Planning spatial sampling of the soil from an uncertain reconnaissance variogram

Abstract

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.

Transferability of a soil variogram for sampling design: A case study of three grasslands in Ireland

“…The kappa coefficient of the Matérn variogram was not included in the MCMC sampling, as it is difficult to estimate (Diggle & Ribeiro, 2007;Lark et al, 2017). The kappa coefficients of the transferred and local variograms were fixed at the REML estimates.…”

“…To transfer a variogram of a donor field to derive a tolerable grid spacing for mapping of a recipient field by ordinary kriging, we propose the following procedure. In this procedure a Bayesian approach, as proposed by Lark et al (2017), is used to derive a probability distribution of tolerable grid spacings from an uncertain variogram. (Minasny, Vrugt, & McBratney, 2011).…”

“…For MCMC sampling from the posterior multivariate distribution of the variogram parameters we used the DREAM algorithm of Vrugt et al (2009). Parameters to run the algorithm were similar to those of Lark et al (2017), that is, nine chains with four chain pairs used to generate the jump at each sample and default values for the others. The first 10% of the sampled variograms were discarded to avoid the effects of the initial parameter vector, while every tenth of the remaining variograms were extracted.…”

“…In practice we are uncertain about the variograms of the donor and recipient fields due to sampling and measurement errors. Ideally, the uncertainty about the variogram of the donor field is accounted for in deriving the tolerable grid spacing for the recipient field (Lark et al, 2017). Besides, to evaluate the tolerable grid spacing as estimated from the transferred variogram of a donor field, uncertainty in the local variogram should be accounted for as well.…”

Digital soil mapping based on empirical mode decomposition components of environmental covariates

“…The spatial dependence part of RK was modelled based on variogram functions frequently used in DSM, including spherical, Gaussian and Matérn functions, and the best one, based on AIC, was chosen. For the Matérn function, a series of kappa values from 0.1 to 3 by an interval of 0.1 was tried, because a kappa value is usually difficult to estimate (Lark et al, 2017). Note that the Matérn function with a kappa value of 0.5 is equivalent to the exponential function (i.e.…”