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The aim of the present work is to show the existence of symmetric periodic solutions of a class of perturbed generalized Galatic-Tidal models. Combining the discrete symmetries of the Hamiltonian and the Poincaré’s continuation method, we give sufficient conditions over the parameters of the problem, for the existence of symmetric periodic solutions. Moreover, we determine the linear stability of these symmetric periodic solutions.

We report on the results of about 9 months of gravimetric recordings acquired at Mt. Somma-Vesuvius (SV) volcano (Southern Italy) with the new generation relative gravimeter gPhoneX#116 (gPh#116), which is a gravimeter specifically designed for continuous gravity recording. We also present the outcomes of an intercomparison experiment of the gPhone#116 conducted at the J9 gravity observatory in Strasbourg (France). In this intercomparison, we were able to check the scale factor of the meter with a high degree of precision by means of an intercomparison with 2 superconducting gravimeters (SGs) and a FG5-type absolute ballistic gravimeter. Multiple calibration approaches allowed us to validate the manufacturer's original calibration constants to a level of 1% accuracy and 0.1% precision. Moreover, we carried out a comparative study of the noise level of the gPh#116 with respect to the SGs and other spring meters routinely used in both prospecting and time-lapse gravimetry. It turns out that gPh#116 exhibits lower levels at hourly time-scales than other compared spring gravimeters (Graviton, gPhone#054, Scintrex-CG5). It was also possible to carry out a detailed study of the instrumental drift, a crucial topic for reliable monitoring of the long-term gravity variations in active volcanic areas. In fact, a challenge in time-lapse gravimetry is the proper separation of the instrumental variations from real gravity changes eventually attributable to recharge or drainage processes of magma or fluids in the feeding systems of active volcanoes. A negative finding coming out from the intercomparison is that, even when applying the tilt correction, the gravimetric residuals obtained with the gPh#116 are an order of magnitude larger and quite inconsistent with those obtained with co-located superconducting gravimeters. We guess this problem could be overcome by installing the gravimeter on an auto-levelling platform. From the analysis of the gravity records, a reliable tidal gravity model was derived, which we believe will help to improve the accuracy of volcano monitoring, as it will allow appropriate correction of tidal effects for both relative and absolute gravity measurements acquired in the area. Two further interesting elements arose from our study: (1) a peculiar cavity effect of the SV underground laboratory that seems to influence the tilt change; (2) the small residual gravity signals are time correlated with the rainfall peaks and are compatible with gravity decreases induced by increases in soil moisture above the gravimeter.

EOT20 is the latest in a series of empirical ocean tide (EOT) models derived using residual tidal analysis of multi-mission satellite altimetry at DGFI-TUM. The amplitudes and phases of 17 tidal constituents are provided on a global 0.125∘ grid based on empirical analysis of seven satellite altimetry missions and four extended missions. The EOT20 model shows significant improvements compared to the previous iteration of the global model (EOT11a) throughout the ocean, particularly in the coastal and shelf regions, due to the inclusion of more recent satellite altimetry data as well as more missions, the use of the updated FES2014 tidal model as a reference to estimated residual signals, the inclusion of the ALES retracker and improved coastal representation. In the validation of EOT20 using tide gauges and ocean bottom pressure data, these improvements in the model compared to EOT11a are highlighted with the root sum square (RSS) of the eight major tidal constituents improving by ∼ 1.4 cm for the entire global ocean with the major improvement in RSS (∼ 2.2 cm) occurring in the coastal region. Concerning the other global ocean tidal models, EOT20 shows an improvement of ∼ 0.2 cm in RSS compared to the closest model (FES2014) in the global ocean. Variance reduction analysis was conducted comparing the results of EOT20 with FES2014 and EOT11a using the Jason-2, Jason-3 and SARAL satellite altimetry missions. From this analysis, EOT20 showed a variance reduction for all three satellite altimetry missions with the biggest improvement in variance occurring in the coastal region. These significant improvements, particularly in the coastal region, provide encouragement for the use of the EOT20 model as a tidal correction for satellite altimetry in sea-level research. All ocean and load tide data from the model can be freely accessed at https://doi.org/10.17882/79489 (Hart-Davis et al., 2021). The tide gauges from the TICON dataset used in the validation of the tide model, are available at https://doi.org/10.1594/PANGAEA.896587 (Piccioni et al., 2018a).

