Previous satellite estimates of internal tides are usually based on 25 years of sea surface height (SSH) data from 1993 to 2017 measured by exact-repeat (ER) altimetry missions. In this study, new satellite estimates of internal tides are based on eight years of SSH data from 2011 to 2018 measured mainly by non-repeat (NR) altimetry missions. The two datasets are labeled ER25yr and NR8yr, respectively. NR8yr has advantages over ER25yr in observing internal tides, because of its shorter time coverage and denser ground tracks. Mode-1 M2 internal tides are mapped from both datasets following the same procedure that consists of two rounds of plane wave analysis with a spatial bandpass filter in between. The denser ground tracks of NR8yr makes it possible to examine the impact of window size in the first-round plane wave analysis. Internal tide mapped using six different windows ranging from 40 to 160 km have almost the same results on global average, but smaller windows can better resolve isolated generation sources. The impact of time coverage is studied by comparing NR8yr160km and ER25yr160km, which are mapped using 160-km windows in the first-round plane wave analysis. They are evaluated using independent satellite altimetry data in 2020. NR8yr160km has larger model variance and can cause larger variance reduction, suggesting that NR8yr160km is a better model than ER25yr160km. Their global energies are 43.6 and 33.6 PJ, respectively, with a difference of 10 PJ. Their energy difference is a function of location.

The yearly mode-1 M₂ internal tide model in 2019 is constructed using sea-surface height measurements made by six concurrent satellite altimetry missions: Jason-3, Sentinel-3A, Sentinel-3B, CryoSat-2, Haiyang-2A and SARAL/AltiKa. The model is developed following a three-step procedure consisting of two rounds of plane wave analysis with a spatial bandpass filter in between. Prior mesoscale correction is made on the altimeter data using AVISO gridded mesoscale fields. The model is labeled Y2019, because it represents the one-year-coherent internal tide field in 2019. In contrast, the model developed using altimeter data from 1992–2017 is labeled MY25, because it represents the multi-year-coherent internal tide field in 25 years. Thanks to the new mapping technique, model errors in Y2019 are as low as those in MY25. Evaluation using independent altimeter data confirms that Y2019 reduces slightly less variance (∼6%) than MY25. Further analysis reveals that the altimeter data from five missions (without Jason-3) can yield an internal tide model of almost same quality. Comparing Y2019 and MY25 shows that mode-1 M₂ internal tides are subject to significant interannual variability in both amplitude and phase, and their interannual variations are a function of location. Along southward internal tides from Amukta Pass, the energy flux in Y2019 is two times large and the phase speed is about 1.1% faster. This mapping technique has been applied successfully to 2017 and 2018. This work demonstrates that yearly internal tides can be observed by concurrent altimetry missions and their interannual variations can be determined.

Shoaling internal solitary waves near the Dongsha Atoll in the South China Sea dissipate their energy and enhance diapycnal mixing, which have an important impact on the oceanic environment and primary productivity. The enhanced diapycnal mixing is patchy and instantaneous. Evaluating its spatiotemporal distribution requires comprehensive observation data. Fortunately, seismic oceanography meets the requirements, thanks to its high spatial resolution and large spatial coverage. In this paper, we studied three internal solitary waves in reversing polarity near the Dongsha Atoll and calculated their spatial distribution of diapycnal diffusivity. Our results show that the average diffusivities along three survey lines are 2 orders of magnitude larger than the open-ocean value. The average diffusivity in internal solitary waves with reversing polarity is 3 times that of the non-polarity reversal region. The diapycnal diffusivity is higher at the front of one internal solitary wave and gradually decreases from shallow to deep water in the vertical direction. Our results also indicate that (1) the enhanced diapycnal diffusivity is related to reflection seismic events, (2) convective instability and shear instability may both contribute to the enhanced diapycnal mixing in the polarity-reversing process, and (3) the difference between our results and Richardson-number-dependent turbulence parameterizations is about 2–3 orders of magnitude, but its vertical distribution is almost the same.

The seasonal variability of mode-1 M₂ internal tides is investigated using 25 years of multi-satellite altimeter data from 1992–2017. Four seasonal internal tide models are constructed using seasonally-subsetted altimeter data and World Ocean Atlas seasonal climatologies. This work is made possible by a newly-developed mapping procedure that can significantly suppress model errors. Seasonal-mean and seasonally-variable internal tide models are derived from the four seasonal models. All the models are inter-compared and evaluated using independent CryoSat-2 data. The seasonal-mean model is overall the best model because averaging the four seasonal models further reduces model errors. The seasonally-variable models are better in the tropical zone, where large seasonal signals may overcome model errors. Each seasonal model works best in its own season and worst in its opposite season. These internal tide models reveal that mode-1 M₂ internal tides are subject to significant seasonal variability and their seasonal variations are a function of location. Large seasonal variations dominantly occur in the tropical zone, where the World Ocean Atlas climatology shows strong seasonal variations in ocean stratification. Seasonal phase variations are obtained from the directionally-decomposed internal tide components. They are dominantly ±60° at the equator and up to ±120° in the central Arabian Sea. Incoherence caused by seasonal phase variations is usually <10%, but may be up to 40–50% in the tropical zone.

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology.

The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the "Green" Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments' development and satellite missions' evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion.

Internal solitary waves (ISWs) make important contributions to the energy cascade, ocean mixing and material transport in the ocean. However, there are few observational studies on the vertical structure of ISWs. In this article, we describe and analyze 11 ISWs near Dongsha Atoll in the South China Sea directly observed using two-dimensional seismic data. We calculate the vertical structures of these ISWs, and compared them with two theories. We find that three ISWs conform to the linear vertical structure function, four conform to the first-order nonlinear vertical structure function, and the remaining conform to neither function. We use the empirical mode decomposition (EMD) method to analyze reasons for the difference between the observed and theoretical vertical structures. The results show that the vertical structure is mainly determined by nonlinearity, which is an important dynamic characteristics of ISW. Therefore, whether the theory conforms to the observation depends on the ability of theory to describe the nonlinear characteristics of ISWs. In addition, topography and background flow affect the vertical structure.

Altimeter measurements are corrected for several geophysical parameters in order to access ocean signals of interest, like mesoscale or sub-mesoscale variability. The ocean tide is one of the most critical corrections due to the amplitude of the tidal elevations and to the aliasing phenomena of high-frequency signals into the lower-frequency band, but the internal-tide signatures at the ocean surface are not yet corrected globally.

Internal tides can have a signature of several centimeters at the surface with wavelengths of 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 correction of all tidal variability becomes mandatory to access accurate measurements of other oceanic signals.

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. The results show a significant altimeter variance reduction when using internal-tide corrections in all ocean regions where internal tides are generating or 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. This work led to the implementation of a new internal-tide correction (ZARON'one) in the next geophysical data records version-F (GDR-F) standards.

