Kriging

Determining the kriging parameters

The kriging algorithm estimates concentration over a regular grid across the site, and the sum of the kriging weights are used to determine the overall weight assigned to each data point. For a particular grid location, the surrounding data points within a specified search window are used to calculate the estimated concentration. The kriging parameters define that grid and search window, and determine how the kriged estimates are calculated.

Grid size:

Determines the resolution of the concentration estimate map. The ideal choice depends on the application and the data distribution, but it's important to ensure that the grid size is not too small relative to site size, since that would require a large number of estimates to be calculated and could result in a long execution time.

Kriging type:

Ordinary kriging re-estimates the mean within the local search area, this can help account for trends in the data. Simple kriging uses a constant, site-wide mean, so should only be used if the data distribution and variogram support that assumption.

Number of points to use:

Minimum and maximum number of data points within the search window to be used in kriging each estimate. If there isn't at least the minimum number of points within the search ellipse, no estimate will be calculated. The maximum number of points to use can also be specified to limit the computational time required. Larger maximum numbers increase the size of the matrices that are inverted for the estimation of each grid node, which increases the computational time.

Block kriging:

Estimates concentrations for blocks of a specified size instead of a grid of points. Point kriging is more commonly used in environmental applications

Octant search:

If octant search is enabled, the search ellipse is divided into eight equal-angle sectors, and only the specified maximum number of points from each octant will be used.

Search ellipsoid:

These parameters determine how far out to search for data to support a particular kriged estimate.

Max and min horizontal radii:

These are the semi-major and semi-minor axes of the search ellipse, respectively. They each should be greater than the range of the variogram model. These values should only need to differ (i.e. define an ellipse instead of a circle) if anisotropy is present. Changing the azimuth angle defining the orientation of the search ellipsoid is also only necessary for a site with anisotropy.

Create map contours

Check this box to automatically create contours of the kriged data when it is applied to the map.

References:

Cameron, K, and P Hunter. 2002. Using Spatial Models and Kriging Techniques to Optimize Long-Term Ground-Water Monitoring Networks: A Case Study. Environmetrics 13:629-59.

Deutsch, C.V. and A.G. Journel. 1998. GSLIB Geostatistical Software Library and User's Guide, 2nd Edition, Applied Geostatistics Series, Oxford University Press, Inc. New York, NY.

Gilbert, RO. 1987. Statistical Methods for Environmental Pollution Monitoring. Van Nostrand Reinhold, New York.

Isaaks, EH, and RM Srivastava. 1989. An Introduction to Applied Geostatistics. Oxford University Press, New York.

Webster, R, and MA Oliver. 1993. How Large a Sample Is Needed to Estimate the Regional Variogram Adequately? . Geostatistics Troia '92 , ed. A Soares, Vol 1, pp. 155-66. Kluwer Academic Publishers, Dordrecht.