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Deep Learning Denoising of Real SWOT Sea Surface Height Observations

Gaétan Meis, Anaëlle Tréboutte, Maxime Ballarotta, Marie-Isabelle Pujol, Gérald Dibarboure

arXiv:2610.03739v1physics.ao-phcs.LGeess.IV

TL;DR

KaRIn noise can alter high-frequency SSH and complicate interpretation of fine-scale ocean dynamics, while existing denoising can have side effects in atypical conditions. This paper revises U-Net training and evaluates the filter with a benchmark; reported results show satisfactory performance and an approximately 4.5 mm RMS improvement over unfiltered SSHA at crossover points, while some small-scale waves remain difficult to preserve.

  • Problem

    KaRIn noise can alter high-frequency SSH content, and denoising has shown side effects under atypical conditions such as high waves and internal-tide solitons.

    Source: §1 · p. 3

  • Method

    The study revises the Tréboutte et al. (2023) U-Net training strategy using simulated ocean data and tests possible model overfitting with artificial signals inserted into SWOT observations.

    Source: §1 · p. 3, c. Addition of non-oceanic signals to… · p. 23

  • Results

    The filter yields satisfactory benchmark results without major identified issues, and improves crossover agreement with Sentinel-3A 20 Hz measurements by approximately 4.5 mm RMS versus unfiltered SSHA.

    Source: §6 · pp. 27–28

  • Takeaways & Limitations

    The denoiser retains SSHA energy below 15 km that a regular Lanczos filter would eliminate, while its local effective cutoff varies by region from 15 km to 28 km.

    Source: §6 · p. 27

    The filter eliminates the smallest 250-m-scale wave groups and very fine solitary waves, which are difficult to distinguish from noise and absent from the training model’s resolved features.

    Source: §5 · p. 26

Abstract

from arXiv · show

The SWOT (Surface Water Ocean Topography) mission is currently providing unpreceded high-resolution measurements of Sea Surface Height (SSH), revealing ocean features at finer scales. Nevertheless, the two-dimensional observations of KaRIn altimeter of SWOT suffer from instrumental errors. This noise degradation is altering the high frequencies of SWOT signal, and the small to sub-mesoscale dynamics of interest for some oceanographers. For this reason, Tr\'eboutte et al. (2023) have developed a convolutional neural network (CNN) based on U-Net architecture to separate the noise from the physical signals contained in the SSH. Their approach has demonstrated great potential on simulated SWOT measurements, and Dibarboure et al. (2024) report a positive influence on actual flight data from SWOT. However, degraded denoising performance, and occasional negative side-effects have been observed in atypical conditions (e.g. very high surface waves, internal tides solitons). In this study, we illustrate some of these limitations and we present an improved approach of the CNN-based denoising: we modified the training procedure to obtain a more robust version of the algorithm, to avoid biases and artifacts in the denoised SSH. This paper also presents a more complete validation process with a robust and standardized evaluation benchmark: these metrics could be of interest to assess other SWOT filtering and denoising algorithms.

1. Introduction

SWOT’s high-resolution KaRIn observations reveal fine-scale ocean dynamics, but noise can distort high-frequency SSH content and denoising can have side effects in atypical conditions. This paper revises the U-Net training strategy for 2-km and 250-m products and develops a benchmark to evaluate filters without a trustworthy ground truth.

1. Introduction

  • SWOT’s 120-km KaRIn swaths provide 250-m and 2-km SSH observations that reveal mesoscale, submesoscale, internal-wave, and coastal-flow features.KaRIn was designed to capture structures down to 15 km.Source: §1 · p. 2
  • KaRIn noise can alter high-frequency SSH content, while reported side effects include unusually high waves, internal-tide solitons, and rain-cell pixels.The existing U-Net filter has been used globally in the KaRIn Level-3 v2.0 product.Source: §1 · p. 3
  • The revised U-Net targets both 2-km and 250-m KaRIn SSH, with an improved training strategy and a benchmark for assessing filtering and denoising algorithms.The benchmark addresses the absence of ground truth for fully demonstrating denoiser behavior.Source: §1 · p. 3
  • The paper’s section plan covers input data and training, denoising results, supervised-learning effects, limitations, and a benchmark description.Appendix B compares the revised filter with the original Tréboutte et al. (2023, 2024) filter on the benchmark.Source: §1 · p. 3

2. Data & Method

The study trains revised U-Nets for 2-km and 250-m SWOT Level-3 SSH anomaly products using realistic simulated inputs and a loss that also emphasizes spatial derivatives. The pipeline accounts for observed noise characteristics and incomplete or contaminated swaths, and compares denoising with low-pass smoothing.

