Ocean Tide Models Research Articles

ALBATROSS: Advancing Southern Ocean tide modelling with high resolution and enhanced bathymetry

The knowledge of bathymetry and ocean tides plays a pivotal role at the crossroads of various scientific fields, especially in the Polar regions. Its significance extends to ocean circulation modeling and understanding the coupled dynamical response of the ocean, sea-ice and ice-sheet systems. In the Southern Ocean, conventional satellite altimetry measurements are rare below the 66° parallel. Hydrodynamic models are thus useful tools to provide spatially continuous information about ocean tides. However, the accuracy of ocean tide models around the Antarctic continent is currently limited by the quality of bathymetry. Recent reprocessing of decade-long CryoSat-2 data has facilitated a new computation of bathymetry around Antarctica, bringing innovative information on bathymetry gradients. This, combined with new compilations of bathymetry, ice draft, coastline, and grounding line datasets in ice-shelf regions, allows improving models and knowledge of ocean tides in the Southern Ocean. We developed a new high-resolution tidal model that implements the improved bathymetry data and includes data assimilation of satellite-altimetry tidal retrievals computed from CryoSat-2, filling the gap between the 66°S-limited coverage of the TOPEX-Jason suite missions and the Antarctic coast. Comparisons with tidal estimates derived from tide gauge measurements showed very good consistencies with an RMSE of 3 cm.

Estimation of tidal energy potential in the Vietnam East Sea: A comprehensive analysis using semi-empirical tide models

This study assesses the tidal energy potential in the Vietnam East Sea (VES), a region with complex hydrodynamics and significant interactions with the Western Pacific Ocean. A rigorous validation of six prominent semi-empirical global ocean tide models (FES2014, DTU16, EOT20, GOT4.10c, HAMTIDE12, OSU12.V1) was conducted against an extensive network of 34 tide gauge stations in the VES region. The validation identified FES2014 as the superior model, exhibiting the closest agreement with observations due to its advanced data assimilation techniques, high-resolution grids, and robust hydrodynamic representation influenced by the complex VES bathymetry. Leveraging the FES2014 model, the influential role of the semi-diurnal component (M2) in dictating energy distribution is prominently evident. Evaluation results of tidal amplitudes revealed three emerging hotspots: the Batang Lupar estuary (Malaysia), Anpu Gang (China), and Bac Lieu (Vietnam), with tidal amplitudes up to 326.2 cm. The Anpu Gang exhibited the highest theoretical potential tidal energy of 14.90 Wh/m2, making it the most promising site for localized tidal power development. Although moderate compared to globally renowned sites, the identified VES hotspots merit consideration for small-to-medium scale projects tailored to local conditions. While limited to potential energy assessments, this study provides a crucial baseline for the VES region, highlighting opportunities for sustainable tidal energy exploitation.

Accuracy assessment of recent global ocean tide models in coastal waters of the European North West Shelf

The accuracy of global ocean tide models is assessed in coastal waters of the European North West Shelf to ascertain where higher resolution local (forecast) models are most needed for geophysical and navigational applications, and which global models are most suitable for providing boundary conditions for regional and local tide models. Five recent global ocean tide models (FES2014b, EOT20, TPXO9-atlas-v5, GOT4.10c, and DTU16) are considered, with the models first compared by interpolating them onto common grids and computing the mean absolute deviation at each grid point. Coastline tide gauge and offshore bottom pressure sensor data were collated from several sources to give a total of 279 observation sites for evaluating model accuracy, including observational values from 137 locations that have not previously been released and have therefore not been assimilated into any of the global models tested. The residual errors between each model’s predicted phasor and the corresponding observed phasor were calculated at each observation location, and quantified using the root mean square (RMS) and median absolute residual (MAR) for the eight tidal constituents M2, S2, N2, O1, K1, K2, P1, and Q1. To avoid RMS values being biased by observation point density, a Voronoi-weighted RMS based on the water area of the Voronoi polygon about each observation location was also developed and used. Four zones were defined based on ocean depth to gauge model performance, and model inaccuracy is again demonstrated in near-shore regions. Seven further zones were defined based on geographical areas, which reveals inhomogeneity among the global models. The smallest overall root sum square (RSS) RMS error across all eight constituents arises with FES2014b, although TPXO9-atlas-v5 has the best performance when using the MAR and Voronoi-weighted RMS metrics. Using only the 137 observation sites that have not been assimilated by any model and therefore provide an independent accuracy assessment, FES2014b exhibits the smallest errors at the coastline, with an RSS RMS of 24.46 cm. All models exhibit larger errors with the 137 independent observation sites than with all 279 observation sites, with an average overall increase in RSS RMS error of 12%, and an increase of 30% for coastline tide gauges, highlighting the need for local model development in these areas.

