Uncertainty and non-stationarity of empirical streamflow sensitivities

Abstract. The sensitivity of streamflow to changes in driving variables such as precipitation and potential evaporation is a key signature of catchment behaviour. Due to increasing interest in climate change impacts, streamflow sensitivities derived from observations have become a widely used metric for catchment characterization, model evaluation, and observation-constrained projections. However, there remain open questions regarding the robustness and stationarity of empirically-derived sensitivities. In this paper, we revisit theoretical and empirical approaches to estimate streamflow sensitivities to precipitation and potential evaporation. First, we compare different estimation methods – primarily based on linear regression – using a synthetic dataset for which the sensitivities are known. Second, we extend this comparison and use two methods selected based on the previous analysis to estimate sensitivities for >1000 near-natural catchments. Third, we investigate how sensitivities change over time due to changes in the ratio between potential evaporation and precipitation (i.e., aridity index). Our results confirm that multiple regression is preferable to single regression, but that in presence of noise and correlation between precipitation and potential evaporation, even multiple regression methods can lead to high uncertainty, especially for potential evaporation. When analysing real catchments, sensitivity to precipitation is estimated consistently across methods, while sensitivity to potential evaporation is highly uncertain and often yields unrealistic values. Further, as the aridity index increases over time – a trend found in observational data – sensitivities decrease (by 22–70 % over 50 years) and are thus non-stationary. These results should urge caution in the use of empirical streamflow sensitivities and call for further investigation.