On the predictability of Lagrangian trajectories in the ocean

Abstract

The predictability of particle trajectories in oceanic flows is investigated in the context of a primitive equation, idealized, double-gyre ocean model. This study is motivated not only by the fact that this is an important conceptual problem but also by practical applications, such as searching for objects lost at sea, and ecological problems, such as the spreading of pollutants or fish larvae. The original aspect of this study is the use of Lagrangian drifter data to improve the accuracy of predicted trajectories. The prediction is performed by assimilating velocity data from the surrounding drifters into a Gauss-Markov model for particle motion. The assimilation is carried out using a simplified Kalman filter. The performance of the prediction scheme is quantified as a function of a number of factors: 1) dynamically different flow regimes, such as interior gyre, western boundary current, and midlatitude jet regions; 2) density of drifter data used in assimilation; and 3) uncertainties in the knowledge of the mean flow field and the initial conditions. The data density is quantified by the number of data per degrees of freedom N(R), defined as the number of drifters within the typical Eulerian space scale from the prediction particle. The simulations indicate that the actual World Ocean Circulation Experiment sampling (1 particle/[5°X 5°] or N(R) << 1) does not improve particle prediction, but predictions improve significantly when N(R) >> 1. For instance, a coverage of 1 particle/[1°X 1°] or N(R) ~ O(1) is already able to reduce the errors of about one-third or one-half. If the sampling resolution is increased to 1 particle/[0.5°X 0.5°] or 1 particle/[0.25°X 0.25°] or N(R) >> 1, reasonably accurate predictions (rms errors of less than 50 km) can be obtained for periods ranging from one week (western boundary current and midlatitude jet regions) to three months (interior gyre region). Even when the mean flow field and initial turbulent velocities are not known accurately, the information derived from the surrounding drifter data is shown to compensate when N(R) > 1. Theoretical error estimates are derived that are based on the main statistical parameters of the flow field. Theoretical formulas show good agreement with the numerical results, and hence, they may serve as useful a priori estimates of Lagrangian prediction error for practical applications.