Chapter 11 Optimization of Sample Configurations for Digital Mapping of Soil Properties with Universal Kriging

Abstract

Digital soil mapping makes extensive use of auxiliary information, such as that contained in remote sensing images and digital elevation models. However, it cannot do without taking samples of the soil itself. Therefore, methods and guidelines need to be developed that assist users in designing spatial sample configurations for use in digital soil mapping. Existing geostatistical methods are insufficient because these typically have been developed for situations in which there is no auxiliary information. In this chapter, we explore how the existing methods may be extended to the case in which the auxiliary information is spatially exhaustive and where soil mapping is done using universal kriging. We develop and illustrate a methodology that optimizes the spatial configuration of observations by minimizing the spatially averaged universal kriging variance. The universal kriging variance incorporates trend estimation error as well as spatial interpolation error. Hence, the optimized sample configuration strikes a balance between an optimal distribution of observations in feature and geographic space. The results show that optimal distribution in feature space prevails over optimal distribution in geographic space when the stochastic component of the universal kriging model is weakly spatially autocorrelated. It also prevails when the total number of observations is small. In all other cases, the optimal configuration is close to that obtained with minimization of only the spatial interpolation error. Application to a variety of real-world cases with multiple predictors and different spatial dependence structures is needed to support and generalise these preliminary findings.