Abstract: Ensembles of process-based crop models are increasingly used to simulate crop growth for scenarios of temperature and/or precipitation changes corresponding to different projections of atmospheric CO2 concentrations. This approach generates large datasets with thousands of simulated crop yield data. Such datasets potentially provide new information but it is difficult to summarize them in a useful way due to their structural complexities. An associated issue is that it is not straightforward to compare crops and to interpolate the results to alternative climate scenarios not initially included in the simulation protocols. Here we demonstrate that statistical models based on random-coefficient regressions are able to emulate ensembles of process-based crop models. An important advantage of the proposed statistical models is that they can interpolate between temperature levels and between CO2 concentration levels, and can thus be used to calculate temperature and [CO2] thresholds leading to yield loss or yield gain, without rerunning the original complex crop models. Our approach is illustrated with three yield datasets simulated by 19 maize models, 26 wheat models, and 13 rice models. Several statistical models are fitted to these datasets, and are then used to analyze the variability of the yield response to [CO2] and temperature. Based on our results, we show that, for wheat, a [CO2] increase is likely to outweigh the negative effect of a temperature increase of +2 degrees C in the considered sites. Compared to wheat, required levels of [CO2] increase are much higher for maize, and intermediate for rice. For all crops, uncertainties in simulating climate change impacts increase more with temperature than with elevated [CO2].

Abstract: Efforts to limit global warming to below 2 degrees C in relation to the pre-industrial level are under way, in accordance with the 2015 Paris Agreement. However, most impact research on agriculture to date has focused on impacts of warming >2 degrees C on mean crop yields, and many previous studies did not focus sufficiently on extreme events and yield interannual variability. Here, with the latest climate scenarios from the Half a degree Additional warming, Prognosis and Projected Impacts (HAPPI) project, we evaluated the impacts of the 2015 Paris Agreement range of global warming (1.5 and 2.0 degrees C warming above the pre-industrial period) on global wheat production and local yield variability. A multi-crop and multi-climate model ensemble over a global network of sites developed by the Agricultural Model Intercomparison and Improvement Project (AgMIP) for Wheat was used to represent major rainfed and irrigated wheat cropping systems. Results show that projected global wheat production will change by -2.3% to 7.0% under the 1.5 degrees C scenario and -2.4% to 10.5% under the 2.0 degrees C scenario, compared to a baseline of 1980-2010, when considering changes in local temperature, rainfall, and global atmospheric CO2 concentration, but no changes in management or wheat cultivars. The projected impact on wheat production varies spatially; a larger increase is projected for temperate high rainfall regions than for moderate hot low rainfall and irrigated regions. Grain yields in warmer regions are more likely to be reduced than in cooler regions. Despite mostly positive impacts on global average grain yields, the frequency of extremely low yields (bottom 5 percentile of baseline distribution) and yield inter-annual variability will increase under both warming scenarios for some of the hot growing locations, including locations from the second largest global wheat producer-India, which supplies more than 14% of global wheat. The projected global impact of warming <2 degrees C on wheat production is therefore not evenly distributed and will affect regional food security across the globe as well as food prices and trade.

Abstract: Crop models of crop growth are increasingly used to quantify the impact of global changes due to climate or crop management. Therefore, accuracy of simulation results is a major concern. Studies with ensembles of crop models can give valuable information about model accuracy and uncertainty, but such studies are difficult to organize and have only recently begun. We report on the largest ensemble study to date, of 27 wheat models tested in four contrasting locations for their accuracy in simulating multiple crop growth and yield variables. The relative error averaged over models was 24-38% for the different end-of-season variables including grain yield (GY) and grain protein concentration (GPC). There was little relation between error of a model for GY or GPC and error for in-season variables. Thus, most models did not arrive at accurate simulations of GY and GPC by accurately simulating preceding growth dynamics. Ensemble simulations, taking either the mean (e-mean) or median (e-median) of simulated values, gave better estimates than any individual model when all variables were considered. Compared to individual models, e-median ranked first in simulating measured GY and third in GPC. The error of e-mean and e-median declined with an increasing number of ensemble members, with little decrease beyond 10 models. We conclude that multimodel ensembles can be used to create new estimators with improved accuracy and consistency in simulating growth dynamics. We argue that these results are applicable to other crop species, and hypothesize that they apply more generally to ecological system models.