Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2024, Vol. 21, No. 3, pp. 84-93
Scale terrain statistics: Linear scale parameter, Horton exponents, raster characteristics
1 Space Research Institute RAS, Moscow, Russia
Accepted: 21.05.2024
DOI: 10.21046/2070-7401-2024-21-3-84-93
The article describes the results of a study of multiscale relief characteristics obtained from a DEM (digital elevation model) of a region of the Far East using hydrological GIS (geographic information system) tools. It is proposed to use a linear parameter as a scale parameter, that is, the maximum length of the drainage line from the source to a given point. By approximating experimental data, a relation was found between this characteristic and the average number (per unit area) of points with a certain length of a drainage line, with the average catchment area at these points (Hack’s law), and with the density of all pieces with the same or greater length of the drainage line. These dependencies have a uniform power-law nature, thus creating a set of exponents which we call Horton exponents. These indices, along with those that were found earlier for such a scale parameter as drainage area, reflect the properties of the relief better than Horton coefficients. Formulas for the interrelation between Horton exponents are given. With their help, one can simply and clearly move from indices for one scale parameter to those for another, as well as calculate new ones. All results are obtained from the analysis of the runoff line length raster and the runoff raster (catchment area at a point), without identification and scale grouping of stream lines. It is shown how, from such “raster” interdependencies of characteristics, dependencies for watercourses divided into sections are found. The constancy of the catchment area was confirmed at the raster level: the total catchment area of all pixels with the same drainage line length is about a third of the study area.
Keywords: DTM, pixel catchment area, length of drainage line in pixel, scale of streams, statistical characteristics of streams, Horton’s laws, Horton’s exponents, Hack’s law
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