======================================= Lunar Gravitational Maps 2026 (LGM2026) ======================================= 1. Introduction =============== LGM2026 is a suite of maps showing the lunar gravitational field at the lunar topography and on its circumscribing sphere. Depicted are the gravitational potential, the gravitational vector and the gravitational tensor at a spatial resolution of 128 pixels per degree (~250 m at the equator). LGM2026 relies on observed GRAIL gravity (harmonic degrees up to 500, wavelengths up to 11 km at the equator) and gravity modeled from topography using a 3D crustal density model (harmonic degrees beyond 500, wavelengths shorter than 11 km at the equator). The maps on the circumscribing sphere have been transformed into a spherical-harmonic expansion of the lunar gravitational field up to degree 11519. 1.1 Recommendation ------------------ Before working with LGM2026, read at least Section 3.2. 1.2 Data points --------------- The resolution of LGM2026 is 1/128 degree. Each map thus consists of 23040 by 46080 pixels that are organized in a 2D grid. The grids are stored in the pixel registration (in the jargon of Generic Mapping Tools); that is, all data refer to the pixel centers. Vertically, the points of the lunar surface gravitational maps reside 0.1 m above the lunar topography as represented by the LDEM128_PA_pixel_202405 model (Neumann, 2024). The points on the circumscribing sphere have a constant spherical radius of 1749 km. Neumann, G. (2024). LOLA MOON_PA gridded dataset [Data set]. NASA Goddard Space Flight Center Planetary Geodesy Data Archive. doi: https://doi.org/10.60903/LOLA_PA 1.3 Coordinate system of the maps --------------------------------- All maps use the Moon's principal axes coordinate system. 1.4 Coordinate system of the gravitational vector and tensor ------------------------------------------------------------ The gravitational vector and the gravitational tensor are expressed in the local north-oriented reference frame, which has the origin at the data point, the x-axis points to the north, the y-axis points to the west and the z-axis points radially outwards. 1.5 Gravitational field ----------------------- LGM2026 shows quantities of the gravitational field. Neither the centrifugal field nor the normal gravity field is accounted for in LGM2026. Given that the position of all LGM2026 points is published along with the maps, these contributions can be easily evaluated whenever necessary. 1.6 Accuracy ------------ The accuracy of the LGM2026 surface maps is estimated as follows: * 13 m**2 * s**-2 for the gravitational potential; once the normal gravitational potential is subtracted, the accuracy improves by three to four orders of magnitude, * 2 mGal for the gravitational vector (1 mGal = 10**-5 m * s**-2), * 250 E for the diagonal elements of the gravitational tensor and a few tens of E for the off-diagonal elements (1 E = 10**-9 s**-2). The maps on the circumscribing sphere should be more accurate than the surface maps at least by two orders of magnitude for the gravitational potential, one order of magnitude for the gravitational vector and three orders of magnitude for the gravitational tensor. 1.7 Limitations --------------- * Beyond degree 500, that is, at wavelengths shorter than ~11 km at the equator, LGM2026 does not incorporate any observed gravitational data and therefore it must not be geophysically or geologically interpreted at these scales. * Noise is present in the grids on the circumscribing sphere at scales shorter than ~9 km for the gravitational potential, ~2 km for the gravitational vector and ~650 meters for the gravitational tensor. The surface maps are not affected by this issue. * The LDEM128_PA_pixel_202405 topography model contains artifacts which propagated into LGM2026. The artifacts are found mostly (but not only) at latitudes beyond +-60 degrees towards the poles. 1.8 Citation ------------ Bucha, B. (2026). Lunar gravitational maps from GRAIL gravity, LRO and Kaguya topography and 3D crustal density. Submitted to Icarus. 1.9 Contact ----------- Blazej Bucha, blazej.bucha@stuba.sk 2. Input Data and Methods ========================= LGM2026 has two main constituents. * Long wavelengths are derived from the Kaula-constrained GRGM1200B (Goossens et al., 2020) up to degree 500 (~11 km at the equator). GRGM1200B is a spherical-harmonic model of the lunar gravitational field derived from GRAIL observations. * Short-scale gravitational signals were obtained by gravity-forward modeling of lunar topography using a 3D crustal density model. The topography was represented by the LDEM128_PA_pixel_202405 model (Neumann, 2024) and the crustal density model was due to Goossens et al. (2020) (the 3D linear density variant with the cap radius of 15 deg and the degree range 250--650). The long wavelength component of LGM2026 was obtained by spherical-harmonic synthesis of GRGM1200B up to degree 500. The short-scale signals were obtained by residual terrain modeling (RTM) using 