2. Data & Method

  • The denoising inputs are edited Level-3 SSHA products, with land, ice, coastal pixels, and quality-flagged outliers excluded; the study uses v2.0 inputs at 250 m and v3.0 at 2 km.The editing retains plain-ocean SSHA and includes eclipse events.Source: a. Input data from SWOT/KaRIn · p. 4
  • The 2-km U-Net has 231,000 parameters, while the deeper 250-m model has approximately 2.5 million parameters.The architecture uses encoder and decoder parts with three double-convolution blocks; the 250-m network adds two depth levels and a larger convolution kernel.Source: b. Deep learning denoising approach · p. 6, Figure 3 · p. 7
  • Training minimizes L1 error on valid ocean values and adds first- and second-derivative losses to improve reconstruction of SSHA gradients.Horizontal and/or vertical flips augment the 2-km training set, but were not used at 250 m because they slowed convergence without clear improvement.Source: b. Deep learning denoising approach · p. 7
  • The supervised target is simulated SSHA from the eddy-resolving eNATL60 North Atlantic ocean model, whose effective resolution is approximately 10 km.The model includes explicit tides and uses 3-hourly atmospheric forcing.Source: c. Simulated noiseless SSHA data · pp. 7–8
  • The simulated inputs combine model SSHA with KaRIn noise designed to reflect real measurement properties, then apply real editing masks to mimic incomplete swaths.Artificial spurious pixels are also added to 250-m simulations to train the CNN not to propagate incorrect denoised values around outliers.Source: c. Simulated noiseless SSHA data · p. 8, d. Final simulated realistic SWOT data · p. 9
  • A Lanczos low-pass filter with a fixed 20-km cutoff provides the smoothing baseline, while denoising aims to reduce random noise while preserving correlated physical signal.The 20-km cutoff was chosen to match the denoiser’s globally averaged cutoff frequency.Source: e. Low-pass filter as baseline for… · p. 10

3. Results

U-Net v3.0 removes much of the random noise from real SWOT 2-km and 250-m SSHA while largely preserving physical structures, but its performance is weaker for small internal tides and solitons. Spectral, spatial, and benchmark analyses characterize its scale-dependent behavior and limitations.

Denoising the real SWOT 2-km product

Denoising the real SWOT LR 250-m product

  • At 250 m, the removed-content spectrum matches the noise plateau; its integrated energy estimates 2.6 cm noise standard deviation and an overall 22 km LECW.The denoised spectrum follows the 2-km K^-2 slope from 70 to 15 km before rolling off, with little removed content above 20 km.Source: b. Denoising the real SWOT LR 250-m… · pp. 17–18, Figure 12 · p. 18
  • At 250 m, U-Net v3.0 removes most random noise, but its poor signal-to-noise ratio makes the filter more like a smoother below 15 km.The authors report no major bias or artifact problems yet, while both resolutions struggle with the smallest internal tide and soliton signals.Source: b. Denoising the real SWOT LR 250-m… · pp. 17, 19

4. Does the neural network reproduce ocean dynamics from simulation

The authors test whether a U-Net trained on North Atlantic simulations reproduces those dynamics when denoising different-model swaths and artificial signals. It generally separates simulated noise from ocean signal, but underestimates noise in high-wave conditions and removes some fine internal-tide content.

4. Does the neural network reproduce ocean dynamics from simulation

  • The authors identify two risks of simulation-supervised training: the ocean model may not represent global or smallest-scale dynamics, and limited samples plus a large CNN may encourage overfitting.They require denoised SSH to remain consistent with unfiltered observations even in atypical scenes.Source: model to real SWOT data? · p. 20

a. Impact of the simulation model

  • The evaluation applies the trained network without retraining to simulated SWOT swaths generated from the global MITgcm model, whose dynamics differ from the North Atlantic training model.The authors chose MITgcm to represent a broader diversity of ocean signals, including regions unlike the North Atlantic.Source: a. Impact of the simulation model · p. 20
  • U-Net v3.0’s denoised spectrum fits MITgcm’s noiseless spectrum to 10 km, while the 15-km Lanczos filter mixes signal and noise and loses energy below 15 km.The test uses South Australia, with wave levels higher than in the Gulf Stream; the network had not seen that region’s dynamics during training.Source: Figure 15 · p. 21, a. Impact of the simulation model · p. 21
  • The removed content on global MITgcm swaths closely matches simulated noise, but its amplitude is slightly low in high-wave conditions not encountered during training.The authors report no signs of U-Net hallucinations in these swaths; coastal highs may reflect missed editing pixels.Source: a. Impact of the simulation model · pp. 21–22, Figure 16 · p. 22

