1. How to forecast the likelihood of thunderstorms!!!
Stability Indices
How to forecast the likelihood of thunderstorms!!!
Thermodynamics
M. D. Eastin

2. Stability Indices Outline: Useful Parameters for Rising Air Parcels
Review of Stability
Useful Parameters for Rising Air Parcels
Convective Condensation Level (CCL)
Convective Temperature (Tc)
Lifting Condensation Level (LCL)
Level of Free Convection (LFC)
Equilibrium Level (EL)
Positive and Negative Areas
Stability Indices
Showalter Index (SI)
Lifted Index (LI)
K Index (K)
Total Totals (TT)
Severe Weather Threat Index (SWEAT)
Convective Inhibition (CIN)
Convective Available Potential Energy (CAPE)
Thermodynamics
M. D. Eastin

3. Concept of Stability Three Categories of Stability: Stable:
Returns to its original position
after displacement
Neutral:
Remains in new position after
being displaced
Unstable:
Moves further away from its original
position after being displaced
Thermodynamics
M. D. Eastin

4. Concept of Stability Basic Idea:
Ability of an air parcel to return to is level of origin after a displacement
Depends on the temperature structure of the atmosphere
Temperature
Dewpoint
Thermodynamics
M. D. Eastin

5. Concept of Stability Cool Hot Cool
How is air displaced? Spontaneous Ascent
Air parcel is warmer than its environment
which means the parcel is “buoyant”
Air becomes buoyant through “heating”
Warm
Cool
Hot
Cool
Thermodynamics
M. D. Eastin

6. Concept of Stability How is air displaced? Forced Ascent
Flow over mountains
Flow over fronts (cold, warm, stationary, occluded, etc.)
Thermodynamics
M. D. Eastin

7. Atmospheric Stability Analysis
Combined Criteria for Moist Air (either saturated or unsaturated):
Absolutely Unstable:
Dry Neutral:
Temperature
Height Γs Γ Γd
Unsaturated
parcel becomes
warmer
than nearby
environment
Saturated
parcel becomes
warmer
than nearby
environment Γd
Unsaturated
parcel becomes
equivalent to
the nearby
environment
Saturated
parcel becomes
warmer
than nearby
environment Γs Γ
Height
Temperature
Thermodynamics
M. D. Eastin

8. Atmospheric Stability Analysis
Combined Criteria for Moist Air (either saturated or unsaturated):
Conditionally Unstable:
The vertical temperature profile at most locations in our atmosphere
is conditionally unstable Γ
Unsaturated
parcel becomes
colder
than nearby
environment
Saturated
parcel becomes
warmer
than nearby
environment Γs Γd
Height
Temperature
Thermodynamics
M. D. Eastin

9. Atmospheric Stability Analysis
Combined Criteria for Moist Air (either saturated or unsaturated):
Moist Neutral:
Absolutely Stable: Γ
Unsaturated
parcel becomes
colder
than nearby
environment
Saturated
parcel becomes
equivalent to
the nearby
environment Γs Γd
Height
Temperature Γs Γ
Unsaturated
parcel becomes
colder
than nearby
environment
Saturated
parcel becomes
colder
than nearby
environment Γd
Height
Temperature
Thermodynamics
M. D. Eastin

10. Useful Parameters for Rising Air Parcels
Convective Condensation Level (CCL):
Definition: Altitude to which an unsaturated moist air parcel, if heated
sufficiently from below, will rise dry adiabatically until it just
becomes saturated
Altitude of the base of cumuliform
clouds that are produced by thermal
convection from surface heating
Hot
Cool
Warm
CCL
Thermodynamics
M. D. Eastin

11. Useful Parameters for Rising Air Parcels
Convective Condensation Level (CCL):
Skew-T Procedure: Start at the surface Td
2. Move upward along a saturated mixing ratio line
until it intersects the T profile
3. The CCL is the altitude (or pressure) at this intersection Td T
Convective
Condensation
Level
(CCL)
CCL = 850 mb
Thermodynamics
M. D. Eastin

