An Adaptive CNN-Based Approach for Improving SWOT-Derived Sea-Level Observations Using Drifter Velocities

Abstract

The Surface Water and Ocean Topography (SWOT) mission provides unprecedented high-resolution observations of sea-surface height. However, their direct use in ocean circulation studies is complicated by the presence of small-scale unbalanced motion signals and instrumental noise, which hinder accurate estimation of geostrophic velocities. To address these limitations, we developed an adaptive convolutional neural network (CNN)-based filtering technique that refines SWOT-derived sea-level observations. The network includes multi-head attention layers to exploit information on concurrent wind fields and standard altimetry interpolation errors. We train the model with a custom loss function that accounts for the differences between geostrophic velocities computed from SWOT sea-surface topography and simultaneous in-situ drifter velocities. We compare our method to existing filtering techniques, including a U-Net-based model and a variational noise-reduction filter. Our adaptive-filtering CNN produces accurate velocity estimates while preserving small-scale features and achieving a substantial noise reduction in the spectral domain. By combining satellite and in-situ data with machine learning, this work demonstrates the potential of an adaptive CNN-based filtering approach to enhance the accuracy and reliability of SWOT-derived sea-level and velocity estimates, providing a valuable tool for global oceanographic applications.

1. Introduction

Satellite altimetry has revolutionized our understanding of ocean dynamics by providing global observations of sea-surface height (SSH) over the past several decades [1,2]. Traditional altimeters, such as those onboard Jason and Sentinel-3 missions, only provide measurements along nadir tracks, and are thus limited in terms of spatial coverage and effective resolution. The launch of the Surface Water and Ocean Topography (SWOT) satellite on 16 December 2022 marked a significant advancement in altimetry by introducing wide-swath interferometric measurements [3,4]. SWOT employs the Ka-band Radar Interferometer (KaRIn) instrument, allowing for high-resolution observations of sea-surface height (SSH) across two swaths, with the capability to resolve oceanic structures down to scales of 15 km [5]. This unprecedented resolution opens new opportunities for studying mesoscale and submesoscale ocean dynamics, internal waves, and other fine-scale processes. Since the first data became available in mid 2023, SWOT has already provided detailed insights into the dynamics of global ocean circulation [6,7,8]. Despite its technological advancements, SWOT instrument and data processing present several challenges. High-frequency noise arising from instrumental limitations and processing artifacts disproportionately affects smaller spatial scales, complicating the retrieval of geostrophic velocities [9]. The necessity of taking spatial derivatives of SSH to estimate velocity further amplifies this noise, making robust filtering essential to obtain reliable oceanographic measurements.

Previous studies have explored various de-noising techniques [10], including spectral filtering [11], data assimilation [12], variational filtering [13], and machine learning-based approaches [14], to mitigate noise in altimetry datasets. However, many of these methods have been applied primarily to conventional altimetry or simulated SWOT data, leaving an important gap in filtering strategies for real SWOT observations. The growing application of deep learning in oceanography highlights the potential of data-driven techniques to enhance satellite-derived SSH measurements [15]. Recently, Dibarboure et al. [16] released a SWOT Level-3 product in which a convolutional neural network (CNN), developed by Tréboutte et al. [14], was applied to SWOT observations. However, the available filtering approaches for SWOT data did not explicitly incorporate constraints based on satellite/in-situ data matchups during their development. Including observation-based information on surface features and velocity differences during model training could instead ensure an improved consistency between SSH-derived geostrophic velocities and real oceanic flow measurements. In this study, we propose an adaptive CNN-based filtering technique that leverages drifter velocity measurements from the Global Drifter Program to improve SWOT-derived SSH observations, also learning from concurrent SSH data provided by standard altimetry [17]. The key innovation of our approach lies in the definition of a custom loss function designed to minimize discrepancies between geostrophic velocities inferred from SWOT data and in-situ drifter velocities. The paper is structured as follows: Section 2 introduces the datasets used in this study, including SWOT SSH, altimetry data, drifter velocity observations, surface wind data, and the SWOT Level-3 product. Section 3 explains the SWOT SSH filtering methodology, detailing the CNN architecture, the data pre-processing and the training strategy. Section 4 presents the results, focusing on the evaluation of geostrophic velocities and spectral analysis. The performance of our denoising filter is also compared to other filtering methods in this section. Finally, Section 5 discusses the implications of our findings and concludes with potential future directions.

2. Datasets

This study utilizes multiple datasets, including SWOT SSH observations, drifter velocity measurements, sea-surface height anomalies (SSHAs), and errors on sea-level anomalies from altimetry as well as wind data. These datasets serve as inputs for the CNN model described in Section 3.1. Additionally, we compare our filtered SWOT product with the SWOT Level-3 dataset from Dibarboure et al. [16].

