Models of Yield, Grain Protein, and Residual Mineral Nitrogen Responses to Applied Nitrogen for Winter Wheat

The proper use of N fertilizer is fundamental for farm profitability and environmental protection. In France, fertilizer recommendations are generally based on the balance‐sheet method, which is not sensitive to the economic or regulatory context. A way to generalize the balance‐sheet method is to use models that describe crop response to applied N. The goal of this paper is to propose, in the case of winter wheat ( Triticum aestivum L.), functional forms for the response of yield, grain protein content, and residual mineral N left in the soil at harvest to applied N. The originality of our models is that all three responses (yield, protein, and residual mineral N) are modeled, using N uptake as an intermediate variable. Furthermore, these models have two clear links with the balance‐sheet method. First, the parameters of the balance‐sheet method appear explicitly in the models. Second, the N dose recommended by the balance‐sheet method appears in our models as the smallest N dose that maximizes yield. Within this general modeling framework, three variants of the yield model, three variants of the grain protein content model, and two variants of the residual mineral N model are considered. The different models are adjusted, site‐year by site‐year, to 28 site‐years of data. All models give satisfactory fits to the data. For example, the root mean square error varies between 0.21 and 0.23 Mg ha −1 for the yield models. Almost all the adjusted parameter values vary widely from site‐year to site‐year. This must be taken into account when calculating optimal N doses for new site‐years.