  Lagrangian data assimilation is a complex problem in oceanic and atmospheric
modeling. Tracking drifters in large-scale geophysical flows can involve
uncertainty in drifter location, complex inertial effects, and other factors
which make comparing them to simulated Lagrangian trajectories from numerical
models extremely challenging. Temporal and spatial discretization, factors
necessary in modeling large scale flows, also contribute to separation between
real and simulated drifter trajectories. The chaotic advection inherent in
these turbulent flows tends to separate even closely spaced tracer particles,
making error metrics based solely on drifter displacements unsuitable for
estimating model parameters. We propose to instead use error in the coherent
structure coloring (CSC) field to assess model skill. The CSC field provides a
spatial representation of the underlying coherent patterns in the flow, and we
show that it is a more robust metric for assessing model accuracy. Through the
use of two test cases, one considering spatial uncertainty in particle
initialization, and one examining the influence of stochastic error along a
trajectory and temporal discretization, we show that error in the coherent
structure coloring field can be used to accurately determine single or multiple
simultaneously unknown model parameters, whereas a conventional error metric
based on error in drifter displacement fails. Because the CSC field enhances
the difference in error between correct and incorrect model parameters, error
minima in model parameter sweeps become more distinct. The effectiveness and
robustness of this method for single and multi-parameter estimation in
analytical flows suggests that Lagrangian data assimilation for real oceanic
and atmospheric models would benefit from a similar approach.

Fluid Dynamics;Machine Learning;Atmospheric and Oceanic Physics;Data Analysis, Statistics and Probability;Machine Learning