Efficient and Accurate Bulk Parameterizations of Air–Sea Fluxes for Use in General Circulation Models

A. Birol Kara Sverdrup Technology Incorporated, Stennis Space Center, Mississippi

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Peter A. Rochford Naval Research Laboratory, Stennis Space Center, Mississippi

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Harley E. Hurlburt Naval Research Laboratory, Stennis Space Center, Mississippi

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Abstract

Efficient and computationally inexpensive simple bulk formulas that include the effects of dynamic stability are developed to provide wind stress, and latent and sensible heat fluxes at the air–sea interface in general circulation models (GCMs). In these formulas the exchange coefficients for momentum and heat (i.e., wind stress drag coefficient, and latent and sensible heat flux coefficients, respectively) have a simple polynomial dependence on wind speed and a linear dependence on the air–sea temperature difference that are derived from a statistical analysis of global monthly climatologies according to wind speed and air–sea temperature difference intervals. Using surface meteorological observations from a central Arabian Sea mooring, these formulas are shown to yield air–sea fluxes on daily timescales that are highly accurate relative to those obtained with the standard algorithm used by the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE), where the latter includes the effect of dynamic stability in calculating wind stress and air–sea heat fluxes. Direct comparisons in calculating the wind stress, and latent and sensible heat fluxes with these formulas and the TOGA COARE algorithm demonstrate that the methodology presented here is computationally inexpensive because iterative calculations are not required in the present methodology. Wind stress and air–sea fluxes can be calculated ≈30 times faster with these bulk formulas than by using the TOGA COARE algorithm. This methodology is of direct practical value for GCMs of high spatial resolution, where the severe computational demands of performing GCM simulations encourage computing air–sea fluxes in the most computationally efficient manner possible. The combination of accuracy and ease of computation of this method makes it the preferred one for computing air–sea fluxes in such GCMs.

Corresponding author address: Peter A. Rochford, Naval Research Laboratory, Bldg. 1009, Stennis Space Center, MS 39529.

Email: rochford@nrlssc.navy.mil

Abstract

Efficient and computationally inexpensive simple bulk formulas that include the effects of dynamic stability are developed to provide wind stress, and latent and sensible heat fluxes at the air–sea interface in general circulation models (GCMs). In these formulas the exchange coefficients for momentum and heat (i.e., wind stress drag coefficient, and latent and sensible heat flux coefficients, respectively) have a simple polynomial dependence on wind speed and a linear dependence on the air–sea temperature difference that are derived from a statistical analysis of global monthly climatologies according to wind speed and air–sea temperature difference intervals. Using surface meteorological observations from a central Arabian Sea mooring, these formulas are shown to yield air–sea fluxes on daily timescales that are highly accurate relative to those obtained with the standard algorithm used by the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE), where the latter includes the effect of dynamic stability in calculating wind stress and air–sea heat fluxes. Direct comparisons in calculating the wind stress, and latent and sensible heat fluxes with these formulas and the TOGA COARE algorithm demonstrate that the methodology presented here is computationally inexpensive because iterative calculations are not required in the present methodology. Wind stress and air–sea fluxes can be calculated ≈30 times faster with these bulk formulas than by using the TOGA COARE algorithm. This methodology is of direct practical value for GCMs of high spatial resolution, where the severe computational demands of performing GCM simulations encourage computing air–sea fluxes in the most computationally efficient manner possible. The combination of accuracy and ease of computation of this method makes it the preferred one for computing air–sea fluxes in such GCMs.

Corresponding author address: Peter A. Rochford, Naval Research Laboratory, Bldg. 1009, Stennis Space Center, MS 39529.

Email: rochford@nrlssc.navy.mil

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  • Atlas, R., 1987: The role of oceanic fluxes and initial data in the numerical prediction of an intense coastal storm. Dyn. Atmos. Oceans,10, 359–388.

  • ——, A. J. Busalacchi, M. Ghil, S. Bloom, and E. Kalnay, 1987: Global surface wind and flux fields from model assimilation of Seasat data. J. Geophys. Res.,92, 6477–6487.

