The following equation provides the static stability:
sigma=-(R/P)*(1000/P)-R/cp
*(partial theta/partial p)
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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
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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
)
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-(dp1)theta(p0
-dp2)]/(2*dp1
*dp2)
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At 200 mb, a backward difference gives the static stability:
partial theta/partial p |p=p0=
[theta(p0)-theta(p0
-dp)]/dp
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Units: m2 s-2 kPa-2
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