how to forecast the likelihood of thunderstorms!!!

Thermodynamics M. D. Eastin

How to forecast the likelihood of thunderstorms!!!

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)

Stability Indices


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


Basic Idea:

Ability of an air parcel to return to is level of origin after a displacementDepends on the temperature structure of the atmosphere


Temperature

DewpointTemperature


How is air displaced? Spontaneous Ascent

• Air parcel is warmer than its environment which means the parcel is “buoyant”

• Air becomes buoyant through “heating”


HotHotCoolCool CoolCool

Warm


How is air displaced? Forced Ascent

• Flow over mountains

• Flow over fronts (cold, warm, stationary, occluded, etc.)



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



equivalent tothe nearby

environment

Temperature

Hei

gh

t Γs Γ

Γd Saturatedparcel becomes




Conditionally Unstable:

The vertical temperature profile at most locations in our atmosphere is conditionally unstable



colderthan nearbyenvironment

Temperature

Hei

gh

t Γs Γ

Γd

Saturatedparcel becomes




Moist Neutral:

Absolutely Stable:




Temperature

Hei

gh

t Γs Γ

Γd


equivalent tothe nearby

environment

ΓΓΓ sd Unsaturatedparcel becomes


Temperature

Hei

gh

t

Γs Γ

Γd




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


Warm

CCL


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



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


Warm

CCL

Tc Tc



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



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



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



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


TTd

LCL

Altitude at whicha lifted parcel first

becomes warmer than the

environment


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


TTd

LCL

Level of FreeConvection

LFC = 660 mb

Tp < Te

Tp > Te

Tp < Te


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


TTd

LCL

Altitude at whichthe temperature

of a buoyant parcelequals the

environmentaltemperature

LFC


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


TTd

LCL

EquilibriumLevel

LFC

Tp < Te

Tp > Te

EL = 400 mbTp < Te

Tp < Te


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)


TTd

LCL

NegativeArea

LFC

Tp < Te

Tp > Te

ELTp < Te

Tp < Te

NegativeArea


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)


TTd

LCL

PositiveArea

LFC

Tp < Te

Tp > Te

ELTp < Te

Tp < Te


Application:

Find the CCL and TC



Application:

Find the LCL, LFC, and EL

for thesurface air parcel



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


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


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


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


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


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


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


Stability IndicesLifted Index (LI):


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


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


Stability IndicesK Index (K):


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


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


Stability IndicesTotal Totals (TT):


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


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



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





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



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


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


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


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


Stability IndicesConvective Inhibition (CIN):


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):


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


Stability Indices

Time for you to forecast thunderstorms…


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


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

how to forecast the likelihood of thunderstorms!!!

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