Small-perturbation (linearized) model for topographic response of ice shelves to localized melting. Also includes finite element code to solve the fully nonlinear problem. This code accompanies the manuscript:

Stubblefield, A.G., Wearing, M.G., & Meyer, C.R. (2023). Linear analysis of ice-shelf topography response to basal melting and freezing. https://eartharxiv.org/repository/view/5330/

This repository contains a simple model for ice-shelves undergoing localized basal melting or freezing perturbations. The figures in the manuscript can be reproduced with the Jupyter notebooks in the "notebooks" directory. A derivation and analysis of the model is outlined in the first two notebooks. The final notebook "4_nonlinear.ipynb" relies on FEniCSx (https://fenicsproject.org) code in the "nonlinear-model" directory. This notebook can be run via Docker (https://www.docker.com) with the command: docker run --init -ti -p 8888:8888 -v $(pwd):/home/fenics/shared -w /home/fenics/shared dolfinx/lab:stable

The "linear-model" directory contains:

1. params.py: sets the physical and numerical parameters
2. kernel_fcns.py: defines the functions that appear in the solution operators
3. operators.py: defines steady-state and time-dependent solution operators

Examples for running the code are provided in the Jupyter notebooks ("notebooks" directory).

The "nonlinear-model" directory is essentially a fork of the repo https://github.com/agstub/grounding-line-methods that has been translated into Dolfinx. The model is organized in 6 python files in the source directory as follows.

1. params.py contains all of the model parameters and model options.

2. stokes.py contains the Stokes system solver and related functions.

3. mesh_routine.py contains functions that solve the surface kinematic equations, move the mesh, and some post-processing functions.

4. bdry_conds.py contains functions that mark the mesh boundary and apply boundary conditions.

5. smb.py contains surface mass balance functions: basal melting/freezing rate and surface accumulation/ablation rate.

6. main.py runs the model. It contains the time-stepping loop that calls the Stokes solver and mesh-related functions at each timestep, and returns the output.