Estimating Four-Dimensional Internal Wave Spectrum in the Northern South China Sea

Hui Sun Physical Oceanography Laboratory, Collaborative Innovation Center of Marine Science and Technology, Ocean University of China, and Qingdao National Laboratory for Marine Science and Technology, Qingdao, China

Search for other papers by Hui Sun in
Current site
Google Scholar
PubMed
Close
,
Wei Zhao Physical Oceanography Laboratory, Collaborative Innovation Center of Marine Science and Technology, Ocean University of China, and Qingdao National Laboratory for Marine Science and Technology, Qingdao, China

Search for other papers by Wei Zhao in
Current site
Google Scholar
PubMed
Close
,
Qingxuan Yang Physical Oceanography Laboratory, Collaborative Innovation Center of Marine Science and Technology, Ocean University of China, and Qingdao National Laboratory for Marine Science and Technology, Qingdao, China

Search for other papers by Qingxuan Yang in
Current site
Google Scholar
PubMed
Close
,
Shuqun Cai State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, and Institution of South China Sea Ecology and Environmental Engineering, Chinese Academy of Sciences, Guangzhou, China

Search for other papers by Shuqun Cai in
Current site
Google Scholar
PubMed
Close
,
Xinfeng Liang College of Marine Science, University of South Florida, St. Petersburg, Florida

Search for other papers by Xinfeng Liang in
Current site
Google Scholar
PubMed
Close
, and
Jiwei Tian Physical Oceanography Laboratory, Collaborative Innovation Center of Marine Science and Technology, Ocean University of China, and Qingdao National Laboratory for Marine Science and Technology, Qingdao, China

Search for other papers by Jiwei Tian in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Internal waves can transfer energy from large-scale to microscale processes; however, the spectra of these waves remain poorly known. A method that combines modal harmonic decomposition and maximum-likelihood method is proposed in this study to estimate four-dimensional internal wave spectrum using limited mooring observations. Using this method, a four-dimensional internal wave spectrum was obtained for the first time based on the mooring measurements collected during the South China Sea (SCS) Internal Wave Experiment in July 2014. The spectrum was then validated by comparing with the spectrum based on Fourier analysis and with the modified Garrett–Munk internal wave spectrum, respectively. The power of the internal wave spectrum decreased obviously with increasing frequency and wavenumber, with a falloff rate of ω−2 beyond tidal frequencies, and with falloff rates of kh2 and kz2.5 for horizontal and vertical wavenumbers, respectively. In addition, at a fixed frequency and vertical wavenumber, the propagation direction and phase speed of internal waves can be obtained through the four-dimensional spectrum. In summary, we verified the feasibility of estimating four-dimensional internal wave spectrum using limited mooring observations in this study, and the method we proposed should be applicable to other regions where such mooring observations are available.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JTECH-D-18-0046.s1.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding authors: Q. Yang, yangqx@ouc.edu.cn; J. Tian, tianjw@ouc.edu.cn

Abstract

Internal waves can transfer energy from large-scale to microscale processes; however, the spectra of these waves remain poorly known. A method that combines modal harmonic decomposition and maximum-likelihood method is proposed in this study to estimate four-dimensional internal wave spectrum using limited mooring observations. Using this method, a four-dimensional internal wave spectrum was obtained for the first time based on the mooring measurements collected during the South China Sea (SCS) Internal Wave Experiment in July 2014. The spectrum was then validated by comparing with the spectrum based on Fourier analysis and with the modified Garrett–Munk internal wave spectrum, respectively. The power of the internal wave spectrum decreased obviously with increasing frequency and wavenumber, with a falloff rate of ω−2 beyond tidal frequencies, and with falloff rates of kh2 and kz2.5 for horizontal and vertical wavenumbers, respectively. In addition, at a fixed frequency and vertical wavenumber, the propagation direction and phase speed of internal waves can be obtained through the four-dimensional spectrum. In summary, we verified the feasibility of estimating four-dimensional internal wave spectrum using limited mooring observations in this study, and the method we proposed should be applicable to other regions where such mooring observations are available.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JTECH-D-18-0046.s1.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding authors: Q. Yang, yangqx@ouc.edu.cn; J. Tian, tianjw@ouc.edu.cn

