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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 July 2001 Downtown LA PBL top 10km**

Griffith Observatory 1000 to die annually in LA from heart disease resulting from SMOG.

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**California stratocumulus and forest fires**

Wolf Fire (6 June 2002) Downtown LA MODIS on Terra (res. 250m) visibleearth.nasa.gov

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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 Re = UL/ν > 2000, ν ~ 10-5 m2/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 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. cyclones microscale turbulence diurnal cycle spectral gap 100 hours 1 hour 0.01 hour data: 1957

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**Power spectrum … which spectral gap?**

10000 1000 100 10 1 Period in Hours -8 -7 -6 -5 -4 -3 -2 Power Spectrum of Wind / Period Cabauw Data 1987 (10m) 24h diurnal harmonics 12h 30-80 days (t,radiative) cyclones 8h cyclones t-5/3 diurnal cycle spectral gap Brookhaven Data 1957 10000 hours 100 hours 1 hour

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**Spectrum from time series of wind (Stratus buoy)**

Amplitude spectrum ( ) -5/6 (3D turbulence) diurnal cycle 24 hours 2 hours

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**Wave number spectra near tropopause**

5000 km cyclones k-3 500 km k-5/3 2 km shifted GASP aircraft data near tropopause Nastrom and Gage (1985)

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**Wave number spectra at z=150m below stratocumulus**

U Spectrum Reynolds Decomposition? V Spectrum W Spectrum 500m Duynkerke 1998

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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**

z0~1-10cm z0~50cm z0~1m Ocean: z0~0.1-1mm Neutral: Oke 1978

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**U-Profile … Effects of Stability**

Height Neutral Stable Unstable surface layer ln (Height) Neutral: Oke 1978

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**Diurnal cycle of boundary layer height**

Sunrise Sunset (residual BL) Local Time stable BL convective BL stable BL Oke 1978

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**Diurnal cycle of profiles**

convective BL stable BL Oke 1978

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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: pot. temperature dry static energy For moist processes: liq. wat. pot. temperature liq. water static energy total water

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**Buoyancy parameter unstable stable**

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. 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**

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

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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 K-diffusion method: analogy to molecular diffusion**

Mass-flux method: mass flux (needs M closure) entraining plume model

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**Turbulent Kinetic Energy equation**

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

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**Mixed layer turbulent kinetic energy budget**

dry PBL Stull 1988 normalized

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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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