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Trends in the deep-ocean M 2 barotropic tide, deduced from nearly three decades of satellite altimetry and recently presented by Opel et al. (Commun Earth Environ 5:261, https://doi.org/10.1038/s43247-024-01432-5, 2024), are here updated with a slightly longer time series and with a focus on potential systematic errors. Tidal changes are very small, of order 0.2 mm/year or less, with a tendency for decreasing amplitudes, which is evidently a response to the ocean's increasing stratification and an increasing energy loss to baroclinic motion. A variety of systematic errors in the satellite altimeter system potentially corrupt these small trend estimates. The Dynamic Atmosphere Correction (DAC), derived from an ocean model and used for de-aliasing, introduces a spurious trend (exceeding 0.1 mm/year in places) caused by changes in ECMWF atmospheric tides. Both operational and reanalysis atmospheric tides have spurious trends over the altimeter era. Tidally coherent errors in satellite orbits, including from use of inconsistent tidal geocenter models, are more difficult to bound, although differences between two sets of satellite ephemerides are found to reach 0.1 mm/year for M 2 . Orbit errors are more deleterious for some other constituents, including the annual cycle. Tidal leakage in the "mesoscale correction," needed here to suppress non-tidal ocean variability, is a known potential problem, and if the leakage changes over time, it impacts ocean-tide trend estimation. Tests show the error is likely small in the open ocean ( < 0.04 mm/year) but large in some marginal seas ( > 0.2 mm/year). Potential contamination from other altimeter corrections (e.g., ionospheric path delay) is likely negligible for M 2 but can be difficult to bound. [ABSTRACT FROM AUTHOR]

Ocean tide generated magnetic fields contain information about changes in ocean heat content and transport that can potentially be retrieved from remotely sensed magnetic data. To provide an important baseline towards developing this potential, tidal signals are extracted from 288 land geomagnetic observatory records having observations within the 50-year time span 1965–2015. The extraction method uses robust iteratively reweighted least squares for a range of models using different predictant and predictor assumptions. The predictants are the time series of the three vector components at each observatory, with versional variations in data selection and processing. The predictors fall into two categories: one using time-harmonic bases and the other that directly use lunar and solar ephemerides with gravitational theory to describe the tidal forces. The ephemerides predictors are shown to perform better (fitting more variance with fewer predictors) than do the time-harmonic predictors, which include the traditional 'Chapman–Miller method'. In fitting the oceanic lunar tidal signals, the predictants with the highest signal/noise involve the 'vertical' magnetic vector component following principle-component rotation. The best simple semidiurnal predictor is the ephemeris series of lunar azimuth weighted by the inverse-cubed lunar distance. More variance is fitted with predictors representing the lunar tidal potential and gradients calculated for each location/time. This article is part of the theme issue 'Magnetometric remote sensing of Earth and planetary oceans'. [ABSTRACT FROM AUTHOR]

The tidal flow of seawater across the Earth's magnetic field induces electric currents and magnetic fields within the ocean and solid Earth. The amplitude and phase of the induced fields depend on the electrical properties of both seawater and the solid Earth, and thus can be used as proxies to study the seabed properties or potentially for monitoring long-term trends in the global ocean climatology. This article presents new global oceanic tidal magnetic field models and their uncertainties for four tidal constituents, including M2,N2,O1 and even Q1 , which was not reliably retrieved previously. Models are obtained through a robust least-squares analysis of magnetic field observations from the Swarm and CHAMP satellites using a specially designed data selection scheme. We compare the retrieved magnetic signals with several alternative models reported in the literature. Additionally, we validate them using a series of high-resolution global three-dimensional (3D) electromagnetic simulations and place constraints on the conductivity of the sub-oceanic mantle for all tidal constituents, revealing an excellent agreement between all tidal constituents and the oceanic upper mantle structure. This article is part of the theme issue 'Magnetometric remote sensing of Earth and planetary oceans'. [ABSTRACT FROM AUTHOR]

Studying ocean tides with satellite altimetry has traditionally been difficult in coastal regions. The 1 day repeat of the Cal/Val phase of SWOT provides a unique dataset that can be exploited for tidal analysis. In this work, KaRIn data from the SWOT Cal/Val phase are analyzed in two coastal regions to present a first look at the possibilities for tidal analysis from SWOT. The areas are: (a) Bristol Channel and (b) Great South Bay. When benchmarked against in situ measurements in these regions, substantial improvements over tide models, which typically report errors exceeding tens of centimeters and degrees, are seen. Specifically, the SWOT ocean‐tide estimates exhibit amplitude discrepancies ranging from 1.75 to 3 cm and phase lag discrepancies between 1.75° and 2.75° when compared with in situ tide gauge data. These findings underscore the value of SWOT for tidal research in complex coastal regions. Plain Language Summary: Estimating ocean tides in the coastal region has challenged tide modelers for decades. The recently launched SWOT satellite provides the opportunity to derive estimations of ocean tides at unprecedented spatial scales thanks to the innovative wide‐swath measurement principle, particularly in complex coastal regions. The mission's Calibration and Validation (Cal/Val) phase is particularly interesting for tidal research, as the tide‐favorable orbit allows for the derivation of the major tidal constituents with a relatively short time series of SWOT data. This manuscript evaluates the largest tidal constituent, the principal lunar M2 ${\mathrm{M}}_{2}$ tide, derived from SWOT's Cal/Val phase within two complex coastal regions. Results within the Bristol Channel and the Great South Bay demonstrate unprecedented spatial variability in the amplitude and phase lag of the M2 ${\mathrm{M}}_{2}$ tide. Additionally, with respect to in situ measurements, SWOT‐derived estimates resulted in reduced errors compared with global tide models in these complex coastal regions. The initial insights demonstrated several strengths and opportunities for using SWOT to improve tide models and new avenues of research with satellite measurements of ocean tides, particularly within fjords and estuaries. Key Points: SWOT KaRIn data from the Cal/Val phase is used to derive M2 ${\mathrm{M}}_{2}$ tide in two complex coastal regionsResults demonstrate the spatial variability of amplitude and phase lag of coastal tidesSWOT KaRIn measurements are useful for studying tidal flats and ocean tides in river mouths and estuaries [ABSTRACT FROM AUTHOR]

Sea level information, and its understanding, are essential for research in oceanography and coastal engineering. This paper describes sea level variability in the Clyde using data from 10 tide gauges. High coherence of sea level variability is found between the Firth of Clyde and estuary of the River Clyde, and between the Firth and estuary and the upstream part of the river. Consequently, if gaps exist in any of the records, missing information can be inferred from others. This applies to timescales of typically hours and longer, appropriate for storm surge or mean sea level change studies. No evidence exists for ‘see-saw’ oscillations of the river on subtidal timescales, as reported for the River Thames, but higher-frequency variability (typical period 45 minutes) is found with equal, or opposite, phase at different river locations. Such a standing wave behaviour would be one of the few reported examples of ‘river seiches’. Data from several agencies are used: two gauges of the UK National Network of the Environment Agency, five from the Scottish Environment Protection Agency, and three from Peel Ports. Only the former tend to be used in academic studies, but the present paper has demonstrated how useful complementary sources can be. [ABSTRACT FROM AUTHOR]

