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: Field-scale crop models are increasingly applied at spatio-temporal scales that range from regions to the globe and from decades up to 100 years. Sufficiently detailed data to capture the prevailing spatio-temporal heterogeneity in weather, soil, and management conditions as needed by crop models are rarely available. Effective sampling may overcome the problem of missing data but has rarely been investigated. In this study the effect of sampling weather data has been evaluated for simulating yields of winter wheat in a region in Germany over a 30-year period (1982-2011) using 12 process-based crop models. A stratified sampling was applied to compare the effect of different sizes of spatially sampled weather data (10, 30, 50,100, 500, 1000 and full coverage of 34,078 sampling points) on simulated wheat yields. Stratified sampling was further compared with random sampling. Possible interactions between sample size and crop model were evaluated. The results showed differences in simulated yields among crop models but all models reproduced well the pattern of the stratification. Importantly, the regional mean of simulated yields based on full coverage could already be reproduced by a small sample of 10 points. This was also true for reproducing the temporal variability in simulated yields but more sampling points (about 100) were required to accurately reproduce spatial yield variability. The number of sampling points can be smaller when a stratified sampling is applied as compared to a random sampling. However, differences between crop models were observed including some interaction between the effect of sampling on simulated yields and the model used. We concluded that stratified sampling can considerably reduce the number of required simulations. But, differences between crop models must be considered as the choice for a specific model can have larger effects on simulated yields than the sampling strategy. Assessing the impact of sampling soil and crop management data for regional simulations of crop yields is still needed.