Reconstructing tidal signals is indispensable for verifying altimetry products, forecasting water levels, and evaluating long-term trends. Uncertainties in the estimated tidal parameters must be carefully assessed to adequately select the relevant tidal constituents and evaluate the accuracy of the reconstructed water levels. Customary harmonic analysis uses ordinary least squares (OLS) regressions for their simplicity. However, the OLS may lead to incorrect estimations of the regression coefficient uncertainty due to the neglect of the residual autocorrelation. This study introduces two residual resamplings (moving-block and semiparametric bootstraps) for estimating the variability of tidal regression parameters and shows that they are powerful methods to assess the effects of regression errors with nontrivial autocorrelation structures. A Monte Carlo experiment compares their performance to four analytical procedures selected from those provided by the RT_Tide, UTide, and NS_Tide packages and the robustfit.m MATLAB function. In the Monte Carlo experiment, an iteratively reweighted least squares (IRLS) regression is used to estimate the tidal parameters for hourly simulations of one-dimensional water levels. Generally, robustfit.m and the considered RT_Tide method overestimate the tidal amplitude variability, while the selected UTide and NS_Tide approaches underestimate it. After some substantial methodological corrections the selected NS_Tide method shows adequate performance. As a result, estimating the regression variance–covariance with the considered RT_Tide, UTide, and NS_Tide methods may lead to the erroneous selection of constituents and underestimation of water level uncertainty, compromising the validity of their results in some applications.

We quantify the vertical wave energy flux and global wave power due to upward propagating tides in the 80–200 km altitude range, based on observations. Our approach utilizes fluid dynamical equations, and Hough Mode Extension (HME) fits to tidal wind and temperatures observed by the TIDI and SABER instruments on board the Thermosphere‐Ionosphere‐Mesosphere Energetics and Dynamics (TIMED) satellite. The global annual mean vertical energy flux due to diurnal and semidiurnal migrating and non‐migrating tides for the year 2009 (solar minimum conditions) is about 10−5${10}^{-5}$  W/m2 or equivalent to 5 GW of global wave power at 100 km. Observation‐based wave energy flux values for the migrating diurnal and semidiurnal tidal components DW1 and SW2 for spring 2009 equinox conditions compare well with SD‐WACCM‐X predicted values but are somewhat smaller than early theoretical results. We find that SW2 is the most dominant tidal component contributing to wave energy throughout the thermosphere. Plain Language Summary Atmospheric tides couple the lower and upper atmosphere by transferring energy and momentum from their source regions in the troposphere and stratosphere to the thermosphere. Nevertheless, how much energy the upward propagating tides transport per unit time and area (vertical wave energy flux) is poorly known. Though a few studies have been conducted in the past to assess wave energy flux, most approaches were solely based on theory and models rather than on observations. To address this gap in observation‐based assessment, we derive the vertical wave energy flux and global wave power for solar minimum conditions from Thermosphere‐Ionosphere‐Mesosphere Energetics and Dynamics (TIMED) satellite observations. This approach utilizes fluid dynamical equations and empirical tidal modeling of temperature and wind observations in the lower thermosphere. Our results compare well with the vertical wave energy flux values predicted by the Specified Dynamics Whole Atmosphere Community Climate Model with thermosphere‐ionosphere eXtension (SD‐WACCM‐X) but are smaller than earlier theoretical numbers for migrating diurnal and semidiurnal tidal components. Key Points The global annual mean wave power due to upward propagating tides is ∼5 GW at 100 km, based on observations The semidiurnal tide is the largest contributor in the thermosphere, whereas the diurnal tide dominates the upper mesosphere About 35% of the global annual mean wave energy flux contribution at 100 km originates from non‐migrating tides

The Singapore Strait connects the South China Sea, where tides are dominantly diurnal, to the dominantly semidiurnal Indian Ocean. At this transition, the tidal water level oscillations are observed to be semidiurnal while the tidal current oscillations are mixed, diurnal to fully diurnal. Due to the interaction of the diurnal constituents with the semidiurnal M2 tide, the tides are strongly asymmetric. Both residual flows and subtidal flows, with periodicities of 2 weeks to 1 year, are strong. In order to analyze and explain the hydrodynamics around Singapore, a well‐documented and calibrated regional tidal model application was further improved and validated. Analysis of the results of this model shows that the diurnal tidal wave is primarily standing, with an amphidromic point close to Singapore, explaining the dominantly diurnal current and semidiurnal water level oscillations. Analysis of the model results further indicates that the fortnightly constituents in the subtidal flow are probably compound tides, with a combined amplitude over 10 cm/s. Pronounced yearly and half‐yearly cycles in spring tidal current amplitude and asymmetry exist, resulting from interaction of the diurnal and the semidiurnal spring‐neap cycles, compound tides, and the monsoon currents. A simple analytical transport formula was applied to determine the relative importance of tidal asymmetry and residual flows, verified with a full sediment transport model. With fine sediment being more sensitive for residual flow and coarser sediment for tidal flow, a pronounced divergence in sediment transport pathways may exist, depending on the grain size. Key Points A pronounced difference in horizontal and vertical tide exists near Singapore Tidal flow velocities near Singapore are strongly asymmetric Transport by tidal asymmetry is in opposite direction of that by residual flow

