Transcript The Thermal Wind: Forecasting Problems and the Analysis of Fronts

Atms 4320 / 7320 – Lab 7
The Thermal Wind:
Forecasting Problems and
the Analysis of Fronts
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
Thermal wind: Bluestein p 181 - 187, and
Holton p 68 - 71.
The “thermal” wind: The thermal wind links
the temperature field to the wind field via
hydrostatic balance.
dp p

  g
dz z
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
We know that in a geostrophically balanced
world we can link the wind field with the mass
field (pressure or height).

kˆ
kˆ
Vg 
  h p   ,   gz
f
f
Thus, in order to talk about thermal wind
balance we must specify two balance conditions
to exist simultaneously. Thus, thermal wind
balance is considered a “higher order” balance
state.
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
The Thermal wind is simply the vertical
wind shear vector:
VT = Vgeo (upper level) - Vgeo (lower
level)
Thus if we substitute in for Vgeo we get:



kˆ
kˆ
VT  Vgu  Vgl    h  u     l
f
f
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
Carrying out the subtraction,

 Vg kˆ
kˆ

VT 
   p  u   l     p
p
f
f
p
put into differential form,

 Vg kˆ

VT 
 p
p
f
p
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
Then using the equation of state:

VT 

Vg
Rkˆ
    pT
p
fp
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
In component form:
u g
1  
R T
uT 


p
f y p
fp y
v g 1   R T
vT 


p f x p fp x
 where 

 thickness
p
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
Note that the thermal wind is simply a
measure of the vertical wind shear.
Vertical wind shear: Baroclinicity


V V

p z
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
Recall that in a barotropic atmosphere,
there is no vertical wind shear. The
definition of a baroclinic atmosphere is that
there is speed and or directional shear in
the vertical.
Thus we can regard the strength of
Thermal Wind as a measure of
baroclinicity.
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
The thermal wind “blows” parallel to the
isotherms, or the thickness lines with
warm air on the right and cold air on the
left. Thus, the thermal wind “blows”
perpendicular to both gradient quantities.


VT || T ,   VT  T , ()
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
The map (Thanks OU)
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
Thus, the thickness lines can also be used
to deduce areas of warm and cold air
advections, and locate fronts in the
atmosphere.
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
Another view (Dr. Brad Muller)
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
Cold advection (winds back with height):
In the Northern Hemisphere, cold
advection will be associated with thermal
wind with a southerly component.
Geostrophic Wind Shear and Thermal
Advection
Case 2: Geostrophic wind backs
(i.e., turns counterclockwise)
with height.
cold
 

Vg
1
Lower level wind is from N.
Upper level wind is from NW.
Since colder air must lie to the left of
the thermal wind, the layer average
wind blows from cold to warm, which
implies cold advection.
 

Vg
warm

VT
2
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
Warm advection (winds veer with height).
(thanks to Dr. Broccoli, Rutgers)
In the northern hemisphere, warm air
advection will tend to be associated with a
thermal wind with a westerly component.
Geostrophic Wind Shear and Thermal
Advection
Case 1: Geostrophic wind
veers (i.e., turns
clockwise) with height.
 

Vg
1
Lower level wind is from SW.
Upper level wind is from W.
Since colder air must lie to the left of
the thermal wind, the layer average
wind blows from warm to cold, which
implies warm advection.
cold

VT
 

Vg
warm
2
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
Areas of low pressure will tend propagate
along with the thermal wind where it is
strong (along packed thickness or height
contours), and at the speed of the thermal
wind.
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
Also, we can deduce fronts from the
thickness field. The warm front is located
on the equatorward edge of a zonal
thickness gradient as we move poleward
(or perpendicular to the thermal wind
moving over it from right to left):
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
The cold front is located on the
downstream edge of a meridional
thickness gradient as we move from west
to east (zonally) (or perpendicular to the
thermal wind moving over it from right to
left)
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
In the Southern Hemisphere, the thermal
wind blows with warm air to the left and
cold air to the right. Why?

VT 

Vg
Rkˆ
    pT
p
fp
Coriolis Force is negative! We must “flip”
all the arguments made above.
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
Example (SH):
A backing wind represents represents
Warm air advection
A veering wind represents cold air
advection
The Thermal Wind: Forecasting Problems
and the Analysis of Fronts
The End!