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An internal tide model, ZHAO30yr, is developed using 30 years of satellite altimetry sea surface height (SSH) measurements from 1993 to 2022 by a recently improved mapping technique that consists of two rounds of plane wave analysis with a spatial bandpass filter in between. Prerequisite wavelengths are calculated using climatological annual mean hydrographic profiles in the World Ocean Atlas 2018. ZHAO30yr only extracts the 30-year phase-locked internal tide component, lacking the incoherent component caused by the time-varying ocean environment. The model contains 12 internal tide constituents: eight mode-1 constituents (M2, S2, N2, K2, K1, O1, P1, and Q1) and four mode-2 constituents (M2, S2, K1, and O1). Model errors are estimated to be lower than 1 mm in the SSH amplitude on global average, thanks to the long data record and improved mapping technique. The model is evaluated by making internal tide correction to independent altimetry data for 2023. A total of 10 constituents (but for K2 and Q1) can reduce variance on global average. K2 and Q1 can only cause variance reductions in their source regions. The model decomposes the multiconstituent, multimodal, multidirectional internal tide field into a series of simple plane waves at each grid point. The decomposition reveals unprecedented features previously masked by multiwave interference. The model divides each internal tide constituent into components by propagation direction. The directionally decomposed components show numerous long-range internal tidal beams associated with notable topographic features. The semidiurnal internal tidal beams off the Amazon shelf and the diurnal internal tidal beams in the Arabian Sea are examined in detail. ZHAO30yr is available at https://doi.org/10.6084/m9.figshare.28078523 (Zhao, 2024b). Model errors are available at https://doi.org/10.6084/m9.figshare.28559978.v3 (Zhao, 2025). 

Seventy‐five days of sea surface height measurements made by the Surface Water and Ocean Topography (SWOT) mission from 7 September to 21 November 2023 are used to explore SWOT's capability of observing internal tides. Mode‐1 internal tides are mapped by our updated mapping technique. SWOT‐75d represents a 75‐day instantaneous model. Nadir‐30y is constructed using 30 years of nadir altimetry data from 1993 to 2022 and represents a climate normal. The nadir altimetry data in 2023 are used for model evaluation. Despite its large errors, SWOT‐75d reveals the basic features of the global mode‐1 internal tide field, and causes positive variance reduction in regions of strong internal tides. Nadir‐30y performs better overall, but SWOT‐75d performs better in the tropical South Atlantic Ocean, the central North Pacific Ocean, and the Melanesian region. Evaluation using seasonally subsetted altimetry data reveals that internal tides have significant temporal variations. SWOT‐75d performs the best in fall, because the model is constructed using data largely in fall. SWOT‐75d has large phase anomalies, which are spatially smoothed and used to adjust the phases in Nadir‐30y. The phase‐adjusted model can better make internal tide correction for SWOT and its performance is improved by 20%. Our results demonstrate that (a) mode‐1 internal tides can be extracted from 75 days of SWOT data by our mapping technique, and (b) the instantaneous internal tide model can be used to improve internal tide correction for SWOT. 

Satellite altimetry sea surface height measurements from 1993 to 2022 are used to show the strengthened mode‐1 M₂internal tides in the past 30 years. Two mode‐1 M₂internal tide models M9509 and M1019 are constructed using the data in 1995–2009 and 2010–2019, respectively. The results show that the global mean M₂internal tides strengthened by 6% in energy. However, the internal tide strengthening is spatially inhomogeneous. Significantly strengthened internal tides are observed in a number of regions including the Aleutian Ridge and the Madagascar‐Mascarene region. Weakened internal tides are observed in the central Pacific. On global average, M1019 leads M9509 by about 10° (20 min in time), suggesting that the propagation speed of M₂internal tides increased. M9509 and M1019 are evaluated using independent altimetry data. The results show that M9509 and M1019 perform better for the data in 1993–1994 and 2020–2022, respectively. 

