Two-step harmonic analysis for capturing seasonally-varying amplitudes and phase lags of the predominant tidal constituents

Abstract. The seasonal variation of tides plays a significant role in water level changes in coastal regions. In this study, seasonal variations of four principal tidal constituents, M2, S2, K1, and O1, in the Bohai Sea, China, were studied by applying an enhanced harmonic analysis method to two time series: 1-year sea level observations at a mooring station (named E2) located in the western Bohai Sea and 17-year sea level observations at Dalian. At E2, the M2 amplitude and phase lag have annual frequencies, with large values in summer and small values in winter, while the frequencies of S2 and K1 amplitudes are also nearly annual. In contrast, the O1 amplitude increases constantly from winter to autumn. The maxima of phase lags appear twice in 1 year for S2, K1, and O1, taking place near winter and summer. The seasonal variation trends estimated by the enhanced harmonic analysis at Dalian are different from those at E2, except for the M2 phase lag. The M2 and S2 amplitudes show semi-annual and annual cycles, respectively, which are relatively significant at Dalian. The results of numerical experiments indicate that the seasonality of vertical eddy viscosity induces seasonal variations of the principal tidal constituents at E2. However, the tested mechanisms, including seasonally varying stratification, vertical eddy viscosity, and mean sea level, do not adequately explain the observed seasonal variations of tidal constituents at Dalian.

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The amplitudes and phases of tidal constituents from Harmonic Analysis at two stations in the Gulf of Aden

Earth Systems and Environment ◽

10.1007/s41748-020-00152-y ◽

2020 ◽

Vol 4 (2) ◽

pp. 321-328

Author(s):

Fawaz A. Madah

Keyword(s):

Harmonic Analysis ◽

Gulf Of Aden ◽

Tidal Constituents

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Extraction of Tide Constituents by Harmonic Analysis Using Altimetry Satellite Data in the Brazilian Coast

Journal of Atmospheric and Oceanic Technology ◽

10.1175/jtech-d-14-00091.1 ◽

2015 ◽

Vol 32 (3) ◽

pp. 614-626 ◽

Cited By ~ 4

Author(s):

Victor Bastos Daher ◽

Rosa Cristhyna de Oliveira Vieira Paes ◽

Gutemberg Borges França ◽

João Bosco Rodrigues Alvarenga ◽

Gregório Luiz Galvão Teixeira

Keyword(s):

Harmonic Analysis ◽

Shallow Water ◽

Deep Water ◽

Global Ocean ◽

Ocean Tide ◽

Brazilian Coast ◽

Latitude Range ◽

Comparison Results ◽

Major Discrepancy ◽

Tidal Constituents

AbstractThis paper analyzes the sea surface height dataset from the TOPEX, Jason-1, and Jason-2 satellites of a 19-yr time series in order to extract the tide harmonic constituents for the region limited by latitude 5°N–35°S and longitude 55°–20°W. The harmonic analysis results implemented here were compared with the tidal constituents estimated by three classical tidal models [i.e., TOPEX/Poseidon Global Inverse Solution 7.2 (TPXO7.2), Global Ocean Tide 4.7 (GOT4.7), and Finite Element Solution 2102 (FES2102)] and also with those extracted from in situ measurements. The Courtier criterion was used to define the tide regimes and regionally they are classified as semidiurnal between the latitude range from approximately 5°N to 22°S, semidiurnal with diurnal inequality from 22° to about 29°S, and mixed southward of latitude 22°S. The comparison results among all tide approaches were done by analyzing the root-sum-square misfit (RSSmisfit) value. Generally, the RSSmisfit difference values are not higher than 12 cm among them in deep-water regions. On the other hand, in shallow water, all models have presented quite similar performance, and the RSSmisfit values have presented higher variance than the previous region, as expected. The major discrepancy results were particularly noted for two tide gauges located in the latitude range from 5°N to 2°S. The latter was investigated and conclusions have mainly pointed to the influence of the mouth of the Amazon River and the considerable distance between tide measurements and the satellite reference point, which make it quite hard to compare those results. In summary, the results have showed that all models presently generate quite reliable results for deep water; however, further study should done in order to improve them in shallow-water regions too.

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STUDIES ON THE CORRELATION OF TIDAL ELEVATION CHANGES ALONG THE WESTERN COASTLINE OF TAIWAN

Coastal Engineering Proceedings ◽

10.9753/icce.v20.23 ◽

1986 ◽

Vol 1 (20) ◽

pp. 23 ◽

Cited By ~ 2

Author(s):

H.H. Hwung ◽

C.L. Tsai ◽

C.C. Wu

Keyword(s):

Energy Density ◽

Harmonic Analysis ◽

Water Level ◽

High Water ◽

Maximum Energy ◽

Phase Lag ◽

Tidal Elevation ◽

Elevation Changes ◽

Tidal Constituents ◽

Phase Angles

In order to understand the characteristics of tidal elevation changes along the western coastline of Taiwan, the authors collected the tidal records at the same duration from eleven stations and made an elaborate analysis in this paper. First step, the main tidal constituents were picked out from spectrum analysis, and the amplitudes and phase angles of these tidal constituents would be obtained by harmonic analysis. Then the variations of amplitude and phase lag of the main constituents and the variations of mean high water level and mean low water level along the coastline would be presented in the figures respectively. Finally, based on the results of harmonic analysis, the energy density of tide for every station could be calculated separately, and the location of the maximum energy density would be determined by cubic spline method.