    • Crossref
    • Export Citation
  • Barnier, B., 1998: Forcing the ocean. Ocean Modeling and Parameterization, E. P. Chassignet and J. Verron, Eds., Kluwer, 45–80.

    • Crossref
    • Export Citation
  • Blanc, T. V., 1985: Variation of bulk-derived surface flux, stability, and roughness results due to the use of different transfer coefficient schemes. J. Phys. Oceanogr.,15, 650–669.

    • Crossref
    • Export Citation
  • Buck, A. L., 1981: New equations for computing vapor pressure and enhancement factor. J. Appl. Meteor.,20, 1527–1532.

    • Crossref
    • Export Citation
  • Bunker, A. F., 1976: Computations of surface energy flux and annual air–sea interaction cycles of the North Atlantic Ocean. Mon. Wea. Rev.,104, 1122–1140.

    • Crossref
    • Export Citation
  • Caldwell, D. R., and W. P. Elliott, 1971: Surface stresses produced by rainfall. J. Phys. Oceanogr.,1, 145–148.

    • Crossref
    • Export Citation
  • Chen, D., A. J. Busalacchi, and L. M. Rothstein, 1994: The roles of vertical mixing, solar radiation, and wind stress in a model simulation of the sea surface temperature seasonal cycle in the tropical Pacific Ocean. J. Geophys. Res.,99, 20 345–20 359.

    • Crossref
    • Export Citation
  • Chu, P. C., Y. Chen, and S. Lu, 1998: On Haney-type surface boundary conditions for ocean circulation models. J. Phys. Oceanogr.,28, 890–901.

    • Crossref
    • Export Citation
  • Cummings, J. A., C. Szczechowski, and M. R. Carnes, 1997: Global and regional ocean thermal analysis systems. Mar. Technol. Soc. J.,31, 63–75.

  • da Silva, A. M., C. C. Young, and S. Levitus, 1994: Algorithms and Procedures. Vol. 1, Atlas of Surface Marine Data 1994, NOAA Atlas NESDIS, 83 pp.

  • DeCosmo, J., K. B. Katsaros, S. D. Smith, R. J. Anderson, W. A. Oast, K. Bumke, and H. Chadwick, 1996: Air–sea exchange of water vapor and sensible heat: The Humidity Exchange Over the Sea (HEXOS) results. J. Geophys. Res.,101, 12 001–12 016.

    • Crossref
    • Export Citation
  • Dyer, A. J., 1974: A review of flux–profile relationships. Bound.-Layer Meteor.,7, 363–372.

    • Crossref
    • Export Citation
  • Fairall, C. W., J. Kepert, and G. J. Holland, 1994: The effect of sea spray on surface energy transports over the ocean. Global Atmos. Ocean Syst.,2, 121–142.

  • ——, 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, 3747–3764.

    • Crossref
    • Export Citation
  • Findlater, J., 1966: Cross-equatorial jet stream at low level over Kenya. Meteor. Mag.,95, 353–364.

  • Friehe, C. A., and K. B. Schmitt, 1976: Parameterization of air–sea interface fluxes of sensible heat and moisture by the bulk aerodynamic formulas. J. Phys. Oceanogr.,6, 801–809.

    • Crossref
    • Export Citation
  • Garratt, J. R., 1977: Review of drag coefficients over oceans and continents. Mon. Wea. Rev.,105, 915–929.

    • Crossref
    • Export Citation
  • Geernaert, G. L., 1990: Bulk parameterizations for the wind stress and heat fluxes. Surface Waves and Fluxes, G. L. Geernaert and W. J. Plant, Eds., Kluwer, 91–172.

    • Crossref
    • Export Citation
  • ——, K. B. Katsaros, and K. Richter, 1986: Variation of the drag coefficient and its dependence on sea state. J. Geophys. Res.,91, 7667–7679.

    • Crossref
    • Export Citation
  • Godfrey, J. S., and A. C. M. Beljaars, 1991: On the turbulent fluxes of buoyancy, heat, and moisture at the air–sea interface at low wind speeds. J. Geophys. Res.,96, 22 043–22 048.