The disintegration of the equatorward-propagating K₁ internal tide in the South China Sea (SCS) by parametric subharmonic instability (PSI) at its critical latitude of 14.52°N is investigated numerically. The multiple-source generation and long-range propagation of K₁ internal tides are successfully reproduced. Using equilibrium analysis, the internal wave field near the critical latitude is found to experience two quasi-steady states, between which the subharmonic waves develop constantly. The simulated subharmonic waves agree well with classic PSI theoretical prediction. The PSI-induced near-inertial waves are of half the K₁ frequency and dominantly high modes, the vertical scales ranging from 50 to 180 m in the upper ocean. From an energy perspective, PSI mainly occurs in the critical latitudinal zone from 13–15°N. In this zone, the incident internal tide loses ~14% energy in the mature state of PSI. PSI triggers a mixing elevation of O(10^-5 – 10^-4 m²/s) in the upper ocean at the critical latitude, which is several times larger than the background value. The contribution of PSI to the internal tide energy loss and associated enhanced mixing may differ regionally and is closely dependent on the intensity and duration of background internal tide. The results elucidate the far-field dissipation mechanism by PSI in connecting interior mixing with remotely generated K₁ internal tides in the Luzon Strait.

Understanding the temporal variability of internal tides plays a crucial role in identifying sources and sinks of energy in the ocean. Using a 10‐month‐long time series from moored instruments inside a tidal beam south of the Azores, the magnitude and the underlying causes of temporal variability in the first two modes of the internal tide energy flux was studied. We analyzed changes of the direction and coherence of the energy flux, its modal structure, and the impact of two eddies. Semidiurnal energy fluxes were further compared with estimates from a 1/10° ocean global circulation model, as well as with fluxes derived from satellite altimetry. All energy fluxes correlate reasonably well in direction, deviations from its fixed phase relation to astronomical forcing, and modal composition while model and satellite underestimate the total energy flux. A pronounced damping of the in situ fluxes coincides with the passing of two eddies. In the presence of a surface‐intensified eddy, the coherent part of the energy flux in the first two modes is lowered by more than 40%, a subsurface eddy coincides with a decrease of the energy flux mainly in the second mode. These observations support the hypothesis that eddy interactions increase the incoherent part of the energy flux and transfer energy from low modes into higher modes, which can lead to increased local dissipation. It remains an open question how much of the energy converted from lower to higher modes results in local dissipation, a crucial part in creating energetically consistent ocean‐climate models.

The M₂ internal tides in the northeastern South China Sea are studied using satellite altimeter data from 1992–2018. By an improved mapping technique that combines plane wave analysis and two‐dimensional spatial filtering, multiple internal tides are separately extracted with weak internal tides becoming detectable. The satellite results reveal for the first time a 300‐km‐long southward M₂ internal tidal beam in the northeastern South China Sea. The generation source is on the steep continental slope at the southern entrance to the Taiwan Strait. It ranges from 118–120°E along 22°N. Combining satellite‐observed internal solitary waves and internal tides, it is found that the onshore radiation evolves into nonlinear solitary waves and the offshore radiation in the form of linear internal tides. Based on the 26‐year‐coherent satellite results, the integrated southward energy flux is 0.18 GW, about 10% of the westward energy flux from the Luzon Strait. In the northeastern South China Sea, the westward and southward internal tides form a multiwave interference field, which features significant spatial variations in the magnitude and direction of energy flux. Further analyses reveal that the steep continental slope radiates southward semidiurnal M₂ and S₂ internal tides, but not diurnal K₁ and O₁ internal tides.

Observations show ocean temperatures are rising due to climate change, resulting in a fivefold increase in the incidence of regional-scale coral bleaching events since the 1980s; analyses based on global climate models forecast bleaching will become an annual event for most of the world's coral reefs within 30–50 yr. Internal waves at tidal frequencies can regularly flush reefs with cooler waters, buffering the thermal stress from rising sea-surface temperatures. Here we present the first global maps of the effects these processes have on bleaching projections for three IPCC-AR5 emissions scenarios. Incorporating semidiurnal temperature fluctuations into the projected water temperatures at depth creates a delay in the timing of annual severe bleaching ≥ 10 yr (≥ 20 yr) for 38% (9%), 15% (1%), and 1% (0%) of coral reef sites for the low, moderate, and high emission scenarios, respectively; regional averages can reach twice as high. These cooling effects are greatest later in twenty-first century for the moderate emission scenarios, and around the middle twenty-first century for the highest emission scenario. Our results demonstrate how these effects could delay bleaching for corals, providing thermal refugia. Identification of such areas could be a factor for the selection of coral reef marine protected areas.

Highlights

• The doubling of the horizontal resolution doubles the number of resolved vertical modes.
• The increased resolution both affects surface and internal tide damping.
• Higher-resolution simulations need less parameterized internal-tide damping.
• The higher-resolution simulation agrees with validation data sets to within 10%.
• A correction factor is applied to allow for the comparison of stationary tide signals.

Mixing in the Samoan Passage has implications for the abyssal water properties of the entire North Pacific — nearly 20% of the global ocean's volume. Dense bottom water formed near Antarctica encounters the passage — a gap in a ridge extending from north of Samoa eastward across the Pacific at around 10°S — and forms an energetic cascade much like a river flowing through a canyon. The 2011–2014 Samoan Passage Abyssal Mixing Experiment explored the importance of topography to the dense water flow on a wide range of scales, including (1) constraints on transport due to the overall passage shape and the heights of its multiple sills, (2) rapid changes in water properties along particular pathways at localized mixing hotspots where there is extreme topographic roughness and/or downslope flow acceleration, and (3) diversion and disturbance of flow pathways and density surfaces by small-scale seamounts and ridges. The net result is a complex but fairly steady picture of interconnected pathways with a limited number of intense mixing locations that determine the net water mass transformation. The implication of this set of circumstances is that the dominant features of Samoan Passage flow and mixing (and their responses to variations in incoming or background properties) can be described by the dynamics of a single layer of dense water flowing beneath a less-dense one, combined with mixing and transformation that is determined by the small-scale topography encountered along flow pathways.

Satellite altimetry is one practical technique for observing internal tides on the global scale. However, it is a great challenge to extract weak internal tide signals. This paper presents a new technique for mapping internal tides from satellite altimeter data. Along‐track high‐pass filtering is needed to remove long‐wavelength nontidal noise and the barotropic tidal residual; however, the filter also removes internal tides having large angles with respect to satellite ground tracks. It thus causes blind directions in mapping internal tides from satellite altimetry: Generally west‐east propagating internal tides are missed. The new technique addresses the blind‐direction issue by replacing the problematic one‐dimensional (1‐D) high‐pass filter with a two‐dimensional (2‐D) band‐pass filter. This mapping technique is able to retrieve ubiquitous westbound and eastbound internal tides not captured in previous estimates. Long‐range westbound and eastbound waves travel over thousands of km from numerous generation sites such as the Emperor seamount chain, the Hawaiian Ridge, and the Kermadec trench. Evaluation using independent Cryosat‐2 data reveals that the new internal tide model may reduce more SSH variance than a model built in 2016 does in regions of strong internal tides. However, this mapping technique makes no improvement in strong boundary current regions, due to the dominance of mesoscale motions. Moreover, the new internal tide model contains leaked noise from westward propagating tropical instability waves (TIWs), which can be suppressed by prior along‐track high‐pass filtering. This paper suggests that better internal tide models may be constructed using both 1‐D and 2‐D filters with optimized parameters.

