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 investiga te scaling properties and the form of the probability distribution for basi n areas along a coastal boundary. The Horton/Strahler approach used in the classical description of the drainage network within a single basin is exte nded to a series of independent though conterminous basins with outlet to t he 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 a lso defined as the average ratio between the number of independent basins o f a given order omega and those of order omega + 1. The cumulative area dis tribution (CAD) for drainage basins that drain along the coastal boundary i s obtained as a power law in the form P[A > a] proportional to a(-gamma), w ith gamma log R-C/log R-A, The derived form and parameters of the CAD are s hown 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 literat ure for optimal channel networks.