Sea Surface Height (SSH) observations describing scales in the range 10 - 100 km are crucial to betterunderstand energy transfers across scales in the open ocean and to quantify vertical exchanges of heatand biogeochemical tracers. The Surface Water Ocean Topography (SWOT) mission is a new wide-swathaltimetric satellite which is planned to be launched in 2022. SWOT will provide information on SSH at akilometric resolution, but uncertainties due to various sources of errors will challenge our capacity to extractthe physical signal of structures below a few tens of kilometers. Filtering SWOT noise and errors is a keystep towards an optimal interpretation of the data.The aim of this study is to explore image de-noising techniques to assess the capabilities of the future SWOTdata to resolve the oceanic fine scales. Pseudo-SWOT data are generated with the SWOT simulator forOcean Science, which uses as input the SSH outputs from high-resolution Ocean General Circulation Models(OGCMs). Several de-noising techniques are tested, to find the one that renders the most accurate SSHand its derivatives fields while preserving the magnitude and shape of the oceanic features present. Thetechniques are evaluated based on the root mean square error, spectra and other diagnostics.In Chapter 3, the pseudo-SWOT data for the Science phase is analyzed to assess the capabilities of SWOT toresolve the meso- and submesoscale in the western Mediterranean. A Laplacian diffusion de-noising techniqueis implemented allowing to recover SSH, geostrophic velocity and relative vorticity down to 40 - 60 km. Thisfirst step allowed to adequately observe the mesoscale, but space is left for improvement at the submesoscale,specially in better preserving the intensity of the SSH signal.In Chapter 4, another de-noising technique is explored and implemented in the same region for the satellite’sfast-sampling phase. This technique is motivated by recent advances in data assimilation techniques to removespatially correlated errors based on SSH and its derivatives. It aims at retrieving accurate SSH derivatives,by recovering their structure and preserving their magnitude. A variational method is implemented whichcan penalize the SSH derivatives of first, second, third order or a combination of them. We find that thebest parameterization is based on a second order penalization, and find the optimal parameters of this setup.Thanks to this technique the wavelengths resolved by SWOT in this region are reduced by a factor of 2,whilst preserving the magnitude of the SSH fields and its derivatives.

In Chapter 5, we investigate the finest spatial scale that SWOT could resolve after de-noising in severalregions, seasons and using different OGCMs. Although a method is found to mitigate the impact of SWOTinstrumental noise and errors, large uncertainties remain due to the incomplete understanding of the impactof fast unbalanced motions (e.g. internal gravity waves) on SSH signals, and therefore the impact on theperformance of the de-noising algorithm. Our study focuses on different regions and seasons in order todocument the variety of regimes that SWOT will sample. The de-noising algorithm performs well even inthe presence of intense unbalanced motions, and it systematically reduces the smallest resolvable wavelength.Advanced de-noising algorithms also allow to reliably reconstruct SSH gradients (related to geostrophicvelocities) and second order derivatives (related to geostrophic vorticity). Our results also show that asignificant uncertainty remains about SWOT’s finest resolved scale in a given region and season because ofthe large spread in the level of variance predicted among our high-resolution ocean model simulations.The de-noising technique developed, implemented and tested in this doctoral thesis allows to recover, insome cases, SWOT spatial scales as low as 15 km. This method is a very useful contribution to achieving theobjectives of the SWOT mission. The results found will help better understand the ocean’s dynamics andoceanic features and their role in the climate system.

I would like to acknowledge CNES and FP7 funding, which made possible this PhD. Also, I would like toacknowledge other sources of funding that allowed me to carry out different activities during my PhD: thePre-SWOT project and COST Action ES140.

Tesis Doctoral.-- Doctoral programme of Physics.-- Doctor by the Université Grenoble Alpes and the Universitat de les Illes Balears.