Numerical model output provides a flow description u(x, t) that is suitable for use to identify LCSs. Also, it has the advantage of allowing for a spatio-temporal coverage that is impossible to attain with existing observational systems. Here we consider a year-long record of surface currents produced by a Hybrid-Coordinate Ocean Model (HYCOM) simulation along the WFS for the year 2004.
The year-long record of simulated currents consists of daily surface velocity fields extracted in the WFS domain from a 0.04°-resolution, free-running HYCOM simulation of the GoM, itself nested within a 0.08°-resolution Atlantic basin data assimilative nowcast, which was generated at the Naval Research Laboratory as part of a National Oceanographic Partnership Program in support of the Global Ocean Data Assimilation Experiment [Chassignet et al., 2006a
]. The Atlantic nowcast was forced with realistic high-frequency forcing obtained from the U. S. Navy NOGAPS operational atmospheric model. It assimilated sea surface temperature and anomalous sea surface height from satellite altimetry with downward projection of anomalous temperature and salinity profiles. The nested GoM model was free-running and driven by the same high-frequency atmospheric forcing. The topography used in both models was derived from the ETOPO5 dataset, with the coastline in the GoM model following the 2 m isobath. Both models included river runoff.
shows snapshots of FTLE field, which were computed using the software package MANGEN, a dynamical systems toolkit designed by F. Lekien that is available at http://www.lekien.com/~francois/software/mangen
. At each time t
the algorithm coded in MANGEN performs the following tasks. First, system (2
) is integrated using a fourth-order Runge–Kutta–Fehlberg method for a grid of particles at time t
to get their positions at time t
, which are the values of the flow map at each point. This requires a smooth velocity field, which is attained by using a cubic interpolation method. Second, the spatial gradient of the flow map is obtained at each point in the initial grid by central differencing with neighboring grid points. Third, the FTLE is computed at each point in the initial grid by evaluating (1
). The previous three steps are repeated for a range of t
values to produce a time series of FTLE field. Here we have set τ
= −60 d so that the ridges of the FTLE fields shown in correspond to attracting LCSs. The choice τ
= −60 d was chosen because 60 d is approximately the time it takes a typical fluid particle to leave the WFS domain. Clearly, some particles will exit the domain before 60 d of integration. In this case, MANGEN evaluates expression (1
) using the position of each such particles prior exiting the domain. Note that due to the choice τ
=−60 d, the time series of computed FTLE fields based on our year-long record of simulated currents can only have a 10-month maximum duration.
The regions of most intense red tones in each plot of roughly indicate maximizing ridges of FTLE field. These regions are seen to form smooth, albeit structured, curves that constitute the desired LCSs or transport barriers. Of particular interest is the triangular-shaped area on the southern portion of the WFS with small FTLEs bounded by the western Florida coast on the east, the lower Florida keys on the south, and large maximizing ridges of FTLE field on the west. The latter constitute a cross-shelf transport barrier that approximately coincides in position with the western boundary of the FZ identified by Yang et al. 
. This is most clearly visible during the period May through September. The sequence of snapshots of FTLE field in also reveals a seasonal movement of the cross-shelf transport barrier, being farthest offshore during the winter and closest to the coast during the summer, which is in agreement with drifter observations [Morey et al., 2003
We have also computed FTLEs forward in time to produce repelling LCS fields (not shown). The combination of attracting and repelling LCS fields allows one to approximately identify the hyperbolic region where the aforementioned cross-shelf transport barrier originates. The hyperbolic region identified in this manner coincides approximately with that identified by Toner et al. 
where the computational domains overlap. In the Toner et al. 
work, stable and unstable manifolds were calculated using the straddling technique of Miller et al. 
based on velocity fields produced by a Princeton Ocean Model (POM) simulation of the GoM.