A Homogeneous Stochastic Model of the Madden–Julian Oscillation

This paper presents a new empirical model to simulate the Madden–Julian oscillation (MJO), which is the most prominent mode of tropical intraseasonal variability. Zonal wind components at 850 and 200 hPa from reanalysis (1948–2007) and outgoing longwave radiation from satellites (1979–2007) are used to identify MJOs and characterize their statistical properties. The temporal variability of the MJO is represented with a nine-state first-order Markov chain in which state 0 represents quiescent days and states 1–8 are phases of the MJO when it is active. Transition probabilities are estimated based on the historical record of MJO events, and sensitivity tests were performed to evaluate the best estimates for a homogeneous model. Once the model simulates time series of phase transitions, composites of convective and circulation anomalies determine the spatial structure of the events. The amplitudes of the MJOs are stochastically generated with an amplitude factor that has a Gaussian frequency distribution. MJO events generated by the homogeneous stochastic model occur irregularly in time and can appear as single isolated events or sequences of successive MJOs. The MJO in the model can have different eastward propagations and the zonal scale is consistent with the observations. The simulated MJOs have different durations (30–90 days), and each event can be stronger or weaker than the mean composite according to a normal distribution. The results show that the homogeneous stochastic model simulates the irregularity of the MJO and model biases are small. Possible applications and future extensions of the homogeneous stochastic model are discussed.