Abstract
Abstract. We present a new algorithm for solving the common problem of flow trapped in closed depressions within digital elevation models, as encountered in many applications relying on flow routing. Unlike other approaches (e.g., the Priority-Flood depression filling algorithm), this solution is based on the explicit computation of the flow paths both within and across the depressions through the construction of a graph connecting together all adjacent drainage basins. Although this represents many operations, a linear time complexity can be reached for the whole computation, making it very efficient. Compared to the most optimized solutions proposed so far, we show that this algorithm of flow path enforcement yields the best performance when used in landscape evolution models. In addition to its efficiency, our proposed method also has the advantage of letting the user choose among different strategies of flow path enforcement within the depressions (i.e., filling vs. carving). Furthermore, the computed graph of basins is a generic structure that has the potential to be reused for solving other problems as well, such as the simulation of erosion. This sequential algorithm may be helpful for those who need to, e.g., process digital elevation models of moderate size on single computers or run batches of simulations as part of an inference study.
Highlights
Finding flow paths on a topographic surface represented as a digital elevation model (DEM) is a very common task that is required by many applications in domains such as hydrology, geomorphometry, soil erosion, and landscape evolution modeling, and for which various algorithms have been proposed for either gridded DEMs (e.g., O’Callaghan and Mark, 1984; Jenson and Domingue, 1988; Quinn et al, 1991; Tarboton, 1997) or unstructured meshes (e.g., Jones et al, 1990; Banninger, 2007)
Most of the examples below are shown within the context of landscape evolution modeling, using a simple model of block uplift vs. channel erosion by the stream power law
The local gradient ∇z is chosen as the slope between the eroded node and its receiver. We choose this algorithm which is well suited to our flow routing method, some discussion on the limits of this algorithm can be found in Campforts and Govers (2015) for steep topography
Summary
Finding flow paths on a topographic surface represented as a digital elevation model (DEM) is a very common task that is required by many applications in domains such as hydrology, geomorphometry, soil erosion, and landscape evolution modeling, and for which various algorithms have been proposed for either gridded DEMs (e.g., O’Callaghan and Mark, 1984; Jenson and Domingue, 1988; Quinn et al, 1991; Tarboton, 1997) or unstructured meshes (e.g., Jones et al, 1990; Banninger, 2007). We have developed a new method of flow enforcement that is based on the explicit building of a graph of drainage basins (possibly encompassing depressions) and the computation of the flow paths both within and across those basins This idea was first introduced in a Computer Graphics implementation of the stream power law (Cordonnier et al, 2016), but with a sub-optimal complexity. This approach may appear naive at first glance, we have improved it by using fast algorithms of linear complexity at each step of the procedure, which makes the whole computation very efficient Does this method enable the use of a wide range of techniques of flow enforcement within the closed depressions (e.g., depression filling, channel carving, or more advanced techniques), but it provides generic data structures that could potentially be reused for solving other problems like modeling the behavior of erosion–deposition processes within those depressions. We will discuss the assets and limitations of our method, with some focus on landscape evolution modeling applications
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