Mesoscale ocean eddies transport heat, salt, energy, and nutrients across oceans. As a result, accurately identifying and tracking such phenomena are crucial for understanding ocean dynamics and marine ecosystem sustainability. Traditionally, ocean eddies are monitored through two phases: identification and tracking. A major challenge for such an approach is that the tracking phase is dependent on the performance of the identification scheme, which can be susceptible to noise and sampling errors. In this paper, we focus on tracking, and introduce the concept of multiple hypothesis assignment (MHA), which extends traditional multiple hypothesis tracking for cases where the features tracked are noisy or uncertain. Under this scheme, features are assigned to multiple potential tracks, and the final assignment is deferred until more data are available to make a relatively unambiguous decision. Unlike the most widely used methods in the eddy tracking literature, MHA uses contextual spatio-temporal information to take corrective measures autonomously on the detection step a pos- teriori and performs significantly better in the presence of noise. This study is also the first to empirically analyze the relative robustness of eddy tracking algorithms.

Rotating coherent structures of water known as ocean eddies are the oceanic analog of storms in the atmosphere and a crucial component of ocean dynamics. In addition to dominating the ocean's kinetic energy, eddies play a significant role in the transport of water, salt, heat, and nutrients. Therefore, understanding current and future eddy activity is a central challenge to address future sustainability of marine ecosystems. The emergence of sea surface height observations from satellite radar altimeter has recently enabled researchers to track eddies at a global scale. The majority of studies that identify eddies from observational data employ highly parametrized connected component algorithms using expert filtered data, effectively making reproducibility and scalability challenging. In this paper, we improve upon the state-of-the-art connected component eddy monitoring algorithms to track eddies globally. This work makes three main contributions: first, we do not pre-process the data therefore minimizing the risk of wiping out important signals within the data. Second, we employ a physically-consistent convexity requirement on eddies based on theoretical and empirical studies to improve the accuracy and computational complexity of our method from quadratic to linear time in the size of each eddy. Finally, we accurately separate eddies that are in close spatial proximity, something existing methods cannot accomplish. We compare our results to those of the state of the art and discuss the impact of our improvements on the difference in results.