Editorial Type:
Article
Article Type:
Research Article

A Diagnostic for Evaluating the Representation of Turbulence in Atmospheric Models at the Kilometric Scale

Rachel Honnert CNRM/GAME, Toulouse, France

Search for other papers by Rachel Honnert in
Current site
Google Scholar
PubMed Close
,
Valéry Masson CNRM/GAME, Toulouse, France

Search for other papers by Valéry Masson in
Current site
Google Scholar
PubMed Close
, and
Fleur Couvreux CNRM/GAME, Toulouse, France

Search for other papers by Fleur Couvreux in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Dec 2011
DOI:
https://doi.org/10.1175/JAS-D-11-061.1
Page(s):
3112–3131
Restricted access

Abstract

Turbulence is well represented by atmospheric models at very fine grid sizes, from 10 to 100 m, for which turbulent movements are mainly resolved, and by atmospheric models with grid sizes greater than 2 km, for which those movements are entirely parameterized. But what happens at intermediate scales, Wyngaard’s so-called terra incognita?

Here an original method is presented that provides a new diagnostic by calculating the subgrid and resolved parts of five variables at different scales: turbulent kinetic energy (TKE), heat and moisture fluxes, and potential temperature and mixing ratio variances. They are established at intermediate scales for dry and cumulus-topped convective boundary layers. The similarity theorem allows the determination of the dimensionless variables of the problem. When the subgrid and resolved parts are studied, a new dimensionless variable, the dimensionless mesh size , needs to be added to the Deardorff free convective scaling variables, where h is the boundary layer height and hc is the height of the cloud layer. Similarity functions for the subgrid and resolved parts are assumed to be the product of the similarity function of the total (subgrid plus resolved) variables and a “partial” similarity function that depends only on . In order to determine the partial similarity function form, large-eddy simulations (LES) of five dry and cloudy convective boundary layers are used. The resolved and subgrid parts of the variables at coarser grid sizes are then deduced from the LES fields.

The evolution of the subgrid and resolved parts in the boundary layer with is as follows: fine grids mainly resolve variables. As the mesh becomes coarser, more eddies are subgrid. Finally, for very large meshes, turbulence is entirely subgrid. A scale therefore exists for which the subgrid and resolved parts are equal. This is obtained for in the case of TKE, 0.4 for the potential temperature variance, and 0.8 for the mixing ratio variance, indicating that the velocity structures are smaller than those for the potential temperature, which are smaller than those for the mixing ratio. Furthermore, boundary layers capped by convective clouds have structures larger than dry boundary layer ones as displayed by the scaling in the partial similarity functions.

This new diagnostic gives a reference for evaluating current and future parameterizations at kilometric scales. As an illustration, the parameterizations of a mesoscale model are eventually evaluated at intermediate scales. In its standard version, the model produces too many resolved movements, as the turbulence scheme does not sufficiently represent the impact of the subgrid thermal. This is not true when a mass-flux scheme is introduced. However in this case, a completely subgrid thermal is modeled leading to an overestimation of the subgrid part.

Corresponding author address: Rachel Honnert, CNRM/GAME, 42, avenue Gaspard Coriolis, 31057 Toulouse CEDEX 01, France. E-mail: rachel.honnert@meteo.fr

Abstract

Turbulence is well represented by atmospheric models at very fine grid sizes, from 10 to 100 m, for which turbulent movements are mainly resolved, and by atmospheric models with grid sizes greater than 2 km, for which those movements are entirely parameterized. But what happens at intermediate scales, Wyngaard’s so-called terra incognita?

Here an original method is presented that provides a new diagnostic by calculating the subgrid and resolved parts of five variables at different scales: turbulent kinetic energy (TKE), heat and moisture fluxes, and potential temperature and mixing ratio variances. They are established at intermediate scales for dry and cumulus-topped convective boundary layers. The similarity theorem allows the determination of the dimensionless variables of the problem. When the subgrid and resolved parts are studied, a new dimensionless variable, the dimensionless mesh size , needs to be added to the Deardorff free convective scaling variables, where h is the boundary layer height and hc is the height of the cloud layer. Similarity functions for the subgrid and resolved parts are assumed to be the product of the similarity function of the total (subgrid plus resolved) variables and a “partial” similarity function that depends only on . In order to determine the partial similarity function form, large-eddy simulations (LES) of five dry and cloudy convective boundary layers are used. The resolved and subgrid parts of the variables at coarser grid sizes are then deduced from the LES fields.

