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Extracting tidal frequencies using multivariate harmonic analysis of sea level height time series

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Abstract

This contribution is seen as a first attempt to extract the tidal frequencies using a multivariate spectral analysis method applied to multiple time series of tide-gauge records. The existing methods are either physics-based in which the ephemeris of Moon, Sun and other planets are used, or are observation-based in which univariate analysis methods—Fourier and wavelet for instance—are applied to tidal observations. The existence of many long tide-gauge records around the world allows one to use tidal observations and extract the main tidal constituents for which efficient multivariate methods are to be developed. This contribution applies the multivariate least-squares harmonic estimation (LS-HE) to the tidal time series of the UK tide-gauge stations. The first 413 harmonics of the tidal constituents and their nonlinear components are provided using the multivariate LS-HE. A few observations of the research are highlighted: (1) the multivariate analysis takes information of multiple time series into account in an optimal least- squares sense, and thus the tidal frequencies have higher detection power compared to the univariate analysis. (2) Dominant tidal frequencies range from the long-term signals to the sixth-diurnal species interval. Higher frequencies have negligible effects. (3) The most important tidal constituents (the first 50 frequencies) ordered from their amplitudes range from 212 cm (M2) to 1 cm (OQ2) for the data set considered. There are signals in this list that are not available in the 145 main tidal frequencies of the literature. (4) Tide predictions using different lists of tidal frequencies on five different data sets around the world are compared. The prediction results using the first significant 50 constituents provided promising results on these locations of the world.

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Acknowledgments

We would like to acknowledge the British Oceanographic Data Center (BODC) for its free tide data we used in this paper. Useful comments of the editor-in-chief and anonymous reviewers are kindly acknowledged.

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Authors and Affiliations

  1. Section of Geodesy, Department of Surveying Engineering, Faculty of Engineering, University of Isfahan, 81746-73441 , Isfahan, Iran

    A. R. Amiri-Simkooei

  2. Chair Acoustics, Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS , Delft, The Netherlands

    A. R. Amiri-Simkooei

  3. Geodesy Division, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, North-Kargar Ave., Amir-Abad, 1439-5515, Tehran, Iran

    S. Zaminpardaz & M. A. Sharifi

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  1. A. R. Amiri-Simkooei
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  2. S. Zaminpardaz
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  3. M. A. Sharifi
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Correspondence to S. Zaminpardaz.

Appendices

Appendix A: UK tide-gauge stations’ names and coordinates

No.

St. name

Latitude (\(^\circ \))

Longitude (\(^\circ \))

No.

St. name

Latitude (\(^\circ \))

Longitude (\(^\circ \))

1

Aberdeen

57.1440

\(-\)2.0803

24

Milford Haven

51.7064

\(-\)5.0514

2

Avonmouth

51.5108

\(-\)2.7151

25

Millport

55.7496

\(-\)4.9058

3

Bangor

54.6648

\(-\)5.6695

26

Moray firth

57.5992

\(-\)4.0002

4

Barmouth

52.7193

\(-\)4.0450

27

Mumbles

51.5703

\(-\)3.9749

5

Bournemouth

50.7143

\(-\)1.8749

28

Newhaven

50.7818

0.0570

6

Cromer

52.9343

1.3016

29

Newlyn

50.1030

\(-\)5.5428

7

Devonport

50.3684

\(-\)4.1853

30

Newport

51.5500

\(-\)2.9874

8

Dover

51.1144

1.3225

31

North Shields

55.0074

\(-\)1.4398

9

Felixstowe

51.9577

1.3466

32

Port Ellen

55.6276:

\(-\)6.1899

10

Fishguard

52.0137

\(-\)4.9832

33

Port Erin

54.0852

\(-\)4.7681

11

Harwich

51.9480

1.2921

34

Port Patric

54.8426

\(-\) 5.1200

12

Heysham

54.0318

\(-\)2.9203

35

Portrush

55.2068

\(-\)6.6568

13

Hinkley point

51.2153

\(-\)3.1345

36

Portsmooth

50.8026

\(-\)1.1118

14

Holyhead

53.3139

\(-\)4.6206

37

St Mary

49.9185

\(-\)6.3165

15

Ilfracombe

51.2109

\(-\)4.1111

38

Sheerness

51.4456

0.7434

16

Immingham

53.6310

\(-\)0.1868

39

Stornoway

58.2070

\(-\)6.3889

17

St. Helier

49.1833

\(-\)2.1167

40

Tobermory

56.6229

\(-\)6.0640

18

Kinlochbervie

58.4567

\(-\)5.0504

41

Ullapool

57.8953

\(-\)5.1581

19

Leith

55.9898

\(-\)3.1817

42

Waymouth

50.6085

\(-\)2.4479

20

Lerwick

60.154

\(-\)1.1403

43

Whitby

54.4894

\(-\)0.6199

21

Liverpool

53.4497

\(-\)3.0181

44

Wick

58.4410

\(-\)3.0865

22

Llandudno

53.3317

\(-\)3.8252

45

Workington

54.6508

\(-\)3.5678

23

Lowestoft

52.4820

1.7516

    
Table 6 Tidal frequencies (most important constituents) detected by least-squares power spectrum of 18.24-year multivariate time series (11 series used) that have approximately the same effect as tide prediction using the entire 413 frequencies in Tables 1 and 2
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Appendix B: different lists of tidal frequencies

See Appendix Tables 4, 5 and 6.

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Amiri-Simkooei, A.R., Zaminpardaz, S. & Sharifi, M.A. Extracting tidal frequencies using multivariate harmonic analysis of sea level height time series. J Geod 88, 975–988 (2014). https://doi.org/10.1007/s00190-014-0737-5

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