Learning Regionalization Using Accurate Spatial Cost Gradients Within a Differentiable High‐Resolution Hydrological Model: Application to the French Mediterranean Region

Estimating spatially distributed hydrological parameters in ungauged catchments poses a challenging regionalization problem and requires imposing spatial constraints given the sparsity of discharge data. A possible approach is to search for a transfer function that quantitatively relates physical descriptors to conceptual model parameters. This paper introduces a Hybrid Data Assimilation and Parameter Regionalization (HDA‐PR) approach incorporating learnable regionalization mappings, based on either multi‐linear regression or artificial neural networks (ANNs), into a differentiable hydrological model. This approach demonstrates how two differentiable codes can be linked and their gradients chained, enabling the exploitation of heterogeneous data sets across extensive spatio‐temporal computational domains within a high‐dimensional regionalization context, using accurate adjoint‐based gradients. The inverse problem is tackled with a multi‐gauge calibration cost function accounting for information from multiple observation sites. HDA‐PR was tested on high‐resolution, hourly and kilometric regional modeling of 126 flash‐flood‐prone catchments in the French Mediterranean region. The results highlight a strong regionalization performance of HDA‐PR especially in the most challenging upstream‐to‐downstream extrapolation scenario with ANN, achieving median Nash‐Sutcliffe efficiency (NSE) scores from 0.6 to 0.71 for spatial, temporal, spatio‐temporal validations, and improving NSE by up to 30% on average compared to the baseline model calibrated with lumped parameters. Multiple evaluation metrics based on flood‐oriented hydrological signatures also indicate that the use of an ANN leads to better performances than a multi‐linear regression in a validation context. ANN enables to learn a non‐linear descriptors‐to‐parameters mapping which provides better model controllability than a linear mapping for complex calibration cases.