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

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

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

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)

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)

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

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’ > 0 w’ v’ > 0 source v’ < 0 , w’ > 0 or v’ > 0 , w’ < 0 w’ v’ < 0 sink

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

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 < 0 strongly unstable PBL 0 < L < 10 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,

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,

PBL: Diurnal variation Clear convective PBL Cloudy convective PBL

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

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

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

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

Boundary layer clouds over oceans EQ 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

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

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

Characterisation of a stratocumulus topped PBL rt (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

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

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

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

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)

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)

Diurnal cycle during observed during FIRE-I experiment Cloud top LWP Cloud base 8 LT 12 LT 16 LT 20LT 0LT Hignett, 1991 (data from FIRE-I)

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

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

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

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

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:

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

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, 271-311 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, 89-125, 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 2012 140:8, 2373-2423 Wyngaard, J.C. (1992) Atmospheric turbulence, Annu. Rev. Fluid Mech. 24, 205-233