advanced synopticm. d. eastin qg analysis: upper-level systems will this upper-level trough...

Advanced Synoptic M. D. Eastin

QG Analysis: Upper-Level Systems

Will this upper-level trough intensify or weaken?

Where will the trough move?


QG Analysis

QG Theory

• Basic Idea• Approximations and Validity• QG Equations / Reference

QG Analysis

• Basic Idea• Estimating Vertical Motion

• QG Omega Equation: Basic Form• QG Omega Equation: Relation to Jet Streaks• QG Omega Equation: Q-vector Form

• Estimating System Evolution• QG Height Tendency Equation

• Diabatic and Orographic Processes• Evolution of Low-level Systems• Evolution of Upper-level Systems


Goal: We want to use QG analysis to diagnose and “predict” the formation,evolution, and motion of upper-level troughs and ridges

Which QG Equation?

• We could use the QG omega equation

• Would require additional steps to convert vertical motions to structure change• No prediction → diagnostic equation → we would still need more information!

• We can apply the QG height-tendency equation

• Ideal for evaluating structural change above the surface• Prediction of future structure → exactly what we want!


VerticalMotion

Differential ThermalAdvection

VorticityAdvection

DiabaticForcing

TopographicForcing+ +

TVp

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pfVf

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Evaluate Total Forcing:

You must consider the combined effects from each forcing type in order to infer the expected total geopotential height change

• Sometimes one forcing will “precondition” the atmosphere for another forcing and the combination will enhance amplification of the trough / ridge• Other times, forcing types will oppose each other, inhibiting (or limiting) any amplification of the trough / ridge

Note: Nature continuously provides us with a wide spectrum of favorable and unfavorable combinations…see the case study and your homework


VerticalMotion


VorticityAdvection

DiabaticForcing


TVp

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Evaluate Total Forcing:

• Forcing for height falls: → PVA (trough amplification) → Increase in WAA with height

→ Increase in diabatic heating with height→ Increase in downslope flow with height

• Forcing for height rises: → NVA (ridge amplification) → Increase in CAA with height

→ Increase in diabatic cooling with height→ Increase in upslope flow with height


VerticalMotion


VorticityAdvection

DiabaticForcing


TVp

Rf

pfVf

p

fg

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Important Aspects of Vorticity Advection:

Vorticity maximum at trough axis:

• PVA and height falls downstream• NVA and height rises upstream• No height changes occur at the trough axis

• Trough amplitude does not change

• Trough simply moves downstream (to the east)



Important Aspects of Vorticity Advection:

Vorticity maximum upstream of trough axis:

• PVA (or CVA) at the trough axis• Height falls occur at the trough axis

• Trough amplitude increases

• Trough “digs” equatorward

Vorticity maximum downstream of trough axis:

• NVA (or AVA) at the trough axis• Height rises occur at the trough axis

• Trough amplitude decreases

• Trough ”lifts” poleward


Digs

Lifts AVA


QG Analysis: Upper-Level SystemsImportant Aspects of Vorticity Advection: Digging Trough

500mb Wind Speeds 500mb Wind Speeds

500mb Absolute Vorticity 500mb Absolute Vorticity

t = 0 hr

t = 0 hr

t = 24 hr

t = 24 hr


QG Analysis: Upper-Level SystemsImportant Aspects of Vorticity Advection: Lifting Trough

500mb Wind Speeds 500mb Wind Speeds

500mb Absolute Vorticity 500mb Absolute Vorticity

t = 0 hr

t = 0 hr

t = 24 hr

t = 24 hr


Example Case: Formation / Evolution



Trough Axis

Vorticity Advection:



Trough Axis

NVAExpect Height Rises

Χ > 0

PVAExpect Height Falls

Χ < 0

Weak PVA at trough axisExpect trough to “dig” slightly

Vorticity Advection:



500mbTrough Axis

System has westwardtilt with height

Differential Temperature Advection:



500mbTrough Axis

Low-level CAANo temperature advection aloft

Expect upper-level Height Falls

Χ < 0

Low-level WAANo temperatureadvection aloft

Expect upper-levelHeight Rises

Χ > 0

Expect upper-leveltrough to “dig”

System has westwardtilt with height

Differential Temperature Advection:



Diabatic Forcing:

500mbTrough Axis



Deep ConvectionDiabatic Heating

Expect upper-levelHeight Falls

Χ < 0Expect northern portion

of upper-leveltrough to “dig”

Diabatic Forcing:


500mbTrough Axis


Topographic Forcing:

500mbTrough Axis



Topographic Forcing:

500mbTrough Axis


Upslope flow (CAA) at low-levelsNo “topo” flow at 500mb

Increase in WAA with heightExpect upper-level

Height FallsΧ < 0

Expect northern portionof upper-level

trough to “dig”



Trough Axis

Initial Time

Expect upper-leveltrough to “dig”

Summary of Forcing Expectations:



InitialTrough Axis

Trough “dug”(intensified)

“Results”

6-hr Later



QG Analysis: Upper-Level System Motion

InitialTrough Axis

CurrentTrough Axis

Trough moved eastWhy?

