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papers have suggested that the lack of knowledge of soil heterogeneity is a fundamental constraint on the
accuracy of distributed models (e.g. Beven, 2001; Hansen et al. , 2007; Refsgaard et al. , 2010) although
some numerical studies have also suggested that this may not be such an issue in predicting catchment
scale responses (Canfield and Goodrich, 2006).
Similar software is required for post-processing of the results. The finer the elements the more data
that are produced by each simulation. The only way to assess such information easily is visually, in the
form of computer graphics, and this form of distributed model has become more and more sophisticated
in interacting with geographical information systems, both in setting up the model and in presenting the
results (see Maidment, 2002; Refsgaard et al. , 2010). This is even more the case if it is necessary to convey
the uncertainities in the spatial predictions of such models (e.g. Leedal et al. , 2010; see Figure 3.7).
5.2.2 Models Based on Grid Elements: The SHE Model
The Systeme Hydrologique Europeen (SHE) model is the most widely known rainfall-runoff model based
on grid elements. It was started in 1977 as a joint collaboration, between the UK Institute of Hydrology,
the Danish Hydraulics Institute (DHI) and SOGREAH of Grenoble in France. An early description of
the model was published by Beven et al. (1980), an explanation of the modelling philosophy was pro-
vided by Abbott et al. (1986a, 1986b), and the first full application (to the Institute of Hydrology River
Wye experimental catchments at Plynlimon, Wales (10 km 2 )) was published in a series of articles by
Bathurst (1986a, 1986b). Other applications have been published, ranging from the 1.4 km 2 Rimbaud
catchment in the south of France (Parkin et al. , 1996) to the 820 km 2 Kolar and 4955 km 2 Narmada
catchments in India (Refsgaard et al. , 1992; Jain et al. , 1992). A summary of the history and appli-
cation of SHE, particularly the DHI commercial version (MIKE SHE) is given by Refsgaard et al.
(2010), who note that there are now nearly 400 installed copies of the MIKE SHE software around
the world.
SHE is a grid-based model that splits the catchment into a number of square or rectangular grid
elements, linked to channel reaches that run along the boundaries of the hillslope grid. The size of
grid used has varied in different applications, ranging from 50 m on a side for the small 40 ha Upper
Sheep Creek catchment in Idaho up to 2 km on a side for the Kolar and Narmada catchments in India.
Note that in the latter case the grid size is so large that the model cannot be considered to be representing
flow on the hillslopes or in the smaller channels of the catchment in any meaningful way.
Each hillslope grid element (Figure 5.3) has a specified surface elevation and model components
for interception, evapotranspiration, snowmelt, and one-dimensional vertical unsaturated zone flow
where appropriate. The grid elements are linked by two-dimensional surface runoff and groundwater
components. Internal boundary conditions allow the coupling of surface flow and infiltration into the
unsaturated zone, the unsaturated and saturated zones at the local water table, and groundwater and
channel flows. Great effort has been made to ensure that the processes are properly coupled and that
the numerical solutions are stable for a wide range of conditions. The model can predict a variety of
runoff generation processes on each grid element, including both infiltration excess and saturation ex-
cess runoff, and the groundwater flow component can be used to simulate subsurface contributions to
the hydrograph under suitable conditions. The description of the unsaturated and saturated zones are
based on Darcy's law; overland and channel flows are described by a diffusion wave approximation
to the St. Venant equations and various options are included for simulating interception and evapo-
transpiration, including the Penman-Monteith equation (see Box 3.1). Snowmelt is simulated, either
using a degree-day method or a full energy balance (Bathurst and Cooley (1996) make a comparison of
both implementations).
The types of parameter values required are similar to those listed in Table 5.1 and there is the potential
to have different parameters for every grid element and within each grid element for different layers in
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