ISSN 2070-7401 (Print), ISSN 2411-0280 (Online)
Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa


Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2022, Vol. 19, No. 5, pp. 113-122

Ordinal statistics of the valleys found by the digital terrain model: Scale factor and Horton’s equations

A.A. Zlatopolsky 1 , E.A. Shekman 2 
1 Space Research Institute RAS, Moscow, Russia
2 Pacific Geographical Institute FEB RAS, Vladivostok, Russia
Accepted: 26.09.2022
DOI: 10.21046/2070-7401-2022-19-5-113-122
The article presents a continuation of the study of the average structural characteristics of a network of watercourses constructed using a digital terrain model (DTM) by a standard algorithm for modeling a river network. We call such networks M-networks consisting of M-valleys. M-valleys are divided into scale levels according to the Horton-Strahler system of orders. The scale level of the M-valley is determined by its order number and initial scale (threshold for the minimum catchment area in km2). The experiment on 6 large territories showed that the average characteristics of M-valleys of the same scale level for all the studied territories are very close. Based on this empirical fact, the Horton relations were transformed into equations called Horton equations, which allow us to calculate the expected average values of the characteristics of M-valleys, if their order and initial scale are given. Based on the average value of one of the characteristics, these equations allow us to calculate the average values of the other characteristics for the same group of M-valleys. The Horton equations are given in several variants, which allows one to choose parameters that are convenient to rely on in a specific situation. Comparison of the density values and the number of M-valleys obtained by the Horton equations with practical measurements showed that the difference between the calculated and experimental data is less than 10 % (and often less than 2 %) if 2 conditions are met: 1) there are a large number of M-valleys of the selected order (more than 100) in the study area; 2) the construction of M-valleys is carried out according to the DTM with a good resolution. In the case of a rough DTM, when valleys of the 1st order begin with a small (in pixels) catchment area (for example, 50 pixels), the difference doubles. Most likely, in both situations, the accuracy of experimental measurement results of average values is insufficient.
Keywords: DTM, valley network calculation, valley order, statistical characteristics of valleys, Horton ratios, scale factor
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