Combining input uncertainty and residual error in crop model predictions: A case study on vineyards

Abstract As crop modelling has matured and been proposed as a tool for many practical applications, there is increased need to evaluate the uncertainty in model predictions. A particular case of interest that has not been treated before is that where one takes into account both uncertainty in the model explanatory variables and model residual error (the uncertainty in model predictions even when the explanatory variables are perfectly known). The specific case we consider is that of a model for predicting water stress of a vineyard. For many of the model explanatory variables, the vine grower (or the farmer advisor) has a choice between approximate values which are easily obtainable and more precise values that are more difficult (and more expensive) to obtain. We specifically discuss the explanatory variable “initial water stress” which is directly based on the initial soil water content and can be estimated or measured (precise but expensive). The vine grower is interested in the decrease in uncertainty that would result from measuring initial water stress, but it is the decrease in total uncertainty, including model residual error, that is of importance. We propose using accurate measurements of water stress over time in multiple vineyards, to estimate model residual error. The uncertainty in initial water stress can be estimated if one has approximate and precise values of initial water stress in several vineyards. We then combine the two sources of error by simulation thanks to an independence hypothesis; the model is run multiple times with a distribution of values for initial water stress, and on each day a distribution of model residual errors is added to the result. The results show that the resulting uncertainty is quite different in different fields. In some cases, uncertainty in initial water stress becomes negligible a short time after the start of simulations, in other cases that uncertainty remains important, compared to model residual error, throughout the growing season. In all cases, residual error is a substantial percentage of overall error and thus should be taken into account.