Surface and boundary layer parameterization Pathways of Information Clouds (CP/MP) Radiation Surface The “atmosphere” Boundary Layer Surface Layer Typical boundary layer evolution over land Parametrization of the planetary boundary layer (PBL) Martin Köhler & Anton Beljaars • Introduction. Martin • Surface layer and surface fluxes. Anton • Outer layer. Martin • Stratocumulus. Martin • PBL evaluation. Maike • Exercises. Martin & Maike Los Angeles PBL July 2001 Downtown LA PBL top 10km Griffith Observatory 1000 to 10000 die annually in LA from heart disease resulting from SMOG. California stratocumulus and forest fires Wolf Fire (6 June 2002) Downtown LA MODIS on Terra (res. 250m) visibleearth.nasa.gov 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? -5 2 • high Reynolds numbers Re = UL/ν > 2000, ν ~ 10 m /s g ∂θv θv ∂z • low Richardson number Ri = 2 <1/ 4 ⎛ ∂u ⎞ ⎜ ⎟ ⎝ ∂z ⎠ Laboratory observations: transition to turbulence Laboratory observations: laminar and turbulent BL 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 data: 1957 100 hours 1 hour 0.01 hour Power spectrum … which spectral gap? 10-2 Cabauw Data 1987 (10m) 24h diurnal harmonics 10-3 12h 30-80 days cyclones (t,radiative) 8h 10-4 10-5 cyclones t-5/3 -6 diurnal 10 cycle Power Spectrum of Wind / Period Wind Power of Spectrum 10-7 spectral gap Brookhaven Data 1957 10-8 10000 1000 100 10 1 Period in Hours 10000 hours 100 hours 1 hour Spectrum from time series of wind (Stratus buoy) Amplitude spectrum ( Power spectrum ) -5/6 (3D turbulence) diurnal cycle 24 hours 2 hours Wave number spectra near tropopause 5000 km k-3 cyclones 500 km k-5/3 2 km shifted GASP aircraft data near tropopause Nastrom and Gage (1985) Wave number spectra at z=150m below stratocumulus U Spectrum Reynolds Decomposition? V Spectrum W Spectrum 500m Duynkerke 1998 T-tendencies due to turbulence scheme [K/day] Jan. 1999 T-tendencies due to convection scheme [K/day] Jan. 1999 U-Profile … Effects of Terrain z0~1-10cm z0~50cm z0~1m Ocean:! uz* Neutral: U = ln z0~0.1-1mm κ z0 Oke 1978 U-Profile … Effects of Stability Neutral Stable Unstable " Height " uz* Neutral: U = ln κ z0 ln (Height) surface layer Oke 1978 Diurnal cycle of boundary layer height Sunrise Sunset (residual BL) Local Time stable BL convective BL stable BL Oke 1978 Diurnal cycle of profiles convective BL stable BL Oke 1978 Conserved variables For turbulent transport in the vertical, quantities are needed that are conserved for adiabatic ascent/descent. R/c p For dry processes: θ = T( po / p) , pot. temperature dry static energy or s = cpT + gz. Lθ For moist processes: θl =θ − ( )ql , liq. wat. pot. temperature cpT or sl = cpT + gz − Lql , liq. water static energy and qt = q + ql . total water 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. dθ dθ v < 0 v > 0 Virtual potential temperature and dz dz virtual dry static energy are suitable parameters to describe stability: {1 ( Rv 1)q q }, θv =θ + Rd − − l s c T{1 ( Rv 1)q q } gz, Rv 1 0.61 v = p + Rd − − l + Rd − ≈ Basic equations ∂u ∂u ∂u ∂u 1 ∂p 2 + u + v + w − fv = − +ν∇ u ∂t ∂x ∂y ∂z ρ ∂x mom. ∂v ∂v ∂v ∂v 1 ∂p 2 + u + v + w + fu = − +ν∇ v equ.’s ∂t ∂x ∂y ∂z ρ ∂y ∂w ∂w ∂w ∂w 1 ∂p 2 + u + v + w = − +ν∇ w − g ∂t ∂x ∂y ∂z ρ ∂z ∂u ∂v ∂w 1 dρ continuity + + = ∂x ∂y ∂z ρ dt Reynolds decomposition u =U + u', v =V + v', w =W + w' ρ = ρo + ρ', p = P + p'. 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: u ≡U + u' =U ≡U After Reynolds decomposition and averaging ∂U ∂U ∂U ∂U 1 ∂P 2 +U +V +W − fV = − +ν∇ U nd ∂t ∂x ∂y ∂z ρo ∂x 2 order ∂u'u' ∂u'v' ∂u'w' − − − ∂x ∂y ∂z ∂V ∂V ∂V ∂V 1 ∂P 2 +U +V +W + fU = − +ν∇ V nd ∂t ∂x ∂y ∂z ρo ∂y 2 order ∂u'v' ∂v'v' ∂v'w' − − − ∂x ∂y ∂z 1 ∂P 0 = − − g ρo ∂z ∂U ∂V ∂W + + = 0 ∂x ∂y ∂z The 2nd order correlations are unknown (closure problem) and need to be parametrized (i.e. expressed in terms of large scale variables). Reynolds equations Boundary layer approximation ∂u'u' ∂u'w' << (horizontal scales >> vertical scales), e.g. : ∂x ∂z High Reynolds number approximation ∂u'w' ν∇2U << (molecular diffusion << turbulent transports), e.g.: ∂z ∂∂∂∂UUUU1'' ∂∂ Puw +++U V W− fV =− − ∂∂∂txyz ∂ρo ∂∂ xz ∂∂∂∂VVVV1'' ∂∂ Pvw ++++=U V W fU − − ∂∂∂txyz ∂ρo ∂∂ yz Reynolds Stress Simple closures K-diffusion method: ∂U u'w' ≈ −K ∂z ∂∂∂uw'' U ∂2 analogy to ⎛⎞KKU ≈−⎜⎟ ≈−2 molecular diffusion ∂∂zz⎝⎠ ∂ z ∂ z Mass-flux method: up u'w' ≈ M (u −U ) mass flux (needs M closure) ∂ up up u = −ε(u −U ) entraining plume model ∂z Turbulent Kinetic Energy equation local TKE: Euvw'1/2('≡22++ ' ') 2 mean TKE: E ≡1/ 2(u'2 + v'2 + w'2 ) Derive equation for E by combining equations of total velocity components and mean velocity components: Storage Mean flow TKE advection ∂∂∂∂EEEE +++UVW = Pressure ∂∂∂txyz ∂ correlation ∂∂∂∂UVgpw'' −−Ew' ' uw ' ' −− vw ' 'ρε ' w ' +− ∂∂∂∂zzzzρρo Turbulent Shear production Buoyancy transport Dissipation Mixed layer turbulent kinetic energy budget dry PBL Stull 1988 normalized 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. Parametrization of surface fluxes: Outline • Surface layer (Monin Obukhov) similarity • Surface fluxes: Alternative formulations • Roughness length over land – Definition – Orographic contribution – Roughness lengths for heat and moisture • Ocean surface fluxes – Roughness lengths and transfer coefficients – Low wind speeds and the limit of free convection – Air-sea coupling at low wind speeds: Impact training course: boundary layer; surface layer Mixing across steep gradients Stable BL Dry mixed layer Cloudy BL θ θ θ Surface flux parametrization is sensitive because of large gradients near the surface. training course: boundary layer; surface layer Boundary conditions for T and q have different character over land and ocean Surface fluxes of heat and moisture are proportional to temperature and moisture differences: Lowest model level T1,q1 HcCUTT=ρ pH1 ()1 − s H E z1 ECUqq=ρ Es1 ()1 − Ts, qs Surface Ocean boundary condition Land boundary condition TT= s HEQG++=λ qq= () T cC U() T T C U { q q ()} T Q G sat s ρρλαpH1111− s+ E− sats += training course: boundary layer; surface layer Parametrization of surface fluxes: Outline • Surface layer (Monin Obukhov) similarity • Surface fluxes: Alternative formulations • Roughness length over land – Definition – Orographic contribution – Roughness lengths for heat and moisture • Ocean surface fluxes – Roughness lengths and transfer coefficients – Low wind speeds and the limit of free convection – Air-sea coupling at low wind speeds: Impact training course: boundary layer; surface layer Surface layer similarity (Monin Obukhov similarity) h For z/h << 1 flux is approximately equal to surface flux. Flux profile Considerations about the nature surface layer of the process: surf . • z/zo >> 1 0 τ o • distance to surface determines turbulence length scale • shear scales with surface Scaling parameters: friction rather than with zo z height or eddy size() m u* friction velocity= τρo /(/) m s −u3 L Obukhov length= * () m g H κ o training θρc course: vp boundary layer; surface layer MO similarity for gradients The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. ∂Uzκ z φm = is a universal function of ∂zu* L ∂Θ κ z φh = dimensionless shear Stability parameter∂z θ* κφ(von Karman constant) is defined such thatm == 1 forzL / 0 ∂Θ κ z z φh = is a universal function of ∂z θ* L dimensionless Stability parameter z potential temperatureL gradient −1 K 1 Note that with ⎛⎞∂U we obtain: m Kuwm =− ''⎜⎟ = ⎝⎠∂z κϕzu* m training course: boundary layer; surface layer MO gradient functions Observations of φ m as a function of z/L, with κ = 0.4 Empirical gradient functions to describe these observations: −1/ 4 φm = (1−16z / L) for z / L < 0 φm =1+ 5z / L for z / L > 0 unstable stable training course: boundary layer; surface layer Parametrization of surface fluxes: Outline • Surface layer (Monin Obukhov) similarity • Surface fluxes: Alternative formulations • Roughness length over land – Definition