# An extended transfer operator approach for time-consistent coherent set analysis

## TL;DR

This paper introduces a novel transfer operator-based method for detecting long-term coherent structures in oceanic velocity data, improving robustness and stability in identifying mesoscale oceanic features relevant to climate and marine ecosystems.

## Contribution

The paper develops a time-centralized transfer operator approach with practical modifications to enhance detection of weakly-mixing coherent volumes over extended periods.

## Key findings

- Successfully identifies coherent structures in toy models.
- Yields promising results on real oceanic data.
- Provides insights into the stability of detected structures.

## Abstract

Coherent oceanic mesoscale structures, especially the non-filamenting cores of oceanic eddies, have gained a lot of attention in recent years. These Lagrangian structures are considered to play a significant role in oceanic transport processes which, in turn, impact marine life, weather and potentially even the climate itself. Answering questions regarding these phenomena requires robust tools for the detection and identification of these structures. In this article, we use transfer operator ideas to develop a novel method for the identification of weakly-mixing coherent volumes in oceanic velocity field data sets. Unlike other methods, the approach focuses on maximizing consistency over longer time periods. We employ a time-centralized transfer operator approach with practical modifications to identify potential structures in predetermined domains and couple adjacent time steps to decide how to conduct the final partitioning. The analysis pipeline includes plausibility checks that give further insights into the stability and coherence of the inferred structure. The presented method is able to find changing masses of maximal coherence in stationary and non-stationary toy models and yields good results when applied to field data.