Global Models¶
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HVR-Met: A Hypothesis-Verification-Replanning Agentic System for Extreme Weather Diagnosis¶
While deep learning-based weather forecasting paradigms have made significant strides, addressing extreme weather diagnostics remains a formidable challenge. This gap exists primarily because the...While deep learning-based weather forecasting paradigms have made significant strides, addressing extreme weather diagnostics remains a formidable challenge. This gap exists primarily because the diagnostic process demands sophisticated multi-step logical reasoning, dynamic tool invocation, and expert-level prior judgment. Although agents possess inherent advantages in task decomposition and autonomous execution, current architectures are still hampered by critical bottlenecks: inadequate expert knowledge integration, a lack of professional-grade iterative reasoning loops, and the absence of fine-grained validation and evaluation systems for complex workflows under extreme conditions. To this end, we propose HVR-Met, a multi-agent meteorological diagnostic system characterized by the deep integration of expert knowledge. Its central innovation is the “Hypothesis-Verification-Replanning” closed-loop mechanism, which facilitates sophisticated iterative reasoning for anomalous meteorological signals during extreme weather events. To bridge gaps within existing evaluation frameworks, we further introduce a novel benchmark focused on atomic-level subtasks. Experimental evidence demonstrates that the system excels in complex diagnostic scenarios. more
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Phys-Diff: A Physics-Inspired Latent Diffusion Model for Tropical Cyclone Forecasting¶
Tropical cyclone (TC) forecasting is critical for disaster warning and emergency response. Deep learning methods address computational challenges but often neglect physical relationships between TC...Tropical cyclone (TC) forecasting is critical for disaster warning and emergency response. Deep learning methods address computational challenges but often neglect physical relationships between TC attributes, resulting in predictions lacking physical consistency. To address this, we propose Phys-Diff, a physics-inspired latent diffusion model that disentangles latent features into task-specific components (trajectory, pressure, wind speed) and employs cross-task attention to introduce prior physics-inspired inductive biases, thereby embedding physically consistent dependencies among TC attributes. Phys-Diff integrates multimodal data including historical cyclone attributes, ERA5 reanalysis data, and FengWu forecast fields via a Transformer encoder-decoder architecture, further enhancing forecasting performance. Experiments demonstrate state-of-the-art performance on global and regional datasets. more
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Scaling Laws of Global Weather Models¶
Data-driven models are revolutionizing weather forecasting. To optimize training efficiency and model performance, this paper analyzes empirical scaling laws within this domain. We investigate the...Data-driven models are revolutionizing weather forecasting. To optimize training efficiency and model performance, this paper analyzes empirical scaling laws within this domain. We investigate the relationship between model performance (validation loss) and three key factors: model size (\(N\)), dataset size (\(D\)), and compute budget (\(C\)). Across a range of models, we find that Aurora exhibits the strongest data-scaling behavior: increasing the training dataset by 10x reduces validation loss by up to 3.2x. GraphCast demonstrates the highest parameter efficiency, yet suffers from limited hardware utilization. Our compute-optimal analysis indicates that, under fixed compute budgets, allocating resources to more total training data yields greater performance gains than increasing model size. Furthermore, we analyze model shape and uncover scaling behaviors that differ fundamentally from those observed in language models: weather forecasting models consistently favor increased width over depth. These findings suggest that future weather models should prioritize wider architectures and larger effective training datasets to maximize predictive performance. more
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A Synergistic Approach: Dynamics-AI Ensemble in Tropical Cyclone Forecasting¶
This study addresses a critical challenge in AI-based weather forecasting by developing an AI-driven optimized ensemble forecast system using Orthogonal Conditional Nonlinear Optimal Perturbations...This study addresses a critical challenge in AI-based weather forecasting by developing an AI-driven optimized ensemble forecast system using Orthogonal Conditional Nonlinear Optimal Perturbations (O-CNOPs). The system bridges the gap between computational efficiency and dynamic consistency in tropical cyclone (TC) forecasting. Unlike conventional ensembles limited by computational costs or AI ensembles constrained by inadequate perturbation methods, O-CNOPs generate dynamically optimized perturbations that capture fast-growing errors of FuXi model while maintaining plausibility. The key innovation lies in producing orthogonal perturbations that respect FuXi nonlinear dynamics, yielding structures reflecting dominant dynamical controls and physically interpretable probabilistic forecasts. Demonstrating superior deterministic and probabilistic skills over the operational Integrated Forecasting System Ensemble Prediction System, this work establishes a new paradigm combining AI computational advantages with rigorous dynamical constraints. Success in TC track forecasting paves the way for reliable ensemble forecasts of other high-impact weather systems, marking a major step toward operational AI-based ensemble forecasting. more
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On Using Medium-Range Ensemble Forecasts for Storm Transposition of Synoptic-Scale Systems in Probable Maximum Precipitation Estimation¶
