### Abstract

The capability of using imperfect stochastic reduced-order models to capture crucial passive tracer statistics is investigated. The passive scalar field is advected by a two-layer baroclinic turbulent flow which can generate various representative regimes in atmosphere and ocean. Much simpler and more tractable block-diagonal linear Gaussian stochastic models are proposed to approximate the complex and high-dimensional advection flow equations. The imperfect model prediction skill is improved through a judicious calibration of the model errors using leading order statistics of the background advection flow, while no additional prior information about the passive tracer field is required. A systematic framework of correcting model errors with empirical information theory is introduced, and optimal model parameters under this unbiased information measure can be achieved in a training phase before the prediction. It is demonstrated that crucial principal statistical quantities like the tracer spectrum and fat-tails in the tracer probability density functions in the most important large scales can be captured efficiently with accuracy using the reduced-order tracer model in various dynamical regimes of the flow field with distinct statistical structures. The skillful linear Gaussian stochastic modeling algorithm developed here should also be useful for other applications such as accurate forecast of mean responses and efficient algorithms for state estimation or data assimilation.

Original language | English (US) |
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Pages (from-to) | 17-51 |

Number of pages | 35 |

Journal | Communications in Mathematical Sciences |

Volume | 16 |

Issue number | 1 |

DOIs | |

State | Published - 2018 |

### Keywords

- Intermittency
- Low-order stochastic model
- Passive tracer turbulence

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics