Abstract: Crop models are important tools for impact assessment of climate change, as well as for  exploring management options under current climate. It is essential to evaluate the  uncertainty associated with predictions of these models. Several ways of quantifying  prediction uncertainty have been explored in the literature, but there have been no  studies of how the different approaches are related to one another, and how they are  related to some overall measure of prediction uncertainty. Here we show that all the  different approaches can be related to two different viewpoints about the model; either  the model is treated as a fixed predictor with some average error, or the model can be  treated as a random variable with uncertainty in one or more of model structure, model  inputs and model parameters. We discuss the differences, and show how mean squared  error of prediction can be estimated in both cases. The results can be used to put  uncertainty estimates into a more general framework and to relate different uncertainty  estimates to one another and to overall prediction uncertainty. This should lead to a  better understanding of crop model prediction uncertainty and the underlying causes of  that uncertainty. This study was published as (Wallach et al. 2016)

Abstract: Genotypic adaptation involves the incorporation of novel traits in crop varieties so as to enhance food productivity and stability and is expected to be one of the most important adaptation strategies to future climate change. Simulation modelling can provide the basis for evaluating the biophysical potential of crop traits for genotypic adaptation. This review focuses on the use of models for assessing the potential benefits of genotypic adaptation as a response strategy to projected climate change impacts. Some key crop responses to the environment, as well as the role of models and model ensembles for assessing impacts and adaptation, are first reviewed. Next, the review describes crop-climate models can help focus the development of future-adapted crop germplasm in breeding programmes. While recently published modelling studies have demonstrated the potential of genotypic adaptation strategies and ideotype design, it is argued that, for model-based studies of genotypic adaptation to be used in crop breeding, it is critical that modelled traits are better grounded in genetic and physiological knowledge. To this aim, two main goals need to be pursued in future studies: (i) a better understanding of plant processes that limit productivity under future climate change; and (ii) a coupling between genetic and crop growth models-perhaps at the expense of the number of traits analysed. Importantly, the latter may imply additional complexity (and likely uncertainty) in crop modelling studies. Hence, appropriately constraining processes and parameters in models and a shift from simply quantifying uncertainty to actually quantifying robustness towards modelling choices are two key aspects that need to be included into future crop model-based analyses of genotypic adaptation.

Abstract: Crop models of crop growth are increasingly used to quantify the impact of global changes due to climate or crop management. Therefore, accuracy of simulation results is a major concern. Studies with ensembles of crop models can give valuable information about model accuracy and uncertainty, but such studies are difficult to organize and have only recently begun. We report on the largest ensemble study to date, of 27 wheat models tested in four contrasting locations for their accuracy in simulating multiple crop growth and yield variables. The relative error averaged over models was 24-38% for the different end-of-season variables including grain yield (GY) and grain protein concentration (GPC). There was little relation between error of a model for GY or GPC and error for in-season variables. Thus, most models did not arrive at accurate simulations of GY and GPC by accurately simulating preceding growth dynamics. Ensemble simulations, taking either the mean (e-mean) or median (e-median) of simulated values, gave better estimates than any individual model when all variables were considered. Compared to individual models, e-median ranked first in simulating measured GY and third in GPC. The error of e-mean and e-median declined with an increasing number of ensemble members, with little decrease beyond 10 models. We conclude that multimodel ensembles can be used to create new estimators with improved accuracy and consistency in simulating growth dynamics. We argue that these results are applicable to other crop species, and hypothesize that they apply more generally to ecological system models.