2.1. SWOT Sea-Surface Height Anomalies

In this study, we use the Level-2 KaRIn low-rate SWOT product (L2_LR_SSH_Expert [18], hereafter referred to as SWOT_L2), which provides SSH measurements along the satellite’s swaths, with corrections applied for tides, atmospheric effects, and geophysical biases [19]. SWOT operates in a wide-swath configuration, measuring SSH across two swaths, each approximately 60 km wide, separated by a 20 km nadir gap. The satellite follows a 21-day repeat orbit, ensuring global coverage with overlapping swaths. Depending on latitude, the effective ground-track length of a single pass can extend over several thousand kilometers. While SWOT_L2 data are provided at a native pixel resolution of 250 m, the effective resolution for geophysical applications, due to instrument noise, is estimated to be around 15–20 km after appropriate filtering [5]. In this work, we use the SWOT Level-2 Expert KaRIn product, which provides SSHA data on a geographically fixed, swath-aligned grid with a resolution of 2 × 2 km. The model is trained on 20 × 20 pixel tiles, corresponding to 40 × 40 km areas, which are suitable for resolving mesoscale geostrophic features across most of the ocean. We specifically use the KaRIn2 SSHA data from the Expert Dataset, downloaded from NASA’s PODAAC portal for the period from July 2023 to April 2024 (https://podaac.jpl.nasa.gov/dataset/SWOT_L2_LR_SSH_Expert_2.0#faceted-browse-dataAccess, last accessed on 15 March 2025). We also compute the absolute dynamic topography (ADT) by combining SSHA from SWOT with the Mean Dynamic Topography (MDT) included in the SWOT SSH file, which is derived from the CNES/CLS 2022 model [20].

2.2. DUACS Altimetry Data

In addition to SWOT observations, we use ADT and SSHA error fields from the Data Unification and Altimeter Combination System (DUACS), a multi-mission altimetry product distributed by the Copernicus Marine Environment Monitoring Service (CMEMS). DUACS provides optimally interpolated daily fields at a 1/4° spatial resolution, merging observations from multiple altimetry missions to generate a globally consistent dataset. ADT is computed by adding sea-level anomalies to CLS MDT [17]. While DUACS ADT is primarily a large-scale, low-resolution product, it serves as a valuable reference for understanding SWOT-derived signals. We use the DUACS product delivered in near-real time (product ID: SEALEVEL_GLO_PHY_L4_NRT_008_046) for the period from July 2023 to April 2024. DUACS data are accessible from the CMEMS data portal (last accessed in March 2025). Before analysis, the DUACS data were interpolated onto the SWOT Level_L2 2 × 2 km grid using bicubic interpolation to enable spatial alignment with SWOT.

2.3. Drifter Velocity Observations

Surface-current velocity measurements are obtained from the Global Drifter Program from NOAA [21], a long-term observational network providing in-situ ocean-surface velocity estimates. The data are accessible at https://www.aoml.noaa.gov/phod/gdp/interpolated/data/all.php (last accessed on 10 December 2024). The drifters, which follow ocean currents, measure near-surface velocities at a depth of approximately 15 m when drogued. These velocity components are crucial for validating satellite-derived geostrophic currents and serve as reference data in the training of the CNN model. The dataset is pre-processed to remove outliers. We selected all available drogued drifter data from July 2023 to April 2024, which represented the maximum data availability at the time of download. To filter out inertial oscillations and internal waves, a low-pass filter is applied to the 6-hourly drifter observations. The filtering consists of averaging the data over a moving time window inversely scaled with the Coriolis parameter, following the methodology described in Buongiorno Nardelli et al. [22]. While this approach effectively attenuates variability near the local inertial frequency, it may not fully remove tidal signals, particularly diurnal tides at latitudes where the inertial period is shorter than 24 h.

2.4. Surface Wind Data

To account for wind-driven effects on surface currents, we use wind data from the CMEMS Global L4 product, which provides daily wind fields at 0.125° spatial resolution at 10 m (product ID: WIND_GLO_PHY_L4_MY_012_006). This dataset is derived from a combination of satellite and model-based analyses, offering a comprehensive representation of surface wind patterns. The wind fields are based on the ECMWF ERA5 Reanalysis winds, bias-corrected using scatterometer observations. The original hourly data were downloaded from July 2023 to April 2024 and converted into daily fields through temporal averaging. The wind-velocity components are included as additional inputs in the CNN model to help distinguish between geostrophic and wind-driven motions. These data are available from the CMEMS data portal (https://data.marine.copernicus.eu, last accessed on 10 December 2024). To ensure spatial consistency across inputs, CMEMS wind data were interpolated onto the 2 × 2 km SWOT Level_2 grid using bicubic interpolation.

2.5. SWOT Level-3 Product

For comparison with our filtered SSHA product, we use the SWOT_L3_LR_SSH dataset (hereafter referred to as SWOT_L3), recently developed by Dibarboure et al. [16], with a spatial resolution of approximately 2 km. A distinctive feature of this product is the application of a CNN filtering technique, specifically a U-Net, to SWOT observations, aimed at reducing noise and enhancing the retrieval of geophysical signals [14]. The SWOT_L3 dataset serves as a benchmark to assess the effectiveness of our proposed CNN-based filtering approach. As before, we combine SSHA and MDT to compute the ADT. The SWOT_L3 product is derived from the Level-2 KaRIn low-rate ocean data product (L2_LR_SSH from NASA/JPL and CNES) and is produced by the AVISO and DUACS teams as part of the DESMOS Science Team project. The dataset is freely available from the AVISO data portal. We downloaded SWOT_L3 data from July 2023 to April 2024, consistent with the time period of our study (last accessed on 10 December 2024).