Most methods for estimating probable maximum precipitation (PMP) -- the greatest depth of precipitation that is physically possible over a given area and duration -- rely on storm transposition (ST),...Most methods for estimating probable maximum precipitation (PMP) -- the greatest depth of precipitation that is physically possible over a given area and duration -- rely on storm transposition (ST), the process of transporting a storm, either historically observed or simulated, from its original location to a target basin. Existing ST approaches, whether classical or physically based, involve assumptions and manipulations that can introduce inconsistencies, leaving the physical validity of the transposed storm uncertain. In this study, the internal variability leveraging (IVL) approach is used to transpose an atmospheric river cluster that affected the U.S. West Coast during 20-29 October 2021. Steering the storm toward the target basin and determining its transposition region are achieved by considering an ensemble of plausible storm evolutions and trajectories obtained from archived ECMWF medium-range forecasts. The Willamette River and Nass River watersheds, located approximately 6 deg N, 2 deg W and 16 deg N, 8 deg W, respectively, from the area most affected by the observed precipitation, were selected as target basins. For each basin, the IVL realization yielding the largest 24-h basin-average precipitation depth was identified, and the initial and boundary condition shifting method was subsequently applied to further enhance its impact, producing 24-h precipitation depths of 119 mm for the Willamette and 98 mm for the Nass. more
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Exploring Novel Data Storage Approaches for Large-Scale Numerical Weather Prediction¶
Driven by scientific and industry ambition, HPC and AI applications such as operational Numerical Weather Prediction (NWP) require processing and storing ever-increasing data volumes as fast as...Driven by scientific and industry ambition, HPC and AI applications such as operational Numerical Weather Prediction (NWP) require processing and storing ever-increasing data volumes as fast as possible. Whilst POSIX distributed file systems and NVMe SSDs are currently a common HPC storage configuration providing I/O to applications, new storage solutions have proliferated or gained traction over the last decade with potential to address performance limitations POSIX file systems manifest at scale for certain I/O workloads. This work has primarily aimed to assess the suitability and performance of two object storage systems -namely DAOS and Ceph- for the ECMWF's operational NWP as well as for HPC and AI applications in general. New software-level adapters have been developed which enable the ECMWF's NWP to leverage these systems, and extensive I/O benchmarking has been conducted on a few computer systems, comparing the performance delivered by the evaluated object stores to that of equivalent Lustre file system deployments on the same hardware. Challenges of porting to object storage and its benefits with respect to the traditional POSIX I/O approach have been discussed and, where possible, domain-agnostic performance analysis has been conducted, leading to insight also of relevance to I/O practitioners and the broader HPC community. DAOS and Ceph have both demonstrated excellent performance, but DAOS stood out relative to Ceph and Lustre, providing superior scalability and flexibility for applications to perform I/O at scale as desired. This sets a promising outlook for DAOS and object storage, which might see greater adoption at HPC centres in the years to come, although not necessarily implying a shift away from POSIX-like I/O. more
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PDE foundation models are skillful AI weather emulators for the Martian atmosphere¶
We show that AI foundation models that are pretrained on numerical solutions to a diverse corpus of partial differential equations can be adapted and fine-tuned to obtain skillful predictive weather...We show that AI foundation models that are pretrained on numerical solutions to a diverse corpus of partial differential equations can be adapted and fine-tuned to obtain skillful predictive weather emulators for the Martian atmosphere. We base our work on the Poseidon PDE foundation model for two-dimensional systems. We develop a method to extend Poseidon from two to three dimensions while keeping the pretraining information. Moreover, we investigate the performance of the model in the presence of sparse initial conditions. Our results make use of four Martian years (approx.~34 GB) of training data and a median compute budget of 13 GPU hours. We find that the combination of pretraining and model extension yields a performance increase of 34.4% on a held-out year. This shows that PDEs-FMs can not only approximate solutions to (other) PDEs but also anchor models for real-world problems with complex interactions that lack a sufficient amount of training data or a suitable compute budget. more
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PuYun-LDM: A Latent Diffusion Model for High-Resolution Ensemble Weather Forecasts¶
Latent diffusion models (LDMs) suffer from limited diffusability in high-resolution (<=0.25°) ensemble weather forecasting, where diffusability characterizes how easily a latent data distribution can...Latent diffusion models (LDMs) suffer from limited diffusability in high-resolution (<=0.25°) ensemble weather forecasting, where diffusability characterizes how easily a latent data distribution can be modeled by a diffusion process. Unlike natural image fields, meteorological fields lack task-agnostic foundation models and explicit semantic structures, making VFM-based regularization inapplicable. Moreover, existing frequency-based approaches impose identical spectral regularization across channels under a homogeneity assumption, which leads to uneven regularization strength under the inter-variable spectral heterogeneity in multivariate meteorological data. To address these challenges, we propose a 3D Masked AutoEncoder (3D-MAE) that encodes weather-state evolution features as an additional conditioning for the diffusion model, together with a Variable-Aware Masked Frequency Modeling (VA-MFM) strategy that adaptively selects thresholds based on the spectral energy distribution of each variable. Together, we propose PuYun-LDM, which enhances latent diffusability and achieves superior performance to ENS at short lead times while remaining comparable to ENS at longer horizons. PuYun-LDM generates a 15-day global forecast with a 6-hour temporal resolution in five minutes on a single NVIDIA H200 GPU, while ensemble forecasts can be efficiently produced in parallel. more
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Hierarchical Testing of a Hybrid Machine Learning-Physics Global Atmosphere Model¶
