Abstract
An expression is derived for the height of the stationary boundary layer during stable lapse rate conditions. It satisfies the conventional limits for neutral conditions and for large values of stability. Comparison with acoustic sounder observations near the meteorological mast at Cabauw (the Netherlands) shows that the steady-state height is not attained for large stability values. The observations are also used to investigate how the similarity functions A and B in the resistance laws depend on the stability parameters μ0 = u */f L and Μ = h/L. The function B shows a clear trend as a function of stability, which can be described in terms of μ. The dependence of A is masked by scatter in the data points. The general conclusion leads to the concept of a non-steady boundary layer during stable lapse rate conditions.
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References
Arya, S. P. S.: 1975, ‘Geostrophic Drag and Heat Transfer Relations for the Atmospheric Boundary Layer’, Quart. J. Roy. Meteorol. Soc., 101, 147–161.
Arya, S. P. S.: 1978, ‘Comparative Effects of Stability, Baroclinicity and Scale-Height Ratio on Drag Laws for the Atmospheric Boundary Layer’, J. Atmos. Sci. 35, 40–46.
Arya, S. P. S. and Wyngaard, J. C.: 1975, ‘Effect of Baroclinicity on Wind Profiles and the Geostrophic Drag Law for the Convective Planetary Boundary Layer’, J. Atmos. Sci. 32, 767–778.
Arya, S. P. S. and Sundararajan, A.: 1976, ‘An Assessment of Proposed Similarity Theories for the Atmospheric Boundary Layer’, Boundary-Layer Meteorol. 10, 149–166.
Blackadar, A. K. and Tennekes, H.: 1968, ‘Asymptotic Similarity in Neutral Barotropic Planetary Boundary Layers’, J. Atmos. Sci. 25, 1015–1020.
Brost, R. A. and Wyngaard, J. C.: 1978, ‘A Model Study of the Stably Stratified Planetary Boundary Layer’, J. Atmos. Sci. 35, 1427–1440.
Businger, J. A. and Arya, S. P. S.: 1974, ‘Height of the Mixed Layer in the Stably Stratified Planetary Boundary Layer’, Adv. Geophys. 18A, Academic Press, 73–92.
Carson, D. J.: 1973, ‘The Development of a Dry Inversion-Capped Convectively Unstable Boundary Layer’, Quart. J. Roy. Meteorol. Soc. 99, 450–467.
Cats, G. J.: 1977, ‘The Calculation of the Geostrophic Wind’, Royal Netherlands Meteorological Institute, Scientific Report, 77-2 (in Dutch).
Clarke, R. H. and Hess, G. D.: 1974, ‘Geostrophic Departure and the Functions A and B of Rossby-Number Similarity Theory’, Boundary-Layer Meteorol. 7, 267–287.
Caughey, S. J., Wyngaard, J. C., and Kaimal, J. C.: 1979, ‘Turbulence in the Evolving Stable Boundary Layer’, J. Atmos. Sci. 36, 1041–1052.
Driedonks, A. G. M., van Dop, H., and Kohsiek, W. H.: 1978, ‘Meteorological Observations on the 213 m Mast at Cabauw, in the Netherlands’, Reprints fourth Symp. Meteorological observations and instrumentation, Denver, Amer. Meteorol. Soc., 41–46.
Hess, G. D.: 1973, ‘On Rossby-Number Similarity Theory for a Baroclinic Planetary Boundary Layer’, J. Atmos. Sci. 30, 1722–1723.
Hicks, B. B.: 1978, ‘Some Limitations of Dimensional Analysis and Power Laws’, Boundary-Layer Meteorol. 14, 567–569.
Mahrt, L., Heald, R. C., Lenschow, D. H., and Stankov, B. B.: 1979, ‘An Observational Study of the Structure of the Nocturnal Boundary Layer’, Boundary-Layer Meteorol. 17, 247–264.
Melgarejo, J. W. and Deardorff, J. W.: 1974, ‘Stability Functions for the Boundary-Layer Resistance Laws Based upon Observed Boundary-Layer Heights’, J. Atmos. Sci. 31, 1324–1333.
Nieuwstadt, F.: 1978, ‘The Computation of the Friction Velocity u * and the Temperature Scale T * from Temperature and Wind Velocity Profiles by Least-Square Methods’, Boundary-Layer Meteorol. 14, 235–246.
Nieuwstadt, F. T. M.: 1980, ‘A rate equation for the inversion height in a nocturnal boundary layer’, to appear in J. Appl. Meteorol.
Nieuwstadt, F. T. M. and Driedonks, A. G. M.: 1979, ‘The Nocturnal Boundary Layer: a Case Study Compared with Model Calculations’, J. Appl. Meteorol. 18, 1397–1405.
Rao, K. S. and Snodgrass, H. F.: 1979, ‘Some Parameterizations of the Nocturnal Boundary Layer’, Boundary-Layer Meteorol. 17, 15–28.
Sundararajan, A.: 1979, ‘Comments on observational studies on the similarity functions C and D of the convective planetary boundary layer over the ocean’, J. Meteorol. Soc. Japan, 57, 367–368.
Tennekes, H.: 1973a, ‘Similarity Laws and Scale Relations in Planetary Boundary Layers’, Workshop on Micrometeorology Amer. Meteorol. Soc., Boston, Mass.
Tennekes, H.: 1973b, ‘A Model for the Dynamics of the Inversion above a Convective Boundary Layer’, J. Atmos. Sci. 30, 558–567.
van Ulden, A. P., van der Vliet, J. G., and Wieringa, J.: 1976, ‘atTemperature and Wind Observations at Heights from 2 to 200 m at Cabauw 1973’, Royal Netherlands Meteorological Institute, Scientific Report 76-7.
Yamada, T.: 1976, ‘On the Similarity Functions A, B and C of the Planetary Boundary Layer’, J. Atmos. Sci. 33, 781–793.
Yamada, T.: 1979, ‘Prediction of the Nocturnal Surface Inversion Height’, J. Appl. Meteorol. 18, 526–531.
Yu, T. W.: 1978, ‘Determining Height of the Nocturnal Boundary Layer’, J. Appl. Meteorol. 17, 28–33.
Zeman, O.: 1979, ‘Parameterization of the Dynamics of Stable Boundary Layers and Nocturnal Jets’, J. Atmos. Sci. 36, 792–804.
Zilitinkevich, S. S.: 1972, ‘On the Determination of the Height of the Ekman Boundary Layer’, Boundary-Layer Meteorol., 3, 141–145.
Zilitinkevich, S. S.: 1975, ‘Resistance Laws and Prediction Equations for the Depth of the Planetary Boundary Layer’, J. Atmos. Sci. 32, 741–752.
Zilitinkevich, S. S. and Deardorff, J. W.: 1974, ‘Similarity Theory for the Planetary Boundary Layer of Time-Dependent Height’, J. Atmos. Sci. 31, 1449–1452.
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Nieuwstadt, F.T.M. The steady-state height and resistance laws of the nocturnal boundary layer: Theory compared with cabauw observations. Boundary-Layer Meteorol 20, 3–17 (1981). https://doi.org/10.1007/BF00119920
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DOI: https://doi.org/10.1007/BF00119920