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QG Analysis: Additional Processes
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: Vertical Motion
Review: The BASIC QG Omega Equation
 2 f 02  2 
  

2 
 p 




f0 
V    g  f 
 p g
Term A

R 2
 Vg   T 
p
Term B
Term C
Term B: Differential Vorticity Advection
Z-top
PVA
PVA
ΔZ
PVA
ΔZ
Rising
Motions
Adiabatic
Cooling
ΔZ decreases
Z-400mb
ΔZ decreases Z-700mb
Z-bottom
Sinking
Motions
Hydrostatic
Balance
Thickness
decreases
must occur
with cooling
Adiabatic
Warming
• Therefore, in the absence of geostrophic vorticity advection and diabatic processes:
 An increase in PVA with height will induce rising motion
 An increase in NVA with height will induce sinking motion
Advanced Synoptic
M. D. Eastin
QG Analysis: Vertical Motion
Review: The BASIC QG Omega Equation
 2 f 02  2 
  

2 
 p 

Term A



f0 
V    g  f 
 p g

Term B
R 2
 Vg   T 
p
Term C
Term C: Thermal Advection
• WAA (CAA) leads to local temperature / thickness increases (decreases)
• In order to maintain geostrophic flow, ageostrophic flows and mass continuity
produce a vertical motion through the layer
Z-top
Z-400mb
WAA
ΔZ
Surface
Rose
Z-top
Z-400mb
ΔZ increase
Z-700mb
Z-bottom
Surface
Fell
Z-700mb
Z-bottom
• Therefore, in the absence of geostrophic vorticity advection and diabatic processes:
 WAA will induce rising motion
 CAA will induce sinking motion
Advanced Synoptic
M. D. Eastin
Vertical Motion: Diabatic Heating/Cooling
What effect does diabatic heating or cooling have?
Diabatic Heating: Latent heat release due to condensation (Ex: Cumulus convection)
Strong surfaces fluxes
(Ex: CAA over the warm Gulf Stream)
(Ex: Intense solar heating in the desert)
• Heating always leads to temperature increases → thickness increases
• Consider the three-layer model with a deep cumulus cloud
Surface
Rose
ΔZ
Z-top
Z-400mb
ΔZ increases
Surface
Fell
Z-700mb
Z-bottom
• Again, the maintenance of geostrophic flow requires rising motion through the layer
• Identical to the physical response induced by WAA
• Therefore:
Advanced Synoptic
Diabatic heating induces rising motion
M. D. Eastin
Vertical Motion: Diabatic Heating/Cooling
What effect does diabatic heating or cooling have?
Diabatic Cooling: Evaporation (Ex: Precipitation falling through sub-saturated air)
Radiation
(Ex: Large temperature decreases on clear nights)
Strong surface fluxes (Ex: WAA over snow/ice)
• Cooling always leads to temperature decreases → thickness decreases
• Consider the three-layer model with evaporational / radiational cooling
Z-top
ΔZ
ΔZ decreases
Surface
Fell
Surface
Rose
Z-400mb
Z-700mb
Z-bottom
• Again, maintenance of geostrophic flow requires sinking motion through the layer
• Identical to the physical response induced by CAA
• Therefore:
Advanced Synoptic
Diabatic cooling aloft induces sinking motion
M. D. Eastin
Vertical Motion: Topography
What effect does flow over topography have?
Downslope Motions: Flow away from the Rockies Mountains
Flow away from the Appalachian Mountains
• Subsiding air always adiabatically warms
• Subsidence leads to temperature increases → thickness increases
• Consider the three-layer model with downslope motion at mid-levels
Z-top
ΔZ
Surface
Rose
Z-400mb
Surface
Fell
Z-700mb
ΔZ increases
Z-bottom
• Again, maintenance of geostrophic flow requires rising motion through the layer
• Identical to the physical response induced by WAA and diabatic heating
• Therefore:
Advanced Synoptic
Downslope flow induces rising motion
M. D. Eastin
Vertical Motion: Topography
What effect does flow over topography have?
Upslope Motions: Flow toward the Rockies Mountains
Flow toward the Appalachian Mountains
• Rising air always adiabatically cools
• Ascent leads to temperature decreases → thickness decreases
• Consider the three-layer model with upslope motion at mid-levels
Z-top
ΔZ
ΔZ decreases
Surface
Fell
Surface
Rose
Z-400mb
Z-700mb
Z-bottom
• Again, maintenance of geostrophic flow requires sinking motion through the layer
• Identical to the physical processes induced by CAA and diabatic cooling
• Therefore:
Advanced Synoptic
Upslope flow induces sinking motion
M. D. Eastin
QG Analysis: Vertical Motion
Update: The Modified QG Omega Equation
 2 f 02  2 
  

2 
 p 




f0 
V    g  f 
 p g
Vertical
Motion
Differential Vorticity
Advection
+
Diabatic
Forcing
+