Tidal forces generate time‐varying currents in bodies with fluid layers, such as the icy ocean moons of the outer solar system. The expectation has been that tidal currents are periodic—they average to zero over a forcing period—so that they are not associated with a mean flow. This expectation arises from the assumption of linearity. Here, we relax this assumption and develop a theory that predicts the emergence of mean currents driven by any periodic forcing. The theory, derived in the context of a global, uniform, shallow ocean, constitutes a set of mean flow equations forced by non‐linear eddy fluctuations. The latter are the canonical, periodic tidal currents predicted by the Laplace Tidal equations. We show that the degree‐2 tide‐raising potential due to obliquity and/or orbital eccentricity can drive time‐averaged currents with zonal wavenumbers from 0 to 4. The most prominent of these is a retrograde zonal jet driven by the obliquity‐forcing potential. Assuming Cassini state obliquities, this jet has speeds ranging from 0.01 to 1 mm s−1, which can exert torques up to roughly 1015 N m at the ice–ocean interfaces of Europa, Callisto, Titan, and Triton. Depending on the viscosity of the ice shell, these torques could drive ice shell drift rates of tens to potentially hundreds of meters a year. Thinner or stably stratified global oceans can experience much faster mean currents. Plain Language Summary: Icy moons with subsurface oceans experience tidal forces as they circle around their host planets. These forces make such oceans flow back and forth. Most models of these tidal flows predict that the ebb and flow of the tide cancel each other out over time, so that a parcel of ocean does not, on average, move. We develop a model of ocean tides that shows this is not the case, and predicts permanent tidal currents that are generated from periodic tidal forces. Our model shows that the most significant of these leads the ocean to flow slightly toward the west. This flow acts to slow down the rotation of the icy crust floating on the ocean, potentially causing the ice to drift slowly to the west over geological time. Key Points: We develop a theory to predict time‐mean ocean circulation driven by periodic tidal forces and apply this to solar system icy satellitesThe dominant tidally driven time‐mean circulation is a single retrograde jetThe time‐mean tidal circulation can reorient the ice shells of Europa, Callisto, Titan, and Triton via frictional torques [ABSTRACT FROM AUTHOR]

Tides and Earth-Moon system evolution are coupled over geological time. Tidal energy dissipation on Earth slows Earth's rotation rate, increases obliquity, lunar orbit semi-major axis and eccentricity, and decreases lunar inclination. Tidal and core-mantle boundary dissipation within the Moon decrease inclination, eccentricity and semi-major axis. Here we integrate the Earth-Moon system backwards for 4.5 Ga with orbital dynamics and explicit ocean tide models that are "high-level" (i.e., not idealized). To account for uncertain plate tectonic histories, we employ Monte Carlo simulations, with tidal energy dissipation rates (normalized relative to astronomical forcing parameters) randomly selected from ocean tide simulations with modern ocean basin geometry and with 55, 116, and 252 Ma reconstructed basin paleogeometries. The normalized dissipation rates depend upon basin geometry and Earth's rotation rate. Faster Earth rotation generally yields lower normalized dissipation rates. The Monte Carlo results provide a spread of possible early values for the Earth-Moon system parameters. Of consequence for ocean circulation and climate, absolute (un-normalized) ocean tidal energy dissipation rates on the early Earth may have exceeded today's rate due to a closer Moon. Prior to ∼3Ga , evolution of inclination and eccentricity is dominated by tidal and core-mantle boundary dissipation within the Moon, which yield high lunar orbit inclinations in the early Earth-Moon system. A drawback for our results is that the semi-major axis does not collapse to near-zero values at 4.5 Ga, as indicated by most lunar formation models. Additional processes, missing from our current efforts, are discussed as topics for future investigation.

Ground-based magnetic observatories and geomagnetic satellites can observe the induced magnetic field generated by the motion of seawater containing sodium and chlorine ions. Calculating the three-dimensional (3-D) spatial distribution of tide-induced magnetic fields (TIMF) is crucial for inverting the electrical conductivity structure of the oceanic lithosphere. It also serves as an essential basis for designing optimal geomagnetic observatories and satellite orbits. However, existing methods for simulating TIMF suffer from limitations in inaccurately modeling realistic coastlines, heterogeneous land and sea surface properties, and complex deep Earth structures, thereby the interpretational level of TIMF data is reduced. To overcome this issue, we developed a tetrahedral-based finite element method for simulating TIMF, which can efficiently approximate realistic coastlines, heterogeneous land and sea surface properties, and complex deep Earth structures. Firstly, we derived the boundary value problem for the seawater motion-induced electromagnetic field, which was solved using the vector finite element method based on tetrahedral elements. Secondly, using the latest ocean depth and seafloor sediment layer models, we constructed a 3-D conductivity model of the Earth, which includes realistic coastlines, heterogeneous land and sea conductivity distributions. We then computed the TIMF using the M2 tidal source as an example and validated our method by comparing it with results obtained from spherical harmonic finite element and integral equation methods. Finally, utilizing the computed high-precision M2, N2, and O1 TIMF signals, we marked global observatories capable of observing strong M2, N2, and O1 TIMF signals and predicted alternative stations suitable for tide signal observations. Additionally, we calculated TIMF at heights of 450 and 200 km for the Macau Science Satellite 1 and its subsequent satellites. The results indicate that the amplitude of the tidal-induced magnetic field at 200 km is approximately twice that at 450 km. The maximum amplitudes of M2, N2 and O1 TIMF at 200 km are eight, two, and three times the measurement accuracy of the magnetic sensing payload (0.5 nT), respectively. The 200 km orbit has great potential for detecting high-resolution electrical structures of the seafloor lithosphere and asthenosphere in regions such as New Zealand, southern Iceland, the southern Indian Ocean, the Ross Sea region of Antarctica, and the Sea of Okhotsk. It also holds the potential for studying large-scale oceanic dynamic processes and properties. [ABSTRACT FROM AUTHOR]

We present a novel approach to modeling the tidal response of icy moons with subsurface oceans. The problem is solved in the time domain and the flow in the ocean is calculated simultaneously with the deformation of the core and the ice shell. To simplify the calculations, we assume that the internal density interfaces are spherical and the effective viscosity of water is equal to or greater than 100 Pa s. The method is used to study the effect of an unconsolidated core on tidal dissipation in Enceladus' ocean. We show that the partitioning of tidal heating between the core and the ocean strongly depends on the thickness of the ocean layer. If the ocean thickness is significantly greater than 1 km, heat production is dominated by tidal dissipation in the core and the amount of heat produced in the ocean is negligible. In contrast, when the ocean thickness is less than about 1 km, tidal heating in the core diminishes and dissipation in the ocean increases, leaving the total heat production unchanged. Extrapolation of our results to realistic conditions indicates that tidal flow is turbulent which suggests that the linearized Navier‐Stokes equation may not be appropriate for modeling the tidal response of icy moons. Finally, we compare our results with those obtained by solving the Laplace tidal equations and discuss the limitations of the two‐dimensional models of ocean circulation. Plain Language Summary: The origin of the heat powering Enceladus' geological activity and preventing its ocean from freezing has been debated since the discovery of a plume of icy particles above Enceladus' south pole in 2005. Here, we evaluate the heat generated by tides in Enceladus' ocean assuming that the internal density interfaces are spherical and the flow in the ocean is primarily driven by the deformation of Enceladus' unconsolidated core. We find that the heat production in the ocean can explain only a small fraction of Enceladus' heat budget under the present day conditions (i.e., for an ocean thickness of about 40 km) but can be as high as 25 GW if the thickness of the ocean layer is less than about 1 km. Analysis of the flow field suggests that the simplifying assumptions often used in previous studies may not be appropriate. In particular, we show that, regardless of ocean thickness, the dissipation rate obtained by solving the shallow water equations corrected for the dampening effect of the ice shell can be significantly different from that obtained by solving the three‐dimensional Navier‐Stokes equations. Key Points: The heat production in the ocean depends on the ocean thickness and the material properties of the coreDissipation is likely to be negligible for ocean thicknesses >1 km but can exceed 20 GW if the ocean is thin and the core is easy to deformThe shallow water approach, widely used in previous studies, can lead to incorrect results regardless of ocean thickness [ABSTRACT FROM AUTHOR]

