The Madden-Julian Oscillation (MJO) is a significant source of weather predictability on sub-seasonal timescales, influencing tropical weather patterns and impacting both tropical and extratropical regions through atmospheric teleconnections. Its influence extends to monsoon systems, tropical cyclone development, and even the El Niño-Southern Oscillation (ENSO). Accurate MJO prediction is crucial for improving forecasts of extreme weather events. While dynamical models have shown improvements in MJO prediction skill, reaching up to 28 days (ECMWF) and 24 days (ABOM2) in 2014, with later improvements to 4 weeks for ECMWF and 20-25 days for most models, this skill remains limited and is sensitive to model physics, initial conditions, and factors such as initial amplitude and phase, season, and extratropical influence. Boreal winter generally shows higher prediction skill. Machine learning (ML) algorithms offer a promising alternative for improving MJO prediction by potentially better representing processes like ocean mixing and atmospheric convection, which are challenging for traditional models. Previous studies have applied ML to climate phenomena like ENSO but not directly to MJO prediction. This study aims to fill this gap by using ANNs to predict the real-time multivariate MJO (RMM) index, a commonly used metric for MJO description, over a period from 1979 to 2020. The study focuses on the performance of FFNN and AR-RNN architectures, evaluating prediction skill using the bivariate correlation coefficient (COR) and root-mean-squared error (RMSE).

Existing literature extensively documents the MJO's impact on various aspects of weather and climate. Studies have highlighted the MJO's influence on monsoon systems (Taraphdar et al., 2018; Díaz et al., 2020), tropical cyclones (Camargo et al., 2009), and extratropical regions (Alvarez et al., 2017; Ungerovich et al., 2021). The interaction between MJO and ENSO has also been investigated (Bergman et al., 2001). Significant progress has been made in dynamical MJO prediction, with models like ECMWF and ABOM showing improved skill over time (Neena et al., 2014; Kim et al., 2018; Jiang et al., 2020). However, the limitations of dynamical models, particularly in representing complex physical processes, motivate the exploration of alternative methods. While machine learning has been applied to other climate phenomena (O’Gorman & Dwyer, 2018; Dijkstra et al., 2019), its application to direct MJO prediction was limited prior to this study, primarily focusing on bias correction of dynamical model outputs (Kim et al., 2021). The use of the RMM index (Wheeler & Hendon, 2004) provides a common framework for evaluating MJO prediction across different models and methods. Previous studies have used various metrics for evaluating MJO prediction skill, including COR and RMSE (Rashid et al., 2011; Vitart, 2017; Wheeler & Weickmann, 2001; Lin et al., 2006; Seo, 2009; Wu et al., 2016; Liu et al., 2019; Lin et al., 2008).

This study employed two artificial neural networks (ANNs): a feed-forward neural network (FFNN) and an autoregressive recurrent neural network (AR-RNN). Both networks had an input layer of 300 units. The FFNN used the last point of the input layer and linked it to a hidden layer of 64 units, connected to an output layer of τ units (where τ represents the forecast lead time, varying from 5 to 100 days in increments of 5). The AR-RNN utilized a single gated recurrent unit (GRU) layer with 64 units. The GRU architecture was chosen to mitigate the vanishing gradient problem. Both networks used two inputs (RMM1 and RMM2) from the real-time multivariate MJO (RMM) index (Wheeler & Hendon, 2004). The RMM data, covering the period from January 1, 1979, to December 31, 2020, were obtained from [source]. The dataset was divided into training, validation, and testing sets while preserving the temporal order. The FFNN used a rectified linear unit (ReLU) activation function, and the Adam optimizer was used for training with a maximum of ten epochs and early stopping based on validation error. The mean squared error (MSE) was used as the loss function. For both ANNs, the prediction skill was quantified using the bivariate correlation coefficient (COR) and the root-mean-squared error (RMSE), with thresholds of COR = 0.5 and RMSE = 1.4 used to define prediction skill. Amplitude and phase errors were calculated using a change of coordinates from Cartesian (RMM1, RMM2) to polar (amplitude, phase). The analysis examined average prediction skill, seasonal variations in prediction skill, and the dependence of skill on the initial MJO phase.

Both the FFNN and AR-RNN exhibited comparable prediction skill, averaging around 26-27 days based on the COR threshold. The AR-RNN showed a slightly better performance for short-term predictions (up to 10 days), while the FFNN was slightly better for longer lead times. However, based on the RMSE, the prediction skill extended beyond 60 days for both models. The ANNs demonstrated good accuracy in predicting the MJO phase but underestimated the amplitude, with amplitude error increasing with lead time. A seasonal analysis revealed significant variation in prediction skill. Boreal winter (DJF) showed the highest skill (around 45 days using COR), followed by boreal summer (JJA, around 31 days), while spring (MAM) and fall (SON) exhibited lower skill (23-24 days and 16-17 days, respectively). However, the RMSE indicated better accuracy in JJA despite lower COR than DJF. The analysis of initial phase dependence revealed that the prediction skill varied considerably across different initial phases and seasons. In boreal winter, phases 1, 2, 5, and 8 showed very high prediction skill (60 days or longer for some phases), while phase 7 exhibited low skill. Other seasons showed similar dependence, highlighting the influence of the initial MJO state on predictability.

This study demonstrates the potential of ANNs for MJO prediction, achieving a level of skill comparable to, and in some cases exceeding, that of computationally demanding state-of-the-art dynamical models. The relatively simple FFNN and AR-RNN architectures used in this study provide a competitive baseline for future research exploring more complex ANN architectures and data representation techniques. The observed underestimation of MJO amplitude suggests potential avenues for model improvement, focusing on better capturing the amplitude dynamics. The significant seasonal and initial phase dependence of prediction skill emphasizes the importance of considering these factors when developing MJO prediction systems. The high prediction skill in some specific phases and seasons suggests that the incorporation of more sophisticated methods for feature engineering or using more advanced architectures could help further improve the model's overall prediction skill. The results offer valuable insights for operational sub-seasonal forecasting.

This research successfully demonstrated the effectiveness of artificial neural networks (ANNs) for predicting the Madden-Julian Oscillation (MJO). Both the FFNN and AR-RNN models achieved significant prediction skill, exceeding that of some existing dynamical models for certain initial phases and seasons. Future research could explore the use of more complex network architectures, incorporating additional predictive variables, and improving the representation of MJO amplitude dynamics to further enhance prediction accuracy. The findings highlight the potential of machine learning for improving sub-seasonal forecasting and enhancing our understanding of MJO variability.

The study primarily focused on predicting the RMM index, which is a simplified representation of the MJO. Future studies should investigate the applicability of the models to other MJO indices and evaluate their performance in predicting regional impacts of the MJO. The temporal limitations of the dataset, particularly the relatively recent availability of high-quality data, might affect the generalizability of the findings. Further research with longer datasets is encouraged to assess the robustness of the models over extended periods. The model's reliance on historical data may limit its ability to accurately predict unprecedented MJO events or those influenced by long-term climate change.