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A novel methodology is presented for the identification of the mean cycle of the Madden–Julian oscillation (MJO) along the equator. The methodology is based on a nonlinear principal component (NLPC) computed with a neural network model. The bandpass-filtered input data encompass 30 yr with zonal winds at 850 and 200 hPa plus outgoing longwave radiation (OLR). The NLPC is conditioned on a sufficiently strong MJO activity and is computed both for the pooled dataset and for the dataset stratified into seasons. The NLPC for all data depicts a circular mode formed by the first two linear principal components (LPCs) with marginal contributions by the higher-order LPCs. Hence, the mean MJO cycle throughout the year is effectively captured by the amplitude of the leading two LPCs varying in quadrature. The NLPC for individual seasons shows additional variability, which mainly arises from a subordinate oscillation of the second pair of LPCs superimposed on the annual MJO signal. In reference to the all-year solution, the difference in resolved variability approximately accounts for 9% in solstitial seasons and 3% in equinoctial seasons. The phasing of the third LPC is such that convective activity oscillations over the Maritime Continent as well as wind oscillations over the Indian Ocean appear enhanced (suppressed) during boreal winter (summer). Also, convective activity oscillations appear more pronounced at the date line during both winter and summer. The phasing of the fourth LPC is such that upper-level westerlies over the Atlantic region are more persistent during boreal spring than during other seasons.

Seasonal Modulations of the Active MJO Cycle Characterized by Nonlinear Principal Component Analysis