Exploring the World of Ordinary Kriging. Dennis J. J. Walvoort. Wageningen University & Research Center Wageningen, The Netherlands
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1 Exploring the World of Ordinary Kriging Wageningen University & Research Center Wageningen, The Netherlands July 2004 (version 0.2)
2 What is? What is it about? Potential Users 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!
3 What is? What is it about? Potential Users 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!
4 What is? What is it about? Potential Users 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!
5 Who may benefit from it? What is it about? Potential Users 1 Students, who need to understand those mysterious kriging equations; 2 Lecturers, who want to explain kriging in an intuitive way; 3 Others, who just want to know what they are doing when using geostatistical software.
6 Who may benefit from it? What is it about? Potential Users 1 Students, who need to understand those mysterious kriging equations; 2 Lecturers, who want to explain kriging in an intuitive way; 3 Others, who just want to know what they are doing when using geostatistical software.
7 Who may benefit from it? What is it about? Potential Users 1 Students, who need to understand those mysterious kriging equations; 2 Lecturers, who want to explain kriging in an intuitive way; 3 Others, who just want to know what they are doing when using geostatistical software.
8 (GUI) Data Configuration Panel Semivariogram Panel Kriging Panel The GUI consists of three panels: 1 data configuration panel 2 semivariogram panel 3 kriging panel
9 (GUI) Data Configuration Panel Semivariogram Panel Kriging Panel The GUI consists of three panels: 1 data configuration panel 2 semivariogram panel 3 kriging panel
10 (GUI) Data Configuration Panel Semivariogram Panel Kriging Panel The GUI consists of three panels: 1 data configuration panel 2 semivariogram panel 3 kriging panel
11 (GUI) Data Configuration Panel Semivariogram Panel Kriging Panel The GUI consists of three panels: 1 data configuration panel 2 semivariogram panel 3 kriging panel
12 Data Configuration Panel Data Configuration Panel Semivariogram Panel Kriging Panel The prediction point is red and labelled 0.
13 Data Configuration Panel Data Configuration Panel Semivariogram Panel Kriging Panel The n sampling points are blue and labelled from 1 to n.
14 Data Configuration Panel Data Configuration Panel Semivariogram Panel Kriging Panel The configuration of points can be changed by means of the mouse (drag n drop).
15 Data Configuration Panel Data Configuration Panel Semivariogram Panel Kriging Panel The range is represented by a solid circle. A dashed circle represents the practical range. definition
16 Data Configuration Panel Data Configuration Panel Semivariogram Panel Kriging Panel The number of sampling points has to be specified here (see ellipse).
17 Data Configuration Panel Data Configuration Panel Semivariogram Panel Kriging Panel The values at the sampling locations have to be entered here.
18 Semivariogram Panel Data Configuration Panel Semivariogram Panel Kriging Panel The following semivariogram models can be selected: Spherical model details Exponential model details Gaussian model details
19 Semivariogram Panel Data Configuration Panel Semivariogram Panel Kriging Panel Use the sliders to set the semivariogram parameters: nugget (c 0 ) partial sill (c 1 ) range parameter (a)
20 Semivariogram Panel Data Configuration Panel Semivariogram Panel Kriging Panel This section gives the nugget variance, the (practical) range and the sill variance (c 0 + c 1 ).
21 Semivariogram Panel Data Configuration Panel Semivariogram Panel Kriging Panel The resulting semivariogram will be shown here.
22 Kriging Panel Introduction Data Configuration Panel Semivariogram Panel Kriging Panel The ordinary kriging weights are shown as bars. Click on the bars for numerical values.
23 Kriging Panel Introduction Data Configuration Panel Semivariogram Panel Kriging Panel Use the radiobuttons to switch between ordinary point kriging and ordinary block kriging.
24 Kriging Panel Introduction Data Configuration Panel Semivariogram Panel Kriging Panel The block size can be set by means of the sliders.
25 Kriging Panel Introduction Data Configuration Panel Semivariogram Panel Kriging Panel Check this checkbox to enforce square prediction blocks.
26 Kriging Panel Introduction Data Configuration Panel Semivariogram Panel Kriging Panel The ordinary kriging prediction and the associated variance of the prediction error are given here.
27 Kriging Panel Introduction Data Configuration Panel Semivariogram Panel Kriging Panel Press this button to get a glimpse of the underlying maths.
28 Effects of sampling point configuration Effect of semivariogram Distance effect Discover that points outside the range affect predictions differently than points within the range (cf. inverse squared distance interpolation).
29 Effects of sampling point configuration Effect of semivariogram Declustering effect Discover how ordinary kriging reduces the influence of clustered sampling points (cf. inverse squared distance interpolation).
