Linear layout of multiple flow-direction networks for landscape-evolution simulations

TL;DR

This paper introduces an efficient linear algorithm for arranging multiple flow-direction networks in landscape evolution models, enabling accurate simulations of erosion and landscape dissection.

Contribution

The paper presents a linear-time algorithm for the layout of multiple flow-direction networks, improving computational efficiency and accuracy in landscape evolution simulations.

Findings

Algorithm has linear time complexity with respect to nodes.

Accurately captures transition from smooth to channelized landscapes.

Numerical solutions match theoretical temporal elevation changes.

Abstract

We present an algorithm that is well suited to find the linear layout of the multiple flow-direction network (directed acyclic graph) for an efficient implicit computation of the erosion term in landscape evolution models. The time complexity of the algorithm varies linearly with the number of nodes in the domain, making it very efficient. The resulting numerical scheme allows us to achieve accurate steady-state solutions in conditions of high erosion rates leading to heavily dissected landscapes. We also establish that contrary to single flow-direction methods such as D8, D$\infty$ multiple flow-direction method follows the theoretical prediction of the linear stability analysis and correctly captures the transition from smooth to the channelized regimes. We finally show that the obtained numerical solutions follow the theoretical temporal variation of mean elevation.