Abstract
Geostatistics provides a suite of methods, summarized as kriging, to analyze a finite data set to describe a continuous property of the Earth. Kriging methods consist of moving window optimum estimation techniques, which are based on a least-squares principle and use a spatial structure function, usually the variogram. Applications of kriging techniques have become increasingly wide-spread, with ordinary kriging and universal kriging being the most popular ones. The dependence of the final map or model on the input, however, is not generally understood. Herein we demonstrate how changes in the kriging parameters and the neighborhood search affect the cartographic result. Principles are illustrated through a glaciological study. The objective is to map ice thickness and subglacial topography of Storglaciären, Kebnekaise Massif, northern Sweden, from several sets of radio-echo soundings and hot water drillings. New maps are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andréasson, P. G., and Gee, D. G., 1989, Bedrock Geology and Morphology of the Tarfala Area, Kebnekaise Mountains, Swedish Caledonides: Geogr. Ann. v. 71, n. A3-4, p. 235–239.
Björnsson, H., 1981, Radio-Echo Sounding Maps of Storglaciären, Isfallglaciären and Rabots Glaciär, Northern Sweden: Geogr. Ann., v. 63, n. A3-4, p. 225–231.
Caress, D., and Parker, R. L., 1989, Spectral Interpolation and Downward Continuation of Marine Magnetic Anomaly Data: J. Geophys. Res., v. 94, n. B12, p. 17397–17407.
Cressie, N., 1989, The Many Faces of Spatial Prediction,in M. Armstrong (ed.),Geostatistics: Kluwer Acad. Publ., Dordrecht, v. 1, p. 163–176.
Davis, J. C., 1986,Statistics and Data Analysis in Geology: John Wiley & Sons, New York, 646 p.
Eriksson, M. G., 1990, Storglaciären Bottentopografi Uppmätt Genom Radioekosondering: Examensarbete, Department of Physical Geography, University of Stockholm, Sweden, 29 p.
Eriksson, M. G., Björnsson, H., Herzfeld, U. C., and Holmlund, P., 1993, The Bottom Topography of Storglaciären. Forskningsrapport 95, STOU-NG95, Naturgeografiska Institutionen, Stockholms Universitet, Stockholm, 48 p.
Herzfeld, U. C., 1990. Geostatistical Software for Evaluation of Line Survey Data, Applied to Radio-Echo Soundings in Glaciology,in J. T. Hanley and D. F. Merriam (eds.),Microcomputer Applications in Geology II, Computers and Geology (Vol. 6): Pergamon Press, New York, p. 119–136.
Herzfeld, U. C., 1992, Least Squares Collocation, Geophysical Inverse Theory, and Geostatistics: A Bird's Eye View: Geophys. J. Int., v. 111, p. 237–249.
Herzfeld, U. C., and Holmlund, P., 1988, Geostatistical Analyses of Radio-Echo Data from Scharffenbergbotnen, Dronning Maud Land, East Antarctica: Z. Gletscherkunde Glazialgeol., v. 24, no. 2, p. 95–110.
Herzfeld, U. C., and Holmlund, P., 1990, Geostatistics in Glaciology: Implications of a Study of Scharffenbergbotnen, Dronning Maud Land, East Antartica: Ann. Glaciol., v. 14, p. 107–110.
Holmlund, P., 1987, Mass Balance of Storglaciären During the 20th Century (Including a Map of the Glaciers in Tarfala Basin, Kebnekaise Massif, Scale 1:10000, edited by P. Holmlund and V. Schytt), Geogr. Ann., v. 69, n. A3-4, p. 439–447.
Holmlund, P., 1988, Is the Longitudinal Profile of Storglaciären, Northern Sweden, in Balance with the present Climate? J. Glaciol., v. 34, n. 118, p. 269–273.
Holmlund, P., and Eriksson, M., 1989, The Cold Surface Layer of Storglaciären: Geogr. Ann., v. 71, n. A3-4, p. 213–227.
