Online Reinforcement Learning in the Met Office Unified Model through Distributed Model-Agent Coupling

Machine-learnt corrections can complement numerical weather prediction only if they adapt to the evolving model state while preserving dynamical consistency and numerical stability. To test this within a global forecasting model, we couple the Met Office (UKMO) Unified Model (UM) with distributed RL agents through rank-local tensors. A DDPG actor shares weights across the 70 vertical model levels of each atmospheric column and applies bounded potential-temperature corrections to the model tendencies. Across ten nudged training forecasts, nudging calculations towards the UKMO operational analysis provides an immediate counterfactual target. The frozen policy is then evaluated in a non-nudged forecast for inference. The coupled workflow successfully completes training and remains numerically stable in the evaluated case. Relative to a matched native UM forecast at +6 h, the learnt policy reduces Z$_{500}$ MAE in four of six latitude bands, including reductions of 45.8% and 40.8% in the northern and southern tropics. MSLP error too decreases in three bands, with a maximum reduction of 27.3% at 0-30°N. This single-case experiment demonstrates significant promise and feasibility of distributed online learning followed by non-nudged inference, laying the groundwork for RL-based bias correction and parametrisations within operational systems.

Precipitation Downscaling Using Foundation Model-Conditioned Diffusion

High-resolution precipitation fields are essential for hydrological impact assessment, yet global climate model outputs are too coarse and biased for direct use. AI-based statistical downscaling with diffusion models offers a promising approach, but the mechanism by which large-scale atmospheric predictors condition generation remains largely unexplored. We investigate three conditioning strategies for a denoising diffusion probabilistic model applied to daily precipitation downscaling: channel concatenation of upsampled coarse predictors, cross-attention conditioning with a learned convolutional encoder, and cross-attention conditioning with the frozen encoder of the pretrained Prithvi WxC weather foundation model. All strategies are evaluated against an unconditioned baseline under identical conditions using probabilistic, distributional, spectral, and extreme-event metrics for the Colorado River Basin. Concatenation conditioning achieves the lowest point-wise CRPS and MSE, but tends to produce over-smoothed fields that suppress high-intensity events. In contrast, cross-attention conditioning provides substantially better distributional realism and modest improvements in spectral fidelity. Improvements are greatest for extremes: the Prithvi-WxC conditioned model retains over half of >100mm/day events, although estimates are uncertain due to limited samples. When trained on the full dataset, the learned convolutional model performs similarly to the foundation model-conditioned approach while requiring lower computational resources. However, the Prithvi-WxC-conditioned model achieves comparable performance with only five years of training data. These results indicate that cross-attention conditioning offers advantages over simple concatenation for probabilistic precipitation downscaling, and that pre-trained foundation model representations may offer benefits in data-limited settings.

UHI-Bench: Benchmarking Dual-Source Urban Heat Island Modeling Across Cities in Diverse Climate Regimes

Urban heat islands (UHIs) are intensifying under climate change, exacerbating thermal exposure risks. Their two primary observations, land surface temperature UHI (LST-UHI) and near-surface air temperature UHI (AirT-UHI), capture physically distinct aspects of urban heat. However, most studies rely on a single source, and substituting one for the other can substantially bias the magnitude and spatial variability of human heat exposure. Accurate UHI modeling also requires dynamic meteorological drivers and static urban morphology features, but spatiotemporal incompatibilities hinder their alignment. Cloud gaps in LST observations and sparse AirT station networks further limit dual-source UHI modeling, motivating cross-city transfer across diverse climates. To bridge these gaps, we introduce UHI-Bench, the first UHI benchmark for dual-source UHI modeling that integrates dynamic and static environmental context. Following a unified signal, mechanism, and transfer framework, it evaluates over 20 baselines from four model families on five tasks across 20 cities and nine Köppen climate classes. Results show that no model is uniformly best, although foundation models remain consistently competitive and stable. Environmental covariates generally improve performance, but their utility varies across sources and tasks. Cross-city transferability is better explained by overlap in UHI regimes than by climate-zone similarity. With the dataset and standardized pipeline, our work provides practical guidance for urban heat modeling, promotes climate data equity, and supports future advances in climate research.

