When advection destroys balance vertical circulations arise
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When advection destroys balance, vertical circulations arise. ppt started from one by James T. Moore Saint Louis University Cooperative Institute for Precipitation Systems. Brian Mapes. COMET-MSC Winter Weather Course 29 Nov. - 10 Dec. 2004. Quasi-Geostrophic Theory.

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When advection destroys balance vertical circulations arise

When advection destroys balance, vertical circulations arise

ppt started from one by

James T. Moore

Saint Louis University

Cooperative Institute for Precipitation Systems

Brian Mapes

COMET-MSC Winter Weather Course

29 Nov. - 10 Dec. 2004


Quasi geostrophic theory

Quasi-Geostrophic Theory

  • It provides a framework to understand the evolution of balanced three-dimensional velocity fields.

  • It reveals how the dual requirements of hydrostatic and geostrophic balance (encapsulated as thermal wind balance) constrain atmospheric motions.

  • It helps us to understand how the balanced, geostrophic mass and momentum fields interact on the synoptic scale to create vertical circulations which result in sensible weather.


Stable balanced dynamics

Stable balanced dynamics

  • Deviations from balance lead to force imbalances that drive ageostrophic and vertical motions which adjust the state back toward balance.

  • Consider hydrostatic, geostrophic as simplest case of balances.

  • Houze chapter 11 - use Boussinesq, hydrostatic equation set as we did for gravity waves.

  • Introduce pseudoheight

  • Assume wind is mostly geostrophic ug, vg

    • Note: f-plane approximation means Vg =0


Balance in atmospheric dynamics

Balance in atmospheric dynamics

  • The vertical equation of motion: imbalance between the 2 terms on the RHS results in small vertical motions that restore balance - unless the state is gravitationally unstable

  • The horizontal equation of motion: imbalance between the major terms on the RHS leads to small ageostrophic motions that restore balance - unless the state is inertially unstable

  • Between lies symmetric instability. Like gravitional instability, it has moist (potential, conditional) cousins. For now, STABLE CASE


When advection destroys balance vertical circulations arise

Old school: Quasi-Geostrophic Omega Equation

(vorticity-oriented form)

A B C

Term A: three-dimensional Laplacian of omega

Term B: vertical variation of the geostrophic advection of the absolute geostrophic vorticity

Term C: Laplacian of the geostrophic advection of thickness


When advection destroys balance vertical circulations arise

  • Problems with the Traditional Form of Q-G Diagnostic Omega Equation

  • The two forcing functions are NOT independent of each other

  • The two forcing functions often oppose one another (e.g., PVA and cold air advection – who wins?)

  • You need more than one level of information to estimate differential geostrophic vorticity advection

  • You cannot estimate the Laplacian of the geostrophic thickness advection by eye!

  • The forcing functions depend upon the reference frame within which they are measured (i.e., the forcing functions are NOT Galilean invariant)


When advection destroys balance vertical circulations arise

PV view of how maintenance of balance requires vertical motions


When advection destroys balance vertical circulations arise

warm

Thermal wind balance prevails: There is a Z trough (trof) for geostrophic balance, with a cold core beneath it, supporting it hypsometrically (in hydrostatic balance).

cyclonic z

(Trof)

COOL

CORE


When advection destroys balance vertical circulations arise

Unshearedadvection of T, u, v, vort, PV:

no problem, whole structure moves

warm

cyclonic

(Trof)

COOL

CORE


Sheared advection breaks thermal wind balance

Sheared advection breaks thermal wind balance

warm

cyclonic z

(Trof)

COOL

CORE


Sheared advection breaks thermal wind balance1

Sheared advection breaks thermal wind balance

Coriolis forces

COOL

CORE

Z Trof

(hypsometric)


Sheared advection breaks thermal wind balance2

Sheared advection breaks thermal wind balance

imbalanced force = acceleration

COOL

CORE

Z Trof

(hypsometric)


When advection destroys balance vertical circulations arise

The PV view of balanced circulation:

(Rob Rogers’s fig)

