Martre, P., Wallach, D., Asseng, S., Ewert, F., Jones, J. W., Rötter, R. P., et al. (2015). Multimodel ensembles of wheat growth: many models are better than one. Glob. Chang. Biol., 21(2), 911–925.
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.
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Hoffmann, H., Zhao, G., Asseng, S., Bindi, M., Biernath, C., Constantin, J., et al. (2016). Impact of spatial soil and climate input data aggregation on regional yield simulations. PLoS One, 11(4), e0151782.
Abstract: We show the error in water-limited yields simulated by crop models which is associated with spatially aggregated soil and climate input data. Crop simulations at large scales (regional, national, continental) frequently use input data of low resolution. Therefore, climate and soil data are often generated via averaging and sampling by area majority. This may bias simulated yields at large scales, varying largely across models. Thus, we evaluated the error associated with spatially aggregated soil and climate data for 14 crop models. Yields of winter wheat and silage maize were simulated under water-limited production conditions. We calculated this error from crop yields simulated at spatial resolutions from 1 to 100 km for the state of North Rhine-Westphalia, Germany. Most models showed yields biased by <15% when aggregating only soil data. The relative mean absolute error (rMAE) of most models using aggregated soil data was in the range or larger than the inter-annual or inter-model variability in yields. This error increased further when both climate and soil data were aggregated. Distinct error patterns indicate that the rMAE may be estimated from few soil variables. Illustrating the range of these aggregation effects across models, this study is a first step towards an ex-ante assessment of aggregation errors in large-scale simulations.
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Webber, H., Ewert, F., Olesen, J. E., Müller, C., Fronzek, S., Ruane, A. C., et al. (2018). Diverging importance of drought stress for maize and winter wheat in Europe. Nat. Comm., 9, 4249.
Abstract: Understanding the drivers of yield levels under climate change is required to support adaptation planning and respond to changing production risks. This study uses an ensemble of crop models applied on a spatial grid to quantify the contributions of various climatic drivers to past yield variability in grain maize and winter wheat of European cropping systems (1984-2009) and drivers of climate change impacts to 2050. Results reveal that for the current genotypes and mix of irrigated and rainfed production, climate change would lead to yield losses for grain maize and gains for winter wheat. Across Europe, on average heat stress does not increase for either crop in rainfed systems, while drought stress intensifies for maize only. In low-yielding years, drought stress persists as the main driver of losses for both crops, with elevated CO2 offering no yield benefit in these years.
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Wallach, D., Thorburn, P., Asseng, S., Challinor, A. J., Ewert, F., Jones, J. W., et al. (2016). Overview paper on comprehensive framework for assessment of error and uncertainty in crop model predictions (Vol. 8).
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)
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Rivington, M., & Wallach, D. (2015). Quantified Evidence of Error Propagation (Vol. 6).
Abstract: Error propagation within models is an issue that requires a structured approach involving the testing of individual equations and evaluation of the consequences of error creation from imperfect equation and model structure on estimates of interest made by a model. This report briefly covers some of the key issues in error propagation and sets out several concepts, across a range of complexity, that may be used to organise an investigation into error propagation. No Label
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