Residual and Unmodeled Ocean Tide Signal From 20+ Years of GRACE and GRACE‐FO Global Gravity Field Models

AbstractWe analyze remaining ocean tide signal in K/Ka‐band range‐rate (RR) postfit residuals, obtained after estimation of monthly gravity field solutions from 21.5 years of Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On sensor data. Low‐pass filtered and numerically differentiated residuals are assigned to grids and a spectral analysis is performed using Lomb‐Scargle periodograms. We identified enhanced amplitudes at over 30 ocean tide periods. Spectral replicas revealed several tides from sub‐semidiurnal bands. Increased ocean tide amplitudes are located in expected regions, that is, in high‐latitude, coastal and shallow water regions, although some tides also show distinct patterns over the open ocean. While most identified tides are considered during processing, and therefore the amplitudes represent residual signal w.r.t. the ocean tide model, several unmodeled tides were found, including astronomical degree‐3 tides , , , , and radiational and/or compound tides , , , and . The astronomical degree‐3 tides were observed on a global level for the first time a few years ago in altimeter data. We are unaware of any global data‐constrained solutions for the other tides. The amplitude patterns of these tides exhibit similarities to purely hydrodynamic solutions, and altimeter observations (astronomical degree‐3 only). The sensitivity of the satellites to these rather small tidal effects demands their inclusion into the gravity field recovery processing to reduce orbit modeling errors and a possible aliasing. The conducted study shows enormous potential of RR postfit residuals analysis for validating ocean tide models and improving gravity field recovery processing strategies.

A comparison of global and regional ocean tide models with tide gauges in the East Asian marginal seas

To enhance storm surge forecasting and establish open boundary conditions for sophistical numerical simulation of tides and tidal currents in the Bohai Sea, Yellow Sea, and East China Sea, this study evaluated the accuracy of eight global and regional tide models (EOT20, FES2014, NAO.99Jb, TPXO9, DTU16, HAMTIDE12, OSU12, and GOT4.10c) based on 41 tide gauges in the region. The differences between tide models and 8 offshore tide gauges were notable, with the root mean square (RMS) values ranging from 12.67 to 25.97 cm for M2, 6.09–13.73 cm for S2, 2.96–6.56 cm for K1, and 2.50–4.20 cm for O1. For the offshore stations, the NAO.99Jb model demonstrated superior performance with the root square sum (RSS) value of 12.63 cm among the eight tide models. For the island and coastal stations, the EOT20 model performed the best for M2 (RMS 13.03 cm), the FES2014 model for S2 (RMS 6.26 cm), and the DTU16 model for K1 and O1 (RMS 2.73 cm and 2.26 cm, respectively). Overall, the EOT20 model also exhibited the lowest RSS value (15.22 cm) among the eight models for 24 island and coastal stations. The EOT20 model slightly outperformed others with the RSS of 14.88 cm across all 32 tide gauges. Regarding the Sa tidal component, great discrepancies were found between TIDAL CONSTANTS (TICON) harmonic constant data and tide gauges. The reason for this is that the Doodson number for the Sa tidal component derived from tide gauge data, which is influenced by meteorological factors, should be (0,0,1,0,0,0), while the TICON harmonic constant data employed the Doodson number of (0,0,1,0,0,−1) corresponding to the basic astronomical variables. A correction method was proposed to adjust tidal constants from inconsistent Doodson numbers. Comparing with the harmonic constants of the Sa tidal component at 28 coastal tide stations revealed large errors in the NAO.99b, FES2014, and EOT20 models, with RMS values of 19.03, 22.08, and 13.61 cm, respectively. Consequently, caution should be taken when using the Sa results from these ocean tide models.

