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A comparison of local and non-local turbulence closure methods for the case of a cold air outbreak

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Abstract

Numerical experiments have shown that large-eddy-simulation models (LES) are able to reproduce the common features of convective boundary layers (CBL) quite well. Models which cannot resolve the convective motions due to their grid structure (1D-models or models with coarse horizontal and/or vertical resolution) have to take into account the effects of large eddies within their subgrid diffusion terms. Turbulent fluxes are frequently parameterized through first-order-closure methods (K-theory). Recently, non-local closure schemes have also been developed. In this paper we compare 1D-and 2D-models using different local and non-local first-order closure methods. The analysis is carried out for the case of an idealized cold air outbreak (CAO). One of the non-local closures is based on the so-called transilient turbulence theory. The reference states are given by a bulk-model and a 2D-model which resolves the large eddies explicitly. A comparison of the results is presented for characteristic quantities such as evolution of boundary-layer height and surface heat flux as well as mean wind and temperature profiles. It is found that simple local first-order closure does not give good agreement with the reference models. The results of the transilient turbulence model shows that a non-local closure is able to parameterize the effects of the large eddies. Comparable results are produced by a local closure where eddy diffusivities are parameterized by dimensionless gradient-functions.

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References

  • Blackadar, A. K.: 1962, ‘The Vertical Distribution of Wind and Turbulence Exchange in a Neutral Atmosphere’, J. Geophys. Res. 67 3095–3102.

    Google Scholar 

  • Brown, R. A.: 1980, ‘Longitudinal Instabilities and Secondary Flows in the Planetary Boundary Layer: A Review’, Rev. Geophys. Space Phys. 18 683–697.

    Google Scholar 

  • Caughey, S. J. and Palmer, S. G.: 1979, ‘Some Aspects of Turbulence Structure through the Depth of the Convective Layer’, Q.J.R. Meteorol. Soc. 105 811–827.

    Google Scholar 

  • Charnock, H.: 1955, ‘Wind Stress on a Water Surface’, Q.J.R. Meteorol. Soc. 81 639–640.

    Google Scholar 

  • Chou, S.-H. and Atlas, D.: 1982, ‘Satellite Estimates of Ocean-Air Heat Fluxes during Cold Air Outbreaks’, Mon. Wea. Rev. 110 1434–1450.

    Google Scholar 

  • Chou, S.-H., Atlas, D., and Yeh, E.-N.: 1986, ‘Turbulence in a Convective Marine Atmospheric Boundary Layer’, J. Atmos. Sci. 43 547–564.

    Google Scholar 

  • Chrobok, G.: 1988, Zur numerischen Simulation Konvektiver Grenzschichten mit integralen Schlieβungsansätzen, Diploma Thesis, Faculty of Physics, University Hannover, F.R.G.

    Google Scholar 

  • Deardorff, J. W.: 1966, ‘The Counter Gradient Heat Flux in the Lower Atmosphere and in the Laboratory’, J. Atmos. Sci. 23 503–506.

    Google Scholar 

  • Deardorff, J. W.: 1970, ‘Convection Velocity and Temperature Scales for the Unstable Planetary Boundary Layer and for Rayleigh Convection’, J. Atmos. Sci. 27 1211–1213.

    Google Scholar 

  • Deardorff, J. W.: 1972, ‘Numerical Investigation of Neutral and Unstable Planetary Boundary Layers’, J. Atmos. Sci. 29 91–115.

    Google Scholar 

  • Deardorff, J. W.: 1979, ‘Prediction of Convective Mixed-Layer Entrainment for Realistic Capping Inversion Structure’, J. Atmos. Sci. 36 424–436.

    Google Scholar 

  • Deardorff, J. W., Willis, G. and Lilly, D. K.: 1969, ‘Laboratory Investigation of Non-Steady Penetractive Convection’, J. Fluid Mech. 35 7–31.