Potential temperature and potential vorticity cross sections

Long-lived Great Plains MCV

Hurricane Andrew after landfall


When advection destroys balance vertical circulations arise

Q-vector Form of the Q-G Diagnostic Omega Equation

Alternate approach developed by Hoskins et al. (1978, Q. J.) – manipulated the equations so forcing is 1 term, not 2:


When advection destroys balance vertical circulations arise

Q-vector Form of the Q-G Diagnostic Omega Equation

Treat Laplacian as a “sign flip” Then,

If -2•Q > 0 (convergence of Q)then w < 0 (upward vertical motion)

If -2•Q < 0 (divergence of Q)then w > 0 (downward vertical motion)

The Q vector points along the ageostrophic wind in the lower branch of the secondary circulation

Q vectors point toward the rising motion and are proportional to the strength of the horizontal ageostrophic wind


When advection destroys balance vertical circulations arise

  • Advantages of Using Q Vectors

  • You only need one isobaric level to compute the total forcing (although layers are probably better to use)

  • Only one forcing term, so no cancellation between terms

  • Plotting Q vectors indicates where the forcing for vertical motion is located and they are a good approximation for the ageostrophic wind

  • The forcing function is not dependent on the reference frame (I.e., it is Galilean invariant

  • Plotting Q vectors and isentropes can indicate regions of Q-G frontogenesis/frontolysis

  • No term is neglected (as in the Trenberth method which neglects the deformation term)


When advection destroys balance vertical circulations arise

Interpreting Q Vectors

Expanding Q and assuming adiabatic conditions yields the following expression for Q:

Setting aside the coefficients,


When advection destroys balance vertical circulations arise

Interpretation of Qx

Geostrophic stretching deformation weakens

Geostrophic shearing deformation turns

cold

vg

ug

cold

warm

to



warm



cold

to+t



cold

warm

warm




When advection destroys balance vertical circulations arise

Interpretation of Qy

Geostrophic shearing deformation turns

Geostrophic stretching deformation strengthens

cold

vg

ug

cold

warm

to



warm



cold

to+t

cold

warm



warm




When advection destroys balance vertical circulations arise

An Alternative form of Q in “natural” coordinates

Keyser et al. (1992, MWR) derived a form of the Q vector in “natural” coordinates where one component is oriented parallel to isotherms and another component is oriented normal to the isotherms.

In this form one component (Qs) has the two shearing deformation terms, expressing rotation of isotherms, that normally show up in Qx and Qy . Meanwhile, the other component (Qn) has the two stretching deformation terms expressing the contraction or expansion of isotherms.

We will see that this novel form of the Q vector has distinct advantages, in terms of interpretation.


When advection destroys balance vertical circulations arise

Defining the Orientation of Qs and Qn with Respect to 

Qn

Q

cold

-1

Qs

+1

+2

n

warm



s

Qs is the component of Q associated with rotating the thermal gradient.

Qn is the component of Q associated with changing the magnitude of the thermal gradient.

Martin (1999, MWR)

Keyser et al. (1992, MWR)


When advection destroys balance vertical circulations arise

DefiningQn and Interpreting What It Means


When advection destroys balance vertical circulations arise

DefiningQn and Interpreting What It Means (cont.)

+1

  • Couplets of div Qn:

  • Tend to line up across the isotherms

  • Show the ageostrophic response to the geostrophically-forced packing/unpacking of the isotherms

  • Often exhibit narrow banded structures typical of the “frontal” scale

  • Give an indication of how “active” a front might be

+2

Qn



vg/y < 0; therefore Qn <0;

Qn points from cold to warm air; confluence (diffluence) in wind field implies frontogenesis (frontolysis)


When advection destroys balance vertical circulations arise

Interpreting Q vectors: Qn

Advection by geostrophic stretching deformation acts to change the magnitude of the thermal gradient vector, .

But the same geostrophic advection changes the wind shear in the direction OPPOSITE to that needed to restore balance. This is why the forcing for ageostrophic secondary circ is -2x(.Q)!

