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Abstract
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In this study we investigate a data-driven stochastic methodology to parametrize
small-scale features in a prototype multiscale dynamical system, the Lorenz ’96
(L96) model. We propose to model the small-scale features using a vector
autoregressive process with exogenous variables (VARX), estimated from
given sample data. To reduce the number of parameters of the VARX we
impose a diagonal structure on its coefficient matrices. We apply the VARX to
two different configurations of the 2-layer L96 model, one with common
parameter choices giving unimodal invariant probability distributions for the
L96 model variables, and one with nonstandard parameters giving trimodal
distributions. We show through various statistical criteria that the proposed VARX
performs very well for the unimodal configuration, while keeping the number
of parameters linear in the number of model variables. We also show that
the parametrization performs accurately for the very challenging trimodal
L96 configuration by allowing for a dense (nondiagonal) VARX covariance
matrix.
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Keywords
stochastic parametrization, constrained autoregressive
models, linear number parameters, multiscale modeling,
Lorenz '96
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Mathematical Subject Classification 2010
Primary: 62F30, 60H10, 65C20, 68U20, 70K70
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Milestones
Received: 29 July 2019
Revised: 24 July 2020
Accepted: 13 September 2020
Published: 19 January 2021
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