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A recent Maxey–Riley theory for Sargassum raft motion, which models a raft as a network of elastically interacting finite size, buoyant particles, predicts the carrying flow velocity to be given by the weighted sum of the water and air velocities (1−α)v+αw. The theory provides a closed formula for parameter α, referred to as windage, depending on the water-to-particle-density ratio or buoyancy (δ). From a series of laboratory experiments in an air–water stream flume facility under controlled conditions, we estimate α ranging from 0.02% to 0.96%. On average, our windage estimates can be up to nine times smaller than that considered in conventional Sargassum raft transport modeling, wherein it is customary to add a fraction of w to v chosen in an ad hoc piecemeal manner. Using the formula provided by the Maxey–Riley theory, we estimate δ ranging from 1.00 to 1.49. This is consistent with direct δ measurements, ranging from 0.9 to 1.25, which provide support for our α estimation.more » « less
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Ulam’s method is a popular discretization scheme for stochastic operators that involves the construction of a transition probability matrix controlling a Markov chain on a set of cells covering some domain. We consider an application to satellite-tracked undrogued surface-ocean drifting buoy trajectories obtained from the National Oceanic and Atmospheric Administration Global Drifter Program dataset. Motivated by the motion of Sargassum in the tropical Atlantic, we apply Transition Path Theory (TPT) to drifters originating off the west coast of Africa to the Gulf of Mexico. We find that the most common case of a regular covering by equal longitude–latitude side cells can lead to a large instability in the computed transition times as a function of the number of cells used. We propose a different covering based on a clustering of the trajectory data that is stable against the number of cells in the covering. We also propose a generalization of the standard transition time statistic of TPT that can be used to construct a partition of the domain of interest into weakly dynamically connected regions.more » « less
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Abstract In this note, we apply transition path theory (TPT) from Markov chains to shed light on the problem of Iceland–Scotland Overflow Water (ISOW) equatorward export. A recent analysis of observed trajectories of submerged floats demanded revision of the traditional abyssal circulation theory, which postulates that ISOW should steadily flow along a deep boundary current (DBC) around the subpolar North Atlantic prior to exiting it. The TPT analyses carried out here allow attention to be focused on the portions of flow from the origin of ISOW to the region where ISOW exits the subpolar North Atlantic and suggest that insufficient sampling may be biasing the aforementioned demand. The analyses, appropriately adapted to represent a continuous input of ISOW, are carried out on three time-homogeneous Markov chains modeling the ISOW flow. One is constructed using a high number of simulated trajectories homogeneously covering the flow domain. The other two use much fewer trajectories which heterogeneously cover the domain. The trajectories in the latter two chains are observed trajectories or simulated trajectories subsampled at the observed frequency. While the densely sampled chain supports a well-defined DBC, whether this is a peculiarity of the simulation considered or not, the more heterogeneously sampled chains do not, irrespective of the nature of the trajectories used, i.e., observed or simulated. Studying the sampling sensitivity of the Markov chains, we can give recommendations for enlarging the existing float dataset to improve the significance of conclusions about long-time-asymptotic aspects of the ISOW circulation.more » « less
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By analyzing a time-homogeneous Markov chain constructed using trajectories of undrogued drifting buoys from the NOAA Global Drifter Program, we find that probability density can distribute in a manner that resembles very closely the recently observed recurrent belt of high Sargassum concentration in the tropical Atlantic between 5 and 10°N, coined the Great Atlantic Sargassum Belt ( GASB). A spectral analysis of the associated transition matrix further unveils a forward attracting almost-invariant set in the northwestern Gulf of Mexico with a corresponding basin of attraction weakly connected with the Sargasso Sea but including the nutrient-rich regions around the Amazon and Orinoco rivers mouths and also the upwelling system off the northern coast of West Africa. This represents a data-based inference of potential remote sources of Sargassum recurrently invading the Intra-Americas Seas (IAS). By further applying Transition Path Theory (TPT) to the data-derived Markov chain model, two potential pathways for Sargassum into the IAS from the upwelling system off the coast of Africa are revealed. One TPT-inferred pathway takes place along the GASB. The second pathway is more southern and slower, first going through the Gulf of Guinea, then across the tropical Atlantic toward the mouth of the Amazon River, and finally along the northeastern South American margin. The existence of such a southern TPT-inferred pathway may have consequences for bloom stimulation by nutrients from river runoff.more » « less
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Abstract Recently introduced in oceanography to interpret the near surface circulation, Transition Path Theory ( TPT ) is a methodology that rigorously characterizes ensembles of trajectory pieces flowing out from a source last and into a target next, i.e., those that most productively contribute to transport. Here we use TPT to frame, in a statistically more robust fashion than earlier analysis, equatorward routes of North Atlantic Deep Water (NADW) in the subpolar North Atlantic. TPT is applied on all available RAFOS and Argo floats in the area by means of a discretization of the Lagrangian dynamics described by their trajectories. By considering floats at different depths, we investigate transition paths of NADW in its upper (UNADW) and lower (LNADW) layers. We find that the majority of UNADW transition paths sourced in the Labrador and southwestern Irminger Seas reach the western side of a target arranged zonally along the southern edge of the subpolar North Atlantic domain visited by the floats. This is accomplished in the form of a well-organized deep boundary current (DBC). LNADW transition paths sourced west of the Reykjanes Ridge reveal a similar pattern, while those sourced east of the ridge are found to hit the western side of the target via a DBC and also several other places along it in a less organized fashion, indicating southward flow along the eastern and western flanks of the Mid-Atlantic Ridge. Naked-eye inspection of trajectories suggest generally much more diffusive equatorward NADW routes. A source-independent dynamical decomposition of the flow domain into analogous backward-time basins of attraction, beyond the reach of direct inspection of trajectories, reveals a much wider influence of the western side of the target for UNADW than for LNADW. For UNADW, the average expected duration of the pathways from the Labrador and Irminger Seas was found to be of 2 to 3 years. For LNADW, the duration was found to be influenced by the Reykjanes Ridge, being as long as 8 years from the western side of the ridge and of about 3 years on average from its eastern side.more » « less
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Abstract Consistent with satellite‐tracked trajectories of drogued drifters, but at odds with Eulerian assessment of satellite‐altimetry measurements of sea‐surface height, we show that North Brazil Currents Rings (NBCRs) are incapable of bypassing the Lesser Antilles as structures that coherently transport material. We arrive at this conclusion by applying
geodesic eddy detection on the altimetric data set over nearly its entire extent. While we detect northwestward translating NBCRs that can be classified as coherent Lagrangian eddies, they typically experience strong filamentation and complete loss of coherence prior to reaching the Lesser Antilles. Moreover, the filamented material hardly penetrates into the Caribbean Sea, let alone the Gulf of Mexico, and not without substantively mixing with the ambient fluid east of the archipelago. The nature of the inability of the de‐facto oceanographic Eulerian, streamline‐based eddy detection technique to produce a correct assessment of the connectivity between the tropical Atlantic and the Gulf of Mexico is rooted in its lack of objectivity.