QG Analysis: Low-Level Systems
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Advanced Synoptic M. D. Eastin
QG Analysis: Low-Level Systems
Will these Surface Lows Intensify or Weaken?
Where will they Move?
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Advanced Synoptic M. D. Eastin
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
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Advanced Synoptic M. D. Eastin
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
QG Analysis: Low-Level Systems
TVp
RfV
p
f
p
fggg
202
2202
VerticalMotion
ThermalAdvection
Differential VorticityAdvection
DiabaticForcing
TopographicForcing+ +
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Advanced Synoptic M. D. Eastin
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
QG Analysis: Low-Level Systems
py
v
x
u agag
p
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Advanced Synoptic M. D. Eastin
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+ +
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Advanced Synoptic M. D. Eastin
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
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Advanced Synoptic M. D. Eastin
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
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Advanced Synoptic M. D. Eastin
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
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Advanced Synoptic M. D. Eastin
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
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Advanced Synoptic M. D. Eastin
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
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Advanced Synoptic M. D. Eastin
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
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Advanced Synoptic M. D. Eastin
Example Case: Formation / Evolution
Will these Surface Lows Intensify or Weaken?
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Advanced Synoptic M. D. Eastin
Differential Vorticity Advection:
L
LL
Example Case: Formation / Evolution
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Advanced Synoptic M. D. Eastin
Differential Vorticity Advection:
L
L
PVA
Assume NO vorticityadvection below
Rising Motion
Surface PressureDecreases
L
Example Case: Formation / Evolution
NVA
Assume NO vorticityadvection below
Sinking Motion
Surface PressureIncreases
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Advanced Synoptic M. D. Eastin
Thermal Advection:
L
L
L
Example Case: Formation / Evolution
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Advanced Synoptic M. D. Eastin
Thermal Advection:
L
L
L
WAA
Rising Motion
Surface PressureDecreases
CAA
Sinking Motion
Surface PressureIncreases
Example Case: Formation / Evolution
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Advanced Synoptic M. D. Eastin
Diabatic Forcing:
L
L
L
Example Case: Formation / Evolution
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Advanced Synoptic M. D. Eastin
Diabatic Forcing:
L
L
LDiabatic Cooling
Sinking Motion
Surface PressureIncreases
Diabatic Heating
Rising Motion
Surface PressureDecreases
Note the snowand cloud cover
Note: Time is 12Z or 5:00-7:00 am (before or at sunrise)
Note the clear skies
Example Case: Formation / Evolution
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Advanced Synoptic M. D. Eastin
Topographic Forcing:
L
L
L
Note direction of surface winds from the previous slide
Example Case: Formation / Evolution
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Advanced Synoptic M. D. Eastin
Topographic Forcing:
L
L
LDownslope Flow
Rising Motion
Surface PressureDecreases
Note direction of surface winds from the two slides ago
Example Case: Formation / Evolution
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Advanced Synoptic M. D. Eastin
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
Example Case: Formation / Evolution
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Advanced Synoptic M. D. Eastin
Will this SurfaceLow Move?
QG Analysis: Low-level System Motion
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Advanced Synoptic M. D. Eastin
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
QG Analysis: Low-level System Motion
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Advanced Synoptic M. D. Eastin
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
Downslope Flow → Pressure Decrease
QG Analysis: Low-level System Motion
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Advanced Synoptic M. D. Eastin
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
Downslope Flow → Pressure Decrease
WAA → Pressure DecreaseT
T-ΔTT-2ΔT
L
Weaker Upslope Flow → Pressure Increase
Weaker Downslope Flow → Pressure Decrease
WAA → Pressure DecreaseT
T-ΔTT-2ΔT
QG Analysis: Low-level System Motion
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Advanced Synoptic M. D. Eastin
Example Case: Motion
Where will this Surface
Low Move?
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Advanced Synoptic M. D. Eastin
Differential Vorticity Advection:
L
Example Case: Motion
Maximum PVA
Assume NO vorticityadvection below
Expect motion toward the south
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Advanced Synoptic M. D. Eastin
Thermal Advection:
L
Maximum WAA
Expect motion toward the southeast
Example Case: Motion
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Advanced Synoptic M. D. Eastin
Diabatic Heating:
L
Maximum Heating
Expect motion toward the northwest
Example Case: Motion
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Advanced Synoptic M. D. Eastin
Flow over Orography:
L
Maximum Downslope Flow
Expect motion toward the southwest
Example Case: Motion
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Advanced Synoptic M. D. Eastin
Motion Summary
LL
WAAPVA
Heating
Downslope
ExpectedMotion
Initial Location
Later Location
Example Case: Motion
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Advanced Synoptic M. D. Eastin
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
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Advanced Synoptic M. D. Eastin
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.