Though unresolved by Argo floats, internal waves still impart an aliased signal onto their profile measurements. Recent studies have yielded nearly global characterization of several constituents of the stationary internal tides. Using this new information in conjunction with thousands of floats, we quantify the influence of the stationary, mode-1 M₂ and S₂ internal tides on Argo-observed temperature. We calculate the in situ temperature anomaly observed by Argo floats (usually on the order of 0.1°C) and compare it to the anomaly expected from the stationary internal tides derived from altimetry. Globally, there is a small, positive correlation between the expected and in situ signals. There is a stronger relationship in regions with more intense internal waves, as well as at depths near the nominal mode-1 maximum. However, we are unable to use this relationship to remove significant variance from the in situ observations. This is somewhat surprising, given that the magnitude of the altimetry-derived signal is often on a similar scale to the in situ signal, and points toward a greater importance of the nonstationary internal tides than previously assumed.

The energy radiated by the Earth toward space does not compensate the incoming radiation from the Sun leading to a small positive energy imbalance at the top of the atmosphere (0.4–1 Wm^-2). This imbalance is coined Earth’s Energy Imbalance (EEI). It is mostly caused by anthropogenic greenhouse gas emissions and is driving the current warming of the planet. Precise monitoring of EEI is critical to assess the current status of climate change and the future evolution of climate. But the monitoring of EEI is challenging as EEI is two orders of magnitude smaller than the radiation fluxes in and out of the Earth system. Over 93% of the excess energy that is gained by the Earth in response to the positive EEI accumulates into the ocean in the form of heat. This accumulation of heat can be tracked with the ocean observing system such that today, the monitoring of Ocean Heat Content (OHC) and its long-term change provide the most efficient approach to estimate EEI. In this community paper we review the current four state-of-the-art methods to estimate global OHC changes and evaluate their relevance to derive EEI estimates on different time scales. These four methods make use of: (1) direct observations of in situ temperature; (2) satellite-based measurements of the ocean surface net heat fluxes; (3) satellite-based estimates of the thermal expansion of the ocean and (4) ocean reanalyses that assimilate observations from both satellite and in situ instruments. For each method we review the potential and the uncertainty of the method to estimate global OHC changes. We also analyze gaps in the current capability of each method and identify ways of progress for the future to fulfill the requirements of EEI monitoring. Achieving the observation of EEI with sufficient accuracy will depend on merging the remote sensing techniques with in situ measurements of key variables as an integral part of the Ocean Observing System.

Low‐mode internal waves propagate over large distances and provide energy for turbulent mixing when they break far from their generation sites. A realistic representation of the oceanic energy cycle in ocean and climate models requires a consistent implementation of their generation, propagation, and dissipation. Here we combine the long‐term mean energy flux from satellite altimetry with results from a 1/10° global ocean general circulation model that resolves the low modes of internal waves and in situ observations of stratification and horizontal currents to study energy flux and dissipation along a 1000 km internal tide beam in the eastern North Atlantic. Internal wave fluxes were estimated from twelve 36‐ to 48‐hr stations in along‐ and across‐beam direction to resolve both the inertial period and tidal cycle. The observed internal tide energy fluxes range from 5.9 kW m^-1 near the generation sites to 0.5 kW m^-1 at distant stations. Estimates of energy dissipation come from both finestructure and upper ocean microstructure profiles and range, vertically integrated, from 0.5 to 3.3 mW m^-2 along the beam. Overall, the in situ observations confirm the internal tide pattern derived from satellite altimetry, but the in situ energy fluxes are more variable and decrease less monotonically along the beam. Internal tides in the model propagate over shorter distances compared to results from altimetry and in situ measurements, but more spatial details close the main generation sites are resolved.

The M₂ internal tide field contains waves of various baroclinic modes and various horizontal propagation directions. This paper presents a technique for decomposing the sea surface height (SSH) field of the multimodal multidirectional internal tide. The technique consists of two steps: First, different baroclinic modes are decomposed by two-dimensional (2D) spatial filtering, utilizing their different horizontal wavelengths; second, multidirectional waves in each mode are decomposed by 2D plane wave analysis. The decomposition technique is demonstrated using the M₂ internal tide field simulated by the MITgcm. This paper focuses on a region lying off the US West Coast ranging 20° – 50°N, 220° – 245°E. The lowest three baroclinic modes are separately resolved from the internal tide field; each mode is further decomposed into five waves of arbitrary propagation directions in horizontal. The decomposed fields yield unprecedented details on the internal tide’s generation and propagation, which cannot be observed in the harmonically fitted field. The results reveal that the mode-1 M₂ internal tide in the study region is dominantly from the Hawaiian Ridge to the west, but also generated locally at the Mendocino Ridge and continental slope. The mode-2 and mode-3 M₂ internal tides are generated at isolated seamounts, as well as the Mendocino Ridge and continental slope. The Mendocino Ridge radiates both southbound and northbound M₂ internal tides for all three modes. Their propagation distances decrease with increasing mode number: Mode-1 waves can travel over 2000 km; while mode-3 waves can only be tracked for 300 km. The decomposition technique may be extended to other tidal constituents and to the global ocean.

Turbulent mixing in the ocean is key to regulate the transport of heat, freshwater and biogeochemical tracers, with strong implications for Earth’s climate. In the deep ocean, tides supply much of the mechanical energy required to sustain mixing via the generation of internal waves, known as internal tides, whose fate — the relative importance of their local versus remote breaking into turbulence — remains uncertain. Here, we combine a semi-analytical model of internal tide generation with satellite and in situ measurements to show that from an energetic viewpoint, small-scale internal tides, hitherto overlooked, account for the bulk (>50%) of global internal tide generation, breaking and mixing. Furthermore, we unveil the pronounced geographical variations of their energy proportion, ignored by current parameterisations of mixing in climate-scale models. Based on these results, we propose a physically consistent, observationally supported approach to accurately represent the dissipation of small-scale internal tides and their induced mixing in climate-scale models.

The surface tide flowing over bottom topography converts part of its energy into the internal tide. The internal tide propagates away from the generation site and eventually dissipates in the ocean. The propagation distance may be up to 3,500 km. The global internal tide is very complicated because (1) the internal tide can be generated over numerous generation sites and (2) the internal tide is a superposition of orthogonal baroclinic modes. Previously, I have addressed the first issue by developing a plane wave analysis method, which is a variant of harmonic analysis. My previous studies focus on the dominant mode‐1 internal tide. In this study, I address the second issue. This is an important and challenging scientific question, because different modes have different vertical structures and dissipation rates. To fully understand the internal tide field, we should investigate the internal tide's generation and propagation for each mode. In this study, I construct the first global map of the mode‐2 M₂ internal tide. I find that mode 2 makes significant contributions to internal tidal energetics and sea surface height variance. My satellite results contain rich information on the global internal tide and reveal some unprecedented fundamental features.

Mooring data collected on the continental slope of the South China Sea show that along‐slope deep sea bottom currents are generated when large spring internal tides (internal waves with tidal frequency) are observed, with the maximum velocity amplitude exceeding 0.15 m/s. The observations are consistent with predictions that near‐bottom breaking of internal waves can result in generation of along‐slope flows when these waves obliquely approach the slope. A linear internal tide model in one horizontal dimension with realistic topography and stratification is used to show that the breaking of internal tides is likely due to near‐critical reflection on the slope. Combining the mooring observations and the model simulation, an along‐slope near‐bottom transport of ~0.5 Sv is estimated. Along‐slope bottom flows caused by breaking internal waves potentially provide a significant way to deform continental slopes and affect deep water exchange between the marginal sea and open ocean.

