  The contribution to the potential caused by the atmosphere is 
computed using the surface pressure field at an equi-angular 
latitude/longitude grid with resolution 2048x4096 computed from 
the output of the 4D numerical weather model.

  The atmospheric surface pressure is multiplied by the land-sea mass 
function of dimension 2048x4096 over latitude/longitude (~10 km) which 
is the fraction of land in a grid cell. Then the spherical harmonic 
transform of degree/order 1023 is performed. The spherical harmonics 
expansion coefficients S(k,n) are scaled by factors 

  Sv(k,n) = 3/(4*pi)*K_n/(2*n+1)/(mean_dens*mean_grav*Earth_rad) * S(k,n)

where K_n is the loading Love numbers, k is order, n is degree, 
mean_dens is the mean density of the Earth, mean_grav is the mean 
gravity acceleration at the sea level, and Earth_rad is the Earth's
equatorial radius.

  The ocean area, as defined in the land-sea mask, is excluded 
from the integration, thus hypothesis of inverted barometer is
exploited.  However, the water mass conservation correction is
applied: it is assumed that the atmosphere pressure over the
entire ocean induces the uniform bottom pressure equal to the
ratio of the integral of the atmosphere pressure over the ocean
to the area of the ocean. 

  The expansion is truncated to degree/order 64.

  NB: The harmonic model that contains 20 terms, annual, semi-annual, 
diurnal, semi-diurnal etc, was evaluated with least squared are removed 
from the surface pressure. Therefore, these Stokes coefficients do not
contain harmonic variations at these frequencies.

  The loading Love numbers are defined for the total Earth
system (solid Earth + here atmosphere). They were 
computed by P. Gegout (private communication, 2005). 
In accordance with this definition the Stokes coefficients,
(0,0), (1,0) and (1,1) are zero.

  Normalization: the Stokes coefficients are so-called "4-pi 
fully normalized" according to Heikassen and Moritz, 1979.

This mean for any m,n, the integral over the entire sphere

\int Y_m^n(\phi,\lambda) \cdot Y_m^n(\phi,\lambda) \cdot
\cos ( \phi ) d \phi d \lambda \cdot = 4 \pi


References:

1) L. Petrov, J.-P. Boy, "Memo on computing Stokes coefficients
   of the expansion of the atmosphere contribution to the
   geopotential into a series of spherical harmonics", 2005,
   Unpublished, 
   http://gemini.gsfc.nasa.gov/agra/agra_memo_01.ps

2) L. Petrov, J.-P. Boy, "Study of the atmospheric pressure 
   loading signal in very long baseline interferometry 
   observations", J. Geophys. Res., vol. 109, p. B03405,
   doi:10.1029/2003JB002500, 2004.

3) Lefevre, F., C. Le Provost and F.H. Lyard, How can we 
   improve a global ocean tide model at a regional scale?
   A test on the Yellow Sea and the East China Sea, 
   J. Geophys. Res., vol. vol. 105, 8707--8725, 2000.

4) W. Heikassen, H. Moritz, Physical geodesy, Graz, 1979, p. 31.

