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 standardDUACS 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.

For decades now, satellite altimetric observations have been successfully integrated in numerical oceanographic models using data assimilation (DA). So far, sea surface height (SSH) data were provided by one-dimensional nadir altimeters. The next generation Surface Water and Ocean Topography (SWOT) satellite altimeter will provide two-dimensional wide-swath altimetric information with an unprecedented high resolution. This new type of SSH data is expected to strongly improve altimetric assimilation. However, the SWOT data is also expected to be affected by spatially correlated errors and, hence, can not be assimilated as easily as nadir altimeters. The present paper proposes to embed a state-of-the-art correlated-error reduction (CER) method for the SWOT data into an ensemble-based DA scheme. The DA with the new correlated-error reduced-data (CER-data) is implemented and tested in a simple SSH reconstruction problem using artificial SWOT data and a quasi-geostrophic model. The results show that, in an energetic large scale region, the DA with CER-data-in comparison to the classical DA-reduces the root-mean-square-error (RMSE) of the reconstruction in SSH by approximately 10%, in relative vorticity by 5% and in surface currents by 5-10%, and also slightly improves the noise-to-signal ratio and spectral coherence of the SSH signal at mesoscale (100-200 km) but with a small degradation on the large scales (>300 km). In a less energetic region, the DA with CER-data cuts down the RMSE in SSH by more than 50% on average therefore allowing a significantly more accurate reconstruction of SSH at mesoscale in terms of noise-to-signal ratio, spectral coherence, and power spectral density.