Optimization of second-phase sampling for multivariate soil mapping purposes: Case study from a wine region, Hungary

Over the last decades extensive work has been done on sampling optimization. Many of the related papers focused on the optimization of sampling for only one soil property. However, there is a necessity to prepare a sampling strategy which is optimized for multivariate digital soil mapping (DSM) purposes. The aim of our work was to elaborate a sampling optimization methodology for multivariate DSM considering the demands on economic efficiency. We presented and tested it through a real-time survey at Tokaj Wine Region, Hungary. The soil properties of interest were pH, soil organic matter (SOM), and calcium carbonate (CaCO3) content. The end-users defined the minimal requested precision for the DSM products (in terms of the average range of the 90% prediction interval), and priority areas on which more detailed survey was requested. We planned a two-phase soil survey based on regression kriging (RK). The results from the first-phase sampling were used to parameterize the second-phase sampling in which spatial simulated annealing (SSA) was applied. The spatially averaged range of the 90% prediction interval was the pre-survey quality measure which can be readily derived from the RK variance. The workflow can be summarized as follows: (1) rank the soil properties considering their spatial variabilities, and precision requests, (2) optimize the sampling design by SSA for the dominant soil property, (3) optimize the sampling by the invers application of SSA for the next soil property using the optimized design from the previous step, and (4) repeat the previous step until all soil property are being selected. In our case, SOM was the dominant property. According to the plot of the sample size vs. quality measure, the optimized design with 500 samples will ensure the minimal requested precision for the SOM map (i.e. 0.5%). In the next step, the optimal removal of those sampling points was targeted which have less information content. In the cases of pH and CaCO3, 100 and 175 could be removed from the 500 samples, and the remaining 400 and 325 samples will ensure the requested precision for the pH (i.e. 1.2) and CaCO3 (i.e. 5%) maps. We computed the relative sampling density on priority and non-priority areas for each sampling designs which showed that densities on priority areas were at least 1.5 times higher than on non-priority areas. We could conclude that the methodology is able to optimize the sampling design for multivariate DSM purposes considering numerous sampling constraints such as the predefined precision, priority areas, and economic efficiency.