ATS/ESS 452: Synoptic Meteorology
Friday 09/26/2014
• Continue Review Material
• Geopotential
• Thickness
• Thermal Wind
Geopotential, Thickness, and the Thermal Wind
What is geopotential?
Work needed to lift a unit of mass from sea level to a given altitude…
Why do we use it?
The shape of the Earth’s surface is not a perfect sphere… a slight equatorial bulge
occurs due to the centrifugal force, which also disrupts from a perfect gravitational
force. It becomes convenient to define a slightly modified gravitational force
combining the true gravitational force with the effects of Earth’s rotation.
Surfaces of constant geopotential are exactly aligned with the Earth’s oblate surface,
leading to a gravitational force given by the gradient in geopotential
A change in geopotential is expressed as:
Geopotential, Thickness, and the Thermal Wind
Using the change in geopotential, the hydrostatic equation, and the gas law, we can
obtain a useful relation known as the hypsometric equation
This equation tells us that the vertical distance between two pressure surfaces (a.k.a.
the thickness) is proportional to the mean virtual temperature in the layer
Example… for two given pressure surfaces, the 1000- and 500-mb levels, the colder the
mean layer temperature, the smaller the thickness.
In other words, pressure decreases more rapidly with height in cold air relative to warm
air.
Applications of the hypsometric equation:
1.) Temperature forecasting
2.) Precipitation-type forecasting
3.) Understanding atmospheric structure
Consider the cross section through a midlatitude cyclone:
Now, based on thickness relation, sketch the approximate shape of the 500-mb surface:
Hypothetical situation
Consider the sfc pressure
at all points 1000-mb. The
sfc pressure is flat.
In the 1000-850-mb layer,
the layer average virtual
temperature gets gradually
colder from south to north.
Since thickness is
proportional to
temperature, the thickness
of that layer must decrease
to the north – reason for
the sloping 850-mb line
NP
EQ
A similar situation occurs in the 850-500-mb and 500-250-mb layers, and we find that the
slope of each pressure surface increases as we ascend in altitude.
BUT, the temperature structure changes at the tropopause (near 200-300-mb) – it is lower in
altitude over the poles.
Reversal of the temperature gradient in the stratosphere
200-mb and higher, temperatures are much colder in the tropics relative to the polar
regions
From Eq (1.33), we know
that the geostrophic wind
is proportional to the
gradient of geopotential
height
As mentioned before, the
slope of the pressure
surfaces increase with
height, due to the northsouth temp gradient.
The greatest slope is
found near 250-mb in this
example.
NP
EQ
Thus, the geostrophic wind speed increases with height up to the 250-mb level.
However, this changes at the tropopause… we find that the wind speed decreases with
height.
**So the fastest wind speed is located near 200-300-mb… the (polar) jet stream!
Let’s consider a tropical cyclone, which is just a large heat engine.
They are often referred to as a “warm core” systems.
Link Between Fronts and the Jet Stream?
Temperature gradients linked to fronts are
associated with a regions of enhanced height
gradients aloft
This in turn, corresponds to strong wind speeds
aloft… greater slope of pressure surfaces!
**Jet stream aloft is due to
thermal contrasts below
**Fronts are zones of
thermal contrasts
Thermal Wind
What is the “thermal wind”? Is it really a true wind?
NO! The thermal wind is simply a difference between winds –
vector difference of the geostrophic wind at 2 levels
**It is the vertical shear of the geostrophic wind!
A thermal wind vector example:
Why is the thermal wind important?
Since the geostrophic wind is proportional to the geopotential
height… the vertical shear of the geostrophic wind is related to the
difference in height (thickness).
In other words… the relation between thermal wind & thickness is
exactly analogous to the relation between geostrophic wind &
geopotential height.
 Geostrophic Wind (natural coordinates)
If we take the geostrophic wind at two different levels (U for upper
and L for lower):
We now have formulations for an upper level geostrophic wind and a lower
level geostrophic wind.
The thermal wind is the vertical shear of geostrophic wind, so we need to
subtract the upper level from the lower level:
The right-hand portion of the above equation is just thickness [ZU – ZL] which is
given by the hypsometric equation:
If we substitute the hypsometric eqn into the thermal wind eqn:
**This tells us that vertical shear of the geostrophic wind (thermal wind) is
directly related to the horizontal (virtual) temperature gradient!
