New efficient methods to calculate watersheds

TL;DR

This paper introduces a fast, scalable algorithm based on Invasion Percolation for accurately determining watershed lines on large Digital Elevation Models, revealing their fractal nature across various landscapes.

Contribution

The paper presents a novel sub-linear time algorithm for watershed calculation, enabling high-precision analysis of large-scale systems and demonstrating the fractal properties of watersheds.

Findings

Watershed lines exhibit fractal dimensions around 1.11.

The algorithm processes systems with 10^8 sites in seconds.

High accuracy in measuring watershed fractal dimensions across landscapes.

Abstract

We present an advanced algorithm for the determination of watershed lines on Digital Elevation Models (DEMs), which is based on the iterative application of Invasion Percolation (IIP). The main advantage of our method over previosly proposed ones is that it has a sub-linear time-complexity. This enables us to process systems comprised of up to 10^8 sites in a few cpu seconds. Using our algorithm we are able to demonstrate, convincingly and with high accuracy, the fractal character of watershed lines. We find the fractal dimension of watersheds to be Df = 1.211 +/- 0.001 for artificial landscapes, Df = 1.10 +/- 0.01 for the Alpes and Df = 1.11 +/- 0.01 for the Himalaya.