Parameterizing the Sea Surface Drag Coefficient over Aiyetoro in Ilaje Local Government Area, Ondo State, Southwestern Nigeria

Adekunle Ayodotun Osinowo

Department of Marine Science and Technology, Federal University of Technology, Akure 340252, Nigeria

Lateef Adesola Afolabi

Department of Engineering, University of Campania Luigi Vanvitelli, 81031 Aversa, Italy

Pasquale Contestabile

Department of Engineering, University of Campania Luigi Vanvitelli, 81031 Aversa, Italy

Segun Ohunayo Ekudehinwa

Department of Meteorology, Nigerian Maritime University, Okerenkoko 332105 Nigeria

Gideon Efeoghene Ovwuwonye

Department of Marine Science and Technology, Federal University of Technology, Akure 340252, Nigeria

DOI: https://doi.org/10.36956/sms.v7i3.1989

Received: 11 April 2025 | Revised: 6 May 2025 | Accepted: 26 May 2025 | Published Online: 21 July 2025

Copyright © 2025 Adekunle Ayodotun Osinowo, Lateef Adesola Afolabi, Pasquale Contestabile, Segun Ohunayo Ekudehinwa, Gideon Efeoghene Ovwuwonye. Published by Nan Yang Academy of Sciences Pte. Ltd.

Creative Commons LicenseThis is an open access article under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) License.


Abstract

Ocean surface waves and upper sea circulation are primarily propelled by wind force and are usually expressed in terms of sea surface drag coefficient (cd) that increases with sea surface roughness and wind speed. This work discussed the cd parameterization at Aiyetoro, Ilaje Local Government Area, Ondo State, Southwestern Nigeria, to quantify the exchange of momentum in this region, The dependence of cd on some one hourly averaged variables sourced from ERA5 Reanalysis over a 71 year period (1950–2020) was clearly analysed. Results of the monthly mean and variability of cd and u10 over the study area showed that November had the lowest monthly mean cd and u10, with values of 0.000825 and 3.38 m/s, respectively, and August had the highest values of 0.001031 and 5.66 m/s, respectively. Furthermore, the cd variability is lowest (63.24%) in November and highest (106.35%) in August. The variability for u10 is lowest in March (198.18%) and greatest in October (304.37%). For the study location, five parameterizations, were statistically evaluated for the predictive power of cd on an annual, seasonal and monthly basis. Furthermore, the cd showed improved performance when using monthly values than when using annual and seasonal values. The equations yielded better performance in the wet season than in the dry season.

Keywords: Era5 Reanalysis Data; Sea Surface Drag; Parameterization; Wind-Sea Interaction; Wave Dynamics; Momentum


References

[1] Gao, Z., Wang, Q., Zhou, M., 2009. Wave-dependence of friction velocity, roughness length, and drag coefficient over coastal and open water surfaces by using three databases. Advances in Atmospheric Sciences. 26, 887–894. DOI: https://doi.org/10.1007/s00376-009-8130-7

[2] Shi, J., Zhong, Z., Li, R., et al., 2011. Dependence of sea surface drag coefficient on wind-wave parameters. Acta Oceanologica Sinica. 30(2), 14–24. DOI: https://doi.org/10.1007/s13131-011-0101-z

[3] Guan, C., Xie, L., 2004. On the linear parameterization of drag coefficient over sea surface. Journal of Physical Oceanography. 34, 2847–2851. DOI: https://doi.org/10.1175/JPO2664.1

[4] Wang, J., Song, J., Huang, Y., and Fan, C., 2013. On the parameterization of drag coefficient over sea surface. Acta Oceanol. Sin., 2013, Vol. 32, No. 5, P. 68-74 DOI: 10.1007/s13131-013-0315-3.