Gravity field recovery of inter-satellite links between Beidou navigation satellite system (BDS) and LEO based on geodesy and time reference in space (GETRIS)

The goal of this contribution is to construct the inter-satellite links (ISLs) between Global Navigation Satellite System (GNSS) and Low Earth Orbit (LEO) satellite to recover the Earth’s gravity field based on the concept of Geodesy and Time Reference in Space (GETRIS). Taking the constellation of the Beidou Navigation Satellite System (BDS) as an example, several types of high-low satellite-to-satellite tracking (H-L SST) modes combining BDS and GETRIS are used to research the tracking mode of high orbit satellites and the distribution of LEO satellite constellations to explore the optimal mode for gravity field recovery. The effects of multiple H-L SST modes on the accuracy of gravity field recovery are studied. In addition, the contribution of each error source is also analyzed. Finally, this study varies LEO satellite constellations to show reduced errors in the temporal gravity field solutions for the improved ISLs. The results showed that the Inclined GeoSynchronous Orbit (IGSO) satellite greatly improved the Geosynchronous orbit (GEO) satellite tracking LEO satellite mode in the high latitude regions. Compared with the Medium Earth Orbit (MEO) satellite tracking LEO satellite, the error of gravity field recovered by combining with GEO, IGSO and MEO can be reduced by 16 %. The largest error is the non-tidal signal, followed by the ocean tidal model difference, and the smallest is the instrument error. For a single LEO satellite, the combination model is more sensitive to the satellite orbital altitude, the cumulative error was decreased from 5.08 mm (550 km) to 0.33 mm (250 km). For LEO constellations, adding inclined orbit satellites can improve the accuracy of the solution to some extent. But the optimal solution can be obtained by the constellation composed of polar orbit satellites with different Right Ascension of Ascending Node (RAAN), the cumulative errors are 0.27 mm (two satellites), 0.19 mm (three satellites), and 0.19 mm (four satellites).

ArcTiCA: Arctic tidal constituents atlas

Tides in the Arctic Ocean affect ocean circulation and mixing, and sea ice dynamics and thermodynamics. However, there is a limited network of available in situ tidal coefficient data for understanding tidal variability in the Arctic Ocean; e.g., the global TICON-3 database contains only 111 sites above 60°N and 21 above 70°N. At the same time, the presence of sea ice and latitude limits of satellite altimetry complicate altimetry-based retrievals of Arctic tidal coefficients. This leads to a reliance on ocean tide models whose accuracy depend on having sufficient in situ data for validation and assimilation. Here, we present a comprehensive new dataset of tidal constituents in the Arctic region, combining analyses of in situ measurements from tide gauges, ocean bottom pressure sensors and GNSS interferometric reflectometry. The new dataset contains 914 measurement sites above 60°N and 399 above 70°N, with each site being quality-assessed and expert guidance provided to help maximise the usage of the dataset. We also compare the dataset to recent tide models.

Modelling of ocean currents and distribution of total suspended solids in Citarum River estuary

The Citarum River is an important river in West Java, which empties into the Java Sea carrying large suspended sediment concentrations. The purpose of this study is to examine the interaction of current patterns and distribution of total suspended solids (TSS) in the Northwest and Southeast Monsoons using hydrodynamic Modelling. The flow model and TSS used were 2-dimensional models with the OpenFlows FLOOD software. The ocean tide model results were validated using the Root Mean Square Error (RMSE) method with a value of 0.10. The current velocity in the West and East monsoons ranges from 0.07 - 0.35 m/s. Currents flow north and northeast during high-tide conditions and move south and southwest during low-tide conditions in both seasons. The movement of TSS was influenced by the current patterns. The highest concentration of TSS is in the Northwest Monsoon at low tide, which was in the range of 560–575 mg/L. The lowest TSS concentration was in the Southeast Monsoon during high tide conditions, ranging from 80 to 120 mg/L. The high concentration of TSS in the Northwest Monsoon was influenced by higher rainfall, with an average in January and only 23.2 mm/day while in the Southeast Monsoon it is only 7.8 mm/day.

