1. Section 2: The Planetary Boundary Layer
Chapter 5 in “Dynamic Meteorology”

2. Definition
The planetary boundary layer is that portion of the atmosphere in which the flow field is strongly influenced directly by interaction with the surface of the earth.
How does the surface of the earth influence the flow field?

3. Boundary layer meteorologists roughly divide the PBL into three regions:
1. The viscous sublayer
The layer extending from the surface to a few millimeters above the surface
Characterized by: -molecular diffusion
-extreme shear
-wind at surface (molecular scale) = 0
2. The surface layer
The layer extending from the top of the viscous sublayer to about 10% of the depth of the PBL
Characterized by: -vertical momentum transfer by turbulent eddies
-not directly dependent on Coriolis and PG forces
3. The Ekman layer
The layer extending from the top of the surface layer to the top of the PBL
Characterized by: -turning wind with height as the effect of
friction diminishes and the wind approaches its geostrophic value

4. Eddies transport heat, moisture and momentum.
Such small eddies can transport momentum of different directions. The flux of momentum of each direction generally is non-uniform. Or briefly speaking, eddies transport heat and moisture from the surface and momentum to the surface. The moisture and heat transport is important for the surface energy balance, and the momentum transport would significantly alter the momentum balance in the PBL and cause departure of the large-scale wind from geostrophic balance.
Eddies transport heat, moisture and momentum.
The mechanical impact of all subgrid-scale motions upon an observable flow is collectively called a frictional force.

5. Force Balance At the surface Within the PBL Top of the PBL PGF PGF PGF
p −δp p
p −2δp
PGF Co V
Three-way balance
p −2δp
p −δp p
PGF Fr
PGF ~ Fr V
PGF Co
PGF ~ Co
p −2δp
p −δp p
the wind at all levels of an EL has a component in the direction from high towards low pressure  convergence over the surface low in the PBL  upward motion

6. A Tea Cup Experiment

7. Ekman pumping (or Ekman suction) and Secondary Circulation
The flow in the free atmosphere is indirectly affected by the friction near the surface through Ekman pumping or Ekman suction.

8. Mass convergence into low pressure centers and mass divergence out of high pressure centers will eventually destroy the weather systems while forcing upward vertical motion in low and downward vertical motion in high.

9. Equations in the PBL Do we have a closed equation set?
Overbars denote average over a time interval long enough to smooth out the small-scale eddy fluctuations but still short enough to preserve the trends of the large-scale flow field.
Do we have a closed equation set?
No! Closure assumptions must be made to approximate the unknown fluxes in terms of the mean state variables.

10. Assume horizontal homogeneous…

11. Assume horizontal homogeneous…
Assume force balance in the PBL…

12. Apply the flux-gradient theory
Assume the vertical flux of a given field is proportional to the local gradient of the mean:
where Km is the eddy viscosity coefficient and Kh is the eddy diffusion of heat.
Assuming Km is a constant, we have:
There are limitations in the K theory.
These are two coupled 2nd order ordinary differential equations governing two unknowns u and v . The wind in an Ekman layer has the same horizontal structure as the geostrophic wind aloft, and its z dependence is explicitly governed by the two equations.

13. We will examine the effect of friction on the wind in the Ekman layer:
How does the wind field change with height?
What determines the Ekman pumping (or Ekman suction)?
How is the Ekman layer coupled to the free atmosphere?

14. Limitations
The Ekman layer solution does not apply to the surface layer.
The flux-gradient approximation may not be valid.
Km is not a constant in the PBL.
The atmosphere is not neutral.

15. Barotropic, neutral atmosphere

16. Stable Stratification
This vertically confined secondary flow will quickly spin down the vorticity at the top of the Ekman layer without appreciably affecting the higher levels. When the geostrophic vorticity at the top of the boundary layer is reduced to zero, the pumping action of the Ekman layer is eliminated. The result is a baroclinic vortex with a vertical shear of the azimuthal velocity.
Spin-down above the PBL
Adiabatic cooling

17. BL drag + free atmosphere rotation  convergence over cyclonic circulation  upward mass transport out of the Ekman layer  divergence above the Ekman layer  spin- down of the cyclone in the free atmosphere
BL drag + free atmosphere rotation  convergence over cyclonic circulation  Ekman pumping  adiabatic cooling (stable stratification)  thermal wind balance