Machine learning (ML)-based models have demonstrated high skill and computational efficiency, often outperforming conventional physics-based models in weather and subseasonal predictions. While prior...Machine learning (ML)-based models have demonstrated high skill and computational efficiency, often outperforming conventional physics-based models in weather and subseasonal predictions. While prior studies have assessed their fidelity in capturing synoptic-scale atmospheric dynamics, their performance across timescales and under out-of-distribution forcing, such as +3K or +4K uniform-warming forcings, and the sources of biases remain elusive, to establish the model reliability for Earth science. Here, we design three sets of experiments targeting synoptic-scale phenomena, interannual variability, and out-of-distribution uniform-warming forcings. We evaluate the Neural General Circulation Model (NeuralGCM), a hybrid model integrating a dynamical core with ML-based component, against observations and physics-based Earth system models (ESMs). At the synoptic scale, NeuralGCM captures the evolution and propagation of extratropical cyclones with performance comparable to ESMs. At the interannual scale, when forced by El Niño-Southern Oscillation sea surface temperature (SST) anomalies, NeuralGCM successfully reproduces associated teleconnection patterns but exhibits deficiencies in capturing nonlinear response. Under out-of-distribution uniform-warming forcings, NeuralGCM simulates similar responses in global-average temperature and precipitation and reproduces large-scale tropospheric circulation features similar to those in ESMs. Notable weaknesses include overestimating the tracks and spatial extent of extratropical cyclones, biases in the teleconnected wave train triggered by tropical SST anomalies, and differences in upper-level warming and stratospheric circulation responses to SST warming compared to physics-based ESMs. The causes of these weaknesses were explored. more
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UniPhy: Unifying Riemannian-Clifford Geometry and Biorthogonal Dynamics for Planetary-Scale Continuous Weather Modeling¶
While data-driven weather models have achieved remarkable deterministic accuracy, they fundamentally rely on discrete-time mappings and closed-system assumptions, failing to capture the multi-scale...While data-driven weather models have achieved remarkable deterministic accuracy, they fundamentally rely on discrete-time mappings and closed-system assumptions, failing to capture the multi-scale continuous dynamics and thermodynamic openness of the atmosphere. To address these limitations, we propose UniPhy, a continuous-time non-Hermitian neural stochastic partial differential equation (SPDE) solver. Geometrically, we employ Riemannian-Clifford gauge transformations to flatten planetary heterogeneity, enabling globally consistent operations. Dynamically, we construct non-Hermitian biorthogonal spectral operators integrated with a global flux tracker to capture transient energy growth and open-system exchange. Computationally, by identifying the algebraic associativity of the analytic solution, we reformulate adaptive physical integration as a parallel prefix-sum problem, achieving log-linear sequence parallelism. UniPhy establishes a physically complete foundation model architecture that unifies geometric adaptivity, thermodynamic consistency, and computational efficiency. Our code is available at https://github.com/yrqUni/UniPhy. more
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Decision-oriented benchmarking to transform AI weather forecast access: Application to the Indian monsoon¶
Artificial intelligence weather prediction (AIWP) models now often outperform traditional physics-based models on common metrics while requiring orders-of-magnitude less computing resources and time....Artificial intelligence weather prediction (AIWP) models now often outperform traditional physics-based models on common metrics while requiring orders-of-magnitude less computing resources and time. Open-access AIWP models thus hold promise as transformational tools for helping low- and middle-income populations make decisions in the face of high-impact weather shocks. Yet, current approaches to evaluating AIWP models focus mainly on aggregated meteorological metrics without considering local stakeholders' needs in decision-oriented, operational frameworks. Here, we introduce such a framework that connects meteorology, AI, and social sciences. As an example, we apply it to the 150-year-old problem of Indian monsoon forecasting, focusing on benefits to rain-fed agriculture, which is highly susceptible to climate change. AIWP models skillfully predict an agriculturally relevant onset index at regional scales weeks in advance when evaluated out-of-sample using deterministic and probabilistic metrics. This framework informed a government-led effort in 2025 to send 38 million Indian farmers AI-based monsoon onset forecasts, which captured an unusual weeks-long pause in monsoon progression. This decision-oriented benchmarking framework provides a key component of a blueprint for harnessing the power of AIWP models to help large vulnerable populations adapt to weather shocks in the face of climate variability and change. more
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Role of the ocean for fast atmospheric evolution revealed by machine learning¶
There have recently been many efforts to create machine learnt atmospheric emulators designed to replace physical models. So far these have mainly focused on medium-range weather forecasting, where...There have recently been many efforts to create machine learnt atmospheric emulators designed to replace physical models. So far these have mainly focused on medium-range weather forecasting, where these ‘Machine Learnt Weather Prediction’ (MLWP) models can outperform leading operational forecasting centres. However, because of this focus on shorter timescales, many of these emulators ignore the effects of the ocean, and take no ocean variables as inputs. We hypothesise that such MLWP models have learnt a best-guess of the evolution of the atmosphere, by implicitly inferring ocean conditions from atmospheric states, with no access to ocean data. Turning this limitation into a strength, we use it as a means to study the role of the oceans on the evolution of the atmosphere. By exploring how model forecast errors relate to properties of the air-sea interface, we infer what ocean information these atmospheric emulators are able to derive from atmospheric data alone, and what they cannot. This highlights the regions and processes through which the ocean independently influences the atmosphere on fast timescales. We perform this analysis for GraphCast, finding clear relationships between air-sea properties and the forecast errors over the ocean, including clear seasonal effects. We then explore what this reveals about GraphCast's internal representation of the ocean. In addition to understanding real-world ocean-atmosphere interactions, this analysis provides guidance for improving forecast skill and physical realism in MLWP models, and for informing how future machine learning models should use ocean information on short timescales. more
