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Thermodynamics M. D. Eastin
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)
Stability Indices
Thermodynamics M. D. Eastin
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
Concept of Stability
Thermodynamics M. D. Eastin
Basic Idea:
Ability of an air parcel to return to is level of origin after a displacementDepends on the temperature structure of the atmosphere
Concept of Stability
Temperature
DewpointTemperature
Thermodynamics M. D. Eastin
How is air displaced? Spontaneous Ascent
• Air parcel is warmer than its environment which means the parcel is “buoyant”
• Air becomes buoyant through “heating”
Concept of Stability
HotHotCoolCool CoolCool
Warm
Thermodynamics M. D. Eastin
How is air displaced? Forced Ascent
• Flow over mountains
• Flow over fronts (cold, warm, stationary, occluded, etc.)
Concept of Stability
Thermodynamics M. D. Eastin
Combined Criteria for Moist Air (either saturated or unsaturated):
Absolutely Unstable:
Dry Neutral:
Atmospheric Stability Analysis
sd ΓΓΓ Unsaturatedparcel becomes
warmerthan nearbyenvironment
Temperature
Hei
gh
t Γs
Γ
Γd Saturatedparcel becomes
warmerthan nearbyenvironment
sd ΓΓΓ Unsaturatedparcel becomes
equivalent tothe nearby
environment
Temperature
Hei
gh
t Γs Γ
Γd Saturatedparcel becomes
warmerthan nearbyenvironment
Thermodynamics M. D. Eastin
Combined Criteria for Moist Air (either saturated or unsaturated):
Conditionally Unstable:
The vertical temperature profile at most locations in our atmosphere is conditionally unstable
Atmospheric Stability Analysis
sd ΓΓΓ Unsaturatedparcel becomes
colderthan nearbyenvironment
Temperature
Hei
gh
t Γs Γ
Γd
Saturatedparcel becomes
warmerthan nearbyenvironment
Thermodynamics M. D. Eastin
Combined Criteria for Moist Air (either saturated or unsaturated):
Moist Neutral:
Absolutely Stable:
Atmospheric Stability Analysis
sd ΓΓΓ Unsaturatedparcel becomes
colderthan nearbyenvironment
Temperature
Hei
gh
t Γs Γ
Γd
Saturatedparcel becomes
equivalent tothe nearby
environment
ΓΓΓ sd Unsaturatedparcel becomes
colderthan nearbyenvironment
Temperature
Hei
gh
t
Γs Γ
Γd
Saturatedparcel becomes
colderthan nearbyenvironment
Thermodynamics M. D. Eastin
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
Useful Parameters for Rising Air Parcels
HotHotCoolCool CoolCool
Warm
CCL
Thermodynamics M. D. Eastin
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
TTd
ConvectiveCondensation
Level(CCL)
CCL = 850 mb
Useful Parameters for Rising Air Parcels
Thermodynamics M. D. Eastin
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 convective clouds will not form
HotHotCoolCool CoolCool
Warm
CCL
Tc Tc
Useful Parameters for Rising Air Parcels
Thermodynamics M. D. Eastin
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
TTd
ConvectiveTemperature
(Tc)
CCLTc = 12ºC
Useful Parameters for Rising Air Parcels
Thermodynamics M. D. Eastin
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
Useful Parameters for Rising Air Parcels
Thermodynamics M. D. Eastin
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
TTd
Lifting Condensation
Level(LCL)
LCL = 870 mb
Useful Parameters for Rising Air Parcels
Thermodynamics M. D. Eastin
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
Useful Parameters for Rising Air Parcels
TTd
LCL
Altitude at whicha lifted parcel first
becomes warmer than the
environment
Thermodynamics M. D. Eastin
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
Useful Parameters for Rising Air Parcels
TTd
LCL
Level of FreeConvection
LFC = 660 mb
Tp < Te
Tp > Te
Tp < Te
Thermodynamics M. D. Eastin
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
Useful Parameters for Rising Air Parcels
TTd
LCL
Altitude at whichthe temperature
of a buoyant parcelequals the
environmentaltemperature
LFC
Thermodynamics M. D. Eastin
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
Useful Parameters for Rising Air Parcels
TTd
LCL
EquilibriumLevel
LFC
Tp < Te
Tp > Te
EL = 400 mbTp < Te
Tp < Te
Thermodynamics M. D. Eastin
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)
Useful Parameters for Rising Air Parcels
TTd
LCL
NegativeArea
LFC
Tp < Te
Tp > Te
ELTp < Te
Tp < Te
NegativeArea
Thermodynamics M. D. Eastin
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)
Useful Parameters for Rising Air Parcels
TTd
LCL
PositiveArea
LFC
Tp < Te
Tp > Te
ELTp < Te
Tp < Te
Thermodynamics M. D. Eastin
Application:
Find the CCL and TC
Useful Parameters for Rising Air Parcels
Thermodynamics M. D. Eastin
Application:
Find the LCL, LFC, and EL
for thesurface air parcel
Useful Parameters for Rising Air Parcels
Thermodynamics M. D. Eastin
Stability IndicesBasic 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 IndicesShowalter 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 KTp 500 Parcel temperature at 500 mb in K
