EAS 486 Lecture Content for Day 5: Frontogenesis: 2-D and QG

The lecture covered the following:

  1. Fronts and Jet Streaks (cont)
    1. Frontogenesis
    2. Pettersen (1936) Two-Dimensional Frontogenesis
      1. Definition (see class notes): note the presence of substantial derivative
      2. Derivation assumptions
        1. Assume that the x-axis is parallel to the front and the y-axis points towards the colder air
        2. All isentropes are parallel to the front
        3. No along-front variations in u or T.
      3. Frontogenesis produced through
        1. Confluent flow (Term 1)
          1. Warm-air advection on warm side; cold-air advection on cold side
        2. Rising cold air, sinking warm air (Tilting Term)
          1. Thermally indirect circulation (as in exit region of straight jet streak)
        3. Less diabatic heating on cold side and/or more diabatic heating on warm side (Differential Diabatic Heating Term)
          1. Daytime example: cloudy on cold side of front; sunny on warm side of front
          2. Example 2: Diabatic heating from open lake on warm side of front when air temperature < lake temperature.
      4. Frontolysis produced through
        1. Diffluent flow (Term 1)
          1. Cold advection on warm side; Warm advection on cold side
        2. Rising warm air, sinking cold air (Tilting Term)
          1. Thermally direct circulation (as in entrance region of straight jet streak)
        3. More diabatic heating on cold side and/or less diabatic heating on warm side (Differential Diabatic Heating Term)
          1. Example: Weak cold front with deeper mixed layer on cold side
            1. Inversion aloft on warm side limits diabatic heating and/or produces clouds
            2. Deeper mixed layer with modest cold advection at 850 mb or 700 mb allows surface air on cold side of front to be warmer
      5. If diabatic heating and vertical velocity assumed to be small, then the reexpression of frontogenesis is produced by:
        1. Deformation when the angle between the isentropes and the axis of dilatation is less than 45°
          1. Results change for different isentrope orientation (not Gallilean invariant)
        2. Convergence
          1. Example 2: Diabatic heating from open lake on warm side of front when air temperature < lake temperature.
      6. In strong lower tropospheric front
        1. Horizontal confluence or deformation produces frontogenesis which is strongest in lower troposphere
        2. Tilting term results in frontolysis in middle and upper troposphere due to direct circulation
    3. Miller (1948) Three-Dimensional Frontogenesis
      1. Used for calculation of frontogenesis for a data set with gridded atmospheric parameters
      2. If vertical advection terms dropped and assumed adiabatic, get two-dimensional adiabatic form (still get tilting effects from horizontal gradients of vertical motion)
  2. Quasi-geostrophic frontogenesis
    1. Assumptions
      1. No diabatic effects
      2. Level surface (omega is zero at the lower boundary)
      3. v is replaced by vg in confluence term
      4. Confluence expressed by (-dvg/dy) (all partial derivatives) and is held fixed
    2. Produces odd looking front
      1. Isentropes like "Japanese fan"
      2. Static instability on warm side of front
      3. "e-folding time" for frontal strengthing = 10**5 seconds or 1 day
      4. To get typical frontal gradient takes 2.5 days
        1. In nature, frontal collapse takes a matter of hours
    3. Is positive if Q-vector has a component (Qn) pointing from cold side to warm side of front
    4. So, QG Theory fails for frontogenesis
      1. Any process involving strong frontogenesis would throw off QG views of dynamics (differential vorticity advection, Laplacian of thermal advection; Q-vector analysis)
      2. Especially bad during early frontal development stages.

Last updated: February 22, 2007

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