![Page 1: AOSS 401, Fall 2006 Lecture 19 October 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e4f5503460f94b45b88/html5/thumbnails/1.jpg)
AOSS 401, Fall 2006Lecture 19
October 26, 2007
Richard B. Rood (Room 2525, SRB)[email protected]
734-647-3530Derek Posselt (Room 2517D, SRB)
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Class NewsOctober 26, 2007
• Homework – Homework 5 posted today– Includes a programming assignment that will
be posted this afternoon/evening– Focus your attention on question 1
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Today
• Bring together physical concepts and preview the rest of the course
• Material from Chapter 6 – Middle Latitude Structure– Quasi-geostrophic theory
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Flow over a mountain rangeWest to East
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What is happening with planetary vorticity?(In the (east-west, north-south) plane)
Dep
th,
H
Dep
th,
H +ΔH
west easts
n Dep
th,
H -ΔH
Dep
th,
H +ΔH
f is greater for deflections to north
f is less for deflections to south
f + ζ is less than earth’s vorticity and wants to turn north.
Arrives here wanting vorticity. “Overshoots”
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Flow over a mountain rangeEast to West
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What is happening with planetary vorticity?(In the (east-west, north-south) plane)
Dep
th,
H
Dep
th,
H +ΔH
west easts
n Dep
th,
H -ΔH
Dep
th,
H +ΔH
Flow from east planetary and relative vorticity interact together, no overshoot or undershoot.
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Wind and geopotential 200 hPa
Note: Troughs associated with
mountain ranges, continents
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Observations of the Atmosphere
• Vorticity– Small scale flow– Large-scale flow
• Large scale flow and the climate system– Heat transport– Jet streams– Development of mid-latitude cyclones
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Vorticity on Small Scales
• From the southern California fires:
http://video.nbc11.com/player/?id=171454
• What is the cause?http://aoss-web.engin.umich.edu/class/aoss102/tools/swf/?url=class/aoss102/tools/swf/
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Vorticity on Large Scales
• Remember, vorticity is caused by– Wind shear– Rotation in the flow
• Can we identify these on weather maps?
• (The following maps come from http://www.aos.wisc.edu/weather/)
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300 mb Wind Speed
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Where is there positive vorticity?
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500 mb Vorticity
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Thermal Wind
• Remember, thermal wind relates– Vertical shear of geostrophic wind– Horizontal temperature gradients
• Can we identify these on weather maps?
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Where are the strongest ?T
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850 mb Temperature
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Convergence/Divergence
• Remember, vertical motion on large scales directly related to– Convergence/divergence of ageostrophic
wind– Curvature in the flow
• Can we identify these on weather maps?
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Where are surface lows/highs?
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Surface Precipitation
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850 mb Temperature
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Concepts
• Vorticity: shear and curvature– Why is curvature vorticity (as opposed to
shear vorticity) usually associated with developing low pressure systems?
• Divergence and convergence and location of surface high and low pressure systems
• Thermal wind—vertical shear of the horizontal wind and horizontal temperature gradients
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Concepts
• Features commonly found together– Jet stream– Upper level positive vorticity– Fronts– Midlatitude cyclones (low pressure systems)
• Coincidence?
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Large scale flow and the climate system
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Transfer of heat north and south is an important element of the climate at the Earth’s surface.
Redistribution by atmosphere, ocean, etc.
SURFACE
Top of Atmosphere / Edge of Space
ATMOSPHERECLOUD
heat is moved to poles
cool air moved towards equator cool air moved towards equator
This is a transfer. Both ocean and atmosphere are important!
Large scale weather systems transport large quantities of thermal energy from equator toward the poles
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Hurricanes and heat
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Hurricanes and heat
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Mid-latitude cyclones
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Mid-latitude cyclones & Heat
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Mid-latitude Cyclones & Jet Stream
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An estimate of the January mean temperature
northwinter
southsummer
tropopause
stratopause
mesosphere
stratosphere
troposphere
note where the
horizontal temperature gradients are
large
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An estimate of the January mean zonal wind
northwinter
southsummer
note the jet streams
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An estimate of the July mean zonal wind
northsummer
southwinter
note the jet streams
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Wind and geopotential 200 hPa
Note: Variability in east-west of the wind
field.
Note: Troughs associated with
mountain ranges, continents
Note: Time variability of the wind field.
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Waves in the atmosphere
• 300 mb Jet Stream Animation
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Short summary
• We have strong mean zonal winds.
