Stability Indices
How to forecast the likelihood of thunderstorms!!!
Thermodynamics
M. D. Eastin
Stability Indices
Outline:
 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
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
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
Temperature
Thermodynamics
M. D. Eastin
Concept of Stability
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
Thermodynamics
Hot
Cool
M. D. Eastin
Concept of Stability
How is air displaced? Forced Ascent
• Flow over mountains
• Flow over fronts (cold, warm, stationary, occluded, etc.)
Thermodynamics
M. D. Eastin
Atmospheric Stability Analysis
Combined Criteria for Moist Air (either saturated or unsaturated):
Absolutely Unstable:
Saturated
parcel becomes
warmer
than nearby
environment
Γd
Height
Γ  Γd  Γs
Unsaturated
parcel becomes
warmer
than nearby
environment
Γs
Γ
Temperature
Dry Neutral:
Unsaturated
parcel becomes
equivalent to
the nearby
environment
Saturated
parcel becomes
warmer
than nearby
environment
Γd
Height
Γ  Γd  Γs
Γs
Γ
Temperature
Thermodynamics
M. D. Eastin
Atmospheric Stability Analysis
Combined Criteria for Moist Air (either saturated or unsaturated):
Conditionally Unstable:
Saturated
parcel becomes
warmer
than nearby
environment
Γ
Height
Γd  Γ  Γs
Unsaturated
parcel becomes
colder
than nearby
environment
Γd
Γs
Temperature
 The vertical temperature profile at most locations in our atmosphere
is conditionally unstable
Thermodynamics
M. D. Eastin
Atmospheric Stability Analysis
Combined Criteria for Moist Air (either saturated or unsaturated):
Moist Neutral:
Saturated
parcel becomes
equivalent to
the nearby
environment
Γ
Height
Γd  Γ  Γs
Unsaturated
parcel becomes
colder
than nearby
environment
Γs
Γd
Temperature
Absolutely Stable:
Saturated
parcel becomes
colder
than nearby
environment
Γs
Height
Γ d  Γs  Γ
Unsaturated
parcel becomes
colder
than nearby
environment
Γ
Γd
Temperature
Thermodynamics
M. D. Eastin
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
Warm
• Altitude of the base of cumuliform
clouds that are produced by thermal
convection from surface heating
Cool
Thermodynamics
CCL
Hot
Cool
M. D. Eastin
Useful Parameters for Rising Air Parcels
Convective Condensation Level (CCL):
Skew-T Procedure:
1. 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
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.
Warm
• Often compared to the forecast
high temperature for the day
CCL
• If Tforecast > Tc then
convective clouds
will form
• If Tforecast < Tc then
convective clouds
will not form
Tc Tc
Cool
Thermodynamics
Hot
Cool
M. D. Eastin
Useful Parameters for Rising Air Parcels
Convective Temperature (Tc):
Skew-T Procedure:
1. 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
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
Thermodynamics
LCL
M. D. Eastin
Useful Parameters for Rising Air Parcels
Lifting Condensation Level (LCL):
Skew-T Procedure:
1. 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
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
Useful Parameters for Rising Air Parcels
Level of Free Convection (LFC):
Skew-T Procedure:
1. 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
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
Useful Parameters for Rising Air Parcels
Equilibrium Level (EL):
Skew-T Procedure:
1. 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
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
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
Useful Parameters for Rising Air Parcels
Application:
Find the
CCL and TC
Thermodynamics
M. D. Eastin
Useful Parameters for Rising Air Parcels
Application:
Find the
LCL, LFC, and EL
for the
surface air parcel
Thermodynamics
M. D. Eastin
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
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.
SI  Te 500  Tp 500
where:
Thermodynamics
Te 500
Tp 500
Environmental temperature at 500 mb in K
Parcel temperature at 500 mb in K
M. D. Eastin
Stability Indices
Showalter Index (SI):
Skew-T Procedure:
1. 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
500 mb
T
Te500
SI = Te500 – Tp500
Tp500
SI = (-32ºC) – (-25ºC)
SI = (241 K) – (248 K)
SI = –7
LCL
850 mb
Thermodynamics
M. D. Eastin
Stability Indices
Showalter Index (SI):
SI  Te 500  Tp 500
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
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
LI  Te 500  Tp 500
where:
Te 500
Tp 500
Environmental temperature at 500 mb in K
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
Stability Indices
Lifted Index (LI):
Skew-T Procedure:
1. 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
500 mb
T
Te500
mean wsw
880 mb
980 mb
Thermodynamics
LI = Te500 – Tp500
Tp500
LI = (-32ºC) – (-26ºC)
LI = (241 K) – (247 K)
LI = –6
LCL
mean θ
M. D. Eastin
Stability Indices
Lifted Index (LI): Finding the mean wsw and θ:
1.
