Identifying Finite-Time Coherent Sets from Limited Quantities of Lagrangian Data

TL;DR

This paper introduces a data-driven method to identify transport barriers in time-varying flows using limited Lagrangian data, by partitioning the space into coherent sets through an optimization approach that leverages smooth functions for better accuracy.

Contribution

The paper presents a novel optimization-based approach for detecting coherent sets from limited Lagrangian data, improving accuracy with globally supported basis functions over traditional indicator functions.

Findings

Effective identification of coherent sets in synthetic and real data

Method outperforms traditional indicator-based approaches with limited data

Successfully applied to complex geophysical flow examples

Abstract

A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into pairs of coherent sets, which are sets of initial conditions chosen to minimize the number of trajectories that "leak" from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by posing an optimization problem, which once solved, yields a pair of functions whose signs determine set membership. From prior experience with synthetic, "data rich" test problems and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. As a result, given a fixed amount of data our approach, which can use sets of globally supported basis functions, has the potential to more accurately approximate the desired functions than other functions tailored to use compactly supported indicator functions. This difference enables our approach to produce effective approximations of pairs of coherent sets in problems with relatively limited quantities of Lagrangian data, which is usually the case with real geophysical data. We apply this method to three examples of increasing complexity: the first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.