Few studies have utilized machine learning techniques to predict or understand the Madden-Julian oscillation (MJO), a key source of subseasonal variability and predictability. Here we present a simple framework for real-time MJO prediction using shallow artificial neural networks (ANNs). We construct two ANN architectures, one deterministic and one probabilistic, that predict a real-time MJO index using maps of tropical variables. These ANNs make skillful MJO predictions out to ~17 days in October-March and ~10 days in April-September, outperforming conventional linear models and efficiently capturing aspects of MJO predictability found in more complex, dynamical models. The flexibility and explainability of simple ANN frameworks is highlighted through varying model input and applying ANN explainability techniques that reveal sources and regions important for ANN prediction skill. The accessibility, performance, and efficiency of this simple machine learning framework is more broadly applicable to predict and understand other Earth system phenomena.

We develop and demonstrate a new interpretable deep learning model specifically designed for image analysis in earth system science applications. The neural network is designed to be inherently interpretable, rather than explained via post hoc methods. This is achieved by training the network to identify parts of training images that act as prototypes for correctly classifying unseen images. The new network architecture extends the interpretable prototype architecture of a previous study in computer science to incorporate absolute location. This is useful for earth system science where images are typically the result of physics-based processes, and the information is often geo-located. Although the network is constrained to only learn via similarities to a small number of learned prototypes, it can be trained to exhibit only a minimal reduction in accuracy compared to non-interpretable architectures. We apply the new model to two earth science use cases: a synthetic data set that loosely represents atmospheric high- and low-pressure systems, and atmospheric reanalysis fields to identify the state of tropical convective activity associated with the Madden-Julian oscillation. In both cases, we demonstrate that considering absolute location greatly improves testing accuracies. Furthermore, the network architecture identifies specific historical dates that capture multivariate, prototypical behaviour of tropical climate variability.

The subseasonal Madden-Julian oscillation (MJO) is among the most important modes of tropical variability on the planet and is a dominant driver of subseasonal-to-seasonal (S2S) prediction globally. The past decade has seen substantial advances in MJO prediction using dynamical forecast models, which now routinely outperform traditional statistical MJO forecasts (e.g. multiple linear regression models). At the same time, an increasing body of literature has demonstrated that machine-learning methods represent a new frontier in Earth science, opening the door to more advanced statistical forecast models of the MJO. In this study, we explore whether state-of-the-art machine learning methods can be used to make real-time MJO forecasts that outperform traditional statistical models and do comparably well to dynamical models. In particular, we utilize neural networks trained on observational tropical fields to attempt to make skillful forecasts of MJO convection out to several weeks lead time. Through contrasting the machine-learning models’ behavior with simpler statistical models and dynamical forecast models, we explore the advantages and disadvantages of statistical versus dynamical forecasts. A novel aspect of our analysis is the use of cutting-edge techniques to allow us to visualize how our neural network models makes their predictions. These techniques, such as layer-wise relevance propagation, can lead to new insights into regions of MJO predictability, allowing us to better interpret sources of MJO prediction skill within the machine-learning model. We further diagnose whether our machine-learning models contain well-known aspects of MJO prediction found in dynamical models, such as an increase in prediction skill during boreal winter or during certain phases of the stratospheric quasi-biennial oscillation.