Geoscience Reference
In-Depth Information
5. Determine whether you have any models left on your list. If not, review the previous steps, relaxing
the criteria used. If predictions are really required for an application, one model at least will need to
be retained at this stage!!
1.8 Model Calibration and Validation Issues
Once one or more models have been chosen for consideration in a project, it is necessary to address
the problem of parameter calibration. It is unfortunate that it is not, in general, possible to estimate
the parameters of models by either measurement or prior estimation. Studies that have attempted to do
so have generally found that, even using an intensive series of measurements of parameter values, the
results have not been entirely satisfactory (Beven
et al.
, 1984; Refsgaard and Knudsen, 1996; Loague
and Kyriakidis, 1997). Prior estimation of feasible ranges of parameters also often results in ranges of
predictions that are wide and may still not encompass the measured responses all of the time (Parkin
et al.
, 1996; Bathurst
et al.
, 2004).
There are two major reasons for these difficulties in calibration. The first is that the scale of the
measurement techniques available is generally much less than the scale at which parameter values are
required. For example, there may be a hydraulic conductivity parameter in a particular model structure.
Techniques for measuring hydraulic conductivities of the soil generally integrate over areas of less than
1m
2
. Even the most finely distributed models however, require values that effectively represent the
response of an element with an area of 100 m
2
or, in many cases, much larger. For saturated flow, there
have been some theoretical developments that suggest how such effective values might change with
scale, given some underlying knowledge of the fine scale structure of the conductivity values. In general,
however, obtaining the information required to use such a theory at the hillslope or catchment scale would
be very time consuming and expensive and would result in a large number of holes in the hillslope! Thus
it may be necessary to accept that the small scale values that it is possible to measure and the effective
values required at the model element scale are different quantities (a technical word is that they are
incommensurate
) - even though the hydrologist has given them the same name. The effective parameter
values for a particular model structure still need to be calibrated in some way. It is also often the case that
the time and space scales of model-predicted variables may be different from the scale at which variables
of the same name can be measured (for example, soil water content). In this case, the variables used in
calibration may also be incommensurate.
Most calibration studies in the past have involved some form of
optimisation
of the parameter values by
comparing the results of repeated simulations with whatever observations of the catchment response are
available. The parameter values are adjusted between runs of the model, either manually by the modeller
or by some computerised optimisation algorithm until some “best fit” parameter set has been found.
There have been many studies of optimisation algorithms and measures of goodness of fit or
objective
functions
in hydrological modelling (see Chapter 7). The essence of the problem is to find the peak in the
response surface
in the
parameter space
defined by one or more objective functions. An example of such
a response surface is shown in Figure 1.7. The two basal axes are two different parameter values, varied
between specified maximum and minimum values. the vertical axis is the value of an objective function,
based on the sum of squared differences between observed and predicted discharges, that has the value
1 for a perfect fit. It is easy to see why optimisation algorithms are sometimes called “hill climbing”
algorithms in this example, since the highest point on the surface will represent the optimum values of
the two parameters. Such a response surface is easy to visualise in two-parameter space. It is much more
difficult to visualise the response surface in an N-dimensional parameter hyperspace. Such surfaces can
often be very complex and much of the research on optimisation algorithms has been concerned with
finding algorithms that are robust with respect to the complexity of the surface in an N-dimensional space
and find the
global optimum
set of parameter values. The complexity of the surface might also depend on
