Duchemin et al. (2025) Data-driven estimation of the hydrologic response using generalized additive models

Identification

• Journal: Geoscientific model development
• Year: 2025
• Date: 2025-11-17
• Authors: Quentin Duchemin, Maria Grazia Zanoni, Marius G. Floriancic, Hansjörg Seybold, Guillaume Obozinski, James W. Kirchner, Paolo Benettin
• DOI: 10.5194/gmd-18-8663-2025

Research Groups

• Swiss Data Science Center, ETH Zürich & EPFL, Zürich & Lausanne, Switzerland
• Department of Environmental Systems Science, ETH Zürich, Zürich, Switzerland
• Department of Civil, Environmental and Geomatic Engineering, ETH Zürich, Zürich, Switzerland
• Swiss Federal Research Institute WSL, Birmensdorf, Switzerland
• Department of Earth and Planetary Science, University of California, Berkeley, California, USA
• Institute of Earth Surface Dynamics (IDYST), Faculty of Geosciences and Environment, Université de Lausanne, Lausanne, Switzerland

Short Summary

This paper introduces GAMCR, a novel data-driven approach employing Generalized Additive Models (GAM) to estimate time-dependent Catchment Responses (CR) from rainfall-runoff data. GAMCR successfully estimates hydrologic response functions, showing consistency with an alternative data-driven approach (ERRA) and physical catchment properties across synthetic and six diverse Swiss basins.

Objective

• To develop and validate GAMCR, a novel data-driven approach using Generalized Additive Models (GAM) to estimate time-dependent Catchment Responses (CR) from rainfall-runoff data.
• To compare GAMCR's performance with the existing Ensemble Rainfall-Runoff Analysis (ERRA) approach and demonstrate its potential for systematic analysis of hydrological responses in diverse watersheds.

Study Configuration

• Spatial Scale: Six Swiss watersheds (Sonceboz, Euthal, Salmsach, Lavertezzo, Magliaso, Chiasso) ranging from 34 km² to 185 km² in area, with diverse hydrological regimes and physical characteristics. Synthetic data generation was based on a Swiss station (Lugano/Chiasso).
• Temporal Scale: 15-year record (2005–2019) of hourly precipitation-runoff data for observed catchments, with 13 years for training and 2 years for testing. Synthetic data covered 40 years at hourly resolution. Analysis focused on snow-free periods (May/June to October). Maximum lag time for response estimation was 10 days (240 hours).

Methodology and Data

• Models used:
  • GAMCR (Generalized Additive Models for Catchment Response): A novel data-driven machine learning model that estimates time-dependent transfer functions using Generalized Additive Models (GAM) and B-spline basis functions.
  • ERRA (Ensemble Rainfall-Runoff Analysis): An existing data-driven approach used for comparison and validation.
  • Lumped nonlinear and nonstationary conceptual model: Used to generate synthetic streamflow time series.
• Data sources:
  • Synthetic Data: Precipitation and air temperature measurements from MeteoSwiss (Lugano station), and streamflow data from Chiasso, Ponte di Polenta (Breggia River).
  • Observed Data:
    • Streamflow time series: Federal Office for the Environment (FOEN).
    • Precipitation data: 'CombiPrecip' product by MeteoSwiss.
    • Potential Evapotranspiration: Computed using the Hargreaves method based on MeteoSwiss air temperatures.
    • Catchment attributes: Extracted for the six Swiss watersheds (e.g., mean elevation, mean slope, area, mean soil depth, mean permeability).

Main Results

• GAMCR accurately estimates transfer functions on synthetic data, with curves nearly overlapping the benchmark for flashy and damped scenarios. While peak value and tail are well captured in the base case, peak timing is systematically early.
• GAMCR accurately estimates key quantities such as Nonlinear Response Function (NRF) peak height (in m s⁻²) and runoff volume across different precipitation bins, showing strong consistency with ERRA. Both models, however, face challenges in predicting peak lag.
• When applied to observed data from six diverse Swiss catchments, GAMCR's estimated hydrological responses (Runoff Response Distributions (RRDs) in s⁻¹ and NRFs in m s⁻²) are broadly consistent with ERRA and align well with the physical and hydrological characteristics of each basin. For instance, Salmsach, with flatter topography and deeper soils (mean soil depth 0.6957 m, mean permeability 6.04 × 10⁻⁶ m s⁻¹), exhibited a slower and less marked average response compared to Euthal (mean soil depth 0.3387 m, mean permeability 6.28 × 10⁻⁶ m s⁻¹).
• RRD peak heights do not vary systematically with precipitation intensity but show clear increasing trends with increasing antecedent wetness. Chiasso, for example, displays RRD peak heights spanning almost an order of magnitude (from 1.67 × 10⁻⁶ s⁻¹ to 1.39 × 10⁻⁵ s⁻¹), highlighting a strong nonstationary response influenced by antecedent conditions.
• GAMCR is computationally efficient, with model training on 20 years of hourly data typically taking around 30 minutes for a maximum lag of 10 days.
• The model was trained using a precipitation intensity threshold of 1.39 × 10⁻⁸ m s⁻¹.
• Key hydrological statistics for the observed catchments (snow-free Q10, Q50, Q90) range from 8.33 × 10⁻¹⁰ m s⁻¹ to 1.21 × 10⁻⁷ m s⁻¹.

Contributions

• Introduction of GAMCR, a novel, flexible, and interpretable data-driven approach for estimating time-dependent Catchment Responses using Generalized Additive Models and spline basis functions.
• Comprehensive validation of GAMCR on synthetic data with known ground truth, demonstrating its accuracy in estimating the magnitude and shape of hydrologic responses.
• Successful application and demonstration of GAMCR's capabilities on diverse real-world Swiss catchments, showing consistency with an alternative data-driven method (ERRA) and the physical properties of the basins.
• Provision of a robust framework for systematic analysis of hydrological responses, enabling investigation into the effects of precipitation intensity and antecedent wetness on catchment behavior.
• Public release of the GAMCR v1.0 software (Python) and associated data, promoting reproducibility and facilitating further research in hydrological modeling.

Funding

• Swiss Data Science Center Fifth Call for Data Science Projects (project C21-09).

Citation

@article{Duchemin2025Datadriven,
  author = {Duchemin, Quentin and Zanoni, Maria Grazia and Floriancic, Marius G. and Seybold, Hansjörg and Obozinski, Guillaume and Kirchner, James W. and Benettin, Paolo},
  title = {Data-driven estimation of the hydrologic response using generalized additive models},
  journal = {Geoscientific model development},
  year = {2025},
  doi = {10.5194/gmd-18-8663-2025},
  url = {https://doi.org/10.5194/gmd-18-8663-2025}
}