    Google Scholar 

  • Driedonks, A. G. M.: 1982, ‘Models and Observations of the Growth of the Atmospheric Boundary Layer’, Boundary-Layer Meteorol. 23 283–306.

    Google Scholar 

  • Driedonks, A. G. M. and Tennekes, H.: 1984, ‘Entrainment Effects in the Well-Mixed Atmospheric Boundary Layer’, Boundary-Layer Meteorol. 30 75–105.

    Google Scholar 

  • Ebert, E. E., Schumann, U. and Stull, R. B.: 1989, ‘Nonlocal Turbulent Mixing in the Convective Boundary Layer Evaluated from Large-Eddy Simulation’, J. Atmos. Sci. 46 2178–2207.

    Google Scholar 

  • Fiedler, B. H.: 1984, ‘An Integral Closure Model for the Vertical Turbulent Flux of a Scalar in a Mixed Layer’, J. Atmos. Sci. 41 674–680.

    Google Scholar 

  • Fiedler, B. H. and Moeng, C.-H.: 1985, ‘A Practical Integral Closure Model for Mean Vertical Transport of a Scalar in a Convective Boundary Layer’, J. Atmos. Sci. 42 359–363.

    Google Scholar 

  • Garratt, J. R.: 1977, ‘Review of Drag Coefficients over Oceans and Continents’, Mon. Wea. Rev. 105 915–929.

    Google Scholar 

  • Huang, C. Y. and Raman, S.: 1988, ‘A Numerical Study of the Marine Boundary Layer over the Gulfstream during Cold Air Advection’, Boundary-Layer Meteorol. 45 251–290.

    Google Scholar 

  • Lenschow, D. H.: 1974, ‘Model of the Height Variation of the Turbulence Kinetic Energy Budget in the Unstable Planetary Boundary Layer’, J. Atmos. Sci. 31 465–474.

    Google Scholar 

  • Moeng, C.-H.: 1984, ‘A Large-Eddy-Simulation Model for the Study of Planetary Boundary Layer Turbulence’, J. Atmos. Sci. 41 2052–2062.

    Google Scholar 

  • Moeng, C. H. and Wyngaard, J. C.: 1984, ‘Statistics of Conservative Scalars in the Convective Boundary Layer’, J. Atmos. Sci. 41 3161–3169.

    Google Scholar 

  • Moeng, C. H. and Wyngaard, J. C.: 1989, ‘Evaluation of Turbulent Transport and Dissipation Closures in Second-Order Modeling’, J. Atmos. Sci. 46 2311–2330.

    Google Scholar 

  • Raasch, S.: 1988, Numerische Simulation zur Entwicklung von Wirbelrollen und Konvektiver Grenzschicht bei Kaltluftausbrüchen über dem Meer, Ber. Instit. Meteorol. Klimatol. Univ. Hannover, 33, 154 pp.

  • Raasch, S.: 1990a, ‘Numerical Simulation of the Development of the Convective Boundary Layer During a Cold Air Outbreak’, Boundary-Layer Meteorol. 52 349–375.

    Google Scholar 

  • Raasch, S.: 1990b ‘Two Numerical Case Studies of Horizontal Roll Vortices in Near-Neutral Inversion Capped Planetary Boundary Layers’, Beitr. Phys. Atmos. 63 205–227.

    Google Scholar 

  • Holt, T. and Raman, S.: 1988, ‘A Review and Comparative Evaluation of Multilevel Boundary Layer Parameterizations for First Order and Turbulent Kinetic Energy Closure Schemes’, Rev. Geophys. 26 761–786.

    Google Scholar 

  • Schmidt, H. and Schumann, U.: 1989, ‘Coherent Structure of the Convective Boundary Layer Derived from Large-Eddy Simulations’, J. Fluid Mech. 200 511–562.