3D variable density. Near-zone gravitational effects (up to 10 deg from data points) were forward-modeled using tesseroids with radially variable density. Far-zone gravitational effects (beyond 10 deg) were obtained by a spherical-harmonic gravity-forward modeling modified to spherical caps and 3D densities. The low-frequency RTM correction was applied to all LGM2026 quantities. The high-frequency RTM correction was not relevant due to the use of the spherical-harmonic spectral gravity-forward modeling. Goossens S., Sabaka T. J., Wieczorek M. A., Neumann G. A., Mazarico E., Lemoine F. G., Nicholas J. B., Smith D. E., Zuber M. T. (2020). High-resolution gravity field models from GRAIL data and implications for models of the density structure of the Moon's crust. Journal of Geophysical Research: Planets 125:e2019JE006086, https://doi.org/10.1029/2019JE006086 3. Structure of the repository ============================== The structure of the LGM2026 repository is as follows: . |-- lgm2026-grd-checksums.zip -- Checksums for all "h5" files |-- lgm2026-grd-example-read.py -- Example reading of an "h5" file in | Python |-- lgm2026-grd-figures.zip -- Simple plots of data from the "h5" | files |-- lgm2026-grd-N00E000.h5 -- 36 HDF5 files with LGM2026 grids |-- lgm2026-grd-N00E060.h5 |-- ... |-- lgm2026-grd-S90E300.h5 |-- lgm2026-manuscript.pdf -- Manuscript on LGM2026 |-- lgm2026-shcs-checksums.zip -- Checksums for "lgm2026-shcs.gfc" |-- lgm2026-shcs-figures.zip -- Plot of degree amplitudes of LGM2026 |-- lgm2026-shcs.gfc -- Spherical-harmonic coefficients of | the gravitational field up to degree | 11519 |-- lgm2026-visualization.mp4 -- Video visualization of LGM2026 |-- LICENSE -- CC BY 4.0 license, under which | LGM2026 data are published `-- README -- This file The size of the entire LGM2026 repository is about 167 GB. LGM2026 grids are stored in the "./lgm2026-grd-*.h5" files using the HDF5 file format (suffix "h5"; see Section 3.1). Each "h5" data file (4.6 GB) contains all LGM2026 maps within a range of 30 degrees in latitude and 60 degrees in longitude (3840 by 7680 pixels). The files are named by the coordinates of the south-westernmost pixel corner. The pattern is lgm2026-grd-[N|S]xxEyyy.h5 where "N" and "S" denote the northern and southern hemisphere, respectively, "xx" is the latitude of the southernmost pixel grid line, "E" denotes longitudes measured positively to the east and "yyy" is the longitude of the westernmost pixel grid line. For instance, the latitude and the longitude of the south-westernmost (bottom left) pixel corner of the region in "./lgm2026-grd-N60E180.h5" are 60 degrees and 180 degrees, respectively. For this tile, the latitude and the longitude of the south-westernmost pixel center are thus "60 + 1 / (2 * 128)" degrees and "180 + 1 / (2 * 128)" degrees, respectively. The spherical-harmonic coefficients of the lunar external gravitational field up to degree 11519 are stored in "./lgm2026-shcs.gfc". The file format is defined by International Center for Global Earth Models (ICGEM; https://icgem.gfz.de/home). 3.1 Structure of HDF5 files --------------------------- HDF5 is an open format to store and organize large datasets (https://www.hdfgroup.org/). It organizes "datasets" into containers called "groups". Datasets and groups may have attached small objects to them called "attributes". HDF5 can be read by all commonly used programming languages. All "h5" files share the same structure. The first-level groups are: "/position" -- 3D position of data points "/gravitational-field" -- Full-scale gravitational maps (the main product) "/residual-gravitational-field" -- Residual gravitational maps from RTM (a by-product) Each first-level group contains two second-level groups: "topography" -- Data associated with the maps residing at the lunar topography "sphere" -- Data associated with the maps residing on the circumscribing sphere The second-level groups: "/position/topography" "/position/sphere" contain three datasets: "latitude" -- Spherical latitude of LGM2026 points (centers of the pixels) "longitude" -- Spherical longitude of LGM2026 points (centers of the pixels) "radius" -- Spherical radius of LGM2026 points (the vertical offset of 0.1 m mentioned in Section 1.2 is already accounted for in this dataset; do not add the 0.1 m offset) The second-level groups: "/gravitational-field/topography" "/gravitational-field/sphere" "/residual-gravitational-field/topography" "/residual-gravitational-field/sphere" contain 10 datasets (all in single precision): "v" -- The gravitational potential "vx" -- The x-element of the gravitational vector "vy" -- The y-element of the gravitational vector "vz" -- The z-element of the gravitational vector "vxx" -- The xx-element of the gravitational tensor "vxy" -- The xy-element of the gravitational tensor "vxz" -- The xz-element of the gravitational tensor "vyy" -- The yy-element of the gravitational tensor "vyz" -- The yz-element of the gravitational tensor "vzz" -- The zz-element of the gravitational