b. Impact on the dynamics in presence of internal tides

  • In northeastern Indonesia, U-Net v3.0 absorbs some internal-tide energy near 20–25 km and misses finer variations, though these effects are marginal compared with Lanczos filtering.Larger-scale internal-tide signals are generally denoised even though internal tides are absent from training.Source: b. Impact on the dynamics in presence… · p. 22, Figure 17 · p. 23

c. Addition of non-oceanic signals to real swaths before denoising

5. Discussion: limitations and outlook

The authors report that U-Net v3.0 is a major improvement over v2.0, while noting that its validation lacks trustworthy matching ground truth. Remaining concerns include high-wave behavior, missing fine-scale ocean features in simulations, and limited validation of 250-m denoising.

5. Discussion: limitations and outlook

  • Despite the lack of trustworthy matching ground truth, the authors report that benchmark metrics show U-Net v3.0 is a major improvement over v2.0.They found no anomalous or unexplained results on SWOT data, while acknowledging that v3.0 is not perfect.Source: §5 · p. 25
  • In high significant-wave-height conditions, the filter may remove too much ocean signal, likely because training data were not balanced across wave heights.The authors call for denoising that adapts better to high-wave conditions.Source: §5 · p. 25
  • Supervised training relies on simulated ocean data, but current models do not realistically reproduce all KaRIn features, including smaller internal waves.The authors suggest real-data self-supervised training as a possible alternative; they also propose more advanced models and training strategies.Source: §5 · pp. 25–26
  • Assessing the physical realism of small-scale content that survives denoising remains difficult; the authors call for new metrics using high-resolution independent data.The current Appendix A reference low-pass filter is simple; a fairer comparison would use more sophisticated adaptive filtering.Source: §5 · p. 25
  • At 250 m, the filter eliminates the smallest-scale wave groups and fine solitary waves; realistic training features may require ocean-model resolution 5–9 times finer than the Unsmoothed pixels.The authors say 250-m validation is still at an early stage and plan comparisons with other satellites and measurement techniques.Source: §5 · p. 26
  • Denoising performance depends on upstream product corrections: high-frequency residuals in the Mean Sea Surface model are absorbed, and missed editing pixels can cause poor predictions, especially at 250 m.The v3.0 Mean Sea Surface model has fewer small-scale artifacts than the previous version, so denoising absorbs fewer of them.Source: §5 · pp. 26–27

6. Conclusion

U-Net v3.0, trained on simulated data, removes SWOT noise while generally preserving ocean dynamics, but high-wave and internal-wave conditions remain challenging. The benchmark reports improvements in crossover agreement and spectral behavior, although the absence of ground truth prevents definitive validation.

6. Conclusion

  • The benchmark finds no major issues overall, but high-wave noise is not perfectly handled and the filter absorbs some internal-wave amplitude.The denoising is better than a standard Lanczos filter for internal waves; denoised 250-m and 2-km dynamics are very close, with neither showing clear artifacts or biases.Source: §6 · p. 27
  • The removed SSHA content is spectrally flat, while denoised SSHA retains energy below 15 km that a regular Lanczos filter would eliminate.The Local Effective Cut-off Wavelength ranges from 15 km in internal-tide regions to 28 km in high-wave regions, averaging 22 km; removed content is almost fully decorrelated day to day, with 10% missing variance.Source: §6 · p. 27
  • Approximately 4.5 mm RMS improvement brings SWOT observations closer to Sentinel-3A measurements at crossover points versus unfiltered SSHA.The authors state that this comparison does not prove the denoised SSHA is accurate without ground truth.Source: §6 · p. 28
  • The authors caution that simulated training data may be imperfect and that denoising accuracy cannot be proven without ground truth.They plan to continue studying how simulation models influence the approach.Source: §6 · p. 28
  • On MITgcm simulated swaths, U-Net v3.0 outperforms a low-pass filter and fits noiseless-swath spectral slopes across varied ocean conditions.In tests using artificial letter shapes embedded in real KaRIn swaths, it mitigates noise without altering the shapes, unlike the Lanczos filter.Source: §6 · p. 28

APPENDIX A

Appendix A benchmarks U-Net v3.0 against Lanczos without noiseless ground truth and evaluates denoising using temporal-coherence, mean-removed-content, and independent satellite-crossover metrics. The evaluations assess small-scale signal preservation and consistency while identifying residual errors, limitations in high-wave and fine-scale conditions, and challenges in interpreting the metrics.

