When and why to predict using the mean or median of a crop multi-model ensemble

Abstract

The systematic use of crop multi-model ensembles (MMEs) has recently become widespread. In these studies, it has often been noted that ensemble predictors, in particular the mean (emean) or median (emedian) of the ensemble simulated values, are in close agreement with observations. If this is the case in general, using ensemble predictors could be an important pathway to improved model predictions and as a consequence to more widespread use of crop models. However, only a single study has specifically targeted the quality of ensemble predictors, and that was based on only limited data.The purpose of this study was to analyze the behavior of the ensemble predictors over a much wider range of situations, and to propose a random effects statistical model of model error to explain and generalize the empirical findings. We analyze the results of applying MMEs to simulate five separate experiments, each designed to study the effects of a specific range of environmental conditions.The basic finding, which confirms and extends previous studies, is that emedian and emean are the best or among the best predictors for every experiment and every response variable considered. Emedian in most cases is preferred to emean, but the differences are small. The empirical results also show that emedian and emean in general have high skill values. Finally, the results show that the skill values increase with the number of models in the ensemble.The statistical model shows how these conclusions depend on overall bias of the models in the ensemble, and the variances of the random model effect, the treatment effect and their interaction.