Download Lesson 7

SO441 Synoptic Meteorology
Quasi-geostrophic theory
Lesson 7: Weeks 8-10
Every day the operational meteorologist is asked to absorb a tremendous amount of weather
data and make a forecast. [There are many model products] which can be used to formulate
the forecast. However, “good” forecasters do not rely exclusively on computer-generated
guidance when making a forecast. They examine developing weather patterns and attempt
to understand the factors which are likely to be responsible for the current and next day’s
weather.
D. Durran and L. Snellman, “The diagnosis of synoptic-scale vertical motion in an operational environment” (1987)
What is “quasi-geostrophic theory”?
• Quasi-geostrophic theory (QG theory, for short) is a
cornerstone of understanding mid-latitude weather
– We have already used QG theory extensively this semester
(without even knowing it!)
• Rising motion to the east of a trough axis
– But why?
• Vorticity & temperature advection, and their relationship to
surface low formation
– Again, why?
• It is a set of assumptions that reduce the predictive
equations for air motion into diagnostic equations for
vertical velocity and height tendency
Goal of QG theory
• Goal is to get to two equations:
– Rising motion (the “omega equation”),
– Change in geopotential height (the “height
tendency equation”)
 2 f02  2 
 RT  
f0 
1 2






V



f


V

   g  p 

2 
 g  g


p


p





A
B
C
 2 f02  2 
 RT
  f0
   f 0Vg   g  f    Vg  
 
2 


p
p  
p



B
A
C



Assumptions to get to QG equations
• Small Rossby number
– Ratio of ageostrophic flow to geostrophic flow is
very small (< 0.1)
• Adiabatic, frictionless flow
• Horizontally uniform static stability
• Hydrostatic balance
Let’s now derive the QG equations for
omega and height tendency . . .
• See handout.
Application of the QG height-tendency
equation: vorticity advection
• Digging and lifting troughs
– The “CVA” (cyclonic vorticity advection) in (a) causes heights to fall
behind the trough axis
• The trough digs
– CVA in (b) ahead of the jet streak (not marked clearly) causes heights
to fall ahead of the trough axis
• The trough lifts
Application of the QG height-tendency
equation: differential temperature advection
• Warm-air advection centered at 700 mb causes heights to rise
above it and fall below it (panel a)
– The warm air must occupy more space, so it displaces air (away from
it)
• Cold-air advection centered at 700 mb causes heights to fall
above it and rise below it (panel b)
– The cold air occupies less space, so it also displaces the air (toward it)