Global Ocean Tide Models Research Articles

Precise determination of ocean tide loading gravity effect for absolute gravity stations in coastal area of China: Effects of land–sea boundary and station coordinate

Gravity effect due to ocean tide loading (OTL) is an important signal and correction in various gravimetric applications. In this paper, we assessed the OTL gravity effects at four absolute gravity (AG) stations in coastal China from several perspectives. The integrated Green's function of the Newtonian part was derived analytically and that of the elastic part was computed based on the PREM earth model. Ocean tide (OT) records near the four AG stations were used to enhance the accuracy of the global ocean tide model of NAO99b and the regional model of NAO99jb for the innermost field (<0.02°). The high-resolution digital elevation model (DEM) from the Shuttle Radar Topography Mission (SRTM) was used to define the land–sea boundary in the optimized near field (<1.0°). Results show that the high-resolution land–sea boundary is indispensible for OTL gravity modeling when the shoreline near a coastal station is complex. The SRTM-based OTL model outperforms the GMT-based model shoreline in terms of the agreement between modeled and observed gravity residuals at the four stations. The final gravity residuals, corrected for OTL, at the four stations are significantly smaller than those without OTL corrections. We give examples of accuracy requirements in coordinates at Qingdao for different station heights. At a station height of 80m and to ensure a 0.1μgal accuracy in OTL modeling, the required accuracies in the horizontal and vertical coordinate are 2.5 and 1. 3m, respectively. For a new coastal station and an expected OTL accuracy, one should inspect the variation of OTL due to coordinate variation to find a best strategy to determine the required accuracy of coordinate.

Global Ocean Tide Models: Assessment and Use within a Surface Model of Lowest Astronomical Tide

The UK Hydrographic Office (UKHO)-sponsored Vertical Offshore Reference Frames (VORF) project aims to develop tidal level transformation models that are referenced to the GRS80 ellipsoid and thus compatible with GNSS positioning; in particular, heighting. Benefits include increasing the efficiency of hydrographic surveying, providing a stable consistent reference frame and enabling integration with land data in the coastal zone. Seven contemporary global ocean tide models are used to derive Lowest Astronomical Tide (LAT) surfaces which are each assessed by comparison with LAT values from the 7,389-strong UKHO tide gauge database, with the results correlated with distance from land. The proportion of truly offshore and pelagic gauges is relatively limited; however, the transition zone whereby the global ocean tide models commence to deteriorate in accuracy is evident at approximately 30km from the coast. The DTU10 model was selected as the strongest candidate overall. Subsequently, a thin plate spline method is used with the tide gauge dataset to enhance the DTU10 LAT surface in the coastal zone, creating a high resolution global LAT surface with respect to mean sea level. It is seen by cross-validation that the method may be used to predict LAT in near-shore locations with a standard error of 0.23 m.

Vertical displacement loading tides and self-attraction and loading tides in the Bohai, Yellow, and East China Seas

The loading tides are calculated by means of the Green’s function method based on a high-resolution regional ocean tide model, the TOPO7.0 global ocean tide model, and the Gutenberg-Bullen A Earth model. The results show that the maximal amplitude of M2 vertical displacement loading (VDL) tide in the Bohai, Yellow, and East China Seas exceeding 28 mm appears 150 km off the Zhejiang coast; the second maximum exceeding 20 mm appears in Inchon Bay; and the third maximum exceeding 14 mm is located in the northeast of the North Yellow Sea. The maximal amplitudes of S2 VDL tide at the above three locations exceed 10, 8, and 4 mm, respectively. The maximal amplitudes of the K1 and O1 VDL tides, exceeding 13 and 10 mm respectively, appear near the central and north Ryukyu Islands; the amplitudes tend to decease toward the inward areas. The phases of semidiurnal VDL tides are basically opposite to those of corresponding ocean tides. The phases of diurnal VDL tides are basically opposite to those of corresponding ocean tides in the most part of the East China Sea and the eastern part of the South Yellow Sea. This anti-phase relationship generally does not hold in the rest parts of the Bohai and Yellow Seas. The distribution patterns of self-attraction and loading (SAL) tides are very similar to those of VDL tides. The SAL tides have amplitudes about 1.2–1.7 times of the corresponding VDL tides and their phases are basically opposite to the corresponding VDL tides. The maximal amplitude of M2 SAL tide also appears off the Zhejiang coast, with a magnitude exceeding 42 mm. Bohai Sea, Yellow Sea, East China Sea, ocean tides, loading tides, self-attraction and loading tides