Physics-Knowledge-Guided Hybrid Neural Learning for Arctic Sea Ice Concentration Evolution and Short-Range Prediction

Accurate modeling of sea ice concentration (SIC) evolution is essential for polar climate assessment and short?range sea ice prediction. Numerical and data-driven approaches constitute major foundations for SIC modeling, but the former often require complex parameterizations and substantial compu?tation, whereas the latter rarely encode physical dependencies explicitly. This study presents the Physics-Informed Hybrid Ice Model (PIHIM), a differentiable data-driven hybrid ice model for daily SIC evolution that organizes its network structure according to the physical dependencies encoded in the sea ice continuity equation and explicitly accounts for dynamical transport, ther?modynamically driven areal growth and loss, and unresolved local processes. PIHIM preserves the representation capacity of deep learning while providing a process-decomposed formulation of ice displacement, freeze-melt areal change, and local error closure. Two evaluation settings are adopted: reanalysis-forced simulation examines SIC evolution stability under reanalysis forcing, and forecast-forced prediction assesses short-range performance un?der forecast-forced conditions, with reanalysis and observational SIC serving as verification references. Results indicate enhanced ice-edge preservation and error-growth control in reanalysis?forced simulation, while PIHIM retains measurable short-range prediction skill under forecast-forced conditions. Our code will be made publicly available after the paper is accepted.

SAE-Xplainers: Rule-Based Feature Interpretation for Extreme Earth Events

The emergence of large-scale Weather and Climate (W&C) datasets offers new opportunities for modeling extreme Earth events (ExEE) and their impacts using deep learning. However, their adoption in operational settings remains limited by the lack of models' interpretability. While for conventional text and image modalities, tools such as Sparse Autoencoders (SAEs) have proven effective for extracting human-understandable concepts, their use for the analysis of ExEE remains challenging due to the nature of W&C data. To address this, we introduce (i) a geographic location-based modulation of the inputs of SAE to capture the local semantic meaning of environmental patterns, and (ii) an ensemble of rule-based SAE-Xplainers to interpret the resulting high-dimensional features derived from complex, multi-modal environmental predictors. We evaluate our method on three ExEE types: the prediction of fires, and the detection of tropical cyclones and atmospheric rivers. We show that SAE input modulation improves both reconstruction performance and feature utilization, and that our SAE-Xplainers enable faithful interpretation of complex climatic patterns by unfolding them into human-understandable rules that are consistent with the scientific literature, while also supporting the identification of feature absorption.

Learning piecewise-smooth dynamical systems

Discovering dynamical systems from trajectory data is a central problem in applied mathematics and engineering. Whilst recent advances in machine learning have led to strong progress in data-driven system identification, much less attention has been given to systems with discontinuous dynamics. These systems are nevertheless highly relevant in applications, including climate dynamics and mechanical systems with friction. In this work, we consider the problem of identifying piecewise-smooth dynamical systems directly from trajectory data. Compared with the smooth setting, this requires recovering the governing equations and detecting the switching hyperplanes that separate different dynamical regimes and characterising their behaviour, such as sliding motion. We present a modular framework for discovering such systems by first estimating switching hyperplanes from data and then learning smooth dynamics within each region using geometry-constrained neural networks. The geometry-learning phase is studied from a statistical perspective, analysing the identifiability of the discontinuities and the robustness of the procedure. We also introduce a novel neural network architecture with a prescribed discontinuity set, and provide a theoretical analysis of its approximation properties. The approach is tested on low-dimensional benchmark problems, including dry-friction oscillators and the PP04 climate model for the ice ages.

Koopman early warning signals for bifurcation and rate-induced tipping

Abrupt transitions in complex systems are often preceded by early warning signals. However, most indicators rely on the notion of critical slowing down and do not generally extend to rate-induced tipping where transitions can occur without local loss of stability. This is problematic in stochastic, nonautonomous systems where internal variability and time-varying variables interact to shape tipping onset. We use Koopman operator theory to develop a unified early warning framework for both bifurcation and rate-induced tipping in stochastic systems. Our approach builds on residual Koopman mode decomposition that measures discrepancies between dynamics and their finite-dimensional approximation, and extends it to the control setting by augmenting the observable space with time-varying control variables. In idealized examples, the resulting indicators recover expected signatures near bifurcation points and improve detection in rate-induced regimes where classical indicators fail. We further show that learned embeddings through deep learning outperform prescribed dictionaries, especially in a high-dimensional setting. Applied to simulations of the Atlantic Meridional Overturning Circulation, our Koopman-based indicators distinguish tipping from non-tipping trajectories and reveal interpretable spectral signatures prior to critical transition.

