Passive tracer advection in the equatorial Pacific region: statistics, correlations and a model of fractional Brownian motion

Abstract

Evaluating passive tracer advection is a common tool to study flow structures, particularly Lagrangian trajectories ranging from molecular scales up to the atmosphere and oceans. Here we report on numerical experiments in the region of the tropical Pacific (20∘ S–20∘ N), where 6600 tracer parcels are advected from a regular initial configuration (along a meridional line at 110∘ W between 15∘ S and 15∘ N) during periods of 1 year for 25 years altogether. We exploit AVISO surface flow fields and solve the kinematic equation for passive tracer movement in the 2D advection tests. We demonstrate that the strength of the advection defined by mean monthly westward displacements of the tracer clouds exhibit surprisingly large inter- and intra-annular variabilities. Furthermore, an analysis of cross-correlations between advection strength and the El-Niño and Southern Oscillation (SOI) indices reveal a significant anticorrelation between advection intensity and ONI (the Oceanic Niño Index) and a weaker positive correlation with SOI, both with a time lag of about 3 months (the two indices are strongly anticorrelated near real time). The statistical properties of advection (time-dependent mean squared displacement and first passage time distribution) suggest that the westward-moving tracers can be mapped into a simple 1D stochastic process, namely fractional Brownian motion. We fit the model parameters and show by numerical simulations of the fractional Brownian motion model that it is able to reproduce the observed statistical properties of the tracers' trajectories well. We argue that a traditional explanation based on the superposition of ballistic drift and a diffusion term yields different statistics and is incompatible with our observations.