Pressure tide gauge records from the Atlantic shelf off Tierra del Fuego, southernmost South America

Based on pressure tide gauge observations at three sites off the Atlantic coast of Tierra del Fuego main island, time series spanning one to seven months of bottom pressure and sea-level variations are derived and analysed to reveal the major driving mechanisms. Ocean tides account for 99.5% of the total energy of the sea-level variations. The amplitudes and phases of a comprehensive set of tidal constituents resulting from a harmonic tidal analysis are presented. Exceptionally large shallow-water tides are identified. The second largest contribution is due to the local inverse barometer model accounting for up to 65% of the variance of the tide residual sea-level variations. Close to the shore a significant topographic modulation of the sea-level variations is revealed. The in situ observations are compared with six recent global ocean tide models, official tide tables, and sea-surface heights derived from satellite altimetry data. The amplitudes and phases predicted by the ocean tide models for the semidiurnal and diurnal constituents agree with those derived from our tide gauge records on average within 2cm and 5°, respectively. In the time domain the tidal signal represented by the models deviates typically by a few decimetres from that extracted from our records. Absolute altimeter biases were determined for the Jason-2, Jason-1 extended mission, and Envisat satellite altimeters. Relative sea-level variations are represented by the altimetry data with an accuracy of the order of 5cm.

Ocean tides from satellite altimetry and GRACE

Satellite altimetry and GRACE observations carry both the signature of ocean tides and have in general complementary potential to resolve tidal constituents. It is therefore straightforward to perform a combined estimation of a global ocean tide model based on these two data sources. The present paper develops and applies a three step procedure for generating such a combined ocean tide model. First, the processing of multi-mission altimetry data is described along with the harmonic analysis applied to derive initially a pure empirical ocean tide model. Then the capability of GRACE to sense particular tidal constituents is elaborated and an approach to estimate tidal constituents from GRACE is outlined. In a third step a combination strategy with optimal stochastic data treatment is developed and applied to the altimetry-only tide model EOT08a and four years of GRACE observations, leading to the combined model EOT08ag. The differential contributions of GRACE to EOT08ag remain small and are mainly concentrated to the Arctic Ocean, an area with little or poor altimetry data. In comparison with other tide models, EOT08ag is validated by K-band range residuals, the impact on gravity field modelling and on precise orbit determination and by variance reduction of crossover differences. None of these comparison exhibits a significant improvement over the altimetry-only tide model except for a few areas above 60°N. Overall the improvements of the combination remain small and appear to stay below the current GRACE baseline accuracy.

Three months of local sea level derived from reflected GNSS signals

By receiving Global Navigation Satellite System (GNSS) signals that are reflected off the sea surface, together with directly received GNSS signals (using standard geodetic‐type receivers), it is possible to monitor the sea level using regular single difference geodetic processing. We show results from our analysis of three months of data from the GNSS‐based tide gauge at the Onsala Space Observatory (OSO) on the west coast of Sweden. The GNSS‐derived time series of local sea level is compared with independent data from two stilling well gauges at Ringhals and Gothenburg about 18 km south and 33 km north of OSO, respectively. A high degree of agreement is found in the time domain, with correlation coefficients of up to 0.96. The root‐mean‐square differences between the GNSS‐derived sea level and the stilling well gauge observations are 5.9 cm and 5.5 cm, which is lower than for the stilling well gauges together (6.1 cm). A frequency domain comparison reveals high coherence of the data sets up to 6 cycles per day, which corresponds well to the propagation of gravity waves in the shallow waters at the Kattegat coast. Amplitudes and phases of some major tides were determined by a tidal harmonic analysis and compared to model predictions. From the GNSS‐based tide gauge results we find significant ocean tidal signals at fortnightly, diurnal, semi‐diurnal, and quarter‐diurnal periods. As an example, the amplitudes of the semi‐diurnal M2 and the diurnal O1 tide are determined with 1σ uncertainties of 11 mm and 12 mm, respectively. The comparison to model calculations shows that global ocean tide models have limited accuracy in the Kattegat area.

