Researchers: (alphabetic order) - Haza, Angelique1 - Griffa, Annalisa1,2 - Mariano, Arthur1 - Molcard, Anne3 - Özgökmen, Tamay1 - Piterbarg, Leonid4 - Poje, Andrew5 - Poulain, Pierre6 - Ricsen, Michel7 - 1RSMAS, Miami - 2CNR- ISMAR, Sp, Italy - 3LSEET, Toulon, Fr - 4USC, Los Angeles - 5CUNY, New York - 6OGS, Tr, Italy - 7NURC, NATO Sponsors: - ONR Publications: - A.C. Haza, A.C. Poje, P. Martin, T.M. Ozgokmen, 2008: Relative dispersion from a high resolution coastal model of the Adriatic Sea. Ocean Modelling, 22, 48-65. - Haza, A., A. Griffa, P. Martin, A. Molcard, T.M. Ozgokmen, A.C. Poje, R. Barbanti, J. Book, P.M. Poulain, M. Rixen, and P. Zanasca, 2007: Model-based directed drifter launches in the Adriatic Sea: Results from the DART experiment. Geophys. Res. Letters, 34, L10605, doi:10.1029/2007GL029634. - Piterbarg, L.I., T.M. Özgökmen, A. Griffa, and A.J. Mariano, 2007: Predictability of Lagrangian motion in the upper ocean. In: Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics, Eds: A. Griffa, A.D. Kirwan, A.J. Mariano, T.M. Özgökmen and T. Rossby , Cambridge University Press, 500 pg. - Griffa A., L.I. Piterbarg and T.M. Özgökmen, 2004: Predictability of Lagrangian particle trajectories: effects of uncertainty in the underlying Eulerian flow. J. Mar. Res., 62, 1-35. - Piterbarg, L.I., and T.M. Özgökmen, 2002: A simple prediction algorithm for the Lagrangian motion in 2D turbulent flows. SIAM J. Appl. Math., 63/1, 116-148. - Castellari, S., A. Griffa, T.M. Özgökmen and P.-M. Poulain, 2001: Prediction of particle trajectories in the Adriatic Sea using Lagrangian data assimilation. J. Mar. Sys., 29, 33-50. - Özgökmen, T.M., L.I. Piterbarg, A.J. Mariano, and E.H. Ryan, 2001: Predictability of drifter trajectories in the tropical Pacific Ocean. J. Phys. Oceanogr., 31/9, 2691-2720. - Özgökmen, T.M., A. Griffa, A.J. Mariano and L.I. Piterbarg, 2000: On the predictability of Lagrangian trajectories in the ocean. J. Atmos. Ocean. Tech., 17/3, 366-383.

Predicting particle trajectories in the ocean is of practical importance for problems such as searching for objects lost at sea, tracking floating mines, and studying ecological issues such as spreading of pollutants and fish larvae and designing oceanic observing systems. It is well known that prediction of particle motion is an intrinsically difficult problem because Lagrangian motion often exhibits chaotic behavior, even in regular and simple Eulerian flows. Chaos implies strong dependence on initial conditions, which are usually not known with great accuracy, so that the task of predicting particle motion is often extremely difficult. Also, velocity errors accumulate as errors of prediction position, further reducing the limits of predictability. Various methods have been developed to improve predictability, and applications have been performed to coastal and open ocean flows.  1) Improving predictability using simultaneous Lagrangian information  2) Effects of smoothing of the Eulerian velocity field on particle prediction  3) Directed drifter launches using a high resolution model and Finite Size Lyapunov Exponents 1. Improving predictability using simultaneous Lagrangian information It is hard to give a reasonable particle prediction based only on the imprecise knowledge of the current, either from model simulations or from historical knowledge of mean currents in a certain area. One can expect a real help from the knowledge of other floating objects in the same area. For example, in practical applications such as search and rescue, or mine detections, ad-hoc launches of drifting buoys can be envisioned, which can be directly observed from planes or satellites. A method to use these additional information has been developed, in the framework of Lagrangian Stochastic (LS) models, where the velocity of a particle is decomposed in a large scale deterministic component (assumed known) and a velocity fluctuation described by a stochastic differential equation. The knowledge of the velocity fluctuation is constrained by the knowledge of the nearby trajectories. The methodology has been tested using historical drifter clusters. One of the drifters, called the "predictand", is assumed to be unobservable, while the remaining drifters, called the "predictors", are observed. The problem is to predict the position of the unobservable drifter at any time given its initial position (known with an initial error) and the predictor observations (Fig. 1.1). Tests using historical drifters in the Adriatic Sea (Fig. 1.2) and in the Tropical Pacific have been performed. They show that the method is very effective, provided that there is at least one predictor in a circle of radius R (Rossby radius of deformation) from the predictand. Figure 1.1 Schematic illustration of particle prediction using simultaneous information. The blue line represents the unobserved trajectory ("predictand"), whose initial position is known within an error of radius dr. The red lines represent the observed "predictors", which are used to reconstruct the unobserved trajectory. Figure 1.2: Example of particle prediction applied to drifter clusters in the Adriatic Sea (Mediterranea Sea). The complete drifter data set is shown in the upper panel, while the prediction results using a 5 drifter cluster are shown in the 2 lower panel. In the left panel, the reconstructed trajectory (dotted) is compared with the observed one (solid) and with an estimate obtained using only historical information on the mean flow (dashed). In the right panel, the prediction error (solid) is compared with the error using only the mean flow (dotted) and with the dispersion (dashed). 