Low-mode internal tides, a dominant part of the internal wave spectrum, carry energy over large distances, yet the ultimate fate of this energy is unknown. Internal tides in the Tasman Sea are generated at Macquarie Ridge, south of New Zealand, and propagate northwest as a focused beam before impinging on the Tasmanian continental slope. In situ observations from the Tasman Sea capture synoptic measurements of the incident semidiurnal mode-1 internal-tide, which has an observed wavelength of 183 km and surface displacement of approximately 1 cm. Plane-wave fits to in situ and altimetric estimates of surface displacement agree to within a measurement uncertainty of 0.3 cm, which is the same order of magnitude as the nonstationary (not phase locked) mode-1 tide observed over a 40-day mooring deployment. Stationary energy flux, estimated from a plane-wave fit to the in situ observations, is directed toward Tasmania with a magnitude of 3.4 ± 1.4 kW m^-1, consistent with a satellite estimate of 3.9 ± 2.2 kW m^-1. Approximately 90% of the time-mean energy flux is due to the stationary tide. However, nonstationary velocity and pressure, which are typically 1/4 the amplitude of the stationary components, sometimes lead to instantaneous energy fluxes that are double or half of the stationary energy flux, overwhelming any spring–neap variability. Despite strong winds and intermittent near-inertial currents, the parameterized turbulent-kinetic-energy dissipation rate is small (i.e., 10^-10 W kg^-1) below the near surface and observations of mode-1 internal tide energy-flux convergence are indistinguishable from zero (i.e., the confidence intervals include zero), indicating little decay of the mode-1 internal tide within the Tasman Sea.

The M₂ internal tide in the Tasman Sea is investigated using sea surface height measurements made by multiple altimeter missions from 1992 to 2012. Internal tidal waves are extracted by two-dimensional plane wave fits in 180 km by 180 km windows. The results show that the Macquarie Ridge radiates three internal tidal beams into the Tasman Sea. The northern and southern beams propagate respectively into the East Australian Current and the Antarctic Circumpolar Current and become undetectable to satellite altimetry. The central beam propagates across the Tasman Sea, impinges on the Tasmanian continental slope, and partially reflects. The observed propagation speeds agree well with theoretical values determined from climatological ocean stratification. Both the northern and central beams refract about 15° toward the equator because of the beta effect. Following a concave submarine ridge in the source region, the central beam first converges around 45.5°S, 155.5°E and then diverges beyond the focal region. The satellite results reveal two reflected internal tidal beams off the Tasmanian slope, consistent with previous numerical simulations and glider measurements. The total energy flux from the Macquarie Ridge into the Tasman Sea is about 2.2 GW, of which about half is contributed by the central beam. The central beam loses little energy in its first 1000-km propagation, for which the likely reasons include flat bottom topography and weak mesoscale eddies.

The life cycle of semidiurnal internal tides over the Mid-Atlantic Ridge (MAR) sector south of the Azores is investigated using in situ, a high-resolution mooring and microstructure profiler, and satellite data, in combination with a theoretical model of barotropic-to-baroclinic tidal energy conversion. The mooring analysis reveals that the internal tide horizontal energy flux is dominated by mode 1 and that energy density is more distributed among modes 1–10. Most modes are compatible with an interpretation in terms of standing internal tides, suggesting that they result from interactions between waves generated over the MAR. Internal tide energy is thus concentrated above the ridge and is eventually available for local diapycnal mixing, as endorsed by the elevated rates of turbulent energy dissipation ε estimated from microstructure measurements. A spring–neap modulation of energy density on the MAR is found to originate from the remote generation and radiation of strong mode-1 internal tides from the Atlantis-Meteor Seamount Complex. Similar fortnightly variability of a factor of 2 is observed in ε, but this signal’s origin cannot be determined unambiguously. A regional tidal energy budget highlights the significance of high-mode generation, with 81% of the energy lost by the barotropic tide being converted into modes >1 and only 9% into mode 1. This has important implications for the fraction (q) of local dissipation to the total energy conversion, which is regionally estimated to be ~0.5. This result is in stark contrast with the Hawaiian Ridge system, where the radiation of mode-1 internal tides accounts for 30% of the regional energy conversion, and q < 0.25.

The superposition of two waves of slightly different wavelengths has long been used to illustrate the distinction between phase velocity and group velocity. The first-mode M₂ and S₂ internal tides exemplify such a two-wave model in the natural ocean. The M₂ and S₂ tidal frequencies are 1.932 and 2 cycles per day, respectively, and their superposition forms a spring-neap cycle in the semidiurnal band. The spring-neap cycle acts like a wave, with its frequency, wave number, and phase being the differences of the M₂ and S₂ internal tides. The spring-neap cycle and energy of the semidiurnal internal tide propagate at the group velocity. Long-range propagation of M₂ and S₂ internal tides in the North Pacific is observed by satellite altimetry. Along a 3,400 km beam spanning 24° – 54°N, the M₂ and S₂ travel times are 10.9 and 11.2 days, respectively. For comparison, it takes the spring-neap cycle 21.1 days to travel over this distance. Spatial maps of the M₂ phase velocity, the S₂ phase velocity, and the group velocity are determined from phase gradients of the corresponding satellite observed internal tide fields. The observed phase and group velocities agree with theoretical values estimated using the World Ocean Atlas 2013 annual-mean ocean stratification.

The global mode-1 S₂ internal tide is observed using sea surface height (SSH) measurements from four satellite altimeters: TOPEX/Poseidon, Jason-1, Jason-2, and Geosat Follow-On. Plane wave analysis is employed to extract three mode-1 S₂ internal tidal waves in any given 250 km by 250 km window, which are temporally coherent over a 20 year period from 1992 to 2012. Depth-integrated energy and flux of the S₂ internal tide are calculated from the SSH amplitude and a conversion function built from climatological hydrographic profiles in the World Ocean Atlas 2013. The results show that the S₂ and M₂ internal tides have similar spatial patterns. Both S₂ and M₂ internal tides originate at major topographic features and propagate over long distances. The S₂ internal tidal beams are generally shorter, likely because the relatively weaker S₂ internal tide is easily overwhelmed by nontidal noise. The northbound S₂ and M₂ internal tides from the Hawaiian Ridge are observed to travel over 3500 km across the Northeast Pacific. The globally integrated energy of the mode-1 S₂ internal tide is 7.8 PJ (1 PJ = 10¹⁵ J), about 20% that of M₂ (36.4 PJ). The histogram of S₂ to M₂ SSH ratios peaks at 0.4, consistent with the square root of their energy ratio. In terms of SSH, S₂ is greater than M₂ in math formula ~10% of the global ocean and ≥50% of M₂ in about half of the global ocean.

Recent advances in our understanding of internal-wave driven turbulent mixing in the ocean interior are summarized. New parameterizations for global climate ocean models, and their climate impacts, are introduced.

Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean and, consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Away from ocean boundaries, the spatio-temporal patterns of mixing are largely driven by the geography of generation, propagation and dissipation of internal waves, which supply much of the power for turbulent mixing. Over the last five years and under the auspices of US CLIVAR, a NSF- and NOAA-supported Climate Process Team has been engaged in developing, implementing and testing dynamics-based parameterizations for internal-wave driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here we review recent progress, describe the tools developed, and discuss future directions.

