Fd

dt y

u

y x

v

y y

w

y z y

d

d t

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

To start today: let’s revisit Frontogenesis, both the equation and the physical interpretations

Scratch paper

uu 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

0u

y

0u

y

0u

y

y

x

0u

y

0u

y

Scratch paper

vv 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

0u

y

0v

y

0v

y

0v

y

0v

y

Scratch paper

θθ 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,

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).

0p

R

cpT

p

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?

0p

R

cpT

p

-1 -1

-1 -1

287 J kg K

1004 J kg K998 mb270.6 K

700 mb

299.5 K = 26.4 C

Frontogenesis: Shear Term (A)

uF

y x

- -Individual contribution to F

Because both terms have negative contributions, F is positive and the front is created / strengthened

Frontogenesis: Confluence Term (B)

Cold advection to the north

Warm advection to the south

Carlson, 1991 Mid-Latitude Weather Systems

vF

y y

- -Individual contribution to F

Because both terms have negative contributions, F is positive and the front is created / strengthened

Carlson (Mid-latitude Weather Systems, 1991)

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

Frontogenesis: Tilting Term (C)

Adiabatic cooling to north and warming to south increases horizontal thermal gradient

Carlson, 1991 Mid-Latitude Weather Systems

+Individual contribution to F

Because both terms have positive contributions, F is positive and the front is created / strengthened

wF

y z

+

Frontogenesis: Diabatic Heating/Cooling Term (D)

frontogenesis

frontolysis

small dθ/dt

Carlson, 1991 Mid-Latitude Weather Systems

large dθ/dt

dF

y dt

- -F is positive (two negatives become positive)

large dθ/dt small dθ/dt

dF

y dt

-F is negative

+

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. Airmass

2. Squall line

3. Multi-cell

4. 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

Main “cell” updraft

LCL (point where condensation

occurs)

Tropopause

Anvil part of the cloud

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 straight-

line winds– Can produce hail and/or tornadoes, too

• Called “squall” because of the abrupt wind changes

Squall line thunderstorms

Squall line thunderstorms

LL

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: derechoDefinition of a derecho:

“A widespread convectively induced straight-line 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 derecho27 May 2001

Visible satellite image of the thunderstorm complex that produced the derecho

Photos from 27 May 2001

1 Death4 Injuries

160,000 without powerOver $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