AI Emulation of Stochastic Sudden Stratospheric Warming with Interpretable Latent Structure
Authors: C. Daniel Boscu, Daniel Hernandez, Fabio Alvarez Ventura, Justin Finkel, Ashesh Chattopadhyay, Pedram Hassanzadeh, Dorian S. Abbot
Organizations: Department of Geophysical Sciences, University of Chicago, Chicago, 60637, IL · Data Science Institute, University of Chicago, Chicago, 60637, IL · Department of Applied Mathematics, University of California, Santa Cruz, Santa Cruz, 95064, CA · Committee on Computational and Applied Mathematics, University of Chicago, Chicago, 60637, IL
Rare weather regime transitions pose a challenge for data-driven modeling due to class imbalance. In this study, we develop a probabilistic deep learning emulator for a prototypical system with regime transitions, the stochastic Holton--Mass model of stratospheric variability, and analyze the structure of its learned latent space. The Holton--Mass model exhibits two metastable regimes, a strong and a weak polar vortex, maintained by nonlinear wave--mean flow interactions, with weak stochastic forcing intermittently triggering rare transitions between these regimes that qualitatively represent SSW events. We employ a ResNet-inspired Conditional Variational Autoencoder with six-layer encoder and decoder layers and explicit current-state conditioning to model the distribution of the system's state at the next time step (one day). The emulator accurately reproduces short-term dynamics, steady-state probability distributions, regime persistence statistics, rare transition rates, the transition committor function, and the transition expected lead time of the physical model. Beyond emulation fidelity, we interrogate the learned latent representation to understand how the model internalizes the underlying metastable structure of the dynamics. Principal Component Analysis of the 32-dimensional latent space reveals a clear and unsupervised separation into four physically interpretable clusters corresponding to strong versus weak vortex regimes and stable versus transition-prone configurations. Such emergent regime separation in latent space is hard to identify for deep generative models applied to high-dimensional stochastic systems. Our results show that carefully designed probabilistic emulators can uncover physically meaningful manifolds governing extreme-event dynamics, potentially aiding the development of improved operational advanced warning systems.
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Figure 1: The research pipeline. (a) Visual representation of the Holton-Mass model data and the metastable system of the Polar Vortex. (b) Architecture of the Conditional Variational Autoencoder (CVAE) emulator. The encoder qϕ(z∣X(t)) , implemented as a six-layer residual fully connected network with learnable parameters ϕ , maps the current system state X(t) to a 32-dimensional latent mean and log-variance. A latent variable z is sampled and concatenated with the resolved streamfunction perturbation field Ψ(t) . The decoder pθ(X(t+Δt)∣Ψ(t),z) , also implemented as a six-layer residual fully connected network, outputs the predicted next state at one-day expected lead time. This probabilistic architecture enables the emulator to represent the metastability, stochastic variability, and noise-induced regime transitions of the Holton-Mass model. (c) Four techniques we use to compare the long-term behavior of the Emulator with the Holton-Mass model: the state PDF, the return period complementary cumulative distribution function ( CCDF(τ)=1−CDF(τ)=P{return period>τ ), the transition probability (committor function), and the transition lead time. (d) PCA analysis of the emulator’s latent mean vector, μ , which clusters into the four dynamical categories.
Figure 2: Sample timeseries (left) and Probability Density Function (right, PDF) of the zonal velocity at an altitude of 30 km, U (30 km), for the Holton-Mass Model (blue, 6×104 days) and the emulator (red, 106 days). The PDF of the emulator is accompanied by the kernel density estimate (KDE) of the Holton-Mass model’s PDF.
Figure 3: One-step RMSE of the zonal wind, U , as a function of altitude, z , computed from 500-member ensembles and averaged over 200 initial conditions sampled from each dynamical state. Results are shown for the emulator (red) and the Holton-Mass stochastic model (green) in state A (left) and state B (right). The dashed grey curves shows the climatological zonal wind Uˉ for each state.
