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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, 2024, Vol. 21, No. 2, pp. 103-121

Scale terrain statistics—orders, ranges, tributary distribution, orientation, age, scaling

A.A. Zlatopolsky 1 
1 Space Research Institute RAS, Moscow, Russia
Accepted: 15.03.2024
DOI: 10.21046/2070-7401-2024-21-2-103-121
The results of a long-term experimental study using a digital elevation model (DEM) of the properties of fluvial relief are presented. The scale of streams is usually characterized by the Horton order value. A more flexible method of division by scale, “range,” is proposed, in case where the interval of values of the catchment area is directly specified. For both options of watercourses grouping, laws called Horton’s laws have been found, which determine the number and density of watercourses of a certain scale. These laws work independently of the orders structure and can be written as homogeneous power laws with Horton exponents. From these laws, the following were analytically derived and experimentally tested: the principle and formulas for the distribution of watercourses of the same order among watercourses of higher orders; formula for the Tokunaga coefficient and formula for the catchment area of direct runoff. The difference base surfaces constructed from watercourses, which are selected by range and order, are similar. Using the LESSA (Lineament Extraction and Stripe Statistical Analysis) program made it possible to find the valley axes in the DEM and carry out their statistical analysis. The scale factor for valleys is their width. For the valley width, a correspondence with the catchment area has been established in the form of Horton’s law. The orientation characteristics and density of valleys and watercourses of the same scale are very similar. But with the help of the analysis of watercourses, it is possible to obtain results that are much more detailed in scale. It made it possible to clarify the scale at which an abrupt change in the orientation of relief elements occurs. To search for a formal correspondence between the scale of watercourses and their age, order dating scales found by researchers of three territories were compared. For one of the territories, the relationship between scale and age is presented in the form of Horton’s law. The scale invariance of relief properties manifested itself in the power-law nature of the laws, in the constancy of the total areas (catchment and valleys) and in the constancy of a number of characteristics measured in pixels.
Keywords: DTM, approximation, density of watercourse lines, catchment area, Horton’s laws, Horton’s exponent, scaling, valley age, valley orientation
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References:

  1. Gartsman B. I., Bugaets A. N., Tegai N. D., Krasnopeev S. M., Analysis of the structure of river systems and prospects for modeling hydrological processes, River system of Pacifick Russia: A quarter century of research, Vladivostok: Dalnauka, 2015, pp. 273–285 (in Russian).
  2. Zlatopolsky A. A., Multiscale digital terrain map analysis. Experimental regularities, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2015, Vol. 12, No. 3, pp. 21–29 (in Russian).
  3. Zlatopolsky A. A., Using LESSA technology to obtain territory orientation characteristics. Methodology and testing using digital elevation model for the pre-Baikal region, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2020, Vol. 17, No. 4, pp. 98–110 (in Russian), DOI: 10.21046/2070-7401-2020-17-4-98-110.
  4. Zlatopolsky A. A., Ordinal statistics of the valleys found by the digital terrain model. Basic calculation and converted order, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2021, Vol. 18, No. 6, pp. 141–151 (in Russian), DOI: 10.21046/2070-7401-2021-18-6-141-151.
  5. Zlatopolsky A. A. (2023a), 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.
  6. Zlatopolsky A. A. (2023b), The structure of the flow raster calculated from a digital terrain model, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2023, Vol. 20, No. 4, pp. 123–132 (in Russian), DOI: 10.21046/2070-7401-2023-20-4-123-132.
  7. Zlatopolsky A. A. (2023c), 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, Vol. 20, No. 4, pp. 123–132 (in Russian), DOI: 10.21046/2070-7401-2023-20-5-120-129.
  8. Zlatopolsky A. A., Zaitsev V. A., Relationship between order and width of valleys automatically found using a digital terrain model, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2021, Vol. 18, No. 6, pp. 141–151 (in Russian), DOI: 10.21046/2070-7401-2021-18-6-141-151.
  9. Zlatopolsky A. A., Shekman E. A., Ordinal statistics of the valleys found by the digital terrain model. Scale factor and Horton’s equations, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2022, Vol. 19, No. 5, pp. 113–122 (in Russian), DOI: 10.21046/2070-7401-2022-19-5-113-122.
  10. 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.
  11. Zlatopolsky A. A., Simonov D. A., Zakharov V. S., Ordinal statistics of valleys — length, width, direction (applied to Bureya ridge), Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2021, Vol. 18, No. 5, pp. 97–107 (in Russian), DOI: 10.21046/2070-7401-2021-18-5-97-107.
  12. Mamedov V. I., Zaitse V. A., Makarova M. A., Chausov A. A., Pashkov V. S., Ob”yasnitel’naya zapiska k karte geomorfologicheskikh tsiklov boksitonosnoi provintsii Futa Dzhallon-Mendingo i ee obramleniya (Zapadnaya Afrika) (Explanatory notes for map of geomorphic cycles of Fouta Djallon-Mandingo bauxite province and environs (West Africa)), Moscow: Akvarel, 2022, 76 p.
  13. Petukhov A. V., Shelepov I. V., Petukhov A. A., Kuklin A. I., Power law and self-similarity principle for investigation of fractured reservoirs and hydrodynamical simulation, Oil-and-gas geology, Theory and practice, 2012, Vol. 7, No. 2, 21 p. (in Russian), http://www.ngtp.ru/rub/3/33_2012.pdf.
  14. Simonov D. A., Zakharov V. S., Gilmanova G. Z., Didenko A. N., Neotectonic vertical movements of Northern Sikhote-Alin and adjacent territories and its relationship with the characteristics of the stream network, Vestnik Moskovskogo universiteta, Ser. 4: Geologiya, 2021, No. 5, pp. 19–30 (in Russian).
  15. 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, Geoinformatika, 2010, No. 4, pp. 9–23 (in Russian).
  16. Chernova I. Yu., Nurgaliev D. K., Nurgalieva N. G., Nugmanov I. I., Chernova O.S, Kadyrov R. I., Reconstruction of history of the Tatar Arch in the Neogene-Quaternary time by means of the morphometric analysis, Neftyanoe khozyaistvo, 2013, No. 6, pp. 12–15 (in Russian).
  17. Horton R. E., Erosional development of streams and their drainage basins. Hydrophysical approach to quantitative morphology, Bull. Geological Society of America, 1945, Vol. 56, pp. 275–370.
  18. Pelletier J. D., Self-organization and scaling relationships of evolving river networks, J. Geophysical Research, 1999, Vol. 104(B4), pp. 7359–7375.
  19. 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, Vol. 9, Article 792289, DOI: 10.3389/fenvs.2021.792289