e{z}-kriging - exploring the world of ordinary kriging · introduction graphical user interface...

E{Z}-KrigingExploring the World of Ordinary Kriging

Dennis J. J. Walvoort

Wageningen University & Research CenterWageningen, The Netherlands

July 2004 (version 0.2)

IntroductionGraphical User Interface

Interesting features to exploreConcluding Remarks

What is it about?Potential Users

What is E{Z}-Kriging?

a computer program for exploring ordinary kriging;

interactive, self-explanatory, and easy to use.Hence, ‘easy kriging’

and last but not least: it’s freeware!

Dennis J. J. Walvoort E{Z}-Kriging

Who may benefit from it?

1 Students, who need to understand those ‘mysterious’ krigingequations;

2 Lecturers, who want to explain kriging in an intuitive way;

3 Others, who just want to know what they are doing whenusing geostatistical software.

Data Configuration PanelSemivariogram PanelKriging Panel

Graphical User Interface (GUI)

The GUI consists of threepanels:

1 data configurationpanel

2 semivariogram panel

3 kriging panel

Data Configuration Panel

The prediction point isred and labelled 0.

The n sampling pointsare blue and labelledfrom 1 to n.

The configuration ofpoints can be changedby means of the mouse(drag ’n’ drop).

The range isrepresented by a solidcircle. A dashed circlerepresents the practicalrange.

definition

The number ofsampling points has tobe specified here (seeellipse).

The values at thesampling locations haveto be entered here.

Semivariogram Panel

The followingsemivariogram modelscan be selected:

Spherical modeldetails

Exponential modeldetails

Gaussian modeldetails

Semivariogram Panel

Use the sliders to setthe semivariogramparameters:

nugget (c0)

partial sill (c1)

range parameter (a)

Semivariogram Panel

This section gives thenugget variance, the(practical) range and thesill variance (c0 + c1).

Semivariogram Panel

The resultingsemivariogram will beshown here.

Kriging Panel

The ordinary krigingweights are shown asbars. Click on the barsfor numerical values.

Kriging Panel

Use the radiobuttons toswitch between ordinarypoint kriging andordinary block kriging.

Kriging Panel

The block size can beset by means of thesliders.

Kriging Panel

Check this checkboxto enforce squareprediction blocks.

Kriging Panel

The ordinary krigingprediction and theassociated variance ofthe prediction error aregiven here.

Kriging Panel

Press this button toget a glimpse of theunderlying maths.

Effects of sampling point configurationEffect of semivariogramEffect of aggregation

Interesting features to explore

Distance effect

Discover that points outside the rangeaffect predictions differently than pointswithin the range (cf. inverse squareddistance interpolation).

Declustering effect

Discover how ordinary kriging reduces theinfluence of clustered sampling points (cf.inverse squared distance interpolation).

Screening effect

Recall that ordinary kriging is a non-convexinterpolator, i.e., its predictions can beoutside the data range. Explore dataconfigurations and semivariogram settingsthat enhance this effect.

Effect of data values

Discover how data values affect theweights, the prediction and the variance ofthe prediction error.

Effect of semivariogram model

Study how model shape, nugget, sill andrange affect the kriging results.

Effect of semivariogram scale

Explore how multiplying the semivariogramby a positive value affects the krigingweights, the kriging prediction, and thevariance of the prediction error.

Effect of aggregation

Experiment with block size and see how itaffects the kriging results.

Further readingGeostatistical softwareLicense

Suggestions for further reading

E.H. Isaaks and R.M. Srivastava.An Introduction to Applied Geostatistics.Oxford University Press, New York, 1989.

P. Goovaerts.Geostatistics for Natural Resources Evaluation.Oxford University Press, New York, 1997.

Geostatistical software

Vesper (www.usyd.edu.au/su/agric/acpa/vesper/vesper.html)

GStat (www.gstat.org),GStat is also available as R-package (www.r-project.org)

License

E{Z}-Kriging is freeware and provided as is without warranty ofany kind, either express or implied.

Enjoy E{Z}-Kriging!

Definitions

Spherical model

γs(h) =

{3h2a −

)3 ∀ h < a1 ∀ h ≥ a

γ(h) = c0 + c1γs(h)

where:a : range parameterc0 : nugget variancec1 : partial sill varianceh : lag distanceγs standardised semivarianceγ semivariance

Return

Definitions

Exponential model

γs(h) = 1− exp

γ(h) = c0 + c1γs(h)

Return

Definitions

Gaussian model

γs(h) = 1− exp

(−h2

)γ(h) = c0 + c1γs(h)

Return

Definitions

Practical range

Lag h for which γ(h) = 0.95γ(∞),i.e., that distance at which the semivariance is 95% of the sill.

Return

e{z}-kriging - exploring the world of ordinary kriging · introduction graphical user interface...

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