Visual validation

  • In strong-wave conditions, U-Net v3.0 removes noise without visibly damaging SSHA, but small millimeter-scale biases remain and realistic high-wave noise simulation is still needed.The removed content shows large red and blue patterns of a few millimeters; the authors call for improved noise simulation to better represent high-significant-wave-height regions.Source: a. Visual validation · pp. 30–31, Figure A1 · p. 30
  • U-Net v3.0 retrieves small internal-tide wavefronts and preserves finer velocity and vorticity details than Lanczos, although subtle fronts remain difficult to separate from noise.The training simulations lack fine-scale motions, limiting the network’s ability to denoise these signals; the authors suggest adding fine-scale motions to the training data.Source: a. Visual validation · pp. 31–32, Figure A2 · p. 31, Figure A3 · p. 31

b. Binned maps of removed SSHA content

  • Below 20 km, U-Net v3.0 absorbs less variance than Lanczos by 1.1 mm on average, yet both filters show internal-tide regions and the denoiser removes more content in high-wave regions.Above 60 km, U-Net v3.0 removes little content, while the 20–60 km removed-content map is homogeneous with a background around 1.5 mm; rainfall regions are also visible, likely from missed spurious pixels.Source: b. Binned maps of removed SSHA content · pp. 32–34, Figure A6 · p. 34

c. SSHA Power Spectral Densities (PSDs)

  • U-Net v3.0 retains some of the noisy spectrum’s 70-to-20-km K-2 slope break, whereas Lanczos removes all SSHA energy below 20 km; both filters’ removed-content spectra are largely flat.A flat removed-content spectrum is consistent with predominantly removing noise, though spectral interpretation is ambiguous without a noiseless reference because ocean processes and red-colored KaRIn errors also contribute.Source: c. SSHA Power Spectral Densities (PSDs) · pp. 34–35, Figure A7 · p. 35, Figure A8 · p. 36
  • Near 20 km, almost 15% of total KaRIn energy lies in U-Net v3.0’s covariance, indicating unretrieved signal; Lanczos has lower covariance across wavelengths partly because it removes all signal below its cutoff.Covariance is positive for both filters at all scales, consistent with some true ocean variability entering the removed content.Source: c. SSHA Power Spectral Densities (PSDs) · pp. 37–38, Figure A9 · p. 37
  • The 24-hour-difference analysis finds about 10% missing variance for U-Net v3.0, versus about 18% for Lanczos, with the U-Net gap mostly explained by mean-sea-surface artifacts.The removed U-Net content decorrelates within 24 hours, consistent with primarily removing random noise; Lanczos also has a missing-variance gap and removes more temporally coherent signals.Source: c. SSHA Power Spectral Densities (PSDs) · pp. 38–39, Figure A10 · p. 39

d. Local Effective Cut-off Wavelength (LECW)

  • The Lanczos filter’s local effective cutoff is spatially homogeneous at about 20 km, while LECW is a visualization measure rather than an absolute performance score without noiseless SSHA.LECW is defined where the approach absorbs more than 50% of total SSHA energy; its optimal value requires a true noiseless reference.Source: d. Local Effective Cut-off Wavelength… · pp. 39–40, Figure A11 · p. 40

SSIM evaluation

  • Because noiseless real SSHA is unavailable, the appendix repurposes SSIM to compare consecutive one-day swaths and evaluates local segments in the high-wave ACC rather than using a global score.The one-day revisit enables comparisons because mesoscale structures change little over 24 hours; the authors note that crossover diamonds could provide an even shorter revisit window.Source: e. One-day regional SSIM · pp. 40–41

