When currents associated with the surface tide (Fig. 16a) impact undersea topography, internal waves of tidal frequency (i.e., internal tides) can be generated. The internal vertical displacements can be quite large, dozens of meters or more; the associated displacements at the surface are very small, a few cm or smaller, but these can be detected and now mapped with altimeters (Fig. 16b). Because the density contrasts within the water column are much smaller than at the air-water interface, the phase velocity of internal tides is much smaller than the surface tide, and the wavelengths are correspondingly short—of order 100 km, as in Fig. 16b. That satellite altimetry can map such small waves has opened up a new path in the study of internal tides (Zhao et al. 2012; Zaron 2019). The dissipation of these waves has possibly profound implications for ocean mixing (Munk 1997; Vic et al. 2019).

By the nature of how they are mapped, the internal tide signals, seen in Fig. 16b, are coherent (phase-locked) with the surface tide. Yet as the ocean stratification or the background (non-tidal) currents change, the generation as well as the propagation of internal tides must also change. For many years our picture of internal tides was one of waves highly incoherent in both space and time, sometimes even intermittent. That coherent waves as depicted in Fig. 16b even exist is somewhat surprising. It is likely, in fact, that Fig. 16b misses a large portion of internal waves that do not remain phase-locked and that are therefore much harder to map with an altimeter.

Mapping internal tides and understanding the degree that they remain stationary and phase-locked with the surface tide is an important topic of current research, with implications for all altimetry missions, including the future SWOT mission. The wavelengths in Fig. 16b fall within the mesoscale/submesoscale band that SWOT is designed to study. Unless SWOT is confined to measuring internal tides, these signals must be predicted and removed from the data, just like the surface tide must be predicted and removed from standard altimeter data. The prediction problem here, however, is far more challenging, and not only in terms of the short wavelengths that must be mapped. If a significant part of the internal tide variance is non-stationary and dependent on the ocean state, as seems possible and even likely, then the tidal problem becomes entangled with the problem of mapping the non-tidal variability. Studying the internal tides that are generated in high-resolution general circulation models that are forced by both the atmosphere and the tidal potential is helping clarify the problem and our understanding of the generation, propagation, and decay of internal tides (Arbic et al. 2018), and the comparison of the performance of several models (Carrere et al. 2021) in the end may be necessary to help with the prediction problem that is needed for high-resolution alongtrack and swath altimetry. The realism of these internal-tide models can be further improved by assimilating observations to correctly represent the mesoscale structures that interact with the tidal waves, and contribute to their non-phase-locked signals.

# 10 Assimilation in Ocean Circulation Models and Oceanic Reanalyses

Ocean data assimilation combines ocean observations and ocean models taking into account their respective errors to derive an optimal 4D estimation of the ocean state (e.g., see Moore et al. 2019 for a recent review). This is an essential step that transforms satellite and in situ observations into 4D ocean fields that are used to describe the state of the ocean in near real time (analyses) and to initialize ocean and coupled ocean/atmosphere models generating short term ocean forecasts and seasonal and long-term ocean/atmosphere forecasts.
<figure><img src="image_24.png" /><figcaption>**Fig. 17** Surface currents 7-day forecasts for mid-August 2021 from the Mercator Ocean/Copernicus Marine Service global 1/12° data assimilation system. The system assimilates data from all available altimeter missions, satellite sea surface temperature data and a wide range of in situ observations (Argo, moorings, gliders, ships, and marine mammals)</figcaption></figure>

Ocean data assimilation is also used to generate ocean reanalyses (e.g., Stammer et al. 2016; Storto et al. 2019; Lellouche et al. 2021) that provide consistent longtime series of the 4D ocean state (e.g., using the same model and same data assimilation system). The contribution of ocean reanalyses to the understanding of ocean dynamics has been demonstrated in numerous regional and global studies. Artana et al. (2019) have thus shown, for example, the major contributions of Mercator Ocean global ocean reanalyses to better understand variations in the Malvinas Current, the Brazil Current and in their confluence, a region with highly complex ocean dynamics.

Ocean modeling and data assimilation systems now operationally assimilate in situ and satellite data to provide regular and systematic reference information on the physical state (Fig. 17), variability, and dynamics of the ocean and marine biogeochemistry from global to coastal scales (e.g., Chassignet et al. 2018; Le Traon et al. 2019). Products serve a wide range of applications and downstream services (e.g., Bell et al. 2009, 2015; Le Traon et al. 2019). Modeling and data assimilation systems are a fundamental component of the value chain that goes from observations to applications and users (Le Traon et al. 2019).

There are a wide range of data assimilation techniques ranging from relatively simple schemes such as optimal interpolation or 3D-VAR, to more sophisticated ones, such as 4D-VAR, Kalman filters and smoothers and/or ensemble techniques (see Moore et al. 2019). The choice of a data assimilation scheme depends on the application and of the modeling and data assimilation system characteristics, in particular, the resolution and the associated computing cost.

Satellite altimetry is a critical observing system required for modeling and data assimilation (e.g., Le Traon et al. 2017). It provides global, real time, all-weather sea level measurements (SSH) with high space and time resolution. SSH is an integral of the ocean interior properties (SSH is related to depth-integrated density perturbations and barotropic motions) and is a strong constraint for inferring the 4D ocean circulation through data assimilation. Only altimetry can constrain, in particular, the 4D mesoscale circulation in ocean models which is required for most operational oceanography applications. High resolution from multiple altimeters is required to adequately represent ocean eddies and associated currents in models. Both Observing System Evaluations (OSEs) (e.g., Hamon
<figure><img src="image_25.png" /><figcaption>**Fig. 17** Surface currents 7-day forecasts for mid-August 2021 from the Mercator Ocean/Copernicus Marine Service global 1/12° data assimilation system. The system assimilates data from all available altimeter missions, satellite sea surface temperature data and a wide range of in situ observations (Argo, moorings, gliders, ships, and marine mammals)</figcaption></figure>

Ocean data assimilation is also used to generate ocean reanalyses (e.g., Stammer et al. 2016; Storto et al. 2019; Lellouche et al. 2021) that provide consistent longtime series of the 4D ocean state (e.g., using the same model and same data assimilation system). The contribution of ocean reanalyses to the understanding of ocean dynamics has been demonstrated in numerous regional and global studies. Artana et al. (2019) have thus shown, for example, the major contributions of Mercator Ocean global ocean reanalyses to better understand variations in the Malvinas Current, the Brazil Current and in their confluence, a region with highly complex ocean dynamics.

Ocean modeling and data assimilation systems now operationally assimilate in situ and satellite data to provide regular and systematic reference information on the physical state (Fig. 17), variability, and dynamics of the ocean and marine biogeochemistry from global to coastal scales (e.g., Chassignet et al. 2018; Le Traon et al. 2019). Products serve a wide range of applications and downstream services (e.g., Bell et al. 2009, 2015; Le Traon et al. 2019). Modeling and data assimilation systems are a fundamental component of the value chain that goes from observations to applications and users (Le Traon et al. 2019).

There are a wide range of data assimilation techniques ranging from relatively simple schemes such as optimal interpolation or 3D-VAR, to more sophisticated ones, such as 4D-VAR, Kalman filters and smoothers and/or ensemble techniques (see Moore et al. 2019). The choice of a data assimilation scheme depends on the application and of the modeling and data assimilation system characteristics, in particular, the resolution and the associated computing cost.

Satellite altimetry is a critical observing system required for modeling and data assimilation (e.g., Le Traon et al. 2017). It provides global, real time, all-weather sea level measurements (SSH) with high space and time resolution. SSH is an integral of the ocean interior properties (SSH is related to depth-integrated density perturbations and barotropic motions) and is a strong constraint for inferring the 4D ocean circulation through data assimilation. Only altimetry can constrain, in particular, the 4D mesoscale circulation in ocean models which is required for most operational oceanography applications. High resolution from multiple altimeters is required to adequately represent ocean eddies and associated currents in models. Both Observing System Evaluations (OSEs) (e.g., Hamon
et al. 2019) and Observing System Simulation Experiments (OSSEs) (e.g., Verrier et al. 2017) demonstrate the major contribution of altimetry. At least four altimeters are required to constrain modeling and data assimilation systems. This is particularly true with high-resolution data assimilation systems. The new generation of nadir altimeters now provides enhanced capability, thanks to a Synthetic Aperture Radar (SAR) mode that reduces measurement noise. Verrier et al. (2018) demonstrated that the use of SAR multiple altimeter missions with high-resolution models will improve the capability of the ocean analysis and forecasting systems. A challenge in using nadir altimetry and future SWOT data for data assimilation is to estimate the data errors and characterize their space–time structures. Estimates are available for alongtrack altimetry (e.g., Taburet et al. 2019) and proposed for SWOT based on simulations (Chelton et al. 2019), but there is a need to continue research efforts on this issue.

Accurate knowledge of the Mean Dynamic Topography (MDT) is also a fundamental element for assimilation into ocean models. Thanks to new and improved altimetric, in situ and gravimetric (GRACE and GOCE satellite missions) data, MDTs are regularly updated, leading to considerable improvements in both forecasts and analyses. Hamon et al. (2019) showed, for example, that, in terms of the impact on reducing SSH errors, assimilating an updated release of the MDT is comparable to assimilating a fourth time-varying altimeter.

The role of satellite altimetry to ocean forecasting is essential but remains limited due to 1D nature of the sampling by nadir altimeters. Even with 3 to 4 altimeters, only wavelengths longer than 200 km can be adequately monitored. The development of wide-swath altimetry that will be demonstrated with the SWOT mission opens up very promising perspectives to improve our ability to monitor and forecast the smaller space and time scales (e.g., d'Addezio et al. 2019; Tchonang et al. 2021). Through a series of Observing System Simulation Experiments, Benkiran et al. (2021) and Tchonang et al. (2021) demonstrated that SWOT data could be readily assimilated in a global high resolution (1/12°) analysis and forecasting system with a positive impact everywhere and very good performances. Adding SWOT observations to those of three nadir altimeters globally reduced the variance of SSH and surface velocities analyses and forecasts by about 30% and 20%, respectively. The main limitation of SWOT is, however, related to its longtime repeat period. On the longer run, flying a constellation of two or three wide-swath altimeters would thus be highly beneficial to further improve the performances, in particular, for the small space and time scales.

# 11 Future Developments in Ocean Circulation from Space

Over the next decade, there are a number of key issues to ensure the continuity of the present observing system of ocean circulation from space, but also to extend and enhance our present capabilities. As this paper has discussed, the satellite-based ocean circulation observing system is largely constrained by multiple nadir altimeter missions, based on conventional or SAR technology. It is important that these altimetric missions continue to be maintained, and their orbits and space–time coverage be well coordinated to allow the optimal sampling of the ocean circulation as well as the continuity of the long-term time series. This continuity will be maintained by the European Sentinel-3 A-B and their extension with C-D, by the Sentinel-6A Michael Freilich and later with Sentinel-6B along the long-term Topex/Poseidon-Jason climate orbit, and will be completed by the Chinese/CNES HY-2 series. Other missions currently in flight complete this constellation (see Fig. 1).
et al. 2019) and Observing System Simulation Experiments (OSSEs) (e.g., Verrier et al. 2017) demonstrate the major contribution of altimetry. At least four altimeters are required to constrain modeling and data assimilation systems. This is particularly true with high-resolution data assimilation systems. The new generation of nadir altimeters now provides enhanced capability, thanks to a Synthetic Aperture Radar (SAR) mode that reduces measurement noise. Verrier et al. (2018) demonstrated that the use of SAR multiple altimeter missions with high-resolution models will improve the capability of the ocean analysis and forecasting systems. A challenge in using nadir altimetry and future SWOT data for data assimilation is to estimate the data errors and characterize their space–time structures. Estimates are available for alongtrack altimetry (e.g., Taburet et al. 2019) and proposed for SWOT based on simulations (Chelton et al. 2019), but there is a need to continue research efforts on this issue.

Accurate knowledge of the Mean Dynamic Topography (MDT) is also a fundamental element for assimilation into ocean models. Thanks to new and improved altimetric, in situ and gravimetric (GRACE and GOCE satellite missions) data, MDTs are regularly updated, leading to considerable improvements in both forecasts and analyses. Hamon et al. (2019) showed, for example, that, in terms of the impact on reducing SSH errors, assimilating an updated release of the MDT is comparable to assimilating a fourth time-varying altimeter.

The role of satellite altimetry to ocean forecasting is essential but remains limited due to 1D nature of the sampling by nadir altimeters. Even with 3 to 4 altimeters, only wavelengths longer than 200 km can be adequately monitored. The development of wide-swath altimetry that will be demonstrated with the SWOT mission opens up very promising perspectives to improve our ability to monitor and forecast the smaller space and time scales (e.g., d'Addezio et al. 2019; Tchonang et al. 2021). Through a series of Observing System Simulation Experiments, Benkiran et al. (2021) and Tchonang et al. (2021) demonstrated that SWOT data could be readily assimilated in a global high resolution (1/12°) analysis and forecasting system with a positive impact everywhere and very good performances. Adding SWOT observations to those of three nadir altimeters globally reduced the variance of SSH and surface velocities analyses and forecasts by about 30% and 20%, respectively. The main limitation of SWOT is, however, related to its longtime repeat period. On the longer run, flying a constellation of two or three wide-swath altimeters would thus be highly beneficial to further improve the performances, in particular, for the small space and time scales.

