pyslfp is a Python package for computing elastic sea level "fingerprints". It provides a robust and user-friendly framework for solving the sea level equation, accounting for the Earth's elastic deformation, gravitational self-consistency between the ice, oceans, and solid Earth, and rotational feedback effects.

The core of the library is the FingerPrint class, which implements an iterative solver to determine the unique pattern of sea-level change that results from a change in a surface load, such as the melting of an ice sheet.

• Elastic Sea Level Equation Solver: Implements an iterative solver for the sea level equation and the generalised sea level equation needed within adjoint calculations.
• Comprehensive Physics: Accounts for Earth's elastic response (via load Love numbers), self-consistent gravity, and rotational feedbacks (polar wander).
• Ice History Models: Includes a data loader for the ICE-5G, ICE-6G, and ICE-7G global ice history models, allowing for easy setup of realistic background states.
• Forward and Adjoint Modeling: Provides a high-level interface for both forward calculations (predicting sea level change from a load) and adjoint modeling (for use in inverse problems), powered by pygeoinf, and based on the theory of Al-Attar et al.(2024)
• Built-in Visualization: Comes with high-quality map plotting utilities built on matplotlib and cartopy for easy visualization of global data grids.

You can install pyslfp directly from PyPI using pip. The package requires Python 3.11+ and its dependencies will be installed automatically.

pip install pyslfp

Alternatively, for development purposes, you can install pyslfp using Poetry. First, clone the repository and then run:

poetry install 

To include the development dependencies (for running tests, building documentation, etc.), use the --with dev flag:

poetry install --with dev

If you use pyslfp in your published work, please cite the following paper:

• Al-Attar, D., Syvret, F., Crawford, O., Mitrovica, J.X. and Lloyd, A.J., 2024. Reciprocity and sensitivity kernels for sea level fingerprints. Geophysical Journal International, 236(1), 362-378.

Additionally, please cite the appropriate ice history model if you use the IceNG class from

• Peltier group data sets

You can run the interactive tutorials directly in Google Colab to get started with the core concepts of the library.

Tutorial Name	Link to Colab
Tutorial 1 - Calculating a Basic Sea Level Fingerprint
Tutorial 2 - A Deeper Dive into the Sea Level Equation
Tutorial 3 - Reciprocity and Generalised Sea Level Forcing
Tutorial 4 - Adjoints and Sensitivity Kernels with pygeoinf
Tutorial 5 - A Bayesian Inverse Problem - Inferring Ice Melt from Tide Gauges

Here's a simple example of how to compute and plot the sea level fingerprint for the melting of 10% of the Northern Hemisphere's ice sheets.

import matplotlib.pyplot as plt
from pyslfp import FingerPrint, plot, IceModel

# 1. Initialise the fingerprint model
# lmax sets the spherical harmonic resolution.
fp = FingerPrint(lmax=256)

# 2. Set the background state (ice and sea level) to the present day
# This uses the built-in ICE-7G model loader.
fp.set_state_from_ice_ng(version=IceModel.ICE7G, date=0.0)

# 3. Define a surface mass load
# This function calculates the load corresponding to melting 10% of
# the Northern Hemisphere's ice mass.
direct_load = fp.northern_hemisphere_load(fraction=0.1)

# 4. Solve the sea level equation for the given load
# This returns the sea level change, surface displacement, gravity change,
# and angular velocity change. In this instance, only the first of the
# returned fields is used. 
sea_level_change, _, _, _ = fp(direct_load=direct_load)

# 5. Plot the resulting sea level fingerprint,
# showing the result only over the oceans.
fig, ax, im = plot(
    sea_level_change * fp.ocean_projection(),
)

# Customize the plot
ax.set_title("Sea Level Fingerprint of Northern Hemisphere Ice Melt", y=1.1)
cbar = fig.colorbar(im, ax=ax, orientation="horizontal", pad=0.05, shrink=0.7)
cbar.set_label("Sea Level Change (meters)")

plt.show()

The output of the above script will look similar to the following figure:

• The library is organized into a few key modules:

• finger_print.py: Contains the main FingerPrint class, which orchestrates the calculations.

• ice_ng.py: Provides the IceNG class for loading and interpolating global ice history models.

• plotting.py: Includes the plot function for visualizing pyshtools.SHGrid objects.

• physical_parameters.py: Defines the EarthModelParameters class, which manages physical constants and non-dimensionalization schemes.

pyslfp is built on top of a robust stack of scientific Python packages:

• numpy & scipy: For numerical operations.

• pyshtools: For spherical harmonic transforms and grid representations.

• pygeoinf: For formulating and solving associated inverse problems

• Cartopy & matplotlib: For creating high-quality map projections and plots.

• regionmask & cf-xarray: For working with geospatial masks.

• pyqt6: As a backend for interactive plotting.

This project is licensed under the BSD-3-Clause License.

If you use pyslfp in your published work, please cite the following paper:

• Al-Attar, D., Syvret, F., Crawford, O., Mitrovica, J.X. and Lloyd, A.J., 2024. Reciprocity and sensitivity kernels for sea level fingerprints. Geophysical Journal International, 236(1), pp.362-378.

Furthermore, if you use the ice models contained in the IceNG class, please cite the appropriate ice history model:

Peltier Group Data Sets

Contributions are welcome! If you have a suggestion or find a bug, please open an issue. Pull requests are also encouraged.