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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.
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Improving the stability of temporal statistics in transition path theory with sparse data
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.
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- Award ID(s):
- 2148499
- PAR ID:
- 10424976
- Date Published:
- Journal Name:
- Chaos: An Interdisciplinary Journal of Nonlinear Science
- Volume:
- 33
- Issue:
- 6
- ISSN:
- 1054-1500
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0144706
