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# SASA 2011 presentation

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### SASA 2011 presentation

1. 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. 2. OUTLINE1. Introduction o Geostatistics o Model-based geostatistics1. Spatial prediction & Kriging o Model-based approach o Kriging predictor & variance o Estimation of parameters1. Case Study o Description o Motivation for study o Analysis1. Conclusions
3. 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
4. 4. SPATIAL PREDICTION & KRIGING
5. 5.  2.1 Model-based approach
6. 6.  2.2 Kriging predictor & variance
7. 7.  2.3 Estimation of parameters 0.70 0.65 0.60 semivariance 0.55 0.50 0.45 0.40 0.0 0.5 1.0 1.5 2.0 2.5 distance
8. 8. 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
9. 9. STUDY AREA
10. 10.  3.3 Analysis -25 -26 1.827 North (km) 7.086 12.5 20.186 -27 236.85 -28 -29 27 28 29 30 East (km)
11. 11. Y Coord data -29 -28 -27 -26 -25 0 50 100 150 200 27 27 28 28 X Coord X Coord 29 29 30 30 31 31 Density 0.00 0.01 0.02 0.03 Y Coord -29 -28 -27 -26 -25 0 0 50 50 100 100data data 150 150 200 200
12. 12. Y Coord data -29 -28 -27 -26 -25 1 2 3 4 5 27 27 28 28 X Coord X Coord 29 29 30 30 31 31 Density 0.0 0.1 0.2 0.3 0.4 0.5 Y Coord -29 -28 -27 -26 -25 1 1 2 2 3 3data data 4 4 5 5
13. 13. 0.70 0.65 0.60semivariance 0.55 0.50 exponential matern (kappa=1.5) 0.45 matern (kappa=2.5) spherical gaussian 0.0 0.5 1.0 1.5 2.0 2.5 distance
14. 14. ESTIMATES OF PARAMETERS FOR FITTED ORDINARY KRIGING MODELS
15. 15. PROFILE LOG-LIKELIHOODS OF ESTIMATED PARAMETERS OF BEST MODEL
16. 16. LOG SCALE KRIGING PREDICTIONS 3.5 -25 3.0 -26 KRIGING VARIANCESY Coord -27 0.64 2.5 -25 0.62 -28 -26 0.60 2.0 Y Coord -29 0.58 27 28 29 30 -27 X Coord 0.56 -28 0.54 0.52 -29 27 28 29 30 X Coord
17. 17. ORIGINAL SCALE KRIGING PREDICTIONS 50 -25 40 -26 KRIGING VARIANCESY 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
18. 18. 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
19. 19. 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.