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Spectral methods in oceanography with applications

Abstract

This paper is a survey of the main spectral methods potentially useful in Oceanography. These methods are applied to the analysis of tides, seasonal variations and ocean geophysical oscillations. Further topics on the Response Method, the Maximum Entropy method and Rotary Components are briefly summarized. Examples of successful appli cations are presented.


Spectral methods in oceanography with applications* * - This work was partially supported by Projeto FINEP-IOUSP, Sub-Projeto nº 3 - Hidrodinâmica Costeira, and Fundação de Amparo á Pesquisa do Estado de São Paulo (FAPESP). - Paper presented at the 1977 Annual Meeting of the American Statistical Association, August 15-18, 1977, Chicago, Illinois.

Pedro Alberto Morettin; Afrânio Rubens de Mesquita

Instituto de Matemática e Estatística e Instituto Oceanográfico da Universidade de São Paulo

SYNOPSIS

This paper is a survey of the main spectral methods potentially useful in Oceanography. These methods are applied to the analysis of tides, seasonal variations and ocean geophysical oscillations. Further topics on the Response Method, the Maximum Entropy method and Rotary Components are briefly summarized. Examples of successful appli cations are presented.

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BIBLIOGRAPHY

AKAIKE, H. 1969a. Fitting auto-regressive models for prediction. In: Rosenblatt, M. & Van Atta, C, ed. - Statistical models and turbulence. New York, Springer-Verlag.

______ 1969b. Power spectrum estimation through auto-regressive model fitting. Ann. Inst, statist. Math., Tokyo, 21:407-419.

______ 1970. Statistical predictor identification. Ann. Inst. statist. Math., Tokyo, 22:203-217.

BARBER, F. G. & TAYLOR, J. 1977. A note on free oscillations of Chedabucto Bay. Manuscr. Rep. Ser., Mar. Sci. Directorate, Ottawa, (47).

BRILLINGER, D. R. 1965. An introduction to polyspectra. Ann. math. Statist., 36(5):1351-1373.

______ 1970. The identification of polynomial systems by means of higher order spectra. J. Sound Vibr., 12(3):301-313.

______ 1975. Time series - data analysis and theory. New York, Holt, Rinehart & Winston.

______ & ROSENBLATT, M. 1967a. Asymptotic theory of estimates of K-th order spectra. In: Harris, B., ed. - Spectral analysis of time series. New York, Wiley & Sons, p.153-188.

______ 1967b. Computations interpretation of K-th order spectra. In: Harris, B., ed. - Spectral analysis of time series. New York, Wiley & Sons, p.189-231.

CARTWRIGHT, D. E. 1971. Some ocean tide measurements of the Eighteenth Century, and their relevance today. Proc. R. Soc, ser. B, 72(32):331-339.

______ & EDDEN, A. C. 1973. Corrected tables of tidal harmonics. Geophys. J. R. astr. Soc, 33:253-264.

______ & TAYLER, R. J. 1971. New computations of the tide generating potential. Geophys. J. R. astr. Soc, 23:45-74.

CHEN, W. Y. & STEGEN, G. R. 1974. Experiments with maximum entropy power of sinusoids. J. geophys. Res., 79:3019-3022.

COHEN, A. & JONES, R, H. 1969. Regression on a random field. J. Am. statist. Ass., 64:1172-1182.

CRAWFORD, W. R. 1976 Turbulent energy dissipation in the Atlantic Equatorial undercurrent PhD These. University of British Columbia, Oceanographic Institute.

DOODSON, A. T. 1921. The harmonic development of the tide generating potential. Proc. R. Soc, ser. A, 100:305-328.

______ 1957. The analysis and prediction of tides in shallow waters. Int. hydrogr. Rev., 33:85-126.

DÜING, W.; HIZARD, P.; KATZ, E. ; MEINCKE, J.; MILLER, L.; MOROSHKIN, K. V.; PHILANDER, G.; RYBNIKOV, A. A.; VOIGT, K. & WEISBERG, R. 1975. Meanders and longwaves in the Equatorial Atlantic. Nature, Lond.; 257(5524).

ECKERT, E. R. & DRAKE, R. M. 1959. Heat and mass transfere New York, MacGraw-Hill.

FRANCO, A. dos S. 1964. Harmonic analysis of tides for 7 days o hourly observations. Int. hydrogr. Rev., 41(2):109-142.

