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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]

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]

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]

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]

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]

The resonance associated with the ellipticity of the core-mantle boundary is usually measured with observations of either the Earth’s nutations, or of tidal gravity, strain, or tilt. But, improbably, it can also be seen in a dataset collected and processed with older and simpler technologies: the harmonic constants for the ocean tides. One effect of the resonance is to decrease the ratio of the amplitude of the P1 constituent to the amplitude of the K1 constituent to 0.96 of the ratio in the equilibrium tidal potential. The compilation of ocean-tide harmonic constants prepared by the International Hydrographic Bureau between 1930 and 1980 shows considerable scatter in this ratio; however, if problematic stations and regions are removed, this dataset clearly shows a decreased ratio. While these data apply only a weak constraint to the frequency of the resonance, they also show that the effect could have been observed long before it actually was. [ABSTRACT FROM AUTHOR]

We present results from the generation of 10-year-long continuous time series of the Earth's polar motion at 15-min temporal resolution using Global Positioning System ground data. From our results, we infer an overall noise level in our high-rate polar motion time series of 60 $$\upmu \hbox {as}$$ (RMS). However, a spectral decomposition of our estimates indicates a noise floor of 4 $$\upmu \hbox {as}$$ at periods shorter than 2 days, which enables recovery of diurnal and semidiurnal tidally induced polar motion. We deliberately place no constraints on retrograde diurnal polar motion despite its inherent ambiguity with long-period nutation. With this approach, we are able to resolve damped manifestations of the effects of the diurnal ocean tides on retrograde polar motion. As such, our approach is at least capable of discriminating between a historical background nutation model that excludes the effects of the diurnal ocean tides and modern models that include those effects. To assess the quality of our polar motion solution outside of the retrograde diurnal frequency band, we focus on its capability to recover tidally driven and non-tidal variations manifesting at the ultra-rapid (intra-daily) and rapid (characterized by periods ranging from 2 to 20 days) periods. We find that our best estimates of diurnal and semidiurnal tidally induced polar motion result from an approach that adopts, at the observation level, a reasonable background model of these effects. We also demonstrate that our high-rate polar motion estimates yield similar results to daily-resolved polar motion estimates, and therefore do not compromise the ability to resolve polar motion at periods of 2-20 days. [ABSTRACT FROM AUTHOR]

The ring laser gyroscope (RLG) technique has been investigated for about 20 years as a potential complement to space geodetic techniques in measuring variations of Earth rotation. The technique is of great interest, especially in the context of monitoring rapid changes of rotation with sub-daily resolution. In this paper, we review how the known high frequency signals in Earth rotation parameters, including the so-called diurnal polar motion, diurnal and semidiurnal ocean tide effects in polar motion and UT1 and librations, prograde diurnal in polar motion and semidiurnal in UT1, contribute to the RLG observable, the Sagnac frequency. Our results suggest that at the current accuracy level of the technique, the signals coming from diurnal polar motion and ocean tides should be taken into account in analysis while the influence of libration can be neglected. We also point out that the contributing signals are superimposed upon each other and can hardly be separated from the data from a single instrument. Our computations are done taking parameters of the RLG at the Wettzell Observatory in Germany. However, we also consider how the strength of a particular signal depends on the geographic location of a horizontally mounted instrument. Finally, we discuss the relationship between the geographical location and terrestrial orientation of RLG and its consequence for the observed Sagnac signal. [ABSTRACT FROM AUTHOR]