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STATE OF THE ART IN TIDE PREDICTIONS

Coastal Engineering Proceedings ◽

10.9753/icce.v18.12 ◽

1982 ◽

Vol 1 (18) ◽

pp. 12

Author(s):

B.D. Zelter

Keyword(s):

Nineteenth Century ◽

Twentieth Century ◽

Harmonic Analysis ◽

Deep Water ◽

State Of The Art ◽

Numerical Models ◽

Least Square ◽

Response Analysis ◽

The Subject ◽

Tidal Constituents

By the end of the nineteenth century, scientists had succeeded in achieving the ability to make reasonably accurate tide predictions by the harmonic method (Schureman, 1941). Except for the building of larger and more sophisticated mechanical tide prediction machines using the harmonic technique, tidal mathematicians more or less rested on their laurels during the first half of the twentieth century; indeed, many scientists assumed there was no need for further tidal research. It is ironic that one of the very few geophysical sciences that already had acceptable methods of prediction should become the subject of significant improvement during the last half of this century. These improvements include: 1) least square analysis for all tidal constituents simultaneously, 2) response analysis and prediction, 3) extended harmonic analysis, 4) tidal measurements in deep water on the ocean floor, and 5) global numerical models of tides.

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HIGH AND LOW WATER PREDICTION AT LAGOS HARBOUR, NIGERIA

Nigerian Journal of Technology ◽

10.4314/njt.v36i3.39 ◽

2017 ◽

Vol 36 (3) ◽

pp. 944-952

Author(s):

OT Badejo ◽

SO Akintoye

Keyword(s):

Prediction Model ◽

White Noise ◽

Harmonic Analysis ◽

Least Squares ◽

Water Level ◽

Observational Period ◽

Tidal Constituent ◽

Tidal Harmonic ◽

Tidal Data ◽

Tidal Constituents

In this work, 500 hourly water level tidal data were used to perform least squares tidal harmonic analysis. Eleven tidal constituents were used for the harmonic analysis. Astronomical arguments (v + u) and the nodal factor (f) were computed for each tidal constituent and at each observational period with a programme written in Matlab environment. The harmonic constants determined from the least squares tidal harmonic analysis were substituted into a tidal prediction model to predict hourly tidal data and tidal predictions at 5 minutesâ€™ intervals. Series of high and low water heights from the tidal predictions made at 5 minutesâ€™ intervals were determined and matched with their corresponding times. Autocorrelation at lags 1 to 30 for the residuals of the observed and predicted tidal data shows that there is no significant correlation in the range of the 30 lags. The series of residuals of the observed and predicted tidal data is therefore white noise. Â Â http://dx.doi.org/10.4314/njt.v36i3.39

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Study of tides and sea levels at Deception and Livingston islands, Antarctica

Antarctic Science ◽

10.1017/s095410201100068x ◽

2011 ◽

Vol 24 (2) ◽

pp. 193-201 ◽

Cited By ~ 10

Author(s):

Juan Vidal ◽

Manuel Berrocoso ◽

Alberto Fernández-Ros

Keyword(s):

Harmonic Analysis ◽

Sea Level ◽

Seawater Temperature ◽

Pressure Sensors ◽

Geodetic Network ◽

South Shetland Islands ◽

Bottom Pressure ◽

Sea Levels ◽

Phase Lags ◽

Tidal Characteristics

AbstractDuring the 2007–08 Spanish Antarctic campaign, two moorings of bottom pressure sensors were carried out over a ten week period. This paper presents the results of the tidal analysis from sea level records obtained at Deception and Livingston islands (South Shetland Islands, Antarctica). The main objective of this paper is to present a detailed study of the tidal characteristics at these two islands, for which statistical and harmonic analysis techniques are applied to the tidal records. A geodetic network was used to reference the pressure sensors. Geometric levelling, with an accuracy of 1 mm, allowed us to link the tidal marks with geodetic vertices located on Livingston and Deception islands. The amplitudes and phase lags obtained by harmonic analysis are compared to the harmonic constants of several coastal stations and co-tidal and co-range charts. Results show an evident influence of tides in the sea level signal, with a clear mixed semi-diurnal behaviour and a daily inequality between high and low waters. Measurements of salinity and temperature were made using electronic sensors. Results from this study showed that salinity and temperature were strongly influenced by tides. Seawater temperature varied in a manner that was consistent with the time series of residual bottom pressure.

