An updated length‐scale formulation for turbulent mixing in clear and cloudy boundary layers

A new mixing-length scale is presented for turbulence-closure schemes, with special emphasis on neutral-to-convective conditions in clear and cloudy boundary layers. The length scale is intended for a prognostic turbulent-kinetic-energy closure. It is argued that present-day length-scale formulations may easily fail in one of two limiting situations. Schemes based on a local stability measure (e.g. the Richardson number) display unrealistic behaviour and instabilities in the convective limit. This strongly limits the representation of mixing in cloudy boundary layers. On the other hand, it is shown that non-local parcel methods may misrepresent mixing near the surface. The new length-scale formulation combines local and non-local stability in a new way; it uses vertical integrals over the stability (the Richardson number) in a simple ‘parcel’ framework. The length scale matches with surface-layer similarity for near-neutral conditions and displays a realistic convective limit. The use of the length-scale formulation can be extended easily to cloudy boundary layers. The scheme is numerically stable and computationally cheap. The behaviour of the length scale is evaluated in a single-column model (SCM) and in a high-resolution limited-area model (LAM). The SCM shows good behaviour in three cases with and without boundary-layer clouds. The prediction of the near-surface wind and temperature in the LAM compares favourably with tower measurements at Cabauw (the Netherlands). Copyright © 2004 Royal Meteorological Society

[1]  J. Deardorff,et al.  Theoretical expression for the countergradient vertical heat flux , 1972 .

[2]  R. Stull.  An Introduction to Boundary Layer Meteorology , 1988 .

[3]  A. P. Siebesma,et al.  The diurnal cycle of shallow cumulus clouds over land: A single‐column model intercomparison study , 2004 .

[4]  P. Bechtold,et al.  A Simple Parameterization of Cloud Water Related Variables for Use in Boundary Layer Models , 1995 .

[5]  A. Holtslag,et al.  Evaluation of the ECHAM4 cloud-turbulence scheme for stratocumulus , 2000 .

[6]  C. Bretherton,et al.  The Atlantic Stratocumulus Transition Experiment - ASTEX , 1995 .

[7]  Albert A. M. Holtslag,et al.  Flux Parameterization over Land Surfaces for Atmospheric Models , 1991 .

[8]  P. Lacarrére,et al.  Improving the Eddy Kinetic Energy model for planetary boundary layer description , 1983 .

[9]  F. Nieuwstadt.  The Turbulent Structure of the Stable, Nocturnal Boundary Layer , 1984 .

[10]  J. Redelsperger,et al.  A turbulence scheme allowing for mesoscale and large‐eddy simulations , 2000 .

[11]  J. Wieringa,et al.  Atmospheric boundary layer research at Cabauw. , 1996 .

[12]  A. Holtslag,et al.  Evaluation of the Kinetic Energy Approach for Modeling Turbulent Fluxes in Stratocumulus , 2000 .

[13]  Jean-Christophe Golaz,et al.  Large‐eddy simulation of the diurnal cycle of shallow cumulus convection over land , 2002 .

[14]  Larry Mahrt,et al.  Simple formulation of turbulent mixing in the stable free atmosphere and nocturnal boundary layer , 1992 .

[15]  J. Louis.  A parametric model of vertical eddy fluxes in the atmosphere , 1979 .

[16]  Albert A. M. Holtslag,et al.  Impact of Skewness and Nonlocal Effects on Scalar and Buoyancy Fluxes in Convective Boundary Layers , 1998 .

[17]  Christopher S. Bretherton,et al.  A Moist PBL Parameterization for Large-Scale Models and Its Application to Subtropical Cloud-Topped Marine Boundary Layers , 2001 .

[18]  Brian H. Fiedler,et al.  Grid Adaption and Its Effect on Entrainment in an E–l Model of the Atmospheric Boundary Layer , 2002 .

[19]  A. Holtslag,et al.  Evaluation and model impacts of alternative boundary-layer height formulations , 1996 .

[20]  A. P. Siebesma,et al.  Model Impacts of Entrainment and Detrainment Rates in Shallow Cumulus Convection. , 1996 .

[21]  J. Walter Strapp,et al.  An Examination of Local versus Nonlocal Aspects of a TKE-Based Boundary Layer Scheme in Clear Convective Conditions , 1999 .

[22]  João Paulo Ramos Teixeira,et al.  Intercomparison of Three- and one-Dimensional Model Simulations and Aircraft Observations of Stratocumulus , 1999 .

[23]  G. Lenderink,et al.  Can an E–l Turbulence Closure Simulate Entrainment in Radiatively Driven Convective Boundary Layers? , 1999 .

[24]  A. Dyer.  A review of flux-profile relationships , 1974 .

[25]  Y. Delage,et al.  PARAMETERISING SUB-GRID SCALE VERTICAL TRANSPORT IN ATMOSPHERIC MODELS UNDER STATICALLY STABLE CONDITIONS , 1997 .

[26]  P. Duynkerke,et al.  Large Eddy Simulation of Trade Wind Cumulus Clouds. , 1993 .

[27]  P. Lacarrére,et al.  Parameterization of Orography-Induced Turbulence in a Mesobeta--Scale Model , 1989 .

[28]  M. Claussen,et al.  The atmospheric general circulation model ECHAM-4: Model description and simulation of present-day climate , 1996 .

[29]  A. Grant,et al.  Cloud‐base fluxes in the cumulus‐capped boundary layer , 2001 .

[30]  Albert A. M. Holtslag,et al.  Local Versus Nonlocal Boundary-Layer Diffusion in a Global Climate Model , 1993 .

[31]  Albert A. M. Holtslag,et al.  Eddy Diffusivity and Countergradient Transport in the Convective Atmospheric Boundary Layer , 1991 .

[32]  A. Blackadar.  The vertical distribution of wind and turbulent exchange in a neutral atmosphere , 1962 .

[33]  N. McFarlane,et al.  Modelling Boundary-Layer Clouds With a Statistical Cloud Scheme and a Second-Order Turbulence Closure , 2001 .

[34]  M. Tiedtke.  A Comprehensive Mass Flux Scheme for Cumulus Parameterization in Large-Scale Models , 1989 .

[35]  Roel Neggers,et al.  An Evaluation of Mass Flux Closures for Diurnal Cycles of Shallow Cumulus , 2004 .