500p500e TTSI
Thermodynamics M. D. Eastin
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
Stability Indices
TTd
LCL
SI = Te500 – Tp500
Te500
850 mb
Tp500500 mb
SI = (-32ºC) – (-25ºC)SI = (241 K) – (248 K)SI = –7
Thermodynamics M. D. Eastin
Stability IndicesShowalter Index (SI):
Forecast Guidelines:
+1 to +3 Showers are probable, Thunderstorms possibleneed strong forced ascent
0 to -3 Unstable – Thunderstorms probable
-4 to -6 Very Unstable – Heavy thunderstorms probable
less than -6 Extremely Unstable – Strong thunderstorms probableTornadoes are possible
Usage Guidelines:
• Good for forecasting mid-level convection• Does not account for moisture in boundary layer
500p500e TTSI
Thermodynamics M. D. Eastin
Stability IndicesLifted 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 KTp 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
500p500e TTLI
Thermodynamics M. D. Eastin
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
Stability Indices
TTd
LCL
LI = Te500 – Tp500
Te500
880 mb
Tp500500 mb
LI = (-32ºC) – (-26ºC)LI = (241 K) – (247 K)LI = –6
980 mb
mean θ
mean wsw
Thermodynamics M. D. Eastin
Lifted Index (LI): Finding the mean wsw and θ:
1. Identify the lowest 100 mb2. Identify the maximum and minimum θ within the 100 mb3. Mean θ is located 50 mb above the surface halfway between θmax and θmin
4. Identify the maximum and minimum wsw within the 100 mb5. 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
Stability Indices
100 mb
TdT
50 mb
θmin θmax
wsw-min wsw-max
Thermodynamics M. D. Eastin
Stability IndicesLifted 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
500p500e TTLI
Thermodynamics M. D. Eastin
Stability IndicesK 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)
where: T850 Temperature at 850 mb in ºCT500 Temperature at 500 mb in ºCTd 850 Dewpoint temperature at 850 mb in ºCT700 Temperature at 700 mb in ºCTd 700 Dewpoint temperature at 700 mb in ºC
)T(TT)T(TK 700d700850d500850
Thermodynamics M. D. Eastin
Stability IndicesK Index (K):
Forecast Guidelines:
K < 15 0% chance of thunderstorms15 – 20 < 20% chance of thunderstorms21 – 25 20-40% chance of thunderstorms26 – 30 40-60% chance of thunderstorms31 – 35 60-80% chance of thunderstorms36 – 40 80-90% chance of thunderstormsK > 40 > 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
)T(TT)T(TK 700d700850d500850
Thermodynamics M. D. Eastin
Stability IndicesTotal 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 ºCT500 Temperature at 500 mb in ºCTd 850 Dewpoint temperature at 850 mb in ºC
500850 d850 2T)T(TTT
Thermodynamics M. D. Eastin
Stability IndicesTotal Totals (TT):
Forecast Guidelines:
TT < 45 No thunderstorm activity45 – 50 Weak potential for thunderstorm activity50 – 55 Moderate potential for thunderstorm activityTT > 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
500850 d850 2T)T(TTT
Thermodynamics M. D. Eastin
Stability IndicesSevere 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)
where: Td 850 Dewpoint temperature at 850 mb in ºCTT Total Totals in ºCvv850 Wind speed at 850 mb in knotsvv500 Wind speed at 500 mb in knotsdd850 Wind direction at 850 mb in degreesdd500 Wind direction at 500 mb in degrees
0.2])dd(dd[sin125vv2vv49)20(TTT12SWEAT 850500500850850d
Thermodynamics M. D. Eastin
Stability IndicesSevere 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
0.2])dd(dd[sin125vv2vv49)20(TTT12SWEAT 850500500850850d
Thermodynamics M. D. Eastin
Stability IndicesSevere Weather Threat Index (SWEAT):
Forecast Guidelines:
SWEAT > 300 Severe ThunderstormsSWEAT > 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
0.2])dd(dd[sin125vv2vv49)20(TTT12SWEAT 850500500850850d
Thermodynamics M. D. Eastin
Stability IndicesConvective 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
TTd
LCL
NegativeArea
LFC
Thermodynamics M. D. Eastin
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
Stability Indices
TTd
LCL
CIN
LFC
Thermodynamics M. D. Eastin
Stability IndicesConvective 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
TTd
LCL
PositiveArea
LFC
EL
Thermodynamics M. D. Eastin
Stability IndicesConvective 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
TTd
LCL
CAPE
LFC
EL
Thermodynamics M. D. Eastin
Stability IndicesConvective Inhibition (CIN):
Forecast Guidelines:
CIN > -10 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):
Forecast Guidelines:
CAPE < 500 J/kg Unlikely development of strong storms 500 – 2000 J/kg Potential for strong or severe stormsCAPE > 2000 J/kg Strong or severe storms likely
Thermodynamics M. D. Eastin
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)
Stability Indices
Thermodynamics M. D. Eastin
ReferencesPetty, 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