Geoscience Reference
In-Depth Information
of the length of the reach). This means that the transfer function of the Muskingum-Cunge model often
shows an initially negative response (e.g. Venetis, 1969) as a way of producing a time delay. The more
general transfer function techniques, described in Chapter 4, that include the possibility of a time delay
are a better approach to defining a simple flow routing model where observed hydrographs are available
for model calibration. The Muskingum-Cunge model is, in fact, a specific case of the general linear
transfer functions outlined in Box 4.1, mathematically equivalent to a first-order (one
a
coefficient)
model, with two
b
coefficients and zero time delay, although versions have also been developed that
allow the parameters to change nonlinearly with time (Todini, 2007; Price, 2009).
The simplicity of the kinematic wave equation with its straightforward combination of the continuity
equation and a storage-discharge function, makes it very appealing as an approximation of the real
physics. It is particularly appealing in cases where some “effective” storage-discharge function might be
required to take account of limited understanding of flow over rilled surfaces or flow through structured
soils that might not be well represented by the normal theory used for surface and subsurface flow (e.g
Beven and Germann, 1981; Faeh
et al.
, 1997). This degree of flexibility makes it valuable as a modelling
strategy. It remains necessary, however, to be aware of the limitations of the approach to essentially
one-dimensional flows and the possible effects of kinematic shocks.
5.6 Case Study: Distributed Modelling of Runoff Generation
at Walnut Gulch, Arizona
One of the real challenges of semi-arid hydrology is still to model the extensive data set collected by
the USDA Agricultural Research Service on the well-known Walnut Gulch experimental catchment
(150 km
2
) in Arizona (Stone
et al.
, 2008). This has been the subject of numerous experimental and mod-
elling studies, a selection of which are discussed in this section. Walnut Gulch is a semi-arid catchment,
with 11 nested subcatchments that range from 2.3 to 150 km
2
and an additional 13 small catchment areas
from 0.004 to 0.89 km
2
. Spatial variability in rainfall is assessed using a network of 92 gauges. The
catchment has been the subject of two intensive field campaigns combining field measurements with
aircraft platform remote sensing (Kustas and Goodrich, 1994; Houser
et al.
, 1998). The perception of
runoff generation in this environment is that it is almost exclusively by an infiltration excess mechanism
(Goodrich
et al.
, 1994).
At the hillslope runoff plot scale in Walnut Gulch, Parsons
et al.
(1997) have compared observed and
predicted discharges, together with flow depths and velocities at several cross-sections. The model used
the simplified storage-based infiltration model of Box 5.2 with two-dimensional kinematic wave routing
downslope. The storage-discharge relationship used was a power law with parameters that varied with
the percentage cover of desert pavement in each grid cell of the model. In the first application, to a
shrubland site, the model underpredicted the runoff generation but was relatively successful in predicting
the shape of the experimental hydrograph (Figure 5.12). The second application, to a grassland plot, was
less successful, despite a number of modifications to the model including the introduction of stochastic
parameter values.
At a somewhat larger scale, Goodrich
et al.
(1994) and Faures
et al.
(1995) have applied KINEROS
(Smith
et al.
, 1995) to the 4.4 ha Lucky Hills LH-104 subcatchment to examine the importance of different
antecedent soil moisture estimates and the effects of wind and rainfall pattern on the predicted discharges
(Figure 5.13). KINEROS uses a Smith-Parlange infiltration equation (see Box 5.2) coupled to 1-D
kinematic wave overland flow routing on hillslope planes and in channel reaches. At this scale, both studies
conclude that an adequate representation of the rainfall pattern is crucial to accurate runoff prediction in
this environment. Using average initial soil moisture contents from different remote sensing and modelling
methods had little effect on the predictions, as did trying to take account of the effects of wind direction and