Satellite Gravity Field Recovery Using Variance‐Covariance Information From Ocean Tide Models

AbstractMonthly gravity field recovery using data from the GRACE and GRACE Follow‐On missions includes errors limiting the spatial and temporal resolution of the estimated gravity fields. The major error contributions, besides the noise of the accelerometer instruments, arise from temporal aliasing errors due to imperfections in the non‐tidal atmospheric and oceanic de‐aliasing models and ocean tide models. We derive uncertainty information for the eight major tidal constituents from five different ocean tide models and introduce it into the gravity field recovery process in terms of a constrained normal equation system while expanding the parameter space by additional tidal parameters to be adjusted. We prove the effectiveness of the ocean tide variance‐covariance information through realistic simulations and we assess its potential based on microwave and laser interferometer observations from the GRACE Follow‐On mission. We show that errors are reduced by more than 20% ocean wRMS for a Gaussian filter radius of 300 km if uncertainty information for ocean tides is considered and stochastic modeling of instrument errors is applied, compared to the latest GFZ release 6.1. Our results also show the limited visibility of the effectiveness of the ocean tide variance‐covariance information due to the dominating error contribution of non‐tidal atmospheric and oceanic mass variations. Additionally, we investigate the option of estimating ocean tide parameters over a 1‐year period while including ocean tide uncertainty information in order to improve ocean tide background modeling.

Polar Ocean Tides—Revisited Using Cryosat-2

With the availability of more than 9 years of Cryosat-2, it is possible to revisit polar ocean tides, which have traditionally been difficult to determine from satellite altimetry. The SAMOSA+ physical retracker is a stable retracker developed particularly for Cryosat-2. Being a physical retracker, it enables the determination of the sea state bias. Correcting for the sea state bias enables more reliable sea level estimates compared with traditional empirical retrackers used before. Cryosat-2 data have been analyzed for residual ocean tides to the FES2014 ocean tide model in the Arctic Ocean and Antarctic Ocean using the response formalism. We utilize data from the sub-cycle of Cryosat-2, which follows a repeating pattern of approximately 28.33 days. This sub-repeat period makes it an advantageous alias period for the majority of significant constituents. This allowed for the estimation and mapping of the major tidal constituents in the open ocean and also in floating ice shelves from data extracted from leads in the sea ice. A novel empirical ocean tide model designed specifically for the polar region, DTU22, is introduced. Our findings reveal substantial enhancements in semi-diurnal tides within the Arctic Ocean and improvement in diurnal constituents within the Southern Ocean. In the Southern Ocean, the diurnal constituents are particularly improved using the empirical model by more than a factor of two to around 3 cm for both constituents compared with FES2014b. These outcomes underscore the significance of incorporating the reprocessed and retracted Cryosat-2 data into tidal modeling, highlighting its pivotal role in advancing the field.

Estimation of free core nutation parameters and availability of computing options

