Understandably soil properties of scientific nature vary continuously in space and time, and as such it is a very difficult if not impossible process to measure soil variables at every point in space. Thus, in order to represent the spatial variation of soil properties in nature, sample points have to be used. However deciding on the sampling design is another challenge because of complexity, variability and dynamic processes of nature. To minimize errors, sample points need to be dispersed strategically over the study area to ensure representativity of phenomena to be measured in the area. In spatial analysis sampling is often performed on regular grid or irregular set of points which however might not depict the true variation of the studied phenomena in space. Nonetheless at the present moment this is one of the only few feasible and economical methods to study soil spatial variability. In general stratified random sampling is often recommended for spatial analysis.
Based on the sampled data values, estimated values are assigned in all other unsampled locations to define spatial variation of the phenomena. Geostatistics is largely the application of this theory, and provides a set of stochastic techniques that account for both random and structured nature of spatial variables, the spatial distribution of sampling sites and the uniqueness of any spatial observation. The most important and common tool of geostatistics is the interpolation process which relies on estimation and prediction. Interpolation process is based on the fact that objects that are nearer to each other are more related or similar in behavior than those that are far apart. As such the output of the interpolation process is influenced by the number and distribution of sampled points, physiographic setup of the study area, and understanding of spatial variation of the phenomena. There are a number of interpolation methods available but the most commonly used method in GIS is Kriging. Different authors have used this technique in comparing between different spatial prediction methods, as well as between different kriging methods since kriging itself has different methods (e.g. ordinary kriging, universal kriging, simple, co-kriging, kriging with external drift, etc). Nonetheless, Luan and Quang classify spatial prediction (interpolation) methods into three main groups:
Local interpolation which is usually based on arithmetic average weights of nearest points.
Global interpolation, of which the common approach is trend surface analysis
Interpolation by kriging which is based on both surface analysis and average weights methods. The surface analysis finds a mathematical formula for describing the general trend without taking into account local variation. The average weights method is used to calculate deviation from global trend and considers variation due to local irregularities.
Hengl[36] has also classified spatial prediction models into two groups based on the amount of statistical analysis involved:
Mechanical/Empirical models: where arbitrary or empirical model parameters are used without estimation of model error and strict consideration of variability of a feature. The most common techniques include but not limited to, Thiessen polygon, inverse distance weighting, regression on coordinates and spline.
Statistical/Probability models: where models parameters are estimated objectively following the probability theory. The prediction outputs are accompanied by the estimate of prediction error. Four groups of statistical models are mentioned by Hengl here including Kriging (plain geostatistics), environmental correlation (regression based), Bayesian-based models and mixed models (regression-kriging).
In general the mechanical prediction models are comparatively more flexible and easy to use than statistical models but are considered primitive and often sub-optimal. The statistical models follow several statistical data analysis steps making the mapping process more complicated. Moreover the input datasets need to satisfy strict statistical assumptions. Nevertheless, these models produce more reliable and objective maps, can reveal sources of errors, and depict problematic areas, and are thus more preferred in the scientific fraternity. In the present study more emphasis will be given on Kriging.
References
Hengl, T., A Practical Guide to Geostatistical Mapping of Environmental Variables. Vol. 2007, Italy: Luxembourg: Office for Official Publications of the European Communities.
Luan Truong Xuan and Q.T. Xuan. Geostatistics combined with the function of interpolation in GIS. in International Symposium on Geoinformatics for Spatial Infrastructure Development in Earth and Allied Sciences. 2004: Hanoi University of Mining and Geology, Dong Ngac, Tu Liem, Hanoi.
Metternicht, G.I. and J.A. Zinck, Remote sensing of soil salinity: potentials and constraints. Remote Sensing of Environment, 2003. 85(1): p. 1-20
Navarro-Pedre?o , J. et al., Estimation of soil salinity in semi-arid land using a geostatistical model. Land Degradation & Development, 2007. 18(3):
p. 339-353.
Siska Peter P. and H. I-Kuai, Assessment of Kriging Accuracy in the GIS Environment, College of Forestry, Stephen F. Austin University.
Triantafilis, J., I.O.A. Odeh, and A.B. McBratney, Five Geostatistical Models to Predict Soil Salinity from Electromagnetic Induction Data Across Irrigated Cotton. Soil Sci Soc Am J, 2001. 65(3): p. 869-878.
Development of Methodologies for
Land Degradation Assessment Applied to
Land Use Planning in Thailand
Hengl, T., A Practical Guide to Geostatistical Mapping of Environmental Variables. Vol. 2007, Italy: Luxembourg: Office for Official Publications of the European Communities.