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: Eleven widely used crop simulation models (APSIM, CERES, CROPSYST, COUP, DAISY, EPIC, FASSET, HERMES, MONICA, STICS and WOFOST) were tested using spring barley (Hordeum vulgare L.) data set under varying nitrogen (N) fertilizer rates from three experimental years in the boreal climate of Jokioinen, Finland. This is the largest standardized crop model inter-comparison under different levels of N supply to date. The models were calibrated using data from 2002 and 2008, of which 2008 included six N rates ranging from 0 to 150 kg N/ha. Calibration data consisted of weather, soil, phenology, leaf area index (LAI) and yield observations. The models were then tested against new data for 2009 and their performance was assessed and compared with both the two calibration years and the test year. For the calibration period, root mean square error between measurements and simulated grain dry matter yields ranged from 170 to 870 kg/ha. During the test year 2009, most models failed to accurately reproduce the observed low yield without N fertilizer as well as the steep yield response to N applications. The multi-model predictions were closer to observations than most single-model predictions, but multi-model mean could not correct systematic errors in model simulations. Variation in soil N mineralization and LAI development due to differences in weather not captured by the models most likely was the main reason for their unsatisfactory performance. This suggests the need for model improvement in soil N mineralization as a function of soil temperature and moisture. Furthermore, specific weather event impacts such as low temperatures after emergence in 2009, tending to enhance tillering, and a high precipitation event just before harvest in 2008, causing possible yield penalties, were not captured by any of the models compared in the current study.