# 11 Future Developments in Ocean Circulation from Space

Over the next decade, there are a number of key issues to ensure the continuity of the present observing system of ocean circulation from space, but also to extend and enhance our present capabilities. As this paper has discussed, the satellite-based ocean circulation observing system is largely constrained by multiple nadir altimeter missions, based on conventional or SAR technology. It is important that these altimetric missions continue to be maintained, and their orbits and space–time coverage be well coordinated to allow the optimal sampling of the ocean circulation as well as the continuity of the long-term time series. This continuity will be maintained by the European Sentinel-3 A-B and their extension with C-D, by the Sentinel-6A Michael Freilich and later with Sentinel-6B along the long-term Topex/Poseidon-Jason climate orbit, and will be completed by the Chinese/CNES HY-2 series. Other missions currently in flight complete this constellation (see Fig. 1).
A key aspect of the success of the altimetric monitoring of ocean circulation is due to the regular meetings and discussions between scientists and engineers within the international Ocean Surface Topography Science Team (OSTST). This annual forum allows for technical discussions on the data quality, external calibration and validation, inter-calibration between all altimetric missions, and scientific discussions on new results and applications. It is also a forum for programmatic discussions to help coordinate the data quality and sampling between different altimetric missions, and different space agencies. Individual altimetric missions have their own internal meetings, but the continuity of the international OSTST forum is critical for the precise data and good functioning of the entire altimetric constellation. Every 5 years, we also hold review meetings with the 15, 20 and 25 Years of Progress in Radar Altimetry Symposia (e.g., http://www.altimetry2018.org).

Global and regional high-resolution models with enhanced space–time resolution and more complex dynamics will be widely available over the next decade (Fox-Kemper et al. 2019). Developing a satellite and in situ observing system with enhanced spatial and temporal resolution is key to accompany these models (see Sect. 10), and to understand and develop better parameterizations of the finer, rapidly evolving ocean dynamics. In a changing climate, it is critical to extend these observations into regions that have strong societal applications yet are poorly sampled today, including coastal and regional seas and the polar regions (Sect. 8).

A major revolution in our ocean circulation observing capabilities over the next few years will be wide-swath altimetry, with the arrival of the SWOT mission (see Sect. 4). These global observations over two 50 km wide swaths, with improved signal-to-noise, will allow us to observe the fine-scale ocean dynamics in 2D right up to the coast, extending into the estuaries, with greatly improved coverage in regional seas and in polar regions up to 78° in latitude. In addition to the 2 km resolution in 2-D SSH coverage, for the first time we will have fine-scale cross-swath gradients of sea surface height, to directly derive the 2D geostrophic velocity and vorticity/strain fields after removing the noise (see Sect. 7). These geostrophic vorticity and strain fields can be used to derive the finer-scale upper ocean 3D circulation, including vertical velocities below the mixed layer (Qiu et al. 2016) or the ageostrophic secondary circulation at fronts (e.g., Zhang et al. 2019). Full global coverage of daily SSH and geostrophic currents will still require interpolation of the multi-mission altimetry constellation including SWOT, or assimilation into ocean models (see Sect. 10). SWOT will fly for 3.5 years from early 2023 to late 2026, and other wide-swath altimeter missions may follow, including the Chinese Guanlan mission and the Sentinel-3 New Generation Topography mission from 2030 onwards.

SWOT’s orbit has also been chosen to resolve the major ocean tide constituents, and after the 3.5 year mission, we expect a major improvement in coastal, regional and high-latitude barotropic tides, and a better observation of internal tides (see Sect. 9). This will allow improved tidal models ingesting SWOT data, leading to improved barotropic and coherent internal tide corrections for reprocessing of past altimetric missions, for predicting more accurate tide corrections for future missions, and tidal heights and currents for many coastal, regional and high-latitude applications.

A precise mean ocean circulation is required to calculate the ocean surface currents from the altimeter-derived ocean surface geostrophic current anomalies. We are expecting a major improvement in the mean sea surface products with the extended fine-scale coverage at 2 km resolution of SWOT, including in the coastal, regional, and polar seas. Once again, after 3-years of global coverage, SWOT should improve the mean sea surface and geoid models at short space scales, including the east–west gradients that are poorly sampled by alongtrack altimetry today (see Sect. 5). Improving the mean ocean
A key aspect of the success of the altimetric monitoring of ocean circulation is due to the regular meetings and discussions between scientists and engineers within the international Ocean Surface Topography Science Team (OSTST). This annual forum allows for technical discussions on the data quality, external calibration and validation, inter-calibration between all altimetric missions, and scientific discussions on new results and applications. It is also a forum for programmatic discussions to help coordinate the data quality and sampling between different altimetric missions, and different space agencies. Individual altimetric missions have their own internal meetings, but the continuity of the international OSTST forum is critical for the precise data and good functioning of the entire altimetric constellation. Every 5 years, we also hold review meetings with the 15, 20 and 25 Years of Progress in Radar Altimetry Symposia (e.g., http://www.altimetry2018.org).

Global and regional high-resolution models with enhanced space–time resolution and more complex dynamics will be widely available over the next decade (Fox-Kemper et al. 2019). Developing a satellite and in situ observing system with enhanced spatial and temporal resolution is key to accompany these models (see Sect. 10), and to understand and develop better parameterizations of the finer, rapidly evolving ocean dynamics. In a changing climate, it is critical to extend these observations into regions that have strong societal applications yet are poorly sampled today, including coastal and regional seas and the polar regions (Sect. 8).

A major revolution in our ocean circulation observing capabilities over the next few years will be wide-swath altimetry, with the arrival of the SWOT mission (see Sect. 4). These global observations over two 50 km wide swaths, with improved signal-to-noise, will allow us to observe the fine-scale ocean dynamics in 2D right up to the coast, extending into the estuaries, with greatly improved coverage in regional seas and in polar regions up to 78° in latitude. In addition to the 2 km resolution in 2-D SSH coverage, for the first time we will have fine-scale cross-swath gradients of sea surface height, to directly derive the 2D geostrophic velocity and vorticity/strain fields after removing the noise (see Sect. 7). These geostrophic vorticity and strain fields can be used to derive the finer-scale upper ocean 3D circulation, including vertical velocities below the mixed layer (Qiu et al. 2016) or the ageostrophic secondary circulation at fronts (e.g., Zhang et al. 2019). Full global coverage of daily SSH and geostrophic currents will still require interpolation of the multi-mission altimetry constellation including SWOT, or assimilation into ocean models (see Sect. 10). SWOT will fly for 3.5 years from early 2023 to late 2026, and other wide-swath altimeter missions may follow, including the Chinese Guanlan mission and the Sentinel-3 New Generation Topography mission from 2030 onwards.

SWOT’s orbit has also been chosen to resolve the major ocean tide constituents, and after the 3.5 year mission, we expect a major improvement in coastal, regional and high-latitude barotropic tides, and a better observation of internal tides (see Sect. 9). This will allow improved tidal models ingesting SWOT data, leading to improved barotropic and coherent internal tide corrections for reprocessing of past altimetric missions, for predicting more accurate tide corrections for future missions, and tidal heights and currents for many coastal, regional and high-latitude applications.

A precise mean ocean circulation is required to calculate the ocean surface currents from the altimeter-derived ocean surface geostrophic current anomalies. We are expecting a major improvement in the mean sea surface products with the extended fine-scale coverage at 2 km resolution of SWOT, including in the coastal, regional, and polar seas. Once again, after 3-years of global coverage, SWOT should improve the mean sea surface and geoid models at short space scales, including the east–west gradients that are poorly sampled by alongtrack altimetry today (see Sect. 5). Improving the mean ocean
circulation not only requires having better Mean Sea Surface and geoid models, but also
additional information about the ocean circulation from in situ measurements (drifting
buoy velocities, HF radar,...) or from space (e.g., SAR Doppler velocities).

SWOT will cover the Antarctic seas, but extending and enhancing our observations
into the Arctic Ocean also requires more polar-orbiting altimeters, since CryoSat and
Saral/AltiKa are approaching their end of life. It is critical that future missions such as
the bi-frequency Copernicus CRISTAL mission are launched soon (expected in 2027) to
provide continuity and enhancement of our coverage of the polar oceans, and to better
estimate the ocean circulation response to snow and sea ice variations in these rapidly
evolving regions (Sect. 8).

This paper has concentrated on altimetric geostrophic currents that provide a strong
constraint on our ocean state estimation (Sect. 10). However, today, total surface cur-
rents including the ageostrophic component of the ocean circulation cannot be observed
directly from space, although the Ekman current component can be estimated from sat-
ellite scatterometer winds, the Stokes drift from wave models, and total surface currents
can be derived from in situ data. The future may be with SAR Doppler surface velocity
satellite missions: A number of propositions are being considered (e.g., OdySea–NASA/
CNES, HARMONY—ESA, see Arduin et al. 2019 for a review) and airborne versions
of the instrument are providing very good results. A future combination of SAR Dop-
pler surface currents, combined with the depth-integrated geostrophic currents from
swath and nadir altimetry, and polar-orbiting satellites, would better respond to our
requirements for space observations of the ocean circulation.

**Funding** R.M. was supported by the French CNES TOSCA programs via SWOT project funding. L.-L.F. was supported by the Jet Propulsion Laboratory, California Institute of Technology, under NASA SWOT Project funding. R.R. was supported by NASA Sentinel-6 and SWOT project funding.

Declarations

**Conflict of interest** All authors declare that they have no conflict of interest.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

References

Abernathey RP, Marshall J (2013) Global surface eddy diffusivities derived from satellite altimetry. J Geophys Res Oceans 118:901–916. https://doi.org/10.1002/jgrc.20066

Ablain M, Cazenave A, Larnicol G, Balmaseda M, Cipollini P, Faugère Y, Fernandes MJ, Henry O, Johannessen JA, Knudsen P, Andersen O, Legeais J, Meyssignac B, Picot N, Roca M, Rudenko S, Scharffenberg MG, Stammer D, Timms G, Benveniste J (2015) Improved sea level record over the satellite altimetry era (1993–2010) from the climate change initiative project. Ocean Sci 11:67–82. https://doi.org/10.5194/os-11-67-2015

Abraham ER, Law CS, Boyd PW, Lavender SJ, Maldonado MT, Bowie A (2000) Importance of stirring in the development of an iron-fertilized phytoplankton bloom. Nature 407:727–730

Andersen OB, Knudsen P, Stenseng, L (2015) The DTU13 MSS (mean sea surface) and MDT (mean dynamic topography) from 20 years of satellite altimetry. In: S Jin, R Barzaghi (Eds), International
circulation not only requires having better Mean Sea Surface and geoid models, but also
additional information about the ocean circulation from in situ measurements (drifting
buoy velocities, HF radar,...) or from space (e.g., SAR Doppler velocities).

SWOT will cover the Antarctic seas, but extending and enhancing our observations
into the Arctic Ocean also requires more polar-orbiting altimeters, since CryoSat and
Saral/AltiKa are approaching their end of life. It is critical that future missions such as
the bi-frequency Copernicus CRISTAL mission are launched soon (expected in 2027) to
provide continuity and enhancement of our coverage of the polar oceans, and to better
estimate the ocean circulation response to snow and sea ice variations in these rapidly
evolving regions (Sect. 8).

This paper has concentrated on altimetric geostrophic currents that provide a strong
constraint on our ocean state estimation (Sect. 10). However, today, total surface cur-
rents including the ageostrophic component of the ocean circulation cannot be observed
directly from space, although the Ekman current component can be estimated from sat-
ellite scatterometer winds, the Stokes drift from wave models, and total surface currents
can be derived from in situ data. The future may be with SAR Doppler surface velocity
satellite missions: A number of propositions are being considered (e.g., OdySea–NASA/
CNES, HARMONY—ESA, see Arduin et al. 2019 for a review) and airborne versions
of the instrument are providing very good results. A future combination of SAR Dop-
pler surface currents, combined with the depth-integrated geostrophic currents from
swath and nadir altimetry, and polar-orbiting satellites, would better respond to our
requirements for space observations of the ocean circulation.

**Funding** R.M. was supported by the French CNES TOSCA programs via SWOT project funding. L.-L.F. was supported by the Jet Propulsion Laboratory, California Institute of Technology, under NASA SWOT Project funding. R.R. was supported by NASA Sentinel-6 and SWOT project funding.