Figure 4: Forecast error growth ( RMSE ) averaged over 2000 initial conditions sampled from the model climatology. The dark blue line shows the mean RMSE, with the medium blue region indicating the interquartile range (IQR, 25–75%) and the light blue region showing the 95% confidence interval. Horizontal dashed blue lines show the asymptotic values of each quantile. Red horizontal dashed lines show the corresponding quantiles for the Holton-Mass model, showing close agreement. The sharp uptick in 75th-percentile error near 200 days for the mid-stratosphere is due to the onset of regime transitions at this timescale.
Figure 5: Two-dimensional projections of the PDF of the Holton-mass (left) and the Emulator (right) with respect to U (30 km) and IHF(30 km).
Figure 6: Complementary cumulative distribution functions (CCDFs) of persistence times for the Holton–Mass model (red) and the emulator (blue). Top: τAB , persistence in set A before transitioning to set B. Bottom: τBA , persistence in state B before transitioning to state A. Solid lines show the median empirical CCDFs, and the shaded regions indicate 95% bootstrap confidence intervals based on 1000 resamplings. The figure uses fixed 500-day bins and logarithmic axes to highlight differences in the tail behavior of the persistence-time distribution.
Figure 7: Distribution of transition durations between vortex regimes for the emulator (blue) and the Holton–Mass model (red). Bars are normalized histograms on shared bins. Solid curves are kernel density estimates (KDE) fit in log-duration space and mapped back to days as P(t)=Q(logt)/t , where Q is a kernel density estimate of the log durations; this construction guarantees the estimated density is zero for non-positive durations. The emulator’s transition durations are skewed slightly toward faster transitions than the Holton–Mass model’s.
Figure 8: Committor functions calculated for the HM model (left) and the emulator (right) as a function of U (30 km) and IHF(30 km). The two dashed lines are the bounds of set A and set B , respectively, and the black line is the level set q+=0.5
Figure 9: Expected lead time with respect to U (30 km) and IHF(30 km) of (left) the Holton-Mass Model, and (right) the emulator. The two dashed lines represent the bounds of state A and state B , respectively.
Figure 10: The four dynamical regimes emerge from the latent space without supervision. Latent mean vectors are projected onto the first two principal components for the Holton–Mass model (top) and the emulator (bottom). Left: points colored by their current and future physical regime classes— AA,AB,BB , and BA —with × marking the regime centroids. Right: the same points colored by the cluster assigned by a four-component Gaussian mixture model fit to the latent coordinates alone (dashed curves show the 1σ and 2σ covariance ellipses), with each cluster colored by the physical regime it best matches. The title is the fraction of states whose cluster matches their regime. The unsupervised clusters closely reproduce the physically defined regime classes.
Figure 11: LASSO regularization paths for PC2 (left) and PC3 (right) of the emulator’s latent space. Each row is one of the 75 state variables, grouped by field (real and imaginary parts of the streamfunction Ψ and the zonal wind U ) and ordered by altitude; columns run from weak to strong regularization, labeled by the number of surviving (nonzero) coefficients; color is the standardized regression coefficient. A variable stays colored as long as the model retains it, so the rows still colored toward the right are those kept under strong regularization. For both PCs the variables that survive the strongest regularization are at low altitude; the prominent upper-level zonal-wind bands in the least-regularized fits are dropped first, indicating that pattern is spread across many correlated levels rather than carried by a single essential variable.
Department of Technology, Management, and Economics Technical University of Denmark · Department of Applied Mathematics and Theoretical Physics University of Cambridge · Department of Mathematics and Statistics University of Exeter
Allen Institute for Artificial Intelligence (Ai2), Seattle, WA, USA · Pacific Northwest National Laboratory, Richland, WA, USA · Los Alamos National Laboratory, Los Alamos, NM, USA +2
1Hydro-Climate Extremes Lab (H-CEL), Department of Environment, Ghent University, Ghent, Belgium. · 2European Centre for Medium-Range Weather Forecasts (ECMWF), Reading, United Kingdom.