Satellite altimetry sea surface height (SSH) measurements from 1993 to 2017 are used to investigate the seasonal variability of mode‐1 M₂internal tides from the Luzon Strait. The 25 years of SSH data are divided into four seasonal subsets, from which four seasonal internal tide models are constructed following the same mapping procedure. Climatological seasonal hydrography in the World Ocean Atlas 2013 is used to calculate two seasonally variable parameters required in the mapping procedure: Wavelength and the transfer function from the SSH amplitude to depth‐integrated energy flux. The M₂internal tides from the Luzon Strait are extracted using propagation direction determined in plane wave analysis. The satellite results show that the westward and eastward M₂internal tides both demonstrate significant seasonal variation. The westward and eastward internal tides seesaw seasonally: The westward internal tides strengthen (weaken) in summer and fall (winter and spring); while the eastward internal tides strengthen (weaken) in winter and spring (summer and fall). We suggest that the seasonal seesaw is mainly determined by ocean stratification and the Kuroshio Current; however, further studies are needed to quantify their relative contributions. 

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 8 years of SSH data from 2011 to 2018 measured mainly by nonrepeat (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 M₂internal 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 make it possible to examine the impact of window size in the first-round plane wave analysis. Internal tides 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. Significance StatementOur understanding of internal tides is mainly limited by the scarcity of field measurements with sufficient spatiotemporal resolution. Satellite altimetry offers a unique technique for observing and predicting internal tides on a global scale. Previous satellite observations of internal tides are mainly based on 25 years of data from exact-repeat altimetry missions. This paper demonstrates that internal tides can be mapped using 8 years of data made by nonrepeat altimetry missions. The new dataset has shorter time coverage and denser ground tracks; therefore, one can examine the impact of window size and time coverage on mapping internal tides from satellite altimetry. A comparison of models mapped from the two datasets sheds new light on the spatiotemporal variability of internal tides. 

Abstract Two moorings deployed for 75 days in 2019 and long‐term satellite altimetry data reveal a spatially complex and temporally variable internal tidal field at the Surface Water and Ocean Topography (SWOT) Cal/Val site off central California due to the interference of multiple seasonally‐variable sources. These two data sets offer complementary insights into the variability of internal tides in various time scales. The in situ measurements capture variations occurring from days to months, revealing ∼45% coherent tides. The north mooring displays stronger mode‐1 M₂with an amplitude of ∼5.1 mm and exhibits distinct time‐varying energy and modal partitioning compared to the south mooring, which is only 30‐km away. The 27‐year altimetry data unveils the mean and seasonal variations of internal tides. The results indicate that the complex internal tidal field is attributed to multiple sources and seasonality. Mode‐1 tides primarily originate from the Mendocino Ridge and the 36.5–37.5°N California continental slope, while mode‐2 tides are generated by local seamounts and Monterey Bay. Seasonality is evident for mode‐1 waves from three directions. The highest variability of energy flux is found in the westward waves (±22%), while the lowest is in the southward waves (±13%). The large variability observed from the moorings cannot be solely explained by seasonality; additional factors like mesoscale eddies also play a role. This study emphasizes the importance of incorporating the seasonality and spatial variability of internal tides for the SWOT internal tidal correction, particularly in regions characterized by multiple tidal sources. 

