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The water level changes in the estuarine area are influenced by various factors with different mechanisms and periodicities, including runoff, astronomical tides and storm surges, resulting in relatively low forecasting accuracy of the residual water level. To improve the forecast accuracy of residual water levels, an estuary-tidal residual water level forecasting method based on VMD-BPNN (variational mode decomposition and back propagation neural network) is proposed. By conducting tidal harmonic analysis on the long-term water level data of estuarine areas, astronomic water levels and residual water levels can be obtained. The residual water level is subjected to VMD, obtaining multiple intrinsic mode functions of the residual water level in the time series. Then, the BPNN is used to train each intrinsic mode function, and an accurate forecast of residual water levels in the estuary area is achieved through the forecast and superposition of each intrinsic mode function. Water level data from four typical tidal stations in estuarine areas of the United States and France were used for experimental analysis. The method was verified by using Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Nash-Sutcliffe Efficiency (NSE) as evaluation indicators, and the results showed that it had a good comprehensive performance, and high stability and accuracy in the forecasting of the residual water level. This study thereby provides a valuable foundation and insightful reference for future research into the complex mechanisms driving water level changes and the development of high-precision tidal forecasting systems in estuarine environments.

A statistical reassessment of the tide gauge record concludes that sea level rose at a rate of about 1.2 millimetres per year from 1901 to 1990, slightly lower than prior estimates and now consistent with estimates based on individual contributions to sea-level change; the estimates reported here from 1990 onwards are consistent with other work, suggesting that the recent acceleration in sea-level rise is greater than previously thought. Twentieth century sea levels revisited Rates of sea-level rise calculated from tide gauge data tend to exceed bottom-up estimates derived from summing loss of ice mass, thermal expansion and changes in land storage. Carling Hay et al . provide a statistical reassessment of the tide gauge record — which is subject to bias due to sparse and non-uniform geographic coverage and other uncertainties — and conclude that sea-level rose by about 1.2 millimetres per year from 1901 to 1990. This is slightly lower than prior estimates and is consistent with the bottom-up estimates. The same analysis applied to the period 1993–2010, however, indicates a sea-level rise of about three millimetres per year, consistent with other work and suggesting that the recent acceleration in sea-level rise has been greater than previously thought. Estimating and accounting for twentieth-century global mean sea-level (GMSL) rise is critical to characterizing current and future human-induced sea-level change. Several previous analyses of tide gauge records 1 , 2 , 3 , 4 , 5 , 6 —employing different methods to accommodate the spatial sparsity and temporal incompleteness of the data and to constrain the geometry of long-term sea-level change—have concluded that GMSL rose over the twentieth century at a mean rate of 1.6 to 1.9 millimetres per year. Efforts to account for this rate by summing estimates of individual contributions from glacier and ice-sheet mass loss, ocean thermal expansion, and changes in land water storage fall significantly short in the period before 1990 7 . The failure to close the budget of GMSL during this period has led to suggestions that several contributions may have been systematically underestimated 8 . However, the extent to which the limitations of tide gauge analyses have affected estimates of the GMSL rate of change is unclear. Here we revisit estimates of twentieth-century GMSL rise using probabilistic techniques 9 , 10 and find a rate of GMSL rise from 1901 to 1990 of 1.2 ± 0.2 millimetres per year (90% confidence interval). Based on individual contributions tabulated in the Fifth Assessment Report 7 of the Intergovernmental Panel on Climate Change, this estimate closes the twentieth-century sea-level budget. Our analysis, which combines tide gauge records with physics-based and model-derived geometries of the various contributing signals, also indicates that GMSL rose at a rate of 3.0 ± 0.7 millimetres per year between 1993 and 2010, consistent with prior estimates from tide gauge records 4 . The increase in rate relative to the 1901–90 trend is accordingly larger than previously thought; this revision may affect some projections 11 of future sea-level rise.

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).

