U. of Delaware College of Earth, Ocean, and Environment


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Helga S. Huntley's Research

Lagrangian Ocean Dynamics

Lagrangian Analysis: A Summary

Our research group has been studying Lagrangian structures in the ocean, their associated transport properties, their evolution, and their predictability. This work is carried out in the context of the practical problems of optimizing deployment strategies for drifting sensors and autonomous underwater vehicles, but addresses more fundamental issues of ocean transport mechanisms as well.

Most ocean models these days are Eulerian in nature. Validation is performed using Eulerian data, and reasonably good agreement with Eulerian fields can be expected from state-of-the-art data assimilating models. Yet many of the questions these models attempt to answer are of fundamentally Lagrangian nature: Ultimately, not the velocity field itself, but the origin and fate of particles are the goal. Unfortunately, intuition built on an instantaneous snapshot of the velocity field or even on an evolving series of them can be misleading for determining particle trajectories. An alternative, and possibly more relevant, method of model validation then is to evaluate the model's predicted drifter trajectories. This is inherently a harsher test, since the integration of model velocities leads to cumulative errors, which, given the chaotic nature of the ocean, can lead to fast divergence between observation and simulation. Moreover, model resolution is limited, so that some of the processes affecting in situ drifters are not represented at all or only in form of a parameterization in the model.

Dynamical systems theory suggests that Lagrangian predictability is not uniform across the ocean. In fact, it is possible, at least in theory, to locate so-called "critical" trajectories (also known as distinguished hyperbolic trajectories) with inflowing stable and outflowing unstable manifolds, which separate regions of exponentially divergent flow. Drifters launched near such a hyperbolic region would be particularly challenging to track. Some of the issues and challenges related to finding and analyzing critical trajectories are outlined in Mancho et al., 2006, and Kirwan, 2006.

Lagrangian Predictability

(In collaboration with Denny Kirwan, Jr. and Bruce Lipphardt, Jr..)

In recent work, we have evaluated the performance of one of the Navy's operational models (EAS16) in terms of Lagrangian predictions. The data set consists of thirty drifters launched within a fairly small area of the East China Sea and within four days of each other in early October 2007. Locations for these drifters are logged at roughly fifteen minute intervals. Each trajectory is simulated in the model by integrating a linearly interpolated velocity field. The most straight-forward metric for evaluating the forecast is separation distance between observation and simulation after a set time. Even within this relatively similar (in launch space and time) group, there is large variation, with an average of about 17 km after one day and 29 km after two days, but a range of 2-50 km and 0-120 km, respectively. A more complex metric is time-in-circle, which attempts to account for initial position uncertainty by following a circle of trajectories centered initially at the drifter's launch time and recording the time when the observation leaves this envelope. Again, wide variation was found, with a mean of around 25 hours for a circle with initial radius 15 km. By grouping the drifters into subsets organized by launch time or launch location, it is possible to distinguish some of the factors influencing the predictability. Thus, for example, drifters launched near the Kuroshio Current were noticeably harder to track than those further away. Similarly, trajectories started shortly after an extreme weather event turned out to be less predictable. Eulerian forecasts, like the Lagrangian ones, lose accuracy near extreme weather events or strong features such as the Kuroshio. However, an Eulerian analysis of the same data shows that an unusually poor velocity prediction does not necessarily lead to an unusually low time-in-circle, or vice versa. To study the effects of resolution, we repeated the analysis with a coarsened model database, aware that the underlying dynamics remain resolved at the original 6 km resolution. The separation statistics and times-in-circle are remarkably insensitive to such database decimation. The results are similar for coarsening in time, up to the tidal frequency.

While there are clear limitations to the predictability of individual drifter trajectories, the larger picture of Lagrangian statistics may be valuable for identifying regions of the ocean that exhibit particular characteristics, such as being especially dispersive or acting as a channeling "highway" for particles. The Lagrangian behavior of many particles can be presented concisely in the form of synoptic Lagrangian maps, depicting such metrics as residence time or escape fate. (The concept was introduced by Lipphardt et al., 2006, using radar data from Monterrey Bay.) We used the EAS16 model to generate a series of maps of residence time, escape fate, trajectory length, and similar quantities. Interestingly, some features can be traced across different maps. For example, thin lines of high residence time (as opposed to centers of eddies) tend to correspond not only to longer trajectory length but also to a curve of particles separating broad regions of similar escape fate. At the same time, these structures cannot be detected in an Eulerian velocity field.