Traditionally, ocean tides have been modeled in frequency domain with a forcing from selected tidal constituents. It is a natural approach; however, it implicitly neglects non-linearities of ocean dynamics. An alternative approach is time-domain modeling with a forcing given by the full lunisolar potential, i.e., all tidal waves are a priori included. This approach has been applied in several ocean tide models; however, some challenging tasks still remain, for example, assimilation of satellite altimetry data. In this paper, we introduce the assimilative scheme applicable in a time-domain model, which is an alternative to existing techniques used in assimilative ocean tide models. We present results from DEBOT, a global barotropic ocean tide model, which has two modes: DEBOT-h, a purely hydrodynamical mode, and DEBOT-a, an assimilative mode. The accuracy of DEBOT in both modes is assessed through a series of tests against tide gauge data which demonstrate that DEBOT is comparable to state-of-the-art global ocean tide models for major tidal constituents. Furthermore, as signals of all tidal frequencies are included in DEBOT, we also discuss modeling of minor tidal constituents and non-linear compound tides. Our modeling approach can be useful for those applications where the frequency domain approach is not suitable. [ABSTRACT FROM AUTHOR]

This paper discusses the differences between mean tide level (MTL) and mean sea level (MSL) as demonstrated using information from a global tide gauge data set. The roles of the two main contributors to differences between MTL and MSL (the M4 harmonic of the M2 semidiurnal tide, and the combination of the diurnal tides K1 and O1) are described, with a particular focus on the spatial scales of variation in MTL-MSL due to each contributor. Findings from the tide gauge data set are contrasted with those from a state-of-the-art global tide model. The study is of interest within tidal science, but also has practical importance regarding the type of mean level used to define land survey datums. In addition, an appreciation of MTL-MSL difference is important in the use of the historical sea level data used in climate change research, with implications for some of the data stored in international databanks. Particular studies are made of how MTL and MSL might differ through the year, and if MTL is measured in daylight hours only, as has been the practice of some national geodetic agencies on occasions in the past. [ABSTRACT FROM AUTHOR]

Diurnal S $$_1$$ tidal oscillations in the coupled atmosphere-ocean system induce small perturbations of Earth's prograde annual nutation, but matching geophysical model estimates of this Sun-synchronous rotation signal with the observed effect in geodetic Very Long Baseline Interferometry (VLBI) data has thus far been elusive. The present study assesses the problem from a geophysical model perspective, using four modern-day atmospheric assimilation systems and a consistently forced barotropic ocean model that dissipates its energy excess in the global abyssal ocean through a parameterized tidal conversion scheme. The use of contemporary meteorological data does, however, not guarantee accurate nutation estimates per se; two of the probed datasets produce atmosphere-ocean-driven S $$_1$$ terms that deviate by more than 30 $$\upmu $$ as (microarcseconds) from the VLBI-observed harmonic of $$-16.2+i113.4$$ $$\upmu $$ as. Partial deficiencies of these models in the diurnal band are also borne out by a validation of the air pressure tide against barometric in situ estimates as well as comparisons of simulated sea surface elevations with a global network of S $$_1$$ tide gauge determinations. Credence is lent to the global S $$_1$$ tide derived from the Modern-Era Retrospective Analysis for Research and Applications (MERRA) and the operational model of the European Centre for Medium-Range Weather Forecasts (ECMWF). When averaged over a temporal range of 2004 to 2013, their nutation contributions are estimated to be $$-8.0+i106.0$$ $$\upmu $$ as (MERRA) and $$-9.4+i121.8$$ $$\upmu $$ as (ECMWF operational), thus being virtually equivalent with the VLBI estimate. This remarkably close agreement will likely aid forthcoming nutation theories in their unambiguous a priori account of Earth's prograde annual celestial motion. [ABSTRACT FROM AUTHOR]

Satellite Laser Ranging (SLR) to LAGEOS has a remarkable contribution to high-precise geodesy and geodynamics through deriving and validating various global geophysical models. This paper validates ocean tide models based on the analysis of satellite altimetry data, coastal tide gauges, and hydrodynamic data, i.e., CSR3.0, TOPEX4.0, CSR4.0A, FES2004, GOT00.2, and the CSRC Schwiderski model. LAGEOS orbits and SLR observation residuals from solutions based on different ocean tide models are compared and examined. It is found that LAGEOS orbits are sensitive to tidal waves larger than 5 mm. The analysis of the aliasing periods of LAGEOS orbits and tidal waves reveals that, in particular, the tidal constituent S2 is not well established in the recent ocean tide models. Some of the models introduce spurious peaks to empirical orbit parameters, which can be associated with S2, Sa, and K2 tidal constituents, and, as a consequence, can be propagated to fundamental parameters derived from LAGEOS observations [ABSTRACT FROM AUTHOR]

