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 Atmospheric Profiling Station (KNMI)

A View of the Convective Boundary Layer Courtesy: Adriaan Schuitemaker

Encroachment

Encroachment

Encroachment

2. Large Eddy Simulations

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)

Dynamics of thermodynamical variables in LES

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

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

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

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

Internal Structure of PBL Rescale profiles

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

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

Courtesy: Harm Jonker

Courtesy : Harm Jonker

Courtesy : Harm Jonker

3. Parameterized dry convection in Climate Models

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

Spectral Gap

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

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

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)

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)

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: z/zinv 1 0.1 K w* /zinv Optional: Prescribe K at the top of the boundary layer as to get the right entrainment rate. (Operational in ECMWF model)

“flux against the gradient” 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

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.

“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……………. zinv

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

ED-CG ED LES ED Mean profile after 10 hrs

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