Simplifying a hydrological ensemble prediction system with a backward greedy selection of members – Part 1: Optimization criteria

Hydrological Ensemble Prediction Systems (HEPS), obtained by forcing rainfall-runoff models with Meteorological Ensemble Prediction Systems (MEPS), have been recognized as useful approaches to quantify uncertainties of hydrological forecasting systems. This task is complex both in terms of the coupling of information and computational time, which may create an operational barrier. The main objective of the current work is to assess the degree of simplification (reduction of the number of hydrological members) that can be achieved with a HEPS configured using 16 lumped hydrological models driven by the 50 weather ensemble forecasts from the European Centre for Medium-range Weather Forecasts (ECMWF). Here, Backward Greedy Selection (BGS) is proposed to assess the weight that each model must represent within a subset that offers similar or better performance than a reference set of 800 hydrological members. These hydrological models' weights represent the participation of each hydrological model within a simplified HEPS which would issue real-time forecasts in a relatively short computational time. The methodology uses a variation of the k-fold cross-validation, allowing an optimal use of the information, and employs a multi-criterion framework that represents the combination of resolution, reliability, consistency, and diversity. Results show that the degree of reduction of members can be established in terms of maximum number of members required (complexity of the HEPS) or the maximization of the relationship between the different scores (performance).