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Encyclopedia of Complexity and Systems Science pp 1–19Cite as

Application of Percolation Theory to Statistical Topographies

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Introduction

Percolation theory (Saberi 2015) provides a suitable platform to study the properties of real and artificial landscapes (Isichenko 1992). A landscape is a height profile {h(x)} usually defined on a square lattice where each cell’s elevation value at position x = (x, y) represents the average elevation over the entire footprint of the cell (site). Now imagine that the water is dripping uniformly over the landscape and fills it from the valleys to the mountains, letting the water flow out through the open boundaries. During the raining, watershed lines may also form which divide the landscape into different drainage basins – see Fig. 1. Watersheds play a fundamental role in geomorphology in, e.g., water management (Vorosmarty et al. 1998) and landslide and flood prevention (Lee and Lin 2006). For a given landscape represented as a digital elevation map (DEM), it is possible to determine the watershed lines based on the iterative application of invasion percolation (Fehr et...

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  1. Department of Physics, University of Tehran, Tehran, Iran

    Abbas Ali Saberi

  2. Institut fur Theoretische Physik, Universitat zu Köln, Köln, Germany

    Abbas Ali Saberi

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Saberi, A.A. (2020). Application of Percolation Theory to Statistical Topographies. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_747-1

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