• Quasi-geostrophic system:
  • advantages:
    1. changes in Z, T, and V are linked
    2. relations between variables are simple (expediting the math and the interpretation)
    3. energetically consistent
    4. captures the gross features observed in middle latitudes
  • Some properties:
    • theta (= potential temperature) is proportional to dZ/dp.
    • advected velocities are geostrophic.
    • advecting velocities are geostrophic -- except where there is a large contribution to the vertical derivative (i.e. in Dtheta/Dt eqn.)
    • Dtheta/Dt = - omega S where S is a horizontal mean static stability.
    • vorticity eqn has 3 parts:
      1. local change,
      2. horizontal advection (of geostrophic absolute vorticity by geostrophic wind)
      3. -fD divergence term.

• The QG omega equation:
  • formed by eliminating time derivatives from vorticity and theta equations
  • RHS:
    • is all geostrophic quantities
    • is viewed as forcing of vertical motion
    • can be estimated (using the "solenoid method") from standard weather maps
    • has differential vorticity advection: larger positive vorticity advection (PVA) above smaller PVA forces upward motion.
    • has temperature advection: warm air advection (WAA) forces upward motion
  • LHS:
    • is all ageostrophic quantities
    • is a linear operator
    • might be approximated as proportional to "minus" omega
  • can link omega equation forcings back to consistent changes that must also be occuring in the vorticity and theta fields (see handout).

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