egm96geoid

Geoid height from Earth Gravitational Model 1996 (EGM96)

Syntaxes of the egm96geoid function that return referencing vectors have been removed. Use a syntax that returns a reference object instead. For more information, see Version History.

Syntax

N = egm96geoid(lat,lon)

N = egm96geoid(R)

[N,globalR] = egm96geoid

Description

N = egm96geoid(lat,lon) returns the height in meters of the geoid at the specified latitude and longitude from the Earth Gravitational Model of 1996 (EGM96). Specify latitude and longitude in degrees.

N = egm96geoid(R) returns geoid heights at the cell center or posting locations specified by the geographic postings reference or geographic cells reference object R.

[N,globalR] = egm96geoid returns geoid heights for the entire globe as a 721-by-1441 matrix spaced at 15-minute intervals with latitude limits [-90 90] and longitude limits [0 360]. The function also returns a geographic postings reference object that contains spatial referencing information for the geoid heights.

Examples

Geoid Height from Latitude and Longitude

Find geoid heights from EGM96 by specifying latitude and longitude values in degrees. The result is returned in meters.

lat = 27.988056;
lon = 86.925278;
N = egm96geoid(lat,lon)

N = 
-28.7444

Geoid Heights within Limits

View geoid heights from EGM96 for an area including Europe.

First, create a GeographicPostingsReference object. Specify the latitude and longitude limits of the area in degrees. Specify the raster size as the number of rows and columns for the grid of geoid heights. Then, return the grid of geoid heights for the area by calling egm96geoid on the reference object.

latlim = [35 72];
lonlim = [-12 51];
rasterSize = [100 100];
R = georefpostings(latlim,lonlim,rasterSize);
N = egm96geoid(R);

Note that the size of N matches the raster size of R.

size(N)

ans = 1×2

   100   100

Load coastline latitude and longitude data into the workspace. Then, plot the geoid height and coastline data on a map.

load coastlines

worldmap(latlim,lonlim)
geoshow(N,R,'DisplayType','surface')
geoshow(coastlat,coastlon,'Color','k')

Geoid Heights for Entire Globe

View geoid heights from EGM96 for the entire globe.

First, return the geoid heights and a referencing object for the globe. The geoid heights are spaced at 15-minute intervals. Load coastline latitude and longitude data into the workspace. Then, plot the geoid heights and coastline data on a world map.

[N,R] = egm96geoid;
load coastlines

worldmap('World')
geoshow(N,R,'DisplayType','surface')
geoshow(coastlat,coastlon,'Color','k')

Input Arguments

lat — Latitude

scalar | vector | matrix

Latitude in degrees, specified as a scalar, vector, or matrix. The dimension of lat depends on the dimension of the geoid heights you want to find.

• To find a single geoid height, specify lat and lon as scalars.

• To find several geoid heights, specify lat and lon as vectors of the same length.

• To find a p-by-q grid of geoid heights, specify lat and lon as p-by-q matrices.

Data Types: single | double

lon — Longitude

scalar | vector | matrix

Longitude in degrees, specified as a scalar, vector, or matrix. The dimension of lon depends on the dimension of the geoid heights you want to find.

• To find a single geoid height, specify lat and lon as scalars.

• To find several geoid heights, specify lat and lon as vectors of the same length.

• To find a p-by-q grid of geoid heights, specify lat and lon as p-by-q matrices.

Data Types: single | double

R — Geographic reference

GeographicPostingsReference object | GeographicCellsReference object

Geographic reference, specified as a GeographicPostingsReference object or a GeographicCellsReference object that contains geospatial referencing information for N. The RasterSize property of the geographic reference object determines the size of the data grid, size(N).

Output Arguments

N — Geoid height

scalar | vector | matrix

Geoid height in meters, returned as a scalar, vector, or matrix.

