[Proj] CEA from an ellipse and +R_A

[David James Brockley]

Hello

I'm trying to convert geodetic lon/lat into CEA xy using the proj API  
initialised with

+proj=cea +long_0=0 +ellps=WGS84 +R_A

What I expect to happen is

y = a * q / 2

where a is the authalic radius calculated from the semi-major of WGS84.

q/2 seems to be a common approximation to q/q_p which is sin 
( authalic latitude)


What actually happens is that proj uses the equation for a sphere  
rather than an ellipse.

y = a sin( phi )

I can get proj to do what I expect by initialising with

+proj=cea +long_0=0 +a=6371007 +e=0.0818191

but that seems somewhat back to front.


Can anyone tell me the correct way to configure proj for what I am  
trying to do?

I'm fairly sure that my expected function for y is correct, since  
I've both copied it from the literature and derived it by hand from  
the spherical case by substituting authalic radius for radius and  
authalic latitude for latitude - I've also realised that the /2 is  
due to the maximum possible value of q_p being 2 when e=0, and that  
it doesn't affect the properties of the transform (still equal area).

Regards, Brock