Download TO 6.2.1 A) Describe the evolution of a typical baroclinic wave from

TO 6.2.1
A) Describe the evolution of a typical baroclinic wave from an incipient wave on a baroclinic
zone, during intensification, through to final occlusion. Relate the development of the wave to
changes in its associated fields and processes.
Stage 1: incipient
1.
2.
3.
Begins along a pre-existing low-level baroclinic (frontal) zone
Perturbation is first started in upper levels prior to the low level with a short wave move in to disturb
the flow aloft, which produces a region of upper-level divergence over the frontal zone of low level
The upper-level divergence results in a wavelike kink near surface
Stage 2: Development
1.
2.
3.
The frontal zone fractures in the vicinity of the low center with cold front pushing south-ward and
warm front moving northward. The low center starts to deepen. The winds cyclonically blow into the
low center
A cooperative interaction starts between the upper level and surface flows: The initiated surface
cyclonic circulation begins to produce and enhance T advection in the low-level, which amplifies the
upper level waves and increases wind aloft. The upper trough intensifies and produces stronger PVA,
which further cause stronger upper-level divergence, and surface convergence. Thus, the cyclonic
circulation strengthens, and surface low becomes deepen. The stronger low-level circulation induces
stronger PTA to amplify upper waves, and so on. A positive feed back starts. This process is called
“self-development” of a cyclone
Meanwhile, warm air rises from the surface low and along warm front, and cold air descends behind the
cold front, a damping (“self-limiting”) influence of the vertical motions occurs as adiabatic cooling in
the regions of ascent (warm air mass) and local warming in the regions of descent (cold air mass),
which decrease the thermal contrast of two air masses. The damping influence latter is largely offset by
the effects of condensation heating as cloud and precipitation set in as a result of vertical motion, the
latent heating is crucial for the further development of the cyclone
Stage 3: Mature
1.
2.
3.
A fully developed open wave with several tight isobars encircle the wave’s apex, the central pressure is
now much lower. The winds blow more vigorously and converge toward the low’s center. The cold
front moves close to the warm front, squeezing the warm sector into a smaller area
Cloud and Precipitation form in a wide band ahead of the warm front and along a narrow band of the
cold front, at the same time, latent heating
The troughs at 500 and 1000mb are nearly in phase. As a consequence, the thermal advection and
energy conversion become weak, amplitude of upper wave reaches its max., and surface pressure
reaches its lowest value
Stage 4: Occluded
1.
2.
3.
Advanced cold front overtakes the warm front, the low system becomes occluded.
Warm sector air gets lifted off surface.
Surface low and upper level low center becomes vertically stacked, storm becomes weaken and
dissipation as this vertical structure is cutting off its energy resource.
(thick lines: 500mb; dashed line: thickness; thin contour: 1000mb)
1
B) Sketch diagrams of a typical baroclinic wave at any stage of its development. Including:
1000-500 hPa thickness, vorticity patterns, surface fronts, surface isobars, relate to upper
level features.
Incipient
Occluded
Development
C) Sketch diagrams of a typical comma at any stage of its development, and relate it to various
surface and upper level features and cloud patterns
A: Multi-layered
cirrostratus shield
B: middle-level
comma cloud
C
B
A
C
B
A
C: deformation
zone cirrus
2
D) Define “Self-development’ and ‘self-limitation’
1. During the advance of an upper-level trough relative to a surface baroclinic zone, the upperlevel divergence initiates the surface circulation. The initiated surface cyclonic circulation
begins to produce and enhance T advection in the low-level, which amplifies the upper level
waves and increases wind aloft. The upper trough intensifies and produces stronger PVA,
which further cause stronger upper-level divergence, and surface convergence. Thus, the
cyclonic circulation strengthens, and surface low becomes deepen. The stronger low-level
circulation induces stronger PTA to amplify upper waves, and so on. A positive feed back
starts. This process is called ‘self-development’ of a cyclone.
2. Meanwhile, warm air rises from the surface low and along warm front, and cold air descends
behind the cold front, a damping (self-limiting) influence of the vertical motions occurs as
adiabatic cooling in the regions of ascent (warm air mass) and local warming in the regions of
descent (cold air mass), which decrease the thermal contrast of two air masses. The damping
influence latter is largely offset by the effects of condensation latent heating as cloud and
precipitation set in as a result of vertical motion.
E) Describe how a secondary circulation is set up over a surface low and high and 500 ridge and
trough
1. During the stage of cyclone development, surface low is usually located downstream (east) of 500mb trough
where PVA and upper level divergence are the strongest; while NVA and convergence are strongest
downstream (east) of 500mb ridge where the surface High is located. Thus, rising motion occurs above the
surface low and subsidence above the surface high.
2. Cold advection dig the trough with downward motion at the rear of the cold front, and warm advection build
the ridge with upward motion ahead of warm front.
3. The secondary circulation (vertical motions) in a developing baroclinic system always acts to oppose the
horizontal advection fields. Thus, the divergent motions tend partly to cancel the vorticity advection and the
adiabatic T changes owing to vertical motion tend to cancel partly the thermal advection.
F) Recognize cyclogenesis patterns on satellite imagery, and be able to identify the stage of
development of the cyclone from the imagery.
3
Type 1: Meridional Trough or Baroclinic Zone Cyclogenesis
1. The short wave disturbance which initiates development moves around the trough within the baroclinic
zone
2. This type is most prevalent along the U.S. east coast and adjacent coastal waters
3. Sequence of development of the major cloud systems:

