### Abstract

A new algorithm is suggested for prediction of a Lagrangian particle position in a stochastic flow, given observations of other particles. The algorithm is based on linearization of the motion equations and appears to be efficient for an initial tight cluster and small prediction time. A theoretical error analysis is given for the Brownian flow and a stochastic flow with memory. The asymptotic formulas are compared with simulation results to establish their applicability limits. Monte Carlo simulations are carried out to compare the new algorithm with two others: the center-of-mass prediction and a Kalman filter-type method. The algorithm is also tested on real data in the tropical Pacific.

Original language | English (US) |
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Pages (from-to) | 116-148 |

Number of pages | 33 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 63 |

Issue number | 1 |

DOIs | |

State | Published - Aug 2002 |

### Fingerprint

### Keywords

- Lagrangian motion
- Oceanographic applications
- Prediction
- Stochastic flow
- Stochastic simulations

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**A simple prediction algorithm for the Lagrangian motion in two-dimensional turbulent flows.** / Piterbarg, Leonid I.; Ozgokmen, Tamay M.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 63, no. 1, pp. 116-148. https://doi.org/10.1137/S003613990139194X

}

TY - JOUR

T1 - A simple prediction algorithm for the Lagrangian motion in two-dimensional turbulent flows

AU - Piterbarg, Leonid I.

AU - Ozgokmen, Tamay M

PY - 2002/8

Y1 - 2002/8

N2 - A new algorithm is suggested for prediction of a Lagrangian particle position in a stochastic flow, given observations of other particles. The algorithm is based on linearization of the motion equations and appears to be efficient for an initial tight cluster and small prediction time. A theoretical error analysis is given for the Brownian flow and a stochastic flow with memory. The asymptotic formulas are compared with simulation results to establish their applicability limits. Monte Carlo simulations are carried out to compare the new algorithm with two others: the center-of-mass prediction and a Kalman filter-type method. The algorithm is also tested on real data in the tropical Pacific.

AB - A new algorithm is suggested for prediction of a Lagrangian particle position in a stochastic flow, given observations of other particles. The algorithm is based on linearization of the motion equations and appears to be efficient for an initial tight cluster and small prediction time. A theoretical error analysis is given for the Brownian flow and a stochastic flow with memory. The asymptotic formulas are compared with simulation results to establish their applicability limits. Monte Carlo simulations are carried out to compare the new algorithm with two others: the center-of-mass prediction and a Kalman filter-type method. The algorithm is also tested on real data in the tropical Pacific.

KW - Lagrangian motion

KW - Oceanographic applications

KW - Prediction

KW - Stochastic flow

KW - Stochastic simulations

UR - http://www.scopus.com/inward/record.url?scp=0036706344&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036706344&partnerID=8YFLogxK

U2 - 10.1137/S003613990139194X

DO - 10.1137/S003613990139194X

M3 - Article

AN - SCOPUS:0036706344

VL - 63

SP - 116

EP - 148

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 1

ER -