Geoscience Reference
In-Depth Information
soils had been available at least since the paper by Green and Ampt (1911). Horton argued, in fact,
that his experiments suggested that infiltration could not be profile controlled, as assumed in the theory
underlying the Green-Ampt equation, but was controlled by surface effects such as the redistribution of
fine particles (Beven, 2004b). Since then, many other infiltration equations have been proposed, mostly
based on various simplifications of the nonlinear Darcy flow problem (see, for example, the review of
Parlange and Haverkamp (1989) and Box 5.2).
All of these equations provide estimates of the local limiting infiltration capacity of the soil over time.
When rainfall during a storm exceeds the infiltration capacity, then water will start to pond at the surface
and, perhaps after the storage in local depressions has been filled, may start to run downslope as overland
flow. Comparison of rainfall rates with infiltration capacities therefore provides a means of estimating
the effective rainfall for a storm (e.g. element B in Figure 2.3) - if runoff is actually being generated by
an infiltration excess mechanism. However, as we saw in Chapter 1, this is not always the case, and even
when surface runoff does occur, infiltration rates may show a high degree of heterogeneity in space. There
is little doubt that this type of approach to estimating effective rainfall has often been misapplied, and
probably continues to be misapplied (or at least misinterpreted) 60 years after the original formulation
of the concepts. Robert Horton understood some of these issues (see Beven, 2004a) but also understood
the value of the infiltration excess approach as an engineering tool.
The reasons for this are functional. The infiltration excess model of effective rainfall and the unit
hydrograph together provide the necessary functional components of a hydrological model, i.e. a way
of estimating how much of the rainfall becomes runoff and a means of distributing that effective rainfall
through time to predict the shape of the hydrograph. It is not therefore necessary to apply this method
under the assumption that it is actually surface runoff in excess of the infiltration capacity of the soil
that is being routed by the unit hydrograph (as in Figure 2.4a). The simplest models of effective rainfall,
assuming either that there is a constant “loss” rate (the
-index method) (Figure 2.4b) or that a constant
proportion of the rainfall is effective rainfall (Figure 2.4c), are also still widely used but are less obviously
surface runoff generation models; rather, they are very simple ways of deriving an approximate runoff
coefficient. This type of estimation of effective rainfall serves the functional requirement of having a
loss function that is nonlinear with respect to total rainfall if the parameter is allowed to vary with
antecedent state of the catchment, regardless of whether the runoff generation process is actually due to
an infiltration excess mechanism. Both methods involve only one parameter but they lead to different
patterns of effective rainfalls in time for the same event. Other ways of calculating effective rainfalls,
with similar functionality, are also commonly used.
Another interesting method for estimating effective rainfalls in the USDA Soil Conservation Service
(SCS) curve number approach (McCuen, 1982). This is also often interpreted as an infiltration equation
(e.g. the recent papers of Yu, 1998, and Mishra and Singh, 1999), but in fact has its origins in the analysis
of runoff volumes from small catchments byMockus (1949, reproduced in Loague, 2010) and which may
not only have included infiltration excess overland flow as the runoff generatingmechanism (see Box 6.3).
The critical assumption of the SCS method is that the ratio of the actual runoff to the potential runoff
(rainfall less some initial abstraction) is equal to the ratio of the actual retention to the potential retention.
There is no physical justification for this assumption. Mockus himself suggested only that it produced
rainfall-runoff curves of the type found on natural watersheds. It is therefore a purely empirical function
for estimating a runoff coefficient and any process interpretation equating the retention to infiltration
and the runoff to surface runoff has been made since the original work. This illustrates how deeply the
Hortonian concepts of runoff generation have permeated the development of rainfall-runoff modelling.
The SCS method remains widely used within a number of current distributed models and is covered in
more detail in Chapter 6.
The calculation of effective rainfalls is a major problem in the use of the unit hydrograph technique,
especially since it is inherently linked to decisions about hydrograph separation to determine the amount
of storm runoff for an event. However, since use of the unit hydrograph is a linear operation, given
