Drainage divides are organized into tree-like networks that may record
information about drainage divide mobility. However, views diverge about how
to best assess divide mobility. Here, we apply a new approach of
automatically extracting and ordering drainage divide networks from digital
elevation models to results from landscape evolution model experiments. We
compared landscapes perturbed by strike-slip faulting and spatiotemporal
variations in erodibility to a reference model to assess which topographic
metrics (hillslope relief, flow distance, and

Example of a mobile drainage divide in the Hindu Kush, Afghanistan.

Divide migration is a time-dependent process that is difficult to quantify.
While the effects of regional-scale drainage captures may be preserved
within sedimentary archives (e.g., Clift et al., 2006), this is unlikely for
smaller-scale drainage captures or gradual divide migration. In such cases,
most studies rely on topographic indicators. Mobile divides are typically
inferred from post-drainage-capture evidence: distorted drainage structures,
low divides (wind gaps), or high tributary junction angles (e.g., Clark et
al., 2004) (Fig. 1). However, divide mobility may
also be expressed in the topography without major drainage captures or flow
reversals but as a result of the more gradual migration of divides. Willett
et al. (2014) inferred drainage divide mobility from across-divide
differences in

In summary, several different metrics have been proposed that may allow for the
quantification of divide mobility in both natural and modeled landscapes.
Forte and Whipple (2018) compared the performance of these metrics with a
landscape evolution model in which they induced divide mobility and
concluded that across-divide differences in relief or gradient better depict
divide motion than

Graphical representation of the model setups in the landscape
evolution experiments. The starting condition of each model is shown at the
top of each rock column. During the experiments, the entire rock column is
eroded and deeper-lying regions are exhumed.

We studied the response of divide networks to stream captures and divide
migration using the TopoToolbox Landscape Evolution Model (TTLEM; Campforts
et al., 2017). In our experiments, we modeled the topographic evolution of
a 20 km

We started from a flat surface with imposed random noise and ran the
experiment for 30 Myr until the topography reached a steady state. The
result of this model, which we termed “Initialize”, provided the starting
point for four other models that we ran for 10 Myr
(Fig. 2). The model “Reference” included no
further changes. In the model “Rotating”, we included a circular (10 km
diameter) left-lateral strike-slip fault that was active throughout the
experiment. Strike-slip faults are well known for enforcing drainage
captures and thus divide mobility (e.g., Castelltort et al., 2012; Duval and
Tucker, 2015). Although the rotating block has, to our knowledge, no
real-world equivalent, this model setup represents a convenient way of
simulating extended periods of strike-slip faulting, as the fault does not
intersect the model boundary (Braun and Sambridge, 1997). The fault slip
rate was fixed at 4 mm yr

Illustration of the junction connectivity (

We analyzed the modeled topography and the associated drainage divide
network. For each modeled topography and at each time step (

The above-described across-divide differences in topographic metrics
essentially aim to quantify divide mobility. In contrast, Spotila (2012)
studied the stability of divides and argued that divide junctions and
pyramidal peaks are more stable than solitary linear divides and might
therefore act as anchor points for drainage divide networks. He proposed
that divide junctions are more difficult to erode than linear divides due
to their greater volume of topography per unit area, their greater
mechanical stability, and their reduction of confluent flows (Spotila,
2012). He also suggested that the stability of divide junctions is related
to the number of joining drainage divides. Because the divide junctions obtained
from our algorithm cannot connect more than four divide segments (Scherler
and Schwanghart, 2020a) – and most often connect three segments – we
introduce a new metric to quantify divide junction connectivity,

Modeled topography and drainage divide network (red solid lines)
at the end of the landscape evolution experiments:

The simulated landscapes, along with their drainage divide networks at the
end of the numerical experiments, are shown in Figs. 4 and 5, and in the “Video supplement”
(Scherler and Schwanghart, 2020b) we provide movies of all simulations. To
provide a measure of the mobility of drainage divides, we computed the
percentages of drainage area that were exchanged during the simulations
between individual catchments that drain to the margin of the model domain
(Fig. 6). Except for the Reference model, all
models are characterized by notable changes in drainage area and mobile
drainage divides. Area changes in the Initialize model are large in the
beginning but level off rapidly during the first 1 Myr. Although area
changes are small after 1 Myr, they continue for another 20 Myr, during
which they are mostly decreasing. In the Rotating model, large area changes
appear as discrete pulses induced by drainage captures of major streams
(Fig. 5b), whereas the background area changes
during rotation and faulting are relatively small (

Erosion rates and divide asymmetry index (DAI) at the end of the
landscape evolution experiments:

Changes in drainage area during the landscape evolution
experiments.

Changes in divide length for divides of different orders during the landscape evolution experiments. Divides have been ordered with the Topo ordering scheme.

We first analyzed the response of the entire drainage network topology to
the perturbations by quantifying the aggregated length of divide segments as
a function of their order (Fig. 7). The first few
million years of the Initialize model are characterized by large changes in divide
lengths and orders. Initially, the divide network extends to orders as high
as 100 but rapidly contracts as the drainage network becomes dendritic.
After about 5 Myr, the highest orders are down to 60. Subsequent changes
result in some scatter of the divide lengths but not in the range of divide
orders. Compared to the Reference model, in which the divide network
structure no longer changes, the Rotating, Inclined, and Spheres
models exhibit changes in the divide network, mostly at divide orders
greater than

We next studied how the above-described disturbances affect drainage divide
metrics during the simulations (Fig. 8). For all
models, we computed the averages of the topographic parameters measured at
drainage divides of specific divide distance intervals
(Fig. 8a–d). As in the analysis of divide-segment
lengths by order, it should be kept in mind that the numbers of divide
segments, or their aggregated lengths (Fig. 7),
are much higher for low orders and distances compared to higher ones. For
reference, a divide order of 20 corresponds to a divide distance of
approximately 9 km. In the Initialize model, all of the studied metrics
attain a constant value that remains unchanged in the Reference model
(Fig. 8) and that may or may not depend on the
divide distance. For example, the mean elevation and junction connectivity
(

Temporal evolution of the drainage divide network during the
landscape evolution experiments. Colored curves show mean values for divide
segments at different divide distances.