Baroclinic Zone Cirrus deck begins to wave into an ‘S’ pattern

Vorticity comma (forms under the cirrus deck, then emerges)

Deformation cirrus
4. During the early phases, the surface low centre and front are on the warm or anticyclonic side of the jet axis.
The low transforms to the cold side of the jet during the developmental cycle
5. The strongest development begins in the middle and lower troposphere and evolves upward with time. The
storm evolves to a type ‘A’ mature storm pattern and may change to a type ‘B’ pattern if development
continues
6. This type of cyclogenesis is most similar to the “classical frontal wave model”
Type 2: Split Flow or Diffluent Flow Cyclogenesis
1.
2.
3.
4.
The short wave disturbance which initiates development moves on the warm side of the established jetfrontal zone, within the diffluent upper air flow pattern.
This type is most prevalent over the great plains east of the Rockies.
Sequence of development of the major cloud systems:

Deformation cirrus.

Vorticity comma. (forms rapidly southeast of the cirrus pattern)

Baroclinic zone cirrus deck (forms over the comma).
During the early phases, the surface low centre and front are not well defined or organized. Surface low
becomes consolidated on the cold or cyclonic side of the jet axis and the surface front tends to lag behind
the upper level baroclinic zone.
4
5.
The closed circulation centre develops sooner and more rapidly in the middle and upper troposphere. The
storm usually evolves directly to a type "B" mature storm pattern; with development east of the divide the
system may evolve with a dry surge structure.
The first two stages of development of split (or diffluent) flow cyclogenesis.
The third and fourth stages of development of split (or diffluent) flow cyclogenesis
Types 3: Cold Air Vortex (3A) and Induced Wave Cyclogenesis (3B)
1.
2.
3.
4.
5.
6.
The short wave disturbance which initiates development moves on the cold side of established jet-front
zone, within a confluent upper air flow pattern.
This type is most prevalent over the open ocean.
Sequence of development of the major cloud systems:
3A:

Vorticity Comma.

Baroclinic zone cirrus.

Deformation zone cirrus.
3B:

Vorticity Comma.

Wave on baroclinic zone.

Deformation zone cirrus.
Early development of weather on the cold side of the jet.
The strongest development begins in the middle troposphere during the early phases, but the nature of
subsequent vertical development is more variable than Type I or II.
The surface low forms or moves within the cold side of the jet.
5
6
TO 6.2.2
A) State and explain the implications of the assumptions of the quasi-geostrophic
approximation
1.
2.
We assume a synoptic scale, nearly geostrophic, and mid-latitude flow.
Quasi-geostrophic assumption: real wind replaced by geo-strophic wind in advection terms, but not in
divergence term (since the small ageostrophic components of the flow describe the development of the
system)
3. Relative vorticity is approximated by the geostrophic vorticity in the vorticity equation
4. Beta-plane approximation (f = fo + βy) is used in the advection term in the vorticiy equation, and fplane approximation (f = fo) elsewhere
5. The relative vorticity (ζ) is typically about an order of magnitude smaller than the planetary vorticity in
mid-latitudes (except for very strongly sheared flows at jet-stream level). The relative vorticity in the
divergence term for the vorticity equation is neglected.
6. The tilting-twisting term is generally ignored since synoptic-scale motions are assumed to be almost
horizontal.
7. Inviscid fluid (frictionless)
8. Incompressible assumption: horizontal inflow must be compensated by vertical outflow.
9. Hydrostatic assumption: states that the rate of decrease of pressure with height is proportional to the
density of the air. Pressure falls more slowly with height in a warm airmass than in a cold airmass. This
is an excellent assumption for synoptic-scale flows (downward gravity force = upward pressure
gradient force). Vertical acceleration << g (no exceeding 0.01 ms-1)
10. Adiabatic assumption: no heat fluxes into or out of the particular volume of air, this is a good shortrange (less than one day) approximation
11. Ideal gas law is used for air.
12. Assumed a static stability parameter
B) Identify and qualitatively explain the terms in the quasi-geostrophic vorticiy,
thermodynamic energy, omega and geopotential tendency equations
Thermodynamic energy equation
Explanation:

Left side: change of thickness

Right-side Term1: thickness advection by geostrophic wind (PTA enhances the thickness)

Right-side Term2: adiabatic T change caused by vertical motion (vertical motion decreases the rate of
thickness change)
Assumptions:

Adiabatic (no latent release, sensible heating)

Hydrostatic (
)

Geostrophic (Vg  V)
To be used for:

Diagnosis temperature changes
7
Vorticity equation: (unsimplified)
(a)
(b)
(c)
(d)
Assumptions:





Ignore “tilting-twisting” term (d), because synoptic-scale motions are assumed to be almost horizontal
The relative vorticity (ζ) is typically about an order of magnitude smaller than the planetary vorticity in
mid-latitudes (except for very strongly sheared flows at jet-stream level). The relative vorticity in the
divergence term (c) is neglected
The velocity in advection term (a) is approximated by Vg (note we cannot do this in divergence term)
Relative vorticity is approximated by geostrophic vorticity (g  )
Beta-plan approximation (f = fo + βy) used in the advection term, while f-plane (f = fo) used elsewhere
So we got Q-G vorticity equation:
Explanation:

Left side: the local rate of change of relative vorticity

Right-side term 1: the advection of absolute vorticity by the geostrophic wind (PVA increase vorticity;
NVA decrease vorticity)

Right-side term 2: local planetary vorticity times divergence of real wind (conservation of absolute angular
momentum: convergence implies “spin-up” or an increase of vorticity, just as the figure skaters spin faster
when they bring in their arms. Conversely, divergence implies a decrease of vorticity)
Use Q-G vorticity equation explain “why short-wave progress eastward”:
In Q-G vorticity Eq. (ignore divergence term):

For short waves, Adv. of g >> Adv. of f  net PVA (NVA) downstream of the trough (ridge)  the
wave moves downwards;

For long waves, Adv. of g ~ Adv. of f  cancel each other out  long waves move slowly (compared
to SW)
8
Geopotential tendency equation: (eliminate  in energy Eq. and Q-G. Vorticity)
Where
Used to:


estimate the rate of change of geopotential heights – in time and in space
assess the relative importance of different physical forcings on the geopotential
Assumptions:

assume synoptic scale, mid-latitude flow

nearly geostrophic

hydrostatic atmosphere (very small vertical accelerations)

no friction (inviscid)

adiabatic flow (constant entropy)
Explanation:

Left side: 3-D Laplacian of , proportional to - (if sinusoidal distribution)




f 
Right-side term1: geostrophic advection of absolute vorticity; = f0   Vg   g  vg  , these two terms will
y 

tend to work against one another. For very short waves, relative vorticity advection will dominate, and the
wave will propagate to the east rapidly. For very long waves the advection of planetary vorticity will
dominate, and the wave will move very slowly westward, i.e., it will retrogress.
Right-side term 2: geostrophic differential advection of thickness;

f 02 R     Vg  T

=
  p 
p





; warm
advection (decreasing with height) increases geopotential, and cold advection (decreasing with height)
reduces geopotential
 fall    
 cold 
Geopotenti al 
   vorticity advection  
advection decrea sing with height
rise


  
 warm 




Other important points:
The vertical impact of PVA or NVA is shallower for short waves than for long waves. For very long
waves the geopotential tendency is impacted all the way to the surface (not so for short waves)
PVA (NVA) can propagate but NOT deepen/strengthen troughs/ridges (as at trough or ridge, VA=0)
Differential cold/warm advection can deepen/strengthen troughs/ridges
9
QG Omega Equation state: (eliminate  in energy Eq. and Q-G. Vorticity)
Assumptions:

assume synoptic scale, mid-latitude flow

scale analysis, dropping very small terms for synoptic scale motions

Q-G approximation (real wind replaced by geostrophic wind in adv. terms, but not in divergence term.
Thus called Quasi-Geostrophic, not Geostrophic)

hydrostatic atmosphere (very small vertical accelerations)

no friction (inviscid)

diabatic heating effects are ignored (adiabatic flow)
Explanation:

Left side: 3-D Laplacian of , proportional to -

Right-side term1: differential geostrophic advection of absolute vorticity; PVA increase (decrease) with
height  ascent (descent);  V500  ( 500  f )

  
 ; PTA
 p 
Right-side term2: 2-D Laplacian (divergence of gradient) of thickness advection;  Vg   
 ascent; NTA  descent
 ri sin g    
 cold 

   vorticity advectionincrease with height  
advection
 warm 
 sin king    

Other important points:

At any level, PVA = divergence; NVA = convergence

Any convergence at SFC forces air up (air uncompressible); any divergence aloft also help air going
up (sucking air from lower levels)

VA and TA can be in opposite sign, so not obvious to see the results (see Figure below)

500-mb VA may not be good indicator of differential VA in 1000-500mb layer.

