The model data used in this study to represent the total ocean signal are the outputs of the mesoscale and submesoscale resolving MITgcm model . The SWOT community has largely used the specific simulation LLC4320, where “LLC” refers to a latitude–longitude polar cap global model grid , which in its higher resolution has a nominal horizontal grid spacing of 1/48∘ globally, similar to the SWOT swath grid spacing of 2 km × 2 km, with an effective resolution of less than 20 km . Outputs are hourly snapshots that span the period from 13 September 2011 to 15 November 2012 . There are 90 vertical levels ranging in thickness from 1 m at the surface to 480 m at a maximum model depth of 7000 m. The LLC4320 is forced at the surface with 6-hourly 0.14∘ atmospheric fields from the European Centre for Medium-Range Weather Forecasts (ECMWF) and by the 16 most significant components of the hourly tidal potential, applied as additional surface pressure, generating both barotropic and baroclinic tidal components . A few details on the validation of the model for the specific use of this study are given in Appendix . Further information about the LLC4320, its construction, and its validation can be found in .

This work focuses on sea surface height and geostrophic currents that would be observed with satellite altimetry in the Agulhas region, represented in Fig. , and our diagnostics are based on the modelled SSH. To reproduce an equivalent altimetry-like SSH field, the model’s barotropic tides and the high-frequency barotropic response to the atmospheric forcing (the so-called dynamical atmospheric correction: DAC) are estimated and removed. The 1/48∘ simulation is known to have minor forcing errors in the tides and an offset on the atmosphere forcing fields (by 6 h) . This results in barotropic and baroclinic tidal artefacts and wind-forcing offsets on the SSH signal. Unrealistic grid-type features at the spatial scale of the atmospheric forcing are also observed in the 1/48∘ SSH field, creating discontinuities when deriving eddy diagnostics from the geostrophic components of the velocity field.

The data used in this work are the outputs of the original high-resolution run of the MITgcm LLC4320, smoothed on a regular global grid at 1/20∘ and subsampled at 1/10∘. This allows us to greatly reduce the discontinuities previously mentioned. Since we do not aim to analyse the ocean geostrophic dynamics at scales smaller than the Surface Water and Ocean Topography (SWOT) resolution (around 15 km at best), we will rely on the 1/10∘ subsampled modelled simulations for our study. This 1/10∘ version was also used to calculate the pseudo-DUACS dataset and for simulating the global SWOT cross-calibration. This dataset is referred to as LLC10 in the following.

Today’s multi-mission Data Unification and Altimeter Combination System (DUACS) altimetry products deliver global and regional sea level and geostrophic current maps for oceanographic applications (distributed by CMEMS). The latest version, the level-4 DUACS-DT (Delayed Time), is constructed by optimal interpolation of level-3 altimeter observations (i.e. with along-track corrections, editing, and processing applied) and is produced on a regular 1/4∘ × 1/4∘ grid with daily sampling . However, found that the capability of retrieving small mesoscale dynamics in level-4 data is limited by the optimal interpolation framework used in DUACS. analysed the effective spatial and temporal resolution of level-4 sea level anomaly (SLA) globally. For the time span of the LLC4320 simulation, the satellites in use for the generation of the DUACS product are Jason-2, ENVISAT, HY-2A, and CryoSat-2 . Further details on this observational product and its benchmarking against its surrogate derived from LLC10 can be found in Appendix .

