A new approach for dealing with depressions in digital elevation models when calculating flow accumulation values

Calculation of flow accumulation (also known as upstream area) matrices from digital elevation models (DEMs) is a very common procedure in hydrological studies, and also has been used in other disciplines within physical geography, such as glaciology. A problem with such calculations has always been the presence of closed depressions in DEMs; flow is directed towards such areas, but then cannot ‘escape’. In many implementations of flow accumulation algorithms such depressions have been removed from the DEM with some form of pre-processing algorithm which typically transform depressions into flat areas, across which area can then be routed. This approach effectively assumes that all depressions in a DEM are therefore artifacts, and not true features within the landscape. The proliferation of very high quality, high precision, and fine spatial resolution DEMs in recent years means that such an assumption is increasingly difficult to support. In this paper, some of the main flow accumulation algorithms and some existing techniques for dealing with closed depressions in DEMs are reviewed. A new algorithm is presented which assumes that such depressions are real features in the landscape, and which allows them to ‘fill’ and then ‘overflow’ into downstream areas within the DEM. Examples with a synthetic and two real DEMs suggest that, at least in these cases, the assumption that depressions are real is justified. These results also suggest that determining the size distribution for depressions within a DEM could form the basis for identifying whether artifact depressions are a problem in individual DEMs.