On the cumulative area distribution of natural drainage basins along a coastal boundary

The natural drainage network ill a region is analyzed in order to investigate scaling properties and the form of the probability distribution for basin areas along a coastal boundary. The Horton/Strahler approach used in the classical description of the drainage network within a single basin is extended to a series of independent though conterminous basins with outlet to the sea, assuming that a regional area ratio R-A, analogous to the Hortonian area ratio, holds for independent basins. A multiplicative factor R-C is also defined as the average ratio between the number of independent basins of a given order omega and those of order omega + 1. The cumulative area distribution (CAD) for drainage basins that drain along the coastal boundary is obtained as a power law in the form P[A > a] proportional to a(-gamma), with gamma log R-C/log R-A, The derived form and parameters of the CAD are shown to hold for the Liguria region of Italy (similar or equal to 5700 km(2) in the northern Mediterranean) as well as for the whole continental Italy (similar or equal to 250,000 km(2)). The fractal dimension of the regional system encompassing all drainage areas of basins with outlet to the sea is derived in the form D = 1/gamma. The analytical results obtained are shown to agree with the theoretical expressions already available in the literature for optimal channel networks.