Skip to main content
SpringerLink
Log in

The depth of the daytime mixed layer at two coastal sites: A model and its validation

  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

A mathematical model of mixed-layer depth based on the thermodynamic analysis of Tennekes (1973) is generalized to include advection and subsidence. The effects of advection on mixed-layer depth have been modelled by setting the model equations in a Lagrangian frame, performing an approximate first integral in order to derive the spatial dependence of the model variables, and using these spatial forms to give a set of Eulerian equations. The effects of subsidence have been modelled by imposing a subsidence velocity on the top of the mixed layer as well as allowing subsidence-induced warming above that layer.

The model thus derived consists of a system of non-linear differential equations which may be numerically solved to elucidate the temporal behaviour of mixed-layer depth. The boundary conditions necessary for such a solution are drawn from field studies at two coastal sites: one with a relatively simple coastline and essentially flat land under agricultural use, the other with a considerably more complex coastline, rolling relief and mixed land use (agricultural, parkland and urban). In both cases the modelled evolution of mixed-layer depth is in good agreement with the measured depth.

The sensitivity of the model to all the input variables is investigated by examining the dependence of the maximum mixed-layer depth on each of these variables in an artificial set.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ball, F. K.: 1960, ‘Control of Inversion Height by Surface Heating’, Quart. J. Roy. Meteorol. Soc. 86, 482–494.

    Google Scholar 

  • Barnum, D. C. and Rao, G. V.: 1975, ‘Role of Advection and Penetrative Convection in Affecting the Mixing-Height Variations over an Idealized Metropolitan Area’, Boundary-Layer Meteorol. 8, 497–514.

    Article  Google Scholar 

  • Betts, A. K.: 1973: ‘Non-Precipitating Convection and Its Parameterization’, Quart. J. Roy. Meteorol. Soc. 99, 178–196.

    Article  Google Scholar 

  • Carson, D. J.: 1973, ‘The Development of a Dry Inversion-Capped Convectively Unstable Boundary Layer’, Quart. J. Roy. Meteorol. Soc. 99, 450–467.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Davidson, K. L., Schacher, G. E., Fairall, C. W., and Houlihan, T. M.: 1980, Observations of Atmospheric Mixed Layer Changes off the California Coast, Preprints Second Conference on Coastal Meteorology, Amer. Meteorol. Soc., Boston, pp. 63–70.

    Google Scholar 

  • Deardorff, J. W.: 1979, ‘Prediction of Convective Mixed-Layer Entrainment for Realistic Capping Inversion Structures’, J. Atmos. Sci. 36, 1070–1076.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Driedonks, A. G. M.: 1981, ‘Dynamics of the Well-Mixed Atmospheric Boundary Layer’, K.N.M.I. Scientific Report, W.R. 81-2, DeBilt, Netherlands, 189 pp.

  • Hay, J. E. and Oke, T. R.: 1976, The Climate of Vancouver, Tantalus Research Ltd., Vancouver, B.C., 48 pp.

    Google Scholar 

  • Heidt, F. D.: 1977, ‘The Growth of the Mixed Layer in a Stratified Fluid Due to Penetrative Convection’, Boundary-Layer Meteorol. 12, 439–461.

    Article  Google Scholar 

  • Kalanda, B. D., Oke, T. R., and Spittlehouse, D.: 1980, ‘Suburban Energy Balance Estimates using the Bowen Ratio-Energy Balance Approach’, J. Appl. Meteorol. 19, 791–802.

    Article  Google Scholar 

  • Kerman, B. R.: 1982, ‘A Similarity Model of Shoreline Fumigation’, Atmos. Envir. 16, 467–478.

    Article  Google Scholar 

  • Kerman, B. R., Mickle, R. E., Portelli, R. V., Trivett, N. B. A., and Misra, P. K.: 1982, ‘Nanticoke Shoreline Diffusion Experiment, June 1978: Part II Internal Boundary Layer Structure’, Atmos. Envir. 16, 423–438.

    Article  Google Scholar 

  • Lapczak, S. and Helferty, M.: 1978, Summary of Synoptic Meteorological Conditions During the Nanticoke Field Study, May 29, 1978–June 16, 1978, Internal Report SSU-78–7, Atmospheric Environment Service, Ontario Region, Toronto, Ontario, 212 pp.

    Google Scholar 

  • Lilly, D. K.: 1968, ‘Models of Cloud Topped Mixed Layers Under a Strong Inversion’, Quart. J. Roy. Meteorol. Soc. 94, 292–309.

    Article  Google Scholar 

  • Mahrt, L. and Lenschow, D. H.: 1976, ‘Growth of the Convectively Mixed Layer’, J. Atmos. Sci. 33, 41–51.

    Article  Google Scholar 

  • Meroney, R. W., Cermak, C. E., and Yang, B. T.: 1975, ‘Modelling of Atmospheric Transport and Fumigation at Shoreline Sites’, Boundary-Layer Meteorol. 9, 69–90.

    Article  Google Scholar 

  • Misra, P. K. and Onlock, S.: 1982, ‘Modelling Continuous Fumigation of Nanticoke Generating Station Plume’, Atmos. Envir. 16, 479–490.

