Interpolation by regularized spline with tension: II. Application to terrain modeling and surface geometry analysis

A general approach to the computation of basic topographic parameters independent of the spatial distribution of given elevation data is developed. The approach is based on an interpolation function with regular first and second order derivatives and on application of basic principles of differential geometry. General equations for computation of profile, plan, and tangential curvatures are derived. A new algorithm for construction of slope curves is developed using a combined grid and vector approach. Resulting slope curves better fulfill the condition of orthogonality to contours than standard grid algorithms. Presented methods are applied to topographic analysis of a watershed in central Illinois.

[1]  Interpolation by Regularized Spline with Tension � , 2022 .

[2]  International symposium on spatial data handling , 1984 .

[3]  S. Auerbach,et al.  Surface representations reproducing given digitized contour lines , 1990 .

[4]  R. Dikau.  The application of a digital relief model to landform analysis in geomorphology , 2020 .

[5]  Karl Auerswald,et al.  Combining a modified Universal Soil Loss Equation with a digital terrain model for computing high resolution maps of soil loss resulting from rain wash , 1990 .

[6]  I. Moore,et al.  Digital terrain modelling: A review of hydrological, geomorphological, and biological applications , 1991 .

[7]  Steven E. Franklin,et al.  Geomorphometric processing of digital elevation models , 1987 .

[8]  T. A. A. Broadbent,et al.  Survey of Applicable Mathematics , 1970, Mathematical Gazette.

[9]  Ian D. Moore,et al.  Terrain analysis : integration into the agricultural nonpoint source (AGNPS) pollution model , 1991 .

[10]  H. Mitásová,et al.  Interpolation by regularized spline with tension: I. Theory and implementation , 1993 .

[11]  R. Heerdegen,et al.  Quantifying source areas through land surface curvature and shape , 1982 .

[12]  D. Mark.  Computer Analysis of Topography: A Comparison of Terrain Storage Methods , 1975 .

[13]  B. Márkus.  TERRAIN ANALYSIS IN CONSIDERATION OF SURFACE CURVATURE CONDITIONS , 1986 .

[14]  C. Thorne,et al.  Quantitative analysis of land surface topography , 1987 .

[15]  H. B. Papo,et al.  Digital terrain models for slopes and curvatures , 1984 .

[16]  Jozef Krcho,et al.  Morphometric analysis of relief on the basis of geometric aspect of field theory , 1973 .