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 4 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 hour period of oscillation.

Plain Language Summary

Ocean surface currents are caused by a variety of phenomena that varies at different space and time scales. Here we mainly consider the two dominant contributions. The first is the current resulting from the quasi‐equilibrium between the sloping sea level and the Coriolis force, slowly evolving over a few days. The second is also associated with the Coriolis force, but out of equilibrium: oscillating currents caused by rapid changes of the wind with a narrow range of periods around a natural period of oscillation that increase with latitude from 12 hours at the poles. For many applications it is desirable to separate these two contributions, for example to compute transports associated to the slowly evolving component and to evaluate the amount of kinetic energy pumped by the wind, mostly in the fast oscillations. This separation is easy with hourly sampled in situ measurements, but few are available. Here we show that we can perform this separation using satellite passes with measurements of sea level and a swath of surface current vectors, as can be measured by proposed future satellites. The fast oscillations can be reproduced even if data is available every few days, thanks to their spatial patterns and temporal coherence.