30 Effects of sampling point configuration Effect of semivariogram Screening effect Recall that ordinary kriging is a non-convex interpolator, i.e., its predictions can be outside the data range. Explore data configurations and semivariogram settings that enhance this effect.
31 Effects of sampling point configuration Effect of semivariogram Effect of data values Discover how data values affect the weights, the prediction and the variance of the prediction error.
32 Effects of sampling point configuration Effect of semivariogram Effect of semivariogram model Study how model shape, nugget, sill and range affect the kriging results.
33 Effects of sampling point configuration Effect of semivariogram Effect of semivariogram model Study how model shape, nugget, sill and range affect the kriging results.
34 Effects of sampling point configuration Effect of semivariogram Effect of semivariogram model Study how model shape, nugget, sill and range affect the kriging results.
35 Effects of sampling point configuration Effect of semivariogram Effect of semivariogram model Study how model shape, nugget, sill and range affect the kriging results.
36 Effects of sampling point configuration Effect of semivariogram Effect of semivariogram model Study how model shape, nugget, sill and range affect the kriging results.
37 Effects of sampling point configuration Effect of semivariogram Effect of semivariogram scale Explore how multiplying the semivariogram by a positive value affects the kriging weights, the kriging prediction, and the variance of the prediction error.
38 Effects of sampling point configuration Effect of semivariogram Effect of semivariogram scale Explore how multiplying the semivariogram by a positive value affects the kriging weights, the kriging prediction, and the variance of the prediction error.
39 Effects of sampling point configuration Effect of semivariogram Effect of semivariogram scale Explore how multiplying the semivariogram by a positive value affects the kriging weights, the kriging prediction, and the variance of the prediction error.
40 Effects of sampling point configuration Effect of semivariogram Effect of semivariogram scale Explore how multiplying the semivariogram by a positive value affects the kriging weights, the kriging prediction, and the variance of the prediction error.
41 Effects of sampling point configuration Effect of semivariogram Effect of semivariogram scale Explore how multiplying the semivariogram by a positive value affects the kriging weights, the kriging prediction, and the variance of the prediction error.
42 Effects of sampling point configuration Effect of semivariogram Effect of semivariogram scale Explore how multiplying the semivariogram by a positive value affects the kriging weights, the kriging prediction, and the variance of the prediction error.
43 Effects of sampling point configuration Effect of semivariogram Effect of semivariogram scale Explore how multiplying the semivariogram by a positive value affects the kriging weights, the kriging prediction, and the variance of the prediction error.
44 Effects of sampling point configuration Effect of semivariogram Experiment with block size and see how it affects the kriging results.
45 Effects of sampling point configuration Effect of semivariogram Experiment with block size and see how it affects the kriging results.
46 Effects of sampling point configuration Effect of semivariogram Experiment with block size and see how it affects the kriging results.
47 Effects of sampling point configuration Effect of semivariogram Experiment with block size and see how it affects the kriging results.
48 Effects of sampling point configuration Effect of semivariogram Experiment with block size and see how it affects the kriging results.
49 Effects of sampling point configuration Effect of semivariogram Experiment with block size and see how it affects the kriging results.
50 Effects of sampling point configuration Effect of semivariogram Experiment with block size and see how it affects the kriging results.
51 Suggestions for further reading Further reading Geostatistical software License E.H. Isaaks and R.M. Srivastava. An Introduction to Applied Geostatistics. Oxford University Press, New York, P. Goovaerts. Geostatistics for Natural Resources Evaluation. Oxford University Press, New York, 1997.
52 Geostatistical software Further reading Geostatistical software License Vesper ( GStat ( GStat is also available as R-package (
53 Further reading Geostatistical software License License is freeware and provided as is without warranty of any kind, either express or implied.
54 Further reading Geostatistical software License Enjoy!
55 Definitions Spherical model γ s (h) = { 3h 2a 1 ( h ) 3 2 a h < a 1 h a γ(h) = c 0 + c 1 γ s (h) where: a : c 0 : c 1 : h : γ s γ range parameter nugget variance partial sill variance lag distance standardised semivariance semivariance Return
56 Definitions Exponential model γ s (h) = 1 exp ( h ) a γ(h) = c 0 + c 1 γ s (h) where: a : c 0 : c 1 : h : γ s γ range parameter nugget variance partial sill variance lag distance standardised semivariance semivariance Return
57 Definitions Gaussian model γ s (h) = 1 exp ( h2 a 2 γ(h) = c 0 + c 1 γ s (h) ) where: a : c 0 : c 1 : h : γ s γ range parameter nugget variance partial sill variance lag distance standardised semivariance semivariance Return
58 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
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