Skip to main content
Springer Nature Link
Log in

Eddy exchange coefficients in numerical models of the planetary boundary layer

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

Abstract

Specification of the eddy exchange coefficients is perhaps one of the most difficult problems in the numerical modeling of the planetary boundary layer. These coefficients have been computed from finite-difference analogs to analytical expressions associated with surface boundary-layer similarity theory, which is based on observations in an equilibrium surface layer. This procedure leads to erroneous results in the region above the surface layer and in a non-equilibrium surface layer. In addition, differencing problems arise in regions of small vertical wind shear. A new turbulence transport model has been obtained through the closure procedures for the transport equations of the Reynolds stress and the turbulent length scale. The new approach could be used to calculate Reynolds stresses and eddy exchange coefficients throughout a non-neutral planetary boundary layer under non-equilibrium conditions.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

  • Ackerman, B. and Appleman, H.: 1975,Thermodynamic Structure Across a City on Days with Convective Rains, Presented at 55th Annual Meeting, American Meteorological Society, Denver.

    Google Scholar 

  • Arya, S. P. S.: 1973, ‘Neutral Planetary Boundary Layer Above a Non-Homogeneous Surface’,Geophys. Fluid. Dyn. 4, 333–355.

    Google Scholar 

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

    Google Scholar 

  • Bornstein, R. D.: 1972, ‘Two Dimensional, Non-Steady Numerical Simulations of Nighttime Flows of a Stable Planetary Boundary Layer over a Rough Warm City’, Ph.D. Thesis, Dept. of Meteorology and Oceanography, New York University. Available from University Microfilm, Inc.

  • Bornstein, R. D.: 1975, ‘The Two Dimensional URBMET Urban Boundary Layer Model’,J. Appl. Meteorol.,14, 1459–1477.

    Google Scholar 

  • Businger, J. A. and Arya, S. P. S.: 1974, ‘Height of the Mixed Layer in the Stably Stratified Planetary Boundary Layer’,Adv. Geophys. 18A, 73–92.

    Google Scholar 

  • Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: 1971, ‘Flux Profile Relationships in the Atmospheric Surface Layer’,J. Atmos. Sci. 28, 181–189.

    Google Scholar 

  • Crawford, T. V.: 1965, ‘Moisture Transfer in Free and Forced Convection’,Quart. J. Roy. Meteorol. Soc. 75, 18–27.

    Google Scholar 

  • Deardorff, J. W.: 1970, ‘Preliminary Results from Numerical Integrations of the Unstable Planetary Boundary Layer’,J. Atmos. Sci. 27, 1209–1211.

    Google Scholar 

  • Elliott, W. P.: 1964, ‘The Height Variation of Vertical Heat Flux Near the Ground’,Quart. J. Roy. Meteorol. Soc. 90, 260–265.

    Google Scholar 

  • Estoque, M. A.: 1961, ‘Theoretical Investigation of the Sea Breeze’,Quart. J. Roy. Meteorol. Soc. 87, 136–146.

    Google Scholar 

  • Estoque, M. A. and Bhumralkar, C. M.: 1968, ‘Theoretical Studies of the Atmospheric Boundary Layer’, Res. and Dev. Tech. Rep., ECOM-G7G2-F, 46 pp.

  • Estoque, M. A. and Bhumralkar, C. M.: 1969, ‘Further Studies on Flow over Non-Homogeneous Terrain’, Tech. Rep. Div. of Atmos. Sci., Univ. of Miami.

  • Fisher, E. L. and Caplan, P.: 1963, ‘An Experiment in Numerical Prediction of Fog and Stratus’,J. Atmos. Sci. 20, 425–437.

    Google Scholar 

  • Heisenberg, W.: 1948, ‘Zur statistischen Theorie der Turbulenz’,Z. Physik 124, 628–657.

    Google Scholar 

  • Kuo, H. L.: 1968, ‘The Thermal Interaction Between the Atmosphere and the Earth and Propagation of Diurnal Temperature Waves’,J. Atmos. Sci. 25, 682–706.