3. SWOT SSHA Filtering Methodology

3.1. Convolutional Neural Network Architecture

In this study, we use a CNN model to denoise the SSHA derived from SWOT satellite data. The main objective is to remove high-frequency noise from SWOT SSHA while preserving physically relevant features, in particular those consistent with surface geostrophic currents. The architecture of the model is illustrated in Figure 1. The core of the CNN model consists of three convolutional layers with an increasing number of filters (32, 64, and 128 filters, each with a 3 × 3 kernel) followed by two multi-head attention modules and a final convolutional layer with 64 filters (3 × 3 kernel). All convolutional layers use the ReLU activation function. The CNN model receives nine input channels during training, each corresponding to a 20 × 20 pixel spatial tile. These include the original SSHA from SWOT, DUACS SSHA, DUACS SSHA error, zonal and meridional wind components, a binary mask identifying valid drifter tile locations, the latitude, the rotation angle (defined as the angle between true north and the spacecraft’s cross-track velocity direction, measured clockwise), and the in-situ drifter velocity components (scalars). During training, the model minimizes a custom loss function that compares the geostrophic velocities inferred from the filtered ADT (derived from the filtered SSHA) with the in-situ drifter velocities. Although the drifter velocities, latitude, rotation angle, and the binary mask are not direct inputs to the prediction, they are essential for defining the physically constrained loss function. To further refine the predictions, the model integrates two attention mechanisms—multi-head attention layers inserted between the third and fourth convolutional layers.These layers help modulate the spatial filtering process by accounting for associated uncertainties in the input data. In these layers, the model looks at different parts of the input image from different “perspectives” using multiple attention heads. Each head focuses on different spatial patterns or relationships in the data. By combining the outputs from all heads, the model can capture more complex and nuanced information about where to focus during the filtering process. In the first attention layer, the DUACS SSHA error is used as the key, allowing the model to emphasize more reliable regions and assign lower weight to noisier ones. The second attention module uses the wind-velocity components as the key, enabling the model to account for the potential influence of wind-driven currents on the difference between total currents (from in-situ drifters) and geostrophic currents (inferred from ADT). The attention-weighted outputs from both mechanisms are then concatenated with the convolutional feature maps before the final prediction layers. Once trained, the model only needs five geophysical variables as input channels for the prediction of filtered SSHA fields: the original SSHA from SWOT, DUACS SSHA, DUACS SSHA error, and zonal and meridional wind components. The final output of the CNN is the filtered SSHA, optimized to produce geostrophic currents consistent with drifter observations.

3.2. The Custom Loss Function

Our custom loss function introduces a constraint based on the geostrophic balance that allows us to estimate surface currents from ADT data. Since the predicted variable is SSHA, the ADT is computed inside the loss function by adding the MDT to the predicted SSHA. It minimizes the mean squared error (MSE) between the predicted geostrophic velocity (derived from ADT) and the in-situ velocity (obtained from the drifters). Although drifter velocities obviously reflect the full dynamical components (including Ekman transport and other ageostrophic motions), using this loss function in combination with ancillary wind data (provided as input to the network) proved effective in filtering unbalanced motions. Gradients of ADT in the across-track and along-track directions are calculated using second-order central finite differences. The geostrophic velocity components are derived by multiplying the gradient components by the gravitational acceleration and dividing them by the Coriolis parameter. Considering the SWOT ground track’s inclination due to its quasi-polar orbit, a final rotation step is needed to project the components along the zonal (u) and meridional directions (v), consistently with the drifter velocities. The complete loss function combines the MSE of the u and v velocity components with an additional quadratic penalty on the mean of the predicted SSHA. This term penalizes deviations of the mean SSHA from zero, helping to prevent systematic bias in the model’s predictions and encourages more balanced and accurate estimates of the SSHA.

3.3. Data Preparation

Matchup Database: 

