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To start today: let’s revisit Frontogenesis, both the
equation and the physical interpretations
Simplified Form of the Frontogenesis Equation
d     u  v  w 
  d 
F



 

 
dt  y   y  x  y  y  y  z y   dt 
A
B
Term A: Shear term
Term B: Confluence term
Term C: Tilting term
Term D: Diabatic Heating/Cooling term
C
D
Scratch paper
u
u is the horizontal, east-west wind. For
this example, u is the left-to-right wind. u
is defined as positive when its vector
points to the east.
Let’s define our coordinate system with
the standard (x,y,z) method, where x
increases to the east, y increases to the
north, and z increases in the vertical.
y
x
y
u
0
y
u
0
y
u
0
y
u
0
y
u
0
y
Scratch paper
v
v is the horizontal, north-south wind. For
this example, v is the top-to-bottom wind.
v is defined as positive when its vector
points to the north.
Let’s define our coordinate system with
the standard (x,y,z) method, where x
increases to the east, y increases to the
north, and z increases in the vertical.
y
x
y
u
0
y
v
0
y
v
0
y
v
0
y
v
0
y
Scratch paper
θ
θ is the potential temperature. It is defined as
the temperature that an air parcel would
acquire if it were displaced from downward
from a certain level (possibly 850 mb, or 500
mb) to a reference level (usually the surface).
θ is related to temperature, T, by Poisson’s
equation,
 p0 
 T  
 p 
R
cp
where p0 is the reference pressure level, R is
the universal gas constant (287 j kg-1 K-1) and
cp is the specific heat at constant pressure
(1004 j kg-1 K-1).
θ example from today
The 700 mb temperature over
Vienna at 0000 UTC on 09 Nov
2006 was -2.5 C. Assume we
transport this air down to the
surface (Vienna’s surface
pressure was 998 mb at 0000
UTC). What temperature will
the air parcel have?
p 
 T  0 
 p 
R
cp
287 J kg -1 K -1
 998 mb 1004 J kg-1 K-1
  270.6 K 

 700 mb 
  299.5 K = 26.4 C
Frontogenesis: Shear Term (A)
F
Individual
contribution
to F
 u 
 y   x
-
Because both terms
have negative
contributions, F is
positive and the front is
created / strengthened
-
Frontogenesis: Confluence Term (B)
F
Individual
contribution
to F
 v 
 y  y
-
-
Cold advection
to the north
Warm advection
to the south
Because both terms
have negative
contributions, F is
positive and the front is
created / strengthened
Carlson, 1991 Mid-Latitude Weather Systems
Why are cold fronts typically stronger than warm fronts?
Look at the shear and confluence terms near cold and
warm fronts
Shear (A) and confluence
(B) terms oppose one
another near warm
fronts
Shear (A) and confluence
(B) terms tend to work
together near cold fronts
Carlson (Mid-latitude Weather Systems, 1991)
Frontogenesis: Tilting Term (C)
F
 w 
 y  z
Individual
contribution
to F
+ +
Because both terms
have positive
contributions, F is
positive and the front is
created / strengthened
Adiabatic
cooling to
north and
warming to
south increases
horizontal
thermal
gradient
Carlson, 1991 Mid-Latitude Weather Systems
Frontogenesis: Diabatic Heating/Cooling Term (D)
  d 

 y  dt 
F
frontogenesis
small dθ/dt
-
large dθ/dt
-
F is positive (two
negatives become
positive)
F
frontolysis
large dθ/dt
small dθ/dt
  d 

