![Earth Gravitational Model 1996](https://upload.wikimedia.org/wikipedia/commons/3/3b/Earth_Gravitational_Model_1996.png)
The Earth Gravitational Models (EGM) are a series of
geopotential model
In geophysics and physical geodesy, a geopotential model is the theoretical analysis of measuring and calculating the effects of Earth's gravitational field (the geopotential).
Newton's law
Newton's law of universal gravitation states that the ...
s of the Earth published by the
National Geospatial-Intelligence Agency
The National Geospatial-Intelligence Agency (NGA) is a combat support agency within the United States Department of Defense whose primary mission is collecting, analyzing, and distributing geospatial intelligence (GEOINT) in support of national ...
(NGA). They are used as the
geoid
The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended ...
reference in the
World Geodetic System
The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also descri ...
.
The NGA provides the models in two formats: as the series of numerical coefficients to the
spherical harmonics
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields.
Since the spherical harmonics form a ...
which define the model, or a dataset giving the geoid height at each coordinate at a given resolution.
Three model versions have been published: EGM84 with n=m=180, EGM96 with n=m=360, and EGM2008 with n=m=2160. n and m are the degree and orders of harmonic coefficients; the higher they are, the more parameters the models have, and the more precise they are. EGM2008 also contains expansions to n=2190.
Developmental versions of the EGM are referred to as Preliminary Gravitational Models (PGMs).
Each version of EGM has its own
EPSG code EPSG Geodetic Parameter Dataset (also EPSG registry) is a public registry of geodetic datums, spatial reference systems, Earth ellipsoids, coordinate transformations and related units of measurement. Originally created by European Petroleum Survey ...
as a
vertical datum
In geodesy, surveying, hydrography and navigation, vertical datum or altimetric datum, is a reference coordinate surface used for vertical positions, such as the elevations of Earth-bound features (terrain, bathymetry, water level, and built stru ...
.
History
EGM84
The first EGM, EGM84, was defined as a part of WGS84. WGS84 combines the old
GRS 80
The Geodetic Reference System 1980 (GRS 80) is a geodetic reference system consisting of a global reference ellipsoid and a normal gravity model.
Background
Geodesy is the scientific discipline that deals with the measurement and representation ...
with the then-latest data, namely available Doppler, satellite laser ranging and Very Long Baseline Interferometry (
VLBI
Very-long-baseline interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy. In VLBI a signal from an astronomical radio source, such as a quasar, is collected at multiple radio telescopes on Earth or in space. The ...
) observations, and a new
least squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...
method called collocation. It allowed for a model with n=m=180 to be defined, providing a raster for every half degree (30', 30 minute) of latitude and longitude of the world. NIMA also computed and made available 30′×30′ mean altimeter derived gravity anomalies from the
GEOSAT
The GEOSAT (GEOdetic SATellite) was a U.S. Navy Earth observation satellite, launched on March 12, 1985 into an 800 km, 108° inclination orbit, with a nodal period of about 6040 seconds. The satellite carried a radar altimeter capable of m ...
Geodetic Mission. 15′×15′ is also available.
EGM96
EGM96 from 1996 is the result of a collaboration between the
National Imagery and Mapping Agency
The National Geospatial-Intelligence Agency (NGA) is a combat support agency within the United States Department of Defense whose primary mission is collecting, analyzing, and distributing geospatial intelligence (GEOINT) in support of national ...
(NIMA), the NASA
Goddard Space Flight Center
The Goddard Space Flight Center (GSFC) is a major NASA space research laboratory located approximately northeast of Washington, D.C. in Greenbelt, Maryland, United States. Established on May 1, 1959 as NASA's first space flight center, GSFC empl ...
(GSFC), and the
Ohio State University
The Ohio State University, commonly called Ohio State or OSU, is a public land-grant research university in Columbus, Ohio. A member of the University System of Ohio, it has been ranked by major institutional rankings among the best publ ...
. It took advantage of new surface
gravity data from many different regions of the globe, including data newly released from the NIMA archives. Major terrestrial gravity acquisitions by NIMA since 1990 include airborne gravity surveys over Greenland and parts of the Arctic and the Antarctic, surveyed by the
Naval Research Lab
The United States Naval Research Laboratory (NRL) is the corporate research laboratory for the United States Navy and the United States Marine Corps. It was founded in 1923 and conducts basic scientific research, applied research, technological ...
(NRL) and cooperative gravity collection projects, several of which were undertaken with the University of Leeds. These collection efforts have improved the data holdings over many of the world's land areas, including Africa, Canada, parts of South America and Africa, Southeast Asia, Eastern Europe, and the former Soviet Union. In addition, there have been major efforts to improve NIMA's existing 30' mean anomaly database through contributions over various countries in Asia. EGM96 also included altimeter derived anomalies derived from
ERS-1
European Remote Sensing satellite (ERS) was the European Space Agency's first Earth-observing satellite programme using a polar orbit. It consisted of 2 satellites, ERS-1 and ERS-2.
