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Wallach, D., Thorburn, P., Asseng, S., Challinor, A. J., Ewert, F., Jones, J. W., et al. (2016). Estimating model prediction error: Should you treat predictions as fixed or random. Env. Model. Softw., 84, 529–539.
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. We compare two criteria of prediction error; MSEPfixed, which evaluates mean squared error of prediction for a model with fixed structure, parameters and inputs, and MSEPuncertain(X), which evaluates mean squared error averaged over the distributions of model structure, inputs and parameters. Comparison of model outputs with data can be used to estimate the former. The latter has a squared bias term, which can be estimated using hindcasts, and a model variance term, which can be estimated from a simulation experiment. The separate contributions to MSEPuncertain(X) can be estimated using a random effects ANOVA. It is argued that MSEPuncertain(X) is the more informative uncertainty criterion, because it is specific to each prediction situation.
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Makowski, D., Asseng, S., Ewert, F., Bassu, S., Durand, J. L., Li, T., et al. (2015). A statistical analysis of three ensembles of crop model responses to temperature and CO2 concentration. Agricultural and Forest Meteorology, 214-215, 483–493.
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].
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Challinor, A. J., Smith, M. S., & Thornton, P. (2013). Use of agro-climate ensembles for quantifying uncertainty and informing adaptation. Agricultural and Forest Meteorology, 170, 2–7.
Abstract: ► Introduces the special issue on Agricultural prediction using climate model ensembles. ► Discuss remaining scientific challenges. ► Develops distinction between projection- and utility-based ensemble modelling. ► Recommendations made RE modelling and the analysis and reporting of uncertainty. Significant progress has been made in the use of ensemble agricultural and climate modelling, and observed data, to project future productivity and to develop adaptation options. An increasing number of agricultural models are designed specifically for use with climate ensembles, and improved methods to quantify uncertainty in both climate and agriculture have been developed. Whilst crop–climate relationships are still the most common agricultural study of this sort, on-farm management, hydrology, pests, diseases and livestock are now also examined. This paper introduces all of these areas of progress, with more detail being found in the subsequent papers in the special issue. Remaining scientific challenges are discussed, and a distinction is developed between projection- and utility-based approaches to agro-climate ensemble modelling. Recommendations are made regarding the manner in which uncertainty is analysed and reported, and the way in which models and data are used to make inferences regarding the future. A key underlying principle is the use of models as tools from which information is extracted, rather than as competing attempts to represent reality.
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