  In Precision Agriculture, the utilization of management zones (MZs) that take
into account within-field variability facilitates effective fertilizer
management. This approach enables the optimization of nitrogen (N) rates to
maximize crop yield production and enhance agronomic use efficiency. However,
existing works often neglect the consideration of responsivity to fertilizer as
a factor influencing MZ determination. In response to this gap, we present a MZ
clustering method based on fertilizer responsivity. We build upon the statement
that the responsivity of a given site to the fertilizer rate is described by
the shape of its corresponding N fertilizer-yield response (N-response) curve.
Thus, we generate N-response curves for all sites within the field using a
convolutional neural network (CNN). The shape of the approximated N-response
curves is then characterized using functional principal component analysis.
Subsequently, a counterfactual explanation (CFE) method is applied to discern
the impact of various variables on MZ membership. The genetic algorithm-based
CFE solves a multi-objective optimization problem and aims to identify the
minimum combination of features needed to alter a site's cluster assignment.
Results from two yield prediction datasets indicate that the features with the
greatest influence on MZ membership are associated with terrain characteristics
that either facilitate or impede fertilizer runoff, such as terrain slope or
topographic aspect.
