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

Classical calibration methods in hydrology typically rely on a single cost function computed on long-term streamflow series. Even when hydrological models achieve acceptable scores in NSE and KGE, imbalances can still arise between overall model performance and its ability to simulate flood events, particularly flash floods. Multi-scale signatures, which refer to hydrological signatures computed at different temporal and/or spatial scales, and distributed flood modeling, which accounts for spatial variability in input variables and model parameters, are important concepts in hydrological modeling. In this study, the potential of using multi-scale signatures is explored to enhance multi-criteria calibration methods for spatially distributed flood modeling, which remains considerable challenges. We present a novel signatures and sensitivity- based calibration approach implemented into a variational data assimilation algorithm capable to deal with high dimensional spatially distributed hydrological optimization problems. It is tested on 141 flash flood prone catchments mostly located in the French Mediterranean region. Our approach involves computing several signatures, including flood event signatures, using an automated flood segmentation algorithm. We select suitable signatures for constraining the model based on their global sensitivity with the input parameters through global signature-based sensitivity analysis (GSSA). We then perform two multi-criteria calibration strategies using the selected signatures, including a single-objective optimization approach, which transforms the multi-criteria problem into a single-objective function, and a multi-objective optimization approach, which uses a simple additive weighting method to select an optimal solution from the Pareto set. Our results show significant improvements in both calibration and temporal validation metrics, especially for flood signatures, demonstrating the robustness and delicacy of our signatures-based calibration framework for enhancing flash flood forecasting systems