Low level wind: pure geostrophic deformation (noting .Vg = 0), here acting to weaken dT/dx.

cold

warm

Upper level wind: addthermal windtolow levelwind. v component is positive and decreases to north, so advection is acting to increase upper-level v.

Thermal wind


When advection destroys balance vertical circulations arise

DefiningQs and Interpreting What It Means


When advection destroys balance vertical circulations arise

Thermal wind

Upper wind

DefiningQs and Interpreting What It Means (cont.)

  • Couplets of div Qs:

  • Tend to line up along the isotherms

  • Show the ageostrophic response to the geostrophically-forced turning of the isotherms

  • Tend to be oriented upstream and downstream of troughs

  • Are associated with the synoptic wave scale of ascent and descent

+1

+2

Qs

Qs



vg/x > 0; therefore Qs > 0.

Qs has cold air is to its left, causes cyclonic rotation of the vector . Thermal wind balance thus requires v to increase aloft, but geostrophic advection acts to decrease v aloft.


When advection destroys balance vertical circulations arise

Estimating Q vectors

Sanders and Hoskins (1990, WAF) derived a form of the Q vector which could be used when looking at weather maps to qualitatively estimate its direction and magnitude:

Where the x axis is defined to be along the isotherms (with cold air to the left) and y is normal to x and to the left.

Thus, Q is large when the temperature gradient is strong and when the geostrophic shear along the isotherms is strong.

To estimate the direction of Q just use vector subtraction to compute the derivative of Vg along the isotherms, then rotate the vector by 90° in the clockwise direction. Example:


When advection destroys balance vertical circulations arise

A

B

-

Col Region

B

A

=

Q vectors

90 deg

Q

A

B

B

A

-

Jet Entrance Region

=

90 deg

This is mainly the cross-front, n component Qn

Q

Holton (1992)


When advection destroys balance vertical circulations arise

Q vectors in a setting where warm air rises

cold

Qn vectors

warm

Direct Thermal Circulation

Confluent Flow

Holton, 1992


When advection destroys balance vertical circulations arise

Q vectors in a setting where COLD air rises

Jet Exit Region

Q

Vageo

Thermally Indirect Circulation

Vageo

South

North


When advection destroys balance vertical circulations arise

Idealized pattern of sea-level isobars (solid) and isotherms (dashed) for a train of cyclones and anticyclones. Heavy bold arrows are Q vectors. This is mostly the along-front or s component Qs.

Holton (1992)


When advection destroys balance vertical circulations arise

  • Semi-geostrophic extension to QG theory

  • Allow advection of b and v by an ageostrophic horizontal wind uain cross-front (x) direction only(following Houze section 11.2.2).

  • An elegant trick: define

  • Using the fact that Dvg/Dt = -fua, the total derivative in X space

  • becomes analogous to Dg/Dt:


When advection destroys balance vertical circulations arise

  • Semi-geostrophic extension to QG theory (cont)

  • More elegant trickery:

    • Defining the geostrophic PV (Houze 11.50)

    • One can get the streamfunction equation (11.60)

    • Comparing the QG case (11.20)

  • PV plays the role of a static stability in this system.


Another form from notes of r johnson csu

Another form (from notes of R. Johnson, CSU)

is met (translation: PV must be positive, so that the system is symmetrically stable)


Frontogenesis definition

Frontogenesis (definition)

(S. Petterssen 1936)

  • The 2-D scalar frontogenesis function (F ):

  • F > 0 frontogenesis, F < 0 frontolysis

  • F: generalization of the quasi-geostrophic version, the Q-vector

    • Can also include diabatic heating gradients, etc.

g

Q


Frontogenesis and symmetric instability

Frontogenesis and Symmetric Instability


When advection destroys balance vertical circulations arise

Symmetric instabilities, contributing to banded precipitation, often north and east of midlatitude cyclones


