On the reliability of finite-size Lyapunov exponents (FSLEs) diagnosis in surface marine flows

There is a recent strong activity in the study of mixing, dispersion and
transport of
oceanic properties from the Lagrangian perspective.
An important Lagrangian tool which is becoming widely used in
oceanography is that of
the Finite-Size Lyapunov Exponents (FSLEs). They are a local measure of
particles
dispersion which, most importantly, serves to characterize coherent
structures in the
turbulent oceanic flow. In this work we show the FLSE capacity for the
identification of
Lagrangian structures and their mixing activity at different spatial
scales, from
coastal to global scales. At the submesoscale, we analyze Palma Bay
using data from a
ROMS model at 300m of spatial resolution. At the mesoscale we use
velocity data from
the DieCast model in the Balearic Sea, and for the global distribution
we use the world
ocean data from JAMSTECH numerical model (Earth Simulator). A seasonal
analysis and a
comparative study between different regions are performed.
Although mathematically appealing, it is rather unclear how robust are
FSLE analyses
when confronted to real data, that is, data affected
by noise and with limited scale sampling. In this study, we analyze the
effect of finite
scale samplings and of diverse types of noise on
FSLE diagnostics. Both effects can be accounted to determine which part
of the
diagnostics is reliable. Most importantly, scale dependence
of FSLE reveals the emergence of a cascade-like structure in oceanic
flows, which can be
used to improve diagnostics and to
better understand ocean dynamics.