A Coupled Dynamic Index for ENSO Periodicity

El Niño–Southern Oscillation (ENSO) is the most active interannual climatic mode, with great global impacts. The state-of-the-art climate models can simulate this dominant mode variability to a large extent. Nevertheless, some of ENSO’s fundamental time–space characteristics still have a large spread in the simulations across the array of recent climate models. For example, the large biases of ENSO periodicity still exist among model simulations from phase 5 of the Coupled Model Intercomparison Project (CMIP5). Based on the recharge oscillator framework, a coupled dynamic index for ENSO periodicity is proposed in this study, referred to as the Wyrtki index, in parallel to the Bjerknes index for ENSO instability. The Wyrtki index provides an approximate dynamic measure for ENSO linear periodicity. It has two main contribution terms: the thermocline and zonal advective feedbacks (or F factor) multiplied by the efficiency factor B of discharging–recharging of the equatorial heat content driven by ENSO wind stress anomalies. It is demonstrated that the diversity of simulated ENSO periodicity in CMIP5 models results from the biases in mean state and several key parameters that control ENSO dynamics. A larger F factor would result in a shorter ENSO period [e.g., BCC_CSM1.1(m)], whereas a smaller B factor would lead to a longer ENSO period (e.g., HadGEM2-ES). The Wyrtki index serves as a useful tool for a quantitative assessment of the sources for ENSO periodicity in reanalysis data and its biases in CMIP5 model simulations.