  Drifters deployed in close proximity collectively provide a unique
observational data set with which to separate mesoscale and submesoscale flows.
In this paper we provide a principled approach for doing so by fitting observed
velocities to a local Taylor expansion of the velocity flow field. We
demonstrate how to estimate mesoscale and submesoscale quantities that evolve
slowly over time, as well as their associated statistical uncertainty. We show
that in practice the mesoscale component of our model can explain much first
and second-moment variability in drifter velocities, especially at low
frequencies. This results in much lower and more meaningful measures of
submesoscale diffusivity, which would otherwise be contaminated by unresolved
mesoscale flow. We quantify these effects theoretically via computing
Lagrangian frequency spectra, and demonstrate the usefulness of our methodology
through simulations as well as with real observations from the LatMix
deployment of drifters. The outcome of this method is a full Lagrangian
decomposition of each drifter trajectory into three components that represent
the background, mesoscale, and submesoscale flow.
