Gnann et al. (2026) Uncertainty, temporal variability, and influencing factors of empirical streamflow sensitivities

Identification

• Journal: Hydrology and earth system sciences
• Year: 2026
• Date: 2026-02-10
• Authors: Sebastian Gnann, Bailey J. Anderson, Markus Weiler
• DOI: 10.5194/hess-30-779-2026

Research Groups

• Faculty of Environment and Natural Resources, University of Freiburg, Freiburg, Germany
• WSL Institute for Snow and Avalanche Research SLF, Davos Dorf, Switzerland
• Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland
• Climate Change, Extremes and Natural Hazards in Alpine Regions Research Center CERC, Davos Dorf, Switzerland

Short Summary

This study systematically evaluates empirical methods for estimating streamflow sensitivities to precipitation and potential evaporation, revealing high uncertainties, particularly for potential evaporation. It demonstrates that these sensitivities are not static but decrease significantly over time (15 %–70 % over 50 years) as aridity increases, urging caution in their use for climate change impact assessments.

Objective

• To test the robustness of different empirical streamflow sensitivity estimation methods using both an analytical model and observational data.
• To investigate the temporal variability of empirically-derived streamflow sensitivities and identify influencing factors.

Study Configuration

• Spatial Scale: Over 1000 (specifically 1121) near-natural catchments across the USA, Great Britain, Australia, and Germany.
• Temporal Scale: Time series of at least 30 years for general analysis, and at least 50 years for temporal trend analysis, aggregated to annual values and analyzed in 20-year moving blocks.

Methodology and Data

• Models used:
  • Theoretical: Turc–Mezentsev model (Budyko-type water balance model).
  • Empirical estimation methods: Non-parametric, Single linear regression, Multiple linear regression #1 (with y-intercept set to 0), Multiple linear regression #2 (using annual variations around the mean with y-intercept set to 0), Log-linear regression.
  • Trend analysis: Theil-Sen trend slope estimator.
• Data sources:
  • Synthetic dataset generated from the Turc–Mezentsev model with varying noise and correlation between precipitation and potential evaporation.
  • Observational data from four large-sample datasets:
    • CAMELS-US (precipitation and potential evaporation from Daymet).
    • CAMELS-GB (precipitation from CEH-GEAR, potential evaporation from CHESS-PE).
    • CAMELS-AUS v2 (precipitation from AGCD, potential evaporation from SILO).
    • CAMELS-DE (precipitation and potential evaporation from DWD-HYRAS).
  • Caravan extension (ERA5-land based) used for comparison.

Main Results

• Univariate sensitivity estimation methods (non-parametric, single regression) are unreliable when precipitation and potential evaporation are correlated (average Pearson correlation ρP = −0.42 in observational data).
• Multiple regression methods are generally preferable, but even they exhibit high uncertainty, particularly for streamflow sensitivity to potential evaporation (sEp), with relative errors up to 12 % in synthetic experiments with noise.
• Streamflow sensitivity to precipitation (sP) is estimated more consistently across methods than sEp.
• When applied to observational data, multiple regression #2 yields unrealistic positive sEp values for 52 % of catchments, while multiple regression #1 (with zero intercept) yields positive sEp for only 3 % of catchments and generally provides more realistic (negative) values, though it may systematically underestimate sEp.
• Empirical sP and sEp generally follow the theoretical pattern of decreasing with increasing aridity, but tend to be lower than Turc–Mezentsev model predictions and show substantial variability.
• Catchments with higher baseflow index (BFI) and larger snow fractions tend to exhibit lower sensitivities.
• Streamflow sensitivities are not static; as the aridity index increases over time (an observed trend), sensitivities decrease (in absolute terms). This decrease ranges from 15 % to 70 % over 50 years in observational data, which is stronger than the 5 % to 26 % decrease predicted by the analytical model.

Contributions

• Provides a systematic and comprehensive comparison of empirical streamflow sensitivity estimation methods using both synthetic data and a large sample of over 1000 catchments.
• Quantifies the robustness and uncertainty of different methods, highlighting the significant challenges in reliably estimating streamflow sensitivity to potential evaporation.
• Demonstrates and quantifies the temporal variability of streamflow sensitivities, showing they are not static metrics but change significantly with evolving aridity.
• Identifies catchment characteristics (e.g., storage processes, snow fraction) that influence the deviation of empirical sensitivities from theoretical predictions.
• Emphasizes the need for caution in using empirical streamflow sensitivities for climate change impact assessments due to inherent uncertainties and temporal non-stationarity.

Funding

This open-access publication was funded by the University of Freiburg.

Citation

@article{Gnann2026Uncertainty,
  author = {Gnann, Sebastian and Anderson, Bailey J. and Weiler, Markus},
  title = {Uncertainty, temporal variability, and influencing factors of empirical streamflow sensitivities},
  journal = {Hydrology and earth system sciences},
  year = {2026},
  doi = {10.5194/hess-30-779-2026},
  url = {https://doi.org/10.5194/hess-30-779-2026}
}