Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2025, V. 22, No. 4, pp. 164-172
Multi-scale statistical analysis of hydrological characteristics of the relief (based on runoff model rasters)
1 Space Research Institute RAS, Moscow, Russia
Accepted: 30.06.2025
DOI: 10.21046/2070-7401-2025-22-4-164-172
We summarize the results of our long-term experimental study of the hydrological characteristics of the relief. We look for regularities common to different territories, generally following Horton’s approach. Our distinction is that we determine the scale of a watercourse not by the number of the order of its inflow, but by its length, L, and we work not with sections of watercourses, but with raster data for all points of the territory. These data contain the results of basic hydrological measurements, which, according to the DTM (digital terrain model), are given by the D8 runoff model. We analyze the territories where this modeling works — the relief is fluvial and quite expressed. Our basic results are the constancy of the total catchment area at runoff points with the same L; the formula for the frequency of runoff points with the same L; the formula for the frequency of the inflow of runoff lines of length L1 into runoff points of length L2 (inflow matrix). We showed how the found dependencies correspond to Hack’s law, Horton’s relations, Tokunaga’s matrix and coefficient, although they were obtained by completely different methods and used different data. The found dependencies allow us to develop these known regularities; in particular, they provide a formal description of the catchment area formation and show the relationship between the inflowing and continuing runoff lines.
Keywords: DTM, runoff model, frequency function of runoff line length, runoff line inflow, statistical characteristics of watercourses, Tokunaga matrix, inflow matrix, scaling
Full textReferences:
- Zlatopolsky A. A. (2024a), Scale terrain statistics — orders, ranges, tributary distribution, orientation, age, scaling, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2024, V. 21, No. 2, pp. 103–121 (in Russian), DOI: 10.21046/2070-7401-2024-21-2-103-121.
- 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.
- Zlatopolsky A. A. (2025a), Tributary distribution statistics — 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.
- Zlatopolsky A. A. (2025b), Statistical regularities of the length of runoff lines (the basis for calculating the hydrological characteristics of the relief), Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2025, V. 22, No. 3, pp. 109–118 (in Russian), DOI: 10.21046/2070-7401-2025-22-3-109-118.
- 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.
- 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).
- Pelletier J. D., Self-organization and scaling relationships of evolving river networks, J. Geophysical Research: Solid Earth, 1999, V. 104, No. B4, pp. 7359–7375.
- 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.