Abstract
Most climate fluctuations may be modulated by a variety of periodic or quasi-periodic deterministic forcing (e.g. diurnal, seasonal or Milankovitch cycles). These process modulations often induce cyclostationary (CS) behaviour defined as periodic correlations. I proposed here that quasi-periodic correlations may appear when the inertia (memory) of a process is modulating its pure CS property. This effect of the phenomenon memory led to CS behaviour ‘in average’ both in time and frequency domains, called Extended CycloStationarity (ECS) which is being rigorously defined in this paper. A new statistical tool has been developed to analyse ECS in a time series with the help of a comfortable timefrequency visualization technique (called DXM). This tool has been applied to the quantification of ENSO interannual ECS quasi-cycles, taking into account the possible ENSO memory. ECS property searched in the SOI and SST (Ni˜no-3) indices perfectly confirmed the well-known interannual periodicities (the quasi-biennial, 28 months, and the quasi-quadrennial, 45 months) and their evolutions discussed in the literature. The main result presented here was that these significant quasicycles were the only ones detected throughout the 50-year datasets, suggesting that various periodicities were detected in the past because ECS quasi-cycles were not taken into account. This result led to the hypothesis that the quasi-biennial cycle belonged to the atmospheric component and that the quasi-quadrennial cycle belonged to the oceanic component of ENSO only. Both quasi-cycle evolutions were significantly (p < 0.01) correlated (r2 = 0.62), with a delayed action (30-month time lag) of the atmosphere upon the ocean. This observation highlighted the nature of the strong coupling between the two components and suggested a possible influence of Pacific atmospheric processes on oceanic processes