On the parameterization of the drag coefficient in mixed seas


  • Héctor García-Nava Instituto de Investigaciones Oceanológicas, Universidad Autónoma de Baja California
  • Francisco J. Ocampo-Torres Departamento de Oceanografía Física, Centro de Investigación Científica y de Educación Superior de Ensenada
  • Paul A. Hwang Remote Sensing Division, Naval Research Laboratory




drag coefficient, sea state, swell, mixed seas


An analysis of the performance of parameterizations for the drag coefficient CD over the ocean is presented. The results were obtained by considering detailed observations from the recent IntOA experiment in which a co-existence of wind sea and swell provides characteristic mixed sea conditions in a wide range of wind speeds. Recent research has advanced our understanding of air-sea fluxes, proposing new functional forms for the drag coefficient, as well as applying wavelength scaling and determining dimensionally consistent expressions for the drag coefficient. Nevertheless, a detailed analysis of the influence of wind sea parameters confirms the need to include the sea state dependence on parameterizing CD for mixed sea conditions. It is also shown that better results are obtained when aerodynamic roughness is considered as a function of wave age and wave steepness, or equivalently if CD is expressed as a function of a characteristic peak frequency defined through the wave momentum spectrum.


Download data is not yet available.


Charnock H. 1955. Wind stress on water surface. Q. J. R. Meteorol. Soc. 81: 639-640. http://dx.doi.org/10.1002/qj.49708135027

Donelan M.A., 1990. Air-sea interaction. In: LeMehaute B., Hanes D.M. (eds.), The Sea, vol. 9, Ocean Engineering Science. John Wiley & Sons Inc., pp. 239-292.

Donelan M.A., Dobson F.W. 2001. The influence of swell on the drag. In: Jones I.S.F., Toba Y. (eds.), Wind Stress Over The Ocean. Cambridge University Press, New York, N.Y., pp. 181-190. http://dx.doi.org/10.1017/CBO9780511552076.009

Donelan M.A., Drennan W.M., Katsaros K.B. 1997. The air-sea momentum flux in conditions of wind sea and swell. J. Phys. Oceanogr. 27: 2087-2099. http://dx.doi.org/10.1175/1520-0485(1997)027<2087:TASMFI>2.0.CO;2

Drennan W.M. 2006. On parameterisations of air-sea fluxes. In: Perrie W. (ed.), Atmosphere-Ocean Interactions, Vol. 2. WIT Press, pp. 1-34. http://dx.doi.org/10.2495/978-1-85312-929-2/01

Drennan W.M., Kahma K.K., Donelan M.A. 1999. On momentum flux and velocity spectra over waves. Bound.-Lay. Meteorol. 92: 489-513. http://dx.doi.org/10.1023/A:1002054820455

Drennan W.M., Graber H.C., Hauser D., Quentin C. 2003. On the wave age dependence of wind stress over pure wind seas. J. Geophys. Res. 108: 8062. http://dx.doi.org/10.1029/2000JC000715

Drennan W.M., Taylor P.K., Yelland M.J. 2005. Parametrizing the sea surface roughness. J. Phys. Oceanogr. 35: 835-848. http://dx.doi.org/10.1175/JPO2704.1

Foreman R.J., Emeis S. 2010. Revisiting the definition of the drag coefficient in the marine atmospheric boundary layer. J. Phys. Oceanogr. 40: 2325-2332. http://dx.doi.org/10.1175/2010JPO4420.1

García-Nava H., Ocampo-Torres F. J., Osuna P., Donelan M.A. 2009. Wind stress in the presence of swell under moderate to strong wind conditions. J. Geophys. Res. 114: C12008. http://dx.doi.org/10.1029/2009JC005389

Geernaert G.L. 1999. Air-sea exchange: Physics, chemistry and dynamics. Kluwer Academic, 578 pp.

