Abstract: Crop models describe the growth and development of a crop interacting with its surrounding agro-environmental conditions (soil, climate and the close conditions of the plant). However, the implementation of such models remains difficult because of the high number of explanatory variables and parameters. It often happens that important discrepancies appear between measured and simulated values. This article aims to highlight the different sources of uncertainty related to the use of crop models, as well as the actual methods that allow a compensation for or, at least, a consideration of these sources of error during analysis of the model results. This article presents a literature review, which firstly synthesises the general mathematical structure of crop models. The main criteria for evaluating crop models are then described. Finally, several methods used for improving models are given. Parameter estimation methods, including frequentist and Bayesian approaches, are presented and data assimilation methods are reviewed.

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 degrees 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 four 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) 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.

Abstract: Models used for climate change impact projections are typically not tested for simulation beyond current climate conditions. Since we have no data truly reflecting future conditions, a key challenge in this respect is to rigorously test models using proxies of future conditions. This paper presents a validation framework and guiding principles applicable across earth science disciplines for testing the capability of models to project future climate change and its impacts. Model test schemes comprising split-sample tests, differential split-sample tests and proxy site tests are discussed in relation to their application for projections by use of single models, ensemble modelling and space-time-substitution and in relation to use of different data from historical time series, paleo data and controlled experiments. We recommend that differential-split sample tests should be performed with best available proxy data in order to build further confidence in model projections.