We show that the current levels of accuracy being achieved for the precise orbit determination (POD) of low-Earth orbiters demonstrate the need for the self-consistent treatment of tidal variations in the geocenter. Our study uses as an example the POD of the OSTM/Jason-2 satellite altimeter mission based upon Global Positioning System (GPS) tracking data. Current GPS-based POD solutions are demonstrating root-mean-square (RMS) radial orbit accuracy and precision of $${<}1$$ cm and 1 mm, respectively. Meanwhile, we show that the RMS of three-dimensional tidal geocenter variations is $${<}6$$ mm, but can be as large as 15 mm, with the largest component along the Earth's spin axis. Our results demonstrate that GPS-based POD of Earth orbiters is best performed using GPS satellite orbit positions that are defined in a reference frame whose origin is at the center of mass of the entire Earth system, including the ocean tides. Errors in the GPS-based POD solutions for OSTM/Jason-2 of $${<}4$$ mm (3D RMS) and $${<}2$$ mm (radial RMS) are introduced when tidal geocenter variations are not treated consistently. Nevertheless, inconsistent treatment is measurable in the OSTM/Jason-2 POD solutions and manifests through degraded post-fit tracking data residuals, orbit precision, and relative orbit accuracy. For the latter metric, sea surface height crossover variance is higher by $$6~\hbox {mm}^{2}$$ when tidal geocenter variations are treated inconsistently. [ABSTRACT FROM AUTHOR]

The seasonal cycle of the main lunar tidal constituent M is studied globally by an analysis of a high-resolution ocean circulation and tide model (STORMTIDE) simulation, of 19 years of satellite altimeter data, and of multiyear tide-gauge records. The barotropic seasonal tidal variability is dominant in coastal and polar regions with relative changes of the tidal amplitude of 5-10 %. A comparison with the observations shows that the ocean circulation and tide model captures the seasonal pattern of the M tide reasonably well. There are two main processes leading to the seasonal variability in the barotropic tide: First, seasonal changes in stratification on the continental shelf affect the vertical profile of eddy viscosity and, in turn, the vertical current profile. Second, the frictional effect between sea-ice and the surface ocean layer leads to seasonally varying tidal transport. We estimate from the model simulation that the M tidal energy dissipation at the sea surface varies seasonally in the Arctic (ocean regions north of 60°N) between 2 and 34 GW, whereas in the Southern Ocean, it varies between 0.5 and 2 GW. The M internal tide is mainly affected by stratification, and the induced modified phase speed of the internal waves leads to amplitude differences in the surface tide signal of 0.005-0.0150 m. The seasonal signals of the M surface tide are large compared to the accuracy demands of satellite altimetry and gravity observations and emphasize the importance to consider seasonal tidal variability in the correction processes of satellite data. [ABSTRACT FROM AUTHOR]

method of analyzing GRACE satellite-to-satellite ranging data is presented which accentuates signals from diurnal ocean tides and dampens signals from long-period non-tidal phenomena. We form a time series of differences between two independent monthly mean gravity solutions, one set computed from range-rate data along strictly ascending arcs and the other set computed from data along descending arcs. The solar and lunisolar diurnal tides having alias periods longer than a few months, such as K, P, and S, present noticeable variations in the monthly ascending and descending 'difference' solutions, while the climate-related signals are largely cancelled. By computing tidal arguments evaluated along the actual GRACE orbits, we decompose and estimate residual tidal signals with respect to our adopted prior model GOT4.7. The adjustment in the tidal height is small yet significant, yielding maximum amplitudes of 4 cm mostly under the Antarctic ice shelves and ~1 cm in general at spatial scales of several hundred kilometer. Moreover, the results suggest there are possible 1-cm errors in the tide model even over oceans well-covered by decades of radar altimetry missions. Independent validation of such small adjustments covering wide areas, however, is difficult, particularly with limited point measurements such as tide gauge. [ABSTRACT FROM AUTHOR]

