Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2023, Vol. 20, No. 3, pp. 87-95
Scale statistics of the valleys found by the digital terrain model: Modified Horton’s laws
1 Space Research Institute RAS, Moscow, Russia
Accepted: 30.03.2023
DOI: 10.21046/2070-7401-2023-20-3-87-95
We continue to publish the results of statistical studies of thalweg networks (watercourse lines) built using digital terrain models. We call these networks M-networks. A section of the Far East measuring about 0.5 million km2 was studied. Watercourses with a catchment area from 1 to 3000 km2 were taken into account. The network was divided into sections with a catchment area in certain intervals. These intervals were smaller (sometimes by tens of times) than the spread of the catchment area of watercourses of the same order in the Horton – Strahler system. Statistical characteristics of sections of the same range were measured directly on the flow raster without dividing it into orders. It turned out that the average values of the characteristics of sections of the same range, such as their number, density and length, obeyed regularity close to the previously proposed by Horton’s laws. For intervals of arbitrary size, generalized Horton’s laws are obtained, which turn into regularities for orders if the value of the intervals is set to be similar to the ordinal ones. Horton’s relations turn out to be a special case of these regularities. Thus, Horton’s laws work independently of the ordinal structure of watercourses. The graphs of regularities obtained as a result of measurements are smooth, there are no signs of ordinal discreteness. It seems that the system of orders is a “palette” that overlays with regularities that exist in addition to it, but this system helped to detect them. The range system is more flexible than the order system, because you can select watercourses of the desired scale (catchment area) for analysis.
Keywords: DTM, watercourse network calculation, watercourse order, statistical characteristics of watercourses, catchment area, Horton ratios, scale factor
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