Signatures-and-sensitivity-based multi-criteria variational calibration for distributed hydrological modeling applied to Mediterranean floods

Classical calibration methods in hydrology are commonly performed with a single cost function computed on long time series. Even though the hydrological model has acceptable scores in NSE and KGE, unbalancing problems can still arise between overall score and the model performance for flood events, and particularly flash floods. Enhancing multi-criteria calibration methods with multi-scale signatures to improve distributed flood modeling remains a challenge. In this study, the potential of hydrological signatures computed continuously and at the scale of flood events on long time series, is employed within various multi-criteria calibration approaches to attain a more efficient hydrological model. This work presents an improved and original signature-based calibration approach, implemented in the variational data assimilation algorithm of SMASH (Spatially distributed Modelling and ASsimilation for Hydrology) platform, applied over 141 catchments mostly located in the French Mediterranean region. Several signatures, especially flood event signatures are firstly computed, relying on a proposed automatic hydrograph segmentation algorithm. Suitable signatures for constraining the model are selected based on their global sensitivity analysis to model parameters. Several multi-criteria calibration strategies with the selected signatures are eventually performed, including a multi-objective optimization approach, and a single-objective optimization approach, that transforms the multi-criteria problem into a single-objective function. Note that in the first approach, the proposed technique based on a simple additive weighting method is used to select an optimal solution obtained from a set of non-inferior solutions. The suggested methods show that, for a global calibration, the average relative error in simulating the peak flow has been dropped from about 0.27 to 0.01-0.08 and from about 0.30 to 0.18-0.21 with various multi-criteria optimization strategies, respectively in calibration and temporal validation. For a distributed calibration, while the average NSE (resp. KGE) still slightly decreases from 0.78 (resp. 0.86) to 0.75 (resp. 0.81) in calibration, the quality of simulated peak flow has been enhanced about 1.5 times in average. In particular, the NSE (resp. KGE) calculated solely on 111 flood events which are picked from 23 downstream gauges has been improved from 0.80 (resp. 0.71) up to 0.83 (resp. 0.78) in median. These results have demonstrated the robustness and delicacy of the model constrained by the signatures for enhancing flash flood forecasting systems