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Low-frequency non-astronomical changes of ocean tides of (1 cm) have been documented in water level measurements around the globe, but their causative mechanisms remain poorly understood in many cases. While anthropogenic developments (e.g., harbor dredging) are certainly a leading factor at individual sites, the spatially coherent tidal variability seen in areas with distributed tide gauge information is revealing of natural processes. Here we use a general circulation model, configured on a 1/12° horizontal grid, to spatially map the influence of ocean stratification changes on the global M2 tide from 1993 to 2019. We partition the problem into separate yearly simulations of short duration (40 days) and relax each forward integration to the year’s “true” stratification, as provided by an eddying ocean reanalysis. The simulations reveal typical stratification-driven M2 amplitude changes of 0.5 cm on interannual time scales, as calculated at positions of 40 coastal tide gauges in three particular regions (New Zealand & Australia, Florida & Gulf of Mexico, Northeast Pacific). Most of the identified fluctuations at the coast are present in the barotropic tidal component, suggesting an origin in changing tidal conversion at remote topography or turbulent energy dissipation in shallow water. In addition, we fit linear rates to the yearly M2 solutions over the 1993–2019 time span and compare the resulting in-phase and quadrature trends to a novel (but still tentative) estimate of M2 trends in the open ocean from TOPEX-Jason satellite altimetry. The two solutions bear gross resemblance to each other and indicate large spatial-scale trends of ~1 cm cy-1 in the barotropic M2 tide in the Indian Ocean, the western and northern Pacific (e.g., in the Gulf of Alaska), and Baffin Bay. Our results highlight that efforts seeking to explain interannual to secular changes of tides at the coast and in the open ocean must consider both sea level rise and contemporary changes in ocean stratification.

SUMMARY Observations of the ψ1 earth tide yield valuable insights into the earth’s free core nutation, especially if the effects of the ψ1 ocean tide can be removed. The ocean tide is extremely small, with amplitudes rarely more than a few millimetres, and developing an accurate model is challenging. Direct observations are inadequate to support a global model. The alternative—numerical simulation—must account for a multitude of possible effects. The ocean tide is forced by the gravitational tidal potential, by pressure loading from atmospheric tides, by seasonal modulation of the nearby K1 constituent, and possibly by non-linear interactions among several other constituents. Here we construct a model of the ψ1 ocean tide which accounts for (or attempts to bound) each of these effects. The radiational component (from atmospheric pressure loading), although relatively small, is complicated by the presence of non-tidal atmospheric variability in the diurnal band. The ocean’s response is dynamic, but there is also high-wavenumber pressure forcing with a near-isostatic response. A general circulation model, forced by both winds and the tidal potential, suggests that annual variability in K1 leads to pronounced ψ1 amplitudes in some marginal seas, especially in the western Pacific.

This special issue marks the 100th anniversary of the founding of the Liverpool Tidal Institute (LTI), one of a number of important scientific developments in 1919. The preface gives a brief history of how the LTI came about and the roles of its first two Directors, Joseph Proudman and Arthur Doodson. It also gives a short overview of the research on tides at the LTI through the years. Summaries are given of the 26 papers in the special issue. It will be seen that the topics of many of them could be thought of as providing a continuation of the research first undertaken at the LTI. Altogether, they provide an interesting snapshot of work on tides now being made by groups around the world.

New determinations of ocean tides are extracted from high-rate Global Positioning System (GPS) solutions at nine stations sitting on the Ross Ice Shelf. Five are multi-year time series. Three older time series are only 2–3 weeks long. These are not ideal, but they are still useful because they provide the only in situ tide observations in that sector of the ice shelf. The long tide-gauge observations from Scott Base and Cape Roberts are also reanalysed. They allow determination of some previously neglected tidal phenomena in this region, such as third-degree tides, and they provide context for analysis of the shorter datasets. The semidiurnal tides are small at all sites, yet M2 undergoes a clear seasonal cycle, which was first noted by Sir George Darwin while studying measurements from the Discovery expedition. Darwin saw a much larger modulation than we observe, and we consider possible explanations - instrumental or climatic - for this difference.

