Atmospheric Planetary Boundary Layer (ABL / PBL): theory, modelling and applications Sergej S. Zilitinkevich Division of Atmospheric Sciences, University of Helsinki, Finland Meteorological Research, Finnish Meteorological Institute, Helsinki Nansen Environmental and Remote Sensing Centre, Bergen, Norway University of Helsinki Part 1 Stably Stratified Atmospheric Boundary Layer (SBL) University of Helsinki References Zilitinkevich, S., and Calanca, P., 2000: An extended similarity-theory for the stably stratified atmospheric surface layer. Quart. J. Roy. Meteorol. Soc., 126, 1913-1923. Zilitinkevich, S., 2002: Third-order transport due to internal waves and non-local turbulence in the stably stratified surface layer. Quart, J. Roy. Met. Soc. 128, 913-925. Zilitinkevich, S.S., Perov, V.L., and King, J.C., 2002: Near-surface turbulent fluxes in stable stratification: calculation techniques for use in general circulation models. Quart, J. Roy. Met. Soc. 128, 1571-1587. Zilitinkevich S. S., and Esau I. N., 2005: Resistance and heat/mass transfer laws for neutral and stable planetary boundary layers: old theory advanced and re-evaluated. Quart. J. Roy. Met. Soc. 131, 1863-1892. Zilitinkevich, S., Esau, I. and Baklanov, A., 2007: Further comments on the equilibrium height of neutral and stable planetary boundary layers. Quart. J. Roy. Met. Soc. 133, 265-271. Zilitinkevich, S. S., and Esau, I. N., 2007: Similarity theory and calculation of turbulent fluxes at the surface for stably stratified atmospheric boundary layers. Boundary-Layer Meteorol. 125, 193-296. Zilitinkevich, S.S., Elperin, T., Kleeorin, N., and Rogachevskii, I., 2007: Energy- and flux-budget (EFB) turbulence closure model for the stably stratified flows. Part I: Steady-state, homogeneous regimes. Boundary-Layer Meteorol. 125, 167-192. Zilitinkevich, S. S., Mammarella, I., Baklanov, A. A., and Joffre, S. M., 2008: The effect of stratification on the roughness length and displacement height. Submitted to Boundary- Layer Meteorol. University of Helsinki Motivation University of Helsinki State of the art University of Helsinki Basic types of the SBL • Until recently ABLs were distinguished accounting only for F =F : bs ∗ neutral at F =0 ∗ stable at F <0 ∗ • Now more detailed classification: truly neutral (TN) ABL: F =0, N=0 ∗ conventionally neutral (CN) ABL:F =0, N>0 ∗ nocturnal stable (NS) ABL: F <0, N=0 ∗ long-lived stable (LS) ABL: F <0, N>0 ∗ • Realistic surface flux calculation scheme should be based on a model applicable to all these types of the ABL University of Helsinki MEAN PROFILES & SURFACE FLUXES Content • Revision of the similarity theory for the stably stratified ABL • Analytical approximations for the wind velocity and potential temperature profiles across the ABL • Validation of new theory against LES and observational data • Improved surface flux scheme for use in operational models _______________________________________________________________ Zilitinkevich, S. S., and Esau, I. N., 2007: Similarity theory and calculation of turbulent fluxes at the surface for stably stratified atmospheric boundary layers. Boundary-Layer Meteorol. 125, 193-296. University of Helsinki Turbulence in atmospheric models r • turbulence closure – to calculate vertical fluxes: τ and F through mean θ r gradients: dU / dz and dΘ / dz • flux-profile relationships – to calculate the surface fluxes: u2 =τ =τ| , ∗ ∗ z=0 F = F | through wind speed U =U | and potential temperature ∗ θ z=0 1 z=z 1 Θ = Θ | at a given level z 1 z=z 1 1 • Warning: In NWP and climate models, the lowest computational level is z ~30 m 1 University of Helsinki Neutral stratification (no problem) From logarithmic wall law: dU τ1/2 dΘ − F τ1/2 z − F z = , = θ , U = ln , Θ − Θ = θ ln dz kz dz k τ1/2z k z 0 k τ1/2 z T 0u T 0u k, k von Karman constants; z aerodynamic roughness length for momentum; T 0u Θ aerodynamic surface potential temperature (at z ) [Θ -Θ through z ] 0 0u 0 s 0T It follows: τ1/2 = kU (ln z / z )−1, F =− kk U (Θ − Θ )(ln z / z )−2 1 1 0u θ1 T 1 1 0 0u τ =τ , F = F when z ≈ 30 m << h (cid:198) OK in neutral stratification 1 ∗ θ1 ∗ 1 University of Helsinki Stable stratification: current theory (i) local scaling, (ii) log-linear Θ-profile (cid:198) both questionable • When z is much above the surface layer (cid:198) τ ≠τ , F ≠ F 1 1 ∗ θ1 ∗ τ3/2 • Monin-Obukhov (MO) theory (cid:198) L = (neglects other scales)(cid:198) −βF θ kz dU k τ1/2z dΘ z = Φ (ξ), T = Φ (ξ), where ξ= τ1/2 dz M F dz H L θ • Φ = 1+ C ξ, Φ = 1+ C ξ from z-less stratification concept M U1 H Θ1 u ⎛ z z ⎞ − F ⎛ z z ⎞ U = ∗ ⎜ln + C ⎟, Θ − Θ = ∗ ⎜ln + C ⎟ ⎜ ⎟ ⎜ ⎟ U1 0 Θ1 k z L k u z L ⎝ ⎠ ⎝ ⎠ u0 s T ∗ u0 s • Ri≡ β(dΘ / dz)(dU / dz)−2 (cid:198) Ri =k 2C k −1C−2 (unacceptable) c Θ1 T U1 • C ~2, C also ~ 2 (factually increases with z\L) U1 Θ1 University of Helsinki