• André, J. C., 1983: On the variability of the nocturnal boundary-layer depth. J. Atmos. Sci., 40 , 23092311.

  • André, J. C., , and L. Mahrt, 1982: The nocturnal surface inversion and influence of clear-air radiative cooling. J. Atmos. Sci., 39 , 864878.

    • Search Google Scholar
    • Export Citation
  • Anfossi, D., , P. Bacci, , and A. Longhetto, 1976: Forecasting of vertical temperature profiles in the atmosphere during nocturnal radiation inversions from air temperature trend at screen height. Quart. J. Roy. Meteor. Soc., 102 , 173180.

    • Search Google Scholar
    • Export Citation
  • Arya, S. P. S., 1981: Parameterizing the height of the stable atmospheric boundary layer. J. Appl. Meteor., 20 , 11921202.

  • Baas, P., , G. J. Steeneveld, , B. J. H. van de Wiel, , and A. A. M. Holtslag, 2006: Exploring self-correlation in flux–gradient relationships for stably stratified conditions. J. Atmos. Sci., 63 , 30453054.

    • Search Google Scholar
    • Export Citation
  • Beare, R. J., and Coauthors, 2006: An intercomparison of large-eddy simulations of the stable boundary layer. Bound.-Layer Meteor., 118 , 247272.

    • Search Google Scholar
    • Export Citation
  • Benkley, C. W., , and L. L. Schulman, 1979: Estimating hourly mixing depths from historical meteorological data. J. Appl. Meteor., 18 , 772780.

    • Search Google Scholar
    • Export Citation
  • Beyrich, F., 1994: Sodar observations of the stable boundary-layer height in relation to the nocturnal low-level jet. Meteor. Z., 3 , 2934.

    • Search Google Scholar
    • Export Citation
  • Beyrich, F., 1997: Mixing height estimation from sodar data: A critical discussion. Atmos. Environ., 31 , 39413953.

  • Beyrich, F., , and V. Kotroni, 1993: Estimation of surface stress over a forest from sodar measurements and its use to parameterize the stable boundary layer height. Bound.-Layer Meteor., 66 , 93103.

    • Search Google Scholar
    • Export Citation
  • Caughey, S. J., , J. C. Wyngaard, , and J. C. Kaimal, 1979: Turbulence in the evolving stable boundary layer. J. Atmos. Sci., 36 , 10411052.

    • Search Google Scholar
    • Export Citation
  • Cuxart, J., , and M. A. Jiménez, 2007: Mixing processes in a nocturnal low-level jet: An LES study. J. Atmos Sci, in press.

  • de Rooy, W. C., , and A. A. M. Holtslag, 1999: Estimation of surface radiation and energy flux densities from single-level weather data. J. Appl. Meteor., 38 , 526540.

    • Search Google Scholar
    • Export Citation
  • Estournel, C., , and D. Guedalia, 1990: Improving the diagnostic relation for the nocturnal boundary layer height. Bound.-Layer Meteor., 53 , 191198.

    • Search Google Scholar
    • Export Citation
  • Franks, S. W., , K. J. Beven, , P. F. Quinn, , and I. R. Wright, 1997: On the sensitivity of soil–vegetation–atmosphere transfer (SVAT) schemes: Equifinality and the problem of robust calibration. Agric. For. Meteor., 86 , 6375.

    • Search Google Scholar
    • Export Citation
  • Garratt, J. R., 1982: Surface fluxes and the nocturnal boundary layer height. J. Appl. Meteor., 21 , 725729.

  • Garratt, J. R., , and R. A. Brost, 1981: Radiative cooling effects within and above the nocturnal boundary layer. J. Atmos. Sci., 38 , 27302746.

    • Search Google Scholar
    • Export Citation
  • Gassmann, M. I., , and N. A. Mazzeo, 2001: Nocturnal stable boundary layer height model and its application. Atmos. Res., 57 , 247259.

  • Gryning, S. E., , A. A. M. Holtslag, , J. S. Irwin, , and B. Siversten, 1987: Applied dispersion modelling based on meteorological scaling parameters. Atmos. Environ., 21 , 7989.

