Transcript Corporate Profile - University of Oklahoma

METR 2413
31 March 2004
Dynamics II:
Thermal wind and
thermal advection
Review
Hydrostatic balance dp    g
dz
Ideal gas law p = ρ RdTv, ρ = p / RdTv

p2
p1
z2
1
p2
g
dp  ln( )   
dz
z1
p
p1
Rd Tv
Take layer average virtual temperature T , R and g as
v
constants and integrate LHS
p2
g
ln( )  
( z2  z1 )
p1
Rd Tv
Thickness
So the height difference, z2-z1, between two pressure levels is
Rd Tv
Rd Tv
p2
p1
z2  z1  
ln( ) 
ln( )
g
p1
g
p2
where Tv is the average virtual temperature over this layer.
This is called the hypsometric equation for the thickness, z2-z1,
between two pressure levels, p1 and p2
Larger thickness means higher mean temperature in the layer.
Thickness
Example: Thickness of the 1000 hPa to 900 hPa layer
T1000  300K , T900  290K , T  295K
1000
287
)  911m
295ln(
z 
900
9.8
T1000  270K , T900  260K , T  265K
1000
287
)  815m
265ln(
z 
900
9.8
Thickness
Most common thickness values are:
1000 – 500 hPa, 1000 – 850 hPa, 1000 – 700 hPa
1000 – 500 hPa thickness used to define “bulk” airmass average
temperature
1000 – 850 hPa thickness used primarily for snow probability
and maximum daytime temperature forecasting
For 1000-500 mb thickness, the 540 dam line (5400 m) is often
used as the separator between rain and snow for low terrain
- When there is precip in a region of thickness < 540 dam, it is
generally snow
- If thickness > 540 dam, it is usually rain
- Contour intervals are typically 60 m (6 dam)
Review
Geostrophic wind, pressure gradient force balanced by
Coriolis force:

1 p
 f cv  0
 x
1 p
g z
ug  

f c y
f c y
1 p g z
vg 

f c x f c x
Coriolisparameter,f c  2 sin 
Thermal wind
In the presence of a horizontal temperature gradient,
the tilt of pressure surfaces increases with height.
p=p2
ug
Δz
p=p1
North
cold
warm
Thermal wind
Horizontal temperature gradient
Increasing tilt of pressure surfaces with height
Increasing pressure gradient force on constant height
surfaces with altitude
Increasing geostrophic wind with height
Vector difference between geostrophic wind at two levels is
called the thermal wind.
Thermal wind
Thermal wind relationship:
The vertical gradient of the geostrophic wind is proportional
to the horizontal temperature gradient
u g
g Tv

,
z
f cTv y
v g
g Tv

z f cTv x
t hickness, z  z 2  z1
g (z )
uth  u g 2  u g1  
f c y
g (z )
vth  v g 2  v g1 
f c x
Thermal advection
“Advection” – generic term for horizontal transport of some
atmospheric property;
- typically used in terms of heat transport, but also for moisture
To have thermal advection:
• must have horizontal motion (stronger winds increase thermal
advection; little advection under calm conditions)
• must have horizontal temperature gradient over a large region
• winds must blow across the zone of strongest horizontal
temperature gradient (no advection if wind blows parallel to
temperature contours)
Thermal advection
Warm air
advection is
occurring in
Indiana,
cold air
advection is
occurring
over South
Dakota and
Nebraska
Thermal advection
Warm air advection (WAA) – movement of warmer air toward a
fixed point on a horizontal plane; warm air replaces cold air;
• Low level WAA is common behind warm fronts and ahead of
cold fronts
• Low level WAA can contribute to rising air
Cold air advection (CAA) – movement of colder air toward a
fixed point on a horizontal plane; cold air replaces warm air
• Low level CAA is common behind cold fronts
• Contributes to sinking air
Caution: other lifting and sinking mechanisms can complicate
rising or sinking due to advection
Thermal advection
Thickness charts often used to infer advection
• thickness used as proxy for temperature
• geostrophic wind used as proxy for average air motion
Thermal advection
Thermal wind and thermal advection:
Thermal wind – the vector difference between geostrophic flow
at 2 different heights (not a real wind!)
Thermal wind can be inferred from the thickness field:
- thermal wind “blows” parallel to the thickness contours, with
cold thickness to the left in the Northern Hemisphere
Thermal wind rule (in the Northern Hemisphere):
• if the geostrophic wind backs (turns counterclockwise with
height), cold advection is indicated
• if the geostrophic wind veers (turns clockwise with height),
warm advection is indicated
Thermal advection
Thermal advection
Can use temperatures at 700 mb as an alternative to thickness:
• temperature at 700 mb close to 1000 – 500 mb thickness
• 700 mb wind approximates the movement of the 1000 – 500 mb
thickness
We can use the geostrophic wind and isotherms at 700 mb to
estimate mean lower tropospheric thermal advection:
• 700 mb thermal advection resembles mean thickness advection
below 500 mb
• spacing of height lines at 700 mb is a measure of wind speed
• wind direction is parallel to height lines
Strength of warm or cold air advection is proportional to the area
formed by the intersection of the isotherms and the height
contours
Thermal advection
Three factors make thermal advection larger:
• a strong wind
• a large temperature gradient
• a small angle between actual wind direction and
temperature gradient (i.e. to maximize heat advection, wind
should blow at right angles to isotherms)
Very little thermal advection occurs at low latitudes since
temperature gradients tend to be very weak.
Summary
• Thickness between two pressure levels is proportional to the
layer mean temperature
• Thermal wind – the vector difference between geostrophic
wind at 2 different heights, is proportional to the horizontal
temperature gradient
• Thermal advection occurs for horizontal wind blowing across
temperature contours
• If the geostrophic wind backs (veers) with height,
cold (warm) advection is indicated