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.

Abstract: • First model inter-comparison on crop rotations. • Continuous simulation of multi-year crop rotations yields outperformed single-year simulation. • Low accuracy of yield predictions in less commonly modelled crops such as potato, radish, grass vegetation. • Multi-model mean prediction was found to minimise the likely error arising from single-model predictions. • The representation of intermediate crops and carry-over effects in the models require further research efforts.
Diversification of crop rotations is considered an option to increase the resilience of European crop production under climate change. So far, however, many crop simulation studies have focused on predicting single crops in separate one-year simulations. Here, we compared the capability of fifteen crop growth simulation models to predict yields in crop rotations at five sites across Europe under minimal calibration. Crop rotations encompassed 301 seasons of ten crop types common to European agriculture and a diverse set of treatments (irrigation, fertilisation, CO2 concentration, soil types, tillage, residues, intermediate or catch crops). We found that the continuous simulation of multi-year crop rotations yielded results of slightly higher quality compared to the simulation of single years and single crops. Intermediate crops (oilseed radish and grass vegetation) were simulated less accurately than main crops (cereals). The majority of models performed better for the treatments of increased CO2 and nitrogen fertilisation than for irrigation and soil-related treatments. The yield simulation of the multi-model ensemble reduced the error compared to single-model simulations. The low degree of superiority of continuous simulations over single year simulation was caused by (a) insufficiently parameterised crops, which affect the performance of the following crop, and (b) the lack of growth-limiting water and/or nitrogen in the crop rotations under investigation. In order to achieve a sound representation of crop rotations, further research is required to synthesise existing knowledge of the physiology of intermediate crops and of carry-over effects from the preceding to the following crop, and to implement/improve the modelling of processes that condition these effects.

Abstract: Highlights • The parameters to be fixed were consistent across sites. • Model calibration must be performed separately for each specific case. • Possible to reduce model parameters from 66 to 45. • Strong model reductions must be avoided. • The error term for the training data were characterised by timing (phase shift). Abstract Proper parameterisation and quantification of model uncertainty are two essential tasks in improvement and assessment of model performance. Bayesian calibration is a method that combines both tasks by quantifying probability distributions for model parameters and outputs. However, the method is rarely applied to complex models because of its high computational demand when used with high-dimensional parameter spaces. We therefore combined Bayesian calibration with sensitivity analysis, using the screening method by Morris (1991), in order to reduce model complexity by fixing parameters to which model output was only weakly sensitive to a nominal value. Further, the robustness of the model with respect to reduction in the number of free parameters were examined according to model discrepancy and output uncertainty. The process-based grassland model BASGRA was examined in the present study on two sites in Norway and in Germany, for two grass species (Phleum pratense and Arrhenatherum elatius). According to this study, a reduction of free model parameters from 66 to 45 was possible. The sensitivity analysis showed that the parameters to be fixed were consistent across sites (which differed in climate and soil conditions), while model calibration had to be performed separately for each combination of site and species. The output uncertainty decreased slightly, but still covered the field observations of aboveground biomass. Considering the training data, the mean square error for both the 66 and the 45 parameter model was dominated by errors in timing (phase shift), whereas no general pattern was found in errors when using the validation data. Stronger model reduction should be avoided, as the error term increased and output uncertainty was underestimated.