The preparation of the data required for the CNN training involves creating a matchup database that pairs tiles from SWOT datasets, drifter velocities, DUACS SSHA and SSHA error, and wind data for the same date. The matchup covers the period July 2023–April 2024. A tile size of 20 × 20 pixels (corresponding to 40 × 40 km, given the 2 × 2 km resolution of the SWOT Expert product) was selected as a trade-off between computational efficiency and the need to capture mesoscale features within the SWOT swath. This size also allows the tiles to be fully contained within the SWOT swath (69 pixels wide), avoiding edge effects and preserving spatial context. The objective is to select 20 × 20 pixel tiles around specific drifter positions, ensuring that the tiles’ edges are positioned at least 5 pixels away from the image borders to reduce spurious edge effects during the training and allow for an accurate estimation of SSHA gradients. For each drifter location, 20 tiles have been selected randomly among all possible tiles, including the drifter locations. This strategy allowed us to generate diverse samples of SWOT data from a single drifter matchup. It served as an augmentation strategy to improve the network ability to associate the most relevant spatial features detected over the relatively small tiles that are positioned differently around the drifter matchup. Once these tiles have been identified, the corresponding 20 × 20 pixel tiles from the other datasets (SWOT_L3, DUACS SSHA, DUACS SSHA error and wind data) were extracted for the same spatial area and date, ensuring consistency across all variables. This procedure resulted in a total of 18634 matchup samples, which thus lead to 372,680 tiles available for network training. This approach was chosen to enhance memory efficiency and processing speed, as working with smaller tiles reduces computational demands, but also considering the small swath of original SWOT observations. By selecting 20 tiles per matchup, our aim was to expose the model to a wide range of oceanographic features within the dataset, allowing it to learn from the diversity of patterns present.

Inputs Pre-processing: 

Before training the CNN, we preprocess the input data to ensure consistency and improve the model’s learning ability. First, we exclude the equatorial band (10°S – 10°N), where geostrophic balance does not hold, and we discard suspect high-velocity drifter points by selecting only locations where $|{\overrightarrow{u}}_{Drifters}|$ < 2 $\mathrm{m}·{\mathrm{s}}^{-1}$. Next, we remove the mean SSHA from each 20 × 20 pixel tile of the DUACS fields to eliminate large-scale biases and regional offsets. For SWOT SSHA, instead of subtracting the tile mean, we apply a large-scale spatial smoothing using a moving average filter with a 30 × 30 kernel. This is implemented using the convolve function from the Astropy 6.0 library in Python 3.11, which acts as a low-pass filter by averaging the SSHA values within a 30 × 30 neighborhood around each pixel. We then subtract this smoothed field from the original SWOT SSHA. This operation isolates mesoscale and smaller-scale features by removing low-frequency variability, allowing the model to focus on resolving local structures and high-frequency variations. Finally, we apply min–max normalization to all input variables to standardize their range and improve model convergence:

$$X_{norm}={\displaystyle \frac{X-X_{min}}{X_{max}-X_{min}}}$$

(1)

where X is the original (non-normalized) variable, $X_{min}$ and $X_{max}$ are the minimum and maximum values of X, respectively, and $X_{norm}$ is the normalized variable.

This normalization scales each variable to the range [0, 1], ensuring that different inputs contribute proportionally during training and preventing numerical instabilities. After training the model, the predicted anomalies are denormalized and the large-scale background—previously removed using the smoothing filter—is summed to reconstruct the full SSHA fields. The dataset is split into 80% for training and 20% for testing, with 15% of the training dataset reserved for validation. This split ensures sufficient data for model optimization while maintaining an independent test set for performance evaluation. The split is applied at the block level, where each block consists of the 20 tiles associated with the same drifter observation. To ensure an unbiased and independent separation, the blocks are randomly assigned to one of the three subsets (training, validation, or testing), ensuring that all tiles corresponding to a single drifter position are assigned to only one subset. This approach prevents model overfitting by avoiding the use of data from the same drifter trajectory across multiple datasets, and further ensures that no duplicate data appears in different subsets.

3.4. Training and Optimization

For training our CNN model, we used the Adam optimizer with a learning rate of 0.001. Early stopping was applied with a patience of 50 epochs, and the model was trained for a maximum of 1000 epochs. Validation data were used to prevent overfitting, and the model’s weights were saved at each epoch where the validation loss improved. The model’s performance was assessed based on both training and validation loss.

3.5. Evaluation Metrics

The accuracy of geostrophic velocity estimates derived from SWOT SSHA filtered by our CNN model was assessed by comparing them to in-situ drifter velocities from the test set. Two metrics were used: the Root Mean Square Error (RMSE) and the coefficient of determination (R²), which reflects the consistency between predicted and observed velocity variability. Both metrics were computed separately for the zonal, meridional, and total velocity components. Confidence intervals were estimated using a bootstrapping approach with 300 resamples. Uncertainties represent ±2 standard deviations, corresponding to a 95% confidence level.

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{(y_i-{\widehat{y}}_i)}^2}$$

(2)

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2}{{\sum }_{i=1}^n{(y_i-\overline{y})}^2}}$$

(3)

where $y_i$ is the drifter value, ${\widehat{y}}_i$ is the predicted“noisy” value (SWOT, DUACS, …), and $\overline{y}$ is the mean of the drifter values.

We also estimate the noise reduction in the spectral domain.

$$NR=100\times {\displaystyle \frac{\int PS{D}_{filtered}-\int PS{D}_{unfiltered}}{\int PS{D}_{unfiltered}}}$$

(4)

where PSD_unfiltered is the power spectral density of the unfiltered data, and PSD_unfiltered is the power spectral density of the filtered data. The integral of the PSD_filtered and PSD_unfiltered represents the total variance (energy) of the denoised and original fields, respectively, in the spectral domain. Therefore, a reduction in this integrated value reflects a decrease in high-frequency variance, which we interpret as spectral noise removal. The integral is computed numerically using Simpson’s rule. This makes spectral noise reduction a meaningful metric for quantifying the efficacy of different filtering approaches in reducing unwanted spectral content while preserving mesoscale features.

