Uncertainty and equifinality in calibrating distributed roughness coefficients in a flood propagation model with limited data

Monte-Carlo simulations of a two-dimensional finite element model of a flood in the southern part of Sicily were used to explore the parameter space of distributed bed-roughness coefficients. For many real-world events specific data are extremely limited so that there is not only fuzziness in the information available to calibrate the model, but fuzziness in the degree of acceptability of model predictions based upon the different parameter values, owing to model structural errors. Here the GLUE procedure is used to compare model predictions and observations for a certain event, coupled with both a fuzzy-rule-based calibration, and a calibration technique based upon normal and heteroscedastic distributions of the predicted residuals. The fuzzy-rule-based calibration is suited to an event of this kind, where the information about the flood is highly uncertain and arises from several different types of observation. The likelihood (relative possibility) distributions predicted by the two calibration techniques are similar, although the fuzzy approach enabled us to constrain the parameter distributions more usefully, to lie within a range which was consistent with the modellers' a priori knowledge of the system.