# A universal approach for drainage basins

## TL;DR

This paper introduces a universal model extending the Invasion Percolation-Based Algorithm to delineate multiple drainage basins, revealing power-law behaviors and invariance across terrestrial, lunar, and Martian landscapes, and proposing a theoretical basis for Hack's law.

## Contribution

The paper presents a novel, robust method for delineating drainage basins applicable to various planetary landscapes, and establishes a theoretical link for Hack's exponent based on fractal dimensions.

## Key findings

- Power-law distributions of basin perimeters and areas.
- Invariance of power-law exponents across different landscapes.
- Similarity between terrestrial and Martian drainage patterns.

## Abstract

Drainage basins are essential to Geohydrology and Biodiversity. Defining those regions in a simple, robust and efficient way is a constant challenge in Earth Science. Here, we introduce a model to delineate multiple drainage basins through an extension of the Invasion Percolation-Based Algorithm (IPBA). In order to prove the potential of our approach, we apply it to real and artificial datasets. We observe that the perimeter and area distributions of basins and anti-basins display long tails extending over several orders of magnitude and following approximately power-law behaviors. Moreover, the exponents of these power laws depend on spatial correlations and are invariant under the landscape orientation, not only for terrestrial, but lunar and martian landscapes. The terrestrial and martian results are statistically identical, which suggests that a hypothetical martian river would present similarity to the terrestrial rivers. Finally, we propose a theoretical value for the Hack's exponent based on the fractal dimension of watersheds, $\gamma=D/2$. We measure $\gamma=0.54 \pm 0.01$ for Earth, which is close to our estimation of $\gamma \approx 0.55$. Our study suggests that Hack's law can have its origin purely in the maximum and minimum lines of the landscapes.