12. Useful Parameters for Rising Air Parcels
Convective Temperature (Tc):
Definition: Surface temperature that must be reached to start the formation
of clouds by solar heating.
Often compared to the forecast
high temperature for the day
If Tforecast > Tc then
convective clouds
will form
If Tforecast < Tc then
will not form
Warm
CCL Tc Tc
Cool
Hot
Cool
Thermodynamics
M. D. Eastin

13. Useful Parameters for Rising Air Parcels
Convective Temperature (Tc):
Skew-T Procedure: Find the CCL
2. Move downward along a dry adiabat to the surface
3. The Tc is the resulting temperature at the surface Td T
Convective
Temperature
(Tc)
CCL
Tc = 12ºC
Thermodynamics
M. D. Eastin

14. Useful Parameters for Rising Air Parcels
Lifting Condensation Level (LCL):
Definition: Altitude at which an unsaturated moist air parcel becomes saturated
when lifted dry-adiabatically.
Lifting can result from:
Convergence
Flow over topography
Fronts
LCL
Thermodynamics
M. D. Eastin

15. Useful Parameters for Rising Air Parcels
Lifting Condensation Level (LCL):
Skew-T Procedure: Move up a saturation mixing ratio line from a Td value
2. Move up a dry adiabat from the corresponding T value
3. The LCL is the altitude or (pressure) of the intersection
Note: An LCL an be determined for a parcel originating
from any level, but the surface is commonly used Td T
Lifting
Condensation
Level
(LCL)
LCL = 870 mb
Thermodynamics
M. D. Eastin

16. Useful Parameters for Rising Air Parcels
Level of Free Convection (LFC):
Definition: Altitude at which a moist air parcel lifted dry adiabatically until
saturated and pseudo-adiabatically thereafter would first
become warmer (less dense) than the surrounding air Td T
Altitude at which
a lifted parcel first
becomes
warmer than the
environment
LCL
Thermodynamics
M. D. Eastin

17. Useful Parameters for Rising Air Parcels
Level of Free Convection (LFC):
Skew-T Procedure: Find the LCL for a parcel lifted from the surface
2. Move up a pseudo-adiabat until the parcel temperature
first becomes warmer than the observed T profile
3. The LFC is the altitude or (pressure) of this location Td T
Level of Free
Convection
Tp > Te
LFC = 660 mb
Tp < Te
LCL
Tp < Te
Thermodynamics
M. D. Eastin

18. Useful Parameters for Rising Air Parcels
Equilibrium Level (EL):
Definition: Altitude at which the temperature of a buoyantly rising air parcel
(i.e. a parcel warmer than its local environment) becomes equal
to the temperature of the environment Td T
Altitude at which
the temperature
of a buoyant parcel
equals the
environmental
temperature
LFC
LCL
Thermodynamics
M. D. Eastin

19. Useful Parameters for Rising Air Parcels
Equilibrium Level (EL):
Skew-T Procedure: Find the LCL for a parcel lifted from the surface
2. Find the LFC for the same parcel
3. Continue moving up a pseudo-adiabat until the
parcel temperature first becomes colder than the
observed T profile
4. The EL is the altitude or (pressure) of this location Td T
Equilibrium
Level
Tp < Te
EL = 400 mb
Tp > Te
LFC
Tp < Te
LCL
Tp < Te
Thermodynamics
M. D. Eastin

20. Useful Parameters for Rising Air Parcels
Negative Area:
Layers within which a parcel requires forced ascent to remain in or rise through
(i.e. the parcel will experience a downward buoyancy force)
Parcel temperature is less than the environmental temperature (Tp < Te) Td T
Negative
Area
Tp < Te EL
Tp > Te
LFC
Negative
Area
Tp < Te
LCL
Tp < Te
Thermodynamics
M. D. Eastin