Supplementary Materials

    • Supplemental Materials (PDF 1.75 MB)
Save
  • Alford, M. H., R.-C. Lien, H. Simmons, J. Klymak, S. Ramp, Y. J. Yang, D. Tang, and M.-H. Chang, 2010: Speed and evolution of nonlinear internal waves transiting the South China Sea. J. Phys. Oceanogr., 40, 13381355, https://doi.org/10.1175/2010JPO4388.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Althaus, A. M., E. Kunze, and T. B. Sanford, 2003: Internal tide radiation from Mendocino Escarpment. J. Phys. Oceanogr., 33, 15101527, https://doi.org/10.1175/1520-0485(2003)033<1510:ITRFME>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Buijsman, M. C., Y. Kanarska, and J. C. McWilliams, 2010: On the generation and evolution of nonlinear internal waves in the South China Sea. J. Geophys. Res., 115, C02012, https://doi.org/10.1029/2009JC005275.

    • Search Google Scholar
    • Export Citation
  • Cairns, J. L., and G. O. Williams, 1976: Internal wave observations from a midwater float, 2. J. Geophys. Res., 81, 19431950, https://doi.org/10.1029/JC081i012p01943.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Capon, J., 1969: High-resolution frequency-wavenumber spectrum analysis. Proc. IEEE, 57, 14081418, https://doi.org/10.1109/PROC.1969.7278.

  • Chang, M. H., R. C. Lien, T. Y. Tang, E. A. D’Asaro, and Y. J. Yang, 2006: Energy flux of nonlinear internal waves in northern South China Sea. Geophys. Res. Lett., 33, L03607, https://doi.org/10.1029/2005GL025196.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, G., Y. Hou, and X. Chu, 2011: Mesoscale eddies in the South China Sea: Mean properties, spatiotemporal variability, and impact on thermohaline structure. J. Geophys. Res., 116, C06018, https://doi.org/10.1029/2010JC006716.

    • Search Google Scholar
    • Export Citation
  • Donelan, M., A. Babanin, E. Sanina, and D. Chalikov, 2015: A comparison of methods for estimating directional spectra of surface waves. J. Geophys. Res. Oceans, 120, 50405053, https://doi.org/10.1002/2015JC010808.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dong, C., H. Song, T. Hao, L. Chen, and Y. Song, 2009: Studying of oceanic internal wave spectra in the northeast South China Sea from seismic reflections (in Chinese). Chin. J. Geophys., 52, 20502055.

    • Search Google Scholar
    • Export Citation
  • Drennan, W. M., H. C. Graber, H. Danièle, and Q. Céline, 2003: On the wave age dependence of wind stress over pure wind seas. J. Geophys. Res., 108, 8062, https://doi.org/10.1029/2000JC000715.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fjeldstad, J. E., 1933: Interne Wellen (in Norwegian). Geofys. Publ., 10, 335.

  • Garrett, C. J., and W. Munk, 1972: Space–time scales of internal waves. Geophys. Fluid Dyn., 3, 225264, https://doi.org/10.1080/03091927208236082.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Garrett, C. J., and W. Munk, 1975: Space–time scales of internal waves: A progress report. J. Geophys. Res., 80, 291297, https://doi.org/10.1029/JC080i003p00291.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gerkema, T., and J. T. F. Zimmerman, 2008: An introduction to internal waves. Royal Netherlands Institute for Sea Research Rep., 207 pp.

  • Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 662 pp.

