1. Parametrization of the planetary boundary layer (PBL) Irina Sandu & Maike Ahlgrimm
Introduction Irina
Surface layer and surface fluxes Irina
Outer layer Irina
PBL& Cloud 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/Equations 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: 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)

6. 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
continuity eq. 
heat 
mean
advection
turbulent
transport
Latent heat release
radiation
total water 
mean
advection
turbulent
transport
precipitation

7. 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

8. 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

9. PBL: Other ways to determine stability (II)
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
L is proportional with the height above the surface at which buoyant factors sominate over mechanical shear production of turbulence,

10. 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,

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

12. 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=  qt l
Conserved variables
Conserved variables

13. 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

14. Clear Convective PBL Buoyantly-driven from surface PBL height:
Entrainment rate: with
(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

15. Clouds effects on climate
Greenhouse effect : warming
Infrared radiation
High clouds, like cirrus
Solar radiation
Umbrella effect : cooling
Boundary layer clouds
(low clouds)
stratocumulus
Shallow cumulus

16. Boundary layer clouds over oceansEQ
warm
cold
SST & surface wind
Sc form in the east part of the oceanic basins, close to coastal regions, in regions where the strong subsidence associated with the descending branch of the Hadley cell and the relatively cold ocean surface lead to strong inversions at the top of the boundary layer
Shallow cumulus
stratocumulus

17. 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

18. Stratocumulus – Why are they important?
Cover in (annual) mean 29% of the planet (Klein and Hartmann, 1993)
Cloud top albedo is 50-80% (in contrast to 7 % at ocean surface).
A 4% increase in global stratocumulus extend would offset 2-3K
global warming from CO2 doubling (Randall et al. 1984).
Coupled models have large biases in stratocumulus extent and SSTs.
Why are the stratocumulus important? Stratocumulus cover a large extent of the planet, and are very important for the radiative budget. This is more particularly the case for marine stratocumulus which reflect a large part of the incoming solar radiation, especially compared with the oceans underneath. Despite of the fact that they are one of the most important cloud regimes, and lots of attention has been paid to understand the processes governing them and to try to improve their representation in models, the stratocumulus still remain one of the most difficult cloud regimes to reproduce in numerical models. Typically, coupled models have large biases in the stratocumulus extent.
Stratocumulus cloud cover (annual mean)
Wood, 2012,based on Han and Waren, 2007

19. Characterisation of a stratocumulus topped PBLrt
(g kg-1)
Subsidence
θl (K)
0.2g/kg
rsat
(g kg-1)
hSTBL
(m)
LWP (kg m-2)
(Liquid Water Path)
STBL
What is particular about a sc is that 1. it contains a very small amount of water compared to the total water content of the boundary layer. The water content in such a cloud is on the order of maximum 1g/kg, where in marine boundary layer the total water content is of 20g/kg. Hence such clouds are extremely sensitive to very fine changes in the thermodynamics...
20g/kg

20. Characterisation of a stratocumulus topped PBL
Subsidence
hSTBL
(m)
0.2g/kg
STBL
LWP (kg m-2)
A diminution of the total water content or an increase in the liquid water potential temperature of , or respectively , can make the cloud dissapear. 2. the evolution of these clouds is regulated by a myriad of interactions , as we are going to see in the following slides.
, which are difficult to represent in a large-scale model
20g/kg
(Liquid Water Path) rt
(g kg-1)
rsat
θl (K)
(g kg-1)
Such a cloudy system is extremely sensitive to thermodynamical conditions

21. Characterisation of a stratocumulus topped PBL
Subsidence
hSTBL
(m)
STBL
LWP (kg m-2)
(Liquid Water Path) rt
(g kg-1)
rsat
θl (K)
(g kg-1)
Such a cloudy system is extremely sensitive to thermodynamical conditions

22. Characterisation of a stratocumulus topped PBL
Subsidence
hSTBL
(m)
STBL
LWP (kg m-2)
0.6K
(Liquid Water Path) rt
(kg kg-1)
rsat
θl (K)
(kg kg-1)
Such a cloudy system is extremely sensitive to thermodynamical conditions

23. Night-time Well-mixed The cloud deepens l qt ql ql,adiabatic
Processes controlling the evolution of a non-precipitating stratocumulus
Night-time
Well-mixed
The cloud deepens
LW radiative cooling
Warm, dry,subsiding free-troposphere l qt ql
Entrainment warming, drying
ql,adiabatic
Surface heat and moisture fluxes
Courtesy of Bjorn Stevens (data from DYCOMS-II)

24. Daytime l qt ql ql,adiabatic The cloud thins Decoupled
Processes controlling the evolution of a non-precipitating stratocumulus
Daytime
Warm, dry, subsiding free-troposphere l qt ql
Entrainment warming, drying
LW radiative cooling
ql,adiabatic
The cloud thins
Decoupled
SW absorption
Stabilisation of the subcloud layer
Surface heat and moisture fluxes
Courtesy of Bjorn Stevens (data from DYCOMS-II)

25. Diurnal cycle during observed during FIRE-I experiment
Cloud top
LWP
Cloud base
8 LT LT LT LT LT
Hignett, 1991 (data from FIRE-I)

26. Precipitation flux
Under cloud evaporation affects the dynamics of the boundary layer
Scenario I v
stable LE
drizzle
Scenario II v
unstable
stable
decoupling
Cumulus

27. 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

28. 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

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

30. 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:

31. 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

32. 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
R. Wood (2012), Stratocumulus Clouds, Monthly Weather Review :8,
Wyngaard, J.C. (1992) Atmospheric turbulence, Annu. Rev. Fluid Mech. 24,