Declarations

**Conflict of interest** All authors declare that they have no conflict of interest.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

References

Abernathey RP, Marshall J (2013) Global surface eddy diffusivities derived from satellite altimetry. J Geophys Res Oceans 118:901–916. https://doi.org/10.1002/jgrc.20066

Ablain M, Cazenave A, Larnicol G, Balmaseda M, Cipollini P, Faugère Y, Fernandes MJ, Henry O, Johannessen JA, Knudsen P, Andersen O, Legeais J, Meyssignac B, Picot N, Roca M, Rudenko S, Scharffenberg MG, Stammer D, Timms G, Benveniste J (2015) Improved sea level record over the satellite altimetry era (1993–2010) from the climate change initiative project. Ocean Sci 11:67–82. https://doi.org/10.5194/os-11-67-2015

Abraham ER, Law CS, Boyd PW, Lavender SJ, Maldonado MT, Bowie A (2000) Importance of stirring in the development of an iron-fertilized phytoplankton bloom. Nature 407:727–730

Andersen OB, Knudsen P, Stenseng, L (2015) The DTU13 MSS (mean sea surface) and MDT (mean dynamic topography) from 20 years of satellite altimetry. In: S Jin, R Barzaghi (Eds), International
Association of Geodesy Symposia. Springer: Switzerland. pp. 1–10. doi: https://doi.org/10.1007/1345_2015_182

Arbic BK, Polzin KL, Scott RB, Richman JG, Shriver JF (2013) On eddy viscosity, energy cascades, and the horizontal resolution of gridded satellite altimeter products. J Phys Oceanogr 43(2):283–300. https://doi.org/10.1175/JPO-D-11-0240.1

Arbic BK et al (2018) A primer on global internal tide and internal gravity wave continuum modeling in HYCOM and MITgcm. In: *New Frontiers in Operational Oceanography* E Chassignet, A Pascual, J Tintoré, J Verron Eds. GODAE Ocean View, 307–392, doi: https://doi.org/10.17125/gov2018.ch13.

Arduuin F, Chapron B, Maes C, Romeiser R, Gommenginger C, Cravatte S, Morrow R, Donlon C, Bourassa M (2019) Satellite doppler observations for the motions of the oceans. B Am Meterol Soc 100:215–219. https://doi.org/10.1175/BAMS-D-19-0039.1

Armitage TWK, Bacon S, Ridout AL, Thomas SF, Aksenov Y, Wingham DJ (2016) Arctic sea surface height variability and change from satellite radar altimetry and GRACE, 2003–2014. Journal of Geophysical Research: Oceans 121(6):4303–4322. https://doi.org/10.1002/2015JC011579

Armitage T, Bacon S, Ridout A, Petty A, Wolbach S, Tsamados M (2017) Arctic ocean geostrophic circulation 2003–2014. Arctic Ocean Geostroph Circulat. https://doi.org/10.5194/tc-2017-22

Armitage TWK, Kwok R, Thompson AF, Cunningham G (2018) Dynamic topography and sea level anomalies of the southern ocean: variability and teleconnections. J Geophys Res Oceans 123(1):613–630. https://doi.org/10.1002/2017JC013534

Artana C, Provost C, Lellouche JM, Rio MH, Ferrari R, Sennéchael N (2019) The malvinas current at the confluence with the brazil current: inferences from 25 years of mercator ocean reanalysis. J Geophys Res Oceans 124:7178–7200. https://doi.org/10.1029/2019JC015289

Athanase M, Provost C, Artana C, Pérez-Hernández MD, Sennéchael N, Bertosio C, Garric G, Lellouche JM, Prandi P (2021) Changes in atlantic water circulation patterns and volume transports north of Svalbard over the last 12 years (2008–2020). J Geophys Res Oceans 126(1):102. https://doi.org/10.1029/2020JC016825

Auger M, Prandi P, Sallée JB (2022) Southern ocean sea level anomaly in the sea ice-covered sector from multimission satellite observations. Sci Data 9(1):70. https://doi.org/10.1038/s41597-022-01166-z

Ballarotta M, Ubelmann C, Pujol MI, Taburet G, Fournier F, Legeais JF, Faugère Y, Delepoulle A, Chelton D, Dibarbourbe G, Picot N (2019) On the resolutions of ocean altimetry maps. Ocean Sci 15:1091–1109. https://doi.org/10.5194/os-15-1091-2019

Balwada D, Xiao Q, Smith S, Abernathey R, Gray AR (2021) Vertical fluxes conditioned on vorticity and strain reveal submesoscale ventilation. J Phys Oceanogr 51(9):2883–2901. https://doi.org/10.1175/JPO-D-21-0016.1

Bell MJ, Lefebvre M, Le Traon PY, Smith N, Wilmer-Becker K (2009) The global ocean data assimilation experiment. Oceanography 22(3):14–21

Bell MJ, Schiller A, Le Traon PY, Smith NR, Dombrowsky E, Wilmer-Becker K (2015) An introduction to GODAE ocean view. J Operat Oceanogr 8(1):s2–s11. https://doi.org/10.1080/1755876X.2015.1022041

Benkiran M, Ruggiero G, Greiner E, Le Traon PY, Rémy E, Lellouche JM, Bourdallé-Badie R, Drillet Y, Tchonang B (2021) Assessing the impact of the assimilation of SWOT observations in a global high-resolution analysis and forecasting system part 1: methods. Front Mar Sci 8:691955. https://doi.org/10.3389/fmars.2021.691955

Boy F, Desjonquères JD, Picot N, Moreau T, Raynal M (2017) CryoSat-2 SAR mode over oceans: processing methods, global assessment and benefits. IEEE Trans Geosci Remote Sens 55:148–158. https://doi.org/10.1109/TGRS.2016.2601958

Brown G (1977) The average impulse response of a rough surface and its applications. IEEE J Oceanic Eng 2(1):67–74. https://doi.org/10.1109/JOE.1977.1145328

Caballero A, Mulet S, Ayoub N, Manso-Narvarte I, Davila X, Boone C, Toublanc F, Rubio A (2020) Integration of HF radar observations for an enhanced coastal mean dynamic topography. Front Mar Sci 7:13. https://doi.org/10.3389/fmars.2020.588713

Cai W, Borlace S, Lengaigne M, van Rensch P, Collins M, Vecchi G, Timmermann A, Santoso A, McPhaden MJ, Wu L, England MH, Wang G, Guilyardi E, Jin FF (2014) Increasing frequency of extreme El Niño events due to greenhouse warming. Nat Clim Chang 4(2):111–116. https://doi.org/10.1038/nclimate2100

Callies J, Ferrari R (2013) Interpreting energy and tracer spectra of upper-ocean turbulence in the submesoscale range (1–200 km). J Phys Oceanogr 43(11):2456–2474. https://doi.org/10.1175/JPO-D-13-063.1

Capotondi A, Wittenberg AT, Newman M, di Lorenzo E, Yu JY, Braconnot P, Cole J, Dewitte B, Giese B, Guilyardi E, Jin FF, Karnauskas K, Kirtman B, Lee T, Schneider N, Xue Y, Yeh SW (2015)
Association of Geodesy Symposia. Springer: Switzerland. pp. 1–10. doi: https://doi.org/10.1007/1345_2015_182

Arbic BK, Polzin KL, Scott RB, Richman JG, Shriver JF (2013) On eddy viscosity, energy cascades, and the horizontal resolution of gridded satellite altimeter products. J Phys Oceanogr 43(2):283–300. https://doi.org/10.1175/JPO-D-11-0240.1

Arbic BK et al (2018) A primer on global internal tide and internal gravity wave continuum modeling in HYCOM and MITgcm. In: *New Frontiers in Operational Oceanography* E Chassignet, A Pascual, J Tintoré, J Verron Eds. GODAE Ocean View, 307–392, doi: https://doi.org/10.17125/gov2018.ch13.

Arduuin F, Chapron B, Maes C, Romeiser R, Gommenginger C, Cravatte S, Morrow R, Donlon C, Bourassa M (2019) Satellite doppler observations for the motions of the oceans. B Am Meterol Soc 100:215–219. https://doi.org/10.1175/BAMS-D-19-0039.1

Armitage TWK, Bacon S, Ridout AL, Thomas SF, Aksenov Y, Wingham DJ (2016) Arctic sea surface height variability and change from satellite radar altimetry and GRACE, 2003–2014. Journal of Geophysical Research: Oceans 121(6):4303–4322. https://doi.org/10.1002/2015JC011579

Armitage T, Bacon S, Ridout A, Petty A, Wolbach S, Tsamados M (2017) Arctic ocean geostrophic circulation 2003–2014. Arctic Ocean Geostroph Circulat. https://doi.org/10.5194/tc-2017-22

Armitage TWK, Kwok R, Thompson AF, Cunningham G (2018) Dynamic topography and sea level anomalies of the southern ocean: variability and teleconnections. J Geophys Res Oceans 123(1):613–630. https://doi.org/10.1002/2017JC013534

Artana C, Provost C, Lellouche JM, Rio MH, Ferrari R, Sennéchael N (2019) The malvinas current at the confluence with the brazil current: inferences from 25 years of mercator ocean reanalysis. J Geophys Res Oceans 124:7178–7200. https://doi.org/10.1029/2019JC015289

Athanase M, Provost C, Artana C, Pérez-Hernández MD, Sennéchael N, Bertosio C, Garric G, Lellouche JM, Prandi P (2021) Changes in atlantic water circulation patterns and volume transports north of Svalbard over the last 12 years (2008–2020). J Geophys Res Oceans 126(1):102. https://doi.org/10.1029/2020JC016825

Auger M, Prandi P, Sallée JB (2022) Southern ocean sea level anomaly in the sea ice-covered sector from multimission satellite observations. Sci Data 9(1):70. https://doi.org/10.1038/s41597-022-01166-z

Ballarotta M, Ubelmann C, Pujol MI, Taburet G, Fournier F, Legeais JF, Faugère Y, Delepoulle A, Chelton D, Dibarbourbe G, Picot N (2019) On the resolutions of ocean altimetry maps. Ocean Sci 15:1091–1109. https://doi.org/10.5194/os-15-1091-2019

Balwada D, Xiao Q, Smith S, Abernathey R, Gray AR (2021) Vertical fluxes conditioned on vorticity and strain reveal submesoscale ventilation. J Phys Oceanogr 51(9):2883–2901. https://doi.org/10.1175/JPO-D-21-0016.1

Bell MJ, Lefebvre M, Le Traon PY, Smith N, Wilmer-Becker K (2009) The global ocean data assimilation experiment. Oceanography 22(3):14–21

Bell MJ, Schiller A, Le Traon PY, Smith NR, Dombrowsky E, Wilmer-Becker K (2015) An introduction to GODAE ocean view. J Operat Oceanogr 8(1):s2–s11. https://doi.org/10.1080/1755876X.2015.1022041

Benkiran M, Ruggiero G, Greiner E, Le Traon PY, Rémy E, Lellouche JM, Bourdallé-Badie R, Drillet Y, Tchonang B (2021) Assessing the impact of the assimilation of SWOT observations in a global high-resolution analysis and forecasting system part 1: methods. Front Mar Sci 8:691955. https://doi.org/10.3389/fmars.2021.691955

Boy F, Desjonquères JD, Picot N, Moreau T, Raynal M (2017) CryoSat-2 SAR mode over oceans: processing methods, global assessment and benefits. IEEE Trans Geosci Remote Sens 55:148–158. https://doi.org/10.1109/TGRS.2016.2601958

Brown G (1977) The average impulse response of a rough surface and its applications. IEEE J Oceanic Eng 2(1):67–74. https://doi.org/10.1109/JOE.1977.1145328

Caballero A, Mulet S, Ayoub N, Manso-Narvarte I, Davila X, Boone C, Toublanc F, Rubio A (2020) Integration of HF radar observations for an enhanced coastal mean dynamic topography. Front Mar Sci 7:13. https://doi.org/10.3389/fmars.2020.588713

Cai W, Borlace S, Lengaigne M, van Rensch P, Collins M, Vecchi G, Timmermann A, Santoso A, McPhaden MJ, Wu L, England MH, Wang G, Guilyardi E, Jin FF (2014) Increasing frequency of extreme El Niño events due to greenhouse warming. Nat Clim Chang 4(2):111–116. https://doi.org/10.1038/nclimate2100

Callies J, Ferrari R (2013) Interpreting energy and tracer spectra of upper-ocean turbulence in the sub-mesoscale range (1–200 km). J Phys Oceanogr 43(11):2456–2474. https://doi.org/10.1175/JPO-D-13-063.1

Capotondi A, Wittenberg AT, Newman M, di Lorenzo E, Yu JY, Braconnot P, Cole J, Dewitte B, Giese B, Guilyardi E, Jin FF, Karnauskas K, Kirtman B, Lee T, Schneider N, Xue Y, Yeh SW (2015)
Understanding ENSO diversity. Bull Am Meteor Soc 96(6):921–938. https://doi.org/10.1175/BAMS-D-13-00117.1

Carrere L, Arbic BK, Dushaw B, Egbert G, Erofeeva S, Lyard F, Ray RD, Ubelmann C, Zaron E, Zhao Z, Shriver JF, Buijsman MC, Picot N (2021) Accuracy assessment of global internal-tide models using satellite altimetry. Ocean Sci 17:147–180. https://doi.org/10.5194/os-17-147-2021

