*Introduction *

The official Earth Gravitational Model EGM2008 has been publicly released by the U.S. National Geospatial-Intelligence Agency (NGA) EGM Development Team. This gravitational model is complete to spherical harmonic degree and order 2159, and contains additional coefficients extending to degree 2190 and order 2159. Full access to the model's coefficients and other descriptive files with additional details about EGM2008 are provided herein.

Those wishing to use EGM2008 to compute **geoid undulation values with respect to WGS 84, **may do so using the self-contained suite of coefficient files, FORTRAN software, and pre-computed geoid grids provided on this web page. For other applications, the previous release of the full 'Geoscience' package for EGM2008 can be accessed through the link at the bottom of this web page.

The WGS 84 constants used to define the reference ellipsoid, and the associated normal gravity field, to which the geoid undulations are referenced are:

*a*=6378137.00 m (semi-major axis of WGS 84 ellipsoid)*f*=1/298.257223563 (flattening of WGS 84 ellipsoid)*GM*=3.986004418 x 10^{14}m^{3}s^{-2}(Product of the Earth's mass and the Gravitational Constant)*ω*=7292115 x 10^{-11}radians/sec (Earth's angular velocity)

All synthesis software, coefficients, and pre-computed geoid grids listed below assume a **Tide Free** system, as far as permanent tide is concerned.

Note that the harmonic synthesis software provided below applies a constant, zero-degree term of -41 cm to all geoid undulations computed using EGM2008 with the height_anomaly-to-geoid_undulation correction model (also provided). Similarly, all pre-computed geoid undulations incorporate this constant zero-degree term. This term converts geoid undulations that are intrinsically referenced to an ideal mean-earth ellipsoid into undulations that are referenced to WGS 84. The value of -41 cm derives from a mean-earth ellipsoid for which the estimated parameters in the Tide Free system are: a=6378136.58 m and 1/f=298.257686.

*Description of Software and Data*

To compute point geoid undulations from spherical harmonic synthesis of the EGM2008 Tide Free Spherical Harmonic Coefficients and its associated Correction Model, at any WGS 84 latitude/longitude coordinate pair listed in a coordinate input file (such as INPUT.DAT), use the FORTRAN harmonic synthesis program, hsynth_WGS84.f.

At present, we are also providing two grids of pre-computed geoid undulations: one at 1 x 1-minute resolution and one at 2.5 x 2.5-minute resolution. To interpolate geoid undulations from the 1 x 1-Minute Geoid Undulation Grid file, for any WGS 84 latitude/longitude coordinate pair listed in a coordinate input file (such as INPUT.DAT), use the FORTRAN interpolation program interp_1min.f. Similarly, the FORTRAN interpolation program interp_2p5min.f, will interpolate geoid undulations from the 2.5 x 2.5-Minute Geoid Undulation Grid file.

Filenames containing a ".gz" in the suffix have been compressed using the Unix "gzip" command.

All files that are SMALL ENDIAN format are highlighted in green. All files that are BIG ENDIAN format are highlighted in purple.

Please carefully review the README_WGS84 file for a complete description of coefficient and data files for computing EGM2008 geoid undulations with respect to WGS 84. Also, before using any of the data files on this web page, please read the disclaimer.

For GIS data formats, please visit the EGM2008 GIS Data Page.

- EGM2008 Harmonic Synthesis Program (hsynth_WGS84.f -184 KB) - Use this FORTRAN program to generate WGS 84 geoid undulations by spherical harmonic synthesis of EGM2008 and its associated height_anomaly-to-geoid_undulation correction model. This program requires that the coefficients for both EGM2008 and the correction model, and an INPUT.DAT file, all be located in the same directory as the hsynth_WGS84.f program.
- Harmonic Synthesis Executable for Windows XP (hsynth_WGS84.exe - 696 KB) - Windows executable version of EGM2008 Harmonic Synthesis Program. Use as described above.
- Spherical Harmonic Coefficients for Earth's Gravitational Potential (Tide Free System)
**-**(EGM2008_to2190_TideFree.gz - 72 MB) - EGM2008 coefficients required by the harmonic synthesis program. - Correction Coefficients (Zeta-to-N_to2160_egm2008.gz - 50 MB) - Height_anomaly-to-geoid_undulation coefficients required by the harmonic synthesis program.
- INPUT.DAT (4 KB) - sample input file of WGS 84 latitude/longitude coordinate pairs for testing the harmonic synthesis program.
- OUTPUT.DAT (4 KB)- sample output file of geoid undulation values, generated by reading INPUT.DAT into the harmonic synthesis program (for test verification).

