Models of topography

Lecture Notes in Geoinformation and Cartography

Volumn 0, Issue , 2008, Pages 29-57

  Shary, Peter A ^a  

^a NONE

Author keywords

Geomorphometry; Gibbs phenomenon; Landform predictability; Scale; Topographic attribute and variable

Indexed keywords

GEOMORPHOLOGY; LANDFORMS;

DIGITAL TERRAIN ANALYSIS; DOUBLE SIDED; GEOMORPHOMETRY; GIBBS PHENOMENA; LANDFORM PREDICTABILITY; NEW APPROACHES; PROPERTY; SCALE; TOPOGRAPHIC ATTRIBUTE AND VARIABLE; VEGETATION PATTERN;

TOPOGRAPHY;

EID: 84872968117     PISSN: 18632246     EISSN: 18632351     Source Type: Book Series    
DOI: 10.1007/978-3-540-77800-4_3     Document Type: Conference Paper

References (55)

1. Akima, H. (1978), A method of bivariate interpolation and smooth surface fitting for irregularly distributed data points, ACM Transactions on Mathematical Software, 4: 148–159.
2. Cayley, A. (1859), On contour and slope lines, Philosophical Magazine, Series 4, (18)120: 264–268.
3. Clarke, K.C., (1988), Scale-based simulation of topographic relief, The American Cartographer, 15: 173–181.
4. Dikau, R., (1988), Case studies in the development of derived geomorphic maps, Geologisches Jahrbuch, A104: 329–338.
5. Dokuchaev, V.V., (1886), Razbor glavneishikh pochvennykh ponyatiy, In Dokuchaev, Izbrannye Sochineniya, Vol.3, 1949: 161–239 (Moscow: Sel’hozgiz, in Russian, original work published 1886).
6. Evans, I.S., (1972), General geomorphometry, derivatives of altitude, and descriptive statistics, In Chorley, R.J. (ed.): Spatial Analysis in Geomorphology, London: Methuen & Co., Ltd.: 17–90.
7. Evans, I.S., (1975), The effect of resolution on gradients calculated from an altitude matrix, Report 3 on Grant DA-ERO-591-73-G0040, ‘Statistical characterization of altitude matrices by computer’, Department of Geography, University of Durham, England.
8. Evans, I.S., (1980), An integrated system of terrain analysis and slope mapping, Zeitschrift für Geomorphologie N.F., Suppl.–Band 36: 274–295.
9. Evans, I.S. and McClean, C.J., (1995), The land surface is not unifractal: variograms, cirque scale and allometry, Zeitschrift für Geomorphologie N.F., Suppl.-Bd., 101: 127–147.
10. Evans, I.S. and Cox, N.J., (1999), Relations between land surface properties: altitude, slope and curvature, In Hergarten, S. and Neugebauer H.J. (eds.): Process Modelling and Landform Evolution, Berlin: Springer: 13–45.
11. Favalli, M. and Pareshi, T.T., (2004), Digital elevation model construction from structured topographic data: The DEST algorithm, Journal of Geophysical Research, 109, F04004.
12. Finn, R., (1986), Equilibrium Capillary Surfaces, New York: Springer-Verlag.
13. Florinsky, I.V., (1998), Accuracy of local topographic variables derived from digital elevation models, International Journal of Geographical Informational Science, 12: 47–61.
14. Freeman, T.G., (1991), Calculating catchment area with divergent flow based on a regular grid, Computers and Geosciences, 17: 413–422.
15. Gauss, K.F., (1827), Disquisitiones generales circa area superficies curves, Göttingen gelehrte Anziegen, No.177: 1761–1768 (In Latin).
16. Goodchild, M., (1982), The fractional Brownian process as a terrain simulation model, Modelling and Simulation, 13: 1133–1137.
17. Gousie, M.B. and Franklin, W.R., (2005), Augmenting grid-based contours to improve thin-plate DEM generation, Photogrammetric Engineering and Remote Sensing, (71)1: 69–79.
18. King, D., Bourennane, H., Isampert, M. and Macaire, J.J., (1999), Relationship of the presence of a non-calcareous clay-loam horizon to DEM attributes in a gently sloping area, Geoderma, 89: 95–111.
19. Klemeš, V., (1983), Conceptualization and scale in hydrology, Journal of Hydrology, 65: 1–23.
20. Koenderink, J.J. and van Doorn, A.J., (1994), Two–plus–one–dimensional differential geometry, Pattern Recognition Letters, 15: 439–443.
21. Li, Z., Zhu, Q., and Gold, C., (2005), Digital Terrain Modeling: Principles and Methodology, Florida, Boca Raton: CRC Press.
22. MacMillan, R.A. and Shary, P.A., (2007). Extraction and classification of landforms and landform elements, In Hengl, T. and Reuter, H.I. (eds.): Geomorphometry: Concepts, Software, Applications, Ch. 9, Joint Research Centre: European Commission: (in press).
23. Mandelbrot, B., (1967), How long is the coast of Britain? Statistical self-similarity and fractional dimension, Science, 156(3775): 636–638.
24. Mark, D.M. and Smith, B., (2004), A science of topography – from qualitative ontology to digital representations, In Bishop, M.P., and Shroder Jr., J.F. (eds.): Geographic Information Science and Mountain Geomorphology, Chichester UK, Praxis Scientific Publishing: Springer-Verlag: 75–110. Available online at: http://ontology.buffalo.edu/smith//articles/topography.pdf (accessed 29 October 2007).
25. Martz, L.W. and de Jong, E., (1988), CATCH: a Fortran program for measuring catchment area from digital elevation models, Computers and Geosciences, 14: 627–640.
