Bogner et al. (2026) Improving sub-seasonal hydrological forecasts utilizing the randomness in Deep Learning models

Identification

• Journal: Stochastic Environmental Research and Risk Assessment
• Year: 2026
• Date: 2026-01-01
• Authors: Konrad Bogner, Ryan S. Padrón
• DOI: 10.1007/s00477-025-03138-2

Research Groups

• Hydrological Forecasting, Swiss Federal Research Institute WSL, Birmensdorf, Switzerland
• Institute for Atmospheric and Climate Science, ETH Zürich, Zürich, Switzerland

Short Summary

This study investigates how the inherent randomness of Deep Learning (DL) models, specifically the Temporal Fusion Transformer (TFT), can be leveraged to improve sub-seasonal hydrological forecasts. By combining predictions from multiple TFT models trained with different random seeds using Nonhomogeneous Gaussian Regression (NGR) and Beta-transformed Linear Pool (BLP), the authors demonstrate a significant enhancement in forecast skill for water temperature and streamflow across Swiss gauging stations.

Objective

• To analyze how the randomness of Deep Learning models influences forecast skill.
• To assess the potential of different forecast combination methods (Nonhomogeneous Gaussian Regression and Beta-transformed Linear Pool) to improve the predictive skill of sub-seasonal hydrological forecasts.

Study Configuration

• Spatial Scale: 22 gauging stations across Switzerland, with catchment areas ranging from approximately 440 km² to 34,500 km². The TFT model is trained globally, optimizing for all stations jointly.
• Temporal Scale: Sub-seasonal forecasts for daily maximum water temperature and daily average streamflow with a forecast horizon of 32 days. Models are trained using daily data from 2012 to 2022 (2022 for validation) and tested in 2023 and 2024. An encoder length of 64 days is used for past information.

Methodology and Data

• Models used:
  • Temporal Fusion Transformer (TFT) Deep Learning model for hydrological forecasting.
  • Nonhomogeneous Gaussian Regression (NGR) for forecast combination.
  • Beta-transformed Linear Pool (BLP) for forecast combination.
• Data sources:
  • Point measurements of water temperature and streamflow from 22 Swiss gauging stations (Federal Office for the Environment, FOEN).
  • Gridded meteorological data (air temperature, precipitation, sunshine duration at 2 km resolution) from MeteoSwiss.
  • Sub-seasonal meteorological forecasts (51 ensemble members) from the European Centre for Medium-Range Weather Forecasts (ECMWF), pre-processed by the Swiss Federal Office for Meteorology and Climatology.
  • Static catchment features (e.g., area, mean elevation, glacierized area, coordinates, station elevation) from FOEN.
  • Wavelet-transformed air temperature data (calculated from MeteoSwiss data).

Main Results

• Combining forecasts from seed-specific TFT models using NGR and BLP significantly improved predictive skill across all lead times for both water temperature and streamflow.
• For water temperature, the average Continuous Ranked Probability Score (CRPS) improved from 0.85 °C (average of 12 seed-specific models) to 0.73 °C for both NGR and BLP.
• For streamflow, the average CRPS improved from 0.95 mm/d (average of 12 seed-specific models) to 0.79 mm/d for BLP, and 0.81 mm/d for NGR (when assuming a lognormal distribution).
• The BLP method demonstrated superior robustness for streamflow (a heavier-tailed distribution) compared to NGR when assuming an underlying normal distribution, but NGR's skill matched BLP's when a lognormal distribution was assumed.
• The improvement in predictive skill from combination methods increased with forecast lead time, reaching 0.18 °C for water temperature and 0.2 mm/d for streamflow at a 32-day lead time.
• An ensemble of approximately 12 seed-specific models was found to be optimal, with diminishing returns beyond this number.
• In an example forecast, the BLP estimate for streamflow achieved a CRPS of 3.78 mm/d, outperforming a multi-model ensemble of process-based hydrological models (CRPS of 4.64 mm/d).
• Including wavelet-transformed air temperature data as input features significantly improved water temperature forecast accuracy, particularly for stations with larger catchment areas.

Contributions

• Demonstrates a systematic approach to leverage the inherent stochasticity of Deep Learning models (random seeds) to build robust ensembles for improved sub-seasonal hydrological forecasting.
• Provides evidence that principled forecast combination methods (NGR and BLP) can significantly enhance the predictive skill of DL models, moving beyond reliance on single-model realizations.
• Highlights the superior flexibility and robustness of BLP for combining forecasts of non-normally distributed hydrological variables like streamflow.
• Shows the value of integrating domain-specific data preprocessing, such as wavelet transforms of meteorological variables, to enhance DL model performance.
• Offers a practical framework for operational hydrological forecasting by reducing the dependency on selecting a single "best" DL model and improving forecast quality, especially at longer lead times.

Funding

• Swiss Federal Institute for Forest, Snow and Landscape Research (EXTREMES program).

Citation

@article{Bogner2026Improving,
  author = {Bogner, Konrad and Padrón, Ryan S.},
  title = {Improving sub-seasonal hydrological forecasts utilizing the randomness in Deep Learning models},
  journal = {Stochastic Environmental Research and Risk Assessment},
  year = {2026},
  doi = {10.1007/s00477-025-03138-2},
  url = {https://doi.org/10.1007/s00477-025-03138-2}
}