We examine the temporal means and variability of the semidiurnal internal tide energy fluxes in 1/25° global simulations of the Hybrid Coordinate Ocean Model (HYCOM) and in a global archive of 79 historical moorings. Low-frequency flows, a major cause of internal tide variability, have comparable kinetic energies at the mooring sites in model and observations. The computed root-mean-square (RMS) variability of the energy flux is large in both model and observations and correlates positively with the time-averaged flux magnitude. Outside of strong generation regions, the normalized RMS variability (the RMS variability divided by the mean) is nearly independent of the flux magnitudes in the model, and of order 23% or more in both the model and observations. The spatially averaged flux magnitudes in observations and the simulation agree to within a factor of about 1.4 and 2.4 for vertical mode-1 and mode-2, respectively. The difference in energy flux computed from the full-depth model output versus model output subsampled at mooring instrument depths is small. The global historical archive is supplemented with six high-vertical resolution moorings from the Internal Waves Across the Pacific (IWAP) experiment. The model fluxes agree more closely with the high-resolution IWAP fluxes than with the historical mooring fluxes. The high variability in internal tide energy fluxes implies that internal tide fluxes computed from short observational records should be regarded as realizations of a highly variable field, not as "means" that are indicative of conditions at the measurement sites over all time.

The variability of internal tides during their generation and long-range propagation in the South China Sea (SCS) is investigated by driving a high-resolution numerical model. The present study clarifies the notably different processes of generation, propagation, and dissipation between diurnal and semidiurnal internal tides. Internal tides in the SCS originate from multiple source sites, among which the Luzon Strait is dominant, and contributes approximately 90% and 74% of the baroclinic energy for M₂ and K₁, respectively. To the west of the Luzon Strait, local generation of K1 internal tides inside the SCS is more energetic than the M2 tides. Diurnal and semidiurnal internal tides from the Luzon Strait radiate into the SCS in a north-south asymmetry but with different patterns because of the complex two-ridge system. The tidal beams can travel across the deep basin and finally arrive at the Vietnam coast and Nansha Island more than 1000–1500 km away. During propagation, M₂ internal tides maintain a southwestward direction, whereas K₁ exhibit complicated wave fields because of the superposition of waves from local sources and island scattering effects. After significant dissipation within the Luzon Strait, the remaining energy travels into the SCS and reduces by more than 90% over a distance of ~1000 km. Inside the SCS, the K₁ internal tides with long crests and flat beam angles are more influenced by seafloor topographical features and thus undergo apparent dissipation along the entire path, whereas the prominent dissipation of M₂ internal tides only occurs after their arrival at Zhongsha Island.

A concept of internal tide oceanic tomography (ITOT) is proposed to monitor ocean warming on a global scale. ITOT is similar to acoustic tomography, but that work waves are internal tides. ITOT detects ocean temperature changes by precisely measuring travel time changes of long-range propagating internal tides. The underlying principle is that upper ocean warming strengthens ocean stratification and thus increases the propagation speed of internal tides. This concept is inspired by recent advances in observing internal tides by satellite altimetry. In particular, a plane wave fit method can separately resolve multiple internal tidal waves and thus accurately determines the phase of each wave. Two examples are presented to demonstrate the feasibility and usefulness of ITOT. In the eastern tropical Pacific, the yearly time series of travel time changes of the M₂ internal tide is closely correlated with the El Niño–Southern Oscillation index. In the North Atlantic, significant interannual variations and bidecadal trends are observed and consistent with the changes in ocean heat content measured by Argo floats. ITOT offers a long-term, cost-effective, environmentally friendly technique for monitoring global ocean warming. Future work is needed to quantify the accuracy of this technique.

This paper evaluates M₂ internal tides observed from multisatellite altimetry (MultiSat20yr) using CryoSat-2 altimeter data. MultiSat20yr is constructed using 20 years of sea surface height measurements made by multiple satellite altimeters from 1992 to 2012. Here it is demonstrated that M₂ internal tides can also be extracted using 4 years of CryoSat-2 data from 2011 to 2014 (CryoSat4yr) by the same plane wave fit method. MultiSat20yr and CryoSat4yr are in good agreement in the central North Pacific, although they are from satellite data of different sampling patterns (1998 versus 10,688 tracks) and different observational periods (20 versus 4 years). Further comparisons are carried out for three isolated wave components. MultiSat20yr and CryoSat4yr agree very well for both Hawaiian components, suggesting that the Hawaiian Ridge is a relatively stable generation site. In contrast, the Aleutian Ridge is a relatively unstable source in that the M₂ amplitudes in MultiSat20yr and CryoSat4yr are very different. With respect to MultiSat20yr, the M₂ internal tide in 2011–2014 propagates slower (faster) to the south (north) of Hawaii, respectively, suggesting that the internal tide's propagation speed is subject to significant interannual variability. This feature is supported by M₂ internal tides observed using multisatellite altimeter data in 2005 (MultiSat2005) and Argo measured upper ocean temperature profiles. MultiSat20yr is used to correct M₂ internal tides in the CryoSat-2 data. Significant and efficient variance reduction suggests that MultiSat20yr is a reliable internal tide model. A phase-adjusted MultiSat20yr is built to account for the interannual variations, and it works better in internal tide correction.

A global map of open-ocean mode-1 M₂ internal tides is constructed using sea-surface height (SSH) measurements from multiple satellite altimeters during 1992–2012, representing a 20-year coherent internal tide field. A two-dimensional plane wave fit method is employed to (1) suppress mesoscale contamination by extracting internal tides with both spatial and temporal coherence, and (2) separately resolve multiple internal tidal waves. Global maps of amplitude, phase, energy and flux of mode-1 M₂ internal tides are presented. M₂ internal tides are mainly generated over topographic features including continental slopes, mid-ocean ridges and seamounts. Internal tidal beams of 100–300 km width are observed to propagate hundreds to thousands of km. Multi-wave interference of some degree is widespread, due to the M₂ internal tide's numerous generation sites and long-range propagation. The M₂ internal tide propagates across the critical latitudes for parametric subharmonic instability (28.8°S/N) with little energy loss, consistent with field measurements by MacKinnon et al. (2013). In the eastern Pacific Ocean, the M₂ internal tide loses significant energy in propagating across the Equator; in contrast, little energy loss is observed in the equatorial zones of the Atlantic, Indian, and western Pacific oceans. Global integration of the satellite observations yields a total energy of 36 PJ (1 PJ = 10¹⁵ J) for the coherent mode-1 M₂ internal tide. The satellite observed M₂ internal tides compare favorably with field mooring measurements and a global eddy-resolving numerical model.