    Google Scholar 

  • Lamb, R. G., Chen, W. H., and Seinfeld, J. H.: 1974, ‘Numerico-Empirical Analyses of Atmospheric Diffusion Theories’, Symposium on Atmos. Diff. and Air Pollution, Santa Barbara, Calif., Sept., 1974.

  • Lettau, H. H.: 1962, ‘Theoretical Wind Spirals in the Boundary Layer of a Barotropic Atmosphere’,Beitr. Phys. Atmos. 35, 195–212.

    Google Scholar 

  • Lettau, H. H. and Dabberdt, W. F.: 1970, ‘Variangular Wind Spirals’,Boundary-Layer Meteorol. 1, 64–79.

    Google Scholar 

  • Lile, R. C.: 1970, ‘Tetroon-Derived Eddy Viscosity in the Region of the Elevated West Coast Temperature Inversion’, San Jose State University Report No. 1, San Jose, Calif.

  • Luther, F. M.: 1969, ‘A Numerical Model of the Energy Transfer Processes in the Lower Atmosphere’, Ph.D. Thesis, Univ. of Calif., Davis.

    Google Scholar 

  • Lumley, J. L. and Khajeh-Nouri, B.: 1974, ‘Computational Modeling of Turbulent Transport’,Adv. Geophys. 18A, 169–192.

    Google Scholar 

  • Lyons, R., Panofsky, H. A., and Wollaston, S.: 1964, ‘The Critical Richardson Number and its Implications for Forecast Problems’,J. Appl. Meteorol. 3, 136–142.

    Google Scholar 

  • McPherson, R. D.: 1970, ‘A Numerical Study of the Effect of a Coastal Irregularity on the Sea Breeze’,J. Appl. Meteorol. 9, 767–777.

    Google Scholar 

  • McVehil, A.: 1964, ‘Wind and Temperature Profiles near the Ground in Stable Stratification’,Quart. J. Roy. Meteorol. Soc. 90, 136–146.

    Google Scholar 

  • Monin, A. S. and Obukhov, A. M.: 1954, ‘Basic Regularity in Turbulent Mixing in the Surface Layer of the Atmosphere’,U.S.S.R. Acad. Sci. Geophys. Inst. No. 24.

  • Neumann, J. and Mahrer, Y.: 1971, ‘A Theoretical Study of the Land and Sea Breeze Circulations’,J. Atmos. Sci. 28, 532–542.

    Google Scholar 

  • O'Brien, J.: 1965, ‘An Investigation of the Adiabatic Wind Profile of the Atmospheric Boundary Layer’,J. Geophys. Res. 70, 2277–2290.

    Google Scholar 

  • O'Brien, J.: 1970, ‘On the Vertical Structure of the Eddy Exchange Coefficient in the Planetary Boundary Layer’,J. Atmos. Sci. 27, 1213–1215.

    Google Scholar 

  • Okamoto, M. and Webb, E. K.: 1970, ‘The Temperature Fluctuations in Stable Stratification’,Quart. J. Roy. Meteorol. Soc. 96, 591–600.

    Google Scholar 

  • Oke, T. R.: 1970a, ‘Turbulent Transport Near the Ground in Stable Conditions’,J. Appl. Meteorol. 9, 778–785.

    Google Scholar 

  • Oke, T. R.: 1970b, ‘The Temperature Profile Near the Ground on Calm Clear Nights’,Quart. J. Roy. Meteorol. Soc. 96, 14–23.

    Google Scholar 

  • Pandolfo, J., Cooley, D., and Newburg, E.: 1963, ‘Preliminary Investigations of Numerical Models for the Short-Period Prediction of Wind, Temperature, and Moisture in the Atmospheric Boundary Layer’, Final Rept. 7047-80, The Travelers Research Center, Inc.

  • Pandolfo, J. and Atwater, M. A.: 1965, ‘The Development of a Numerical Prediction Model for the Planetary Boundary Layer’, Final Rept. 7465-174, Contract Cwb-10960, The Travelers Research Center, Inc.

