Sensitivity and robustness of Lagrangian coherent structures in coastal water systems

TL;DR

This study evaluates how mesh resolution, interpolation, and noise affect the reliability of Lagrangian Coherent Structures in coastal water models, highlighting their robustness and limitations in complex environments.

Contribution

It provides the first systematic analysis of LCS sensitivity to data errors and grid resolution in realistic coastal water simulations.

Findings

LCSs are robust to interpolation errors in data conversion.

Random errors of 1-10% can disrupt LCS ridge continuity.

LCS applicability is limited by flow divergence and data noise.

Abstract

In coastal water systems, horizontal chaotic dispersion plays a significant role in the distribution and fate of pollutants. Lagrangian Coherent Structures (LCSs) provide useful tools to approach the problem of the transport of pollutants and have only recently been applied to coastal waters. While the fundamentals of the LCS approach using idealised analytical flow fields are well established in the literature, there are limited studies on their practical implementations in coastal waters where effects of boundaries and bathymetry frequently become significant. Due to their complex bathymetry and boundaries, unstructured grid systems are commonly used in modelling of coastal waters. For convenient derivation of LCS diagnostics, structured grids are commonly used. Here we examine the effect of mesh resolution, interpolation schemes and additive random noise on the LCS diagnostics in relation to coastal waters. Two kinematic model flows, the double gyre and the meandering jet, as well as validated outputs of a hydrodynamic model of Moreton Bay, Australia, on unstructured grids are used. The results show that LCSs are quite robust to the errors from interpolation schemes used in the data conversion from unstructured to structured grid. Attributed to the divergence in the underlying flow field, the results show that random errors in the order of 1-10 % cause a break down in the continuity of ridges of maximum finite time Lyapunov exponents and closed orbit elliptic LCSs. The result has significant implications on the suitability of applying LCS formulations based on a deterministic flow field to diffusive coastal waters.