    Google Scholar 

  • Stage, S. A. and Businger, J. A.: 1981a, ‘A Model for Entrainment into a Cloud-Topped Marine Boundary Layer. Part I: Model Description and Application to a Cold Air Outbreak Episode’, J. Atmos. Sci. 38 2213–2229.

    Google Scholar 

  • Stage, S. A. and Businger, J. A.: 1981b, ‘A Model for Entrainment into a Cloud-Topped Marine Boundary Layer. Part II: Discussion of Model Behaviour and Comparison with other Models’, J. Atmos. Sci. 38 2230–2242.

    Google Scholar 

  • Stull, R. B.: 1984, ‘Transilient Turbulence Theory. Part I: The Concept of Eddy-Mixing Across Finite Distances’, J. Atmos. Sci. 41 3351–3367.

    Google Scholar 

  • Stull, R. B.: 1986, ‘Transilient Turbulence Theory. Part III: Bulk Dispersion Rate and Numerical Stability’, J. Atmos. Sci. 43 50–57.

    Google Scholar 

  • Stull, R. B.: 1988, An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, Dordrecht, 666 pp.

    Google Scholar 

  • Stull, R. B. and Driedonks, A. G. M.: 1987, ‘Applications of the Transilient Turbulence Parameterization to Atmospheric Boundary-Layer Simulations’, Boundary-Layer Meteorol. 43 209–239.

    Google Scholar 

  • Sun, W.-Y.: 1989, ‘Numerical Study of Dispersion in the Convective Boundary Layer’, Atmos. Environ. 23 1205–1217.

    Google Scholar 

  • Sun, W.-Y. and Hsu, W. R.: 1988, ‘Numerical Study of a Cold Air Outbreak over the Ocean’, J. Atmos. Sci. 45 1205–1227.

    Google Scholar 

  • Sykes, R. L., Lewellen, W. S. and Henn, D. S.: 1990, ‘Numerical Simulation of the Boundary Layer Structure during Cold Air Outbreak of GALE IOP-2’, Mon. Wea. Rev. 118 363–374.

    Google Scholar 

  • Therry, G. and Lacarrere, P.: 1983, ‘Improving the Eddy Kinetic Energy Model for Planetary Boundary Layer Description’, Boundary-Layer Meteorol. 25 63–88.

    Google Scholar 

  • Weil, J. C.: 1990, ‘A Diagnosis of the Asymmetry in Top-Down and Bottom-Up Diffusion using a Lagrangian Stochastic Model’, J. Atmos. Sci. 47 501–515.

    Google Scholar 

  • Wyngaard, J. C.: 1984, ‘Toward Convective Boundary Layer Parameterization: A Scalar Transport Module’, J. Atmos. Sci. 41 1959–1969.

    Google Scholar 

  • Wyngaard, J. C.: 1987, ‘A Physical Mechanism for the Asymmetry in Top-Down and Bottom-Up Diffusion’, J. Atmos. Sci. 44 1083–1087.

    Google Scholar 

  • Wyngaard, J. C. and Brost, R. A.: 1984, ‘Top-Down and Bottom-Up Diffusion of a Scalar in the Convective Boundary Layer’, J. Atmos. Sci. 41 102–112.

    Google Scholar 

  • Young, G. S.: 1988, ‘Turbulence Structure of the Convective Boundary Layer. Part II: Phoenix 78 Aircraft Observations of Thermals and Their Environment’, J. Atmos. Sci. 45 727–735.

    Google Scholar 

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Authors and Affiliations

  1. Institut für Meteorologie und Klimatologie, Universität Hannover, Herrenhäuser Str. 2, 3000, 21, Hannover, Germany

    G. Chrobok, S. Raasch & D. Etling

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  1. G. Chrobok
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  2. S. Raasch
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  3. D. Etling
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Chrobok, G., Raasch, S. & Etling, D. A comparison of local and non-local turbulence closure methods for the case of a cold air outbreak. Boundary-Layer Meteorol 58, 69–90 (1992). https://doi.org/10.1007/BF00120752

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