Accurately defining the life cycle of the Madden-Julian Oscillation (MJO), the dominant mode of intraseasonal climate variability, remains a foundational challenge due to its propagating nature. The established linear-projection method (RMM index) often conflates mathematical artifacts with physical states, while direct clustering in raw data space is confounded by a "propagation penalty." Here, we introduce an "AI-for-theory" paradigm to objectively discover the MJO's intrinsic structure. We develop a deep learning model, PhysAnchor-MJO-AE, to learn a latent representation where vector distance corresponds to physical-feature similarity, enabling objective clustering of MJO dynamical states. Clustering these "MJO fingerprints" reveals the first complete, six-phase anatomical map of its life cycle. This taxonomy refines and critically completes the classical view by objectively isolating two long-hypothesized transitional phases: organizational growth over the Indian Ocean and the northward shift over the Philippine Sea. Derived from this anatomy, we construct a new physics-coherent monitoring framework that decouples location and intensity diagnostics. This framework reduces the rates of spurious propagation and convective misplacement by over an order of magnitude compared to the classical index. Our work transforms AI from a forecasting tool into a discovery microscope, establishing a reproducible template for extracting fundamental dynamical constructs from complex systems.
The pursuit of science is often a pursuit of definition. From the periodic table in chemistry to the classification of elementary particles in physics, precisely identifying fundamental building blocks has repeatedly catalyzed scientific revolutions by establishing a common framework for understanding and predicting. In the geosciences, a paramount challenge is to objectively define the life cycles of planetary-scale fluid dynamical systems, whose intrinsic complexity, nonlinearity, and propagating nature have long resisted unambiguous decomposition.
The Madden-Julian Oscillation (MJO) exemplifies this challenge. First identified through its distinctive signals in tropical winds and pressure (Madden & Julian, 1971;Madden & Julian, 1972), the MJO is now recognized as the dominant mode of intraseasonal climate variability. This planetary-scale system, characterized by a coupled envelope of deep convection and large-scale circulation anomalies, propagates slowly eastward and modulates a vast spectrum of global weather and climate phenomena (Jiang et al., 2020). It orchestrates monsoon rhythms, energizes tropical cyclone activity, and triggers extreme precipitation events across the globe (Zhang, 2013;Stan et al., 2022;Cheng et al., 2025). Its predictability on subseasonal-to-seasonal timescales makes its accurate monitoring essential for advancing extended-range forecasting (Vitart et al., 2017).
However, the MJO’s nature as a propagating mode renders its fundamental definition-and thus its routine monitoring-a uniquely difficult problem. Unlike quasi-stationary phenomena such as the El Niño-Southern Oscillation, trackable via sea surface temperature anomalies in fixed regions (Trenberth, 1997), or compact vortices like tropical cyclones, identifiable by organized eyewall structures (Velden et al., 2006), the MJO is a traveling signal embedded within high-amplitude synoptic noise. Its detection, therefore, cannot rely on local measurements but must instead assess the similarity between the planetary-scale atmospheric state and a set of predefined spatial patterns that capture its essence.
The landmark work of Wheeler and Hendon (2004, WH04) established the operational standard by deriving the Real-time Multivariate MJO (RMM) index from two leading Empirical Orthogonal Function (EOF) modes (Fig. S1 a-b) of filtered, meridionally averaged fields (see Methods). This linear projection framework provided a crucial, globally consistent benchmark. Yet, it suffers from a foundational limitation: it confounds the MJO’s mathematical projection with its physical entity. By coupling the system’s location and intensity into a single two-dimensional vector derived from fixed, zonally averaged patterns, the RMM index is intrinsically vulnerable to contamination by any non-MJO variability that projects onto these static patterns. This often results in diagnosed “MJO centers” that reside within convectively suppressed regions or trajectories that exhibit unphysical retrogression-artifacts that undermine physical interpretation and event demarcation. Crucially, this limitation is inherent to the linear, pattern-based approach. Attempts to simply expand the basis by incorporating higher-order EOF modes fail, as these modes lack the canonical planetary-scale, wavenumber-1 structure of the MJO and instead capture noise or other dynamical processes (Fig. S1 c-j). Thus, the WH04 framework is not merely low-dimensional; it is structurally confined to an approximate, and often physically inconsistent, representation.
Given this impasse, a natural proposal would be to extract the MJO’s recurrent phases directly from historical data-for instance, by clustering-to refine its life cycle and achieve a more precise description. This intuitive path, however, encounters a more fundamental geometric obstacle: the “propagation penalty.” For a propagating phenomenon like the MJO, traditional similarity measures (e.g., Euclidean distance) are vastly more sensitive to spatial displacement than to changes in physical structure. Consequently, in raw data space the same MJO convective-circulation dipole at different longitudes would be treated as distinct classes, preventing any clustering algorithm from identifying the coherent, propagating entity itself (Fig. S2). Defining the MJO objectively therefore requires a new representational paradigm:
one that preserves its essential physical attributes (spatial structure, intensity, relative position) while mapping physically similar MJO systems to mathematically nearby vectors, thereby ensuring that similarity reflects physical kinship rather than incidental positional overlap. In recent years, artificial intelligence (AI), especially deep learning, has demonstrated transformative potential in applied fields such as weather forecasting (Pathak et al., 2022;Bi et al., 2023). This raises a deeper question: Can AI move beyond its role as a “prediction tool” to become a “discovery tool,” helping to solv
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