Monthly 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. Key Points: Application of variance‐covariance information from ocean tide models in Level‐2 satellite gravity field processingReduction of temporal aliasing errors due to ocean tides in time‐varying gravity field solutionsEstimation of ocean tide parameters for an improved ocean tide background modeling [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

With the continued rise in global mean sea level, operational predictions of tidal height and total water levels have become crucial for accurate estimations and understanding of sea level processes. The Dutch Continental Shelf Model in Delft3D Flexible Mesh (DCSM-FM) is developed at Deltares to operationally estimate the total water levels to help trigger early warning systems to mitigate against these extreme events. In this study, a regional version of the Empirical Ocean Tide model for the Northwest European Continental Sea (EOT-NECS) is developed with the aim to apply better tidal forcing along the boundary of the regional DCSM-FM. EOT-NECS is developed at DGFI-TUM by using 30 years of multi-mission along-track satellite altimetry to derive tidal constituents which are estimated both empirically and semi-empirically. Compared to the global model, EOT20, EOT-NECS showed a reduction in the root-square-sum error for the eight major tidal constituents of 0.68 cm compared to in situ tide gauges. When applying constituents from EOT-NECS at the boundaries of DCSM-FM, an overall improvement of 0.29 cm was seen in the root-mean-square error of tidal height estimations made by DCSM-FM, with some regions exceeding a 1 cm improvement. Furthermore, of the fourteen constituents tested, eleven showed a reduction of RMS when included at the boundary of DCSM-FM from EOT-NECS. The results demonstrate the importance of using the appropriate tide model(s) as boundary forcings, and in this study, the use of EOT-NECS has a positive impact on the total water level estimations made in the northwest European continental seas. [ABSTRACT FROM AUTHOR]

The accurate estimation of ocean tide loading displacements is essential and necessary for geodesy, oceanic and geophysical studies. It is common knowledge that K1 and K2 tidal constituents estimated from Global Positioning System (GPS) observations are unsatisfactory because their tidal periods are nearly same to the revisit cycle or orbital period of GPS constellation. To date, this troublesome problem is not fully solved. In this paper, we revisit this important issue and develop a novel method based on the unique characteristic of tidal waves to separate GPS-system errors from astronomical K1/K2 tides. The well-known credo of smoothness indicates that tidal admittances of astronomical constituents in a narrow band can be expressed as smooth functions of tidal frequencies, while the interference of GPS-system errors seriously damages the smooth nature of observed tidal admittances. Via quadratic fitting, smooth functions of tidal frequencies for tidal admittances can be determined, thus, astronomical K1 and K2 tides can be interpolated using fitted quadratic functions. Three GPS stations are selected to demonstrate our method because of their typicality in terms of poor estimates of K1/K2 tidal parameters related to GPS-system errors. After removing GPS-systematical contributions based on our method, corrected K1/K2 tides at three GPS stations are much closer to the modeled K1/K2 tides from FES2014, which is one of the most accurate tide models. Furthermore, the proposed method can be easily applied to other areas to correct GPS-system errors because their smooth nature is valid for global tidal signals. [ABSTRACT FROM AUTHOR]

As one of the most vital passageways worldwide, the Panama Canal plays essential roles in global trade and maritime logistics. Sea levels around the Panama Canal are dominated by ocean tides but local tidal evolution is still unexplored to date, which motivates present study. Two secular tide gauges longer than 110 years (Cristobal and Balboa) around the Panama Canal are analyzed to explore multi-time scale tidal variability. It is found that observed nodal modulations of major constituents are generally consistent with the equilibrium tidal theory. M 4 and Mf nodal modulations notably deviate from the theory possibly due to non-linear processes. Long-term trends exist in main semi-diurnal tides, while main diurnal tides do not have significant secular trends. It is worth mentioning that M 4 and MS 4 amplitudes at Cristobal have halved in the past century. Moreover, tidal parameters of major constituents at Cristobal and Balboa show abnormal mutations in 1908, 1990–1998, and 2013–2018. As a result of changing tides, tidal asymmetries at Cristobal are significantly weakened while the number of high tides per year is notably decreased. Tides at Balboa are almost symmetric. Tidal regimes at Cristobal can periodically shift between mixed diurnal tides and mixed semi-diurnal tides following the 18.61-year nodal cycle. However, such regime shift has disappeared since 1997 due to secular negative trends in M 2 amplitudes. In general, the findings of this study can be helpful for ships navigating in the Panama Canal. • Long-term tidal evolution around the Panama Canal is explored. • Nodal modulations of main tides are generally consistent with the theory. • Main constituents at Cristobal and Balboa have abnormal mutations. • Both high and low tides at Cristobal and Balboa show significant increasing trends. [ABSTRACT FROM AUTHOR]

Titan’s ice shell floats on top of a global ocean, as revealed by the large tidal Love number k _2 = 0.616 ± 0.067 registered by Cassini. The Cassini observation exceeds the predicted k _2 by one order of magnitude in the absence of an ocean, and is 3 σ away from the predicted k _2 if the ocean is pure water resting on top of a rigid ocean floor. Previous studies demonstrate that an ocean heavily enriched in salts (salinity S ≳ 200 g kg ^−1 ) can explain the 3 σ signal in k _2 . Here we revisit previous interpretations of Titan’s large k _2 using simple physical arguments and propose a new interpretation based on the dynamic tidal response of a stably stratified ocean in resonance with eccentricity tides raised by Saturn. Our models include inertial effects from a full consideration of the Coriolis force and the radial stratification of the ocean, typically neglected or approximated elsewhere. The stratification of the ocean emerges from a salinity profile where the salt concentration linearly increases with depth. We find multiple salinity profiles that lead to the k _2 required by Cassini. In contrast with previous interpretations that neglect stratification, resonant stratification reduces the bulk salinity required by observations by an order of magnitude, reaching a salinity for Titan’s ocean that is compatible with that of Earth’s oceans and close to Enceladus’ plumes. Consequently, no special process is required to enrich Titan’s ocean to a high salinity as previously suggested.

The Gulf of Maine's lunar semidiurnal (M2) ocean tide exhibits spatially coherent amplitude changes of ∼1–3 cm on interannual time scales, though no causative mechanism has been identified. Here we show, using a specially designed numerical modeling framework, that stratification changes account for 32%–48% (Pearson coefficient 0.58–0.69) of the observed M2 variability at tide gauges from 1994 to 2019. Masking experiments and energy diagnoses reveal that the modeled variability is primarily driven by fluctuations in barotropic‐to‐baroclinic energy conversion on the continental slope south of the gulf's mouth, with a 1‐cm amplitude increase at Boston corresponding to a ∼7% (0.30 GW) drop in the area‐integrated conversion rate. Evidence is given for the same process to have caused the decade‐long M2 amplitude decrease in the Gulf of Maine beginning in 1980/81. The study has implications for nuisance flooding predictions and space geodetic analyses seeking highest accuracies. Plain Language Summary: The height of the twice‐daily tide at Boston is about 135 cm, but researchers have long noted that this value fluctuates by about 1–3 cm from year to year. Here we show that the annual tidal height changes—seen in fact throughout the Gulf of Maine—are closely linked to how seawater density is distributed three‐dimensionally in the region. In particular, as tidal currents enter the gulf over steep underwater topography, the vertical distribution of density determines how much of the incoming wave energy is scattered back as internal tides into the deeper Northwest Atlantic. In years where this conversion of wave energy drops by 7% from its nominal value of 4 Gigawatt, the surface tide at Boston typically increases by 1 cm. Climate‐induced changes in ocean temperature and density may strengthen or weaken the conversion effect and thus slightly alter the role of tides in coastal flood events. Key Points: We propagate the M2 tide through realistic, annually varying density structures (1993–2019) in a regional Gulf of Maine modelStratification changes explain 32%–48% of the observed, cm‐level M2 amplitude variability at coastal tide gauges from 1994 to 2019Modeled M2 changes mainly reflect fluctuations in the barotropic‐baroclinic energy conversion rate on the New England continental slope [ABSTRACT FROM AUTHOR]