3.6. Reconstruction of the SWOT Track

Before applying the CNN filtering, we extend the SWOT swath by adding five pixels on each side using edge padding, where the border values of the tile are extended outward. This padding enhances the filter’s performance near the borders by minimizing discontinuities without introducing artificial gradients or patterns. This ensures a reduction of potential boundary artifacts during the convolution process. The extended track is then divided into all possible overlapping tiles of size 20 × 20 pixels, ensuring full coverage of the track. The tiles are then passed to the trained CNN as inputs, producing filtered SSHA predictions. After filtering, the full SWOT satellite track is reconstructed by merging the filtered tiles using a weighted averaging approach, a method commonly used in image processing for the seamless blending of overlapping patches [23]. Each tile is multiplied by a two-dimensional weighting mask that assigns higher weights to the central pixels and lower weights towards the edges. The weighting mask is computed as a normalized distance function from the tile center, with the highest value at the center and linearly decreasing toward the borders. This method reduces edge effects and ensures smooth transitions between overlapping tiles. The final filtered SSHA along the SWOT track is obtained by summing the weighted predictions and normalizing by the total weights at each pixel location. After merging, we crop five pixels from each side of the reconstructed swath to remove the initial padding and retain the valid central portion of the track.

3.7. Filtering Methods for Comparison

In addition to our CNN-based filtering approach, we consider two existing methods to process SWOT-derived SSHA as benchmarks. The first is the variational filtering technique developed by Gómez-Navarro et al. [13], which we apply to SWOT observations to obtain denoised ADT product data (hereafter Gómez filter or Gómez method). This method reconstructs geophysical signals by minimizing a cost function that penalizes deviations from the noisy observations. It applies some regularization constraints based on three parameters (${\lambda }_1$, ${\lambda }_2$, and ${\lambda }_3$). In our case, we chose ${\lambda }_1$ = ${\lambda }_3$ = 0 and ${\lambda }_2$ = 4. The second reference product is the SWOT_L3 dataset [16] described in Section 2.5, which uses a U-Net to enhance SWOT observations by reducing instrumental noise and aliasing effects.

4. Results

4.1. Evaluation of Geostrophic Velocity

In this section, we present the results of the trained model applied on the test dataset and compare its performance to other products/methods. We assessed the accuracy of the geostrophic velocity derived from the ADT by comparing them to in-situ drifter velocities. This comparison is illustrated through scatter plots in Figure 2, where we examined the relationship between the velocity components computed from (i) non-filtered SWOT ADT, (ii) CNN-filtered SWOT ADT, (iii) SWOT ADT filtered using the Gómez method, (iv) SWOT_L3 velocities, and (v) DUACS-derived velocities—all compared against drifter velocities. To quantify the performance of each filtering approach, RMSEs and coefficients of determination (R²) were included in each plot and summarized in

Table 1. RMSE (±2 standard deviations) between in-situ drifter velocities and SWOT-derived products, along with DUACS, for zonal (u), meridional (v), and total velocity ($|\overrightarrow{u}|$) components (in $\mathrm{m}·{\mathrm{s}}^{-1}$). The spectral noise reduction indicates the averaged percentage decrease in the spectral energy of filtered products relative to unfiltered SWOT, as computed from the kinetic energy spectra (see Section 4.3).

	SWOT_Unfiltered	SWOT_CNN	SWOT_Gómez	SWOT_L3	DUACS_L4
${\mathrm{RMSE}}_u$	0.355 ± 0.005	0.128 ± 0.003	0.132 ± 0.002	0.175 ± 0.005	0.112 ± 0.003
${\mathrm{RMSE}}_v$	0.438 ± 0.007	0.238 ± 0.005	0.179 ± 0.004	0.277 ± 0.005	0.221 ± 0.004
${\mathrm{RMSE}}_{|\overrightarrow{u}|}$	0.434 ± 0.006	0.163 ± 0.003	0.176 ± 0.004	0.203 ± 0.005	0.156 ± 0.004
${\mathrm{R}}_u^2$	0.150 ± 0.012	0.475 ± 0.017	0.411 ± 0.017	0.435 ± 0.017	0.568 ± 0.017
${\mathrm{R}}_v^2$	0.005 ± 0.002	0.001 ± 0.002	0.002 ± 0.002	0.001 ± 0.002	0.001 ± 0.001
${\mathrm{R}}_{|\overrightarrow{u}|}^2$	0.4068 ± 0.009	0.280 ± 0.017	0.266 ± 0.018	0.296 ± 0.018	0.317 ± 0.024
Spectral Noise Reduction	-	87.0%	89.6%	58.5%	-

).

