1. ATS/ESS 452: Synoptic Meteorology
Monday 09/22/2014
Continue Review Material
Vorticity
Thermodynamics

2. Vorticity What is vorticity, and why do we study it?
Why do we focus on the vertical component?

3. Vorticity
Tornadoes, hurricanes, and extratropical cyclones are all characterized by varying degrees of wind rotation about a vertical axis
Vorticity is the parameter we use to measure the rotation
Vorticity is a measure of rotation in all three directions/axes (x,y,z), however, on the synoptic scale we are primarily interested in the vertical vorticity (scale analysis!)
Relative vorticity represents the the local rotation in a fluid (our atmosphere). If we include the rotation of the Earth, then we refer to it as the absolute vorticity.
In the Northern hemisphere, positive vorticity is associated with cyclonic rotation (counter-clockwise) and negative vorticity is associated with anti-cyclonic rotation (clockwise)
**Advection of the vertical vorticity is related to forcing for vertical air motion (lift) and is a critical parameter for weather forecasting.

4. NAM 500-mb height, absolute vorticity analysis 00UTC 11 Jan 12
Notice the strong cyclonic rotation around the upper-level low pressure over eastern TX and the strongly positive absolute vorticity associated with that. Also, the anti-cyclonic rotation in the ridging over the mountain west and the near negative absolute vorticity.
**Planetary vorticity is always positive and is very large… so difficult to get negative absolute vorticity!!
NAM 500-mb height, absolute vorticity analysis 00UTC 11 Jan 12

5. 500mb GFS 21-hr forecast; shading represents positive absolute vorticity

6. Vorticity
Physically, what do the i (x) and j (y) components of vorticity include?
vertical wind shear
When is this typically important?
convective storms
“Types” of vorticity:
If vorticity is considered a measure of rotation, is it possible to have vorticity in perfectly straight flow, such as that picture below?
Yes! This is called shear vorticity and is caused by a change in wind speed over some distance. It is important on the flanks of jet streams
Where is the vertical vorticity positive?

7. 300mb GFS 30-hr forecast; shading represents wind speeds > 70 kts
Shear vorticity!
300mb GFS 30-hr forecast; shading represents wind speeds > 70 kts

8. Vorticity “Types” of vorticity:
Curvature vorticity is caused by a change in wind direction over some distance and is important in troughs/ridges
What is the sign of vertical vorticity here?
Planetary Vorticity is due to the Earth’s rotation – the air spins with the earth!
Given by, f, and is positive in the NH.

9. Notice the areas where vorticity is elevated on 500 mb is within significant curvature of the winds…. In troughs, positive vorticity!... Don’t confuse this with PVA though.
500mb GFS 168-hr forecast; shading represents positive absolute vorticity

10. Typical wintertime situation showing the relative between the 500-mb heights and vorticity
Left (a): Absolute vorticity  values generally increase toward the North Pole, partly due to the increase in planetary vorticity (f) with latitude
An area of cyclonic curvature vorticity is located in the upper trough centered near the Great Lakes Region. Cyclonic shear vorticity is evident along the northern flank of a strong jet over N. Canada
Right (b): Relative vorticity  now regions of negative vorticity appear in the large upper ridge over western N. America

11. Qualitatively estimate the geostrophic relative vorticity at location A.

12. The Vorticity Equation
Local time-rate-of-change in absolute vorticity (relative + planetary)
Vertical advection (of relative vorticity)
Tilting/twisting term  conversion of horizontal vorticity to vertical vorticity
b) And c) are rather small on the synoptic scale
Wind shear creates horiz vort
Updraft “tilts” the spinning air upright
The updraft then starts rotating  supercell

13. The Vorticity Equation
(d) Stretching or “convergence” term… i.e. the ice skater effect
The spin-up of vorticity is proportional to the convergence
This might explain the rapid development of many strongly rotating cyclonic systems (the rate of vorticity growth is proportional to the vorticity itself)
Also, zones of preexisting cyclonic vorticity (fronts and troughs) and thus preferential sites for the growth of cyclones…. All it needs is a bit of convergence to grow the vorticity!

14. The Vorticity Equation
(e) Friction
(f) Horizontal advection  most important on synoptic scale!

15. Vorticity Advection
Left: 500-mb chart showing the 500-mb winds, isoheights and vorticity
Right: Corresponding 500-mb vorticity advection.

16. Thermodynamic Review What is an adiabatic process?
One in which there is no heat transfer; for example, no heat exchanged between a parcel and its environment would be considered an adiabatic process
dq = 0
Lapse rate – the rate of decrease with height for an atmospheric variable, typically temperature
The dry adiabatic lapse rate (DALR) is the rate of temperature decrease with height for a parcel of dry or unsaturated air rising under adiabatic conditions
No heat exchanged between the parcel and the environment
Pressure decreases as the parcel rises, causing it to expand
As the parcel expands, it pushes on the air around it, causing it to lose internal energy, so the temperature of the parcel decreases
≈ 10 K km-1

17. Potential Temperature, θ
Poisson’s Equation:
where p0 is some reference pressure level, usually 1000 mb
What is the physical interpretation of potential temperature?
The temperature that an air parcel would have if it were dry adiabatically compressed (or expanded) to a reference pressure level
What are some potential uses of potential temperature?
Used to determine static stability
An examination of the horizontal θ distribution is useful in locating frontal boundaries -- especially over uneven terrain where surface temperature differences may be caused by the terrain.
When diabatic processes are neglible, air parcels are typically constrained to travel along surfaces of constant θ, known as isentropic surfaces. This can help identify areas of lift. (Chapter 3).