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**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

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**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

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**Outline Definition Turbulence Stability Classification**

Clear convective boundary layers Cloudy boundary layers (stratocumulus and cumulus) Summary

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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)

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**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

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**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)

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**PBL: Governing equations for the mean state**

Reynolds averaging gas law virtual temperature

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**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

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**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.

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**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

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**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

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**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

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**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

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

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**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

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**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,

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**PBL: Diurnal variation**

Clear convective PBL Cloudy convective PBL

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**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

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**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

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**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

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**Clouds effects on climate**

Solar radiation Umbrella effect cooling Boundary layer clouds warming Greenhouse effect Infrared radiation

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**Cloudy marine boundary layers**

Stratocumulus capped boundary layers Fair weather cumuli Trade wind cumuli

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**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

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**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

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**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

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**Longwave radiative transfer in stratocumulus**

cooling warming At cloud top

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**Cumulus capped boundary layers**

Buoyancy is the main mechanism that forces cloud to rise Active cloud CAPE

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**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:

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**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

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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,

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