The Earth's Free Core Nutation (FCN) causes Earth tides and forced nutation with frequencies close to the FCN that exhibit resonance effects. High-precision superconducting gravimeter (SG) and very long baseline interferometry (VLBI) provide good observation techniques for detecting the FCN parameters. However, some choices in data processing and solution procedures increase the uncertainty of the FCN parameters. In this study, we analyzed the differences and the effectiveness of weight function and ocean tide corrections in the FCN parameter detection using synthetic data, SG data from thirty-one stations, and the 10 celestial pole offset (CPO) series. The results show that significant discrepancies are caused by different computing options for a single SG station. The stacking method, which results in a variation of 0.24–5 sidereal days (SDs) in the FCN period (T) and 103-104 in the quality factor (Q) due to the selection of the weighting function and the ocean tide model (OTM), can effectively suppress this influence. The statistical analysis results of synthetic data shows that although different weight choices, while adjusting the proportion of diurnal tidal waves involved, do not significantly improve the accuracy of fitted FCN parameters from gravity observations. The study evaluated a series of OTMs using the loading correction efficiency. The fitting of FCN parameters can be improved by selecting the mean of appropriate OTMs based on the evaluation results. Through the estimation of the FCN parameters based on the forced nutation, it was found that the weight function P1 is more suitable than others, and different CPO series (after 2009) resulted in a difference of 0.4 SDs in the T and of 103 in the Q. We estimated the FCN parameters for SG (T = 430.4 ± 1.5 SDs and Q = 1.52 × 104 ± 2.5 × 103) and for VLBI (T = 429.8 ± 0.7 SDs, Q = 1.88 × 104 ± 2.1 × 103).

Comparison of state-of-the-art GNSS-observed and predicted ocean tide loading displacements across Australia

We seek to quantify and understand the residual signal in GPS and GLONASS estimates of ocean tide loading displacements (OTLDs) after removing state-of-the-art model estimates. To consider contributions over a broad spatial scale, we estimate OTLD over the Australian continent using sim 5.5 years of continuous GPS and GLONASS data from 360 sites. We compare these with modelled estimates, with a focus on the lunar semidiurnal M_2 and diurnal O_1 constituents. We observe spatially coherent patterns of residual OTLD in each of the east, north, and up coordinate components after the removal of tidal loading using elastic models. We subsequently assess the impact of including anelastic dispersion in the model and show a 0.2 mm reduction in range of the up component residuals at coastal sites. A similar reduction at all sites is observed in the east and north components. Of the seven ocean tide models used, we find that three recent models, FES2014b, GOT4.10c and TPXO9.v1, perform similarly, noting these comparisons are made in the CE frame. However, we show that the latter contains centre of mass (CoM) biases in amplitude up to 0.2 mm and 0.5 mm for M_2 and O_1, respectively, due to the assimilated altimetry data having not been corrected for geocentre motion. We find OTLD estimates are sensitive to the chosen orbit and clock products used in our analysis, with differences of up to 0.5 mm in the east component between solutions using the JPL and either of ESA or CODE products (GPS-only). Our analysis shows that current GNSS estimates of OTLD over Australia are typically accurate to sim 0.2 mm at which point we are unable to explain spatially coherent residuals when compared to modelled quantities. These may depend on the appropriate treatment of the CoM variation, anelasticity and/or three-dimensional Earth structure. As such, we recommend great care is taken when interpreting OTLD at the level of 0.1 or 0.2 mm, even if it is regionally coherent.

Anelastic response of the Earth's crust underneath the Canary Islands revealed from ocean tide loading observations

SUMMARY We report on the analysis of M2 ocean tide loading (OTL) kinematic GPS vertical displacement and tidal gravity measurements using 26 GPS and four gravimetric sites across the Canary Islands archipelago. In this region, the standard deviation among recent ocean tide models is lower than 0.4 cm in amplitude and 0.3° in phase, which are suitably accurate for displacement modelling. However, for gravity we need to model regional ocean tides to achieve enough accuracy in the loading calculations. Particularly, this study improves the predicted OTL gravity variations when global ocean models are replaced with the regional model CIAM2 which assimilates local tide gauge data. These small ocean tide model errors allow us to use the differences between observed and predicted OTL values to study the elastic and anelastic properties of the solid Earth around the Canary Islands. In the prediction of OTL, we first used the recent elastic STW105 and S362ANI seismic models, obtaining average observed minus predicted residuals of 1.2–1.3 mm for vertical displacement and 3 nm s−2 for gravity. After the STW105 and S362ANI models were adjusted for anelasticity, by considering a constant quality factor Q at periods ranging from 1 s to 12.42 hr, the average misfit between observations and predicted OTL values reduced to 0.7–0.8 mm for vertical displacement and to 1 nm s−2 for gravity. However, the average vertical displacement misfit is made up from site misfits less than 0.5 mm in western islands but for the easternmost islands of Lanzarote and Fuerteventura, they still reach up to nearly 2 mm at some sites, which still exceeds the uncertainty in the GPS observations. It is hypothesized that mantle upwelling underneath the Canary Islands, creating spatial variations in the elastic properties, causes the large residuals observed in the eastern islands. We reduced the shear modulus by up to 35 per cent in the upper mantle layer of 24.4–220 km depth. This produced residual observed minus model differences of about 0.7 mm for the sites on Lanzarote and Fuerteventura, comparable to the results obtained for the GPS sites across the rest of the archipelago, whose residuals in turn were also slightly reduced through the VS velocity and shear modulus reductions (by 0.2 mm on average).