Hooke, R. LeB., 1991, Positive Feedbacks Associated with Erosion of Glacial Cirques and Overdeepenings: Geol. Soc. Am. Bull., v. 103, n. 8, p. 1104–1108.
Hooke, R. LeB., Gould, J. E., and Brzozowski, J., 1983, Nearsurface Temperatures Near and Below the Equilibrium Line on Polar and Subpolar Glaciers: Z. Gletscherk. Glazialgeol., v. 19, n. 1, p. 1–25.
Hooke, R. LeB., Brzozowski, J., and Bronge, C., 1983, Seasonal Variations in Surface Velocity, Storglaciären, Sweden: Geogr. Ann., v. 65, n. A3-4, p. 263–278.
Hooke, R. LeB., Pohjola, V. A., Jansson, P., and Kohler, J., in press, Intraseasonal Variations of Internal Deformation, Revealed by Borehole Deformation Measurements in Storglaciären, Sweden: J. Glaciol.
Isaaks, E. H., and Srivastava, R. M., 1988, Spatial Continuity Measures for Probabilistic and Deterministic Geostatistics: Math. Geol., v. 20, n. 4, p. 313–341.
Journel, A. G., and Huijbregts, C. J., 1989. Mining Geostatistics (2nd Ed.) Academic Press, London, 600 p.
Kulling, O., 1964, Översikt Över Norra Norrbottenfjällens Kaledonidberggrund: Sveriges Geologiska Undersökning, v. 19, p. 1–166.
Matheron, G., 1963, Principles of Geostatistics: Econ. Geol., v. 58, n. 8, p. 1246–1266.
Moritz, H., 1980,Advanced Physical Geodesy: H. Wichmann Verlag, Karlsruhe, 500 p.
Nye, J. F., 1957, The Distribution of Stress and Velocity in Glaciers and Ice Sheets: Proc. Roy. Soc. London, Ser. A, v. 239, p. 113–133.
Olea, R. A., 1975, Optimum Mapping Techniques Using Regionalized Variable Theory: Series on Spatial Analysis, v. 2, Kansas Geological Survey, Lawrence, Kansas, 137 p.
Ostrem, G., Haakonsen, N., and Melander, O., 1973, Atlas Over Breer i Nordskandinavia: Meddelande 46 fr. Naturgeografiska Institutionen, Stockholms Universitet, Stockholm, 315 p.
Patterson, W. S. B., 1981,The Physics of Glaciers: Pergamon Press, Oxford, 380 p.
Rasmussen, L. A., and Meier, M. F., 1985, Surface Topography of the Lower Part of the Columbia Glacier, Alaska, 1974–1981: U.S. Geol. Survey Prof. Paper 1258-E, p. E1–E63.
Sampson, R. J., 1975, Surface II, Graphics System, Revision 1: Kansas Geological Survey Publication, Lawrence, Kansas, 240 p.
Schytt, V., 1959, The Glaciers of Kebnekaise Massif: Geogr. Ann., v. 41, n. 4, p. 213–227.
Schytt, V., 1962, Naturgeografisk Fältstation i Kebnekaise: Svensk Naturvetenskap, p. 332–345.
Schytt, V., 1968, Notes on the Glaciological Activities in Kebnekaise, Sweden, During 1966 and 1967; Geogr. Ann., v. 50, n. A2, p. 111–120.
Svenonius, F., 1910, Die Gletscher Schwedens im Jahre 1908: Sveriges Geologiska Undersökning, v. 5, part I, p. 1–54.
Sverisson, M., Jóhannesson, A. E., and Björnsson, H., 1980, Radio-Echo Equipment for Depth Sounding of Temperate Glaciers: J. Glaciol., v. 25, n. 93, p. 477–486.
Warnes, J. J., 1986, A Sensitivity Analysis for Universal Kriging: Math. Geol., v. 18, n. 7, p. 653–676.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Herzfeld, U.C., Eriksson, M.G. & Holmlund, P. On the influence of kriging parameters on the cartographic output—A study in mapping subglacial topography. Math Geol 25, 881–900 (1993). https://doi.org/10.1007/BF00891049
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00891049