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Spatiospectral localization of data from the GRACE mission using Slepian functions

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slepian_delta

Spatiospectral localization of data from the GRACE/GRACE-FO missions using Slepian functions as originally developed by C. Harig & F. J. Simons. This package is hosted by CSDMS at http://csdms.colorado.edu/wiki/Model:SLEPIAN_Delta

Citation information

Please cite our work as appropriate if you find this package useful.

To cite the method:
Harig, Christopher and Frederik J. Simons. Mapping Greeenland's mass loss in space and time. Proc. Natl. Acad. Sc., 109(49), 19934-19937, 2012. doi:10.1073/pnas.1206785109

To cite the code itself:
Persistent DOI of the latest release: DOI

To cite the application to Greenland:
Harig, Christopher and Frederik J. Simons.
Ice mass loss in Greenland, the Gulf of Alaska, and the Canadian Archipelago: Seasonal cycles and decadal trends.
Geophys. Res. Let., 43 (7), 3150-3159, 2016. http://dx.doi.org/10.1002/2016GL067759

Harig, Christopher and Frederik J. Simons.
Mapping Greeenland's mass loss in space and time.
Proc. Natl. Acad. Sc., 109(49), 19934-19937, 2012. doi:10.1073/pnas.1206785109

To cite the application to Antarctica:
Harig, Christopher and Frederik J. Simons.
Accelerated West Antarctic ice mass loss continues to outpace East Antarctica gains. Earth Planet. Sci. Let., 415, 134-141, 2015. http://dx.doi.org/10.1016/j.epsl.2015.01.029

Latest release hosted on View slepian_delta on File Exchange

Where to start? Slepian localization and GRACE: a recipe

Here is a general outline to study regions and signals in GRACE data.

  1. Set up your data and directory structure, and then with GRACE2PLMT read in the GRACE data files into a matrix for use in Matlab. This function does corrections for C2,0 from the SLR values of Cheng and Tapley, [2004] and degree 1 values from Swenson, [2008].

  2. Decide on your choice of basis, depending on your region of interest and the bandwidth you want. Using GRACE2SLEPT, project the results of GRACE2PLMT into your chosen basis. We recommend that your basis is chosen based on a set of synthetic experiments which estimate the leakage/recovery tradeoffs.

  3. Next run SLEPT2RESID to fit a choice of functions (e.g. lines, quadratics, etc.) to the Slepian coefficients. Note: if you want to remove a model of GIA then you should do that before this step, using a function like CORRECT4GIA.

  4. If you want to examine the total mass trend in a region, this information is calculated and returned as a result from SLEPT2RESID. To summarize, each Slepian coefficient up to the Shannon truncation is multiplied by the integral (found using INTEGRATEBASIS) of the corresponding function over the region. This total data is then fit with TIMESERIESFIT which allows fitting with a custom data variance.

  5. If you want the total map of mass change, multiply the difference between estimated signal coefficients by the corresponding Slepian function, and add them up. Remember the appropriate units. This sum can then be expanded to space using PLM2XYZ By limiting the set of coefficients you use, you can instead make this for any date span, such as for several years or a single year.

Note: The demos above and the package in general expects a couple of environmental variables to be set (e.g. your storage location: $IFILES) and a directory tree for data storage to already be created (i.e. subdirectories in $IFILES). The programs will initially display errors instructing the user to set up these shell variables and folders. Also, if you have an open pool of Matlab workers, a few functions such as KERNELCP will take advantage of the parallel computing resources and run much faster than otherwise.

Function List:

Administrative

LICENSE.txt The license file
README.md The masthead for the package
README_Delta.md This file!

Geographic

baffing.m An outline for a region encompassing the glaciers around Baffin Island
ellesmereg.m An outline for a region encompassing the glaciers around Ellesmere Island
getglaciers.m Return the XY coordinates for glaciers from the Randolph Glacier Inventory

Analysis

Clmlmp2Cab.m Given a spectral covariance matrix, turns it into a Slepian covariance matrix
Clmlmp2Crrp.m Given a spectral covariance matrix, evaluates it in space
coarsenmask.m Given a spatial mask, coarsen its resolution by several methods
cov2plm.m Given a spectral covariance matrix, generates spherical harmonics realizations
geopotential.m Plots geopotential fields for Earth, Moon and Mars
getglaciers.m Get XY coordinates for glaciers in RGI database
gldas2TWSt.m Read the GLDAS products and calculate Terrestrial Water Storage (TWS) fields
grace2plmt.m Turns monthly GRACE data files into a single matrix for time-dependent analysis
grace2slept.m Transform the result of GRACE2PLMT into a Slepian basis
grs.m Computes parameters for a certain geodetic reference system
hash.m Makes a hash (NOTE: This is one of the few files not written by us! It was made by Michael Kleder)
integratebasis.m Integrates Slepian eigenfunctions given as spherical harmonics expansions
lovenums.m Returns elastic Love numbers for a certain Earth model
maskfromgmt.m Given a grid and polgon, generate a gridded mask using Generic Mapping Tools
net2mat.m Saves specified variables from netcdf files as MAT files
netvarread.m Read a netcef file and get the variable list in the file
periodfit.m Find and fit periodic cycles through a data set
plm2avg.m Integrates and averages spherical harmonic expansions
plm2pot.m Reads in and scales geopotential coeffficients
plmresid2cov.m Turns GRACE residual time series into a spherical-harmonic spectral covariance matrix
plmt2diff.m Turns monthly GRACE data matrix into a month-to-month difference map
plmt2resid.m Turns monthly GRACE data matrix into residuals after fitting analysis in the spherical harmonic basis
POMME4.m Reads in and scales geomagnetic coeffficients of the POMME-4 model
readgldas.m Read in the GLDAS products and save them in Matlab friendly formats
resid2plot.m Plots GRACE residual time series
slepresid2cov.m Turns GRACE residual time series into a Slepian covariance matrix
slept2resid.m Turns monthly GRACE data matrix into residuals after fitting in the Slepian basis
timeseriesfit.m Fits polynomial functions to time series with an F-test criterion
topography.m Plots topography fields for Earth, Moon and Mars
TWSt2slept.m Project the TWS fields you previously made into a Slepian basis

Other important stuff

This software is distributed under the GNU Public License v2, which can be found at http://geoweb.princeton.edu/people/simons/license.html and also copied below.

Copyright (C) 2014. Developer can be contacted by email.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You can receive a copy of the GNU General Public License by writing to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

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Spatiospectral localization of data from the GRACE mission using Slepian functions

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