21. Useful Parameters for Rising Air Parcels
Positive Area:
Layers within which a parcel can rise freely through the atmosphere
(i.e. the parcel will experience an upward buoyancy force)
Parcel temperature is greater than the environmental temperature (Tp > Te) Td T
Tp < Te EL
Positive
Area
Tp > Te
LFC
Tp < Te
LCL
Tp < Te
Thermodynamics
M. D. Eastin

22. Useful Parameters for Rising Air Parcels
Application:
Find the
CCL and TC
Thermodynamics
M. D. Eastin

23. Useful Parameters for Rising Air Parcels
Application:
Find the
LCL, LFC, and EL
for the
surface air parcel
Thermodynamics
M. D. Eastin

24. Stability Indices Basic Idea:
Single number that characterizes the stability (or instability) of the atmosphere
Advantages:
Easily computed
Easily applied in forecasting
Disadvantages:
Details of atmospheric profile may be ignored
Application Guidelines:
Forecaster must always closely examine the entire sounding
Must be used in conjunction with other forecasting methods
Thermodynamics
M. D. Eastin

25. Stability Indices Showalter Index (SI):
Temperature difference between:
The environmental air at 500 mb and
The temperature of an air parcel at 500 mb lifted
dry-adiabatically from 850 mb to saturation (i.e., the LCL)
and then pseudo-adiabatically thereafter up to 500 mb.
where: Te 500 Environmental temperature at 500 mb in K
Tp 500 Parcel temperature at 500 mb in K
Thermodynamics
M. D. Eastin

26. Stability Indices SI = Te500 – Tp500 Showalter Index (SI):
Skew-T Procedure: Find the LCL for a parcel lifted from 850 mb
2. Find the LFC for the same parcel
3. From the LCL move up a pseudo-adiabat to 500 mb
4. Subtract the parcel temperature (Tp) at 500 mb from
the environmental temperature (Te) at 500 mb Td T
SI = Te500 – Tp500
SI = (-32ºC) – (-25ºC)
SI = (241 K) – (248 K)
SI = –7
Te500
Tp500
500 mb
LCL
850 mb
Thermodynamics
M. D. Eastin

27. Stability Indices Showalter Index (SI): Forecast Guidelines:
+1 to +3 Showers are probable, Thunderstorms possible
need strong forced ascent
0 to -3 Unstable – Thunderstorms probable
-4 to -6 Very Unstable – Heavy thunderstorms probable
less than -6 Extremely Unstable – Strong thunderstorms probable
Tornadoes are possible
Usage Guidelines:
Good for forecasting mid-level convection
Does not account for moisture in boundary layer
Thermodynamics
M. D. Eastin

28. Stability Indices Lifted Index (LI): Definition:
Temperature difference between:
The environmental air at 500 mb and
The temperature of an air parcel at 500 mb lifted dry-adiabatically
from the mean conditions in the boundary layer to saturation
(i.e., the LCL) and then pseudo-adiabatically thereafter up to 500 mb
where: Te 500 Environmental temperature at 500 mb in K
Tp 500 Parcel temperature at 500 mb in K
Mean boundary layer conditions are determined by finding the
average wsw and θ in the lowest 100 mb of the sounding
Thermodynamics
M. D. Eastin

29. Stability Indices LI = Te500 – Tp500 Lifted Index (LI):
Skew-T Procedure: Identify the lowest 100 mb of the sounding
2. Find the mean wsw and mean θ in the lowest 100 mb
3. Follow the mean wsw and mean θ up to the LCL
4. From the LCL move up a pseudo-adiabat to 500 mb
5. Subtract the parcel temperature (Tp) at 500 mb from
the environmental temperature (Te) at 500 mb Td T
LI = Te500 – Tp500
LI = (-32ºC) – (-26ºC)
LI = (241 K) – (247 K)
LI = –6
Te500
Tp500
500 mb
mean wsw
LCL
880 mb
mean θ
980 mb
Thermodynamics
M. D. Eastin