QG vertical motion is not caused by these terms

QG vertical motion is a response to Vg advection which destroys the geostrophic balance

QG Omega is not a physical reality, similar to thermal winds, i.e., not measurable
Ageostrophic flow (which is to restore the destroyed geostrophic balance)
10
C) Describe the effect of wavelength on the motion of upper level waves in terms of planetary
and relative vorticity (Using QG vorticity equation Eq.).
1.
2.
3.
4.
5.
The advection of absolute vorticity is composed of two terms, the relative vorticity advection and the
planetary vorticity advection.
These two terms tend to compete with each other, and the direction of motion of the wave is dependant
upon which component is stronger.
For short waves, the advection of relative vorticity is greater than the advection of planetary vorticity. Thus,
the net vorticity advection is positive/negative downstream of the trough/ridge and the wave moves
downstream.
For long wave, the relative vorticity advections are weaker so the planetary and relative vorticity
advections are comparable and largely cancel each other out. Thus, the long waves move very slowly in
comparison with the short waves.
For very long waves the advection of planetary vorticity dominates, and the wave will move very slowly
westward, i.e., it will retrogress.
D) Explain the effect of vorticity and thickness advection on the movement and amplification of
upper wave, referring to the influence of wavelength (Using potential tendency Eq.)
1. Vorticity advections cannot amplify wave, but can propagate the trough and ridge since such advections are
close to zero in the vicinity of troughs and ridges.
2. Cold air advection decreasing with height results in falling heights. Conversely, warm air advection
decreasing with height results in a rising of heights. It is differential thickness advection that is responsible
for the amplification of upper waves. Cold air flooding into the low levels of a trough will dig the trough and
warm air pushing into a ridge will build the ridge, thereby amplifying the wave.
3. Vertical impact of PVA and NVA is shallower for short wave than for long waves.
E) Explain the effect of vorticity and thickness advection on the vertical velocity fields, including
the influence of airmass stability (Using QG Omega Eq.).
1. PVA contributes to ascent; NVA causes subsidence (more accurately: PVA increases (decreases) with height
 ascent (descent); NVA decreases (increases) with height  ascent (descent))
2. PTA contributes to ascent, NTA tends to induce subsidence.
3. Stable air mass tends to prevent vertical motion, instable air mass favors vertical motion.
F) State and explain in physical terms the wavelength restrictions on baroclinic development
derived from the two-level quasi-geostrophic mode (short wave cut-off and long wave damping)
1. Short wave cut-off: as relative vorticity is larger for shorter wavelength systems than for longer wavelength
systems. Thus, vertical motions are more intense since the magnitudes of the regions of PVA and NVA are
larger. The intense vertical motion results in adiabatic cooling and warming, which reduce the rate of
thickness change, and thus decrease thermal advection, and limit the amplification of shortwave, and
eventually cut-off [in the notes, it says the parcel with considerable vertical velocity will exceed the slope
of the potential temperature slope  EAPE can no longer be produced and the flow becomes barocilinically
stable  producing shortwave cut off]
2. The growth of long waves is damped due to the requirement for conservation of absolute vorticity (f +  =
constant). If a long wave amplifies, the flow between the troughs and ridges becomes more meridional.
Northward (or southward) moving air will feel a greater increase (or decrease) in f. However, if the
wavelength is too long then there will not be enough variation in the relative vorticity along the trajectory to
balance the variations in f. To compensate, the flow will adjust itself so that air moving northward veers
(turns anticyclonically) while southbound air backs (curves cyclonically). Thus, the growth is damped until
the wavelength decreases.
11
G) Define isentropic potential vorticity and explain why it is a useful quantity in the study of
atmospheric flow patterns
1.
Isentropic Potential vorticity (IPV) is a conserved quantity in adiabatic, frictionless flow, and is defined
as the product of the absolute vorticity and static stability on an isentropic surface.
1 PVU = 10-6 KKg-1m2s-1
2.
Why it is useful?
its “elegant” – contains all dynamics in a compact formulation
PV is a conserved quantity following the motion of a parcel, therefore can be used as a tracer of air
movement – used to describe the evolution of flow patterns during significant synoptic events such as
rapid cyclogenesis, blocking and retrogression of longwaves
3) PV fields can be inverted to regain velocity and thermodynamic fields. It is derived directly from the
equations of motion and thermodynamic balances, so it is possible to deduce the T, P and wind fields
from the PV distribution if a number of assumptions are made (like QG)
4) Some atmospheric processes may be described in terms of the interaction of PV anomalies with the
background structure of the atmosphere. For example, when a strong upper-level PV anomaly moves
over a low-level baroclinic zone, cyclogenesis usually results. There is no need to invoke secondary
circulations (vertical motions) as drivers of the development. In addition, a superposition principle may
be used to describe the interaction of PV anomalies at different levels in the atmosphere, interactions
which lead to changes in the circulations at these levels.
1)
2)
* Some other points to know:




PV increase rapidly with height in the stratosphere because of high static stability. So it becomes easy
to identify stratosphere air in contrast to troposphere air
The PV value at the tropopause in mid-latitudes is about 2 PVU
In tropics, the tropopause is hard to define using PV (need to just potential temperature)
In mid-latitudes, some  surfaces consist of both tropospheric and stratospheric air
H) Explain the invertibility principle of potential vorticity.
1.
2.
The invertibility principle of potential vorticity states that a knowledge of the spatial distribution of PV
is sufficient to determine the overall structure of the flow
As it is derived directly from the equations of motion and thermodynamic balances, thus it is possible to
deduce the T, p and wind fields from the PV distribution if a number of assumptions are made
OUT
W
IN
C
isotach
12
I) Explain the role of an isentropic potential vorticity anomaly in cyclogenesis.