Mesoscale instabilities and processes which can result in enhanced precipitation

Mesoscale Instabilities and Processes Which Can Result in Enhanced Precipitation

  • Conditional Instability

  • Convective Instability

  • Inertial Instability

  • Potential Symmetric Instability

  • Conditional Symmetric Instability

  • Weak Symmetric Stability

  • Convective-Symmetric Instability

  • Frontogenesis


Balance in atmospheric dynamics1

Balance in atmospheric dynamics

  • The vertical equation of motion: imbalance between the 2 terms on the RHS results in small vertical motions that restore balance - unless the state is gravitationally unstable

  • The horizontal equation of motion: imbalance between the major terms on the RHS leads to small ageostrophic motions that restore balance - unless the state is inertially unstable

  • Between lies symmetric instability. Like gravitional instability, it has moist (potential, conditional) cousins. For now, STABLE CASE


Schultz et al 1999 mwr

Schultz et al. 1999 MWR


Instabilities nomenclature schultz et al mwr 1999 the intricacies of instabilities

Instabilities: nomenclatureSchultz et al. MWR 1999 “The intricacies of instabilities”


When advection destroys balance vertical circulations arise

Conditional Symmetric Instability: Cross section of esand Mg taken normal to the 850-300 mb thickness contours

s

es-1

es

es+ 1

Mg +1

Symm.

unstable

Note: isentropes of es

are sloped more vertical

than lines of absolute

geostropic momentum,

Mg.

Mg

Vert.

stable

Horiz.

stable

Mg -1


When advection destroys balance vertical circulations arise

Conditional Symmetric Instability in the Presence of Synoptic Scale Lift – Slantwise Ascent and Descent

Multiple Bands with Slantwise Ascent


Frontogenesis and varying symmetric stability

Frontogenesis and varying Symmetric Stability

  • Emanuel (1985, JAS) has shown that in the presence of weak symmetric stability (simulating condensation) in the rising branch, the ageostrophic circulations in response to frontogenesis are changed.

  • The upward branch becomes contracted and becomes stronger. The strong updraft is located ahead of the region of maximum geostrophic frontogenetical forcing.

  • The distance between the front and the updraft is typically on the order of 50-200 km

  • On the cold side of the frontogenetical forcing stability is greater and and the downward motion is broader and weaker than the updraft.


When advection destroys balance vertical circulations arise

Frontal secondary circulation - constant stability

Emanuel (1985, JAS)

Frontal secondary circ - with condensation on ascent


When advection destroys balance vertical circulations arise

Schematic of Convective-Symmetric Instability Circulation

Blanchard, Cotton, and Brown, 1998 (MWR)


When advection destroys balance vertical circulations arise

Convective-Symmetric Instability

Multiple Erect Towers with Slantwise Descent


When advection destroys balance vertical circulations arise

Sanders and Bosart, 1985: Mesoscale Structure in the Megalopolitan Snowstorm of 11-12 February 1983. J. Atmos. Sci.,42, 1050-1061.


Frontogenesis and symmetric instability1

Frontogenesis and Symmetric Instability


When advection destroys balance vertical circulations arise

A Conceptual Model: Plan View of Key Processes

NW

SE

NW-SE cross-section shown on next slide.

Often found in the vicinity of an extratropical cyclone warm front, ahead of a long-wave trough in a region of strong, moist, mid-tropospheric southwesterly flow


When advection destroys balance vertical circulations arise

A Conceptual Model: Cross-Sectional View of Key Processes

Dry Air

CSI

Convectively Unstable

es

Heavy snow area

Arrows = Ascent zone

F = Frontogenesis zone

Shaded area = CSI

CSI may be a precursor to elevated CI, as the vertical circulation associated with CSI may overturn e surfaces with time creating convectively unstable zones aloft


Nolan moore conceptual model

Nolan-Moore Conceptual Model

  • Many heavy precipitation events display different types of mesoscale instabilities including:

    • Convective Instability (CI; edecreasing with height)

    • Conditional Symmetric Instability (CSI; lines of esare more vertical than lines of constant absolute geostrophic momentum or Mg)

    • Weak Symmetric Stability (WSS; lines of esare nearly parallel to lines of constant absolute geostrophic momentum or Mg)


When advection destroys balance vertical circulations arise

Spectrum of Mesoscale Instabilities


Nolan moore conceptual model1

Nolan-Moore Conceptual Model

  • These mesoscale instabilities tend to develop from north to south in the presence of strong uni-directional wind shear (typically from the SW)

  • CI tends to be in the warmer air to the south of the cyclone while CSI and WSS tend to develop further north in the presence of a cold, stable boundary layer.

