“Application Of Ordinary Point Kriging For
Predicting Pollutant Using Gstat R”
Annisa Nur Falah
Presented on SEAMS School 2016
Spatio Temporal Data Mining and Optimization Modeling
Universitas Padjadjaran
2016
Kriging is a method of estimation that provides an unbiasedlinear prediction of the values of a point or block. Ordinary pointkriging is one of the most simple kriging method when the averagepopulation is not known which normally applied to the spatial data, forexample Meuse river floodplain. On the Meuse river floodplain arecontaminating metals are cadmium, it is necessary to predict thelocation that contains cadmium. Calculation of cadmium pollutant canuse the software GStat-R in order to obtain accurate results. In thecalculation of prediction with ordinary point kriging method requiredgstat library and sp library and algorithms in GStat-R, to be applied tothe data meuse river floodplain in order to obtain an index prediction ofpollutant in unobserved locations.
Calculation of the index prediction of pollutant using GStat-R is easy,fast and accurate because the average kriging variance minimumresultant. In GStat-R also can display contours showing the locationpollutant are and the content of cadmium pollutant in each location.
Keywords: Ordinary point kriging, GStat-R, floodplain.
Abstract
Introduction
GEOSTATISTICS
SPATIAL
DATA
KRIGING
METHOD
STATIONARY
ORDINARY POINT
KRIGING
CADMIUM
DATA
1. What is the procedure for use of GStat R program
for Ordinary Point Kriging method?
2. How do I determine the content of cadmium
predicted by Ordinary Point Kriging method?
Identifications of Problem
Scope of Problems
1. We use R 3.2.5 for GStat Program.
2. Predicting the content of cadmium with Ordinary
Point Kriging method of order one.
3. The data is used, stationary secondary data
derived from Gstat Program.
Purpose and Objectives
Purpose
Applying GStat program
for prediction the content
of cadmium in unobserved
location with Ordinary
Point Kriging method.
Objectives
To build an algorithm
and procedure of GStat
R using Ordinary Point
Kriging method and to
predict the content of
cadmium pollutant at
Meuse river using
Ordinary Point Kriging
method
• R program is classified as free software.
• Can showing contours clearer.
• Packages used :
Library sp : class and method for point, line, polygon, and the grid .
Library gstat: basic functions for geostatistical analysis of univariate
and multivariate analyzes.
Library plot3D : function to view 2D data and 3D , including a plot
perspective, sliced plots, surface plots and scatter plots .
R PROGRAM
(Bivand, R. Pebesma, E. and Rubio,V. 2013)
Data of Cadmium Pollutant
(R 3.2.5 Program)
Table of Cadmium DataStatistics Descriptive of Cadmium
Data
Source : Dataset from R 3.2.5 Program
Locations x(m) y(m)Cadmium
(ppm)
1 181072 333611 11.7
2 181025 333558 8.6
… … … …
164 180627 330190 2.7
x y Cadmium
Min. 178605 330179 0.7
1st Qu. 179442 331065 1.8
Median 180283 332213 2.9
Mean 180156 332022 4.689
3rd Qu. 180935 332778 7.05
Max. 181390 333611 18.1
Plot Absis and Ordinat The Content of Cadmium
Stationary
178500 179500 180500 181500
330500
331500
332500
333500
plot Absis dan ordinat
x
y
HistogramHistogram
Transformasi Log
Vallue The Experimental Semivariogram
No Np Distance Experimental
Semivariogram
1 57 79.29244 0.6650872
2 299 163.97367 0.8584648
3 419 267.36483 1.0064382
4 457 372.73542 1.1567136
5 547 478.47670 1.3064732
6 533 585.34058 1.5135658
7 574 693.14526 1.6040086
8 564 796.18365 1.7096998
9 589 903.14650 1.7706890
10 543 1011.29177 1.9875659
11 500 1117.86235 1.8259154
12 477 1221.32810 1.8852099
13 452 1329.16407 1.9145967
14 457 1437.25620 1.8505336
15 415 1543.20248 1.8523791
Plot The Experimental Semivariogram
The Experimental Semivariogram
Fitting The Theoritical Semivariogram Model
MSE The Theorit ical Semivariogram Models
Spherical Gaussian Eksponensial
0.001672666 0.002911202 0.0007050954
Prediction of The Content of Cadmium Pollutant Use
Ordinary Point Kriging Method
Locations x y Prediction Error Variance
1 181180 333740 1.5756351481 1.22283792
2 181140 333700 1.8132411584 0.97966064
3 181180 333700 1.6789480445 1.07323860
4 181220 333700 1.5382721781 1.15795371
5 181100 333660 2.1056764901 0.61503208
... ... ... ... ...
3099 179060 329620 1.1220969724 0.99534179
3100 179100 329620 1.1349347771 1.00937419
3101 179140 329620 1.1513120467 1.00085156
3102 179180 329620 1.1701319249 0.95628549
3103 179220 329620 1.1813989083 0.90547905
Contour Prediction of The Content of Cadmium Pollutant
REFERENCES
Anton, H. 1995. Aljabar Linear Elementer (edisi kelima). (Terjemahanoleh Pantur Silaban & I. Nyoman Susila). Jakarta: Erlangga.
Armstrong, M. 1998. Basic Linear Geostatistics. New York: Springer-veriag berlin heidelberg.
Bain & Engelhardt. 1992. Introduction to Probability andMathematical Statistics 2nd Edition. California: Duxbury Press.
Bivand, R. Pebesma, E. and Rubio,V. 2013. Applied Spatial DataAnalysis with R (Second Edition). New York. Springer.
Cressie, N. A. C. 1993. Statistics For Spatial Data. New York: JohnWiley and Sons, Inc. New York.
Olea, R. A. 1999. Geostatistics for engineers and earth scientists.Kluwer Academic Publishers. United States of America.
THANK YOU FOR YOUR
ATTENTION