Incorporating structural uncertainty of hydrological models in likelihood functions via an ensemble range approach

Abstract

Model ensembles are possibly the most powerful tool to assess uncertainties in runoff predictions stemming from inadequacies in model structure. But in many applications little knowledge is gained about the specific weaknesses of the individual models. Here we introduce the ensemble range approach (ERA). Compared to other ensemble techniques, ERA is primarily intended to facilitate hydrological reasoning about model structural uncertainty. This is attempted by separate modelling of data uncertainty and structural uncertainty with two different error density functions that are combined in one likelihood function. The width of the structural error density is in accordance with the range of runoff predictions calculated by a small model ensemble at each individual time step. Albeit not the only choice, this study is restricted on the use of a modified beta density to represent structural uncertainty. The performance of ERA is assessed in some synthetic and real data case studies. Ensembles of two structurally identical models are applied, made possible by estimating the parameters of ERA and both models simultaneously.