Multimission empirical ocean tide modeling for shallow waters and polar seas

A new global ocean tide model named DTU10 (developed at Technical University of Denmark) representing all major diurnal and semidiurnal tidal constituents is proposed based on an empirical correction to the global tide model FES2004 (Finite Element Solutions), with residual tides determined using the response method. The improvements are achieved by introducing 4 years of TOPEX–Jason 1 interleaved mission into existing 18 years (1993–2010) of primary joint TOPEX, Jason 1, and Jason 2 mission time series. Hereby the spatial distribution of observations are doubled and satellite altimetry should be able to recover twice the spatial variations of the tidal signal which is particularly important in shallow waters where the spatial scale of the tidal signal is scaled down. Outside the ±66° parallel combined Envisat, GEOSAT Follow‐On, and ERS‐2, data sets have been included to solve for the tides up to the ±82° parallel. A new approach to removing the annual sea level variations prior to estimating the residual tides significantly improved tidal determination of diurnal constituents from the Sun‐synchronous satellites (e.g., ERS‐2 and Envisat) in the polar seas. Extensive evaluations with six tide gauge sets show that the new tide model fits the tide gauge measurements favorably to other state of the art global ocean tide models in both the deep and shallow waters, especially in the Arctic Ocean and the Southern Ocean. One example is a comparison with 207 tide gauge data in the East Asian marginal seas where the root‐mean‐square agreement improved by 35.12%, 22.61%, 27.07%, and 22.65% (M2, S2, K1, and O1) for the DTU10 tide model compared with the FES2004 tide model. A similar comparison in the Arctic Ocean with 151 gauge data improved by 9.93%, 0.34%, 7.46%, and 9.52% for the M2, S2, K1, and O1 constituents, respectively.

Lunar tides in Loch Ness, Scotland

Measurements have been made of the astronomical tide in Loch Ness, Scotland, which is not directly connected to marine tides. Our measurements of the loch tide are, so far as we know, the first in a European lake where the tide originates primarily from ocean tide loading. Loch Ness is a readily accessible lake and is in a region for which the neighboring ocean tides are large and described well by modern global ocean tide models. The principal tidal constituent, M2, was observed to have an amplitude of approximately 1.5 mm, and to be in antiphase, at each end of the loch. These values are in close agreement with the theoretical combined effects of the direct gravitational tide (body tide) and the tilt effects due to ocean tide loading, computed using Green's functions based on conventional elastic‐Earth models. By analyzing over long periods for coherent tidal signals, we are able to significantly improve the signal‐to‐noise ratio in the tilt values compared with values obtained by direct level differencing. Our tilt accuracy of better than 10−8, measured over 35 km, demonstrates Loch Ness as one the world's longest and most accurate tiltmeters. Despite this unprecedented accuracy, Earth tidal models are still at least as accurate as our ability to measure them.

A comparison of model estimates of ocean-tide loading displacements in New Zealand

