Statistical Analysis of Large Simulated Yield Datasets for Studying Climate Change Effect.

Many simulation studies have been carried out to predict the effect of climate change on crop yield. Typically, in such study, one or several crop models are used to simulate series of crop yield values for different climate scenarios corresponding to different hypotheses of temperature, CO₂ concentration, and rainfall changes. These studies usually generate large datasets including thousands of simulated yield data. The structure of these datasets is complex because they include series of yield values obtained with different mechanistic crop models for different climate scenarios defined from several climatic variables (temperature, CO₂ etc.). Statistical methods can play a big part for analyzing large simulated crop yield datasets, especially when yields are simulated using an ensemble of crop models. A formal statistical analysis is then needed in order to estimate the effects of different climatic variables on yield, and to describe the variability of these effects across crop models. Statistical methods are also useful to develop meta-models i.e., statistical models summarizing complex mechanistic models. The objective of this paper is to present a random-coefficient statistical model (mixed-effects model) for analyzing large simulated crop yield datasets produced by the international project AgMip for several major crops. The proposed statistical model shows several interesting features; i) it can be used to estimate the effects of several climate variables on yield using crop model simulations, ii) it quantities the variability of the estimated climate change effects across crop models, ii) it quantifies the between-year yield variability, iv) it can be used as a meta-model in order to estimate effects of new climate change scenarios without running again the mechanistic crop models. The statistical model is first presented in details, and its value is then illustrated in a case study where the effects of climate change scenarios on different crops are compared.