# Learning Regionalization using Accurate Spatial Cost Gradients within a Differentiable High-Resolution Hydrological Model: Application to the French Mediterranean Region

arXiv: https://arxiv.org/abs/2308.02040 · HTML: https://mlsanity.com/paper/2308.02040/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 95 references that are in the map.
- First posted on arXiv 2 Aug 2023.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Variational Data Assimilation Models and Solvers](https://mlsanity.com/paper/2007.12941/) (2020)
- [From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling](https://mlsanity.com/paper/2007.15751/) (2020)
- [Differentiable, learnable, regionalized process-based models with physical outputs can approach state-of-the-art hydrologic prediction accuracy](https://mlsanity.com/paper/2203.14827/) (2022)
- [Signatures-and-sensitivity-based multi-criteria variational calibration for distributed hydrological modeling applied to Mediterranean floods](https://mlsanity.com/paper/2305.19307/) (2023)
- [Multi-gauge Hydrological Variational Data Assimilation: Regionalization Learning with Spatial Gradients using Multilayer Perceptron and Bayesian-Guided Multivariate Regression](https://mlsanity.com/paper/2307.02497/) (2023)

## Abstract (arXiv)

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 regressions 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 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 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. ANN enables to learn a non-linear descriptors-to-parameters mapping which provides better model controllability than a linear mapping for complex calibration cases.