Stochastic parameterization with VARX processes

TL;DR

This paper introduces a data-driven stochastic parameterization method using VARX processes to model small-scale features in the Lorenz '96 system, demonstrating high accuracy in different distribution scenarios.

Contribution

It proposes a novel VARX-based stochastic parameterization approach with a diagonal structure to efficiently model multiscale dynamical systems.

Findings

Performs well for unimodal distributions with linear parameters.

Accurately models trimodal distributions with a dense covariance matrix.

Maintains linear parameter growth relative to the number of variables.

Abstract

In this study we investigate a data-driven stochastic methodology to parameterize 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 variable (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 non-standard 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 parameterization performs accurately for the very challenging trimodal L96 configuration by allowing for a dense (non-diagonal) VARX covariance matrix.