A comparison of model estimates of ocean-tide loading displacements in New Zealand We analyze the regional accuracy of the global ocean tide models TPXO7.2, GOT00.2, NAO. 99b, FES2004, and EOT10a using the tide-gauge records from 7 stations along the coastline of New Zealand. The comparison reveals that TPXO7.2 provides the bestfit with the tide-gauge data in this part of the world. The TPXO. 7.2 ocean tide model is then used for computing and analysis of the vertical and horizontal ocean-tide loading displacements in New Zealand. The ocean-tide loading is calculated for the semi-diurnal and diurnal tidal harmonic constituents M 2 , S 2 , N 2 , K 2 , K 1 , O 1 , P 1 , and Q 1 , the long-period tidal components M f and M m , and for the shallow-water (nonlinear) components M 4 , MS 4 , and MN 4 . The charts of the ocean tide (offshore) and the ocean-tide loading (onshore) are compiled on a 5×5 arc-min geographical grid at the study area of New Zealand. The results reveal that the major contribution to the ocean-tide loading displacements up to a few centimeters is attributed to the semi-diurnal and diurnal harmonic constituents. The contribution of the long-period tidal components is to about 1 mm, and the effect of the shallow-water components is less than 0.2 mm. The maxima of vertical and horizontal displacements are typically of the same order of magnitude with larger amplitudes of vertical motions. The maximum amplitudes of vertical motions up to 5.6 cm are found in the upper north region of the North Island. The maximum horizontal motions up to 2.1 cm are in the northwest part of the South Island The ocean-tide loading displacements in New Zealand are finally compared with the crustal deformations due to geodynamic, atmospheric and other phenomena.

A novel high resolution model without open boundary conditions applied to the China Seas: first investigation on tides

We developed a Global Ocean Circulation and Tide Model (GOCTM) with coarse grids in the open deep ocean degrading ‘smoothly’ into the highly resolved China Seas (CS) of refined grids to study the tides and circulation there. GOCTM is based on the framework of the Finite Volume approach for better mass conservation through improved transports across the discrete individual control volume. It also takes a full advantage of the geometric flexibility of unstructured mesh using a realistic global topography including the Arctic Ocean. The CS are given a special focus by refining the unstructured grids, but they are embedded into global domain naturally. Furthermore, GOCTM not only successfully avoids the treatment of the open boundaries, but also optimizes the trade-off between computational cost and model accuracy. Meanwhile, GOCTM is driven by the astronomical tide-generating potential and the secondary tide-generating potential directly, together with the wind stress and heat flux. GOCTM succeeds in reproducing the global eight principal tidal harmonic constants. Particularly, the simulated tidal results in the CS are improved compared to some other regional models with the discrepancy of 3.9 cm for M2 tide. This idea of GOCTM can also be referred for other regional ocean study.

Coastal tides in West Greenland derived from tide gauge records

Based on pressure tide-gauge observations, sea-level records are derived for ten sites along the coast of West Greenland. The ocean tidal signal is extracted by a harmonic tidal analysis. The accuracy of the determined tidal constants is discussed in detail. The tides account for 85% of the observed sea-level standard deviation. The tide gauge records reveal significant shallow-water tidal effects, in particular compound and overtide amplitudes reaching 5 cm. The propagation of the tidal waves into the fjords depends strongly on local conditions and is in some cases accompanied by an amplification of the tidal amplitudes. The observed tidal signals are compared to the predictions of the global ocean tide model FES2004. At the outer coast, a good agreement is found. Inside the fjords, however, the model performs worse and tide gauge observations may still be indispensable when accurate tidal signals are required.

GOTIC2: A Program for Computation of Oceanic Tidal Loading Effect

Oceanic tidal loading signals are in general smaller than solid Earth tide signals, but they can be measured by geodetic technique and need to be accurately corrected for because they are in general a source of noise. In order to meet this requirement we have developed a program to compute the loading tide most accurately in Japanese region by using a combination of global and regional ocean tide models and fine-scale land-sea grids. The program computes six kinds of loading (radial and horizontal displacements, gravity, tilt, strain, and deflection of the vertical) for 21 constituents including long-period tide.

