Warning Signs for Boundary Noise and their Application to an Ocean Boussinesq Model

TL;DR

This paper develops early-warning signs for boundary noise-induced bifurcations in stochastic PDE models, with a focus on an ocean Boussinesq model, using autocovariance and autocorrelation analysis.

Contribution

It introduces new analytical tools for detecting bifurcations in SPDEs with boundary noise and demonstrates their application to an ocean Boussinesq model.

Findings

Autocovariance and autocorrelation serve as reliable early-warning signs.

Analytic results extend previous work on stochastic bifurcations.

Numerical simulations confirm the effectiveness of the proposed signs.

Abstract

In this paper, we construct and discuss early-warning signs of the approach of a parameter to a deterministic bifurcation on a stochastic partial differential equation (SPDE) model with Gaussian white-noise on the boundary. We specifically focus on the qualitative behaviour of the time-asymptotic autocovariance and autocorrelation of the solutions of the linearized system. We also discuss the reliability of the tools from an analytic perspective and through various examples. Among those, the application of the early-warning signs for an ocean Boussinesq model is explored through numerical simulations. The analytic results obtained expand on previous work and present valuable early-warning signs for various applications.