1. Stability Indices
Summarized from “A First Course in Atmospheric Dynamics” by Grant W. Petty, pp

2. Stability Indices
It can be useful to summarize the overall stability of the atmosphere with a single number.
Because stability indices are simple, however, they cannot account for all aspects of the atmosphere, or how the local atmosphere might evolve in the future (advection, fronts, etc.). Each stability index has different strengths and weaknesses.
The following slides show some of the more popular indices. For a more complete descriptions, as well as the pros and cons of each index, see pp in Petty.

3. Lifted Index (LI) LI = T500 – Tparcel500
Average the lowest 100 mb of atmosphere, then raise that parcel adiabatically to 500 mb. The LI is the difference between the parcel temperature and the environment atmosphere at 500 mb.
LI = T500 – Tparcel500
>3 Stable
1 to 3 Weak convection possible if strong lifting is present
0 to -3 Marginally unstable
-3 to -6 Moderately unstable
-6 to -9 Very unstable
< -9 Extremely unstable

4. Showalter Index (SI) SI = T500 – Tparcel500
Same as the Lifted Index, but parcel is lifted from the 850 mb level rather than the lowest 100 mb.
SI = T500 – Tparcel500
>3 No significant activity.
1 to 3 Showers possible with other sources of lift
-2 to 1 Thunderstorms possible (generally weak)
-3 to -2 Thunderstorms more probable (possibly strong)
-6 to -4 Strong or severe thunderstorms possible
< -6 Any thunderstorms likely to be strong or severe

5. Total Totals Index (TT)
The Total Totals Index is equal to the temperature at 850 mb plus the dewpoint at 850 mb minus two times the temperature at 500 mb.
TT = T850 + Td,850 – 2T500
44 to 45 Isolated moderate thunderstorms
46 to 47 Scattered moderate / few heavy thunderstorms
48 to 49 Scattered moderate / few heavy / isolated severe thunderstorms
50 to 51 Scattered heavy / few severe thunderstorms and isolated tornadoes
52 to 55 Scattered to numerous heavy / few to scattered severe thunderstorms / few tornadoes
>55 Numerous heavy / scattered severe thunderstorms and scattered tornadoes

6. K Index (KI) KI = T850 – T500 + Td,850 – (T700 – Td,700)
The K index is defined as follows:
KI = T850 – T500 + Td,850 – (T700 – Td,700)
< 15 0% Air mass thunderstorm probability
15 to 20 <20% Air mass thunderstorm probability
21 to 25 20% to 40% Air mass thunderstorm probability
26 to 30 40% to 60% Air mass thunderstorm probability
31 to 35 60% to 80% Air mass thunderstorm probability
36 to 40 80% to 90% Air mass thunderstorm probability
> 40 >90% Air mass thunderstorm probability

7. SWEAT (Severe Weather thrEAT) Index
The SWEAT index is a more elaborate index. It uses the dewpoint at 850 mb, the Total Totals Index (TT) and wind speeds in knots (f) at 850 mb and 500 mb. S is a shear term (see p. 272 of Petty for details). It is defined as follows:
SWEAT = 12Td, (TT – 49) + 2f850 + f (s + 0.2)
Any term that is negative is set to zero.
< 300 No activity expected
300 to 400 Isolated moderate to heavy thunderstorms
400 to 500 Severe thunderstorms and tornadoes probably
> 500 Severe thunderstorms and tornadoes likely

8. Convective Available Potential Energy (CAPE)
In many ways, knowing CAPE can be more useful than any of the stability indices. However, it cannot be calculated from a simple formula. Instead, it is usually calculated on a computer. An alternative way is to find the area of CAPE on a skew-T, then convert that to energy.
The approximate meaning of the CAPE, expressed in J/kg, is as follows:
< 0 Stable
0 to 1000 Marginally unstable
1000 to 2500 Moderately unstable
2500 to 3500 Very unstable
3500 to 4000 Extremely unstable