Skip to main content
SpringerLink
Log in

Convective Profile Constants Revisited

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

Abstract

This paper examines the interpolation betweenBusinger–Dyer (Kansas-type) formulae,ϕu = (1 -1 6ζ )-1/4 andϕt = (1 - 16ζ )-1/2, and free convection forms. Based on matching constraints, the constants, au and at, in the convective flux-gradient relations, ϕu = (1 - auζ )-1/3 and ϕt = (1 - atζ )-1/3, are determined. It isshown that au and at cannot be completely independent if convective forms are blended with theKansas formulae. In other words, these relationships already carryinformation about au and at. This follows because the Kansas relations cover a wide stability range (up to ζ = - 2), which includes a lower part of the convective sublayer (about 0.1 < - ζ < 2). Thus, there is a subrange where both Kansas and convective formulae are valid. Matching Kansas formulae and free convection relations within thesubrange 0.1 < -ζ < 2 and independently smoothing ofthe blending function are used to determine au and at. The values au = 10 for velocity and at = 34for scalars (temperature and humidity) give a good fit. This new approacheliminates the need for additional independent model constants and yields a`smooth' blending between Kansas and free-convection profileforms in the COARE bulk algorithm.

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

  • Andreas, E. L., Edson, J. B., Monahan, E. C., Rouault, M. P., and Smith, S. D.: 1995, 'The Spray Contribution to Net Evaporation from the Sea', Boundary-Layer Meteorol. 72, 3–52.

    Google Scholar 

  • Bradley, E. F. and Weller, R. A. (eds.): 1998, Fourth Workshop of the TOGA COARE Air-Sea Interaction (Flux) Working Group, 9–11 October, Woods Hole Oceanographic Institution, Woods Hole, MA, 62 pp. [TOGA COARE International Project Office, University Corporation for Atmospheric Research, Boulder, CO, U.S.A.].

    Google Scholar 

  • Brutsaert, W.: 1992, 'Stability Corrections Functions for the Mean Wind Speed and Temperature in the Unstable Surface Layer', Geophys. Res. Lett. 19, 469–472.

    Google Scholar 

  • Businger, J. A.: 1966, 'Transfer of Heat and Momentum in the Atmospheric Boundary Layer', in Proceedings of the Arctic Heat Budget and Atmospheric Circulation, RAND Corporation, Santa Monica, CA, pp. 305–332.

    Google Scholar 

  • Businger, J. A.: 1973, 'A Note on Free Convection', Boundary-Layer Meteorol. 4, 323–326.

    Google Scholar 

  • Businger, J. A.: 1988, 'A Note on the Businger-Dyer Profiles', Boundary-Layer Meteorol. 42, 145–151.

    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 

  • Carl, M. D., Tarbell, T. C., and Panofsky, H. A.: 1973, 'Profiles of Wind and Temperature from Towers over Homogeneous Terrain', J. Atmos. Sci. 30, 788–794.

    Google Scholar 

  • Delage, Y. and Girard, C.: 1992,'Stability Functions Correct at the Free Convection Limit and Consistent for Both the Surface and Ekman Layers', Boundary-Layer Meteorol. 58, 19–31.

    Google Scholar 

  • Dyer, A. J.: 1974, 'A Review of Flux-Profile Relationships', Boundary-Layer Meteorol. 7, 363–372.

    Google Scholar 

  • Dyer, A. J. and Bradley, E. F.: 1982, 'An Alternative Analysis of Flux-Gradient Relationships at the 1976 ITCE', Boundary-Layer Meteorol. 22, 3–19.

    Google Scholar 

  • Fairall, C. W. and Grachev, A. A.: 1996, 'On the Sea-Surface Roughness Length under Free Convection Conditions', in Proceedings of the 8th AMS Conference on Air-Sea Interaction and Conference on the Global Ocean-Atmosphere-Land System (GOALS), 28 January-2 February 1996, Atlanta, Georgia, pp. J134-J138.

  • Fairall, C. W., Bradley, E. F., Rogers, D. P., Edson, J. B., and Young, G. S.: 1996a, 'Air-Sea Flux Parameterization in TOGA COARE', J. Geophys. Res. 101(C2), 3747–3764.