______ & ROCK, N.J. 1971. The fast Fourier transform and its applications to tidal oscillations. Bolm Inst, oceanogr., S Paulo, 20:145-199.

GASSER, T. 1972. System identification, polyspectra and related functions. Dissertation (Doctor of Math.). Swiss Federal Institute of Technology.

GERSH, W. 1970. Spectral analysis of EEG's by auto-regressive decomposition of time series. Math. Biosc, 7:205-222.

GODFREY, M. D, 1965. An exploratory study of the bispectrum of eco nomic time series. Appl. Statist., 14(1):48-69.

GODIN, G. 1972. The analysis of tides. Liverpool, Liverpool University Press, 264p.

GONELLA, J. 1972. A rotary-component method for analysing meteoro logical and oceanographie vector time series. Deep Sea Res., 19:833-846.

HANNAN, E. J. 1966. Spectral analysis for geophysical data. J. R. astr. Soc., 11:225-236.

HORN, W. 1960. Some recent approaches to tidal problems. Int. hydrogr. Rev., 37(2):65-68.

JENKINS, G. M. & WATTS, D. G. 1968. Spectral analysis. Holden-Days, 535p.

JONES, R. H. 1963. Stochastic processes on a sphere as applied to meteorological 500-milibar forecasts. In: Rosenblatt, M., ed. - SIAM Proc of Time Series Analysis. New York, John Wiley, p.119-124.

KATZ, E.; BELEVITSCH, R.; BRUCE, J.; BUBNOV, V.; COCHRANE, J.; DÜING, W.; HIZARD, P.; LASS, H. V.; MESQUITA, A. R. dé; MILLER, L. & RYBNIKOV, A. A. 1977. Zonal pressure gradient along the Equatorial Atlantic. J. mar. Res., 35(2):203-307.

KOOPMANS, L. H. 1974. The spectral analysis of time series. New York, Academic Press.

MESQUITA, A. R. de; MAGLIOCCA, A. & AMBRÓSIO Jr., O. 1977a. Physical and chemical variability at 35-4GºW of the Equatorial Atlantic upper layers. Rel. int. Inst, oceanogr., Univ. S Paulo, (8):1-27.

______ & MORETTIN, P. A. 1976. "Aplicações da analise espectral a oceanografia" (in Portuguese). 2nd Brazilian Symp. on Prob. and Statistics, (in press).

______; SOUZA, J. M. C. de; TUPINAMBÁ, P. M.; WEBER, R.; FESTA, M. & LEITE, J. B. A. 1911b. Correntes rotatórias e variabilidade do campo de massa na plataforma do Estado de São Paulo (Ponto: 25 S; 46 W). Rei. Cruzeiros , ser. N/Oc. "Prof. W. Besnard", Inst. oceanogr. Univ. S Paulo, (3):1-27.

MEUS, J. 1962. Tables of moon and sun. Belgium, Kessleberg Sterrenwacht.

MOEERS, C. N. K. 1973. A technique for the cross spectrum analysis of pairs of complex-valued time series, with emphasis on properties of polarized components and rotational invariants. Deep Sea Res., 20:11291141.

MUNK, W. & CARTWRIGHT, D. E. 1966. Tidal spectroscopy and prediction. Phil. Trans. R. Soc, ser. A, 259:533-581.

______ & HASSELMANN, K. 1964. Super-resolution of tides. In: Yoshida, K., ed. - Studie s on oceanography. Tokyo, University of Tokyo Press, p.339-344.

PARZEN, E. 1972. Some recent advances in the time series analysis. In: Rosenblatt, M. & Van Atta, C, ed. - Statistical models and turbulence. New York, Springer-Verlag.

PHILANDER, G. 1976. Instabilities of zonal equatorial currents. J. geophys. Res., 81(21):3725-3735.

ROY, R. 1976. Spectral analysis for a random process on the sphere. Ann. Inst, statist. Math., Tokyo, 28(1):91-99.

TUKEY, J. W. 1961. Discussion, emphasizing the connection between analysis of variance and spectrum analysis. Technometrics, 3:1-29.

ULRYCH, T. J. & BISHOP, T. N. 1975. Maximum entropy spectral analysis and auto-regressive decomposition. Rev. geophys. space Phys., 13:183-200.

