ATM S 542 Synoptic Meteorology
Overview
Gregory J. Hakim
University of Washington, Seattle, USA
www.atmos.washington.edu/~hakim
• Vertical structure of the atmosphere.
• Atmospheric phenomena by horizontal scale.
• Potential vorticity.
• Tropopause.
Overview
Asymptotic methods
• expand dependent variables in a power series.
• small parameters needed.
• co-operative dialog between math & physics is helpful.
Role of asymptotics in atmosphere/ocean dynamics.
• simplified equations for solution & understanding.
Goals
• survey atmosphere/ocean structure & phenomena.
• bias toward extratropics & atmosphere.
• motivate asymptotic methods for these problems.
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Jets, stirring, organized structures; waves, vortices, convection.
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Atmospheric Structure
•Atmosphere: very thin gas layer.
• depth <<< radius earth.
•Troposphere: “weather layer”
• ~ 10 km deep.
• ~ 80% mass of atmosphere.
• ~ all H2O vapor.
• Tropopause: jet streams.
• wave guide.
• unstable: cyclones.
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Atmospheric Energy Spectrum
Energy increases with
horizontal length scale.
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Atmospheric Phenomena by Scale
Planetary waves
Cyclones
Gravity waves
Convection
L ~ 10 000 km
H/L ~ .001
Ro ~ 0.01
L ~ 1000 km
H/L ~ .01
Ro ~ 0.1
L ~ 10--100 km
H/L ~ .1-1
Ro ~ 1
L ~ 10 km
H/L ~ 1
Ro > 1
Long, slow
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Short, fast
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Jet streams & planetary waves
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Jet Streams
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Jets: ~ Geostrophic Balance
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Jet stream vorticity
Waves & particles
Waves:
Information flows
through the medium by
radiation.
Particles (vortices):
Information flows
through the medium by
material transport.
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Cyclones & Anticyclones
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Cyclone Structure
• Center has lowest pressure.
• ~geostrophic winds.
• Warm air moves poleward.
• and upward.
• warm front.
• Cold air moves equatorward.
• and downward.
• cold front.
• Clouds & precipitation.
•~ “comma” shape.
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North American Cyclone
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Pacific
Extratropical
Cyclone
•Intense vortex
•Cold air: shallow cellular
convection
•Warm air: stratiform cloud
•Sharp frontal boundaries
Zoom in on cold front…
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Scale collapse at cold front: “rope cloud”---narrow line convection.
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Cyclone—Anticyclone Track Density
Hoskins & Hodges (2002)
Primary tracks coincide with time-mean jet stream locations.
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Jet-Level 2.5—6 d Variance
Maximum variance
in storm tracks.
Hoskins & Hodges (2002)
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Baroclinic Waves & Packets
Cyclones & anticyclones often compose
waves within larger wave packets.
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Baroclinic
Waves
Wavelength ~4000 km
Phase speed ~ 15 m/s.
Period ~ 3 d.
Due to baroclinic instability.
Organize into packets.
Lim & Wallace (1991)
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Wave Packet Phase & Group Speed
phase speed
group speed
Chang & Yu (1999)
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Wave Packet Tracks
Jet-stream wave guides.
Storm-track recycling.
Hakim (2003)
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Mesoscale Phenomena
& Smaller Scales
Fronts & frontal waves.
Gravity waves.
Convection.
Shear instabilities.
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Frontal Waves
Paldor et al. (1994)
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Wakimoto & Bosart (2000)
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Tropopause Shear Line Instability
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Tropopause Shear Line Instability
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Tropopause Shear Line Instability
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Tropopause Shear Line Instability
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Moist Convection
tropopause
Strong vertical
mixing
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Kelvin—Helmholtz Instability
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Gravity Waves
Wavelength ~10 km
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Gravity Waves
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How do we better understand
cyclones & anticyclones?
Need to filter other disturbances from the equations…
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Ertel Potential Vorticity
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Vertical Profile of PV
Tropopause
• Well-defined as PV jump.
• Dynamics focus here.
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Tropopause
Topography
(pressure)
• High pressure over poles.
• Low pressure over tropics.
• Strong gradient in mid-latitudes.
• Stronger gradient in winter.
source: Hoinka (1998)
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Height-Latitude Tropopause Profile
Hoinka (1998)
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