Technical note: Machine learning metamodelling for global sensitivity analysis
- 1University of Potsdam (Potsdam, Germany)
- 2GFZ Helmholtz Centre for Geosciences (Potsdam, Germany)
- 3Universidad de Granada (Granada, Spain)
Abstract
Global sensitivity analysis (GSA) plays a central role in hydrologic modelling by supporting model understanding, diagnosis, and decision-making through the identification of influential and non-influential parameters and their interactions. Variance-based methods provide a rigorous framework for GSA but are often computationally expensive, as their estimation requires a large number of model evaluations. Metamodelling has therefore been widely adopted as a strategy to alleviate this issue, with recent advances in machine learning (ML) offering new opportunities to construct accurate and flexible surrogates for complex models. This technical note examines the practical relationship between Sobol' total-effect indices ( T i ) and feature importance measures derived from ML metamodels within a hydrologic modelling context. Building on theoretical results that link T i to permutation variable importance (PVI i ) under independence assumptions, we provide systematic numerical evidence using three hydrologic models of varying complexity (HBV, HyMod, and VIC) applied to three headwater catchments in northern Germany, together with three ML metamodels: a gradient boosting decision tree (GBDT), a neural network (NN), and a linear model (LM). The three metamodels were trained on Monte Carlo samples and used to estimate sensitivities through PVI i and SHapley Additive exPlanations (SHAP i ). The results demonstrate that GBDT and NN metamodels reliably reproduce both the ranking and relative magnitude of T i using PVI i across all hydrologic models, providing clear empirical support for the theoretical connection between the two measures. In contrast, the performance of LM-based estimates depends strongly on the degree of linearity in the underlying model response. Mean absolute SHAP i values exhibit a consistent monotonic relationship with T i and preserve parameter rankings, while sample-specific SHAP i values enable a distributed evaluation of sensitivities across both the parameter space and the target variable space. Overall, this study highlights ML metamodelling as a computationally efficient and conceptually sound framework for GSA in hydrologic modelling and beyond.
Versions
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BibTeX
@article{yeste2026technical,
title = {{Technical note: Machine learning metamodelling for global sensitivity analysis}},
author = {Patricio Yeste and Lieke A. Melsen and João Paulo L. F. Brêda and Nicolás Tacoronte and Andrea Saltelli and Giulia Vannucci and Roberta Siciliano and Axel Bronstert},
journal = {Hydrology and Earth System Sciences},
year = {2026},
month = oct,
doi = {10.5194/hess-30-6579-2026},
url = {https://doi.org/10.5194/hess-30-6579-2026},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Technical note: Machine learning metamodelling for global sensitivity analysis
AU - Patricio Yeste
AU - Lieke A. Melsen
AU - João Paulo L. F. Brêda
AU - Nicolás Tacoronte
AU - Andrea Saltelli
AU - Giulia Vannucci
AU - Roberta Siciliano
AU - Axel Bronstert
PY - 2026
DA - 2026/10/27
JO - Hydrology and Earth System Sciences
DO - 10.5194/hess-30-6579-2026
UR - https://doi.org/10.5194/hess-30-6579-2026
AB - Global sensitivity analysis (GSA) plays a central role in hydrologic modelling by supporting model understanding, diagnosis, and decision-making through the identification of influential and non-influential parameters and their interactions. Variance-based methods provide a rigorous framework for GSA but are often computationally expensive, as their estimation requires a large number of model evaluations. Metamodelling has therefore been widely adopted as a strategy to alleviate this issue, with recent advances in machine learning (ML) offering new opportunities to construct accurate and flexible surrogates for complex models. This technical note examines the practical relationship between Sobol' total-effect indices ( T i ) and feature importance measures derived from ML metamodels within a hydrologic modelling context. Building on theoretical results that link T i to permutation variable importance (PVI i ) under independence assumptions, we provide systematic numerical evidence using three hydrologic models of varying complexity (HBV, HyMod, and VIC) applied to three headwater catchments in northern Germany, together with three ML metamodels: a gradient boosting decision tree (GBDT), a neural network (NN), and a linear model (LM). The three metamodels were trained on Monte Carlo samples and used to estimate sensitivities through PVI i and SHapley Additive exPlanations (SHAP i ). The results demonstrate that GBDT and NN metamodels reliably reproduce both the ranking and relative magnitude of T i using PVI i across all hydrologic models, providing clear empirical support for the theoretical connection between the two measures. In contrast, the performance of LM-based estimates depends strongly on the degree of linearity in the underlying model response. Mean absolute SHAP i values exhibit a consistent monotonic relationship with T i and preserve parameter rankings, while sample-specific SHAP i values enable a distributed evaluation of sensitivities across both the parameter space and the target variable space. Overall, this study highlights ML metamodelling as a computationally efficient and conceptually sound framework for GSA in hydrologic modelling and beyond.
SN - 1607-7938
ER -