Exact knowledge on the seasonal variations of main tidal constituents is beneficial for improving tidal prediction. The semi-annual cycles in K1 and S2 tides are abnormally exaggerated by astronomical P1 and K2 tides, which interferes with our understanding on tidal seasonality. The widely-used tidal inference method in previous studies cannot fully separate astronomical P1 and K2 tides from seasonal P1 and K2 tides due to inaccurate inference relationship. In this study, on the basis of the ‘credo of smoothness’ which indicates that tidal admittances are smooth functions of tidal frequencies, we develop a novel but simple method to address this intractable issue and applied this method to explore the seasonality of tidal currents observed in the deep Timor Passage at the depth of 1800m. We find that the timing and range of seasonal modulations of M2, S2, K1, and O1 tides are distinct. Annual variations in tidal currents are much stronger than semi-annual variations in tidal currents. The annual and semi-annual ranges of M2 tide can reach 2.69 cm/s and 1.51 cm/s, which are largest among main constituents. Although the annual range of K1 tide is only 1.85 cm/s, considering the relatively small amplitude of time-averaged K1 tide (2.87cm/s), K1 the most affected tide by the annual cycle. The seasonal cycles of semi-diurnal tides (M2 and S2) are basically synchronous while those of diurnal tides (K1 and O1) are generally out-of-phase. As a general method, the proposed method can be widely applied to other sea areas to explore local tidal seasonality.

To mitigate temporal aliasing effects in monthly mean global gravity fields from the GRACE and GRACE‐FO satellite tandem missions, both tidal and non‐tidal background models describing high‐frequency mass variability in atmosphere and oceans are needed. To quantify tides in the atmosphere, we exploit the higher spatial (31 km) and temporal (1 hr) resolution provided by the latest atmospheric ECMWF reanalysis, ERA5. The oceanic response to atmospheric tides is subsequently modeled with the general ocean circulation model MPIOM (in a recently revised TP10L40 configuration that includes the feedback of self‐attraction and loading to the momentum equations and has an improved bathymetry around Antarctica) as well as the shallow water model TiME (employing a much higher spatial resolution and more elaborate tidal dissipation than MPIOM). Both ocean models consider jointly the effects of atmospheric pressure variations and surface wind stress. We present the characteristics of 16 waves beating at frequencies in the 1–6 cpd band and find that TiME typically outperforms the corresponding results from MPIOM and also FES2014b as measured from comparisons with tide gauge data. Moreover, we note improvements in GRACE‐FO laser ranging interferometer range‐acceleration pre‐fit residuals when employing the ocean tide solutions from TiME, in particular, for the S1 spectral line with most notable improvements around Australia, India, and the northern part of South America. Plain Language Summary: In addition to many rather slow processes such as the melting of glaciers, rapid mass redistribution related to the weather also measurably affect the Earth's gravity field. The ability of monitoring liquid freshwater changes within the Earth system from the satellite gravity missions GRACE (2002–2017) and GRACE‐FO (since 2018) relies on accurate background models of mass variability in atmosphere and oceans for both tidal and non‐tidal processes. Atmospheric tides are primarily excited in the middle atmosphere by solar energy absorption at periods of 24 hr and its overtones. We find additional tidal signatures in the atmosphere excited by periodic deformations of both crust and sea‐surface of the Earth. We thus introduce here a new data set for the atmospheric tides and their corresponding oceanic response that features both more waves and higher accuracy than other background models previously used for the processing of GRACE and GRACE‐FO satellite gravimetry data. Key Points: Sixteen relevant tidal lines identified in hourly data from ERA5 atmospheric reanalysisDedicated simulations with a high‐resolution global hydrodynamic model to simulate ocean tides with atmospheric influenceNew tidal models reduce pre‐fit residuals in GRACE‐FO Laser Ranging Interferometer data [ABSTRACT FROM AUTHOR]

A constant tidal form factor, defined by the ratio of the sum of K 1 and O 1 tidal amplitudes to the sum of M 2 and S 2 tidal amplitudes, has been widely used to represent tidal feature for nearly 120 years. Tides can be classified as semi-diurnal, mixed semi-diurnal, mixed diurnal and diurnal regimes based on tidal form factors. It is well-known that K 1 and O 1 tidal amplitudes have significant 18.61-year nodal variations. Therefore, the relative strength of semi-diurnal and diurnal tides changes during the 18.61-year nodal cycle. Consequently, local tidal regimes in some sea areas are not fixed, but periodically change during the 18.61-year nodal cycle. Such periodical tidal regime shift cannot be reflected by constant tidal form factor, which motivates present research. The purpose of this study is to propose a time-varying tidal form factor which considers the 18.61-year nodal modulations of main constituents based on the equilibrium tidal theory. 1249 tide gauges and a global tide model (EOT20) derived from multi-satellite altimeters are used to detect potential tidal regime shift related to the 18.61-year nodal cycle in the global ocean. It is found that there are 154 tide gauges and 17.32% ocean grid points in EOT20 model which exist tidal regime shift caused by the 18.61-year nodal cycle. Tidal form factor can be modified by ∼17% during the 18.61-year cycle in the global ocean. Furthermore, the deviations between theoretical and actual nodal modulations in some coastal resonant areas do not significantly influence the calculation of temporal tidal form factors. • Constant tidal from factors cannot reflect periodically tidal regime shift. • A temporal tidal form factor is proposed. • Tidal regime shift related to the nodal cycle widely exists in the global ocean. [ABSTRACT FROM AUTHOR]

This paper presents a tidal current meter that is based on the inertial acceleration principle for offshore infrastructures in deep water. Focusing on the marine installations of the aquaculture industry, we studied the forces of tides at a depth of 15 m by measuring the acceleration. In addition, we used a commercial MEMS triaxial accelerometer to record the acceleration values. A prototype of the tidal measurement unit was developed and tested at a real offshore aquaculture infrastructure in Gran Canaria, which is one of the Canary Islands in the Atlantic Ocean. The proposed tidal measurement unit was used as a recorder to assess the complexity of measuring the frequency of tidal currents in the short (10 min), medium (one day) and long term (one week). The acquired data were studied in detail, in both the time and frequency domains, to determine the frequency of the forces that were involved. Finally, the complexity of the frequency measurements from the captured data was analyzed in terms of sampling ratio and recording duration, from the point of view of using our proposed measurement unit as an ultra-low-power embedded system. The proposed device was tested for more than 180 days using a lithium-ion battery. This working period was three times greater than the best alternative in the literature because of the ultra-low-power design of the on-board embedded system. The measurement accuracy error was lower than 1% and the resolution was 0.01 cm/s for the 0.8 m/s velocity scale. This performance was similar to the best Doppler solution that was found in the literature. [ABSTRACT FROM AUTHOR]

