A statistical analysis of three ensembles of crop model responses to temperature and CO2 concentration
Introduction
Many studies have been carried out in recent decades to assess the effects of climate change on crop yield and other key crop characteristics. In these studies, one or several crop models were used to simulate crop growth and development for different projections of atmospheric CO2 concentration, temperature and precipitation changes (Semenov et al., 1996, Tubiello and Ewert, 2002, White et al., 2011). AgMIP, the Agricultural Model Intercomparison and Improvement Project (Rosenzweig et al., 2013), builds on these studies to explore the value of an ensemble of crop models for assessing effects of climate change scenarios for several crops in contrasting environments.
The AgMIP studies generate large datasets, including thousands of simulated crop yield data. They include series of yield values that are obtained by using standardized protocols that combine several crop models with different climate scenarios defined by several climatic variables (temperature, CO2, precipitation, etc.). Such datasets potentially provide new information on the possible effects of different climate change scenarios on crop yields. However, it is difficult to summarize them in a useful way due to their structural complexity; simulated yield data can differ among contrasting climate scenarios, sites, and crop models. Another issue is that it is not straightforward to interpolate the results obtained for the considered scenarios to alternative climate scenarios not considered in the initial simulation protocols. Additional crop model simulations for new climate scenarios is an option but this approach is costly, especially when a large number of crop models is used to generate the simulated data.
Statistical models have been used to analyze responses of measured yield data to climate variables in past studies (Lobell et al., 2011). They were also recently used in meta-analyses on the effect of climate change on crop yields (Wilcox and Makowski, 2014, Challinor et al., 2014). However, the use of a statistical model to analyze the variability of crop model responses to climate change factors is a rather new idea. We demonstrate herewith that statistical methods can play an important role in analyzing simulated yield datasets obtained with ensembles of process-based crop models using standardized protocols. Formal statistical analysis is helpful to estimate the effects of different climatic variables on yield, and to describe the between-model variability of these effects. Statistical methods can also be used to develop meta-models, i.e., statistical models summarizing process-based crop models. Such meta-models may enable scientists to explore more efficiently the effects of new climate change scenarios not initially included in the simulation protocol.
Our approach is illustrated with three datasets of simulated yields obtained by AgMIP for maize, wheat, and rice generated by ensembles of process-based crop models (Asseng et al., 2013; Bassu et al., 2014; Li et al., 2015). The yield datasets were used to develop a meta-model that provides a simplified representation of the original ensembles of crop models. The proposed meta-model is a statistical regression with random coefficients describing the variability of the simulated yield data across the original crop models. Once fitted to the simulated yield datasets, the meta-models were used to analyze the variability of the projected effects of climate changes among crop models, and between alternative crops. The meta-models were also used to study the effects of temperature-change and CO2-change scenarios that were not initially tested with the original ensemble of crop models. Finally, the results obtained with the meta-model were used to compare simulated uncertainties and to assess the impact of temperature and CO2 concentration changes on yields of maize, wheat, and rice.
Section snippets
Simulated yield data
We used the maize, wheat, and rice datasets presented by Asseng et al. (2013), Bassu et al. (2014), and Li et al. (2015). Yield data were simulated with 19 maize models, 26 wheat models, and 13 rice models. For each crop species, models were calibrated and then run for four contrasting sites located in France (Lusignan), USA (Ames), Brazil (Rio Verde), and Tanzania (Morogoro) for maize, in The Netherlands (Wageningen), Argentina (Balcarce), India (New Delhi), and Australia (Wongan Hills) for
Yield response to increase in temperature
Fig. 3 shows the change in yield from the baseline for one maize site (Fig. 3A), one wheat site (Fig. 3C), and one rice site (Fig. 3E) as affected by an atmospheric CO2 concentration increase of 180 ppm ([CO2] = 540 ppm) and an increase of mean seasonal temperature ranging from 0 °C to 6 °C. Each emulated model yield response is calculated by using the crop model-specific coefficients αeki (k = 0, …, 5, i = 1, …, P) and is plotted with a gray line, and thus can be seen as a substitute for a given crop
Discussion and conclusions
Our study shows how yields simulated by ensembles of process-based dynamic crop models can be summarized by statistical models (meta-models) that are based on random coefficient regressions. These statistical models describe the between-crop model variability of the simulated yield data using probability distributions. They can be used to compute key simulated quantities such as mean yield loss, percentiles of yield loss, and probabilities of yield loss as functions of temperature change and CO2
Acknowledgements
G.J. O’Leary was supported by the Victorian Department of Economic Development Jobs, Transport and Resources, the Australian Department of Agriculture. S. Bassu, P. Bertuzzi, G. De Sanctis, J.-L. Durand, D. Makowski, P. Martre, D. Ripoche and D. Wallach were partly supported by the INRA ACCAF meta-program. S. Gayler was supported by a grant from the Ministry of Science, Research and Arts of Baden-Württemberg (AZ Zu33-721.3-2) and the Helmholtz Centre for Environmental Research – UFZ, Leipzig.
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# Dr. Nadine Brisson passed away in 2011 while this work was being carried out.