Журнал

About Editorial Board Information for authors and reviewers Publication ethics Contacts User Account: send / review a manuscript
Archive
Volume 22, 2025
Number 1 Number 2 Number 3
Volume 21, 2024
Number 1 Number 2 Number 3 Number 4 Number 5 Number 6
Volume 20, 2023
Number 1 Number 2 Number 3 Number 4 Number 5 Number 6
Volume 19, 2022
Number 1 Number 2 Number 3 Number 4 Number 5 Number 6
Volume 18, 2021
Number 1 Number 2 Number 3 Number 4 Number 5 Number 6
Volume 17, 2020
Number 1 Number 2 Number 3 Number 4 Number 5 Number 6 Number 7
Volume 16, 2019
Number 1 Number 2 Number 3 Number 4 Number 5 Number 6
Volume 15, 2018
Number 1 Number 2 Number 3 Number 4 Number 5 Number 6 Number 7
Volume 14, 2017
Number 1 Number 2 Number 3 Number 4 Number 5 Number 6 Number 7
Volume 13, 2016
Number 1 Number 2 Number 3 Number 4 Number 5 Number 6
Volume 12, 2015
Number 1 Number 2 Number 3 Number 4 Number 5 Number 6
Volume 11, 2014
Number 1 Number 2 Number 3 Number 4
Volume 10, 2013
Number 1 Number 2 Number 3 Number 4
Volume 9, 2012
Number 1 Number 2 Number 3 Number 4 Number 5
Volume 8, 2011
Number 1 Number 2 Number 3 Number 4
Volume 7, 2010
Number 1 Number 2 Number 3 Number 4
Issue 6, 2009
Volume 1 Volume 2
Issue 5, 2008
Volume 1 Volume 2
Issue 4, 2007
Volume 1 Volume 2
Issue 3, 2006
Volume 1 Volume 2
Issue 2, 2005
Volume 1 Volume 2
Issue 1, 2004
Volume 1
Search
Find:
русский
ISSN 2070-7401 (Print), ISSN 2411-0280 (Online)
Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa
CURRENT PROBLEMS IN REMOTE SENSING OF THE EARTH FROM SPACE

  

Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2025, V. 22, No. 3, pp. 109-118

Statistical regularities of the length of runoff lines (the basis for calculating hydrological characteristics of the relief)

A.A. Zlatopolsky 1 
1 Space Research Institute RAS, Moscow, Russia
Accepted: 07.03.2025
DOI: 10.21046/2070-7401-2025-22-3-109-118
Formulas describing statistical patterns of distribution of runoff line length, L, allow calculating a number of basic hydrological characteristics of the relief. In the article, we examine how much the proposed formulas match experimental measurements, not on average, but in a detailed comparison. The comparison leaves out sections of functions of large lengths, where statistics are small, and sections of the smallest lengths, where the discreteness of both the measurement and the runoff modeling process significantly affects the experimental results. In four territories, the previously found power approximation of the frequency function of lengths, H(L), coincides well with the experimental ones. The two-dimensional frequency function, which we call the inflow matrix, or rather its main part, which reflects the inflow of some runoff lines into others, is close to the product of frequency functions H(L1)·H(L2). This confirms the hypothesis of “uniform inflow”: runoff lines of length L1 flow into lines of greater length L2 proportionally to the frequency of runoff lines of this length H(L2). A two-dimensional power function is proposed that better matches the experimentally obtained matrices of the four territories. An analogue of the Tokunaga coefficient, which characterizes the distribution of tributaries, is derived from this function. This formula is very close to the formula experimentally found by other authors for watercourses divided into orders. The formulas proposed in this work are scale-invariant.
Keywords: DEM, runoff model, frequency function of runoff line length, runoff line inflow, statistical characteristics of watercourses, Tokunaga matrix, inflow matrix
Full text

References:

  1. Zlatopolsky A. A., Constancy of the area of the total catchment of watercourses of the same scale and the distribution of this catchment between watercourses of a larger scale, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2023, V. 20, No. 5, pp. 120–129 (in Russian), DOI: 10.21046/2070-7401-2023-20-5-120-129.
  2. Zlatopolsky A. A. (2024a), Scale terrain statistics: Linear scale parameter, Horton exponents, raster characteristics, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2024, V. 21, No. 3, pp. 84–93 (in Russian), DOI: 10.21046/2070-7401-2024-21-3-84-93.
  3. Zlatopolsky A. A. (2024b), Statistical scale relationships of relief characteristics (based on runoff model rasters), Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2024, V. 21, No. 6, pp. 159–167 (in Russian), DOI: 10.21046/2070-7401-2024-21-6-159-167.
  4. Zlatopolsky A. A., Tributary distribution statistics — the inflow matrix (analog of Tokunaga matrix), Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2025, V. 22, No. 2, pp. 71–81 (in Russian), DOI: 10.21046/2070-7401-2025-22-2-71-81.
  5. Horton R. E., Erosional development of streams and their drainage basins. Hydrophysical approach to quantitative morphology, Bul. Geological society of America, 1945, V. 56, pp. 275–370.
  6. Chernova I. Yu., Nugmanov I. I., Dautov A. N., Application of GIS analytic functions for improvement and development of the structural morphological methods of the neotectonics studies, Geoinformatica, 2010, No. 4, pp. 9–23 (in Russian).
  7. Entin A. L., Koshel S. M., Lurie I. K., Samsonov T. E., Morphometric analysis of digital terrain models for assessing and mapping of the distribution of surface runoff, Geography Issues, 2017, V. 144, pp. 169–186 (in Russian).
  8. Pelletier J. D., Self-organization and scaling relationships of evolving river networks, J. Geophysical Research: Solid Earth, 1999, V. 104, Iss. B4, pp. 7359–7375, https://doi.org/10.1029/1998JB900110.
  9. Tokunaga E., Ordering of divide segments and law of divide segment numbers, Trans. Japanese Geomorphological Union, 1984, V. 5, No. 2, pp. 71–77.
  10. Wang K., Zhang L., Li T. et al., Side tributary distribution of quasi-uniform iterative binary tree networks for river networks, Frontiers in Environmental Science, 2022, V. 9, Article 792289, DOI: 10.3389/fenvs.2021.792289.