Kerry: As long the variogram model is concave upwards and increasing (i.e. no hole effect), the kriging variance will increase as you move away from existing sample points. So it will depend upon the model that you use and the location of the sample points. If the fitted variogram model is steeper than another one, the kriging variance will increase faster as you move away from existing points.
Since it is simply a function of distance, there are a lot of anologies with location-allocation problems, such as for maximin problems for instance. In the case of spatial sampling where you would like to add a new sample to an existing set, the problem consists of the minimum distance to the closest existing sampling point (locating obnoxious facilities for instance). Let me know if this helps, and I could guide you with some references. Try also those references: Webster R. and T.M. Burgess (1984). Sampling and bulking strategies for estimating soil properties of small regions. Journal of Soil Science, vol. 35: 127-140. Yfantis E.A., Flatman G.T. and J.V. Behar (1987). Efficiency of kriging estimation for square, triangular and hexagonal grids. Mathematical Geology, vol. 19: 183-205. Van Groenigen J.W., Siderius W. and A. Stein (1999). Constrained optimisation of soil sampling for minimisation of the kriging variance. Geoderma vol. 87: 239-259. Arbia G. (1994). Selection techniques in sampling spatial units. Quaderni di Statistica e Matematica Applicata Alle Scienze Economico-Sociali, vol. 16: 81-91. Delmelle (2005). Optimization of Second-Phase Spatial Sampling Using Auxiliary Information, Ph.D. Dissertation, Department of Geography, SUNY at Buffalo http://www.uidaho.edu/~delmelle/RES/PHD-DISSERTATION.pdf Good luck Eric. -- Assistant Professor Department of Geography McClure Hall 305A University of Idaho Moscow, ID 83844 Phone: (208) 885-6452 Email: [EMAIL PROTECTED] www.uidaho.edu/~delmelle -- -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of Kerry Ritter Sent: Thursday, August 10, 2006 3:16 PM To: [email protected] Subject: AI-GEOSTATS: kriging variance as a function of sampling density Hi. I am looking for a simple way to compute the kriging variance as a function of distance between sampling sites for a given spherical and exponential semivariogram. I know that these variances do not depend on the data values, but on location. Thus, it seems like this would be a common enough task where one would use this curve for completing a cost-efficiency analyzes with regard to sample spacing. I currently use Splus/R. Thaniks, Kerry + + To post a message to the list, send it to [email protected] + To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/ + + To post a message to the list, send it to [email protected] + To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
