Landscape Evolution Model (LEM) Stability Analysis

• This is a Python code to numerically compute the solution of the linear stability analysis problem for the detachment-limited landscape evolution model (LEM).
• Using the developed code, the role of m and n (exponents of the specific drainage area and slope, respectively in the fluvial erosion term of the model) on the onset and selection of regular valley spacing can be examined.

Publication

The peer-reviewed publication can be found here: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2022JF006716.

Installation

• numpy and scipy are the required python libraries.

• This repository contains the code as a jupyter notebook, which can be installed using pip as pip install notebook or using Conda conda install -c conda-forge notebook.

• Files s200.mat and w200.mat in the repository contain 200 Quadrature Points and Weight Functions, respectively, for the numerical solver.

Code structure

Each number written in the list below explains the operations and functions for the particular Cell of the Jupyter Notebook.

1. Import relevant packages from numpy and scipy libraries.
2. Import quadrature points and weight functions arrays (s200.mat and w200.mat), define Python functions for trial and test functions used in the weak formulation, and define Python functions to numerically obtain the slope and its derivatives for generic values of m and n.
3. Select values of parameters (C_I,m,n,L,U,k), global variables and arrays used in the solver.
4. For every Channelization Index (C_I) and wavenumber (k), solve the eigenvalue problem using the spectral Galerkin technique with numerical quadrature.
5. Extract the critical Channelization Index C_Icr and the corresponding fastest growing (positive) spatial frequency (k_cr).
6. Save relevant arrays for plotting and further investigations.

Contact Us

For more information about this research, you can reach out to me: Shashank Kumar Anand.

Other Links

Well-commented Python code for the numerical simulations of the Landscape Evolution Model (LEM) by the same author is available at github.com/ShashankAnand1996/LEM. The developed code has been tested to provide efficient and accurate solutions for the LEM in detachment-limited conditions. The published manuscript is also available: Linear layout of multiple flow-direction networks for landscape-evolution simulations.