In Gauss' words, the geoid is "the mathematical figure of the Earth". This figure is an equipotential surface coincident with the idealized mean sea surface. The geoid can be computed from the geodetic boundary value problems that use gravity data as its boundary value. A geoid model computed using gravity data is called a gravimetric geoid. On the other hand, geoid height at bench marks can also be computed using data from spirit leveling and the Global Positioning System (GPS). A geoid model that is fixed to the GPS/leveling data is called a hybrid geoid. Both geoid models can serve as the zero-height-surface of a country's height system by selection. To satisfy this need, National Geodetic Survey has published a series of geoid models (https://geodesy.noaa.gov/GEOID). The vast majority of navigation and positioning applications utilize a hybrid geoid model with the latest model being GEOID18 for CONUS and Puerto Rico/U.S. Virgin Islands and GEOID12B for all other states and territories of the United States. The corresponding gravimetric geoid for these regions is xGEOID19B and USGG2012, respectively. All models are provided at 1 arc-minute resolution.

In Gauss' words, the geoid is "the mathematical figure of the Earth". This figure is an equipotential surface coincident with the idealized mean sea surface. The geoid can be computed from the geodetic boundary value problems that use gravity data as its boundary value. A geoid model computed using gravity data is called gravimetric geoid. On the other hand, geoid height at bench marks can also be computed using data of the spirit leveling and the Global Positioning System (GPS). A geoid model that fixed to the GPS/leveling data is called hybrid geoid. Both geoid models can serve as the zero-height-surface of a country's height system by selection. To satisfy this need, National Geodetic Survey has published a series of geoid models (http://geodesy.noaa.gov/GEOID). The latest models are USGG2012 and GEOID12B, both are at 1 arc-second grids over the territory of the United States.

This 2' geoid height grid for the Principal Hawaiian Islands is distributed as a GEOID96 model. The computation used 61,000 terrestrial and marine gravity data held in the National Geodetic Survey gravity data base in July 1996. These data were augmented by gravity data contributions from NGA (former National Imagery and Mapping Agency (former Defence Mapping Agency)). By means of a Fast Fourier Transform (FFT) technique, high frequency corrections were made to an underlying EGM96 geopotential model through a remove, compute, and restore process. The gravity values are based on the International Gravity Standardization Net 1971 (IGSN71). The geoid heights are referred to the Geodetic Reference System 1980 (GRS80) ellipsoid. Unlike the grid for the conterminous United States, this GEOID96 grid does not incorporate GPS on leveled benchmarks. This model is a gravimetric geoid in a geocentric, ITRF94(1996.0) reference frame. It is necessary to subtract 12.0 cm from these values to obtain the geoid undulation between the best-fit global geopotential surface and the GRS80 ellipsoid (both expressed in a tide free system). Additional information is available at: http://www.ngs.noaa.gov/GEOID/geoid.html We are particularly grateful to NGA (former National Imagery and Mapping Agency) for their assistance and their data contributions.

This 2' geoid height grid for Puerto Rico and the Virgin Islands is distributed as a GEOID96 model. The computation used 26,000 terrestrial and marine gravity data held in the National Geodetic Survey gravity data base in July 1996 These data were augmented by gravity data contributions from NGA (former National Imagery and Mapping Agency (former Defence Mapping Agency)). By means of a Fast Fourier Transform (FFT) technique, high frequency corrections were made to an underlying EGM96 geopotential model through a remove, compute, and restore process. The gravity values are based on the International Gravity Standardization Net 1971 (IGSN71). The geoid heights are referred to the Geodetic Reference System 1980 (GRS80) ellipsoid. Unlike the grid for the conterminous United States, this GEOID96 grid does not incorporate GPS on leveled benchmarks. This model is a gravimetric geoid in a geocentric, ITRF94(1996.0) reference frame. It is necessary to subtract 12.0 cm from these values to obtain the geoid undulation between the best-fit global geopotential surface and the GRS80 ellipsoid (both expressed in a tide free system). Additional information is available at: http://www.ngs.noaa.gov/GEOID/geoid.htmlWe are particularly grateful to NGA (former National Imagery and Mapping Agency) for their assistance and their data contributions.

This 2' x 4' geoid height grid for Alaska is distributed as a GEOID96 model. The computation used 1.1 million terrestrial and marine gravity data held in the National Geodetic Survey gravity data base in July 1996 These data were augmented by gravity data contributions from NGA (former National Imagery and Mapping Agency (former Defence Mapping Agency)). By means of a Fast Fourier Transform (FFT) technique, high frequency corrections were made to an underlying EGM96 geopotential model through a remove, compute, and restore process. The gravity values are based on the International Gravity Standardization Net 1971 (IGSN71). The geoid heights are referred to the Geodetic Reference System 1980 (GRS80) ellipsoid. Unlike the grid for the conterminous United States, this GEOID96 grid does not incorporate GPS on leveled benchmarks. This model is a gravimetric geoid in a geocentric, ITRF94(1996.0) reference frame. It is necessary to subtract 12.0 cm from these values to obtain the geoid undulation between the best-fit global geopotential surface and the GRS80 ellipsoid (both expressed in a tide free system). Additional information is available at: http://www.ngs.noaa.gov/GEOID/geoid.html We are particularly grateful to NGA (former National Imagery and Mapping Agency) for their assistance and their data contributions.

