1. Parametrization of the planetary boundary layer (PBL) Irina Sandu & Anton Beljaars
Introduction Irina
Surface layer and surface fluxes Anton
Outer layer Irina
Stratocumulus Irina
PBL evaluation Maike
Exercises Irina & Maike

2. Why studying the Planetary Boundary Layer ?
Natural environment for human activities
Understanding and predicting its structure
Agriculture, aeronautics, telecommunications, Earth energetic budget
Weather forecast, pollutants dispersion, climate prediction

3. Outline Definition Turbulence Stability Classification
Clear convective boundary layers
Cloudy boundary layers (stratocumulus and cumulus)
Summary

4. PBL: Definitions
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.
The layer where the flow is turbulent.
The fluxes of momentum, heat or matter are carried by turbulent motions on a scale of the order of the depth of the boundary layer or less.
The surface effects (friction, cooling, heating or moistening) are felt on times scales < 1 day.
Free troposphere
50 m
1 - 3 km
Mixed layer
surface layer  qv
Composition
atmospheric gases (N2, O2, water vapor, …)
aerosol particles
clouds (condensed water)

5. PBL: Turbulence U Characteristics of the flow Chaotic flow Properties
Rapid variation in time
Irregularity
Randomness
Properties
Diffusive
Dissipative
Irregular (butterfly effect)
Origin:
Hydrodynamic instability (wind shear) Reynolds number
Thermal instability Rayleigh number
Chaotic flow U
Reynolds – ratio between inertial and viscous forces 3*1e7

6. PBL: Governing equations for the mean state
gas law (equation of state) 
momentum (Navier Stokes) 
continuity eq. (conservation of mass) 
heat (first principle of thermodynamics) 
total water 
Reynolds averaging
Averaging (overbar) is over grid box, i.e. sub-grid turbulent motion is averaged out.
Simplifications
Boussinesq approximation (density fluctuations non-negligible only in buoyancy terms)
Hydrostatic approximation (balance of pressure gradient and gravity forces)
Incompressibility approximation (changes in density are negligible)

7. PBL: Governing equations for the mean state
Reynolds averaging
gas law
virtual temperature 

8. PBL: Governing equations for the mean state
Reynolds averaging
Need to be parameterized !
gas law
virtual temperature 
2nd order
momentum 
mean
advection
gravity
Coriolis
Pressure gradient
Viscous stress
Turbulent transport

9. PBL: Governing equations for the mean state
Reynolds averaging
gas law
virtual temperature 
2nd order
momentum 
mean
advection
gravity
Coriolis
Pressure gradient
Viscous stress
Turbulent transport
continuity eq. 

10. PBL: Governing equations for the mean state
Reynolds averaging
gas law
virtual temperature 
2nd order
momentum 
mean
advection
gravity
Coriolis
Pressure gradient
Viscous stress
Turbulent transport
continuity eq. 
heat 
mean
advection
turbulent
transport
Latent heat release
radiation

11. PBL: Governing equations for the mean state
Reynolds averaging
gas law
virtual temperature 
2nd order
momentum 
mean
advection
gravity
Coriolis
Pressure gradient
Viscous stress
Turbulent transport
continuity eq. 
heat 
mean
advection
turbulent
transport
Latent heat release
radiation
Total water 
total water 
mean
advection
turbulent
transport
precipitation
mean
advection
turbulent
transport
precipitation

12. PBL: Turbulent kinetic energy equation
TKE: a measure of the intensity of turbulent mixing
turbulent
transport
pressure
buoyancy
production
mechanical
shear
dissipation q v = 1 + . 61 - l ( )
virtual potential
temperature 
An example :
v’ < 0 , w’ < 0 or v’ > 0 , w’ > w’ v’ > source
v’ < 0 , w’ > 0 or v’ > 0 , w’ < w’ v’ < sink

13. PBL: Stability (I) stable unstable
Traditionally stability is defined using the temperature gradient
v gradient (local definition):
stable layer
unstable layer
neutral layer
How to determine the stability of the PBL taken as a whole ?
In a mixed layer the gradient of temperature is practically zero
Either v or w’ v’ profiles are needed to determine the PBL stability state
stable
unstable z z v v

14. PBL: Stability (II)
(Stull, 1988)
Stable
Unstable ?

15. PBL: Other ways to determine stability (III)
Bouyancy flux at the surface:
unstable PBL
(convective)
stable PBL
Or dynamic production of TKE integrated over the PBL depth stronger than thermal production
neutral PBL
Monin-Obukhov length:
-105m  L  –100m unstable PBL
-100m < L < strongly unstable PBL
0 < L < strongly stable PBL
10m  L  105m stable PBL
|L| > 105m neutral PBL
Rf <1 static stability is insuficiently strong to compensate mechanical gen of turb
Richardson flux number
Rf < 0 statically unstable flow
Rf > 0 statically stable flow
Rf < 1 dynamically unstable flow
Rf > 1 dynamically stable flow

