Early-Warning Signs for SPDEs under Boundary Noise

The search of early-warning signs able to predict the approach of a parameter to a deterministic bifurcation threshold is relevant in climate as it aims to enable a proper prediction of qualitative changes in the studied models. The observation of such objects in SPDEs (stochastic partial differential equations) permits the consideration of space variables and the ensuing heterogeneity in the behaviour of their solutions.

The presence of Gaussian noise on the boundary of the studied space is used in order to build the signals, whose properties are discussed thoroughly. An example in the form of application of such tools on a climate model is presented and justified. The utility and appropriate use of the results on a more applied perspective are shown.