Permeability controls energy and matter fluxes in deep‐sea hydrothermal systems fueling a 'deep biosphere' of microorganisms. Here, we indirectly measure changes in sub‐seafloor crustal permeability, based on the tidal response of high‐temperature hydrothermal vents at the East Pacific Rise 9°50'N preceding the last phase of volcanic eruptions during 2005–2006. Ten months before the last phase of the eruptions, permeability decreased, first rapidly, and then steadily as the stress built up, until hydrothermal flow stopped altogether ∼2 weeks prior to the January 2006 eruption phase. This trend was interrupted by abrupt permeability increases, attributable to dike injection during last phase of the eruptions, which released crustal stress, allowing hydrothermal flow to resume. These observations and models suggest that abrupt changes in crustal permeability caused by magmatic intrusion and volcanic eruption can control first‐order hydrothermal circulation processes. This methodology has the potential to aid eruption forecasting along the global mid‐ocean ridge network. Plain Language Summary: Permeability governs how fluids such as water and melt flow beneath the seafloor, and is influenced by diverse magmatic, volcanic, and tectonic forces as new oceanic crust is formed and altered over time. Despite being a master variable controlling the fluxes of energy and matter in deep‐sea hydrothermal systems, permeability remains a poorly constrained hydrologic parameter of the oceanic crust. Here, we indirectly measure changes in crustal permeability for the first time, using the tidal response of high‐temperature hydrothermal vents on the East Pacific Rise at 9°50'N preceding the last phase of volcanic eruptions in 2005–2006. We show that abrupt changes in crustal permeability caused by magmatic intrusion and volcanic eruption can control first‐order hydrothermal circulation processes. Key Points: Hydrothermal vent fluid temperature data modeled with ocean tides reveal permeability changes associated with seafloor volcanic eruptionsChanges in crustal permeability caused by magmatic intrusion and volcanic eruption control first‐order hydrothermal circulation processesThis methodology expands the potential of forecasting seafloor eruptions along the global mid‐ocean ridge network [ABSTRACT FROM AUTHOR]

Ocean tide aliasing is one of the largest error sources in satellite gravimetry. Despite its importance, the aliasing mechanism of ocean tides in satellite gravimetry is only partially understood. This paper explains tidal aliasing as a two-step mechanism. The primary aliasing is caused by orbit undersampling of original tidal signals. The secondary aliasing is due to undersampling of the primary aliasing signals through gravity recovery in discrete time intervals. The two-step aliasing mechanism is demonstrated through a closed-loop numerical simulation. The aliasing of the tidal constituents M 2 , N 2 , S 2 , K 2 , O 1 , P 1 , Q 1 and K 1 in CHAMP, GOCE, GRACE and GRACE Follow-On missions is analysed. The primary alias periods of individual constituents change from a few to hundreds of days depending on the orbital geometry. The long-term S 2 aliasing may cause bias in gravity fields derived by GOCE data if the S 2 tide is not well-represented by the ocean tide model applied in the data processing. Comparing the primary aliasing properties of CHAMP with that of GRACE indicates that tuning orbit inclination can improve aliasing properties, i.e. shorter aliasing periods and less couplings with annual/semi-annual signals. The strict definition of secondary alias periods is compromised in case of GRACE and GRACE Follow-On due to non-constant recovery periods, which results in irregular sampling and blurs the sharp spectral lines that are described by the two-step mechanism. The two-step aliasing mechanism can also be used in understanding aliasing of other periodic signals observed by satellite gravimetry. [ABSTRACT FROM AUTHOR]

Several solar system moons harbor subsurface water oceans; extreme internal heating or solar irradiation can form magma oceans in terrestrial bodies. Tidal forces drive ocean currents, producing tidal heating that affects the thermal−orbital evolution of these worlds. If the outermost layers (ocean and overlying shell) are thin, tidal dynamics can be described using thin-shell theory. Previous work assumed that the ocean and shell's thickness and density are uniform. We present a formulation of thin-shell dynamics that relaxes these assumptions and apply it to several cases of interest. The tidal response of unstratified oceans of constant thickness is given by surface gravity and Rossby waves, which can resonate with the tidal force. The oceans of the outer solar system are too thick for gravity wave resonances, but high-amplitude Rossby waves can be excited in moons with high orbital obliquity. We find that meridional ocean thickness variations hinder the excitation of Rossby waves, decreasing tidal dissipation and increasing the inclination damping timescale, which allows us to reconcile the present inclination of the Moon with the existence of a past long-lived magma ocean and to explain the inclination of Titan and Callisto without invoking a recent excitation. Stratified oceans can support internal gravity waves. We show that dissipation due to internal waves can exceed that resulting from surface gravity waves. For Enceladus, it can be close to the moon’s thermal output, even if the ocean is weakly stratified. Shear due to internal waves can result in Kelvin–Helmholtz instabilities and induce ocean mixing.

Tidal modulation of ice streams and their adjacent ice shelves is a real‐world experiment to understand ice‐dynamic processes. We observe the dynamics of Priestley Glacier, Antarctica, using Terrestrial Radar Interferometry (TRI) and GNSS. Ocean tides are predominantly diurnal but horizontal GNSS displacements also oscillate semi‐diurnally. The oscillations are strongest in the ice shelf and tidal signatures decay near‐linearly in the TRI data over >10 km upstream of the grounding line. Tidal flexing is observed >6 km upstream of the grounding line including cm‐scale uplift. Tidal grounding line migration is small and <40% of the ice thickness. The frequency doubling of horizontal displacements relative to the ocean tides is consistent with variable ice‐shelf buttressing demonstrated with a visco‐elastic Maxwell model. Taken together, this supports previously hypothesized flexural ice softening in the grounding‐zone through tides and offers new observational constraints for the role of ice rheology in ice‐shelf buttressing. Plain Language Summary: Temperatures in Antarctica's interior are below zero, so that ice continuously accumulates through snowfall. This mass gain is balanced by ice transport from the interior toward the coast. There, floating ice shelves form on the ocean and ice is eventually lost through iceberg calving and ocean induced melting. Small changes in any of these processes impact global ocean circulation and mean sea level. The speed of the ice varies with ocean tides. We use a specialized instrument that detects this variability and tidal flexing area‐wide and every few hours. We find that although low‐ and high‐tide only occur once a day in this area, ice flow is largest twice a day. This can be explained because ice softens when it is flexed by the ocean tides so that it can flow episodically faster. This is important because the deformation of ice shelves determines to an extent the stability of the entire ice sheet. Key Points: Terrestrial radar interferometry and GNSS identify dynamic changes at Priestley Glacier, Antarctica, forced by diurnal ocean tidesHorizontal displacements vary semi‐diurnally, are strongest in the shelf and decay near‐linearly >10 km upstream of the grounding lineGrounding line migration is small and flexural softening in ice‐shelf shear margins can explain the semi‐diurnal ice flow component [ABSTRACT FROM AUTHOR]

