A Stochastic Conceptual Model for the Coupled ENSO and MJO

Abstract

Understanding the interactions between the El Nino-Southern Oscillation (ENSO) and the Madden-Julian Oscillation (MJO) is essential to studying climate variabilities and predicting extreme weather events. Here, we develop a stochastic conceptual model for describing the coupled ENSO-MJO phenomenon. The model adopts a three-box representation of the interannual ocean component to characterize the ENSO diversity. For the intraseasonal atmospheric component, a low-order Fourier representation is used to describe the eastward propagation of the MJO. We incorporate decadal variability to account for modulations in the background state that influence the predominant types of El Nino events. In addition to dynamical coupling through wind forcing and latent heat, state-dependent noise is introduced to characterize the statistical interactions among these multiscale processes, improving the simulation of extreme events. The model successfully reproduces the observed non-Gaussian statistics of ENSO diversity and MJO spectra. It also captures the interactions between wind, MJO, and ENSO.

Figures (12)

• Figure 4.1: Comparison of model simulations and statistical data with observational records. Observations cover the period from 1950 to 2019 (a total of 70 years). The model simulation spans 2,000 years, with the first 40 years discarded as a burn-in period. The remaining simulations are divided into 28 non-overlapping segments, each corresponding to a 70-year observational period. Confidence intervals are calculated based on these 28 segments. Panel (a): Time series of $T_E$ and $T_C$. Panels (b)–(d): Power spectra, PDFs, and variances as a function of months for $T_E$ and $T_C$, with shaded areas representing 95% confidence intervals. Panel (e): Bivariate distribution of DJF SST peaks. Panel (f): Frequency of ENSO events over 70 years, with bars showing 95% confidence intervals. Model simulations are shown in blue, and observational data are shown in red.
• Figure 4.2: Hovmoller diagrams of the spatially reconstructed SST and MJO from the conceptual model. The x-axis of the SST Hovmoller diagram covers the equatorial Pacific, while the MJO diagram also includes the Indian Ocean. The red vertical line in the MJO panels marks the Western Pacific (WP) boundary at 120$^o$E. In the SST panels, the averaged atmospheric wind over the WP is overlaid on the SST, with red and blue indicating westerly and easterly wind bursts, respectively. The black curve represents the interannual wind. The rectangles along the y-axis indicate different ENSO events occurring during boreal winter: strong and moderate EP El Niño (red), weak EP El Niño (purple), CP El Niño (orange), and La Niña (blue).
• Figure 4.3: Lagged correlation between the MJO and ENSO. Panels (a)--(b): Lagged correlation with $T_E$ for years when El Niño events occur. Panels (c)--(d): lagged correlation with $T_C$ for the same years. Panels (e)--(f): Lagged correlation with $T_E$ for years with only EP El Niño events. Panels (g)--(h): Lagged correlation with $T_C$ for years with only CP El Niño events. On the x-axis, zero corresponds to the peak of the El Niño event, with the unit of the x-axis being months.
• Figure 6.1: Bivariate regression analysis. Panel (a): Regression coefficients $a_E(x)$ and $a_C(x)$ from \ref{['Reconstruction_ENSO']}. Panel (b): Observed sea surface temperature (SST) field. Panel (c): Reconstructed SST field based on the bivariate regression using the coefficients from Panel (a). Panel (d): Residual SST, representing the difference between the observed SST in Panel (b) and the reconstructed SST in Panel (c).
• Figure 6.2: Hovmoller diagrams depicting the evolution of ENSO and MJO patterns during the observation period from 1982 to 2018. The format is similar to Figure \ref{['fig:Hovmoller_ENSO_MJO']}.