The evolution of the subgrid and resolved parts in the boundary layer with is as follows: fine grids mainly resolve variables. As the mesh becomes coarser, more eddies are subgrid. Finally, for very large meshes, turbulence is entirely subgrid. A scale therefore exists for which the subgrid and resolved parts are equal. This is obtained for in the case of TKE, 0.4 for the potential temperature variance, and 0.8 for the mixing ratio variance, indicating that the velocity structures are smaller than those for the potential temperature, which are smaller than those for the mixing ratio. Furthermore, boundary layers capped by convective clouds have structures larger than dry boundary layer ones as displayed by the scaling in the partial similarity functions.

This new diagnostic gives a reference for evaluating current and future parameterizations at kilometric scales. As an illustration, the parameterizations of a mesoscale model are eventually evaluated at intermediate scales. In its standard version, the model produces too many resolved movements, as the turbulence scheme does not sufficiently represent the impact of the subgrid thermal. This is not true when a mass-flux scheme is introduced. However in this case, a completely subgrid thermal is modeled leading to an overestimation of the subgrid part.

Corresponding author address: Rachel Honnert, CNRM/GAME, 42, avenue Gaspard Coriolis, 31057 Toulouse CEDEX 01, France. E-mail: rachel.honnert@meteo.fr
Save
Cover Journal of the Atmospheric Sciences
Journal of the Atmospheric Sciences

  • Bougeault, P., and P. Lacarrère, 1989: Parameterization of orography-induced turbulence in a meso-beta-scale model. Mon. Wea. Rev., 117, 1872–1890.

    • Search Google Scholar
    • Export Citation

  • Brown, A., and Coauthors, 2002: Large-eddy simulation of the diurnal cycle of shallow cumulus convection over land. Quart. J. Roy. Meteor., 128, 1075–1093.

    • Search Google Scholar
    • Export Citation

  • Buckingham, E., 1914: On physically similar systems: Illustrations of the use of dimensional equations. Phys. Rev. E, 4, 345–376.

  • Cheng, A., K.-M. Xu, and B. Stevens, 2010: Effects of resolution on the simulation of boundary-layer clouds and the partition of kinetic energy to subgrid scales. J. Adv. Model. Earth Syst., 2 (3), doi:10.3894/JAMES.2010.2.3

    • Search Google Scholar
    • Export Citation

  • Clarke, R., A. Dyer, D. Reid, and A. Troup, 1971: The Wangara experiment: Boundary layer data. CSIRO Division of Meteorological Physics Tech. Paper 19, Division Meterological Physics Tech. Paper, CSIRO 22 pp.

    • Search Google Scholar
    • Export Citation

  • Côté, J., S. Gravel, A. Méthot, A. Patoine, M. Roch, and A. Staniforth, 1998: The operational CMC-MRB global environmental multiscale (GEM) model. Part I: Design considerations and formulation. Mon. Wea. Rev., 126, 1373–1395.

    • Search Google Scholar
    • Export Citation

  • Couvreux, F., F. Guichard, J.-L. Redelsperger, C. Kiemle, V. Masson, J.-P. Lafore, and C. Flamant, 2005: Water-vapour variability within a convective boundary-layer assessed by large-eddy simulations and IHOP_2002 observations. Quart. J. Roy. Meteor. Soc., 131, 2665–2693.

    • Search Google Scholar
    • Export Citation

  • Cuxart, C., P. Bougeault, and J.-L. Redelsperger, 2000: A turbulence scheme allowing for mesoscale and large-eddy simulations. Quart. J. Roy. Meteor. Soc., 126, 1–30.

    • Search Google Scholar
    • Export Citation

  • Deardorff, J. W., 1970a: Convective velocity and temperature scales for the unstable planetary boundary layer and Rayleigh convection. J. Atmos. Sci., 27, 1211–1213.

    • Search Google Scholar
    • Export Citation

  • Deardorff, J. W., 1970b: A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech., 41, 453–480.

