Non-linear coupling between modes in a low-dimensional model of ENSO

An intermediate coupled model of the tropical Pacific ocean-atmosphere system was reduced by projecting the non-linear model onto a truncated basis set of its own empirical orthogonal functions (EOFs). For moderate coupling strengths, the simulated El Niño/Southern Oscillation (ENSO) variability consists of a dominant quasi-quadrennial mode with a period of approximately four years and a smaller quasi-biennial mode at a period of approximately two years. In the absence of a seasonal cycle, the leading two EOFs capture the dynamics of the leading interannual mode, with a further two EOFs being required to capture the secondary oscillation. The presence of seasonal forcing increases the EOF requirement by two, the leading pair of EOFs being dominated by the annual cycle. Normal mode analysis of the reduced models indicates that the quasi-biennial mode manifests itself, even though it is linearly stable, by non-linear coupling to the quasi-quadrennial mode. The nonlinearity does not produce the quasi-biennial signal unless the spatial degrees of freedom associated with the linear quasi-biennial mode are present. Other linearly stable modes also couple non-linearly to the leading interannual mode and to the seasonal cycle, but the quasi-biennial mode is favoured over other, less-damped linear modes because of its proximity to a multiple of the quasi-quadrennial frequency.