Journal of Oceanography

, Volume 61, Issue 1, pp 91–107 | Cite as

Comparison of Ocean Surface Wind Stress Computed with Different Parameterization Functions of the Drag Coefficient

  • Paul A. Hwang


Depending on the choice of reference wind speed, the quantitative and qualitative properties of the drag coefficient may vary. On the ocean surface, surface waves are the physical roughness at the air-sea interface, and they play an important role in controlling the air-sea exchange processes. The degree of dynamic influence of surface waves scales with wavelength. Drag coefficient computed with the reference wind speed at an elevation proportional to the wavelength (for example, Uλ/2) is fundamentally different from the drag coefficient computed with the wind speed at fixed 10 m elevation (U10). A comparison has been carried out to quantify the difference in wind stress computation using several different parameterization functions of the drag coefficient. The result indicates that the wind stress computed from U10 input using a drag coefficient referenced to Uλ/2 is more accurate than that computed with drag coefficient functions referenced to U10.


Drag coefficient wind stress parameterization functions wavelength wave age dimensionless frequency 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anctil, F. and M. A. Donelan (1996): Air-water momentum flux observed over shoaling waves. J. Phys. Oceanogr., 26, 1344–1353.CrossRefGoogle Scholar
  2. Banner, M. L., W. Chen, E. J. Walsh, J. B. Jensen and S. Lee (1999): The Southern Ocean Waves Experiment. Part I: Overview and mean results. J. Phys. Oceanogr., 29, 2130–2145.Google Scholar
  3. Dobson, F. W., S. D. Smith and R. J. Anderson (1994): Measuring the relationship between wind stress and sea state in the open ocean in the presence of swell. Atmos.-Oceans, 32, 237–256.Google Scholar
  4. Donelan, M. A. (1979): On the fraction of wind momentum retained by waves. p. 141–159. In Marine Forecasting, ed. by J. C. J. Nihoul, Elsevier.Google Scholar
  5. Donelan, M. A. (1990): Air-sea interaction. p. 239–292. In The Sea—Volume 9: Ocean Engineering Science, ed. by B. LeMehaute and D. M. Hanes, Wiley Interscience.Google Scholar
  6. Donelan, M. A., F. W. Dobson, S. D. Smith and R. J. Anderson (1993): On the dependence of sea surface roughness on wave development. J. Phys. Oceanogr., 23, 2143–2149.Google Scholar
  7. Garratt, J. R. (1977): Review of drag coefficients over oceans and continents. Mon. Wea. Rev., 105, 915–929.Google Scholar
  8. Geernaert, G. L. (ed.) (1999): Air-Sea Exchange: Physics, Chemistry and Dynamics. Kluwer Academic Publ., Dordrecht, The Netherlands, 578 pp.Google Scholar
  9. Geernaert, G. L. and W. J. Plant (eds.) (1990): Surface Waves and Fluxes, I and II. Kluwer Academic Publ., Dordrecht, The Netherlands, 372 and 336 pp.Google Scholar
  10. Geernaert, G. L., S. E. Larsen and F. Hansen (1987): Measurements of the wind stress, heat flux, and turbulence intensity during storm conditions over the North Sea. J. Geophys. Res., 92, 13127–13139.Google Scholar
  11. Huang, N. E. (1999): A review of coastal wave modeling: the physical and mathematical problems. p. 1–20. In Advances in Coastal and Ocean Engineering, 4, ed. by P. L.-F. Liu, World Scientific, Singapore.Google Scholar
  12. Hwang, P. A. (2004): Influence of wavelength on the parameterization of drag coefficient and surface roughness. J. Oceanogr., 60, 835–841.Google Scholar
  13. Hwang, P. A. and D. W. Wang (2001): Directional distributions and mean square slopes in the equilibrium and saturation ranges of the wave spectrum. J. Phys. Oceanogr., 31, 1346–1360.Google Scholar
  14. Janssen, J. A. M. (1997): Does wind stress depend on sea-state or not?—A statistical error analysis of HEXMAX Data. Bound.-Layer Meteorol., 83, 479–503.Google Scholar
  15. Jones, I. S. F. and Y. Toba (eds.) (2001): Wind Stress over the Ocean. Cambridge Univ. Press, Cambridge, U.K., 307 pp.Google Scholar
  16. Kinsman, B. (1965): Wind Waves. Prentice-Hall, Inc., Englewood Cliffs, NJ, 542 pp.Google Scholar
  17. Kitaigorodskii, S. A. (1973): The Physics of Air-Sea Interaction. Israel Program for Scientific Translations, Jerusalem (English translation), 237 pp.Google Scholar
  18. Long, S. R., N. E. Huang, E. Mollo-Christensen, F. C. Jackson and G. L. Geernaert (1994): Directional wind wave development. Geophys. Res. Lett., 21, 2503–2506.Google Scholar
  19. Makin, V. K. (2003): A note on a parameterization of the sea drag. Bound.-Layer Meteorol., 106, 593–600.Google Scholar
  20. Makin, V. K. and V. N. Kudryavtsev (1999): Coupled sea surface-atmosphere model. 1. Wind over waves coupling. J. Geophys. Res., 104, 7613–7623.Google Scholar
  21. Makin, V. K. and V. N. Kudryavtsev (2002): Impact of dominant waves on sea drag. Bound.-Layer Meteorol., 103, 83–99.Google Scholar
  22. Merzi, N. and W. H. Graf (1985): Evaluation of the drag coefficient considering the effects of mobility of the roughness elements. Ann. Geophys., 3, 473–478.Google Scholar
  23. Miles, J. W. (1957): On the generation of surface waves by shear flows. J. Fluid Mech., 3, 185–204.Google Scholar
  24. Mitsuyasu, H. (1982): Wind wave problems in engineering. p. 683–729. In Engineering Meteorology, ed. by E. Plate, Elsevier, New York.Google Scholar
  25. Phillips, O. M. (1957): On the generation of waves by turbulent wind. J. Fluid Mech., 2, 417–445.Google Scholar
  26. Phillips, O. M. (1958a): On some properties of the equilibrium of wind-generated ocean waves. J. Mar. Res., 16, 231–245.Google Scholar
  27. Phillips, O. M. (1958b): The equilibrium range in the spectrum of wind-generated waves. J. Fluid Mech., 4, 426–434.Google Scholar
  28. 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, 15467–15472.Google Scholar
  29. Stewart, R. W. (1974): The air-sea momentum exchange. Bound.-Layer Meteorol., 6, 151–167.Google Scholar
  30. Taylor, P. K. and M. J. Yelland (2001): The dependence of sea surface roughness on the height and steepness of the waves. J. Phys. Oceanogr., 31, 572–590.Google Scholar
  31. Toba, Y., N. Iida, H. Kawamura, N. Ebuchi and I. S. F. Jones (1990): Wave dependence of sea-surface wind stress. J. Phys. Oceanogr., 20, 705–721.Google Scholar
  32. Toba, Y., S. D. Smith and N. Ebuchi (2001): Historical drag expressions. p. 35–53. In Wind Stress over the Ocean, ed. by I. S. F. Jones and Y. Toba, Cambridge Univ. Press, New York.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Paul A. Hwang
    • 1
  1. 1.Oceanography Division, Naval Research LaboratoryStennis Space CenterU.S.A.

Personalised recommendations