Metadata-Version: 2.4
Name: erosionfront
Version: 0.1.17
Summary: Tools for simulating rock slope erosion and the emergent geometry of Richter slopes
Author-email: "Colin P. Stark" <cstarkjp@gmail.com>
Keywords: geomorphology,erosion,rockslope,mesa,butte,cliff retreat,Richter slope,non-convex,geomorphic Hamiltonian,Hamilton-Jacobi equation,level-set,Lax-Friedrichs,Finsler geometry
Classifier: Development Status :: 3 - Alpha
Classifier: Framework :: Jupyter
Classifier: Framework :: MkDocs
Classifier: Intended Audience :: Science/Research
Classifier: Programming Language :: Python :: Implementation :: CPython
Classifier: License :: OSI Approved :: GNU General Public License v3 (GPLv3)
Classifier: Operating System :: MacOS
Classifier: Operating System :: POSIX :: Linux
Classifier: Operating System :: Microsoft :: Windows
Classifier: Topic :: Scientific/Engineering :: Physics
Requires-Python: >=3.14
Description-Content-Type: text/markdown
Requires-Dist: numpy
Requires-Dist: matplotlib
Requires-Dist: scipy
Requires-Dist: shapely
Requires-Dist: rasterio
Requires-Dist: ruptures
Requires-Dist: h5py

# [**The emergent geometry of rock slopes**](https://pypi.org/project/erosionfront/)

[![](https://github.com/cstarkjp/ErosionFront/actions/workflows/pypi-publish.yml/badge.svg?style=cache-control=no-cache)](https://github.com/cstarkjp/ErosionFront/actions/workflows/pypi-publish.yml)



**Summary:** Simulation tools in support of a geomorphic, non-convex Hamiltonian theory of rock ramp-cliff retreat and the emergent geometry of Richter-type slopes.


<div align="center">

![3d model of West Mitten Butte rendered in Blender](https://raw.githubusercontent.com/cstarkjp/ErosionFront/main/images/WestMittenButte/BlenderView1_reduced.png?raw=true
)

</div>

### Abstract

An iconic image of the American West is the desert mesa: a steep cliff, rising above a ramp-like rock slope, capped by a flat bench. This famous landform has long been assumed to develop where strong rock overlies weak, and where rockfall debris suppresses ramp erosion. Such an explanation cannot be true in general, however, because the archetypal geometry can arise even in uniform bedrock with no talus armouring. Here we argue instead that the ramp-cliff shape is an emergent property. Theoretical evidence comes from a simple model of scarp retreat whose combined rates of weathering and surface-normal erosion are written as a slowly varying function of gradient. Model analysis and simulation, using geometric mechanics and level sets, reveal the sharp break in slope to form automatically as a transient shock solution of a non-convex Hamilton-Jacobi equation. Strong erodibility contrasts are not needed to explain this behaviour, but when present they lock the landform into its classic shape and allow it to persist long-term.  Comparison of differential cliff recession in geologically homogeneous versus heterogeneous bedrock confirms our hypothesis.



 ### Level-set solution

The purpose of the Python code presented here is to derive, analyze, and numerically solve a geomorphic Hamiltonian[^1] model of rock slope erosion and retreat[^2]. The code is provided as a 
[Python library package](src/erosionfront)
 and associated Jupyter notebooks (e.g., [here](notebooks/simulation/ErosionFront.ipynb) and  [here](notebooks/analysis/3DProfiling.ipynb)).

<div align="center">

 ![Animated set of HJE solutions of ramp-cliff retreat for varying ratio of upper/lower rock layer erodibility](
    https://raw.githubusercontent.com/cstarkjp/ErosionFront/main/notebooks/simulation/combo/time_slices_test_2layer_ηul0p2.png?raw=true
)
</div>

Numerical solution of the model Hamilton-Jacobi equation is achieved with a level-set scheme[^3] that employs Lax-Friedrichs finite differencing to obtain stable viscosity solutions for a non-convex Hamiltonian. The level-set code is custom implemented in Python.

Model analysis is performed using some tools from geometric mechanics[^4]: having converted the rock-slope erosion model into geomorphic Hamiltonian $\mathcal{H}(\mathbf{r}, \mathbf{p})$ form, this Hamiltonian is then used to derive Hamilton's ray tracing equations $(\partial_{\mathbf{p}}\mathcal{H}, -\partial_{\mathbf{r}}\mathcal{H})$ and the co-metric of rock slope erosion tensor $g^{ij} = \partial_{ij}\mathcal{H}$; these properties are then probed to understand model stability, notably to place bounds on the non-convexity of $\mathcal{H}$ and to identify critical angles.


### References

[^1]: [Stark, C.P., & Stark, G.J., 2022. The direction of landscape erosion. Earth Surface Dynamics, 10: 383-419.](https://doi.org/10.5194/esurf-10-383-2022)

[^2]: [Howard, A.D., & Selby, M.J., 2009. Rock Slopes. In: Parsons, A.J., Abrahams, A.D. (eds). Geomorphology of Desert Environments. Springer, Dordrecht. ](https://doi.org/10.1007/978-1-4020-5719-9_8)

[^3]: [Osher, S., & Fedkiw, R., 2003. Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag New York, Inc.](https://link.springer.com/book/10.1007/b98879)  See page 50.

[^4]: [Holm, D.D., 2011. Geometric Mechanics. Part I: Dynamics and Symmetry (2nd Edition)](https://www.ma.imperial.ac.uk/~dholm/classnotes/HolmPart1-GM.pdf)
