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Surface area of latitude-longitude quadrangle

Description

area = areaquad(lat1,lon1,lat2,lon2) returns the surface area bounded by the parallels lat1 and lat2 and the meridians lon1 and lon2. The output area is a fraction of the unit sphere's area of 4π, so the result ranges from 0 to 1.

area = areaquad(lat1,lon1,lat2,lon2,ellipsoid) allows the specification of the ellipsoid model with ellipsoid. ellipsoid is a referenceSphere, referenceEllipsoid, or oblateSpheroid object, or a vector of the form [semimajor_axis eccentricity]. When ellipsoid is input, the resulting area is given in terms of the (squared) units of the ellipsoid. For example, if the ellipsoid referenceEllipsoid('grs80','kilometers') is used, the resulting area is in km2.

area = areaquad(lat1,lon1,lat2,lon2,ellipsoid,units) where units specifies the units of the inputs. The default is 'degrees'.

Examples

Find the fraction of the Earth's surface that lies between 30ºN and 45ºN, and also between 25ºW and 60ºE:

area =
0.0245

Assuming a spherical ellipsoid, find the surface area of the Earth in square kilometers.

earthellipsoid = referenceSphere('earth','km');

area =
5.1006e+08

For comparison,

earthellipsoid.SurfaceArea

ans =
5.1006e+08

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A latitude-longitude quadrangle is a region bounded by two meridians and two parallels. In spherical geometry, it is the intersection of a lune (a section bounded by two meridians) and a zone (a section bounded by two parallels). Algorithms

The areaquad calculation is exact, being based on simple spherical geometry. For nonspherical ellipsoids, the data is converted to the auxiliary authalic sphere. 