Stochastic parameterization with VARX processes
This work addresses the challenge of efficiently modeling multiscale dynamics in climate or fluid systems, but it is incremental as it builds on existing stochastic parameterization methods.
The authors tackled the problem of parameterizing small-scale features in the multiscale Lorenz '96 model by proposing a data-driven stochastic method using a vector autoregressive process with exogenous variable (VARX). They showed that the VARX performs very well for a unimodal configuration with linear parameter scaling and accurately handles a challenging trimodal configuration with a dense covariance matrix.
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.