A High Precision Tidal Model Based on Multisource Tidal Harmonic Constants for Offshore China

As the accuracy of analytical instruments improve, the accuracy of ocean tide load displacement (OTLD) in geodesy and ocean dynamics is becoming increasingly demanding. The method of integrating through the load Green’s function using the ocean tide model is the main means of OTLD correction. However, although different tidal models have high accuracy in open ocean regions, they are less precise and less practical in the offshore areas of China, making it difficult to correct OTLDs accurately in complicated coastline areas of China. In this work, we evaluate the accuracy of 13 different tidal models in offshore China, and construct a new tidal model, new.chinasea.2022, based on the combination of high-precision tidal harmonic parameters. The OTLD correction efficiency of new.chinasea.2022 and conventional tidal models was assessed by wRMS analysis of GPS coordinate time series from the Crustal Movement Observation Network of China (CMONOC). It turns out that (1) the newly released tidal model performs better than the old model in offshore China, and there are differences in the performance of different models for each tidal constituent in different seas; (2) The OTLD correction of new.chinasea.2022 performed better in the offshore region of China, improving the correction of FES2004 by 1%-12% and osu.chinasea.2010 by 1%-6.5%.

Residual M2 and S2 ocean tide signals in complex coastal zones identified by X-Track reprocessed altimetry data

While the reliability of reprocessed altimetry data from X-Track has been examined for sea level studies, it has not previously been used to study ocean tides in tidally complex coastal zones. Using a new dataset of short-term tide gauges, the aim of this study is to demonstrate the improvements in X-Track reprocessed data for studying ocean tides for the first time in tidally complex regions in northwest Australia. We show that X-Track can be used to evaluate and potentially correct ocean tide models in challenging coastal areas. Our study comprises three components: (1) evaluate the tidal constants from X-Track and RADS datasets using nearby (<12 km) short-term tide gauge data, (2) assess three ocean tide models (FES2014, DTU10, TPXO9) using the X-Track altimetry dataset and (3) extract residual M2 and S2 tidal constants from sea level anomalies (SLAs) computed using the optimal model (FES2014) for ocean tide correction and then use these to predict the residual tidal height to use as an additional correction for the recomputation of the SLAs.Our results show that X-Track data provides users with more valid observations close to coastlines (as close as 5 km) so that the derived M2 and S2 tidal constants show better agreement with nearby tide gauges compared to RADS for both Jason-3 (J3) and GFO missions. In Van Diemen Gulf, where the footprints were 7 km or less from the coast, RADS did not have any valid observations, whereas tidal constants of M2 computed from X-Track J3 and GFO data agreed with the tide gauges within ∼6% of the M2 tidal height. In contrast, X-Track J3 and GFO extracted S2 tidal constants agreed with nearby tide gauges within ∼11–24% (GFO extreme of 47%) of the S2 tidal height. The FES2014-detided SLA time series from X-Track were then analysed to detect the remaining signals of M2 and S2 tidal constituents, with co-range maps suggesting the unmodelled amplitudes for M2 reaches 40 cm and S2 up to 30 cm in Collier Bay. In Van Diemen Gulf, M2 contributes more to the residual tidal signal than S2 with an amplitude of 40 cm compared to 10 cm respectively, in contrast to Joseph Bonaparte Gulf with ∼10 cm for both. When the SLAs, are corrected for the residual tide heights of M2 and S2, the standard deviation of the SLA residuals is decreased by as much as ∼70% in Collier Bay indicating that X-Track altimetry can identify M2 and S2 tidal residuals in complex coastal regions.

