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In the near future, the Surface Water Ocean Topography (SWOT) mission will provide images of altimetric data at kilometric resolution. This unprecedented 2-dimensional data structure will allow the estimation of geostrophy-related quantities that are essential for studying the ocean surface dynamics and for data assimilation uses. To estimate these quantities, i.e., to compute spatial derivatives of the Sea Surface Height (SSH) measurements, the uncorrelated, small-scale noise and errors expected to affect the SWOT data must be smoothed out while minimizing the loss of relevant, physical SSH information. This paper introduces a new technique for de-noising the future SWOT SSH images. The de-noising model is formulated as a regularized least-square problem with a Tikhonov regularization based on the first-, second-, and third-order derivatives of SSH. The method is implemented and compared to other, convolution-based filtering methods with boxcar and Gaussian kernels. This is performed using a large set of pseudo-SWOT data generated in the western Mediterranean Sea from a 1/60 ∘ simulation and the SWOT simulator. Based on root mean square error and spectral diagnostics, our de-noising method shows a better performance than the convolution-based methods. We find the optimal parametrization to be when only the second-order SSH derivative is penalized. This de-noising reduces the spatial scale resolved by SWOT by a factor of 2, and at 10 km wavelengths, the noise level is reduced by factors of 104 and 103 for summer and winter, respectively. This is encouraging for the processing of the future SWOT data.

In the near future, the Surface Water Ocean Topography (SWOT) mission will provide images of altimetric data at kilometric resolution. This unprecedented 2-dimensional data structure will allow the estimation of geostrophy-related quantities that are essential for studying the ocean surface dynamics and for data assimilation uses. To estimate these quantities, i.e., to compute spatial derivatives of the Sea Surface Height (SSH) measurements, the uncorrelated, small-scale noise and errors expected to affect the SWOT data must be smoothed out while minimizing the loss of relevant, physical SSH information. This paper introduces a new technique for de-noising the future SWOT SSH images. The de-noising model is formulated as a regularized least-square problem with a Tikhonov regularization based on the first-, second-, and third-order derivatives of SSH. The method is implemented and compared to other, convolution-based filtering methods with boxcar and Gaussian kernels. This is performed using a large set of pseudo-SWOT data generated in the western Mediterranean Sea from a 1/60 ∘ simulation and the SWOT simulator. Based on root mean square error and spectral diagnostics, our de-noising method shows a better performance than the convolution-based methods. We find the optimal parametrization to be when only the second-order SSH derivative is penalized. This de-noising reduces the spatial scale resolved by SWOT by a factor of 2, and at 10 km wavelengths, the noise level is reduced by factors of 104 and 103 for summer and winter, respectively. This is encouraging for the processing of the future SWOT data.

The SurfaceWater and Ocean Topography (SWOT) mission is a next generation satellite mission expected to provide a 2 km-resolution observation of the sea surface height (SSH) on a two-dimensional swath. Processing SWOT data will be challenging because of the large amount of data, the mismatch between a high spatial resolution and a low temporal resolution, and the observation errors. The present paper focuses on the reduction of the spatially structured errors of SWOT SSH data. It investigates a new error reduction method and assesses its performance in an observing system simulation experiment. The proposed error-reduction method first projects the SWOT SSH onto a subspace spanned by the SWOT spatially structured errors. This projection is removed from the SWOT SSH to obtain a detrended SSH. The detrended SSH is then processed within an ensemble data assimilation analysis to retrieve a full SSH field. In the latter step, the detrending is applied to both the SWOT data and an ensemble of model-simulated SSH fields. Numerical experiments are performed with synthetic SWOT observations and an ensemble from a North Atlantic, 1/60° simulation of the ocean circulation (NATL60). The data assimilation analysis is carried out with an ensemble Kalman filter. The results are assessed with root mean square errors, power spectrum density, and spatial coherence. They show that a significant part of the large scale SWOT errors is reduced. The filter analysis also reduces the small scale errors and allows for an accurate recovery of the energy of the signal down to 25 km scales. In addition, using the SWOT nadir data to adjust the SSH detrending further reduces the errors.