River networks around the world exhibit statistical scaling laws, including the distribution of independent basin sizes in landscapes. The widespread occurrence of these patterns in various landscapes suggests that there are fundamental, but not yet fully understood, processes responsible for these power law distributions. This study investigates the distribution of independent basin areas across 25 islands worldwide, revealing a clear adherence to a power law pattern. The research suggests that the power law exponent is influenced by landscape boundary characteristics, such as the compactness coefficient and fractal dimension, with the exponent value increasing with these factors. Furthermore, the study demonstrates the development of power law patterns in basin areas using a probabilistic network growth model. This model, based on a preferential headward growth mechanism, underscores the significant roles of boundary conditions and headward growth dynamics in the self-organization of power law patterns in fluvial landscapes.

The coefficient (k) of the Brutsaert-Niber equation (-dQ/dt = kQ^α, Q being discharge at time t) cannot provide information on streamflow dynamics independently because its unit depends on the exponent α. One way to address this challenge is to compute k after fixing α at α median, which may involve large fitting errors. A recent study has therefore adopted a method to decorrelate k from α by resealing Q and demonstrated that the decorrelated coefficients hold useful information on streamflow dynamics. Here, I argue that decorrelation is not dissociation and propose a framework to evaluate the parameter estimation methods quantitatively. Analysis of real as well as synthetic recession curves suggests that under no circumstance the decorrelation method is superior to the fixed exponent method. To conclude, there seems to be no rational solution to the Brutsaert-Niber parameter association problem.