30. Stability Indices wsw-min wsw-max θmin θmax
Lifted Index (LI): Finding the mean wsw and θ:
Identify the lowest 100 mb
Identify the maximum and minimum θ within the 100 mb
Mean θ is located 50 mb above the surface halfway between θmax and θmin
Identify the maximum and minimum wsw within the 100 mb
Mean wsw is 50 mb above the surface halfway between wsw-max and wsw-min
Note: The mean θ and mean wsw may NOT fall along the sounding
wsw-min
wsw-max
θmin
θmax T Td
100 mb
50 mb
Thermodynamics
M. D. Eastin

31. Stability Indices Lifted Index (LI): Forecast Guidelines:
0 to -2 Thunderstorms possible, need strong forced ascent
-2 to -5 Unstable – Thunderstorms probable
less than -5 Very Unstable – Strong thunderstorms probable
Usage Guidelines:
Good for forecasting surface-based convection
Accounts for moisture in boundary layer
Addresses limitations of Showalter Index
Thermodynamics
M. D. Eastin

32. Stability Indices K Index (K): Definition:
Measure of thunderstorm potential based on:
Vertical temperature lapse rates (T850-T500)
Moisture content of the lower atmosphere (Td 850)
Vertical extent of moist layer (T700-Td 700)
where: T850 Temperature at 850 mb in ºC
T500 Temperature at 500 mb in ºC
Td 850 Dewpoint temperature at 850 mb in ºC
T700 Temperature at 700 mb in ºC
Td 700 Dewpoint temperature at 700 mb in ºC
Thermodynamics
M. D. Eastin

33. Stability Indices K Index (K): Forecast Guidelines:
K < % chance of thunderstorms
15 – < 20% chance of thunderstorms
21 – % chance of thunderstorms
26 – % chance of thunderstorms
31 – % chance of thunderstorms
36 – % chance of thunderstorms
K > > 90% chance of thunderstorms
Usage Guidelines:
Does not require a plotted sounding
Biased toward “air mass” thunderstorms (i.e. not near fronts)
Works best for non-severe thunderstorms
Thermodynamics
M. D. Eastin

34. Stability Indices Total Totals (TT): Definition:
Used to identify areas of potential thunderstorm development:
Temperature lapse rate between 850 and 500 mb (T850 and T500)
Low-level moisture (Td 850)
where: T850 Temperature at 850 mb in ºC
T500 Temperature at 500 mb in ºC
Td 850 Dewpoint temperature at 850 mb in ºC
Thermodynamics
M. D. Eastin

35. Stability Indices Total Totals (TT): Forecast Guidelines:
TT < 45 No thunderstorm activity
45 – 50 Weak potential for thunderstorm activity
50 – 55 Moderate potential for thunderstorm activity
TT > 55 Strong potential for thunderstorm activity
Usage Guidelines:
Does not require a plotted sounding
Good for “air mass” thunderstorms (i.e. not near fronts)
More reliable than K-Index for severe thunderstorm potential
Thermodynamics
M. D. Eastin

36. Stability Indices Severe Weather Threat Index (SWEAT): Definition:
Measure of severe weather potential based on:
Low-level moisture (Td 850)
Instability (Total Totals = TT)
Low-level jet stream (vv850)
Mid-level jet stream (vv500)
Warm air advection (dd500 and dd850)
where: Td 850 Dewpoint temperature at 850 mb in ºC
TT Total Totals in ºC
vv850 Wind speed at 850 mb in knots
vv500 Wind speed at 500 mb in knots
dd850 Wind direction at 850 mb in degrees
dd500 Wind direction at 500 mb in degrees
Thermodynamics
M. D. Eastin

37. Stability Indices Severe Weather Threat Index (SWEAT): Rules:
No term may be negative!
Set 12Td 850 = 0 if Td 850 is negative
Set 20(TT-49) = 0 if TT < 49
Set 125[sin(dd500 – dd850) +0.2] = 0 if any of the following are not met:
dd850 is in the range 130º to 250º
dd500 is in the range 210º to 310º
dd500 – dd850 > 0
vv500 and vv850 are both > 15 knots
Thermodynamics
M. D. Eastin

