Abstract
The regime behavior of the low-order El Niño–Southern Oscillation (ENSO) model, according to an increase in the radiative–convective equilibrium sea surface temperature (SST; Tr), is studied to provide a possible explanation for the observed increase in ENSO irregularity characterized by decadal modulation. During recent decades, a clear increasing trend of the warm-pool SST has been observed. In this study, the increase in the warm-pool maximum SST is interpreted as an increase in Tr following previous studies. A bifurcation analysis with Tr as a control parameter is conducted to reveal that the degree of ENSO irregularity in the model is effectively controlled by the equilibrium states of the model. At a critical value of Tr, bifurcation analysis reveals that period-doubling bifurcation occurs and an amplitude-modulated ENSO emerges. At this point, a subcycle appears within the preexisting ENSO cycle, which initiates decadal modulation of ENSO. As Tr increases further, nested oscillations are successively generated, illustrating clear decadal modulation of ENSO. The qualitative regime changes revealed in this study are supported by the observation of regime shifts in the 1970s. With increasing Tr, the mean zonal SST gradient increases, and the model adjusts toward a “La Niña–like” mean state. Further constraint with shoaling of the mean thermocline depth and increasing stratification causes ENSO to exhibit stronger amplitude modulation. Furthermore, the timing of the period-doubling bifurcation advances with these two effects.
Period-doubling bifurcation analysis of stochastic van der Pol system via Chebyshev polynomial approximation