Communications in Mathematical Sciences

Volume 16 (2018)

Number 1

Predicting extreme events for passive scalar turbulence in two-layer baroclinic flows through reduced-order stochastic models

Pages: 17 – 51

DOI: http://dx.doi.org/10.4310/CMS.2018.v16.n1.a2

Authors

Di Qi (Department of Mathematics and Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, N.Y., U.S.A.)

Andrew J. Majda (Department of Mathematics and Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, N.Y., U.S.A.)

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.

Keywords

passive tracer turbulence; intermittency; low-order stochastic model

2010 Mathematics Subject Classification

62B10, 76F25, 86A32

Full Text (PDF format)

Received 26 April 2017

Accepted 7 August 2017

Published 29 March 2018