We examined the sensitivity of GRACE Follow-On (GRACE-FO) laser ranging interferometer (LRI) measurements to sub-monthly time-variable gravity (TVG) signals caused by transient, high-frequency mass changes in the Earth system. GRACE-FO LRI provides complementary inter-satellite ranging measurements with higher precision over a wider range of frequencies than the baseline K-band microwave ranging system. The common approach for studying mass variation relies on the inverted TVG or mascon solutions over a period of, for example, one month or 10 days which are adversely affected by temporal aliasing and/or smoothing. In this article, we present the alternative along-orbit analysis methodology in terms of line-of-sight gravity difference (LGD) to fully exploit the higher precision LRI measurements for examination of sub-monthly mass changes. The discrepancy between "instantaneous" LGD LRI observations and monthly-mean LGD (from Level-2 data) at satellite altitude indicates the sub-monthly gravitational variability not captured by monthly-mean solutions. In conjunction with the satellite ocean altimetry observations, high-frequency non-tidal atmosphere and ocean models, and hydrology models, we show that the LGD LRI observations detect the high-frequency oceanic mass variability in the Argentine Basin and the Gulf of Carpentaria, and sub-monthly variations in surface (river) water in the Amazon Basin. We demonstrate the benefits gained from repeat ground track analysis of GRACE-FO LRI data in the case of the Amazon surface water flow. The along-orbit analysis methodology based on LGD LRI time series presented here is especially suitable for quantifying temporal and spatial evolution of extreme, rapidly changing mass variations. University of Newcastle; Australian Research Council [DP160104095, DP170100224]; NASA [GRACERFO19-0010]; National Aeronautics and Space Administration [80NM0018D0004]; German Research Foundation [DO 1311/4-1] Published version This work was funded by the University of Newcastle to support NASA's GRACE and GRACE Follow-On projects as an international science team member and by Australian Research Council Discovery Program (DP160104095, DP170100224). Science team funding was provided by NASA (GRACERFO19-0010) to Jeanne Sauber. A portion of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). The work towards AOD1B RL07 is supported by the German Research Foundation (DO 1311/4-1).

Since the early twentieth century, the amplitudes of tidal constituents in the Gulf of Maine and Bay of Fundy display clear secular trends that are among the largest anywhere observed for a regional body of water. The M2 amplitude at Eastport, Maine, increased at a rate of 14.1 ± 1.2 cm per century until it temporarily dropped during 1980–1990, apparently in response to changes in the wider North Atlantic. Annual tidal analyses indicate M2 reached an all‐time high amplitude last year (2018). Here we report new estimates of tides derived from nineteenth century water‐level measurements found in the U.S. National Archives. Results from Eastport, Portland, and Pulpit Harbor (tied to Bar Harbor) do not follow the twentieth century trends and indicate that the Gulf of Maine tide changes commenced sometime in the late nineteenth or early twentieth centuries, coincident with a transition to modern rates of sea‐level rise as observed at Boston and Portland. General agreement is that sea level rise alone is insufficient to cause the twentieth‐century tide changes. A role for ocean stratification is suggested by the long‐term warming of Gulf of Maine waters; archival water temperatures at Boston, Portland, and Eastport show increases of ∼2 °C since the 1880s. In addition, a changing seasonal dependence in M2 amplitudes is reflected in a changing seasonal dependence in water temperatures. The observations suggest that models seeking to reproduce Gulf of Maine tides must consider both sea level rise and long‐term changes in stratification.

In most places extreme high tides undergo a clear seasonal variation. It is well known that semidiurnal tides tend to peak during equinox seasons, and diurnals during solstice seasons. This is a consequence of the solar and lunar declinations, which when large maximize diurnal tides at the expense of semidiurnals. The semiannual range modulation of tidal extremes for a pure semidiurnal tide is determined mainly by the amplitude of the K2 constituent; a pure diurnal is determined mainly by P1. Mixed tidal regimes tend to experience maxima very roughly around the times of solstice, but not always, with the semiannual modulation generally a complicated function of constituent amplitudes and phases. These modulations are here mapped worldwide by analyzing tidal extremes predicted with a global tide model. The known 4.4-year modulation in extreme tides is a consequence of declinational and perigean effects coming in and out of phase. The phase of the 4.4-year modulation is controlled by the phase of the semiannual modulation, irrespective of whether the tide is diurnal, semidiurnal, or mixed.