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EMFormer: Efficient Multi-Scale Transformer for Accumulative Context Weather Forecasting¶
Long-term weather forecasting is critical for socioeconomic planning and disaster preparedness. While recent approaches employ finetuning to extend prediction horizons, they remain constrained by the...Long-term weather forecasting is critical for socioeconomic planning and disaster preparedness. While recent approaches employ finetuning to extend prediction horizons, they remain constrained by the issues of catastrophic forgetting, error accumulation, and high training overhead. To address these limitations, we present a novel pipeline across pretraining, finetuning and forecasting to enhance long-context modeling while reducing computational overhead. First, we introduce an Efficient Multi-scale Transformer (EMFormer) to extract multi-scale features through a single convolution in both training and inference. Based on the new architecture, we further employ an accumulative context finetuning to improve temporal consistency without degrading short-term accuracy. Additionally, we propose a composite loss that dynamically balances different terms via a sinusoidal weighting, thereby adaptively guiding the optimization trajectory throughout pretraining and finetuning. Experiments show that our approach achieves strong performance in weather forecasting and extreme event prediction, substantially improving long-term forecast accuracy. Moreover, EMFormer demonstrates strong generalization on vision benchmarks (ImageNet-1K and ADE20K) while delivering a 5.69x speedup over conventional multi-scale modules. more
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"What is a realistic forecast?" Assessing data-driven weather forecasts, a journey from verification to falsification¶
The artificial intelligence revolution is fuelling a paradigm shift in weather forecasting: forecasts are generated with machine learning models trained on large datasets rather than with...The artificial intelligence revolution is fuelling a paradigm shift in weather forecasting: forecasts are generated with machine learning models trained on large datasets rather than with physics-based numerical models that solve partial differential equations. This new approach proved successful in improving forecast performance as measured with standard verification metrics such as the root mean squared error. At the same time, the realism of data-driven weather forecasts is often questioned and considered an Achilles' heel of machine learning models. How forecast realism can be defined and how this forecast attribute can be assessed are the two questions simultaneously addressed here. Inspired by the seminal work of Murphy (1993) on the definition of forecast goodness, we identify 3 types of realism: a functional realism measured by scoring functions, a structural realism related to the statistical characteristics of the forecasts, and a physical realism that is apprehended through the lenses of our scientific knowledge. This conceptual setting serves as a basis for the design of a new framework for the evaluation of data-driven weather models where falsification arises as a complementary process to the well-established diagnostic and verification tasks. more
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Track-Dependent Links between Tropical Cyclones and Extratropical Predictability in Physical and AI Models¶
Global medium-range weather forecasts suffer occasional failures, often linked to tropical cyclones (TCs). We investigate TC influences on extratropical predictability by comparing forecasts from a...Global medium-range weather forecasts suffer occasional failures, often linked to tropical cyclones (TCs). We investigate TC influences on extratropical predictability by comparing forecasts from a physics-based model (ECMWF-IFS) and an AI-hybrid model (Google-NGCM) initialized near TC genesis. Analyzing 108 out-of-sample Northern Hemisphere cases reveals similar extratropical error growth patterns and comparable performance between the models. This suggests that the NGCM is capable of predicting the bulk upscale effects of tropical convection without directly representing convective processes. Leveraging the NGCM's computational efficiency, we compare forecasts initialized with and without TC genesis to isolate track-dependent forecast impacts. For Week-2 extratropical forecasts, TC impacts are highly time-, metric-, and track-dependent. The analysis confirms that some poleward-moving TCs degrade Week-2 US and European forecasts and suggests significant impacts from westward-moving TCs. The findings highlight the utility of the AI-hybrid model in predictability research and complex tropical-extratropical teleconnections that warrant future research. more
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Physics Informed Reconstruction of Four-Dimensional Atmospheric Wind Fields Using Multi-UAS Swarm Observations in a Synthetic Turbulent Environment¶
