Static Stability

The following equation provides the static stability:

sigma=-(R/P)*(1000/P)-R/cp *(partial theta/partial p)

Potential temperature was computed using Poisson's equation, except at 1000 mb, where a lapse rate of 6.5K/km was used to bring the 850 mb temperatures to 1000 mb using the 850 mb heights.

Partial theta/partial p is calculated using numerical differences. A forward difference gives the static stability at 1000 mb:

partial theta/partial p |p=p0= [theta(p0+dp)-theta(p0 )]/dp

A centered unequal difference gives the static stability at 850 mb and 500 mb:

partial theta/partial p |p=p0= [(dp2)theta(p0 +dp1)+(dp1 -dp2)theta(p0 )

-(dp1)theta(p0 -dp2)]/(2*dp1 *dp2)

At 200 mb, a backward difference gives the static stability:

partial theta/partial p |p=p0= [theta(p0)-theta(p0 -dp)]/dp