The stochastic skeleton model for the Madden-Julian Oscillation with time-dependent observation-based forcing

TL;DR

The paper addresses how a minimal skeleton dynamics framework can capture Madden-Julian Oscillation (MJO) behavior when forced by time-dependent, observation-based inputs. By implementing $S^q$ (latent heating proxy) and $S^\theta$ (radiative cooling) as monthly-varying forcings and identifying MJO episodes with the SMM index, the authors assess the model’s ability to reproduce MJO lifetimes, propagation extents, and amplitudes, as well as ENSO-related modulation. The findings show that the approach reproduces several key MJO statistics and the planetary-scale convective envelope's characteristics but fails to reproduce MJO seasonal variability and ENSO-driven spatial differences, indicating missing physics such as mean-state wind and ocean coupling. The work highlights both the usefulness and the limitations of a low-dimensional skeleton framework for understanding MJO dynamics and points to necessary extensions to accurately capture ENSO–MJO interactions in practice.

Abstract

We analyze solutions to the stochastic skeleton model, a minimal nonlinear oscillator model for the Madden-Julian Oscillation (MJO). This model has been recognized for its ability to reproduce several large-scale features of the MJO. In previous studies, the model's forcings were predominantly chosen to be mathematically simple and time-independent. Here, we present solutions to the model with time-dependent observation-based forcing functions. Our results show that the model, with these more realistic forcing functions, successfully replicates key characteristics of MJO events, such as their lifetime, extent, and amplitude, whose statistics agree well with observations. However, we find that the seasonality of MJO events and the spatial variations in the MJO properties are not well reproduced. Having implemented the model in the presence of time-dependent forcings, we can analyze the impact of temporal variability at different time scales. In particular, we study the model's ability to reflect changes in MJO characteristics under the different phases of ENSO. We find that it does not capture differences in studied characteristics of MJO events in response to differences in conditions during El Niño, La Niña, and neutral ENSO.

Figures (11)

• Figure 1: Evolution of (a) the latent heating profile $S^q$ estimated from latent heat flux and (b) the radiative cooling profile $S^\theta$ computed according to Eq. \ref{['eq:Stheta_equ']}. The abscissa indicates months of the year 1979.
• Figure 2: Hovmöller diagrams of the skeleton model lower tropospheric wind $u(x,y=0,t)$ and envelope of convective activity $\bar{H}a(x,y=0,t)$ at the equator. (a,b) raw data, (c,d) daily anomalies from the long-term mean, filtered in time and space as described in the text. One westward moving signal (likely of a moist Rossby wave) and one eastward moving signal (likely MJO activity) are marked in white in panel (d).
• Figure 3: Zonal wavenumber - frequency power spectrum of the simulated envelope of convective activity $\bar{H}a$ (in base 10 - logarithm). The dashed lines mark the 90 and 30 days periods.
• Figure 4: (a) Long-term averages of observed and modeled $\bar{H}a$ (envelope of convective activity). (b) Variance of modeled and observed $\bar{H}a$ when all spatial modes from the model output are kept. (c) Variance of modeled and observed $\bar{H}a$ when only the first 14 spatial modes from the model output are kept. Note the different scales in panels (b) and (c).
• Figure 5: Phase-space diagram of the model SMM values for a 52-day period from a simulation forced with observation-based functions. The dots correspond to daily values of (SMM1, SMM2). The first day of the series is labelled 'd1', the last is labeled 'd52'. The circle in the center of the plot has unit radius, indicating the threshold at which the amplitude of SMM exceeds $1$. Points in dark blue indicate an MJO event as defined by the criteria in Section \ref{['sec:rmm_index']}.