  • Henyey, F. S., J. Wright, and S. M. Flatté, 1986: Energy and action flow through the internal wave field: An eikonal approach. J. Geophys. Res., 91, 84878495, https://doi.org/10.1029/JC091iC07p08487.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huang, X., W. Zhao, J. Tian, and Q. Yang, 2014: Mooring observations of internal solitary waves in the deep basin west of Luzon Strait. Acta Oceanol. Sin., 33, 8289, https://doi.org/10.1007/s13131-014-0416-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huang, X., Z. Zhang, X. Zhang, H. Qian, W. Zhao, and J. Tian, 2017: Impacts of a mesoscale eddy pair on internal solitary waves in the northern South China Sea revealed by mooring array observations. J. Phys. Oceanogr., 47, 15391554, https://doi.org/10.1175/JPO-D-16-0111.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jan, S., R. C. Lien, and C. H. Ting, 2008: Numerical study of baroclinic tides in Luzon Strait. J. Oceanogr., 64, 789802, https://doi.org/10.1007/s10872-008-0066-5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kocaoğlu, A. H., and K. Fırtana, 2011: Estimation of shear wave velocity profiles by the inversion of spatial autocorrelation coefficients. J. Seismol., 15, 613624, https://doi.org/10.1007/s10950-011-9239-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Krauss, W., 1966: Interne Wellen. Gebruder Borntraeger, 248 pp.

  • Leaman, K. D., and T. B. Sanford, 1975: Vertical energy propagation of inertial waves: A vector spectral analysis of velocity profiles. J. Geophys. Res., 80, 19751978, https://doi.org/10.1029/JC080i015p01975.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leong, E. C., and A. M. W. Aung, 2012: Weighted average velocity forward modelling of Rayleigh surface waves. Soil. Dyn. Earthquake Eng., 43, 218228, https://doi.org/10.1016/j.soildyn.2012.07.030.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Levine, M. D., 2002: A modification of the Garrett–Munk internal wave spectrum. J. Phys. Oceanogr., 32, 31663181, https://doi.org/10.1175/1520-0485(2002)032<3166:AMOTGM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, X., Z. Zhao, and W. G. Pichel, 2008: Internal solitary waves in the northwestern South China Sea inferred from satellite images. Geophys. Res. Lett., 35, L13605, https://doi.org/10.1029/2008GL034272.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lien, R.-C., T. Y. Tang, M. H. Chang, and E. A. D’Asaro, 2005: Energy of nonlinear internal waves in the South China Sea. Geophys. Res. Lett., 32, L05615, https://doi.org/10.1029/2004GL022012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, A. K., S. R. Ramp, Y. Zhao, and T. Y. Tang, 2004: A case study of internal solitary wave propagation during ASIAEX 2001. IEEE J. Oceanic Eng., 29, 11441156, https://doi.org/10.1109/JOE.2004.841392.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, A. K., Y. Zhao, and M. Hsu, 2005: Nonlinear internal wave study in the South China Sea. Advances in Engineering Mechanics: Reflections and Outlooks, A. T. Chwang, M. H. Teng, and D. T. Valentine, Eds., World Scientific, 297–313.

    • Crossref
    • Export Citation
  • Millard, R., 1972: Further comments on vertical temperature spectra in the MODE region. MODE Hot Line News, No. 18, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, 1–6.

  • Müller, P., D. J. Olbers, and J. Willebrand, 1978: The IWEX spectrum. J. Geophys. Res., 83, 479500, https://doi.org/10.1029/JC083iC01p00479.

  • Munk, W. H., 1981: Internal waves and small-scale processes. Evolution of Physical Oceanography, B. A. Warren and C. Wunsch, Eds., MIT Press, 264–291.