e. Temporal coherence

  • The U-Net v3.0 and Lanczos filters equally and slightly improve SSHA coherence between consecutive swaths, while their SSIM should remain below 1.The rationale is that fast small-scale features can shift within a day, whereas perfect similarity could indicate that denoising removed all small-scale variability.Source: e. One-day regional SSIM · p. 41, Figure A12 · p. 42
  • Both filters produce flat, consistent velocity SSIM and significantly improve coherence between consecutive swaths.The metric should increase after denoising, but not excessively, to avoid absorbing temporally coherent ocean features.Source: e. One-day regional SSIM · p. 42, Figure A14 · p. 43

f. Mean Profile of removed SSHA content

  • Mean removed-content profiles reveal that U-Net v3.0 absorbs static, small-scale residuals in high-frequency mean sea surface corrections, which also helps remove an error.This confirms that the network partially absorbs very small-scale signals; the identified residuals are blended with 2-km noise.Source: f. Mean Profile of removed SSHA content · p. 43, Figure A15 · p. 44
  • U-Net v3.0 removed-content profiles are centered near zero, with a 0.6 mm absolute mean and 2.5 mm standard deviation; these values depend on MSS quality.The newer CNES_CLS_2025 MSS in L3 LR product version 3.0 mitigates most artifacts; the mean-profile metric was not computed for Lanczos, but is recommended for comparing methods.Source: f. Mean Profile of removed SSHA content · p. 44

g. SWOT KaRIn/S3A crossovers

  • The U-Net v3.0 filter reduces KaRIn–S3A crossover RMS by a median 4 mm, though spurious differences remain near Antarctica and coastal areas.The benchmark relies on strong assumptions, including measurement independence, and is sensitive to the time gap between satellite observations.Source: g. SWOT KaRIn/S3A crossovers · pp. 45–47, Figure A17 · p. 47
  • The Butterworth low-pass filter and U-Net v3.0 achieve almost the same S3A coherence gain, but smoothing can favor shared mesoscale signals when Δt_max ≥ 60 min.S3A does not detect some small-scale motions observed by SWOT, so preserving them can reduce the measured gain.Source: g. SWOT KaRIn/S3A crossovers · p. 47, Figure A18 · p. 48

APPENDIX B

Appendix B evaluates U-Net v2.0 and documents hallucinations and signal removal that compromise denoising in several conditions. Its problems include large-scale biases, absorption of ocean signal, and reduced coherence with other observations.

High-wave artifacts

  • High-wave conditions produce centimeter-scale biases at swath borders, false structures, and strong smoothing of real structures; the style-transfer noise proxy detached noise from ocean conditions and v3.0 greatly improved predictions.The artifacts can also create cross-track and along-track discontinuities, especially visible in velocity and relative vorticity; v3.0 avoids hallucinations by abandoning style transfer.Source: Evaluative Benchmark, results of U-Net… · pp. 48–49, Figure B2 · p. 50

Internal waves

Removed SSHA content binned maps

  • Removed-content variability is strongly hallucinated above 60 km (>1 cm), while maps at 60–20 km are homogeneous and below 20 km show no clear difference from other filters.The above-60-km patterns are described as large-scale hallucinations.Source: b. Removed SSHA content binned maps · p. 50, Figure B4 · p. 51

SSHA power spectral densities

  • The denoised SSHA spectrum retains the initial K-3.7 slope down to 15 km, while removed-content energy follows a K-0.5 slope that may reflect feature absorption or mitigation of red KaRIn errors.The excess removed-content energy above 100 km relative to v3.0 is attributed to v2.0 hallucinations.Source: c. SSHA Power Spectral Densities (PSD) · p. 51, Figure B5 · p. 51
  • Negative covariance through 80 km indicates invented large-scale biases, while positive covariance below 80 km reflects KaRIn energy absorption that could hide local artifacts.The large-scale covariance issue is stated to no longer exist with U-Net v3.0.Source: c. SSHA Power Spectral Densities (PSD) · pp. 51–52, Figure B5 · p. 51

Mean profile of removed content

Local Effective Cut-off Wavelength

  • Average LECW is 22 km, with values around 15 km in major western boundary currents and the Mediterranean and higher values in high-wave regions; this metric reveals no clear issue.The filter absorbs less SSHA content in the currents and Mediterranean than in high-wave regions.Source: c. SSHA Power Spectral Densities (PSD) · p. 52, Figure B6 · p. 52

SSIM and SWOT/ S3A crossovers

Supplemental Material

The section is labeled as supplementary material for SWOT L3 denoising.

Supplemental Material

  • The section is identified as supplementary materials for SWOT L3 denoising.An access/download prompt is also present.Source: Supplemental Material · p. 59
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