Geoscience Reference
In-Depth Information
indeed, to the extent that the drainable porosity
n
e
represents the mobile water in the
soil (so that (
n
e
) can be considered immobile water as indicated in Figure 10.12),
Equation (10.151) is also the true velocity of the water in the aquifer. Therefore, it is
perhaps preferable to refer to this phenomenon as kinematic flow, rather than kinematic
wave. It can be seen that the reason for this equality of fluid and wave velocity is the
inherent linearity of (10.150). On the other hand, it should also be remembered that, in
spite of its name, the real physical significance of
n
e
is not obvious; it was introduced
as a mere parameter to compensate for the neglect of the partly saturated flow above
the water table in the soil by the free surface approximation. While the fraction of the
soil volume below the water table occupied by flowing water is not as large as the total
porosity
n
0
, it is probably larger than
n
e
, because not all the flowing water is removed
by the drainage process. Therefore, the true velocity of the water in the aquifer is not
likely to be as large as (10.151). This means that it can be expected that the water table
motion down a steep slope may still have certain features of a wave; but on account of
the obscure physical nature of
n
e
, these features are unclear and the phenomenon will
require further study.
The applicability of the kinematic wave approach was studied by Henderson and
Wooding (1964), by comparing their results presented in Section 6.2.2 applied to ground-
water, i.e. for the case
a
θ
0
−
0, with those obtainable with the full Boussinesq equation.
They concluded that the differences can be significant for the decay phase, as obtain-
able, for example, from the groundwater analog of Equation (6.27). As mentioned, in
the kinematic approach the hydraulic gradient is assumed to be equal to the bed slope;
in practice, this is usually taken to be the same as the ground surface slope. The main
practical drawback of this approach is that it is unsuitable when a wide range of slopes
has to be considered, including very small ones in relatively flat terrain. However, for
steep slopes or large values of the hillslope flow number Hi this approach can be a useful
tool to describe the flow. Because the motion is strictly translatory, it also provides some
justification for the application of the rational method (see Section 12.2.2) to describe
subsurface storm runoff from very permeable hillslopes in hilly catchments for engineer-
ing design. The kinematic approach has been used in some catchment scale simulations
of hillslope storm runoff (Beven, 1981).
=
10.6
CATCHMENT-SCALE BASE FLOW PARAMETERIZATIONS
10.6.1
General features
Base flow is the discharge rate in a river that results from the natural release of the water
stored in the upstream river channels and adjoining riparian aquifers in the absence of
precipitation, snowmelt, or other inputs. In general, this type of flow depends primarily
on the physiographic characteristics of the basin, on the distribution of water storage in
river channels and in groundwater aquifers, and possibly also on the evaporation from
the basin. These physiographic characteristics are mainly the geomorphology of the
landscape and of the stream network, and the configuration and nature of the riparian
aquifers and near-surface soils; these characteristics reflect the geology and the climate
