![Page 1: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/1.jpg)
AOSS 401, Fall 2006Lecture 18
October 24, 2007
Richard B. Rood (Room 2525, SRB)[email protected]
734-647-3530Derek Posselt (Room 2517D, SRB)
![Page 2: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/2.jpg)
Class News
• Final exam will be last day of class
• Derek and I decided to think about good homework problems for another day.– No homework posted today.
![Page 3: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/3.jpg)
Material from Chapter 4
• Vorticity, Vorticity, Vorticity
– Relative and planetary vorticity– Mid-latitude disturbances– Vorticity, divergence, in 3-D
![Page 4: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/4.jpg)
Weather
• National Weather Service– http://www.nws.noaa.gov/– Model forecasts:
http://www.hpc.ncep.noaa.gov/basicwx/day0-7loop.html
• Weather Underground– http://www.wunderground.com/cgi-bin/findweather/getForecast?
query=ann+arbor
– Model forecasts: http://www.wunderground.com/modelmaps/maps.asp?model=NAM&domain=US
![Page 5: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/5.jpg)
Two important definitions
• barotropic – density depends only on pressure. And by the ideal gas equation, surfaces of constant pressure, are surfaces of constant density, are surfaces of constant temperature.
• baroclinic – density depends on pressure and temperature.
![Page 6: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/6.jpg)
Absolute (or total) Vorticity
fy
u
x
veartha
vorticityabsolute
vorticityrelativevorticityplanetary vorticityabsolute
ukukUk
![Page 7: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/7.jpg)
Relative and planetary vorticity
• Planetary vorticity is cyclonic is positive vorticity
• Planetary vorticity, in middle latitudes, is usually larger than relative vorticity
![Page 8: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/8.jpg)
We derived the vorticity equation
x
p
yy
p
x
z
u
y
w
z
v
x
w
y
v
x
uf
y
fv
t
11
)(
))((u
TERMS
DIVERGENCE
TILTING
SOLENOIDAL or
BAROCLINIC
![Page 9: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/9.jpg)
Comments on the terms
• There are important dynamical features in the atmosphere where all of these terms are important.
• Baroclinic terms are due to there being gradients of temperature on pressure surfaces. (Are they explicitly there in pressure coordinates?) Like a thermodynamic “source” of rotation.
![Page 10: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/10.jpg)
Tilting Term
rotation in, say, (y, z)
plane, “vorticity” in x
plane
as the wheel is turned there is a
component of “vorticity” in the z
plane
![Page 11: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/11.jpg)
Divergence influence on vorticity
![Page 12: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/12.jpg)
Divergence influence on vorticity
![Page 13: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/13.jpg)
Scale factors for “large-scale” mid-latitude
s 10 /
m 10
m 10
! s cm 1
s m 10
5
4
6
1-
-1
UL
H
L
unitsW
U
1-1-11-
14-0
2
3-
sm10
10
10/
m kg 1
hPa 10
y
f
sf
P
![Page 14: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/14.jpg)
Assume balance among terms of 10-10s-2
)(
0)(
y
v
x
uf
y
fv
yv
xu
t
y
fv
y
v
x
uf
yv
xu
t
![Page 15: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/15.jpg)
A nuance on vorticity and the scaled equation: potential vorticity
![Page 16: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/16.jpg)
A simple version of potential vorticity
0)( H
f
Dt
Dhorizontal
Integrate with height,z1 z2 over a layer of depth H.
![Page 17: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/17.jpg)
A simple version of potential vorticity
vorticitypotentialH
f
This is the potential vorticity under the set of assumptions that we used to derive the equation. Constant density, constant temperature so only in a shallow layer might this be relevant to the atmosphere.
Potential vorticity is a measure of absolute vorticity relative to the depth of the vortex.
![Page 18: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/18.jpg)
Relative vorticity with change of depth
![Page 19: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/19.jpg)
Vorticity and depth
• We can see that there is a relationship between depth and vorticity.
• As the depth of the vortex changes, the relative vorticity has to change in order to conserve the potential vorticity.
• This is the play between relative and planetary vorticity.
![Page 20: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/20.jpg)
Scaled vorticity equation
))(()(
y
v
x
uf
Dt
fDhorizontal
![Page 21: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/21.jpg)
An observation
• The vorticity is dominated by the geostrophic component of the wind.
• The divergence requires the wind to be away from geostrophic balance.
