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: Crop models can be sensitive to climate input data aggregation and this response may differ among models. This should be considered when applying field-scale models for assessment of climate change impacts on larger spatial scales or when coupling models across scales. In order to evaluate these effects systematically, an ensemble of ten crop models was run with climate input data on different spatial aggregations ranging from 1, 10, 25, 50 and 100 km horizontal resolution for the state of North Rhine-Westphalia, Germany. Models were minimally calibrated to typical sowing and harvest dates, and crop yields observed in the region, subsequently simulating potential, water-limited and nitrogen-limited production of winter wheat and silage maize for 1982-2011. Outputs were analysed for 19 variables (yield, evapotranspiration, soil organic carbon, etc.). In this study the sensitivity of the individual models and the model ensemble in response to input data aggregation is assessed for crop yield. Results show that the mean yield of the region calculated from climate time series of 1 km horizontal resolution changes only little when using climate input data of higher aggregation levels for most models. However, yield frequency distributions change with aggregation, resembling observed data better with increasing resolution. With few exceptions, these results apply to the two crops and three production situations (potential, water-, nitrogen-limited) and across models including the model ensemble, regardless of differences among models in simulated yield levels and spatial yield patterns. Results of this study improve the confidence of using crop models at varying scales.