Hyperbolic and Elliptic Points Tracking Algorithm (HEPTA) in two-dimensional non-stationary velocity fields defined on a discrete grid

TL;DR

HEPTA is a new algorithm for automatically tracking elliptic and hyperbolic stationary points in two-dimensional non-stationary velocity fields, aiding in oceanographic and climate research.

Contribution

The paper introduces HEPTA, a novel algorithm that accurately tracks stationary points in discrete velocity fields, addressing bifurcations and boundary transitions.

Findings

HEPTA accurately identifies and tracks eddies in satellite data.

The algorithm effectively handles rapid eddy drift and complex hydrodynamics.

HEPTA provides a reliable tool for mesoscale oceanic feature analysis.

Abstract

This article presents a new algorithm, the Hyperbolic and Elliptic Points Tracking Algorithm (HEPTA), designed for automated tracking of elliptic and hyperbolic stationary points in two-dimensional non-stationary velocity fields defined on a discrete grid. HEPTA analyzes the stability, bifurcations, and Lagrangian dynamics of stationary points. By leveraging bilinear interpolation, Jacobian matrix analysis, and trajectory tracking, the algorithm accurately identifies the locations of vortex centers (elliptic points) and strain zones (hyperbolic points). A methodology has been developed to address bifurcation events and transitions across grid cell boundaries that occur during the evolution of stationary points in a discrete velocity field. The algorithm was tested on AVISO satellite altimetry data in the Kuroshio Current region, which is characterized by intense eddy formation. These data represent a two-dimensional discrete velocity field with a daily time step. The results show that HEPTA accurately identifies and tracks both cyclonic and anticyclonic eddies, even under conditions of rapid eddy drift and complex hydrodynamic conditions. This study provides a reliable and efficient tool for analyzing the dynamics of mesoscale formations, which may be useful in oceanographic research, climate modeling, and operational oceanography.