The error in agricultural systems model prediction depends on the variable being predicted

Abstract

Models are generally evaluated based on the squared error of model predictions compared with individual data. However, if major interest is in some quantity averaged over time or space it would be more pertinent to evaluate how well the model predicts this average quantity. We show that the model squared error for predictions averaged over space or time will always be smaller than average squared prediction error and how to estimate the difference between the two, using commonly available data. We illustrate with two case studies concerning irrigation management, (where major interest is in yield averaged over years) and nitrous oxide emissions (where major interest is in emissions averaged over a growing season). Squared error of the average was estimated to be only 57% and 10% of the average squared error for the irrigation and nitrous oxide emissions studies, respectively, in the limit of averaging over long times.