Chafik L, Nilsen JEØ, Dangendorf S et al (2019) North atlantic ocean circulation and decadal sea level change during the altimetry era. Nat Sci Rep 9:1041. https://doi.org/10.1038/s41598-018-37603-6

Chassignet EP, Pascual A, Tintoré J, Verron J (2018) New frontiers in operational oceanography. GODAE Ocean View 102:815. https://doi.org/10.17125/gov2018

Chelton DB, Xie SP (2010) Coupled ocean-atmosphere interaction at oceanic mesoscales. Oceanogr 23:52–69

Chelton DB, deSzoeke RA, Schlax MG, El Naggar K, Siwertz N (1998) Geographical variability of the first baroclinic rossby radius of deformation. J Phys Oceanogr 28(3):433–460. https://doi.org/10.1175/1520-0485(1998)028%3c0433:GVOTFB%3e2.0.CO;2

Chelton DB, Ries JC, Haines BJ, Fu LL, Callahan PS (2001). In: Fu LL, Cazenave A (eds) Satellite altimetry and Earth sciences: a handbook of techniques and applications. Academic Press, San Diego, pp 1–131

Chelton DB, Schlax MG, Samelson RM, de Szoeke RA (2007) Global observations of large oceanic eddies. Geophys Res Lett 34:L15606. https://doi.org/10.1029/2007GL030812

Chelton DB, Schlax MG, Samelson RM (2011) Global observations of nonlinear mesoscale eddies. Prog Oceanogr 91:167–216. https://doi.org/10.1016/j.pocean.2011.01.002

Chelton DB, Schlax MG, Samelson RM, Farrar JT, Molemaker MJ, McWilliams JC, Gula J (2019) Prospects for future satellite estimation of small-scale variability of ocean surface velocity and vorticity. Prog Oceanogr 173(2019):256–350. https://doi.org/10.1016/j.pocean.2018.10.012

Chen G, Tang J, Zhao C, Wu S, Yu F, Ma C, Xu Y, Chen W, Zhang Y, Liu J, Wu L (2019) Concept design of the “guanlan” science mission: china’s novel contribution to space oceanography. Front Mar Sci 6:194. https://doi.org/10.3389/fmars.2019.00194

Cheney RE, Marsh JG, Beckley BD (1983) Global me- soscale variability from repeat tracks of SEASAT altimeter data. J Geophys Res 88:4343–4354. https://doi.org/10.1029/JC088iC07p04343

Cohen J, Screen JA, Furtado JC, Barlow M, Whittleston D, Coumou D, Francis J et al (2014) Recent arc- tic amplification and extreme mid-latitude weather. Nat Geosci 7(9):627–37. https://doi.org/10.1038/ ngeo2234

D'Addezio JM, Smith S, Jacobs GA, Helber RW, Rowley C, Souopgui I et al (2019) Quantifying wave-lengths constrained by simulated SWOT observations in a submesoscale resolving ocean analysis/ forecasting system. Ocean Model 135:40–55. https://doi.org/10.1016/j.ocemod.2019.02.001

d'Ovidio F, Isern-Fontanet J, López C, Hernández-García E, García-Ladona E (2009) Comparison between Eulerian diagnostics and finite-size Lyapunov exponents computed from altimetry in the Algerian basin. Deep Sea Res, Part I 56(1):15–31

Desprès A, Reverdin G, D' Ovidio F (2011) Mechanisms and spatial variability of meso scale frontogenesis in the northwestern subpolar gyre. Ocean Model 39:97–113. https://doi.org/10.1016/j.ocemod.2010. 12.005

Dibarboure G, Boy F, Desjonqueres JD, Labroue S, Lasne Y, Picot N, Poisson JC, Thibaut P (2014) Investi-gating short wavelength correlated errors on low-resolution mode altimetry. J Atmos Oceanic Technol 31:1337. https://doi.org/10.1175/JTECH-D-13-00081

Doddridge EW, Meneghello G, Marshall J, Scott J, Lique C (2019) A three-way balance in the beaufort gyre: the ice-ocean governor, wind stress, and eddy diffusivity. J Geophys Res Oceans 124(5):3107– 3124. https://doi.org/10.1029/2018JC014897

Dong C, McWilliams JC, Liu Y, Chen D (2014) Global heat and salt transports by eddy movement. Nat Commun. https://doi.org/10.1038/ncomms4294

Dotto TS, Naveira Garabato A, Bacon S, Tsamados M, Holland PR, Hooley J, Frajka-Williams E, Ridout A, Meredith MP (2018) Variability of the ross gyre, southern ocean: drivers and responses revealed by satellite altimetry. Geophys Res Lett 45(12):6195–6204. https://doi.org/10.1029/2018GL078607

Dufau C, Orsztynowicz M, Dibarboure G, Morrow R, Le Traon PY (2016) Mesoscale resolution capability of altimetry: present & future. J Geophys Res Oceans 121:4910–4927. https://doi.org/10.1002/2015J C010904

Egbert GD, Erofeeva SY (2002) Efficient inverse modeling of barotropic ocean tides. J Atmos Oceanic Tech 19:183–204

Egbert GD, Ray RD (2000) Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature 405:775–778. https://doi.org/10.1038/35015531
Understanding ENSO diversity. Bull Am Meteor Soc 96(6):921–938. https://doi.org/10.1175/BAMS-D-13-00117.1

Carrere L, Arbic BK, Dushaw B, Egbert G, Erofeeva S, Lyard F, Ray RD, Ubelmann C, Zaron E, Zhao Z, Shriver JF, Buijsman MC, Picot N (2021) Accuracy assessment of global internal-tide models using satellite altimetry. Ocean Sci 17:147–180. https://doi.org/10.5194/os-17-147-2021

Chafik L, Nilsen JEØ, Dangendorf S et al (2019) North atlantic ocean circulation and decadal sea level change during the altimetry era. Nat Sci Rep 9:1041. https://doi.org/10.1038/s41598-018-37603-6

Chassignet EP, Pascual A, Tintoré J, Verron J (2018) New frontiers in operational oceanography. GODAE Ocean View 102:815. https://doi.org/10.17125/gov2018

Chelton DB, Xie SP (2010) Coupled ocean-atmosphere interaction at oceanic mesoscales. Oceanogr 23:52–69

Chelton DB, deSzoeke RA, Schlax MG, El Naggar K, Siwertz N (1998) Geographical variability of the first baroclinic rossby radius of deformation. J Phys Oceanogr 28(3):433–460. https://doi.org/10.1175/1520-0485(1998)028%3c0433:GVOTFB%3e2.0.CO;2

Chelton DB, Ries JC, Haines BJ, Fu LL, Callahan PS (2001). In: Fu LL, Cazenave A (eds) Satellite altimetry and Earth sciences: a handbook of techniques and applications. Academic Press, San Diego, pp 1–131

Chelton DB, Schlax MG, Samelson RM, de Szoeke RA (2007) Global observations of large oceanic eddies. Geophys Res Lett 34:L15606. https://doi.org/10.1029/2007GL030812

Chelton DB, Schlax MG, Samelson RM (2011) Global observations of nonlinear mesoscale eddies. Prog Oceanogr 91:167–216. https://doi.org/10.1016/j.pocean.2011.01.002

Chelton DB, Schlax MG, Samelson RM, Farrar JT, Molemaker MJ, McWilliams JC, Gula J (2019) Prospects for future satellite estimation of small-scale variability of ocean surface velocity and vorticity. Prog Oceanogr 173(2019):256–350. https://doi.org/10.1016/j.pocean.2018.10.012

Chen G, Tang J, Zhao C, Wu S, Yu F, Ma C, Xu Y, Chen W, Zhang Y, Liu J, Wu L (2019) Concept design of the “guanlan” science mission: china’s novel contribution to space oceanography. Front Mar Sci 6:194. https://doi.org/10.3389/fmars.2019.00194

Cheney RE, Marsh JG, Beckley BD (1983) Global me- soscale variability from repeat tracks of SEASAT altimeter data. J Geophys Res 88:4343–4354. https://doi.org/10.1029/JC088iC07p04343

Cohen J, Screen JA, Furtado JC, Barlow M, Whittleston D, Coumou D, Francis J et al (2014) Recent arc- tic amplification and extreme mid-latitude weather. Nat Geosci 7(9):627–37. https://doi.org/10.1038/ ngeo2234

D'Addezio JM, Smith S, Jacobs GA, Helber RW, Rowley C, Souopgui I et al (2019) Quantifying wave-lengths constrained by simulated SWOT observations in a submesoscale resolving ocean analysis/ forecasting system. Ocean Model 135:40–55. https://doi.org/10.1016/j.ocemod.2019.02.001

d'Ovidio F, Isern-Fontanet J, López C, Hernández-García E, García-Ladona E (2009) Comparison between Eulerian diagnostics and finite-size Lyapunov exponents computed from altimetry in the Algerian basin. Deep Sea Res, Part I 56(1):15–31

Desprès A, Reverdin G, D' Ovidio F (2011) Mechanisms and spatial variability of meso scale frontogenesis in the northwestern subpolar gyre. Ocean Model 39:97–113. https://doi.org/10.1016/j.ocemod.2010. 12.005

Dibarboure G, Boy F, Desjonqueres JD, Labroue S, Lasne Y, Picot N, Poisson JC, Thibaut P (2014) Investi-gating short wavelength correlated errors on low-resolution mode altimetry. J Atmos Oceanic Technol 31:1337. https://doi.org/10.1175/JTECH-D-13-00081

Doddridge EW, Meneghello G, Marshall J, Scott J, Lique C (2019) A three-way balance in the beaufort gyre: the ice-ocean governor, wind stress, and eddy diffusivity. J Geophys Res Oceans 124(5):3107– 3124. https://doi.org/10.1029/2018JC014897

Dong C, McWilliams JC, Liu Y, Chen D (2014) Global heat and salt transports by eddy movement. Nat Commun. https://doi.org/10.1038/ncomms4294

Dotto TS, Naveira Garabato A, Bacon S, Tsamados M, Holland PR, Hooley J, Frajka-Williams E, Ridout A, Meredith MP (2018) Variability of the ross gyre, southern ocean: drivers and responses revealed by satellite altimetry. Geophys Res Lett 45(12):6195–6204. https://doi.org/10.1029/2018GL078607

Dufau C, Orsztynowicz M, Dibarboure G, Morrow R, Le Traon PY (2016) Mesoscale resolution capability of altimetry: present & future. J Geophys Res Oceans 121:4910–4927. https://doi.org/10.1002/2015J C010904

Egbert GD, Erofeeva SY (2002) Efficient inverse modeling of barotropic ocean tides. J Atmos Oceanic Tech 19:183–204

Egbert GD, Ray RD (2000) Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature 405:775–778. https://doi.org/10.1038/35015531
Egido A, Smith WHF (2017) Fully focused SAR altimetry: theory and applications. IEEE Trans Geosci Remote Sens 55:1. https://doi.org/10.1109/TGRS.2016.2607122

Faghmous J, Frenger I, Yao Y et al (2015) A daily global mesoscale ocean eddy dataset from satellite altimetry. Sci Data 2:150028. https://doi.org/10.1038/sdata.2015.28

Farrar JT (2011) Barotropic rossby waves radiating from tropical instability waves in the Pacific Ocean. J Phys Oceanogr 41:1160–1181. https://doi.org/10.1175/2011JPO4547.1

Farrar JT, Durland TS (2012) Wavenumber-frequency spectra of inertia-gravity and mixed rossby-gravity waves in the equatorial Pacific Ocean. J Phys Oceanogr 42:1859–1881

Farrar JT, Durland T, Jayne SR, Price JF (2021) Long-distance radiation of rossby waves from the equatorial current system. J Phys Oceanogr 51(6):1947–1966. https://doi.org/10.1175/JPO-D-20-0048.1

Fox-Kemper B, Acroft A, Böning CW, Chassignet EP, Curchitser E, Danabasoglu G, Eden C, England MH, Gerdes R, Greatbatch RJ, Griffies SM, Hallberg RW, Hanert E, Heimbach P, Hewitt HT, Hill CN, Komuro Y, Legg S, Le Sommer J, Masina S, Marsland SJ, Penny SG, Qiao F, Ringler TD, Treguier AM, Tsujino H, Uotila P, Yeager SG (2019) Challenges and prospects in ocean circulation models. Front Mar Sci. https://doi.org/10.3389/fmars.2019.00065

Frajka-Williams E (2019) Atlantic meridional overturning circulation: observed transport and variability. Front Mar Sci. https://doi.org/10.3389/fmars.2019.00260

Frappart F, Blumstein D, Cazenave A, Ramillien G, Birol F, Morrow R, Rémy F (2017) Satellite altimetry: principle and major applications in Earth Sciences. In: Webster J (ed) Wiley encyclopedia of electrical and electronics engineering. Wiley, New Jersey, pp 1–25

Frenger I, Münnich M, Gruber N, Knutti R (2015) Southern ocean eddy phenomenology. J Geophys Res Oceans 120:7413–7449. https://doi.org/10.1002/2015JC011047

