Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2026, V. 23, No. 1, pp. 140-149
Statistical relationship of local longitudinal slope of watercourse with other local characteristics (slope matrix)
1 Space Research Institute RAS, Moscow, Russia
Accepted: 13.11.2025
DOI: 10.21046/2070-7401-2026-23-1-140-149
A description of relief characteristics by a slope matrix is proposed. This matrix reflects the statistical relationship of the local longitudinal slope values with the current length of the runoff line and the current height above sea level. An experimental calculation of the slope matrix using the DTM (digital terrain model) of a section of the Far East (500,000 km2) is described. The runoff line length is obtained by simulating the runoff in a geographic information system. A relationship between the slope value and the length of the watercourse and the height above sea level is experimentally established. Variants of a formal description of the experimental slope matrix by power functions of length and height are given. The proposed formulas describe the matrix well as a whole, but poorly correspond to the data obtained from the lowland section. Most likely, this is due to the fact that this section has small slopes that are measured with a relatively large error. It is also possible that the accuracy of these heights in the DTM is insufficient. Further, it is necessary to conduct similar studies in significantly different areas. It is proposed to study the relationship between the drop in height along the runoff line and the length of the runoff line, which is closely related to the considered statistical dependence of the longitudinal slope.
Keywords: DTM, runoff model, longitudinal slope, runoff line length, height, slope matrix, statistical dependence, power function
Full textReferences:
- Gartsman B. I., Analysis of geomorphological conditions for primary streams formation using digital elevation models, Geography and Natural Resources, 2013, V. 34, No. 1, pp. 69–78, DOI: 10.1134/S1875372813010101.
- Zlatopolsky A. A., Multi-scale statistical analysis of hydrological characteristics of the relief (based on runoff model rasters), Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2025, V. 22, No. 4, pp. 164–172 (in Russian), DOI: 10.21046/2070-7401-2025-22-4-164-172.
- 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).
- 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.