Abstract
Quality of data used in the GIS-support tools is a critical issue, as the decisions that affect locations or areas are to be made effectively, in time and with adequate accuracy. At present, a number of European Union and national policy strategies rely on the use of quality digital elevation model (DEM) data. The accuracy, smoothness and representativeness are properties of DEM determining outputs of the support systems that are designed for assessment of renewable energy resources, flood forecasting, disaster and security management. Similarly, suitability analysis, calculating of environmental indicators and water quality monitoring within the catchments are based on the use of DEM and the decisions taken have financial and legal implications. Thus, a prerequisite for full exploitation of the potential of DEMs is to make them available for the community at sufficient accuracy and detail for a variety of applications.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramowitz M and Stegun IA (1964) Handbook of mathematical functions. Dover, New York, pp 297–300, 228–231
Cebecauer T, Hofierka J, Šúri M (2002) Processing digital terrain models by regularized spline with tension: tuning interpolation parameters for different input datasets. In: Ciolli M, Zatelli P (eds) Proceedings of the Open Source Free Software GIS — GRASS users conference 2002, Trento, Italy, 11–13 September 2002
Custer GS, Fames P, Wilson JP, Snyder RD (1996) A comparison of hand-and spline-drawn precipitation maps for Mountainous Montana. Water Resources Bulletin 32:393–405
Duchon J (1976) Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces: R.A.I.R.O. Analysis Numerique 10:5–12
Franke R (1985) Thin plate spline with tension. Computer Aided Geometrical Design 2:87–95
GRASS 2000 Geographic Resources Analysis Support System, http://grass.itc.it/
Hancock PA and Hutchinson MF (2003) An iterative procedure for calculating minimum generalised cross validation smoothing splines. Australian and New Zealand Industrial and Applied Mathematics Journal 44:290–312
Hofierka J (2005) Interpolation of radioactivity data using regularized spline with tension. Applied GIS, 1:16/01–16/13
Hofierka J, Parajka J, Mitasova H, Mitas L. (2002) Multivariate interpolation of precipitation using regularized spline with tension. Transactions in GIS 6:135–150
Hutchinson MF (1998) Interpolation of rainfall data with thin plate smoothing splines: I. Two dimensional smoothing of data with short range correlation. Journal of Geographic Information and Decision Analysis 2:152–167
Jeffrey SJ, Carter JO, Moodie KB, Beswick AR (2001) Using spatial interpolation to construct a comprehensive archive of Australian climate data. Environmental Modelling and Software 16:309–330
Mitas L and Mitasova H (1988) General vanational approach to the interpolation problem. Computers and Mathematics with Applications 16:983–992
Mitas L and Mitasova H (1999) Spatial interpolation. In: Longley P, Goodchild MF, Maguire DJ, Rhind DW (eds) Geographical information systems: principles, techniques, management and applications. GeoInformation International, Wiley, pp. 481–492
Mitasova H and Hofierka J (1993) Interpolation by regularized spline with tension: II. Application to terrain modeling and surface geometry analysis. Mathematical Geology 25:657–671
Mitasova H and Mitas L (1993) Interpolation by regularized spline with tension: I. Theory and implementation. Mathematical Geology 25:641–655
Mitasova H, Mitas L, Brown BM, Gerdes DP and Kosinovsky I (1995) Modeling spatially and temporally distributed phenomena: new methods and tools for GRASS GIS. International Journal of GIS, Special Issue on Integration of Environmental Modeling and GIS 9: 443–446
Neteler M and Mitasova H (2002) Open source GIS: A GRASS GIS approach. Kluwer Academic Publishers, Boston.
Talmi A and Gilat G (1977) Method for smooth approximation of data. Journal of Computational Physics 23:93–123
Tomczak M (1998) Spatial interpolation and its uncertainty using automated anisotropic inverse distance weighting (IDW) — cross-validation/jackknife approach. Journal of Geographic Information and Decision Analysis 2:18–33
Wahba G (1990) Spline models for observational data. CNMS-NSF Regional Conference Series in Applied Mathematics 59, SIAM, Philadelphia, Pennsylvania
Weibel R and Heller M (1991) Digital Terrain modelling. In: Maguire DJ, Goodchild MF, Rhind DW (eds) Geographical information systems: principles and applications. Longman, Essex, 269–297
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hofierka, J., Cebecauer, T., Šúri, M. (2007). Optimisation of Interpolation Parameters Using Cross-validation. In: Peckham, R.J., Jordan, G. (eds) Digital Terrain Modelling. Lecture Notes in Geoinformation and Cartography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36731-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-36731-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36730-7
Online ISBN: 978-3-540-36731-4
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)