A case of combined use of crop simulation models and general linear models

Crop models predict both the evolution of some crop variable (e.g. biomass, referred to as the intermediate variable) and a final variable of interest (e.g. final yield). These models have proved to be very powerful tools, but the quality of their prediction is generally unknown. This article presents a statistical methodology to improve the yield prediction of those crop models. Their error in simulating the value of a final variable (i.e. the final error) can be estimated through the errors they commit in simulating an intermediate variable (i.e. intermediate errors). The general linear model theory was used to model these errors and to elaborate the Best Linear Unbiased Predictor (BLUP). The properties of this predictor permit the estimation of its variance, and thus gives a confidence interval for the new yield prediction, which the crop models cannot do. The innovative aspect of this methodology resides in the identification of an exponential covariance function to describe the relationships between intermediate errors and of a linear function for the covariance between intermediate and final errors. This methodology was applied on two sets of data using two different crop models, CERES-Wheat and EPIC, respectively. Average 90 and 60% decreases of the Mean Square Error of Prediction (MSEP) were obtained for EPIC and CERES-Wheat, respectively. This method also proved to be more efficient than a simple correction in unbiasing the yield predicted by the model.