Python 计算以纬线 lat1 和 lat2 以及经线 lon1 和 lon2 为界的表面积

Question

I'm looking for an equivalent to this Matlab function areaquad in Python.

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.

Do you happen to know how I can calculate this using Python? Any tips are much appreciated!

Answer 1

It's not that hard to calculate it, if you need it only for spheres. Here is the formula for calculating total area of sphere surface between two latitudes. So:

h = sin(lat2)-sin(lat1)
Az = 2 * pi * h

Now, we can simply find the proportion of the region restricted between two longitudes:

Aq = Az * (lon2-lon1)/(2*pi)

And finally, to make the result a fraction of surface of unit sphere, divide it by 4*pi . Putting all together, with simplification and take angle units into account:

 A = (sind(lat2)-sind(lat1)) * deg2rad(lon2-lon1) / (4*pi);

Hope you can translate it to python.

Edit: This is what I get in R2020b for your test case:

lat1 = -90; lat2 = -89; lon1 = -180; lon2 = 180;
A = (sind(lat2)-sind(lat1)) * deg2rad(lon2-lon1) / (4*pi)

A =
7.6152e-05

Also, about Aq not being present in the final formula:

h = sin(lat2)-sin(lat1)
Az = 2 * pi * h
Aq = Az * (lon2-lon1)/(2*pi)
   = 2*pi*h*(lon2-lon1)/(2*pi) // reducing 2*pi
   = h * (lon2-lon1)
   = (sin(lat2)-sin(lat1))*(lon2-lon1)
A  = Aq/(4*pi)
   = (sin(lat2)-sin(lat1))*(lon2-lon1)/(4*pi)