Is there any standard methodology for the same? What is its approximate value for around 25 degree latitude?
Yes, there is a very standard way to calculate the Rossby radius of deformation for Rossby waves (see, e.g., http://glossary.ametsoc.org/wiki/Rossby_radius_of_deformation ). The formula you want there is the "internal" one for L, where
L = (N H)/f
where
N= average Brunt-Vaisala frequency within depth of wave (e.g., troposphere);
H = depth of troposphere, and
f = coriolis parameter (= 2 *Omega*Sin(latitude), where Omega = earth rotation rate.
Your 25 deg. latitude enters primarily through the Coriolis parameter, which is about 6.15 *10^-5 at that latitude.
N = sqrt( g/theta *(d theta/d z)), where theta = potential temperature, is about 10^-2 (s^-1), given g~10; theta~300 K; delta-theta~30 K; delta-z~ 10,000 m.
Then L is approx. 10^-2 * 10^4 /(6.15* 10^-5) ~ 1.6 *10^6 m = 1,600 km.
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