2.
3.
4.
5.
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
Td
T
100 mb
50 mb
Thermodynamics
M. D. Eastin
Stability Indices
Lifted Index (LI):
LI  Te 500  Tp 500
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
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 500)
• Vertical extent of moist layer (T700-Td 700)
K  (T850  T500 )  Td 850  (T700  Td 700 )
where:
Thermodynamics
T850
T500
Td 850
T700
Td 700
Temperature at 850 mb in ºC
Temperature at 500 mb in ºC
Dewpoint temperature at 850 mb in ºC
Temperature at 700 mb in ºC
Dewpoint temperature at 700 mb in ºC
M. D. Eastin
Stability Indices
K Index (K):
K  (T850  T500 )  Td 850  (T700  Td 700 )
Forecast Guidelines:
K < 15
15 – 20
21 – 25
26 – 30
31 – 35
36 – 40
K > 40
0% chance of thunderstorms
< 20% chance of thunderstorms
20-40% chance of thunderstorms
40-60% chance of thunderstorms
60-80% chance of thunderstorms
80-90% chance of thunderstorms
> 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
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)
TT  (T850  Td 850 )  2T500
where:
Thermodynamics
T850
T500
Td 850
Temperature at 850 mb in ºC
Temperature at 500 mb in ºC
Dewpoint temperature at 850 mb in ºC
M. D. Eastin
Stability Indices
Total Totals (TT):
TT  (T850  Td 850 )  2T500
Forecast Guidelines:
TT < 45
45 – 50
50 – 55
TT > 55
No thunderstorm activity
Weak potential for thunderstorm activity
Moderate potential for thunderstorm activity
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
Stability Indices
Severe Weather Threat Index (SWEAT):
Definition:
Measure of severe weather potential based on:
• Low-level moisture (Td 850)
• Instability (Total Totals)
• Low-level jet stream (vv850)
• Mid-level jet stream (vv500)
• Warm air advection (dd500 and dd850)
SWEAT  12Td 850  20(TT 49) 2vv850  vv500 125[sin(dd500  dd850 )  0.2]
where:
Thermodynamics
Td 850
TT
vv850
vv500
dd850
dd500
Dewpoint temperature at 850 mb in ºC
Total Totals in ºC
Wind speed at 850 mb in knots
Wind speed at 500 mb in knots
Wind direction at 850 mb in degrees
Wind direction at 500 mb in degrees
M. D. Eastin
Stability Indices
Severe Weather Threat Index (SWEAT):
SWEAT  12Td 850  20(TT 49) 2vv850  vv500 125[sin(dd500  dd850 )  0.2]
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
Stability Indices
Severe Weather Threat Index (SWEAT):
SWEAT  12Td 850  20(TT 49) 2vv850  vv500 125[sin(dd500  dd850 )  0.2]
Forecast Guidelines:
SWEAT > 300
SWEAT > 400
Severe Thunderstorms
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
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
Stability Indices
Convective Inhibition (CIN):
Skew-T Procedure:
1. 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
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
Stability Indices
Convective Available Potential Energy (CAPE):
Skew-T Procedure:
1. 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
Stability Indices
Convective Inhibition (CIN):
Forecast Guidelines:
CIN > -10 J/kg
-10 to -100 J/kg
CIN < 100 J/kg
Early development of storms
Late development of storms
(severe weather possible)
No storms (“capped”)
Convective Available Potential Energy (CAPE):
Forecast Guidelines:
CAPE < 500 J/kg
500 – 2000 J/kg
CAPE > 2000 J/kg
Thermodynamics
Unlikely development of strong storms
Potential for strong or severe storms
Strong or severe storms likely
M. D. Eastin
Stability Indices
Time for you to forecast thunderstorms…
Thermodynamics
M. D. Eastin
Stability Indices
Summary:
• 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
References
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