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The linear recharge oscillator model for the El Nino-Southern Oscillation (ENSO) was expanded to a nonlinear model, thus allowing identification of a nonlinear dynamic ENSO index. This index was applied for a dynamic examination of the El Nino-La Nina asymmetry. Here, the nonlinear physical processes including the nonlinear dynamical heating were implemented into the linear recharge oscillator model in the form of quadratic nonlinearity. This nonlinear recharge oscillator model revealed that nonlinear (linear) physical processes play a critical role in the long-term ENSO skewness (amplitude) changes quantitatively. Particularly, the large part of the long-term ENSO skewness change could be explained by the quadratic nonlinearity associated with the nonlinear ocean dynamical heating, which is closely related to change in mean thermocline. This research provides a unified framework to understand better the past-present-future ENSO changes by applying the interdecadal change dynamics on a low hierarchical level.

Plain Language Summary The linear coupled dynamic index so-called "Bjerknes Stability index" for the El Nino-Southern Oscillation (ENSO) has been widely used. This linear stability index provided a detailed dynamical interpretation on change in ENSO amplitude. However, it cannot assess the nonlinearity of ENSO because of the limitation as the linear dynamics. This study expands the linear scope to nonlinear and proposes a nonlinear coupled dynamic index in order to adequately examine the El Nino-La Nina asymmetry. As an application, it is applied for the assessment of the interdecadal change in ENSO skewness and demonstrated that the long-term changes in mean thermocline depth effectively modify the nonlinear dynamical processes to lead the interdecadal change of El Nino-La Nina asymmetry.