Abstract Rain in tropical cyclones is studied using eight time series of underwater ambient sound at 40–50 kHz with wind speeds up to 45 m s⁻¹beneath three tropical cyclones. At tropical cyclone wind speeds, rain- and wind-generated sound levels are comparable, and therefore rain cannot be detected by sound level alone. A rain detection algorithm that is based on the variations of 5–30-kHz sound levels with periods longer than 20 s and shorter than 30 min is proposed. Faster fluctuations (<20 s) are primarily due to wave breaking, and slower ones (>30 min) are due to overall wind variations. Higher-frequency sound (>30 kHz) is strongly attenuated by bubble clouds. This approach is supported by observations that, for wind speeds < 40 m s⁻¹, the variation in sound level is much larger than that expected from observed wind variations and is roughly comparable to that expected from rain variations. The hydrophone results are consistent with rain estimates by the Tropical Rainfall Measuring Mission (TRMM) satellite and with Stepped-Frequency Microwave Radiometer (SFMR) and radar estimates by surveillance flights. The observations indicate that the rain-generated sound fluctuations have broadband acoustic spectra centered around 10 kHz. Acoustically detected rain events usually last for a few minutes. The data used in this study are insufficient to produce useful estimation of rain rate from ambient sound because of limited quantity and accuracy of the validation data. The frequency dependence of sound variations suggests that quantitative rainfall algorithms from ambient sound may be developed using multiple sound frequencies. Significance StatementRain is an indispensable process in forecasting the intensity and path of tropical cyclones. However, its role in the air–sea interaction is still poorly understood, and its parameterization in numerical models is still in development. In this work, we analyzed sound measurements made by hydrophones on board Lagrangian floats beneath tropical cyclones. We find that wind, rain, and breaking waves each have distinctive signatures in underwater ambient sound. We suggest that the air–sea dynamic processes in tropical cyclones can be explored by listening to ambient sound using hydrophones beneath the sea surface. 

Abstract The yearly mode-1 M₂internal 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, andSARAL/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 1-yr-coherent internal tide field in 2019. In contrast, the model developed using altimeter data from 1992 to 2017 is labeled MY25, because it represents the multiyear-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 (withoutJason-3) can yield an internal tide model of almost the same quality. Comparing Y2019 and MY25 shows that mode-1 M₂internal 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 2 times larger 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. Significance StatementThis work is motivated to study the interannual variations of internal tides using observation-based yearly internal tide models from satellite altimetry. Previous satellite observations of internal tides are usually based on 25 years of altimeter data from 1993 to 2017. The yearly subsetted altimeter data are short, so that the resultant yearly models are overwhelmed by noise. A new mapping technique is developed and demonstrated in this paper. It paves a path to study the interannual and decadal variations of internal tides on a global scale and monitor the global ocean changes by tracking long-range internal tides. 

Abstract The M₂internal 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 M₂internal 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 M₂and S₂internal tides, but not diurnal K₁and O₁internal tides. 

The effects of horizontal resolution and wave drag damping on the semidiurnal M2 tidal energetics are studied for two realistically-forced global HYbrid Coordinate Ocean Model (HYCOM) simulations with 41 layers and horizontal resolutions of 8 km (H12) and 4 km (H25). In both simulations, the surface tidal error is minimized by tuning the strength of the linear wave drag, which is a parameterization of the surface-tide energy conversion to the unresolved baroclinic wave modes. In both simulations the M2 surface tide error with TPXO8-atlas, an altimetry constrained model, is 2.6 cm. Compared to H12, the surface tide energy conversion to the resolved vertical modes is increased by 50% in H25. This coincides with an equivalent reduction in the tuned loss of energy from the surface tide to the wave drag. For the configurations studied here, the horizontal and not the vertical resolution is the factor limiting the number of vertical modes that are resolved in most of the global ocean: modes 1–2 in H12 and modes 1–5 in H25. The wave drag also dampens the resolved internal tides. The 40% reduction in wave-drag strength does not result in a proportional increase in the mode-1 energy density in H25. In the higher-resolution simulations, topographic mode-scattering and wave–wave interactions are better resolved. This allows for an energy flux out of mode 1 to the higher modes, mitigating the need for an internal tide damping term. The HYCOM simulations are validated with analytical conversion models and altimetry-inferred sea-surface height, fluxes, and surface tide dissipation. H25 agrees best with these data sets to within 10%. To facilitate the comparison of stationary tide signals extracted from time series with different durations, we successfully apply a spatially-varying correction factor.