If we assume that our modelled SSH represents reality, our first step is to verify how this SSH would be observed by today's along-track altimetric sampling and mapping, so we built a pseudo-DUACS product. This product consists of the same DUACS mapping technique described above; however, the data are subsampled from the LLC10 fields along the altimeter mission tracks. These altimeter-like model data are then processed using the DUACS optimal interpolation mapping algorithm, applying the same mapping parameters used for the real DUACS maps, thereby providing pseudo-DUACS daily maps on a regular 1/10∘ grid. Since the original model has no data assimilation, its eddy field may be shifted compared to the real eddy position, and the advantage of the pseudo-DUACS is to have better colocation of the modelled large- and small-scale features. So in this study, the pseudo-DUACS product is used as a proxy for the current observational capability of satellite altimetry in our region, in terms of spatial and temporal resolution. In the region of the Agulhas Current, the effective resolution of the pseudo-DUACS gridded maps is larger than 150 km and represents dynamics with temporal variability greater than 10 d. SWOT will potentially observe all scales included in the LLC10 SSH fields. In the computation, the smaller-scale processes observable with SWOT have been defined as the residual between the total LLC10 fields (corrected for the high-frequency motions) and the pseudo-DUACS fields. This derived product, referred to as “SSH residuals”, is analysed to investigate the new dynamics that SWOT will observe.

Figure  illustrates the SSH spectral power of the different products derived from the LLC10 in terms of time and spatial frequencies, calculated over the annual model period. The top panels show the LLC10 original SSH (a) and the same field (b) after removing the high-frequency correction for the barotropic tide and DAC. As expected, most of the higher-frequency tidal energy (6 h, 12 h, 1 d) disappears in the corrected version of the spectrum. There are weaker residual energy signals at tidal frequencies that may be due to errors in the barotropic tide correction or at smaller scales, internal tides. Although the MITgcm LLC4320 is known to overestimate the tide forcing by a factor of 1.1121 , in our Agulhas region, the residual internal tide signal is very low compared to the energetic mesoscale SSH field shown in Fig. b. The DAC correction removes much of the large-scale, high-frequency energy at timescales <10 d; since this has a large-scale structure, it does not impact the eddy diagnostics we derive that are shaped by the smaller-scale SSH gradients. The SSH spectral power for the reconstructed pseudo-DUACS product is shown in Fig. c and for the SSH residual high frequencies in Fig. d. The time frequencies of the pseudo-DUACS product and the SSH residuals are cut at the Nyquist frequency of 2 d because of their daily time sampling. We note that even if the pseudo-DUACS mapping decorrelation scales are around 150 km in the Agulhas region , its frequency–wavenumber spectra have some residual power in scales smaller than the effective resolution of 150 km in Fig. c and smaller lobes of energy around 30 km in wavelength, whereas the SSH residuals (d) represent the residual SSH power (b–c) at scales <150 km and between 2–10 d well.

The Surface Water Ocean Topography (SWOT) mission, launched on 16 December 2022, will provide the first global SAR interferometry observations providing collocated 2D surface topography and 250 m resolution SAR images . SWOT observations are made over two 50 km wide swaths, with a Jason-class nadir altimeter in the centre. An onboard processor allows for a 250 m × 250 m expert product and a precise 2 km × 2 km grid product over all oceans. The measurement is very precise, with an expected root mean square (rms) SSH noise at 2 km of 1.37 cm, an order of magnitude smaller than conventional Jason-class altimeters . SWOT will have two orbit phases: a daily revisit over a limited number of tracks during the first 6 months (January to June 2023) of the mission's commissioning and a calibration and validation phase (the CalVal orbit). From July 2023, the satellite had moved into the science orbit with a 21 d revisit and global coverage. Both orbits cover latitudes of up to 78∘ . SWOT is the first altimeter mission whose science requirements are specified in terms of wavenumber spectra and observable wavelengths; these requirements are that the SSH signal should exceed the noise (for 2 m wave height conditions) at 15 km wavelength globally . During the daily CalVal phase of the SWOT mission, a series of international in situ validation campaigns are proposed (https://www.swot-adac.org/, last access: 16 August 2023). One of these campaigns, QUICCHE (QUantifying Interocean fluxes in the Cape Cauldron Hotspot of Eddy kinetic energy), targets the Agulhas Cape Cauldron region (https://www.swot-adac.org/campaigns/quicche/, last access: 16 August 2023) where a SWOT cross-over exists (SWOT tracks 5 and 20; Fig. ). This region is used as a test site in our study to evaluate the projected SWOT signal-to-noise ratio.

