Search and rescue at sea aided by hidden flow structures

The high number of deaths at sea annually due to vessel and airplane accidents necessitates more efficient Search and Rescue (SAR) algorithms. Current SAR procedures rely on Bayesian techniques and ensemble integrations over uncertain parameters, resulting in probability distribution maps for the lost object's location. This approach, while accounting for uncertainties, can be slow and less precise, especially crucial in time-sensitive situations involving human lives. The challenge lies in developing a readily interpretable tool using key ocean surface dynamics features to narrow down the search area, identifying the most attracting regions for objects fallen in the water (PIW). This research addresses this by utilizing the concept of Objective Eulerian coherent structures (OECSs) and their associated Transient Attracting Profiles (TRAPs). TRAPs, quickly computable from a single velocity field snapshot, reveal the strongest regions of accumulation for floating objects, offering precise information for optimized search-asset allocation. The study uses three field experiments to validate the predictive power of TRAPs in emulating SAR scenarios, comparing results from remotely sensed data and ocean model data.

Existing SAR methods address uncertainties using Bayesian techniques and ensemble integrations, generating probability maps for the lost object's location. However, this approach can be slow and may not provide readily interpretable information for immediate action. Lagrangian coherent structures (LCSs) have been used to predict tracer behavior in geophysical flows, but their application to SAR is limited by the sensitivity to release time, location, observation period, and errors in velocity fields. Traditional Eulerian diagnostics (streamlines, velocity magnitude, etc.) are observer-dependent and unsuitable for robust SAR applications. The study builds upon the recently developed concept of Objective Eulerian Coherent Structures (OECSs) to overcome these limitations. OECSs are observer-independent and provide short-term limits of LCSs, predicting pathways and barriers to material transport. Hyperbolic OECSs, specifically attracting OECSs (TRAPs), identify the strongest short-term attractors.

The study employs the concept of Objective Eulerian Coherent Structures (OECSs) to identify Transient Attracting Profiles (TRAPs) in ocean surface velocity data. TRAPs are computed from a single snapshot of the velocity field and represent the strongest short-term attractors for floating objects. The methodology involves computing the Jacobian of the velocity field, the rate-of-strain tensor, its eigenvalues and eigenvectors. TRAPs are then computed as solutions of an ordinary differential equation (ODE) based on the eigenvector field associated with the largest eigenvalue, ensuring local smoothness and focusing on regions with significant attraction. Three field experiments are conducted south of Martha's Vineyard to validate the TRAP approach. The first experiment uses high-frequency radar (HFR) data to compute TRAPs and track the movement of CODE drifters. The second and third experiments use ocean model velocity data (MIT-MSEAS) assimilating in situ measurements, deploying drifters and manikins to test TRAP predictions. The experiments compare TRAPs with instantaneous streamlines and horizontal divergence fields, demonstrating TRAPs' ability to predict short-term attraction even in regions of positive divergence. A comparison of computational times between the TRAP-based method and traditional SAR planning methods is provided in the supplementary materials.

The study demonstrates that TRAPs accurately predict the short-term attracting regions for objects fallen in the water (PIW) in three distinct field experiments. In the first experiment using HFR data, drifters are observed to align with the computed TRAPs within two hours, with the average drifter-to-TRAP distance decreasing significantly over time. The second and third experiments, using model velocity data, further confirm the predictive power of TRAPs in attracting both drifters and manikins, even when accounting for uncertainties in the initial conditions and model errors. The results show a remarkable robustness of TRAPs under uncertainty; they invariably attract floating objects within two to three hours, regardless of whether inertial or windage effects are considered. Importantly, TRAPs often remain hidden to instantaneous streamlines and horizontal divergence fields, highlighting their unique contribution to SAR. The study demonstrates the superiority of the TRAPs-based approach by showing that even though drifter, manikins, and ensemble trajectories all differ from each other due to uncertainties, they all converge to nearby TRAPs.

The findings demonstrate the significant potential of TRAPs for improving SAR operations. The ability of TRAPs to quickly identify and pinpoint regions of high attraction for floating objects, even under significant uncertainty, offers a substantial advantage over traditional methods. The instantaneous nature of TRAP computation allows for real-time updates, enabling rapid decision-making in emergency situations. Unlike probability maps generated by traditional Bayesian methods, TRAPs offer readily interpretable information for efficient search-asset allocation. The short prediction time scales (two to three hours) are particularly relevant for SAR, where rapid action is critical for successful rescue operations. The robustness of TRAPs under various uncertainties, including model errors and unknown object properties, makes them a valuable tool for emergency response.

This research introduces Transient Attracting Profiles (TRAPs) as a novel and effective tool for enhancing Search and Rescue (SAR) operations at sea. TRAPs provide easily interpretable, localized information about short-term attracting regions, enabling faster and more efficient search-asset allocation. The field experiments confirm the predictive power of TRAPs in various SAR scenarios, demonstrating their robustness under uncertainty and their ability to predict the movement of floating objects within crucial timeframes. Future research could focus on incorporating additional factors like windage, wave effects, and object inertia for improved accuracy and longer-term predictions. Integration of TRAPs into existing SAR systems holds significant promise for saving lives and mitigating the impact of environmental disasters.

While the study demonstrates the effectiveness of TRAPs in short-term predictions (2-3 hours), their predictive power diminishes over longer time scales due to their instantaneous nature. The accuracy of TRAPs is directly dependent on the accuracy of the underlying velocity field data, whether from HFR measurements or ocean models. The experiments were conducted in a specific geographic location, and further research is needed to assess the generalizability of the findings to other oceanographic regions and conditions. The study focused primarily on passive drifters and manikins, and future research could investigate the applicability of TRAPs to objects with greater inertia or complex dynamics.