Abstract
A simple prognostic model of the depth of the stable boundary layer is developed which includes both the possibilities of growth due to entrainment and decreasing depth associated with turbulence decay. The model is designed to avoid requirement of surface fluxes and instead uses information on profiles of mean wind and temperature. Resulting coefficients for the model are estimated by comparisons with existing studies in the literature and comparison with Wangara data.
Similar content being viewed by others
References
Alexander, R. C. and Kim, J.-W.: 1976, ‘Diagnostic Model Study of Mixed-Layer Depths in the Summer North Pacific’, J. Phys. Ocean. 6, 293–298.
Andre, J. C., De Moor, G., Lacarrere, P., Therry, G., and du Vachat, R.: 1978, ‘Modeling the 24 Hour Evolution of the Mean and Turbulent Structures of the Planetary Boundary Layer’, J. Atmos. Sci. 35, 1861–1883.
Anfossi, D., Bacci, P., and Longhetto, A.: 1976, ‘Forecasting of Vertical Temperature Profiles in the Atmosphere during Nocturnal Radiation Inversions from Air Temperature Trend at Screen Height’, Quart. J. Roy, Meteorol. Soc. 102, 173–180.
Anisimova, Ye. P., Porborchaya, L. V., and Speranskaya, A. A.: 1978, ‘Velocity Profile in the Boundary Layer of Stratified Turbulent Flow’, Izv. Acad. Sci., U.S.S.R., Atmospheric and Oceanic Physics 14, 785–788.
Arya, S. P. S.: 1977, ‘Suggested Revisions to Certain Boundary Layer Parameterization Schemes Used in Atmospheric Circulation Models’, Mon. Weather Rev. 105, 215–226.
Blackadar, A. K.: 1976, ‘Modeling the Nocturnal Boundary Layer’, Reprints Third Symp. Atmospheric Turbulence, Diffusion and Air Quality, Raleigh, American Meteorological Society, pp. 46–49.
Brost, R. A. and Wyngaard, J. C.: 1978, ‘A Model Study of the Stably Stratified Planetary Boundary Layer’, J. Atmos. Sci. 35, 1427–1440.
Brutsaert, Wilfried: 1972, ‘Radiation, Evaporation and the Maintenance of Turbulence under Stable Conditions in the Lower Atmosphere’, Boundary-Layer Meteorol. 2, 309–325.
Businger, J. A.: 1969, ‘Note on the Critical Richardson Number’, Quart. J. Roy. Meteorol. Soc. 95, 653–654.
Businger, J. A. and Arya, S. P. S.: 1974, ‘Height of the Mixed Layer in the Stable Planetary Boundary Layer’, Adv. Geophys. 18A, Academic Press, 73–92.
Caughey, S. J., Wyngaard, J. C., and Kaimal, J. C.: 1979, ‘Turbulence in the Evolving Stable Boundary Layer’, J. Atmos. Sci. 36, 1041–1052.
Clarke, R. H., Dyer, A. J., Brooke, R. R, Reid, D. G. and Troup, A. J.:1971, ‘The Wangara Experiment: Boundary Layer Data’. CSIRO Div. Meteor. Phys. Tech. Paper No. 19.
Deardorff, J. W.: 1972, ‘Parameterization of the Planetary Boundary Layer for Use in General Circulation Models’, Mon. Weather Rev. 100, 93–106.
Delage, Y.: 1974, ‘A Numerical Study of the Nocturnal Atmospheric Boundary Layer’, Quart. J. Roy. Meteorol. Soc. 100, 351–364.
Ellison, T. H. and Turner, J. S.: 1959, ‘Turbulent Entrainment in Stratified Flows’, J. Fluid Mech. 6, 423–448.
Emmanuel, C. B.: 1973, ‘Richardson Number Profiles Through Shear Instability Wave Regions Observed in the Lower Planetary Boundary Layer’, Boundary-Layer Meteorol. 5, 19–27.
Eymard, L. and Weill, A.: 1979, ‘A Study of Gravity Waves in the Planetary Boundary Layer by Acoustic Sounding’, Boundary-Layer Meteorol. 17, 231–245.
Hanna, S. R.: 1969, ‘The Thickness of the Planetary Boundary Layer’, Atmos. Environ. 3, 519–536.
Hooke, W. H., Hall, F. F., and Gossard, E E.: 1973, ‘Observed Generation of an Atmospheric Gravity Wave by Shear Instability in the Mean Flow of the Planetary Boundary Layer’, Boundary-Layer Meteorol. 5, 29–41.
Khakimov, I. R.: 1976, ‘The Wind Profile of the Neutrally Stratified Atmosphere Boundary Layer’, Izv. Acad. Sci., U.S.S.R., Atmospheric and Oceanic Physics 12, 628–630.