Our first objective is to analyse the different eddy diagnostics based on the larger and smaller mesoscale dynamics observable with today’s altimetric mapping and with the future SWOT observations, using the LLC10 as our ocean reality in the Agulhas Current region. Figure  shows the geographical distribution of the average EKE and the strain standard deviation (SD) over the 1-year period of the LLC10 simulation for three separate cases: the top row is calculated from the total model (LLC10) geostrophic currents, computed from the SSH after correction for barotropic tide and DAC, and represents the total field to be observed by SWOT; the middle row represents the results computed with the pseudo-DUACS data, a proxy of the capability of products derived from current-generation altimeters to measure the larger mesoscale structures; and the bottom data represent their difference: the new scales to be observed with SWOT. We use it to tease out the circulation variability currently not included in the operational products.

In terms of mean surface geostrophic EKE over this 1-year period, the maximum for the total corrected LLC10 current occurs in the Agulhas Retroflection (0.256 m2 s-2), which is close to the reported observations of the geostrophic EKE computed from DUACS DT2021 data on CMEMS over a longer period (from 1 January 1993 to 3 June 2020, not shown). The larger scales in the pseudo-DUACS (Fig. c) are responsible for most of the energy in the Agulhas Retroflection (0.171 m2 s-2) compared to the smaller-scale residuals (0.085 m2 s-2) (Fig. e). The larger-scale energy follows the meanders of the main current in the Agulhas Extension. The LLC10 simulation represents physics down to 20 km (Fig. b), whereas the pseudo-DUACS is limited by the interpolation scheme. The residual and smaller scales, representing the missing dynamics, have a weaker signature in EKE except along the Agulhas Shelf, especially near Gqeberha (formerly Port Elizabeth) (around 26∘ E) where the LLC10 current dynamics present greater smaller-scale turbulence. In the CMEMS observations in Fig. a, the larger mesoscale develops further south, whereas the model develops weaker large-scale energy offshore, all along the Agulhas Current, with smaller scales dominating on the shelf. This is characteristic of the DUACS interpolation that forces the reconstructed dynamics close to zero near the coasts and thus underestimates the boundary currents and their variability. The strain root mean square variations show a different behaviour. The mean annual strain structure is dominated by the larger scales (not shown). However, Fig.  shows that the small-scale, high-frequency dynamics (f) are predominant in terms of variance over the full Agulhas Current system and that as an average over the year, the larger scales (d) are quite stable. The majority of the small-scale strain variability comes from the coastal Agulhas Current and the Agulhas Retroflection and loses its intensity along the Agulhas Extension.

As illustrated in Fig. , the SSH variance in the Agulhas region is essentially dominated by the rich variability occurring at synoptic to intra-seasonal timescales. In order to analyse the spatial coherency of such variability, we compute the Hovmöller diagrams of the LLC10 geostrophic EKE (Fig. ), focusing on the region delimited by the time-average current position (grey contours in Fig. ) along the Agulhas coast and extending our focus to the Agulhas Retroflection (orange line in the geographic plot of Fig. ). Four zones can be distinguished in the area: zone 1 is the northern part of the coastal region, from where the Agulhas Current starts flowing southwards in the study area. Zone 2 is the coastal extension south of Gqeberha. Zone 3 is the retroflection of the current, and zone 4 is the Cape Cauldron region to the west, surveyed by the QUICCHE CalVal campaign. The first three zones are located along the mean current and are marked on the Hovmöller diagram, from which two sets of distinctive physical processes are distinguishable.

