Learning Regionalization within a Differentiable High-Resolution Hydrological Model using Accurate Spatial Cost Gradients

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.

Multi-gauge Hydrological Variational Data Assimilation: Regionalization Learning with Spatial Gradients using Multilayer Perceptron and Bayesian-Guided Multivariate Regression

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.