Evaluation of Ocean Tide Models Used for Jason-2 Altimetry Corrections

It has been more than a decade since the last comprehensive accuracy assessment of global ocean tide models. Here, we conduct an evaluation of the barotropic ocean tide corrections, which were computed using FES2004 and GOT00.2, and other models on the Jason-2 altimetry Geophysical Data Record (GDR), with a focus on selected coastal regions with energetic ocean dynamics. We compared nine historical and contemporary ocean tide models with pelagic tidal constants and with multiple satellite altimetry mission (T/P, ERS-1/-2, Envisat, GFO, Jason-1/-2) sea level anomalies using variance reduction studies. All accuracy assessment methods show consistent results. We conclude that all the contemporary ocean tide models evaluated have similar performance in the selected coastal regions. However, their accuracies are region-dependent and overall are significantly worse than those in the deep-ocean, which are at the 2–3 cm RMS (root-mean-square) level. The Gulf of Mexico and Northwest Atlantic regions present the least reduction of altimetry sea surface height variability after ocean tides are removed, primarily because of large oceanic variability associated with loop currents in the Gulf of Mexico and the Gulf Stream in the Northwest Atlantic.

Determination of ocean tide loading displacements in Hong Kong using GPS technique

Ocean tide loading (OTL) displacements of eight principal constituents at 12 sites in Hong Kong were determined using more than eight years of continuous GPS observations. Parameters of the OTL displacements were estimated using daily GPS solutions obtained with precise point positioning (PPP) technique. The results were compared with predictions from seven latest global ocean tide models. Gravity measurements of OTL in Hong Kong were also used to validate the GPS results. The study shows that the results from both the GPS and gravity measurements agree best with the GOT4.7 and NAO99b models, when the K1 and K2 constituents are excluded. The agreements between the GPS and the model estimates are generally at sub-millimeter level in both the horizontal and vertical directions, except for S2, K2 and K1 constituents that have relatively larger errors. After removing the systematic biases between the GPS and the model estimates, the misfits of M2, S2, N2, O1, P1 and Q1 at all sites are within 0.5 and 1.0 mm in the horizontal and the vertical directions, respectively, whereas K1 and K2 show relatively larger misfits of up to 2.3 mm. Both the GPS and the gravity S2 estimates have large biases with unknown reasons when compared with the modeled values, which needs to be further investigated. The study demonstrates that GPS is capable of estimating the OTL displacements with the same accuracy as the model predictions, especially for coastal areas.

Accuracy Assessment of Global Ocean Tide Models Base on Satellite Altimetry

Tidal harmonics of 8 principal constituents (M2,S2,K1,O1,N2,K2,P1 and Q1)derived from ground observations at 152 tidal gauge stations are used to assess the accuracy of 7 global ocean tidal models.It is shown that for the deep ocean area these models have high accuracy.The root-mean-square values of tidal height differences (RMSd) are within the range from 1.0 to1.3 cm for M2,and the root-sum-square values of the RMSd of these 8 constituents lie in the range from 2.0 to 2.3 cm.Comparison of the global tidal models to 18 offshore and island tide gauge observations in the seas adjacent to China shows that the accuracy significantly decreases.The RMSd values of constituent M2 lie in the range of 4.4 to 10 cm,which is significantly greater than that in the deep ocean area.Among these models,the model NAO99 that assimilates T/P altimeter data and tide gauge observations into a hydrodynamic model,developed by the National Astronomical Observatory of Japan,has the best accuracy for the seas adjacent to China.

Tidal Simulation around Japanese Coastal Region with a Global Ocean Tide Model

This study examines the sensitivity of tidal simulation to the model-domain size, and validates the accuracy of tidal simulation with broad model domain as the storm surge simulation. The tidal simulation models which adopt the driving force given by the global ocean tide model are developed. The models cover the Seto Inland Sea and coastal region of Kyushu-Shikoku with three different model-domain sizes. The size of the broadest domain is just as the storm surge simulation. Validation with the tide-gauge data shows that the accuracy is high in the narrower domain cases, however, in the broadest domain case the calculational error of tide becomes large in Bungo Channel and eastern coastal region of Kyushu.