    • Search Google Scholar
    • Export Citation
  • Halldin, S., Ed. 1999: Final report for WINTEX. NOPEX Tech. Rep. 29, 70 pp. [Available from NOPEX Central Office, Institute of Earth Sciences, Uppsala University, Norbyvägen 18B, SE-75236 Uppsala, Sweden.].

  • Hicks, R. B., , D. Smith, , P. J. Irwin, , and T. Mathews, 1977: Preliminary studies of atmospheric acoustic sounding at Calgary. Bound.-Layer Meteor., 12 , 201212.

    • Search Google Scholar
    • Export Citation
  • Holtslag, A. A. M., , and F. T. M. Nieuwstadt, 1986: Scaling the atmospheric boundary layer. Bound.-Layer Meteor., 36 , 201209.

  • Holtslag, A. A. M., , and H. A. R. de Bruin, 1988: Applied modeling of the nighttime surface energy balance over land. J. Appl. Meteor., 27 , 689704.

    • Search Google Scholar
    • Export Citation
  • Holtslag, A. A. M., , and B. A. Boville, 1993: Local versus nonlocal boundary-layer diffusion in a global climate model. J. Climate, 6 , 18251842.

    • Search Google Scholar
    • Export Citation
  • Joffre, S. M., , and M. Kangas, 2002: Determination and scaling of the atmospheric boundary layer height under various stability conditions over a rough surface. COST Action 715 Workshop on Urban Boundary Layer Parameterisations (Zurich, 24–25 May 2001), M. Rotach, B. Fisher, and M. Piringer, Eds., Office for Official Publications of the European Communities, EUR 20355, 111–118.

  • Joffre, S. M., , M. Kangas, , M. Heikinheimo, , and S. A. Kitaigorodskii, 2001: Variability of the stable and unstable boundary layer height and its scales over a boreal forest. Bound.-Layer Meteor., 99 , 429450.

    • Search Google Scholar
    • Export Citation
  • Karppinen, A., , S. Joffre, , J. Kukkonen, , and P. Bremer, 2001: Evaluation of inversion strengths and mixing heights during extremely stable atmospheric stratification. Int. J. Environ. Pollut., 16 , 111.

    • Search Google Scholar
    • Export Citation
  • Kitaigorodskii, S. A., , and S. Joffre, 1988: In search of a simple scaling for the height of the stratified atmospheric boundary layer. Tellus, 40A , 419433.

    • Search Google Scholar
    • Export Citation
  • Koracin, D., , and R. Berkowicz, 1988: Nocturnal boundary-layer height: Observations by acoustic sounders and prediction in terms of surface-layer parameters. Bound.-Layer Meteor., 43 , 6583.

    • Search Google Scholar
    • Export Citation
  • Kosovic, B., , and J. A. Curry, 2000: A large eddy simulation study of a quasi-steady, stably stratified atmospheric boundary layer. J. Atmos. Sci., 57 , 10521068.

    • Search Google Scholar
    • Export Citation
  • Kosovic, B., , and J. K. Lundquist, 2004: Influences on the height of the stable boundary layer. Preprints, 16th Symp. on Boundary Layers and Turbulence, Portland, ME, Amer. Meteor. Soc., CD-ROM, 4.20.

  • Langhaar, H. L., 1951: Dimensional Analysis and Theory of Models. John Wiley and Sons, 166 pp.

  • Lena, F., , and F. Desiato, 1999: Intercomparison of nocturnal mixing height estimate methods for urban air pollution modeling. Atmos. Environ., 33 , 23852393.

    • Search Google Scholar
    • Export Citation
  • Lenschow, D. H., , X. S. Li, , C. J. Zhu, , and B. B. Stankov, 1988: The stably stratified boundary layer over the Great Plains, I. Mean and turbulent structure. Bound.-Layer Meteor., 42 , 95121.

    • Search Google Scholar
    • Export Citation
  • Mahrt, L., 1981: Modelling the height of the stable boundary-layer. Bound.-Layer Meteor., 21 , 319.

  • Mahrt, L., , and R. C. Heald, 1979: Comments on “Determining height of the nocturnal boundary layer.”. J. Appl. Meteor., 18 , 383.

  • Mahrt, L., , and D. Vickers, 2002: Contrasting vertical structures of nocturnal boundary layers. Bound.-Layer Meteor., 105 , 351363.