The effects of a parameterized linear internal wave drag on the semidiurnal barotropic and baroclinic energetics of a realistically forced, three-dimensional global ocean model are analyzed. Although the main purpose of the parameterization is to improve the surface tides, it also influences the internal tides. The relatively coarse resolution of the model of ~8 km only permits the generation and propagation of the first three vertical modes. Hence, this wave drag parameterization represents the energy conversion to and the subsequent breaking of the unresolved high modes. The total tidal energy input and the spatial distribution of the barotropic energy loss agree with the Ocean Topography Experiment (TOPEX)/Poseidon (TPXO) tidal inversion model. The wave drag overestimates the high-mode conversion at ocean ridges as measured against regional high-resolution models. The wave drag also damps the low-mode internal tides as they propagate away from their generation sites. Hence, it can be considered a scattering parameterization, causing more than 50% of the deep-water dissipation of the internal tides. In the near field, most of the baroclinic dissipation is attributed to viscous and numerical dissipation. The far-field decay of the simulated internal tides is in agreement with satellite altimetry and falls within the broad range of Argo-inferred dissipation rates. In the simulation, about 12% of the semidiurnal internal tide energy generated in deep water reaches the continental margins.

Underwater ambient sound levels beneath tropical cyclones were measured using hydrophones onboard Lagrangian floats, which were air deployed in the paths of Hurricane Gustav (2008) and Typhoons Megi (2010) and Fanapi (2010). The sound levels at 40 Hz – 50 kHz from 1- to 50-m depth were measured at wind speeds up to 45 m s^-1. The measurements reveal a complex dependence of the sound level on wind speed due to the competing effects of sound generation by breaking wind waves and sound attenuation by quiescent bubbles. Sound level increases monotonically with increasing wind speed only for low frequencies (<200 Hz). At higher frequencies (>200 Hz), sound level first increases and then decreases with increasing wind speed. There is a wind speed that produces a maximum sound level for each frequency; the wind speed of the maximum sound level decreases with frequency. Sound level at >20 kHz mostly decreases with wind speed over the wind range 15–45 m s^-1. The sound field is nearly uniform with depth in the upper 50 m with nearly all sound attenuation limited to the upper 2 m at all measured frequencies. A simple model of bubble trajectories based on the measured float trajectories finds that resonant bubbles at the high-frequency end of the observations (25 kHz) could easily be advected deeper than 2 m during tropical cyclones. Thus, bubble rise velocity alone cannot explain the lack of sound attenuation at these depths.

The M₂, K₁, and O₁ internal tides originating in the Luzon Strait are investigated using the sea surface height measurements by multiple satellites ERS-2, Envisat, TOPEX/Poseidon, Jason-1/2, and Geosat Follow-On. A plane wave fit method is used to resolve multiple internal tides in arbitrary horizontal directions. The Luzon Strait is an energetic internal tide generation site, and radiates internal tides both westward into the South China Sea (SCS) and eastward into the western Pacific (WP). In the SCS, the K₁ and O₁ internal tides propagate over 1600 km, reaching the Vietnam coast; in the WP, they propagate over 2500 km and arrive to the Mariana Ridge and Guam. The K₁ and O₁ internal tides refract toward the Equator during propagation. The M₂ internal tides in the SCS bifurcate into two beams. The northwestward beam is coincident with the frequent occurrence of internal solitary waves in this region, implying their causative relation. The phase speeds inferred from the altimetric along-beam propagation agree with the theoretical values. Due to the influence of the Earth's rotation, the K₁ and O₁ phase speeds decrease remarkably from high to low latitudes. For the diurnal internal tides, the eastward radiation is about 50% greater than the westward radiation. For M₂, the westward radiation is about two times the eastward radiation. The altimetric energy fluxes are about 50% of those in numerical model simulations.

Monterey Submarine Canyon is a large, sinuous canyon off the coast of California, the upper reaches of which were the subject of an internal tide observational program using moored profilers and upward-looking moored ADCPs. The mooring observations measured a near-surface stratification change in the upper canyon, likely caused by a seasonal shift in the prevailing wind that favoured coastal upwelling. This change in near-surface stratification caused a transition in the behaviour of the internal tide in the upper canyon from a partly standing wave during pre-upwelling conditions to a progressive wave during upwelling conditions. Using a numerical model, we present evidence that either a partly standing or a progressive internal tide can be simulated in the canyon, simply by changing the initial stratification conditions in accordance with the observations. The mechanism driving the transition is a dependence of down-canyon (supercritical) internal tide reflection from the canyon floor and walls on the depth of maximum stratification. During pre-upwelling conditions, the main pycnocline extends down to 200 m (below the canyon rim) resulting in increased supercritical reflection of the up-canyon propagating internal tide back down the canyon. The large up-canyon and smaller down-canyon progressive waves are the two components of the partly standing wave. During upwelling conditions, the pycnocline shallows to the upper 50 m of the watercolumn (above the canyon rim) resulting in decreased supercritical reflection and allowing the up-canyon progressive wave to dominate.

Internal solitary waves (ISWs) occur ubiquitously in China's waters: the South China Sea (SCS), the East China Sea (ECS), the Yellow Sea (YS), and the Bohai Sea (BS). ISWs have long attracted much research interest because of their important role in ocean acoustics, offshore engineering, ocean mixing, primary productivity, and submarine navigation. ISWs have sea surface signatures that can be detected by satellite synthetic aperture radar (SAR) and optical sensors. Satellite remote-sensing images provide excellent two-dimensional views of the ISW field. Our understanding of ISWs in the China Seas has been greatly improved using satellite remote-sensing techniques. The primary objectives of this paper are to review the development of remote-sensing techniques in the study of ISWs and to summarize ISW characteristics in the China seas, mainly demonstrated by remote-sensing techniques. In addition, several issues with remote-sensing techniques and interesting research topics are discussed.

Internal solitary waves (ISWs) are observed 2 times within 30 min in synthetic aperture radar (SAR) image pairs from the Envisat and ERS-2 tandem satellites. Three pairs of SAR images were acquired in the South China Sea (SCS) in April 2007, August 2008, and March 2009, and 13 ISWs were tracked between the image pair in an ArcGIS environment. The phase speeds of these ISWs are calculated from their spatial displacement and time interval. The resultant ISW speeds agree well with the theoretical values estimated from the Sturm-Louisville equation using local bathymetric and monthly climatology ocean stratification data. This technique reveals the spatial variation in the ISWs speed in the water depth between 100 and 4000 m in the SCS. The study shows that ISWs speed is mainly affected by bottom topography and generally decreases from deep to shallow water from east to west and from south to north.

Observational evidence is presented for transfer of energy from the internal tide to near-inertial motions near 29°N in the Pacific Ocean. The transfer is accomplished via parametric subharmonic instability (PSI), which involves interaction between a primary wave (the internal tide in this case) and two smaller-scale waves of nearly half the frequency. The internal tide at this location is a complex superposition of a low-mode waves propagating north from Hawaii and higher-mode waves generated at local seamounts, making application of PSI theory challenging. Nevertheless, a statistically significant phase locking is documented between the internal tide and upward- and downward-propagating near-inertial waves. The phase between those three waves is consistent with that expected from PSI theory. Calculated energy transfer rates from the tide to near-inertial motions are modest, consistent with local dissipation rate estimates. The conclusion is that while PSI does befall the tide near a critical latitude of 29°N, it does not do so catastrophically.