  • Panofsky, H. A., Blackadar, A. K., and McVehil, G. E.: 1960, ‘The Adiabatic Wind Profile’,Quart. J. Roy. Meteorol. Soc. 86, 390–398.

    Google Scholar 

  • Panofsky, H. A. and Prasad, B.: 1965, ‘Similarity Theories and Diffusion’,Inter. J. Air Water Poll. 9, 419–430.

    Google Scholar 

  • Peterson, E. W.: 1971, ‘Predictions of the Momentum Exchange Coefficient for Flow over Heterogeneous Terrain’,J. Appl. Meteorol. 10, 958–961.

    Google Scholar 

  • Priestley, C. H. B.: 1959,Turbulent Transfer in the Lower Amtosphere, Univ. of Chicago Press.

  • Reiter, E. R. and Lester, P. F.: 1967, ‘The Dependence of the Richardson Number on Scale Length’, Atmos. Sci. Paper No. 111, Colorado State Univ., Fort Collins, Colorado.

    Google Scholar 

  • Sasamori, T.: 1970, ‘A Numerical Study of Atmospheric and Soil Boundary Layer’,J. Atmos. Sci. 27, 1122–1137.

    Google Scholar 

  • Shir, C. C.: 1972, ‘A Numerical Computation of Air Flow over a Sudden Change of Surface Roughness’,J. Atmos. Sci. 29, 304–310.

    Google Scholar 

  • Shir, C. C.: 1973, ‘A Preliminary Numerical Study of Atmospheric Turbulent Flows in the Idealized Planetary Boundary Layer’,J. Atmos. Sci. 30, 1327–1339.

    Google Scholar 

  • Stevens, D. W.: 1959, ‘Numerical Experiments in Forecasting Air and Soil Temperature Profiles’, GRD Note No. 12, Air Force Cambridge Research Lab., Bedford, Mass.

    Google Scholar 

  • Tag, P. M.: 1969, ‘Surface Temperatures in an Urban Environment’, M.S. Thesis, Dept. of Meteorol., The Pennsylvania State Univ., Univ. Park. Penn., 69 pp.

    Google Scholar 

  • Takeuchi, K.: 1961, ‘On the Structure of the Turbulent Field in the Surface Boundary Layer’,J. Meteorol. Soc. Japan 39, 346–367.

    Google Scholar 

  • Webb, E. K.: 1970, ‘Profile Relationships: The Log-Linear Range and Extension to Strong Stability’,Quart. J. Roy. Meteorol. Soc. 96, 67–90.

    Google Scholar 

  • Wu, S. S.: 1965, ‘A Study of Heat Transfer Coefficients in the Lowest 400 meters of the Atmosphere’,J. Geophys. Res. 70, 1801–1807.

    Google Scholar 

  • Wyngaard, J. C.: 1973, ‘On Surface Layer Turbulence’, in D. A. Haugen (ed.),Workshop on Micrometeorology, Am. Meteorol. Soc., Boston, pp. 101–149.

    Google Scholar 

  • Wyngaard, J. C., Coté, O. R., and Rao, K. S.: 1974, ‘Modeling the Atmospheric Boundary Layer’,Adv. Geophys. 18A, 193–212.

    Google Scholar 

  • Yamamoto, G.: 1959, ‘Theory of Turbulent Transfer in Non-Neutral Conditions’,J. Meteorol. Soc. Japan 37, 60–70.

    Google Scholar 

  • Zdundowski, W., Henderson, D., and Hales, J. V.: 1967, ‘Prediction of Nocturnal Temperature Changes During a Calm Night’,Beiträge Physik Atmosphäre 40, 144–157.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IBM Research Laboratory, San Jose, Calif., USA

    C. C. Shir

  2. Dept. of Meteorology, San Jose State University, San Jose, Calif., USA

    R. D. Bornstein

Authors
  1. C. C. Shir
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. R. D. Bornstein
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shir, C.C., Bornstein, R.D. Eddy exchange coefficients in numerical models of the planetary boundary layer. Boundary-Layer Meteorol 11, 171–185 (1977). https://doi.org/10.1007/BF02166803

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02166803

Keywords