• Generally vg/va >= 10
![Page 22: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/22.jpg)
Let’s explicitly map these ideas to the Earth
![Page 23: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/23.jpg)
Local vertical / planetary vorticity
![Page 24: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/24.jpg)
relative vorticity/planetary vorticity
relative vorticity
planetary vorticity
![Page 25: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/25.jpg)
Compare relative vorticity to planetary vorticity
NumberRossby Ro
10
10
10
0
1
0
140
15
Lf
U
f
sf
sL
U
planetary vorticity
is usually larger than
relative vorticity
for large-scale and
middle latitudes
![Page 26: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/26.jpg)
Relative and planetary vorticity
• Planetary vorticity is cyclonic is positive vorticity• Planetary vorticity, in middle latitudes, is usually
larger than relative vorticity• A growing cyclone “adds to” the planetary
vorticity.– Lows intense
• A growing anticyclone “opposes” the planetary vorticity.– Highs less intense
![Page 27: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/27.jpg)
Compare relative vorticity to planetary vorticity and
to divergence
100
10
10
0
0
yv
xuf
yv
xu
f
Flow is rotationally dominated, but divergence is crucial to understanding
flow.
![Page 28: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/28.jpg)
Consider our simple form of potential vorticity
vorticitypotential
0)(
H
fH
f
Dt
Dhorizontal
From scaled equation, with assumption of constant density and temperature.
![Page 29: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/29.jpg)
Fluid of changing depth
![Page 30: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/30.jpg)
Two things that we have learned about vorticity.
• Convergence and divergence in a column of fluid, impacts the vorticity throughout the column.– Specifically, divergence above causes low
pressure at the surface.
• Stretching and shrinking of a column of vorticity will change the relative vorticity.
![Page 31: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/31.jpg)
Possible development of a surface low.
Earth’s surface
pressure surfaces
![Page 32: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/32.jpg)
Lets return to our simple problem
Earth’s surface
pressure surfaces
warming
cooling
![Page 33: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/33.jpg)
Lets return to our simple problem
Earth’s surface
pressure / height
surfacesrisewarming
cooling
pressure / height
surfacessink
![Page 34: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/34.jpg)
Lets return to our simple problem
Earth’s surface
warming
cooling
PGF H
L
![Page 35: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/35.jpg)
Lets return to our simple problem
Earth’s surface
warming
cooling
PGF H
L mass leaves
column / low forms at groundL
![Page 36: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/36.jpg)
Lets return to our simple problem
Earth’s surface
warming
cooling
PGF H
L mass leaves
column / low forms at groundL
mass enters column / high
forms at ground
H
![Page 37: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/37.jpg)
Lets return to our simple problem
Earth’s surface
warming
cooling
PGF H
L mass leaves
column / low forms at groundL
mass enters column / high
forms at ground
H PGF
![Page 38: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/38.jpg)
Mass continuity?
• What are the implications of mass continuity?
• What is your law, your equation, your tool to answer that question?
![Page 39: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/39.jpg)
Temperature
• Assuming the air moves isentropically, what happens to the temperature?
• What is your law, your equation, your tool to answer that question?
![Page 40: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/40.jpg)
Lets return to our simple problem
Earth’s surface
warming
cooling
PGF H
L
LH PGF
![Page 41: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/41.jpg)
Simple Thermal Circulation
• There is the sense of the air moves to counter the heating.
• If the heating ended, then the circulation would end, acting to bring back the original equilibrium situation.
• This sort of low is cause by heating, is called a “thermal” low, warm core. It tends to damp out.
![Page 42: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/42.jpg)
Lets return to our simple problem
Earth’s surface
warmcore
coldcore
PGFHL
LH PGF
![Page 43: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/43.jpg)
Simple Thermal Circulation
• This sort of low is cause by heating, is called a “thermal” low, warm core. It tends to damp out.– Remember the question about the hurricane
being warm core.
• What about the divergence and convergence?
![Page 44: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/44.jpg)
Lets return to our simple problem
Earth’s surface
warmcore
coldcore
PGF HL
LH PGF
DIVERGENCE
CONVERGENCE
CONVERGENCE
DIVERGENCE
![Page 45: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/45.jpg)
Simple Thermal Circulation
• What about the divergence and convergence?– Convergence and Divergence are aligning
over top of each other in the vertical.– Again, in this case there is a tendency for the
circulation to damp out.
![Page 46: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/46.jpg)
Back to the earth again
![Page 47: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/47.jpg)
Still in the atmosphere
![Page 48: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/48.jpg)
Flow over a hill
HILL
![Page 49: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/49.jpg)
Derived a simple form of potential vorticity
vorticitypotential
0)(
H
fH
f
Dt
Dhorizontal
From scaled equation, with assumption of constant density and temperature.
