An optimisation-based approach to generate interpretable within-field zones

The paper proposes a numerical criterion to evaluate zoning quality for a given number of classes. The originality of the criterion is to simultaneously quantify how zones are heterogeneous on the whole field under study and how neighbouring zones are similar. This approach allows comparison between maps either with different zones or different labels, which is of importance for zone delineation algorithms aiming at maximizing inter-zone variability. In addition, this study also proposes an optimisation procedure that yields interpretable within-field zones in which each zone is assigned a clear label. The zoning procedure involves contour delineation based on quantile values. The key point of the paper is to use the proposed numerical zoning quality criterion to guide the optimisation procedure showing the complementarity of both proposals in delineating relevant within-field zones. In order to demonstrate the relevancy of the criterion, the zoning procedure and the implementation of both together, the method was tested on 50 theoretical fields with known variability and known spatial structure. A real plot with yield monitoring data was also used to demonstrate the value of the approach on a real case. Results show the relevancy of the methodology to compare maps with different zones and to sort them. Results also demonstrate the interest of the optimisation procedure to provide a ranked set of possible maps with different within-field zones. This set of relevant maps may constitute a decision support for practitioners who may consider additional expert information to choose the most appropriate map in the specific conditions under consideration.