Direct statistical simulation of Lorenz96 system in model reduction approaches

TL;DR

This paper explores two methods to reduce the computational complexity of direct statistical simulation for the Lorenz-96 system, enabling efficient and accurate statistical analysis of complex dynamical systems.

Contribution

It introduces two dimensionality reduction techniques for DSS using approximate closures, demonstrated through numerical experiments on Lorenz-96.

Findings

Significant reduction in computational effort achieved.

Accuracy of DSS maintained despite dimensionality reduction.

Methods applicable to turbulent fluid and magnetohydrodynamical systems.

Abstract

Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations (DNS) by solving the equations that govern the statistics themselves. DSS suffers, however, from the curse of dimensionality as the statistics (such as correlations) generally have higher dimension than the underlying dynamical variables. Here we investigate two approaches to reduce the dimensionality of DSS, illustrating each method with numerical experiments with the Lorenz-96 dynamical system. The forms of DSS chosen here involve approximate closures at second and third order in the equal time cumulants. We demonstrate significant reduction in computational effort that can be achieved without sacrificing the accuracy of DSS. The methods developed here can be applied to turbulent fluid and magnetohydrodynamical systems.