    • Search Google Scholar
    • Export Citation

  • Deardorff, J. W., 1972: Numerical investigation of neutral and unstable planetary boundary layers. J. Atmos. Sci., 29, 91–115.

  • De Roode, S., P. Duynkerke, and H. Jonker, 2004: Large-eddy simulation: How large is large enough? J. Atmos. Sci., 61, 403–421.

  • Drobinski, P., P. Carlotti, J.-L. Redelsperger, R. Banta, V. Masson, and R. Newsom, 2007: Numerical and experimental investigation of the neutral atmospheric surface layer. J. Atmos. Sci., 64, 137–156.

    • Search Google Scholar
    • Export Citation

  • Huang, J., M. Cassiani, and J. Albertson, 2009: Analysis of coherent structures within the atmospheric boundary layer. Bound.-Layer Meteor., 131, 147–171.

    • Search Google Scholar
    • Export Citation

  • Kolmogorov, A. N., 1942: Equations of turbulent motion of an incompressible fluid. Izυ. Akad. Nauk. SSSR, 6, 56–58.

  • Lafore, J., and Coauthors, 1998: The Méso-NH atmospheric simulation system. Part I: Adiabatic formulation and control simulation. Ann. Geophys., 16, 90–109.

    • Search Google Scholar
    • Export Citation

  • Lenschow, D., J. Wyngaard, and W. T. Pennell, 1980: Mean-field and second-moment budgets in a baroclinic, convective boundary layer. J. Atmos. Sci., 37, 1313–1326.

    • Search Google Scholar
    • Export Citation

  • Moeng, C., and J. Wyngaard, 1984: Statistics of conservative scalars in the convective boundary layer. J. Atmos. Sci., 41, 3161–3169.

  • Pergaud, J., V. Masson, S. Malardel, and F. Couvreux, 2009: A parameterization of dry thermals and shallow cumuli for mesoscale numerical weather prediction. Bound.-Layer Meteor., 132, 83–106.

    • Search Google Scholar
    • Export Citation

  • Redelsperger, J. L., C. D. Thorncroft, T. L. A. Diedhiou, D. J. Parker, and J. Polcher, 2006: African Monsoon Multidisciplinary Analysis: An international research project and field campaign. Bull. Amer. Meteor. Soc., 87, 1739–1746.

    • Search Google Scholar
    • Export Citation

  • Sandu, I., J.-L. Brenguier, O. Geoffroy, O. Thouron, and V. Masson, 2008: Aerosols impacts on the diurnal cycle of marine stratocumulus. J. Atmos. Sci., 65, 2705–2718.

    • Search Google Scholar
    • Export Citation

  • Seity, Y., P. Brousseau, S. Malardel, G. Hello, P. Benard, F. Bouttier, C. Lac, and V. Masson, 2011: The AROME-France convective-scale operational model. Mon. Wea. Rev., 139, 976–991.

    • Search Google Scholar
    • Export Citation

  • Siebesma, P., and Coauthors, 2004: Cloud representation in general-circulation models over the northern Pacific Ocean: A EUROCS intercomparison study. Quart. J. Roy. Meteor. Soc., 130, 3245–3267.

    • Search Google Scholar
    • Export Citation

  • Sorbjan, Z., 1991: Evaluation of local similarity functions in the convective boundary layer. J. Appl. Meteor., 30, 1565–1583.

  • Sullivan, P. P., and E. G. Patton, 2008: A highly parallel algorithm for turbulence simulations in planetary boundary layers: Results with meshes up to 10243. Preprints, 18th Symp. on Boundary Layer and Turbulence, Stockholm, Sweden, Amer. Meteor. Soc., 11B.5. [Available online at http://ams.confex.com/ams/pdfpapers/139870.pdf.]

    • Search Google Scholar
    • Export Citation

  • Weckwerth, T., and Coauthors, 2004: An overview of the International H2O Project (IHOP_2002) and some preliminary highlights. Bull. Amer. Meteor. Soc., 85, 253–277.

    • Search Google Scholar
    • Export Citation

  • Wyngaard, J., 2004: Toward numerical modelling in the “terra incognita.” J. Atmos. Sci., 61, 1816–1826.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1426 418 24
PDF Downloads 1146 352 23