    • Crossref
    • Export Citation
  • Gosnell, R., C. W. Fairall, and P. J. Webster, 1995: The sensible heat of rainfall in the tropical ocean. J. Geophys. Res.,100, 18 437–18 442.

    • Crossref
    • Export Citation
  • Greenhut, G. K., 1982: Stability dependence of fluxes and bulk transfer coefficients in a tropical boundary layer. Bound.-Layer Meteor.,24, 253–264.

    • Crossref
    • Export Citation
  • Haltiner, G. J., and R. T. Williams, 1980: Numerical Prediction and Dynamic Meteorology. 2d ed. John Wiley and Sons, 477 pp.

  • Hasse, L., 1993: Observations of air sea fluxes. Energy and Water Cycles in the Climate System, E. Raschke and D. Jacop, Eds., Springer-Verlag, 263–293.

    • Crossref
    • Export Citation
  • Hogan, T. F., and T. E. Rosmond, 1991: The description of the navy operational global atmospheric prediction system’s spectral forecast model. Mon. Wea. Rev.,119, 1786–1815.

    • Crossref
    • Export Citation
  • Hurlburt, H. E., A. J. Wallcraft, W. Schmitz Jr., P. J. Hogan, and E. J. Metzger, 1996: Dynamics of the Kuroshio/Oyashio current system using eddy-resolving models of the North Pacific Ocean. J. Geophys. Res.,101, 941–976.

    • Crossref
    • Export Citation
  • Isemer, H. J., and L. Hasse, 1987: The Bunker Climate Atlas of the North Atlantic Ocean. Vol. 2. Springer-Verlag, 252 pp.

    • Crossref
    • Export Citation
  • ——, J. Willebrand, and L. Hasse, 1989: Fine adjustment of large scale air–sea energy flux parameterizations by direct estimates of ocean heat transport. J. Climate,2, 1173–1184.

    • Crossref
    • Export Citation
  • Jourdan, D., and C. Gautier, 1995: Comparison between global latent heat flux computed from multisensor (SSM/I and AVHRR) and from in situ data. J. Atmos. Oceanic Technol.,12, 46–72.

    • Crossref
    • Export Citation
  • Kallberg, P., 1998: Aspects of the re-analysed climate. ECMWF Re-Analysis Project Report Series, Vol. 2, European Centre for Medium-Range Weather Forecasts, 89 pp.

  • Kantha, L. H., and C. A. Clayson, 1994: An improved mixed layer model for geophysical applications. J. Geophys. Res.,99, 25 235–25 266.

    • Crossref
    • Export Citation
  • Kara, A. B., J. B. Elsner, and P. H. Ruscher, 1998: Numerical models of boundary layer processes over and around the Gulf of Mexico during a return-flow event. Wea. Forecasting,13, 921–933.

    • Crossref
    • Export Citation
  • Large, W. G., and S. Pond, 1982: Sensible and latent heat flux measurements over the ocean. J. Phys. Oceanogr.,12, 464–482.

    • Crossref
    • Export Citation
  • Latif, M., A. Sterl, M. Assenbaum, M. M. Junge, and E. Maier-Reimer, 1994: Climate variability in a coupled GCM. Part II: The Indian Ocean and monsoon. J. Climate,7, 1449–1462.

  • Laurent, H., I. Jobart, and A. Toma, 1998: Validation of satellite and ground-based estimates of precipitation over the Sahel. Atmos. Res.,47–48, 651–670.

    • Crossref
    • Export Citation
  • Liu, W. T., 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, 1722–1735.

    • Crossref
    • Export Citation
  • Lo, A. K., and G. A. McBean, 1978: On the relative errors in methods of flux calculations. J. Appl. Meteor.,17, 1704–1711.

    • Crossref
    • Export Citation
  • Marsden, R. F., and S. Pond, 1983: Synoptic estimates of air–sea fluxes. J. Mar. Res.,41, 349–373.

