ATS/ESS 452: Synoptic MeteorologyFriday 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:

NP EQ

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

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 stratosphere200-mb and higher, temperatures are much colder in the tropics relative to the polar regions

NP EQ

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 north-south temp gradient.

The greatest slope is found near 250-mb in this example.

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.

If we take the geostrophic wind at two different levels (U for upper and L for lower):

Geostrophic Wind (natural coordinates)

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?

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?

Frictional Veering

GSO sounding from 00Z 25 August 2008

What is the wind profile doing here?

Clockwise with height

Veering Wind Profile

What type of thermal advection does this imply?

Warm Air Advection (WAA)

BUT… what can you say about the PBL?

It’s relatively deep

So this is likely frictional veering… no implications for WAA

GSO sounding from 00Z 27 August 2008

What is the wind profile doing here?

Veering

What type of thermal advection does this imply?

WAA

How about the PBL?Shallow, so the

deep veering observed IS geostrophic veering.

WAA is likely occurring.

This is also consistent with the saturated atmospheric profile