Using QG theory: an upper level vorticity maxium induces upward motion in the PVA area. Stretching of
the column due to vertical motion can help to spin-up the low-level circulation which is aided by low-level
warm advection and more vertical motion.

Using PV theory:
1. The positive IPV anomaly at upper levels has a strong cyclonic circulation associated with it. A weaker
extension of this circulation extends down to the surface
2. As the anomaly moves over the baroclinic zone, this low level circulation induces a wave in the thermal
field, the wave crest forming a positive temperature anomaly. This positive temperature anomaly is
equivalent to a positive IPV anomaly.
3. This new centre establishes its own cyclonic circulation, the upwards extension of which can eventually
reinforce the flow about the upper centre, and slow down the eastward progression of upper level PV
anomaly. Thus, a process of mutual reinforcement (positive feedback) is established.
4. The circulations induced by both centers can be superimposed to yield the net circulation. Note that the
warm center on surface is slightly to the east of the upper IPV anomaly
This schematic picture shows cyclogenesis associated with the arrival of an upper air IPV anomaly over a low level baroclinic region. On
the left, the upper air cyclonic IPV anomaly, indicated by a solid plus sign and associated with the low tropopause shown, has just
arrived over a region of significant low level baroclinicity. The circulation induced by the anomaly is indicated by solid arrows, and
potential temperature contours are shown on the ground. The low level circulation is shown above the ground for clarity. The advection
by this circulation leads to a warm temperature anomaly somewhat ahead of the upper IPV anomaly as indicated on the right, and
marked with an open plus sign. This warm anomaly induces the cyclonic circulation indicated by the open arrows. If the equatorward
motion at upper levels advects high-PV polar lower-stratospheric air, and the poleward motion advects low-PV subtropical uppertropospheric air, then the action of the upper-level circulation induced by the surface potential temperature anomaly will, in effect,
reinforce the upper air IPV anomaly and slow down its eastward progression.
13
T.O. 6.2.3
A) Describe methods of estimating vertical velocity, including their limitations
1. Kinematic method:
Based on continuity equation
Thus, increasing div. with height  ascent, decreasing div. with height  descent

Problems:

Small error in u and v can result in large error in vertical velocity

Cumulative errors of all lower levels
2. Dynamic methods:
1) QG omega equation:

QG vertical motion is a response to Vg advection which destroys the thermal wind balance.

upward vertical motion  PVA + PTA ; downward vertical motion  NVA + NTA

Limitation: VA and TA can be in opposite signs; 500-mb VA may not be a good indicator of the
differential VA in the 1000-500-mb layer


2)

Q-vector:
Problem: time-consuming to identify the area of convergence of Q vector.
B) Describe situations in which the quasi-geostrophic omega equation is liable to be inaccurate
1.
2.
3.
4.
When the scale is less than synoptic motions such as frontal zone, convection, hurricane etc.
When diabatic heating processes occur (latent heat release; sensible heat)
When strong boundary layer forcing such as friction stress and local terrain effect
Out of mid-latitude
C) List and describe the terms in the full omega equation which are important to consider when
estimating vertical velocity in both the boundary layer and free atmosphere


In boundary layer: Besides differential vorticity advection and thickness advection, frictional stress at the
surface, latent heat release, sensible heat transfer, surface terrain effect are important to consider when
estimating vertical velocity.
In free atmosphere: Besides the differential vorticity advection and the Laplacian of thickness advection,
differential deformation, divergence, and twisting effects, Beta effect, differential vertical advection of
vorticity, latent heat release and sensible heat transfer are important to consider when estimating vertical
velocity.
14
D) Explain the relationship between divergence and vertical velocity


Low level convergence and upper level divergence results in upward motion
Low level divergence and upper-level convergence lead to subsidence.
E) Given upper level and surface charts for idealized synoptic situations, describe the vertical
velocity profile.





