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Abstract 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.

Abstract 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.

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.

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.

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 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.

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.

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.

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.

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.

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.

Ocean tides, and the atmospherically forced oceanic general circulation and its associated mesoscale eddy field, have long been run separately in high-resolution global models. They are now being simulated concurrently in a high-resolution version of the HYbrid Coordinate Ocean Model (HYCOM). The incorporation of horizontally varying stratification with the addition of atmospheric forcing yields internal tides (internal waves of tidal frequency) in high-latitude, low-stratification regions that are qualitatively different from those in earlier global internal tide models, in which atmospheric forcing and horizontally variable stratification were absent. The internal tides in the new concurrent HYCOM simulations compare well with those measured in along-track satellite altimeter data. The new concurrent simulations demonstrate that the wavenumber spectrum of sea surface height—a measure of the energy contained in different length scales—is dominated in some locations by internal tides and in others by mesoscale eddies. Tidal kinetic energies in the new concurrent simulations compare well with those in current-meter observations, as long as sufficient spatial averaging is performed. The new concurrent simulations are being used in the planning of future-generation satellite altimeters, in the provision of boundary conditions for coastal ocean models, and in studies of ocean mixing.

Since the launch of the first altimetry satellites, ocean tide models have been improved dramatically for deep and shallow waters. However, issues are still found for areas of great interest for climate change investigations: the coastal regions. The purpose of this study is to analyze the influence of the ALES coastal retracker on tide modeling in these regions with respect to a standard open ocean retracker. The approach used to compute the tidal constituents is an updated and along-track version of the Empirical Ocean Tide model developed at DGFI-TUM. The major constituents are derived from a least-square harmonic analysis of sea level residuals based on the FES2014 tide model. The results obtained with ALES are compared with the ones estimated with the standard product. A lower fitting error is found for the ALES solution, especially for distances closer than 20 km from the coast. In comparison with in situ data, the root mean squared error computed with ALES can reach an improvement larger than 2 cm at single locations, with an average impact of over 10% for tidal constituents K 2 , O 1 , and P 1 . For Q 1 , the improvement is over 25%. It was observed that improvements to the root-sum squares are larger for distances closer than 10 km to the coast, independently on the sea state. Finally, the performance of the solutions changes according to the satellite’s flight direction: for tracks approaching land from open ocean root mean square differences larger than 1 cm are found in comparison to tracks going from land to ocean.