Identification and ordering of drainage divides in digital elevation models

Abstract. We propose a novel way to measure and analyse networks of drainage divides from digital elevation models. We developed an algorithm that extracts drainage divides, based on the drainage basin boundaries defined by a stream network. In contrast to streams, there is no straightforward approach to order and classify divides, although it is intuitive that some divides are more important than others. We thus propose a divide-network metric that orders divides based on the average distance one would have to travel down on either side of a divide to reach a common stream location. Because measuring these distances is computationally very expensive, we instead sort divide segments in a tree-like network, starting from endpoints at river junctions. The sorted nature of the network allows assigning distances to points along the divides, which can be shown to scale with the average distance downstream to the common location. Furthermore, because divide segments tend to have characteristic lengths, an ordering scheme in which divide orders increase by one at junctions, mimics these distances. We applied our new algorithm to a natural landscape and to results from landscape evolution model experiments to assess which parameters of divides and divide networks are diagnostic of divide mobility. Results show that stable drainage divides strive to attain a constant hillslope relief as well as flow distance from the nearest stream, provided a distance of > ~ 5 km from endpoints. Disruptions of such pattern can be related to mobile divides that are lower than stable divides, closer to streams, and often asymmetric in shape. In general, we observe that drainage divides high up in the network, i.e., at great distance from endpoints, are more vulnerable than divides closer to endpoints of the network and are more likely to record disturbance for a longer time period. We compared different topographic metrics to assess drainage divide mobility and found that cross-divide differences in hillslope relief proved more useful for assessing divide migration than other tested metrics. Finally, we introduced a new metric to assess divide junction stability, based on the connectivity of junctions with adjacent drainage divide segments.