Spherical harmonic models of the shape of Mercury

<p>The data used to generate these spherical harmonic models is the global digital elevation model (DEM) of Mercury, produced by the U.S. Geological Survey (USGS). The DEM was derived from from stereo image pairs (stereo photogrammetry) captured by the Mercury Dual Imaging System (MDIS) narrow-angle camera (NAC) and multispectral wide-angle camera (WAC) on board the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft.&nbsp;</p> <p>The global DEM was downloaded throught the <a href="https://astrogeology.usgs.gov/search/map/Mercury/Topography/MESSENGER/Mercury_Messenger_USGS_DEM_Global_665m_v2">Astropedia catalog</a> in geoTIFF format and equirectangular projection. &nbsp;Using the <a href="https://rasterio.readthedocs.io/en/stable/">rasterio</a> package, the dataset was loaded in python, scaled to the local height and radius (described in the Astropedia documentation), and exported into .dat format. Then, the file was converted into a netcdf format and resampled into a gridline registration using the <a href="https://www.generic-mapping-tools.org/">generic-mapping-tools</a>&nbsp; as follows:<br><code>gmt xyz2grd filename.dat -Gfilename.grd -R0/360/-90/90 -I0.015625/0.015625 -ZTLd -fg -rp</code><br><code>gmt grdsample filename.grd -Gfilename_gridline.grd -T</code></p> <p>The resulting netcdf file was read into the <a href="https://shtools.github.io/SHTOOLS/index.html">pyshtools</a> software with the <code>SHGrid.from_netcdf()</code> and expanded into spherical harmonics using the function <code>SHGrid.expand()</code>. The spherical harmonic functions were chosen to be "4pi" normalized and to exclude the Condon-Shortley phase factor of (-1)m. The units of the coefficients are meters.</p> <p>The four files in this archive are</p> <p>- Mercury_shape_5759.sh.gz<br>- Mercury_shape_2879.sh.gz<br>- Mercury_shape_1439.sh.gz<br>- Mercury_shape_719.sh.gz</p> <p>The numbers 5759, 2879, 1439, and 719 in the filename refer to the maximum spherical harmonic degree of file, which corresponds to effective spatial resolutions of 64, 32, 16, and 8 pixels per degree, respectively. The files are stored in the binary "bshc" format as described in the pyshtools documentation and are furthermore compressed using gzip. The lower resolution models were generated by truncating the spherical harmonic coefficients of the highest resolution model.</p> <p>The spherical harmonic coefficients can be loaded with pyshtools as follows:<br><code>SHCoeffs.from_file("filename.sh.gz", format='bshc')</code></p>