Stochastic Emulation of a Fully Coupled Preindustrial E3SMv3 Simulation

We present a stochastic coupled emulator of E3SM version 3, built on the SamudrACE framework, which couples an atmosphere emulator (ACE2) with a full-depth ocean emulator (Samudra). We replace the deterministic atmosphere emulator with its stochastic counterpart, ACE2S, and fine-tune the coupled system with a probabilistic objective, so that the atmosphere acts as a source of internal variability for the ocean. Trained on 105 years of a pre-industrial control simulation and evaluated on an independent 400 years, the emulator reproduces E3SMv3's mean climate state with biases much smaller than existing model-to-observation differences. Relative to a deterministic baseline, stochastic training maintains internal variability across timescales, most notably in the ENSO power spectrum, eddy-rich SST anomalies, and sea ice variability in the marginal ice zone. The emulator captures daily precipitation accurately up to the 99.99th percentile, but underestimates the rarest tropical extremes. These results show that stochastic coupled emulators can reproduce long-timescale variability with high fidelity, while extrapolation to unseen extremes remains a key challenge.

Deep Learning-Based Statistical Downscaling of Sea Surface Temperature Using a Residual Corrective Neural Network

The large-scale oceanic and atmospheric forecasts provided by global climate models typically lack sufficient resolution to accurately capture the response of the coastal ocean to atmospheric forcing and coastal circulation that drive fine-scale SST variability. Dynamical downscaling is computationally prohibitive, when applied to extensive coastlines, predictive ensembles, or long time periods. Therefore, this work presents a statistical downscaling of sea surface temperature (SST) from the seasonal coupled ocean-atmosphere forecast system (ACCESS-S2) using machine learning techniques. This study proposes a novel deep learning framework that uses a U-Net to generate an initial high-resolution SST estimate, which is subsequently refined using a residual corrective approach. The target SST fields are derived from the Regional Ocean Modeling System (ROMS). This two step approach called Residual Corrective Neural Network (RCNN) progressively refines initial U-Net predictions by incorporating dynamically scaled residuals at each step, enabling accurate capture of broad patterns and fine-grained features such as eddies and fronts. We also introduce a custom loss-assisted RCNN variant to improve performance during extreme events, which may be absent from training data due to climate-driven shifts in SST extremes. The framework efficiently downscales SST along the west coast of Australia. A 2011 marine heatwave case study shows that the RCNN improves ACCESS-S2 SST predictions by increasing horizontal resolution from 25 km to 2 km, enabling identification of fine-scale anomalies unresolved in the ACCESS-S2 dataset. This balance between computational efficiency and accuracy supports applications in coastal impact assessment and marine ecosystem studies.

A Sequence-to-Sequence ConvLSTM Approach for Leaf Area Index Forecasting over the South-Central United States

Leaf Area Index (LAI) is a fundamental biophysical variable governing land-atmosphere interactions; however, LAI forecasting at high spatial resolution remains an unsolved challenge. While recent machine learning approaches have demonstrated LAI estimation at point or regional scales, none provides a gridded, meteorology-driven prognostic forecast suitable for subseasonal land surface and climate modeling applications. Here we present a sequence-to-sequence Convolutional LSTM (ConvLSTM) framework that generates daily 1-km LAI forecasts up to 30 days ahead, driven by historical LAI sequences and daily meteorological forcing including temperature and precipitation. Trained and evaluated over the South-Central United States -- a region of strong climate gradients and diverse vegetation -- the model achieves a domain-averaged RMSE of 0.36 at a 30-day lead time, more than a third lower than the persistence baseline. Forecast skill remains robust across seasons, geographic distributions, and plant functional types, including forests, grasslands, shrublands, and croplands. To our knowledge, this is the first demonstration of skillful LAI forecasting at a 30-day horizon at 1-km resolution.

A Fortran General-Purpose Transpiler: Proof of Concept

Fortran has been the cornerstone of high-performance computing for decades and remains unmatched in many domains. Yet the language faces an expertise gap: a new generation of scientists is barely familiar with it, while many experienced Fortran developers are only now transitioning to modern ecosystems such as JAX. This gap often results in "Fython" - Python code written with a Fortran mindset - that fails to leverage modern frameworks. We present FGPT, a transpiler framework designed to bridge this gap. It provides a systematic pipeline that transpiles Fortran into GPU-adapted Fortran, auto-differentiable Fortran via Tapenade, or NumPy and JAX scripts. Its architecture comprises three stages: (i) a frontend that parses Fortran and extracts target procedures along with all their dependencies; (ii) a middle-end that lowers the code into an intermediate representation, then into GPU-adapted or auto-differentiable Fortran, or a NumPy class; and (iii) a backend that transforms NumPy scripts into JAX modules optimized for GPU acceleration and automatic differentiation. Large language models fail when applied to the scale of community scientific codes-often spanning hundreds of thousands of lines-where consistent transformations, strict numerical fidelity, and validation against production tests are non-negotiable. FGPT addresses these challenges by preserving program semantics throughout the entire translation. We verified the framework on representative climate modeling kernels and demonstrated that it produces correct, differentiable Python implementations without requiring manual intervention. By combining rigorous compiler techniques with modern accelerator support, FGPT offers a scalable, trustworthy path for modernizing legacy Fortran code.