Important contributors to vertical motion:
1. Vorticity advection
2. Thermal advection
3. Latent heat release
4. Sensible heat transfer
5. Boundary layer forcing: friction stress and orographic lifting
250mb chart: vorticity advection strong along jet streak, right entrance and left exit divergence, upward motion.
Left entrance and right exit of jet, convergence downward motion
500mb chart: vorticity advection and thickness advection. PVA area in downstream of the trough, div.  ascent;
NVA upstream of the trough, descent. PTA  ascent and NTA descent.
700 or 850mb chart: latent heat release (cloud and precipitation area) and thermal advection.
Surface chart: 1. sensible heating by underlying surface. 2. Low center  convergence, high center
divergence. 3. Surface roughness. 4. Pressure tendency effect as pressure fall is the results of divergence aloft.
F) Use the Q-vector approach to estimate vertical motion
1.
A serious limitation of the traditional QG omega equation is that it involves two terms which tend to oppose
one another, and is difficult to qualitatively determine even whether up or down, and need a simpler and
unambiguous depiction of vertical motion.

2.
It points in a direction perpendicular and to the right of the geostrophic change vector along the x-axis
(with cold air to the left) with a magnitude that is proportional to the amplitude of the vector change of
the geostrophic wind multiplied by the strength of the T gradient.
Advantages of Q-Vector:
Forcing terms can be solved on a single constant-pressure surface (as opposed to the multiple vertical
levels required by the quasi-geostrophic omega equation)
2) No partial cancellation among the forcing terms as often in the traditional formulation
3) No terms are neglected as with the Trenberth approximation
4) The forcing terms are independent of the coordinate system on which they are evaluated
5) Q-vector field (or divergence of Q) may be plotted to indicate the synoptic-scale vertical motion field
and the ageostrophic wind etc
1)
3.
Usefulness of Q-vectors:
Qualitatively and unambiguously identify regions of ascent/descent by the divergence of Q.

15



Indicates the enhancement and dissipation of fronts: when Q-vectors point towards warmer (colder) air
one may immediately recognize frontogenesis (frontolysis)
Q-vector points in the same direction as the lower-level ageostrophic motion (always point to the
ascending region) and in the opposite direction to the upper-troposphere ageostrophic motion
Q-vector provides an elegant explanation of the interdependent relationships between geostrophic wind,
vertical motion, and thermal wind balance:

Geostrophic advections destroy geostrophic balance, or likewise, thermal wind balance

Environment responds to this by generating an ageostrophic flow

This flow adjusts the magnitude of the thermal wind to match the modified strength of the thermal
gradient
Q-vectors for barocilnic wave
Q-vector in Jet, and ageostrophic flow (which is to restore the destroyed geostrophic balance)
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Q-vector in frontogenesis, and ageostrophic flow (which is to restore the destroyed thermal wind balance)
Q-vector in frontolysis
G) Describe Zwack’s diagnostic divergence method for calculating the vertical velocity profile

Instead of calculating vertical velocity at a given level, the divergence is estimated at all levels. Vertical motion
is then calculated through a vertical integration of the equation of continuity, i.e., considering the additive
effects of divergence from the ground up.
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H) Construct qualitative vertical velocity profiles given standard upper and surface charts (see
answer to E)
I) Identify physical processes that can contribute to vertical motion but which are not accounted
for by the quasi-geostrophic omega equation
1.
2.
3.
4.
Latent Heat Release: Convection on satellite imagery, precip. on radar)
Sensible Heat Transfer: SFC temp
Boundary layer forcing (frictional stress, orographic lifting, divergence/convergence, wind barbs etc)
Pressure tendency
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TO 6.2.4
A) Illustrate and explain the relationship between the temperature and wind fields based upon
the geostrophic thermal wind equation

Vg
g ˆ
k  T
Z
fT
Thermal wind law relates the vertical structure of the wind fields to the horizontal temperature
distribution. It states in the presence of a horizontal temperature gradient, the wind speed must increase
with increasing height.
Thermal wind is the vector difference between the geostrophic wind at two different levels in the
vertical, it blows ‘parallel’ to the thickness contours with cold air to the left, the magnitude of thermal
wind is proportional to the thickness gradient.
The reason is: the differences in thickness between two pressure levels are a result of differences in the
mean temperature for a layer. Hence, greater thicknesses in a warm region of the atmosphere
contrasted with lower thicknesses in a cold region of the atmosphere lead to increasingly sloped
pressure surfaces aloft, i.e., increasing horizontal pressure gradients which leads to stronger winds aloft:




So, if there is a zone of strong T gradient such as a frontal surface, there must be a corresponding zone
of strong winds somewhere above that surface. Then if at some other point above these strong winds
the T gradient reverses itself, the winds above will begin to diminish. This is how Jet stream and upper
front created.
Backing - Cold air advection and Veering, Warm air advection.