The results clearly show that the CNN-filtered ADT provides a substantial improvement over the non-filtered SWOT ADT, reducing the discrepancy between satellite-derived and drifter-derived velocities. For the zonal velocity, the CNN-filtered product reduces the error to 0.128 $\mathrm{m}·{\mathrm{s}}^{-1}$, representing a notable improvement compared to the non-filtered SWOT (0.355 $\mathrm{m}·{\mathrm{s}}^{-1}$). It also achieves lower errors than both the SWOT_L3 product (0.175 $\mathrm{m}·{\mathrm{s}}^{-1}$) and the Gómez filter (0.132 $\mathrm{m}·{\mathrm{s}}^{-1}$), although the difference between the CNN and Gómez filter is within the uncertainty range and may not be statistically significant. Both methods approach the accuracy of the DUACS velocities. While RMSE reflects the absolute error, the R² values indicate how well the predicted fields capture the variance in drifter-derived velocities. The CNN-filtered zonal velocity explains 47.5% of the variance, a notable improvement over SWOT_L3 (43.5%) and the Gómez filter (41.1%).

For the meridional velocity, the CNN filter achieves an error of 0.238 $\mathrm{m}·{\mathrm{s}}^{-1}$, surpassing the SWOT_L3 product (0.277 $\mathrm{m}·{\mathrm{s}}^{-1}$), but not reaching the performance of the Gómez filter (0.179 $\mathrm{m}·{\mathrm{s}}^{-1}$) or the DUACS velocities (0.221 $\mathrm{m}·{\mathrm{s}}^{-1}$). However, all products show very low R² values (between 0.001 and 0.005), indicating limited skill in capturing the variability of the meridional component. This limitation may be partly attributed to the quasi-meridional orientation of SWOT ground tracks, which provides limited sampling in the zonal direction. As a result, the cross-track SSH gradient estimations (which governs the estimation of meridional geostrophic velocities) may be more sensitive to small-scale variability that is not fully geostrophically balanced or is poorly resolved in the swath.

Considering the total velocity magnitude, the CNN filter once again shows improved performance over the SWOT_L3 product and, in this case, also surpasses the Gómez filtering method, coming close to the accuracy of DUACS, although the latter still performs slightly better overall. The CNN-filtered product reaches an RMSE of 0.163 $\mathrm{m}·{\mathrm{s}}^{-1}$ compared to the non-filtered SWOT’s 0.434 $\mathrm{m}·{\mathrm{s}}^{-1}$, while DUACS velocities have an RMSE of 0.156 $\mathrm{m}·{\mathrm{s}}^{-1}$. DUACS and CCN total velocity RMSE values almost overlap once confidence intervals are taken into account. In terms of R², the CNN-filtered product explains 28.0% of the variance in total velocity, which is comparable to the Gómez filter (26.6%) and SWOT_L3 (29.6%), and approaches the performance of DUACS (31.7%).

4.2. Reconstructed Track

A qualitative comparison of SSHA fields along SWOT tracks in two different regions, the Gulf Stream and the East Indian Ocean, is presented in Figure 3 and Figure 4. These examples highlight the varying degrees of noise reduction and feature preservation among the different products.

Contrary to initial expectations, the noise level in the unfiltered SWOT data does not appear exceptionally higher than the other products in the Gulf Stream region (Figure 3, panels a–e). However, subtle differences and finer details become clearer upon closer inspection. The CNN filter (Figure 3c) and the Gómez filter (Figure 3d) both reduce noise but tend to produce a smoother representation of the SSHA. The U-Net filter (Figure 3b) seems to strike a better balance, preserving more fine-scale features while still mitigating noise. Compared to the reference DUACS_L4 data (Figure 3e), the CNN, Gómez, and U-Net filters demonstrate improved performance in reconstructing the SSHA fields, underscoring their potential for refining oceanographic observations.

The corresponding geostrophic surface currents derived from these ADT fields (Figure 3, panels f–j) further emphasize the impact of filtering. Unlike the SSHA fields, the velocity fields more clearly reveal the noisy nature of the SWOT data. While the unfiltered velocities (Figure 3f) exhibit significant noise and unrealistic intensities, the application of the CNN filter (Figure 3h) effectively reduces this noise while preserving the sharp gradients characteristic of the Gulf Stream, resulting in a smoother and more interpretable velocity field. The Gómez filter (Figure 3i) also reduces noise but tends to oversmooth finer details, potentially losing important information. The SWOT_L3 data (Figure 3g) appears to retain more detail than both the Gómez and CNN filters, although it may still contain residual noise that was not fully filtered. Relative to the DUACS_L4 product (Figure 3j), the CNN filter and the SWOT_L3 product show improved skill in reconstructing velocity fields, underlining their potential to enhance both data resolution and accuracy in ocean studies.