Fu LL, Chelton DB (2001) Large-scale ocean circulation. In: Fu L-L, Cazenave A (eds) Satellite altimetry and earth sciences: a handbook for techniques and applications. Academic Press, New Jersey, pp 133–169

Fu LL, Rodriguez ER (2004) High-resolution measurement of ocean surface topography by radar interferometry for oceanographic and geophysical applications. AGU Geophys Monogr 19:209–224

Fu LL, Rodriguez E, Alsdorf D, Morrow R (eds) (2012) The SWOT mission science document. JPL publication. https://swot.jpl.nasa.gov/files/swot/SWOT_MSD_1202012.pdf

Fu LL, Ubelmann C (2014) On the transition from profile altimeter to swath altimeter for observing global ocean surface topography. J Atmos Ocean Technol 31:560–568. https://doi.org/10.1175/JTECH-D-13-00109.1

Fu L, Chelton DB, Le Traon PY, Morrow R (2010) Eddy dynamics from satellite altimetry. Oceanogr Magaz 23:4

Fu LL, Lee T, Liu WT, Kwok R (2019) Fifty years of satellite remote sensing of the ocean. In: a century of progress in atmospheric and related sciences: celebrating the American meteorological society centennial. Meteor Monogr. https://doi.org/10.1175/AMSMONOGRAPHS-D-18-0010.1

Gaube P, Chelton DB, Samelson RM, Schlax MG, O'Neill LW (2015) Satellite observations of mesoscale eddy-induced Ekman pumping. J Phys Oceanogr 45:104–132

Giles KA, Laxon SW, Ridout AL, Wingham DJ, Bacon S (2012) Western arctic ocean freshwater storage increased by wind-driven spin-up of the beaufort gyre. Nat Geosci 5(3):194–197. https://doi.org/10.1038/ngeo1379

Gourcuff C, Lherminier P, Mercier H, Le Traon P-Y (2011) Altimetry combined with hydrography for ocean transport estimation. J Atmos Ocean Technol 28(10):1324–1337. https://doi.org/10.1175/2011JTECHO818.1

Hamlington BD, Strassburg MW, Leben RR, Han W, Nerem RS, Kim KY (2014) Uncovering an anthropogenic sea-level rise signal in the Pacific Ocean. Nat Clim Chang 4:782–785. https://doi.org/10.1038/nclimate2307

Hamon M, Greiner E, Le Traon P, Remy E (2019) Impact of multiple altimeter data and mean dynamic topography in a global analysis and forecasting system. J Atmos Oceanic Tech 36(7):1255–1266. https://doi.org/10.1175/JTECH-D-18-0236.1

Hart-Davis MG, Piccioni G, Dettmering D, Schwatke C, Passaro M, Seitz F (2021) EOT20: a global ocean tide model from multi-mission satellite altimetry. Earth Syst Sci Data. https://doi.org/10.5194/essd-2021-97

Kelly KA, Willis JK, Reverdin G, Dong S, Thompson L (2017) Monitoring and interpreting mid-latitude oceans by satellite altimetry. In: satellite altimetry over oceans and land surfaces. CRC Press: New York. pp 102

Klein P, Lapeyre G (2009) The oceanic vertical pump induced by mesoscale and submesoscale turbulence. Annu Rev Mar Sci 1:351–375
Egido A, Smith WHF (2017) Fully focused SAR altimetry: theory and applications. IEEE Trans Geosci Remote Sens 55:1. https://doi.org/10.1109/TGRS.2016.2607122

Faghmous J, Frenger I, Yao Y et al (2015) A daily global mesoscale ocean eddy dataset from satellite altimetry. Sci Data 2:150028. https://doi.org/10.1038/sdata.2015.28

Farrar JT (2011) Barotropic rossby waves radiating from tropical instability waves in the Pacific Ocean. J Phys Oceanogr 41:1160–1181. https://doi.org/10.1175/2011JPO4547.1

Farrar JT, Durland TS (2012) Wavenumber-frequency spectra of inertia-gravity and mixed rossby-gravity waves in the equatorial Pacific Ocean. J Phys Oceanogr 42:1859–1881

Farrar JT, Durland T, Jayne SR, Price JF (2021) Long-distance radiation of rossby waves from the equatorial current system. J Phys Oceanogr 51(6):1947–1966. https://doi.org/10.1175/JPO-D-20-0048.1

Fox-Kemper B, Acroft A, Böning CW, Chassignet EP, Curchitser E, Danabasoglu G, Eden C, England MH, Gerdes R, Greatbatch RJ, Griffies SM, Hallberg RW, Hanert E, Heimbach P, Hewitt HT, Hill CN, Komuro Y, Legg S, Le Sommer J, Masina S, Marsland SJ, Penny SG, Qiao F, Ringler TD, Treguier AM, Tsujino H, Uotila P, Yeager SG (2019) Challenges and prospects in ocean circulation models. Front Mar Sci. https://doi.org/10.3389/fmars.2019.00065

Frajka-Williams E (2019) Atlantic meridional overturning circulation: observed transport and variability. Front Mar Sci. https://doi.org/10.3389/fmars.2019.00260

Frappart F, Blumstein D, Cazenave A, Ramillien G, Birol F, Morrow R, Rémy F (2017) Satellite altimetry: principle and major applications in Earth Sciences. In: Webster J (ed) Wiley encyclopedia of electrical and electronics engineering. Wiley, New Jersey, pp 1–25

Frenger I, Münnich M, Gruber N, Knutti R (2015) Southern ocean eddy phenomenology. J Geophys Res Oceans 120:7413–7449. https://doi.org/10.1002/2015JC011047

Fu LL, Chelton DB (2001) Large-scale ocean circulation. In: Fu L-L, Cazenave A (eds) Satellite altimetry and earth sciences: a handbook for techniques and applications. Academic Press, New Jersey, pp 133–169

Fu LL, Rodriguez ER (2004) High-resolution measurement of ocean surface topography by radar interferometry for oceanographic and geophysical applications. AGU Geophys Monogr 19:209–224

Fu LL, Rodriguez E, Alsdorf D, Morrow R (eds) (2012) The SWOT mission science document. JPL publication. https://swot.jpl.nasa.gov/files/swot/SWOT_MSD_1202012.pdf

Fu LL, Ubelmann C (2014) On the transition from profile altimeter to swath altimeter for observing global ocean surface topography. J Atmos Ocean Technol 31:560–568. https://doi.org/10.1175/JTECH-D-13-00109.1

Fu L, Chelton DB, Le Traon PY, Morrow R (2010) Eddy dynamics from satellite altimetry. Oceanogr Magaz 23:4

Fu LL, Lee T, Liu WT, Kwok R (2019) Fifty years of satellite remote sensing of the ocean. In: a century of progress in atmospheric and related sciences: celebrating the American meteorological society centennial. Meteor Monogr. https://doi.org/10.1175/AMSMONOGRAPHS-D-18-0010.1

Gaube P, Chelton DB, Samelson RM, Schlax MG, O'Neill LW (2015) Satellite observations of mesoscale eddy-induced Ekman pumping. J Phys Oceanogr 45:104–132

Giles KA, Laxon SW, Ridout AL, Wingham DJ, Bacon S (2012) Western arctic ocean freshwater storage increased by wind-driven spin-up of the beaufort gyre. Nat Geosci 5(3):194–197. https://doi.org/10.1038/ngeo1379

Gourcuff C, Lherminier P, Mercier H, Le Traon P-Y (2011) Altimetry combined with hydrography for ocean transport estimation. J Atmos Ocean Technol 28(10):1324–1337. https://doi.org/10.1175/2011JTECHO818.1

Hamlington BD, Strassburg MW, Leben RR, Han W, Nerem RS. Kim KY (2014) Uncovering an anthropogenic sea-level rise signal in the Pacific Ocean. Nat Clim Chang 4:782–785. https://doi.org/10.1038/nclimate2307

Hamon M, Greiner E, Le Traon P, Remy E (2019) Impact of multiple altimeter data and mean dynamic topography in a global analysis and forecasting system. J Atmos Oceanic Tech 36(7):1255–1266. https://doi.org/10.1175/JTECH-D-18-0236.1

Hart-Davis MG, Piccioni G, Dettmering D, Schwatke C, Passaro M, Seitz F (2021) EOT20: a global ocean tide model from multi-mission satellite altimetry. Earth Syst Sci Data. https://doi.org/10.5194/essd-2021-97

Kelly KA, Willis JK, Reverdin G, Dong S, Thompson L (2017) Monitoring and interpreting mid-latitude oceans by satellite altimetry. In: satellite altimetry over oceans and land surfaces. CRC Press: New York. pp 102

Klein P, Lapeyre G (2009) The oceanic vertical pump induced by mesoscale and submesoscale turbulence. Annu Rev Mar Sci 1:351–375
Laignel B, Vignudelli S, Almar R, Becker M, Bentamy A, Benveniste J, Birol F, Frappart F, Idier D, Salameh E, Passaro M, Menendez M, Simard M, Turki I, Verpoorter C (2022) Observation of the coastal areas, estuaries and deltas from space. Surveys Geophys. 10:102. https://doi.org/10.1007/s10712-022-09757-6

Le Provost C, Bennett AF, Cartwright DE (1995) Ocean tides for and from topex/poseidon. Science 267:639–642

Le Traon PY et al (2019) From observation to information and users: the copernicus marine service perspective. Front Mar Sci 6(234):22. https://doi.org/10.3389/fmars.2019.00234

Leben RR, Hamlington BD, Haines BJ (2011) Seasat and geosat revisited: using sea level measurements to improve satellite altimeter orbits. J Astronaut Sci 58:479–493

Legeckis R (1977) Long waves in the eastern equatorial pacific ocean: a view from a geostationary satellite. Science 197:1179–1181. https://doi.org/10.1126/science.197.4309.1179

Lellouche JM, Greiner E, Bourdallé-Badie R, Garric G, Melet A, Drevillon M, Bricaud M Hamon, Le Gal-loudec O, Regnier C, Candela T, Testut CE, Gasparin F, Ruggiero G, Benkiran M, Drillet Y, Le Traon PY (2021) The copernicus global 1/12° oceanic and sea ice GLORYS12 reanalysis. Front Earth Sci 9:698876. https://doi.org/10.3389/feart.2021.698876

Levitus S, Antonov JI, Boyer TP, Locarnini RA, Garcia HE, Mishonov AV (2009) Global ocean heat content 1955–2008 in light of recently revealed instrumentation problems. Geophys Res Lett 36:07608. https://doi.org/10.1029/2008GL037155

Levy M, Ferrari R, Franks PJP, Martin AP, Riviere P (2012) Bringing physics to life at the submesoscale. Geophys Res Lett 39:L14602. https://doi.org/10.1029/2012GL052756

Llovel W, Penduff T, Meyssignac B, Molines JM, Terray L, Bessières L, Barnier B (2018) Contributions of atmospheric forcing and chaotic ocean variability to regional sea level trends over 1993–2015. Geophys Res Lett 45(13):405–413. https://doi.org/10.1029/2018GL080838

Lyard F, Allain D, Cancet M, Carrère L, Picot N (2021) FES2014 global ocean tide atlas: design and performance. Ocean Sci 17:615–649. https://doi.org/10.5194/os-17-615-2021

Lyman JM, Chelton DB, de Szoefe RA, Samelson RM (2005) Tropical instability waves as a resonance between equatorial rossby waves. J Phys Oceanogr 35:232–254. https://doi.org/10.1175/JPO-2668.1

Martínez-Moreno J, Hogg AM, England MH et al (2021) Global changes in oceanic mesoscale currents over the satellite altimetry record. Nat Clim Chang 11:397–403. https://doi.org/10.1038/s41558-021-01006-9

Maximenko NA, Niiler PP (2005) Hybrid decade-mean global sea level with mesoscale resolution. In: Saxena N (ed) Recent advances in marine sci-ence and technology. PACON International, Honolulu, pp 55–59

McCarthy GD, Brown PJ, Flagg CN, Goni G, Houpert L, Hughes CW et al (2020) Sustainable observations of the AMOC: methodology and technology. Rev Geophys 58:e2019RG000654. https://doi.org/10.1029/2019RG000654

Mercier H, Lherminier P, Sarafanov A, Gaillard F, Daniault N, Desbruyères D, Falina A, Ferron B, Gourcuff C, Huck T, Thierry V (2015) Variability of the meridional overturning circulation at the Greenland-Portugal OVIDE section from 1993 to 2010. Prog Oceanogr 132:250–261. https://doi.org/10.1016/j.pocean.2013.11.001

Moore AM, Martin MJ, Akella S, Arango HG, Balmaseda M, Bertino L, Ciavatta S, Cornuelle B, Cummings J, Frolov S, Lermusiaux P, Oddo P, Oke PR, Storto A, Teruzzi A, Vidard A, Weaver AT (2019) Synthesis of ocean observations using data assimilation for operational, real-time and reanalysis systems: a more complete picture of the state of the ocean. Front Mar Sci 6:90. https://doi.org/10.3389/fmars.2019.00090

