### Stability indices

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Tephigrams, and static stability
sources:
-handout text
-online module called “Skew T mastery”
1. Aerological diagrams
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–
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Maps
Vertical profiles
Instrument contains:
Hygristor, thermistor, aneroid barometer, and
At the ground, a highly directional radio
direction finding antenna is used to obtain the
wind speed and direction at various levels in
the atmosphere by tracking the radiosonde and
determining the azimuth and elevation angles.
Aerological diagrams
• Hydrostatic balance
• Ideal gas law
• Hypsometric equation
Aerological
diagrams: different
types
emagram
Stuve




pressure
p
 R
 d
 c
 p
temperature
Stuve
Skew T log p
Fig 1d. Elements of a tephigram. First, the 5 lines are shown
separately, and then they are combined in the lower-right image.
2. using a tephigram
tephi
LCL (lifting condensation level)
HLCL
ground
Applications
1. Determine the height of the base of cumulus clouds, given surface
observations of T and Td : H  T  T  T  T
d
LCL
 d   Td
2. Determine the cloud base temperature:
d
8
T cloudbase  T surface  10 H LCL
wet-bulb
potential
temperature
potential
temperature
equivalent
potential
temperature
saturated
equivalent
potential
temperature
wet bulb temperature:
energy balance on the damp sock:
LE = H
LE = 6 u [esat(Tw)-e]
H = 4 u [T-Tw]
(Regnault balance)
Applications
1. Layer thickness (between po and p)
Dz
Dz = 100 DT
2. Precipitable water
3. Chinook (Föhn) effect
west
east
4. subsidence
5. Turbulent mixing, mixed layer (stratus), MCL
Oakland
Conserved or not conserved?
T
Td
Tw
q
qe or qw
qe*
q or r
RH
Evaporation/
condensation
Ascent/descent
Conserved or not conserved?
Evaporation/
condensation
Ascent/descent
T
n
n
n
Td
y
n
n
Tw
n
y
n
q
n
n
y
qe or qw
n
y
y
qe*
n
n
n
q or r
y
n
y
RH
n
n
n
3. stability
stability
Local vs non-local stability
Conditional vs absolute stability
Case II:
d qe* < 0
dz
Absolutely stable
Conditionally unstable
Absolutely unstable
equilibrium
level
benign
severe
LFC
no convection
convective inhibition
Typical wet-season tropical sounding
Conditional instability:
d qe* < 0
dz
Potential instability
Potential instability:
dq e
dz
or
dq w
dz
Lifting a potentially
unstable layer
Latent instability
WLR: wet-bulb lapse rate
deep convection
source layer
Stability indices
Significant level indices
e.g. UW sounding site
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WB0: Wet bulb zero, Tw = 0°C ideally 7-9,000ft MSL, yet well below the FL
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PWAT: Precipitable water (mm) the higher the better
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LCL: Lifting condensation level (mb, from surface data) the lower the better
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TOTL: Total totals index =T 850 +Td
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KINX: K index =T
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SWET: Sweat index or severe weather threat - the higher the better, for severe
850
- 2T
thunderstorms probable when TOTL>50
850
+ Td
850
500
(°C) the higher the better,
-T 500 -(T-Td)700 (°C) the higher the better
storms, SW>300
SWET= 12*Td850 +20*(TOTL-49) + 2*U850 +U500 +125*(0.2+sinf)
where f= [wind direction 500 - wind direction 850 ]
U is expressed in kts and TOTL-49 is set to 0 if TOTL<49
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MLTH and MLMR: mean mixed layer (lowest 500 m) potential temp and mixing
ratio
PARCEL indices
Lifted index uses:
Actual sfc temp
or
Estimated max sfc temp
or
Mean mixed-layer temp
(note: always use virtual
temp!)
Showalter index
SI=T500-Tp,850
PARCEL indices
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LIFT: Lifted index (°C) must be negative
LI = T500 – T parcel,near-sfc [a 50 mb deep mixed layer is often used]
LFTV: lifted index, but Tv is used.
SHOW: Showalter index (°C, as LI but starts from 850mb) must be negative
SHOW = T500 – T parcel,850
CAPE: Convective available potential energy - should be over 500J/kg
CAPV: CAPE using Tv
CINS: Convective inhibition (external energy) - ideally 100-300 J/kg
CINV: CIN using Tv
CAP: Cap strength (C) Tenv –Tparcel @LCL - should be <5°C
LFC: Level free convection (LFCT and LFCT) (mb) - should be close to the LCL
EQL: Equilibrium level or level of neutral buoyancy (EQLT and EQLV)(mb) - should be high
MPL: Maximum parcel buoyancy level (mb) - level where buoyancy (Tp-Tenv) is maximum
Wind parameters
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STM: Estimated storm motion (knts) from 0-20,000ft AGL layer, spd 75%
of mean, dir 30 deg veer (to the right) from mean wind.
HEL: Storm relative helicity 0-10,000ft AG (total value)
SHR+: Positive shear magnitude 0-3000m AG (sum of veering shear values)
SRDS: Storm relative directional shear 0-3000m AG (directional difference
of storm relative winds)
EHI: Energy helicity index (prop to positive helicity * CAPE)
BRN: Bulk Richardson number 500-6000m AG (BRN = CAPE/.5BSHR2)
BSHR: Bulk shear value (magnitude of shear over layer), shear calculated
between 1000-500 mb or 500 m –6000 m AGL
example mid-term questions
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As a rule of thumb, thunderstorms are possible when LI<0, and severe thunderstorms
are likely if LI<-8. Assuming surface values T=32°C, Td=22°C, T500=-7°C, calculate Tv
at the surface, and the lifted index LI based on both T and Tv.
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Note that traditionally LI was calculated based on T, but the more correct procedure uses
Tv. The difference is small but not negligible!
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Using a given sounding on a tephigram, graphically determine, for an air parcel at 850
mb, the following: LCL, Tw , r, rs, e, es, RH, q, qw, qe*, qe,
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Using a given sounding on a tephigram, graphically determine layers of:
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–
–
–
absolute instability
conditional instability
potential instability
draw a parcel ascent path and shade the areas of
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positive energy (CAPE)
negative energy (CIN)
LIFT=-7 K
CAPE=1974 J/kg
CIN=-24 J/kg
LCL= 900 mb
LFL= 836 mb
```