Ocean general circulation models simulate total ocean transport averaged over surface waves

We argue that ocean general circulation models and observations based on Ekman or geostrophic balance provide estimates of the Lagrangian-mean ocean velocity field averaged over surface waves -- the total time-averaged velocity that advects oceanic tracers, particles, and water parcels. This interpretation contradicts an assumption often made in ocean transport studies that numerical models and observations based on dynamical balances estimate the Eulerian-mean velocity -- the velocity time-averaged at a fixed position and only part of the total ocean velocity. Our argument uses the similarity between the wave-averaged Lagrangian-mean momentum equations appropriate at large oceanic scales, and the momentum equations solved by "wave-agnostic" general circulation models that neglect surface wave effects. We further our case by comparing a realistic, global, "wave-agnostic" general circulation ocean model to a wave-averaged Lagrangian-mean general circulation ocean model at eddy-permitting 1/4$^\circ$ resolution, and find that the wave-agnostic velocity field is almost identical to the wave-averaged Lagrangian-mean velocity.