  Vertical transport in the ocean plays a critical role in the exchange of
freshwater, heat, nutrients, and other biogeochemical tracers. While there are
situations where vertical fluxes are important, studying the vertical transport
and displacement of material requires analysis over a finite interval of time.
One such example is the subduction of fluid from the mixed layer into the
pycnocline, which is known to occur near density fronts. Divergence has been
used to estimate vertical velocities indicating that surface measurements,
where observational data is most widely available, can be used to locate these
vertical transport conduits. We evaluate the correlation between surface
signatures derived from Eulerian (horizontal divergence, density gradient, and
vertical velocity) and Lagrangian (dilation rate and finite time Lyapunov
exponent) metrics and vertical displacement conduits. Two submesoscale
resolving models of density fronts and a data-assimilative model of the western
Mediterranean were analyzed. The Lagrangian surface signatures locate
significantly more of the strongest displacement features and the difference in
the expected displacements relative to Eulerian ones increases with the length
of the time interval considered. Ensemble analysis of forecasts from the
Mediterranean model demonstrates that the Lagrangian surface signatures can be
used to identify regions of strongest downward vertical displacement even
without knowledge of the true ocean state.