Accurate reconstruction of atmospheric wind fields is essential for applications such as weather forecasting, hazard prediction, and wind energy assessment, yet conventional instruments leave...Accurate reconstruction of atmospheric wind fields is essential for applications such as weather forecasting, hazard prediction, and wind energy assessment, yet conventional instruments leave spatio-temporal gaps within the lower atmospheric boundary layer. Unmanned aircraft systems (UAS) provide flexible in situ measurements, but individual platforms sample wind only along their flight trajectories, limiting full wind-field recovery. This study presents a framework for reconstructing four-dimensional atmospheric wind fields using measurements obtained from a coordinated UAS swarm. A synthetic turbulence environment and high-fidelity multirotor simulation are used to generate training and evaluation data. Local wind components are estimated from UAS dynamics using a bidirectional long short-term memory network (Bi-LSTM) and assimilated into a physics-informed neural network (PINN) to reconstruct a continuous wind field in space and time. For local wind estimation, the bidirectional LSTM achieves root-mean-square errors (RMSE) of 0.064 and 0.062 m/s for the north and east components in low-wind conditions, increasing to 0.122 to 0.129 m/s under moderate winds and 0.271 to 0.273 m/s in high-wind conditions, while the vertical component exhibits higher error, with RMSE values of 0.029 to 0.091 m/s. The physics-informed reconstruction recovers the dominant spatial and temporal structure of the wind field up to 1000 m altitude while preserving mean flow direction and vertical shear. Under moderate wind conditions, the reconstructed mean wind field achieves an overall RMSE between 0.118 and 0.154 m/s across evaluated UAS configurations, with the lowest error obtained using a five-UAS swarm. These results demonstrate that coordinated UAS measurements enable accurate and scalable four-dimensional wind-field reconstruction without dedicated wind sensors or fixed infrastructure. more
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Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecasting¶
Recent machine-learning approaches to weather forecasting often employ a monolithic architecture, where distinct physical mechanisms (advection, transport), diffusion-like mixing, thermodynamic...Recent machine-learning approaches to weather forecasting often employ a monolithic architecture, where distinct physical mechanisms (advection, transport), diffusion-like mixing, thermodynamic processes, and forcing are represented implicitly within a single large network. This representation is particularly problematic for advection, where long-range transport must be treated with expensive global interaction mechanisms or through deep, stacked convolutional layers. To mitigate this, we present PARADIS, a physics-inspired global weather prediction model that imposes inductive biases on network behavior through a functional decomposition into advection, diffusion, and reaction blocks acting on latent variables. We implement advection through a Neural Semi-Lagrangian operator that performs trajectory-based transport via differentiable interpolation on the sphere, enabling end-to-end learning of both the latent modes to be transported and their characteristic trajectories. Diffusion-like processes are modeled through depthwise-separable spatial mixing, while local source terms and vertical interactions are modeled via pointwise channel interactions, enabling operator-level physical structure. PARADIS provides state-of-the-art forecast skill at a fraction of the training cost. On ERA5-based benchmarks, the 1 degree PARADIS model, with a total training cost of less than a GPU month, meets or exceeds the performance of 0.25 degree traditional and machine-learning baselines, including the ECMWF HRES forecast and DeepMind's GraphCast. more
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Demystifying Data-Driven Probabilistic Medium-Range Weather Forecasting¶
The recent revolution in data-driven methods for weather forecasting has lead to a fragmented landscape of complex, bespoke architectures and training strategies, obscuring the fundamental drivers of...The recent revolution in data-driven methods for weather forecasting has lead to a fragmented landscape of complex, bespoke architectures and training strategies, obscuring the fundamental drivers of forecast accuracy. Here, we demonstrate that state-of-the-art probabilistic skill requires neither intricate architectural constraints nor specialized training heuristics. We introduce a scalable framework for learning multi-scale atmospheric dynamics by combining a directly downsampled latent space with a history-conditioned local projector that resolves high-resolution physics. We find that our framework design is robust to the choice of probabilistic estimator, seamlessly supporting stochastic interpolants, diffusion models, and CRPS-based ensemble training. Validated against the Integrated Forecasting System and the deep learning probabilistic model GenCast, our framework achieves statistically significant improvements on most of the variables. These results suggest scaling a general-purpose model is sufficient for state-of-the-art medium-range prediction, eliminating the need for tailored training recipes and proving effective across the full spectrum of probabilistic frameworks. more
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HealDA: Highlighting the importance of initial errors in end-to-end AI weather forecasts¶
AI weather models now rival leading numerical weather prediction (NWP) systems in medium-range skill. However, almost all still rely on NWP data assimilation (DA) to provide initial conditions, tying...AI weather models now rival leading numerical weather prediction (NWP) systems in medium-range skill. However, almost all still rely on NWP data assimilation (DA) to provide initial conditions, tying them to expensive infrastructure and limiting the practical speed and accuracy gains of ML. More recently, ML-based DA systems have been proposed, which are often trained and evaluated end-to-end with a forecast model, making it difficult to assess the quality of their analysis fields. We introduce HealDA, a global ML-based DA system that maps a short window of satellite and conventional observations directly to a 1° atmospheric state on the HEALPix grid, using a smaller sensor suite than operational NWP. We treat HealDA strictly as a DA module: its analyses are used to initialize off-the-shelf ML forecast models without any fine-tuning of either. For a variety of off-the-shelf ML forecast models, including FourCastNet3 (FCN3), Aurora, and FengWu, HealDA-initialized forecasts lose less than one day of effective lead time when scored against ERA5. HealDA-initialized FCN3 ensembles similarly trail those of the ECMWF IFS ENS system by < 24 h. We find that forecast error growth in these models is unchanged from HealDA initialization, and the skill gap primarily arises from the larger initial error of the HealDA analysis. Spectral analysis reveals that this stems from overfitting to the large scales and upper-tropospheric fields. We also demonstrate that small changes in the verification setup can shift apparent skill by 12--24h, underscoring the need for consistent scoring. Taken together, these results clarify the current performance of ML-based DA systems and show that a relatively simple, direct observation-to-state network can already provide initial conditions that are usable by state-of-the-art ML forecast models with only modest loss in medium-range skill. more
