Power law Scaling in Drainage Basin Areas of Independent landscapes

Power-law distributions occur in a diverse range of phenomena. Natural drainage networks also exhibit distinctive fractal properties and certain power-law scaling relationships irrespective of the underlined controls, such as geology, topography, and climate. Here we study the distribution of basin areas of continents as well as some islands. We used area-fraction vs. rank distribution, where the area fraction represents the area of a basin with respect to the total landscape area. To obtain the basin area distribution, we used HydroRivers data for the nine continent regions and performed DEM analysis for 12 islands. The results show that basin area distribution follows a power law in the case of all continents with scaling exponent ranging from -1.15 to -1.4. In the case of islands, the majority of them followed power law scaling with exponent ranging from -1.2 to around -2.5; however, distributions of some islands deviated from the power laws.

We also looked at the basin area distribution with the optimal channel network model with all boundary pixels modelled as outlets. We got the scaling exponent around -1.8. Our recently proposed probabilistic model for drainage network evolution (Borse & Biswal, 2023) shows the capability to produce networks with different distributions. This model can capture the varying range of exponents with its flexible parameters. Further studies would be needed to understand the significance of this basin area distribution scaling exponent and whether it could be used as a metric to characterize landscapes.