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: An environmental dynamic system is usually modeled as a nonlinear system described by a set of nonlinear ODEs. A central challenge in computational modeling of environmental systems is the determination of the model parameters. In these cases, estimating these variables or parameters from other easily obtained measurements can be extremely useful. This work addresses the problem of monitoring and modeling a leaf area index and soil moisture model (LSM) using state estimation. The performances of various conventional and state-of-the-art state estimation techniques are compared when they are utilized to achieve this objective. These techniques include the extended Kalman filter (EKF), particle filter (PF), and the more recently developed technique variational filter (VF). Specifically, two comparative studies are performed. In the first comparative study, the state variables (the leaf-area index LAI, the volumetric water content of the soil layer 1, HUR1 and the volumetric water content of the soil layer 2, HUR2) are estimated from noisy measurements of these variables, and the various estimation techniques are compared by computing the estimation root mean square error (RMSE) with respect to the noise-free data. In the second comparative study, the state variables as well as the model parameters are simultaneously estimated. In this case, in addition to comparing the performances of the various state estimation techniques, the effect of number of estimated model parameters on the accuracy and convergence of these techniques are also assessed. The results of both comparative studies show that the PF provides a higher accuracy than the EKF, which is due to the limited ability of the EKF to handle highly nonlinear processes. The results also show that the VF provides a significant improvement over the PF because, unlike the PF which depends on the choice of sampling distribution used to estimate the posterior distribution, the VF yields an optimum choice of the sampling distribution, which also accounts for the observed data. The results of the second comparative study show that, for all techniques, estimating more model parameters affects the estimation accuracy as well as the convergence of the estimated states and parameters. However, the VF can still provide both convergence as well as accuracy related advantages over other estimation methods. (C) 2013 Elsevier B.V. All rights reserved.

Abstract: This study presents a Bayesian approach for the parameters’ identification of the STICS crop model based on the recently developed Differential Evolution Adaptive Metropolis (DREAM) algorithm. The posterior distributions of nine specific crop parameters of the STICS model were sampled with the aim to improve the growth simulations of a winter wheat (Triticum aestivum L) culture. The results obtained with the DREAM algorithm were initially compared to those obtained with a Nelder-Mead Simplex algorithm embedded within the OptimiSTICS package. Then, three types of likelihood functions implemented within the DREAM algorithm were compared, namely the standard least square, the weighted least square, and a transformed likelihood function that makes explicit use of the coefficient of variation (CV). The results showed that the proposed CV likelihood function allowed taking into account both noise on measurements and heteroscedasticity which are regularly encountered in crop modelling. (C) 2013 Elsevier Ltd. All rights reserved.