38. Stability Indices Severe Weather Threat Index (SWEAT):
Forecast Guidelines:
SWEAT > Severe Thunderstorms
SWEAT > 400 Tornadic Thunderstorms
Usage Guidelines:
Does not require a plotted sounding
Only indicates potential for severe weather
Includes vertical wind shear terms required for deep convection
Forced ascent is needed to realize the potential
Thermodynamics
M. D. Eastin

39. Stability Indices Convective Inhibition (CIN): Definition:
The energy that must be overcome to make a parcel buoyant
Energy is overcome by forced ascent
The negative area below the LFC between the environmental sounding
and the temperature of a lifted parcel Td T
LFC
Negative
Area
LCL
Thermodynamics
M. D. Eastin

40. Stability Indices Convective Inhibition (CIN):
Skew-T Procedure: Find the LCL for a parcel lifted from the surface
2. Find the LFC for the same parcel
3. Identify those layers below the LFC in which the
parcel temperature is less than the environmental
temperature
4. The CIN is the total negative area Td T
LFC
CIN
LCL
Thermodynamics
M. D. Eastin

41. Stability Indices Convective Available Potential Energy (CAPE):
Definition:
Buoyant energy available in the atmosphere
Forced ascent is usually required to tap into this energy
The positive area above the LFC between the environmental sounding
and the temperature of a lifted parcel Td T EL
Positive
Area
LFC
LCL
Thermodynamics
M. D. Eastin

42. Stability Indices Convective Available Potential Energy (CAPE):
Skew-T Procedure: Find the LCL for a parcel lifted from the surface
2. Find the LFC and EL for the same parcel
3. Identify those layers below the LFC and EL in which the
parcel temperature is greater than the environmental
temperature
4. The CAPE is the total positive area Td T EL
CAPE
LFC
LCL
Thermodynamics
M. D. Eastin

43. Stability Indices Convective Inhibition (CIN): Forecast Guidelines:
CIN > J/kg Early development of storms
-10 to -100 J/kg Late development of storms
(severe weather possible)
CIN < 100 J/kg No storms (“capped”)
Convective Available Potential Energy (CAPE):
CAPE < 500 J/kg Unlikely development of strong storms
500 – J/kg Potential for strong or severe storms
CAPE > J/kg Strong or severe storms likely
Thermodynamics
M. D. Eastin

44. Time for you to forecast thunderstorms…
Stability Indices
Time for you to forecast thunderstorms…
Thermodynamics
M. D. Eastin

45. Stability Indices Summary: Useful Parameters for Rising Air Parcels
Review of Stability
Useful Parameters for Rising Air Parcels
Convective Condensation Level (CCL)
Convective Temperature (Tc)
Lifting Condensation Level (LCL)
Level of Free Convection (LFC)
Equilibrium Level (EL)
Positive and Negative Areas
Stability Indices
Showalter Index (SI)
Lifted Index (LI)
K Index (K)
Total Totals (TT)
Severe Weather Threat Index (SWEAT)
Convective Inhibition (CIN)
Convective Available Potential Energy (CAPE)
Thermodynamics
M. D. Eastin

46. References Thermodynamics M. D. Eastin
Petty, G. W., 2008: A First Course in Atmospheric Thermodynamics, Sundog Publishing, 336 pp.
Tsonis, A. A., 2007: An Introduction to Atmospheric Thermodynamics, Cambridge Press, 197 pp.
Wallace, J. M., and P. V. Hobbs, 1977: Atmospheric Science: An Introductory Survey, Academic Press, New York, 467 pp.
Also (from course website):
NWSTC Skew-T Log-P Diagram and Sounding Analysis, National Weather Service, 2000
The Use of the Skew-T Log-P Diagram in Analysis and Forecasting, Air Weather Service, 1990
Thermodynamics
M. D. Eastin