Rescene: band-limited stochastic forcing turns a frozen neural weather operator into a climate emulator

Over the past few years, the rapid development of machine learning (ML) models for weather forecasting has produced deterministic models whose medium-range skill matches or exceeds that of the European Centre for Medium-Range Weather Forecasts (ECMWF)'s high-resolution forecast (HRES). However, when these models are integrated freely beyond the horizon they were trained for, they blow up, drift, or lose their seasonal cycle, and retraining them for stability is expensive. We therefore ask what can be recovered from a strictly frozen backbone. We present Rescene, a 0.4 M-parameter wrapper around a frozen 1.5 degree, 6-hourly vision-transformer operator, developed using ERA5 reanalysis data and comprising a deterministic "slow clock" (0.33 M) that blends the forecast toward a lead-aware day-of-year climatology and a generative head (0.06 M) that adds a spectrally shaped stochastic perturbation at every step. The performance evaluation demonstrates that the deterministic wrapper alone is stable for decades but collapses daily variability to 40% of ERA5. Adding the generative head restores 126% (Z500) and 130% (MSLP) of the observed daily variability with pattern correlations of 0.89 and 0.92, recovers 82% of the observed blocking frequency, keeps the ensemble calibrated (spread-skill ratio 0.78-0.97 from day 7 to day 90), and integrates for 100 years with no detectable drift (+0.008 +/- 0.014 K per century). Moreover, because the perturbation is band-limited to total wavenumber $k \le 20$, the small scales are never forced, yet realistic $k \ge 20$ power is sustained: a direct decomposition of the 6-hourly energy budget shows that the frozen operator supplies 28 times more energy than the perturbation at $k \ge 40$, with a fractional growth rate 247 times larger at the grid scale than at planetary scales.

A Spatial Persistence Gradient in European Warming Consistent with North Atlantic Cold-Blob Influence

Europe is warming faster than the global mean, yet the spatial organisation of this acceleration remains incompletely understood. Using ERA5 reanalysis for 1950--2024 across 28 IPCC AR6 European sub-regions, we identify two connected empirical results. First, the DFA1 Hurst exponent of interannual temperature residuals is strongly and negatively associated with the 1996--2024 warming rate ($r=-0.792$, $p=5.1\times10^{-7}$). High-persistence, mainly Atlantic-proximal regions warm more slowly, whereas low-persistence continental regions warm faster. This relationship is robust to five residualisation schemes, three memory estimators, leave-one-region-out analysis, and five null-test families, including spatial block permutation. It also persists across warming windows ($r=-0.550$ for 1981--2024, $-0.792$ for 1996--2024, and $-0.875$ for 2000--2024), but vanishes under DFA2, indicating that the signal lies in low-frequency interannual-to-decadal persistence rather than trend curvature. The pattern is consistent with, but does not prove, North Atlantic cold-blob and thermohaline influence on European land temperatures. Second, under a strict 2006--2024 holdout, contemporaneous Mediterranean SST reduces mean annual temperature RMSE by 43% (from $0.787$ to $0.449,^{\circ}\mathrm{C}$). A causal lag-weight predictor based on prior-year Mediterranean and Atlantic SST also outperforms AR(2) ($0.578$ versus $0.695,^{\circ}\mathrm{C}$) and remains informative after removing NAO, AO, and PNA effects. Similar skill from five-year moving-average and exponentially weighted predictors shows that short Mediterranean SST persistence at 1--5-year lags is the key predictive ingredient. Together, the results support a two-regime interpretation: Atlantic-proximal regions exhibit stronger memory and oceanic buffering, while continental interiors show faster warming and weaker interannual persistence.

Projected climate memory and inherited warm-tail risk in accelerated European summer warming

European summer warming reflects interactions among background change, persistent ocean--land--circulation states, and same-season variability. We develop an empirical reduced-dynamics framework that decomposes regional summer indicators into inherited slow-state memory, its predictable component, and contemporaneous innovation. Projection-operator theory motivates the decomposition, implemented with finite causal filters, ridge-regularised prediction, and logistic risk models. Using ERA5-derived summer indicators for 28 IPCC AR6 European sub-regions over 1950--2024, with validation on 2006--2024, we find that Mediterranean-state memory improves mean summer-temperature prediction relative to trend-only and ARX baselines. The gain over ARX is modest, while moving-average, exponentially weighted, and tempered filters contain similar annual information, indicating that the data identify useful slow-state memory more robustly than a unique kernel shape. Predictable-state reconstruction is ridge-sensitive and therefore treated diagnostically rather than as a forecasting model. The strongest result concerns warm-tail risk. In parsimonious logistic models, high accumulated Mediterranean memory raises predicted upper-tail event probability by about 8--11 percentage points for annual maximum summer temperature, warm-day frequency, and warm-spell duration at 1-, 3-, and 5-year horizons. Regional bootstrap intervals remain positive for all targets and horizons. Circular-shift placebos yield one-sided probabilities of approximately 0.05--0.14 and do not survive strict family-wise correction across nine tests, so the evidence is moderate rather than decisive. Overall, annual projected memory is not a universal short-horizon predictor, but a physically interpretable inherited risk-loading variable identifying years and regions predisposed to warm-tail outcomes.

