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Efforts to extract information about climate and tectonics from topography commonly assume that river networks are static. Drainage divides can migrate through time, however, and recent work has shown that divide mobility can potentially induce changes in river profiles comparable to changes caused by variation in rock uplift, climate, or rock properties. We use 1‐D river profile and 2‐D landscape evolution simulations to evaluate how mobile divides influence the interpretation of river profiles in tectonically active settings. We define a nondimensional divide migration number, NDm, as the ratio of the timescale of channel profile response to a change in drainage area (TdA) to the timescale of divide migration (TDm). In simulations of headward divide migration, NDm is much less than unity with no measurable perturbation of channel profiles. Only in simulations configured to induce rapid lateral divide migration are there occasional large stream capture events and zones where localized drainage area loss is fast enough to support NDm values near unity. The rapid response of channel profiles to changes in drainage area ensures that under most conditions profiles maintain quasi‐equilibrium forms and thus generally reflect spatiotemporal variation in rock uplift, climate, or rock properties even during active divide migration. This implies that channel profile form may not reliably record divide mobility, so we evaluate alternate metrics of divide mobility. In our simulations and an example in Taiwan, we find that simple measures of cross‐divide contrasts in topography are more robust metrics of divide mobility than measures of drainage network topology.

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[1] Recent experimental and theoretical studies support the notion that bed load in mountain rivers can both enhance incision rates through wear and inhibit incision rates by covering the bed. These effects may play an important role in landscape evolution and, in particular, the response of river channels to tectonic or climatic perturbation. We use the channel-hillslope integrated landscape development (CHILD) numerical model with two different bedrock incision models that include the dual role of the sediment flux to explore the transient behavior of fluvial landscapes. Both models predict that steady state channel slopes increase in landscapes with higher rock uplift rates. However, the incision models predict different transient responses to an increase in uplift rate, and the behavior of each incision model depends on both the magnitude of change in uplift rate and the local drainage area. In some cases, the transient channel behavior is indistinguishable from that predicted for transport-limited alluvial rivers. In other cases, knickpoints form in some or all of the drainage network, as predicted by the detachmentlimited stream power model. In all cases the response in the lower parts of the network is highly dependent on the response in the upper parts of the network as well as the hillslopes. As the upper parts of the network send more sediment downstream, channel incision rates may rise or fall, and slopes in the lower parts of the channel may, in fact, decrease at times during the transient adjustment to an increase in rock uplift rate. In some cases, channel incision in the upper parts of the network ceases during the transient while the hillslopes adjust to the new uplift rate; drainage density may also change as a function of uplift rate. Our results suggest that if the sediment flux strongly controls bedrock incision rates, then (1) the transient fluvial response will take longer than predicted by the detachment-limited stream power model, (2) changes in channel slope may be much more complex than predicted by the detachment-limited stream power model, and (3) changes in the fluvial system will be closely tied to sediment delivery from the hillslopes. Importantly, our results outline quantitative differences in system behavior produced by competing models and provide a framework for identifying locations in natural systems where differences in channel morphology can be used to discern between competing fluvial erosion models.Citation: Gasparini, N. M., K. X. Whipple, and R. L. Bras (2007), Predictions of steady state and transient landscape morphology using sediment-flux-dependent river incision models,

[1] Although only recently recognized, hanging tributary valleys in unglaciated, tectonically active landscapes are surprisingly common. Stream power-based river incision models do not provide a viable mechanism for the formation of fluvial hanging valleys. Thus these disequilibrium landforms present an opportunity to advance our understanding of river incision processes. In this work, we demonstrate that thresholds apparent in sediment flux-dependent bedrock incision rules provide mechanisms for the formation of hanging valleys in response to transient pulses of river incision. We simplify recently published river incision models in order to derive analytical solutions for the conditions required for hanging valley formation and use these results to guide numerical landscape evolution simulations. Analytical and numerical results demonstrate that during the response to base level fall, sediment flux-dependent incision rules may create either temporary or permanent hanging valleys. These hanging valleys form as a consequence of (1) rapid main stem incision oversteepening tributary junctions beyond some threshold slope or (2) low tributary sediment flux response during the pulse of main stem incision, thus limiting the tributary's capacity to keep pace with main stem incision. The distribution of permanent and temporary hanging valleys results from four competing factors: the magnitude of base level fall, the upstream attenuation of the incision signal, the lag time of the sediment flux response, and the nonsystematic variation in tributary drainage areas within the stream network. The development of hanging valleys in landscapes governed by sediment flux-dependent incision rules limits the transmission of base level fall signals through the channel network, ultimately increasing basin response time.

Abstract. The ability to model surface processes and to couple them to both subsurface and atmospheric regimes has proven invaluable to research in the Earth and planetary sciences. However, creating a new model typically demands a very large investment of time, and modifying an existing model to address a new problem typically means the new work is constrained to its detriment by model adaptations for a different problem.Landlab is an open-source software framework explicitly designed to accelerate the development of new process models by providing (1) a set of tools and existing grid structures -including both regular and irregular gridsto make it faster and easier to develop new process components, or numerical implementations of physical processes; (2) a suite of stable, modular, and interoperable process components that can be combined to create an integrated model; and (3) a set of tools for data input, output, manipulation, and visualization. A set of example models built with these components is also provided. Landlab's structure makes it ideal not only for fully developed modelling applications but also for model prototyping and classroom use. Because of its modular nature, it can also act as a platform for model intercomparison and epistemic uncertainty and sensitivity analyses. Landlab exposes a standardized model interoperability interface, and is able to couple to third-party models and software. Landlab also offers tools to allow the creation of cellular automata, and allows native coupling of such models to more traditional continuous differential equation-based modules. We illustrate the principles of component coupling in Landlab using a model of landform evolution, a cellular ecohydrologic model, and a flood-wave routing model.

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Playfair's law (J. Playfair, illustrations of the Huttonian Theory of the Earth, 1802) requires any two tributaries in a river network to lower at the same rate near their junction. Although this law holds exactly at the junction, it is unclear how well it holds in the vicinity of the junction. This issue has practical importance because Playfair's law has been used to estimate parameters for detachment-limited models of erosion. If the incision rate of a stream is modelled asˇA m S n , whereˇis an erodibility parameter, A is the area drained by the stream, and S is the local gradient of the channel, then the ratio of the parameters m/n can be estimated from junctions by assuming that Playfair's law holds over the distance used to determine S for each tributary. In this paper, Playfair's law and associated m/n estimates are evaluated for simulated basins with constant and temporally varying uplift rates (or baselevel lowering rates). The results demonstrate that estimates of m/n may be biased for basins with upward-concave stream profiles because the local slope must be approximated with an average upstream slope. In addition, when uplift rate varies temporally, knickpoints are shown to travel through the basins with constant vertical velocity. Because incision rates vary within the basin, Playfair's law only holds exactly at the junctions. These effects are more important when slopes are measured over longer distances. Finally, measurement techniques are presented which address these potential biases.