The Samoan islands are an archipelago hosting a quarter million people mostly residing inthree major islands, Savai'i and Upolu (Samoa), and Tutuila (American Samoa). The islands haveexperienced sea level rise by 2-3 mm/year during the last half century. The rate, however, has dramaticallyincreased following the Mw 8.1 SamoaTonga earthquake doublet (megathrust + normal faulting) inSeptember 2009. Since the earthquake, we found largescale gravity increase (0.5 Gal/year) around theislands and ongoing subsidence (8-16 mm/year) of the islands from our analysis of Gravity Recovery AndClimate Experiment gravity and GPS displacement data. The postseismic horizontal displacement is faster inSamoa, while the postseismic subsidence rate is considerably larger in American Samoa. The analysis oflocal tide gauge records and satellite altimeter data also identified that the relative sea level rise becomesfaster by 7-9 mm/year in American Samoa than Samoa. A simple viscoelastic model with a Maxwellviscosity of 2–3×10(exp 18) Pa s for the asthenosphere explained postseismic deformation at nearby GPS sites aswell as Gravity Recovery And Climate Experiment gravity change. It is found that the constructiveinterference of viscoelastic relaxation from both megathrust and normal faulting has intensified thepostseismic subsidence at American Samoa, causing ~5 times faster sea level rise than the global average.Our model indicates that this trend is likely to continue for decades and result in sea level rise of 30-40 cm,which is independent of and in addition to anticipated climaterelated sea level rise. It will worsen coastalflooding on the islands leading to regular nuisance flooding.

SUMMARY Seven years of GRACE intersatellite range-rate measurements are used to test the new ocean tide model FES2014 and to compare against similar results obtained with earlier models. These qualitative assessments show that FES2014 represents a marked improvement in accuracy over its earlier incarnation, FES2012, with especially notable improvements in the Arctic Ocean for constituents K1 and S2. Degradation appears to have occurred in two anomalous regions: the Ross Sea for the O1 constituent and the Weddell Sea for M2.

Satellite altimetry and gravimetry are used to determine the mean seasonal cycle in relative sea level, a quantity relevant to coastal flooding and related applications. The main harmonics (annual, semiannual, terannual) are estimated from 25 years of gridded altimetry, while several conventional altimeter “corrections” (gravitational tide, pole tide, and inverted barometer) are restored. To transform from absolute to relative sea levels, a model of vertical land motion is developed from a high-resolution seasonal mass inversion estimated from satellite gravimetry. An adjustment for annual geocenter motion accounts for use of a center-of-mass reference frame in satellite orbit determination. A set of 544 test tide gauges, from which seasonal harmonics have been estimated from hourly measurements, is used to assess how accurately each adjustment to the altimeter data helps converge the results to true relative sea levels. At these gauges, the median annual and semiannual amplitudes are 7.1 cm and 2.2 cm, respectively. The root-mean-square differences with altimetry are 3.24 and 1.17 cm, respectively, which are reduced to 1.93 and 0.86 cm after restoration of corrections and adjustment for land motion. Example outliers highlight some limitations of present-day coastal altimetry owing to inadequate spatial resolution: upwelling and currents off Oregon and wave setup at Minamitori Island.

Ocean tides produce significant gravitational perturbations that affect near-Earth orbiting spacecraft. The gravitational potential induced by tidal mass redistribution is routinely modelled for global gravity analysis and orbit determination, although generally by assuming a spherical Earth and a uniform seawater density. The inadequacy of these simplifications is here addressed. We have developed an accurate yet efficient algorithm to compute the ocean tidal geopotential, allowing for Earth’s elliptical shape and variable seawater density. Using this new computation, we find that (1) the effect of ellipticity is several percent of the tide signal over mid to high latitude regions, which is comparable to elevation error in the state-of-the-art ocean tide models; (2) the effect of seawater density variations on the potential is as large as 2-3 cm in water-height equivalent, primarily in deep water where density increases 2-3% from compressibility. Our analysis of new GRACE Follow-On (GRACE-FO) laser ranging interferometer measurements reveals evident errors when ellipticity and density variations are ignored. When accounted for, the GRACE-FO residual tidal gravity perturbations are reduced by half, depending on the adopted tide model; only the remaining half likely represents actual model elevation error. The use of a spherical surface and a uniform seawater density is no longer tenable given the precision of gravity measurements from GRACE and GRACE-FO satellites.

Astronomical variations in tidal magnitude can strongly modulate the severity of coastal flooding on daily, monthly, and interannual timescales. Here, we present a new quasi-nonstationary skew surg...

