Geoscience Reference
In-Depth Information
Figure 7.7
Pareto optimal set calibration of the Sacramento ESMA rainfall-runoff model to the Leaf River
catchment, Mississippi (after Yapo
et al.
, 1998, with kind permission of Elsevier): (a) grouping of Pareto
optimal set of 500 model parameter sets in the plane of two of the model parameters; (b) prediction limits for
the 500 Pareto optimal parameter sets.
ranges of discharges predicted by the original randomly chosen parameter sets and the final Pareto optimal
set (from Gupta
et al.
, 1998). A major advantage of the Pareto optimal set methodology is that it does
not require different performance measures to be combined into one overall measure. Gupta
et al.
(1999)
suggest that this method is now competitive with interactive methods carried out by a modelling expert
in achieving a calibration that satisfies the competing requirements on the model in fitting the data.
As shown in Figure 7.7a the set of models that is found to be Pareto optimal reflects the sometimes
conflicting requirements of satisfying more than one performance measure. Figure 7.7b, however, shows
that this does not guarantee that the predictions from the sample of Pareto optimal models will bracket the
observations since it cannot compensate completely for model structural error or discharge observations
that are not error free. The original randomly chosen sets do bracket the observations, but with limits
that are considerably wider (note the log discharge scale in Figure 7.7b). It must be remembered that
the method is not intended to estimate prediction limits in any statistical sense, but one feature of this
approach is that it does seem to result in an over-constrained set of predictions in comparison with the