Observations show that outside the tropics, the atmosphere is generally close to a state
of thermal wind balance
So, regions with strong horizontal temperature contrasts (tight gradients) imply vertical
wind shear!
What does this tell us about frontal zones?
They are zones of strong vertical wind shear!
Can you think of some important operational forecasting implications of this?
Thunderstorms/convection/tornadoes?
Convective storms that form in regions of strong shear are more likely to exhibit
rotation and become severe relative to those that form in weak shear. Thus,
convection that takes place in zones of strong thermal contrasts must be monitored
carefully
Hurricanes?
Vertical wind shear is detrimental to tropical cyclones; frontal zones and regions of
strong temperature contrasts are not favorable for tropical cyclone activity
Also, horizontal temperature advection is related to the geostrophic shear… this has
useful forecasting applications that will be discussed in detail with QG Theory
How must the N-S temperature gradient be oriented to have westerly winds increasing
with height?
Using the Cartesian coordinate form of the thermal wind equation:
we see that if colder temperatures are located to the north, then the westerly winds will
increase with height within the troposphere.
This figure is consistent with the
previous one, except it features a
narrow horizontal jet.
The jet stream increases in strength
with height up to the tropopause, and
then weakens with height in the lower
stratosphere.
At the level of the jet core, the
temperature gradient is weak to zero.
Red arrows indicate the meridional temperature
gradient
Temperature Advection & Thermal Wind
Regions where the 1000-mb height contours are crossing 500-mb
height contours at a strong angle correspond to regions of strong
horizontal temperature (thickness) gradient
The thermal wind is oriented parallel to thickness contours with lower
(colder) values to the left
If we consider thickness contours as layer-average isotherms, then it
becomes useful in evaluating the temperature advection within that
layer.
At point A, the northerly 1000-mb geostrophic wind is associated with
cold advection (moving low (cold) thickness values to point A).
The westerly 500-mb geostrophic wind is also associated with cold
advection.
There is clearly geostrophic cold air advection taking place at point A in
the 1000-500-mb layer
Temperature Advection & Thermal Wind
Temperature Advection & Thermal Wind
Notice how the geostrophic wind profile turns counter-clockwise with height.
This is known as a backing wind profile.
In the NH, backing winds are associated with cold air advection.
When the geostrophic wind turns clockwise with height, it is called a
veering wind profile and is associated with warm air advection.
Using QG-theory, we will learn that thermal advection is related to the
forcing for vertical air motion
WAA is often associated with ascent (lift)
CAA is often associated with descent (sinking air)
Can often use SLP in place of the 1000-mb geopotential height. So a
MSLP and 500-mb height map is often used for a resonable estimate of
thermal advection
*BUT…
The link between veering/backing winds and
thermal advection only applies to the
GEOSTROPHIC wind
Why is this?
Frictional Veering
The actual wind can veer or back due to other mechanisms that may not
be related to thermal advection
For example, in the PBL, friction can cause a departure from
geostrophic balance. Notice below, that the inclusion of the friction has
caused the sfc wind to blow towards the lower pressure.
The influence of friction diminishes with height, and the flow becomes
more geostrophic
So in this example, how does the wind change with height?
Implications?
GSO sounding from 00Z 25
August 2008
GSO sounding
What is the wind profile
from 00Z 25
doing here?
A 2008
Aug
Clockwise
with height
Veering Wind Profile
What is the wind
doing?
What typeprofile
of thermal
advection does this imply?
can we
WarmHow
Air Advection
(WAA) determine
thermal
advection?
BUT… what can you say
about the PBL?
It’s relatively deep
So
this is veering,
likely frictional
Frictional
PBL
veering… no implications
No implications for ascent
for WAA
GSO sounding
GSO sounding
from 00Z
27 August
2008
from
00Z 27
Aug 2008
What is the wind profile
doing here?
What is the wind
Veering
profile doing?
What type
of thermal
How
can we
advection
does this imply?
determine
WAA
thermal
advection?
How about
the PBL?
Shallow, so the deep
veering observed IS
geostrophic veering.
Shallow PBL, so deep
veering
is geostrophic
WAA
is likely
occurring.
veering
g
This is also consistent
Consistent w/ saturation
with the saturated
atmospheric profile