Abstract: The development of methodologies for predicting crop yield, in real-time and in response to different agro-climatic conditions, could help to improve the farm management decision process by providing an analysis of expected yields in relation to the costs of investment in particular practices. Based on the use of crop models, this paper compares the ability of two methodologies to predict wheat yield (Triticum aestivum L.), one based on stochastically generated climatic data and the other on mean climate data. It was shown that the numerical experimental yield distribution could be considered as a log-normal distribution. This function is representative of the overall model behaviour. The lack of statistical differences between the numerical realisations and the logistic curve showed in turn that the Generalised Central Limit Theorem (GCLT) was applicable to our case study. In addition, the predictions obtained using both climatic inputs were found to be similar at the inter and intra-annual time-steps, with the root mean square and normalised deviation values below an acceptable level of 10% in 90% of the climatic situations. The predictive observed lead-times were also similar for both approaches. Given (i) the mathematical formulation of crop models, (ii) the applicability of the CLT and GLTC to the climatic inputs and model outputs, respectively, and (iii) the equivalence of the predictive abilities, it could be concluded that the two methodologies were equally valid in terms of yield prediction. These observations indicated that the Convergence in Law Theorem was applicable in this case study. For purely predictive purposes, the findings favoured an algorithm based on a mean climate approach, which needed far less time (by 300-fold) to run and converge on same predictive lead time than the stochastic approach. (C) 2015 Elsevier B.V. All rights reserved.

Abstract: This study presents a Bayesian approach for the parameters’ identification of the STICS crop model based on the recently developed Differential Evolution Adaptive Metropolis (DREAM) algorithm. The posterior distributions of nine specific crop parameters of the STICS model were sampled with the aim to improve the growth simulations of a winter wheat (Triticum aestivum L) culture. The results obtained with the DREAM algorithm were initially compared to those obtained with a Nelder-Mead Simplex algorithm embedded within the OptimiSTICS package. Then, three types of likelihood functions implemented within the DREAM algorithm were compared, namely the standard least square, the weighted least square, and a transformed likelihood function that makes explicit use of the coefficient of variation (CV). The results showed that the proposed CV likelihood function allowed taking into account both noise on measurements and heteroscedasticity which are regularly encountered in crop modelling. (C) 2013 Elsevier Ltd. All rights reserved.

Abstract: Crop growth simulation models can differ greatly in their treatment of key processes and hence in their response to environmental conditions. Here, we used an ensemble of 26 process-based wheat models applied at sites across a European transect to compare their sensitivity to changes in temperature (−2 to +9°C) and precipitation (−50 to +50%). Model results were analysed by plotting them as impact response surfaces (IRSs), classifying the IRS patterns of individual model simulations, describing these classes and analysing factors that may explain the major differences in model responses.   The model ensemble was used to simulate yields of winter and spring wheat at sites in Finland, Germany and Spain. Results were plotted as IRSs that show changes in yields relative to the baseline with respect to temperature and precipitation. IRSs of 30-year means and selected extreme years were classified using two approaches describing their pattern.   The expert diagnostic approach (EDA) combines two aspects of IRS patterns: location of the maximum yield (nine classes, Figure 1) and strength of the yield response with respect to climate (four classes), resulting in a total of 36 combined classes defined using criteria pre-specified by experts. The statistical diagnostic approach (SDA) groups IRSs by comparing their pattern and magnitude, without attempting to interpret these features. It applies a hierarchical clustering method, grouping response patterns using a distance metric that combines the spatial correlation and Euclidian distance between IRS pairs. The two approaches were used to investigate whether different patterns of yield response could be related to different properties of the crop models, specifically their genealogy, calibration and process description.   Although no single model property across a large model ensemble was found to explain the integrated yield response to temperature and precipitation perturbations, the application of the EDA and SDA approaches revealed their capability to distinguish: (i) stronger yield responses to precipitation for winter wheat than spring wheat; (ii) differing strengths of response to climate changes for years with anomalous weather conditions compared to period-average conditions; (iii) the influence of site conditions on yield patterns; (iv) similarities in IRS patterns among models with related genealogy; (v) similarities in IRS patterns for models with simpler process descriptions of root growth and water uptake compared to those with more complex descriptions; and (vi) a closer correspondence of IRS patterns in models using partitioning schemes to represent yield formation than in those using a harvest index.   Such results can inform future crop modelling studies that seek to exploit the diversity of multi-model ensembles, by distinguishing ensemble members that span a wide range of responses as well as those that display implausible behaviour or strong mutual similarities.   The full manuscript of this study is currently under revision (Fronzek et al. 2017).