RoughNet: Mapping Arctic Sea Ice Roughness Using Diffusion-Based Super-Resolution of Satellite Imagery

Accurate estimation of landfast sea ice roughness is critical for climate modeling and safe Arctic over-ice travel, yet existing approaches rely on costly airborne surveys or sparse in-situ measurements, limiting spatial coverage and operational scalability. Here we show that high-resolution sea ice topography can be reconstructed directly from optical satellite imagery using a conditional diffusion framework. Our approach, RoughNet, learns to map 10 m Sentinel-2 multispectral images to locally normalized 1 m surface elevation residual fields, enabling fine-scale roughness characterization from widely available satellite data. Trained on airborne LiDAR data from two Arctic regions and evaluated on an unseen third Arctic region, the model generalizes across diverse ice conditions and partially reproduces small-scale topographic structure. The best-performing model achieves an out-of-domain root mean squared error of 9 cm while preserving the statistical and spectral properties of the underlying roughness field. These results demonstrate that generative diffusion models can recover physically meaningful surface structure from optical imagery alone, providing a scalable pathway for high-resolution sea ice mapping and roughness estimation in data-sparse environments.

Disentangling Forced and Internal Climate Variability in Single Realizations using Dynamic Mode Decomposition with Control

We show that a single climate realization can be decomposed into forced and internal components by treating external forcing as a dynamical driver within a linear stochastic system, an idea grounded in pullback attractor theory. In doing so, we address a central methodological challenge in climate science with direct implications for climate projection and the detection and attribution of the forced response, disentangling the forced climate response from internal variability in a single observed record. Statistical methods range from approaches trained on large ensembles to techniques operating on single realizations. The latter often rely on linear frameworks such as linear inverse models (LIMs) and linear regression. LIMs ignore forcing predictors, whereas linear regression omits climate system dynamics. Here we introduce PullbackDMDc, a method grounded in non-autonomous dynamical systems theory and dynamic mode decomposition with control (DMDc), incorporating pullback attractor estimation to decompose a single climate realization into spatial modes and their associated forced and internal components, yielding a physically interpretable picture of the underlying dynamics. We illustrate the utility of PullbackDMDc for Earth System Model (ESM) evaluation by applying it to near-surface air temperature and sea-level pressure from reanalysis and four ESM large ensembles. PullbackDMDc estimates the forced response with skill matching or exceeding established baselines and identifies optimal forcing predictors against model-based ground truth. Its internal variability components reveal that ESMs qualitatively capture interannual and decadal modes while exhibiting systematic differences relative to each other and to observations. Skillful forced response estimation and a novel decomposition position PullbackDMDc as a practical tool for single-realization climate analysis and ESM evaluation.

Exploring Convolutional Neural Processes for Weather Downscaling

Global reanalysis products such as ERA5-Land provide spatially complete weather fields but at resolutions too coarse for local applications, particularly in mountainous regions where temperature can vary by several degrees over short distances. This project investigates Convolutional Conditional Neural Processes (ConvCNPs) for statistical downscaling of daily maximum temperature from the ~11km resolution ERA5-Land grid to ~1km resolution over Switzerland, building upon the architecture of Vaughan et al. (2022) and adapting it to the topographically complex Swiss domain with high-resolution elevation features from the swisstopo DHM25. The best model, trained on ten years of data (2014-2023) with five-fold temporal cross-validation, achieves a mean absolute error of 1.31 Celsius and a CRPS-based skill score of 0.524 relative to bilinear interpolation, reducing the expected prediction error by more than half. An ablation study reveals that the elevation MLP is the indispensable component - without it, the model diverges entirely - while explicit seasonal features and Topographic Position Index provide secondary benefits. Under sparse on-grid input the model degrades gracefully, maintaining positive skill down to approximately 10% of the input grid; however, zero-shot deployment on off-grid station observations does not achieve positive skill at any density tested. All configurations exhibit severely overconfident uncertainty estimates, a structural limitation of the Gaussian likelihood training objective. These results demonstrate that ConvCNPs are a viable and effective approach to climate downscaling in complex terrain, and identify uncertainty calibration and native support for non-gridded input as the key challenges for operational deployment.