To assess the generalizability of these findings, a second example from the Indian Ocean west of Australia is shown in Figure 4. In this region, the unfiltered SWOT SSHA appears significantly noisier than the other products. Nonetheless, the overall patterns are consistent with those observed in the Gulf Stream. Both the CNN and Gómez filters reduce noise in the SSHA fields (Figure 4, panels c and d). The SWOT_L3 product (Figure 4b) displays intermediate behavior, while the DUACS reference (Figure 4e) lacks much of the smaller-scale variability. The geostrophic velocities (Figure 4, panels f–j) reinforce these observations: unfiltered SWOT velocities (Figure 4f) are extremely noisy, while the CNN and SWOT_L3 products (Figure 4g,h) deliver the most realistic and spatially coherent current patterns. The results in this region are even more favorable than in the Gulf Stream case, with the CNN preserving finer-scale features than the Gómez filter, while also achieving a stronger noise reduction than the U-Net. These two examples demonstrate that the CNN-based filtering approach generalizes well across different dynamical regimes, effectively reducing noise while retaining key oceanographic features in both SSHA and derived geostrophic velocities.

4.3. Spectral Analysis

Following the qualitative comparison of SSHA and velocity fields presented earlier, we conducted a spectral analysis to assess the distribution of kinetic energy (KE) across spatial scales. This analysis focuses on the along-track segments shown in Figure 3 and Figure 4. The power spectral density (PSD) of surface geostrophic KE was computed using Welch’s method, applied to 256-point cross-track segments (i.e., 512 km spatial windows, given the 2 km resolution of SWOT), and averaged to derive the mean along-track spectrum. The spectral range thus extends from 4 km (Nyquist) to 512 km (segment length). This analysis compares unfiltered SWOT data, our CNN model, the Gómez filter, SWOT_L3, and the DUACS_L4 product, offering further insights into the noise reduction and feature preservation across spatial scales.

As shown in Figure 5a, all products display similar energy levels at large scales (low wavenumbers), reflecting consistent large-scale ocean dynamics. This example focuses on a portion of the Gulf Stream region, characterized by intense mesoscale activity. Around 100 km, the CNN, Gómez, and DUACS_L4 spectra begin to diverge from the unfiltered SWOT spectrum, indicating the start of noise filtering. The DUACS_L4 spectrum drops off more steeply beyond 70 km, consistent with its known limitations in resolving mesoscale and submesoscale variability due to strong smoothing [24,25]. In contrast, both the CNN and Gómez-filtered spectra display higher power density at these scales, suggesting improved preservation of dynamic features compared to DUACS_L4. The CNN-filtered product displays a smooth and continuous decay across scales, indicating a balance between effective denoising and signal retention. The SWOT_Gómez spectrum, while broadly comparable to the CNN product, exhibits slightly lower energy at intermediate-to-small scales. Notably, it shows a secondary steepening around 20 km, followed by a flattening between 20 and 5 km, before dropping again. This flattening suggests the spectrum is approaching the noise floor, the spatial scale below which signal and noise become indistinguishable, and residual noise dominates the PSD. Such a plateau is a common artifact of filtering approaches that dampen small-scale variability as signal energy approaches the noise level. At high wavenumbers (small spatial scales), the unfiltered SWOT spectrum shows elevated PSD levels, indicative of strong noise contamination. The SWOT_L3 product, while improved relative to the raw SWOT data, still shows elevated power at small scales compared to both the SWOT_CNN and SWOT_Gómez spectra, suggesting residual high-frequency noise.

In the East Indian Ocean example (Figure 5b), all products exhibit lower overall power spectral density (PSD) levels compared to the Gulf Stream case (Figure 5a), reflecting the generally weaker KE in this region. Despite this, the spectral behaviors across products remain broadly consistent. At large spatial scales (low wavenumbers, <${10}^{-2}$ ${\mathrm{km}}^{-1}$), all spectra align closely, confirming agreement in representing broad-scale ocean variability. Divergence begins between 100 and 70 km, where filtering effects become evident. As in the Gulf Stream example, the DUACS_L4 spectrum drops off more sharply beyond 70 km due to its strong smoothing and limited capacity to retain mesoscale variability. Interestingly, the SWOT_Gómez spectrum also exhibits a marked steepening around 70–50 km. However, unlike DUACS_L4, it begins to flatten beyond 50 km, eventually reaching a quasi-plateau around 0.08 ${\mathrm{km}}^{-1}$ (∼12 km), suggesting that the filter approaches the noise floor more gradually. The CNN-filtered spectrum behaves similarly in this region: it drops around 70 km, then reaches a relatively flat plateau between 50 km and ∼12 km before steepening again at higher wavenumbers. While both filters perform comparably, the CNN-filtered spectrum maintains higher PSD levels than the Gómez-filtered product at scale smaller than 50 km, indicating better retention of fine-scale energy. At high wavenumbers, the unfiltered SWOT spectrum remains dominated by noise, showing elevated PSD levels. The SWOT_L3 product, although improved, still retains more small-scale energy than both CNN and Gómez filters. These results reinforce the earlier findings in the Gulf Stream, confirming that the CNN filter generalizes well across different dynamical regime. It effectively suppresses noise while preserving the spectral characteristics of surface ocean variability, offering a favorable compromise between denoising and the retention of physically relevant structures, even in lower-energy environments like the East Indian Ocean.

