Description of the terrain surface through digital elevation models (DEMs) strongly depends on data collection methods and DEM data structures. For eciency and availability reasons regular point distributions are most common, which yield artefacts such as depressions and preferential ¯ow directions. These facts need to be considered when natural phenomena are modelled, as is shown for handling depressions and for estimation of ¯ow paths and upslope contributing areas. Analysis of the main reasons for the occurrence of depressions shows that they usually better re¯ect the terrain than their surroundings. Thus, the most common remedial method of raising depressions is rejected. Algorithms that `cut' a ¯ow path from the depression through its bounding barrier are favoured instead. Several ¯ow routing algorithms are evaluated for their behaviour in regular grids. It is shown that the multiple ¯ow direction (mfd) algorithm that distributes water from a grid cell to the lower of its eight neighbours proportionally to their elevation dierences (slope) exhibits correct ¯ow directions and the best rotation invariance. It is suggested that the estimation of upslope contributing areas (TCAs) is undertaken in two steps: ®rst, a high quality ¯ow direction data set is derived by a well-behaved mfd algorithm or by subgrid modelling of ¯ow paths; secondly, the upslope contributing areas are obtained by counting the upslope elements.