YAO, N.-C; NESHYBA, S. & CREW, H. 1975. Rotary cross-bispectra and energy transfer functions between non-gaussian vector processes.I. De velopment and example. J. phys. Oceanogr., 5(1):164-172.

YAGLOW, A. M. 1961. Second-order homogeneous random fields. Proc. Berkekey Symp. math. Statist. Probab., 4th, 2:593-622.

(Received November 18/1977)

  • AKAIKE, H. 1969a Fitting auto-regressive models for prediction. In: Rosenblatt, M. & Van Atta, C, ed. - Statistical models and turbulence. New York, Springer-Verlag.
  • ______ 1969b Power spectrum estimation through auto-regressive model fitting. Ann. Inst, statist. Math., Tokyo, 21:407-419.
  • ______ 1970. Statistical predictor identification. Ann. Inst. statist. Math., Tokyo, 22:203-217.
  • BARBER, F. G. & TAYLOR, J. 1977. A note on free oscillations of Chedabucto Bay. Manuscr. Rep. Ser., Mar. Sci. Directorate, Ottawa, (47).
  • BRILLINGER, D. R. 1965. An introduction to polyspectra. Ann. math. Statist., 36(5):1351-1373.
  • ______ 1970. The identification of polynomial systems by means of higher order spectra. J. Sound Vibr., 12(3):301-313.
  • ______ 1975. Time series - data analysis and theory. New York, Holt, Rinehart & Winston.
  • ______ & ROSENBLATT, M. 1967a Asymptotic theory of estimates of K-th order spectra. In: Harris, B., ed. - Spectral analysis of time series. New York, Wiley & Sons, p.153-188.
  • ______ 1967b Computations interpretation of K-th order spectra. In: Harris, B., ed. - Spectral analysis of time series. New York, Wiley & Sons, p.189-231.
  • CARTWRIGHT, D. E. 1971. Some ocean tide measurements of the Eighteenth Century, and their relevance today. Proc. R. Soc, ser. B, 72(32):331-339.
  • ______ & EDDEN, A. C. 1973. Corrected tables of tidal harmonics. Geophys. J. R. astr. Soc, 33:253-264.
  • ______ & TAYLER, R. J. 1971. New computations of the tide generating potential. Geophys. J. R. astr. Soc, 23:45-74.
  • CHEN, W. Y. & STEGEN, G. R. 1974. Experiments with maximum entropy power of sinusoids. J. geophys. Res., 79:3019-3022.
  • COHEN, A. & JONES, R, H. 1969. Regression on a random field. J. Am. statist. Ass., 64:1172-1182.
  • CRAWFORD, W. R. 1976 Turbulent energy dissipation in the Atlantic Equatorial undercurrent PhD These. University of British Columbia, Oceanographic Institute.
  • DOODSON, A. T. 1921. The harmonic development of the tide generating potential. Proc. R. Soc, ser. A, 100:305-328.
  • ______ 1957. The analysis and prediction of tides in shallow waters. Int. hydrogr. Rev., 33:85-126.
  • DÜING, W.; HIZARD, P.; KATZ, E. ; MEINCKE, J.; MILLER, L.; MOROSHKIN, K. V.; PHILANDER, G.; RYBNIKOV, A. A.; VOIGT, K. & WEISBERG, R. 1975. Meanders and longwaves in the Equatorial Atlantic. Nature, Lond.; 257(5524).
  • ECKERT, E. R. & DRAKE, R. M. 1959. Heat and mass transfere New York, MacGraw-Hill.
  • FRANCO, A. dos S. 1964. Harmonic analysis of tides for 7 days o hourly observations. Int. hydrogr. Rev., 41(2):109-142.
  • ______ & ROCK, N.J. 1971. The fast Fourier transform and its applications to tidal oscillations. Bolm Inst, oceanogr., S Paulo, 20:145-199.
  • GASSER, T. 1972. System identification, polyspectra and related functions. Dissertation (Doctor of Math.). Swiss Federal Institute of Technology.
  • GERSH, W. 1970. Spectral analysis of EEG's by auto-regressive decomposition of time series. Math. Biosc, 7:205-222.
  • GODFREY, M. D, 1965. An exploratory study of the bispectrum of eco nomic time series. Appl. Statist., 14(1):48-69.
  • GODIN, G. 1972. The analysis of tides. Liverpool, Liverpool University Press, 264p.
