Climatology Lectures 6 7

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Climatology Lectures 6 7
General Circulation Midlatitudes Richard
Washington
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Recap..

• Pressure gradient between subtropics and poles
• westerly wind
• Rossby waves develop in the westerlies
• vorticity used to understand why the waves
  develop (absolute and potential vorticity)
• Gradient wind equation (see Lect 5) causes air
  flow through wave to either speed up or slow down
• Upper air divergence leads to uplift and surface
  low
• Upper air convergence leads to subsidence and
  surface high
• Surface lows mix heat across the latitudes the
  prime means by which the general circulation does
  its work in the mid latitudes

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Outline

• Some background Air pressure, temperature and
  thickness what drives the large scale flow
• Westerlies major wind system of the midlatitudes
• Waves in the Westerlies
• What they do.
• Why they form
• potential and absolute vorticity
• Dynamical View of Midlatitude Weather Systems
  convergence, divergence and surface weather

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Outline

• Some background Air pressure, temperature and
  thickness what drives the large scale flow
• Westerlies major wind system of the midlatitudes
• Waves in the Westerlies
• What they do.
• Why they form
• potential and absolute vorticity
• Dynamical View of Midlatitude Weather Systems
  convergence, divergence and surface weather

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Radiation Budget across the latitudes
HOT
COLD
latitude
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Radiation Budget across the latitudes
What does this heating do to the atmosphere?
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Air columns
700 hPa
3100m

• Each slab contains the same mass
• The depth of each mass is not the same
• As density decreases the depth increases

800 hPa
1900m
900 hPa
900m
1000 hPa
0 m
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Cold Warm
2900m
1750m
800m
0 m
0 m
COLD
WARM
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900hPa isobaric surface

• Gradient at 900 hPa

Low
High
900 m
950 m
850 m
WARM
COLD
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800hPa isobaric surface

• Gradient at 800 hPa

High
1800 m
1900 m
2000 m
Low
WARM
COLD
No pressure gradient at the surface
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700hPa isobaric surface

• Gradient at 700 hPa

Low
High
2950 m
3100 m
3250 m
WARM
COLD
No pressure gradient at the surface
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700 hPa
HOT
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• How can we explain this?
• On a simple level we can say that a positive net
  radiation budget warms the air column and it
  expands (vertically) while a negative net
  radiation budget cools the air column which
  contracts (vertically)
• We can be more definitive about this by using the
  hydrostatic equation
• dp p g dzchange in pressure in a vertical
  slice
• density X gravity X height of the slice

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dP g ? dZ cold air, ? increases, dZ must
decrease warm air, ? decreases, dZ must increase
For given dp
700 hPa
HOT
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dP g ? dZ cold air, ? increases, dZ must
decrease warm air, ? decreases, dZ must increase
For given dp
dP 1000 700 300 hPa, 300 00 Pag
10dz 2900m in cold air 3250m in warm air
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dP g ? dZ cold air, ? increases, dZ must
decrease warm air, ? decreases, dZ must increase
For given dp
dP 1000 700 300 hPa, 300 00 Pag
10dz 2900m in cold air 3250m in warm air
p dP/gdz Cold air example 30000/102900
1.03 kg/m3 warm air example
30000/103250 0.92 kg/m3
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dP g ? dZ cold air, ? increases, dZ must
decrease warm air, ? decreases, dZ must increase
For given dp
700 hPa
HOT
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dP g ? dZ cold air, ? increases, dp must
increase warm air, ? decreases, dp must decrease
For given dz
2900m
700 hPa
800 hPa
HOT
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X Section latitude-height
Poles
Subtropics
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X Section latitude-height
Poles
Subtropics
Pressure Gradient Force Available Potential
Energy
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Outline

• Some background Air pressure, temperature and
  thickness what drives the large scale flow
• Westerlies major wind system of the midlatitudes
• Waves in the Westerlies
• What they do.
• Why they form
• potential and absolute vorticity
• Dynamical View of Midlatitude Weather Systems
  convergence, divergence and surface weather

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Poles
Subtropics
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So how does the a purely westerly wind help to
mix up energy differences between the poles and
the equator?
Plan View
Poles
Westerlies
Equator
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By converting potential energy to kinetic
energy..an inefficient process! Potential
energy height or pressure difference between the
subtropics and the midlatitudes Kinetic energy
the motion of the westerly wind
X-Section
Poles
Subtropics
Pressure Gradient Force
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Outline

• Some background Air pressure, temperature and
  thickness what drives the large scale flow
• Westerlies major wind system of the midlatitudes
• Waves in the Westerlies
• What they do.
• Why they form
• potential and absolute vorticity
• Dynamical View of Midlatitude Weather Systems
  convergence, divergence and surface weather

