lake-altimetry-inversions

Author: Aaron Stubblefield (Dartmouth College)

Overview

This program inverts for a basal vertical velocity anomaly "w_inv" given the observed surface elevation change data "h_obs" as input by solving a least-squares optimization problem.

The motivation is that the basal vertical velocity anomaly is associated with subglacial lake activity that produces the elevation anomaly. Once we invert for the basal vertical velocity anomaly, we can try to estimate the subglacial water-volume change or the areal extent of the lake.

The main model assumptions are (1) Newtonian viscous ice flow, (2) a linear basal sliding law, and (3) that all fields are small perturbations from a simple reference flow state. These assumptions allow for efficient solution of the problem: 2D (map-plane) Fourier transforms and convolution in time are the main operations. The model and numerical method are described in a forthcoming manuscript.

Dependencies

As of this commit, this code runs with the latest SciPy (https://www.scipy.org/) release.

Plotting relies on Matplotlib (https://matplotlib.org/).

Required data

The following data are needed to run the code with ICESat-2 ATL15 data.

(Note: you can run the inversion with synthetic data without downloading this data--see description below)

1. ICESat-2 ATL15, Version 2 (1 km resolution):

   *website: https://nsidc.org/data/atl15/versions/2

   *filename: ATL15_AA_0314_01km_002_02.nc

2. WAVI model output (for basal drag and ice viscosity )

   *website: https://ramadda.data.bas.ac.uk/repository/entry/show?entryid=5f0ac285-cca3-4a0e-bcbc-d921734395ab

   *filename: WAVI_5km_Initial.nc

   *reference:

   Arthern, R. J., Hindmarsh, R. C., & Williams, C. R. (2015). Flow speed within the Antarctic ice sheet and its controls inferred from satellite observations. Journal of Geophysical Research: Earth Surface, 120(7), 1171-1188.

3. MEaSUREs Phase-Based Antarctica Ice Velocity Map, Version 1 (NSIDC-0754)

   *webiste: https://nsidc.org/data/nsidc-0754/versions/1

   *filename: antarctic_ice_vel_phase_map_v01.nc

   *reference:

   Mouginot, J., E. Rignot, and B. Scheuchl. (2019). MEaSUREs Phase-Based Antarctica Ice Velocity Map, Version 1 [Data Set]. Boulder, Colorado USA. NASA National Snow and Ice Data Center Distributed Active Archive Center. https://doi.org/10.5067/PZ3NJ5RXRH10.

4. Antarctic Subglacial Lake inventory

   *website: https://github.com/mrsiegfried/Siegfried2021-GRL

   *filename: SiegfriedFricker2018-outlines.h5

   *references:

   Siegfried, M. R., & Fricker, H. A. (2018). Thirteen years of subglacial lake activity in Antarctica from multi-mission satellite altimetry. Annals of Glaciology, 59(76pt1), 42-55.

   Siegfried, M. R., & Fricker, H. A. (2021). Illuminating active subglacial lake processes with ICESat‐2 laser altimetry. Geophysical Research Letters, 48(14), e2020GL091089.

5. MEaSUREs BedMachine Antarctica, Version 3 (NSIDC-0756) *website: https://nsidc.org/data/nsidc-0756/versions/3

   *filename: BedMachineAntarctica-v3.nc

   *reference:

   Morlighem, M. (2022). MEaSUREs BedMachine Antarctica, Version 3 [Data Set]. Boulder, Colorado USA. NASA National Snow and Ice Data Center Distributed Active Archive Center. https://doi.org/10.5067/FPSU0V1MWUB6. Date Accessed 02-17-2023.

Running the inversion

Follow the example in the Inversion notebook in the notebooks directory.

Contents

The inversion code is in the inverse-model directory.

Source files

The inversion code is organized in several python files in the inverse-model/source directory as follows.

1. inversion.py is the inverse problem solver: this defines the normal equations and calls the conjugate gradient solver.

2. conj_grad.py defines the conjugate gradient method that is used to solve the normal equations.

3. operators.py defines the forward and adjoint operators that appear in the normal equations.

4. kernel_fcns.py defines the relaxation and transfer functions that the forward and adjoint operators depend on.

5. regularizations.py defines the regularization.

6. params.py defines all of the model options and parameters.

There are two auxiliary functions as well:

7. localization.py defines a function that remove the off-lake component from fields when necessary.

8. post_process.py defines functions to estimate the water-volume change from the elevation change and inversion.

Scripts

The inverse-model/scripts contains files for running the model, pre-processing the data, and plotting the results. The main scripts are:

1. make_synth_data.py makes synthetic data that can be inverted to verify the code.

2. proc_icesat_data.py obtains and interpolates the ICESat-2 ATL15 data around a given lake location (from the inventory listed above), and also obtains some auxiliary parameters (ice thickness, viscosity, basal drag coefficient, flow speed).

3. plot_results.py is a plotting script for visualizing the inversion results.

Plotting can be modified in the plot_results.py script.

Notebooks

1. Inversion.ipynb demonstrates how to select the subglacial lake, pre-process the data, run the inversion, and plot the results.

2. PlotMap.ipynb plots a map of Antarctic ATL15 data with zoom-ins on some of our favorite subglacial lakes.

Miscellaneous

There is also some FEniCS (https://fenicsproject.org/) code in the misc directory for producing synthetic data with a fully nonlinear finite element model. See the repository agstub/grounding-line-methods for a description. The version herein assumes radial symmetry.