• Three least square methods are compared. • Ridge regression can notably reduce the uncertainties of tidal estimates. • Ridge regression can solve the problem of over-fitting. • Ridge regression needs 75-h data to resolve eight main tides. To fully resolve eight major tides from short-term records, classical harmonic analysis model usually infers unresolved constituents with the help of inference relationships from nearby long-term tide gauges. Our previous study developed a modified harmonic analysis model using the credo of smoothness (i.e., MHACS) which can achieve this without inference relationships. Via introducing the inherent natural links between major tides, MHACS breaks the restrictions of the Rayleigh criterion and requires only ∼9-day hourly records to resolve eight major tides. However, when data length is shorter than 9 days, the results of MHACS become problematic due to over-fitting. In this study, we introduce ridge regression to replace ordinary least squares (OLS) in the MHACS. Practical experiments on short-term hourly tide gauge records and satellite altimeter observations indicate that ridge regression can effectively eliminate meaningless mathematical artifacts obtained by OLS. The minimum length of records for MHACS to resolve eight major tides dramatically decreases from ∼210 h to ∼75 h as a result of using ridge regression. It is also found that ridge regression can notably reduce the uncertainties of tidal estimates from MHACS. Moreover, other modified harmonic analysis models such as NS_TIDE designed for river tides also suffer from over-fitting which can be solved by ridge regression in a similar way. [ABSTRACT FROM AUTHOR]

The differential probability gain approach is used to estimate quantitatively the change in aftershock rate at various levels of ocean tides relative to the average rate model. An aftershock sequences are analyzed from two regions with high ocean tides, Kamchatka and New Zealand. The Omori-Utsu law is used to model the decay over time, hypothesizing an invariable spatial distribution. Ocean tide heights are considered rather than phases. A total of 16 sequences of M ≥6 aftershocks off Kamchatka and 15 sequences of M ≥6 aftershocks off New Zealand are examined. The heights of the ocean tides at various locations were modeled using FES 2004. Vertical stress changes due to ocean tides are here about 10–20 kPa, that is, at least several times greater than the effect due to Earth tides. An increase in aftershock rate is observed by more than two times at high water after main M ≥6 shocks in Kamchatka, with slightly less pronounced effect for the earthquakes of M = 7.8, December 15, 1971 and M = 7.8, December 5, 1997. For those two earthquakes, the maximum of the differential probability gain function is also observed at low water. For New Zealand, we also observed an increase in aftershock rate at high water after thrust type main shocks with M ≥6. After normal-faulting main shocks there was the tendency of the rate increasing at low water. For the aftershocks of the strike-slip main shocks we observed a less evident impact of the ocean tides on their rate. This suggests two main mechanisms of the impact of ocean tides on seismicity rate, an increase in pore pressure at high water, or a decrease in normal stress at low water, both resulting in a decrease of the effective friction in the fault zone.

Abstract The magnetic signatures of ocean $$\hbox {M}_{2}$$ M2 tides have been successfully detected by the low-orbit satellite missions CHAMP and Swarm. They have been also used to constrain the electrical conductivity in the uppermost regions of the Earth’s mantle. Here, we concentrate on the problem of accurate numerical modelling of tidally induced magnetic field, using two different three-dimensional approaches: the contraction integral equation method and the spherical harmonic-finite element method. In particular, we discuss the effects of numerical resolution, self-induction, the galvanic and inductive coupling between the oceans and the underlying mantle. We also study the applicability of a simplified two-dimensional approximation, where the ocean is approximated by a single layer with vertically averaged conductivity and tidal forcing. We demonstrate that the two-dimensional approach is sufficient to predict the large-scale tidal signals observable on the satellite altitude. However, for accurate predictions of $$\hbox {M}_{2}$$ M2 tidal signals in the areas with significant variations of bathymetry, and close to the coastlines, full three-dimensional calculations are required. The ocean–mantle electromagnetic coupling has to be treated in the full complexity, including the toroidal magnetic field generated by the vertical currents flowing from and into the mantle.

We derive an empirical model of the sub-daily polar motion (PM) based on the multi-GNSS processing incorporating GPS, GLONASS, and Galileo observations. The sub-daily PM model is based on 3-year multi-GNSS solutions with a 2 h temporal resolution. Firstly, we discuss differences in sub-daily PM estimates delivered from individual GNSS constellations, including GPS, GLONASS, Galileo, and the combined multi-GNSS solutions. Secondly, we evaluate the consistency between the GNSS-based estimates of the sub-daily PM with three independent models, i.e., the model recommended in the International Earth Rotation and Reference Systems Service (IERS) 2010 Conventions, the Desai–Sibois model, and the Gipson model. The sub-daily PM estimates, which are derived from system-specific solutions, are inherently affected by artificial non-tidal signals. These signals arise mainly from the resonance between the Earth rotation period and the satellite revolution period. We found strong spurious signals in GLONASS-based and Galileo-based results with amplitudes up to 30 µas. The combined multi-GNSS solution delivers the best estimates and the best consistency of the sub-daily PM with external geophysical and empirical models. Moreover, the impact of the non-tidal spurious signals in the frequency domain diminishes in the multi-GNSS combination. After the recovery of the tidal coefficients for 38 tides, we infer better consistency of the GNSS-based empirical models with the new Desai–Sibois model than the model recommended in the IERS 2010 Conventions. The consistency with the Desai–Sibois model, in terms of the inter-quartile ranges of tidal amplitude differences, reaches the level of 1.6, 5.7, 6.3, 2.2 µas for the prograde diurnal tidal terms and 1.2/2.1, 2.3/6.0, 2.6/5.5, 2.1/5.1 µas for prograde/retrograde semi-diurnal tidal terms, for the combined multi-GNSS, GPS, GLONASS, and Galileo solutions, respectively. [ABSTRACT FROM AUTHOR]

Primary and secondary microseism originating in the world oceans and peaking at around 14 and 7 s, respectively, characterize the Earth's background noise in that frequency range. Microseism generated in marginal seas with partly shorter periods and higher spatial and temporal variability is less studied and requires stations in immediate proximity to the source to be observed. Such studies can help to elucidate the exact microseism generation areas and mechanisms in a constrained area. We analyze 15 years of broadband data recorded at the seismic station on Helgoland island in the marginal North Sea. In addition to remote primary (RPM) and secondary microseism (RSM) originating in the North Atlantic, we observe strong and dominant local secondary microseism (LSM) with on average higher frequencies above 0.2 Hz, in accordance with shorter wave periods of about 4–8 s in the shallow North Sea. During times with low RSM activity we observe local primary microseism (LPM) at frequencies in agreement with local ocean wave periods. The higher horizontal to vertical (H/V) ratio of LPM with respect to LSM indicates a major non‐Rayleigh wave contribution. LSM and LPM show a strong modulation with local semidiurnal ocean tides and microseism energy maxima preceding the water level maximum by 2.5 and 1.5 hr, respectively. This time shift might be influenced by stronger currents during rising than falling tides. Active sources of tide‐modulated microseism migrate along the North Sea coast in sync with the ocean tidal signal as evidenced by comparison of LSM maxima at stations distributed along the coast. Key Points: At an island in the marginal North Sea, we observe strong local primary and secondary microseism at shorter periods than remote microseismLocal microseism exhibits a strong tidal modulation and high horizontal to vertical (H/V) ratios in the primary microseism signalThe source region of the tidal‐modulated local microseism seems to migrate in sync with the progression of the ocean tides Plain Language Summary: Ocean sea waves cause seismic waves in the solid earth. These seismic waves have either the same period or half that period. They are caused by interaction of water waves with shallow seafloor structures or the interference of waves with equal period and opposite propagation directions, respectively. The period of ocean waves depends, among other factors, on the size of the water body. A smaller water body causes shorter wave periods. At an island station in the North Sea, a marginal sea of the North Atlantic, we observe simultaneously seismic wave energy generated nearby in the North Sea and far away in the North Atlantic. The North Atlantic in general generates seismic waves with longer periods. We observe seismic waves with the period and half the period of water waves in the North Sea. In addition, a modulation of the locally generated seismic wave energy with ocean tides is observed. The sources of this tidal‐modulated energy move with the tidal front. This is interesting, as the exact conditions necessary to generate these seismic waves are not well understood. Our station location in direct vicinity to the generation area allows for the novel observations presented here. [ABSTRACT FROM AUTHOR]

