Improving the stability of temporal statistics in transition path theory with sparse data.

Area of Science:

• Oceanography
• Dynamical Systems
• Computational Physics

Background:

• Ulam's method discretizes stochastic operators using Markov chains for domain analysis.
• Transition Path Theory (TPT) analyzes trajectories, such as those of ocean drifters.
• Understanding drifter movement is crucial for tracking marine phenomena like Sargassum.

Purpose of the Study:

• To investigate the stability of Ulam's method for analyzing satellite-tracked drifter data.
• To apply TPT to drifter trajectories from West Africa to the Gulf of Mexico, inspired by Sargassum motion.
• To develop a more robust discretization scheme for TPT analysis.

Main Methods:

• Applied Ulam's method and TPT to Global Drifter Program data.
• Compared standard longitude-latitude cell covering with a novel data-clustering approach.
• Investigated the impact of cell number on transition time stability.
• Proposed a generalized TPT transition time statistic.

Main Results:

• Standard regular grid discretization in Ulam's method shows significant instability in transition times with varying cell numbers.
• A data-clustering-based discretization provides stable transition time calculations.
• The generalized TPT statistic enables partitioning domains into dynamically connected regions.

Conclusions:

• The choice of discretization significantly impacts the reliability of TPT analysis for oceanographic data.
• Data-driven clustering offers a more stable and accurate approach for Ulam's method.
• The proposed methods enhance the analysis of complex oceanic transport phenomena.