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Vertical mixing is often regarded as the Achilles' heel of ocean models. In particular, few models include a comprehensive and energy‐constrained parameterization of mixing by internal ocean tides. Here, we present an energy‐conserving mixing scheme which accounts for the local breaking of high‐mode internal tides and the distant dissipation of low‐mode internal tides. The scheme relies on four static two‐dimensional maps of internal tide dissipation, constructed using mode‐by‐mode Lagrangian tracking of energy beams from sources to sinks. Each map is associated with a distinct dissipative process and a corresponding vertical structure. Applied to an observational climatology of stratification, the scheme produces a global three‐dimensional map of dissipation which compares well with available microstructure observations and with upper‐ocean finestructure mixing estimates. This relative agreement, both in magnitude and spatial structure across ocean basins, suggests that internal tides underpin most of observed dissipation in the ocean interior at the global scale. The proposed parameterization is therefore expected to improve understanding, mapping, and modeling of ocean mixing. Plain Language Summary When tidal ocean currents flow over bumpy seafloor, they generate internal tidal waves. Internal waves are the subsurface analog of surface waves that break on beaches. Like surface waves, internal tidal waves often become unstable and break into turbulence. This turbulence is a primary cause of mixing between stacked ocean layers—a key process regulating ocean currents and biology and a key ingredient of computer models of the global ocean. In this article, a three‐dimensional global map of mixing induced by internal tidal waves is presented. This map incorporates a large variety of energy pathways from the generation of tidal waves to turbulence, accounting for the conservation of energy. The map is compared to available observations of turbulence across the globe and found to reproduce with good fidelity the main patterns identified in observations. This relatively good agreement suggests that internal tidal waves are the main source of turbulence in the subsurface ocean and implies that the map may serve a range of applications. In particular, the three‐dimensional map provides an efficient and realistic means to represent mixing by internal tidal waves in global ocean models. Key Points A global three‐dimensional map of mixing induced by internal tides is presented The map can serve as a comprehensive and energy‐constrained tidal mixing parameterization in global ocean models The map compares well to available microstructure and upper‐ocean finestructure mixing estimates

For science applications of the gravity recovery and climate experiment (GRACE) monthly solutions, the GRACE estimates of C 20 (or J 2 ) are typically replaced by the value determined from satellite laser ranging (SLR) due to an unexpectedly strong, clearly non-geophysical, variation at a period of ∼ 160 days. This signal has sometimes been referred to as a tide-like variation since the period is close to the perturbation period on the GRACE orbits due to the spherical harmonic coefficient pair C 22 / S 22 of S2 ocean tide. Errors in the S2 tide model used in GRACE data processing could produce a significant perturbation to the GRACE orbits, but it cannot contribute to the ∼ 160-day signal appearing in C 20 . Since the dominant contribution to the GRACE estimate of C 20 is from the global positioning system tracking data, a time series of 138 monthly solutions up to degree and order 10 ( 10 × 10 ) were derived along with estimates of ocean tide parameters up to degree 6 for eight major tides. The results show that the ∼ 160-day signal remains in the C 20 time series. Consequently, the anomalous signal in GRACE C 20 cannot be attributed to aliasing from the errors in the S2 tide. A preliminary analysis of the cross-track forces acting on GRACE and the cross-track component of the accelerometer data suggests that a temperature-dependent systematic error in the accelerometer data could be a cause. Because a wide variety of science applications relies on the replacement values for C 20 , it is essential that the SLR estimates are as reliable as possible. An ongoing concern has been the influence of higher degree even zonal terms on the SLR estimates of C 20 , since only C 20 and C 40 are currently estimated. To investigate whether a better separation between C 20 and the higher-degree terms could be achieved, several combinations of additional SLR satellites were investigated. In addition, a series of monthly gravity field solutions ( 60 × 60 ) were estimated from a combination of GRACE and SLR data. The results indicate that the combination of GRACE and SLR data might benefit the resonant orders in the GRACE-derived gravity fields, but it appears to degrade the recovery of the C 20 variations. In fact, the results suggest that the poorer recovery of C 40 by GRACE, where the annual variation is significantly underestimated, may be affecting the estimates of C 20 . Consequently, it appears appropriate to continue using the SLR-based estimates of C 20 , and possibly also C 40 , to augment the existing GRACE mission.

