Abstract
Third-generation wave models have been evolved in 1980s with the state-of-the-art physics of wave generation. Using these models, the real time wave estimation is made possible but, in general, it is found to be underpredicted. This is mainly due to the smoothened wind vectors from the atmospheric model. An accurate prediction of wind is thus necessary to improve the wave prediction further. A better way of overcoming the discrepancies in the wind is by the way of wave data assimilation. In the present study, an operationally efficient yet a versatile assimilation model, optimal interpolation (OI), has been presented. The weighting matrix, so-called gain matrix, has been formulated according to the model physics by which the wind generates waves. The efficiency of the assimilative model using real time buoy observations at the Arabian Sea has been evaluated and described in this article. The root mean square error reduction of wave height is found to be of the order of 30–50% at the validation stations.
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References
Barzel G, Long RB (1994) Wave model fitting using the adjoint technique. In: Komen GJ, Cavaleri L, Donelan M, Hasselmann K, Hasselmann S, Janssen PAEM (eds) Dynamics and modeling of ocean waves. Cambridge University Press, New York
Bauer E, Young IR, Hasselmann K (1994) Data assimilation using a Green’s function approach. In: Komen GJ, Cavaleri L, Donelan M, Hasselmann K, Hasselmann S, Janssen PAEM (eds) Dynamics and modeling of ocean waves. Cambridge University Press, New York
Booij N, Ris RC, Holthuijsen LH (1999) A third-generation wave model for coastal regions 1. Model description and validation. J Geophys Res 104(C4):7649–7666. doi:10.1029/98JC02622
de las Heras MM, Burgers G, Janssen PAEM (1995) Wave data assimilation in the WAM wave model. J Mar Syst 6:77–85. doi:10.1016/0924-7963(94)00019-8
de Valk CF (1994) A wind and wave data assimilation scheme based on the adjoint technique. In: Komen GJ, Cavaleri L, Donelan M, Hasselmann K, Hasselmann S, Janssen PAEM (eds) Dynamics and modeling of ocean waves. Cambridge University Press, New York
de Valk CF, Calkoen CJ (1989) Wave data assimilation in a third generation wave prediction model for the North sea—an optimal control approach. Report X38, Delft Hydraulics, Delft, 123 pp
Golding B (1983) A wave prediction system for real time sea state forecasting. Q J R Meteorol Soc 109(460):393–416. doi:10.1002/qj.49710946011
Hasselmann S, Bruning C, Lionello P (1994) Towards a generalized optimal interpolation method for the assimilation of ERS-1 SAR retrieved wave spectra in a wave model. In: Proceedings of second ERS-1 symposium, Hamburg, 11–14 Oct 1993, ESA SP-361, pp 21–25
Hasselmann S, Bruning C, Hasselmann K, Heimbach P (1996) An improved algorithm for the retrieval of ocean wave spectra from SAR image spectra. J Geophys Res 101:16615–16629. doi:10.1029/96JC00798
Hasselmann S, Lionello P, Hasselmann K (1997) An optimal interpolation scheme for the assimilation of spectral wave data. J Geophys Res 102(C7):15823–15836. doi:10.1029/96JC03453
Hersbach H (1998) Application of adjoint of the WAM model to inverse wave modeling. J Geophys Res 103(C5):10469–10487. doi:10.1029/97JC03554
Holthuijsen LH, Booij N, van Endt M, Caires S, Gueded Soares C (1997) Assimilation of buoy and satellite data in wave forecasts with integral control variables. J Mar Syst 13:21–31. doi:10.1016/S0924-7963(96)00121-2
Janssen PAEM, Lionello P, Reistad M, Hollingsworth A (1989) Hindcasts and data assimilation studies with the WAM model during the Seasat period. J Geophys Res 94(C1):973–993. doi:10.1029/JC094iC01p00973
Komen GJ, Cavaleri L, Donelan M, Hasselmann K, Hasselmann S, Janssen PAEM (1994) Dynamics and modeling of ocean waves. Cambridge University Press, New York
Lionello P, Günter H (1992) Assimilation of altimeter data in a global third-generation model. J Geophys Res 97(C9):14453–14474. doi:10.1029/92JC01055
Lionello P, Günter H, Hansen B (1995) A sequential assimilation scheme applied to global wave analysis and prediction. J Mar Syst 6:87–107. doi:10.1016/0924-7963(94)00010-9
Mellor GL, Ezer T (1991) A Gulf stream model and an altimetry assimilation scheme. J Geophys Res 96:8779–8795. doi:10.1029/91JC00383
Miles JW (1957) On the generation of surface waves by shear flow. J Fluid Mech 3:185–204. doi:10.1017/S0022112057000567
Phillips OM (1957) On the generation of waves by turbulent wind. J Fluid Mech 2:417–445. doi:10.1017/S0022112057000233
Pinto JP, Bernardino MC, Pires SA (2005) A Kalman filter application to a spectral wave model. Nonlinear Process Geophys 12:775–782
Robinson AR, Lermusianx PFJ (2000) Overview of data assimilation. Technical Note No. 62, Division of Engineering and Applied Sciences, Harward University, Cambridge
Sannasiraj SA, Babovic V, Chan ES (2006) Wave data assimilation using ensemble error covariances for operational wave forecast. Ocean Model 14:102–121. doi:10.1016/j.ocemod.2006.04.001
Snyder RL, Dobson FW, Elliot JA, Long RB (1981) Array measurements of atmospheric pressure fluctuations above surface gravity waves. J Fluid Mech 102:1–59. doi:10.1017/S0022112081002528
The WAMDI Group (Hasselmann S, Hasselmann K, Bauer E, Janssen PAEM, Komen GJ, Bertotti L, Lionello P, Guillaume A, CardoneVC, Greenwood JA, Reistad M, Zambresky L, Ewing JA) (1988) The WAM model—a third generation ocean wave prediction model. J Phys Oceanogr 18:1775–1810. doi :10.1175/1520-0485(1988)018<1775:TWMTGO>2.0.CO;2
Thomas J (1988) Retrieval of energy spectra from measured data for assimilation into a wave model. Q J R Meteorol Soc 114:781–800. doi:10.1256/smsqj.48111
Tolman HL (1999) User manual and system documentation of WAVEWATCH-III, version 1.18. Technical Note No. 166, National Oceanic and Atmospheric Administration, Washington, DC
Acknowledgment
The authors would like to express their sincere gratitude to the Programme Director, National Data Buoy Program, India, for providing the buoy wave measurements and National Centre for Medium Range Weather Forecasting (NCMRWF) Centre, India, for providing the analyzed wind field for the required time period.
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Sannasiraj, S.A., Goldstein, M.G. Optimal interpolation of buoy data into a deterministic wind–wave model. Nat Hazards 49, 261–274 (2009). https://doi.org/10.1007/s11069-008-9291-x
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DOI: https://doi.org/10.1007/s11069-008-9291-x