- Interpolation Program for 1 x 1-Minute Geoid Grid (interp_1min.f - 28 KB) - Use this FORTRAN program to interpolate geoid undulations from the 1 x 1-Minute Geoid Undulation Grid file, for any WGS 84 latitude/longitude coordinate pair listed in a coordinate input file (such as INPUT.DAT). When applied to the 1 x 1-Minute Geoid Undulation Grid file, this interp_1min.f program will generate geoid undulation values that match the corresponding values generated by harmonic synthesis (hsynth_WGS84.f or hsynth_WGS84.exe above) to within 1 mm. The interp_1min.f program requires that the 1 x 1-Minute Geoid Undulation Grid file and the INPUT.DAT are located in the same directory as interp_1min.f.
- 1 x 1-Minute Grid Interpolation Executable for Windows XP (interp_1min.exe - 434 KB) - Windows executable version of the Interpolation Program for 1 x 1-Minute Geoid Grid. Use as described above. To be used with the SMALL ENDIAN Geoid Undulation Grid below.
- 1 x 1-Minute Geoid Undulation Grid in WGS 84 - SMALL ENDIAN (Und_min1x1_egm2008_isw=82_WGS84_TideFree_SE.gz - 825 MB) - 1 x 1-minute global grid of pre-computed geoid undulations. This file has a SMALL ENDIAN internal binary representation.
- 1 x 1-Minute Geoid Undulation Grid in WGS 84 - BIG ENDIAN (Und_min1x1_egm2008_isw=82_WGS84_TideFree.gz - 828 MB) - 1 x 1-minute global grid of pre-computed geoid undulations. This file has a BIG ENDIAN internal binary representation.
- INPUT.DAT (4 KB) - sample input file of WGS 84 latitude/longitude coordinate pairs for testing the Interpolation Program for 1 x 1-Minute Geoid Grid.
- OUTPUT.DAT (4 KB)- sample output file of geoid undulation values, generated by reading INPUT.DAT into the Interpolation Program for 1 x 1-Minute Geoid Grid above (for test verification).
- Interpolation Program for 2.5 x 2.5 Minute Geoid Grid (interp_2p5min.f - 28 KB) - Use this FORTRAN program to interpolate geoid undulations from the 2.5 x 2.5-Minute Geoid Undulation Grid file, for any WGS 84 latitude/longitude coordinate pair listed in a coordinate input file (such as INPUT.DAT). When applied to the 2.5 x 2.5-Minute Geoid Undulation Grid file, this interp_2p5min.f program will generate geoid undulation values that match the corresponding values generated by harmonic synthesis (hsynth_WGS84.f or hsynth_WGS84.exe above) to within 1 cm. The interp_2p5min.f program requires that the 2.5 x 2.5-Minute Geoid Undulation Grid file and the INPUT.DAT are located in the same directory as interp_2p5min.f.
- 2.5 x 2.5-Minute Interpolation Executable for Windows XP (interp_2p5min.exe - 434 KB) - Windows executable version of the Interpolation Program for 2.5 x 2.5 Minute Geoid Grid. Use as described above. To be used with the SMALL ENDIAN Geoid Undulation Grid below.
- 2.5 x 2.5-Minute Geoid Undulation Grid in WGS 84 - SMALL ENDIAN (Und_min2.5x2.5_egm2008_isw=82_WGS84_TideFree_SE.gz - 135 MB) - 2.5 x 2.5-minute global grid of pre-computed geoid undulations. This file has a SMALL ENDIAN internal binary representation.
- 2.5 x 2.5-Minute Geoid Undulation Grid in WGS 84 - BIG ENDIAN (Und_min2.5x2.5_egm2008_isw=82_WGS84_TideFree.gz - 135 MB) - 2.5 x 2.5-minute global grid of pre-computed geoid undulations. This file has a BIG ENDIAN internal binary representation.
- INPUT.DAT (4 KB) - sample input file of WGS 84 latitude/longitude coordinate pairs for testing the Interpolation Program for 2.5 x 2.5-Minute Geoid Grid.
- OUTPUT.DAT (4 KB)- sample output file of geoid undulation values, generated by reading INPUT.DAT into the Interpolation Program for 2.5 x 2.5-Minute Geoid Grid above (for test verification).