[5] Zhao, D., Li, M., 2018. Dependence of wind stress across an air–sea interface on wave states. Journal of Oceanography. 75, 207–223. DOI: https://doi.org/10.1007/s10872-018-0494-9

[6] Charnock, H., 1955. Wind stress on a water surface. Quarterly Journal of theRoyal Meteorological Society. 81, 639–640. DOI: https://doi.org/10.1002/qj.49708135027

[7] Gao, Z., Zhou, S., Zhang, J., et al., 2021. Parameterization of Sea Surface Drag Coefficient for All Wind Regimes Using 11 Aircraft Eddy-Covariance Measurement Databases. Atmosphere. 12(11), 1485. DOI: https://doi.org/10.3390/atmos12111485

[8] Zhao, D., Li, M., 2024. Dependence of drag coefficient on the spectral width of ocean waves. Journal of Oceanography. 80, 129–143. DOI: https://doi.org/10.1007/s10872-023-00712-6

[9] Shi, J., Feng, Z., Sun, Y., et al., 2021. Relationship between Sea Surfacedrag coefficient and Wave State. Journal of Marine Science and Engineering. 9(11), 1248. DOI: https://doi.org/10.3390/jmse9111248

[10] Gao, Z., Peng, W., Gao, C.Y., et al., 2020. Parabolic dependence of the drag coefficient on wind speed from aircraft eddy-covariance measurements over the tropical Eastern Pacific. Scientific Reports. 10, 1805. DOI: https://doi.org/10.1038/s41598-020-58699-9

[11] Zhang, X., Bi, X., Gao, Z., et al., 2021. Parameterizations of drag coefficient and aerodynamic roughness length using the turbulence data collected during typhoons Hagupit and Chanthu. Journal of Tropical Oceanography. 40(2), 1–6.

[12] Zhou, X., Hara, T., Ginis, I., et al., 2022. Drag coefficient and its sea state dependence under tropical cyclones. Journal of Physical Oceanography. 52(7), 1447–1470. DOI: https://doi.org/10.1175/JPO-D-21-0246.1

[13] Hsu, J.Y., Lien, R.C., D’Asaro, E.A., et al., 2019. Scaling of drag coefficients under five tropical cyclones. Geophysical Research Letters. 46, 3349–3358. DOI: https://doi.org/10.1029/2018GL081574

[14] Shi, H., Li, Q., Wang, Z., et al., 2022. The Influence of Sea Sprays on Drag Coefficient at High Wind Speed. Journal of Ocean University of China. 22, 21–27. DOI: https://doi.org/10.1007/s11802-022-5050-y

[15] Kim, S-H., Kang, H-W., Moon, I-J., et al., 2022. Effects of the reduced air-sea drag coefficient in high winds on the rapid intensification of tropical cyclones and bimodality of the lifetime maximum intensity. Frontiers in Marine Science. 9, 1032888. DOI: https://doi.org/10.3389/fmars.2022.1032888

[16] Curcic, M., Haus, B.K., 2020. Revised Estimates of Ocean Surface Drag in Strong Winds. Geophysical Research Letters. 47(10), e2020GL087647. DOI: https://doi.org/10.1029/2020GL087647

[17] Takagaki, N., Komori, S., Suzuki, N., et al., 2012. Strong correlation between the drag coefficient and the shape of the wind sea spectrum over a broad range of wind speeds. Geophysical Research Letters. 39, L23604. DOI: https://doi.org/10.1029/2012GL053988

[18] Kuznetsova, A., Baydakov, G., Dosaev, A., et al., 2023. Drag coefficient Parameterization under Hurricane Wind Conditions. Water. 15(10), 1830. DOI: https://doi.org/10.3390/w15101830

[19] Hu, Y., Shao, W., Xu, Y., et al., 2024. Improvement of drag coefficient parameterization of WAVEWATCH-III using remotely sensed products during tropical cyclones. Ocean Dynamics. 74(10), 843–858. DOI: https://doi.org/10.1007/s10236-024-01638-3

[20] Feng, X., Sun, J., Yang, D., et al., 2021. Effect of drag coefficient Parameterizations on Air–Sea Coupled Simulations: A Case Study for Typhoons Haima and Nida in 2016. Journal of Atmospheric and Oceanic Technology. 38(5), 977–993. DOI: https://doi.org/10.1175/JTECH-D-20-0133.1

[21] Hwang, P.A., 2020. Impact on Sea-Surface Electromagnetic Scattering and Emission Modeling of Recent Progress on the Parameterization of Ocean Surface Roughness, Drag Coefficient, and Whitecap Coverage in High Wind Conditions. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing. 13, 1879–1887. DOI: https://doi.org/10.1109/JSTARS.2020.2977420

[22] Lin, S., Sheng, J., 2020. Revisiting dependences of the drag coefficient at the sea surface on wind speed and sea state. Continental Shelf Research. 207, 104188. DOI: https://doi.org/10.1016/j.csr.2020.104188