![Page 50: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/50.jpg)
Flow over a hill(long in the north-south)(can’t go around the hill)
west east
![Page 51: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/51.jpg)
Flow over a hill
HILL
west east
Dep
th,
H
![Page 52: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/52.jpg)
Flow over a hill(assume flow is adiabatic)
HILL
west east
Dep
th,
H
θ
θ + Δθ
![Page 53: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/53.jpg)
Flow over a hill(far upstream constant zonal flow)
HILL
west east
Dep
th,
H
θ
θ + Δθ
ζ=0
![Page 54: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/54.jpg)
Derived a simple form of potential vorticity
vorticitypotential
0)(
H
fH
f
Dt
Dhorizontal
From scaled equation, with assumption of constant density and temperature.
![Page 55: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/55.jpg)
What happens as air gets to hill?
HILL
west east
Dep
th,
H
θ
θ + Δθ
ζ=0
![Page 56: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/56.jpg)
What happens as air gets to hill?
HILL
west east
Dep
th,
H
θ
θ + Δθ
ζ=0
Air is lifted. Lifting higher at ground than upper air.(pressure gradient force spreads it out)
![Page 57: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/57.jpg)
What happens as air gets to hill?
HILL
west east
Dep
th,
H +ΔH
θ
θ + Δθ
ζ=0
Air is lifted. Lifting higher at ground than upper air.(pressure gradient force spreads it out)
![Page 58: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/58.jpg)
What happens as air gets to hill?
HILL
west east
Dep
th,
H +ΔH
θ
θ + Δθ
ζ must increase
Air is lifted. Lifting higher at ground than upper air.(pressure gradient force spreads it out)
![Page 59: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/59.jpg)
How does vorticity increase?
![Page 60: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/60.jpg)
What happens in these waves?
Gains cyclonic vorticity
Loses cyclonic vorticitySame as gains
anticyclonic vorticity
![Page 61: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/61.jpg)
Or schematically
Cyclonic Anticyclonic
Rotational
Shear
![Page 62: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/62.jpg)
What happens as air gets to hill?
HILL
west east
Dep
th,
H +ΔH
θ
θ + Δθ
ζ must increase
Air turns cyclonically to increase vorticity.In northern hemisphere turns north.
![Page 63: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/63.jpg)
In the (east-west, north-south) planeD
epth
, H
Dep
th,
H +ΔH
west easts
n
![Page 64: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/64.jpg)
What happens as air goes over hill?
HILL
west east
Dep
th,
H -ΔH
θ
θ + Δθ
Air turns anti-cyclonically to decrease vorticity.In northern hemisphere turns south.
ζ must decrease
![Page 65: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/65.jpg)
In the (east-west, north-south) planeD
epth
, H
Dep
th,
H +ΔH
west easts
n Dep
th,
H -ΔH
![Page 66: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/66.jpg)
What happens as air goes down hill?
HILL
west eastD
epth
, H
+ΔH
θ
θ + Δθ
Air turns cyclonically to increase vorticity.In northern hemisphere turns north.
ζ must increase
![Page 67: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/67.jpg)
In the (east-west, north-south) planeD
epth
, H
Dep
th,
H +ΔH
west easts
n Dep
th,
H -ΔH
Dep
th,
H +ΔH
![Page 68: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/68.jpg)
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
![Page 69: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/69.jpg)
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 + ζ is less than earth’s vorticity and wants to turn north.
Arrives here wanting vorticity. “Overshoots”
![Page 70: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/70.jpg)
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
![Page 71: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/71.jpg)
What happens if wind is from east?
HILL
west east
θ
θ + Δθ
![Page 72: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/72.jpg)
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.
![Page 73: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/73.jpg)
Excursion into the atmosphere
![Page 74: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/74.jpg)
Middle latitude cyclones
![Page 75: AOSS 401, Fall 2006 Lecture 18 October 24 , 2007](https://reader035.vdocuments.site/reader035/viewer/2022081603/56813e47550346895da830a7/html5/thumbnails/75.jpg)
Weather
• National Weather Service– http://www.nws.noaa.gov/– Model forecasts:
http://www.hpc.ncep.noaa.gov/basicwx/day0-7loop.html
• Weather Underground– http://www.wunderground.com/cgi-bin/findweather/getForecast?
query=ann+arbor
– Model forecasts: http://www.wunderground.com/modelmaps/maps.asp?model=NAM&domain=US