39 pages, 8 figures, 3 tables.-- Gridded Surface Height Anomalies Version 1801. Ver. 1801 available from NASA JPL PO.DAAC, CA, USA(https://doi.org/10.5067/SLREF-CDRV1). Data are also available through Wiese et al. (2017), Global sea level provides an important indicator of the state of the warming climate, but changes in regional sea level are most relevant for coastal communities around the world. With improvements to the sea‐level observing system, the knowledge of regional sea‐level change has advanced dramatically in recent years. Satellite measurements coupled with in situ observations have allowed for comprehensive study and improved understanding of the diverse set of drivers that lead to variations in sea level in space and time. Despite the advances, gaps in the understanding of contemporary sea‐level change remain and inhibit the ability to predict how the relevant processes may lead to future change. These gaps arise in part due to the complexity of the linkages between the drivers of sea‐level change. Here we review the individual processes which lead to sea‐level change and then describe how they combine and vary regionally. The intent of the paper is to provide an overview of the current state of understanding of the processes that cause regional sea‐level change and to identify and discuss limitations and uncertainty in our understanding of these processes. Areas where the lack of understanding or gaps in knowledge inhibit the ability to provide the needed information for comprehensive planning efforts are of particular focus. Finally, a goal of this paper is to highlight the role of the expanded sea‐level observation network—particularly as related to satellite observations—in the improved scientific understanding of the contributors to regional sea‐level change, The research was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The authors acknowledge support from the National Aeronautics and Space Administration under Grants 80NSSC17K0565, 80NSSC170567, 80NSSC17K0566, 80NSSC17K0564, and NNX17AB27G. A. A. acknowledgessupport under GRACE/GRACEFO Science Team Grant (NNH15ZDA001N‐GRACE). T. W. acknowledges support by the National Aeronautics and Space Administration (NASA) under the New (Early Career) Investigator Program in Earth Science (Grant: 80NSSC18K0743). C. G. P was supported by the J. Lamar Worzel Assistant Scientist Fund and the Penzance Endowed Fund in Support of Assistant Scientists at the Woods Hole Oceanographic Institution, With the funding support of the ‘Severo Ochoa Centre of Excellence’ accreditation (CEX2019-000928-S), of the Spanish Research Agency (AEI)

In order to access the targeted ocean signal, altimeter measurements are corrected for several geophysical parameters among which the ocean tide correction is one of the most critical, but the internal tide signature at the surface are not yet corrected globally. Internal tides can have a signature of several cm at the surface with wavelengths about 50–250 km for the first mode and even smaller scales for higher order modes. The goals of the upcoming Surface Water Ocean Topography (SWOT) mission and other high-resolution ocean measurements make the correction of these small scale signals a challenge, as the separation of all tidal variability from other oceanic signals becomes mandatory. In this context, several scientific teams are working on the development of new internal tide models, taking advantage of the very long altimeter time series now available, which represent an unprecedented and valuable global ocean database. The internal tide models presented here focus on the coherent internal tide signal and they are of three types: empirical models based upon analysis of existing altimeter missions, an assimilative model, and a three-dimensional hydrodynamic model. A detailed comparison and validation of these internal tide models is proposed using existing satellite altimeter databases. The analysis focuses on the four main tidal constituents M2, K1, O1 and S2. The validation process is based on a statistical analysis of multi-mission altimetry including Jason-2 and Cryosphere Satellite-2 data, taking advantage of the long-term altimeter databases available. The results show a significant altimeter variance reduction when using internal tide corrections on all ocean regions where internal tides are generating/propagating. A complementary spectral analysis also gives some estimation of the performance of each model as a function of wavelength, and some insight into the residual non-stationary part of internal tides in the different regions of interest.

