THE CUMULATIVE DISTRIBUTION CURVE FOR DRAINAGE AREAS

Abstract

In this paper, an equation for describing the cumulative area distribution for river basins is theoretically derived by using a link magnitude law of drainage area and the bifurcation structures of channel networks obtained from Horton’s laws. Analyzed here are 109 large river basins in Japan, which have a wide variety of features in size, geology and climate. The GIS analysis of DEMs for the 109 basins shows that the Shreve’s link magnitude law of drainage areas has a universal scaling property in all of the 109 river basins with the same constant slope. As for the cumulative area distribution, previous researches in GIS analysis and theoretical examination have revealed that it has a power law distribution with a constant slope in lower stream orders. The equation derived here can represent the cumulative area distribution over the whole river basins including the portion of the power law distribution.