A Spatial Statistical Analysis of Geochemical Data in the Soil of ASA Experimental Forest

Malin Jönsson

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology
Lund University

Detecting soil properties are today of major interest due to various reasons such as preventing acidification of certain areas, detecting contaminated land areas, and optimizing agriculture and forestry. The problem associated with examining soil is the spatial variability of soil properties. Hence, a good interpolation method is needed to minimize the number of sampling points in a specified area.

In this study the interpolation method kriging is used to examine the soil properties of Asa experimental forest. The kriging technique uses a weighted linear combination of known points to predict unknown points by minimizing the estimation error. Kriging depends on a so-called variogram function, which describes the spatial variation of the investigated variable. The variogram function determines the weights used when predicting the map of the investigated soil property. This method was used to investigating the Asa forest, situated 40 km north of Växjö in Southern Sweden (57o08'N and 14o47' E).

In the investigated area, 94 pits were dug in which samples were taken from the B/C- or C-horizon and analysed with respect to the elemental concentrations (Al, Ca, Cu, Fe, K, Mg, Mn, Na, Ni, P, Si, Ti, Zn, and Zr).

The aim of the study is to produce predicted maps of the elemental concentrations in the investigated area by using the kriging technique. However, the study also aims to determine which properties effect the kriging method and thereby set up a procedure of the kriging technique. A simulation of Ca data based on the modelled data of Asa forest has also been done as an attempt to estimate the minimum number of points needed to perform a kriging interpolation.

The result of this report indicates variogram modelling to be very sensitive to so-called outliers. Variogram modelling have been performed on two different data sets of Ca concentrations, one including all sample points and one data set excluding two outliers. The result suggests that the sampling grid used for detecting Ca should have minimum spacings of less than 2000 m when using the complete data set, whereas Ca data of excluded outliers suggests that minimum spacings should be less than 200 m. Furthermore minimum spacings for detecting Al should be less than 500 m and 200 m for K, Mg and Ti. The elements Fe, Mn, Na, Si and Zr have shown to need very high sampling densities. In fact, the existent data sets from the Asa forest do not have a sufficiently close grid of sampling pints to estimate the variogram function. Hence kriging interpolation was not performed for Fe, Mn, Na, Si and Zr. The results of the simulations of Ca data have shown the minimum number of points needed for kriging prediction, on an area of the same size as the Asa area, to be approximately 25. Furthermore the estimation error of the kriging method has been shown to decreases for increasing number of points up to 80-100 points, after which the estimation error does not improve much.