  • It is not unusual to see CI move north and become elevated, producing thundersnow.


Nolan moore conceptual model2

Nolan-Moore Conceptual Model

  • CSI may be a precursor to elevated CI, as the vertical circulation associated with CSI may overturn esurfaces with time creating convectively unstable zones aloft.

  • We believe that most thundersnow events are associated with elevated convective instability (as opposed to CSI).

  • CSI can generate vertical motions on the order of 1-3 m s-1 while elevated CI can generate vertical motions on the order of 10 m s-1 which are more likely to create charge separation and lightning.


Parting thoughts on banded precipitation jim moore

Parting Thoughts on Banded Precipitation (Jim Moore)

  • Numerical experiments suggest that weak positive symmetric stability (WSS) in the warm air in the presence of frontogenesis leads to a single band of ascent that narrows as the symmetric stability approaches neutrality.

  • Also, if the forcing becomes horizontally widespread and EPV < 0, multiple bands become embedded within the large scale circulation; as the EPV decreases the multiple bands become more intense and more widely spaced.

  • However, more research needs to be done to better understand how bands form in the presence of frontogenesis and CSI.


When advection destroys balance vertical circulations arise

Figure from Nicosia and Grumm(1999,WAF).Potential symmetric instability occurs where the mid-level dry tongue jet overlays the low-level easterly jet (or cold conveyor belt), north of the surface low. In this area dry air at mid-levels overruns moisture-laden low-level easterly flow, thereby steepening the slope of the e surfaces.


Nicosia and grumm 1999 waf conceptual model for csi

Nicosia and Grumm (1999, WAF) Conceptual Model for CSI

  • Also….since the vertical wind shear is increasing with time the Mg surfaces become more horizontal (become flatter). Thus, a region of PSI/CSI develops where the surfaces of e or esare more vertical than the Mg surfaces.

  • In this way frontogenesis and the develop- ment of PSI/ CSI are linked.


Frontogenesis definition1

Frontogenesis (definition)

(S. Petterssen 1936)

  • The 2-D scalar frontogenesis function (F ):

  • F > 0 frontogenesis, F < 0 frontolysis

  • F: generalization of the quasi-geostrophic version, the Q-vector

    • Can also include diabatic heating gradients, etc.

g

Q


Vector frontogenesis function

Vector Frontogenesis Function

(Keyser et al. 1988, 1992)

  • Change in magnitude

  • Corresponds to vertical motion on the frontal scale (mesoscale bands), as cross-frontal F vector points along low-level Va, toward upward motion.

  • Change in direction (rotation)

  • Corresponds to vertical motion on the scale of the baroclinic wave itself: rotation of T gradient by a cyclone’s winds causes along-front F vectors to converge on east side of low pressure


When advection destroys balance vertical circulations arise

Three-Dimensional Frontogenesis Equation

1

2

4

3

5

6

7

8

9

10

11

12

Terms 1, 5, 9: Diabatic Terms

Terms 2, 3, 6, 7: Horizontal Deformation Terms

Terms 10 and 11: Vertical Deformation Terms

Terms 4 and 8: Tilting Terms

Term 12: Vertical Divergence Terms

Bluestein (Synoptic-Dynamic Met. In Mid-Latitudes, vol. II, 1993)


When advection destroys balance vertical circulations arise

Assumptions to Simplify the Three-Dimensional Frontogenesis Equation

y’

+ 1

x’

+ 2

  • y’ axis is set normal to the frontal zone, with y’ increasing towards the cold air (note: y’ might not always be normal to the isentropes)