[23] Zhao, Z., Shi, J., Wang, H., et al., 2024. Parameterization scheme of the sea surface drag coefficient considering the influence of wave states and sea spray stress. Frontiers in Marine Science. 11, 1336709. DOI: https://doi.org/10.3389/fmars.2024.1336709

[24] Chen, S., Jiang, W.Z., Xue, Y., et al., 2024. A New Wave-State-Based Drag Coefficient Parameterization for Coastal Regions. Journal of Physical Oceanography. 54(3), 809–821. DOI: https://doi.org/10.1175/JPO-D-23-0081.1

[25] Zhang, C., Chen, L., Brett, M.T., 2024. Adaptation of wind drag coefficient parameterization: Improvement of hydrodynamic modeling by a wave‐dependent cd in large shallow lakes. Water Resources Research. 60, e2023WR035914. DOI: https://doi.org/10.1029/2023WR035914

[26] Shi, J., Zhao, D., Li, X., et al., 2009. New wave-dependent formulae for sea spray flux at air-sea interface. Journal of Hydrodynamics. 21, 573–581. DOI: https://doi.org/10.1016/S1001-6058(08)60186-9

[27] Rizza, U., Canepa, E., Ricchi, A., et al., 2018. Influence of wave state and sea spray on the roughness length: feedback on medicanes atmosphere. Atmosphere. 9(8), 301. DOI: https://doi.org/10.3390/atmos9080301

[28] Powell, M.D., Vickery, P.J., Reinhold, T.A., 2003. Reduced drag coefficient for high wind speeds in tropical cyclones. Nature. 422, 279–283. DOI: https://doi.org/10.1038/nature01481

[29] Moon, I.J., Ginis, I., Hara, T., et al., 2007. A physics-based parameterization of air–sea momentum flux at high wind speeds and its impact on hurricane intensity predictions. Monthly Weather Review. 135(8), 2869–2878. DOI: https://doi.org/10.1175/MWR3432.1

[30] Andreas, E.L., Emanuel, K.A., 2001. Effects of sea spray on tropical cyclone intensity. Journal of the Atmospheric Sciences. 58, 3741–3751. DOI: https://doi.org/10.1175/1520-0469(2001)058<3741: EOSSOT>2.0.CO;2

[31] Xu, X., Voermans, J.J., Ma, H., et al., 2021. A wind–wave-dependent sea spray volume flux model based on field experiments. Journal of Marine Science and Engineering. 9(11), 1168. DOI: https://doi.org/10.3390/jmse9111168

[32] Andreas, E.L., 2004. Spray stress revisited. Journal of Physical Oceanography. 34(6), 1429–1440. DOI: https://doi.org/10.1175/1520-0485(2004)034<1429: SSR>2.0.CO;2

[33] Lafon, C., Piazzola, J., Forget, P., et al., 2004. Analysis of the variations of the whitecap fraction as measured in a coastal zone. Boundary-Layer Meteorology. 111, 339–360. DOI: https://doi.org/10.1023/B:BOUN.0000016490.83880.63

[34] Andreas, E.L., Decosmo, J., 2002. The signature of sea spray in the hexos turbulent heat flux data. Boundary-Layer Meteorology. 103, 303–333. DOI: https://doi.org/10.1023/A:1014564513650

[35] Nilsson, E.D., Hultin, K.A.H., Mårtensson, E.M., et al., 2021. Baltic sea spray emissions: in situ eddy covariance fluxes vs. Simulated tank sea spray. Atmosphere. 12(2), 274. DOI: https://doi.org/10.3390/atmos12020274

[36] Lenain, L., Melville, W.K., 2017. Evidence of sea-state dependence of aerosol concentration in the marine atmospheric boundary layer. Journal of Physical Oceanography. 47(1), 69–84. DOI: https://doi.org/10.1175/JPO-D-16-0058.1

[37] Song, A., Li, J., Tsona, N., et al., 2023. Parameterizations for sea spray aerosol production flux. Applied Geochemistry. 157, 105776. DOI: https://doi.org/10.1016/j.apgeochem.2023.105776

[38] Zhao, D., Toba, Y., Sugioka, K., et al., 2006. New sea spray generation function for spume droplets. Journal of Geophysical Research Oceans. 111(C2), C02007. DOI: https://doi.org/10.1029/2005JC002960

[39] Austin, M.J., Unsworth, C.A., Van Landeghem, K.J.J., et al., 2025. Enhanced bed shear stress and mixing in the tidal wake of an offshore wind turbine monopile. Ocean Science. 21(1), 81–91. DOI: https://doi.org/10.5194/os-21-81-2025.