    Google Scholar 

  • Fairall, C. W., Bradley, E. F., Godfrey, J. S., Wick, G. A., Edson, J. B., and Young, G. S.: 1996b, 'Cool-Skin and Warm-layer Effects on Sea Surface Temperature', J. Geophys. Res. 101(C1),1295–1308.

    Google Scholar 

  • Fairall, C.W., White, A. B., Edson, J. B., and Hare, J. E.: 1997, 'Integrated Shipboard Measurements of the Marine Boundary Layer', J. Atmos. Oceanic Tech. 14, 338–359.

    Google Scholar 

  • Friehe, C. A., Burns, S. P., Khelif, D, and Song, X.: 1996, 'Meteorological and Flux Measurements from the NOAA WP3D Aircraft in TOGA COARE', in 8th AMS Conference on Air-Sea Interaction and Conference on the Global Ocean-Atmosphere-Land System (GOALS), 28 January-2 February 1996, Atlanta, Georgia, pp. J42-J45.

  • Garratt, J. R.: 1992, The Atmospheric Boundary Layer, Cambridge University Press, U.K., 316 pp.

    Google Scholar 

  • Godfrey, J. S. and Beljaars, A. C. M.: 1991, 'On the Turbulent Fluxes of Buoyancy, Heat, and Moisture at the Air-Sea Interface at Low Wind Speeds', J. Geophys. Res. 96, 22043–22048.

    Google Scholar 

  • Grachev, A. A., Fairall, C. W., and Zilitinkevich, S. S.: 1997, 'Surface-Layer Scaling for the Convection-Induced Stress Regime', Boundary-Layer Meteorol. 83, 423–439.

    Google Scholar 

  • Grachev, A. A., Fairall, C. W., and Larsen, S. E.: 1998, 'On the Determination of the Neutral Drag Coefficient in the Convective Boundary Layer', Boundary-Layer Meteorol. 86, 257–278.

    Google Scholar 

  • Gurvich, A. S.: 1965, 'Vertical Temperature and Wind Velocity Profiles in the Atmospheric Surface layer', Izvestiya, Acad. Sci., USSR, Atmos. Oceanic Phys. 1, 31–36 (English edition).

    Google Scholar 

  • Högström, H.: 1988, 'Non-Dimensional Wind and Temperature Profiles in the Atmospheric Surface Layer: A Re-Evaluation', Boundary-Layer Meteorol. 42, 55–78.

    Google Scholar 

  • Kader, B. A.: 1988, 'Three-Level Structure of an Unstably Stratified Atmospheric Surface Layer', Izvestiya, Acad. Sci., USSR, Atmos. Oceanic Phys. 24, 907–918 (English edition).

    Google Scholar 

  • Kader, B. A. and Perepelkin, V. G.: 1989, 'Effect of Unstable Stratification on the Wind Speed and Temperature Profiles in the Surface Layer', Izvestiya, Acad. Sci., USSR, Atmos. Oceanic Phys. 25, 583–588 (English edition).

    Google Scholar 

  • Kader, B. A. and Yaglom, A. M.: 1990, 'Mean Fields and FluctuationMoments in Unstably Stratified Turbulent Boundary Layers', J. Fluid Mech. 212, 637–662.

    Google Scholar 

  • Large, W. G., McWilliams, J. C., and Doney, S. C.: 1994, 'Ocean Vertical Mixing: A Review and a Model with a Nonlocal Boundary Layer Parameterization', Rev. Geophys. 32, 363–403.

    Google Scholar 

  • Mahrt, L. and Sun, J.: 1995, 'The Subgrid Velocity Scale in the Bulk Aerodynamic Relationship for Spatially Averaged Scalar Fluxes', Mon. Wea. Rev. 123, 3032–3041.

    Google Scholar 

  • Mahrt, L., Vickers, D., Howell J., Højstrup, J., Wilczak, J. M., Edson, J., and Hare, J.: 1996, 'Sea Surface Drag Coefficients in the Risø Air Sea Experiment', J. Geophys. Res. 101(C6), 14327–14335.