16. PBL: Classification and scaling
Neutral PBL :
turbulence scale l ~ 0.07 H, H being the PBL depth
Quasi-isotropic turbulence
Scaling - adimensional parameters : z0, H, u*
Stable PBL:
l << H (stability embeds turbulent motion)
Turbulence is local (no influence from surface), stronger on horizontal
Scaling : , , H
Unstable (convective) PBL
l ~ H (large eddies)
Turbulence associated mostly to thermal production
Turbulence is non-homogeneous and asymmetric (top-down, bottom-up)
Scaling: H,

17. PBL: Diurnal variation
Clear convective PBL
Cloudy convective PBL

18. PBL: State variables Clear PBL Cloudy PBL q = T p æ è ç ö ø ÷ q » - L
Specific
humidity
Total water content q = T p æ è ç ö ø ÷ - R d / c
Liquid water potential temperature q l - L v c p
Potential temperature
Evaporation
temperature
ql= qt-qsat
qsat 
Cloud base qv
l= 
Conserved variables qt l

19. Stephan de Roode, Ph.D thesis
Clear Convective PBL qt
qsat v
Stephan de Roode, Ph.D thesis
Free atmosphere
Inversion layer
mixed layer
surface layer

20. Clear Convective PBL Buoyantly-driven from surface
turbulent fluxes : a function of convective
scaling variables:
PBL height:
Entrainment rate:
(a possible parameterization )
Fluxes at PBL top:
Key parameters:
inversion
Main source of TKE production
Turbulent transport and pressure term
0.7 H
level of neutral buoyancy

21. Clouds effects on climate
Solar radiation
Umbrella effect
cooling
Boundary layer clouds
warming
Greenhouse effect
Infrared radiation

22. Cloudy marine boundary layers
Stratocumulus capped boundary layers
Fair weather cumuli
Trade wind cumuli

23. Cloudy boundary layers
Stephan de Roode, Ph.D thesis qt
qsat v
Free atmosphere
Inversion layer
Stratocumulus topped PBL
mixed layer
surface layer qt
qsat v
Free atmosphere
Dry-adiabatic
lapse rate
Inversion layer
Cumulus PBL
Conditionally unstable cloud layer
wet-adiabatic
lapse rate
Subcloud mixed
surface layer

24. Cloudy boundary layers
Stephan de Roode, Ph.D thesis qt
qsat v
Free atmosphere
Inversion layer
Stratocumulus topped PBL
mixed layer
surface layer qt
qsat v
Free atmosphere
Dry-adiabatic
lapse rate
Inversion layer
Cumulus PBL
Conditionally unstable cloud layer
wet-adiabatic
lapse rate
Subcloud mixed
surface layer

25. Stratocumulus topped boundary layer
Complicated turbulence structure
Cloud top entrainment
Buoyantly driven by radiative cooling
at cloud top
Surface latent and heat flux play an
important role
Cloud top entrainment an order of
magnitude stronger than in clear PBL
Solar radiation transfer essential for
the cloud evolution
Key parameters:
condensation
Long-wave cooling
Long-wave warming

26. Longwave radiative transfer in stratocumulus
cooling
warming
At cloud top

27. Cumulus capped boundary layers
Buoyancy is the main mechanism that forces cloud to rise
Active cloud
CAPE

28. Cumulus capped boundary layers
Buoyancy is the main mechanism that forces cloud to rise
Represented by mass flux convective
schemes
Decomposition: cloud + environment
Lateral entrainment/detrainment rates
prescribed
Key parameters:

29. PBL: Summary Characteristics : Classification: Clear convective
several thousands of meters – 2-3 km above the surface
turbulence, mixed layer
convection
Reynolds framework
Classification:
neutral (extremely rare)
stable (nocturnal)
convective (mostly diurnal)
Clear convective
Cloudy (stratocumulus or cumulus)
Importance of boundary layer clouds (Earth radiative budget)
Small liquid water contents, difficult to measure

30. Bibliography
Deardorff, J.W. (1973) Three-dimensional numerical modeling of the planetary boundary layer, In Workshop on Micrometeorology, D.A. Haugen (Ed.), American Meteorological Society, Boston,
P. Bougeault, V. Masson, Processus dynamiques aux interfaces sol-atmosphere et ocean-atmosphere, cours ENM
Nieuwstad, F.T.M., Atmospheric boundary-layer processes and influence of inhomogeneos terrain. In Diffusion and transport of pollutants in atmospheric mesoscale flow fields (ed. by Gyr, A. and F.S. Rys), Kluwer Academic Publishers, Dordrecht, The Netherlands, , 1995.
Stull, R. B. (1988) An introduction to boundary layer meteorology, Kluwer Academic Publisher, Dordrecht, The Netherlands.
S. de Roode (1999), Cloudy Boundary Layers: Observations and Mass-Flux Parameterizations, Ph.D. Thesis
Wyngaard, J.C. (1992) Atmospheric turbulence, Annu. Rev. Fluid Mech. 24,