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Rossby Waves and the meandering jet stream plan
view

• Jet follows isotherms
• Strongest when gradient is greatest
• Associated with fronts
• Mixes energy (heat) across the lines of latitude

L A T I T U D E
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Rossby Waves and the meandering jet stream plan
view

• Heat transport advection

Cold air advection
Cold air advection
warm air advection
warm air advection
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Outline

• Some background Air pressure, temperature and
  thickness what drives the large scale flow
• Westerlies major wind system of the midlatitudes
• Waves in the Westerlies
• What they do.
• Why they form
• potential and absolute vorticity
• Dynamical View of Midlatitude Weather Systems
  convergence, divergence and surface weather

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Why do Rossby Waves form..

• What is vorticity?
• a measure of the intensity of a vortex
• related to the spin in 3 dimensions, only
  vertical is used
• twice the rate of angular rotation
• for cyclonic, - for anticyclonic (in the
  Northern Hemisphere)

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Defining relative vorticity

• Solid body rotation
• ?r 2V/r
• V/r positive

V
r
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Vorticity on weather maps

• Look for areas of
• cyclonic curvature ?

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Vorticity on weather maps

• Look for areas of
• cyclonic curvature ?

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Potential vorticity

• If the depth of a layer of wind changes, then the
  wind will start to meander sideways and waves
  will therefore form in the wind flow
• This characteristic is explained by the
  conservation of potential vorticity

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Potential vorticity

• c ?r /?d
• ?d is change in depth of flow
• ?r is relative vorticity (i.e. local spin)
• c is a constant
• Therefore conservation of potential vorticity
• Change in ?d must be balanced by changes in ?r
• If ?d decreases, then so must ?r
• If ?d increases, then so must ?r

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Mountain lee waves

• Assume air with no vorticity moving west to east
  towards a mountain range

Plan view
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?r /??d is constant

• Vortex shrinks, ?d reduced
• ?r becomes -ve, anticyclonic spin

Plan view
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?r /??d is constant

• Vortex starts to stretch, ?d increases
• ?r becomes ve, cyclonic spin

LOW
Plan view
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?r /??d is constant

• Back to original trajectory

LOW
Plan view
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Mountain lee waves

• Trough of low pressure in the lee of the mountain
  range

LOW
Plan view
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Potential Vorticity

• Mountains set up waves in westerlies (Rockies,
  Andes)
• Regions of strong thermal heating also set up
  waves (Amazon - S.Atlantic)
• Regions of strong thermal contrast cold land to
  warm sea

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Earths vorticity

• Spin is maximum at poles
• Spin is zero at equator
• Vorticity is twice spin
• Vorticity 2 ? at poles
• Vorticity 2 ? sin ? at latitude ?
• Earths vorticity Coriolis parameter
• f 2 ? sin ?

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Absolute vorticity

• Vorticity of air relative to the Earth, ?r
• Earths vorticity, f
• Absolute vorticity, ?a ?r f
• For horizontal motion absolute vorticity is
  conserved
• Increase (decrease) in ?r is balanced by decrease
  (increase) in f (change in latitude)

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Absolute vorticity

• Absolute vorticity, ?a ?r f
• where Vorticity of air relative to the Earth
  ?r and Earths vorticity f
• Absolute vorticity, ?a ?r f
• For horizontal motion absolute vorticity is
  conserved
• Increase (decrease) in ?r is balanced by decrease
  (increase) in f (i.e. change in latitude)

T-1
2
1
T1
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Absolute vorticity

• Increase (decrease) in ?r is balanced by decrease
  (increase) in f (i.e. change in latitude)
• Point 1 to2, f increases so ?r decreases ,
  curvature becomes anticyclonic

T-1
2
1
T1
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Absolute vorticity NH example

• Increase (decrease) in ?r is balanced by decrease
  (increase) in f (i.e. change in latitude)
• Point 1 to2, f increases so ?r decreases ,
  curvature becomes anticyclonic
• Flow is forced south in the anticyclonic flow
  although the anticyclonic flow is not completed
  as the arrow below shows because..

North
T-1
2
1
T1
South
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Absolute vorticity NH example

• Increase (decrease) in ?r is balanced by decrease
  (increase) in f (i.e. change in latitude)
• Point 1 to 2, f increases so ?r decreases ,
  curvature becomes anticyclonic
• Flow is forced south
• Point 2 to 3, f decreases so so ?r increases,
  curvature becomes cyclonic
• Flow is forced north

North
T-1
2
1
3
T1
South
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Absolute vorticity NH example

• Increase (decrease) in ?r is balanced by decrease
  (increase) in f (i.e. change in latitude)
• Point 1 to 2, f increases so ?r decreases ,
  curvature becomes anticyclonic
• Flow is forced south
• Point 2 to 3, f decreases so so ?r increases,
  curvature becomes cyclonic
• Flow is forced north
• Point 3 to 4, increases so ?r decreases ,
  curvature becomes anticyclonic
• Flow is forced southetc.

