, as the
catchment contains more or less water, different flow paths and mechanisms come into
play in the production of the runoff, and this results in a non-stationary response.
In general, one can distinguish two ways of describing non-stationarity. One type
of formulation makes use of a coarse time variable describing changes in catchment
response at monthly and annual time scales; these changes could conceivably be cyclical,
that is seasonal, or in the nature of a trend in the case of changes in land use or climate.
