Stochastic model reduction: convergence and applications to climate equations

TL;DR

This paper develops a stochastic model reduction framework for infinite-dimensional evolution equations, proving convergence results and applying them to climate modeling equations.

Contribution

It introduces a convergence analysis for stochastic model reduction in infinite dimensions, including applications to climate equations.

Findings

Proved weak and strong convergence of reduced models.

Applied the theoretical results to climate-related equations.

Established conditions for convergence depending on noise interactions.

Abstract

We study stochastic model reduction for evolution equations in infinite dimensional Hilbert spaces, and show the convergence to the reduced equations via abstract results of Wong-Zakai type for stochastic equations driven by a scaled Ornstein-Uhlenbeck process. Both weak and strong convergence are investigated, depending on the presence of quadratic interactions between reduced variables and driving noise. Finally, we are able to apply our results to a class of equations used in climate modeling.