Crop Model Calibration: a Statstical Perspective.

It is common practice to calibrate crop models. This involves estimating some of the model parameters in order to give a better fit of the model to data.  The purpose of this presentation is to propose a statistical treatment of crop model calibration, which has not previously been done and is important in order to better understand the properties of the calibrated model. The major difficulty is proposing a realistic statistical description of model error. Our approach is to begin with a statistical model of error for the underlying process equations. Those are in general fairly simple, so it is reasonable to assume that they conform to standard simple regression assumptions. We then show that a crop model, made up of coupled process equations, does not satisfy the same assumptions. In statistical terms, the crop model is “misspecified”.  We then concentrate on the consequences of misspecification. A first consequence is that the calibrated parameters do not tend toward the true parameter values of the process equations, even in the limit of very large amounts of data. Thus, calibration cannot in general be used to recover the true underlying parameter values. A second consequence is that calibration using some particular output variable will improve prediction quality for that output variable,  but need not improve prediction quality for other output variables. Thus there is no assurance that calibration will improve prediction of variables that are calculated by the crop model but which have not been measured.