Distributed Error Propagation Analysis for Automatic Drainage Basin Delineation

Delineation of drainage basins is a popular terrain analysis method for digital elevation model (DEM) data. Currently, a deterministic delineation method is available in a number of terrain analysis software applications. The method uses elevation data for defining flow directions for each elevation point of a DEM and then follows flow paths from a pour point to all upstream points. The influence of a DEM error in the delineation process can be handled by replacing a single DEM D with the distribution of possible correct DEMs p(D). This uncertainty can be integrated into automatic delineation by using the Monte Carlo method, which uses realisations of DEMs drawn from p(D) to calculate probability maps for drainage basin delineations. The benefits of using Monte Carlo-based probability estimation in comparison with deterministic delineation are numerous. Firstly, the Monte Carlo method gives additional information by providing a clear ‘probability band’ for the catchment boundary, where the width of the band is dependent on local topography and the parameters of the DEM error model. In the extreme case, the band covers large areas around the drainage divide. Secondly, in some cases there exist two or more alternative boundaries that will become visible using the Monte Carlo method, whereas a deterministic approach is forced to pick only one of them. The number of samples required to accurately estimate the uncertainties in delineations is not clear, but according to earlier studies, estimation can require hundreds or thousands of samples. Our experiments on a single computer have shown that the use of the Monte Carlo method together with drainage basin delineation algorithms is a computationally demanding problem. In addition, the problem in current terrain analysis software applications is that they are not designed for large DEMs, which require distribution of the processed data and computations between multiple computers. In this paper, we improve existing drainage basin delineation methods for uncertain DEM data by improving and comparing distributed algorithms, used for computing probability maps of the delineations. We measure the performance and behavior of algorithms in different cases and compare the results of MPI (with spatial distribution of the data) and GRID (without spatial distribution) based implementations.