Harmonic Analysis in the Simulation of Multiple Constituents: Determination of the Optimum Length of Time Series

An-Zhou Cao Key Laboratory of Physical Oceanography, Ocean University of China, Ministry of Education, Qingdao, China

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Dao-Sheng Wang Key Laboratory of Physical Oceanography, Ocean University of China, Ministry of Education, Qingdao, China

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Xian-Qing Lv Key Laboratory of Physical Oceanography, Ocean University of China, Ministry of Education, Qingdao, China

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Abstract

To investigate the optimum length of time series (TS) for harmonic analysis (HA) in the simulation of multiple constituents, a two-dimensional tidal model is used to simulate the M2, S2, K1, and O1 constituents in the Bohai and Yellow Seas. By analyzing the HA results of several nonoverlapping TS of the same length, which varies from 15 to 365 days, a field-average deviation of HA results is calculated. A deviation that is sufficiently small means that HA results are independent of the choice of TS, and the corresponding TS length is regarded as the optimum. Results indicate that the range of 180–195 days is the optimum length of TS for HA in the simulation of the four principal constituents. To investigate what determines the optimum length, experiments with different computed area and model settings are carried out. Results indicate that the optimum length is independent of advection, nodal corrections, and computed area, and only depends on bottom friction. Nonlinear bottom friction results in the appearance of higher harmonics and explains why the optimum length of TS for HA is 180–195 days.

Corresponding author address: Xian-Qing Lv, Key Laboratory of Physical Oceanography, Ocean University of China, Ministry of Education, 238 Songling Road, Qingdao 266001, China. E-mail: xqinglv@ouc.edu.cn

Abstract

To investigate the optimum length of time series (TS) for harmonic analysis (HA) in the simulation of multiple constituents, a two-dimensional tidal model is used to simulate the M2, S2, K1, and O1 constituents in the Bohai and Yellow Seas. By analyzing the HA results of several nonoverlapping TS of the same length, which varies from 15 to 365 days, a field-average deviation of HA results is calculated. A deviation that is sufficiently small means that HA results are independent of the choice of TS, and the corresponding TS length is regarded as the optimum. Results indicate that the range of 180–195 days is the optimum length of TS for HA in the simulation of the four principal constituents. To investigate what determines the optimum length, experiments with different computed area and model settings are carried out. Results indicate that the optimum length is independent of advection, nodal corrections, and computed area, and only depends on bottom friction. Nonlinear bottom friction results in the appearance of higher harmonics and explains why the optimum length of TS for HA is 180–195 days.

Corresponding author address: Xian-Qing Lv, Key Laboratory of Physical Oceanography, Ocean University of China, Ministry of Education, 238 Songling Road, Qingdao 266001, China. E-mail: xqinglv@ouc.edu.cn
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  • Cao, A. Z., Guo Z. , and Lv X. Q. , 2012: Inversion of two-dimensional tidal open boundary conditions of M2 constituent in the Bohai and Yellow Seas. Chin. J. Oceanol. Limnol., 30, 868875, doi:10.1007/s00343-012-1185-9.

    • Search Google Scholar
    • Export Citation
  • Cummins, P. F., and Oey L. Y. , 1997: Simulation of barotropic and baroclinic tides off north British Columbia. J. Phys. Oceanogr., 27, 762781, doi:10.1175/1520-0485(1997)027<0762:SOBABT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Egbert, G. D., and Erofeeva S. Y. , 2002: Efficient inverse modeling of barotropic ocean tides. J. Atmos. Oceanic Technol., 19, 183204, doi:10.1175/1520-0426(2002)019<0183:EIMOBO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Fang, G. H., Kwok Y. K. , Yu K. J. , and Zhu Y. H. , 1999: Numerical simulation of principal tidal constituents in the South China Sea, Gulf of Tokin and Gulf of Thailand. Cont. Shelf Res., 19, 845869, doi:10.1016/S0278-4343(99)00002-3.

    • Search Google Scholar
    • Export Citation
  • Foreman, M. G. G., Henry R. F. , Walters R. A. , and Ballantyne V. A. , 1993: A finite element model for tides and resonance along the north coast of British Columbia. J. Geophys. Res., 98, 25092531, doi:10.1029/92JC02470.

    • Search Google Scholar
    • Export Citation
  • He, R. Y., and Weisberg R. H. , 2002: Tides on the West Florida shelf. J. Phys. Oceanogr., 32, 34553473, doi:10.1175/1520-0485(2002)032<3455:TOTWFS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kang, S. K., Lee S. R. , and Lie H. J. , 1998: Fine grid tidal modeling of the Yellow and East China Seas. Cont. Shelf Res., 18, 739772, doi:10.1016/S0278-4343(98)00014-4.

    • Search Google Scholar
    • Export Citation
  • Lu, X. Q., and Zhang J. C. , 2006: Numerical study on spatially varying bottom friction coefficient of a 2D tidal model with adjoint method. Cont. Shelf Res., 26, 19051923, doi:10.1016/j.csr.2006.06.007.

    • Search Google Scholar
    • Export Citation
  • Rosenfeld, L., Shulman I. , Cook M. , Paduan J. , and Shulman L. , 2009: Methodology for a regional tidal model evaluation, with application to central California. Deep-Sea Res. II, 56, 199218, doi:10.1016/j.dsr2.2008.08.007.

    • Search Google Scholar
    • Export Citation
  • Wang, X. C., and Coauthors, 2013: Modeling tides and their influence on the circulation in Prince William Sound, Alaska. Cont. Shelf Res., 63, S126S137, doi:10.1016/j.csr.2012.08.016.

    • Search Google Scholar
    • Export Citation
  • Wijeratne, E. M. S., Pattiaratchi C. B. , Eliot M. , and Haigh I. D. , 2012: Tidal characteristics in Bass Strait, south-east Australia. Estuarine Coastal Shelf Sci., 114, 156165, doi:10.1016/j.ecss.2012.08.027.

    • Search Google Scholar
    • Export Citation
  • Zhang, J. C., X. Q. Lu, P. Wang, and Y. P. Wang, 2011: Study on linear and nonlinear bottom friction parameterizations for regional tidal models using data assimilation. Cont. Shelf Res.,31, 555–573, doi: 10.1016/j.csr.2010.12.011.

  • Zu, T. T., Gan J. P. , and Erofeeva S. Y. , 2008: Numerical study of the tide and tidal dynamics in the South China Sea. Deep-Sea Res. I, 55, 137154, doi:10.1016/j.dsr.2007.10.007.

    • Search Google Scholar
    • Export Citation
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