A Simple Dynamical Model Capturing the Key Features of Central Pacific

This SI Appendix is formed by three sections. Section 1 contains a brief discussion of the derivations of the dynamical model and its low-order meridional truncation. The details of boundary conditions, numerical solvers as well as a list of the parameter values are also included. The mathematical formula of the Walker circulation is shown at the end of this section. Section 2 involves the basic information of the two-state Markov jump process that is utilized in the article. Section 3 contains more supporting information of the results. In Section 3.1, Hovmoller diagrams of atmospheric wind, ocean zonal current, thermocline depth and SST associated with the deterministic advective modes in different regimes are shown. In Section 3.2, the important roles of the stochasticity, the nonlinear advection and the mean easterly trade wind anomaly are all emphasized.