A blueprint for process-based modeling of uncertain hydrological systems

We present a probability based theoretical scheme for building process-based models of uncertain hydrological systems, thereby unifying hydrological modeling and uncertainty assessment. Uncertainty for the model output is assessed by estimating the related probability distribution via simulation, thus shifting from one to many applications of the selected hydrological model. Each simulation is performed after stochastically perturbing input data, parameters and model output, this latter by adding random outcomes from the population of the model error, whose probability distribution is conditioned on input data and model parameters. Within this view randomness, and therefore uncertainty, is treated as an inherent property of hydrological systems. We discuss the related assumptions as well as the open research questions. The theoretical framework is illustrated by presenting real-world and synthetic applications. The relevant contribution of this study is related to proposing a statistically consistent simulation framework for uncertainty estimation which does not require model likelihood computation and simplification of the model structure. The results show that uncertainty is satisfactorily estimated although the impact of the assumptions could be significant in conditions of data scarcity.