B) Define a front dynamically in terms of temperature, wind, stability and vorticity





Front is an elongated zone (~ 1000km long; ~100 km wide) of
strong horizontal T gradient (hyperbaroclinic zone)
cyclonic wind shear and vorticity
relatively large static stability
vertical depth to at leas 850mb (for surface fronts)
C) Discuss the applicability of an idealized frontal model to actual fronts, indicating where and
when the model is most successful and how observed fronts depart from the ideal
1. Frontal zone in the Bergon model continuously extends from surface up to upper troposphere, in the real case,
surface fronts and upper fronts can exist independently of one another and they form in different processes.
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2. The classical model of fronts included a model of the precipitation patterns with a broad area of stratiform
precipitation associated with the warm front, and the narrow line of convective precipitation along the cold
front. In reality, the weather relative to the cold front varied from case to case. This prompted Bergeron to
introduce “anafront” and “katafront”. Anafronts resemble the original polar front model. Cloud forms along
and behind the surface front, and heavier convective precipitation is confined to a narrow band along the front.
The katafront has warm air flowing down the frontal surface, and usually develops in conjunction with a
mature system or a rapidly developing synoptic disturbance. In this case, mid-level cloud and its associated
precipitation occur ahead of the surface frontal position.
3. Idealized model of front is continuous, but in reality, it could be incontinuous.
4. Idealized model thought jet stream was near the tropopause, but in reality, it could be much lower than that.
D) Discuss the formation and evolution of a surface front including the processes of
frontogenesis and frontlysis.
1.
2.
3.
4.
At the first stage, the surface stationary front usually forms along the axis of dilatation in a horizontal
deformation zone where horizontal T gradient and wind shear tend to be increased by the stretching of the
flow. If convergence is presented along with deformation, see figure bellow, frontogenesis is greatly
enhanced. Near the surface, convergence is created by friction with air flow inward to the low
With the support from upper level and the surface cyclone development, the frontal zone fractures in the
vicinity of the low center with cold front pushing south-ward and warm front moving northward
The cold front is more active and moves faster than the warm front, squeezing the warm air off the ground,
and forming a trowal with cloud and precipitation associated.
With combined effects from adiabatic cooling of warm air and heating of cold air, diabatic processes, and
turbulence mixing, the warm air and cold air eventually mix together and diffuse, the temperature contrast
no longer exit, Trowal disappear.
E) Discuss the contribution of the following processes to surface frontogenesis and frontlysis
1.
2.
3.
4.
Geostrophic deformation is the dominant processes leading to frontogenesis, which increases horiz. T
gradient and wind shear. A front will form along the axis of dilatation. It would be frontolytic if the
isotherms were oriented to lie within 45 degrees of the axis of contraction.
Divergence: frontogenesis is enhanced if convergence is present along with deformation, which causes
packing of isotherms, frontogenesis; divergence  frontolysis
Surface friction increases the possibility of frontogenesis. When high values of vorticity are maintained in
frontal zone, the convergence is greatly enhanced by the effects of surface friction on the surface wind field.
The added convergence hastens frontogenesis. If without the convergence of frontal zone, friction would
dissipate vorticity and cause frontlysis
Diabatic processes: sensible heating (radiative heating/cooling, conduction from the surface) and latent
heat release are very important to low level thermal structure. If diabatic processes causes greater thermal
contrast between two airmasses, then contribute to frontogenesis, otherwise, causes frontolysis. It may mask
presence of surface or low-level front
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F) Explain the formation and structure of upper tropospheric fronts
1.
2.
3.
4.
The formation of upper fronts was coupled to tropopause folding where intrusions of air from stratosphere
can be found, in some cases, in the lower troposphere
Vertical motions play an important role in the formation of upper level frontogenesis, the transverse
circulation (associated with tropopause folding) with subsidence on both sides of the upper front, but
ascent ahead of the upper front
In order for the thermal contrast to develop, the orientation of the axis of deformation must be such that
adiabatic warming (due to subsidence) is maximized on the warm side of the frontal zone
Because of point 2 (mentioned above), it is appropriate to analyze the upper front at the back edge of the
cloud and precipitation area.
G) Define and describe the jet-stream and define the jet axis and core
1.
2.
3.
The jet stream refers to

a narrow current of strong winds concentrated along a quasi-horizontal axis (jet axis) in the upper
troposphere

Typically, a jet stream is thousands of kilometers long, a few hundred kilometers wide and a few
kilometers in depth

It has one or more velocity maxima, the strongest vertical and horizontal wind shears are in the frontal
mixing zone
The core is the strongest winds in the stream, is located at the level where the horizontal temperature
gradient vanishes, and in the warm air below the tropopause.
Upper tropospheric fronts and jet streams are so closely linked that they are often considered two ways of
talking about the same thing. The latter emphasizes the winds while the former refers to the T or density
field.
H) Based on the thermal wind relationship, explain the position and intensity of the jet with
relation to the front and the tropopause.


Throughout the troposphere, air is warmer near the equator, colder at the poles, and there is a frontal zone at
mid-latitudes where T rapidly decreases toward the north. This sharp horizontal T gradient along the frontal
zone causes geostrophic wind increasing with height and the greatest wind aloft in the middle latitudes based
on the thermal wind relationship; The Jet core must be located in the warm side of the front zone, otherwise
the thermal wind law doesn’t help explain the high speed of upper level wind (the strong T gradient zone
must be under the Jet in vertical)
However, the tropopause is lower near the poles than near the equator, thus, temperature begins increasing
with height at a lower altitude near the poles than near the equator. This causes a T reversal in the
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stratosphere, where the air is cold near the equator and warmer over the poles, thus, above the tropopause, the
wind becomes weaken because of the reversed horizontal T gradient. Thus jet core is located below the
tropopause.
J) Describe and explain the secondary circulations about jet maxima.


