E{Z }-Kriging
Exploring the World of Ordinary Kriging Dennis J. J. Walvoort
Wageningen University & Research Center Wageningen, The Netherlands
July 2004 (version 0.2)
Introduction Graphical User Interface Interesting features to explore Concluding 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: its freeware!
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding 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: its freeware!
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding 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: its freeware!
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
What is it about? Potential Users
Who may benet from it?
Students, who need to understand those mysterious kriging equations; Lecturers, who want to explain kriging in an intuitive way; Others, who just want to know what they are doing when using geostatistical software.
2 3
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
What is it about? Potential Users
Who may benet from it?
Students, who need to understand those mysterious kriging equations; Lecturers, who want to explain kriging in an intuitive way; Others, who just want to know what they are doing when using geostatistical software.
2 3
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
What is it about? Potential Users
Who may benet from it?
Students, who need to understand those mysterious kriging equations; Lecturers, who want to explain kriging in an intuitive way; Others, who just want to know what they are doing when using geostatistical software.
2 3
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Graphical User Interface (GUI)
The GUI consists of three panels:
1
data conguration panel semivariogram panel kriging panel
2 3
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Graphical User Interface (GUI)
The GUI consists of three panels:
1
data conguration panel semivariogram panel kriging panel
2 3
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Graphical User Interface (GUI)
The GUI consists of three panels:
1
data conguration panel semivariogram panel kriging panel
2 3
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Graphical User Interface (GUI)
The GUI consists of three panels:
1
data conguration panel semivariogram panel kriging panel
2 3
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Data Conguration Panel
The prediction point is red and labelled 0.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Data Conguration Panel
The n sampling points are blue and labelled from 1 to n.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Data Conguration Panel
The conguration of points can be changed by means of the mouse (drag n drop).
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Data Conguration Panel
The range is represented by a solid circle. A dashed circle represents the practical range.
denition
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Data Conguration Panel
The number of sampling points has to be specied here (see ellipse).
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Data Conguration Panel
The values at the sampling locations have to be entered here.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Semivariogram Panel
The following semivariogram models can be selected: Spherical model
details
Exponential model
details
Gaussian model
details
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Semivariogram Panel
Use the sliders to set the semivariogram parameters: nugget (c0 ) partial sill (c1 ) range parameter (a)
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Semivariogram Panel
This section gives the nugget variance, the (practical) range and the sill variance (c0 + c1 ).
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Semivariogram Panel
The resulting semivariogram will be shown here.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Kriging Panel
The ordinary kriging weights are shown as bars. Click on the bars for numerical values.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Kriging Panel
Use the radiobuttons to switch between ordinary point kriging and ordinary block kriging.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Kriging Panel
The block size can be set by means of the sliders.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Kriging Panel
Check this checkbox to enforce square prediction blocks.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Kriging Panel
The ordinary kriging prediction and the associated variance of the prediction error are given here.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Data Conguration Panel Semivariogram Panel Kriging Panel
Kriging Panel
Press this button to get a glimpse of the underlying maths.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Distance eect Discover that points outside the range aect predictions dierently than points within the range (cf. inverse squared distance interpolation).
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Declustering eect Discover how ordinary kriging reduces the inuence of clustered sampling points (cf. inverse squared distance interpolation).
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Screening eect Recall that ordinary kriging is a non-convex interpolator, i.e., its predictions can be outside the data range. Explore data congurations and semivariogram settings that enhance this eect.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of data values Discover how data values aect the weights, the prediction and the variance of the prediction error.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of semivariogram model Study how model shape, nugget, sill and range aect the kriging results.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of semivariogram model Study how model shape, nugget, sill and range aect the kriging results.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of semivariogram model Study how model shape, nugget, sill and range aect the kriging results.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of semivariogram model Study how model shape, nugget, sill and range aect the kriging results.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of semivariogram model Study how model shape, nugget, sill and range aect the kriging results.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of semivariogram scale Explore how multiplying the semivariogram by a positive value aects the kriging weights, the kriging prediction, and the variance of the prediction error.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of semivariogram scale Explore how multiplying the semivariogram by a positive value aects the kriging weights, the kriging prediction, and the variance of the prediction error.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of semivariogram scale Explore how multiplying the semivariogram by a positive value aects the kriging weights, the kriging prediction, and the variance of the prediction error.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of semivariogram scale Explore how multiplying the semivariogram by a positive value aects the kriging weights, the kriging prediction, and the variance of the prediction error.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of semivariogram scale Explore how multiplying the semivariogram by a positive value aects the kriging weights, the kriging prediction, and the variance of the prediction error.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of semivariogram scale Explore how multiplying the semivariogram by a positive value aects the kriging weights, the kriging prediction, and the variance of the prediction error.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of semivariogram scale Explore how multiplying the semivariogram by a positive value aects the kriging weights, the kriging prediction, and the variance of the prediction error.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of aggregation Experiment with block size and see how it aects the kriging results.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of aggregation Experiment with block size and see how it aects the kriging results.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of aggregation Experiment with block size and see how it aects the kriging results.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of aggregation Experiment with block size and see how it aects the kriging results.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of aggregation Experiment with block size and see how it aects the kriging results.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of aggregation Experiment with block size and see how it aects the kriging results.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Eects of sampling point conguration Eect of semivariogram Eect of aggregation
Interesting features to explore
Eect of aggregation Experiment with block size and see how it aects the kriging results.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Further reading Geostatistical software License
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.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Further reading Geostatistical software License
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)
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Further reading Geostatistical software License
License E{Z }-Kriging is freeware and provided as is without warranty of any kind, either express or implied.
Dennis J. J. Walvoort
E{Z }-Kriging
Introduction Graphical User Interface Interesting features to explore Concluding Remarks
Further reading Geostatistical software License
Enjoy E{Z }-Kriging!
Dennis J. J. Walvoort
E{Z }-Kriging
Denitions
Spherical model
s (h) =
3h 2a
1 2
h 3 a
h<a ha
(h) = c0 + c1 s (h)
where: a: c0 : c1 : h: s
range parameter nugget variance partial sill variance lag distance standardised semivariance semivariance
Return
Dennis J. J. Walvoort
E{Z }-Kriging
Denitions
Exponential model
h s (h) = 1 exp a (h) = c0 + c1 s (h)
where: a: c0 : c1 : h: s
range parameter nugget variance partial sill variance lag distance standardised semivariance semivariance
Return
Dennis J. J. Walvoort
E{Z }-Kriging
Denitions
Gaussian model
h2 s (h) = 1 exp 2 a (h) = c0 + c1 s (h)
where: a: c0 : c1 : h: s
range parameter nugget variance partial sill variance lag distance standardised semivariance semivariance
Return
Dennis J. J. Walvoort
E{Z }-Kriging
Denitions
Practical range Lag h for which (h) = 0.95 (), i.e., that distance at which the semivariance is 95% of the sill.
Return
Dennis J. J. Walvoort
E{Z }-Kriging
