1. ATS/ESS 452: Synoptic Meteorology
Cyclone Structure
QG Theory

2. NAM Forecast Sounding for this Saturday at 03 UTC (i. e
NAM Forecast Sounding for this Saturday at 03 UTC (i.e., tonight near 9pm)
In the sfc to ~700-mb layer, how are the winds turning with height?
Counter-clockwise
Is this a veering or backing wind profile?
Backing
What type of temperature advection is this indicative of?
Cold Air Advection

3. NAM Forecast Sounding for this Saturday at 03 UTC (i. e
NAM Forecast Sounding for this Saturday at 03 UTC (i.e., tonight near 9pm)
Notice the temperature and dew point profile from ~850-mb to just above the sfc. Describe what’s going on here and does it make sense based on the temperature advection that’s occurring within that layer.
CAA  sinking air  compressional warming in that layer  air dries and temp warms / parallels a dry adiabat

4. (4 pts) In an absolute vorticity conserving flow, if an air parcel is displaced to the north, what happens to the relative vorticity (ζ) and in what direction does the parcel begin to rotate? Assume initial ζ = 0. An illustration may be used to describe this process.
If a parcel is displaced to the north, then f increases, so through the conservation of absolute vorticity, the relation vorticity must decrease.
ζ < 0; the parcel begins to rotate clocks, or anti-cyclonically
(2 pts) In the Northern Hemisphere, shortwave troughs and ridges are dominated by
( planetary / relative ) vorticity advection, which causes them to ( prograde / retrograde)

5. Convergence;
sinking air
Divergence;
rising air
Convergence;
sinking air
Divergence;
rising air

6. Healthy Westward Tilt of Pressure Systems with HeightZ H L W E

7. Healthy Westward Tilt of Pressure Systems with Height
Note that the thermal ridges and troughs depicted in Fig. 6.6 tilt eastward with height and are out of phase with the pressure ridges and troughs. This means that:
Baroclinic ridges (highs) are cold at the surface and warm aloft
Baroclinic troughs (lows) are warm at the surface and cold aloft
This allows for significant temperature advection to take place in the presence of cyclones

8. Vertically Stacked Systems
As cyclones mature and become occluded, they become vertically stacked with their upper-level system H L Z
Note that sub-tropical highs are vertically stacked… but its not a baroclinic high (barotropic) H L W E

9. Vertically Stacked Systems
As a result, the pressure trough and temperature trough lose their vertical tilt. They also become aligned. (This is common as cyclones move poleward toward 60N and 60S latitudes)
The same happens with the pressure ridge and temperature ridge as an aging polar high moves equatorward and merges with the subtropical high near 30N and 30S
i.e. systems began to lose their baroclinic nature
As a consequence, the thermal advection with these systems becomes quite weak (or non-existent). Thus, energy conversion from the jet stream to these surface systems becomes negligible
 No thermal contrasts, then the jet stream retreats
So basically, with a vertically stacked system, the surface cyclone pulls back into the colder air (it’s under a low height center!)
**When the system becomes totally vertical, that means it has moved away from the energy source (thermal gradient) and it will soon begin to die out

10. Vertically Stacked Systems
These vertically-stacked systems become more barotropic in nature (equivalent barotropic) with the wind direction being uniform with height (no wind shear)

11. Westward tilt of pressure systems with height
Vertically stacked

12. Unhealthy Eastward Tilt
If the pressure trough displays an eastward tilt with height, there is an up-scale energy cascade whereby the eddies must give their energy back to the mean flow H L Z
**So now, the sfc features are giving its energy back to the jet
** This is really the kiss of death for any weather system**  this is important stuff to look for when doing weather analysis
**Huge deep lows will very likely die very quickly…. See the large pacific lows that come in on the west coast H L W E

13. Thus, individual cyclones and anticyclones will weaken or dissipate as they lose energy to the larger jet-stream westerlies
The surface cyclone or anticyclone must give up its kinetic and potential energy to the jet stream
The surface system rapidly dissipates
This is characterized on weather maps by the upper trough (ridge) tending to “outrun” the surface low (high)
This is common with landfalling cyclones on the West Coast

14. A simplistic diagram of baroclinic troughs and ridges is displayed in your handout
The surface trough (i.e. convergence) is overlain by the upper-tropospheric ridge (i.e. divergence)
Thus, mass continuity requires that upward vertical motion occur in the vicinity of baroclinic surface lows
The surface ridge (i.e. divergence) is overlain by the upper-tropospheric trough (i.e. convergence)
Thus, mass continuity requires that downward vertical motion occur in the vicinity of baroclinic surface highs

15. BUT, in actuality, this vertical view of baroclinic systems is too simplistic. In reality:
The greatest upper-tropospheric convergence and divergence occurs in between upper-tropospheric troughs and ridges (via the gradient wind relationship):
Super-geostrophic flow in the ridges
Sub-geostrophic flow in the troughs
And other factors not yet discussed

16. What is the gradient wind?
Similar to geostrophic wind, but allows for curved flow
A balance between the pressure gradient, Coriolis AND centrifugal forces
Air still blows parallel to isobars (isoheights) with low values to the left
Example
For low pressure cases, the PGF must be balanced by the Centrifugal + Coriolis forces
Because the PGF doesn’t change, this means that the Coriolis force must decrease to achieve the desired balance
This in turn decreases the overall wind speed
In other words, the gradient wind blows parallel to the isobars at a less than geostrophic wind speed (subgeostrophic)
For high pressure cases, the Coriolis force must be balanced by the Centrifugal + PG forces
Again, the PGF doesn’t change, so now the Coriolis force must increase to achieve the desired balance
This in turn increases the overall wind speed
So now, the gradient wind blows parallel to the isobars at a greater than geostrophic wind speed (supergeostrophic)

