Abstract
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 10 4 and 10 3 for summer and winter, respectively. This is encouraging for the processing of the future SWOT data.
Highlights
The Surface Water Ocean Topography (SWOT) [1] mission will provide an unprecedented two-dimensional view of ocean surface topography at a pixel resolution of 2 km
This paper presents a method designed to remove the random, small-scale noise of the future SWOT data, which explicitly relies upon the regularity of the first three orders of Sea Surface Height (SSH) derivatives
To remove the small-scale SWOT noise, we propose a de-noising method that performs better than conventional convolution-based methods both in terms of Root Mean Square Errors (RMSE) and spectra
Summary
The Surface Water Ocean Topography (SWOT) [1] mission will provide an unprecedented two-dimensional view of ocean surface topography at a pixel resolution of 2 km. This paper presents a method designed to remove the random, small-scale noise of the future SWOT data, which explicitly relies upon the regularity (bounded variations) of the first three orders of SSH derivatives. This approach is of interest as it has a direct impact on SSH and on important oceanic variables like geostrophic velocity and vorticity. Our approach is to acknowledge that our image is a smooth physical field with relatively smooth derivatives and that the estimation of derivatives is an important issue Remote Sens. 2020, 12, 734 and 5 present the results, and Section 6 summarizes the study, draws the most relevant conclusions, discusses them, and suggests possible future research paths
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