An Analysis of Nonlinear Relationship between the MJO and ENSO

Using the Hilbert Singular Value Decomposition (HSVD) and the Nonlinear Canonical Correlation Analysis (NLCCA), we analyzed the statistical relationship of MJO (Madden-Julian Oscillation) and ENSO (El Nino and Southern Oscillation). It was found that while a linear analysis produced no significant relationship between MJO and ENSO, a low-order nonlinear analysis based on the quadratic function of HSVD led to statistically significant lagged correlations. When their nonlinear relationship was further extracted by the NLCCA, stronger correlation was obtained, with the maximum correlation coefficient appearing while the MJO signals preceding the ENSO signals by around 2 months and 5-6 months respectively. The time lags producing the maximum correlation are respectively consistent with the characteristic time of MJO influencing ENSO dominated by two physical processes: the equatorial Kelvin waves and air-sea feedback. Corresponding to the two different physical processes, ENSO shows different features of development. In the former scenario, the westerly winds in the western Pacific excite the equatorial Kelvin waves which propagate eastward and deepen the thermocline in the eastern Pacific, resulting in the sea surface warming at the far eastern Pacific near the coast. In the latter scenario, the westerly anomalies in the western Pacific precede the development of El Nino through bringing surface warm water into the central and eastern Pacific, thus the sea surface warming occurs across the whole eastern Pacific ocean.