Material Based on Chapter 5

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Material Based on Chapter 5
The Planetary Boundary Layer
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The Planetary Boundary Layer
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Red w(t) Blue q(t)
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is the radiative heating rate.
Note
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Derive TKE Equation
Similarly for v and w
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• Frictional dissipation (molecular diffusion)
• gt 0

TR Redistribution by transport pressure
forces (no new TKE created)
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Analogue in large-scale flow
How does this circulation lower center of mass?
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BPL - TKE increase for unstable PBL
If PBL heated from below, then ?(z)
BPL gt 0 Primary energy source for unstable
PBL (In stable PBL, BPL term gives energy loss)
w lt 0 ? lt 0
w gt 0 ? gt 0
z
?
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BPL - Side Note
More precise ?(z) when well-mixed PBL is fully
developed.
Homogeneous, well-mixed layer Unstable layer
maintained near surface by surface heating
z
?
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(See figures)
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(Add friction? See Figure 5.3 in Holton.)
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(See Figures 5.4 and 5.5 in Holton.)
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(See Fig. 5.5 in Holton additional figures.)
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Horizontal Wind in PBL
In PBL, wind component toward lower pressure
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giving horizontal convergence around low center
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Vertical Wind in PBL
Mass convergence around low pressure
PBL top
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gives upward motion over low. Effect on vortex?
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Slowing Vortex Vortex Compression
Ekman pumping reduces vorticity in free
troposphere by vortex compression
Tropopause (w 0)
PBL top
L
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Slowing Vortex Conservation of Angular Momentum
Alternatively, outward secondary circulation in
free troposphere slows vortex by conservation of
angular momentum
PBL top
L
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Spin-Down Time
te H 2/(fKm) 1/2

• Use H 10 km
• and previous values for other constants
• Then, ?e 7 days
• Longer than synoptic time scale
• A reason why PBL was ignored when introducing
  quasi-geostrophic motion

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Ekman-Pumping Torque
Outward (secondary ) flow gives torque against
primary flow by Coriolis force.
L
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Ekman-Pumping Effectiveness

• Ekman pumping more effective than diffusion
• Works not by mixing high/low vorticity air
• Rather by forcing mass divergence in free
  troposphere
• Angular momentum (moment of intertia) x
  (rotation rate)
• Outward mass movement
• gt increased moment of inertia
• gt reduced rotation to conserve angular mom.

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Baroclinic Atmosphere?

• If atmosphere baroclinic (not barotropic)
• Circulation confined closer to surface
• Shear created in vortex gt more damping closer to
  surface
• Shear balanced by induced ?T uplifted air at
  center cooler than air at vortex edge

• Final note all rests on Ekman PBL
• Qualitatively OK
• Gives correct approximate physics (cross isobar
  flow)

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END