Yeste et al. (2026) Technical note: Machine learning metamodelling for global sensitivity analysis

Identification

• Journal: Hydrology and earth system sciences
• Year: 2026
• Date: 2026-10-27
• Authors: Patricio Yeste, Lieke Anna Melsen, João Paulo Lyra Fialho Brêda, Nicolás Tacoronte, Andrea Saltelli, Giulia Vannucci, Roberta Siciliano, Axel Bronstert
• DOI: 10.5194/hess-30-6579-2026

Research Groups

• Institute of Environmental Science and Geography, University of Potsdam, Germany
• GFZ Helmholtz Centre for Geosciences, Germany
• Department of Applied Physics, University of Granada, Spain
• Hydrology and Environmental Hydraulics Group, Wageningen University, the Netherlands
• Instituto de Pesquisas Hidráulicas, Universidade Federal do Rio Grande do Sul (IPH/UFRGS), Brazil
• University Pompeu Fabra, Barcelona School of Management, Spain
• Centre for the Study of the Sciences and the Humanities, University of Bergen, Norway
• Department of Electrical Engineering and Information Technology, Polytechnic and Basic Sciences School, University of Naples Federico II, Italy

Short Summary

This technical note empirically examines the relationship between variance-based Sobol’ total-effect indices (Ti) and machine learning (ML) metamodel-derived feature importance measures (PVIi and SHAPi) in hydrologic modeling. The study demonstrates that GBDT and Neural Network metamodels reliably reproduce the ranking and relative magnitude of Ti, establishing ML metamodelling as a computationally efficient and conceptually sound framework for global sensitivity analysis.

Objective

• To examine the practical relationship between Sobol’ total-effect indices (Ti) and feature importance measures derived from ML metamodels within a hydrologic modelling context.
• To provide systematic numerical evidence using three hydrologic models of varying complexity (HBV, HyMod, and VIC) applied to three headwater catchments in northern Germany.
• To evaluate the capabilities of different ML metamodels to accurately approximate Ti in a computationally cheaper way than traditional variance-based sensitivity analysis.
• To assess the potential of alternative approaches in ML metamodelling to estimate sensitivities, such as SHapley Additive exPlanations (SHAPi).

Study Configuration

• Spatial Scale: Three headwater catchments in northern Germany: Sude River (gauge Garlitz, 675 km²), Treene River (gauge Augaard, 136 km²), and Trave River (gauge Schackendorf, 349 km²).
• Temporal Scale: Hydrologic models run with a daily time step over the period 1 October 2001 to 30 September 2020.

Methodology and Data

• Models used:
  • Hydrologic models: Hydrologiska Byråns Vattenbalansavdelning (HBV, 13 parameters), HyMod (5 parameters), and Variable Infiltration Capacity (VIC) version 5 (9 parameters). All models were implemented in a lumped configuration.
  • Machine Learning (ML) metamodels: Gradient Boosting Decision Tree (GBDT) (XGBoost), Neural Network (NN) (TensorFlow), and Linear Model (LM) (scikit-learn).
• Data sources:
  • Monte Carlo samples (n = 10 000) of hydrologic model parameters, generated using the Sobol’ quasi-random sequence scheme from the SALib Python package.
  • Model output of interest: Kling–Gupta Efficiency (KGE) of daily streamflow.
  • Catchment data: CAMELS-DE dataset (Garlitz (ID DE812200), Schackendorf (ID DEF13760), and Augaard (ID DEF10190)).

Main Results

• GBDT and NN metamodels reliably reproduced both the ranking and the relative magnitude of Sobol’ total-effect indices (Ti) using permutation variable importance (PVIi) across all three hydrologic models (HBV, HyMod, and VIC), showing only minor discrepancies.
• The performance of LM-based PVIi estimates was strongly dependent on the degree of linearity in the underlying model response, exhibiting larger deviations for HBV compared to HyMod and VIC.
• Mean absolute SHapley Additive exPlanations (SHAPi) values demonstrated a consistent monotonic relationship with Ti and preserved parameter rankings, albeit with greater dispersion than PVIi.
• Sample-specific SHAPi values provided a distributed evaluation of parameter sensitivities across both the parameter space and the target variable space, revealing how parameter influence varies with model performance.
• ML metamodelling offers a substantial computational advantage for Global Sensitivity Analysis (GSA), requiring only 'n' model evaluations for training the surrogate, compared to 'n(p+2)' evaluations for classical variance-based Ti estimation.

Contributions

• Provides robust empirical evidence supporting the theoretical link between variance-based total-effect sensitivity indices (Ti) and ML-based permutation variable importance (PVIi) in a hydrologic modeling context.
• Demonstrates the applicability and reliability of various ML metamodel classes (GBDT, NN, LM) for approximating GSA measures across hydrologic models of differing complexity.
• Establishes ML metamodelling as a computationally efficient and conceptually sound framework for GSA, addressing the prohibitive computational cost of traditional methods for complex models.
• Introduces SHAPi values as a valuable complementary diagnostic tool for distributed sensitivity analysis, offering detailed insights into parameter influence across parameter and target variable spaces, thereby overcoming limitations of single aggregated sensitivity measures.
• Bridges methodological advancements in GSA and Explainable Artificial Intelligence (XAI) with practical applications in hydrologic modeling.

Funding

• Alexander von Humboldt Foundation (Humboldt Research Fellowship for postdoctoral researchers)
• UGR-Banco Santander (postdoctoral fellowship)
• Italian Ministry of Research (Grant # PNC0000007, complementary actions to the NRRP “Fit4MedRob - Fit for Medical Robotics”)

Citation

@article{Yeste2026Technical,
  author = {Yeste, Patricio and Melsen, Lieke Anna and Brêda, João Paulo Lyra Fialho and Tacoronte, Nicolás and Saltelli, Andrea and Vannucci, Giulia and Siciliano, Roberta and Bronstert, Axel},
  title = {Technical note: Machine learning metamodelling for global sensitivity analysis},
  journal = {Hydrology and earth system sciences},
  year = {2026},
  doi = {10.5194/hess-30-6579-2026},
  url = {https://doi.org/10.5194/hess-30-6579-2026}
}