Morrow R, Le Traon PY (2012) Recent advances in observing mesoscale ocean dynamics with satellite altimetry. Adv Space Res 50(8):1062–1076. https://doi.org/10.1016/j.asr.2011.09.033

Morrow R, Blumstein D, Dibarboure G (2018) Finescale altimetry and the future SWOT mission. In: New frontiers in operational oceanography GODAE ocean view international school special edition. pp 815. https://doi.org/10.17125/gov2018

Morrow R, Fu LL, Ardhuin F, Benkiran M, Chapron B, Cosme E, d'Ovidio F, Farrar JT, Gille ST, Lapeyre G, Le Traon P-Y, Pascual A, Ponte A, Qiu B, Rascle N, Ubelmann C, Wang J, Zaron E (2019) Global observations of fine-scale ocean surface topography with the surface water and ocean topography (SWOT) mission. Front Mar Sci. https://doi.org/10.3389/fmars.2019.0023

Mulet S, Rio MH, Mignot A, Guinehut S, Morrow R (2012) A new estimate of the global 3D geostrophic ocean circulation based on satellite data and in-situ measurements. Deep Sea Res Part II 77–80:70–81. https://doi.org/10.1016/j.dsr2.2012.04.012
Laignel B, Vignudelli S, Almar R, Becker M, Bentamy A, Benveniste J, Birol F, Frappart F, Idier D, Salameh E, Passaro M, Menendez M, Simard M, Turki I, Verpoorter C (2022) Observation of the coastal areas, estuaries and deltas from space. Surveys Geophys. 10:102. https://doi.org/10.1007/s10712-022-09757-6

Le Provost C, Bennett AF, Cartwright DE (1995) Ocean tides for and from topex/poseidon. Science 267:639–642

Le Traon PY et al (2019) From observation to information and users: the copernicus marine service perspective. Front Mar Sci 6(234):22. https://doi.org/10.3389/fmars.2019.00234

Leben RR, Hamlington BD, Haines BJ (2011) Seasat and geosat revisited: using sea level measurements to improve satellite altimeter orbits. J Astronaut Sci 58:479–493

Legeckis R (1977) Long waves in the eastern equatorial pacific ocean: a view from a geostationary satellite. Science 197:1179–1181. https://doi.org/10.1126/science.197.4309.1179

Lellouche JM, Greiner E, Bourdallé-Badie R, Garric G, Melet A, Drevillon M, Bricaud M Hamon, Le Gal-loudec O, Regnier C, Candela T, Testut CE, Gasparin F, Ruggiero G, Benkiran M, Drillet Y, Le Traon PY (2021) The copernicus global 1/12° oceanic and sea ice GLORYS12 reanalysis. Front Earth Sci 9:698876. https://doi.org/10.3389/feart.2021.698876

Levitus S, Antonov JI, Boyer TP, Locarnini RA, Garcia HE, Mishonov AV (2009) Global ocean heat content 1955–2008 in light of recently revealed instrumentation problems. Geophys Res Lett 36:07608. https://doi.org/10.1029/2008GL037155

Levy M, Ferrari R, Franks PJP, Martin AP, Riviere P (2012) Bringing physics to life at the submesoscale. Geophys Res Lett 39:L14602. https://doi.org/10.1029/2012GL052756

Llovel W, Penduff T, Meyssignac B, Molines JM, Terray L, Bessières L, Barnier B (2018) Contributions of atmospheric forcing and chaotic ocean variability to regional sea level trends over 1993–2015. Geophys Res Lett 45(13):405–413. https://doi.org/10.1029/2018GL080838

Lyard F, Allain D, Cancet M, Carrère L, Picot N (2021) FES2014 global ocean tide atlas: design and performance. Ocean Sci 17:615–649. https://doi.org/10.5194/os-17-615-2021

Lyman JM, Chelton DB, de Szoefe RA, Samelson RM (2005) Tropical instability waves as a resonance between equatorial rossby waves. J Phys Oceanogr 35:232–254. https://doi.org/10.1175/JPO-2668.1

Martínez-Moreno J, Hogg AM, England MH et al (2021) Global changes in oceanic mesoscale currents over the satellite altimetry record. Nat Clim Chang 11:397–403. https://doi.org/10.1038/s41558-021-01006-9

Maximenko NA, Niiler PP (2005) Hybrid decade-mean global sea level with mesoscale resolution. In: Saxena N (ed) Recent advances in marine sci-ence and technology. PACON International, Honolulu, pp 55–59

McCarthy GD, Brown PJ, Flagg CN, Goni G, Houpert L, Hughes CW et al (2020) Sustainable observations of the AMOC: methodology and technology. Rev Geophys 58:e2019RG000654. https://doi.org/10.1029/2019RG000654

Mercier H, Lherminier P, Sarafanov A, Gaillard F, Daniault N, Desbruyères D, Falina A, Ferron B, Gourcuff C, Huck T, Thierry V (2015) Variability of the meridional overturning circulation at the Green-land-Portugal OVIDE section from 1993 to 2010. Prog Oceanogr 132:250–261. https://doi.org/10.1016/j.pocean.2013.11.001

Moore AM, Martin MJ, Akella S, Arango HG, Balmaseda M, Bertino L, Ciavatta S, Cornuelle B, Cummings J, Frolov S, Lermusiaux P, Oddo P, Oke PR, Storto A, Teruzzi A, Vidard A, Weaver AT (2019) Synthesis of ocean observations using data assimilation for operational, real-time and reanalysis systems: a more complete picture of the state of the ocean. Front Mar Sci 6:90. https://doi.org/10.3389/fmars.2019.00090

Morrow R, Le Traon PY (2012) Recent advances in observing mesoscale ocean dynamics with satellite altimetry. Adv Space Res 50(8):1062–1076. https://doi.org/10.1016/j.asr.2011.09.033

Morrow R, Blumstein D, Dibarboure G (2018) Finescale altimetry and the future SWOT mission. In: New frontiers in operational oceanography GODAE ocean view international school special edition. pp 815. https://doi.org/10.17125/gov2018

Morrow R, Fu LL, Ardhuin F, Benkiran M, Chapron B, Cosme E, d'Ovidio F, Farrar JT, Gille ST, Lapeyre G, Le Traon P-Y, Pascual A, Ponte A, Qiu B, Rascle N, Ubelmann C, Wang J, Zaron E (2019) Global observations of fine-scale ocean surface topography with the surface water and ocean topography (SWOT) mission. Front Mar Sci. https://doi.org/10.3389/fmars.2019.0023

Mulet S, Rio MH, Mignot A, Guinehut S, Morrow R (2012) A new estimate of the global 3D geostrophic ocean circulation based on satellite data and in-situ measurements. Deep Sea Res Part II 77–80:70–81. https://doi.org/10.1016/j.dsr2.2012.04.012
Mulet S, Rio MH, Etienne H, Artana C, Cancet M, Dibarboure G, Feng H, Husson R, Picot N, Provost C, Strub PT (2021) The new CNES-CLS18 global mean dynamic topography. Ocean Sci 17:789–808. https://doi.org/10.5194/os-17-789-2021

Munk W (1997) Once again—tidal friction. Prog Oceanogr 40:7–35

Newton JL, Aagaard K, Coachman LK (1974) Baroclinic eddies in the arctic ocean. Deep-Sea Res Oceanogr Abstr 21(9):707–719. https://doi.org/10.1016/0011-7471(74)90078-3

Pascual A, Faugère Y, Larnicola G, Le Traon PY (2006) Improved description of the ocean mesoscale variability by combining four satellite altimeters. Geophys Res Lett. https://doi.org/10.1029/2005GL024633

Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the earth gravitational model 2008 (EGM2008). J Geophys Res 117:B04406. https://doi.org/10.1029/2011JB008916

Peacock NR, Laxon SW (2004) Sea Surface Height Determination in the Arctic Ocean from ERS Altimetry. J Geophys Res 109(C7):C07001. https://doi.org/10.1029/2001JC001026

Pegliasco C, Chaigneau A, Morrow R, Dumas F (2021) Detection and tracking of mesoscale eddies in the mediterranean sea: a comparison between the sea level anomaly and the absolute dynamic topography fields. Adv Space Res 68:401–419. https://doi.org/10.1016/j.asr.2020.03.039

Penduff T, Juza M, Barnier B, Zika J, Dewar WK, Treguier AM et al (2011) Sea-level expression of intrinsic and forced ocean variabilities at interannual time scales. J Clim 24(21):5652–5670. https://doi.org/10.1175/JCLI-D-11-00077

Poisson JC, Quarterly GD, Kurekin AA, Thibaut P, Hoang D, Nencioli F (2018) Development of an ENVISAT altimetry processor providing sea level continuity between open ocean and arctic leads. IEEE Trans Geosci Remote Sens 56(9):5299–5319. https://doi.org/10.1109/TGRS.2018.2813061

Prandi P, Poisson JC, Faugère Y, Guillot A, Dibarboure G (2021) Arctic sea surface height maps from multi-altimeter combination. Earth Syst Sci Data Discuss. https://doi.org/10.5194/ESSD-2021-123

Pujol M-I, Faugère Y, Taburet G, Dupuy S, Pelloquin C, Ablain M, Picot N (2016) DUACS DT2014: the new multi-mission altimeter data set reprocessed over 20 years. Ocean Sci 12:1067–1090. https://doi.org/10.5194/os-12-1067-2016

Pujol MI, Schaeffer P, Faugere Y, Raynal M, Dibarboure G, Picot N (2018) Gauging the improvement of recent mean sea surface models: A new approach for identifying and quantifying their errors. J Geophys Res Oceans 123:1056. https://doi.org/10.1029/2017JC013503

Qiu B, Chen S (2005) Variability of the kuroshio extension jet, recirculation gyre, and mesoscale eddies on decadal time scales. J Phys Oceanogr 35(11):2090–2103. https://doi.org/10.1175/JPO2807.1

Qiu B, Chen S (2011) Effect of decadal Kuroshio Extension jet and eddy variability on the modification of North Pacific in-termediate water. J Phys Oceanogr 41:503–515. https://doi.org/10.1175/2010JPO4575.1

Qiu B, Chen S, Klein P, Sasaki H, Sasai Y (2014) Seasonal mesoscale and submesoscale eddy variability along the North Pacific subtropical counter current. J Phys Oceanogr 44:3079–3098. https://doi.org/10.1175/JPO-D-14-0071.1

Qiu B, Chen S, Klein P, Ubelmann C, Fu L-L, Sasaki H (2016) Reconstructability of 3-dimensional upper ocean circulation from SWOT sea surface height measurements. J Phys Oceanogr 46:947–963

Quartly GD, Srokosz MA, McMillan AC (2001) Analyzing altimeter artifacts: statistical properties of ocean waveforms. J Atmos Ocean Tech 18(12):2074–2091

Quartly GD, Rinne E, Passaro M, Andersen OB, Dinardo S, Fleury S, Guillot A et al (2019) Retrieving sea level and freeboard in the arctic: a review of current radar altimetry methodologies and future perspectives. Remote Sens. https://doi.org/10.3390/RS11070881

Raney RK (1998) The delay/doppler radar altimeter. IEEE Trans Geosci Remote Sens 36(5):1578–1588. https://doi.org/10.1109/36.718861

Ray RD (2020) First global observations of third-degree ocean tides. Sci Adv 6:4744. https://doi.org/10.1126/sciadv.abd4744

Ray RD, Egbert GD (2017) Tides and satellite altimetry. In: Stammer D, Cazenave A (eds) Satellite altimetry over oceans and land surfaces. CRC Press, New York, pp 427–458

Ray RD, Zaron ED (2016) M2 internal tides and their observed wavenumber spectra from satellite altimetry. J Phys Oceanogr 46(1):3–22. https://doi.org/10.1175/JPO-D-15-0065.1

Richman JG, Arbic BK, Shriver JF, Metzger EJ, Wallcraft AJ (2012) Inferring dynamics from the wavenumber spectra of an eddying global ocean model with embedded tides. J Geophys Res 117:C12012. https://doi.org/10.1029/2012JC008364

Rieck JK, Böning CW, Greatbatch RJ, Scheinert M (2015) Seasonal variability of eddy kinetic energy in a global high-resolution ocean model. Geophys Res Lett 42:9379–9386. https://doi.org/10.1002/2015GL066152
Mulet S, Rio MH, Etienne H, Artana C, Cancet M, Dibarboure G, Feng H, Husson R, Picot N, Provost C, Strub PT (2021) The new CNES-CLS18 global mean dynamic topography. Ocean Sci 17:789–808. https://doi.org/10.5194/os-17-789-2021

Munk W (1997) Once again—tidal friction. Prog Oceanogr 40:7–35

Newton JL, Aagaard K, Coachman LK (1974) Baroclinic eddies in the arctic ocean. Deep-Sea Res Oceanogr Abstr 21(9):707–719. https://doi.org/10.1016/0011-7471(74)90078-3

Pascual A, Faugère Y, Larnicola G, Le Traon PY (2006) Improved description of the ocean mesoscale variability by combining four satellite altimeters. Geophys Res Lett. https://doi.org/10.1029/2005GL024633

Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the earth gravitational model 2008 (EGM2008). J Geophys Res 117:B04406. https://doi.org/10.1029/2011JB008916

Peacock NR, Laxon SW (2004) Sea Surface Height Determination in the Arctic Ocean from ERS Altimetry. J Geophys Res 109(C7):C07001. https://doi.org/10.1029/2001JC001026

Pegliasco C, Chaigneau A, Morrow R, Dumas F (2021) Detection and tracking of mesoscale eddies in the mediterranean sea: a comparison between the sea level anomaly and the absolute dynamic topography fields. Adv Space Res 68:401–419. https://doi.org/10.1016/j.asr.2020.03.039

Penduff T, Juza M, Barnier B, Zika J, Dewar WK, Treguier AM et al (2011) Sea-level expression of intrinsic and forced ocean variabilities at interannual time scales. J Clim 24(21):5652–5670. https://doi.org/10.1175/JCLI-D-11-00077

Poisson JC, Quarterly GD, Kurekin AA, Thibaut P, Hoang D, Nencioli F (2018) Development of an ENVISAT altimetry processor providing sea level continuity between open ocean and arctic leads. IEEE Trans Geosci Remote Sens 56(9):5299–5319. https://doi.org/10.1109/TGRS.2018.2813061

Prandi P, Poisson JC, Faugère Y, Guillot A, Dibarboure G (2021) Arctic sea surface height maps from multi-altimeter combination. Earth Syst Sci Data Discuss. https://doi.org/10.5194/ESSD-2021-123

Pujol M-I, Faugère Y, Taburet G, Dupuy S, Pelloquin C, Ablain M, Picot N (2016) DUACS DT2014: the new multi-mission altimeter data set reprocessed over 20 years. Ocean Sci 12:1067–1090. https://doi.org/10.5194/os-12-1067-2016

Pujol MI, Schaeffer P, Faugere Y, Raynal M, Dibarboure G, Picot N (2018) Gauging the improvement of recent mean sea surface models: A new approach for identifying and quantifying their errors. J Geophys Res Oceans 123:1056. https://doi.org/10.1029/2017JC013503

Qiu B, Chen S (2005) Variability of the kuroshio extension jet, recirculation gyre, and mesoscale eddies on decadal time scales. J Phys Oceanogr 35(11):2090–2103. https://doi.org/10.1175/JPO2807.1

Qiu B, Chen S (2011) Effect of decadal Kuroshio Extension jet and eddy variability on the modification of North Pacific in-termediate water. J Phys Oceanogr 41:503–515. https://doi.org/10.1175/2010JPO4575.1

Qiu B, Chen S, Klein P, Sasaki H, Sasai Y (2014) Seasonal mesoscale and submesoscale eddy variability along the North Pacific subtropical counter current. J Phys Oceanogr 44:3079–3098. https://doi.org/10.1175/JPO-D-14-0071.1

Qiu B, Chen S, Klein P, Ubelmann C, Fu L-L, Sasaki H (2016) Reconstructability of 3-dimensional upper ocean circulation from SWOT sea surface height measurements. J Phys Oceanogr 46:947–963

Quartly GD, Srokosz MA, McMillan AC (2001) Analyzing altimeter artifacts: statistical properties of ocean waveforms. J Atmos Ocean Tech 18(12):2074–2091

Quartly GD, Rinne E, Passaro M, Andersen OB, Dinardo S, Fleury S, Guillot A et al (2019) Retrieving sea level and freeboard in the arctic: a review of current radar altimetry methodologies and future perspectives. Remote Sens. https://doi.org/10.3390/RS11070881

Raney RK (1998) The delay/doppler radar altimeter. IEEE Trans Geosci Remote Sens 36(5):1578–1588. https://doi.org/10.1109/36.718861

Ray RD (2020) First global observations of third-degree ocean tides. Sci Adv 6:4744. https://doi.org/10.1126/sciadv.abd4744

Ray RD, Egbert GD (2017) Tides and satellite altimetry. In: Stammer D, Cazenave A (eds) Satellite altimetry over oceans and land surfaces. CRC Press, New York, pp 427–458

Ray RD, Zaron ED (2016) M2 internal tides and their observed wavenumber spectra from satellite altimetry. J Phys Oceanogr 46(1):3–22. https://doi.org/10.1175/JPO-D-15-0065.1

Richman JG, Arbic BK, Shriver JF, Metzger EJ, Wallcraft AJ (2012) Inferring dynamics from the wavenumber spectra of an eddying global ocean model with embedded tides. J Geophys Res 117:C12012. https://doi.org/10.1029/2012JC008364

Rieck JK, Böning CW, Greatbatch RJ, Scheinert M (2015) Seasonal variability of eddy kinetic energy in a global high-resolution ocean model. Geophys Res Lett 42:9379–9386. https://doi.org/10.1002/2015GL066152
Rieu P, Moreau T, Cadier E, Raynal M, Clerc S, Donlon C, Borde F, Boy F, Maraldi C (2021) Exploiting the Sentinel-3 tandem phase dataset and azimuth oversampling to better characterize the sensitivity of SAR altimeter sea surface height to long ocean waves. Adv Space Res 67:253–265. https://doi.org/10.1016/j.asr.2020.09.037

Rio MH, Hernandez F (2004) A mean dynamic Topography computed over the world ocean from altimetry, in-situ measurements and a geoid mod-el. J Geophys Res 109:12

Rodriguez E, Fernandez DE, Peral E, Chen CW, De Bleser JW, Williams B (2017) Wide-swath altimetry: a review. In: Stammer D, Cazenave A (eds) Satellite altimetry over oceans and land surfaces. CRC Press, New York, pp 71–112

Roemmich D, Johnson GC, Riser S, Davis R, Gilson J, Owens WB, Garzoli SL, Schmid C, Ignaszewski M (2009) The argo program: observing the global ocean with profiling floats. Oceanography 22(2):34–43. https://doi.org/10.5670/oceanog.2009.36

Roessler A, Rhein M, Kieke D, Mertens C (2015) Long-term observations of North Atlantic Current transport at the gateway between western and eastern Atlantic. J Geophys Res C: Oceans. https://doi.org/10.1002/2014JC010662

Rogé M, Morrow R, Dencausse G (2015) Altimetric lagrangian advection to reconstruct Pacific Ocean fine scale surface tracer fields. Ocean Dyn 65:1249–1268. https://doi.org/10.1007/s10236-015-0872-4

Rose SK, Andersen OB, Passaro M, Ludwigsen CA, Schwatke C (2019) Arctic ocean sea level record from the complete radar altimetry Era: 1991–2018. Remote Sens 11(14):16. https://doi.org/10.3390/rs11141672

Sandwell DT, Smith WHF (2009) Global marine gravity from retracked Geosat and ERS-1 altimetry: Ridge segmentation versus spreading rate. J Geophys Res 114:B01411. https://doi.org/10.1029/2008JB006008

Sasaki H, Klein P, Qiu B et al (2014) Impact of oceanic-scale interactions on the seasonal modulation of ocean dynamics by the atmosphere. Nat Commun 5:5636. https://doi.org/10.1038/ncomms6636

Scharffenberg MG, Stammer D (2010) Seasonal variations of the large-scale geostrophic flow field and eddy kinetic energy inferred from the TOPEX/Poseidon and Jason-1 tandem mission data. J Geophys Res 115:C02008. https://doi.org/10.1029/2008JC005242

Schmid C (2014) Mean vertical and horizontal structure of the subtropical circulation in the South Atlantic from three-dimensional observed velocity fields. Deep Sea Res Part I. https://doi.org/10.1016/j.dsr.2014.04.015

Scott RB, Wang F (2005) Direct evidence of an oceanic inverse kinetic energy cascade from satellite altimetry. J Phys Oceanogr 35:1650–1666

Shakespeare CJ, Arbic BK, Hogg AM (2020) The drag on the barotropic tide due to the generation of baroclinic motion. J Phys Oceanogr 50:3467–3481

Shum CK et al (1997) Accuracy assessment of recent ocean tide models. J Geophys Res 102:25173–25194

Smith GC, Allard R, Babin M, Bertino L, Chevallier M, Corlett GK, Crout J et al (2019) Polar ocean observations: a critical gap in the observing system and its effect on environmental predictions from hours to a season. Front Mar Sci 6:1025. https://doi.org/10.3389/fmars.2019.00429

Souza JMAC, de Boyer Montegut C, Le Traon PY (2011) Mesoscale eddies in the South Atlantic. Ocean Sci Discuss 8:483–531. https://doi.org/10.5194/osd-8-483-2011

Stammer D et al (2014) Accuracy assessment of global barotropic ocean tide models. Rev Geophys 52:243–282. https://doi.org/10.1002/2014RG000450

Stammer D, Balmaseda M, Heimbach P, Kohl A, Weaver A (2016) Ocean data assimilation in support of climate applications: status and perspectives. Ann Rev Mar Sci 8:491–518. https://doi.org/10.1146/annurev-marine-122414-034113

Storto A, Alvera-Azcárate A, Balmaseda MA, Barth A, Chevallier M, Counillon F, Domingues CM, Drevil-lon M, Drillet Y, Forget G, Garric G, Haines K, Hernandez F, Iovino D, Jackson LC, Lellouche J-M, Masina S, Mayer M, Oke PR, Penny SG, Peterson KA, Yang C, Zuo H (2019) Ocean reanalyses: recent advances and unsolved challenges. Front Mar Sci 6:418. https://doi.org/10.3389/fmars.2019.00418

Taburet G, Sanchez-Roman A, Ballarotta M, Pujol M-I, Legeais J-F, Fournier F, Faugere Y, Dibarboure G (2019) DUACS DT2018: 25 years of reprocessed sea level altimetry products. Ocean Sci 15:1207–1224. https://doi.org/10.5194/os-15-1207-2019

Tchilibou M, Gourdeau L, Morrow R, Serazin G, Djath B, Lyard F (2018) Spectral signatures of the tropical Pacific dynamics from model and altimetry: a focus on the meso-submesoscale range. Ocean Sci 14:1283–1301. https://doi.org/10.5194/os-14-1283-2018

Tchonang B, Benkiran M, Le Traon PY, Van Gennip SJ, Lellouche JM, Ruggiero G (2021) Assessing the impact of the assimilation of SWOT observations in a global high-resolution analysis and forecasting system Part 2: results. Front Mar Sci 8:691–995
Rieu P, Moreau T, Cadier E, Raynal M, Clerc S, Donlon C, Borde F, Boy F, Maraldi C (2021) Exploiting the Sentinel-3 tandem phase dataset and azimuth oversampling to better characterize the sensitivity of SAR altimeter sea surface height to long ocean waves. Adv Space Res 67:253–265. https://doi.org/10.1016/j.asr.2020.09.037

Rio MH, Hernandez F (2004) A mean dynamic Topography computed over the world ocean from altimetry, in-situ measurements and a geoid mod-el. J Geophys Res 109:12

Rodriguez E, Fernandez DE, Peral E, Chen CW, De Bleser JW, Williams B (2017) Wide-swath altimetry: a review. In: Stammer D, Cazenave A (eds) Satellite altimetry over oceans and land surfaces. CRC Press, New York, pp 71–112

Roemmich D, Johnson GC, Riser S, Davis R, Gilson J, Owens WB, Garzoli SL, Schmid C, Ignaszewski M (2009) The argo program: observing the global ocean with profiling floats. Oceanography 22(2):34–43. https://doi.org/10.5670/oceanog.2009.36

Roessler A, Rhein M, Kieke D, Mertens C (2015) Long-term observations of North Atlantic Current transport at the gateway between western and eastern Atlantic. J Geophys Res C: Oceans. https://doi.org/10.1002/2014JC010662

Rogé M, Morrow R, Dencausse G (2015) Altimetric lagrangian advection to reconstruct Pacific Ocean fine scale surface tracer fields. Ocean Dyn 65:1249–1268. https://doi.org/10.1007/s10236-015-0872-4

Rose SK, Andersen OB, Passaro M, Ludwigsen CA, Schwatke C (2019) Arctic ocean sea level record from the complete radar altimetry Era: 1991–2018. Remote Sens 11(14):16. https://doi.org/10.3390/rs11141672

Sandwell DT, Smith WHF (2009) Global marine gravity from retracked Geosat and ERS-1 altimetry: Ridge segmentation versus spreading rate. J Geophys Res 114:B01411. https://doi.org/10.1029/2008JB006008

Sasaki H, Klein P, Qiu B et al (2014) Impact of oceanic-scale interactions on the seasonal modulation of ocean dynamics by the atmosphere. Nat Commun 5:5636. https://doi.org/10.1038/ncomms6636

Scharffenberg MG, Stammer D (2010) Seasonal variations of the large-scale geostrophic flow field and eddy kinetic energy inferred from the TOPEX/Poseidon and Jason-1 tandem mission data. J Geophys Res 115:C02008. https://doi.org/10.1029/2008JC005242

