Sampling optimization based on secondary information and its utilization in soil carbon mapping

Abstract

We propose a method for optimizing sampling for digital soil mapping in cases where no directly measured prior information of the primary variable of interest is available. Various ancillary variables (soil series, relative elevation, slope, electrical conductivity and soil surface reflectance) were assumed to provide indirect information about the spatial distribution of soil carbon stock (CS, Mg ha − 1 in 0–0.3 m depth) in three fields of 49 to 65 ha size. The secondary information was used for stratifying each field into contiguous spatial clusters. Using this stratification, initial stratified random sampling schemes were allocated and further optimized by constrained spatial simulated annealing. Three optimization approaches were evaluated: minimization of the shortest distance (MMSD), a uniform distribution of point pairs for variogram estimation (WM), and a combination of MMSD (2 / 3 of samples) and WM (1 / 3). Spatially constrained cluster analysis of secondary information resulted in stratifications that accounted for large proportions of the variation of all ancillary variables used in the cluster analysis, but also for 47% to 68% of the spatial variation in measured CS. MMSD-optimized sampling schemes were inappropriate for mapping when the sampling density was low (≤ 1.5 to 2 samples per hectare) because spatial variation occurring at short lag distances was poorly resolved. WM-optimized sampling schemes allowed modeling of spatial variation, but resulted in poor field coverage for mapping purposes. The combined MMSD + WM optimization provided both even field coverage and the ability to estimate variograms for interpolation purposes. Sampling based on secondary information and re-use of the secondary information in regression kriging increased the accuracy of CS maps and allowed a significant reduction in sample size without loss of information. Further improvements could include fitness functions that simultaneously account for variation in feature and geographic space as well as sampling cost.