 y  dt 
-
+
F is negative
Carlson, 1991 Mid-Latitude Weather Systems
Thunderstorms: Airmass and Squall Line
Facts about thunderstorms
• Common world-wide, especially in tropical
and middle latitudes
• Redistribute heat and moisture
– Transport from the surface to upper-levels
• Most (95%) are non-severe
– “Severe” criteria: ¾” or larger hail, 50+ kt
(58+ mph) wind, OR tornado
Types of thunderstorms
•
Four primary types of organization:
1.
2.
3.
4.
•
Airmass
Squall line
Multi-cell
Supercell
Focus today: Airmass and squall line
Elements required for formation
• Source of moisture
• Conditionally unstable atmosphere
• Mechanism to “trigger” an updraft
– Lifting from an advancing frontal boundary or
air flow over a mountain
– Convective heating at the surface (from solar
radiation)
– Convergence of air at the surface
Airmass Thunderstorms
• Occurs away from any frontal boundary
– In fact, typically found in the middle of an
airmass
• “Trigger” mechanism:
– Strong solar heating at the surface
• Formation: typically late afternoon and
evening
– After sun heats the mT airmass for 10+ hours
Airmass Thunderstorms
• Last about 1 hour
• Rain covers maybe a 10 to 15 km area
• Are self-destructive
– Rain/precipitation falls back into the updraft
• Usually form in region of weak upper-level winds
– i.e., little/no vertical wind shear
– Remember the “tropical disturbance”? Simply a large collection
of airmass thunderstorms
• Are not known for most types of severe weather (hail,
straight-line winds, or tornadoes)
– We will see later that air mass thunderstorms are responsible for
microbursts
Parts of airmass thunderstorm
Anvil part of
the cloud
Tropopause
Main “cell”
updraft
LCL (point where
condensation
occurs)
Airmass Thunderstorm:
stages of development
Airmass Thunderstorm:
stages of development
1. Cumulus stage:
– Cloud consists of warm, buoyant plume of
rising air
– Cloud consists of mostly small cloud
droplets; there are only a few raindrops or
ice crystals
Airmass Thunderstorm:
stages of development
2. Mature stage:
–
–
As storm updraft rises to regions well below
freezing, ice crystals form
Graupel forms
•
–
–
•
Graupel: small (a few millimeters) ice particles with
consistency of a snowball
Downdrafts begin to form as raindrops fall back to
earth
Light rain is noticed at the ground
Key point in “mature” stage: Because there is
no vertical wind shear, precipitation must fall
back down through the main updraft.
Airmass Thunderstorm:
stages of development
3. Dissipation stage
– Downdrafts formed by rain falling back down
into the updraft
– Downdrafts overwhelm the main updraft
– Heavy rain falls out of the base of the
thunderstorm
– Dissipation occurs
Squall Line
• Long line of thunderstorms
– individual “cells” are so close together the heavy
precipitation forms a long continuous line
• Typically form along an advancing cold front
• Can be hundreds of miles long!
• Most commonly associated with strong straightline winds
– Can produce hail and/or tornadoes, too
• Called “squall” because of the abrupt wind
changes
Squall line thunderstorms
Squall line thunderstorms
L
A squall line
approaching
Memphis, TN.
Note the heaviest
precip is along the
leading (eastern)
edge of the line,
with moderate –
but still continuous
– rainfall occurring
100+ km behind
(to the west) of the
“line”
Structure of a squall line
• Already noted the “trigger” is typically an advancing
(cold) frontal boundary
• The squall line will sustain itself by producing its own lift
due to outflow boundaries
• Again, tropopause acts as a “lid” to the thunderstorm
updraft
– Thus, anvil clouds also form in squall lines
• Heavy rain / strong winds occur beneath the convective
region
– Strongest updrafts occur in the convective region
• As long as instability and moisture remain present out
ahead of the squall line, the squall line will continue to
propagate
Structure of a squall line
Looking THROUGH the line … i.e., the “line” is
coming out of / going into the page
Squall line “gust front”
Also called a “bow echo”
Squall line
• Self-propagating (not self-destructive like
airmass thunderstorm)
• Evaporatively-cooled air pushes out
slightly ahead of the squall line
– Acts as the “trigger” mechanism
• i.e., lifts the warm air up and into the squall line
– Easily noticed as a “shelf cloud”
Squall line photos
More photos of a squall line
More photos of a squall line
Dangers from air mass
thunderstorms: microbursts
Not easily detected
because
1. the ambient
thunderstorm (or
even cumuliform
cloud) is usually
considered
benign
2. The scale is
typically very
small (perhaps 1
or 2 km across)
Two primary types of microbursts:
1. Dry microburst. Occurs when surface layer is very dry (low relative
humidity). Rain evaporates and accelerates downward through the
warm, dry surface layer
2. Wet microburst. Occurs when the surface layer is very moist and
upper-levels are very dry. Dry downdraft entrained (mixed) from
above the cloud penetrates through the cloud, evaporatively-cooling
as it mixes with rainwater
** Both types of microbursts are associated with evaporating rainwater **
Danger comes from two sources:
1. Rush of cool, stable air out from
the microburst center once it
reaches the surface
2. Turbulence associated with the
“rotor cloud” – the leading edge of
the microburst
Photos of microbursts
More photos of microbursts
Microbursts can be deadly
• Eastern Airlines flight 66
– June 24, 1975, John F.
Kennedy, New York
– 112 fatalities (12 survivors)
• Pan-Am flight 759
– July 9, 1982, New Orleans,
Louisiana
– 153 fatalities (0 survivors)
• Delta Airlines flight 191
– August 2, 1985, Dallas-Fort
Worth, Texas
– 135 fatalities (29 survivors)
• US Airways flight 1016
– July 2, 1994, Charlotte,
North Carolina
– 37 fatalities (25 survivors)
The threat from a squall line: derecho
Definition of a derecho:
“A widespread convectively induced straightline windstorm.” (AMS Glossary of
Meteorology)
Conditions for a calling an event a “derecho”:
1. There must be a concentrated area of reports
consisting of convectively-induced wind damage
or convective gusts of more than 26 ms-1 (50
kt).
2. The reports within this area must also exhibit a
nonrandom pattern of occurrence. That is, the
reports must show a pattern of chronological
progression, either as a singular swath
(progressive) or as a series of swaths (serial).
3. Within the area there must be at least three
reports, separated by 64 km or more, of either
F1 damage or convective gusts of 33 ms-1 (65
kt) or greater.
4. No more than 3 h can elapse between
successive wind damage (gust) events.
Trajectories and annual frequency
of derechos in the US
A typical derecho event: 19 July 1983.
Map shows location and time of derecho line; max wind
gusts are given in miles per hour
Photo of the incoming derecho,
19 July 1983
Another photo of the incoming derecho,
19 July 1983
A particularly damaging derecho
event: 30-31 May 1998
Storm reports from derecho event
The event did not start out as a
derecho . . .
Radar sequence images of 30-31
May 1998 derecho event
Clip: animated radar display
Final example of a strong derecho
27 May 2001
Visible satellite
image of the
thunderstorm
complex that
produced the
derecho
Photos from 27 May 2001
1 Death
4 Injuries
160,000 without power
Over $300 million damage
27 May 2001 derecho event
Photo taken
here at 7:23
pm CDT
*
Finally, derechos are not only found
in the US