Researchers: (alphabetic order) - Griffa, Annalisa1,2 - Mariano, Arthur1 - Özgökmen, Tamay1 - Piterbarg, Leonid3 - 1RSMAS, Miami - 2CNR, Italy - 3USC, Los Angeles Sponsors: - ONR Publications: - 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. Two problems have been considered in the framework of the problem of particle predictability: a) Methods to improve 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). Tests using historical drifters in the Adriatic Sea (Fig. 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. b) Study of the effects of smoothing of the Eulerian velocity field on particle prediction. Despite the increasing realism of ocean circulation models, there is still a significant gap between the spatial scales of model resolution and that of forces acting on Lagrangian particles and influencing their motion. This is studied considering a turbulent quasi-geostrophic (QG) field smoothed in space (Fig. 3), 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. 4) that i) CM trajectories are strongly dependent on smoothing, and ii) LS results provide a good qualitative descriptions of the errors. Figures: Figure 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 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). Figure 3 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 4 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.