2
4
1
3
T1
South
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Outline

• Some background Air pressure, temperature and
  thickness what drives the large scale flow
• Westerlies major wind system of the midlatitudes
• Waves in the Westerlies
• What they do.
• Why they form
• potential and absolute vorticity
• Dynamical View of Midlatitude Weather Systems
  convergence, divergence and surface weather

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The Dynamical View of Midlatitude Weather Systems

• Life of a wave cyclone
• Birth
• Energy source Deepening
• Maturity
• Changing shape Energy of winds Movement
  Vertical motion
• Death
• End of movement Filling pressure Winds die out

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Birth energy source

• Strong temperature difference between polar and
  tropical air

LOW
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Airflow through the upper level wave
Cyclonic curvature gradient wind for cyclonic
flow Sub Geostrophic Wind slows down!
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Airflow through the upper level wave
LOW
Anticyclonic curvature gradient wind for
anticyclonic flow Super Geostrophic Wind
speeds up!
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Birth deepening

• Upper divergence and convergence develop in wave

LOW
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Birth deepening

• Upper divergence from weak wave produces reduced
  surface pressure

LOW
Increasing pressure
Reducing pressure
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Maturitychanging shape

• Surface trough and ridge grow due to convergence
  and divergence

LOW
LOW
Increasing pressure
Reducing pressure
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Maturity changing shape

• Upper trough deepens due to temperature advection

Low
LOW
Decreasing contour heights
Warm air advection
Cold air advection
LOW
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Maturity vertical motion

• Divergence and convergence produce upward and
  downward motion

LOW
Vortex stretching - increasing vorticity
LOW
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Maturity vertical motion

• Horizontal motion is larger than vertical and
  combines with it

LOW
Vorticity maximum
LOW
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Maturity energy of winds

• Wind speed increases Kinetic energy increase
  Potential energy decreases
• More cold air, less warm air at surface

LOW
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Maturity movement

• Upper trough moves with jet stream Deepening
  moves ahead of trough

LOW
Most rapid decrease
LOW
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Death end of movement

• Upper trough moves faster than surface system
  divergence now out of sync

LOW
LOW
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Death filling pressure

• Convergence aloft replaces divergence

LOW
Increasing pressure
LOW
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Long term mean zonal wind doesnt show the work
done by the midlatitude atmosphere
The main agents doing the energy transport in the
midlatitudes have life times of around 6 days
and tend to move from west to east. Their
presence is lost when the atmosphere is time
averaged.
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Breakdown of the annual and zonal mean northward
energy flux into the mean meridional circulation,
total eddy and transient eddy
Note equatorward transport for MMC in the
midlatitudes (Ferrel cell) Relative contribution
of transients to the total eddy transport
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Recap..

• Pressure gradient between subtropics and poles
• westerly wind
• Rossby waves develop in the westerlies
• vorticity used to understand why the waves
  develop (absolute and potential vorticity)

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Recap.

• Vorticity is a measure of spin
• Relative vorticity, ?r (relative to Earth)
• Absolute vorticity, ?a (air Earth) (?r f)
• conserved if no vertical motion
• Divergence, shrinking, reduced vorticity
• opposite for convergence
• Potential vorticity, ?r/?d
• also conserved

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Readings for todays lecture

• Barry and Chorley 1997 chapter 6 7
• Briggs et al. 1997 Fundamentals of the Physical
  Environment chp 9
• Henderson-Sellers and Robinson 1999 chp 7 9
• Linacre and Geerts 1997 Climates and Weather
  Explained p 258-264, 271-283
• Musk L F 1992 Weather Systems Chp 12.
• McIlveen 1992 chp 11

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Past Paper Questions..

• What factors determine the speed of the wind in
• a) the western sector of an upper air wave in the
  midlatitudes
• b) a tornado
• c) the trade winds (2003)
• What large-scale mechanisms are responsible for
  generating precipitation in the mid-latitudes?
  (2002)
• What causes Rossby waves and what is their role
  in weather and climate? (1999)
• Compare the geostrophic and gradient wind
  equations (1997)
• Explain the link between upper level and surface
  flow in the midlatitude (1997)
• Cold fronts cannot be understood
  two-dimensionally. Discuss (1996)