[40] Cai, L., Wang, B., Wang, W., et al., 2025. The Impact of Air–Sea Flux Parameterization Methods on Simulating Storm Surges and Ocean Surface Currents. Journal of Marine Science and Engineering. 13(3), 541. DOI: https://doi.org/10.3390/jmse13030541

[41] Ocean Energy Systems (OES), 2017. OES Annual Report 2017. Available from: https://www.ocean-energy-systems.org/publications/oes-annual-reports/document/oes-annual-report-2017/ (cited 13 December 2024).

[42] Soukissian, T., Karathanasi, F., Axaopoulos, P., 2017. Satellite-Based Offshore wind resource assessment in the mediterranean sea. IEEE Journal of Oceanic Engineering. 42(1), 73–86. DOI: https://doi.org/10.1109/JOE.2016.2565018

[43] Energiewende, A., Sandbag, 2018. The European Power Sector in 2017: State of Affairs and Review of Current Developments. Available online at: https://www.agora-energiewende.de/fileadmin/Projekte/2018/EU_Jahresrueckblick_2017/Agora_EU-report-2017_WEB.pdf (cited 16 January 2025).

[44] Onea, F., Ciortan, S., Rusu, E. 2017. Assessment of the potential for developing combined wind-wave projects in the European nearshore. Energy & Environment. 28(5–6), 580–597. DOI: https://doi.org/10.1177/0958305X17716947

[45] McMillan, D., Ault, G.W., 2010. Techno-economic comparison of operational aspects for direct drive and gearbox-driven wind turbines. IEEE Transactions on Energy Conversion. 25(1), 191–198. DOI: https://doi.org/10.1109/TEC.2009.2032596

[46] Liu, Y., Li, Y., He, F., et al., 2017. Comparison study of tidal stream and wave energy technology development between China and some Western Countries. Renewable and Sustainable Energy Reviews. 76, 701–716. DOI: https://doi.org/10.1016/j.rser.2017.03.049

[47] Fusco, F., Nolan, G., Ringwood, J.V., 2010. Variability reduction through optimal combination of wind/wave resources—an Irish case study. Energy. 35(1), 314–325. DOI: https://doi.org/10.1016/j.energy.2009.09.023

[48] Barbier, J., Guichard, F., Bouniol, D., et al., 2018. Detection of Intraseasonal Large-Scale Heat Waves: Characteristics and Historical Trends during the Sahelian Spring. Journal of Climate. 31(1), 61–80. DOI: https://doi.org/10.1175/JCLI-D-170244.1

[49] Bruno, M.F., Molfetta, M.G., Torato, V., et al., 2020. Performance Assessment of ERA5 Wave Data in a Swell Dominated Region. Journal of Marine Science and Engineering. 8(3), 214. DOI: https://doi.org/10.3390/jmse8030214

[50] Enikanselu, P.A., Balogun, A.A., Ewetumo, T., et al., 2025. Exploration of Wind-Wave Energy Potentials for Renewable Energy Development in Parts of Ondo Coastal and Offshore Locations, Southwestern Nigeria. Indian Journal of Energy and Energy Resources (IJEER). 4(2), 1–10. DOI: https://doi.org/10.54105/ijeer.B1039.04020225

[51] Wilks, D.S., 1995. Statistical Methods in the Atmospheric Sciences: An Introduction. Academic Press: San Diego, CA, USA. pp. 1–649.

[52] Osinowo, A.A., Okogbue, E.C., 2013. Estimating Global Solar Radiation from some Readily Measured Climatic Parameters over the Major Climatic Zones of Nigeria. Ife Research Publications in Geography. 12, 62–90.

[53] Iqbal, M., 1983. An introduction to solar radiation. Academic Press: New York, NY, USA. pp. 59–67.

[54] Halouani, N., Nguyem, C.T., Vo-Ngoc, D., 1993. Calculation of monthly average global solar radiation on horizontal surfaces using daily hours of bright sunshine. Solar energy. 50(3), 247–258. DOI: https://doi.org/10.1016/0038-092X(93)90018-J