The first is associated with two strong, large mesoscale events called Natal Pulses, represented by the dashed blue lines in the plots. Natal Pulses are solitary meanders that develop near the Natal Bight (around 31∘ E); they can reach 50 to 200 km in amplitude and have largely been studied with satellite altimetry . They originate south of the Mozambique Channel and travel downstream, westwards towards the tip of the retroflection. Up until the moment they reach the Agulhas Bank (around 24∘ E), continued processes of dissipation and merging occur , and only a fraction of the Natal Pulses reaches this point. The Agulhas Current becomes increasingly unstable downstream, and in addition to the Natal Pulses, shear-edge eddies develop , with diameters between 50 and 100 km, which are difficult to observe with altimetry maps. During 2012 in the LLC10 model simulation, two Natal Pulses were reproduced in the coastal region of the Agulhas Current, propagating at an average speed of 6 km d-1. At the northern limit of the domain, they have a size of around 150 km, consistent with the observations and literature. Around mid-March, when the first Natal Pulse reaches Gqeberha, its structure is stretched along the mean current direction and can reach 300 km. The DUACS-reconstructed data, representing the potential of current altimetry, is able to resolve these slow, large-scale processes (in a similar Hovmöller diagram, not shown) in terms of diameter and phase, but their amplitude is underestimated by about 40 %. This is a well-documented characteristic of the gridded products as a consequence of the mapping algorithms . Figure  highlights that the first Natal Pulse passed box 1 in December 2011, propagated at 6.3 km d-1, and reached box 2 in early March 2012 and then the retroflection box 3 in early May 2012. An EKE animation (not shown) shows that after passing the unstable zone of Gqeberha, part of the Natal Pulse is split into one Agulhas ring and propagates in the region of Cape Cauldron. The rest merges in the Agulhas Current and continues down through the Agulhas Extension.

The Hovmöller diagram highlights a second type of much smaller and faster dynamics that have time-varying amplitudes along the Agulhas Shelf from zones 1 to 2 and are almost always present in the zone of the Agulhas Bank, except in the periods when the large Natal Pulses pass. Similar dynamics are modelled in the Gulf Stream . We find that these submesoscale frontal eddies propagate at a speed of around 20 km d-1 and have a diameter of a tens of kilometres, too small to be observed with gridded altimetry maps. and demonstrate that southwards from Gqeberha, barotropic instabilities are the main cause of smaller mesoscale eddy generation in a period when no Natal Pulses are occurring. Our LLC10 fields are in accordance, and in the proximity of Gqeberha the Natal Pulse loses most of its energy, and the flow becomes highly unstable, generating faster smaller-scale eddies.

We can quantify how well the different datasets represent these dominant large- and small-scale processes by focusing on the temporal evolution of the EKE for each of the four boxes defined in Fig. . Figure  shows the EKE on the full period of the LLC4320 simulation from the LLC10 data as well as from the pseudo-DUACS data and their residual. The mean EKE and strain value for each box are shown in Table . In the highly energetic Agulhas region, the larger mesoscale represented by the pseudo-DUACS product (orange line in Fig. ) structures the flow in the coastal box (a), but the large and small scales have similar mean values. In the retroflection (c) and Cape Cauldron (d) boxes the large scales dominate the EKE, with a mean value close to double the small scales in both cases. Yet, in comparison with the total LLC10 data (blue line), the pseudo-DUACS underestimates the magnitude of the larger eddies in strong events by 30 %–40 %. The biggest features here are the two Natal Pulses propagating downstream from coastal box 1, along the shelf break (box 2) to the retroflection area (box 3), as shown in Fig. .

In these three boxes, the amplitude of the smaller-scale dynamics generally increases in periods when the larger-scale eddies are active, suggesting that energy transfer processes are activated during this period. Certain smaller-scale energetic processes are smoothed out by the pseudo-DUACS reconstruction, such as in November 2011 in box 3 and the large peak in late July 2012 in the Cape Cauldron region. Box 2 is different, being a shelf region dominated by small-scale, rapidly propagating dynamics that are stronger on average than the larger scales in the same region, except during the periods when the two Natal Pulses propagate downstream from box 1. Figure  shows that these small-scale, rapid dynamics have speeds of 20 km d-1 on average, similar to the submesoscale frontal eddies generated by barotropic instabilities on the Agulhas Plateau as described by , , and . They are weakly present in the early period of the simulation, but their amplitude increases during the 3 months in autumn following the passage of the first Natal Pulse. During the following winter–spring months (July–October), the dynamics return to a less energetic state in box 2, as this barotropic instability occurs when the Agulhas Current is not in a meandering state . This critical small-scale adjustment process is undetected in today’s altimetric maps.