tensor Each dataset (including those in the "/position" group) has two attributes: "unit" -- Physical unit of the dataset as a string "offset" -- Value that must be added to the associated dataset. It may or may not be zero. The offset value of the same dataset (e.g., "/gravitational-field/topography/vz") may vary between the tiles. A simple rule that ensures proper data reading is to *always* add the offset value to the dataset, be the offset zero or not, and to always use only that offset, which is found in the same tile as the dataset. All floating points in the datasets and attributes are stored in single precision except for the "latitude" and "longitude" datasets and their "offset" attributes, which are stored in double precision. A brief listing of the groups and datasets of each "h5" file reads: / Group /gravitational-field Group /gravitational-field/sphere Group /gravitational-field/sphere/v Dataset {3840, 7680} /gravitational-field/sphere/vx Dataset {3840, 7680} /gravitational-field/sphere/vxx Dataset {3840, 7680} /gravitational-field/sphere/vxy Dataset {3840, 7680} /gravitational-field/sphere/vxz Dataset {3840, 7680} /gravitational-field/sphere/vy Dataset {3840, 7680} /gravitational-field/sphere/vyy Dataset {3840, 7680} /gravitational-field/sphere/vyz Dataset {3840, 7680} /gravitational-field/sphere/vz Dataset {3840, 7680} /gravitational-field/sphere/vzz Dataset {3840, 7680} /gravitational-field/topography Group /gravitational-field/topography/v Dataset {3840, 7680} /gravitational-field/topography/vx Dataset {3840, 7680} /gravitational-field/topography/vxx Dataset {3840, 7680} /gravitational-field/topography/vxy Dataset {3840, 7680} /gravitational-field/topography/vxz Dataset {3840, 7680} /gravitational-field/topography/vy Dataset {3840, 7680} /gravitational-field/topography/vyy Dataset {3840, 7680} /gravitational-field/topography/vyz Dataset {3840, 7680} /gravitational-field/topography/vz Dataset {3840, 7680} /gravitational-field/topography/vzz Dataset {3840, 7680} /position Group /position/sphere Group /position/sphere/latitude Dataset {3840} /position/sphere/longitude Dataset {7680} /position/sphere/radius Dataset {SCALAR} /position/topography Group /position/topography/latitude Dataset {3840} /position/topography/longitude Dataset {7680} /position/topography/radius Dataset {3840, 7680} /residual-gravitational-field Group /residual-gravitational-field/sphere Group /residual-gravitational-field/sphere/v Dataset {3840, 7680} /residual-gravitational-field/sphere/vx Dataset {3840, 7680} /residual-gravitational-field/sphere/vxx Dataset {3840, 7680} /residual-gravitational-field/sphere/vxy Dataset {3840, 7680} /residual-gravitational-field/sphere/vxz Dataset {3840, 7680} /residual-gravitational-field/sphere/vy Dataset {3840, 7680} /residual-gravitational-field/sphere/vyy Dataset {3840, 7680} /residual-gravitational-field/sphere/vyz Dataset {3840, 7680} /residual-gravitational-field/sphere/vz Dataset {3840, 7680} /residual-gravitational-field/sphere/vzz Dataset {3840, 7680} /residual-gravitational-field/topography Group /residual-gravitational-field/topography/v Dataset {3840, 7680} /residual-gravitational-field/topography/vx Dataset {3840, 7680} /residual-gravitational-field/topography/vxx Dataset {3840, 7680} /residual-gravitational-field/topography/vxy Dataset {3840, 7680} /residual-gravitational-field/topography/vxz Dataset {3840, 7680} /residual-gravitational-field/topography/vy Dataset {3840, 7680} /residual-gravitational-field/topography/vyy Dataset {3840, 7680} /residual-gravitational-field/topography/vyz Dataset {3840, 7680} /residual-gravitational-field/topography/vz Dataset {3840, 7680} /residual-gravitational-field/topography/vzz Dataset {3840, 7680} A more lengthy list that shows not only the groups and datasets but also the attributes and the data types reads (for "./lgm2026-grd-N60E000.h5" as an example): HDF5 "./lgm2026-grd-N60E000.h5" { GROUP "/" { GROUP "gravitational-field" { GROUP "sphere" { DATASET "v" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vx" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vxx" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vxy" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vxz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vy" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vyy" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vyz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vzz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } } GROUP "topography" { DATASET "v" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vx" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vxx" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vxy" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vxz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vy" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vyy" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vyz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vzz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } } } GROUP "position" { GROUP "sphere" { DATASET "latitude" { DATATYPE H5T_IEEE_F64LE DATASPACE SIMPLE { ( 3840 ) / ( 3840 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F64LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "longitude" { DATATYPE H5T_IEEE_F64LE DATASPACE SIMPLE { ( 7680 ) / ( 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F64LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "radius" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } } GROUP "topography" { DATASET "latitude" { DATATYPE H5T_IEEE_F64LE DATASPACE SIMPLE { ( 3840 ) / ( 3840 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F64LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "longitude" { DATATYPE H5T_IEEE_F64LE DATASPACE SIMPLE { ( 7680 ) / ( 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F64LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "radius" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } } } GROUP "residual-gravitational-field" { GROUP "sphere" { DATASET "v" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vx" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vxx" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vxy" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vxz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vy" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vyy" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vyz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vzz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } } GROUP "topography" { DATASET "v" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vx" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vxx" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vxy" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vxz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vy" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vyy" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vyz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } DATASET "vzz" { DATATYPE H5T_IEEE_F32LE DATASPACE SIMPLE { ( 3840, 7680 ) / ( 3840, 7680 ) } ATTRIBUTE "offset" { DATATYPE H5T_IEEE_F32LE DATASPACE SCALAR } ATTRIBUTE "unit" { DATATYPE H5T_STRING { STRSIZE H5T_VARIABLE; STRPAD H5T_STR_NULLTERM; CSET H5T_CSET_UTF8; CTYPE H5T_C_S1; } DATASPACE SCALAR } } } } } } All array elements in the 2D datasets are stored first along latitude parallels (west to east) and then along meridians (north to south). The first record is for the north-westernmost pixel. If you read the files in programming languages that store arrays in the column-major format (Fortran, Julia, GNU Octave, MATLAB, etc.), you may need to transpose the arrays after the reading to get the shape of 3840 by 7680 as shown above. Programming languages following the row-major data storing method (C, C++, NumPy in Python, etc.) should load the arrays in the 3840 by 7680 shape by default. 3.2 Data processing ------------------- Except for the "latitude" and "longitude" datasets and their "offset" attributes, all floating points are stored in single precision (32 bits, see Section 3.1). In order not to lose precision when adding offsets to datasets, the following approach is recommended for the single precision datasets. 1) Read your dataset in single precision. 2) Cast your dataset to double precision. Naturally, this will almost certainly create garbage digits beyond the 7th digit or so, because the datasets cannot be represented exactly in single precision. But this is okay because, as long as the offsets have not been applied, the single precision datasets are not accurate to that many digits anyway. 3) Read your offset in single precision. 4) Cast your offset to double precision. This can be done exactly without any artificial digits (unlike in the step 2), because all offsets take values that can be represented in single precision exactly. 5) Add your double precision offset to your double precision dataset. 6) From now on, use only the double precision output from step 5) in your code. Without the casts, you may lose precision. For instance, the gravitational potential may be rounded to integer values if not explicitly cast to double precision, simply because there are not enough bits in single precision to store all digits after the decimal point. 3.3 Example read in Python -------------------------- See "./lgm2026-grd-example-read.py". Funding ======= Funded by the EU NextGenerationEU through the Recovery and Resilience Plan for Slovakia under the project No. 09I03-03-V04-00273. Disclaimer ========== The dataset provided here is offered "as-is" and without any warranties of any kind, either express or implied, including but not limited to the accuracy, completeness, reliability, or fitness for a particular purpose. By using this dataset, you agree to assume all risks associated with its use. Neither the dataset creator nor Slovak University of Technology in Bratislava take any responsibility for any damages, losses, or legal issues arising from the use of these data.