The size of N depends on the syntax:

Syntax	Size of N
N = egm96geoid(lat,lon)	Size of lat and lon
N = egm96geoid(R)	R.RasterSize
[N,globalR] = egm96geoid	721-by-1441 matrix

Data Types: double

globalR — Geographic reference

GeographicPostingsReference object

Geographic reference, returned as a GeographicPostingsReference object of size 721-by-1441 with latitude limits [-90 90] and longitude limits [0 360].

More About

Earth Gravitational Model of 1996 (EGM96)

The geoid is an equipotential surface of the Earth's gravity field that approximates global mean sea level. You can visualize the geoid as the surface of the ocean without effects such as weather, waves, and land. The Earth Gravitational Model of 1996 (EGM96) is based on the ellipsoid specified by the World Geodetic System of 1984 (WGS84), so the egm96geoid function returns heights above or below the surface of the WGS84 ellipsoid.

Version History

Introduced before R2006a

R2023b: Syntaxes that return referencing vectors have been removed

Syntaxes of the egm96geoid function that return referencing vectors have been removed. Use a syntax that returns a geographic raster reference object instead. Reference objects have several advantages over referencing vectors.

• Unlike referencing vectors, reference objects have properties that document the size of the associated raster, its geographic limits, and the direction of its rows and columns. For more information about reference object properties, see the GeographicCellsReference and GeographicPostingsReference objects.

• You can manipulate the limits of rasters associated with reference objects using the geocrop function.

• You can manipulate the size and resolution of rasters associated with reference objects using the georesize function.

• Most functions that accept referencing vectors as inputs also accept reference objects.

This table shows the syntaxes of the egm96geoid function that return referencing vectors and how to update your code to use syntaxes that return reference objects instead.

Removed	Recommended
[N,refvec] = egm96geoid(samplefactor);	[~,globalR] = egm96geoid; latlim = globalR.LatitudeLimits; lonlim = globalR.LongitudeLimits; globalSize = globalR.RasterSize; rasterSize = 1 + ceil((globalSize-1)/samplefactor); R = georefpostings(latlim,lonlim,rasterSize); N = egm96geoid(R);
[N,refvec] = egm96geoid(samplefactor,latlim,lonlim);	[~, globalR] = egm96geoid; spacing = samplefactor ... * globalR.SampleSpacingInLatitude; R = georefpostings(latlim,lonlim,spacing,spacing); N = egm96geoid(R);

R2022a: Syntaxes that return referencing vectors warn

Syntaxes of the egm96geoid function that return referencing vectors issue a warning that they will be removed in a future release.

R2020b: Syntaxes that return referencing vectors will be removed

Syntaxes of the egm96geoid function that return referencing vectors will be removed in a future release.

R2020a: Return geoid heights referenced to geographic reference object

Return geoid heights from EGM96 that are referenced to a geographic raster reference object. You can specify GeographicCellsReference or GeographicPostingsReference objects, or return geoid heights and a reference object for the entire globe spaced at 15-minute intervals.

R2019b: Return geoid heights at specified latitudes and longitudes

Return geoid heights from EGM96 by specifying latitude and longitude in degrees. For example, find the geoid height at a latitude of 42.3601 degrees and a longitude of -71.589 degrees:

N = egm96geoid(42.3601,-71.589);

R2019b: Improved performance

In previous releases, egm96geoid accessed geoid heights using WW15MGH.GRD, a file that you downloaded from the Internet. Starting in R2019b, a grid of geoid heights from EGM96 is included with Mapping Toolbox™, and egm96geoid no longer reads data from WW15MGH.GRD.

As a result, the egm96geoid function shows improved performance. For example, this code shows about a 15x speed-up when you return the entire grid of geoid heights:

function timingTest
N = egm96geoid(1);
end

The approximate execution times are:

• R2019a: 0.1838 s

• R2019b: 0.0121 s

This code was timed on a Windows^® 10 test system with a 3.6-GHz Intel^® Xeon^® W-2133 CPU using the timeit function:

timeit(@timingTest)