To complete the analysis we focus on the flow's deformation with the potential of generating secondary vertical overturning circulation at different scales . Figure  shows the geostrophic strain rate variability over two of the boxes (box 1: a–b, box 2: c–d). The left column shows the spatial average of strain over the box, whereas the right column shows the spatial SD. This figure, together with Table 1 which quantifies the average strain rate values over the boxes and over 1 year, confirms that the larger-scale pseudo-DUACS geostrophic strain rate contributes around 60 % of the total average LLC10 strain rate amplitude in box 1 (and in boxes 3 and 4, not shown). The residual rapidly evolving small-scale geostrophic strain contributes 40 % of the mean strain rate but most of its variability as shown in Figs. 3d, 3f, 5b, 5d.

The Natal Pulses, the strongest events in terms of EKE, only have a small signature on the strain, especially on the pseudo-DUACS strain. They propagate through the region (a, b, c, d) with very high SSH and EKE values but with a less strong impact on the deformation of the flow: the very large EKE peaks in December 2011 and August 2012 in box 1 (Fig. a) have moderate DUACS strain peaks (Fig. a, b), but other periods with weaker EKE also have moderate pseudo-DUACS strain peaks in box 1, of the same order of magnitude. Indeed, the passage of the Natal Pulses tends to damp out the smaller-scale strain (evident in the SD, Fig. b), but the total strain in box 1 remains fairly constant throughout the year, with a mix of larger- and smaller-scale contributions. In contrast, the effect of the Natal Pulse is evident on the cross-terms (red line in Fig. a), whose effect increases during the pass of the Natal Pulses and causes the dampening of the smaller scales.

An exception is box 2 (Fig. b, c), where the small-scale strain is the most active all year, except when the Natal Pulse passes. Small-scale strain remains present even during the low-EKE period (August to October 2012), with implications for vertical overturning and mixing at small scales in this region. In contrast with , there is no evidence during this 1-year simulation of small mesoscale EKE in winter and spring feeding energy to larger mesoscale EKE in late spring and summer. Indeed, the seasonal averages in this 1-year simulation are dominated by more individual eddy events. The seasonal mixed-layer depth remains shallow all year round, in contrast to the strong seasonal mixed-layer depth changes in the North Pacific (see climatology in Fig. 4 of ). So seasonal dynamics in the Agulhas Retroflection are weak compared to mesoscale events and do not strictly follow the paradigm of mixed-layer instabilities, in contrast to .

One of the main aims of SWOT will be to understand and monitor a wider range of mesoscale structures, whether they act to reinforce or compensate for the larger-scale variability, and to observe the interaction and transfers of energy between the different spatial scales. A direct (or downwards) cascade is defined as the transfer of kinetic energy towards smaller scales. An inverse (or upwards) cascade is the transport of kinetic energy to progressively larger scales. We analyse the geostrophic energy fluxes in our region using the coarse-graining method, as displayed in Fig. . Note that although the SSH observed by SWOT includes both geostrophic and ageostrophic components that dominate submesoscale features, only the geostrophic ones are accessible and can be used for computing energy transfers.