Since the beginning of the altimeter mission TOPEX/Poseidon (T/P), followed by Jason-1 and Jason-2 on similar orbits, and many other missions on different orbits (ERS, EnviSat, etc.), mean sea level (MSL) products became essential for the comprehension of global ocean circulation. Since early in the T/P mission, a suspicious signal, having a period of near 59 days and amplitude of roughly 5 mm, was apparent in the Global MSL record. Compared with the 4–5-mm amplitude of the annual signal, the 59-day signal has understandably attracted attention. Moreover, the same signal has been subsequently detected in Jason-1 and later in Jason-2 MSLs. In 2010, the Ocean Surface Topography Science Team (OSTST) concluded this signal as the aliasing of a higher frequency error inherited from the tide model correction: the semi-diurnal wave S2. The source of this error was mainly attributed to T/P measurements, which were assimilated in ocean tide models. When these models are used in the computation of T/P MSL, most of the error cancels. However, this error is communicated to Jason-1 and Jason-2 MSLs. In order to gather and publish the OSTST analyses on this matter, this paper first attempts to list the myriad possibilities for the puzzling 59-day error in MSL. Then, this paper goes deeper into the description of the main contributor to this list: the tide models error. Indeed, since 2010, considerable efforts have been undertaken within the ocean tide community in order to correct ocean tide S2-waves from this error, particularly in the Goddard Ocean Tide (GOT) and finite element solution (FES) latest versions. Comparing several GOT and FES versions and a pure hydrodynamic tide model, this paper assesses, quantifies, and describes a reduction of the MSL 59-day error thanks to the latest releases. These analyses also confirm that a large part of this error has its origins in the T/P mission and has contaminated ocean tide solutions and Jason-1 and Jason-2 MSLs. They also suggest that ocean tide is not the only possible vector. Jason-1 and Jason-2 MSLs contain additional 59-day error—though to a lesser extent—that may either come from the measurements themselves or from another vector.

Comparison of satellite altimetry against a high-quality network of tide gauges suggests that sea-surface heights from the TOPEX altimeter may be biased by ±5 mm, in an approximate piecewise linear, or U-shaped, drift. This has been previously reported in at least two other studies. The bias is probably caused by use of an internal calibration-mode range correction, included in the TOPEX “net instrument” correction, which is suspect owing to changes in the altimeter's point target response. Removal of this correction appears to mitigate most of the drift problem. In addition, a new time series based on retracking the TOPEX waveforms, again without the calibration-mode correction, also reduces the drift aside for a clear problem during the first 2 years. With revision, the TOPEX measurements, combined with successor Jason altimeter measurements, show global mean sea level rising fairly steadily throughout most of 24 year time period, with rates around 3 mm/yr, although higher over the last few years.

Standard methods of tidal inference should be revised to account for a known resonance that occurs mostly within the K1 tidal group in the diurnal band. The resonance arises from a free rotational mode of Earth caused by the fluid core. In a set of 110 bottom-pressure tide stations, the amplitude of the P1 tidal constituent is shown to be suppressed relative to K1, which is in good agreement with the resonance theory. Standard formulas for the K1 nodal modulation remain essentially unaffected. Two examples are given of applications of the refined inference methodology: one with monthly tide gauge data and one with satellite altimetry. For some altimeter-constrained tide models, an inferred P1 constituent is found to be more accurate than a directly determined one.

Sea level rise necessarily triggers more occurrences of minor, or nuisance, flooding events along coastlines, a fact well documented in recent studies. At some locations nuisance flooding can be brought about merely by high spring tides, independent of storms, winds, or other atmospheric conditions. Analysis of observed water levels at Boston indicates that tidal flooding began to occur there in 2011 and will become more frequent in subsequent years. A compilation of all predicted nuisance-flooding events, induced by astronomical tides alone, is presented through year 2050. The accuracy of the tide prediction is improved when several unusual properties of Gulf of Maine tides, including secular changes, are properly accounted for. Future mean sea-level rise at Boston cannot be predicted with comparable confidence, so two very different climate scenarios are adopted; both predict a large increase in the frequency and the magnitude of tidal flooding events.

The presence of significant tidal mixing in the Indonesian seas is well established from both observations and numerical modeling. One indicator is a clear spring-neap cycle in satellite sea-surface temperature (SST) measurements, as first shown by Ffield and Gordon. Their early results are here updated with SST data of considerably higher spatial and temporal resolution. The largest fortnightly signals are found to be localized to relatively small straits, channels, and sills, while the deep basin of the Banda Sea displays little significant signal. A broader region of somewhat enhanced signal surrounds the Seram Sea. The high resolution of the modern SST data is especially critical for mapping the complex fortnightly signals that arise in, and especially south of, the major straits of the Lesser Sunda Island chain.

