How canyons evolve by incision into bedrock: Rainbow Canyon, Death Valley National Park, United States

Incising rivers may be confined by low-slope, erodible hillslopes or steep, resistant sidewalls. In the latter case, the system forms a canyon. We present a morphodynamic model that includes the essential elements of a canyon incising into a plateau, including 1) abrasion-driven channel incision, 2) migration of a canyon-head knickpoint, 3) sediment feed from an alluvial channel upstream of the knickpoint, and 4) production of sediment by sidewall collapse. We calculate incision in terms of collision of clasts with the bed. We calculate knickpoint migration using a moving-boundary formulation that allows a slope discontinuity where the channel head meets an alluvial plateau feeder channel. Rather than modeling sidewall collapse events, we model long-term behavior using a constant sidewall slope as the channel incises. Our morphodynamic model specifically applies to canyon, rather than river–hillslope evolution. We implement it for Rainbow Canyon, CA. Salient results are as follows: 1) Sediment supply from collapsing canyon sidewalls can be substantially larger than that supplied from the feeder channel on the plateau. 2) For any given quasi-equilibrium canyon bedrock slope, two conjugate slopes are possible for the alluvial channel upstream, with the lower of the two corresponding to a substantially lower knickpoint migration rate and higher preservation potential. 3) Knickpoint migration occurs at a substantially faster time scale than regrading of the bedrock channel itself, underlying the significance of disequilibrium processes. Although implemented for constant climactic conditions, the model warrants extension to long-term climate variation.

The convexity of carbonate hillslopes: the influence of climate, chemical weathering and dust flux

<p>Convex soil-covered hillslopes are ubiquitous in various tectonic and climatic settings and are often modeled based on a mass balance relating hillslope convexity to regolith transport and soil production. In order to account for chemical weathering of carbonate rocks and dust input to the regolith, two fluxes that are commonly neglected in settings with silicate-dominated bedrock,  we modify this mass balance.</p><p>We studied 7 study sites in carbonate rocks across an Eastern Mediterranean gradient in the mean annual rainfall (250 to 900 mm yr<sup>-1</sup>) and dust flux (150 to 40 g m<sup>-2</sup> yr<sup>-1</sup>). Combining cosmogenic <sup>36</sup>Cl-derived hilltops denudation rates with an estimate of the regolith chemical depletion and dust fraction based on immobile elements, we predict the hillslope curvature and compare our predictions with observations based on high-resolution airborne LiDAR.</p><p>Our results demonstrate that soft carbonates (chalk) experience faster denudation rates relative to resistant dolo-limestone. However, the harder carbonates are more prone to chemical weathering, which systematically constitutes around half of their total denudation.  Soil production rates exhibit a humped dependency on soil thickness, with an apparent maximum at a depth of 8-16 cm.</p><p>The observed hillslope curvature vary as function of rainfall and dust flux with a minimum at sub-humid sites with intermediate rainfall of  500-600 mm/yr. The predicted curvature based on our new mass balance is not far from the observed curvature, illustrating the prominent effects of dust flux and chemical weathering on hillslope morphology.  Our model also implies that drier sites in the south probably experienced a more complex history of regolith production due dust flux fluctuations.</p><p>By incorporating dust flux and chemical weathering to the classic hillslope evolution model we identify a complex relation between hillslope curvature, soil production, and climate. These two fluxes are not unique to carbonate bedrock and should be incorporated in hillslope evolution models.</p>

Evidence of late-Holocene mud-volcanic eruptions in the Modena foothills (northern Italy)

Among natural hazards, mud volcanoes can damage property and infrastructures and affect hillslope evolution at different spatial and temporal scales. The results of 10-year-long multidisciplinary investigations performed on a Roman-age archaeological site, La Rovina di Montegibbio, are presented, showing a peculiar example of mutual interplay between human settlement and geological forcing in the mud-volcanic environment. The site (350 m a.s.l.) lies at the termination of the upper Secchia River catchment, near the town of Sassuolo (Modena Province). Here, a 4-km-long mud volcano belt borders the Apennines chain front, comprising one of the most prominent mud volcanoes of Italy ( Salsa di Montegibbio), and the still-active chain hinge tectonics gives origin to gas and oil seeps. Based on geological, geoarchaeological, palaeobotanical, geochemical, geophysical records and analytical data, we unravel the onset, the evolution and the abandonment of the settlement in relation to the existence of a previously unknown mud volcano, belonging to the larger Montegibbio mud volcano system. The damages affecting the Roman-age buildings record the ground deformations in the context of mud volcano tectonics. In particular, the pattern of faults set buried under the archaeological site is shown and compared with that of the main mud volcano conduit. At least two Roman-age eruptive episodes have been recorded, whose ejected muds are geochemically characterized. The first recorded eruption must be regarded as the reason for the initial location and function of the sacred ancient settlement. The final site abandonment was because of subsequent severe ground deformations affecting the hillslope as a consequence of mud volcano activity.