Kondo, J., Kanechika, O., and Yasuda, N.: 1978, ‘Heat and Momentum Transfers under Strong Stability in the Atmospheric Surface Layer’, J. Atmos. Sci. 35, 1012–1021.
Laikhtman, D. L.: 1961, ‘Physics of the Boundary Layer of the Atmosphere’, Translated by the Israel Program for Scientific Translations, Jerusalem, 1964.
Louis, Jean-Francois: 1979, ‘A Parametric Model of Vertical Eddy Fluxes in the Atmosphere’, Boundary-Layer Meteorol. 17, 187–202.
Lyons, Richard, Panofsky, H. A., and Wollaston, Sarah: 1964, ‘The Critical Richardson Number and Its Implication for Forecast Problems’, J. Appl. Meteorol. 3, 136–142.
Mahrt, L.: 1980, ‘The Early Evening Boundary Layer Transition’, to appearQuart. J. Roy. Meteorol. Soc.
Mahrt, L., Heald, R. C., Lenschow, D. H., Stankov, B., and Troen, Ib: 1979, ‘An Observational Study of the Nocturnal Boundary Layer’, Boundary-Layer Meteorol. 17, 247–264.
Manins, P. C. and Sawford, B. L.: 1979a, ‘A Model of Katabatic Winds’, J. Atmos. Sci. 36, 619–630.
Manins, P. C. and Sawford, B. L.: 1979b, ‘Katabatic Winds: A Field Case Study’, Quart. J. Roy. Meteorol. Soc. 105, 1011–1025.
Melgarejo, J. W. and Deardorff, J. W.: 1974, ‘Stability Functions for the Boundary Layer Resistance Laws Based on Observed Boundary-Layer Heights’, J. Atmos. Sci. 31, 1324–1333.
Merrill, John T.: 1977, ‘Observational and Theoretical Study of Shear Instability in the Air Flow Near the Ground’, J. Atmos. Sci. 34, 911–921.
Nieuwstadt, F. T. M.: 1980a, ‘A Rate Equation for the Inversion Height in a Nocturnal Boundary-Layer’, J. of Appl. Meteorol. 19, 1445–1447.
Nieuwstadt, F. T. M.: 1980b, ‘The Steady-State Height and Resistance Laws of the Nocturnal Boundary Layer: Theory Compared with Cabauw Observations’, to appear in Boundary-Layer 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.
Ottersten, Hans, Hardy, R., Little, Kenneth, and Gordon, C.: 1973, ‘Radar and Sodar Probing of Waves and Turbulence in Stratified Stable Clear Layers’, Boundary-Layer Meteorol. 4, 47–89.
Pollard, R. T., Rhines, P. B., and Thompson, R. O. R. Y.: 1973, ‘The Deepening of the Wind Mixed Layer’, Geophysical Fluid Dynamics 3, 381–404.
Rao, K. S. and Snodgrass, H. F.: 1979, ‘Some Parameterizations of the Nocturnal Boundary Layer’, Boundary-Layer Meteorol. 17, 15–28.
Schubert, J. F.: 1977, ‘Acoustic Detection of Momentum Transfer During the Abrupt Transition From a Laminar to a Turbulent Atmospheric Boundary Layer’, J. Appl. Meteor. 16, p1292–1297.
Smeda, M. S.: 1979a, ‘Incorporation of Planetary Boundary-Layer Processes into Numerical Forecasting Models’, Boundary-Layer Meteorol. 16, 115–129.
Smeda, M. S.: 1979b, ‘A Bulk Model for the Atmospheric Planetary Boundary Layer’, Boundary-Layer Meteorol. 14, 411–428.
Turner, J. S.: 1968, ‘The Influence of Molecular Diffusivity on Turbulent Entrainment Across a Density Interface’, J. Fluid Mech. 33, 639–656.
Yamada, Tetsuji: 1978, ‘Prediction of the Nocturnal Surface Inversion Height’, J. Appl. Meteorol. 18, 526–531.
Yamada, Tetsuji, and Mellor, George: 1975, ‘A Simulation of the Atmospheric Boundary Layer’, J. Atmos. Sci. 32, 2309–2329.
Yamamoto, Susumu, Yokoyama, Osayuki, and Gamo, Minoru: 1979, ‘Observational Study on the Turbulent Structure of the Atmospheric Boundary Layer and Stable Conditions’. J. Meteorol. Soc. Japan 57, 423–431.
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 Layer Flow 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., and Monin, A. S.: 1974, ‘Similarity Theory for the Atmospheric Boundary Layer’, Izv. Acad. Sci. U.S.S.R., Atmospheric and Oceanic Physics 10, 587–599.
Author information
Authors and Affiliations
Additional information
On leave from the Dept of Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331, U.S.A.
Rights and permissions
About this article
Cite this article
Mahrt, L. Modelling the depth of the stable boundary-layer. Boundary-Layer Meteorol 21, 3–19 (1981). https://doi.org/10.1007/BF00119363
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00119363