TEMF Boundary Layer and Surface Layer                            March 2011

Release Notes

 

Wayne Angevine (Wayne.M.Angevine@noaa.gov)

 

Concept and purpose

 

The Total Energy – Mass Flux PBL scheme for WRF uses eddy diffusivity and mass flux concepts to determine vertical mixing.  It belongs to a category called EDMF (Eddy Diffusivity – Mass Flux) schemes.  Eddy diffusivity (K formulation) is used in stable parts of the column.  When the surface buoyancy flux is positive, a surface-based updraft is created, which transports heat, moisture, energy, and momentum upward.  The updraft represents non-local transport and takes care of the counter-gradient transport in the upper part of the boundary layer.  The eddy diffusivities (Kh and Km) are prognosed from total turbulent energy TE.  TE is similar to turbulent kinetic energy (TKE) but does not have a buoyancy destruction term.  For the eddy diffusivity part, therefore, TEMF could be considered a Ò1.5 orderÓ or Òlevel 2.5Ó (Mellor-Yamada) scheme.

 

The primary purpose of TEMF is to improve the representation of boundary layers with shallow cumulus clouds, and of stable boundary layers.  The inclusion of an explicit updraft allows natural integration of shallow cumulus cloud into the PBL scheme.  If the updraft condenses before its vertical velocity falls to zero, it is considered cloudy, and liquid water is produced internally.  A cloud fraction is diagnosed as well.  At this time, cloud produced inside TEMF does not affect the microphysics or radiation schemes, and is not included in the grid-scale moisture variables.  The stable boundary layer formulation of TEMF is derived from field data and large-eddy simulations.

 

Angevine et al. (2010) gives the equations implemented in the TEMF scheme and describes its performance in several 1D cases.  Earlier versions are described in Angevine (2005) and Mauritsen et al. (2007).  The WRF implementation includes some limits to improve stability which are not described in the paper, users interested in that level of detail are encouraged to read the code.

 

Compatibility

 

The TEMF PBL must be used with the matching TEMF surface layer.  The surface layer formulation uses a local Richardson number formulation rather than the usual similarity theory.

 

TEMF has been tested extensively with the thermal diffusion land surface scheme (option 1).  It has been tested much less extensively with the Noah LSM.  As far as I know, little or no testing has been done with other LSMs.

 

Caveats

 

There is no known unconditionally stable numerical solution to the EDMF equations.  As a result, TEMF may require a shorter timestep than other PBL schemes.  The possible instability occurs in the vertical column, and is therefore not sensitive to the horizontal grid spacing.  In a nested grid setup, this means that the longest timestep (coarsest domain) governs the stability.  One solution is to use another PBL scheme on the outermost grid.  For example, we have successfully used three grids of 36, 12, and 4 km spacing and 40 vertical levels with the MYJ PBL on the outer domain and 90 s timestep.  The release version uses an average of the current and previous values of the surface velocity scale to improve stability, so some of the above precautions may no longer be necessary.

 

Limits and implementation details

 

To improve stability, limits have been imposed on some variables.  These are intended to prevent extreme values leading to blowups.  The limits are:

á            Mass flux is limited so that mass flux contribution to heat flux at second level is less than or equal to diffusive (K) contribution.  This prevents the formation of a spurious stable layer.

á            Minimum Km = 1.57e-4 (10x molecular)

á            Minimum Kh = 1.57e-4/0.733 (10x molecular)

á            hd, hct <= 4000 m

á            Asymptotic length scale = 200 m

á            Beta terms of Km, Kh removed to prevent negative values

á            PBL height output (PBLH = hd) is only valid when convective

á            TE limited to <= 30

á            As with any scheme, the 10 m winds and 2 m temperature and mixing ratio are only valid if the lowest half-level is above 10 m or 2 m respectively.

 

Future work

 

The subgrid cloud produced by TEMF is represented by internal variables (*temf) for cloud fraction and updraft liquid.  At this time, those variables do not interact with radiation or microphysics.  How to do this is an ongoing research topic.  We welcome input or collaboration on this and other matters from users or prospective users of TEMF.

 

References

 

Angevine, W.M., H. Jiang, and T. Mauritsen, 2010: Performance of an eddy diffusivity – mass flux scheme for shallow cumulus boundary layers. Monthly Weather Review, 138, 2895-2912, doi:10.1175/2010MWR3142.1.

 

Angevine, W. M., 2005:  An integrated turbulence scheme for boundary layers with shallow cumulus applied to pollutant transport.  J.  Appl. Meteor., 44, 1436-1452.

 

Mauritsen, T., G. Svensson, S. S. Zilitinkevich, I. Esau, L. Enger, and B. Grisogono, 2007:  A total turbulent energy closure model for neutrally and stably stratified atmospheric boundary layers.  J. Atmos. Sci., 64, 4113-4126.