This research leads to interesting questions about the interpretation of structures in the synoptic Lagrangian maps and their relationship on the one hand with dynamical systems concepts such as critical trajectories and manifolds and on the other hand with observed features in satellite imagery. A current project seeks to find some answers. We have started applying this type of analysis to the Deepwater Horizon oil spill in the Gulf of Mexico in spring 2010 to explore the predictability of the oil slick's movement.

Lagrangian Data Assimilation

(In collaboration with Denny Kirwan, Jr., Bruce Lipphardt, Jr., Pat Hogan, Tamay Özgökmen, Annalisa Griffa, Yeon Chang, Angelique Haza, David Hammond, and Vincent Taillandier.)

To extend the Lagrangian predictability, it is possible to assimilate Lagrangian data into a model. In collaboration with scientists at several other institutions, we have investigated the effect of blending surface drifter tracks with a general circulation model on sonobuoy trajectory forecasts. We implemented two different methods, one a variational approach and one based on normal mode decomposition. Significant improvement in the predictions was found, reducing the total rms error by approximately 50% and 25% for the two methods, respectively. Neither method has been optimized, however, and future studies will likely lead to even better results. In addition, I plan to investigate further the effectiveness of assimilating different aspects of observed drifter trajectories. In the current project, we have used trajectory-derived velocities and end positions. It is also possible to extract such characteristics as path length or complexity, which has not been done before but could provide richer information for the model to ingest.

Lagrangian Analysis in 4D

(In collaboration with many other scientists...)

In a related effort, we are dealing with the issues around extending primarily three-dimensional (two in space, plus time) Lagrangian analyses to the full four-dimensional problem. In the initial stage, we are focusing on eddy dynamics and applying Eulerian and Lagrangian tools to study their birth, evolution and break-down processes, mainly in the Gulf of Mexico. Our group is also investigating how to extend Lagrangian analyses to ensemble model runs, which have proven to be more reliable in Eulerian metrics.

Oil Spill Modeling

(As a member of the CARTHE consortium)

The Consortium for Advanced Research on Transport of Hydrocarbon in the Environment is a broad coalition of scientists interested in improving the prediction capability for the next oil spill or a similar disaster. In this context, we are pursuing mutiple directions of research, including probabilistic forecasts and why things cluster. In the summer of 2012, CARTHE conducted a large field experiment, releasing more than 300 surface drifters. This data set has proven to be immensely rich, and much of our recent work has focused on analyzing it.

References

Kirwan, A.D., Jr., Dynamics of "critical" trajectories, Prog. Oceanogr., 70, 448-465, 2006.

Lipphardt, B.L., Jr., D. Small, A.D. Kirwan, Jr., S. Wiggins, K. Ide, C.E. Grosch, and J.D. Paduan, Synoptic Lagrangian maps: Application to surface transport in Monterey Bay, J. Mar. Res., 62, 221-247, 2006.

Mancho, A., D. Small, and S. Wiggins, A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues, Physics Reports, 437, 55-124, 2006.

Related publications

Jacobs, G., H.S. Huntley, A.D. Kirwan, Jr., B.L. Lipphardt, Jr., T. Campbell, T. Smith, K. Edwards, and B. Bartels, 2015: Ocean processes underlying surface clustering, J. Geophys. Res. Oceans, under review.

Huntley, H.S., B.L. Lipphardt, Jr., G. Jacobs, and A.D. Kirwan, Jr., 2015: Clusters, deformation, and dilation: Diagnostics for material accumulation regions, J. Geophys. Res. Oceans, doi: 10.1002/2015JC011036, 120.

Muscarelli, P., M. Carrier, H. Ngodock, S. Smith, B.L. Lipphardt, Jr., A.D. Kirwan, Jr., and H.S. Huntley, 2015: Do assimilated drifter velocities improve Lagrangian predictability in an operational ocean model?, Mon. Weather Rev., doi: 10.1175/MWR-D-14-00164.1, 143, 1822--1832.

Coelho, E.F., P. Hogan, G. Jacobs, P. Thoppil, H.S. Huntley, B. Haus, B.L. Lipphardt, Jr., A.D. Kirwan, Jr., E. Ryan, M.J. Olascoaga, F.J. Beron-Vera, A. Poje, A. Griffa, T.M. Özgökmen, A.J. Mariano, G. Novelli, A.C. Haza, D. Bogucki, S.S. Chen, M. Curcic, M. Iskandarani, F. Judt, N. Laxague, A.J.H.M. Reniers, A. Valle-Levinson, and M. Wei, 2015: Ocean current estimation using a multi-model ensemble Kalman filter during the Grand LAgrangian Deployment experiment (GLAD), Ocean Model., doi: 10.1016/j.ocemod.2014.11.001, 87, 86--106.