    Google Scholar 

  • Miller, M. J., Beljaars, A. C. M., and Palmer, T. N.: 1992, 'The Sensitivity of the ECMWF Model to the Parameterization of Evaporation from the Tropical Oceans', J. Climate 5, 418–434.

    Google Scholar 

  • Monin, A. S. and Obukhov, A. M.: 1954, 'Basic Laws of Turbulent Mixing in the Surface Layer of the Atmosphere', Trudy Geofiz. Inst. Acad. Nauk SSSR 24(151), 163–187.

    Google Scholar 

  • Monin, A. S. and Yaglom, A. M.: 1971, Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 1, MIT Press, Cambridge, MA, 769 pp.

    Google Scholar 

  • Obukhov, A. M.: 1946, 'Turbulence in an Atmosphere with a Non-Uniform Temperature', Trudy Inst. Teoret. Geophys. Akad. Nauk SSSR 1, 95–115 (translation in: Boundary-Layer Meteorol. 2, 7–29, 1971).

    Google Scholar 

  • Panofsky, H. A.: 1963, 'Determination of Stress fromWind and Temperature Measurements', Quart. J. Roy. Meteorol. Soc. 89, 85–94.

    Google Scholar 

  • Panofsky, H. A., Blackadar, A. K., and McVehil, G. E.: 1960, 'The Diabatic Wind Profile', Quart. J. Roy. Meteorol. Soc. 86, 495–503.

    Google Scholar 

  • Paulson, C. A.: 1970, 'The Mathematical Representation ofWind Speed and Temperature Profiles in the Unstable Atmospheric Surface Layer', J. Appl. Meteorol. 9, 857–861.

    Google Scholar 

  • Petukhov, B. S. and Polyakov, A. F.: 1988, Heat Transfer in Turbulent Mixed Convection, Hemisphere Pub. Corp., New York, 216 pp.

    Google Scholar 

  • Priestley, C. H. B.: 1960, 'A Determination Hypothesis for the SuperadiabaticWind and Temperature Profiles', Quart. J. Roy. Meteorol. Soc. 86(368), 232–236.

    Google Scholar 

  • Schumann, U.: 1988, 'Minimum Friction Velocity and Heat Transfer in the Rough Surface Layer of a Convective Boundary Layer', Boundary-Layer Meteorol. 44, 311–326.

    Google Scholar 

  • Sorbjan, Z.: 1989, Structure of the Atmospheric Boundary Layer. Prentice Hall, New Jersey, 317 pp.

    Google Scholar 

  • Sugita, M., Hiyama, T., Endo, N., and Tian, S-F.: 1995, 'Flux Determination over a Smooth Surface under Strongly Unstable Conditions', Boundary-Layer Meteorol. 73, 145–158.

    Google Scholar 

  • Webster, P. J. and Lukas, R.: 1992, 'TOGA COARE: The Coupled Ocean Atmosphere Response Experiment, Bull. Amer. Meteorol. Soc. 73, 1377–1416.

    Google Scholar 

  • Zilitinkevich, S. S. and Chalikov, D. V.: 1968, 'Determining the Universal Wind-Velocity and Temperature Profiles in the Atmospheric Boundary Layer', Izvestiya, Acad. Sci., USSR, Atmos. Oceanic Phys. 4, 165–170 (English edition).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Cooperative Institute for Research in Environmental Sciences, University of Colorado, U.S.A.

    A. A. Grachev

  2. Environmental Technology Laboratory, NOAA, 325 Broadway, R/ET7, Boulder, Colorado, 80303-3328, U.S.A.

    A. A. Grachev & C. W. Fairall

  3. CSIRO Land and Water, GPO Box 1666, Canberra, ACT, 2601, Australia

    E. F. Bradley

Authors
  1. A. A. Grachev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. W. Fairall
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. F. Bradley
    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

Grachev, A.A., Fairall, C.W. & Bradley, E.F. Convective Profile Constants Revisited. Boundary-Layer Meteorology 94, 495–515 (2000). https://doi.org/10.1023/A:1002452529672

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1002452529672

Search

Navigation