This paper presents a study on depth modernization, paralleling height modernization for land elevations. Depth modernization integrates mean sea surface (MSS) models, ocean tide models, and precise ship positioning to achieve accurate seafloor depth measurements. Conventional methods rely on tidal corrections and chart datum from temporary tide gauges, which can be challenging in regions with complex tidal patterns and inconsistent chart datums. For depth modernization, we developed (1) a hybrid MSS model using satellite altimeter data, tide gauge records, and a regional geoid model, and (2) a hydrodynamic-driven ocean model with 26 tidal constituents to determine separations between the hybrid MSS and five tidal surfaces, resulting in five ellipsoid-based surfaces analogous to a geoid model for height modernization. Precise ship positioning is demonstrated using GNSS data collected by the Legend research ship in the Pacific Ocean east of Taiwan and the Canadian spatial reference system precise point positioning toolbox. We used measurements in the Taiwan Strait to show how modern depth is implemented. Comparisons of depths in four regions from the conventional and modern methods show small (a few cm) to moderate (a few dm) differences with some variability depending on the region and equipment. Discontinuities in depths from the conventional method are analyzed. Depth modernization has significantly benefited rapid and accurate bathymetric mapping for electronic navigation charts. Future work in MSS and ocean tide models and the availability of PPP tools for depth modernization are discussed. For mapping agencies worldwide, depth modernization should be prioritized alongside height modernization to ensure rapid and accurate depth data provision.

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

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.

Global Positioning System technique has been widely used to estimate ocean tide loading displacements, but classical harmonic analysis with satellite modulation typically disregards the effects of hundreds of minor tides within the same tidal species of major tides. We present an improved harmonic analysis of eight major tidal constituents (M2, S2, N2, K2, K1, O1, P1 and Q1) that are adjusted by more adjacent minor tides in semidiurnal and diurnal species than the usual satellite modulation approach, through the tidal admittance interpolation. Our results show that this approach allows for a more reliable determination of GPS-observed N2, Q1, P1 and S2 constituents in the northwest European shelf than the classical method, as demonstrated by a comparison with FES2014b and TPXO9-Atlas ocean tide model predictions. The advantages of our method are more pronounced in the harmonic analysis of GPS time series of short duration (1–2 years) than long duration. These improvements mainly depend on some inferred minor tides with larger equilibrium amplitudes, which provide effective admittance constraints to major tidal estimation. Among the major tidal estimates, the most significant improvement is seen for the N2 constituent (with the maximum improvement of 9.9%, 9.0% and 9.7% for the up, east and north components in terms of agreement with FES2014b model predictions), particularly along the Wadden Sea coast where significant satellite modulation deviations occur.

We seek to quantify and understand the residual signal in GPS and GLONASS estimates of ocean tide loading displacements (OTLDs) after removing state-of-the-art model estimates. To consider contributions over a broad spatial scale, we estimate OTLD over the Australian continent using ∼ 5.5 years of continuous GPS and GLONASS data from 360 sites. We compare these with modelled estimates, with a focus on the lunar semidiurnal M 2 and diurnal O 1 constituents. We observe spatially coherent patterns of residual OTLD in each of the east, north, and up coordinate components after the removal of tidal loading using elastic models. We subsequently assess the impact of including anelastic dispersion in the model and show a 0.2 mm reduction in range of the up component residuals at coastal sites. A similar reduction at all sites is observed in the east and north components. Of the seven ocean tide models used, we find that three recent models, FES2014b, GOT4.10c and TPXO9.v1, perform similarly, noting these comparisons are made in the CE frame. However, we show that the latter contains centre of mass (CoM) biases in amplitude up to 0.2 mm and 0.5 mm for M 2 and O 1 , respectively, due to the assimilated altimetry data having not been corrected for geocentre motion. We find OTLD estimates are sensitive to the chosen orbit and clock products used in our analysis, with differences of up to 0.5 mm in the east component between solutions using the JPL and either of ESA or CODE products (GPS-only). Our analysis shows that current GNSS estimates of OTLD over Australia are typically accurate to ∼ 0.2 mm at which point we are unable to explain spatially coherent residuals when compared to modelled quantities. These may depend on the appropriate treatment of the CoM variation, anelasticity and/or three-dimensional Earth structure. As such, we recommend great care is taken when interpreting OTLD at the level of 0.1 or 0.2 mm, even if it is regionally coherent.