  • Polzin, K. L., and Y. V. Lvov, 2011: Toward regional characterizations of the oceanic internal wavefield. Rev. Geophys., 49, RG4003, https://doi.org/10.1029/2010RG000329.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Polzin, K. L., J. M. Toole, and R. W. Schmitt, 1995: Finescale parameterizations of turbulent dissipation. J. Phys. Oceanogr., 25, 306328, https://doi.org/10.1175/1520-0485(1995)025<0306:FPOTD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Polzin, K. L., A. C. N. Garabato, T. N. Huussen, B. M. Sloyan, and S. Waterman, 2014: Finescale parameterizations of turbulent dissipation. J. Geophys. Res. Oceans, 119, 13831419, https://doi.org/10.1002/2013JC008979.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ramp, S. R., Y. J. Yang, and F. L. Bahr, 2010: Characterizing the nonlinear internal wave climate in the northeastern South China Sea. Nonlinear Processes Geophys., 17, 481498, https://doi.org/10.5194/npg-17-481-2010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Satoh, T., H. Kawase, T. Iwata, S. Higashi, T. Sato, K. Irikura, and H. C. Huang, 2001: S-wave velocity structure of the Taichung basin, Taiwan, estimated from array and single-station records of microtremors. Bull. Seismol. Soc. Amer., 91, 12671282, https://doi.org/10.1785/0120000706.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shang, X., Z. Lu, X. Xie, and G. Chen, 2009: The characters of internal wave spectra in the northern South China Sea. J. Trop. Oceanogr., 28, 1620.

    • Search Google Scholar
    • Export Citation
  • Simmons, H., M. H. Chang, Y. T. Chang, S. Y. Chao, O. Fringer, C. R. Jackson, and D. S. Ko, 2011: Modeling and prediction of internal waves in the South China Sea. Oceanography, 24 (4), 8899, https://doi.org/10.5670/oceanog.2011.97.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tokimatsu, K., K. Shinzawa, and S. Kuwayama, 1992: Use of short-period microtremors for VS profiling. J. Geotech. Eng., 118, 15441558, https://doi.org/10.1061/(ASCE)0733-9410(1992)118:10(1544).

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, D., Y. Shu, H. Xue, J. Hu, J. Chen, W. Zhuang, T. T. Zu, and J. Xu, 2014: Relative contributions of local wind and topography to the coastal upwelling intensity in the northern South China Sea. J. Geophys. Res. Oceans, 119, 25502567, https://doi.org/10.1002/2013JC009172.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, D., J. Xiao, Y. Shu, Q. Xie, J. Chen, and Q. Wang, 2016: Progress on deep circulation and meridional overturning circulation in the South China Sea. Sci. China Earth Sci., 59, 18271833, https://doi.org/10.1007/s11430-016-5324-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, G., J. Li, C. Wang, and Y. Yan, 2012: Interactions among the winter monsoon, ocean eddy and ocean thermal front in the South China Sea. J. Geophys. Res., 117, C08002, https://doi.org/10.1029/2012JC008007.

    • Search Google Scholar
    • Export Citation
  • Wu, C. F., and H. C. Huang, 2015: S-wave velocity structure of the Taiwan Chelungpu Fault Drilling Project (TCDP) site using microtremor array measurements. Pure Appl. Geophys., 172, 25452556, https://doi.org/10.1007/s00024-014-0773-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xie, X., X. Shang, and G. Chen, 2010: Nonlinear interactions among internal tidal waves in the northeastern South China Sea. Chin. J. Oceanol. Limnol., 28, 9961001, https://doi.org/10.1007/s00343-010-9064-8.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, T. C., and K. Yoo, 1999: Internal wave spectrum in shallow water: Measurement and comparison with the Garrett-Munk model. IEEE J. Oceanic Eng., 24, 333345, https://doi.org/10.1109/48.775295.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Young, I. R., and A. V. Babanin, 2006: Spectral distribution of energy dissipation of wind-generated waves due to dominant wave breaking. J. Phys. Oceanogr., 36, 376394, https://doi.org/10.1175/JPO2859.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhao, Z., 2014: Internal tide radiation from the Luzon Strait. J. Geophys. Res. Oceans, 119, 54345448, https://doi.org/10.1002/2014JC010014.

  • Zhao, Z., and M. H. Alford, 2006: Source and propagation of internal solitary waves in the northeastern South China Sea. J. Geophys. Res., 111, C11012, https://doi.org/10.1029/2006JC003644.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 600 176 3
PDF Downloads 640 116 4