A PHYSICAL EXPLANATION OF THE CUMULATIVE AREA DISTRIBUTION CURVE

A physical explanation for the behavior of the cumulative area distrib ution (CAD) based on the Tokunaga channel network model is given. The CAD is divided into three regions. The first region, for small areas, is dependent on hillslope flow accumulation patterns and represents th e catchment average of the hillslope flow accumulation in the diffusiv e erosion-dominated areas, upstream reaches, of the catchment. The sec ond region represents that portion of the catchment dominated by fluvi al erosion. This region is well described by a log-log linear power la w, which results from the scaling properties of the channel network. T he scale exponent, phi, is highly sensitive to a parameter of the Toku naga stream numbering scheme. The exponent phi converges to -0.5 for h igher order Tokunaga networks for parameters consistent with topologic al random networks. Small networks have lower values of phi, which asy mptotic converges to phi = -0.5 as the catchment scale increase. The t hird region reflects the lowest reaches of the channel network, the sc ale of the catchment, and is a boundary effect. An explicit analytical solution to the scaling properties in the second region is derived on the basis of the Tokunaga network model.