*Users - Please verify results by comparing to OUTPUT.DAT file immediately above.

- Extract 1 x 1-Minute Grid Program (gridget_1min.f -20 KB) - Use this FORTRAN program to extract a user-defined sub-rectangle of geoid undulations from the 1 x 1-Minute Geoid Undulation Grid file. This program prompts the user for a rectangular area of interest and requires the 1 x 1-Minute Geoid Undulation Grid file to be located in the same directory as the gridget_1min.f program.
- Extract 1 x 1-Minute Grid Executable for Windows XP (gridget_1min.exe - 401 KB) - Windows executable version of the Extract 1 x 1-Minute Grid Program. Use as described above. To be used with the SMALL ENDIAN Geoid Undulation Grid below.
- 1 x 1-Minute Geoid Undulation Grid in WGS 84 - SMALL ENDIAN (Und_min1x1_egm2008_isw=82_WGS84_TideFree_SE.gz - 825 MB) - 1 x 1-minute global grid of pre-computed geoid undulations. This file has a SMALL ENDIAN internal binary representation.
- 1 x 1-Minute Geoid Undulation Grid in WGS 84 - BIG ENDIAN (Und_min1x1_egm2008_isw=82_WGS84_TideFree.gz - 828 MB) - 1 x 1-minute global grid of pre-computed geoid undulations. This file has a BIG ENDIAN internal binary representation.
- Extract 2.5 x 2.5-Minute Grid Program (gridget_2p5min.f - 20 KB) - Use this FORTRAN program to extract a user-defined sub-rectangle of geoid undulations from the 2.5 x 2.5-Minute Geoid Undulation Grid file. This program prompts the user for a rectangular area of interest and requires the 2.5 x 2.5-Minute Geoid Undulation Grid file to be located in the same directory as the gridget_2p5min.f program.
- Extract 2.5 x 2.5-Minute Grid Executable for Windows XP (gridget_2p5min.exe - 397 KB) - Windows executable version of the Extract 2.5 x 2.5-Minute Grid Program. Use as described above. To be used with the SMALL ENDIAN Geoid Undulation Grid below.
- 2.5 x 2.5-Minute Geoid Undulation Grid in WGS 84 - SMALL ENDIAN (Und_min2.5x2.5_egm2008_isw=82_WGS84_TideFree_SE.gz - 135 MB) - 2.5 x 2.5-minute global grid of pre-computed geoid undulations. This file has a SMALL ENDIAN internal binary representation.
- 2.5 x 2.5-Minute Geoid Undulation Grid in WGS 84 - BIG ENDIAN (Und_min2.5x2.5_egm2008_isw=82_WGS84_TideFree.gz - 135 MB) - 2.5 x 2.5-minute global grid of pre-computed geoid undulations. This file has a BIG ENDIAN internal binary representation.

- The development and evaluation of the Earth Gravitational Model 2008 (EGM2008) - Nikolaos K. Pavlis, Simon A. Holmes, Steve C. Kenyon, John K. Factor; Journal of Geophysical Research: Solid Earth (1978-2012) Volume 117, Issue B4, April 2012
- EGM2008 JGR Erratum
- Original Release of the EGM2008 Model Coefficients from EGU General Assembly, Vienna, Austria 2008: Geoscience Package
- An Earth Gravitational Model to Degree 2160: EGM2008 (NPavlis&al_EGU2008.ppt - 18.5 MB) - Presentation given at the 2008 European Geosciences Union General Assembly held in Vienna, Austria, April13-18, 2008.
- Background Papers from Earlier Symposiums on the New EGM

Dr. Nikolaos Pavlis NGA, Geodesy and Geophysics Basic and Applied Research wgs84@nga.mil Nikolaos.K.Pavlis@nga.mil |
NGA Office of Geomatics (SN) EGM2008 Development Team wgs84@nga.mil |

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