    • Crossref
    • Export Citation
  • McCreary, J. P., P. K. Kundu, and R. L. Molinari, 1993: A numerical investigation of dynamics, thermodynamics and mixed layer processes in the Indian Ocean. Progress in Oceanography, Vol. 31, Pergamon, 181–244.

    • Crossref
    • Export Citation
  • Morissey, M. K., and J. E. Janowiak, 1996: Sampling-induced conditional biases in satellite climate-scale rainfall estimates. J. Appl. Meteor.,35, 541–548.

    • Crossref
    • Export Citation
  • Murphy, A. H., 1988: Skill scores based on the mean square error and their relationships to the correlation coefficient. Mon. Wea. Rev.,116, 2417–2424.

    • Crossref
    • Export Citation
  • Murtugudde, R., R. Seager, and A. Busalacchi, 1996: Simulation of the tropical oceans with an ocean GCM coupled to an atmospheric mixed-layer model. J. Climate,9, 1795–1815.

    • Crossref
    • Export Citation
  • Neter, J., W. Wasserman, and G. A. Whitmore, 1988: Applied Statistics. Allyn and Bacon, 1006 pp.

  • Price, J. F., R. A. Weller, C. M. Bowers, and M. G. Briscoe, 1987: Diurnal response of sea surface temperature observed at the Long-Term Upper Ocean Study (34°N, 70°W) in the Sargasso Sea. J. Geophys. Res.,92, 14 480–14 490.

    • Crossref
    • Export Citation
  • Roberts, C. M., C. Gordon, and C. Cooper, 1997: The origin of flux adjustments in a coupled model. Mon. Wea. Rev.,125, 909–925.

    • Crossref
    • Export Citation
  • Rochford, P. A., J. C. Kindle, P. C. Gallacher, and R. A. Weller, 2000: Sensitivity of the Arabian Sea mixed layer to 1994–1995 operational wind products. J. Geophys. Res.,105, 14 141–14 162.

    • Crossref
    • Export Citation
  • Sausen, R., K. Barthel, and K. Hasselmann, 1988: Coupled ocean–atmosphere models with flux adjustment. Climate Dyn.,2, 145–163.

    • Crossref
    • Export Citation
  • Shriver, J. F., and H. E. Hurlburt, 1997: The contribution of the global thermohaline circulation to the Pacific to Indian Ocean throughflow via Indonesia. J. Geophys. Res.,102, 5491–5511.

    • Crossref
    • 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, 15 467–15 472.

    • Crossref
    • Export Citation
  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer, 666 pp.

    • Crossref
    • Export Citation
  • Swenson, M. S., and D. V. Hansen, 1999: Tropical Pacific Ocean mixed layer heat budget: The Pacific cold tongue. J. Phys. Oceanogr.,29, 69–81.

    • Crossref
    • Export Citation
  • Weare, B. C., and P. T. Strub, 1981: The significance of sampling biases on calculated monthly mean oceanic surface heat flux. Tellus,33, 211–224.

    • Crossref
    • Export Citation
  • Webster, P. J., 1994: The role of hydrological processes in ocean–atmosphere interactions. Rev. Geophys.,34, 427–476.

    • Crossref
    • Export Citation
  • Weller, R. A., M. F. Baumgartner, S. A. Josey, A. S. Fischer, and J. C. Kindle, 1998: Atmospheric forcing in the Arabian Sea during 1994–1995: Observations and comparisons with climatology models. Deep-Sea Res.,45, 1961–1999.

    • Crossref
    • Export Citation
  • Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences. Academic Press, 467 pp.

  • Yelland, M. J., and P. K. Taylor, 1996: Wind stress measurements from the open ocean. J. Phys. Oceanogr.,26, 541–558.

    • Crossref
    • Export Citation
  • Yuen, C. W., J. Y. Cherniawsky, C. A. Lin, and L. A. Mysak, 1992: An upper ocean general circulation model for climate studies: Global simulation with seasonal cycle. Climate Dyn.,7, 1–18.

    • Crossref
    • Export Citation
  • Zhang, G. J., 1995: Use of monthly mean data to compute surface turbulent fluxes in the tropical Pacific. J. Climate,8, 3084–3090.

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