An application of a spatial simulated annealing sampling optimization algorithm to support digital soil mapping

Abstract

Spatial simulated annealing (SSA) was applied to optimize the sampling confi guration for soil organic matt er mapping through various sampling scenarios in a Hungarian study site. Prediction-error variance of regression kriging was applied as quality measure in the optimization procedures. Requisites of SSA come from a legacy soil dataset and from spatial auxiliary information. Four scenarios were set to represent the major capabilities of SSA. Scenario 1 and 2 represented completely new sampling designs to optimize with predefi ned constraints. In scenario 1, number of new observations was the constraint, whilst in scenario 2, it was the value of the quality measure. In both scenarios, areas inaccessible for sampling (roads, farms etc.) were also taken into account. Scenario 3 and 4 represented complementary sampling confi gurations to optimize taking the previously collected samples into consideration. In scenario 3, the constraint was the number of new observations, whilst in scenario 4, it was the value of the quality measure. In both cases, two types of previously collected sampling design were simulated, a regular and a clustered confi guration. The resulted designs were evaluated by Kolmogorov–Smirnov test, nearest neighbour distribution function and empty space function. In cases of scenario 1 and 3, the results showed that, all of the optimized sampling confi gurations cover properly both geographic and feature space, respectively. In cases of scenario 2 and 4, the resulted calibration curves can be used to determine the sample size for a given quality measure value. Furthermore, we could determine the minimal sample size for a given scenario, which has to be collected to represent properly both geographic and feature space. In conclusion, SSA is a valuable tool to optimize the sampling design considering a lot of constraints.