Use of an entropy-based metric in multiobjective calibration to improve model performance

Parameter estimation for hydrological models is complicated for many reasons, one of which is the arbitrary emphasis placed, by most traditional measures of fit, on various magnitudes of the model residuals. Recent research has called for the development of robust diagnostic measures that provide insights into which model structural components and/or data may be inadequate. In this regard, the flow duration curve (FDC) represents the historical variability of flow and is considered to be an informative signature of catchment behavior. Here we investigate the potential of using the recently developed conditioned entropy difference metric (CED) in combination with the Kling-Gupta efficiency (KGE). The CED respects the static information contained in the flow frequency distribution (and hence the FDC), but does not explicitly characterize temporal dynamics. The KGE reweights the importance of various hydrograph components (correlation, bias, variability) in a way that has been demonstrated to provide better model calibrations than the commonly used Nash-Sutcliffe efficiency, while being explicitly time sensitive. We employ both measures within a multiobjective calibration framework and achieve better performance over the full range of flows than obtained by single-criteria approaches, or by the common multiobjective approach that uses log-transformed and untransformed data to balance fitting of low and high flow periods. The investigation highlights the potential of CED to complement KGE (and vice versa) during model identification. It is possible that some of the complementarity is due to CED representing more information from moments >2 than KGE or other common metrics. We therefore suggest that an interesting way forward would be to extend KGE to include higher moments, i.e., use different moments as multiple criteria.