Relationship between the Monin–Obukhov Stability Parameter and the Bulk Richardson Number at Sea under Unstable Conditions, Derived From a Turbulence-Closure Model

Lech Łobocki Institute of Environmental Engineering Systems, Warsaw University of Technology, Warsaw, Poland

Search for other papers by Lech Łobocki in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Relationships between the Monin–Obukhov stability parameter and the bulk Richardson number are useful for explicit calculation of fluxes through the air–sea interface. The most straightforward method assumes simple proportionality and is supported well by experimental evidence in a recent work by Grachev and Fairall. On the other hand, the reference iterative method is regarded as more accurate. To recognize possible differences, calculated values of the proportionality factor as a function of wind speed and air–sea virtual potential temperature difference are shown. The calculation is based on commonly used sea roughness specifications and the Mellor–Yamada turbulence-closure model, which has been shown in previous studies to reproduce the three-sublayer structure of the atmospheric surface layer under convective conditions and to predict mean flow profiles that are consistent with empirical data. The results show that the proportionality factor varies with the wind speed and virtual potential temperature vertical differences and that this variability has a nonmonotonic character when wind speeds are smaller than 5 m s−1.

Corresponding author address: Dr. Lech Łobocki, Institute of Environmental Engineering Systems, Warsaw University of Technology, Nowowiejska 20, Warsaw 00-653, Poland. lech.lobocki@is.pw.edu.pl

Abstract

Relationships between the Monin–Obukhov stability parameter and the bulk Richardson number are useful for explicit calculation of fluxes through the air–sea interface. The most straightforward method assumes simple proportionality and is supported well by experimental evidence in a recent work by Grachev and Fairall. On the other hand, the reference iterative method is regarded as more accurate. To recognize possible differences, calculated values of the proportionality factor as a function of wind speed and air–sea virtual potential temperature difference are shown. The calculation is based on commonly used sea roughness specifications and the Mellor–Yamada turbulence-closure model, which has been shown in previous studies to reproduce the three-sublayer structure of the atmospheric surface layer under convective conditions and to predict mean flow profiles that are consistent with empirical data. The results show that the proportionality factor varies with the wind speed and virtual potential temperature vertical differences and that this variability has a nonmonotonic character when wind speeds are smaller than 5 m s−1.

Corresponding author address: Dr. Lech Łobocki, Institute of Environmental Engineering Systems, Warsaw University of Technology, Nowowiejska 20, Warsaw 00-653, Poland. lech.lobocki@is.pw.edu.pl

Save
  • Berkowicz, R. and L. P. Prahm. 1982. Evaluation of the profile method for estimation of surface fluxes of momentum and heat. Atmos. Environ. 16:28092819.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W. 1968. Dependence of air–sea transfer coefficients on bulk stability. J. Geophys. Res. 73:25492557.

  • De Bruin, H. A. R., R. J. Ronda, and B. J. H. van de Wiel. 2000. Approximate solutions for the Obukhov length and the surface fluxes in terms of bulk Richardson numbers. Bound.-Layer Meteor. 95:145157.

    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young. 1996. Bulk parameterization of air–sea fluxes for Tropical Ocean Global Atmosphere–Coupled Ocean Atmosphere Response Experiment. J. Geophys. Res. 101:37473764.

    • Search Google Scholar
    • Export Citation
  • Grachev, A. A. and C. W. Fairall. 1997. Dependence of the Monin–Obukhov stability parameter on the bulk Richardson number over the ocean. J. Appl. Meteor. 36:406414.

    • Search Google Scholar
    • Export Citation
  • Grachev, A. A., C. W. Fairall, and S. S. Zilitinkevich. 1997. Surface-layer scaling for free-convection induced stress regime. Bound.-Layer Meteor. 83:423439.

    • Search Google Scholar
    • Export Citation
  • Hsu, S. A. 1989. The relationship between the Monin–Obukhov stability parameter and the bulk Richardson number. J. Geophys. Res. 94:80538054.

    • Search Google Scholar
    • Export Citation
  • Kondo, J. and S. Ishida. 1997. Sensible heat flux from the earth's surface under natural convective conditions. J. Atmos. Sci. 54:498509.

    • Search Google Scholar
    • Export Citation
  • Launiainen, J. 1995. Derivation of the relationship between the Obukhov stability parameter and the bulk Richardson number for flux-profile studies. Bound.-Layer Meteor. 76:165179.

    • Search Google Scholar
    • Export Citation
  • Liu, T. W., K. B. Katsaros, and J. A. Businger. 1979. Bulk parameterization of air–sea exchanges of heat and water vapor including the molecular constraints at the interface. J. Atmos. Sci. 36:17221735.

    • Search Google Scholar
    • Export Citation
  • Łobocki, L. 1993. A procedure for the derivation of surface layer bulk relationships from simplified second-order closure models. J. Appl. Meteor. 32:126138.

    • Search Google Scholar
    • Export Citation
  • Łobocki, L. 2001a. Calculation of surface fluxes under convective conditions by turbulence closure models. J. Appl. Meteor. 40:604621.

    • Search Google Scholar
    • Export Citation
  • Łobocki, L. 2001b. An explicit algorithm for calculating surface layer parameters in convective conditions derived from a turbulence closure model. J. Appl. Meteor. 40:622627.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L. and T. Yamada. 1974. A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 31:17911806.

    • Search Google Scholar
    • Export Citation
  • Nickerson, E. C. and V. E. Smiley. 1975. Surface layer and energy budget parameterizations for mesoscale models. J. Appl. Meteor. 14:297300.

    • Search Google Scholar
    • Export Citation
  • Smith, S. D. 1988. Coefficients for sea surface wind stress, heat flux, and wind profiles as a function of wind speed and temperature. J. Geophys. Res. 93:1546715472.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 487 123 6
PDF Downloads 397 111 5