Near-global and continuous measurements from satellite altimetry have provided accurate estimates of global mean sea level in the past two decades. Extending these estimates further into the past is a challenge using the historical tide gauge records. Not only is sampling nonuniform in both space and time, but tide gauges are also affected by vertical land motion (VLM) that creates a relative sea level change not representative of ocean variability. To allow for comparisons to the satellite altimetry estimated global mean sea level (GMSL), typically the tide gauges are corrected using glacial isostatic adjustment (GIA) models. This approach, however, does not correct other sources of VLM that remain in the tide gauge record. Here we compare Global Positioning System (GPS) VLM estimates at the tide gauge locations to VLM estimates from GIA models, and assess the influence of non-GIA-related VLM on GMSL estimates. We find that the tide gauges, on average, are experiencing positive VLM (i.e., uplift) after removing the known effect of GIA, resulting in an increase of 0.2460.08 mm yr21 in GMSL trend estimates from 1900 to present when using GPS-based corrections. While this result is likely dependent on the subset of tide gauges used and the actual corrections used, it does suggest that non-GIA VLM plays a significant role in twentieth century estimates of GMSL. Given the relatively short GPS records used to obtain these VLM estimates, we also estimate the uncertainty in the GMSL trend that results from limited knowledge of non-GIA-related VLM.

Since the late 1990s the semi-diurnal tide at Churchill, on the western shore of Hudson Bay, has been decreasing in amplitude, with M(sub 2) amplitudes falling from approximately 154 cm in 1998 to 146 cm in 2012 and 142 cm in 2014. There has been a corresponding small increase in phase lag. Mean low water, decreasing throughout most of the twentieth century, has levelled off. Although the tidal changes could reflect merely a malfunctioning tide gauge, the fact that there are no other measurements in the region and the possibility that the tide is revealing important environmental changes calls for serious investigation. Satellite altimeter measurements of the tide in Hudson Bay are complicated by the seasonal ice cover; at most locations less than 40% of satellite passes return valid ocean heights and even those can be impacted by errors from sea ice. Because the combined TOPEX/Poseidon, Jason-1, and Jason-2 time series is more than 23 years long, it is now possible to obtain sufficient data at crossover locations near Churchill to search for tidal changes. The satellites sense no changes in M(sub 2) that are comparable to the changes seen at the Churchill gauge. The changes appear to be localized to the harbour, or to the Churchill River, or to the gauge itself.

Daily harmonics of the ionosphere’s total electron content (TEC) can be mapped using Global Navigation Satellite Systems (GNSS), as recently accomplished by Lean and colleagues. Here those harmonics are determined (over oceans only) by tidal analysis of ionospheric path delay from dual-frequency radar altimetry. Data from TOPEX, Jason-1, and Jason-2 altimeters are used, with focus on periods of medium to high solar activity. Diurnal-band signals are aliased by the altimeter sampling, but TOPEX-Jason orbits were designed to achieve acceptable tidal aliasing. Altimeter maps reveal where corresponding GNSS-based maps are in error, generally near the geomagnetic equator where high-wavenumber features are overly smoothed. When ocean tides are deduced from single-frequency altimetry, a task that relies on accurate GNSS-based ionospheric path corrections, any TEC errors leak directly into the tide solutions. TEC errors near and west of the Weddell Sea are likely problematic for the CryoSat-2 mission.

Increasing sea level rise will lead to more instances of nuisance flooding along the Virginia coastline in the coming decades, causing road closures and deteriorating infrastructure. These minor flood events can be caused by astronomical tides alone, in addition to internal climate variability on annual to decadal timescales. An assessment of nuisance flooding from these two effects is presented up until the year2050 for Norfolk, Virginia. The analysis of water levels indicates that nuisance flooding from tides alone in conjunction with a medium-high sea level scenario will result in flooding beginning in 2030 with frequency increasing thereafter. The addition of climate variability, by use of an empirical mode decomposition, leads to a substantial increase of flooding relative to the tides-alone analysis and shows flood events beginning as soon as 2020. High tides in the future will produce nuisance flooding without the need of other drivers such as coastal storms.

