Nonlinear principal component analysis applied to the tropical MJO cycle

The Madden–Julian Oscillation (MJO) is the dominant pattern of intraseasonal variability in the tropical atmosphere. Traditionally, linear principal components (LPCs) are derived in tropical atmospheric fields to identify the dynamical signal of the MJO. The restriction to a leading subset of the LPCs provides a reduction of dimensionality and ideally discards all computational modes without a physical background.

Here, an alternative MJO definition is presented based on a nonlinear principal component (NLPC) computed by a neural network with a circular bottleneck node. The bandpass–filtered input data encompass 30 years with zonal winds on 850 hPa and 200 hPa plus outgoing longwave radiation (OLR). The NLPC is conditioned on an active MJO and is computed both for the pooled dataset and for the dataset stratified into seasons. Seasonal modulations are derived from the full solutions and then corroborated by means of a residual bootstrap with 250 repetitions.

The NLPC for all data depicts a circular mode within the first pair of LPCs and marginally projects onto the higher–order LPCs. The NLPC for individual seasons shows additional variability which mainly arises from a stronger contribution of the higher–order LPCs. In reference to the all–year solution, the difference of resolved variability approximately accounts for 9% in solstitial seasons and 3% in equinoctial seasons. A secondary oscillation is evoked by the third and fourth LPC and superimposed on the annual MJO signal. The third LPC contributes to the NLPC with a changing sign throughout the year. The spatial structure of the third LPC is characterized by OLR anomalies over the Maritime Continent and baroclinic wind modulations which peak in phase over the Indian and eastern Pacific Oceans. The phase lag in the NLPC is such that convective activity oscillations over the Maritime Continent as well as wind oscillations over the Indian Ocean appear to be enhanced (suppressed) during boreal winter (summer). The fourth LPC contributes less to the NLPC than the third LPC, but causes the upper– level westerlies over the Atlantic region to be more persistent during boreal spring than during other seasons.

Overall, the presented approach provides a clearly arranged mapping of the MJO cycle and sheds some new light on the seasonal variations of the MJO.