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.

Abstract: Working with ensembles of crop models is a recent but important development in crop modeling which promises to lead to better uncertainty estimates for model projections and predictions, better predictions using the ensemble mean or median, and closer collaboration within the modeling community. There are numerous open questions about the best way to create and analyze such ensembles. Much can be learned from the field of climate modeling, given its much longer experience with ensembles. We draw on that experience to identify questions and make propositions that should help make ensemble modeling with crop models more rigorous and informative. The propositions include defining criteria for acceptance of models in a crop MME, exploring criteria for evaluating the degree of relatedness of models in a MME, studying the effect of number of models in the ensemble, development of a statistical model of model sampling, creation of a repository for MME results, studies of possible differential weighting of models in an ensemble, creation of single model ensembles based on sampling from the uncertainty distribution of parameter values or inputs specifically oriented toward uncertainty estimation, the creation of super ensembles that sample more than one source of uncertainty, the analysis of super ensemble results to obtain information on total uncertainty and the separate contributions of different sources of uncertainty and finally further investigation of the use of the multi-model mean or median as a predictor.