The ocean reduces human impact on the climate by absorbing and sequestering CO2. From 1950s to the 1980s, observations of pCO(2) and related ocean carbon variables were sparse and uncertain. Thus, global ocean biogeochemical models (GOBMs) have been the basis for quantifying the ocean carbon sink. The LDEO-Hybrid Physics Data product (LDEO-HPD) interpolates sparse surface ocean pCO(2) data to global coverage by using GOBMs as priors, and applying machine learning to estimate full-coverage corrections. The largest component of the GOBM corrections are climatological. This is consistent with recent findings of large seasonal discrepancies in GOBMs, but contrasts the long-held view that interannual variability is a major source of GOBM error. This supports extension of the LDEO-HPD pCO(2) product back to 1959, using a climatology of model-observation misfits prior to 1982. Consistent with previous studies for 1980 onward, air-sea CO2 fluxes for 1959-2020 demonstrate response to atmospheric pCO(2) growth and volcanic eruptions.