An efficient assignment of drainage direction over flat surfaces in raster digital elevation models

In processing raster digital elevation models (DEMs) it is often necessary to assign drainage directions over flats-that is, over regions with no local elevation gradient. This paper presents an approach to drainage direction assignment which is not restricted by a flat's shape, number of outlets, or surrounding topography. Flow is modeled by superimposing a gradient away from higher terrain with a gradient towards lower terrain resulting in a drainage field exhibiting flow convergence, an improvement over methods which produce regions of parallel flow. This approach builds on previous work by Garbrecht and Martz (1997), but presents several important improvements. The improved algorithm guarantees that flats are only resolved if they have outlets. The algorithm does not require iterative application; a single pass is sufficient to resolve all flats. The algorithm presents a clear strategy for identifying flats and their boundaries. The algorithm is not susceptible to loss of floating-point precision. Furthermore, the algorithm is efficient, operating in O(N) time whereas the older algorithm operates in O(^{N3 / 2}) time. In testing, the improved algorithm ran 6.5 times faster than the old for a 100×100 cell flat and 69 times faster for a 700×700 cell flat. In tests on actual DEMs, the improved algorithm finished its processing 38-110 times sooner while running on a single processor than a parallel implementation of the old algorithm did while running on 16 processors. The improved algorithm is an optimal, accurate, easy-to-implement drop-in replacement for the original. Pseudocode is provided in the paper and working source code is provided in the Supplemental Materials.