Özgökmen, T.M., F.J. Beron-Vera, D. Bogucki, S. Chen, C. Dawson, W. Dewar, A. Griffa, B. Haus, A.C. Haza, H.S. Huntley, M. Iskandarani, G. Jacobs, B. Jagers, A.D. Kirwan, Jr., N. Naxague, B.L. Lipphardt, Jr., J. MacMahan, A.J. Mariano, M.J. Olascoaga, G. Novelli, A.C. Poje, A.J.H.M. Reniers, J.M. Restrepo, B. Rosenheim, E.H. Ryan, C. Smith, A. Soloviev, S. Venkataramani, G.-C. Zha, and P. Zhu, 2014: Research overview of the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE), Intl Oil Spill Conf., doi: 10.7901/2169-3358-2014.1.544, 2014(1), 544--560.

Poje, A.C., T.M. Özgökmen, B.L. Lipphardt, Jr., B. Haus, E. Ryan, A.C. Haza, G. Jacobs, A.J.H.M. Reniers, M.J. Olascoaga, G. Novelli, A. Griffa, F.J. Beron-Vera, S. Chen, E.F. Coelho, P.J. Hogan, A.D. Kirwan, Jr., H.S. Huntley, and A. Mariano, 2014: Submesoscale dispersion in the vicinity of the Deepwater Horizon spill, PNAS, doi: 10.1073/pnas.1402452111, 111(35), 12693--12698.

Olascoaga, M.J., F.J. Beron-Vera, G. Haller, J. Triñanes, M. Iskandarani, E.F. Coelho, B. Haus, H.S. Huntley, G. Jacobs, A.D. Kirwan. Jr., B.L. Lipphardt, Jr., T. Özgökmen, A.J.H.M. Reniers, and A. Valle-Levinson, 2013: Drifter motion in the Gulf of Mexico constrained by altimetric Lagrangian coherent structures, Geophys. Res. Lett., doi: 10.1002/2013GL058624, 40(23), 6171--6175.

Sulman, M.H.M., H.S. Huntley, B.L. Lipphardt, Jr., G. Jacobs, P. Hogan, and A.D. Kirwan, Jr., 2013: Hyperbolicity in temperature and flow fields during the formation of a Loop Current ring, Nonlin. Processes Geophys., doi: 10.5194/npg-20-883-2013, 20(5), 883-892.

Sulman, M.H.M., H.S. Huntley, B.L. Lipphardt, Jr., and A.D. Kirwan, Jr., 2013: Leaving flatland: Diagnostics for Lagrangian coherent structures in three-dimensional flows, Physica D, doi: 10.1016/j.physd.2013.05.005, 258, 77-92.

Sulman, M.H.M., H.S. Huntley, B.L. Lipphardt, Jr., and A.D. Kirwan, Jr., 2013: Out of flatland: Three-dimensional aspects of Lagrangian transport in geophysical fluids, in Lagrangian Modeling fo the Atmosphere, Geophys. Monogr. Ser., vol. 200, edited by J. Lin et al., AGU, doi:10.1029/2012GM001279, 77-84.

Huntley, H.S., B.L. Lipphardt, Jr., and A.D. Kirwan, Jr., 2011: Surface drift predictions of the Deepwater Horizon spill: The Lagrangian perspective, in Monitoring and Modeling the Deepwater Horizon Oil Spill: A Record-Breaking Enterprise, Geophys. Monogr. Ser., vol. 195, edited by Y. Liu et al., AGU, doi:10.1029/2011GM001097, 179-195.

Chang, Y., D. Hammond, A.C. Haza, P. Hogan, H.S. Huntley, A.D. Kirwan, Jr., B.L. Lipphardt, Jr., V. Taillandier, A. Griffa, and T.M. Özgökmen, 2011: Enhanced estimation of sonobuoy trajectories by velocity reconstruction with near-surface drifters, Ocean Model., doi: 10.1016/j.ocemod.2010.11.002, 36, 179-197.

Huntley, H.S., B.L. Lipphardt, Jr., and A.D. Kirwan, Jr., 2011: Lagrangian predictability assessed in the East China Sea, Ocean Model., doi: 10.1016/j.ocemod.2010.11.001, 36, 163-178.


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