Abstract: Crop models are important tools for impact assessment of climate change, as well as for  exploring management options under current climate. It is essential to evaluate the  uncertainty associated with predictions of these models. Several ways of quantifying  prediction uncertainty have been explored in the literature, but there have been no  studies of how the different approaches are related to one another, and how they are  related to some overall measure of prediction uncertainty. Here we show that all the  different approaches can be related to two different viewpoints about the model; either  the model is treated as a fixed predictor with some average error, or the model can be  treated as a random variable with uncertainty in one or more of model structure, model  inputs and model parameters. We discuss the differences, and show how mean squared  error of prediction can be estimated in both cases. The results can be used to put  uncertainty estimates into a more general framework and to relate different uncertainty  estimates to one another and to overall prediction uncertainty. This should lead to a  better understanding of crop model prediction uncertainty and the underlying causes of  that uncertainty. This study was published as (Wallach et al. 2016)

Abstract: Crop models are essential tools for assessing the threat of climate change to local and global food production1. Present models used to predict wheat grain yield are highly uncertain when simulating how crops respond to temperature2. Here we systematically tested 30 different 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.

Abstract: 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°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 development.