GlacierCastAI: Predicting Glacier Retreat from Multi-Modal Satellite Imagery and Climate Signals

ERA5 seasonal climate variables contain predictive information about future glacier retreat beyond what satellite imagery alone provides, yet existing deep learning methods focus on mapping current boundaries rather than forecasting future ones. This paper presents GlacierCastAI, which reframes glacier boundary prediction as a multi-modal spatiotemporal forecasting problem, fusing multi-temporal Landsat imagery with ERA5 reanalysis climate variables and Copernicus DEM terrain features to forecast glacier boundaries across five glaciers spanning four climate regimes. The architecture couples a ResNet50 spatial encoder with a ConvLSTM temporal model and a cross-attention climate fusion module. Because forecasting is inherently more uncertain than mapping current boundaries, the reported IoU values (0.320-0.337) are not directly comparable to state-of-the-art mapping models. Comparisons are against traditional baselines and experimental conditions. Through a pre-registered ablation study, adding ERA5 climate signals improves image-only IoU from 0.326 to 0.337 (+3.4%), suggesting that atmospheric forcing carries predictive information beyond imagery alone. All deep learning models substantially outperform persistence and linear trend baselines (IoU 0.160 and 0.169 respectively), with improvements of 89-99% relative IoU. A lightweight climate-only MLP baseline (661K parameters) achieves an IoU of 0.320 (98% of image-only performance) using 85x fewer parameters, suggesting that ERA5 variables encode substantial predictive signal independently of satellite imagery. SHAP attribution analysis suggests that spring solar radiation (MAM) is the dominant climate driver, consistent with the known role of spring insolation in setting melt season trajectories.

Conditional Tropical Cyclogenesis Rates via Rare-Event Sampling in a Neural Weather Emulator

We couple Forward Flux Sampling (FFS), a non-equilibrium rare-event technique from statistical mechanics, to a neural weather emulator (SDL-WXFormer, 1° grid spacing) to estimate conditional tropical cyclogenesis rates, or how often a tropical cyclone achieves a hurricane-level central pressure, without modifying model dynamics. Tropical cyclogenesis rates vary by orders of magnitude across regimes, yet direct ensemble sampling cannot resolve this variability at operationally feasible ensemble sizes. FFS decomposes the rare disturbance to mature cyclone intensification path into a flux through an initial interface pressure and a product of conditional crossing probabilities across four intermediate interface pressures. We use the 1° emulator because FFS requires O(10^4) model trajectories per initial condition, and because the model's calibrated stochastic layers provide the necessary exploratory spread. Applied to 98 Atlantic basin initial conditions spanning 21 August - 8 October 2022, FFS resolves genesis rates spanning nearly three orders of magnitude, capturing a seasonal cycle qualitatively consistent with observations. A self-consistency check comparing FFS rates to independent direct-sampling rates yields a mean ratio of 1.03 +/- 0.15 across all initial conditions. Computational enhancement factors range from 3X (most active environment) to 140X (most suppressed), with a geometric mean of 14X. Three case studies illustrate the physical diagnostics the method provides: the rate-limiting step is initial tropical organization for the Earl environment, uniformly high crossing probabilities for the Fiona precursor environment, and a compound barrier at the final intensification stages for the Ian environment. More efficient emulators would enable application of FFS to finer resolutions.

Mind the Residual Gap: Probabilistic Downscaling under Real-World Bias

Probabilistic downscaling is the task of modeling the conditional distribution of high-resolution fields given coarse inputs, and is a central challenge to atmospheric science, climate modeling, and other multiscale physical systems. A widely used paradigm decomposes the problem into a deterministic mean predictor followed by a stochastic residual generator. While effective in idealized settings, this mean--residual approach frequently produces biased and under-dispersive ensembles in real-world applications. Is this merely generic predictive uncertainty miscalibration? We show that the root cause is more fundamental: residual target misspecification, the residual distribution induced during training differs systematically from the one required at test time due to downscaling bias. To close this gap, we introduce ReMatch (Residual Distribution Matching). ReMatch aligns the training residual distribution toward the test-time regime via optimal transport in a low-dimensional PCA space. This preserves the statistical benefits of the mean--residual framework while reducing the train--test mismatch in the residual targets seen by the stochastic generator. On a controlled synthetic benchmark with varying bias levels and a real-world HRRR--ERA5 wind field downscaling task, ReMatch substantially reduces under-dispersion, improves calibration (SSR and CRPS), and outperforms strong baselines, including the standard mean--residual model and its variants, as well as state-of-the-art super-resolution models. Our code is available at https://github.com/sdean-group/ReMatch.git.

