Geoscience Reference
In-Depth Information
Recall the criteria that were established in Chapter 1 for model choice. These may be summarised
as follows:
•
Is a model readily available or could one be made available if the investment of time (and money!)
appeared to be worthwhile?
•
Does the model predict the variables required by the aims of the particular project?
•
Are the assumptions made by the model likely to be limiting in terms of what you know about the
response of the catchment you are interested in?
•
Can all the inputs required by the model, for specification of the flow domain, for specification of the
boundary and initial conditions and for specification of the parameters values, be provided within the
time and cost constraints of the project?
At this stage it should be apparent that these criteria essentially provide the basis for model rejection
and, as pointed out way back in Chapter 1, it is all too easy to reject all the available models due to
inadequate assumptions or infeasible demands for input data. This is not very helpful: in very many
projects, the hydrologist is still required to make predictions of what might be expected in terms of flood
peaks, reservoir inflows or other variables under different conditions. Thus one or more models will need
to be retained.
This is, however, where the idea of conditioning of models becomes very important. We can, to some
extent, overcome some of the limitations of the available models by conditioning their predictions on
any available observations or prior knowledge about the catchment of interest. Traditionally, this has
been done by the calibration or optimisation of parameter values: it is suggested in Chapter 7 that a more
general strategy of conditioning within an uncertainty framework is a much more satisfactory approach
for the future. In this framework,
any
model that predicts a variable of interest is a potentially useful
predictor, until there is evidence (or a justifiable opinion) to reject it. The value of conditioning in this
way is that the model or models retained must be consistent with the available data (at least to some
level of acceptability), otherwise they would have been rejected. This gives some basis for belief in the
predictions when those models are used to extrapolate or predict responses for other conditions.
Try to picture the modelling process as a form of mapping of a particular (unique) catchment or element
of a catchment into a model space with dimensions of different model structures and parameter values.
Chapter 7 shows how this mapping can be done using conditioning based on likelihood measures or fuzzy
weights. For many reasons, primarily associated with the limitations of model structure and parameter
estimation, the mapping is necessarily approximate. The mapping can be done for both gauged catchments
and ungauged catchments based on whatever prior information or observations are available, but is likely
to be more exact where observations of hydrological response are available and more approximate for
the ungauged catchment case. There is, however, the potential to refine this mapping by the collection
of more data and this approach to model evaluation also has implications for the types of data collection
exercise that might be used as the basis for a rainfall-runoff modelling study.
In fact, as discussed in Section 7.17, the process of model evaluation can be set up in terms of hypothesis
testing. Given a set of models for a catchment that have survived the initial selection and evaluation
procedure, what hypotheses can be tested by the collection of data to allow some of those models to be
rejected? It would seem that some types of data might be more valuable than others in testing models
and in model rejection. For example Lamb
et al.
(1998b) considered the use of water table information
in predicting the responses of the small Saeternbekken catchment in Norway (see Section 6.4). Their
results highlighted the problem of using spatially distributed observations in model evaluation in that
local water table responses depend strongly on the local transmissivity and storage characteristics of the
soil. Thus it is unlikely, given the heterogeneity of soil characteristics to be expected in a catchment, that
even if the model structure were correct, an effective transmissivity and storage coefficient calibrated
for a catchment would predict local variations in water table depth accurately. Local parameter values
