Connectivity of Pulley Ridge With Remote Locations as Inferred From Satellite‐Tracked Drifter Trajectories

Abstract

Using historical (1994–2017) satellite‐tracked surface drifter trajectory data, we conduct a probabilistic Lagrangian circulation study which sheds light on the connectivity of Pulley Ridge with other locations in the Gulf of Mexico and adjacent areas. The analysis reveals that Pulley Ridge is connected with the North Atlantic, the Caribbean Sea, and most of the Gulf of Mexico. Preferred connecting pathways are identified and arrival times to potential reef sites computed. The study demonstrates the importance of Pulley Ridge as a source for neighboring regions like the Dry Tortugasa, the Florida Keys, Campeche Bank, and the east Florida coast as well as a self‐recruitment area for species with short competence time. The study further suggests that the reefs in the Caribbean Sea, the Dry Tortugas, the western Florida Keys, and the West Florida Shelf can act as sources for Pulley Ridge, indicating the importance of Pulley Ridge as a central refugium for species in the Gulf of Mexico.

Building a Maxey–Riley framework for surface ocean inertial particle dynamics

“…Specifically, we partition the North Atlantic domain into 5 • × 5 • longitude-latitude boxes and construct a matrix of probabilities, P , of the drifters and the inertial particles to transitioning, irrespective of the start time, among them over a short time. Such a time-independent P represents a discrete autonomous transfer operator which governs the evolution of tracer probability densities, satisfying a stationary advection-diffusion process, on a Markov chain defined on the boxes of the partition 23,[95][96][97][98] . Thus given an initial probability vector f , this is forward evolved under left multiplication by P , namely, f n = f P n , n = 1, 2, .…”

Stability of the Malvinas Current

“…Markovian dynamics can be expected to approximately hold as there is negligible memory farther than 2 days into the past. A similar reasoning was applied in earlier applications involving drifter data [35][36][37][67][68][69] . Here the validity of the Markov model was estimated by checking that λ(P (nT )) = λ(P (T )) n holds well with n up to 5 and consistent with this we have verified that the results presented below are largely insensitive to variations of T in the range 2-10 days.…”

“…The other set of tools considered is probabilistic. These tools root in ergodic theory and, under appropriate time-homogeneity assumptions, can unveil from the Lagrangian circulation statistically weak communicating flow regions that form the basis for the construction of Lagrangian geographies [34][35][36][37] . The theoretical foundation for this is provided by a series of results from the study of autonomous dynamical systems using probability densities that have led to the notion of almost-invariant sets [38][39][40][41][42] .…”

Markov-chain-inspired search for MH370

“…Here we have chosen to use n = 5 (equivalently T = 5 d) as this guarantees both good interbox communication and negligible memory into the past. Similar choices have been made in recent applications involving drifter data 23,28,29,32,33 .…”

“…The size of the cells was selected to maximize the grid's resolution while each individual box is sampled by enough trajectories. Similar grid resolutions in analysis involving buoy trajectory data were employed in recent work 23,28,29 , where sensitivity analyses to cell size variations and data amount truncations are presented. The area of the boxes varies from about 400 to 750 km 2 , yet the normalization by box area in the definition of the vector space V N makes this variation inconsequential, i.e., a stochastic transition matrix is obtained without the need of a similarity transformation (e.g., Froyland and Padberg 30 ).…”