Spheroidal equal angular DEMs: The specificity of morphometric treatment

Correspondence Institute of Mathematical Problems of Biology, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences.1, Vitkevich St., Pushchino, Moscow Region, 142290, Russia. Email: iflor@mail.ru Abstract Digital elevation models (DEMs) are commonly constructed using two main types of regular grids: plane square grids and spheroidal equal angular grids. Methods and algorithms intended for plane square-gridded DEMs should not be directly applied to spheroidal equal angular DEMs. This is because these grids have fundamentally different geometry. However, some researchers continue to apply square-grid algorithms to spheroidal equal angular DEMs. It seems appropriate to consider once again the specifity of morphometric treatment of spheroidal equal angular DEMs. This article, first, demonstrates possibilities of direct calculation of local, nonlocal, and combined morphometric variables from spheroidal equal angular DEMs exemplified by slope gradient, catchment area, and topographic index. Second, the article shows computational errors when algorithms for plane square-gridded DEMs are unreasonably applied to spheroidal equal angular DEMs. The study is exemplified by two DEMs. A medium-resolution DEM of a relatively small, high-mountainous area (Mount Elbrus) was extracted from the SRTM1 DEM. A low-resolution DEM of a vast region with the diverse topography (the central and western regions of Kenya) was extracted from the SRTM30_PLUS DEM. The results show that application of square-grid methods to spheroidal equal angular DEMs leads to substantial computational errors in models of morphometric variables.

[1]  I. Florinsky.  Global Morphometric Maps of Mars, Venus, and the Moon , 2008 .

[2]  Margaret Young,et al.  Statistical Characterization of Altitude Matrices by Computer. Report 5. Terrain Analysis: Program Documentation , 1978 .

[3]  John P. Wilson,et al.  Water in the Landscape: A Review of Contemporary Flow Routing Algorithms , 2008 .

[4]  Y. Deng,et al.  New trends in digital terrain analysis: landform definition, representation, and classification , 2007 .

[5]  Jan Pacina,et al.  Third-order geomorphometric variables (derivatives): definition, computation and utilization of changes of curvatures , 2013, Int. J. Geogr. Inf. Sci..

[6]  Patricia J. Wozniak.  Applied Nonparametric Statistics (2nd ed.) , 1991 .

[7]  Peter L. Guth,et al.  Geomorphometry from SRTM: Comparison to NED , 2006 .

[8]  Simon Dadson,et al.  High-resolution global topographic index values for use in large-scale hydrological modelling. , 2015 .

[9]  S. Orlandini,et al.  Determination of surface flow paths from gridded elevation data , 2009 .

[10]  T. Vincenty.  DIRECT AND INVERSE SOLUTIONS OF GEODESICS ON THE ELLIPSOID WITH APPLICATION OF NESTED EQUATIONS , 1975 .

[11]  I. Florinsky,et al.  Virtual morphometric globes: applying the software Blender , 2016 .

[12]  Thomas A. Hennig,et al.  The Shuttle Radar Topography Mission , 2001, Digital Earth Moving.

[13]  K. Beven,et al.  A physically based, variable contributing area model of basin hydrology , 1979 .

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

[15]  S. Brocklehurst.  Tectonics and geomorphology , 2010 .

[16]  Gegam Vagramovich Bagratuni.  COURSE IN SPHEROIDAL GEODESY , 1967 .

[17]  Igor V. Florinsky,et al.  Digital Terrain Analysis in Soil Science and Geology , 2011 .

[18]  A-Xing Zhu,et al.  Artificial surfaces simulating complex terrain types for evaluating grid-based flow direction algorithms , 2013, Int. J. Geogr. Inf. Sci..

[19]  D. Tarboton.  A new method for the determination of flow directions and upslope areas in grid digital elevation models , 1997 .

[20]  D. Fabre,et al.  Global Bathymetry and Elevation Data at 30 Arc Seconds Resolution: SRTM30_PLUS , 2009 .

[21]  I. Florinsky.  Global Lineaments: Application of Digital Terrain Modelling , 2008 .

[22]  T. G. Freeman,et al.  Calculating catchment area with divergent flow based on a regular grid , 1991 .

[23]  T. Hengl,et al.  Geomorphometry: Concepts, software, applications , 2009 .

[24]  L. Martz,et al.  CATCH: a FORTRAN program for measuring catchment area from digital elevation models , 1988 .

[25]  Igor V. Florinsky,et al.  Computation of the third‐order partial derivatives from a digital elevation model , 2009, Int. J. Geogr. Inf. Sci..

[26]  Qing Zhu,et al.  Digital terrain modeling - principles and methodology , 2004 .

[27]  K. Beven,et al.  THE PREDICTION OF HILLSLOPE FLOW PATHS FOR DISTRIBUTED HYDROLOGICAL MODELLING USING DIGITAL TERRAIN MODELS , 1991 .

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

[29]  K. Beven,et al.  The in(a/tan/β) index:how to calculate it and how to use it within the topmodel framework , 1995 .

[30]  P. A. Shary,et al.  Land surface in gravity points classification by a complete system of curvatures , 1995 .

[31]  I. Evans.  Statistical Characterization of Altitude Matrices by Computer. Report 6. An Integrated System of Terrain Analysis and Slope Mapping. , 1979 .

[32]  P. A. Shary,et al.  Fundamental quantitative methods of land surface analysis , 2002 .

[33]  J. Franklin.  Predictive vegetation mapping: geographic modelling of biospatial patterns in relation to environmental gradients , 1995 .

[34]  Igor V. Florinsky,et al.  Derivation of Topographic Variables from a Digital Elevation Model Given by a Spheriodal Trapezoidal Grid , 1998, Int. J. Geogr. Inf. Sci..

[35]  E. M. Sodano,et al.  General non-iterative solution of the inverse and direct geodetic problems , 1965 .

[36]  John F. O'Callaghan,et al.  The extraction of drainage networks from digital elevation data , 1984, Comput. Vis. Graph. Image Process..

[37]  John P. Wilson,et al.  Terrain analysis : principles and applications , 2000 .