Evaluating optimal fertilizer rates using plant measurements

Correctly adjusting the amount of nitrogen fertilizer to crop needs is important for both economic and environmental reasons. A recent development in nitrogen fertilization is the use of plant measurements to indicate plant nitrogen status. We present a theoretical treatment of this practice. We assume that yield response to nitrogen dose can be described using a random parameter model. The lack of precise knowledge of the parameter values leads to calculated nitrogen doses that are not optimal. The plant measurement allows one to calculate a conditional distribution of the parameter values, which leads to improved calculated nitrogen doses. We apply the treatment to a data set for wheat in northern France. It is shown that the use of a plant measurement, compared with no measurement, has only a minor effect on net profit, but achieves this with less nitrogen and, in particular, reduces the probability of large excesses of nitrogen beyond crop needs.