NIVA: A Multimodal Foundation Model for Actionable Earth System Intelligence

Recent advances in AI-driven weather and climate modeling have improved forecast skill while reducing computational cost. However, existing data-driven approaches are limited in their ability to model coupled Earth system dynamics, which is required for extending predictability beyond the ~2-week horizon. To address this, we introduce NIVA, a multimodal foundation model designed to learn unified representations across Earth system components. While the full framework targets atmosphere, ocean, ice, and land interactions, we focus here on a two-modality setting (ocean and atmosphere) as a controlled proof of concept to evaluate whether foundation models can learn coupled dynamics. Trained on large-scale Earth system simulations, NIVA learns physically meaningful cross-modal structure, providing a foundation for subseasonal-to-seasonal prediction. As initial validation, we show that NIVA captures key modes of climate variability through accurate prediction of major climate indices.

Regional Climate Model Emulation with Diffusion Approaches: What is the Added Value of Generative Machine Learning?

Emulators provide a cost-effective alternative to regional climate models (RCMs) by capturing their dynamical downscaling function. They link large-scale predictors simulated by global climate models (GCMs) to RCM-simulated high-resolution fields of the target variable, here precipitation. Machine learning methods, typically deep learning, are cheaper than running RCMs in computation time and energy. Among them, generative models are appealing because they can simulate ensembles of local high-resolution fields consistent with the predictors. This ensemble, which we call the uncertainty envelope, remains to be properly assessed for added value. Here, we make three contributions. First, we introduce ParamDiffusion, a new two-stage diffusion-based framework, and compare it with a state-of-the-art diffusion approach. Second, we expand standard validation through a comprehensive framework aligned with climate-science needs, examining specific precipitation events, including extremes. Third, within this framework, we assess the added value of diffusion approaches relative to deterministic methods. We intercompare four deep-learning models: a deterministic model designed to capture the precipitation tail; a parametric probabilistic model based on it; a recently proposed diffusion approach; and ParamDiffusion, which couples the parametric model with a diffusion model. Our results show that diffusion-based approaches reproduce climatological precipitation statistics with high skill, including distributional tails and spatially compounded extremes, while generating spatially detailed fields. However, none of the assessed models consistently accounts for the most extreme RCM-simulated events within its uncertainty envelope. Diffusion models are therefore promising for probabilistic RCM emulation, but progress is still required before they can reliably represent high-impact precipitation extremes.

AI4Land: Scalable Deep Learning for Global High-Resolution Land Use Reconstruction

Uncertainty in the terrestrial carbon cycle remains a major constraint in climate projections, partly driven by the uncertainties affecting the land surface representation and variability in Earth system models. To address this limitation, we present a data-driven framework AI4Land, for generating high-resolution historical reconstructions and future projections of key land surface variables. The framework follows a two-phase approach using a U-Net architecture. In the first phase, which is the focus of this work, it reconstructs annual land use and land cover by integrating coarse-resolution scenario data with static geophysical features. In a planned second phase, the resulting high-resolution maps will be used to predict dynamic biophysical variables, particularly leaf area index, at finer temporal scales. Trained on Earth observation data, the models learn to reproduce spatially explicit and physically consistent land surface patterns, extending temporal coverage to periods lacking direct observations. AI4Land was developed and trained on MareNostrum5, demonstrating how GPU-accelerated HPC infrastructure enables global-scale climate AI pipelines. The final product is a suite of open-source emulators designed for real-time coupling with digital twin platforms, such as those developed under the Destination Earth initiative. By delivering realistic and evolving land surface conditions on demand, this work aims to reduce critical uncertainties and improve the predictive power of next-generation climate simulations.

COGENT: Continuous Graph Emulators with Neural Ordinary Differential Equations for Long-Term Physical Forecasting

