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 multivariate regressions or neural networks, into a differentiable hydrological model. It enables the exploitation of heterogeneous datasets 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 two flash-flood-prone areas located in the South of France. In both study areas, the median Nash-Sutcliffe efficiency (NSE) scores ranged from 0.52 to 0.78 at pseudo-ungauged sites over calibration and validation periods. These results highlight a strong regionalization performance of HDA-PR, improving NSE by up to 0.57 compared to the baseline model calibrated with lumped parameters, and achieving a performance comparable to the reference solution obtained with local uniform calibration (median NSE from 0.59 to 0.79). Multiple evaluation metrics based on flood-oriented hydrological signatures are also employed to assess the accuracy and robustness of the approach. The regionalization method is amenable to state-parameter correction from multi-source data over a range of time scales needed for operational data assimilation, and it is adaptable to other differentiable geophysical models.
Tackling the difficult problem of estimating spatially distributed hydrological parameters, especially for floods on ungauged watercourses, this contribution presents a novel seamless regionalization technique for learning complex regional transfer functions designed for high-resolution hydrological models. The transfer functions rely on: (i) a multilayer perceptron enabling a seamless flow of gradient computation to employ machine learning optimization algorithms, or (ii) a multivariate regression mapping optimized by variational data assimilation algorithms and guided by Bayesian estimation, addressing the equifinality issue of feasible solutions. The approach involves incorporating the inferable regionalization mappings into a differentiable hydrological model and optimizing a cost function computed on multi-gauge data with accurate adjoint-based spatially distributed gradients.