Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2025, Vol. 22, No. 2, pp. 71-81
Tributary distribution statistics — the inflow matrix (analogue of Tokunaga matrix)
1 Space Research Institute RAS, Moscow, Russia
Accepted: 17.02.2025
DOI: 10.21046/2070-7401-2025-22-2-71-81
A new method for describing relief properties is proposed — the inflow matrix. It records the number of flows from inflow lines of one length to inflow lines of another length. This is an analogue of the Tokunaga matrix, but much more detailed. The inflow matrix is calculated from rasters that are created by a standard GIS (geographical information system) runoff model based on the DEM (digital elevation model). There is no need to identify watercourses and divide them into orders. Experimental calculations were carried out on the DEM of a section of the Far East. The description of the matrix through one-dimensional functions has the form of homogeneous power dependencies. A basis is obtained for assuming that the inflow matrix is described by a two-dimensional quadratic power function. This type of dependencies indicates scale invariance. An algorithm for calculating the inflow coefficient based on the matrix (an analogue of the Tokunaga coefficient) is proposed. To calculate it, the flow lines are divided into sections with a length value in the specified intervals. Like the Tokunaga coefficient, the inflow coefficient demonstrates the scale invariance of runoff characteristics, since it is determined only by the difference in the scales of the main flow lines and tributaries. If the size of the intervals is close to ordinal, then the formulas for these coefficients are almost the same. The difference in scales can be measured by the ratio of the lengths of the main flow lines and tributaries. The dependence of the coefficient value on this ratio is close to linear or to a power law with an exponent of about 1. For the inflow matrix, the previously proposed hypothesis of uniform inflow is confirmed: watercourses of the same scale, when flowing, are distributed between watercourses of larger scales proportionally to the total length of watercourses of larger scales.
Keywords: DEM, GIS, flow line length, flow line inflow, statistical characteristics of watercourses, Tokunaga matrix, Tokunaga coefficient, scale invariance
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