Abstract: Within the context of nitrogen (N) management, since 1950, with the rapid intensification of agriculture, farmers have often applied much larger fertiliser quantities than what was required to reach the yield potential. However, to prevent pollution of surface and groundwater induced by nitrates, The European Community launched The European Nitrates Directive 91/6/76/EEC. In 2002, in Wallonia (Belgium), the Nitrates Directive has been transposed under the Sustainable Nitrogen Management in Agriculture Program (PGDA), with the aim of maintaining productivity and revenue for the country’s farmers, while reducing the environmental impact of excessive N application. A feasible approach for addressing climatic uncertainty lies in the use of crop models such as the one commonly known as STICS (simulateur multidisciplinaire pour les cultures standard). These models allow the impact on crops of the interaction between cropping systems and climatic records to be assessed. Comprehensive historical climatic records are rare, however, and therefore the yield distribution values obtained using such an approach can be discontinuous. In order to obtain better and more detailed yield distribution information, the use of a high number of stochastically generated climate time series was proposed, relying on the LARS-Weather Generator. The study focused on the interactions between varying N practices and climatic conditions. Historically and currently, Belgian farmers apply 180 kg N ha(-1), split into three equal fractions applied at the tillering, stem elongation and flag-leaf stages. This study analysed the effectiveness of this treatment in detail, comparing it to similar practices where only the N rates applied at the flag-leaf stage were modified. Three types of farmer decision-making were analysed. The first related to the choice of N strategy for maximising yield, the second to obtaining the highest net revenue, and the third to reduce the environmental impact of potential N leaching, which carries the likelihood of taxation if inappropriate N rates are applied. The results showed reduced discontinuity in the yield distribution values thus obtained. In general, the modulation of N levels to accord with current farmer practices showed considerable asymmetry. In other words, these practices maximised the probability of achieving yields that were at least superior to the mean of the distribution values, thus reducing risk for the farmers. The practice based on applying the highest amounts (60-60-100 kg N ha(-1)) produced the best yield distribution results. When simple economical criteria were computed, the 60-60-80 kg N ha(-1) protocol was found to be optimal for 80-90% of the time. There were no statistical differences, however, between this practice and Belgian farmers’ current practice. When the taxation linked to a high level of potentially leachable N remaining in the soil after harvest was considered, this methodology clearly showed that, in 3 years out of 4,30 kg N ha(-1) could systematically be saved in comparison with the usual practice.

Abstract: This paper deals with the problem of predicting biomass and grain protein content using improved particle filtering (IPF) based on minimizing the Kullback-Leibler divergence. The performances of IPF are compared with those of the conventional particle filtering (PF) in two comparative studies. In the first one, we apply IPF and PF at a simple dynamic crop model with the aim to predict a single state variable, namely the winter wheat biomass, and to estimate several model parameters. In the second study, the proposed IPF and the PF are applied to a complex crop model (AZODYN) to predict a winter-wheat quality criterion, namely the grain protein content. The results of both comparative studies reveal that the IPF method provides a better estimation accuracy than the PF method. The benefit of the IPF method lies in its ability to provide accuracy related advantages over the PF method since, unlike the PF which depends on the choice of the sampling distribution used to estimate the posterior distribution, the IPF yields an optimum choice of this sampling distribution, which also utilizes the observed data. The performance of the proposed method is evaluated in terms of estimation accuracy, root mean square error, mean absolute error and execution times.

Abstract: LAI of winter wheat (Triticum aestivum L.) and soil water content of the topsoil (200 mm) and of the subsoil (500 mm) were considered as state variables of a dynamic soil-crop system. This system was assumed to progress according to a Bayesian probabilistic state space model, in which real values of LAI and soil water content were daily introduced in order to correct the model trajectory and reach better future evolution. The chosen crop model was mini STICS which can reduce the computing and execution times while ensuring the robustness of data processing and estimation. To predict simultaneously state variables and model parameters in this non-linear environment, three techniques were used: extended Kalman filtering (EKF), particle filtering (PF), and variational filtering (VF). The significantly improved performance of the VF method when compared to EKF and PF is demonstrated. The variational filter has a low computational complexity and the convergence speed of states and parameters estimation can be adjusted independently. Detailed case studies demonstrated that the root mean square error of the three estimated states (LAI and soil water content of two soil layers) was smaller and that the convergence of all considered parameters was ensured when using VF. Assimilating measurements in a crop model allows accurate prediction of LAI and soil water content at a local scale. As these biophysical properties are key parameters in the crop-plant system characterization, the system has the potential to be used in precision farming to aid farmers and decision makers in developing strategies for site-specific management of inputs, such as fertilizers and water irrigation.