  • x’ axis is parallel to the frontal zone

  • Neglect vertical and horizontal diffusion effects


When advection destroys balance vertical circulations arise

Simplified Form of the Frontogenesis Equation

A B C D

Term A: Shear term

Term B: Confluence term

Term C: Tilting term

Term D: Diabatic Heating/Cooling term


When advection destroys balance vertical circulations arise

Frontogenesis: Shear Term

Shearing Advection changes orientation of isotherms

Carlson, 1991 Mid-Latitude Weather Systems


When advection destroys balance vertical circulations arise

Frontogenesis: Confluence Term

Cold advection to the north

Warm advection to the south

Carlson, 1991 Mid-Latitude Weather Systems


When advection destroys balance vertical circulations arise

Shear and Confluence Terms near Cold and Warm Fronts

Shear and confluence

terms oppose one another near warm fronts

Shear and confluence

terms tend to work together

near cold fronts

Carlson (Mid-latitude Weather Systems, 1991)


When advection destroys balance vertical circulations arise

Frontogenesis: Tilting Term

Adiabatic cooling to north and warming to south increases horizontal thermal gradient

Carlson, 1991 Mid-Latitude Weather Systems


When advection destroys balance vertical circulations arise

Frontogenesis: Diabatic Heating/CoolingTerm

frontogenesis

T constant

T increases

frontolysis

T increases

T constant

Carlson, 1991 Mid-Latitude Weather Systems


When advection destroys balance vertical circulations arise

Frontogenesis/Frontolysis with Deformation with No Diabatic Effects or Tilting Effects

where:

and

= angle between the isentropes and the axis of dilatation

Petterssen (1968)


When advection destroys balance vertical circulations arise

Kinematic Components of the Wind

Vorticity

Translation

Divergence

Deformation


When advection destroys balance vertical circulations arise

Stretching and Shearing Deformation Patterns

Stretching

Deformation

Shearing

Deformation


When advection destroys balance vertical circulations arise

Stretching Deformation Patterns

Stretching along the flow

Translational component of wind removed

Stretching normal to the flow

Translational component of wind removed

Bluestein (1992, Synoptic-Dynamic Met)


When advection destroys balance vertical circulations arise

Shearing Deformation Patterns

Stretching in a direction 45° to the left of the flow

Translational component of wind removed

Stretching in a direction 45° to the right of the flow

Translational component of wind removed

Bluestein (1992, Synoptic-Dynamic Met)


When advection destroys balance vertical circulations arise

 < 45°

Frontogenesis

Axis of dilatation

 > 45°

Frontolysis

Axis of dilatation

Petterssen (Weather Analysis and Forecasting, vol. 1, 1956)


When advection destroys balance vertical circulations arise

Pure Deformation Wind Field Acting on a Thermal Gradient

Isotherms are rotated and brought closer together

Keyser et al. (MWR, 1988)


When advection destroys balance vertical circulations arise

  • Deficiencies of Kinematic Frontogenesis

  • Fronts can double their intensity in a matter of several hours; kinematic frontogenesis suggests that it takes on the order of a day.

  • Kinematic frontogenesis does not account for changes in the divergence of momentum fields; values of divergence and vorticity in frontal zones are on scales <= 100 km, suggesting highly ageostrophic flow.

  • Kinematic frontogenesis fails since temperature is treated as a passive scalar. As the thermal gradient changes the thermal wind balance is upset, therefore there is a continual readjustment of the winds in the vertical in an attempt to re-establish geostrophic balance.

Carlson (Mid-Latitude Weather Systems, 1991)


Frontogenetical circulation

Frontogenetical Circulation

  • As the thermal gradient strengthens the geostrophic wind aloft and below must respond to maintain balance with the thermal wind.

  • Winds aloft increase and “cut” to the north while winds below decrease and “cut” to the south, thereby creating regions of div/con.

  • By mass continuity upward motion develops to the south and downward motion to the north – a direct thermal circulation.

  • This direct thermal circulation acts to weaken the frontal zone with time and works against the original geostrophic frontogenesis.