  • GONELLA, J. 1972. A rotary-component method for analysing meteoro logical and oceanographie vector time series. Deep Sea Res., 19:833-846.
  • HANNAN, E. J. 1966. Spectral analysis for geophysical data. J. R. astr. Soc., 11:225-236.
  • HORN, W. 1960. Some recent approaches to tidal problems. Int. hydrogr. Rev., 37(2):65-68.
  • JENKINS, G. M. & WATTS, D. G. 1968. Spectral analysis. Holden-Days, 535p.
  • JONES, R. H. 1963. Stochastic processes on a sphere as applied to meteorological 500-milibar forecasts. In: Rosenblatt, M., ed. - SIAM Proc of Time Series Analysis. New York, John Wiley, p.119-124.
  • KATZ, E.; BELEVITSCH, R.; BRUCE, J.; BUBNOV, V.; COCHRANE, J.; DÜING, W.; HIZARD, P.; LASS, H. V.; MESQUITA, A. R. dé; MILLER, L. & RYBNIKOV, A. A. 1977. Zonal pressure gradient along the Equatorial Atlantic. J. mar. Res., 35(2):203-307.
  • KOOPMANS, L. H. 1974. The spectral analysis of time series. New York, Academic Press.
  • MESQUITA, A. R. de; MAGLIOCCA, A. & AMBRÓSIO Jr., O. 1977a Physical and chemical variability at 35-4GşW of the Equatorial Atlantic upper layers. Rel. int. Inst, oceanogr., Univ. S Paulo, (8):1-27.
  • ______ & MORETTIN, P. A. 1976. "Aplicações da analise espectral a oceanografia" (in Portuguese). 2nd Brazilian Symp. on Prob. and Statistics, (in press).
  • MEUS, J. 1962. Tables of moon and sun. Belgium, Kessleberg Sterrenwacht.
  • MOEERS, C. N. K. 1973. A technique for the cross spectrum analysis of pairs of complex-valued time series, with emphasis on properties of polarized components and rotational invariants. Deep Sea Res., 20:11291141.
  • MUNK, W. & CARTWRIGHT, D. E. 1966. Tidal spectroscopy and prediction. Phil. Trans. R. Soc, ser. A, 259:533-581.
  • ______ & HASSELMANN, K. 1964. Super-resolution of tides. In: Yoshida, K., ed. - Studie s on oceanography. Tokyo, University of Tokyo Press, p.339-344.
  • PARZEN, E. 1972. Some recent advances in the time series analysis. In: Rosenblatt, M. & Van Atta, C, ed. - Statistical models and turbulence. New York, Springer-Verlag.
  • PHILANDER, G. 1976. Instabilities of zonal equatorial currents. J. geophys. Res., 81(21):3725-3735.
  • ROY, R. 1976. Spectral analysis for a random process on the sphere. Ann. Inst, statist. Math., Tokyo, 28(1):91-99.
  • TUKEY, J. W. 1961. Discussion, emphasizing the connection between analysis of variance and spectrum analysis. Technometrics, 3:1-29.
  • ULRYCH, T. J. & BISHOP, T. N. 1975. Maximum entropy spectral analysis and auto-regressive decomposition. Rev. geophys. space Phys., 13:183-200.
  • YAO, N.-C; NESHYBA, S. & CREW, H. 1975. Rotary cross-bispectra and energy transfer functions between non-gaussian vector processes.I. De velopment and example. J. phys. Oceanogr., 5(1):164-172.
  • YAGLOW, A. M. 1961. Second-order homogeneous random fields. Proc. Berkekey Symp. math. Statist. Probab., 4th, 2:593-622.
  • *
    - This work was partially supported by Projeto FINEP-IOUSP, Sub-Projeto nº 3 - Hidrodinâmica Costeira, and Fundação de Amparo á Pesquisa do Estado de São Paulo (FAPESP).
    - Paper presented at the 1977 Annual Meeting of the American Statistical Association, August 15-18, 1977, Chicago, Illinois.
  • Publication Dates

    • Publication in this collection
      06 June 2012
    • Date of issue
      1978

    History

    • Received
      18 Nov 1977
    Instituto Oceanográfico da Universidade de São Paulo Praça do Oceanográfico, 191, 05508-120 São Paulo SP Brasil, Tel.: (55 11) 3091 6513, Fax: (55 11) 3032 3092 - São Paulo - SP - Brazil
    E-mail: amspires@usp.br