Tidal currents and surface amplitudes are calculated globally for the dominating diurnal and semidiurnal constituents using an established tidal model under a range of altered bathymetry. The purpose is to evaluate if the well-known amplification of the global tides during the Last Glacial Maximum (LGM) is related to changed propagation properties for the tidal wave or to changed damping due to removal of shelf seas. The response of the tides and tidal dissipation to future sea-level rise is also discussed. The tides in the present and LGM oceans were simulated first, followed by runs where the present day bathymetry was used but the shelf seas removed by the introduction of vertical walls or where sea level is allowed to rise. Previously reported results regarding tidal amplitudes and dissipation rates are reproduced in the control runs. The runs without shelf seas show significantly enhanced tidal amplitudes in the North Atlantic, whereas sea-level rise of 5 m above present levels show a significant shift in the amphidromic points on a local and regional scale but had a limited effect on the open ocean tides. Simulations with very large sea-level rise show a significantly decreased global tidal dissipation, whereas experiments without friction in present-day shallow water display results similar to those with no shelf seas. The results all point towards changing damping properties due to the removal of shelf seas as being the mechanism behind the LGM amplification, and they imply the importance of implementing future sea-level changes properly in tidal simulations. [ABSTRACT FROM AUTHOR]

By exchanging angular momentum with the solid earth, tidal variations in ocean currents and sea level cause the rotation of the solid earth to change. Observations of earth rotation variations can therefore be used to evaluate ocean tide models. The rotational predictions of a spherical harmonic ocean tide model that is not constrained by any type of data are compared here to the predictions of numerical ocean tide models and to earth rotation observations from which atmospheric and non-tidal oceanic effects have been removed. The spherical harmonic ocean tide model is shown to account for the observed variations at the fortnightly tidal period in polar motion excitation but not in length-of-day. Overall, its long-period polar motion excitation predictions fit the observed tidal signals better than do the predictions of the numerical ocean tide models studied here. It may be possible to improve its agreement with length-of-day observations by tuning certain model parameters, as was done to obtain the close agreement reported here between the modeled and observed polar motion excitation; alternatively, the discrepancy in length-of-day may point to the need to revise current models of mantle anelasticity and/or models of the oceanic response to atmospheric pressure variations. [ABSTRACT FROM AUTHOR]

We study the ratio between the gravity variation and vertical displacement on the surface of a self-gravitating earth model when a surface load is applied. We adopt a theoretical and numerical point of view, excluding any observations. First, we investigate the spectral behavior of the ratio of the harmonic components of the gravity variation and vertical displacement. Then, we model the gravity-to-height ratio for different surface loads (continental hydrology, atmospheric pressure, ocean tides) using outputs of global numerical models in order to relate the predicted spatial values to theoretical mean values deduced from the spectral domain. For locations inside loaded areas, the ratio is highly variable because of the Newtonian attraction of the local masses and depends on the size of the load. For the hydrological loading (soil moisture and snow), the mean ratio over the continents is −0.87 μGal mm−1, but increases with decreasing size of the river basins. For the atmospheric loading, assuming an inverted-barometer response of the ocean, the ratio is positive, with larger values for high latitudes (0.49 μGal mm−1)—particularly on the coasts—than for lower latitudes (0.30 μGal mm−1). The ratio, however, is much less variable outside the loaded areas: in desert areas such as the Sahara and Arabia, its mean value is −0.28 μGal mm−1. For the ocean tidal loading, we find a mean ratio of −0.26 μGal mm−1 over the continents for the diurnal tidal waves. Both results are close to the theoretical mean value of −0.26 μGal mm−1 combining elastic and remote attraction contributions. [ABSTRACT FROM AUTHOR]

