1. 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)

2. 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

3. Goal of QG theory Goal is to get to two equations:
Rising motion (the “omega equation”),
Change in geopotential height (the “height tendency equation”)

4. 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

5. Let’s now derive the QG equations for omega and height tendency . . .
See handout.

6. 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

7. 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)