Accounting for sample support in geostatistical analyses of soil properties

Abstract

The support of a soil sample defines the size and shape of the volume of soil material that is collected and then analysed to give a single datum. This includes both the horizontal and vertical dimensions of the sampled material. For instance, in the vertical dimension some samples might be collected over 10-cm intervals, whilst others might be over 30-cm intervals, giving data with different supports. In horizontal space, data might represent the value of a soil property in a single soil core, whilst others might be measurements of a sample composed of multiple composited soil cores collected from locations across a sampling unit. Support can refer to that on which the data are collected, or to that on which predictions are required, and in both cases can play an important role in mapping soil properties. Generally, the larger the extent of the sample support, the more variation is averaged out of the data. Hence composite soil samples are often collected to reduce noise in the data, and predictions calculated on block support to produce smoother maps. Geostatistical approaches have proven to be extremely useful for modelling and mapping the spatial distributions of soil properties, although they have most commonly been applied under the assumption that the sample supports of all data are identical. In this thesis, we investigate some aspects of sample support, and how data from different sample supports might be used in the same geostatistical analysis. We consider four specific types of support, two where the data differ in their vertical supports, and two where they differ in their horizontal supports. Our general strategy is to employ a model-based geostatistical approach, based on the formulation of a statistical model that describes the distribution of all raw measurements whilst accounting for their different supports. This same statistical model is also applied for prediction, again accounting for prediction sample support. Our aim in each research chapter is to describe and test methods that can adequately deal with each sample-support issue, and to investigate whether the proposed methods can be used to analyse such data and give (i) reliable inference, (ii) competitive predictions when compared with existing methods and (iii) a fair assessment of prediction uncertainty.