A geostatistical method to account for the number of aliquots in composite samples for normal and lognormal random variables

Geostatistical methods can be used to calculate predictions of soil variables at unsampled locations, but the methodology is typically based on samples collected on identical sample supports. In this paper, we provide and test theory that allows the inclusion of data from mixed sample supports in a single analysis. In particular, we consider composite sample supports that are defined by the number of aliquots used to form a single composite sample, n_i, and the set of locations, x_i, from which the aliquots were collected. We allow both n_i and x_i to vary between samples (x_i can vary in the extent and geometry of the aliquot locations), and thereby show how point data (a special case of composite data, defined by n_i = 1 and x_i as the known sample point) can be included in the same geostatistical analysis as composite data. A further complication arises when data are not normally distributed, rather their logarithm is. When composite sampling is used for such lognormal data, the sample support affects not only the variance but also the mean. We give the theory for normally distributed variables, and also derive an approximation that can be used when the point-support variable is lognormal. We focus on this latter case, and test the approach with a series of simulation experiments. Finally, we illustrate the approach on a dataset of soil organic carbon (SOC) values from a grazing property in Queensland, Australia, where soil information from two measurement phases was obtained on different supports.