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Toward Trustworthy Short-Range Forecasts with AFNO: From Skill Metrics to Conservation Checks¶
Data driven weather models now approach traditional numerical weather prediction (NWP) skill at short to medium lead times, but their dynamical consistency during autoregressive rollout remains...Data driven weather models now approach traditional numerical weather prediction (NWP) skill at short to medium lead times, but their dynamical consistency during autoregressive rollout remains uncertain. more
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Searth Transformer: A Transformer Architecture Incorporating Earth's Geospheric Physical Priors for Global Mid-Range Weather Forecasting¶
Accurate global medium-range weather forecasting is fundamental to Earth system science. Most existing Transformer-based forecasting models adopt vision-centric architectures that neglect the Earth's...Accurate global medium-range weather forecasting is fundamental to Earth system science. Most existing Transformer-based forecasting models adopt vision-centric architectures that neglect the Earth's spherical geometry and zonal periodicity. In addition, conventional autoregressive training is computationally expensive and limits forecast horizons due to error accumulation. To address these challenges, we propose the Shifted Earth Transformer (Searth Transformer), a physics-informed architecture that incorporates zonal periodicity and meridional boundaries into window-based self-attention for physically consistent global information exchange. We further introduce a Relay Autoregressive (RAR) fine-tuning strategy that enables learning long-range atmospheric evolution under constrained memory and computational budgets. Based on these methods, we develop YanTian, a global medium-range weather forecasting model. YanTian achieves higher accuracy than the high-resolution forecast of the European Centre for Medium-Range Weather Forecasts and performs competitively with state-of-the-art AI models at one-degree resolution, while requiring roughly 200 times lower computational cost than standard autoregressive fine-tuning. Furthermore, YanTian attains a longer skillful forecast lead time for Z500 (10.3 days) than HRES (9 days). Beyond weather forecasting, this work establishes a robust algorithmic foundation for predictive modeling of complex global-scale geophysical circulation systems, offering new pathways for Earth system science. more
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Efficient Parameter Calibration of Numerical Weather Prediction Models via Evolutionary Sequential Transfer Optimization¶
The configuration of physical parameterization schemes in Numerical Weather Prediction (NWP) models plays a critical role in determining the accuracy of the forecast. However, existing parameter...The configuration of physical parameterization schemes in Numerical Weather Prediction (NWP) models plays a critical role in determining the accuracy of the forecast. However, existing parameter calibration methods typically treat each calibration task as an isolated optimization problem. This approach suffers from prohibitive computational costs and necessitates performing iterative searches from scratch for each task, leading to low efficiency in sequential calibration scenarios. To address this issue, we propose the SEquential Evolutionary Transfer Optimization (SEETO) algorithm driven by the representations of the meteorological state. First, to accurately measure the physical similarity between calibration tasks, a meteorological state representation extractor is introduced to map high-dimensional meteorological fields into latent representations. Second, given the similarity in the latent space, a bi-level adaptive knowledge transfer mechanism is designed. At the solution level, superior populations from similar historical tasks are reused to achieve a "warm start" for optimization. At the model level, an ensemble surrogate model based on source task data is constructed to assist the search, employing an adaptive weighting mechanism to dynamically balance the contributions of source domain knowledge and target domain data. Extensive experiments across 10 distinct calibration tasks, which span varying source-target similarities, highlight SEETO's superior efficiency. Under a strict budget of 20 expensive evaluations, SEETO achieves a 6% average improvement in Hypervolume (HV) over two state-of-the-art baselines. Notably, to match SEETO's performance at this stage, the comparison algorithms would require an average of 64% and 28% additional evaluations, respectively. This presents a new paradigm for the efficient and accurate automated calibration of NWP model parameters. more
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Hybrid SARIMA LSTM Model for Local Weather Forecasting: A Residual Learning Approach for Data Driven Meteorological Prediction¶
Accurately forecasting long-term atmospheric variables remains a defining challenge in meteorological science due to the chaotic nature of atmospheric systems. Temperature data represents a complex...Accurately forecasting long-term atmospheric variables remains a defining challenge in meteorological science due to the chaotic nature of atmospheric systems. Temperature data represents a complex superposition of deterministic cyclical climate forces and stochastic, short-term fluctuations. While planetary mechanics drive predictable seasonal periodicities, rapid meteorological changes such as thermal variations, pressure anomalies, and humidity shifts introduce nonlinear volatilities that defy simple extrapolation. Historically, the Seasonal Autoregressive Integrated Moving Average (SARIMA) model has been the standard for modeling historical weather data, prized for capturing linear seasonal trends. However, SARIMA operates under strict assumptions of stationarity, failing to capture abrupt, nonlinear transitions. This leads to systematic residual errors, manifesting as the under-prediction of sudden spikes or the over-smoothing of declines. Conversely, Deep Learning paradigms, specifically Long Short-Term Memory (LSTM) networks, demonstrate exceptional efficacy in handling intricate time-series data. By utilizing memory gates, LSTMs learn complex nonlinear dependencies. Yet, LSTMs face instability in open-loop forecasting; without ground truth feedback, minor deviations compound recursively, causing divergence. To resolve these limitations, we propose a Hybrid SARIMA-LSTM architecture. This framework employs a residual-learning strategy to decompose temperature into a predictable climate component and a nonlinear weather component. The SARIMA unit models the robust, long-term seasonal trend, while the LSTM is trained exclusively on the residuals the nonlinear errors SARIMA fails to capture. By fusing statistical stability with neural plasticity, this hybrid approach minimizes error propagation and enhances long-horizon accuracy. more
