Geoscience Reference
In-Depth Information
Figure 1.7
Response surface for two TOPMODEL parameters (see Chapter 6) in an application to modelling
the stream discharge of the small Slapton Wood catchment in Devon, UK; the objective function is the Nash-
Sutcliffe efficiency that has a value of 1 for a perfect fit of the observed discharges.
the nature of the model equations, especially if there are thresholds involved, and the correct numerical
integration of the equations in time (Kavetski and Clark, 2010).
However, for most hydrological modelling problems, the optimisation problem is ill-posed in that if
the optimisation is based on the comparison of observed and simulated discharges alone, there may not
be enough information in the data to support the robust optimisation of the parameter values. Experience
suggests that even a simple model with only four or five parameter values to be estimated may require at
least 15 to 20 hydrographs for a reasonably robust calibration and, if there is strong seasonal variability
in the storm responses, a longer period still (see, for example, Kirkby, 1975; Gupta and Sorooshian,
1985; Hornberger
et al.
, 1985; Yapo
et al.
, 1996). For more complex parameter sets, much more data
and different types of data may be required for a robust optimisation unless many of the parameters are
fixed beforehand.
These are not the only problems with finding an optimum parameter set. Optimisation generally
assumes that the observations with which the simulations are compared are error free and that the model
is a true representation of that data. We know, however, at least for hydrological models, that both the
model structure and the observations are not error free. Thus, the optimum parameter set found for
a particular model structure may be sensitive to small changes in the observations, to the period of
observations considered in the calibration, to the way in which the model predictions are evaluated,
and possibly to changes in the model structure (such as a change in the element discretisation for a
distributed model).
There may also be an issue about whether all the observed data available for use in a model cali-
bration exercise are useful. Where, for example, there is an inconsistency between measured rainfalls
and measured discharges, or incommensurability between observed and predicted soil moisture vari-
ables, then not all the observed data may be informative (Beven and Westerberg, 2011). The issue of
identifying
disinformation
in calibration data does not, however, appear to have received much atten-
tion. In some cases, inconsistencies might be obvious, such as hydrographs that are recorded when no
rainfall has been measured in any of the rain gauges in a catchment or, more generally, when runoff
coefficients appear to be more than 100%. However, heavy rainfalls observed in one or more raingauges