Schmid C (2014) Mean vertical and horizontal structure of the subtropical circulation in the South Atlantic from three-dimensional observed velocity fields. Deep Sea Res Part I. https://doi.org/10.1016/j.dsr.2014.04.015

Scott RB, Wang F (2005) Direct evidence of an oceanic inverse kinetic energy cascade from satellite altimetry. J Phys Oceanogr 35:1650–1666

Shakespeare CJ, Arbic BK, Hogg AM (2020) The drag on the barotropic tide due to the generation of baroclinic motion. J Phys Oceanogr 50:3467–3481

Shum CK et al (1997) Accuracy assessment of recent ocean tide models. J Geophys Res 102:25173–25194

Smith GC, Allard R, Babin M, Bertino L, Chevallier M, Corlett GK, Crout J et al (2019) Polar ocean observations: a critical gap in the observing system and its effect on environmental predictions from hours to a season. Front Mar Sci 6:1025. https://doi.org/10.3389/fmars.2019.00429

Souza JMAC, de Boyer Montegut C, Le Traon PY (2011) Mesoscale eddies in the South Atlantic. Ocean Sci Discuss 8:483–531. https://doi.org/10.5194/osd-8-483-2011

Stammer D et al (2014) Accuracy assessment of global barotropic ocean tide models. Rev Geophys 52:243–282. https://doi.org/10.1002/2014RG000450

Stammer D, Balmaseda M, Heimbach P, Kohl A, Weaver A (2016) Ocean data assimilation in support of climate applications: status and perspectives. Ann Rev Mar Sci 8:491–518. https://doi.org/10.1146/annurev-marine-122414-034113

Storto A, Alvera-Azcárate A, Balmaseda MA, Barth A, Chevallier M, Counillon F, Domingues CM, Drevil-lon M, Drillet Y, Forget G, Garric G, Haines K, Hernandez F, Iovino D, Jackson LC, Lellouche J-M, Masina S, Mayer M, Oke PR, Penny SG, Peterson KA, Yang C, Zuo H (2019) Ocean reanalyses: recent advances and unsolved challenges. Front Mar Sci 6:418. https://doi.org/10.3389/fmars.2019.00418

Taburet G, Sanchez-Roman A, Ballarotta M, Pujol M-I, Legeais J-F, Fournier F, Faugere Y, Dibarboure G (2019) DUACS DT2018: 25 years of reprocessed sea level altimetry products. Ocean Sci 15:1207–1224. https://doi.org/10.5194/os-15-1207-2019

Tchilibou M, Gourdeau L, Morrow R, Serazin G, Djath B, Lyard F (2018) Spectral signatures of the tropical Pacific dynamics from model and altimetry: a focus on the meso-submesoscale range. Ocean Sci 14:1283–1301. https://doi.org/10.5194/os-14-1283-2018

Tchonang B, Benkiran M, Le Traon PY, Van Gennip SJ, Lellouche JM, Ruggiero G (2021) Assessing the impact of the assimilation of SWOT observations in a global high-resolution analysis and forecasting system Part 2: results. Front Mar Sci 8:691–995
Tourain C, Piras F, Ollivier A, Hauser D, Poisson JC, Boy F, Thibaut P, Hermozo L, Tison C (2021) Benefits of the adaptive algorithm for retracking altimeter nadir echoes: results from simulations and CFOSAT/SWIM observations. IEEE Trans Geosci Remote Sens. https://doi.org/10.1109/TGRS.2021.3064236

Le Traon PY, Morrow R (2001) Ocean currents and eddies. In: L.-L. Fu and A. Cazenave (eds) satellite altimetry and earth sciences: a handbook for techniques and applications, pp 171–210, Academic Press, San Diego

Le Traon, PY, G Dibarboure, G Jacobs, M Martin, E Remy, A Schiller (2017) Use of satellite altimetry for operational oceanography in satellite altimetry over oceans and land surfaces, CRC Press: Taylor, Editors: Stammer Cazenave. pp. 581–608. doi https://doi.org/10.1201/9781315151779-18

Vergara O, Morrow R, Pujol I, Dibarboure G, Ubelmann C (2019) Revised global wave number spectra from recent altimeter observations. J Geophys Res Oceans 124:3523–3537. https://doi.org/10.1029/2018JC014844

Verrier S, Le Traon PY, Remy E (2017) Assessing the impact of multiple altimeter missions and Argo in a global eddy-permitting data assimilation system. Ocean Sci 13(6):1077–1092. https://doi.org/10.5194/os-13-1077-2017

Verrier S, Le Traon PY, Remy E, Lellouche JM (2018) Assessing the impact of SAR altimetry for global ocean analysis and forecasting. J Operat Oceanogr. https://doi.org/10.1080/1755876X.2018.1505028

Vic C, Naveira Garabato A, Green JAM, Waterhouse AF, Zhao Z, Melet A, de Lavergne C, Buijsman MC, Stephenson GR (2019) Deep-ocean mixing driven by small-scale internal tides. Nat Commun 10:2099. https://doi.org/10.1038/s41467-019-10149-5

Vivier F, Kelly KA, Thompson L (1999) Contributions of wind forcing, waves, and surface heating to sea surface height observations in the Pacific Ocean. J Geophys Res 104(9):20767–20788. https://doi.org/10.1029/1999JC900096

Wang J, Fu LL, Torres HS, Chen S, Qiu B, Menemenlis D (2019a) On the spatial scales to be resolved by the surface water and ocean topography ka-band radar interferometer. J Atmos Oceanic Tech 36(1):87–99. https://doi.org/10.1175/JTECH-D-18-0119.1

Wang S, Qiao F, Dai D et al (2019b) Anisotropy of the sea surface height wavenumber spectrum from altimeter observations. Sci Rep 9:15896. https://doi.org/10.1038/s41598-019-52328-w

Waugh DW, Abraham ER (2008) Stirring in the global surface ocean. Geophys Res Lett 35:L20605. https://doi.org/10.1029/2008GL035526

Willis JK (2010) Can in situ floats and satellite altimeters detect long-term changes in Atlantic Ocean overturning? Geophys Res Lett 37:L06602. https://doi.org/10.1029/2010GL042372

Willis JK, Fu LL (2008) Combining altimeter and subsurface float data to estimate the time-averaged circulation in the upper ocean. J Geophys Res Oceans 113:C12017. https://doi.org/10.1029/2007JC004690

Wunsch C (2010) Towards a midlatitude ocean frequency–wavenumber spectral density and trend determination. J Phys Oceanogr 40:2264–2281. https://doi.org/10.1175/2010JPO4376.1

Wunsch C, Ferrari R (2018) One hundred years of the ocean general circulation. Meteorol Monograph 59:7.1–7.32. https://doi.org/10.1175/AMSMONOGRAPHHS-D-18-0002.1

Wunsch C, Gill AE (1976) Observations of equatorially trapped waves in Pacific sea level variations. Deep Sea Res 23:371–390. https://doi.org/10.1016/0011-7471(76)90835-4

Xu Y, Fu LL (2012) The effects of altimeter instrument noise on the estimation of the wavenumber spectrum of sea surface height. J Phys Oceanogr 42:2229–2233. https://doi.org/10.1175/JPO-D-12-0106.1

Zaron ED (2017) Mapping the nonstationary internal tide with satellite altimetry. J Geophys Res Oceans 122:539–554. https://doi.org/10.1002/2016JC012487

Zaron ED (2019) Baroclinic tidal sea level from exact-repeat mission altimetry. J Phys Oceanogr 49:193–210. https://doi.org/10.1175/JPO-D-18-0127.1

Zhang Z, Wang W, Qiu B (2014) Oceanic mass transport by mesoscale eddies. Science 345:322–324

Zhang Z, Qiu B, Klein P et al (2019) The influence of geostrophic strain on oceanic ageostrophic motion and surface chlorophyll. Nat Commun 10:2838. https://doi.org/10.1038/s41467-019-10883-w

Zhao Z, Alford MH, Girton JB (2012) Mapping low-mode internal tides from multisatellite altimetry. Oceanography 25:42–51. https://doi.org/10.5670/oceanog.2012.40

<footnote>**Publisher's Note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</footnote>
Tourain C, Piras F, Ollivier A, Hauser D, Poisson JC, Boy F, Thibaut P, Hermozo L, Tison C (2021) Benefits of the adaptive algorithm for retracking altimeter nadir echoes: results from simulations and CFOSAT/SWIM observations. IEEE Trans Geosci Remote Sens. https://doi.org/10.1109/TGRS.2021.3064236

Le Traon PY, Morrow R (2001) Ocean currents and eddies. In: L.-L. Fu and A. Cazenave (eds) satellite altimetry and earth sciences: a handbook for techniques and applications, pp 171–210, Academic Press, San Diego

Le Traon, PY, G Dibarboure, G Jacobs, M Martin, E Remy, A Schiller (2017) Use of satellite altimetry for operational oceanography in satellite altimetry over oceans and land surfaces, CRC Press: Taylor, Editors: Stammer Cazenave. pp. 581–608. doi https://doi.org/10.1201/9781315151779-18

Vergara O, Morrow R, Pujol I, Dibarboure G, Ubelmann C (2019) Revised global wave number spectra from recent altimeter observations. J Geophys Res Oceans 124:3523–3537. https://doi.org/10.1029/2018JC014844

Verrier S, Le Traon PY, Remy E (2017) Assessing the impact of multiple altimeter missions and Argo in a global eddy-permitting data assimilation system. Ocean Sci 13(6):1077–1092. https://doi.org/10.5194/os-13-1077-2017

Verrier S, Le Traon PY, Remy E, Lellouche JM (2018) Assessing the impact of SAR altimetry for global ocean analysis and forecasting. J Operat Oceanogr. https://doi.org/10.1080/1755876X.2018.1505028

Vic C, Naveira Garabato A, Green JAM, Waterhouse AF, Zhao Z, Melet A, de Lavergne C, Buijsman MC, Stephenson GR (2019) Deep-ocean mixing driven by small-scale internal tides. Nat Commun 10:2099. https://doi.org/10.1038/s41467-019-10149-5

Vivier F, Kelly KA, Thompson L (1999) Contributions of wind forcing, waves, and surface heating to sea surface height observations in the Pacific Ocean. J Geophys Res 104(9):20767–20788. https://doi.org/10.1029/1999JC900096

Wang J, Fu LL, Torres HS, Chen S, Qiu B, Menemenlis D (2019a) On the spatial scales to be resolved by the surface water and ocean topography ka-band radar interferometer. J Atmos Oceanic Tech 36(1):87–99. https://doi.org/10.1175/JTECH-D-18-0119.1

Wang S, Qiao F, Dai D et al (2019b) Anisotropy of the sea surface height wavenumber spectrum from altimeter observations. Sci Rep 9:15896. https://doi.org/10.1038/s41598-019-52328-w

Waugh DW, Abraham ER (2008) Stirring in the global surface ocean. Geophys Res Lett 35:L20605. https://doi.org/10.1029/2008GL035526

Willis JK (2010) Can in situ floats and satellite altimeters detect long-term changes in Atlantic Ocean overturning? Geophys Res Lett 37:L06602. https://doi.org/10.1029/2010GL042372

Willis JK, Fu LL (2008) Combining altimeter and subsurface float data to estimate the time-averaged circulation in the upper ocean. J Geophys Res Oceans 113:C12017. https://doi.org/10.1029/2007JC004690

Wunsch C (2010) Towards a midlatitude ocean frequency–wavenumber spectral density and trend determination. J Phys Oceanogr 40:2264–2281. https://doi.org/10.1175/2010JPO4376.1

Wunsch C, Ferrari R (2018) One hundred years of the ocean general circulation. Meteorol Monograph 59:7.1–7.32. https://doi.org/10.1175/AMSMONOGRAPHHS-D-18-0002.1

Wunsch C, Gill AE (1976) Observations of equatorially trapped waves in Pacific sea level variations. Deep Sea Res 23:371–390. https://doi.org/10.1016/0011-7471(76)90835-4

Xu Y, Fu LL (2012) The effects of altimeter instrument noise on the estimation of the wavenumber spectrum of sea surface height. J Phys Oceanogr 42:2229–2233. https://doi.org/10.1175/JPO-D-12-0106.1

Zaron ED (2017) Mapping the nonstationary internal tide with satellite altimetry. J Geophys Res Oceans 122:539–554. https://doi.org/10.1002/2016JC012487

Zaron ED (2019) Baroclinic tidal sea level from exact-repeat mission altimetry. J Phys Oceanogr 49:193–210. https://doi.org/10.1175/JPO-D-18-0127.1

Zhang Z, Wang W, Qiu B (2014) Oceanic mass transport by mesoscale eddies. Science 345:322–324

Zhang Z, Qiu B, Klein P et al (2019) The influence of geostrophic strain on oceanic ageostrophic motion and surface chlorophyll. Nat Commun 10:2838. https://doi.org/10.1038/s41467-019-10883-w

Zhao Z, Alford MH, Girton JB (2012) Mapping low-mode internal tides from multisatellite altimetry. Oceanography 25:42–51. https://doi.org/10.5670/oceanog.2012.40