Distributed computation of drainage basin delineations from uncertain digital elevation models

Abstract

Automatic delineation of drainage basins from digital elevation models (DEMs) is a well established technique used in terrain analysis. The conventional methodological framework was first developed in the 1980s, after which time complexities and memory requirements of the algorithms for N-cell DEMs have been improved to the point where they are optimal O(N) or nearly optimal O(N log(N)). In addition to algorithmic developments, uncertainty in the drainage basin delineation results has been handled with spatial probability models, which replace a single DEM D with a distribution of possible correct DEMs p(D). If a probability model is used, results are in the form of distributions and can be visualized as a probability map of uncertain drainage basin delineations. In this paper, we improve existing algorithms by deriving distributed algorithms for computing probability maps of the delineations. Our work is based on the use of Monte Carlo integration, process convolution, and Wang & Liu's fast method for removal of DEM depressions. The new algorithms are designed to large, high resolution DEMs. When distributed algorithms process DEM data in a computer cluster with K nodes, the memory requirements for a single node grow according to O(N/K). The performance and behaviour of algorithms are measured in different settings.