The basic purpose of this study was to develop the method for analyzing the stream network structure of basin geometry and to clarify the relation between quantitative properties of basin geomorphology and the hydrological characteristics of runoff phenomenon in an actual river basin.
As a part of the study on such a theoretical procedure in quantitative geomorphology, this paper discussed on the various stream classification methods suggested in the past and the distribution characteristics of ordered stream numbers.
Then, the numerical calculation based on the concept of stream order was carried out by the statistical theory of stream network systems, which was found on the basic postulate that natural stream network systems in the absence of strong geologic controls are very nearly topologically random.
As the ordering method of stream network systems, Strahler and N_1 ordering systems were applied.
The main results were as follows : 1) Topologically distinct channel networks were evaluated in too extreame numbers cdmparing with ones based on the ambilateral classification. 2) Strahler and N_1 ordering systems were the practical method of stream classification for evaluation in the macro scale of river basin geometry. 3) The frequency distributions of Strahler and N_1 stream numbers drawn from an infinite topologically random stream network systems with respect to each order were approximately given by the normal probability density function. And the standard deviation of stream numbers increased rapidly at the rate of exponential function. 4) The mean stream number and the standard deviation of stream numbers were evaluated in relation to the numbers of first -order streams in random topology stream network systems. 5) The geomorphologic index for orderd stream numbers in an actual river basin was defined and the measuring examples in river basins were shown.