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Phenomenology, Simulation and Parameterization of Atmospheric Convection

Phenomenology, Simulation and Parameterization of Atmospheric Convection. Pier Siebesma. Today: “ Dry” Atmospheric Convection Tomorrow: “Moist” Convection and Clouds. 1. Phenomenology. The Place of the Convective Boundary Layer. Evolution of the Convective Boundary Layer. Cabauw

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Phenomenology, Simulation and Parameterization of Atmospheric Convection

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  1. Phenomenology, Simulation and Parameterization of Atmospheric Convection Pier Siebesma Today: “Dry” Atmospheric Convection Tomorrow: “Moist” Convection and Clouds

  2. 1. Phenomenology

  3. The Place of the Convective Boundary Layer

  4. Evolution of the Convective Boundary Layer Cabauw Atmospheric Profiling Station (KNMI)

  5. A View of the Convective Boundary Layer Courtesy: Adriaan Schuitemaker

  6. Encroachment

  7. Encroachment

  8. Encroachment

  9. 2. Large Eddy Simulations

  10. Large Eddy Simulation (LES) Model (Dx<100m) • High Resolution non-hydrostatic Model (Boussinesq or Anelastic) 10~50m • Large eddies explicitly resolved by NS-equations • inertial range partially resolved • Therefore: subgrid eddies can be realistically parametrised by using Kolmogorov theory • Used for parameterization development of turbulence, convection, clouds Inertial Range Resolution LES 5 3 ln(Energy) DissipationRange ln(wave number)

  11. Dynamics of thermodynamical variables in LES

  12. :average over the horizontal domain Remark: Richardson law!!

  13. LES example: Classic Dry Convection PBL Case • Nx=Ny=128, Nz=150 • Lx=Ly=6.4km, Lz=3km • Dx=Dy=50m, Dz=20m • Lapse Rate: G= 2 10-3 K m-1 • Prescribed Surface Heat Flux :Qs = 6 10-2 K ms-1 Siebesma et al JAS 2007

  14. Potential Temperature:q Vertical velocity: w Courtesy: Chiel van Heerwaarden

  15. Quasi-Stationarity <-> Linear Fluxes Non-dimensionalise:

  16. Internal Structure of PBL Rescale profiles

  17. Growth of the PBL PBL height : Height where potential temperature has the largest gradient

  18. Mixed Layer Model of PBL growth Assume well-mixed profiles of q. Use simple top-entrainment assumption. q Boundary layer height grows as: Encroachment:

  19. Courtesy: Harm Jonker

  20. Courtesy : Harm Jonker

  21. Courtesy : Harm Jonker

  22. 3. Parameterized dry convection in Climate Models

  23. Energy Spectra in the atmosphere (1) Classic Picture (Frisch 86) Horizontal Kinetic Energy 1km 2d-turbulence 3d-turbulence E E Notation: 10000 km 10km 1 mm

  24. Spectral Gap

  25. k-3 Spectral Gap? 5000 km cyclones 500 km k-5/3 2 km GASP aircraft data near tropopause Nastrom and Gage (1985)

  26. Large scale advection Large scale subsidence turbulent transport Net Condensation Rate Grid Averaged Equations of thermodynamic variables DX=DY~100km , DZ~100m

  27. Mixed Layer Models? • Mixed Layer models useful for understanding, but….. • Not easily implementable in large scale models • No information on the internal structure • Only applicable under convective conditions • No transition possibe to other regimes (neutral, sheardriven, stable)

  28. Classic Parameterization of Turbulent Transport in de CBL Eddy-diffusivity models, i.e. • Natural Extension of Surface Layer Similarity theory • Diffusion tends to make profiles well mixed • Extension of mixing-length theory for shear-driven turbulence (Prandtl 1932)

  29. 1 z/zinv 0 0.1 K w* /zinv K-profile: The simplest Practical Eddy Diffusivity Approach (1) The eddy diffusivity K should forfill three constraints: • K-profile should match surface layer similarity near zero • K-profile should go to zero near the inversion • Maximum value of K should be around: Optional: Prescribe K at the top of the boundary layer as to get the right entrainment rate. (Operational in ECMWF model)

  30. A critique on the K-profile method (or an any eddy diffusivity method) (1) Diagnose the K that we would need from LES: K>0 Forbidden area “flux against the gradient” K<0 K>0 Down-gradient diffusion cannot account for upward transport in the upper part of the PBL

  31. Physical Reason! • In the convective BL undiluted parcels can rise from the surface layer all the way to the inversion. • Convection is an inherent non-local process. • The local gradientof the profile in the upper half of the convective BL is irrelevant to this process. • Theories based on the local gradient (K-diffusion) fail for the Convective BL.

  32. zinv “Standard “ remedy Add the socalled countergradient term: Long History: Ertel 1942 Priestley 1959 Deardorff 1966,1972 Holtslag and Moeng 1991 Holtslag and Boville 1993 B. Stevens 2003 And many more…………….

  33. Single Column Model tests for convective BL Only Diffusion: ED Diffusion + Counter-Gradient: ED-CG and solve (Analytical quasi-stationary solutions: B. Stevens MWR 2003) • Lapse Rate: G= 2 10-3 K m-1 • Prescribed Surface Heat Flux :Qs = 6 10-2 K ms-1 • Dz =20m Siebesma et al JAS 2007

  34. ED-CG ED LES ED Mean profile after 10 hrs

  35. Breakdown of the flux into an eddy diffusivity and a countergradient contribution No entrainment flux since the countergradient (CG) term is balancing the ED-term. LES ED-CG CG ED • Countergradient approach • Correct internal structure but….. • Underestimation of ventilation to free atmosphere • Cannot be extended to cloudy boundary layer total

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