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Seasonal Variation of GPS-Derived the Principal Ocean Tidal Constituents’ Loading Displacement Parameters Based on Moving Harmonic Analysis in Hong Kong

Remote Sensing ◽

10.3390/rs13020279 ◽

2021 ◽

Vol 13 (2) ◽

pp. 279 ◽

Cited By ~ 1

Author(s):

Maosheng Zhou ◽

Xin Liu ◽

Jiajia Yuan ◽

Xin Jin ◽

Yupeng Niu ◽

...

Keyword(s):

Hong Kong ◽

Seasonal Variation ◽

Harmonic Analysis ◽

Seasonal Variations ◽

Ocean Tide ◽

Atmospheric Loading ◽

Global Positioning ◽

Ocean Loading ◽

Tidal Constituents ◽

Annual Signal

The classical harmonic analysis (CHA) method only can be used to obtain the harmonic constants (amplitude and phase) of ocean tide loading displacement (OTLD). In fact, there are significant seasonal variations in the harmonic constants of OTLD. A moving harmonic analysis (MHA) method is proposed, which can effectively capture the seasonal variation of OTLD parameters. Based on 5 years of kinematic coordinate time series in direction U of six Global Positioning System (GPS) stations in Hong Kong, the MHA method is used to explore the seasonal variation of the OTLD parameters of the 6 principal tidal constituents (M2, S2, N2, K1, O1, Q1). The influence of mass loading on the seasonal variation of OTLD parameters is analyzed. The results show that there are obviously seasonal variations in OTLD parameters of the 6 principal tidal constituents in Hong Kong. The OTLD’s amplitude’s changes of the 6 principal tidal constituents are around 4–25.1% and the oscillation ranges of OTLD’s phase parameters vary from 8.8° to 20.4°. Among the seasonal variations of OTLD parameters, the annual signal, the semi-annual signal, and the ter-annual signal are the most significant. By analyzing the influence of atmospheric loading on the seasonal variation of OTLD parameters, it is found that atmospheric loading has certain contribution to the seasonal variation of OTLD parameters. Hydrological loading and non-tidal ocean loading have little influence on the seasonal variation of OTLD parameters.

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Seasonal variability of the M2 tide in the Bohai Bay: development and application of modified enhanced harmonic analysis

10.5194/egusphere-egu2020-12217 ◽

2020 ◽

Author(s):

Daosheng Wang ◽

Haidong Pan ◽

Lin Mu

Keyword(s):

Harmonic Analysis ◽

Sea Level ◽

Seasonal Variability ◽

The Other ◽

Major Influence ◽

Bohai Bay ◽

Phase Lag ◽

Phase Lags ◽

Ocean Environment ◽

One Year

The seasonal variability of the M2 tide exerts a major influence on the coastal ocean environment. In this study, a novel method, namely modified enhanced harmonic analysis (MEHA), is developed to synchronously extract the temporally varying amplitudes and phase lags of significant tides and the constant values of the other constituents. The seasonal variability of the M2 tide in the Bohai Bay, China, is investigated by analyzing one-year sea level observations at two stations with MEHA.In ideal twin experiments, the artificial sea level observations were analyzed. Both the estimated temporally varying amplitude and phase lag of the M2 tide and constant values of the S2, K1 and O1 tides using MEHA were much closer to the prescribed values than those obtained using the other methods, indicating the capability and efficacy of MEHA. When the real sea level observations were analyzed using MEHA, the estimated M2 tidal amplitude has significant seasonal variability, with large values in summer and small values in winter, which is robust and not affected by experimental settings. The results of numerical experiments indicate that the seasonality of vertical eddy viscosity induces seasonal variations of the M2 tide in the Bohai Bay.

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Modeling the Paranagua Estuarine Complex, Brazil: tidal circulation and cotidal charts

Revista Brasileira de Oceanografia ◽

10.1590/s1413-77392003000100003 ◽

2003 ◽

Vol 51 (unico) ◽

pp. 23-31 ◽

Cited By ~ 7

Author(s):

Ricardo de Camargo ◽

Joseph Harari

Keyword(s):

Bottom Topography ◽

Grid Point ◽

Ocean Model ◽

Southern Brazil ◽

Tidal Circulation ◽

Open Boundaries ◽

Near Shore ◽

Phase Lags ◽

Residual Flows ◽

Tidal Constituents

The tidal circulation in Paranagua Bay (Parana State, Southern Brazil) was studied based on the Princeton Ocean Model. The model domain covered the near shore region and the estuarine area, with about 1 km grid resolution in cross-shore and along-shore directions. Homogeneous and diagnostic distributions for temperature and salinity were used and 12 tidal constituents were considered to specify the elevations at the open boundaries. Tidal analysis of 29-days time series of elevations and currents for each grid point generated corange and cophase lines as well as the correspondent axes of the current ellipses for each constituent. These computed values reproduced well the observed amplifications and phase lags of surface elevations and currents. Residual flows show the formation of tidal eddies, related to coastal geometry and bottom topography.

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