This study considers year-to-year and decadal variations in as well as secular trends of the sea-air CO.sub.2 flux over the 1957-2020 period, as constrained by the pCO.sub.2 measurements from the SOCATv2021 database. In a first step, we relate interannual anomalies in ocean-internal carbon sources and sinks to local interannual anomalies in sea surface temperature (SST), the temporal changes in SST (dSST/dt), and squared wind speed (u.sup.2 ), employing a multi-linear regression. In the tropical Pacific, we find interannual variability to be dominated by dSST/dt, as arising from variations in the upwelling of colder and more carbon-rich waters into the mixed layer. In the eastern upwelling zones as well as in circumpolar bands in the high latitudes of both hemispheres, we find sensitivity to wind speed, compatible with the entrainment of carbon-rich water during wind-driven deepening of the mixed layer and wind-driven upwelling. In the Southern Ocean, the secular increase in wind speed leads to a secular increase in the carbon source into the mixed layer, with an estimated reduction in the sink trend in the range of 17 % to 42 %. In a second step, we combined the result of the multi-linear regression and an explicitly interannual pCO.sub.2 -based additive correction into a "hybrid" estimate of the sea-air CO.sub.2 flux over the period 1957-2020. As a pCO.sub.2 mapping method, it combines (a) the ability of a regression to bridge data gaps and extrapolate into the early decades almost void of pCO.sub.2 data based on process-related observables and (b) the ability of an auto-regressive interpolation to follow signals even if not represented in the chosen set of explanatory variables. The "hybrid" estimate can be applied as an ocean flux prior for atmospheric CO.sub.2 inversions covering the whole period of atmospheric CO.sub.2 data since 1957.