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Error in ERA5 2m Temperature identified using GraphCast¶
Reanalyses such as ERA5 have long been foundational for weather and climate science. They have also found a new use case, as training and verification data for machine-learnt weather prediction...Reanalyses such as ERA5 have long been foundational for weather and climate science. They have also found a new use case, as training and verification data for machine-learnt weather prediction (MLWP) models. Here we compare short-lead time (6h) forecasts from the MLWP model GraphCast against ERA5. In doing so, we identify a recurrent, spatially coherent error in 2m Temperature centred on the Ethiopian Highlands, that occurs predominantly at 0600 UTC. We show that these error events are not an error in the forecast from GraphCast, but are in fact an error in ERA5, and are also present in the ECMWF operational analysis. They arise from the 2D optimal interpolation procedure, when surface reports are assimilated that are temporally displaced compared to the background forecast. This produces spuriously warm analysis increments over Ethiopia on approximately 7% of dates at 0600 UTC across the reanalysis record. The spread from the ensemble of data assimilation partially flags these cases but is underdispersive. We assess the impact on GraphCast, which was trained on ERA5. While GraphCast can largely ignore these unphysical error events, a small systematic degradation in forecast skill over the region is observed. We discuss implications for using reanalysis as truth in machine learning training and verification, and recommend simple changes to reduce such artefacts in future analyses. more
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Probabilistic Transformers for Joint Modeling of Global Weather Dynamics and Decision-Centric Variables¶
Weather forecasts sit upstream of high-stakes decisions in domains such as grid operations, aviation, agriculture, and emergency response. Yet forecast users often face a difficult trade-off. Many...Weather forecasts sit upstream of high-stakes decisions in domains such as grid operations, aviation, agriculture, and emergency response. Yet forecast users often face a difficult trade-off. Many decision-relevant targets are functionals of the atmospheric state variables, such as extrema, accumulations, and threshold exceedances, rather than state variables themselves. As a result, users must estimate these targets via post-processing, which can be suboptimal and can introduce structural bias. The core issue is that decisions depend on distributions over these functionals that the model is not trained to learn directly. In this work, we introduce GEM-2, a probabilistic transformer that jointly learns global atmospheric dynamics alongside a suite of variables that users directly act upon. Using this training recipe, we show that a lightweight (~275M params) and computationally efficient (~20-100x training speedup relative to state-of-the-art) transformer trained on the CRPS objective can directly outperform operational numerical weather prediction (NWP) models and be competitive with ML models that rely on expensive multi-step diffusion processes or require bespoke multi-stage fine-tuning strategies. We further demonstrate state-of-the-art economic value metrics under decision-theoretic evaluation, stable convergence to climatology at S2S and seasonal timescales, and a surprising insensitivity to many commonly assumed architectural and training design choices. more
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Rainfall forecasts in daily use over East Africa improved by machine learning¶
Ensemble forecasting has proven over the years to be a vital tool for predicting extreme or only partially predictable weather events. In particular life-threatening weather events. Many National...Ensemble forecasting has proven over the years to be a vital tool for predicting extreme or only partially predictable weather events. In particular life-threatening weather events. Many National Meteorological Services in East Africa do not have the computing resources to enable them to run their local area models in full ensemble mode over the full period of the 2 week medium range. As a result, weather users in these countries are not being given sufficient information about weather risk that is needed to make reliable decisions about taking preventative action. Consequently, society in many parts of the world is not as resilient to weather events as they could be. In this paper we test the performance of our forecast system, cGAN, which is the only high-resolution (10 km) ensemble rainfall product that does real-time, probabilistic correction of global forecasts for East Africa. Compared to existing state-of-the-art AI models, our system offers higher spatial resolution. It is cheap to train/run and requires no additional post-processing. It is run on laptops and can generate many thousands of ensemble members at little computational cost (compared with physical local area models). It is ideally suited to Meteorological Services with limited computational facilities. more
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Towards mechanistic understanding in a data-driven weather model: internal activations reveal interpretable physical features¶
