aoss 401, fall 2006 lecture 9 september 26, 2007 richard b. rood (room 2525, srb) [email protected]...
TRANSCRIPT
![Page 1: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/1.jpg)
AOSS 401, Fall 2006Lecture 9
September 26, 2007
Richard B. Rood (Room 2525, SRB)[email protected]
734-647-3530Derek Posselt (Room 2517D, SRB)
![Page 2: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/2.jpg)
Class News
• Contract with class.– First exam October 10.
• Will make it completely through Chapter 3.
![Page 3: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/3.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 4: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/4.jpg)
Outline
• Thermal Wind
• Equations of motion in pressure coordinates
• Maps
![Page 5: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/5.jpg)
Full equations of motion
1 and
)1
(
)()cos(21v
)v()sin(21v)tan(v
)()cos(2)sin(v21)vtan(
222
22
2
RTp
JDt
Dp
Dt
DTc
Dt
D
wΩugz
p
a
u
Dt
Dw
Ωuy
p
a
w
a
u
Dt
D
uΩwΩx
p
a
uw
a
u
Dt
Du
v
u Tangential coordinate system.z, height, as a vertical coordinate.zonal, meridional, vertical
![Page 6: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/6.jpg)
• What are the three major balances we have discussed?– What are the assumptions of those balances?
![Page 7: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/7.jpg)
The geostrophic balance
y
pfu
z
x
pfv
z
1
1
Take a vertical derivative of the equation.
![Page 8: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/8.jpg)
The geostrophic balance
y
T
fT
g
z
u
x
T
fT
g
z
v
z
T
T
u
y
T
fT
g
z
u
z
T
T
v
x
T
fT
g
z
v
Use equation of state to eliminate density.
Thermal wind relationship in height (z) coordinates
![Page 9: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/9.jpg)
moving fluid
Shear? (3)
• Shear is a word used to describe that velocity varies in space.
more slowly moving fluid
wind.zonal ofshear verticalz
u
z
![Page 10: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/10.jpg)
The geostrophic balance
y
T
fT
g
z
u
y
T
fT
g
z
u
What does this equation tell us?
Zonal wind a a level is a function of average meridional temperature BELOW.
Thermal wind relationship in height (z) coordinates
![Page 11: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/11.jpg)
An estimate of the July mean zonal wind
northsummer
southwinter
note the jet streams
![Page 12: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/12.jpg)
Now we return to our march to pressure coordinates.
![Page 13: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/13.jpg)
Pressure altitude
Under virtually all conditions pressure (and density) decreases with height. ∂p/∂z < 0. That’s why it is a good vertical coordinate. If ∂p/∂z = 0, then utility as a vertical coordinate falls apart. What does this look like?
![Page 14: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/14.jpg)
Use pressure as a vertical coordinate?
• What do we need.– Pressure gradient force in pressure
coordinates.– Way to express derivatives in pressure
coordinates.– Way to express vertical velocity in pressure
coordinates.
![Page 15: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/15.jpg)
Expressing pressure gradient force
![Page 16: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/16.jpg)
Integrate in altitude
gz
p
z
z
gdzzp
gdzzpp
)(
)()(
Pressure at height z is force (weight) of air above height z.
![Page 17: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/17.jpg)
Concept of geopotential
kF g
gdz
d
Define a variable such that the gradient of is equal to g. This is called a potential function.
We have assumed here that is a function of only z.
![Page 18: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/18.jpg)
Integrating with height
gdz
d
z
z
gdzz
gdzz
gdzd
0
0
)(
0)0(
)0()(
![Page 19: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/19.jpg)
What is geopotential?
• Potential energy that a parcel would have if it was lifted from surface to the height z.
• It is analogous to the height of a pressure surface.– We seek to have an analogue for pressure on
a height surface, which will be height on a pressure surface.
![Page 20: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/20.jpg)
xx
zg
x
p
x
zg
x
p
1
1
Implicit that this is on a constant z surface
Implicit that this is on a constant p surface
![Page 21: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/21.jpg)
Horizontal pressure gradient force in pressure coordinate is the gradient of geopotential
pz
pz
yy
p
xx
p
1
1
![Page 22: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/22.jpg)
Our horizontal momentum equation(rotating coordinate system)
p
pp
pp
fDt
D
fuyDt
D
fxDt
Du
uku
)()v
(
v)()(
Assume no viscosity
Other assumptions in these equations?
![Page 23: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/23.jpg)
2.4) Homework question
• Below the transformation of some scalar Ψ from the vertical coordinate z to the vertical coordinate p, pressure, is expressed symbolically. Write expressions for the horizontal (x and y) derivatives of Ψ and the vertical derivative (z) of Ψ in the pressure coordinate system.
Ψ (x, y, z, t) = Ψ (x, y, p(x, y, z, t), t)
What happens if ∂p/∂z = 0?
![Page 24: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/24.jpg)
2.4) Answer
Ψ (x, y, z, t) = Ψ (x, y, p(x, y, z, t), t)
z
p
pz
y
p
pyy
x
p
pxx
pz
pz
If ∂p/∂z=0 then the transform cannot be made, because p does not depend on z. It is not a monotonic function.
![Page 25: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/25.jpg)
What do we do with the material derivative?
Tt
T
Dt
DT
z
Tw
y
Tv
x
Tu
t
T
Dt
DT
Dt
Dz
z
T
Dt
Dy
y
T
Dt
Dx
x
T
t
T
Dt
DT
U
By definition: wDt
Dzv
Dt
Dyu
Dt
Dx ,,
Implicit that horizontal and time derivatives at constant z
![Page 26: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/26.jpg)
What do we do with the material derivative?
