GrainHill cellular hillslope model: GIF animations of hillslope evolution

This collection includes ten animations showing simulated evolution of hypothetical hillslope cross-sectional profiles. The animations accompany a paper by Tucker et al. (2018) in Earth Surface Dynamics.<br

Illustration of weathering and disturbance rules in Grain Hill cellular model of hillslope evolution

Transitions representing rock-to-regolith transformation by weathering (top), and regolith disturbance (bottom), in which a stationary particle becomes mobile and switches position with a air cell. Illustration represents one of the six possible orientations

Illustration of gravitational rules in continuous-time stochastic Lattice Grain model

Illustration of gravitational rules. The bottom row shows the ``falling on a slope'' rule, which effectively imposes a 30-degree angle of repose. Modified from Tucker et al. (2016).<br

Schematic illustration of lattice transitions in Grain Hill model

Example of a four-by-four lattice, illustrating the first nine states in the Grain Hill model and including an example transition in which a falling grain trades places with the fluid cell below it

How might sediment size heterogeneity inhibit river incision?

<div>This is a talk presented on November 4th, 2015 at the Geological Society of America annual meeting in Baltimore, MD, USA. It describes field evidence, theory, and a 1-D numerical model for the influence of large blocks of rock on river erosion. This model was eventually published in Shobe et al (2016, <i>Geophysical Research Letters</i>).</div><div><br></div><div>The presentation includes two model simulation videos, which are also individually included in this repository. The PDF version of the talk has still images in place of the videos. The video "sped_up_control.mp4" accompanies slide 10 and "sped_up_blocks_20s.mp4" accompanies slide 11.</div><div><br></div>Abstract:<div><br></div><div>Rapidly eroding rivers influence adjacent hillslopes by setting their lower boundary conditions, while hillslopes and canyon walls affect rivers by supplying sediment of varying size and lithology. Much progress has been made in identifying the influence of sediment mass flux on river incision, and specifically in identifying the prevalence of erosion-inhibiting bed armor at high sediment supplies. Sediment supplied to rapidly eroding rivers is often very heterogeneous in size, and we argue that significant bed armoring by the largest grains may occur even if sediment mass flux does not exceed a river's carrying capacity. This leads to cases where rivers that quickly cut steep-walled canyons incite a negative feedback on incision by receiving an increased supply of large, immobile sediment from the canyon walls that shields significant portions of the bed from erosion. We use a simple analytical model to demonstrate that this effect is controlled by the sediment size distribution supplied from the hillslopes, the input rate of new large grains, and the rate at which large grains degrade. In model cases where the channel is decoupled from the hillslopes (i.e., increased incision does not increase the supply of large grains), the pace of river incision remains consistent through time. In cases where rapid river incision leads to an increased influx of large grains from the hillslopes (reflecting the hypothesis that steeper slopes will be more prone to releasing large grains), erosion slows as the fraction of the bed shielded by immobile grains increases. This result suggests an inherent negative feedback on incision in channels with access to a supply of large grains. Preliminary results from field surveys in the canyons of the Wind River and Beartooth ranges suggest that the residence time of large boulders and blocks in a single channel reach is long enough to cause significant long-term bed armoring. Our results show that changes in sediment size distribution may exert significant control over rates of river and landscape evolution. The critical governing timescales of this effect are the input rate of large, immobile grains from the hillslopes and the degradation rate of large grains in the channel, both of which warrant further investigation.<br></div

