Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2023, Vol. 20, No. 4, pp. 123-132
The structure of the flow raster calculated from a digital terrain model
1 Space Research Institute RAS, Moscow, Russia
Accepted: 04.07.2023
DOI: 10.21046/2070-7401-2023-20-4-123-132
A study of the structure of the flow raster built in GIS using a digital elevation model (DEM) is proposed. The histogram of this raster, i.e. the number of pixels with a certain catchment area, is analyzed. This histogram reflects both the area of watercourses and areas of initial flow. It turned out that in half of the territory, the flow comes from only one neighbor or there is no flow at all, and 3/4 of the territory receives flow from less than 7 nearby points. The watercourse lines include areas with a catchment area of at least 10 points, more confidently with a catchment area of more than 20 points, and possibly 46 points, because the further part of the histogram is well approximated by a power law with an almost constant exponent. For a well-populated part of the histogram, a formula for the dependence of the normalized density of network sections with a certain catchment area is obtained. For a large part of the histogram, a formula is obtained that approximates the function inverse to the distribution function. Equations are derived analytically from both functions for calculating the density of watercourses with the catchment area in a given range of values. In both cases, the results obtained are very close to each other and close to the previously obtained Horton’s law for the density. All these results are preserved during the study of 4 different territories with different resolutions of the DEM. We believe this is due to the fact that the histogram of the flow raster reflects the general properties of the relief, possibly, the fluvial relief. The similarity of histograms at different resolutions of the DEM can be determined by the fact that the structure of the power law acting in the main part of the histogram does not depend on the catchment area, and the form of the initial counts of the histogram is uniformly affected by the discreteness of the DEM representation.
Keywords: DEM, flow raster, histogram, approximation, density of watercourse lines, catchment area, Horton’s ratios
Full textReferences:
- Zlatopolsky A. A., Scale statistics of the valleys found by the digital terrain model. Modified Horton’s laws, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2023, Vol. 20, No. 3, pp. 87–95 (in Russian), DOI: 10.21046/2070-7401-2023-20-3-87-95.
- Zlatopolsky A. A., Shekman E. A., Ordinal and scale statistics of the valleys found by the digital terrain model, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2023, Vol. 20, No. 2, pp. 125–134 (in Russian), DOI: 10.21046/2070-7401-2023-20-2-125-134.
- Nugmanov I. I., Nugmanova E. V., Chernova I. Yu., Osnovy morfometricheskogo metoda poiska neotektonicheskikh struktur: uchebno-metodicheskoe posobie (Fundamentals of the morphometric method of searching for neotectonic structures: Educational and methodological manual), Kazan: Kazanskii universitet, 2016, 53 p. (in Russian).