In this analysis, our subsampled model at 1/10∘ around 45∘ in latitude has a Nyquist sampling of around 15 km, in line with the SWOT observability (not far off from 15 km) from Sect. . Since the objective is to perform a comparison with the pseudo-DUACS products, Fig.  shows the geostrophic energy flux at 60 km (top) and 150 km (bottom) for the LLC10 data (a, c) and for the pseudo-DUACS product (b, d). Shorter wavelengths would not be representative of the pseudo-DUACS data. In line with , the inverse cascade's (blue) strength and spatial distribution increase at the larger 150 km scale. The full “SWOT-like” LLC10 presents a stronger inverse cascade, and the change of sign between upscale and downscale fluxes occurs at shorter wavelengths. This has already been observed by in the Agulhas Current and the Gulf Stream and indicates that current altimetric maps are unable to accurately estimate the spatial scales at which the energy cascade changes from an inverse to a direct cascade. The “patched” shape of the flux may be due to the limited duration of our model: only 1 year of data may not be long enough in this active region to provide stabilized mean fluxes, especially given the very energetic and diverse events shown in Fig. . Both and use a multi-year simulation for their flux computation which shows an inverse cascade dominated by the balanced flow, becoming stronger as larger wavelengths are analysed. At 150 km, the zone of the direct cascade is larger than at 60 km, and it is concentrated east of Gqeberha (around 26∘ E). It corresponds to the zone and wavelengths where found the generation of smaller eddies after the passage of the Natal Pulses, in relation with the downstream decrease in the number of Natal Pulses south of Port Edward (31∘ S, 30∘ E). In Fig. a the Natal Pulse propagating downstream from the Natal Bight breaks into many smaller and faster dynamics, shown in Fig. b, creating a direct geostrophic energy cascade. As seen in the time series, this very large and energetic event is the only one that is fairly well represented by the pseudo-DUACS product, although the inverse cascade it is largely underestimated.

This coarse-graining diagnostic will not be reproduced at the maximum resolution along the SWOT tracks due to the narrow width of the two 50 km swaths. The diagnostics could be revisited once SWOT is included in future multi-mission CMEMS maps.

The objective of this section is to analyse the impact of KarIn noise on the SSH measurements and therefore on the derived eddy diagnostics. We also infer the capability of the U-Net noise mitigation technique, trained on eNATL60, to treat a different model (LLC10) in a different and very energetic zone. After de-noising, we expect to be able to see the smallest possible ocean structures. , , and showed that KarIn's random error adds noise to the signal features that could lead to a misinterpretation of the observed variable or completely mask the signal, making it impossible to interpret the data. The impact of the small-scale random noise increases when making first- or second-order spatial derivatives, such as the EKE or the strain. Figure  demonstrates this point, showing the SSH (left), EKE (centre), and strain (right) in the ideal LLC10 model scenario (top), when random noise is added (centre) and after U-Net is applied to remove the noise (bottom). All plots refer to pass number 5 (geographically shown in Fig. ). The noisy SSH (b) presents the same large-scale features with respect to the simulated true field (a), but smaller-scale features are introduced or modified, leading to a misrepresentation of the SSH variability at small spatial scales. The noisy EKE (e) only shows the strongest feature in the middle of the swath, and the strain (h) is completely covered by the noise, preventing any interpretation of this variable. The U-Net noise mitigation technique, with parameters derived from a different model in the North Atlantic, suitably restores the input signal in the three cases. For the SSH, for wavelengths between 15 and 50 km, the noise is reduced by 1 order of magnitude. However, U-Net also removes part of the signal by a few percent points over this interval. Thus, the ocean SSH dynamics observed after noise reduction will have the correct positioning and phase, but their amplitude is slightly underestimated. The interval in which the signal is slightly underestimated is larger for higher-order derivatives, being between 10 and 100 km for the strain.

The scores used to assess the impact of U-Net are defined in Sect. . The RMSE is shown in Fig. . A synthetic overview of the overall noise mitigation efficiency in the Agulhas Current zone with the MITgcm model is given in Table , comparing the scores and observability of this study to the original U-Net simulation based on the eNAtl60 North Atlantic study and the use of the filter implemented by . The results are promising, with a homogeneous RMSE for the four daily-sampled tracks in the Agulhas region, ranging between 0.20 and 0.45 cm, which is in line with the findings from for the North Atlantic. The RMSE across-track shape reflects the simulated random error that increases towards the inner and outer swath borders .

