Is Water Stress the Root Cause of the Observed Nonlinear Relationship Between Yield Losses and Temperature?

Observational analyses consistently find that yields of major rainfed crops increase with temperature up to a threshold of approximately 32$°$C, above which they reduce sharply. Two damage pathways have been suggested to explain this relationship: that high temperatures directly stress crops and drive yield loss, or that high temperatures induce water stress in crops, which in turn drives yield loss. Here we explore a third pathway: that soil water stress limits both agricultural productivity and evaporative cooling, giving rise to the nonlinear relationship between temperature and yield. Determining which of these pathways underpins the yield-temperature relationship is important for predicting future crop productivity because climate change is expected to alter the co-variability between temperature and water availability. To examine this third pathway, we use cumulative growing-season transpiration from an idealized land surface model as a proxy for yield. This approach reproduces the observed yield-temperature relationship, even though the model includes no mechanisms that limit productivity at high temperatures. In experiments where the influence of temperature on soil moisture is suppressed, yields still decline during hot, dry periods in a manner consistent with the observations. We conclude that water stress, and its influence on evaporative cooling, temperature, and agricultural productivity, drives the yield-temperature relationship found in crops that experience episodic water stress. This framework explains the muted sensitivity of irrigated yields to high atmospheric temperatures, and suggests that future yield outcomes depend more critically on changes in rainfall than suggested by estimates that attribute yield losses primarily to temperature variations.