1. Parametrization of the planetary boundary layer (PBL) Martin Köhler & Anton Beljaars (rooms 108/114)
Introduction. Martin
Surface layer and surface fluxes. Anton
Outer layer. Martin
Stratocumulus. Martin
PBL evaluation. Maike
Exercises. Martin & Maike

2. Los Angeles PBL July 2001 Downtown LA PBL top 10km
Griffith Observatory
1000 to die annually in LA from heart disease resulting from SMOG.

3. California stratocumulus and forest fires
Wolf Fire (6 June 2002)
Downtown LA
MODIS on Terra (res. 250m)
visibleearth.nasa.gov

4. Boundary layer: definition
The PBL is the layer close to the surface within which vertical transports by turbulence play dominant roles in the momentum, heat and moisture budgets.
Turbulent flows are characterized by fluctuating dynamical quantities in space and time in a “disordered” manner (Monin and Yaglon, 1973).
Why is PBL turbulent?
high Reynolds numbers Re = UL/ν > 2000, ν ~ 10-5 m2/s
low Richardson number

5. Laboratory observations: transition to turbulence

6. Laboratory observations: laminar and turbulent BL

7. Space and time scales
Diffusive transport in the atmosphere is dominated by turbulence.
Time scale of turbulence varies from seconds to half hour.
Length scale varies from mm for dissipative eddies to 100 m for transporting eddies.
The largest eddies are the most efficient ones for transport.
cyclones
microscale
turbulence
diurnal cycle
spectral gap
100 hours
1 hour
0.01 hour
data: 1957

8. Power spectrum … which spectral gap?
10000
1000
100 10 1
Period in Hours -8 -7 -6 -5 -4 -3 -2
Power Spectrum of Wind / Period
Cabauw Data 1987 (10m)
24h
diurnal harmonics
12h
30-80 days
(t,radiative)
cyclones 8h
cyclones
t-5/3
diurnal cycle
spectral gap
Brookhaven Data 1957
10000 hours
100 hours
1 hour

9. Spectrum from time series of wind (Stratus buoy)
Amplitude spectrum
( )
-5/6 (3D turbulence)
diurnal cycle
24 hours
2 hours

10. Wave number spectra near tropopause
5000 km
cyclones
k-3
500 km
k-5/3
2 km
shifted
GASP aircraft data near tropopause
Nastrom and Gage (1985)

11. Wave number spectra at z=150m below stratocumulus
U Spectrum
Reynolds
Decomposition?
V Spectrum
W Spectrum
500m
Duynkerke 1998

12. T-tendencies due to turbulence scheme
[K/day]
Jan. 1999

13. T-tendencies due to convection scheme
[K/day]
Jan. 1999

14. U-Profile … Effects of Terrain
z0~1-10cm
z0~50cm
z0~1m
Ocean:
z0~0.1-1mm
Neutral:
Oke 1978

15. U-Profile … Effects of Stability
Height
Neutral
Stable
Unstable
surface layer
ln (Height)
Neutral:
Oke 1978

16. Diurnal cycle of boundary layer height
Sunrise
Sunset
(residual BL)
Local Time
stable BL
convective BL
stable BL
Oke 1978

17. Diurnal cycle of profiles
convective BL
stable BL
Oke 1978

18. Conserved variables
For turbulent transport in the vertical, quantities are needed that are conserved for adiabatic ascent/descent.
For dry processes:
pot. temperature
dry static energy
For moist processes:
liq. wat. pot. temperature
liq. water static energy
total water

19. Buoyancy parameter unstable stable
To determine static stability, move a fluid parcel adiabatically in the vertical and compare the density of the parcel with the density of the surrounding fluid.
Virtual potential temperature and virtual dry static energy are suitable parameters to describe stability:

20. Basic equations
mom.
equ.’s
continuity

21. Reynolds decomposition
Substitute, apply averaging operator,
Boussinesq approximation (density in buoyancy terms only) and
hydrostatic approximation (vertical acceleration << buoyancy).
Averaging (overbar) is over grid box,
i.e. sub-grid turbulent motion is averaged out.
Property of averaging operator:

22. After Reynolds decomposition and averaging
2nd order
2nd order
The 2nd order correlations are unknown (closure problem) and need to be parametrized (i.e. expressed in terms of large scale variables).

23. Reynolds equations Boundary layer approximation
(horizontal scales >> vertical scales), e.g. :
High Reynolds number approximation
(molecular diffusion << turbulent transports), e.g.:
Reynolds Stress

24. Simple closures K-diffusion method: analogy to molecular diffusion
Mass-flux method:
mass flux (needs M closure)
entraining plume model

25. Turbulent Kinetic Energy equation
local TKE:
mean TKE:
Derive equation for E by combining equations of total velocity components and mean velocity components:
Storage
Mean flow TKE advection
Pressure correlation
Turbulent
transport
Shear production
Buoyancy
Dissipation

26. Mixed layer turbulent kinetic energy budget
dry PBL
Stull 1988
normalized

27. Literature
General:
Stull (1988): An introduction to boundary layer meteorology, Kluwer publishers.
Oke(1978): Boundary layer climate, Halsted press.
Boundary layer in large scale atmospheric models:
Holtslag and Duynkerke (eds., 1999): Clear and cloudy boundary layers, North Holland Press.
Surface fluxes:
Brutsaert (1982): Evaporation into the atmosphere, Reidel publishers.
Sensitivity of ECMWF boundary layer scheme:
Beljaars (1995): The impact of some aspects of the boundary layer scheme in the ECMWF model, ECMWF-seminar 1994.