Advanced Synoptic M. D. Eastin
QG Analysis: Low-Level Systems
Will these Surface Lows Intensify or Weaken?
Where will they Move?
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
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+ +
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
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+ +
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
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
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
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
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
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
Advanced Synoptic M. D. Eastin
Example Case: Formation / Evolution
Will these Surface Lows Intensify or Weaken?
Advanced Synoptic M. D. Eastin
Differential Vorticity Advection:
L
LL
Example Case: Formation / Evolution
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
Advanced Synoptic M. D. Eastin
Thermal Advection:
L
L
L
Example Case: Formation / Evolution
Advanced Synoptic M. D. Eastin
Thermal Advection:
L
L
L
WAA
Rising Motion
Surface PressureDecreases
CAA
Sinking Motion
Surface PressureIncreases
Example Case: Formation / Evolution
Advanced Synoptic M. D. Eastin
Diabatic Forcing:
L
L
L
Example Case: Formation / Evolution
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
Advanced Synoptic M. D. Eastin
Topographic Forcing:
L
L
L
Note direction of surface winds from the previous slide
Example Case: Formation / Evolution
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
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
Advanced Synoptic M. D. Eastin
Will this SurfaceLow Move?
QG Analysis: Low-level System Motion
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
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
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
Advanced Synoptic M. D. Eastin
Example Case: Motion
Where will this Surface
Low Move?
Advanced Synoptic M. D. Eastin
Differential Vorticity Advection:
L
Example Case: Motion
Maximum PVA
Assume NO vorticityadvection below
Expect motion toward the south
Advanced Synoptic M. D. Eastin
Thermal Advection:
L
Maximum WAA
Expect motion toward the southeast
Example Case: Motion
Advanced Synoptic M. D. Eastin
Diabatic Heating:
L
Maximum Heating
Expect motion toward the northwest
Example Case: Motion
Advanced Synoptic M. D. Eastin
Flow over Orography:
L
Maximum Downslope Flow
Expect motion toward the southwest
Example Case: Motion
Advanced Synoptic M. D. Eastin
Motion Summary
LL
WAAPVA
Heating
Downslope
ExpectedMotion
Initial Location
Later Location
Example Case: Motion
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
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.
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