In this work, we present COGENT, a continuous graph emulator with Neural Ordinary Differential Equations for long-term physical forecasting on irregular geospatial meshes. COGENT encodes a finite history of system states and associated forcing fields and external forcings with a graph-based history encoder, producing node-wise context vectors that capture both local spatial interactions and temporal evolution. These context vectors initialize and condition a latent Neural Ordinary Differential Equation whose dynamics are driven by interpolated future forcings and explicit relative rollout time. By modeling the forecast trajectory as a continuous latent dynamical system, COGENT can generate predictions at arbitrary future times rather than being restricted to a fixed temporal discretization. A residual decoder maps the resulting latent trajectories back to future physical states, enabling direct multi-step forecasting without repeatedly feeding predicted states back into the model. This formulation combines graph-based spatial representation, history-conditioned latent dynamics, and continuous-time rollout in a unified framework for mesh-based physical simulation emulation. In order to stabilize training with long-horizon supervision, we also propose effective rollout-horizon sampling and a progressive rollout-horizon scheduling strategy. We evaluate COGENT on transient ice-sheet simulations generated by the Ice-sheet and Sea-level System Model, demonstrating improved long-range stability over autoregressive graph baselines. These results suggest that continuous graph Neural ODEs provide a promising methodology for scalable physical forecasting on irregular geospatial meshes, particularly in applications that require stable long-horizon predictions and the ability to query system states at arbitrary times.

Gaussian Process Latent Factor Regression for Low-Data, High-Dimensional Output Problems

In the sciences, regression tasks often require predicting high-dimensional outputs from few training examples. Multi-output Gaussian processes excel in low-data regimes but typically struggle with high-dimensional outputs. Compress-then-predict pipelines such as PCA-GP (principal component analysis plus Gaussian process regression) handle high dimensionality, but rely on bases optimized for reconstruction rather than prediction. To address this gap, we propose a model that represents each output as a linear-Gaussian decoding of a low-dimensional latent state drawn from a Gaussian process prior. By analytically marginalizing the decoder weights, we couple compression and prediction in a single objective that scales to high-dimensional outputs. We refer to this model as Gaussian process latent factor regression (GPLFR). We demonstrate GPLFR by building the first spatially resolved emulator of global climate models for rocky exoplanets.

Decomposing Ensemble Spread in Lorenz '96 With Learned Stochastic Parameterizations

Weather and climate forecasts are inherently uncertain due to chaotic dynamics, imperfect initial conditions, and incomplete representation of the underlying physical processes. Operational ensemble forecasts aim to represent these uncertainties through forecast spread, yet many approaches yield underdispersive estimates, with spread that grows too slowly relative to forecast error. Using the two-scale Lorenz 1996 system as a widely used, controlled testbed, we design a systematic approach to disentangle intrinsic variability, initial-condition perturbations, and stochastic model uncertainty. We compare multiple ensemble configurations and parameterization strategies, including existing deterministic and autoregressive as well as novel Bayesian and flow-based approaches. Our results show that ensemble perturbations do not increase the system's long-term variance; rather, they regulate how rapidly trajectories decorrelate and explore the invariant measure. Stochastic parameterizations, particularly those with temporally persistent structure, enhance early spread growth and improve spread-error consistency. Overall, we bring clarity to how different sources of uncertainty interact in a chaotic system and provide guidance for the design and evaluation of stochastic parameterizations in weather and climate models.

Deep Learning Surrogates for Emulating Stochastic Climate Tipping Dynamics

This work explores a dynamics-informed Temporal Fusion Transformer (TFT) as a data-driven surrogate for computationally intensive Earth system simulations. Focusing on multivariate time series describing global ocean transport, we demonstrate the surrogate's ability to forecast tip events across thousands of time steps. The data involve up to 21 non-stationary time series in addition to static covariates describing free parameters and initial conditions. Modifications to the architecture and objective function yield a surrogate that anticipates the timing of Atlantic and Pacific collapses to high fidelity and captures the stochastic uncertainty in transition timing across ensemble predictions. The learned surrogate achieves a 465x computational speedup over the numerical simulator while maintaining differentiability with respect to parameters and initial conditions.

The Bayesian Reflex: Online Learning as the Autonomic Nervous System of Modern and Future AI

This chapter introduces the Bayesian reflex -- an analogy with the autonomic nervous system -- as a unifying framework for online learning in AI. Bayesian online algorithms automatically maintain equilibrium in dynamic environments via three mechanisms: belief maintenance through probabilistic representations, sequential updating via Bayes' theorem, and uncertainty-driven action balancing exploration and exploitation. We survey online Bayesian methods, highlighting two computational principles: the look-up table principle for sequential inference in function space, and the ellipsoidal decomposition framework for nearly exact i.i.d. sampling from arbitrary posteriors. These principles are generalized across dynamic emulation, nonparametric state-space models, circular time series, inverse regression for climate model evaluation, and deep architectures via Recursive Gaussian Processes. Decision-making is explored via Thompson sampling and restless bandits. We extend the framework to assess infinite series convergence (applied to climate dynamics and the Riemann Hypothesis), model prime number distributions leading to the discovery of 184 strong Mersenne prime candidates, detect stationarity, and characterize point processes. The Bayesian reflex provides a foundational infrastructure for adaptive AI that continuously learns in a complex world.