During the past 25 years, altimetric observations of the ocean surface from space have been mapped to provide two dimensional sea surface height (SSH) fields which are crucial for scientific research and operational applications. The SSH fields can be reconstructed from conventional altimetric data using temporal and spatial interpolation. For instance, the standard DUACS products are created with an optimal interpolation method which is effective for both low temporal and low spatial resolution. However, the upcoming next-generation SWOT mission will provide very high spatial resolution but with low temporal resolution. The present paper makes the case that this temporal-spatial discrepancy induces the need for new advanced mapping techniques involving information on the ocean dynamics. An algorithm is introduced, dubbed the BFN-QG, that uses a simple data assimilation method, the back-and-forth nudging, to interpolate altimetric data while respecting quasigeostrophic dynamics. The BFN-QG is tested in an observing system simulation experiments and compared to the DUACS products. The experiments consider as reference the high-resolution numerical model simulation NATL60 from which are produced realistic data: four conventional altimetric nadirs and SWOT data. In a combined nadirs and SWOT scenario, the BFN-QG substantially improves the mapping by reducing the root-mean-square errors and increasing the spectral effective resolution by 40km. Also, the BFN-QG method can be adapted to combine large-scale corrections from nadirs data and small-scale corrections from SWOT data so as to reduce the impact of SWOT correlated noises and still provide accurate SSH maps.

The future Surface Water and Ocean Topography (SWOT) mission will soon provide Sea Surface Height (SSH) measurements resolving scales of a few tens of kilometers. Over a large fraction of the globe, the SSH signal at these scales is essentially a superposition of a component due to balanced motions (BM) and another component due to internal tides (IT). Several oceanographic applications require the separation of these components and their mapping on regular grids. For that purpose, the paper introduces an alternating minimization algorithm that iteratively implements two data assimilation techniques, each specific to the mapping of one component: a quasi-geostrophic model with Back-and-Forth Nudging for BM, and a linear shallow-water model with 4-Dimensional Variational (4DVar) assimilation for IT. The algorithm is tested with Observation System Simulation Experiments (OSSE) where the truth is provided by a primitive-equation ocean model in an idealized configuration simulating a turbulent jet and a mode-one IT. The algorithm reconstructs almost 80\% of the variance of BM and IT, the remaining 20\% being mostly due to dynamics that cannot be described by the simple models used. Importantly, in addition to the reconstruction of stationary IT, the amplitude and phase of nonstationary IT are reconstructed. Although idealized, this study represents a step forward towards the disentanglement of BM and IT signals from real SWOT data.