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Although interannual streamflow variability is primarily a result of precipitation variability, temperature also plays a role. The relative weakness of the temperature effect at the annual time scale hinders understanding, but may belie substantial importance on climatic time scales. Here we develop and evaluate a simple theory relating variations of streamflow and evapotranspiration (E) to those of precipitation (P) and temperature. The theory is based on extensions of the Budyko water-balance hypothesis, the Priestley-Taylor theory for potential evapotranspiration (E-p), and a linear model of interannual basin storage. The theory implies that the temperature affects streamflow by modifying evapotranspiration through a Clausius-Clapeyron-like relation and through the sensitivity of net radiation to temperature. We apply and test (1) a previously introduced strong extension of the Budyko hypothesis, which requires that the function linking temporal variations of the evapotranspiration ratio (E/P) and the index of dryness (E-p/P) at an annual time scale is identical to that linking interbasin variations of the corresponding long-term means, and (2) a weak extension, which requires only that the annual evapotranspiration ratio depends uniquely on the annual index of dryness, and that the form of that dependence need not be known a priori nor be identical across basins. In application of the weak extension, the readily observed sensitivity of streamflow to precipitation contains crucial information about the sensitivity to potential evapotranspiration and, thence, to temperature. Implementation of the strong extension is problematic, whereas the weak extension appears to capture essential controls of the temperature effect efficiently.

Plain Language Summary Human communities, economies, and natural ecosystems require a reliable supply of water, and this often is provided by rivers. It has at times been noted that rivers deliver less water in warm years than in cool years, even after adjustment for variations in precipitation. This dependence on temperature raises concerns about the effect of heat waves or climatic warming on water supply. Just why and how much the flow of rivers depends on temperature has not been well understood, but the answers to these questions are relevant for ensuring future water security. Here we present and evaluate a process-based theory that attempts to answer both questions. In those river basins where long-term observations of river flow, temperature, and precipitation data are available, the theory is consistent overall with observed sensitivities of river flows to temperature. This success implies potential applicability of the theory also where such observations are not available.