ERS-1
ERS-1 launched 17 July 1991 from Guiana Space Centre ...
by Kort & Matrikelstyrelsen (KMS), (National Survey and Cadastre, Denmark) over portions of the Arctic, and the Antarctic, as well as the altimeter derived anomalies of Schoene
996
Year 996 ( CMXCVI) was a leap year starting on Wednesday (link will display the full calendar) of the Julian calendar.
Events
By place
Japan
* February - Chotoku Incident: Fujiwara no Korechika and Takaie shoot an arrow at Retired Em ...
over the
Weddell Sea
The Weddell Sea is part of the Southern Ocean and contains the Weddell Gyre. Its land boundaries are defined by the bay formed from the coasts of Coats Land and the Antarctic Peninsula. The easternmost point is Cape Norvegia at Princess Martha ...
. The raster from EGM96 is provided at 15'x15' resolution.
EGM96 is a composite solution, consisting of:
# a combination solution to degree and order 70,
# a block diagonal solution from degree 71 to 359,
# and the quadrature solution at degree 360.
PGM2000A
PGM may refer to:
Math and science
* probabilistic graphical model, which can be directed or undirected
* Phosphoglycerate mutase, an enzyme that catalyses step 8 of glycolysis
* Phosphoglucomutase, an enzyme that interconverts G6P and G1P
* P ...
is an EGM96 derivative model that incorporates normal equations for the dynamic ocean topography implied by the
POCM4B ocean general circulation model
Ocean general circulation models (OGCMs) are a particular kind of general circulation model to describe physical and thermodynamical processes in oceans. The oceanic general circulation is defined as the horizontal space scale and time scale large ...
.
EGM2008
The official Earth Gravitational Model EGM2008 has been publicly released by the National Geospatial-Intelligence Agency (NGA) EGM Development Team. Among other new data sources, the
GRACE
Grace may refer to:
Places United States
* Grace, Idaho, a city
* Grace (CTA station), Chicago Transit Authority's Howard Line, Illinois
* Little Goose Creek (Kentucky), location of Grace post office
* Grace, Carroll County, Missouri, an uninco ...
satellite mission provided a very high resolution model of the global gravity. This gravitational model is complete to
spherical harmonic
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields.
Since the spherical harmonics form a ...
degree and order 2159 (block diagonal), and contains additional coefficients extending to degree 2190 and order 2159. It provides a raster of 2.5′×2.5′ and an accuracy approaching 10 cm. 1'×1' is also available in non-float but lossless
PGM,
but original .gsb files are better. Indeed, some libraries like GeographicLib use uncompressed PGM, but it is not original float data as was present in .gsb format. That introduces an error of up to 0.3 mm because of 16 bit quantisation, using lossless float GeoTIFF or original .gsb files is a good idea.
The two grids can be recreated by using program in Fortran and source data from NGA. "Test versions" of EGM2008 includes PGM2004, 2006, and 2007.
As with all spherical harmonic models, EGM2008 can be truncated to have fewer coefficients with lower resolution.
EGM2020
EGM2020 is to be a new release (still not released as of February 2022) with the same structure as EGM2008, but with improved accuracy by incorporating newer data. It was originally planned to be released in April 2020. The precursor version XGM2016 (X stands for experimental) was released in 2016 up to degree and order (d/o) 719. XGM2019e was released in 2020 up to spheroidal d/o 5399 (that corresponds to a spatial resolution of 2′ which is ~4 km) and spherical d/o 5540 with a different
spheroidal harmonic
Spheroidal wave functions are solutions of the Helmholtz equation that are found by writing the equation in spheroidal coordinates and applying the technique of separation of variables, just like the use of spherical coordinates lead to spherical h ...
construction followed by conversion back into spherical harmonics. XGM2020 was also released recently.
See also
*
Geoid
The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended ...
*
ETRS89
The European Terrestrial Reference System 1989 (ETRS89) is an ECEF (Earth-Centered, Earth-Fixed) geodetic Cartesian reference frame, in which the Eurasian Plate as a whole is static. The coordinates and maps in Europe based on ETRS89 are not sub ...
*
NAD83
The North American Datum (NAD) is the horizontal datum now used to define the geodetic network in North America. A datum is a formal description of the shape of the Earth along with an "anchor" point for the coordinate system. In surveying, ca ...
*
WGS84
The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also descr ...
References
{{reflist
External links
EGM96: The NASA GSFC and NIMA Joint Geopotential ModelEarth Gravitational Model 2008 (EGM2008)GeographicLibprovides a utility GeoidEval (with source code) to evaluate the
geoid
The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended ...
height for the EGM84, EGM96, and EGM2008 Earth gravity models. Here is a
online version of GeoidEval
The Tracker Component Libraryfrom the
United States Naval Research Laboratory
The United States Naval Research Laboratory (NRL) is the corporate research laboratory for the United States Navy and the United States Marine Corps. It was founded in 1923 and conducts basic scientific research, applied research, technological ...
is a free
Matlab
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation ...
library with a number of gravitational synthesis routines. The function
getEGMGeoidHeight
can be used to evaluate the geoid height under the EGM96 and EGM2008 models. Additionally, the gravitational potential, acceleration, and gravity gradient (second spatial derivatives of the potential) can be evaluated using the
spherHarmonicEval
function, as demonstrated in
DemoGravCode
.
Geodesy