Secondary circulation: Divergence (ascent) in the right entrance and left exit, convergence (descent) in the
left-entrance and right exit, therefore, there is a thermally (warm air rising, and cold air descending) direct
vertical circulation in the entrance region, and a thermally indirect circulation in the exit region.
Explanation:
1. Ageostrophic wind:

As an air parcel enters a jet streak, its geostrophic wind speed increase. But the Coriolis force needs
time to adjust, and can not balance the increased pressure gradient, therefore, ageostrophic wind
blows to the left towards lower height

As the air parcel exits the jet streak, its geostrophic wind speed decreases, coriolis force is bigger
than pressure gradient force, and an ageostrophic wind blows toward greater height
2. From energy point of view, air gains kinetic energy and therefore must lose potential energy. The loss of
potential energy means the air parcel must move to lower geopotential heights
3. Vorticity advection: PVA in the left exit and right entrance at jet-streak, causing divergence; NVA in the
left entrance and right exit, causing convergence.
4. Q-vector
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K) Explain the propagation of jet maxima in relation to the secondary circulation.
As ahead of the jet maximum, there will be subsidence to the right of the jet stream, and ascent to the left. According
to the thermal wind law, this means that there will be subsidence in the warm air and ascent in the cold air ahead of
the jet. So, in this area, the warm air will warm adiabatically and the cold air will cool, increasing the thermal
contrast, meaning that this circulation is frontogenetic. To the rear of the jet maximum, the opposite circulation is
taking place, meaning that this area is frontolytic. Hence by the thermal wind law the maximum winds aloft will
move downstream where the maximum temperature gradient is being formed. This is why you will see jet maxima
always moving downstream in the 250mb flow.
L) Explain the life cycle of a mid-latitude cyclone and its relationship to the polar front as
described by the Bergen school.
According to Bergen model, an extratropical cyclone begins as a small perturbation superimposed on a pre-existing
front – the polar front. This creates a cyclonic circulation with a warm front developing east of the cyclone and a cold
front to the west. These fronts progress with the cyclonic circulation and the cold front eventually catches up to the
warm front, forcing all of the warm air aloft near the centre of the cyclone and leaving a vortex to weaken in the cold
air.
M) Describe some of the modifications that have been proposed to the Bergen model, including
split fronts, trowals and cold fronts aloft.
1. A “trowal” is the trough of warm air aloft, and is analyzed at the back edge of middle cloud and
precipitation south of the low center

Occlusion: The process of the cold front catching up to the warm front is called an occlusion. The
occlusion is a surface feature.

Warm occlusion develops when the cold air wrapping around the low center is modified so that it is
warmer when it arrives to meet the cold air that is unmodified

Cold occlusion develops if the cold air is cooled as it wraps around the low
Warm occlusion
Cold occlusion
2. Upper cold front (UCF) or Cold front aloft (CFA):

A warm front at the surface

a cold front aloft (CFA), which produces the main precipitation at the surface
23

a surface trough, some 200-300 km behind the leading edge of the CFA, which may or may not take
the form of a cold front
The cold front aloft (CFA) model (from Hobbs, et al 1990)
3. Split front model: a cold front aloft, a surface cold front in the trough
The split front model
4.
5.
6.
7.
Three airmass cyclone model
Conveyor belt model
marine cyclone model (mentioned in next page)
rapidly deepening cyclones over land (many similarities the horizontal and vertical structures to the
marine cyclone model; One of the main differences was the absence of the secluded pool of warm air at the
surface near the centre of the cyclone in its later stages)
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N) Explain the life cycle and potential applications of the marine cyclone model
1. The incipient cyclone forms along a broad, continuous baroclinic zone.
2. The previously continuous front “fractures” near the centre of the intensifying cyclone, leaving a relatively
barotropic area near the low centre. At the same time the frontal gradients intensify along the warm and
cold fronts.
3. The cold front propagates eastward perpendicular to the warm front. This stage of cyclogenesis is termed
the “T-bone”, which is what the frontal structure resembles. At this point the warm front is “bent-back”
north of the low centre.
4. The bent-back warm front encircles the low centre, forming a relatively warm core “seclusion” about the
low centre. It should be noted that the warm air near the low centre did not originate in the warm sector of
the low. The seclusion near the centre of the cold low develops from the manner in which the baroclinic
zone wraps around the low.
* Main drawback: it may apply to only one specific area of the world, so that it cannot be universally applied to
cyclones. It is yet to be shown conclusively that this life cycle occurs in rapidly deepening cyclones over land
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