Turbulent mixing rates are inferred from measurements spanning 25°–37°N in the Pacific Ocean. The observations were made as part of the Internal Waves Across the Pacific experiment, designed to investigate the long-range fate of the low-mode internal tide propagating north from Hawaii. Previous and companion results argue that, near a critical latitude of 29°N, the internal tide loses energy to high-mode near-inertial motions through parametric subharmonic instability. Here, the authors estimate mixing from several variations of the finescale shear–strain parameterization, as well as Thorpe-scale analysis of overturns. Though all estimated diffusivities are modest in magnitude, average diffusivity in the top kilometer shows a factor of 2%u20134 elevation near and equatorward of 29°N. However, given intrinsic uncertainty and the strong temporal variability of diffusivity observed in long mooring records, the meridional mixing pattern is found to be near the edge of statistical significance.

The time variability of the energetics and turbulent dissipation of internal tides in the upper Monterey Submarine Canyon (MSC) is examined with three moored profilers and five ADCP moorings spanning February–April 2009. Highly resolved time series of velocity, energy, and energy flux are all dominated by the semidiurnal internal tide and show pronounced spring-neap cycles. However, the onset of springtime upwelling winds significantly alters the stratification during the record, causing the thermocline depth to shoal from about 100 to 40 m. The time-variable stratification must be accounted for because it significantly affects the energy, energy flux, the vertical modal structures, and the energy distribution among the modes. The internal tide changes from a partly horizontally standing wave to a more freely propagating wave when the thermocline shoals, suggesting more reflection from up canyon early in the observational record. Turbulence, computed from Thorpe scales, is greatest in the bottom 50–150 m and shows a spring-neap cycle. Depth-integrated dissipation is 3 times greater toward the end of the record, reaching 60 mW m^-2 during the last spring tide. Dissipation near a submarine ridge is strongly tidally modulated, reaching 10^-5 W kg^-1 (10–15-m overturns) during spring tide and appears to be due to breaking lee waves. However, the phasing of the breaking is also affected by the changing stratification, occurring when isopycnals are deflected downward early in the record and upward toward the end.

The low-frequency oceanography of the Washington continental shelf has been studied in great detail over the last several decades owing in part to its high productivity but relatively weak upwelling winds compared to other systems. Interestingly, though many internal wave-resolving measurements have been made, there have been no reports on the region's internal wave climate and the possible feedbacks between internal waves and lower-frequency processes. This paper reports observations over two summers obtained from a new observing system of two moorings and a glider on the Washington continental shelf, with a focus on internal waves and their relationships to lower-frequency currents, stratification, dissolved oxygen, and nutrient distributions. We observe a rich, variable internal wave field that appears to be modulated in part by a coastal jet and its response to the region's frequent wind reversals. The internal wave spectral level at intermediate frequencies is consistent with the model spectrum of Levine (2002) developed for continental shelves. Superimposed on this continuum are (1) a strong but highly temporally variable semidiurnal internal tide field and (2) an energetic field of high-frequency nonlinear internal waves (NLIWs). Mean semidiurnal energy flux is about 80 W m^-1 to the north-northeast. The onshore direction of the flux and its lack of a strong spring/neap cycle suggest it is at least partly generated remotely. Nonlinear wave amplitudes reach 38 m in 100 m of water, making them among the strongest observed on continental shelves of similar depth. They often occur each 12.4 hours, clearly linking them to the tide. Like the internal tide energy flux, the NLIWs are also directed toward the north-northeast. However, their phasing is not constant with respect to either the baroclinic or barotropic currents, and their amplitude is uncorrelated with either internal-tide energy flux or barotropic tidal forcing, suggesting substantial modulation by the low-frequency currents and stratification.

Low-mode internal tides propagate over thousands of kilometers from their generation sites, distributing tidal energy across the ocean basins. Though internal tides can have large vertical displacements (often tens of meters or more) in the ocean interior, they deflect the sea surface only by several centimeters. Because of the regularity of the tidal forcing, this small signal can be detected by state-of-the-art, repeat-track, high-precision satellite altimetry over nearly the entire world ocean. Making use of combined sea surface height measurements from multiple satellites (which together have denser ground tracks than any single mission), it is now possible to resolve the complex interference patterns created by multiple internal tides using an improved plane-wave fit technique. As examples, we present regional M2 internal tide fields around the Mariana Arc and the Hawaiian Ridge and in the North Pacific Ocean. The limitations and some perspective on the multisatellite altimetric methods are discussed.

Satellite altimetric sea surface height anomaly (SSHA) data from Geosat Follow-on (GFO) and European Remote Sensing (ERS), as well as TOPEX/Poseidon (T/P), are merged to estimate M₂ internal tides around the Hawaiian Ridge, with higher spatial resolution than possible with single-satellite altimetry. The new estimates are compared with numerical model runs. Along-track analyses show that M₂ internal tides can be resolved from both 8 years of GFO and 15.5 years of ERS SSHA data. Comparisons at crossover points reveal that the M₂ estimates from T/P, GFO, and ERS agree well. Multisatellite altimetry improves spatial resolution due to its denser ground tracks. Thus M₂ internal tides can be plane wave fitted in 120 km x 120 km regions, compared to previous single-satellite estimates in 4° lon x 3° lat or 250 km x 250 km regions. In such small fitting regions the weaker and smaller-scale mode 2 M₂ internal tides can also be estimated.

The higher spatial resolution leads to a clearer view of the M₂ internal tide field around the Hawaiian Ridge. Discrete generation sites and internal tidal beams are clearly distinguishable, and consistent with the numerical model runs. More importantly, multisatellite altimetry produces larger M₂ internal tidal energy fluxes, which agree better with model results, than previous single-satellite estimates. This study confirms that previous altimetric underestimates are partly due to the more widely spaced ground tracks and consequently larger fitting region. Multisatellite altimetry largely overcomes this limitation.

The Mariana Arc of ridges and islands forms an ~1300-km-long arc of a circle, ~630 km in radius centered at 17N, 139.6E. The hypothesis that the westward-propagating internal tides originating from the arc converge in a focal region is tested by examining the dominant M2 internal tides observed with air-launched expendable bathythermographs (AXBTs) and altimetric data from multiple satellites. The altimetric and AXBT observations agree well, though they measure different aspects of the internal tidal motion. M2 internal tides radiate both westward and eastward from the Mariana Arc, with isophase lines parallel to the arc and sharing the same center. The westward-propagating M2 internal tides converge in a focal region, and diverge beyond the focus. The focusing leads to energetic M2 internal tides in the focal region. The spatially smoothed energy flux is about 6.5 kW/m, about four times the mean value at the arc; the spatially un-smoothed energy flux may reach up to 17 kW/m. The size of the focus is close to the Rayleigh estimate; it is thus a perfect focus.

The northeastward progression of the semidiurnal internal tide from French Frigate Shoals (FFS), Hawaii, is studied with an array of six simultaneous profiling moorings spanning 25.5–37.1 deg N (~1400 km) and 13-yr-long Ocean Topography Experiment (TOPEX)/Poseidon (T/P) altimeter data processed by a new technique. The moorings have excellent temporal and vertical resolutions, while the altimeter offers broad spatial coverage of the surface manifestation of the internal tide's coherent portion. Together these two approaches provide a unique view of the internal tide's long-range propagation in a complex ocean environment. The moored observations reveal a rich, time-variable, and multimodal internal tide field, with higher-mode motions contributing significantly to velocity, displacement, and energy. In spite of these contributions, the coherent mode-1 internal tide dominates the northeastward energy flux, and is detectable in both moored and altimetric data over the entire array. Phase and group propagation measured independently from moorings and altimetry agree well with theoretical values. Sea surface height anomalies (SSHAs) measured from moorings and altimetry agree well in amplitude and phase until the northern end of the array, where phase differences arise presumably from refraction by mesoscale flows. Observed variations in SSHA, energy flux, and kinetic-to-potential energy ratio indicate an interference pattern resulting from superposed northeastward radiation from Hawaii and southeastward from the Aleutian Ridge. A simple model of two plane waves explains most of these features.

