Spherical harmonic models of the shape of Mercury

The data used to generate these spherical harmonic models is the global digital elevation model (DEM) of Mercury. The DEM is derived from observations made by the Mercury Dual Imaging System (MDIS) narrow-angle camera (NAC) and multispectral wide-angle camera (WAC) on board of the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft. The global DEM was downloaded throught the Astropedia catalog in geoTIFF format and equirectangular projection. Using the rasterio 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 generic-mapping-tools as follows:gmt xyz2grd filename.dat -Gfilename.grd -R0/360/-90/90 -I0.015625/0.015625 -ZTLd -fg -rpgmt grdsample filename.grd -Gfilename_gridline.grd -T The resulting netcdf file was read into the pyshtools software with the SHGrid.from_netcdf() and expanded into spherical harmonics using the function SHGrid.expand(). 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. The four files in this archive are - Mercury_shape_5759.sh.gz- Mercury_shape_2879.sh.gz- Mercury_shape_1439.sh.gz- Mercury_shape_719.sh.gz 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. The spherical harmonic coefficients can be loaded with pyshtools as follows:SHCoeffs.from_file("filename.sh.gz", format='bshc')用于生成此类球谐模型（spherical harmonic models）的数据，取自水星全球数字高程模型（digital elevation model, DEM）。该DEM源自“水星表面、空间环境、地球化学与测距”（MErcury Surface, Space ENvironment, GEochemistry, and Ranging, MESSENGER）探测器搭载的水星双成像系统（Mercury Dual Imaging System, MDIS）的窄角相机（narrow-angle camera, NAC）与多光谱广角相机（multispectral wide-angle camera, WAC）的观测数据。 该全球DEM通过Astropedia目录下载，格式为geoTIFF，投影方式为等经纬度投影（equirectangular projection）。借助rasterio库，我们在Python环境中加载该数据集，按照Astropedia文档所述对其进行局部高度与半径缩放，并导出为.dat格式。随后将该文件转换为netCDF格式，并通过通用制图工具（Generic Mapping Tools, GMT）按如下步骤重采样为网格线配准： gmt xyz2grd filename.dat -Gfilename.grd -R0/360/-90/90 -I0.015625/0.015625 -ZTLd -fg -rp gmt grdsample filename.grd -Gfilename_gridline.grd -T 将得到的netCDF文件通过pyshtools软件的`SHGrid.from_netcdf()`函数读取，并通过`SHGrid.expand()`函数展开为球谐函数形式。本次选用的球谐函数采用“4pi”归一化方式，且排除了(-1)^m的康登-肖特利相位因子（Condon-Shortley phase factor）。球谐系数的单位为米（meters）。 本存档共包含四个文件： - Mercury_shape_5759.sh.gz - Mercury_shape_2879.sh.gz - Mercury_shape_1439.sh.gz - Mercury_shape_719.sh.gz 文件名中的数字5759、2879、1439与719分别对应各文件的最大球谐阶数，其对应的有效空间分辨率分别为每度64、32、16与8个像素。上述文件以pyshtools文档中描述的二进制“bshc”格式存储，并通过gzip进行压缩。低分辨率模型均通过截断最高分辨率模型的球谐系数生成。 可通过如下代码使用pyshtools加载该球谐系数： SHCoeffs.from_file("filename.sh.gz", format='bshc')