Over the last years, the number of studies that investigate or utilize the electromagnetic (EM) signals generated by ocean tides is steadily growing. However, the majority of these studies focuses on the amplitudes of EM tidal signals. This study investigates the phases of EM tidal signals and their changes. Twenty‐six years of monthly observation‐based datasets of tidal velocities, geomagnetic field, and oceanic conductivity are fed into an EM induction solver to generate varying EM tidal signals. The sensitivities of the resulting EM signals are analyzed by forbidding or allowing the input datasets to vary in time. We report on the phase's sensitivities with respect to changes in the EM properties, that is, secular variation of the geomagnetic field and changes in oceanic conductivity. Distinct temporal behavior and distinct geographic pattern for the two sensitivities can be reported. In general, apart from global phase shifts of 3–5 degrees, concentrated areas with phase shifts of up to 45 degrees occur all over the globe, over the oceans, for example, Arctic and Atlantic Ocean, as well as on coastal land regions, for example, Southwest Greenland and Japan. Very locally, phase shifts of 90 degree or higher occur. Key Points: Electromagnetic tidal signals show significant spatiotemporal phase changesAnnual and monthly phase anomalies are found to be of oceanic originDecadal transient phase anomalies are generated by secular variation and changing oceanic conductivity [ABSTRACT FROM AUTHOR]

Exact tidal information is essential for multifarious human activities in the global ocean. Satellite altimeters especially Topex/Poseidon (T/P) and Jason series play fundamental roles in improving our understanding of global tides. Compared to T/P-Jason series, other satellite altimeters such as Geosat Follow-On (GFO) have been rarely used in tidal studies mainly due to their unfavorable aliasing features for tidal estimates. Classical harmonic analysis requires 12-year GFO records to fully resolve eight major tidal constituents while the longest GFO data is only 8-year. As a result, it is challenging for classical harmonic analysis to derive reliable tidal estimates from short GFO records. In this study, a modified tidal harmonic analysis algorithm based on the credo of smoothness (i.e. MHACS) is introduced to extract ocean tides from GFO records in the Bohai Sea. Via utilizing the inherent natural links between main constituents, MHACS breaks the constraint of the Rayleigh criterion and effectively solves tidal aliasing problems in GFO records. Practical experiments indicate that GFO-derived tidal constants via MHACS have high consistencies with the tidal theory and satellite-based EOT20 tidal model. Spatially-averaged vector difference between the EOT20 model and GFO results in the Bohai Sea is only 2.12 cm (eight major constituents averaged). Moreover, except for GFO, MHACS also has the potential to be applied to sun-synchronous satellites such as Envisat, Sentinel series, and Haiyang series. • CHA cannot derive reliable tidal estimates from short GFO data. • MHACS is introduced to extract ocean tides from GFO records. • MHACS effectively solves tidal aliasing problems in GFO records. • MHACS has the potential to be applied to sun-synchronous satellites. [ABSTRACT FROM AUTHOR]

Radiational tides derived from solar radiation are important components of ocean tides. Understanding dynamical features of radiational tides can be beneficial for further promoting the accuracy of water level prediction. Generally, radiational S 2 amplitudes are only 10%–30% of gravitational S 2 amplitudes, which has been verified by numerous studies. However, a previous study indicated that radidational S 2 amplitudes can reach 60% of gravitational S 2 amplitudes in the Gulf of Tonkin and related physical processes are unknown. In this paper, we revisit this abnormal phenomenon and find that such large radiational S 2 amplitudes are not real, but artifacts induced by the inadaptation of the method based on the credo of smoothness. Specifically, observed semi-diurnal tidal admittances in the Gulf of Tonkin are not smooth due to strong nonlinear interactions between large main diurnal tides. We quantitatively estimate and remove the contributions of quadratic and quartic nonlinear interactions to main semi-diurnal tides and find that the real ratio of radiational S 2 amplitude to astronomical S 2 amplitude is only 0.17 at Beihai, which is basically consistent with previous model results. Our study highlights the importance of eliminating the interference of nonlinear interactions to semi-diurnal tidal admittances in all diurnal resonant sea areas like the Gulf of Tonkin and the Gulf of Thailand when extracting radiational S 2 tides from sea level observations. • Large radiational S2 amplitudes in the Gulf of Tonkin are not real. • Observed semi-diurnal tidal admittances are distorted by nonlinear interactions. • Our method is universal for all diurnal resonant sea areas. [ABSTRACT FROM AUTHOR]

One of the fundamental problems of modern geodesy is precise defi nition of the gravitational fi eld and its changes in time. This is essential in positioning and navigation, geophysics, geodynamics, oceanography and other sciences related to the climate and Earth’s environment. One of the major sources of gravity data is satellite altimetry that provides gravity data with almost 75% surface of the Earth. Satellite altimetry also provides data to study local, regional and global geophysical processes, the geoid model in the areas of oceans and seas. This technique can be successfully used to study the ocean mean dynamic topography. The results of the investigations and possible products of altimetry will provide a good material for the GGOS (Global Geodetic Observing System) and institutions of IAS (International Altimetry Service). This paper presents the achievements in satellite altimetry in all the above disciplines obtained in the last years. First very shorly basic concept of satellite altimetry is given. In order to obtain the highest accuracy on range measurements over the ocean improved of altimetry waveforms performed on the ground is described. Next, signifi cant improvements of sea and ocean gravity anomalies models developed presently is shown. Study of sea level and its extremes examined, around European and Australian coasts using tide gauges data and satellite altimetry measurements were described. Then investigations of the phenomenon of the ocean tides, calibration of altimeters, studies of rivers and ice-sheets in the last years are given.

Satellite altimetry observations have provided a significant contribution to the understanding of global sea surface processes, particularly allowing for advances in the accuracy of ocean tide estimations. Currently, almost three decades of satellite altimetry are available which can be used to improve the understanding of ocean tides by allowing for the estimation of an increased number of minor tidal constituents. As ocean tide models continue to improve, especially in the coastal region, these minor tides become increasingly important. Generally, admittance theory is used by most global ocean tide models to infer several minor tides from the major tides when creating the tidal correction for satellite altimetry. In this paper, regional studies are conducted to compare the use of admittance theory to direct estimations of minor tides from the EOT20 model to identify which minor tides should be directly estimated and which should be inferred. The results of these two approaches are compared to two global tide models (TiME and FES2014) and in situ tide gauge observations. The analysis showed that of the eight tidal constituents studied, half should be inferred (2N2, ϵ2, MSF and T2), while the remaining four tides (J1, L2, μ2 and ν2) should be directly estimated to optimise the ocean tidal correction. Furthermore, for certain minor tides, the other two tide models produced better results than the EOT model, suggesting that improvements can be made to the tidal correction made by EOT when incorporating tides from the two other tide models. Following on from this, a new approach of merging tidal constituents from different tide models to produce the ocean tidal correction for satellite altimetry that benefits from the strengths of the respective models is presented. This analysis showed that the tidal correction created based on the recommendations of the tide gauge analysis provided the highest reduction of sea-level variance. Additionally, the combination of the EOT20 model with the minor tides of the TiME and FES2014 model did not significantly increase the sea-level variance. As several additional minor tidal constituents are available from the TiME model, this opens the door for further investigations into including these minor tides and optimising the tidal correction for improved studies of the sea surface from satellite altimetry and in other applications, such as gravity field modelling.