Qualitative comparisons of global ocean tide models by analysis of intersatellite ranging data

Four global ocean tide models are compared in terms of their contribution to Gravity Recovery and Climate Experiment (GRACE) satellite‐to‐satellite tracking residuals. The residuals are computed relative to a comprehensive model of Earth's time‐varying gravity, including allowance for mass motions in the atmosphere, ocean, terrestrial hydrology, and mantle, in addition to tides. For each analyzed tide model, 4 years of GRACE range rate data are processed. Range and range acceleration residuals are tidally analyzed by geographic location. All four global tide models are shown to be error prone in various ways, leaving tidally coherent residuals especially in polar regions but also in some lower‐latitude regions. Considerable power in the solar semidiurnal S2 tide in low latitudes suggests errors in our adopted model of atmospheric tides, which is based on 3 hourly European Centre for Medium‐Range Weather Forecasts operational analyses. Anomalies in the μ2 tidal constituent over some shallow seas suggest the presence of unmodeled nonlinear compound tides, in this case 2MS2. Similarly, anomalies in the nonlinear M4 tide are seen if this constituent is omitted from the models. Errors in assumed seawater density may be contributing to some residuals.

Estimates of ocean tide loading displacements and its impact on position time series in Hong Kong using a dense continuous GPS network

Three-dimensional ocean tide loading (OTL) displacements of eight diurnal and semidiurnal constituents at 12 sites in Hong Kong were estimated using 3–7 years of continuous global positioning system (GPS) observations. OTL displacements were estimated using the precise point positioning (PPP) technique on a daily basis and then combined. The OTL displacements obtained by GPS were compared with predictions using seven recent global ocean tide models. The effect of OTL displacements on GPS position time series was also investigated. The study shows that the GPS-derived OTL displacements (excluding K1 and K2 constituents) agree best with those predicted by the GOT4.7 and NAO99b models. The GPS/model agreement is generally at the sub-millimeter level, except for S2, K1, and K2 constituents with relatively large errors. After systematic biases between the GPS and model values are removed, the misfits of all sites for M2, S2, N2, O1, P1, and Q1 are less than 0.5 and 1.0 mm in the horizontal and vertical components, respectively, while larger misfits (within 2.5 mm) are observed for K1 and K2. Integer ambiguity fixing slightly improves the east component of OTL displacement estimates. The study also finds that GPS-derived OTL corrections, instead of model predicts, can be used in daily data processing with the exception of K1 and K2. Including K2 corrections, a secular vertical rate of up to 1 mm/year in position time series can be induced, which needs to be confirmed by further studies.

Accurate Correction Models for Tidal Gravity in Chinese Continent

AbstractAccurate correction models for tidal gravity in Chinese continent are developed by using the recent theoretical and experimental models for the Earth's tidal gravity, in which the loading effects of the global and local ocean tides are combined. The relative difference of tidal gravity variations induced from different Earth's tidal gravity models is less than 0.06%. The ocean tide loading effects are about 4% of the total tidal gravity in coastal area while they are about 1% in inland. The difference between the ocean tide loading effects estimated from global ocean tide models and modified global models with local tides is about 10% of the total ocean tide loading effects. And the interpolated and extrapolated ocean tide loading effects are about 3% of the total ones. Comparing the observed tidal gravity variations by superconducting gravimeter with the ones calculated through the correction models, it is confirmed that the models developed in this study can accurately predict the tidal gravity signatures with a precision much better than 0.5 × 10−8 m·s−2. Consequently, it is expected that the models should provide an effective reference and accurate correction models for gravity measurements.

Coral microatoll as geodetic tool in North Andaman and Little Andaman, India

Coral microatolls were examined from North Andaman and Little Andaman to understand the relative sea level change due to vertical tectonic deformation above the subduction interface. The highest level of survival of coral microatoll before the 26 December, 2004 earthquake at eastern coast of North Andaman has been determined by Global Ocean Tide Model. The present position of recently dead flat top microatoll with preserved internal structure at the eastern coast of North Andaman mainland indicates 31.21 cm uplift due to the 26 December, 2004 earthquake. Comparatively old cup shaped microatoll at the eastern fringe of North Andaman group of islands and highly bioeroded fossil microatolls at the intertidal zone of Little Andaman bear the signature of permanent vertical deformation in the past.