  • Mahrt, L., , J. C. André, , and R. C. Heald, 1982: On the height of the nocturnal boundary layer. J. Appl. Meteor., 21 , 9092.

  • Mason, P. J., , and D. J. Thomson, 1987: Large-eddy simulations of the neutral-static-stability planetary boundary layer. Quart. J. Roy. Meteor. Soc., 113 , 413443.

    • Search Google Scholar
    • Export Citation
  • Melgarejo, J. W., , and J. W. Deardorff, 1974: Stability functions for the boundary-layer resistance laws based upon observed boundary-layer heights. J. Atmos. Sci., 31 , 13241333.

    • Search Google Scholar
    • Export Citation
  • Newsom, R. K., , and R. M. Banta, 2003: Shear-flow instability in the stable nocturnal boundary layer as observed by Doppler lidar during CASES-99. J. Atmos. Sci., 60 , 1633.

    • Search Google Scholar
    • Export Citation
  • Nieuwstadt, F. T. M., 1980a: A rate equation for the inversion height in a nocturnal boundary layer. J. Appl. Meteor., 19 , 14451447.

  • Nieuwstadt, F. T. M., 1980b: Some aspects of the turbulent stable boundary layer. Bound.-Layer Meteor., 30 , 3155.

  • Nieuwstadt, F. T. M., , and H. Tennekes, 1981: A rate equation for the nocturnal boundary-layer height. J. Atmos. Sci., 38 , 14181429.

  • Nieuwstadt, F. T. M., , and P. G. Duynkerke, 1996: Turbulence in the atmospheric boundary layer. Atmos. Res., 40 , 111142.

  • Pollard, R. T., , P. B. Rhines, , and R. O. R. Y. Thompson, 1973: The deepening of the wind-mixed layer. Geophys. Fluid Dyn., 3 , 381404.

  • Poulos, G. S., and Coauthors, 2002: CASES-99: A comprehensive investigation of the stable nocturnal boundary layer. Bull. Amer. Meteor. Soc., 83 , 555581.

    • Search Google Scholar
    • Export Citation
  • Salmond, J. A., , and I. G. McKendry, 2005: A review of turbulence in the very stable boundary layer and its implications for air quality. Prog. Phys. Geogr., 29 , 171188.

    • Search Google Scholar
    • Export Citation
  • Seibert, P., , F. Beyrich, , S. E. Gryning, , S. Joffre, , A. Rasmussen, , and P. Tercier, 2000: Review and intercomparison of operational methods for the determination of the mixing height. Atmos. Environ., 34 , 10011027.

    • Search Google Scholar
    • Export Citation
  • Stull, R. B., 1988: An Introduction to Boundary-Layer Meteorology. Kluwer Academic, 666 pp.

  • Troen, I. B., , and L. Mahrt, 1986: A simple model of the atmospheric boundary layer; sensitivity to surface evaporation. Bound.-Layer Meteor., 37 , 129148.

    • Search Google Scholar
    • Export Citation
  • van de Wiel, B. J. H., 2002: Intermittent turbulence and oscillations in the stable boundary layer over land. Ph.D. thesis, Wageningen University, 129 pp.

  • van de Wiel, B. J. H., , A. F. Moene, , O. K. Hartogensis, , H. A. R. de Bruin, , and A. A. M. Holtslag, 2003: Intermittent turbulence and oscillations in the stable boundary layer over land. Part III: A classification for observations during CASES99. J. Atmos. Sci., 60 , 25012513.

    • Search Google Scholar
    • Export Citation
  • van Pul, W. A. J., , A. A. M. Holtslag, , and D. P. J. Swart, 1994: A comparison of ABL heights inferred routinely from lidar and radiosondes at noon. Bound.-Layer Meteor., 68 , 173191.

    • Search Google Scholar
    • Export Citation
  • van Ulden, A. P., , and J. Wieringa, 1996: Atmospheric boundary layer research at Cabauw. Bound.-Layer Meteor., 78 , 3969.

  • Venkatram, A., 1980: Estimating the Monin–Obukhov length in the stable boundary layer for dispersion calculations. Bound.-Layer Meteor., 19 , 481485.

