Nonlinear Recharge Oscillator

The El Nino-Southern Oscillation (ENSO) is not a simple linear system but a non-linear system. Obviously, nonlinear properties of ENSO cannot be explained by a simple linear recharge oscillator model (linear ROM). Therefore, we develop a nonlinear ROM by adding square terms into a linear ROM. The square terms are dynamically derived from nonlinear dynamical heating. The nonlinear dynamical heating has been known as a driver of amplitude asymmetry of ENSO. Using a Fokker Plank equation, we compute a probability function of a nonlinear and linear ROMs. The probability function of nonlinear ROM clearly demonstrates a skewed probability density and a non-symmetric oscillatory behavior as seen in the observation. Finally, the linear ROM well explains amplitude and period of ENSO, while the nonlinear ROM additionally explains the skewness and non-symmetric oscillatory feature of ENSO.