# Non-universality in the erosion of tilted landscapes

## TL;DR

This study uses the nonperturbative renormalization group to analyze an erosion model, revealing that the roughness exponent varies with soil and erosion details, explaining the diversity of landscape roughness observed in nature.

## Contribution

It demonstrates the nonuniversality of the erosion model's roughness exponent due to a line of fixed points, challenging previous assumptions of universality.

## Key findings

- The roughness exponent depends weakly on soil and erosion details.
- The model exhibits a line of fixed points leading to nonuniversality.
- This explains the wide range of roughness exponents in natural landscapes.

## Abstract

The anisotropic model for landscapes erosion proposed by Pastor-Satorras and Rothman in [R. Pastor-Satorras and D. H. Rothman, Phys. Rev. Lett. 80, 4349 (1998)] is believed to capture the physics of erosion at intermediate length scale ($\lesssim3$ km), and to account for the large value of the roughness exponent $\alpha$ observed in real data at this scale. Our study of this model -- conducted using the nonperturbative renormalization group (NPRG) -- concludes on the nonuniversality of this exponent because of the existence of a line of fixed points. Thus the roughness exponent depends (weakly) on the details of the soil and the erosion mechanisms. We conjecture that this feature, while preserving the generic scaling observed in real data, could explain the wide spectrum of values of $\alpha$ measured for natural landscapes.