• We have latitudinal and time variability of the zonal winds– Quasi-stationary long waves.
• On these quasi-stationary long waves, mid-latitude cyclones form and propagate.
![Page 37: AOSS 401, Fall 2006 Lecture 19 October 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e4f5503460f94b45b88/html5/thumbnails/37.jpg)
Mid-latitude cyclones
• What we know:– Low pressure systems– Form through spinup of low-level positive
vorticity– Divergence/convergence is key
• This is just the beginning…– Always closely associated with fronts—why?– Sometimes develop rapidly, sometimes not at
all—why?
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The mid-latitude cyclone
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Mid-latitude cyclones: Norwegian Cyclone Model
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Fronts and Precipitation
CloudSat Radar
Norwegian Cyclone Model
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Relationship between upper troposphere and surface
note tilt with height
![Page 42: AOSS 401, Fall 2006 Lecture 19 October 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e4f5503460f94b45b88/html5/thumbnails/42.jpg)
Idealized vertical cross section
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What’s at work here?
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Mid-latitude cyclone development
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Mid-latitude cyclones: Norwegian Cyclone Model
• http://www.srh.weather.gov/jetstream/synoptic/cyclone.htm
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Cold and warm advection
cold
warm
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Lifting and sinking
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Increasing the pressure gradient force
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Relationship between upper troposphere and surface
divergence over low enhances surface low
//increases vorticity
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Relationship between upper troposphere and surface
vertical stretching //
increases vorticity
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Modern education at its best.
• http://aoss.engin.umich.edu/class/aoss102/tools/swf/
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Analysis Tools
• We have used many of the concepts and tools that we have introduced and explored.– Observed characteristics of the atmosphere– Conservation principles– Scale analysis: Geostrophic and hydrostatic– Thermal wind– Divergence and convergence
• These ideas are integrated into quasi-geostrophic theory (analysis and prediction)
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Programming Exercise
• Gain experience writing programs to– Read data– Analyze data– Plot data
• Tools for research/analysis
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Remember the vertical structure of the atmosphere
zRT
pgp
RT
p
gz
p
Hydrostatic
Eq. of State
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If we assume T is constant with height (Isothermal)
zRT
g
p
p
zRT
pgp
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If we assume T varies with height (Realistic)
p
p
z
p
p
z
sfc
sfc
T
z
R
gp
T
z
R
g
p
p
zRT
g
p
p
0
0
ln
![Page 57: AOSS 401, Fall 2006 Lecture 19 October 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e4f5503460f94b45b88/html5/thumbnails/57.jpg)
If we assume T varies linearly with height (Not a bad assumption, in general)
sfc
sfc
sfc
p
p
z
sfc
sfc
sfc
T
zT
R
g
p
p
zT
z
R
g
p
p
zT
z
R
g
p
p
zTT
sfc
lnln
0 constant,
0
![Page 58: AOSS 401, Fall 2006 Lecture 19 October 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e4f5503460f94b45b88/html5/thumbnails/58.jpg)
If we assume T varies linearly with height (Not a bad assumption, in general)
Rg
sfcsfc
Rg
sfc
sfcsfc
sfc
sfc
sfc
T
Tpp
T
zTpp
T
zT
R
g
p
p
/
/
)(
)(
lnln
![Page 59: AOSS 401, Fall 2006 Lecture 19 October 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e4f5503460f94b45b88/html5/thumbnails/59.jpg)
Programming Exercise
• Read in data from two sounding files– Height– Potential temperature
• Compute pressure on each level– Isothermal atmosphere– Varying temperature– Constant lapse rate
• Use this information– Geostrophic wind– Temperature gradients
![Page 60: AOSS 401, Fall 2006 Lecture 19 October 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e4f5503460f94b45b88/html5/thumbnails/60.jpg)
Programming Exercise
• Goals: programming concepts– Reading data– Arrays– Loops– Iteration
• Materials posted to ctools this afternoon/evening– Skeleton MatLAB program– Data– Instructions
![Page 61: AOSS 401, Fall 2006 Lecture 19 October 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader035.vdocuments.site/reader035/viewer/2022062516/56649e4f5503460f94b45b88/html5/thumbnails/61.jpg)
Next Week
• Programming exercise in class Monday
• Start looking at quasi-geostrophic system– Scale analysis of equations in pressure
coordinates– Quantify wave movement and development