We study the computation of the flow of water on imprecise terrains. We
consider two approaches to modeling flow on a terrain: one where water flows
across the surface of a polyhedral terrain in the direction of steepest
descent, and one where water only flows along the edges of a predefined graph,
for example a grid or a triangulation. In both cases each vertex has an
imprecise elevation, given by an interval of possible values, while its
(x,y)-coordinates are fixed. For the first model, we show that the problem of
deciding whether one vertex may be contained in the watershed of another is
NP-hard. In contrast, for the second model we give a simple O(n log n) time
algorithm to compute the minimal and the maximal watershed of a vertex, where n
is the number of edges of the graph. On a grid model, we can compute the same
in O(n) time