Crop models are essential tools for assessing the threat of climate change to local and global food production 1 . Present models used to predict wheat grain yield are highly uncertain when simulating how crops respond to temperature 2 . Here we systematically tested 30 di erent wheat crop models of the Agricultural Model Intercomparison and Improvement Project against field experiments in which growing season mean temperatures ranged from 15 • C to 32 • C, including experiments with artificial heating. Many models simulated yields well, but were less accurate at higher temperatures. The model ensemble median was consistently more accurate in simulating the crop temperature response than any single model, regardless of the input information used. Extrapolating the model ensemble temperature response indicates that warming is already slowing yield gains at a majority of wheat-growing locations. Global wheat production is estimated to fall by 6% for each • C of further temperature increase and become more variable over space and time.Understanding how different climate factors interact and impact food production 3 is essential when reaching decisions on how to adapt to the effects of climate change. To implement such strategies the contribution of various climate variables on crop yields need to be separated and quantified. For instance, a change in temperature will require a different adaptation strategy than a change in rainfall 4 . Temperature changes alone are reported to have potentially large negative impacts on crop production 5 , and hotspots-locations where plants suffer from high temperature stress-have been identified across the globe 6,7 . Crop simulation models are useful tools in climate impact studies as they deal with multiple climate factors and how they interact with various crop growth and yield formation processes that are sensitive to climate. These models have been applied in many studies, including the assessment of temperature impacts on crop production 1,8 . However, none of the crop models have been tested systematically against experiments at different temperatures in field conditions. Although many glasshouse and controlled-environment temperature experiments have been described, they are often not suitable for model testing as the heating of root systems in pots 9 and effects on micro-climate differ greatly from field conditions 10 . Detailed information on field experiments with a wide range of sowing dates and infrared heating recently became available for wheat 11,12 . Such experiments are well suited for testing the ability of crop models to quantify temperature responses under field conditions. Testing the temperature responses of crop models is particularly important for assessing the impact of climate change on wheat production, because the largest uncertainty in simulated impacts on yield arises from increasing temperatures 2 .In a 'Hot Serial Cereal' (HSC) well-irrigated and fertilized experiment with a single cultivar, the observed days after sowing (DAS) to maturity declined...

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This study explored the utility of the impact response surface (IRS) approach for investigating model ensemble crop yield responses under a large range of changes in climate. IRSs of spring and winter wheat Triticum aestivum yields were constructed from a 26-member ensemble of process-based crop simulation models for sites in Finland, Germany and Spain across a latitudinal transect. The sensitivity of modelled yield to systematic increments of changes in temperature (-2 to + 9 degrees C) and precipitation (-50 to + 50%) was tested by modifying values of baseline (1981 to 2010) daily weather, with CO2 concentration fixed at 360 ppm. The IRS approach offers an effective method of portraying model behaviour under changing climate as well as advantages for analysing, comparing and presenting results from multi-model ensemble simulations. Though individual model behaviour occasionally departed markedly from the average, ensemble median responses across sites and crop varieties indicated that yields decline with higher temperatures and decreased precipitation and increase with higher precipitation. Across the uncertainty ranges defined for the IRSs, yields were more sensitive to temperature than precipitation changes at the Finnish site while sensitivities were mixed at the German and Spanish sites. Precipitation effects diminished under higher temperature changes. While the bivariate and multi-model characteristics of the analysis impose some limits to interpretation, the IRS approach nonetheless provides additional insights into sensitivities to inter-model and inter-annual variability. Taken together, these sensitivities may help to pinpoint processes such as heat stress, vernalisation or drought effects requiring refinement in future model developmen

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