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: Highlights • Regularization techniques for regression outperformed the classical regression techniques in predicting crop yields. • Different regression techniques with similar prediction accuracy showed different responses of major climatic variables to crop yield. • The regression models showed some responses of crop yield to climatic conditions that is mostly absent in process based crop models. Abstract Statistical regression models represent alternatives to process-based dynamic models for predicting the response of crop yields to variation in climatic conditions. Regression models can be used to quantify the effect of change in temperature and precipitation on yields. However, it is difficult to identify the most relevant input variables that should be included in regression models due to the high number of candidate variables and to their correlations. This paper compares several regression techniques for modeling response of winter oilseed rape yield to a high number of correlated input variables. Several statistical regression methods were fitted to a dataset including 689 observations of winter oilseed rape yield from replicated field experiments conducted in 239 sites in Denmark, covering nearly all regions of the country from 1992 to 2013. Regression methods were compared by cross-validation. The regression methods leading to the most accurate yield predictions were Lasso and Elastic Net, and the least accurate methods were ordinary least squares and stepwise regression. Partial least squares and ridge regression methods gave intermediate results. The estimated relative yield change for a +1°C temperature increase during flowering was estimated to range between 0 and +6 %, depending on choice of regression method. Precipitation was found to have an adverse effect on yield during autumn and winter. It was estimated that an increase in precipitation of +1 mm/day would result in a relative yield change ranging from 0 to −4 %. Soil type was also important for crop yields with lower yields on sandy soils compared to loamy soils. Later sowing was found to result in increased crop yield. The estimated effect of climate on yield was highly sensitive to the chosen regression method. Regression models showing similar performance led in some cases to different conclusions with respect to effect of temperature and precipitation. Hence, it is recommended to apply an ensemble of regression models, in order to account for the sensitivity of the data driven models for projecting crop yield under climate change.