Multi-objective calibration and fuzzy preference selection of a distributed hydrological model

Multi-objective evaluation of distributed hydrological models enables an analysis of prediction behaviour of individual sub-systems within a catchment. The aim of this paper is to demonstrate an application of multi-response, multisite calibration strategy for a distributed hydrological model, so that model limitations can be identified and subsequently improved. The study was carried out for calibration of flows from two gauging stations in a 152 km2 catchment in Elbe Basin in Germany. The multi-objective optimisation tool NSGA-II was used for the calibration of distributed hydrological modelling code WaSiM-ETH. A fuzzy set theory based methodology was formulated for selection of preferred solution from numerous Pareto solutions in four-dimensional space. The methodology consistently led to selection of the solution which is able to reasonably represent the magnitude and dynamics of streamflow hydrograph. For a reasonable simulation of water balance in the downstream gauge, overprediction of water balance in the upstream gauge was necessary. The analysis of precipitation–discharge data and geological conditions in the river channel support the possibility of flow reduction in the upstream gauge and increase in the downstream gauge. Due to this limitation in observation data, additional optimisation runs were carried out by explicitly considering the effect. This led to a significant improvement in the performance of the model. Therefore, the study provides an effective implementation of the multi-objective calibration strategy for a distributed hydrological model, which can be used for the analysis of different catchments using a combination of different objective functions.