As global climate change intensifies, hurricane‐induced storm surges are becoming more frequent and severe. While Global Navigation Satellite System‐Interferometric Reflectometry (GNSS‐IR) is widely used to monitor sea level variations, its capability to detect rapid and extreme events remains limited. We propose a short‐time feature extraction GNSS‐IR strategy constrained by astronomical tidal models. By analyzing the continuity and stability of spectral reflections, the method identifies coherent signals from transient sea level changes and effectively addresses the typical 10–20 min temporal bias introduced by the static‐surface assumption. Validation results show that the method achieves a long‐term monitoring accuracy of 4.6 cm over 1 year, and maintains a stable accuracy of approximately 10 cm during storm surges. It also achieves 4.0 cm accuracy over 12‐hr period and enables short‐term sea level prediction with an accuracy of 7 cm. These findings highlight the potential of near‐shore GNSS‐IR to strengthen tide gauge networks and marine assessments.

As a ubiquitous movement in the ocean, tides are vital for marine life and numerous marine activities such as fishing and ocean engineering. Tidal dynamics are complicated in the East Asian marginal seas (EAMS) due to changing complex topography and coastlines related to human activities (e.g., land reclamation and channel deepening) and natural variability (e.g., seasonal variations of ocean stratification and river flow). As an important tool, numerical models are widely used because they can provide basin-scale patterns of tidal dynamics compared to point-based tide gauges. This paper aims to overview the development history of the numerical simulation of tides in the EAMS, including the Bohai Sea, the Yellow Sea, the East China Sea, the East/Japan Sea, and the South China Sea, provide comprehensive understanding of tidal dynamics, and address contemporary research challenges. The basic features of major tidal constituents obtained by tidal models are reviewed, and the progress in the inversion of spatially and temporally changing model parameters via the adjoint method are presented. We review numerical research on how a changing ocean environment induces tidal evolution and how tides and tidal mixing influence ocean environment in turn. The generation, propagation, and dissipation of internal tides in the EAMS are also reviewed. Although remarkable progresses in tidal dynamics have been made, nonstationary tidal variations are not fully explained yet, and further efforts are needed. In addition, tidal influences on ocean environment still receive limited attention, which deserves special attention.

We have discovered that the peak phase time of predawn thermosphere‐ionosphere Na (TINa) layers (∼110–150 km altitude) undergoes clear annual variations with the earliest occurrence in summer and latest in winter over Boulder (40.13°N, 105.24°W), which are closely correlated to annual phase variations of sunrise and tidal winds. Such discoveries were enabled by the first characterization of 12 monthly composites of TINa layers from January through December using 7 years of lidar observations (2011–2017). Despite their tenuous densities, the predawn TINa layers have nearly 100% occurrence rate (160 out of 164 nights of observations). Monthly composites show downward‐phase‐progression TINa descending at similar phase speeds as Climatological Tidal Model of the Thermosphere tidal winds. These TINa layers occur in ion convergence but neutral divergence regions, modeled using tidal winds. These results support the formation mechanism (neutralization of converged TINa+ forming TINa) proposed previously and suggest that migrating tidal winds experience annual phase variations. Plain Language Summary With tons of cosmic dust falling on Earth every day, metallic atoms and ions (e.g., Fe, Na, K, and Ca+) are released via meteor ablation and sputtering into the upper atmosphere, forming permanent metal layers (∼75–105 km) that have been known for nearly a century. What was unknown until 2011 was the existence of thermosphere‐ionosphere metal (TIMt) layers that were discovered with high‐sensitivity lidar observations first from Antarctica and then were observed globally. These neutral TIMt layers locate above the permanent layers with an upper reach to ∼200 km and exhibit intermittent occurrence. In 2021 surprising regular occurrence of TIMt layers in Na species (TINa) was reported for the first time from lidar observations over Boulder, Colorado, where TINa layers occur before dawn and after dusk nearly every night. By analyzing 7 years of lidar data, we have further discovered that the Boulder predawn TINa layers occur in earlier hours in summer than in winter. Such annual phase variations are correlated with sunrise and solar‐heating‐driven tidal winds. These TIMt layers are of great scientific interest as they provide unique tracers for making direct measurements in the least understood but crucially important “thermospheric gap” region of 100–200 km. Key Points First characterization of 12 monthly composites of Na mixing ratios reveals annual phase variations of predawn thermosphere‐ionosphere Na (TINa) layers (110–150 km) Predawn TINa occur ∼2.5 hr earlier in summer than in winter, closely correlating to annual phase variations of sunrise and Climatological Tidal Model of the Thermosphere semidiurnal westward‐propagating tidal winds TINa layers descend at similar rates as and in tidal‐wind‐modeled ion convergence regions, supporting neutralization of TINa+ forming TINa