Ocean observability is defined as the wavelength for which the NSR equals 1, meaning that the noise and the signal have equivalent energy. Following , for noisy fields where the error is always more energetic than the signal (NSR always higher than 1), we consider the observability to be larger than 1000 km. Previous findings by show that SWOT observability is expected to be degraded and to resolve wavelengths up to 35–45 km at high latitudes due to SWH-induced instrumental noise. This is especially true in the Antarctic Circumpolar Current (ACC) where the wave-induced random error has a large seasonality. In their simulation, used the realistic WAVEWATCH III (WW3) model as input data for waves, and they showed that spatial filtering of the data to smooth the noisy smaller wavelengths destroys much of the information contained in the small-scale SSH field. Figure  shows the LLC10 SSH noise-to-signal ratio, before and after applying the U-Net method over our four SWOT tracks. Even though we are using a noise simulated for a 2 m wave field, as in , the wavelength SWOT should resolve in this region before de-noising is 40 km, whereas when U-Net is applied to the noisy data, an observable wavelength of 17.5 km can be restored. The resolved observable scale is also calculated on the EKE and on the strain rate. For noisy data, the observability decreases by a factor of 3 for first-order derivatives such as EKE, resolving scales of more than 120 km with noisy data. For second-order derivatives such as geostrophic strain, the noise dominates the signal for all wavelengths, since the NSR spectrum is always > 1. After U-Net application, the observability is restored to wavelengths of the order of 15 km in both cases.

Considering the results for these de-noising scores and the comparison with other noise reduction techniques used in the literature, the U-Net method is very promising for the Agulhas Current when analysing a realistic simulation. In terms of SSH mean RMSE, without any noise treatment, the values in the Agulhas region and in the North Atlantic are comparable, 1.17 cm and 1.27 respectively. Using the U-Net method in the Agulhas region, the final RMSE is 0.24 cm, which is the same found by with specific tuning of their algorithms for the North Atlantic. The U-Net performance in the North Atlantic has an even better error reduction of 0.19 cm. In terms of the variance of the SSH residuals, the results are similar, with the best result found with U-Net in the North Atlantic and U-Net in the Agulhas region and the Gomez filter in the North Atlantic having comparable values. This result was expected because the Gomez filter was parameterized specifically on their study zone, and the U-Net training was performed in the North Atlantic with a different model. What is remarkable about the U-Net performance is that even with a different model and in a different zone, the mean RMSE and variance of SSH residuals are comparable with the original parametrization of the other methods. The SSH observable wavelengths give the most surprising result in this sense. The two zones have comparable observability before noise reduction (40.5 km in the Agulhas region and 42 km in the North Atlantic). U-Net in the Agulhas region manages to retrieve wavelengths down to 17 km. This result in the Agulhas region could be improved in the future by performing new training in this specific zone. This is encouraging for the early SWOT processing, since the U-Net parameters, trained in the North Atlantic, could be applied directly to the early SWOT data and then be improved by retraining U-Net once enough SWOT data have been retrieved.

Finally, this study was conducted in preparation for the real SWOT data that will represent a new challenge, since in the early months of the mission’s data analysis, no training dataset will be available for the U-Net algorithm. Note that in all the noise mitigation techniques presented in Table , the simulated random noise is estimated in the same way, based on the SWOT project’s best spectral estimates of the random noise for 2 m SWH . In reality, the SWOT random noise will vary in amplitude and could be impacted by small-scale anomalies that will need extra editing (e.g. presence of isolated ships, icebergs, platforms, extreme waves). However, the U-Net performance in a different region and using a different model from the original training is very encouraging, not just for the restored SSH, but also for the key high-order eddy diagnostics such as EKE and strain.