Estimation of Error and Compliance in Surveys by Kriging
Publication: Journal of Surveying Engineering
Volume 125, Issue 2
Abstract
This paper demonstrates how a geostatistical method called kriging can be used to establish limits on the minimum allowable contour interval (MACI) that complies with National Map Accuracy Standards (NMAS). Kriging works with the same survey point file as ordinarily required by a digital terrain model in a conventional mapping assignment, but extracts more information from the data set. The method is not appropriate for surveys of man-made features, but it is well suited for large surveys of predeveloped parcels and GIS base mapping. Because field surveys are nonrandom samples by design, kriging is unable to calculate a precise compliance contour. However, a suitably narrow interval for the MACI can be determined. Although kriging is not as definitive as a second independent survey, it can offer an effective, expedient, and inexpensive screening tool for assessing NMAS compliance. A detailed example demonstrates application of the proposed kriging method.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Acharya, B., and Chaturvedi, A. (1997). “Digital terrain model: Elevation extraction and accuracy assessment.”J. Surv. Engrg., ASCE, 123(2), 70–77.
2.
Ackermann, F. ( 1987). “Experimental investigation into the accuracy of contouring from DTM.” Photogrammetric Engrg. and Remote Sensing, 44(12), 1537–1548.
3.
Armstrong, M. ( 1984). Common problems seen in variograms. Math. Geol., 16(3), 305–313.
4.
Bras, R. L., and Rodriguez-Iturbe, I. ( 1985). Random functions and hydrology, Addison Wesley, Reading, Mass.,359–425.
5.
Christakos, G. ( 1984). “On the problem of permissible covariance and variogram models.” Water Resour. Res., 20(2), 251–265.
6.
Davis, B. ( 1987). “Uses and abuses of cross-validation in geostatistics.” Math. Geol., 19(3), 241–248.
7.
Davis, M. W., and Culhane, P. G. ( 1984). “Contouring very large data sets using Kriging.” Geostatistics for Natural Resour. Characterizations, Part 2. Reidel, Dortrecht, The Netherlands, 599–619.
8.
Davis, R. E., Foote, F. S., Anderson, J. M., and Mikhail, E. M. ( 1981). Surveying theory and practice. McGraw-Hill, New York, Chap. 13.
9.
Delhomme, J. P. ( 1983). “Kriging in the hydrosciences.” Flow through Porous Media, G. P. Findler, ed., 99–113.
10.
Deutsch, C. V., and Journel, A. G. ( 1992). GSLIB geostatistical software library and user's guide. Oxford Univ. Press, New York, 123–132.
11.
Dowd, P. A. ( 1984). “The variogram and Kriging: Robust and resistant estimators.” Geostatistics for Natural Resour. Characterizations, Part 2. Reidel, Dortrecht, The Netherlands, 91–106.
12.
Georgakakos, A. P., Kitanidis, P. K., Loaiciga, H. A., Olea, R. A., Yates, S. R., and Rouhani, S. (ASCE Task Committee) (1990). “Review of geostatistics in geohydrology I: Basic concepts.”J. Hydr. Engrg., 116(5), 612–632.
13.
Hannah, M. ( 1981). “Error detection and correction in digital terrain models.” Photogrammetric Engineering and Remote Sensing, 47(1), 63–69.
14.
Hardy, R. L. ( 1990). “Theory and applications of the multiquadradic-biharmonic method: 20 years of discovery.” Comp. and Math. with Applic., 19(8/9), 163–208.
15.
Marcotte, D. ( 1991). “Cokriging with MATLAB.” Comp. and Geosci., 17(9), 1265–1280.
16.
Matheron, G. ( 1973). “The intrinsic random functions and their applications.” Adv. Appl. Prob., 5, 439–468.
17.
Omre, H. ( 1984). “The variogram and its estimation.” Geostatistics for Natural Resour. Characterization, Part 1. Reidel, Dortrecht, The Netherlands, 107–125.
18.
Schut, G. H. ( 1976). “Review of interpolation methods for digital terrain models.” The Canadian Surveyor, 30(5), 389–412.
19.
Thorpe, J. ( 1997). “Two foot contours from 1″ = 800′ photography: Are we fooling ourselves? or worse still: Are we fooling our customers?” EOM. June, 30–32.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 125 • Issue 2 • May 1999
Pages: 87 - 108
History
Received: Feb 19, 1998
Published online: May 1, 1999
Published in print: May 1999
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.