The paper deals with the themes of the Earth's orientation and rotation. The parameters of the Earth's orientation can be determined by several methods. The emphasis in this paper is the influence of ocean tides to determine the parameters of the Earth's orientation with one of the space-geodetic techniques, called Very long baseline interferometry (VLBI). After determining the parameters, the results obtained using the VLBI were compared between reference system VieVS and Vrf2008, as well as influence of ocean tides and without its impact. When processing the data, the obtained results were compared using different reference systems and various that influence their changes were analyzed. The used data belong to different series of programs that are continuously observed. The results are the product of software VieVS with data from a continuing series CONT14. [ABSTRACT FROM AUTHOR]

S 2 ocean tide, as one of the most important semi-diurnal constituents, is composed of astronomical S 2 tide originated from gravitational forcing and radiational S 2 tide derived from solar radiation. Although there are lots of researches which have explored the features of radiational S 2 tides in the globe, less known and less discussed, are the radiational S 2 tides in the East China Sea due to lack of water level observations. In present study, radiational S 2 tides in the East China Sea are estimated and discussed via the combination of 39 coastal tide gauges and EOT20 tidal model derived from multi-satellite altimeter records. We find that radiational S 2 tides obtained from tide gauges and satellite-derived EOT20 model are roughly consistent in the East China Sea: (1) The largest radiational S 2 amplitude can be as high as 14 cm. (2) Radiational and astronomical S 2 tidal amplitudes are large in the coastal zones but small in the open sea. (3) Radiational S 2 amplitudes are ∼12% of astronomical S 2 amplitudes while phase differences between radiational and astronomical S 2 tides are ∼114°. The inconsistency between coastal tide gauges and EOT20 model in coastal zones should be induced by the temporal evolution of tides and the inaccuracy of satellite altimeter observations in this region. Furthermore, the methods used in the East China Sea can be easily applied to other sea areas, except diurnal resonant sea areas where the smooth nature of semi-diurnal admittances may be corrupted by nonlinear interactions between anomalously large diurnal tides. • The largest radiational S 2 amplitude in the East China Sea can be as high as 14 cm. • Radiational S 2 tidal amplitudes are large in the coastal zones but small in the open sea. • Radiational S 2 amplitudes are ∼12% of astronomical S 2 amplitudes. • Phase differences between radiational and astronomical S 2 tides are ∼114°. [ABSTRACT FROM AUTHOR]

Tidal constants of major semi-diurnal and diurnal constituents are essential for understanding tidal features and long-term tidal prediction. Widely-used classical harmonic analysis (CHA) model requires at least half-year hourly sea level records to resolve eight major semi-diurnal and diurnal constituents based on the Rayleigh criterion. When the analyzed records are short (typically shorter than one month), most previous studies adopt tidal inference method to infer more constituents in the CHA model. The performance of tidal inference method depends on the accuracy of given inference relationships. In this paper, we propose a modified harmonic analysis model on the basis of the credo of smoothness (i.e. MHACS) which indicates inherent natural links between major astronomical diurnal and semi-diurnal constituents. In the CHA, tidal constituents are independent of each other and estimated individually. However, in the MHACS, major constituents are connected via smooth functions of frequency (linear or quadratic functions) indicated by the credo of smoothness. MHACS aims to determine such smooth functions via least squares and then calculate all major tides simultaneously. A series of ideal and practical experiments are conducted to examine the effectiveness of MHACS. It is found that MHACS can derive relatively accurate tidal constants of eight major tides from short-term hourly tide gauge records and satellite altimeter observations. As a general and understandable method, MHACS is easy to realize and can be widely used to analyze diverse tidal signals in the global ocean except diurnal resonant regions where semi-diurnal tidal admittances may be distorted by nonlinear interactions. Furthermore, it should be noted that widely-used tidal inference method can be considered as a special case of MHACS when tidal admittances are assumed as constant functions of frequency. • A modified tidal harmonic analysis model based on the rule of smoothness is proposed. • The new method can estimate accurate tidal constants from very short water level records. • The new method can be widely used in the global ocean except diurnal resonant sea areas. [ABSTRACT FROM AUTHOR]

Highlights • Oceanic tidal heating from eccentricity forcing is strongly suppressed on Enceladus and other small satellites by the ice shell's mechanical forcing. • For large satellites, oceanic tidal heating from eccentricity forcing is enhanced due to the ice shell's self-gravity. • An ice shell increases oceanic obliquity tide heating on most satellites, except Triton, due to self-gravity and the flow properties of Rossby-Haurwitz waves. • Non-linear tidal heating in barotropic ocean tides is still found to be small compared to radiogenic decay, except for Triton. • Dynamic tidal forcing drives a time-varying pressure excess at the ocean surface due to the restrictive nature of the ice shell. Abstract Subsurface ocean tides act as a mechanism to dissipate tidal energy in icy satellite interiors. We numerically model the effect of an ice shell on ocean tides using non-linear bottom drag for the first time. We demonstrate that subsurface oceans experience tidal pressurization due to the confining nature of the ice shell, and find that Enceladus' eccentricity forcing can generate up to 2.2 kPa of pressure excess at the ocean surface. Existing free-surface oceanic energy dissipation scaling laws are extended to subsurface oceans, and are benchmarked against our numerical results to within 10 %. We show that for the large bodies Ganymede, Europa and Titan, an ice shell increases eccentricity tidal heating due to self-gravity, whereas the shell's suppressive mechanical forcing reduces eccentricity tide dissipation on Enceladus and Dione by several orders of magnitude due to their high effective rigidities. In contrast, the ice shell enhances obliquity-forced dissipation in all satellites investigated, except Triton, because the largely divergence-free ocean response is unaffected by the shell's rigidity but is still enhanced by self-gravity. We conclude that the fundamental difference in ocean response to obliquity and eccentricity forcing, combined with self-gravity, results in increased obliquity heating and suppressed eccentricity heating in small satellites. For large satellites with low effective rigidities, the type of ocean response is less important because the shell's mechanical forcing has little impact on the flow, whereas self-gravity will enhance the response, and consequently dissipation, regardless of the forcing. Overall, obliquity tides are likely to dominate the tidal heating budget of icy satellite oceans, remaining the most prominent source of fluid dissipation in subsurface barotropic ocean tides. [ABSTRACT FROM AUTHOR]

Due to limit of coverage in TOPEX/Poseidon (T/P) satellite and sparseness of in-situ tide gauges around Antarctica, the accuracy of global ocean tide models in Antarctic seas is relatively poorer than in low- and mid-latitude regions. To better understand ocean tides in Prydz Bay, east Antarctica, a GPS receiver was deployed on floating sea ice to measure tide-induced ice motion in multiple campaigns. Four online Precise Point Positioning (PPP) services are used to process the GPS data in the kinematic PPP mode, and UTide software is used to separate the major tidal constituents. Comparison between results from different processing methods (relative processing solutions from Track, kinematic PPP solutions from online services) and with bottom pressure gauge (BPG) shows that, high-accuracy tidal information can be obtained from GPS observations on floating sea ice, the root-sum-square (RSS) for the eight major constituents (O1, K1, P1, Q1, M2, S2, N2, K2) is below 4 cm. We have also studied the impacts of data span and filter edge effects at daily boundaries on the accuracy of tide estimates, and found that to obtain reliable tide estimates and neglect the filter edge effects, continuous observation longer than 30 days is necessary. Our study suggests that GPS provides an independent method to estimate tides in Prydz Bay, and can be an alternative to tidal gauges, which are costly and hard to maintain in Antarctica. [ABSTRACT FROM AUTHOR]