A lattice grain model of hillslope evolution

This paper describes and explores a new continuous-time stochastic cellular automaton model of hillslope evolution. The Grain Hill model provides a computational framework with which to study slope forms that arise from stochastic disturbance and rock weathering events. The model operates on a hexagonal lattice, with cell states representing fluid, rock, and grain aggregates that are either stationary or in a state of motion in one of the six cardinal lattice directions. Cells representing near-surface soil material undergo stochastic disturbance events, in which initially stationary material is put into motion. Net downslope transport emerges from the greater likelihood for disturbed material to move downhill than to move uphill. Cells representing rock undergo stochastic weathering events in which the rock is converted into regolith. The model can reproduce a range of common slope forms, from fully soil mantled to rocky or partially mantled, and from convex-upward to planar shapes. An optional additional state represents large blocks that cannot be displaced upward by disturbance events. With the addition of this state, the model captures the morphology of hogbacks, scarps, and similar features. In its simplest form, the model has only three process parameters, which represent disturbance frequency, characteristic disturbance depth, and base-level lowering rate, respectively. Incorporating physical weathering of rock adds one additional parameter, representing the characteristic rock weathering rate. These parameters are not arbitrary but rather have a direct link with corresponding parameters in continuum theory. Comparison between observed and modeled slope forms demonstrates that the model can reproduce both the shape and scale of real hillslope profiles. Model experiments highlight the importance of regolith cover fraction in governing both the downslope mass transport rate and the rate of physical weathering. Equilibrium rocky hillslope profiles are possible even when the rate of base-level lowering exceeds the nominal bare-rock weathering rate, because increases in both slope gradient and roughness can allow for rock weathering rates that are greater than the flat-surface maximum. Examples of transient relaxation of steep, rocky slopes predict the formation of a regolith-mantled pediment that migrates headward through time while maintaining a sharp slope break.

Glassy dynamics of landscape evolution

Soil creeps imperceptibly downhill, but also fails catastrophically to create landslides. Despite the importance of these processes as hazards and in sculpting landscapes, there is no agreed-upon model that captures the full range of behavior. Here we examine the granular origins of hillslope soil transport by discrete element method simulations and reanalysis of measurements in natural landscapes. We find creep for slopes below a critical gradient, where average particle velocity (sediment flux) increases exponentially with friction coefficient (gradient). At critical gradient there is a continuous transition to a dense-granular flow rheology. Slow earthflows and landslides thus exhibit glassy dynamics characteristic of a wide range of disordered materials; they are described by a two-phase flux equation that emerges from grain-scale friction alone. This glassy model reproduces topographic profiles of natural hillslopes, showing its promise for predicting hillslope evolution over geologic timescales.

A lattice grain model of hillslope evolution

This paper describes and explores a new continuous-time stochastic cellular automaton model of hillslope evolution. The Grain Hill model provides a computational framework with which to study slope forms that arise from stochastic disturbance and rock weathering events. The model operates on a hexagonal lattice, with cell states representing fluid, rock, and grain aggregates that are either stationary or in a state of motion in one of the six cardinal lattice directions. The model can reproduce a range of common slope forms, from fully soil mantled to rocky or partially mantled, and from convex-upward to planar shapes. An optional additional state represents large blocks that cannot be displaced upward by disturbance events. With the addition of this state, the model captures the morphology of hogbacks, scarps, and similar features. In its simplest form, the model has only three process parameters, which represent disturbance frequency, characteristic disturbance depth, and baselevel lowering rate, respectively. Incorporating physical weathering of rock adds one additional parameter, representing the characteristic rock weathering rate. These parameters are not arbitrary but rather have a direct link with corresponding parameters in continuum theory. Comparison between observed and modeled slope forms demonstrates that the model can reproduce both the shape and scale of real hillslope profiles. Model experiments highlight the importance of regolith cover fraction in governing both the downslope mass transport rate and the rate of physical weathering. Equilibrium rocky hillslope profiles are possible even when the rate of baselevel lowering exceeds the nominal bare-rock weathering rate, because increases in both slope gradient and roughness can allow for rock weathering rates that are greater than the flat-surface maximum. Examples of transient relaxation of steep, rocky slopes predict the formation of a regolith-mantled pediment that migrates headward through time while maintaining a sharp slope break.

The SPACE 1.0 model: A Landlab component for 2-D calculation of sediment transport, bedrock erosion, and landscape evolution

Models of landscape evolution by river erosion are often either transport-limited (sediment is always available, but may or may not be transportable) or detachment-limited (sediment must be detached from the bed, but is then always transportable). While several models incorporate elements of, or transition between, transport-limited and detachment-limited behavior, most require that either sediment or bedrock, but not both, are eroded at any given time. We present SPACE (Stream Power with Alluvium Conservation and Entrainment) 1.0, a new model for simultaneous evolution of an alluvium layer and a bedrock bed based on conservation of sediment mass both on the bed and in the water column. The model treats sediment transport and bedrock erosion simultaneously, embracing the reality that many rivers (even those commonly defined as "bedrock" rivers) flow over a partially alluviated bed. The SPACE model is a component of the Landlab modeling toolkit, a Python-language library used to create models of earth surface processes. Landlab allows efficient coupling between the SPACE model and components simulating basin hydrology, hillslope evolution, weathering, lithospheric flexure, and other surface processes. Here, we first derive the governing equations of the SPACE model from existing sediment transport and bedrock erosion formulations and explore the behavior of local analytical solutions for sediment flux and alluvium thickness. We derive steady-state analytical solutions for channel slope, alluvium thickness, and sediment flux, and show that SPACE matches predicted behavior in detachment-limited, transport-limited, and mixed conditions. We provide an example of landscape evolution modeling in which SPACE is coupled with hillslope diffusion, and demonstrate that SPACE provides an effective framework for simultaneously modeling 2-D sediment transport and bedrock erosion.