How well-connected is the surface of the global ocean?

Abstract

The Ekman dynamics of the ocean surface circulation is known to contain attracting regions such as the great oceanic gyres and the associated garbage patches. Less well-known are the extents of the basins of attractions of these regions and how strongly attracting they are. Understanding the shape and extent of the basins of attraction sheds light on the question of the strength of connectivity of different regions of the ocean, which helps in understanding the flow of buoyant material like plastic litter. Using short flow time trajectory data from a global ocean model, we create a Markov chain model of the surface ocean dynamics. The surface ocean is not a conservative dynamical system as water in the ocean follows three-dimensional pathways, with upwelling and downwelling in certain regions. Using our Markov chain model, we easily compute net surface upwelling and downwelling, and verify that it matches observed patterns of upwelling and downwelling in the real ocean. We analyze the Markov chain to determine multiple attracting regions. Finally, using an eigenvector approach, we (i) identify the five major ocean garbage patches, (ii) partition the ocean into basins of attraction for each of the garbage patches, and (iii) partition the ocean into regions that demonstrate transient dynamics modulo the attracting garbage patches. V C 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4892530]Ocean dynamics operate and affect climate on timescales of months to millenia. In this paper, we investigate phenomena on the ocean's surface that manifest over very long time periods: we look for regions in which water, biomass, and pollutants become trapped "forever" (which we refer to as attracting regions), or for long periods of time before eventually exiting (which we refer to as almostinvariant regions). While attracting regions may be quite small in size or irregular in shape, they can nonetheless exert great influence on the global ocean surface dynamics if their basins of attraction are large.

Lagrangian based methods for coherent structure detection

“…30 Using the global drifter data set, the FCM method was able to identify global ocean partitioning results similar to those found using transfer operator methods. 33 While the FCM method is quite robust for sparse and intermittent data, there are some limitations. The approach limits the consideration of relative movement between trajectories to just the prescribed distance metric.…”

“…A related study used the transfer operator to divide the ocean into distinct regions, in an attempt to quantify the connectivity of different parts of the ocean. 33 To better represent the ocean surface dynamics, this study allowed for the loss of trajectories by considering an open domain, which accounted for the beaching of trajectories and advection to the poles. By considering by the Perron-Frobenius operator and its dual, the Koopman operator, the study was extended to both forwards and backwards time, which allowed identification of regions of upwelling and downwelling in the ocean.…”

Lagrangian Flow Network approach to an open flow model

“…[23] it was shown that, under the standard approximation of Markovian dynamics (i.e. P(t 0 , τ 1 +τ 2 ) ≈ P(t 0 , τ 1 )P(t 0 + τ 1 , τ 2 )) [28,29,45]), for velocity fields either steady or periodic with period T , and for values of τ multiple of T , C c i is non-zero at nodes containing the position at time t 0 of a periodic trajectory of period 3τ . In open flows, periodic orbits can only appear on the non-escaping set, i.e.…”

Lagrangian Transport of Marine Litter in the Mediterranean Sea

“…In oceanographic flows, particle retention has been assessed with tools derived from dynamical systems theory (e.g., Castiglione et al, 1999;Cencini et al, 1999); the attractive properties of Lagrangian coherent structures may play an important trapping role (Peacock and Haller, 2013; for a Mediterranean application see Rossi et al, 2014). Froyland et al (2014) quantitatively assessed the location and effectiveness of particle attraction areas in the world ocean on the basis of synthetic Lagrangian trajectories interpreted in a Markovian approximation. Here we will limit ourselves to the most straightforward accumulation definition, i.e., a mediumand/or long-term local increase of FLP density (see also below, Section Lagrangian Transport Reconstruction).…”