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: The phenological development of cereal crops from emergence through flowering to maturity is largely controlled by temperature, but also affected by day length and potential physiological stresses. Responses may vary between species and varieties. Climate change will affect the timing of cereal crop development, but exact changes will also depend on changes in varieties as affected by plant breeding and variety choices. This study aimed to assess changes in timing of major phenological stages of cereal crops in Northern and Central Europe under climate change. Records on dates of sowing, flowering, and maturity of wheat, oats and maize were collected from field experiments conducted during the period 1985-2009. Data for spring wheat and spring oats covered latitudes from 46 to 64°N, winter wheat from 46 to 61°N, and maize from 47 to 58°N. The number of observations (site-year-variety combinations) varied with phenological phase, but exceeded 2190, 227, 2076 and 1506 for winter wheat, spring wheat, spring oats and maize, respectively. The data were used to fit simple crop development models, assuming that the duration of the period until flowering depends on temperature and day length for wheat and oats, and on temperature for maize, and that the duration of the period from flowering to maturity in all species depends on temperature only. Species-specific base temperatures were used. Sowing date of spring cereals was estimated using a threshold temperature for the mean air temperature during 10 days prior to sowing. The mean estimated temperature thresholds for sowing were 6.1, 7.1 and 10.1°C for oats, wheat and maize, respectively. For spring oats and wheat the temperature threshold increased with latitude. The effective temperature sums required for both flowering and maturity increased with increasing mean annual temperature of the location, indicating that varieties are well adapted to given conditions. The responses of wheat and oats were largest for the period from flowering to maturity. Changes in timing of cereal phenology by 2040 were assessed for two climate model projections according to the observed dependencies on temperature and day length. The results showed advancements of sowing date of spring cereals by 1-3 weeks depending on climate model and region within Europe. The changes were largest in Northern Europe. Timing of flowering and maturity were projected to advance by 1-3 weeks. The changes were largest for grain maize and smallest for winter wheat, and they were generally largest in the western and northern part of the domain. There were considerable differences in predicted timing of sowing, flowering and maturity between the two climate model projections applied.