2. Effects of smoothing of the Eulerian velocity field on particle prediction Despite the increasing realism of ocean circulation models, often there is still a significant gap between the spatial scales of model resolution and that of forces acting on Lagrangian particles, especially when considering large scale ocean models. This is studied considering a turbulent quasi-geostrophic (QG) field smoothed in space (Fig. 2.1), and releasing particle clusters in the different fields obtained with different smoothing scales. The particle statistics are compared, in terms of trajectories of center of mass (CM) and in terms of average spreading. Parameterizations using LS models are considered. The results show (Fig. 2.2) that i) CM trajectories are strongly dependent on smoothing, and ii) LS results provide a good qualitative descriptions of the errors. Figure 2.1 Impact of smoothing on the results of a quasi-geostrophic (QG) model. The smoothing scale h is increased (left to right and top to bottom panels) from h=20 km to h= 600 km. Figure 2.2 Errors on the position of cluster center of mass (CM) due to progressive smoothing for the QG solutions (upper panel) and for the LSM solutions (lower panels). Results for smoothing scales h=20, 50 are indicated with a blue and red line respectively. Qualitative agreement between QG and LSM results is shown. 3. Directed drifter launches using a high resolution model and Finite Size Lyapunov Exponents during the DART experiment While single particle trajectories are very difficult to accurately predict, the main Lagrangian structures controlling transport processes appear to be more robust to diagnose, still providing crucial information about particle transport. A number of new methods based on dynamical system theory have been put forth to identify these structures (e.g. Haller and Poje, 1998; Shadden et al., 2005), and they are now mature for applications. During The 2006 DART experiment in the Adriatic Sea, a high-resolution numerical model (NCOM) has been used in real time to predict Lagrangian coherent structure boundaries, quantified by finite-size Lyapunov exponents (FSLE) (Haza et al., 2007). Flow features in the region of the Gargano Peninsula have been targeted. FSLE fields computed from two-day model forecasts of the surface velocity indicate distinct regions of high relative drifter dispersion (Fig.3.1). Model predictions of such regions located on available ship-tracks were used to direct the launching of pairs of drifters on three days during March 2006, with the goal of maximize coverage of the sampling area (Fig.3.2). For two of the three launches, the observed trajectories separated at locations and along directions closely approximated by those predicted from the model FSLE fields. The third case acted as an inadvertent control experiment. Model predictions at release-time showed minimal FSLE structure at the launch locations and the observed drifter pair advected in a coherent fashion for two days. While there are considerable differences between individual drifter observations and trajectory envelopes computed from ensembles of synthetic drifters, the experiment confirms the model's ability to approximate the location and shape of energetic flow features controlling the near-time fate of quasi-Lagrangian particles. Overall, the combined use of FSLEs with high-resolution, realistic coastal circulation models appears to be a promising avenue to aid real-time-directed drifter launches in observational programs. Figure 3.1: The location of the DART experiment domain within the Adriatic Sea (right panel) and the forecasted surface NCOM model velocity field on March 15, 2006 in the DART region (left panel). Superimposed are the 2-day model based FSLE field , the ship track (regular line) and the location of a hyperbolic point determined by the intersection of in-flowing/stable (blue) and out flowing/unstable (red) FSLE branches (green circle). Figure 3.2: The initial 2-day trajectories for real (gray: upper panels, green and purple: lower panels) drifters launched on March 16, March 19 and March 23 (launch position indicated by circles). Superimposed are the FSLE computed at launch time (a)-(c), and synthetic drifters released in regular arrays (d)-(f). Red (blue) dots indicate initial (final positions .