Mapping Toolbox™

areaint - Surface area of polygon on sphere or ellipsoid

Syntax

area = areaint(lats,longs)
area = areaint(lats,longs,ellipsoid)
area = areaint(lats,longs,ellipsoid,units)

area = areaint(lats,longs) returns the surface area enclosed by the polygon defined by the column vectors lats and longs. Multiple polygons can be delineated by NaNs. The output area is a fraction of the unit sphere's area of 4π, so the result ranges from 0 to 1.

area = areaint(lats,longs,ellipsoid) allows the specification of the ellipsoid model with the two-element ellipsoid vector ellipsoid. When an 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 = areaint(lats,longs,ellipsoid,units) specifies the units of the inputs lats and longs, which are 'degrees' by default.

Description

This function allows the measurement of areas enclosed by arbitrary polygons. This is a numerical estimate, using a line integral based on Green's Theorem. As such, it is limited by the accuracy and resolution of the input data.

Examples

Consider the area enclosed by a 30º lune from pole to pole and bounded by the prime meridian and 30ºE. You can use the function areaquad to get an exact solution:

area = areaquad(90,0,-90,30)
area =
    0.0833

This is 1/12 the spherical area. The more points used to define this polygon, the more integration steps areaint takes, improving the estimate. This first attempt takes a point every 30º of latitude:

lats = [-90:30:90,60:-30:-60]';
longs = [zeros(1,7),30*ones(1,5)]';
area = areaint(lats,longs)
area =
    0.0792

Now, a little finer, perhaps one point every 1º of latitude:

lats = [-90:1:90,89:-1:-89]';
longs = [zeros(1,181),30*ones(1,179)]';
area = areaint(lats,longs)
area =
    0.0833

Limitations

As noted above, this is a line integral estimation, only as good as the accuracy and the density of the polygon vertex data. However, given sufficient data, the areaint function is the best method for determining the areas of complex polygons, such as continents, cloud cover, and other natural or derived features. The calculations in this function employ a spherical Earth assumption. For nonspherical ellipsoids, the latitude data is converted to the auxiliary authalic sphere.

See Also

almanac, areamat, areaquad

arcgridread

areamat