Geoscience Reference
In-Depth Information
do not make calculations for every point in the catchment but for a distribution function of charac-
teristics. TOPMODEL, discussed in Chapter 6, is a model of this type, but has the feature that the
predictions can be mapped back into space for comparison with any observations of the hydrological
response of the catchment. It could therefore be called, perhaps, a semi-distributed model. Chapter 9
discusses the next generation of hydrological models, which will, at least in part, start to resolve some of
these issues.
A second consideration is whether to use a
deterministic
or a
stochastic
model. Deterministic models
permit only one outcome from a simulation with one set of inputs and parameter values. Stochastic models
allow for some randomness or uncertainty in the possible outcomes due to uncertainty in input variables,
boundary conditions or model parameters. The vast majority of models used in rainfall-runoff modelling
are used in a deterministic way, although again the distinction is not clear cut since there are examples of
models which add a stochastic error model to the deterministic predictions of the hydrological model and
there are models that use a probability distribution function of state variables but make predictions in a
deterministic way. A working rule is that if the model output variables are associated with some variance
or other measure of predictive dispersion the model can be considered stochastic; if the output values are
single valued at any time step, the model can be considered deterministic, regardless of the nature of the
underlying calculations.
There is one other modelling strategy, based on
fuzzy logic
methods, that looks highly promising
for the future. The number of fuzzy models is currently few (see, for example, Bardossy
et al.
, 1995;
Hundecha
et al.
2001; Ozelkan and Duckstein, 2001) but the range of application would appear to be
large. In particular fuzzy models would appear to offer the potential for a more direct translation from the
complexity of the perceptual model into a procedural model. Applications to date, however, have often
used an intermediate conceptual model to formulate the fuzzy rules and have defuzzified the results so
as to run as essentially deterministic solutions.
So, these are the broad generic classes of rainfall-runoff model. Within each class there is a range of
possible model structures. How then to go about choosing a particular model structure for a particular
application? The following suggested procedure is based, in essence, on considerations of the
function
of possible modelling structures:
1. Prepare a list of the models under consideration. This list may have two parts: those models that
are readily available and those that might be considered for a project if the investment of time (and
money!) appears to be worthwhile.
2. Prepare a list of the variables predicted by each model. Decide whether the model under consideration
will produce the outputs needed to meet the aims of a particular project. If you are interested in the
rise in the water table in valley bottoms due to deforestation, for example, a model predicting the
lumped response of the catchment may not fulfill the needs of the project. If, however, you are only
interested in predicting the discharge response of a catchment for real-time flood forecasting, then it
may not be necessary to choose a distributed modelling strategy.
3. Prepare a list of the assumptions made by the model (see the guides in the chapters that follow). Are
the assumptions likely to be limiting in terms of what you know about the response of the catchment
you are interested in (your perceptual model)? Unfortunately the answer is likely to be yes for all
models, so this assessment will generally be a relative one, or at best a screen to reject those models
that are obviously based on incorrect representations of the catchment processes (i.e. any reasonable
hydrologist should not try to use a model based on Hortonian overland flow to simulate the Coweeta
catchments mentioned in Section 1.4).
4. Make a list of the inputs required by the model, for specification of the flow domain, the boundary
and initial conditions and the parameter values. Decide whether all the information required can be
provided within the time and cost constraints of the project.
