Continuum Model for River Networks

TL;DR

This paper introduces a stochastic PDE model capturing erosion, avalanching, and precipitation effects, leading to self-organized river networks with power-law basin area distributions and tributary piracy.

Contribution

It presents a novel continuum model that reproduces key statistical features of river networks, including basin area distribution and area-length relationships.

Findings

Algebraic distribution of basin areas

Power law between basin area and river length

Self-organized structured landscape

Abstract

The effects of erosion, avalanching and random precipitation are captured in a simple stochastic partial differential equation for modelling the evolution of river networks. Our model leads to a self-organized structured landscape and to abstraction and piracy of the smaller tributaries as the evolution proceeds. An algebraic distribution of the average basin areas and a power law relationship between the drainage basin area and the river length are found.