Graber H.C., Terray E.A., Donelan M.A., Drennan W.M., Leer J.C.V., Peters D.B. 2000. ASIS-A New Air-Sea Interaction Spar Buoy: Design and Performance at Sea. J. Atmos. Oceanic. Technol. 17: 708-720. http://dx.doi.org/10.1175/1520-0426(2000)017<0708:AANASI>2.0.CO;2

Guan C., Xie, L. 2004. On the linear parameterization of drag coefficient over sea surface. J. Phys. Oceanogr. 34: 2847-2851. http://dx.doi.org/10.1175/JPO2664.1

Hara T., Belcher S.E. 2004. Wind profile and drag coefficient over mature ocean surface wave spectra. J. Phys. Oceanogr. 34: 2345-2358. http://dx.doi.org/10.1175/JPO2633.1

Hwang P.A. 2004. Influence of wavelength on the parameterization of drag coefficient and surface roughness. J. Oceanogr. 60: 835-841.

Hwang P.A., García-Nava H., Ocampo-Torres F.J. 2011. Dimensionally consistent similarity relation of ocean surface friction coefficient in mixed seas. J. Phys. Oceanogr. 41: 1227-1238. http://dx.doi.org/10.1175/2011JPO4566.1

Jones I.S.F., Toba Y. 2001. Wind stress over the ocean. Cambridge University Press, 303 pp. http://dx.doi.org/10.1017/CBO9780511552076

Komen G. J., Janssen P.A.E.M., Makin V., Oost W. 1998. On the sea state dependence of the Charnock parameter. Global Atmos. Ocean Syst. 5: 367-388.

Large W.G., Pond S. 1981. Open ocean momentum flux measurements in moderate to strong winds. J. Phys. Oceanogr. 11: 324-336. http://dx.doi.org/10.1175/1520-0485(1981)011<0324:OOMFMI>2.0.CO;2

Moon I., Ginis I., Hara T. 2004. Effect of surface waves on Charnock coefficient under tropical cyclones. Geophys. Res. Lett. 31: L20302. http://dx.doi.org/10.1029/2004GL020988

Ocampo-Torres F.J., García-Nava H., Durazo R., Osuna P., Díaz Méndez G.M., Graber H.C. 2011. The IntOA experiment: A study of ocean-atmosphere interactions under moderate to strong offshore winds and opposing swell conditions in the Gulf of Tehuantepec, Mexico. Bound.-Lay. Meteorol. 138: 433-451. http://dx.doi.org/10.1007/s10546-010-9561-5

Pan J., Wang D.W., Hwang P.A. 2005. A study of wave effects on wind stress over the ocean in a fetch-limited case. J. Geophys. Res. 110: C02020. http://dx.doi.org/10.1029/2003JC002258

Romero R., Zavala J., Gallegos A., O'Brien J.J. 2003. Isthmus of Tehuantepec wind climatology and ENSO signal. J. Climate 16: 2628-2639. http://dx.doi.org/10.1175/1520-0442(2003)016<2628:IOTWCA>2.0.CO;2

Smith S.D. 1980. Wind stress and heat flux over the ocean in gale force winds. J. Phys. Oceanogr. 10: 709-726. http://dx.doi.org/10.1175/1520-0485(1980)010<0709:WSAHFO>2.0.CO;2

Sreenivasan K.R., Chambers S.J., Antonia R.A. 1978. Accuracy of moments of velocity and scalar fluctuations in the atmospheric surface layer. Bound.-Lay. Meteorol. 14: 341-359. http://dx.doi.org/10.1007/BF00121044

Taylor P.K., Yelland, M.J. 2001. The dependence of sea surface roughness on the height and steepness of the waves. J. Phys. Oceanogr. 31: 572-590. http://dx.doi.org/10.1175/1520-0485(2001)031<0572:TDOSSR>2.0.CO;2

Veron F., Melville W.K., Lenain L. 2008. Wave-coherent air-sea heat flux. J. Phys. Oceanogr. 38: 788-802. http://dx.doi.org/10.1175/2007JPO3682.1

Yelland M., Taylor P.K. 1996. Wind stress measurements form the open ocean. J. Phys. Oceanogr. 26: 541-555. http://dx.doi.org/10.1175/1520-0485(1996)026<0541:WSMFTO>2.0.CO;2




How to Cite

García-Nava H, Ocampo-Torres FJ, Hwang PA. On the parameterization of the drag coefficient in mixed seas. scimar [Internet]. 2012Sep.30 [cited 2023May31];76(S1):177-86. Available from: https://scientiamarina.revistas.csic.es/index.php/scientiamarina/article/view/1383