    • Search Google Scholar
    • Export Citation
  • Vickers, D., , and L. Mahrt, 2004: Evaluating formulations of the stable boundary layer height. J. Appl. Meteor., 43 , 17361749.

  • Vogelezang, D. H. P., , and A. A. M. Holtslag, 1996: Evaluation and model impacts of alternative boundary-layer height formulations. Bound.-Layer Meteor., 81 , 245269.

    • Search Google Scholar
    • Export Citation
  • Willmott, C. J., 1982: Some comments on the evaluation of model performance. Bull. Amer. Meteor. Soc., 63 , 13091313.

  • Yamada, T., 1979: Prediction of the nocturnal surface inversion height. J. Appl. Meteor., 18 , 526531.

  • Yu, T. W., 1978: Determining height of the nocturnal boundary layer. J. Appl. Meteor., 17 , 2833.

  • Zilitinkevich, S. S., 1972: On the determination of the height of the Ekman boundary layer. Bound.-Layer Meteor., 3 , 141145.

  • Zilitinkevich, S. S., , and D. V. Mironov, 1996: A multi-limit formulation for the equilibrium height of a stably stratified boundary layer. Bound.-Layer Meteor., 81 , 325351.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S. S., , and A. Baklanov, 2002: Calculation of the height of the stable boundary layer in practical applications. Bound.-Layer Meteor., 105 , 389409.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S. S., , and I. N. Esau, 2003: The effect of baroclinicity on the equilibrium depth of the neutral and stable planetary boundary layers. Quart. J. Roy. Meteor. Soc., 129 , 33393356.

    • Search Google Scholar
    • Export Citation
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Diagnostic Equations for the Stable Boundary Layer Height: Evaluation and Dimensional Analysis

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  • 1 Meteorology and Air Quality Group, Wageningen University, Wageningen, Netherlands
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Abstract

The performance of diagnostic equations for the stable boundary layer height h is evaluated with four observational datasets that represent a broad range of latitudes, land use, and surface roughness. In addition, large-eddy simulation results are used. Special care is given to data-quality selection. The diagnostic equations evaluated are so-called multilimit equations as derived by Zilitinkevich and coworkers in a number of papers. It appears that these equations show a serious negative bias, especially for h < 100 m, and it was found that the parameters involved could not be determined uniquely with calibration. As an alternative, dimensional analysis is used here to derive a formulation for h that is more robust. The formulation depends on the surface friction velocity u*, surface buoyancy flux Bs, Coriolis parameter, and the free-flow stability N. The relevance of the Coriolis parameter for the boundary layer height estimation in practice is also discussed. If the Coriolis parameter is ignored, two major regimes are found: hu*/N for weakly stable conditions and h ∼ (|Bs|/N3)1/2 for moderate to very stable conditions.

Corresponding author address: G. J. Steeneveld, Wageningen University, Meteorology and Air Quality Group, P.O. Box 47, 6700 AA Wageningen, the Netherlands. Email: gert-jan.steeneveld@wur.nl

Abstract

The performance of diagnostic equations for the stable boundary layer height h is evaluated with four observational datasets that represent a broad range of latitudes, land use, and surface roughness. In addition, large-eddy simulation results are used. Special care is given to data-quality selection. The diagnostic equations evaluated are so-called multilimit equations as derived by Zilitinkevich and coworkers in a number of papers. It appears that these equations show a serious negative bias, especially for h < 100 m, and it was found that the parameters involved could not be determined uniquely with calibration. As an alternative, dimensional analysis is used here to derive a formulation for h that is more robust. The formulation depends on the surface friction velocity u*, surface buoyancy flux Bs, Coriolis parameter, and the free-flow stability N. The relevance of the Coriolis parameter for the boundary layer height estimation in practice is also discussed. If the Coriolis parameter is ignored, two major regimes are found: hu*/N for weakly stable conditions and h ∼ (|Bs|/N3)1/2 for moderate to very stable conditions.

Corresponding author address: G. J. Steeneveld, Wageningen University, Meteorology and Air Quality Group, P.O. Box 47, 6700 AA Wageningen, the Netherlands. Email: gert-jan.steeneveld@wur.nl

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