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
QG Analysis: Low-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
 2 f 02  2 
  

2 
 p 

Vertical
Motion



Differential Vorticity
Advection
+
Advanced Synoptic

f0 
Vg    g  f 
 p
Diabatic
Forcing
R 2
 Vg   T 
p
Thermal
Advection
+
Topographic
Forcing
M. D. Eastin
QG Analysis: Low-Level Systems
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:

0
p
Recall:
 uag vag  
 
 


x

y

 p
QG continuity equation
Equivalent to low-level
convergence
• We can then infer from the QG vorticity equation that:
 g
t
0
Recall:
 g
t
 f0

p
• Using the relationship between vorticity tendency and height tendency we thus know:

0
t
Recall:
 g
t

1 2
   
f0
and


t
• Finally, using the height / pressure tendency relationship via hydrostatic balance:
p
0
t
 Therefore:
Advanced Synoptic
Since:
1  p 
  

   
 t  p   t  z
Rising motions aloft
Sinking motions aloft
→
→
via
p   
Surface pressure decreases
Surface pressure increases
M. D. Eastin
Combined Effects of Forcing
Evaluate Total Forcing:
 2 f 02  2 
  

2 


p


Vertical
Motion



f0 
Vg    g  f 
 p

Differential Vorticity
Advection
+
Diabatic
Forcing
R 2
 Vg   T 
p
Thermal
Advection
+
Topographic
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
Advanced Synoptic
M. D. Eastin
Favorable Combinations of Forcing
Vorticity 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
Vort
Upper Levels
Max
WAA
Lower Levels
Advanced Synoptic
M. D. Eastin
Favorable Combinations of Forcing
Temperature 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 Forcing
Vorticity 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
PVA
Vort
Upper Levels
Max
WAA
Advanced Synoptic
Lower Levels
M. D. Eastin
Favorable Combinations of Forcing
Vorticity 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
Upper Levels
Vort
Max
Downslope
Motions
Advanced Synoptic
Lower Levels
M. D. Eastin
Unfavorable Combinations of Forcing
Vorticity 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
Vort
Upper Levels
Max
Lower Levels
CAA
Advanced Synoptic
M. D. Eastin
Unfavorable Combinations of Forcing
Vorticity 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
Upper Levels
Vort
Max
Downslope
Motions
Advanced Synoptic
Lower Levels
M. D. Eastin
Example Case: Formation / Evolution
Will these Surface Lows
Intensify or Weaken?
Advanced Synoptic
M. D. Eastin
Example Case: Formation / Evolution
Differential Vorticity Advection:
L
L
L
Advanced Synoptic
M. D. Eastin
Example Case: Formation / Evolution
Differential Vorticity Advection:
L
L
NVA
Assume NO vorticity
advection below
L
PVA
Sinking Motion
Assume NO vorticity
advection below
Surface Pressure
Increases
Rising Motion
Surface Pressure
Decreases
Advanced Synoptic
M. D. Eastin
Example Case: Formation / Evolution
Thermal Advection:
L
L
L
Advanced Synoptic
M. D. Eastin
Example Case: Formation / Evolution
Thermal Advection:
L
WAA
L
L
Rising Motion
CAA
Surface Pressure
Decreases
Sinking Motion
Surface Pressure
Increases
Advanced Synoptic
M. D. Eastin
Example Case: Formation / Evolution
Diabatic Forcing:
L
L
L
Advanced Synoptic
M. D. Eastin
Example Case: Formation / Evolution
Diabatic Forcing:
Note: Time is 12Z or 5:00-7:00 am
(before or at sunrise)
Note the snow
and cloud cover
Diabatic Cooling
L
Sinking Motion
L
Surface Pressure
Increases
Note the clear
skies
Diabatic Heating
Rising Motion
L
Advanced Synoptic
Surface Pressure
Decreases
M. D. Eastin
Example Case: Formation / Evolution
Topographic Forcing:
Note direction of
surface winds from
the previous slide
L
L
L
Advanced Synoptic
M. D. Eastin
Example Case: Formation / Evolution
Topographic Forcing:
Note direction of
surface winds from
the two slides ago