Tidal flats are shrinking in extent globally. The dynamics of the response of estuarine tidal flats to global environmental changes remain unclear. Tidal-flat morphology is shaped by the interplay among wave and tidal forces, river discharge and sediment supply, and preservation of tidal flats requires a balance between erosional and depositional processes be maintained. Here we assess tidal-flat morphodynamic changes of 40 globally distributed estuaries with contrasting tidal amplitudes between 1986 and 2011 from analyses of 4,939 satellite images. We consider both vegetated and unvegetated intertidal areas. From comparisons with remote-sensing-derived turbidity estimates, we identify a critical turbidity threshold indicative of a minimum sediment supply along with the hydrodynamic forces, which is necessary to maintain tidal flats. Tidal flats in intertidal areas in estuaries with low turbidity face retreat, with the critical turbidity threshold increasing with increasing tidal amplitudes. By contrast, estuaries with high turbidity tend to exhibit laterally or vertically expanding tidal flats. However, despite estuaries with limited tidal ranges having relatively low turbidity thresholds, environmental or anthropogenic alterations can still adversely affect the morphology of tidal flats. Our findings demonstrate the need to consider sediment supply in integrated estuarine management strategies to maintain the ecological integrity and flood defence function of tidal flats. Maintenance of estuarine tidal flats requires a minimum turbidity level that increases with tidal range, according to a global analysis of tidal-flat changes from satellite imagery.

Internal tides (ITs) play a critical role in ocean mixing, and have strong signatures in ocean observations. Here, global IT sea surface height (SSH) in nadir altimetry is compared with an ocean forecast model that assimilates de‐tided SSH from nadir altimetry. The forecast model removes IT SSH variance from nadir altimetry at skill levels comparable to those achieved with empirical analysis of nadir altimetry. Accurate removal of IT SSH is needed to fully reveal lower‐frequency mesoscale eddies and currents in altimeter data. Analysis windows of order 30–120 days, made possible by the frequent (hourly) outputs of the forecast model, remove more IT SSH variance than longer windows. Forecast models offer a promising new approach for global internal tide mapping and altimetry correction. Because they provide information on the full water column, forecast models can also help to improve understanding of the underlying dynamics of ITs. Plain Language Summary Tidal flow over topographic features on the seafloor generates vertical displacements along the interfaces of ocean layers that have different densities. These vertical displacements at tidal frequencies are known as internal tides. Internal tide displacements are largest well below the sea surface, but also display a sea surface height (SSH) signature that is large enough to be measured by satellite altimeters. Removing internal tide signals from satellite altimeter SSH allows for a more accurate accounting of non‐tidal features, including slowly evolving ocean currents and eddies, that are also measured by altimeters. Here, we show that supercomputer ocean forecast simulations of the global internal tide field are able to remove internal tide SSH from satellite altimeter measurements with a skill level that is comparable to the skill of internal tide SSH removal based upon analysis of the satellite altimeter data itself. Thus, forecast models offer a complementary method for this important task. In addition, forecast models provide information on the entire ocean water column, not just the sea surface. Finally, the hourly outputs of forecast models allow for a greater variety of tidal analysis record lengths than can be achieved with altimeter outputs, which report sea surface height fields much less frequently. Key Points Global ocean forecast models can accurately simulate both long‐term (phase‐locked) internal tides and their short‐term modulations Ocean forecast models offer a useful complement to empirical models for mapping internal tides and correcting altimetry for internal tides In regions of strong internal tides, optimal variance reduction in nadir altimetry is attained through short‐term tidal analyses (∼60 days)

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

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.