Evolution of Global Ocean Tide Levels Since the Last Glacial Maximum

AbstractThis study addresses the evolution of global tidal dynamics since the Last Glacial Maximum focusing on the extraction of tidal levels that are vital for the interpretation of geologic sea‐level markers. For this purpose, we employ a truly‐global barotropic ocean tide model which considers the non‐local effect of Self‐Attraction and Loading. A comparison to a global tide gauge data set for modern conditions yields agreement levels of 65%–70%. As the chosen model is data‐unconstrained, and the considered dissipation mechanisms are well understood, it does not have to be re‐tuned for altered paleoceanographic conditions. In agreement with prior studies, we find that changes in bathymetry during glaciation and deglaciation do exert critical control over the modeling results with minor impact by ocean stratification and sea ice friction. Simulations of 4 major partial tides are repeated in time steps of 0.5–1 ka and augmented by 4 additional partial tides estimated via linear admittance. These are then used to derive time series from which the tidal levels are determined and provided as a global data set conforming to the HOLSEA format. The modeling results indicate a strengthened tidal resonance by M2, but also by O1, under glacial conditions, in accordance with prior studies. Especially, a number of prominent changes in local resonance conditions are identified, that impact the tidal levels up to several meters difference. Among other regions, resonant features are predicted for the North Atlantic, the South China Sea, and the Arctic Ocean.

A superconducting gravimeter on the island of Heligoland for the high-accuracy determination of regional ocean tide loading signals of the North Sea

SUMMARY The superconducting gravimeter GWR iGrav 047 has been installed on the small offshore island of Heligoland in the North Sea approximately at sea level with the overall aim of high-accuracy determination of regional tidal and non-tidal ocean loading signals. For validation, a second gravimeter (gPhoneX 152) has been setup within a gravity gradiometer approach to observe temporal gravity variations in parallel on the upper land of Heligoland. This study covers the determination of regional ocean tide loading (OTL) parameters based on the two continuous gravimetric time-series after elimination of the height-dependent gravity component by empirical transfer functions between the local sea level from a nearby tide gauge and local attraction effects. After reduction of all gravity recordings to sea level, both gravimeters provide very similar height-independent OTL parameters for the eight major diurnal and semidiurnal waves with estimated amplitudes between 0.3 nm s−2 (Q1) and 11 nm s−2 (M2) and RMSE of 0.1–0.2 nm s−2 for 2 yr of iGrav 047 observations and a factor of 2 worse for 1.5 yr of gPhoneX 152 observations. The mean absolute OTL amplitude differences are 0.3 nm s−2 between iGrav 047 and gPhoneX 152, 0.4 nm s−2 between iGrav 047 and the ocean tide model FES2014b and 0.7 nm s−2 between gPhoneX 152 and FES2014b which is in good agreement with the uncertainty estimations. As by-product of this study, OTL vertical displacements are estimated from the height-independent OTL gravity results from iGrav 047 applying proportionality factors ${\rm d}h/{\rm d}g$ for the eight major waves. These height-to-gravity ratios and the corresponding phase shifts are derived from FES2014b. The OTL vertical displacements from iGrav 047 are estimated with amplitudes between 0.4 mm (Q1) and 5.1 mm (M2) and RMSE of 0.1–0.7 mm. These OTL amplitudes agree with FES2014b within 0.0 (M2) and 0.8 mm (K1) with a mean difference of 0.3 mm only. The OTL amplitudes from almost 5 yr of GNSS observations show deviations of up to 6 mm (M2) compared to vertical displacements from both iGrav 047 and FES2014b, which suggests systematic effects included in the estimation of OTL vertical displacements from GNSS. With the demonstrated accuracy, height-independent sensitivity in terms of gravity and vertical displacements along with the high temporal resolution and the even better performance with length of time-series, iGrav 047 delivers the best observational signal for OTL which is representative for a large part of the North Sea.

