Simplified Form of the Frontogenesis Equation

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To start today lets revisit Frontogenesis,
both the equation and the physical interpretations
Simplified Form of the Frontogenesis Equation
A B C
D
Term A Shear term Term B Confluence term Term
C Tilting term Term D Diabatic
Heating/Cooling term
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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. Lets 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
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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. Lets 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
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Scratch paper
? ? 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). ? is
related to temperature, T, by Poissons
equation, 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).
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? 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 (Viennas surface
pressure was 998 mb at 0000 UTC). What
temperature will the air parcel have?
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Frontogenesis Shear Term (A)
Individual contribution to F
Because both terms have negative contributions, F
is positive and the front is created /
strengthened
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Frontogenesis Confluence Term (B)
Cold advection to the north
Warm advection to the south
Individual contribution to F
Because both terms have negative contributions, F
is positive and the front is created /
strengthened
Carlson, 1991 Mid-Latitude Weather Systems
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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)
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Frontogenesis Tilting Term (C)
Adiabatic cooling to north and warming to south
increases horizontal thermal gradient
Individual contribution to F


Because both terms have positive contributions, F
is positive and the front is created /
strengthened
Carlson, 1991 Mid-Latitude Weather Systems
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Frontogenesis Diabatic Heating/Cooling Term (D)
frontogenesis
small d?/dt
large d?/dt
F is positive (two negatives become positive)
frontolysis
large d?/dt
small d?/dt

F is negative
Carlson, 1991 Mid-Latitude Weather Systems
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Thunderstorms Airmass and Squall Line
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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

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Types of thunderstorms

• Four primary types of organization
• Airmass
• Squall line
• Multi-cell
• Supercell
• Focus today Airmass and squall line

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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

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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

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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

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Parts of airmass thunderstorm
Anvil part of the cloud
Tropopause
Main cell updraft
LCL (point where condensation occurs)
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Airmass Thunderstorm stages of development
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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

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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.

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Airmass Thunderstorm stages of development

• 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

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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
  straight-line winds
• Can produce hail and/or tornadoes, too
• Called squall because of the abrupt wind
  changes

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Squall line thunderstorms
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Squall line thunderstorms
L
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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
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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

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Structure of a squall line
Looking THROUGH the line i.e., the line is
coming out of / going into the page
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Squall line gust front
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Also called a bow echo
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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

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Squall line photos
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More photos of a squall line
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More photos of a squall line
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Dangers from air mass thunderstorms microbursts

• Not easily detected because
• the ambient thunderstorm (or even cumuliform
  cloud) is usually considered benign
• The scale is typically very small (perhaps 1 or 2
  km across)

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• Two primary types of microbursts
• Dry microburst. Occurs when surface layer is
  very dry (low relative humidity). Rain
  evaporates and accelerates downward through the
  warm, dry surface layer
• 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-coolin
  g as it mixes with rainwater
• Both types of microbursts are associated with
  evaporating rainwater

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• Danger comes from two sources
• Rush of cool, stable air out from the microburst
  center once it reaches the surface
• Turbulence associated with the rotor cloud
  the leading edge of the microburst

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Photos of microbursts
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More photos of microbursts
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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)

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The threat from a squall line derecho

• Definition of a derecho
• A widespread convectively induced straight-line
  windstorm. (AMS Glossary of Meteorology)
• Conditions for a calling an event a derecho
• 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).
• 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).
• 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.
• No more than 3 h can elapse between successive
  wind damage (gust) events.

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Trajectories and annual frequency of derechos in
the US
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A typical derecho event 19 July 1983.
Map shows location and time of derecho line max
wind gusts are given in miles per hour
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Photo of the incoming derecho, 19 July 1983
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Another photo of the incoming derecho, 19 July
1983
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A particularly damaging derecho event 30-31 May
1998
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Storm reports from derecho event
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The event did not start out as a derecho . . .
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Radar sequence images of 30-31 May 1998 derecho
event
Clip animated radar display
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Final example of a strong derecho27 May 2001
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Visible satellite image of the thunderstorm
complex that produced the derecho
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Photos from 27 May 2001
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1 Death
4 Injuries
160,000 without power
Over 300 million damage
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27 May 2001 derecho event
Photo taken here at 723 pm CDT

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Finally, derechos are not only found in the US