The adiabatic temperature gradient (lapse rate) is temperature dependent
 

Some additional info, updates and corrections.

Other factors in meteorology are much less precise than 0.2% so this will not improve much of prognosis making.

With longitudinal direction above I mean east-west direction.

Another thing is that molecular motion in the north-south direction will also alter the speed in the centrifugal force calculation so an additional term has to be added. This speed is perpendicular to the surface speed so net molecular speed becomes (v^2 + v_rms^2)^0.5 .
acceleration = (G mEarth)/((rEquator+rPole)/2)^2 - 2/3*v^2 - (v + v_rms)^2/6r - (v - v_rms)^2/6r - ((v^2 + v_rms^2)^0.5)^2/3r =
= (G mEarth)/((rEquator+rPole)/2)^2 - v^2/r - 2*v_rms^2/3r

This leads to
g = 9.7725
which is 0.38 % smaller that the definition from 1901.

I have used the following m-script that can be run with Matlab, FreeMat, Scilab or Octave.

rPole = 6356752.3;
rEquator = 6378137;
G = 6.67428e-11;
mEarth = 5.9736e24;
v_rms=500;
g=(G*mEarth)/((rEquator+rPole)/2)^2
ang = cos(45.5*2*pi/360)
ac=(2*pi/86164.0905)^2 *ang* rEquator
ac_old=(2*pi/86400)^2 *ang* rEquator
act=2*v_rms^2/(3 *ang* rEquator)
g0org_old = g - ac_old
g0org = g - ac
g0 = g - ac - act

David