To quantitatively assess the noise reduction achieved by the different filtering techniques, we computed the spectral noise reduction as defined in Equation (4) across the entire spectral domain. This metric is derived by integrating the PSD of KE over the full wavenumber range. This integral represents the total variance of the KE field contained in the signal. Therefore, a decrease in the PSD integral after filtering indicates that less variance (energy) is present and directly reflects the removal of high-frequency energy interpreted as noise. On average across both the Gulf Stream and East Indian Ocean regions (see Figure 3 and Figure 4), the SWOT_CNN filter demonstrates a significant reduction in noise, with a 87.0% decrease in power spectral density. The Gómez filter shows slightly higher effectiveness, achieving a 89.6% reduction while the SWOT_L3 product shows a more modest 58.5% reduction. These results indicate that both the CNN-based and Gómez filters significantly reduce high-frequency noise across all scales, whereas the SWOT_L3 product retains a larger portion of unresolved variability. All spectral noise reduction values are reported in Table 1.

The scatter plots of velocity shown in Section 4.1 further support these findings. Since geostrophic velocities are derived from ADT gradients, excessive small-scale energy, often dominated by noise, can lead to overestimated velocities, while excessive smoothing can result in underestimation. When compared to drifter velocities, SWOT_CNN demonstrates superior performance relative to other filtering methods (SWOT_L3 and SWOT_Gómez), particularly for the zonal component and the total velocity magnitude. While the SWOT_Gómez filter performs slightly better for the meridional component, the CNN filter achieves an overall balance between high-frequency noise reduction and the preservation of mesoscale structures, with an accuracy approaching that of DUACS_L4.

5. Discussion/Conclusions

In this study, we presented a convolutional neural network (CNN)-based approach to filter SWOT-derived SSHA observations by leveraging in-situ drifter velocities, satellite observations, and wind data. The proposed methodology aimed to enhance the accuracy of geostrophic velocities inferred from SWOT data by reducing high-frequency noise contamination while preserving mesoscale-to-submesoscale signals. A key feature of our approach was the development of a custom loss function, which incorporated in-situ drifter velocities to guide the filtering process. The evaluation of the filtered geostrophic velocities demonstrated the effectiveness of the CNN filter compared to existing techniques and conventional altimetry products.

The scatter-plot analysis revealed that the CNN-filtered SSHA product significantly improved the consistency between satellite-derived and drifter-derived velocities, particularly for the zonal component and total velocity magnitude, where the CNN filter achieved the lowest RMSE among all products considered (except DUACS_L4).

While the filtering method of [13] performed slightly better for the meridional component, the CNN approach consistently delivered more accurate overall results. Notably, the CNN filter approached the performance of the operational DUACS_L4 product while enhancing the variance and sharpness of fine-scale features.

Spectral analysis further supported these findings. When assessing the reduction in spectral KE across the entire wavenumber domain, the SWOT_CNN filter achieved a 77.9% reduction in noise, compared to 81.3% for the Gómez filter and 32.4% for SWOT_L3. These results highlight the ability of the CNN to effectively suppress high-frequency noise while avoiding excessive smoothing. Moreover, the CNN-filtered product preserved mesoscale energy levels up to approximately 100 km, confirming its effectiveness in balancing noise reduction with the retention of physically relevant signals.

Overall, these results demonstrate that the proposed CNN-based filtering strategy provides a robust and adaptive solution for enhancing SWOT-derived SSHA and geostrophic velocity fields. By integrating additional observational datasets such as wind, DUACS SSHA, and associated uncertainties, the CNN model better captures the sources of error and delivers improved filtering performance. The superior accuracy of the CNN-filtered product in both velocity reconstruction and spectral characteristics suggests its potential for operational applications and broader use in oceanographic research.

Future work will focus on extending the CNN filtering approach to global SWOT observations, including equatorial regions by incorporating second-order dynamic balance terms to account for non-geostrophic processes. With the ongoing expansion of the drifter dataset and ongoing SWOT acquisitions, a larger set of in-situ/satellite data matchups will be available, enabling the model to be trained more effectively and enhancing its generalization ability. The inclusion of other relevant variables, such as sea-surface temperature, which has been shown to improve the estimation of geostrophic currents (as demonstrated in [26,27,28]), could also be considered. The promising results obtained in this study suggest that deep learning methods hold great potential to improve the processing and analysis of high-resolution satellite altimetry observations, ultimately contributing to a more detailed understanding of ocean dynamics at fine scales. Importantly, the present study offers a unique contribution in the context of SWOT-specific filtering by training the CNN model on real SWOT data, in combination with surface velocity estimates derived from in-situ drifters. This contrasts with previous deep learning approaches, which relied on simulated SWOT observations and synthetic noise. In addition, our method integrates wind stress data to account for ageostrophic effects, enhancing the model’s ability to distinguish signal from noise. The adaptive nature of the CNN also allows for spatially variable filtering depending on the features present in the inputs. Taken together, these methodological elements offer a novel and practical strategy design for SWOT’s specific characteristics and challenges.