Short-Term Prediction of Lagrangian Trajectories

Abstract

Lagrangian particles in a cluster are divided in two groups: observable and unobservable. The problem is to predict the unobservable particle positions given their initial positions and velocities based on observations of the observable particles. A Markov model for Lagrangian motion is formulated. The model implies that the positions and velocities of any number of particles form a multiple diffusion process. A prediction algorithm is proposed based on this model and Kalman filter ideas. The algorithm performance is examined by the Monte Carlo approach in the case of a single predictand. The prediction error is most sensitive to the ratio of the velocity correlation radius and the initial cluster radius. For six predictors, if this parameter equals 5, then the relative error is less than 0.1 for the 15-day prediction, whereas for the ratio close to 1, the error is about 0.9. The relative error does not change significantly as the number of predictors increases from 4?7 to 20.