Abstract: Crop models are important tools for impact assessment of climate change, as well as for  exploring management options under current climate. It is essential to evaluate the  uncertainty associated with predictions of these models. Several ways of quantifying  prediction uncertainty have been explored in the literature, but there have been no  studies of how the different approaches are related to one another, and how they are  related to some overall measure of prediction uncertainty. Here we show that all the  different approaches can be related to two different viewpoints about the model; either  the model is treated as a fixed predictor with some average error, or the model can be  treated as a random variable with uncertainty in one or more of model structure, model  inputs and model parameters. We discuss the differences, and show how mean squared  error of prediction can be estimated in both cases. The results can be used to put  uncertainty estimates into a more general framework and to relate different uncertainty  estimates to one another and to overall prediction uncertainty. This should lead to a  better understanding of crop model prediction uncertainty and the underlying causes of  that uncertainty. This study was published as (Wallach et al. 2016)

Abstract: We compare 27 wheat models’ yield responses to interannual climate variability, analyzed at locations in Argentina, Australia, India, and The Netherlands as part of the Agricultural Model Intercomparison and Improvement Project (AgMIP) Wheat Pilot. Each model simulated 1981-2010 grain yield, and we evaluate results against the interannual variability of growing season temperature, precipitation, and solar radiation. The amount of information used for calibration has only a minor effect on most models’ climate response, and even small multi-model ensembles prove beneficial. Wheat model clusters reveal common characteristics of yield response to climate; however models rarely share the same cluster at all four sites indicating substantial independence. Only a weak relationship (R-2 <= 0.24) was found between the models’ sensitivities to interannual temperature variability and their response to long-term warming, suggesting that additional processes differentiate climate change impacts from observed climate variability analogs and motivating continuing analysis and model development efforts. Published by Elsevier Ltd.

Abstract: We consider predictions of the impact of climate warming on rice development times in Sri Lanka. The major emphasis is on the uncertainty of the predictions, and in particular on the estimation of mean squared error of prediction. Three contributions to mean squared error are considered. The first is parameter uncertainty that results from model calibration. To take proper account of the complex data structure, generalized least squares is used to estimate the parameters and the variance-covariance matrix of the parameter estimators. The second contribution is model structure uncertainty, which we estimate using two different models. An ANOVA analysis is used to separate the contributions of parameter and model uncertainty to mean squared error. The third contribution is model error, which is estimated using hindcasts. Mean squared error of prediction of time from emergence to maturity, for baseline +2 °C, is estimated as 108 days2, with model error contributing 86 days2, followed by model structure uncertainty which contributes 15 days2 and parameter uncertainty which contributes 7 days2. We also show how prediction uncertainty is reduced if prediction concerns development time averaged over years, or the difference in development time between baseline and warmer temperatures.