Mean sea level (MSL) is a prominent indicator of climatic change (Ablain et al., 2015; Cazenave et al., 2014; Leuliette and Willis, 2011), and is therefore of great scientific and societal interest. Since the beginning of the altimeter mission TOPEX/Poseidon, followed by Jason-1 and Jason-2 on similar orbits, and many other missions on different orbits (ERS, EnviSat, etc.), MSL products became essential to the comprehension of Global ocean circulation. Since early in the TOPEX/Poseidon mission (Nerem, 1995) a suspicious signal, having period near 59 days and amplitude of roughly 5 mm, was apparent in the GMSL record. Compared with the 4–5 mm amplitude of the annual signal (Minster et al., 1999), the suspicious 59-day signal has understandably attracted attention. Moreover, the same signal has been subsequently detected in Jason-1 and later Jason-2 MSLs. In 2010, it was the subject of a dedicated session at the Ocean Surface Topography Science Team (OSTST) meeting in Lisbon. The conclusions were this signal is the aliasing of a higher frequency error inherited from the tide model correction: the semi-diurnal wave S2. The source of this error was mainly attributed to TOPEX measurements which are assimilated in ocean tide models. When these models are used in the computation of TOPEX/Poseidon MSL, most of the error cancels. However, this error is communicated to Jason-1 and Jason-2 MSLs. Since 2010, considerable efforts have been undertaken within the ocean tide community in order to correct ocean tide S2-waves from this error, particularly in the Goddard Ocean Tide (GOT) and Finite Element Solution (FES) latest versions. The present paper aims at assessing, quantifying and characterizing the reduction of the 58.77-day error thanks to the latest releases.

Like most fields of science over the past century or two, the subject of oceanic tides appears to have progressed through a few major phases that, in hindsight at least, can be readily identified. When observing tides with a satellite altimeter, the problem of aliasing can scarcely be avoided. There is an underlying pattern to the tidal aliasing for any satellite, and to understand this it is helpful to return to basic aliasing concepts. Some tidal aliasing problems, especially those involving mapping the broad-scale barotropic tides, can be mitigated somewhat by combining the additional phase observations from neighboring tracks or from ascending and descending tracks. One area where great progress has been made since the Le Provost review concerns the energetics and dissipation of the barotropic tide. Internal or baroclinic tides are internal gravity waves with tidal periodicity. They are generated by the interaction of barotropic tides with bottom topography.

The astronomer Manuel Johnson, a future President of the Royal Astronomical Society, recorded the ocean tides with his own instrument at St. Helena in 1826–1827, while waiting for an observatory to be built. It is an important record in the history of tidal science, as the only previous measurements at St. Helena had been those made by Nevil Maskelyne in 1761, and there were to be no other systematic measurements until the late 20th century. Johnson's tide gauge, of a curious but unique design, recorded efficiently the height of every tidal high and low water for at least 13 months, in spite of requiring frequent re-setting. These heights compare very reasonably with a modern tidal synthesis based on present-day tide gauge measurements from the same site. Johnson's method of timing is unknown, but his calculations of lunar phases suggest that his tidal measurements were recorded in Local Apparent Time. Unfortunately, the recorded times are found to be seriously and variably lagged by many minutes. Johnson's data have never been fully published, but his manuscripts have been safely archived and are available for inspection at Cambridge University. His data have been converted to computer files as part of this study for the benefit of future researchers.

Tidal geocenter motion has been previously ignored when developing ocean tide models from satellite altimetry. Accounting for tidal geocenter motion is necessary because the best orbit determinations for altimetric satellites position sea-surface heights relative to the center of mass of the total Earth system, including the ocean tides. But the ocean tides are presumed relative to the Earth's crust and thus are effectively relative to the center of figure. By accounting for this effect, we find improved agreement between an altimeter-based ocean tide model and bottom pressure recorder observations. The variance of differences between these two observations is reduced by 31% and 43% for the two tidal constituents with the largest contributions to geocenter variations, O1 and K1, respectively. With this accommodation the predicted contribution from altimeter-based ocean tide models to geocenter variations is amplified by 15–22%, providing improved agreement with observations, especially for the K1 component.

A new model of long-period tidal variations in length of day is developed. The model comprises 80 spectral lines with periods between 18.6 years and 4.7 days, and it consistently includes effects of mantle anelasticity and dynamic ocean tides for all lines. The anelastic properties follow Wahr and Bergen; experimental confirmation for their results now exists at the fortnightly period, but there remains uncertainty when extrapolating to the longest periods. The ocean modeling builds on recent work with the fortnightly constituent, which suggests that oceanic tidal angular momentum can be reliably predicted at these periods without data assimilation. This is a critical property when modeling most long-period tides, for which little observational data exist. Dynamic ocean effects are quite pronounced at shortest periods as out-of-phase rotation components become nearly as large as in-phase components. The model is tested against a 20 year time series of space geodetic measurements of length of day. The current international standard model is shown to leave significant residual tidal energy, and the new model is found to mostly eliminate that energy, with especially large variance reduction for constituents Sa, Ssa, Mf, and Mt.