New efficient methods for calculating watersheds

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 (IP). The main advantage of our method over previously proposed ones is that it has a sub-linear time-complexity. This enables us to process systems comprising up to 108 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 Alps and Df = 1.11 ± 0.01 for the Himalayas.

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