The socioeconomic impact of weather extremes draws the attention of researchers to the development of novel methodologies to make more accurate weather predictions. The Madden–Julian oscillation (MJO) is the dominant mode of variability in the tropical atmosphere on sub-seasonal time scales, and can promote or enhance extreme events in both, the tropics and the extratropics. Forecasting extreme events on the sub-seasonal time scale (from 10 days to about 3 months) is very challenging due to a poor understanding of the phenomena that can increase predictability on this time scale. Here we show that two artificial neural networks (ANNs), a feed-forward neural network and a recurrent neural network, allow a very competitive MJO prediction. While our average prediction skill is about 26–27 days (which competes with that obtained with most computationally demanding state-of-the-art climate models), for some initial phases and seasons the ANNs have a prediction skill of 60 days or longer. Furthermore, we show that the ANNs have a good ability to predict the MJO phase, but the amplitude is underestimated.

Identifying, from time series analysis, reliable indicators of causal relationships is essential for many disciplines. Main challenges are distinguishing correlation from causality and discriminating between direct and indirect interactions. Over the years many methods for data-driven causal inference have been proposed; however, their success largely depends on the characteristics of the system under investigation. Often, their data requirements, computational cost or number of parameters limit their applicability. Here we propose a computationally efficient measure for causality testing, which we refer to as pseudo transfer entropy (pTE), that we derive from the standard definition of transfer entropy (TE) by using a Gaussian approximation. We demonstrate the power of the pTE measure on simulated and on real-world data. In all cases we find that pTE returns results that are very similar to those returned by Granger causality (GC). Importantly, for short time series, pTE combined with time-shifted (T-S) surrogates for significance testing strongly reduces the computational cost with respect to the widely used iterative amplitude adjusted Fourier transform (IAAFT) surrogate testing. For example, for time series of 100 data points, pTE and T-S reduce the computational time by $$82\%$$ 82 % with respect to GC and IAAFT. We also show that pTE is robust against observational noise. Therefore, we argue that the causal inference approach proposed here will be extremely valuable when causality networks need to be inferred from the analysis of a large number of short time series.

The Madden-Julian Oscillation (MJO) is a major source of predictability on the sub-seasonal (10 to 90 d) timescale. An improved forecast of the MJO may have important socioeconomic impacts due to the influence of MJO on both tropical and extratropical weather extremes. Although in the last decades state-of-the-art climate models have proved their capability for forecasting the MJO exceeding the 5-week prediction skill, there is still room for improving the prediction. In this study we use multiple linear regression (MLR) and a machine learning (ML) algorithm as post-processing methods to improve the forecast of the model that currently holds the best MJO forecasting performance, the European Centre for Medium-Range Weather Forecasts (ECMWF) model. We find that both MLR and ML improve the MJO prediction and that ML outperforms MLR. The largest improvement is in the prediction of the MJO geographical location and intensity.

Abstract. The Madden–Julian Oscillation (MJO) is one of the main sources of sub-seasonal atmospheric predictability in the tropical region. The MJO affects precipitation over highly populated areas, especially around southern India. Therefore, predicting its phase and intensity is important as it has a high societal impact. Indices of the MJO can be derived from the first principal components of zonal wind and outgoing longwave radiation (OLR) in the tropics (RMM1 and RMM2 indices). The amplitude and phase of the MJO are derived from those indices. Our goal is to forecast these two indices on a sub-seasonal timescale. This study aims to provide an ensemble forecast of MJO indices from analogs of the atmospheric circulation, computed from the geopotential at 500 hPa (Z500) by using a stochastic weather generator (SWG). We generate an ensemble of 100 members for the MJO amplitude for sub-seasonal lead times (from 2 to 4 weeks). Then we evaluate the skill of the ensemble forecast and the ensemble mean using probabilistic scores and deterministic skill scores. According to score-based criteria, we find that a reasonable forecast of the MJO index could be achieved within 40 d lead times for the different seasons. We compare our SWG forecast with other forecasts of the MJO. The comparison shows that the SWG forecast has skill compared to ECMWF forecasts for lead times above 20 d and better skill compared to machine learning forecasts for small lead times.

Abstract. The Madden–Julian Oscillation (MJO) is a major source of predictability on the sub-seasonal (10 to 90 d) timescale. An improved forecast of the MJO may have important socioeconomic impacts due to the influence of MJO on both tropical and extratropical weather extremes. Although in the last decades state-of-the-art climate models have proved their capability for forecasting the MJO exceeding the 5-week prediction skill, there is still room for improving the prediction. In this study we use multiple linear regression (MLR) and a machine learning (ML) algorithm as post-processing methods to improve the forecast of the model that currently holds the best MJO forecasting performance, the European Centre for Medium-Range Weather Forecasts (ECMWF) model. We find that both MLR and ML improve the MJO prediction and that ML outperforms MLR. The largest improvement is in the prediction of the MJO geographical location and intensity.