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: Understanding the relationship between climate and crop productivity is a key component of projections of future food production, and hence assessments of food security. Climate models and crop yield datasets have errors, but the effects of these errors on regional scale crop models is not well categorized and understood. In this study we compare the effect of synthetic errors in temperature and precipitation observations on the hindcast skill of a process-based crop model and a statistical crop model. We find that errors in temperature data have a significantly stronger influence on both models than errors in precipitation. We also identify key differences in the responses of these models to different types of input data error. Statistical and process-based model responses differ depending on whether synthetic errors are overestimates or underestimates. We also investigate the impact of crop yield calibration data on model skill for both models, using datasets of yield at three different spatial scales. Whilst important for both models, the statistical model is more strongly influenced by crop yield scale than the process-based crop model. However, our results question the value of high resolution yield data for improving the skill of crop models; we find a focus on accuracy to be more likely to be valuable. For both crop models, and for all three spatial scales of yield calibration data, we found that model skill is greatest where growing area is above 10-15 %. Thus information on area harvested would appear to be a priority for data collection efforts. These results are important for three reasons. First, understanding how different crop models rely on different characteristics of temperature, precipitation and crop yield data allows us to match the model type to the available data. Second, we can prioritize where improvements in climate and crop yield data should be directed. Third, as better climate and crop yield data becomes available, we can predict how crop model skill should improve.