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 models of crop growth are increasingly used to quantify the impact of global changes due to climate or crop management. Therefore, accuracy of simulation results is a major concern. Studies with ensembles of crop models can give valuable information about model accuracy and uncertainty, but such studies are difficult to organize and have only recently begun. We report on the largest ensemble study to date, of 27 wheat models tested in four contrasting locations for their accuracy in simulating multiple crop growth and yield variables. The relative error averaged over models was 24-38% for the different end-of-season variables including grain yield (GY) and grain protein concentration (GPC). There was little relation between error of a model for GY or GPC and error for in-season variables. Thus, most models did not arrive at accurate simulations of GY and GPC by accurately simulating preceding growth dynamics. Ensemble simulations, taking either the mean (e-mean) or median (e-median) of simulated values, gave better estimates than any individual model when all variables were considered. Compared to individual models, e-median ranked first in simulating measured GY and third in GPC. The error of e-mean and e-median declined with an increasing number of ensemble members, with little decrease beyond 10 models. We conclude that multimodel ensembles can be used to create new estimators with improved accuracy and consistency in simulating growth dynamics. We argue that these results are applicable to other crop species, and hypothesize that they apply more generally to ecological system models.

Abstract: Croplands and grasslands are agricultural systems that contribute to land–atmosphere exchanges of carbon (C). We evaluated and compared gross primary production (GPP), ecosystem respiration (RECO), net ecosystem exchange (NEE) of CO2, and two derived outputs – C use efficiency (CUE=-NEE/GPP) and C emission intensity (IntC= -NEE/Offtake [grazed or harvested biomass]). The outputs came from 23 models (11 crop-specific, eight grassland-specific, and four models covering both systems) at three cropping sites over several rotations with spring and winter cereals, soybean and rapeseed in Canada, France and India, and two temperate permanent grasslands in France and the United Kingdom. The models were run independently over multi-year simulation periods in five stages (S), either blind with no calibration and initialization data (S1), using historical management and climate for initialization (S2), calibrated against plant data (S3), plant and soil data together (S4), or with the addition of C and N fluxes (S5). Here, we provide a framework to address methodological uncertainties and contextualize results. Most of the models overestimated or underestimated the C fluxes observed during the growing seasons (or the whole years for grasslands), with substantial differences between models. For each simulated variable, changes in the multi-model median (MMM) from S1 to S5 was used as a descriptor of the ensemble performance. Overall, the greatest improvements (MMM approaching the mean of observations) were achieved at S3 or higher calibration stages. For instance, grassland GPP MMM was equal to 1632 g C m−2 yr-1 (S5) while the observed mean was equal to 1763 m-2 yr-1 (average for two sites). Nash-Sutcliffe modelling efficiency coefficients indicated that MMM outperformed individual models in 92.3 % of cases. Our study suggests a cautious use of large-scale, multi-model ensembles to estimate C fluxes in agricultural sites if some site-specific plant and soil observations are available for model calibration. The further development of crop/grassland ensemble modelling will hinge upon the interpretation of results in light of the way models represent the processes underlying C fluxes in complex agricultural systems (grassland and crop rotations including fallow periods).