Motional induction is the process by which the motion of conductive seawater in the ambient geomagnetic main field generates electromagnetic (EM) variations, which are observable on land, at the seafloor, and sometimes at satellite altitudes. Recent years have seen notable progress in our understanding of motional induction associated with tsunamis and with ocean tides. New studies of tsunami motional induction were triggered by the 2004 Sumatra earthquake tsunami and further promoted by subsequent events, such as the 2010 Chile earthquake and the 2011 Tohoku earthquake. These events yielded observations of tsunami-generated EM variations from land and seafloor stations. Studies of magnetic fields generated by ocean tides attracted interest when the Swarm satellite constellation enabled researchers to monitor tide-generated magnetic variations from low Earth orbit. Both avenues of research benefited from the advent of sophisticated seafloor instruments, by which we may exploit motional induction for novel applications. For example, seafloor EM measurements can serve as detectors of vector properties of tsunamis, and seafloor EM data related to ocean tides have proved useful for sounding Earth’s deep interior. This paper reviews and discusses the progress made in motional induction studies associated with tsunamis and ocean tides during the last decade.

A modern third-generation interferometric water level tilt meter was developed at the Finnish Geodetic Institute in 2000. The tilt meter has absolute scale and can do high-precision tilt measurements on earth tides, ocean tide loading and atmospheric loading. Additionally, it can be applied in various kinds of geodynamic and geophysical research. The principles and results of the historical 100-year-old Michelson–Gale tilt meter, as well as the development of interferometric water tube tilt meters of the Finnish Geodetic Institute, Finland, are reviewed. Modern Earth tide model tilt combined with Schwiderski ocean tide loading model explains the uncertainty in historical tilt observations by Michelson and Gale. Earth tide tilt observations in Lohja2 geodynamic station, southern Finland, are compared with the combined model earth tide and four ocean tide loading models. The observed diurnal and semidiurnal harmonic constituents do not fit well with combined models. The reason could be a result of the improper harmonic modelling of the Baltic Sea tides in those models.

A global ocean tide model (NAO.99b model) representing major 16 constituents with a spatial resolution of 0.5° has been estimated by assimilating about 5 years of TOPEX/POSEIDON altimeter data into barotropic hydrodynamical model. The new solution is characterized by reduced errors in shallow waters compared to the other two models recently developed; CSR4.0 model (improved version of Eanes and Bettadpur, 1994) and GOT99.2b model (Ray, 1999), which are demonstrated in comparison with tide gauge data and collinear residual reduction test. This property mainly benefits from fine-scale along-track tidal analysis of TOPEX/POSEIDON data. A high-resolution (1/12°) regional ocean tide model around Japan (NAO.99Jb model) by assimilating both TOPEX/POSEIDON data and 219 coastal tide gauge data is also developed. A comparison with 80 independent coastal tide gauge data shows the better performance of NAO.99Jb model in the coastal region compared with the other global models. Tidal dissipation around Japan has been investigated for M2 and K1 constituents by using NAO.99Jb model. The result suggests that the tidal energy is mainly dissipated by bottom friction in localized area in shallow seas; the M2 ocean tidal energy is mainly dissipated in the Yellow Sea and the East China Sea at the mean rate of 155 GW, while the K1 energy is mainly dissipated in the Sea of Okhotsk at the mean rate of 89 GW. TOPEX/POSEIDON data, however, detects broadly distributed surface manifestation of M2 internal tide, which observationally suggests that the tidal energy is also dissipated by the energy conversion into baroclinic tide.