• We saw a connection between divergence and height change when discussing the vorticity equation
  • from "bowstring" model below a level of maximum upward motion: D<0.
  • vorticity tendency (partial zeta)/(partial t) >0 = - f D + horiz. advection.
  • for convergence ( D <0 ) ahead of a surface low, the above means vorticity tendency >0.
  • since geostrophic vorticity ~ LaPlacian of Z ~ -Z, the height tendency <0.
• form of equation:
  (- Z tend.) ~ (Abs. vort. advection) + (d/dP) of (thickness advection) + d Q-dot/dP
  where d/dp is a partial derivative w.r.t. pressure
• Absolute Vorticity advection term:
  • PVA => P falls, NVA => P rises
  • simply put: P falls if higher vorticity is approaching
• Differential temperature advection term:
  • WAA that INCREASES with elevation makes heights fall (and vice versa)
  • CAA that INCREASES with elevation makes heights rise (and vice versa)
  • 3 examples shown
    1. vertical compensation between WAA and CAA: WAA in layer above layer having CAA and vice versa
       • temperature advection changes thickness in layer
       • interface between layers deflected up or down. For example, WAA above CAA is WAA increasing with height and heights fall.
    2. First example is approximation to troposphere and lower stratosphere response to temperature advection in troposphere.
       • The "interface" referred to above becomes the tropopause
       • sinking or rising of tropopause (and lower stratosphere) changes temps in lower stratosphere by adiabatic heating or cooling
    3. What about the surface?
       • consider WAA:
       • causes temperature to increase which increases thickness
       • increased thickness causes high pressure at layer top
       • high pressure creates ageostrophic horizontal motion
       • ageostrophic motion not balanced at first, some mass lost from layer
       • lost mass lowers heights: creates low P at layer bottom, still high P at layer top
       • trof at layer bottom causes ageostrophic motion inward below
       • motion is now balanced in that inflow = outflow with upward motion in between
       • Note: upward motion here for WAA consistent with "omega" eqn.
  • Some properties of T advection:
    • "thermal wind" (V_T) parallel to isotherms so can't advect T if isotherms have same orientation w/ elevation.
    • T gradient often decreases with increasing elevation. Main exception: T gradient associated with Subtropical jet is often mainly in upper troposphere.
    • T advection tends to decrease w/ increasing elevation (low level winds more perpendicular to isotherms)
    • T gradient is larger on the "cold air side" of both warm and cold fronts.
• differential diabatic heating term
  • where d/dP of Q-dot is >0 height rises and vice versa
  • picture a precipitating cloud:
    • Q-dot >0 inside cloud, zero at top and bottom of cloud
    • pressure derivative of Q-dot >0 in upper cloud --> height rises
    • pressure derivative of Q-dot <0 in lower cloud --> height falls

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