Sampling design optimization for multivariate soil mapping

Much attention has been paid to sampling design optimization over the past decades. Many methods have been developed and applied, but only a few of these deal with simultaneous optimization of the sampling design for multiple soil variables. In this paper we present a method implemented as R-code that minimizes the average kriging variance (AKV) for multiple soil variables simultaneously. The method is illustrated with real soil data from an experimental field in central Czech Republic. The goal of the method is to minimize the sample size while keeping the AKV values of all tested soil variables below given thresholds. We defined and tested two different objective functions, critical AKV optimization and weighted sum of AKV optimization, both based on the AKV minimization with annealing algorithm. The crucial moment for such an optimization is defining the mutual spatial relationship between all soil variables with the Linear Model of Coregionalization and proper modelling of all (cross)variograms which are used in the optimization process. In addition, a separate optimization was made for each of the tested soil characteristics to evaluate a possible gain of the simultaneous approach. The results showed that the final design for multivariate sampling is “fully-optimal” for one soil variable — optimal number of observations and optimal structure of sampling pattern, and “sub-optimal” for the others, while no clear difference between the two optimization criteria was found. We can recommend using the method in situations where periodical soil surveys are planned and where multivariate soil characteristics are determined from the same soil samples at once