    Article  Google Scholar 

  • Munn, R. E., Findlay, B., Hirt, M., Van Toen, G., and Herscovitch, H.: 1970, ‘Atmospheric Inventory and Air Pollution Analysis’, in V. Chanasyk, (ed.), The Haldimand-Norfolk Environmental Appraisal, Ont. Ministry of Treasury, Economics and Intergovernmental Affairs, Toronto, 22–53.

    Google Scholar 

  • Portelli, R. V.: 1979, The Nanticoke Study: Experimental Investigation of Diffusion from Tall Stacks in a Shoreline Environment. Presented to 10th NATO/CCMSS Meeting, Rome, Nov., 1979.

  • Portelli, R. V.: 1982, ‘Nanticoke Shoreline Diffusion Experiment, June, 1978: Part I. Experimental Design and Program Overview’, Atmos. Envir. 16, 413–422.

    Article  Google Scholar 

  • Raynor, G. S., Michael, P., Brown, R. M., and Sethuraman, S.: 1975, ‘Studies of Atmospheric Diffusion from a Nearshore Oceanic Site’, J. Appl. Meteorol. 14, 1080–1094.

    Article  Google Scholar 

  • Raynor, G. S., Sethuraman, S., and Brown, R. M.: 1979, ‘Formation and Characteristics of Coastal Internal Boundary Layers During Onshore Flows’, Boundary-Layer Meteorol. 16, 487–514.

    Article  Google Scholar 

  • Shampine, L. F. and Gordon, M. K.: 1974, Computer Solution of Ordinary Differential Equations: The Initial Value Problem, Freeman. 162 pp.

  • Smith, F. B. and Carson, D. J.: 1977, ‘Some Thoughts on the Specification of the Boundary Layer Relevant to Numerical Modelling’, Boundary-Layer Meteorol. 12, 307–330.

    Article  Google Scholar 

  • Steyn, D. G.: 1980, ‘Turbulence, Diffusion and the Daytime Mixed Layer Depth over a Coastal City’, Ph.D. Thesis, The University of British Columbia, Vancouver, British Columbia, Canada, 161 pp.

    Google Scholar 

  • Stull, R. B.: 1976a, ‘The Energetics of Entrainment Across a Density Interface’, J. Atmos. Sci. 33, 1260–1267.

    Article  Google Scholar 

  • Stull, R. B.: 1976b, ‘Mixed-Layer Depth Model Based on Turbulence Energetics’, J. Atmos. Sci. 33, 1268–1278.

    Article  Google Scholar 

  • Stull, R. B.: 1976c, ‘Internal Gravity Waves Generated by Penetrative Convection’, J. Atmos. Sci. 33, 1279–1286.

    Article  Google Scholar 

  • Summers, P. W.: 1964, ‘An Urban Ventilation Model Applied to Montreal’, Ph.D. Thesis, McGill University, P.Q., Canada.

    Google Scholar 

  • Tennekes, H.: 1973, ‘A Model for the Dynamics of the Inversion above a Convective Boundary Layer’, J. Atmos. Sci. 30, 558–567.

    Article  Google Scholar 

  • Tennekes, H.: 1974, ‘The Atmospheric Boundary Layer’, Physics Today 27, 52–63.

    Article  Google Scholar 

  • Tennekes, H. and Driedonks, A. G. M.: 1981, ‘Basic Entrainment Equations for the Atmospheric Boundary Layer’, Boundary-Layer Meteorology 20, 515–531.

    Article  Google Scholar 

  • van Dop, H. R., Steenkist, S., and Nieuwstadt, F. T. M.: 1979, ‘Revised Estimates for Continuous Shoreline Fumigation’, J. Appl. Meteorol. 18, 133–137.

    Article  Google Scholar 

  • Venkatram, A.: 1977, ‘A Model of Internal Boundary-Layer Development’, Boundary-Layer Meteorol. 11, 419–437.

    Article  Google Scholar 

  • Weisman, B. and Hirt, M. S.: 1975, Dispersion Governed by the Thermal Internal Boundary Layer, 68th Meeting of the Air Pollution Control Association, June 1975, Boston, Mass.

  • Willis, G. E. and Deardorff, J. W.: 1974, ‘A Laboratory Model of the Unstable Planetary Boundary Layer’, J. Atmos. Sci. 31, 1297–1307.

    Article  Google Scholar 

  • Yamada, T. and Berman, S.: 1979, ‘A Critical Evaluation of a Simple Mixed-Layer Model with Penetrative Convection’, J. Appl. Meteorol. 18, 781–786.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geography, The University of British Columbia, V6T 1W5, Vancouver, B.C., Canada

    D. G. Steyn & T. R. Oke

Authors
  1. D. G. Steyn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. R. Oke
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Steyn, D.G., Oke, T.R. The depth of the daytime mixed layer at two coastal sites: A model and its validation. Boundary-Layer Meteorol 24, 161–180 (1982). https://doi.org/10.1007/BF00121666

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00121666

Keywords

Search

Navigation