When advection destroys balance vertical circulations arise

Ageostrophic Adjustments in Response to Frontogenetical Forcing

West

East

West

East


When advection destroys balance vertical circulations arise

Frontogenetical Circulation

North

South

COLD

WARM

Thermally Direct Circulation

Carlson (Mid-latitude Weather Systems, 1991)

Strength and Depth of the vertical circulation is modulated by static stability


When advection destroys balance vertical circulations arise

  • Sawyer-Eliassen Description of the Frontogenetic Circulation

  • Includes advections by the ageostrophic component of the wind normal to the frontal zone or jet streak.

  • The ageostrophic and vertical components of the wind are viewed as nearly instantaneous responses to the geostrophic advection of temperature and geostrophic deformation near the frontal zone.

  • The cross-frontal (transverse) ageostrophic component of the tranverse/vertical circulations is significant and can become as large in magnitude as the geostrophic wind velocity.

  • Thus, divergence/convergence and vorticity production in the vicinity of the front take place more rapidly than predicted by purely kinematic frontogenesis.

Carlson (Mid-latitude Weather Systems,1991)


When advection destroys balance vertical circulations arise

  • Frontogenetical Circulation Factors

  • According to the Sawyer-Eliassen equations (see Carlson, Mid-Latitude Weather Systems, 1991):

  • The major and minor axes of the elliptical circulation are determined by the relative magnitudes of the static stability and the absolute geostrophic vorticity; the vertical slope is a function of the baroclinicity.

  • High static stability compresses and weakens the circulation cells.

  • If the absolute geostrophic vorticity is small (weak inertial stability) in the presence of high static stability the circulation ellipses are oriented horizontally.

  • If the absolute geostrophic vorticity is large (strong inertial stability) in the presence of small static stability the circulation cells are oriented vertically.


When advection destroys balance vertical circulations arise

  • High static stability and low inertial stability

Result is a shallow but broad circulation.

With high static stability, a little vertical motion results in large change in temperature.

With low inertial stability, takes longer for Coriolis force to balance the pressure gradient force.

Greg Mann, 2004


When advection destroys balance vertical circulations arise

  • Low static stability and high inertial stability

With low static stability, need large vertical motion to change the temperature.

With high inertial stability, Coriolis force quickly balances the pressure gradient force.

Greg Mann, 2004


Role of symmetric stability

Role of symmetric stability

  • Symmetric stability plays a large role in determining the strength and width of the ageostrophic frontal circulation

    • Small symmetric stability

      • Intense and narrow updraft

    • Large symmetric stability

      • Broad and weak updraft.

Greg Mann, 2004


When advection destroys balance vertical circulations arise

Defining Fs and Fn Vectors from the Frontogenesis Function

Keyser et al. (1988, MWR)


When advection destroys balance vertical circulations arise

Defining Fs and Fn Vectors from the Frontogenesis Function

Keyser et al. (1988, MWR) and Augustine and Caracena (1994, WAF)


When advection destroys balance vertical circulations arise

  • Interpreting F Vectors

  • The component of F normal to the isentropes (Fn) is the frontogenetic component; it is equivalent but opposite in sign to the Petterssen frontogenesis function. When F is directed from cold to warm (Fn < 0), the local forcing is frontogenetic, i.e., the large scale is acting to fortify the frontal boundary by strengthening the horizontal potential temperature gradient and increasing the slope of the isentropes.

  • Conversely, when F is directed from warm to cold (Fn > 0), the forcing is acting in a frontolytic fashion.

  • The component of F parallel to the isentropes (Fs) quantifies how the forcing acts to rotate the potential temperature gradient.

  • The F vector is equivalent to the Q vector only when the horizontal wind is geostrophic; thus F is less restrictive. The divergence of F is a only a good approximation of the Q-G forcing for vertical motion when the wind is in approximate geostrophic balance.

  • However, F vector convergence does NOT necessarily imply upward vertical motion.


When advection destroys balance vertical circulations arise

Application of Frontogenetical Vectors for MCS Formation

Synoptic setting favorable for large MCS development.

Dashed lines are isentropes and arrows are F vectors, at 850 hPa. Red arrow indicates the low-level jet.

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Augustine and Caracena (1994, WAF)


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