Large data-driven physics models like DeepMind's weather model GraphCast have empirically succeeded in parameterizing time operators for complex dynamical systems with an accuracy reaching or in some...Large data-driven physics models like DeepMind's weather model GraphCast have empirically succeeded in parameterizing time operators for complex dynamical systems with an accuracy reaching or in some cases exceeding that of traditional physics-based solvers. Unfortunately, how these data-driven models perform computations is largely unknown and whether their internal representations are interpretable or physically consistent is an open question. Here, we adapt tools from interpretability research in Large Language Models to analyze intermediate computational layers in GraphCast, leveraging sparse autoencoders to discover interpretable features in the neuron space of the model. We uncover distinct features on a wide range of length and time scales that correspond to tropical cyclones, atmospheric rivers, diurnal and seasonal behavior, large-scale precipitation patterns, specific geographical coding, and sea-ice extent, among others. We further demonstrate how the precise abstraction of these features can be probed via interventions on the prediction steps of the model. As a case study, we sparsely modify a feature corresponding to tropical cyclones in GraphCast and observe interpretable and physically consistent modifications to evolving hurricanes. Such methods offer a window into the black-box behavior of data-driven physics models and are a step towards realizing their potential as trustworthy predictors and scientifically valuable tools for discovery. more
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Controllable Probabilistic Forecasting with Stochastic Decomposition Layers¶
AI weather prediction ensembles with latent noise injection and optimized with the continuous ranked probability score (CRPS) have produced both accurate and well-calibrated predictions with far less...AI weather prediction ensembles with latent noise injection and optimized with the continuous ranked probability score (CRPS) have produced both accurate and well-calibrated predictions with far less computational cost compared with diffusion-based methods. However, current CRPS ensemble approaches vary in their training strategies and noise injection mechanisms, with most injecting noise globally throughout the network via conditional normalization. This structure increases training expense and limits the physical interpretability of the stochastic perturbations. We introduce Stochastic Decomposition Layers (SDL) for converting deterministic machine learning weather models into probabilistic ensemble systems. Adapted from StyleGAN's hierarchical noise injection, SDL applies learned perturbations at three decoder scales through latent-driven modulation, per-pixel noise, and channel scaling. When applied to WXFormer via transfer learning, SDL requires less than 2% of the computational cost needed to train the baseline model. Each ensemble member is generated from a compact latent tensor (5 MB), enabling perfect reproducibility and post-inference spread adjustment through latent rescaling. Evaluation on 2022 ERA5 reanalysis shows ensembles with spread-skill ratios approaching unity and rank histograms that progressively flatten toward uniformity through medium-range forecasts, achieving calibration competitive with operational IFS-ENS. Multi-scale experiments reveal hierarchical uncertainty: coarse layers modulate synoptic patterns while fine layers control mesoscale variability. The explicit latent parameterization provides interpretable uncertainty quantification for operational forecasting and climate applications. more
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Predicting Forecast Error for the HRRR Using LSTM Neural Networks: A Comparative Study Using New York and Oklahoma State Mesonets¶
Long Short-Term Memory (LSTM) models are trained to predict forecast errors for the High-Resolution Rapid Refresh (HRRR) model using the New York State Mesonet and Oklahoma State Mesonet near-surface...Long Short-Term Memory (LSTM) models are trained to predict forecast errors for the High-Resolution Rapid Refresh (HRRR) model using the New York State Mesonet and Oklahoma State Mesonet near-surface weather observations as ground truth. When evaluated using mean-absolute-error and percent improvement relative to the HRRR, LSTMs predict precipitation error most accurately, providing, on average, a 48% improvement relative to the HRRR forecast, followed by wind error, providing, on average, a 15% improvement, and then temperature error, providing, on average, a 25% improvement. Precipitation errors exhibit an asymmetry, with overforecast precipitation detected more accurately than underforecast, while wind error predictions are consistent across over- and underforecast predictions. Temperature error predictions are relatively accurate but smoother, with respect to variance, than true observations. This paper describes an overview of LSTM performance with the expressed intent of providing forecasters with real-time predictions of forecast error at the point of use within the New York State and Oklahoma State Mesonets. In practice, the predicted errors can be used to adjust deterministic HRRR forecasts at the point of use, identify locations and variables with elevated uncertainty, and provide supplemental guidance for high-impact decision-making. This research demonstrates the potential of LSTM-based machine learning models to provide actionable, location-specific predictions of forecast error for high-resolution operational numerical weather prediction (NWP) systems. However, model performance is variable-dependent, and the approach relies on the availability of dense mesonet observations, which may limit applicability in data-sparse regions. more
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Evaluating Weather Forecasts from a Decision Maker's Perspective¶
Standard weather forecast evaluations focus on the forecaster's perspective and on a statistical assessment comparing forecasts and observations. In practice, however, forecasts are used to make...Standard weather forecast evaluations focus on the forecaster's perspective and on a statistical assessment comparing forecasts and observations. In practice, however, forecasts are used to make decisions, so it seems natural to take the decision-maker's perspective and quantify the value of a forecast by its ability to improve decision-making. Decision calibration provides a novel framework for evaluating forecast performance at the decision level rather than the forecast level. We evaluate decision calibration to compare Machine Learning and classical numerical weather prediction models on various weather-dependent decision tasks. We find that model performance at the forecast level does not reliably translate to performance in downstream decision-making: some performance differences only become apparent at the decision level, and model rankings can change among different decision tasks. Our results confirm that typical forecast evaluations are insufficient for selecting the optimal forecast model for a specific decision task. more