Hi

Check the definition of the adiabatic heat gradient http://en.wikipedia.org/wiki/Lapse_rate
gamma = g/cp
where g is the total acceleration from gravity and centrifugal acceleration..
That definition of g is speed dependent and according to definition the speed for the centrifugal acceleration is taken to be the angular velocity multiplied with distance from rotation axis: http://en.wikipedia.org/wiki/Standard_gravity
However, considering the gas to be composed of a lot of smaller particles with thermal motion makes the speed in the centrifugal calculation different.. I found it to be like this instead
g = (G mEarth)/((rEquator+rPole)/2)^2 - (2 pi/86164.0905)^2 cos(45.5) rEquator - v_rms^2/(3 cos(45.5) rEquator)

First, the sidereal rotation time of Earth should be used and secondly the molecular speed should be used and not the Earth surface speed. The figure 3 in the denominator in the last term is due to the fact that only the thermal speed component in the longitudinal direction should be used. One sixth of the gas is considered to move at the Earth surface speed v plus the thermal v_rms speed and another sixth is considered to move with Earth surface speed v minus v_rms. 2/3 of the remaining gas moves at Earth surface speed v. This results in
acceleration = (G mEarth)/((rEquator+rPole)/2)^2 - 2/3*v^2 - (v + v_rms)^2/6r - (v - v_rms)^2/6r =
= (G mEarth)/((rEquator+rPole)/2)^2 - v^2/r - v_rms^2/3r

The value for g with this higher precision becomes, with v_rms = 500 m/s:
9.7911 m/s^2
compared to the value derived with sidereal time but no thermal correction:
9.8098 m/s^2

The difference is 0.19 %. This might be to small to be noticeable on Earth in most cases but can be higher in other atmospheres on other planets and moons or in machines like centrifuges.

I hope weather services reprogram their computers in order to improve weather forecasting. Those 0.19% could be the difference between rain or no rain..

David