Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2026, V. 23, No. 2, pp. 141-149
Formal description of the runoff profile based on statistical analysis of the digital terrain model: Part 1
1 Space Research Institute RAS, Moscow, Russia
Accepted: 16.02.2026
DOI: 10.21046/2070-7401-2026-23-2-141-149
The article demonstrates the possibility of finding a first approximation of a formal description of the statistically average profile of runoff lines. These lines are obtained through digital runoff modeling. We propose considering in the formula not only the length of the runoff line but also its elevation above sea level. It turned out that the profile formula, previously obtained from the analysis of the slope matrix, which includes these characteristics, coincides well with the average profile experimentally found over a large area of the Far East. The formula was refined by switching to an analysis of a tabular function of one variable (instead of two), which provides more reliable statistical data and more measurements per cell of the tabular function. The scatter of measured values relative to the average profile turned out to be quite large due, in part, to the insufficiently accurate consideration of the influence of elevation in the profile formula. Using approximation, we found the dependence of two parameters of the formula on height and, on this basis, obtained a more accurate formal description of the fall of the runoff lines. The derivatives of the original and refined profile functions yield similar dependences of the longitudinal slope on the runoff length and elevation. These dependences are described by a common formula with different parameters.
Keywords: DTM, runoff model, runoff line profile, fall of the runoff line, longitudinal slope, runoff line length, source height, statistical dependence
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