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

Ngo Nghi Truyen Huynh, Pierre-André Garambois, François Colleoni, Benjamin Renard, Hélène Roux, Julie Demargne, Maxime Jay-Allemand, Pierre Javelle

TL;DR

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, demonstrating how two differentiable codes can be linked and their gradients chained, enabling the exploitation of heterogeneous datasets within a high-dimensional regionalization context.

Abstract

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.

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

TL;DR

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, demonstrating how two differentiable codes can be linked and their gradients chained, enabling the exploitation of heterogeneous datasets within a high-dimensional regionalization context.

Abstract

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.
Paper Structure (15 sections, 11 equations, 13 figures, 3 tables, 1 algorithm)

This paper contains 15 sections, 11 equations, 13 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Forward-Inverse Algorithms
  3. Forward Model with Regionalization
  4. Calibration Cost Function
  5. The Variationnal Data Assimilation Algorithm
  6. Optimization Algorithm for Polynomial Regionalization
  7. Optimization Algorithm for Neural Network-based Regionalization
  8. Data and Numerical Experiment
  9. Study Area and Experimental Design
  10. Regional Learning Performance and Computational Efficiency
  11. Interpretation of the Learning Process and Inferred Parameters
  12. Discussions
  13. Conclusion
  14. Metrics
  15. Incorporating ANN into the Differentiable Hydrological Model

Figures (13)

  • Figure 1: Flowchart of the forward-inverse algorithm used in HDA-PR. The forward hydrological model is a gridded model (spatio-temporal regular grid at 1 $\mathrm{km}^2$ and 1 $\mathrm{h}$) using GR operators perrin2003improvement.
  • Figure 2: Map of France highlighting the ArcMed study area, covering 150,000 $\mathrm{km}^2$ (100,000 $\mathrm{km}^2$ excluding sea), comprising 126 catchments categorized as 38 catchments located upstream, 33 intermediate catchments, 24 catchments positioned downstream, and 31 independent catchments, representing a total drainage area of 26,000 $\mathrm{km^2}$.
  • Figure 3: Observed and simulated discharges (in $\mathrm{m}^3/\mathrm{s}$) at several locations during the validation period P2, using three multi-gauge regional calibration methods (columns) within the first calibration setup, where upstream catchments are used for calibration on P1. The first row hence corresponds to temporal validation assessments, while the subsequent three rows correspond to spatio-temporal validation assessments.
  • Figure 4: Boxplots of NSE scores (optimal value = 1) across calibration and validation catchments for both calibration setups which are upstream (top) and downstream (bottom), compared to reference solutions obtained by local calibration methods (Uniform (loc) and Distributed (loc)). From left to right: results are displayed for calibration catchments on period P1 ("Cal"), validation catchments on P1 for spatial validation ("S_Val"), calibration catchments on P2 for temporal validation ("T_Val"), and validation catchments on P2 for spatio-temporal validation ("S-T_Val"). The numbers in parentheses indicate the count of catchments included in each boxplot.
  • Figure 5: Boxplots of KGE scores (optimal value = 1) across calibrated (with NSE cost function) and validation catchments for both calibration setups (upstream (top) and downstream (bottom)), compared to reference solutions obtained by local calibration methods (Uniform (loc) and Distributed (loc)). From left to right: results are displayed for calibration catchments on period P1 ("Cal"), validation catchments on P1 for spatial validation ("S_Val"), calibration catchments on P2 for temporal validation ("T_Val"), and validation catchments on P2 for spatio-temporal validation ("S-T_Val"). The numbers in parentheses indicate the count of catchments included in each boxplot.
  • ...and 8 more figures