Observing and quantifying kinematic properties and lagrangian coherent structures of ocean flows using drifter experiments

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2021.This thesis analyzes data from two types of unique drifter experiments in order to characterize two aspects of ocean flows that are often difficult to study. First, vertical velocities and their associated transport processes are often challenging to observe in the real ocean since vertical velocities are typically orders of magnitude smaller than horizontal velocities in mesoscale and submesoscale flows. Second, Lagrangian coherent structures (LCS) are features which categorize ocean flows into regimes of distinct behavior. These structures are also difficult to quantify in the real ocean, since sets of gridded trajectories from real ocean data (rather than model fields) are rarely available. The first experiment uses drifters drogued at multiple depths in the Alboran Sea to observe and characterize the ocean’s vertical structure, particularly near a strong front where vertical velocities are expected to be much stronger than other regions of the Ocean. The second experiment uses a roughly gridded pattern of surface drifters in the Gulf of Mexico to study LCSs as quantified by methods from dynamical systems such as finitetime Lyapunov exponents (FTLEs), trajectory arc-length, correlation dimension, dilation, Lagrangian-averaged vorticity deviation (LAVD), and spectral clustering. This thesis includes the first attempt to apply these dynamical systems techniques to real drifters for LCS detection. Overall, these experiments and the methods used in this paper are shown to be promising new techniques for quantifying both the vertical structure of ocean flows and Lagrangian Coherent Structures of flows using real drifter data. Future work may involve modified versions of the experiments, with denser sets of ocean drifters in the horizontal and/or vertical directions.My Masters studies in the MIT/WHOI Joint Program were funded by the US Navy Civilian Institution Office

Applying dynamical systems techniques to real ocean drifters

This paper presents the first comprehensive comparison of several different dynamical-systems-based measures of stirring and Lagrangian coherence, computed from real ocean drifters. Seven commonly used methods (finite-time Lyapunov exponent (FTLE), trajectory path length, trajectory correlation dimension, trajectory encounter volume, Lagrangian-averaged vorticity deviation, dilation, and spectral clustering) were applied to 144 surface drifters in the Gulf of Mexico in order to map out the dominant Lagrangian coherent structures. Among the detected structures were regions of hyperbolic nature resembling stable manifolds from classical examples, divergent and convergent zones, and groups of drifters that moved more coherently and stayed closer together than the rest of the drifters. Many methods highlighted the same structures, but there were differences too. Overall, five out of seven methods provided useful information about the geometry of transport within the domain spanned by the drifters, whereas the path length and correlation dimension methods were less useful than others.</p

Observing and Quantifying Kinematic Properties and Lagrangian Coherent Structures of Ocean Flows using Drifter Experiments

This thesis analyzes data from two types of unique drifter experiments in order to characterize two aspects of ocean flows that are often difficult to study. First, vertical velocities and their associated transport processes are often challenging to observe in the real ocean since vertical velocities are typically orders of magnitude smaller than horizontal velocities in mesoscale and submesoscale flows. Second, Lagrangian coherent structures (LCS) are features which categorize ocean flows into regimes of distinct behavior. These structures are also difficult to quantify in the real ocean, since sets of gridded trajectories from real ocean data (rather than model fields) are rarely available. The first experiment uses drifters drogued at multiple depths in the Alboran Sea to observe and characterize the ocean’s vertical structure, particularly near a strong front where vertical velocities are expected to be much stronger than other regions of the Ocean. The second experiment uses a roughly gridded pattern of surface drifters in the Gulf of Mexico to study LCSs as quantified by methods from dynamical systems such as finitetime Lyapunov exponents (FTLEs), trajectory arc-length, correlation dimension, dilation, Lagrangian-averaged vorticity deviation (LAVD), and spectral clustering. This thesis includes the first attempt to apply these dynamical systems techniques to real drifters for LCS detection. Overall, these experiments and the methods used in this paper are shown to be promising new techniques for quantifying both the vertical structure of ocean flows and Lagrangian Coherent Structures of flows using real drifter data. Future work may involve modified versions of the experiments, with denser sets of ocean drifters in the horizontal and/or vertical directions.S.M

Observing and quantifying ocean flow properties using drifters with drogues at different depths

Author Posting. © American Meteorological Society, 2021. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 51(8),(2021): 2463–2482, https://doi.org/10.1175/JPO-D-20-0291.1.This paper presents analyses of drifters with drogues at different depths—1, 10, 30, and 50 m—that were deployed in the Mediterranean Sea to investigate frontal subduction and upwelling. Drifter trajectories were used to estimate divergence, vorticity, vertical velocity, and finite-size Lyapunov exponents (FTLEs) and to investigate the balance of terms in the vorticity equation. The divergence and vorticity are O(f) and change sign along trajectories. Vertical velocity is O(1 mm s−1), increases with depth, indicates predominant upwelling with isolated downwelling events, and sometimes changes sign between 1 and 50 m. Vortex stretching is one of the significant terms, but not the only one, in the vorticity balance. Two-dimensional FTLEs are 2 × 10−5 s−1 after 1 day, 2 times as large as in a 400-m-resolution numerical model. Three-dimensional FTLEs are 50% larger than 2D FTLEs and are dominated by the vertical shear of horizontal velocity. Bootstrapping suggests uncertainty levels of ~10% of the time-mean absolute values for divergence and vorticity. Analysis of simulated drifters in a model suggests that drifter-based estimates of divergence and vorticity are close to the Eulerian model estimates, except when drifters get aligned into long filaments. Drifter-based vertical velocity is close to the Eulerian model estimates at 1 m but differs at deeper depths. The errors in the vertical velocity are largely due to the lateral separation between drifters at different depths and are partially due to only measuring at four depths. Overall, this paper demonstrates how drifters, heretofore restricted to 2D near-surface observations, can be used to learn about 3D flow properties throughout the upper layer of the water column.Authors Rypina and Pratt were supported by U.S. Office of Naval Research (ONR) Grant N000141812417. Author Getscher acknowledges support from the U.S. Navy Civilian Institution Office with the MIT–WHOI Joint Program. Author Mourre acknowledges support from ONR Grant N00014-16-1-3130. We also thank Eugenio Cutolo for the initial technical support in the implementation of the ultra-high-resolution WMOP simulation. CALYPSO is a Departmental Research Initiative funded by the ONR.2022-01-1