A lattice grain model of hillslope evolution

Thispaperdescribesandexploresanewcontinuous-timestochasticcellularautomatonmodelofhill- slope 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 stochas- tic 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, characteris- tic 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

Fresh shallow valleys in the Martian midlatitudes as features formed by meltwater flow beneath ice

Significant numbers of valleys have been identified in the Martian midlatitudes (30–60°N/S), spatially associated with extant or recent ice accumulations. Many of these valleys date to the Amazonian, but their formation during these cold, dry epochs is problematic. In this study, we look in detail at the form, distribution, and quantitative geomorphology of two suites of these valleys and their associated landforms in order to better constrain the processes of their formation. Since the valleys themselves are so young and thus well preserved, uniquely, we can constrain valley widths and courses and link these to the topography from the Mars Orbiter Laser Altimeter and High-Resolution Stereo Camera data. We show that the valleys are both qualitatively and quantitatively very similar, despite their being >5000 km apart in different hemispheres and around 7 km apart in elevation. Buffered crater counting indicates that the ages of these networks are statistically identical, probably forming during the Late Amazonian, ~100 Ma. In both localities, at least tens of valleys cross local drainage divides, apparently flowing uphill. We interpret these uphill reaches to be characteristic of flow occurring beneath a now absent, relatively thin (order 101–102 m), regionally extensive ice cover. Ridges and mounds occasionally found at the foot of these valley systems are analogous to eskers and aufeis-like refreezing features. On the basis of their interaction with these aufeis-like mounds, we suggest that this suite of landforms may have formed in a single, short episode (perhaps order of days), probably forced by global climate change

Modeling the shape and evolution of normal-fault facets

Facets formed along the footwalls of active normal-fault blocks display a variety of longitudinal profile forms, with variations in gradient, shape, degree of soil cover, and presence or absence of a slope break at the fault trace. We show that a two-dimensional, process-oriented cellular automaton model of facet profile evolution can account for the observed morphologic diversity. The model uses two dimensionless parameters to represent fault slip, progressive rock weathering, and downslope colluvial-soil transport driven by gravity and stochastic disturbance events. The parameters represent rock weathering and soil disturbance rates, respectively, scaled by fault slip rate; both can be derived from field-estimated rate coefficients. In the model's transport-limited regime, slope gradient depends on the ratio of disturbance to slip rate, with a maximum that represents the angle of repose for colluvium. In this regime, facet evolution is consistent with nonlinear diffusion models of soil-mantled hillslope evolution. Under the weathering-limited regime, bedrock becomes partly exposed but microtopography helps trap some colluvium even when facet gradient exceeds the threshold angle. Whereas the model predicts a continuous gradient from footwall to colluvial wedge under transport-limited behavior, fully weathering-limited facets tend to develop a slope break between footwall and basal colluvium as a result of reduced transport efficiency on the rocky footwall slope. To the extent that the model provides a reasonable analogy for natural facets, its behavior suggests that facet profile morphology can provide useful constraints on relative potential rates of rock weathering, soil disturbance, and fault slip

The Landlab v1.0 OverlandFlow component: a Python tool for computing shallow-water flow across watersheds

Representation of flowing water in landscape evolution models (LEMs) is often simplified compared to hydrodynamic models, as LEMs make assumptions reducing physical complexity in favor of computational efficiency. The Landlab modeling framework can be used to bridge the divide between complex runoff models and more traditional LEMs, creating a new type of framework not commonly used in the geomorphology or hydrology communities. Landlab is a Python-language library that includes tools and process components that can be used to create models of Earth-surface dynamics over a range of temporal and spatial scales. The Landlab OverlandFlow component is based on a simplified inertial approximation of the shallow water equations, following the solution of de Almeida et al. (2012). This explicit two-dimensional hydrodynamic algorithm simulates a flood wave across a model domain, where water discharge and flow depth are calculated at all locations within a structured (raster) grid. Here we illustrate how the OverlandFlow component contained within Landlab can be applied as a simplified event-based runoff model and how to couple the runoff model with an incision model operating on decadal timescales. Examples of flow routing on both real and synthetic landscapes are shown. Hydrographs from a single storm at multiple locations in the Spring Creek watershed, Colorado, USA, are illustrated, along with a map of shear stress applied on the land surface by flowing water. The OverlandFlow component can also be coupled with the Landlab DetachmentLtdErosion component to illustrate how the nonsteady flow routing regime impacts incision across a watershed. The hydrograph and incision results are compared to simulations driven by steady-state runoff. Results from the coupled runoff and incision model indicate that runoff dynamics can impact landscape relief and channel concavity, suggesting that on landscape evolution timescales, the OverlandFlow model may lead to differences in simulated topography in comparison with traditional methods. The exploratory test cases described within demonstrate how the OverlandFlow component can be used in both hydrologic and geomorphic applications

Sedimentology and climatic environment of alluvial fans in the Martian Saheki Crater and a comparison with terrestrial fans in the Atacama Desert

