ATS/ESS 452: Synoptic Meteorology

- Cyclone Structure- QG Theory

NAM Forecast Sounding for this Saturday at 03 UTC (i.e., tonight near 9pm)

a) In the sfc to ~700-mb layer, how are the winds turning with height?

Counter-clockwise

b) Is this a veering or backing wind profile?

Backing

c) What type of temperature advection is this indicative of?

Cold Air Advection

NAM Forecast Sounding for this Saturday at 03 UTC (i.e., tonight near 9pm)

d) 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

2. (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

3. (2 pts) In the Northern Hemisphere, shortwave troughs and ridges are dominated by ( planetary / relative ) vorticity advection, which causes them to ( prograde / retrograde)

Convergence;sinking air

Convergence;sinking airDivergence;

rising air

Divergence;rising air

Healthy Westward Tilt of Pressure Systems with Height

Z

W E

H L

H L

• 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

Healthy Westward Tilt of Pressure Systems with Height

Vertically Stacked Systems

Z

W E

H L

H L

• As cyclones mature and become occluded, they become vertically stacked with their upper-level system

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

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)

Westward tilt of pressure systems with height

Vertically stacked

Unhealthy Eastward Tilt

Z

W E

H L

H L

• 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

• 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

• 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

• 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

• 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)

300-mb Isobaric Surface

Upper Level Gradient Wind Relationship

970 dam

990 dam

970 dam

990 dam

Ridge Ridge

Trough

(Supergeostrophic Winds) (Supergeostrophic Winds)

(Subgeostrophic Winds)

Speed Convergence

Speed Divergence

300-mb Isobaric Surface

Upper Level Gradient Wind Relationship

970 dam

990 dam

970 dam

990 dam

Region of Subsidence (dashed line)

Region of Lifting (dashed line)

H L

Aloft: Speed Convergence Aloft: Speed Divergence

SFCSFC

• 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

• 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

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

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

Vertical Motions in Mid-Latitude Synoptic Systems

• 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

Quasi-Geostrophic 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

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

Main Assumptions 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)

Main Limitations of Q-G Theory

The Q-G ApproximationsFundamental assumption for Q-G equations: Rossby number is small (on the order of 0.1).

**Define the Rossby number**