When hillslope-derived blocks alter river evolution: A sensitivity analysis

This is a poster presented on December 15th, 2016 at the American Geophysical Union annual meeting in San Francisco, California, USA. It presents initial results for sensitivity analysis of a numerical model of river incision in the presence of hillslope-derived blocks of rock (Shobe et al., 2016; <i>Geophysical Research Letters</i>).<div><br></div><div>Abstract:</div><div><br></div><div>Many studies rely on simple models of river channel evolution for predicting channel response to perturbations and landscape evolution outcomes, as well as extracting climatic and tectonic signals from river longitudinal profiles. However, recent work has shown that large, hillslope-derived blocks delivered to rivers in response to rapid incision may noticeably alter the form and evolution of river profiles from the behavior predicted by the most common models. We use a 1-D model of fluvial erosion and block dynamics to investigate the conditions under which this channel-hillslope feedback influences river erosion and landscape evolution. In the model, block delivery by hillslopes occurs in response to channel bed lowering, and blocks inhibit further erosion by covering the bed and reducing effective bed shear stress. Using formal sensitivity analysis techniques including Morris one-at-a-time screening and variance-based decomposition, we seek to explore the full model parameter space and determine which landscape parameters set the influence of blocks on river incision. We use eight response functions to evaluate model behavior, including the mean, standard deviation, and range of the distributions of elevation and slope in the model domain. Preliminary results indicate that baselevel lowering rate, bed erodibility, initial block size, and a parameter governing the connection between river erosion and volume flux of blocks to the channel control whether or not channel evolution will be influenced by hillslope-derived blocks. Surprisingly, block erodibility and the delay timescale separating channel incision from hillslope response have relatively little influence on model outcomes. Results also show that parameter sensitivity is strongly dependent on the chosen response function, highlighting the need for multiple model metrics. Identification of the most important model parameters allows confident identification of landscapes strongly influenced by block delivery to rivers, where special care may be needed when inverting river profiles for tectonic and climatic signals. Our results support the need for comprehensive model sensitivity analysis in geomorphology, which has the potential to reveal model dynamics that may be missed by simple “brute force” parameter space exploration.<br></div

Exploring river response to tectonic perturbations with the open source, 2-D SPACE model

This is a poster presented on October 25th, 2017 at the Geological Society of America annual meeting in Seattle, WA, USA. The poster presents the SPACE (Stream Power with Alluvium Conservation and Entrainment) model, described fully in Shobe et al (2017, <i>Geoscientific Model Development</i>). A case study is shown in which SPACE is used in conjunction with a hillslope evolution model to explore the development of Basin and Range-type landscapes.<div><br></div><div>Abstract:</div><div><br></div><div>Understanding landscape response to tectonic perturbation requires models that can evolve both sediment and bedrock. However, most models of river channel evolution only treat erosion into a single substrate, or use substrate layering systems that preclude co-evolution of a sediment layer and in-channel bedrock. For example, basic sediment-flux-dependent incision models parameterize the effects of sediment flux on bedrock incision, but do not actually compute sediment transport dynamics explicitly. In these models, high sediment fluxes result in cessation of bedrock incision, but cannot cause aggradation of sediment. We present a new algorithm (the SPACE model) for modeling the simultaneous evolution of sediment and bedrock in river channels in 2-D. SPACE explicitly incorporates sediment entrainment, transport, and deposition as well as bedrock erosion, rather than parameterizing the effects of sediment on bedrock erosion into a flux-dependent function. The model tracks sediment thickness and bedrock elevation, and allows self-organization of sediment flux, channel slope, and sediment thickness in response to model forcings. SPACE can therefore transition freely between, and match known analytical solutions for, both detachment-limited and transport-limited behavior. We develop steady state analytical solutions for channel slope, sediment thickness, and sediment flux in the more complex case of a mixed bedrock-alluvial river, and show that a 2-D numerical implementation of SPACE matches the predictions and need not be constrained by detachment-limited or transport-limited assumptions. SPACE is one of few models equipped to embrace the reality that most channel systems on earth transition between bedrock, bedrock-alluvial, and fully alluviated states over geologic time in response to tectonics. The model is particularly useful for modeling landscape response to tectonic forcing as it can treat the storage and evacuation of sediment as well as bedrock incision. We present an example in which SPACE is coupled with a hillslope diffusion model to explore the dynamics of erosion and sedimentation resulting from topographic growth and decay. As a component of the open source Landlab modeling toolkit, SPACE is easily customized and coupled with other models.<br></div

Hillslope-derived blocks and erosion rate-channel steepness scaling: Emergence of variable-threshold behavior

