“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.

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