calculate grid area a function of latitude and longitude on earth'ssurface

[Steve Knox <stevek@xxxxxxxxxxxxxxxxxx>]

I think I found what I needed from the Dr. Math Archives. For anyone who 
is interested here it is:

We started with 
the formula for the area of the earth between a line of latitude and 
the north pole (the area of a spherical cap, listed in the Dr. Math 
FAQ on Geometric Formulas).

 A = 2*pi*R*h

where R is the radius of the earth and h is the perpendicular distance 
from the plane containing the line of latitude to the pole. We can 
calculate h using trigonometry as

 h = R*(1-sin(lat))

Thus the area north of a line of latitude is

 A = 2*pi*R^2(1-sin(lat))

The area between two lines of latitude is the difference between the 
area north of one latitude and the area north of the other latitude:

 A = |2*pi*R^2(1-sin(lat2)) - 2*pi*R^2(1-sin(lat1))|
   = 2*pi*R^2 |sin(lat1) - sin(lat2)|

The area of a lat-long rectangle is proportional to the difference in 
the longitudes. The area I just calculated is the area between 
longitude lines differing by 360 degrees. Therefore the area we seek 
is

 A = 2*pi*R^2 |sin(lat1)-sin(lat2)| |lon1-lon2|/360
   = (pi/180)R^2 |sin(lat1)-sin(lat2)| |lon1-lon2|

- Doctor Rick, The Math Forum
 http://mathforum.org/dr.math/ 


--
_________________________
Steve Knox
NREL
Colorado State University
(970)491-1972