This is an oral presentation given on December 13th, 2017 at the American Geophysical Union annual meeting in New Orleans, Louisiana, USA. It presents a numerical modeling study exploring steady-state erosion rate-slope and erosion rate-channel steepness relationships in channels influenced by hillslope-derived blocks of rock. The modeling results have been published as Shobe et al (2018; <i>Journal of Geophysical Research: Earth Surface</i>). This study uses the numerical model of Shobe et al (2016; <i>Geophysical Research Letters</i>). The final figure was produced using the model of Lague et al (2005; <i>Journal of Geophysical Research</i>).<div><br></div><div>Abstract:</div><div><br></div><div>The combination of erosion thresholds and time-varying flow in stream channels has been shown to significantly influence channel form and evolution. Mathematical models that describe the relationship between stream channel gradient and erosion rate typically assume a time- and space-invariant erosion threshold, which is dictated either by the size of in-channel sediment or bedrock properties, and is constant across a range of erosion rates and stream gradients. This assumption becomes suspect in cases where the physical mechanisms that impose erosion thresholds may co-vary with erosion rate. For example, recent modeling and field efforts have suggested that large, hillslope-derived blocks of rock delivered to channels may significantly impede erosion and alter channel morphology and evolution. Given that rapid river erosion can lead to hillslope steepening and increased delivery of large grains to channels, it is reasonable to hypothesize that the erosion threshold in a channel may be correlated with its erosion rate. Using a 1-D fluvial erosion model that incorporates incision-rate-dependent delivery of large blocks, we explore the effects of block delivery on the relationship between erosion rate and channel steepness, and assess whether that relationship supports a fixed threshold or one that varies with erosion rate. Unsurprisingly, delivery of blocks to the channel results in steeper steady-state channel profiles than those obtained in the no-blocks case. The increase in steepness relative to the no-blocks case is greater with more rapid block delivery. Above a critical slope, channel steepness ceases to increase with increased block delivery, as blocks become mobile and no longer influence channel evolution. Modeled channel steepness values over a wide range of erosion rates are inconsistent with a single threshold value, but are instead well described by a threshold that increases with increasing erosion rate. The positive relationship between erosion rate and threshold arises as a result of increased erosion rates driving rapid block delivery from hillslopes, which increases the effective erosion threshold in the channel. Our results suggest that a variable-threshold incision model may be more appropriate than a single threshold in steep landscapes with tightly coupled channels and hillslopes.<br></div

pub_shobe_etal_GMD

This repository includes a user guide for the Landlab SPACE component (presented in Shobe et al, in Geosci. Mod. Dev.), an iPython notebook with a working example of the code presented in the user guide, and an example driver script that replicates the example from section 7.3 in the manuscript

Variable thresholds in mountain rivers imposed by hillslope-derived blocks

This is an oral presentation given on October 25th, 2017 at the Geological Society of America annual meeting in Seattle, Washington, USA. It presents a numerical modeling study exploring steady-state erosion rate-slope and erosion rate-channel steepness relationships in channels influenced by hillslope-derived blocks of rock. The modeling results have been published as Shobe et al (2018; <i>Journal of Geophysical Research: Earth Surface</i>). This study uses the numerical model of Shobe et al (2016; <i>Geophysical Research Letters</i>). Data came from Ouimet et al (2009; <i>Geology</i>), Safran et al (2005; <i>Earth Surface Processes and Landforms</i>), and Rossi et al (2017; <i>Geological Society of America Bulletin</i>). The final figure was produced using the model of Lague et al (2005; <i>Journal of Geophysical Research</i>).<div><br></div><div>Abstract:</div><div><br></div><div>Recent field and modeling studies have shown that large, hillslope-derived blocks of rock delivered to channels may alter the course of river profile evolution in ways not accounted for by simple channel evolution models. Block delivery can set up a negative feedback in which blocks retard incision, which leads to a reduction in hillslope relief, and hence a reduction in block supply rate. Here we investigate the implications of these channel-hillslope feedbacks for the predicted relationships between erosion rate and channel slope. We use a 1-D model of fluvial erosion in the presence of hillslope-derived blocks to explore the influence of blocks on channel evolution across a wide range of erosion rates and block delivery scenarios. In general, hillslope block delivery causes increases in channel slope relative to the control (block free) case, and the magnitude of the increase in slope is proportional to the rate of block delivery. This behavior holds for channel slope gradients less than that required to mobilize blocks, beyond which point blocks are easily transported and block-influenced channels exhibit the same behavior as those in the control case. The behavior of the block-influenced channels is not well described by a shear stress/stream power type model with a constant erosion threshold. Instead, a shear stress/stream power model with an erosion threshold that depends on the imposed baselevel lowering rate successfully replicates the scaling of channel slope with baselevel lowering rate in block-influenced channels. We argue that the form of the function relating the erosion threshold to the baselevel lowering rate depends on the relationship between channel incision rate and hillslope block delivery. Our results indicate that the effects of hillslope-derived blocks may be easily incorporated into simple landscape evolution models. The use of a variable-threshold model has important implications for the relationship between erosion rate and channel steepness, showing lower steepness values at low erosion rates and higher steepness at higher erosion rates than equivalent constant-threshold models. The variable-threshold model that arises from considering block dynamics in fluvial erosion yields field-testable predictions for how channels might deviate from the predictions of simpler models.<br></div