18. Upper Level Gradient Wind Relationship
(Supergeostrophic Winds)
(Supergeostrophic Winds)
Ridge
Ridge
Speed Convergence
Speed Divergence
970 dam
990 dam
970 dam
990 dam
Trough
**Winds blowing FASTER than the height gradient allows in the ridge
**Winds blowing SLOWER than the height gradient allows in the trough
So what happens in between these areas?
(Subgeostrophic Winds)
300-mb Isobaric Surface

19. H L Upper Level Gradient Wind Relationship 300-mb Isobaric Surface
Aloft: Speed Convergence
Aloft: Speed Divergence H L
970 dam
990 dam
970 dam
990 dam
SFC
SFC
**So low pressure development at the sfc to the right of trough axis
** High pressure development at the sfc to the left of trough axis
Region of Lifting (dashed line)
Region of Subsidence (dashed line)
300-mb Isobaric Surface

21. Also, much of the upward and downward vertical motion in a baroclinic system is slant-wise
So just by using the basic wave pattern construct, we can determine where “stormy” weather might be
Example

22. Vertical Motions in Mid-Latitude Synoptic Systems
Evaluation of synoptic scale vertical motion fields are of primary importance in analyzing and forecasting synoptic scale weather
Vertical motions in the atmosphere are extremely difficult to observe and forecast
Large-scale (i.e. synoptic scale) horizontal winds in the troposphere usually have magnitudes between 5 and 50 m/s (10 – 100 kt)
Synoptic scale vertical winds in the troposphere are much smaller, with magnitudes generally between 0.05 and 5 cm/s (0.1 and 3 knot)
The continuity equation for mass links divergence (convergence) of the horizontal wind to vertical motion

23. Vertical Motions in Mid-Latitude Synoptic Systems
Small changes in the speed or direction of the horizontal wind may have HUGE effects on the lifting or sinking (you see this at the jet level).
The actual horizontal wind direction and speed cannot be measured with enough accuracy to allow direct calculations of the resulting vertical wind. There are many disruptions to the flow, such as storms, mountains and buildings, which produce irregular wind flow and generate turbulence/eddies
Thus, actual winds measured by rawinsonde balloons, aircraft, surface weather stations, and satellite cloud motions cannot be used for accurate calculations of divergence and vertical motion in the classical sense
**ROABs are not close enough together for enough accuracy
**And we don’t measure with enough accuracy. For examples, our wind directions have a + or – of 5 degrees, which is not good enough for our calculations.
** Also, the horizontal wind speed could be up to 50 m/s whereas DIV is on the order of 1*10-5 m/s…. Orders of magnitude difference in order to get real accurate calculations

24. Vertical Motions in Mid-Latitude Synoptic Systems
Therefore, alternative “indirect” vertical motion methods must be developed which may be partially or totally independent of the actual wind.
Two of the most popular indirect methods are the Omega Equation and Q-Vector methods, both of which are derived from Quasi-Geostrophic (Q-G) wind relationships
Another method, depicts wind flow, moisture, and isobar patterns on an isentropic surface. Isentropic vertical motions will be discussed at a later date in Synoptic

25. Quasi-Geostrophic Theory
On the synoptic scale (and outside of the tropics), wind flow can be generally assumed to be quasi-geostrophic.
That is, wind flow is approximately in geostrophic balance with only small amounts of divergence/convergence occurring
Q-G theory is designed for baroclinic systems within the mid-latitude westerlies

26. Main Assumptions of Q-G Theory
The atmosphere is in hydrostatic balance (i.e. the atmosphere is thermodynamically stable)
Hydrostatic balance is destroyed near thunderstorms where the atmosphere is unstable
The wind is quasi-geostrophic (i.e. flows essentially parallel the height contours)
Advantages to this assumption are that height contour patterns may replace the actual wind flow and that no actual wind observations are required
No small-scale weather features required
Only a single analysis of vorticity, isobaric heights, and temperatures are required

27. Main Assumptions of Q-G Theory
Divergence/Convergence is small
This is representative of inactive weather regions and small vertical motions
Vorticity is represented by geostrophic vorticity
Geostrophic vorticity can be derived from the height pattern on isobaric surfaces
Vorticity advection can be inferred from the intersection of vorticity and height contours
Thermal advection can be represented by the intersection of isobars (or isoheights) with isotherms

28. Main Limitations of Q-G Theory
Provides only a first inference of where and why vertical motion may be occurring in the atmosphere
Should not be applied in the tropics where synoptic-scale flow is more ageostrophic in nature
Should be used with great caution in active weather regions where divergence is large and non-hydrostatic conditions may exist
Vertical motion produced by topography (i.e. friction), latent heating (i.e. convection), evaporative cooling, radiational heating and cooling, and small-scale processes will not be represented by Q-G theory and the omega equation.
Strictly a diagnostic equation (here and now – not future)
Q-G theory can not be used to “predict” future vertical motions (no time derivative)
On the other hand, Q-G theory may be used to diagnose vertical motion in model forecast patterns
Some error is introduced in Q-G analyses when smoothed contour patterns are used (all model analyses are smoothed)

29. The Q-G Approximations
Fundamental assumption for Q-G equations: Rossby number is small (on the order of 0.1).
**Define the Rossby number**