Two methods for the mapping of ocean surface currents from satellite measurements of sea level and future current vectors are presented and contrasted. Both methods rely on the linear and Gaussian analysis framework with different levels of covariance definitions. The first method separately maps sea level and currents with single‐scale covariance functions and leads to estimates of the geostrophic and ageostrophic circulations. The second maps both measurements simultaneously and projects the circulation onto four contributions: geostrophic, ageostrophic rotary, ageostrophic divergent, and inertial. When compared to the first method, the second mapping moderately improves the resolution of geostrophic currents but significantly improves estimates of the ageostrophic circulation, in particular near‐inertial oscillations. This method offers promising perspectives for reconstructions of the ocean surface circulation. Even the hourly dynamics can be reconstructed from measurements made locally every few days because nearby measurements are coherent enough to help fill the gaps. Based on numerical simulation of ocean surface currents, the proposed SKIM mission that combines a nadir altimeter and a Doppler scatterometer with a 300 km wide swath (with a mean revisit time of 3 days) would allow the reconstruction of 50% of the near‐inertial variance around an 18 h period of oscillation.

This study proposes an approach to estimate the ocean sea surface height signature of coherent internal tides from a 25-year along-track altimetry record, with a single inversion over time, resolving both internal tide contributions and mesoscale eddy variability. The inversion is performed on a reduced-order basis of topography and practically achieved with a conjugate gradient. The particularity of this approach is to mitigate the potential aliasing effects between mesoscales and internal tide estimation from the uneven altimetry sampling (observing the sum of these components) by accounting for their statistics simultaneously, while other methods generally use a prior mesoscale. The four major tidal components are considered (M2, K1, S2, O1) over the period 1992–2017 on a global configuration. From the solution, we use altimetry data after 2017 for independent validation in order to evaluate the performance of the simultaneous inversion and compare it with an existing model.

The Surface Water and Ocean Topography (SWOT) mission will be affected by various sources of systematic errors, which are correlated in space and in time. Their amplitude before calibration might be as large as tens of centimeters, i.e., able to dominate the mission error budget. To reduce their magnitude, we developed so-called data-driven (or empirical) calibration algorithms. This paper provided a summary of the overall problem, and then presented the calibration framework used for SWOT, as well as the pre-launch performance simulations. We presented two complete algorithm sequences that use ocean measurements to calibrate KaRIN globally. The simple and robust Level-2 algorithm was implemented in the ground segment to control the main source of error of SWOT’s hydrology products. In contrast, the more sophisticated Level-3 (multi-mission) algorithm was developed to improve the accuracy of ocean products, as well as the one-day orbit of the SWOT mission. The Level-2 algorithm yielded a mean inland error of 3–6 cm, i.e., a margin of 25–80% (of the signal variance) with respect to the error budget requirements. The Level-3 algorithm yielded ocean residuals of 1 cm, i.e., a variance reduction of 60–80% with respect to the Level-2 algorithm.

Over the last few years, a very active field of research has aimed at exploring new data-driven and learning-based methodologies to propose computationally efficient strategies able to benefit from the large amount of observational remote sensing and numerical simulations for the reconstruction, interpolation and prediction of high-resolution derived products of geophysical fields. In this paper, we investigate how they might help to solve for the oversmoothing of the state-of-the-art optimal interpolation (OI) techniques in the reconstruction of sea surface height (SSH) spatio-temporal fields. We focus on two small $10°\times 10°$ GULFSTREAM and $8°\times 10°$ OSMOSIS regions, part of the North Atlantic basin: the GULFSTREAM area is mainly driven by energetic mesoscale dynamics, while OSMOSIS is less energetic but with more noticeable small spatial patterns. Based on observation system simulation experiments (OSSE), we used a NATL60 high resolution deterministic ocean simulation of the North Atlantic to generate two types of pseudo-altimetric observational dataset: along-track nadir data for the current capabilities of the observation system and wide-swath SWOT data in the context of the upcoming SWOT (Surface Water Ocean Topography) mission. We briefly introduce the analog data assimilation (AnDA), an up-to-date version of the DINEOF algorithm, and a new neural networks-based end-to-end learning framework for the representation of spatio-temporal irregularly-sampled data. The main objective of this paper consists of providing a thorough intercomparison exercise with appropriate benchmarking metrics to assess whether these approaches help to improve the SSH altimetric interpolation problem and to identify which one performs best in this context. We demonstrate how the newly introduced NN method is a significant improvement with a plug-and-play implementation and its ability to catch up the small scales ranging up to 40 km, inaccessible by the conventional methods so far. A clear gain is also demonstrated when assimilating jointly wide-swath SWOT and (aggregated) along-track nadir observations.

The SWOT satellite, carrying the KaRIN first wide-swath onboard altimeter, was launched in December 2022, and has now delivered more than a year of surface water elevation data over the ocean and inland lakes/rivers. These data are affected by systematic errors which constitute the dominant part of the error budget at scales larger than a few thousands of kilometers. Some strategies for their estimation and calibration were explored during the pre-launch studies with performance estimations. Now, based on the real data, we propose in this study to assess the systematic error budget with statistical methods relying on spectral and co-spectral analysis. From this assessment, suggesting very low error levels (below requirements), we propose the implementation of the calibration algorithms at Level-2 and Level-3 with a few minor adjustments justified by the error spectra. The calibrated products are then validated with usual CalVal metrics.

The Surface Water and Ocean Topography (SWOT) mission offers two-dimensional measurements of Sea Surface Height (SSH), capturing scales of a few tens of kilometers and enabling the study of previously unobserved short mesoscale dynamical structures. However, the mission faces technical challenges in maximizing scientific benefits, particularly during the science phase with its 21-day repeat orbit, which limits observations of small-scale structure evolution over time.To address the challenge of high spatial and low temporal samplings, we propose an original dynamic interpolation scheme that we call 4Dvar-QG. This innovative method combines a weakly constrained, reduced-order, 4-dimensional variational scheme with a quasi-geostrophic model. The weak constraint of the quasi-geostrophic model on the inversion procedure ensures that the estimated maps closely match the observations while preserving the space-time continuity of the reconstructed structures.The 4Dvar-QG method is applied in the North Atlantic Ocean on a constellation of real conventional altimeters and SWOT, during both the SWOT’s fast sampling and science phases. Performance evaluations are conducted through Observing System Experiments, utilizing independent data (such as altimetric and drifter data) as ground truth and comparing results to operational products like the Multiscale Interpolation Ocean Science Topography product (MIOST). The 4Dvar-QG method significantly improves the mapping of short energetic structures, reducing the root mean square error by up to 50% and increasing the effective resolutions by up to 30% compared to MIOST, while maintaining good reconstruction of large-scale and/or low energetic structures.