This paper introduces a distillation framework for an ensemble of entropy-optimal Sparse Probabilistic Approximation (eSPA) models, trained exclusively on satellite-era observational and reanalysis data to predict ENSO phase up to 24 months in advance. While eSPA ensembles yield state-of-the-art forecast skill, they are harder to interpret than individual eSPA models. We show how to compress the ensemble into a compact set of "distilled" models by aggregating the structure of only those ensemble members that make correct predictions. This process yields a single, diagnostically tractable model for each forecast lead time that preserves forecast performance while also enabling diagnostics that are impractical to implement on the full ensemble. An analysis of the regime persistence of the distilled model "superclusters", as well as cross-lead clustering consistency, shows that the discretised system accurately captures the spatiotemporal dynamics of ENSO. By considering the effective dimension of the feature importance vectors, the complexity of the input space required for correct ENSO phase prediction is shown to peak when forecasts must cross the boreal spring predictability barrier. Spatial importance maps derived from the feature importance vectors are introduced to identify where predictive information resides in each field and are shown to include known physical precursors at certain lead times. Case studies of key events are also presented, showing how fields reconstructed from distilled model centroids trace the evolution from extratropical and inter-basin precursors to the mature ENSO state. Overall, the distillation framework enables a rigorous investigation of long-range ENSO predictability that complements real-time data-driven operational forecasts.

The ocean is a crucial component of the Earth's system.

The ocean is a crucial component of the Earth's system.

Robust generalization under climate change remains a major challenge for machine learning applications in climate science. Most existing approaches struggle to extrapolate beyond the climate they were trained on, leading to a strong dependence on training data from model simulations of warm climates. Use of climate-invariant inputs improves generalization but requires challenging manual feature engineering. Here, we present CERA (Climate-invariant Encoding through Representation Alignment), a machine learning framework consisting of an autoencoder with explicit latent-space alignment, followed by a predictor for downstream process estimation. We test CERA on the problem of parameterizing moist-physics processes. Without training on labeled data from a +4K climate, CERA leverages labeled control-climate data and unlabeled warmer-climate inputs to improve generalization to the warmer climate, outperforming both raw-input and physically informed baselines in predicting key moisture and energy tendencies. It captures not only the vertical and meridional structures of the moisture tendencies, but also shifts in the intensity distribution of precipitation including extremes. Ablation experiments show that latent alignment improves both accuracy and the robustness across random seeds used in training. While some reduced skill remains in the boundary layer, the framework offers a data-driven alternative to manual feature engineering of climate invariant inputs. Beyond parameterizations used in hybrid ML-physics systems, the approach holds promise for other climate applications such as statistical downscaling.

Accurate Subseasonal-to-Seasonal (S2S) climate forecasting is pivotal for decision-making including agriculture planning and disaster preparedness but is known to be challenging due to its chaotic nature. Although recent data-driven models have shown promising results, their performance is limited by inadequate consideration of geometric inductive biases. Usually, they treat the spherical weather data as planar images, resulting in an inaccurate representation of locations and spatial relations. In this work, we propose the geometric-inspired Circular Transformer (CirT) to model the cyclic characteristic of the graticule, consisting of two key designs: (1) Decomposing the weather data by latitude into circular patches that serve as input tokens to the Transformer; (2) Leveraging Fourier transform in self-attention to capture the global information and model the spatial periodicity. Extensive experiments on the Earth Reanalysis 5 (ERA5) re-analysis dataset demonstrate our model yields a significant improvement over the advanced data-driven models, including PanguWeather and GraphCast, as well as skillful ECMWF systems. Additionally, we empirically show the effectiveness of our model designs and high-quality prediction over spatial and temporal dimensions. The code link is: https://github.com/compasszzn/CirT . Subseasonal-to-seasonal (S2S) forecasting, which predicts meteorological variables 2 to 6 weeks in advance, is crucial for agriculture, resource allocation, and disaster preparedness (e.g., heatwaves and droughts) (Mouatadid et al., 2024). Despite its high socioeconomic benefits, such a task has long been considered a "predictability desert" (Vitart et al., 2012) due to the chaotic nature of the atmosphere. Compared with medium-range (up to 15 days) and seasonal predictions (3-6 months) (Vitart et al., 2017), the S2S timescale is long enough to lose much of the memory of atmospheric initial conditions, while it is too short for slowly evolving earth system components such as the ocean that strongly influence the atmosphere (Black et al., 2017; Phakula et al., 2024).

Multi-year-to-decadal climate prediction is a key tool in understanding the range of potential regional and global climate futures. Here, we present a framework that combines machine learning and analog forecasting for predictions on these timescales. A neural network is used to learn a mask, specific to a region and lead time, with global weights based on relative importance as precursors to the evolution of that prediction target. A library of mask-weighted model states, or potential analogs, are then compared to a single mask-weighted observational state. The known future of the best matching potential analogs serve as the prediction for the future of the observational state. We match and predict 2-meter temperature using the Berkeley Earth Surface Temperature dataset for observations, and a set of CMIP6 models as the analog library. We find improved performance over traditional analog methods and initialized decadal predictions.

Machine learning (ML) is a revolutionary technology with demonstrable applications across multiple disciplines. Within the Earth science community, ML has been most visible for weather forecasting, producing forecasts that rival modern physics-based models. Given the importance of deepening our understanding and improving predictions of the Earth system on all time scales, efforts are now underway to develop forecasting models into Earth-system models (ESMs), capable of representing all components of the coupled Earth system (or their aggregated behavior) and their response to external changes. Modeling the Earth system is a much more difficult problem than weather forecasting, not least because the model must represent the alternate (e.g., future) coupled states of the system for which there are no historical observations. Given that the physical principles that enable predictions about the response of the Earth system are often not explicitly coded in these ML-based models, demonstrating the credibility of ML-based ESMs thus requires us to build evidence of their consistency with the physical system. To this end, this paper puts forward five recommendations to enhance comprehensive, standardized, and independent evaluation of ML-based ESMs to strengthen their credibility and promote their wider use.

One of the major sources of uncertainty in the current generation of Global Climate Models (GCMs) is the representation of sub-grid scale physical processes. Over the years, a series of deep-learning-based parameterization schemes have been developed and tested on both idealized and real-geography GCMs. However, datasets on which previous deep-learning models were trained either contain limited variables or have low spatial-temporal coverage, which can not fully simulate the parameterization process. Additionally, these schemes rely on classical architectures while the latest attention mechanism used in Transformer models remains unexplored in this field. In this paper, we propose Paraformer, a "memory-aware" Transformer-based model on ClimSim, the largest dataset ever created for climate parameterization. Our results demonstrate that the proposed model successfully captures the complex non-linear dependencies in the sub-grid scale variables and outperforms classical deep-learning architectures. This work highlights the applicability of the attenuation mechanism in this field and provides valuable insights for developing future deep-learning-based climate parameterization schemes.