Constancy of the Area of the Total Catchment of Watercourses of the Same Scale and the Distribution of This Catchment between Larger-Scale Watercourses

The article begins with a test of the assumption that the size of the total catchment area of watercourses of the same order (according to Horton–Strahler) is a constant part of the study area, this size is the same for all orders. This assumption follows from Horton ratios, and Horton law proposed earlier gives the size of this part. Our GIS measurements on the DEM of the Far East confirmed this assumption. A hypothesis is proposed about the uniform distribution of watercourses between watercourses of higher orders. This hypothesis, combined with the established constancy of the catchment area, made it possible to formally describe how watercourses are distributed among watercourses of higher orders. The obtained formulas made it possible to analytically describe: Tokunaga coefficients; distribution of the catchment area of watercourses of one order between catchment areas of subsequent orders; formation of the catchment area of watercourses of one order from catchment areas of previous orders; the total catchment area of direct runoff into watercourses of each order. Our direct measurements, as well as the experimental data of other researchers, confirmed the results obtained analytically. It has been suggested that these patterns—both the constancy of the total catchment area and the distribution of this area over larger catchment areas—are not related to the ordinal organization of watercourses, but are dictated by the scale of watercourses. We obtained very close experimental results by distributing watercourses into sections of the same scale not with the help of a system of orders, but directly according to their catchment area, on the basis of whether it falls within a given range of values. It is likely that the hypothesis of a uniform distribution of watercourses between watercourses of a larger scale can be formulated without mentioning orders. The statements in the article are of a statistical nature; they are carried out in the measurements over large areas and for scales with a large number of watercourses.