R 2
 Vg   T 
p
Thermal
Advection
Topographic
Forcing
Note: The text includes a modified equation
with only diabatic effects [Section 2.5]
Application Tips:
• Differential vorticity advection and thermal advection are the dominant terms
in the majority of situations → weight these terms more
• Diabatic forcing can be important when deep convection or dry/clear air are present
• Topographic forcing is only relevant near large mountain ranges
Advanced Synoptic
M. D. Eastin
QG Analysis: Vertical Motion
Application Tips:
Diabatic Forcing
• Use radar
• Use IR satellite
• Use VIS satellite
• Use WV satellite
→
→
→
→
→
more intense convection → more vertical motion
cold cloud tops → deep convection or high clouds?
warm cloud tops → shallow convection or low clouds?
clouds or clear air?
clear air → dry or moist?
Topographic Forcing
• Topographic maps → Are the mountains high or low?
• Use surface winds → Is flow downslope, upslope, or along-slope?
Advanced Synoptic
M. D. Eastin
QG Analysis: System Evolution
Review: The BASIC QG Height Tendency Equation
 2 f 02  2 
  

2 
 p 




f o  Vg    g  f 
Term A

  f o2 R


 

V


T
g


p   p

Term B
Term C
Term B: Vorticity Advection
• Positive vorticity advection (PVA)
causes local vorticity increases
PVA →  g  0
t
• From our relationship between ζg and χ, we know that PVA is equivalent to:
 g
t

1 2
 p  therefore: PVA →  2p   0
f0
or, since: 2    
PVA →   0
 Thus, we know that PVA at a single level leads to height falls
 Using similar logic, NVA at a single level leads to height rises
Advanced Synoptic
M. D. Eastin
QG Analysis: System Evolution
Review: The BASIC QG Height Tendency Equation
 2 f 02  2 
  

2 
 p 

Term A



f o  Vg    g  f 
Term B

  f o2 R


 

V


T
g


p   p

Term C
Term C: Differential Thermal Advection
• Consider an atmosphere with an arbitrary vertical profile of temperature advection
• Thickness changes throughout the profile will result from the type (WAA/CAA) and
magnitude of temperature advection though the profile
•Therefore:
Advanced Synoptic
An increase in WAA advection with height leads to height falls
An increase in CAA advection with height leads to height rises
M. D. Eastin
System Evolution: Diabatic Heating/Cooling
Recall:
Clear Regions
• Local diabatic heating produces the
same response as local WAA
• Likewise local diabatic cooling is
equivalent to local CAA
Z
Diabatic heating max
located near surface
due to surface fluxes
Evaluation:
• Examine / Estimate the vertical profile
of diabatic heating / cooling from all
available radar / satellite data
Net Result: Increase in cooling with height
Height Rises
Regions of Deep Convection
Z
Diabatic Heating max
located in upper-levels
due to condensation
Diabatic cooling max
located below cloud base
due to evaporation
Net Result: Increase in heating with height
Height Falls
Advanced Synoptic
Diabatic Cooling max
located in upper-levels
due to radiational cooling
Regions of Shallow Convection
Z
Diabatic Cooling max
located in upper-levels
due to radiational cooling
Diabatic heating max
located in lower-levels
due to condensation
Net Result: Increase in cooling with height
Height Rises
M. D. Eastin
System Evolution: Topography
Recall:
• Local downslop flow produces the
same response as local WAA
• Likewise local upslope flow is
equivalent to local CAA
Evaluation:
• Examine / Estimate the vertical profile
of heating due to topographic effects
Upslope Flow
Downslope Flow
Z
Z
No adiabatic heating
No topographic effects
above the mountains
No adiabatic heating
No topographic effects
above the mountains
Adiabatic Heating
due to downslope flow
Adiabatic Cooling
due to upslope flow
Net Result: Decrease in heating with height
above heating max → height rises
Decrease in heating with height
below heating max → height falls
Advanced Synoptic
Net Result: Decrease in cooling with height
above cooling max → height falls
Decrease in cooling with height
below cooling max → height rises
M. D. Eastin
QG Analysis: System Evolution
The Modified QG Height Tendency Equation
 2 f 02  2 
  

2 
 p 




f 0  Vg    g  f 
Height
Tendency
Vorticity
Advection
+
Diabatic
Forcing

  f o2 R

  
 Vg   T 
p   p

Differential Thermal
Advection
+
Topographic
Forcing
Application Tips:
• Differential vorticity advection and thermal advection are the dominant terms
in the majority of situations → weight these terms more
• Diabatic forcing can be important when deep convection or dry/clear air are present
• Topographic forcing is only relevant near large mountain ranges
Advanced Synoptic
M. D. Eastin
QG Analysis: System Evolution
Application Tips:
Diabatic Forcing
• Use radar
• Use IR satellite
• Use VIS satellite
• Use WV satellite
→
→
→
→
→
more intense convection → more vertical motion
cold cloud tops → deep convection or high clouds?
warm cloud tops → shallow convection or low clouds?
clouds or clear air?
clear air → dry or moist?
Topographic Forcing
• Topographic maps → Are the mountains high or low?
• Use surface winds → Is flow downslope, upslope, or along-slope?
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