The GRACE mission will map the Earth's gravity fields and its variations with unprecedented accuracy during its 5-year lifetime. Unless ocean tide signals and their load upon the solid earth are removed from the GRACE data, their long period aliases obscure more subtle climate signals which GRACE aims at. In this analysis the results of Knudsen and Andersen (2002) have been verified using actual post-launch orbit parameter of the GRACE mission. The current ocean tide models are not accurate enough to correct GRACE data at harmonic degrees lower than 47. The accumulated tidal errors may affect the GRACE data up to harmonic degree 60. A study of the revised alias frequencies confirm that the ocean tide errors will not cancel in the GRACE monthly avenged temporal gravity fields. The S2 and the K2 terms have alias frequencies much longer than 30 days, so they remain almost unreduced in the monthly averages. Those results have been verified using a simulated 30 days GRACE orbit. The results show that the magnitudes of the monthly averaged values are slightly higher than the previous values. This may be caused by insufficient sampling to hilly resolve and reduce the tidal signals at short wavelengths and close to the poles. [ABSTRACT FROM AUTHOR]

An analytical gravitational perturbation theory for the intersatellite tracking range and range-rate measurement between two satellites is developed. The satellite-to-satellite tracking (SST) range data measure the difference between the position perturbations of two satellites along the direction of the intersatellite range. The SST range-rate data measure the difference between the velocity perturbations along the direction of the intersatellite range, and the difference of the position perturbation along the direction perpendicular to the intersatellite range (cross-range). The SST range and range rate depend on different orbital excitations for mapping the gravity field. For the Gravity Recovery and Climate Experiment (GRACE), approximately 97% of the geopotential coefficient pairs produce perturbations with a root-mean-square larger than 1 m on the range and 0.1 m/sec on the range rate based on the EGM96 gravity field truncated at degree and order 140. Results in this study showed that ocean tides produce significant perturbations in the range and range-rate measurements. An ocean tide field with a higher degree and order (>70) is required to model the ocean tide perturbations on the intersatellite range and range-rate measurement. [ABSTRACT FROM AUTHOR]

The solutions of the CODE Analysis Center submitted to the IGS, the International Global Position System (GPS) Service for Geodynamics, are based on three days of observation of about 80–100 stations of the IGS network. The Earth rotation parameters (ERPs) are assumed to vary linearly over the three days with respect to an a priori model. Continuity at the day boundaries as well as the continuity of the first derivatives are enforced by constraints. Since early April 1995 CODE has calculated a new ERP series with an increased time resolution of 2 hours. Again continuity is enforced at the 2-hours-interval boundaries. The analysis method is described, particularly how to deal with retrograde diurnal terms in the ERP series which may not be estimated with satellite geodetic methods. The results obtained from the first year of data covered by the time series (time interval from 4 April 1995 to 30 June 1996) are also discussed. The series is relatively homogeneous in the sense of the used orbit model and the a priori model for the ERPs. The largest source of excitation at daily and sub-daily periods is likely to be the effect of the ocean tides. There is good agreement between the present results and Topex/Poseidon ocean tide models, as well as with models based on Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging (SLR) data. Non-oceanic periodic variations are also observed in the series. Their origin is most probably a consequence of the GPS solution strategy; other possible sources are the atmospheric tides. [ABSTRACT FROM AUTHOR]

A short general explanation of tidal forces and tidal effects is given. The influences of Earth tides and ocean tides on the Earth's rotation vector are presented. Today, the theoretical models for periodic variations in the Earth's rotation and in polar motion can be compared with precise measurements done by modern space techniques. Secular changes of the Earth's rotation due to interactions within the Earth-Moon-system are also discussed. [ABSTRACT FROM AUTHOR]

The magnetic signatures of ocean 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 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. [ABSTRACT FROM AUTHOR]