1. THE MODEL-BASED APPROACH TO
GEOSTATISTICAL ANALYSIS:
A Case Study of Micro-Nutrient Content in the Soils of the
Witwatersrand Area
Mzabalazo Z. Ngwenya a, Christien Thiart b & Linda M. Haines b
a
Biometry Unit, Agricultural Research Council (ARC),
b
Department of Statistical Sciences, University of Cape Town (UCT)
2. OUTLINE
1. Introduction
o Geostatistics
o Model-based geostatistics
1. Spatial prediction & Kriging
o Model-based approach
o Kriging predictor & variance
o Estimation of parameters
1. Case Study
o Description
o Motivation for study
o Analysis
1. Conclusions
3. INTRODUCTION
1.1 Geostatistics:
The branch of spatial statistics concerned with continuous
spatial variation
Traditional geostatistics developed largely independently
outside mainstream spatial statistics hence the approach
lacks statistical rigor
1.2 Model-based Geostatistics:
The application of formal statistical methods of modeling
and inference to geostatistical problems;
Analyses are carried out under explicitly assumed stochastic
models
12. CASE STUDY
3.1 Description
• 214 soil samples collected at 1000 locations between 2005 &
2008
• Various micronutrients measured; Fe, Zn, Pb, Cd, Co, Cr, Ni,
Mn
3.2 Motivation for study
• Iron (Fe) has important role in plant health. Plays major role in
Energy transfer within plant
Nitrogen fixation
Plant respiration & metabolism
Chlorophyll development & function
• However its accumulation within plant cells can be toxic
21. ORIGINAL SCALE
KRIGING PREDICTIONS
50
-25
40
-26
KRIGING VARIANCES
Y Coord
-27 30
700
-25
-28 20
690
-26 680
-29 10
Y Coord
27 28 29 30 670
X Coord -27
660
-28 650
640
-29
27 28 29 30
X Coord
22. CONCLUSIONS
• Clear methodology
• None of the subjectivity of empirical semivariogram
construction
• Models for kriging selected on the basis of established
statistical criterion
• Can obtain confidence intervals for parameters in models
• Methods extendable to multivariate and non-Gaussian cases
23. REFERENCES
Cressie, N.A.C (1993).
Statistics for Spatial Data (revised edn). John Wiley & Sons, New York.
DeVillers, S. , Thiart, C. & Basson, N.C. (2010).
Identification of sources of environmental lead in South Africa from surface soil
geochemical maps.
Environmental Geochemistry and Health, 32, 451-459.
Diggle, P.J. , Riberio, P.J. & Christensen, O.F. (2003).
An introduction to model-based geostatistics.
In Spatial Statistics and Computational Methods, Møller, J. (ed), Springer, 43-
86.
Diggle, P.J. & Riberio, P.J. (2007).
Model-Based Geostatistics. Springer, New York.
Riberio, P.J. Jr. & Diggle, P. (2001).
geoR: a package for geostatistical analysis.
R News, 2, 14-18.
Schabenberger, O. & Gotway, C.A. (2005).
Statistical Methods for Spatial Data Analysis. Chapman & Hall, New York.