Ocean Tides near Hawaii from Satellite Altimeter Data. Part III

Abstract The Chebyshev polynomial fitting (CPF) method has been proved to be effective to construct reliable cotidal charts for the eight major tidal constituents (M2, S2, K1, O1, N2, K2, P1, and Q1) and six minor tidal constituents (2N2, J1, L2, Mu2, Nu2, and T2) near Hawaii in Part I and Part II, respectively. In this paper, this method is extended to estimate the harmonic constants of four long-period tidal constituents (Mf, Mm, Sa, and Ssa). The harmonic constants obtained by this method were compared with those from the TPXO9, Finite Element Solutions 2014 (FES2014), and Empirical Ocean Tide 20 (EOT20) models, using benchmark data from satellite altimeters and eight tide gauges. The accuracies of the Mf and Mm constituents derived from the CPF method are comparable to those from the models, but the accuracies of the Sa and Ssa constituents are significantly higher than those from the FES2014 and EOT20 models. The results indicate that the CPF method is also effective for estimating harmonic constants of long-period tidal constituents. Furthermore, since the CPF method relies only on satellite altimeter data, it is an easier-to-use method than these ocean tide models.

Influence of Ocean Tidal Loading on Continuous Gravity Observations in Eastern China

Global and regional ocean tide models are used to analyze the gravity effect of ocean tidal loading (OTL) for gravity stations in East China. The accuracies of OTL correction results for 21 gravity stations in East China are evaluated. The global ocean tide model is the most effective for the OTL correction of inland gravity stations (up to 90%) but is less effective for coastal gravity stations (only 60%). Considering regional ocean tide models, the applicability of OTL correction increased to 80% in coastal gravity stations. Based on the root sum square (RSS) method, among 16 combination models, the optimal combination model for OTL correction is the global model FES2014b by combing the regional model OSU.Chinasea.2010 (F14O). The RSS, which has reached 7.1 nms−2, is the minimum of the 16 combination models. Simulating with the F14O in the China Sea and adjacent areas, the gravity amplitude of the OTL is about 10 nms−2 in inland areas and > 50 nms−2 along the coastline. Especially in Southeastern China coastal areas and the southwestern coastal areas of the Korean Peninsula, the gravity amplitude of the OTL reaches about 80 nms−2. Moreover, the OTL changes drastically possibly owing to coastal topography. The results of this study provide a reference for selecting ocean tide models for high-precision analysis of continuous gravity observations in East China.

The impact of nonlinear tide–surge interaction on satellite radar altimeter-derived tides

Both empirical and assimilative global ocean tidal models are significantly more accurate in the deep ocean than in shelf and coastal waters. In this study, we answered whether this is due to the quality of the models used to reduce tide and surge or the general approach to treat tide and surge as two separate components of the water level obtained from stand-alone models, which ignores the nonlinear tide–surge interaction. In doing so, we used tide gauge observations as partially synthetic altimeter time series, tide–surge water-level time series obtained with the 2D Dutch Continental Shelf Model – Flexible Mesh (DCSM), and tide and surge water-level time series obtained using the DCSM, FES2014 (FES) and the Dynamic Atmospheric Correction (DAC) product. Expressed in the root-sum-square (RSS) of the eight main tidal constituents, we obtained a reduction % when removing the DCSM tide–surge water levels compared to when we removed the sum of the DCSM tide and DCSM surge water levels. The RSS obtained in the latter case was only 3.3% lower than with FES and DAC. We conclude that the lower tidal estimates accuracy in shelf-coastal waters derives from the missing nonlinear tide–surge interactions.