Whether the relative or planetary vorticity advection dominates the height changesdetermines if the wave will “progress” or “retrograde”



VerticalMotion


VorticityAdvection

DiabaticForcing


TVp

Rf

pfVf

p

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2202

ggVf 0 fVf g 0 gvOR

Relative Vorticity Advection Planetary Vorticity Advection


Scale Analysis for a Synoptic Wave:

Term B

Absolute Vorticity Advection

OR

Relative Vorticity Advection Planetary Vorticity Advection

• Assume waves are sinusoidal in structure: U = basic current (zonal flow)L = wavelength of waveβ = north-south Coriolis gradient

• Ratio of relative to planetary vorticity is:

ggVf 0 fVf g 0 gv

2

0

0 2

L

U

fVf

Vf

g

gg



Scale Analysis for a Synoptic Wave:

For the Mid-Latitudes: U ~ 10 m s-1

β ~ 10-11 s-1 m-1

Whether relative or planetary vorticity advection dominates the height changes is a function of the wavelength

Short Waves: L < 6000 kmRelative vorticity dominates

Long Waves: L > 6000 kmPlanetary vorticity dominates

12

2

L

U

12

2

L

U


2

0

0 2

L

U

fVf

Vf

g

gg


Short Waves:

• Most synoptic waves are short waves with wavelengths less than 6000 km• Relative vorticity maxima (minima) are often located near trough (ridge) axes

• PVA and height falls east of troughs• NVA and height rises east of ridges

• Short waves move eastward

Trough

Trough

Ridge

Ridge

L < 6000 kmL < 6000 km

L L

Adapted from Bluestein (1993)

VortMax Vort

Min

Note: Several “short waves” can stretch across the entire US at one time



Long Waves:

• Long waves, with wavelengths greater than 6000 km, occur during stationary weather patterns• Planetary vorticity maxima (minima) are located at ridge (trough) axes

• NVA and height rises west of ridges• PVA and height falls west of troughs

• Long waves move westwardTroughRidge

L > 6000 km

Adapted from Bluestein (1993)

VortMax

VortMin

Note: A single “long wave” would stretch across the entire US and beyond



The “Kicker”:

• Long waves are often associated with stationary weather patterns

• When a short wave “kicker” approaches a stationary long wave trough, the wavelength associated with the long wave is effectively decreased

• Hence, the long wave becomes a short wave and begins to move eastward

• The short wave “kicked out” the long wave, and the stationary weather pattern ends

From Bluestein (1993)



Example Case: Motion

Where will this upper-level trough move?


Trough

Trough

RidgeRidge

L < 6000 km Short Wave

Trough

Examinerelativevorticity

advection

Is it a “short wave” or a “long wave”?

Initial Time



Trough Axis

NVAExpect Height Rises

Χ > 0

PVAExpect Height Falls

Χ < 0

Expect trough to move east

Effects of Vorticity Advection:

Assume “local” absolute vort maxare relative vort maxima

Initial Time



InitialTrough Axis

CurrentTrough Axis

6-hr Later

Troughmoved east

Results:



Application Tips: Evolution and Motion

• ALL relevant forcing terms should be analyzed in each situation!!!

• Differential vorticity advection and thermal advection are the dominant terms in the majority of situations → weight these terms more

• Diabatic forcing can be important for system evolution when deep convection or dry/clear air are present. • Diabatic forcing can be important for system motion when the forcing is asymmetric about the system center

• Topographic forcing is only relevant near large mountain ranges or rapid elevation changes over a short horizontal distance



ReferencesBluestein, H. B, 1993: Synoptic-Dynamic Meteorology in Midlatitudes. Volume I: Principles of Kinematics and Dynamics.

Oxford University Press, New York, 431 pp.

Bluestein, H. B, 1993: Synoptic-Dynamic Meteorology in Midlatitudes. Volume II: Observations and Theory of WeatherSystems. Oxford University Press, New York, 594 pp.

Charney, J. G., B. Gilchrist, and F. G. Shuman, 1956: The prediction of general quasi-geostrophic motions. J. Meteor.,13, 489-499.

Durran, D. R., and L. W. Snellman, 1987: The diagnosis of synoptic-scale vertical motionin an operational environment. Weather and Forecasting, 2, 17-31.

Hoskins, B. J., I. Draghici, and H. C. Davis, 1978: A new look at the ω–equation. Quart. J. Roy. Meteor. Soc., 104, 31-38.

Hoskins, B. J., and M. A. Pedder, 1980: The diagnosis of middle latitude synoptic development. Quart. J. Roy. Meteor.Soc., 104, 31-38.

Lackmann, G., 2011: Mid-latitude Synoptic Meteorology – Dynamics, Analysis and Forecasting, AMS, 343 pp.

Trenberth, K. E., 1978: On the interpretation of the diagnostic quasi-geostrophic omega equation. Mon. Wea. Rev., 106,131-137.

advanced synopticm. d. eastin qg analysis: upper-level systems will this upper-level trough...

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