Dt
Dp
p
T
Dt
Dy
y
T
Dt
Dx
x
T
t
T
Dt
DT
Dt
Dpv
Dt
Dyu
Dt
Dx,,By definition:
Implicit that horizontal and time derivatives at constant p
p
T
y
Tv
x
Tu
t
T
Dt
DT
![Page 27: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/27.jpg)
Continuity equation
0)(
py
v
x
u
pyv
xu
t
Dt
D
p
u
u
Think about this derivation!
![Page 28: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/28.jpg)
Thermodynamic equation
Jp
T
y
Tv
x
Tu
t
Tc
Rcc
JDt
Dp
Dt
DTRc
JDt
Dp
Dt
DTc
p
vp
v
v
)(
)(
![Page 29: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/29.jpg)
Thermodynamic equation
pp
pp
p
c
J
pc
RT
p
T
y
Tv
x
Tu
t
T
c
J
cp
T
y
Tv
x
Tu
t
T
Jp
T
y
Tv
x
Tu
t
Tc
)(
)(
)(
Equation of state
![Page 30: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/30.jpg)
Thermodynamic equation
pp
pp
pp
c
JS
y
Tv
x
Tu
t
T
pc
RT
p
TS
c
J
pc
RT
p
T
y
Tv
x
Tu
t
T
)(
)(
Sp is the static stability parameter.What is static stability?
![Page 31: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/31.jpg)
Equations of motion in pressure coordinates(plus hydrostatic and equation of state)
pp
p
p
c
JS
y
Tv
x
Tu
t
T
py
v
x
u
fDt
D
0)(
uku
Tangential coordinate system.p, pressure, as a vertical coordinate.zonal, meridional, vertical
![Page 32: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/32.jpg)
Full equations of motion
1 and
)1
(
)()cos(21v
)v()sin(21v)tan(v
)()cos(2)sin(v21)vtan(
222
22
2
RTp
JDt
Dp
Dt
DTc
Dt
D
wΩugz
p
a
u
Dt
Dw
Ωuy
p
a
w
a
u
Dt
D
uΩwΩx
p
a
uw
a
u
Dt
Du
v
u Tangential coordinate system.z, height, as a vertical coordinate.zonal, meridional, vertical
![Page 33: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/33.jpg)
In the derivation
• Have used the conservation principle.
• Have relied heavily on the hydrostatic assumption.
• Require that the conservation principle holds in all coordinate systems.
• Plus we did some implicit scaling.
![Page 34: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/34.jpg)
Let’s move this to a chart
![Page 35: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/35.jpg)
Geopotential, Φ, in upper troposphere
eastwest
Φ0+ΔΦ
Φ0+3ΔΦ
Φ0
Φ0+2ΔΦ
ΔΦ > 0
south
north
![Page 36: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/36.jpg)
Geopotential, Φ, in upper troposphere
eastwest
Φ0+ΔΦ
Φ0+3ΔΦ
Φ0
Φ0+2ΔΦ
ΔΦ > 0
south
north
Δy
![Page 37: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/37.jpg)
Geopotential, Φ, in upper troposphere
eastwest
Φ0+ΔΦ
Φ0+3ΔΦ
Φ0
Φ0+2ΔΦ
ΔΦ > 0
south
north
Δy
δΦ = Φ0 – (Φ0+2ΔΦ)
![Page 38: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/38.jpg)
Geopotential, Φ, in upper troposphere
eastwest
Φ0+ΔΦ
Φ0+3ΔΦ
Φ0
Φ0+2ΔΦ
ΔΦ > 0
south
north
Δy
yy
2
![Page 39: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/39.jpg)
The horizontal momentum equation
p
pp
pp
fDt
D
fuydt
d
fxdt
du
uku
)()v
(
v)()(
Assume no viscosity
![Page 40: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/40.jpg)
Geostrophic approximation
gp
p
fuy
fx
)(
v)( g
![Page 41: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/41.jpg)
Geopotential, Φ, in upper troposphere
eastwest
Φ0+ΔΦ
Φ0+3ΔΦ
Φ0
Φ0+2ΔΦ
ΔΦ > 0
south
north
Δy
yfug
2
![Page 42: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/42.jpg)
Think a second
• This is the i (east-west, x) component of the geostrophic wind.
• We have estimated the derivatives based on finite differences.– Does this seem like a reverse engineering of the
methods we used to derive the equations?
• There is a consistency– The direction comes out correctly! (towards east)– The strength is proportional to the gradient.
![Page 43: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/43.jpg)
Geopotential, Φ, in upper troposphere
eastwest
Φ0+ΔΦ
Φ0+3ΔΦ
Φ0
Φ0+2ΔΦ
ΔΦ > 0
south
north
Δy
yfug
![Page 44: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/44.jpg)
Return toGeopotential, Φ, in upper troposphere
eastwest
Φ0+ΔΦ
Φ0+3ΔΦ
Φ0
Φ0+2ΔΦ
ΔΦ > 0
south
northDo not assume geostrophic.Are the winds parallel to the height contours?
![Page 45: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/45.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 46: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/46.jpg)
Return toGeopotential, Φ, in upper troposphere
eastwest
Φ0+3ΔΦ
Φ0
Φ0+2ΔΦ
ΔΦ > 0
south
northDo not assume geostrophic.A qualitative velocity contour. Not the same as geopotential, but usually close.
![Page 47: AOSS 401, Fall 2006 Lecture 9 September 26, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu](https://reader033.vdocument.in/reader033/viewer/2022052701/56649f285503460f94c40a8c/html5/thumbnails/47.jpg)
Next Time
• Natural Coordinates
• Balanced Flows