New estimates of mode-1 M₂ internal tide energy flux are computed from an extended Ocean Topography Experiment (TOPEX)/Poseidon (T/P) altimeter dataset that includes both the original and tandem tracks, improving spatial resolution over previous estimates from O(500 km) to O(250 km). Additionally, a new technique is developed that allows separate resolution of northward and southward components. Half-wavelength features previously seen in unseparated estimates are shown to be due to the superposition of northward and southward wave trains.

The new technique and higher spatial resolution afford a new view of mode-1 M₂ internal tides in the central North Pacific Ocean. As with all altimetric estimates, only the coherent or phase-locked signals are detectable owing to the long repeat period of the tracks. Emanating from specific generation sites consistent with predictions from numerical models, internal tidal beams 1) are as narrow as 200 km and 2) propagate a longer distance than previously observed. Two northward internal tidal beams radiating from the Hawaiian Ridge, previously obscured by coarse resolution and the southward Aleutian beam, are now seen to propagate more than 3500 km across the North Pacific Ocean to reach the Alaskan shelf. The internal tidal beams are much better resolved than in previous studies, resulting in better agreement with moored flux estimates.

Internal solitary waves (ISWs) in the northwestern South China Sea are studied from three spaceborne synthetic aperture radar images. ISWs are observed in the same area 18.5–20.5°N, 112–114°E. The common characteristics of the ISWs are: 1) their propagation directions are 270 ~ 300 degrees with respect to north; 2) the wavelength is about 1.2–1.6 km; 3) the distance between two neighboring ISW packets is about 10 km, but it is not a constant; 4) in two images, the easternmost ISWs evolve into multiple rank-ordered soliton on the shelf (ISW fission); and 5) near Shenhu Shoal, a local uplift at 19.5°N, 112.9°E, one ISW packet splits into two ISW packets. Based on their propagation direction and barotropic tidal forcing analysis, we suggest that these ISWs originate from tide-topography interactions in the Luzon Strait. It takes the internal tide about 100 hours to propagate 880 km from the Luzon Strait to the observation site.

The long-range propagation of the semidiurnal internal tide northward from the Hawaiian ridge and its susceptibility to parametric subharmonic instability (PSI) at the "critical latitude," λ_c = 28.8°N, were examined in spring 2006 with intensive shipboard and moored observations spanning 25–37°N along a tidal beam. Velocity and shear at λ_c were dominated by intense vertically-standing, inertially-rotating bands of several hundred meters vertical wavelength. These occurred in bursts following spring tide, contrasting sharply with the downward-propagating, wind-generated features seen at other latitudes. These marginally-stable layers (which have inverse 16-meter Richardson number Ri₁₆^-1 = 0.7) are interpreted as the inertial waves resulting from PSI of the internal tide. Elevated near-inertial energy and parameterized diapycnal diffusivity, and reduced asymmetry in upgoing/downgoing energy, were also observed at and equatorward of λ_c . Yet, simultaneous moored measurements of semidiurnal energy flux and 1-km-deep velocity sections measured from the ship indicate that the internal tide propagates at least to 37°N, with no detectable energy loss or phase discontinuity at λ_c . Our observations indicate that PSI occurs in the ocean with sufficient intensity to substantially alter the inertial shear field at and equatorward of λ_c, but that it does not appreciably disrupt the propagation of the tide at our location.

Extending an earlier attempt to understand long-range propagation of the global internal-wave field, the energy E and horizontal energy flux F are computed for the two gravest baroclinic modes at 80 historical moorings around the globe. With bandpass filtering, the calculation is performed for the semidiurnal band (emphasizing M₂ internal tides, generated by flow over sloping topography) and for the near-inertial band (emphasizing wind-generated waves near the Coriolis frequency). The time dependence of semidiurnal E and F is first examined at six locations north of the Hawaiian Ridge; E and F typically rise and fall together and can vary by over an order of magnitude at each site. This variability typically has a strong spring–neap component, in addition to longer time scales. The observed spring tides at sites northwest of the Hawaiian Ridge are coherent with barotropic forcing at the ridge, but lagged by times consistent with travel at the theoretical mode-1 group speed from the ridge. Phase computed from 14-day windows varies by approximately ±45° on monthly time scales, implying refraction by mesoscale currents and stratification. This refraction also causes the bulk of internal-tide energy flux to be undetectable by altimetry and other long-term harmonic-analysis techniques. As found previously, the mean flux in both frequency bands is O(1 kW m^-1), sufficient to radiate a substantial fraction of energy far from each source. Tidal flux is generally away from regions of strong topography. Near-inertial flux is overwhelmingly equatorward, as required for waves generated at the inertial frequency on a β plane, and is winter-enhanced, consistent with storm generation. In a companion paper, the group velocity is examined for both frequency bands.

Using a set of 80 globally distributed time series of near-inertial and semidiurnal energy E and energy flux F computed from historical moorings, the group velocity is estimated. For a single free wave, observed group speed should equal that expected from linear wave theory. For comparison, the latitude dependence of perceived group speed for perfectly standing waves is also derived. The latitudinal dependence of observed semidiurnal group speed closely follows that expected for free waves at all latitudes, implying that 1) low-mode internal tides obey linear theory and 2) standing internal-tidal waves are rare in the deep ocean for latitudes equatorward of about 35°. At higher latitudes, standing waves cannot be easily distinguished from free waves using this method because their expected group speeds are similar. Near-inertial waves exhibit scattered group speed values consistent with the passage of events generated at various latitudes, with implied frequencies ω ≈ 1.05 – 1.25 x f, as typically observed in frequency spectra.

Large-amplitude internal solitary waves (ISWs) observed near Dongsha Island in the South China Sea originate in tide-topography interactions at Luzon Strait. Their arrival times at two moorings (S7 at 117°17'E, 21°37'N, and Y at 117°13.2'E, 21°2.8'N) are investigated, with respect to model-predicted barotropic tidal currents over Lan-Yu ridge at Luzon Strait. Each ISW packet can be associated with a westward tidal current peak. The time lags between the ISWs and the barotropic tidal currents are 57.6 ± 0.9 hours at S7 and 55.1 ± 1.0 hours at Y, consistent with the mode-one internal waves propagating nondispersively through the region's bathymetry and climatological stratification. Larger ISWs usually arrive earlier than smaller ones, consistent with the theoretical relation between nonlinear wave speed and wave amplitude. The observation that the ISWs are associated with westward tidal currents, with/without the presence of earlier eastward tidal currents, suggests that they are generated by nonlinear steepening of internal tides, rather than by the lee-wave mechanism. An idealized nonlinearization distance, over which the ISWs are generated in internal tide troughs, is estimated to be 260 ± 40 km from Luzon Strait.