The deflated surfaces of the alluvial fans in Saheki crater reveal the most detailed record of fan stratigraphy and evolution found, to date, on Mars. During deposition of at least the uppermost 100 m of fan deposits, discharges from the source basin consisted of channelized flows transporting sediment (which we infer to be primarily sand- and gravel-sized) as bedload coupled with extensive overbank mud-rich flows depositing planar beds of sand-sized or finer sediment. Flow events are inferred to have been of modest magnitude (probably less than ~60 m3/s), of short duration, and probably occupied only a few distributaries during any individual flow event. Occasional channel avulsions resulted in the distribution of sediment across the entire fan. A comparison with fine-grained alluvial fans in Chile’s Atacama Desert provides insights into the processes responsible for constructing the Saheki crater fans: sediment is deposited by channelized flows (transporting sand through boulder-sized material) and overbank mudflows (sand size and finer) and wind erosion leaves channels expressed in inverted topographic relief. The most likely source of water was snowmelt released after annual or epochal accumulation of snow in the headwater source basin on the interior crater rim during the Hesperian to Amazonian periods. We infer the Saheki fans to have been constructed by many hundreds of separate flow events, and accumulation of the necessary snow and release of meltwater may have required favorable orbital configurations or transient global warming

Off-fault deformation rate along the southern San Andreas Fault at Mecca Hills inferred from landscape modeling of curved drainages

Quantifying off-fault deformation (OFD) rates on geomorphic timescales (10^2-10^5 yr) along strike-slip faults is critical for resolving discrepancies between geologic and geodetic slip-rate estimates, improving knowledge of seismic hazard, and understanding the influence of tectonic motion on landscapes. Quantifying OFD over these timescales is challenging without displacement markers such as offset terraces or geologic contacts. We present a landscape evolution model coupled with distributed lateral tectonic shear to show how drainage basins sheared by lateral tectonic motion can reveal OFD rates. The model shows that OFD rate can control the orientation of drainage basin topography: the faster the OFD rate, the greater the deflection of drainage basins towards a fault-parallel orientation. We apply the model to the southern San Andreas Fault near the Mecca Hills, where drainages basins change in orientation with proximity to the fault. Comparison of observed and modeled topography suggests that the OFD rate in the Mecca Hills follows an exponential-like spatial pattern with a maximum rate nearest the fault of 3.5 ± 1.5 mm/yr, which decays to approximately zero at ~600 m distance from the fault. This rate is applicable since the initiation of differential rock uplift in the Mecca Hills at approximately 760 ka. Our results suggest that OFD in this 800 m study area may be as high as 10% of total plate motion. This example demonstrates that curved drainage basins may be used to estimate OFD rates along strike slip faults

On transient semi‐arid ecosystem dynamics using Landlab: vegetation shifts, topographic refugia, and response to climate

Projecting how arid and semi‐arid ecosystems respond to global change requires the integration of a wide array of analytical and numerical models to address different aspects of complex ecosystems. We used the Landlab earth surface modeling toolkit (Hobley et al., 2017, https://doi.org/10.5194/esurf-5-21-2017) to couple several ecohydrologic and vegetation dynamics processes to investigate the controls of exogenous drivers (climate, topography, fires, and grazing) and endogenous grass‐fire feedback mechanisms. Aspect‐controlled ecosystems and historical woody plant encroachment (WPE) narratives in central New Mexico, USA are used to construct simulations. Modeled ecosystem response to climatic wetness (i.e., higher precipitation, lower potential evapotranspiration) on topography follows the Boyko's “geo‐ecological law of distribution.” Shrubs occupy cooler pole‐facing slopes in the dry end of their ecoclimatic range (Mean Annual Precipitation, MAP ≤ 200 mm), and shift toward warmer equator‐facing slopes as regional moisture increases (MAP > 250 mm). Trees begin to occupy pole‐facing slopes when MAP > 200 mm, and gradually move to valleys. Pole‐facing slopes increase species diversity at the landscape scale by hosting relict populations during dry periods. WPE observed in the region since the middle 1800s is predicted as a three‐phase phenomenon. Phase II, rapid expansion, requires the removal of the positive grass‐fire feedback by livestock grazing or fire suppression. Regime shifts from grassland to shrubland are marked by critical thresholds that involve grass cover remaining below 40%, shrub cover increasing to 10%–20% range, and the grass connectivity, Cg, remaining below 0.15. A critical transition to shrubland is predicted when grazing pressure is not removed before shrub cover attains 60%

Short communication: Landlab v2.0: a software package for Earth surface dynamics

Numerical simulation of the form and characteristics of Earth's surface provides insight into its evolution. Landlab is an open-source Python package that contains modularized elements of numerical models for Earth's surface, thus reducing time required for researchers to create new or reimplement existing models. Landlab contains a gridding engine which represents the model domain as a dual graph of structured quadrilaterals (e.g., raster) or irregular Voronoi polygon-Delaunay triangle mesh (e.g., regular hexagons, radially symmetric meshes, and fully irregular meshes). Landlab also contains components - modular implementations of single physical processes - and a suite of utilities that support numerical methods, input/output, and visualization. This contribution describes package development since version 1.0 and backward-compatibility-breaking changes that necessitate the new major release, version 2.0. Substantial changes include refactoring the grid, improving the component standard interface, dropping Python 2 support, and creating 31 new components - for a total of 58 components in the Landlab package. We describe reasons why many changes were made in order to provide insight for designers of future packages. We conclude by discussing lessons about the dynamics of scientific software development gained from the experience of using, developing, maintaining, and teaching with Landlab.</p