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

• Published in: Water resources research 2001-05, Vol.37 (5), p.1503-1509
• Main Authors: La Barbera, P., Lanza, L. G.
• Format: Article
• Language: English
• Subjects: Freshwater; Italy; Italy, Liguria
• ISSN: 0043-1397; 1944-7973
• DOI: 10.1029/2000WR900382

The natural drainage network in 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 RA, analogous to the Hortonian area ratio, holds for independent basins. A multiplicative factor Rc is also defined as the average ratio between the number of independent basins of a given order ω and those of order ω+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] ∝ a−γ, with γ = log Rc/log RA. The derived form and parameters of the CAD are shown to hold for the Liguria region of Italy (≃5700 km2 in the northern Mediterranean) as well as for the whole continental Italy (≃250,000 km2). 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/γ. The analytical results obtained are shown to agree with the theoretical expressions already available in the literature for optimal channel networks.