This file contains a list of geodetic bench marks, identified by a Permanent Identifier (PID), each of which have a precise orthometric height determined by geodetic leveling, a precise ellipsoid height determined by GPS surveying, and a precise modeled hybrid geoid height. The observations were used to constrain a gravimetric geoid model to the surface of a current vertical datum to produce a hybrid geoid model and associated performance metrics. The data is primarily from the US, however some data from Canada and Mexico is included as well.

This 2' geoid height grid for the conterminous United States is the G96SSS model. The computation used about 1.8 million terrestrial and marine gravity data held in the National Geodetic Survey gravity data base in July 1996. These data were augmented by gravity data contributions from NGA (former National Imagery and Mapping Agency (former Defence Mapping Agency)). By means of a Fast Fourier Transform (FFT) technique, high frequency corrections were made to an underlying EGM96 geopotential model through a remove, compute, and restore process. The gravity values are based on the International Gravity Standardization Net 1971 (IGSN71). The geoid heights are referred to the Geodetic Reference System 1980 (GRS80) ellipsoid. Unlike GEOID96, the G96SSS grid does not incorporate GPS on leveled benchmarks. The G96SSS model is a gravimetric geoid in a geocentric, ITRF94(1996.0) reference frame. It is necessary to subtract 12.0 cm from the G96SSS values to obtain the geoid undulation between the best-fit global geopotential surface and the GRS80 ellipsoid (both expressed in a tide free system). Additional information is available at: http://www.ngs.noaa.gov We are particularly grateful to NGA (former National Imagery and Mapping Agency) for their assistance and their data contributions.

This 2' geoid height grid for the conterminous United States is the GEOID96 model. The computation used about 1.8 million terrestrial and marine gravity data held in the National Geodetic Survey gravity data base in July 1996. These data were augmented by gravity data contributions from NGA (former National Imagery and Mapping Agency (former Defence Mapping Agency)). By means of a Fast Fourier Transform (FFT) technique, high frequency corrections were made to an underlying EGM96 geopotential model through a remove, compute, and restore process. The gravity values are based on the International Gravity Standardization Net 1971 (IGSN71). The geoid heights are referred to the Geodetic Reference System 1980 (GRS80) ellipsoid. GEOID96 incorporates the reference system relationship between NAD 83(86) and ITRF94(1996.0), the datum offset of NAVD 88, and the contributions from 2951 GPS on leveled benchmarks. Additional information is available at http://www.ngs.noaa.gov/GEOID/geoid.htmlWe are particularly grateful to NGA (former National Imagery and Mapping Agency) for their assistance and their data contributions.

This 2' surface deflection of the vertical grid for the Principal Hawaiian Islands is the DEFLEC96 model. The computation used about 61,000 terrestrial and marine gravity data held in the National Geodetic Survey gravity data base in July 1996. These data were augmented by gravity data contributions from NGA (former National Imagery and Mapping Agency (former Defence Mapping Agency)). The deflections were obtained by numerical differentiation of cubic spline models along the meridians of the GEOID96 grid. The gravity values are based on the International Gravity Standardization Net 1971 (IGSN71). The deflections are referred to the Geodetic Reference System 1980 (GRS80) ellipsoidal normals. The curvature of the plumb line correction has been applied. We are particularly grateful to NGA (former National Imagery and Mapping Agency) for their assistance and their data contributions.

This 2' geoid height grid for Mexico, and North-Central America, is the MEXICO97 geoid model. The computation used about one million terrestrial and marine gravity measurements held in the NGS database as of March 1997. These gravity measurements were augmented by data contributions from NGA (former National Imagery and Mapping Agency), and satellite altimeter-derived gravity anomalies computed by Sandwell and Smith (1997). Large data gaps south of 20 degrees North latitude were filled with 15'x15' gravity values derived from the EGM96 global geopotential model. This helped control interpolation errors across the data gaps during the gridding of terrain corrected Bouguer anomalies. After gridding of the Bouguer anomalies, the Bouguer plate was restored, a degree 360 model of gravity anomalies (from EGM96) was removed, and the residual free-air anomalies in the data gaps (south of 20 degrees North Latitude) were zeroed. (This zeroing was found to be the best way currently available to yield a reasonable geoid in the data gaps). The residual Faye anomalies were converted to residual co-geoid undulations through a 1-D FFT formulation of Stokes' integral, and finally the EGM96 undulation model was restored, and the indirect effect applied. This means that in the data gaps, long wavelength information is provided by EGM96, short wavelength information is provided by the 2'x2' DTED (during the application of the indirect effect), but medium wavelength information (usually provided by gravity measurements) is missing altogether. Although the exact accuracy of the geoid in the data gaps is difficult to ascertain, the quoted accuracy for EGM96 (which is the primary source of geoid information in the data gaps) is below 50 cm in these areas. The gravity values are based on the International Gravity Standardization Net 1971 (IGSN71). The geoid heights are referred to the Geodetic Reference System 1980 (GRS80) ellipsoid, centered at the origin of the International Terrestrial Reference Frame 1994 (ITRF94(1996.0)). Additional information is available at: http://www.ngs.noaa.gov/GEOID/MEXICO97/ We are particularly grateful to NGA (former National Imagery and Mapping Agency) for their assistance and their data contributions.