Downslope Flow
L
Rising Motion
Surface Pressure
Decreases
L
L
Advanced Synoptic
M. D. Eastin
Example Case: Formation / Evolution
Moderate NVA
Weak CAA
Diabatic Cooling
Downslope Flow
D
D
D
U
Weak PVA
Moderate CAA
Diabatic Heating
Downslope Flow
-----------------------------------------------------------
Net Pressure Rise
D/R
U
D
U
U
-----------------------------------------------------------
-----------------------------------------------------------
15Z: Pressure rose 2 mb
Net Pressure Fall
U/F
------------------------------------------------------------
15Z: Pressure fell 1 mb
Moderate NVA
Weak WAA
Diabatic Cooling
Downslope Flow
D
U
D
U
-----------------------------------------------------------
Net Pressure Rise
D/R
-----------------------------------------------------------
15Z: Pressure rose 3 mb
Advanced Synoptic
M. D. Eastin
QG Analysis: Low-level System Motion
Will this Surface
Low Move?
Advanced Synoptic
M. D. Eastin
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
Motion
(From → To)
Regions of sinking motion
Regions of NVA aloft
Regions of CAA
Regions of diabatic cooling
Regions of upslope flow
→
→
→
→
→
Regions or rising motion
Regions of PVA aloft
Regions of WAA
Regions of diabatic heating
Regions of downslope flow
Anticyclone
Motion
(From → To)
Regions of rising motion
Regions of PVA aloft
Regions of WAA
Regions of diabatic heating
Regions of downslope flow
→
→
→
→
→
Regions of sinking motion
Regions of NVA aloft
Regions of CAA
Regions of diabatic cooling
Regions of upslope flow
Advanced Synoptic
M. D. Eastin
QG Analysis: Low-level System Motion
Influence of Topography:
• Consider a cyclone (low pressure system) east of a mountain range:
• Motion will be to the south
along the range
Upslope Flow → Pressure
Increase
L
Downslope Flow → Pressure
Decrease
• Consider an anticyclone east of a mountain range
• Motion will be to the south
along the range
Downslope Flow → Pressure
Decrease
H
Upslope Flow → Pressure
Increase
Advanced Synoptic
M. D. Eastin
QG Analysis: Low-level System Motion
Influence of Topography and Temperature Advection:
• Consider a low pressure system initially just east of a mountain range:
• Motion will be
to the southeast
Upslope Flow → Pressure
Increase
T-2ΔT
T-ΔT
T
L
WAA → Pressure
Decrease
Downslope Flow → Pressure
Decrease
• Consider the low at a later time southeast of the mountain range
Weaker Upslope Flow → Pressure
Increase
• Motion will now be to
the east-southeast
T-2ΔT
T-ΔT
T
L
WAA → Pressure
Decrease
Weaker Downslope Flow → Pressure
Decrease
 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
Advanced Synoptic
M. D. Eastin
Example Case: Motion
Where will this
Surface
Low Move?
Advanced Synoptic
M. D. Eastin
Example Case: Motion
Differential Vorticity Advection:
L
Maximum PVA
Assume NO vorticity
advection below
Expect motion
toward the south
Advanced Synoptic
M. D. Eastin
Example Case: Motion
Thermal Advection:
L
Maximum WAA
Expect motion
toward the southeast
Advanced Synoptic
M. D. Eastin
Example Case: Motion
Diabatic Heating:
L
Maximum Heating
Expect motion
toward the northwest
Advanced Synoptic
M. D. Eastin
Example Case: Motion
Flow over Orography:
L
Maximum Downslope Flow
Expect motion
toward the southwest
Advanced Synoptic
M. D. Eastin
Example Case: Motion
Motion Summary
Initial Location
Heating
L
Downslope
Expected
Motion
PVA
L
WAA
Later Location
Advanced Synoptic
M. D. Eastin
QG Analysis: Low-level Systems
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
Advanced Synoptic
M. D. Eastin
References
Bluestein, 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 Weather
Systems. 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 Synoptic
M. D. Eastin