qg analysis: low-level systems

Advanced Synoptic M. D. Eastin

QG Analysis: Low-Level Systems

Will these Surface Lows Intensify or Weaken?

Where will they 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 low-level (or surface) cyclones and anticyclones

Which QG Equation?

• We cannot apply the QG height-tendency equation

• Lower boundary condition assumes no height tendency at the surface• Contrary to what we are trying to infer…

• We can use the QG omega equation

• Evaluate above the surface• Then we can use QG theory to infer low-level (or surface) pressure changes


TVp

RfV

p

f

p

fggg

202

2202

VerticalMotion

ThermalAdvection

Differential VorticityAdvection

DiabaticForcing

TopographicForcing+ +


Local application of the QG Theory at the Surface:

• If rising motion (ω < 0) is present above the surface (where ω = 0), then we know:

Recall:

• We can then infer from the QG vorticity equation that:

Recall:

• Using the relationship between vorticity tendency and height tendency we thus know:

Recall: and

• Finally, using the height / pressure tendency relationship via hydrostatic balance:

Since: via

Therefore: Rising motions aloft → Surface pressure decreasesSinking motions aloft → Surface pressure increases

pf

tg

0

0p

QG continuity equationEquivalent to low-level

convergence

0

tg

0t

2

0

1

ftg

t

0t

pzp t

p

t

1


py

v

x

u agag

p


Combined Effects of ForcingEvaluate Total Forcing:

You must consider the combined effects from each forcing type in order to infer the expected total vertical motion and surface pressure change

• Sometimes one forcing will “precondition” the atmosphere for another forcing and the combination will enhance low-level (or surface) cyclogenesis• Other times, forcing types will oppose each other, inhibiting (or limiting) any low-level (or surface) cyclogenesis

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

TVp

RfV

p

f

p

fggg

202

2202

VerticalMotion

ThermalAdvection

Differential VorticityAdvection

DiabaticForcing

TopographicForcing+ +


Favorable Combinations of ForcingVorticity Advection with Temperature Advection:

Scenario: A region of increasing PVA with height (located downstream from a trough) is collocated with a region of strong warm air advection

PVA

Max

Vort

WAA

Upper Levels

Lower Levels


Favorable Combinations of ForcingTemperature Advection with Diabatic Heating:

Scenario: A region of strong warm advection collocated with deep convection Commonly observed near warm fronts and in the warm sector

WAA


Favorable Combinations of ForcingVorticity Advection with Temperature Advection and Diabatic Heating:

Scenario: A region of increasing PVA with height (located downstream from a trough) is collocated with a region of warm air advection and deep convection

Max

Vort

WAA

Upper Levels

Lower Levels

PVA


Favorable Combinations of ForcingVorticity Advection with Downslope Motions:

Scenario: A region of increasing PVA with height (located downstream from a trough) is located over the leeside of a mountain range

PVA

Max

Vort

Downslope Motions

Upper Levels

Lower Levels


Unfavorable Combinations of ForcingVorticity Advection with Temperature Advection:

Scenario: A region of increasing PVA with height (located downstream from a trough) is collocated with a region of strong cold air advection

PVA

Max

Vort

CAA

Upper Levels

Lower Levels


Unfavorable Combinations of ForcingVorticity Advection with Downslope Motions:

Scenario: A region of increasing NVA with height (located upstream from a trough) is located over the leeside of a mountain range

NVA

Max

Vort

Downslope Motions

Upper Levels

Lower Levels


Example Case: Formation / Evolution

Will these Surface Lows Intensify or Weaken?


Differential Vorticity Advection:

L

LL




L

L

PVA

Assume NO vorticityadvection below

Rising Motion

Surface PressureDecreases

L


NVA


Sinking Motion

Surface PressureIncreases


Thermal Advection:

L

L

L



Thermal Advection:

L

L

L

WAA

Rising Motion


CAA

Sinking Motion




Diabatic Forcing:

L

L

L



Diabatic Forcing:

L

L

LDiabatic Cooling

Sinking Motion


Diabatic Heating

Rising Motion


Note the snowand cloud cover

Note: Time is 12Z or 5:00-7:00 am (before or at sunrise)

Note the clear skies



Topographic Forcing:

L

L

L

Note direction of surface winds from the previous slide



Topographic Forcing:

L

L

LDownslope Flow

Rising Motion


Note direction of surface winds from the two slides ago



Moderate NVA DWeak CAA DDiabatic Cooling DDownslope Flow U-----------------------------------------------------------

Net Pressure Rise D/R-----------------------------------------------------------

15Z: Pressure rose 2 mb

Moderate NVA DWeak WAA UDiabatic Cooling DDownslope Flow U-----------------------------------------------------------

Net Pressure Rise D/R-----------------------------------------------------------

15Z: Pressure rose 3 mb

Weak PVA UModerate CAA DDiabatic Heating UDownslope Flow U-----------------------------------------------------------

Net Pressure Fall U/F------------------------------------------------------------

15Z: Pressure fell 1 mb



Will this SurfaceLow Move?

QG Analysis: Low-level System Motion


Goal: Use QG theory to diagnose the motion of low-level (or surface) systems

Application of QG Theory:

• Surface cyclones always move away from regions with pressure increases toward regions with pressure decreases• In essence, surface cyclones “move down the pressure change gradient”

Cyclone Regions of sinking motion → Regions or rising motion Motion Regions of NVA aloft → Regions of PVA aloft (From → To) Regions of CAA → Regions of WAA

Regions of diabatic cooling → Regions of diabatic heatingRegions of upslope flow → Regions of downslope flow

Anticyclone Regions of rising motion → Regions of sinking motion Motion Regions of PVA aloft → Regions of NVA aloft (From → To) Regions of WAA → Regions of CAA

Regions of diabatic heating → Regions of diabatic coolingRegions of downslope flow → Regions of upslope flow



Influence of Topography:

• Consider a cyclone (low pressure system) east of a mountain range:

• Motion will be to the south along the range

• Consider an anticyclone east of a mountain range

• Motion will be to the south along the range

L

Upslope Flow → Pressure Increase

Downslope Flow → Pressure Decrease

HUpslope Flow → Pressure Increase




Influence of Topography and Temperature Advection:

• Consider a low pressure system initially just east of a mountain range:

• Motion will be to the southeast

• Consider the low at a later time southeast of the mountain range

• Motion will now be to the east-southeast

As the low moves further away from the mountain range, it begins to feel less topographic effects and more temperature advection effects → acquires a more northeastward motion

L

Upslope Flow → Pressure Increase


WAA → Pressure DecreaseT

T-ΔTT-2ΔT

L

Weaker Upslope Flow → Pressure Increase

Weaker Downslope Flow → Pressure Decrease

WAA → Pressure DecreaseT

T-ΔTT-2ΔT



Example Case: Motion

Where will this Surface

Low Move?



L


Maximum PVA


Expect motion toward the south


Thermal Advection:

L

Maximum WAA

Expect motion toward the southeast



Diabatic Heating:

L

Maximum Heating

Expect motion toward the northwest



Flow over Orography:

L

Maximum Downslope Flow

Expect motion toward the southwest



Motion Summary

LL

WAAPVA

Heating

Downslope

ExpectedMotion

Initial Location

Later Location



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

QG Analysis: Low-level Systems


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.

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