It is also worth noting that none of the normalized across-divide
differences in the topographic metrics attain zero values in the Reference
model. This means that even at topographic steady state, there are
residual across-divide differences in hillslope relief, flow distance, and

Minimum hillslope relief

Divide junction connectivity (

Motivated by the observation of constant values in hillslope relief and flow
distance in the Reference model, as well as in actual landscapes (Scherler
and Schwanghart, 2020a), and by our expectation that small values in either
one would be found where one catchment loses area to another
(Fig. 1), we next compared how minimum hillslope
relief (HR

The spatial pattern of divide junction connectivity (

Relationship between across-divide differences in the topographic
metrics hillslope relief (HR), chi (

Coefficient of determination for linear regressions between
normalized across-divide differences in different topographic metrics (HR: hillslope relief; FD: flow distance;

The analysis of stream networks has become a standard tool for inferring
tectonic forcing and landscape history (e.g., Wobus et al., 2006; Kirby and
Whipple, 2012; Demoulin, 2012; Schwanghart and Scherler, 2014). The divide
network holds the potential to record similar tectonic forcing, but also
other aspects of landscape history (e.g., Willett et al., 2014). The
question is which divide metrics are useful to analyze, and what do they tell
us about landscape history? Our Rotating model induced relatively sudden
drainage captures (Fig. 6). Because such events
are associated with the dissection of drainage divides, reliable indicators
are values of hillslope relief (HR) and flow distance (FD) that are much lower
compared to the values that divides (

Figure 11 shows how normalized across-divide
differences in

We speculate that the influence of divide distance on topographic metric–erosion rate relationships may also account for the differences in scatter observed by Sassolas-Serrayet et al. (2019) in landscape evolution experiments similar to our Initialize model between larger and smaller basin areas. But even when excluding divides of low order or low divide distance, we still observe considerable scatter in the topographic metric–erosion rate relationships, which, at the very least, demands caution when interpreting divide morphology in terms of mobility. In this regard, studying Fig. 5 and the videos of the landscape evolution experiments (see the “Video supplement”; Scherler and Schwanghart, 2020b) is insightful: where drainage divides are migrating, one typically observes a range of across-divide topographic metric values that vary considerably during the migration. In other words, despite a continuous divide migration at a large scale, there is often small-scale variability in divide morphology that may in part be related to across-divide differences in topographic metrics lagging behind across-divide differences in erosion rate.

As a final note, we emphasize that the above observations are from our numerical experiments, which depict an idealized world. It is clear that the complexities present in nature, such as anisotropic and variable rock properties, hydroclimatic gradients, mass-wasting events, and biological influences on erosion processes and rates, can lead to landscape patterns that bias any of the above topographic metrics and need to be taken into account when inferring divide dynamics from divide metrics in natural landscapes.

Stream networks tend to attain configurations that are in equilibrium with the geological and climatic environment, given an initial condition (e.g., Rinaldo et al., 2014). Because drainage divides are defined by adjacent drainage basins, the geometry of divide networks should attain a similar equilibrium, which expresses itself in both the geometry of divides and the topology of divide networks. Our numerical experiments have shown that during the initial establishment of a stream network, on a relatively flat surface, both stream and divide networks are far from their steady-state configuration and characterized by networks that extend to high orders (Fig. 7) and long divide distances. During the subsequent extension and shrinkage of individual streams towards their steady-state configuration, the divide network contracts and primarily high-order divide segments shorten and become fewer, whereas divides of low orders maintain their frequencies (Fig. 7).

In general, divide segments of high order, i.e., at great distance from
endpoints, appear to be the most responsive to landscape disturbances
(Fig. 8). In the case of the Rotating model, this
is in part expected because the inner rotating part of the landscape
contains the highest-order divide segments (Fig. 4b). In the cases of the Inclined and Spheres models, it may be related to
the increased probability of recording a disturbance because the adjoining
basins cover a larger area compared to lower-order divides. In other words,
if drainage captures happen somewhere within a drainage basin, this will
most likely influence divides further upstream. Over a distance of less than

Our new junction connectivity index (

Based on landscape evolution model experiments in which we forced divides to
migrate, we found that stable drainage divides strive to attain a constant
hillslope relief and flow distance from the nearest stream, provided
a sufficiently large divide distance to avoid confounding influences near
the edges of the divide network. In our experiments this distance is

The divide algorithm developed in Scherler and Schwanghart (2020a) has been
implemented in the TopoToolbox v2 (Schwanghart and Scherler, 2014). The
codes will be made available with the next TopoToolbox release and shall be
accessible at

The “Video supplement” related to this article is available online at

DS conducted the modeling and led the writing of the paper. Both authors contributed to discussions, editing, and revising the paper.

The authors declare that they have no conflict of interest.

We thank two anonymous reviewers for constructive comments that helped improve the paper.

This research has been supported by the Deutsche Forschungsgemeinschaft (DFG; grant no. SCHE 1676/4-1). The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.

This paper was edited by Sebastien Castelltort and reviewed by two anonymous referees.