Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2022, Vol. 19, No. 3, pp. 133-142
Ordinal statistics of the valleys found by the digital terrain model: Basic calculation and converted order
1 Space Research Institute RAS, Moscow, Russia
Accepted: 04.05.2022
DOI: 10.21046/2070-7401-2022-19-3-133-142
According to the digital terrain model (DTM), networks of watercourses (we call them M-valleys) for four large territories: “Amur”, “Shilka”, “Kama”, “Niger” (approx. 400 000 km2 each) were built using a standard algorithm. In all cases, the same basic calculation parameters with a minimum catchment area of 0,85 km2 were used. It was found that the values of the average density of M-valleys of the same order in all territories are very close (the spread of values is 10 %), and the ratio of the average density of M-valleys of successive orders in all cases is about 2. Based on these measurements, we assume that for large areas and M-valleys of the first basic orders, P, an average density of 0,4/2(P–1) km/km2 can be expected. Similar, though less reliable estimates were obtained for the average number of M-valleys per km2 0.27/4,4(P–1), the average length of M-valleys 1,48∙2,2(P–1) km and the average width of M-valleys 2(P–1) km. These formulas correspond to the Horton relations for hydraulic networks. Perhaps the proximity of the absolute M-values of these characteristics for such different territories reflects the deep properties of the relief organization. It is proposed how, with non-basic calculation parameters, to recalculate the order of the M-valleys into the “converted” order of the basic variant, in which the M-valleys have similar statistical characteristics. We provide an example of the methodical use of the M-valleys density relationships stated above to calculate local statistics. It is shown, that the local statistical analysis of M-valleys of definite orders makes it possible to identify the characteristics of relief elements of appropriate sizes. We also provide an example of how the detected statistical properties of the relief can be associated with M-valleys of a certain basic order, and through the use of basic surfaces, these properties can be associated with geological events of a certain time.
Keywords: DTM, valley network calculation, valley order, statistical characteristics of valleys, Horton ratios
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