Ensemble Averaging for Dynamical Systems under Fast Oscillating Random Boundary Conditions

TL;DR

This paper establishes a theoretical foundation for ensemble forecasting in dynamical systems with rapidly fluctuating random boundary conditions and body forcing, using stochastic PDEs and mixing conditions.

Contribution

It proves ensemble averaging principles under mixing conditions and characterizes the deviation process as a linear stochastic PDE.

Findings

Ensemble averaging principles are validated for systems with fast oscillating randomness.

The deviation process is explicitly characterized as a linear stochastic PDE.

The approach provides a rigorous theoretical basis for ensemble forecasting under stochastic boundary conditions.

Abstract

This paper is devoted to provide a theoretical underpinning for ensemble forecasting with rapid fluctuations in body forcing and in boundary conditions. Ensemble averaging principles are proved under suitable `mixing' conditions on random boundary conditions and on random body forcing. The ensemble averaged model is a nonlinear stochastic partial differential equation, with the deviation process (i.e., the approximation error process) quantified as the solution of a linear stochastic partial differential equation.