With the continued acquisition of high-precision tracking data by the Juno spacecraft, significant progress has been made in accurately determining Jupiter’s dynamical parameters. In this study, we utilize the orbit determination and gravity field recovery software SPOT, developed by Wuhan University, to process all available two-way Doppler tracking data of Juno’s perijove passes between 2016 and 2024. Incorporating 19 additional perijoves (PJ39–PJ68) beyond the 26 arcs used in the previous study, a joint estimation of Jupiter’s 40 degree zonal gravity harmonics, four tesseral degree-2 terms, spin-axis orientation parameters, and tidal Love number is determined. The results indicate that, compared with previously published Juno-based gravity field solutions, the accuracy of coefficients J2–J5 has improved by more than a factor of 2, while the J13–J36 terms exhibit an average improvement of about 30%. A stochastic force was introduced to absorb unmodeled small perturbations near perijoves, but its rapidly varying orientation does not point to an identifiable physical origin. The uncertainty of Jupiter’s spin-axis rotation parameter is improved to about 1 × 10–7 rad, indicating no significant deviation between the principal axis of inertia and the rotation axis. The estimated accuracy of the static tidal Love numbers is improved by roughly a factor of 2 compared with earlier Juno-based tidal analyses. Due to limitations in orbital geometry, the satellite-dependent tidal Love numbers cannot be determined with sufficient accuracy to reveal potential dynamical tidal effects. This work provides improved dynamical parameters for constraining Jupiter’s interior structure.

A novel tidal analysis package (red_tide) has been developed to characterize low-amplitude non-phase-locked tidal energy and dominant tidal peaks in noisy, irregularly sampled, or gap-prone time series. We recover tidal information by expanding conventional harmonic analysis to include prior information and assumptions about the statistics of a process, such as the assumption of a spectrally colored background, treated as nontidal noise. This is implemented using Bayesian maximum posterior estimation and assuming Gaussian prior distributions. We utilize a hierarchy of test cases, including synthetic data and observations, to evaluate this method and its relevance to analysis of data with a tidal component and an energetic nontidal background. Analysis of synthetic test cases shows that the methodology provides robust tidal estimates. When the background energy spectrum is nearly spectrally white, red_tide results replicate results from ordinary least squares (OLS) commonly used in other tidal packages. When background spectra are red (a spectral slope of −2 or steeper), red_tide’s estimates represent a measurable improvement over OLS. The approach highlights the presence of tidal variability and low-amplitude constituents in observations by allowing arbitrarily configurable fitted frequencies and prior statistics that constrain solutions. These techniques have been implemented in MATLAB in order to analyze tidal data with non-phase-locked components and an energetic background that pose challenges to the commonly used OLS approach.

Denpasar, the capital city of Bali Province, is a coastal city pivotal for tourism, economy, and investment. However, these activities, compounded by climate change, alter coastal characteristics, potentially increasing coastal hazards. This study aims to determine the coastal region's characteristics and analyze the distribution of coastal multi-hazards in Denpasar using the Coastal Hazard Wheel (CHW). The multi-hazards studied consist of ecosystem disruption, gradual inundation, seawater intrusion, erosion, and flooding. The results showed that Denpasar City has heterogeneous coastal characteristics. Denpasar’s coastal region is composed of a geological layout: a barrier, delta/low estuary island, sedimentary plain, sloping soft rock, and tidal inlet/sand spit/river mouth. Wave exposure in the Denpasar’s coastal region consists of protected and moderately exposed categories with significant wave heights ranging from 0.93 to 1.27 m. Tidal analysis shows that the average tidal range in the Denpasar’s coastal region is 366 cm (meso tidal). Denpasar’s coastal area also has heterogeneous flora/fauna conditions with categories such as mangrove/tidal flat, vegetated slope, not vegetated, and any (there is vegetation, but it does not have a significant effect). Denpasar’s coastal region experienced an increase in shoreline by 4.2 km (8.7%) from 2012 to 2022, dominated by anthropogenic activities. There is no tropical cyclone activity around Denpasar’s coastal area. Based on the conditions of the biogeophysical parameters, the coastal type and the level of existing hazards can identified. Ecosystem disruption has low, medium, and very high hazard levels. Seawater intrusion has a low to high hazard level. Meanwhile, gradual inundation, erosion, and coastal flooding have a low to very high level of hazard.