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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

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

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

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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 R e = UL/ν > 2000, ν ~ m 2 /s low Richardson number

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Laboratory observations: transition to turbulence

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Laboratory observations: laminar and turbulent BL

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Space and time scales 1 hour100 hours0.01 hour microscale turbulence 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. spectral gap diurnal cycle cyclones data: 1957

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

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Spectrum from time series of wind (Stratus buoy) -5/6 (3D turbulence) 2 hours24 hours diurnal cycle Amplitude spectrum ( )

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

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

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

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

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U-Profile … Effects of Terrain Oke 1978 Neutral: z 0 ~1-10cm Ocean: z 0 ~0.1-1mm z 0 ~50cmz 0 ~1m

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U-Profile … Effects of Stability Oke 1978 StableUnstable Height Neutral surface layer ln (Height) Neutral:

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Diurnal cycle of boundary layer height Oke 1978 SunriseSunset stable BLconvective BLstable BL Local Time (residual BL)

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Diurnal cycle of profiles Oke 1978 convective BL stable BL

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

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Buoyancy parameter 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. unstablestable Virtual potential temperature and virtual dry static energy are suitable parameters to describe stability:

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Basic equations mom. equ.s continuity

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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:

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

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

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

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

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Mixed layer turbulent kinetic energy budget normalized Stull 1988 dry PBL

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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.

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