26. Maxwell, J.C., (1870), On hills and dales, Philosophical Magazine, Series 4, (40)269: 421–427.
27. Nikol’sky, S.M., (1975), Kours Matematicheskogo Analiza, 2: 199–203, Moscow: Nauka (in Russian).
28. Pachepsky, Ya.A., Timlin, D.J. and Rawls, W.J., (2001), Soil water retention as related to topographic variables, Soil Science Society of America Journal, 65: 1787–1795.
29. Pennock, D.J., Zebarth, B.J. and de Jong, E., (1987), Landform classification and soil distribution in hummocky terrain, Saskatchewan, Canada, Geoderma, 40: 297–315.
30. Peuquet, D.J., (1984), A conceptual framework and comparison of spatial data models, Cartographica, 21: 66–113.
31. Phillips, J.D., (1988), The role of spatial scale in geomorphic systems, Geographical Analysis, 20: 308–317.
32. Pike, R., (1995), Geomorphometry – progress, practice, and prospect, Zeitschrift für Geomorphometry N.F. Suppl.–Band, 101: 221–238.
33. Richardson, L., (1961), The problem of contiguity: An appendix to statistics of deadly quarrels, In Yearbook of the Society for General Systems Research, Vol.6, Michigan: Ann Arbor, 140–187.
34. Sard, A., (1942), The measure of the critical values of differentiable maps, Bulletin of the American Mathematical Society, 48: 883–890.
35. Schmidt, J., Evans, I.S. and Brinkmann, J., (2003), Comparison of polynomial models for land surface curvature calculation, International Journal of Geographical Information Science, 17: 797–814.
36. Schmidt, J. and Hewitt, A., (2004), Fuzzy land elements classification from DTMs based on geometry and terrain position, Geoderma, 121: 243–256.
37. Shary, P.A., (1995), Land surface in gravity points classification by a complete system of curvatures, Mathematical Geology, 27: 373–390.
38. Shary, P.A., Sharaya, L.S. and Mitusov, A.V., (2002), Fundamental quantitative methods of land surface analysis, Geoderma, 107: 1–32.
39. Shary, P.A., (2005), Geomorphometry and ‘Analytical GIS Eco’ software description and demonstration version, Available on-line at: http://www.giseco.info/(accessed 29 October 2007).
40. Shary, P.A., Sharaya, L.S. and Mitusov, A.V., (2005), The problem of scale-specific and scale-free approaches in geomorphometry, Geografia Fisica e Dinamica Quatrenaria, 28: 81–101.
41. Shary, P.A., (2006a), Variables of geomorphometry: The current state-of-art, In International Symposium on Terrain Analysis and Digital Terrain Mapping (TADTM 2006), November 23–25 in Nanjing, China, Proceedings of TADTM 2006, full paper: CD–ROM.
42. Shary, P.A., (2006b), Unsolved tasks of geomorphometry. In International Symposium on Terrain Analysis and Digital Terrain Mapping (TADTM 2006), November 23–25 in Nanjing, China, Proceedings of TADTM 2006, full paper: CD-ROM.
43. Shary, P.A. and Sharaya, L.S., (2006), Predictable and terrain–specific landform classifications. In International Symposium on Terrain Analysis and Digital Terrain Mapping (TADTM 2006), November 23–25 in Nanjing, China, Proceedings of TADTM 2006, full paper: CD–ROM.
44. Smith, B. and Mark, D.M., (2003), Do mountains exist? Towards an ontology of landforms, Environment & Planning B (Planning and Design), 30: 411–427. Available on-line at: http://ontology.buffalo.edu/smith/articles/Mountains.pdf (accessed 29 October 2007).
45. Sousa, M.C., Foster, K., Wyvill, B. and Samavati, F., (2003), Precise ink drawing of 3d models, EuroGraphics, 22: 47–61.
46. Speight, J.G., (1974). A parametric approach to landform regions. In Progress in Geomorphology. Institute of British Geographers special publ. No.7, Oxford: Alden & Mowbray Ltd. at the Alden Press: 213–230.
47. Tarboton, D.G., (1997), A new method for the determination of flow directions and upslope areas in grid Digital Elevation Models, Water Resources Research, 33: 309–319.
48. Tomer, M.D. and Anderson, J.L., (1995), Variation of soil water storage across a sand plain hillslope, Soil Science Society of America Journal, 59: 1091–1100.
49. Troeh, F.R., (1964), Landform parameters correlated to soil drainage, Soil Science Society of America Proceedings, 28: 808-812.
50. Voronoi, G., (1907), Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Journal für die Reine und Angewandte Mathematik, 133: 97–178 (in French).
51. Wood, J., (1996), The geomorphological characterization of Digital Elevation Models, PhD thesis, University of Leicester, Available on-line at: http://www.soi.city.ac.uk/~jwo/phd/(accessed 27 October 2007).
52. Wilson, J. and Gallant, J. (eds.), (2000), Terrain Analysis: Principles and Applications, New York: John Wiley & Sons, Ltd.
53. Xu, T.B., Moore, I.D. and Gallant, J.C., (1993), Fractals, fractal dimensions and landscapes – a review, Geomorphology, 8: 245–262.
54. Young, M., (1978), Terrain analysis: program documentation. Report 5 on Grant DA-ERO-591-73-G0040, ‘Statistical characterization of altitude matrices by computer’, Department of Geography, University of Durham, England.
55. Zevenbergen, L.W. and Thorne, C.R., (1987), Quantitative analysis of land surface topography, Earth Surface Processes and Landforms, 12: 47–56.