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: This study shows an average yield increase of 415–1,338 kg ha−1 per unit increase of the Shannon diversity index for feed barley cultivar use. There is a global quest to increase food production sustainably. Therefore, judicious farmer choices such as selection of crop cultivars are increasingly important. Cultivar diversity is limited and, as a consequence, corresponding crop yields are highly impacted by local weather variations and global climate change. Actually, there is little knowledge on the relationships between yields of regional crops and cultivar diversity, that is evenness and richness in cultivar use. Here, we hypothesized that higher cultivar diversity is related to higher regional yield. We also assumed that the diversity-yield relationship depends on weather during the growing season. Our data were based on farm yield surveys of feed and malting barley, Hordeum vulgare L.; spring wheat, Triticum aestivum L.; and spring turnip rape, Brassica rapa L. ssp. oleifera, from 1998 to 2009, representing about 4,500–5,500 farms annually. We modeled the relationships between regional yields and Shannon diversity indices in high-yielding (south-west) and low-yielding (central-east) regions of Finland using linear mixed models. Our results show that an increase of Shannon diversity index increases yield of feed barley. Feed barley had also the greatest cultivar diversity. In contrast, an average yield decrease of 1,052 kg ha−1 per unit increase in Shannon index was found for spring rape in 2006 and 2008. Our findings show that cultivar diversification has potential to raise mean regional yield of feed barley. Increasing cultivar diversity thus offers a novel, sustainability-favoring means to promote higher yields.

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.