Using Regularized Least Squares to Break the Data Requirements of Tidal Harmonics Analysis

Recent observation reveals a stunning fact that the coastal tides are experiencing a rapid change in the last century at several places in the world. High-accuracy tide level data is needed to achieve a wide and refined understanding of the phenomenon. In-situ measurements – the traditional and main data source to support tidal harmonic analysis – are often sparse and limited to fixed locations, which are insufficient to provide information about the spatiotemporal variability of tidal processes beyond the tidal gauges. Satellite altimetry may fundamentally change the situation. This technology measures water level with much wider spatial coverage and higher resolution, but it has not been used in tidal analysis due to two major limitations in the harmonic analysis: a) a min-imum length of sampled observed data is required to recognize a sufficient number of tidal constituents according to the Rayleigh criterion and b) data sampling/acquisition frequency must be at least two times the major tidal frequencies to avoid the aliasing issue dictated by the Nyquist theorem. To address these issues, a novel Regularized Least-Square approach is proposed to break the limitations. In this method, the prior information of the regional tidal amplitudes is used to support a least square algorithm to obtain the amplitudes and phases of the tidal constituents for data series with different lengths and time intervals. A numerical experiment showed that the proposed method can determine the tidal amplitudes with a low level of error and the sampling interval can be relaxed to the application level equal to altimetry satellite revisit intervals. The proposed algorithm was also tested using the data of the altimetry mission, Jason-3, and the performance was excellent. The potential use of this method could help identify the changing tides with climate change and anthropogenic activities in the coastal area.

[1]  Hanbo Wang.  Compressed Sensing: Theory and Applications , 2023, Journal of Physics: Conference Series.

[2]  D. Jay,et al.  Evolving tides aggravate nuisance flooding along the U.S. coastline , 2021, Science Advances.

[3]  Colin J. Gleason,et al.  Remote Sensing of River Discharge: A Review and a Framing for the Discipline , 2020, Remote. Sens..

[4]  D. Jay,et al.  Changing Tides: The Role of Natural and Anthropogenic Factors. , 2020, Annual review of marine science.

[5]  Tao Ji,et al.  Observing storm surges in China's coastal areas by integrating multi-source satellite altimeters , 2019, Estuarine, Coastal and Shelf Science.

[6]  Rashmi Shah,et al.  Requirements for a Coastal Hazards Observing System , 2019, Front. Mar. Sci..

[7]  A. Trasviña-Castro,et al.  Coastal currents in the Eastern Gulf of Tehuantepec from coastal altimetry , 2018, Advances in Space Research.

[8]  A. Ellmann,et al.  Examining the Performance of the Sentinel-3 Coastal Altimetry in the Baltic Sea Using a Regional High-Resolution Geoid Model , 2018, 2018 Baltic Geodetic Congress (BGC Geomatics).

[9]  Yijun He,et al.  Identification of tidal mixing fronts from high-resolution along-track altimetry data , 2018 .

[10]  Ole Baltazar Andersen,et al.  ALES+: Adapting a homogenous ocean retracker for satellite altimetry to sea ice leads, coastal and inland waters , 2018, Remote Sensing of Environment.

[11]  J. Bouffard,et al.  Inter-annual variations of surface currents and transports in the Sicily Channel derived from coastal altimetry , 2017 .

[12]  R. Najjar,et al.  Fingerprints of Sea Level Rise on Changing Tides in the Chesapeake and Delaware Bays , 2017 .

[13]  A. Trasviña-Castro,et al.  Poleward currents from coastal altimetry: The west coast of Southern Baja California, Mexico , 2017 .

[14]  A. Vafeidis,et al.  Sea‐level rise impacts on the temporal and spatial variability of extreme water levels: A case study for St. Peter‐Ording, Germany , 2017 .

[15]  B. Sanders,et al.  Cumulative hazard: The case of nuisance flooding , 2017 .

[16]  Jérôme Benveniste,et al.  Cross-calibrating ALES Envisat and CryoSat-2 Delay–Doppler: a coastal altimetry study in the Indonesian Seas , 2016 .

[17]  Bruno Zakardjian,et al.  Exploiting coastal altimetry to improve the surface circulation scheme over the central Mediterranean Sea , 2016 .

[18]  Kristen D. Splinter,et al.  A multi-decade dataset of monthly beach profile surveys and inshore wave forcing at Narrabeen, Australia , 2016, Scientific Data.

[19]  Kristen D. Splinter,et al.  Coastal vulnerability across the Pacific dominated by El Niño-Southern Oscillation , 2015 .

[20]  R. Holman,et al.  Shoreline variability from days to decades: Results of long‐term video imaging , 2015 .

[21]  Stefano Vignudelli,et al.  ALES: a multi-mission adaptive subwaveform retracker for coastal and open ocean altimetry , 2014 .

[22]  V. N. Jonge,et al.  The influence of channel deepening on estuarine turbidity levels and dynamics, as exemplified by the Ems estuary , 2014 .

[23]  J. S. Fleming,et al.  Nyquist—overcoming the limitations , 2005 .

[24]  Gary D. Egbert,et al.  Estimates of M2 Tidal Energy Dissipation from TOPEX/Poseidon Altimeter Data , 2001 .

[25]  W. Press,et al.  Fast algorithm for spectral analysis of unevenly sampled data , 1989 .

[26]  F. Seitz,et al.  The Zone of Influence: Matching sea level variability from coastal altimetry and tide gauges for vertical land motion estimation , 2020 .

[27]  Hui Lin,et al.  Extended Spectral Analysis of Tidal Variability in the North Atlantic Ocean , 2019, Journal of Geophysical Research: Oceans.

[28]  J. Marra,et al.  Patterns and projections of high tide flooding along the U.S. coastline using a common impact threshold , 2018 .

[29]  Frédéric Frappart,et al.  Satellite radar altimetry water elevations performance over a 200 m wide river: Evaluation over the Garonne River , 2017 .

[30]  D. Codiga.  Unified Tidal Analysis and Prediction Using the UTide Matlab Functions , 2011 .

[31]  Yaakov Tsaig,et al.  Extensions of compressed sensing , 2006, Signal Process..

[32]  C. Provost,et al.  Chapter 6 Ocean Tides , 2001 .