Does an upper limit to river water temperature apply in all places?

There remains continued use of non‐linear, logistic regression models for predicting water temperature from air temperature. A dominant feature of these non‐linear models is an upper bound on river water temperature. This upper bound is often attributed to a large increase in evaporative cooling at high air temperatures, but the exact conditions under which such an increase may occur have not been thoroughly explored. To better understand the appropriateness of the non‐linear model for predicting river water temperatures, it is essential to understand the physical basis for the upper bound and when it should and should not be included in the statistical model. This paper applies and validates an energy balance model against 8 river systems spread across different climate regions of the United States. The energy balance model is then used to develop a diagram relating vapour pressure deficit and air temperature to water temperature. With knowledge of present or future vapour pressure deficit (difference between saturation and actual vapour content in the atmosphere) conditions in a given climate, the diagram can be used to predict the likelihood of an upper bound in the air–water temperature relationship. This investigation offers a fundamental physical explanation of the most appropriate form of statistical models that should be used for predicting future water temperature from air temperature in different geographic regions with different climate conditions. In general, climatic regions that have only a slight increase in vapour pressure deficit with increasing air temperature (typically humid regions) would not be expected to have an upper bound. Conversely, climatic regions in which vapour pressure deficit sharply increases with increasing air temperature (typically arid regions) would be expected to have an upper bound.