Articles | Volume 3, issue 4
SOIL, 3, 235–244, 2017
SOIL, 3, 235–244, 2017

Original research article 13 Dec 2017

Original research article | 13 Dec 2017

Planning spatial sampling of the soil from an uncertain reconnaissance variogram

R. Murray Lark1, Elliott M. Hamilton1, Belinda Kaninga2,3, Kakoma K. Maseka4, Moola Mutondo4, Godfrey M. Sakala2,3, and Michael J. Watts1 R. Murray Lark et al.
  • 1Centre for Environmental Geochemistry, British Geological Survey, Keyworth, Nottinghamshire, NG12 5GG, UK
  • 2Zambia Agriculture Research Institute, Mount Makulu, Central Research Station, Lusaka, Zambia
  • 3University of Zambia, Great East Road Campus, Lusaka, Zambia
  • 4Copperbelt University, Jambo Drive, Riverside, Kitwe, Zambia

Abstract. An estimated variogram of a soil property can be used to support a rational choice of sampling intensity for geostatistical mapping. However, it is known that estimated variograms are subject to uncertainty. In this paper we address two practical questions. First, how can we make a robust decision on sampling intensity, given the uncertainty in the variogram? Second, what are the costs incurred in terms of oversampling because of uncertainty in the variogram model used to plan sampling? To achieve this we show how samples of the posterior distribution of variogram parameters, from a computational Bayesian analysis, can be used to characterize the effects of variogram parameter uncertainty on sampling decisions. We show how one can select a sample intensity so that a target value of the kriging variance is not exceeded with some specified probability. This will lead to oversampling, relative to the sampling intensity that would be specified if there were no uncertainty in the variogram parameters. One can estimate the magnitude of this oversampling by treating the tolerable grid spacing for the final sample as a random variable, given the target kriging variance and the posterior sample values. We illustrate these concepts with some data on total uranium content in a relatively sparse sample of soil from agricultural land near mine tailings in the Copperbelt Province of Zambia.

Short summary
An advantage of geostatistics for mapping soil properties is that, given a statistical model of the variable of interest, we can make a rational decision about how densely to sample so that the map is sufficiently precise. However, uncertainty about the statistical model affects this process. In this paper we show how Bayesian methods can be used to support decision making on sampling with an uncertain model, ensuring that the probability of meeting certain levels of precision is high enough.