Geoscience Reference
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Figure 6.4 The ln ( a/ tan ˇ ) topographic index in the small Maimai M8 catchment (3.8 ha), New Zealand,
calculated using a multiple flow direction downslope flow algorithm; high values of topographic index in the
valley bottoms and hillslope hollows indicate that these areas are predicted as saturating first (after Freer, 1998).
of ( a/ tan β ) (see Figure 6.4) may be derived from analysis of a digital terrain model (DTM) or a digital
elevation map (DEM) of the catchment (see Section 6.3.2). Specifying a spatial distribution for T o is
generally much more problematic, since there are no good measurement techniques for obtaining this
parameter. In most applications, it has been assumed to be spatially homogeneous, in which case the
similarity index reduces to the form ( a/ tan β ).
To calculate the surface (or subsurface) contributing area, the catchment topographic index is ex-
pressed in distribution function form (Figure 6.5). Discretisation of the ( a/ tan β ) distribution function
brings computational advantages. Given that all points having the same value of ( a/ tan β ) are assumed
to behave in a hydrologically similar fashion, then the computation required to generate a spatially-
distributed local water table pattern reduces to one calculation for each ( a/ tan β ) class; calculations are
not required for each individual location in space. This approach should be computationally more efficient
than a solution scheme that must make calculations at each of a large number of spatial grid nodes, a
potentially significant advantage when parameter sensitivity and uncertainty estimation procedures are
carried out.
In a time step with rainfall, the model predicts that any rainfall falling upon the saturated source area
will reach the stream by a surface or subsurface route as storm runoff, along with rainfall in excess of
that required to fill areas where the local deficit is small. The calculated local deficits may also be used
to predict the pattern of subsurface stormflow contributing areas or flow through different soil horizons
(Robson et al. , 1992) if they can be defined by some threshold value of deficit (or water table depth).
The model is completed by a representation of the unsaturated zone and a flow routing component.
Both have been kept deliberately simple to facilitate parameter estimation. It is particularly difficult to
account explicitly for the effects of local soil heterogeneity and macroporosity. No entirely satisfactory
mathematical description is currently available of unsaturated flow in structured soils with parameters
that can be identified at a practical prediction scale and if parameter values are to be determined by
calibration then minimal parameterisation is advantageous. Current versions of TOPMODEL use two
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