areaquad - Surface area of latitude-longitude quadrangle

Syntax

area = areaquad(lat1,lon1,lat2,lon2) area = areaquad(lat1,lon1,lat2,lon2,ellipsoid) area = areaquad(lat1,lon1,lat2,lon2,ellipsoid,units)

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 the two-element ellipsoid vector ellipsoid. When ellipsoid is input, the resulting area is given in terms of the (squared) units of the ellipsoid. For example, if the ellipsoid almanac('earth','ellipsoid','kilometers') is used, the resulting area is in km². The default ellipsoid is the unit sphere.

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

Definitions

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).

Examples

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

area = areaquad(30,-25,45,60)

area =
    0.0245

Assuming a spherical ellipsoid, find the surface area of the Earth in square kilometers. (Use the almanac function with the sphere as its reference body.)

earthellipsoid = almanac('earth','ellipsoid','km','sphere');
area = areaquad(-90,-180,90,180,earthellipsoid)

area =
   5.1006e+08

For comparison,

almanac('earth','surfarea','km')

ans =
   5.1006e+08

Algorithm

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