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General circulation models (GCMs) are the foundation of weather and climate prediction. GCMs are physics-based simulators which combine a numerical solver for large-scale dynamics with tuned representations for small-scale processes such as cloud formation. Recently, machine learning (ML) models trained on reanalysis data achieved comparable or better skill than GCMs for deterministic weather forecasting. However, these models have not demonstrated improved ensemble forecasts, or shown sufficient stability for long-term weather and climate simulations. Here we present the first GCM that combines a differentiable solver for atmospheric dynamics with ML components, and show that it can generate forecasts of deterministic weather, ensemble weather and climate on par with the best ML and physics-based methods. NeuralGCM is competitive with ML models for 1-10 day forecasts, and with the European Centre for Medium-Range Weather Forecasts ensemble prediction for 1-15 day forecasts. With prescribed sea surface temperature, NeuralGCM can accurately track climate metrics such as global mean temperature for multiple decades, and climate forecasts with 140 km resolution exhibit emergent phenomena such as realistic frequency and trajectories of tropical cyclones. For both weather and climate, our approach offers orders of magnitude computational savings over conventional GCMs. Our results show that end-to-end deep learning is compatible with tasks performed by conventional GCMs, and can enhance the large-scale physical simulations that are essential for understanding and predicting the Earth system., Comment: 92 pages, 54 figures. Nature (2024)

WeatherBench 2 is an update to the global, medium-range (1-14 day) weather forecasting benchmark proposed by Rasp et al. (2020), designed with the aim to accelerate progress in data-driven weather modeling. WeatherBench 2 consists of an open-source evaluation framework, publicly available training, ground truth and baseline data as well as a continuously updated website with the latest metrics and state-of-the-art models: https://sites.research.google/weatherbench. This paper describes the design principles of the evaluation framework and presents results for current state-of-the-art physical and data-driven weather models. The metrics are based on established practices for evaluating weather forecasts at leading operational weather centers. We define a set of headline scores to provide an overview of model performance. In addition, we also discuss caveats in the current evaluation setup and challenges for the future of data-driven weather forecasting.

Climate projection uncertainty can be partitioned into model uncertainty, scenario uncertainty and internal variability. Here, we investigate the different sources of uncertainty in the projected frequencies of daily maximum temperature and precipitation extremes, which are defined as events that exceed the 99.97th percentile. This is done globally using initial-condition large ensembles. For maximum temperature extremes, internal variability dominates in the next two decades. Around the middle of the 21st century model and scenario uncertainty become the dominant contribution in the tropics but internal variability remains dominant in the extra-tropics. Towards the end of the century, model and scenario uncertainty increase to near equal contributions of ~40% each globally with large regional fluctuations. For precipitation extremes, internal variability dominates throughout the 21st century, except for some tropical regions, for example, West Africa. In regions where internal variability constitutes the major source of uncertainty, the potential impact of reducing model uncertainty on the signal-to-noise ratio of the climate projection is estimated to be small. We discuss the caveats of the methodology used and impact of our findings for the design of future climate models. The importance of internal variability found here emphasizes that large ensembles are a vital tool for understanding climate projections.

WeatherBench is a benchmark dataset for medium-range weather forecasting of geopotential, temperature and precipitation, consisting of preprocessed data, predefined evaluation metrics and a number of baseline models. WeatherBench Probability extends this to probabilistic forecasting by adding a set of established probabilistic verification metrics (continuous ranked probability score, spread-skill ratio and rank histograms) and a state-of-the-art operational baseline using the ECWMF IFS ensemble forecast. In addition, we test three different probabilistic machine learning methods -- Monte Carlo dropout, parametric prediction and categorical prediction, in which the probability distribution is discretized. We find that plain Monte Carlo dropout severely underestimates uncertainty. The parametric and categorical models both produce fairly reliable forecasts of similar quality. The parametric models have fewer degrees of freedom while the categorical model is more flexible when it comes to predicting non-Gaussian distributions. None of the models are able to match the skill of the operational IFS model. We hope that this benchmark will enable other researchers to evaluate their probabilistic approaches.

Accurately forecasting extreme rainfall is notoriously difficult, but is also ever more crucial for society as climate change increases the frequency of such extremes. Global numerical weather prediction models often fail to capture extremes, and are produced at too low a resolution to be actionable, while regional, high-resolution models are hugely expensive both in computation and labour. In this paper we explore the use of deep generative models to simultaneously correct and downscale (super-resolve) global ensemble forecasts over the Continental US. Specifically, using fine-grained radar observations as our ground truth, we train a conditional Generative Adversarial Network -- coined CorrectorGAN -- via a custom training procedure and augmented loss function, to produce ensembles of high-resolution, bias-corrected forecasts based on coarse, global precipitation forecasts in addition to other relevant meteorological fields. Our model outperforms an interpolation baseline, as well as super-resolution-only and CNN-based univariate methods, and approaches the performance of an operational regional high-resolution model across an array of established probabilistic metrics. Crucially, CorrectorGAN, once trained, produces predictions in seconds on a single machine. These results raise exciting questions about the necessity of regional models, and whether data-driven downscaling and correction methods can be transferred to data-poor regions that so far have had no access to high-resolution forecasts., Comment: To appear in AISTATS 2022

Projecting climate change is a generalization problem: we extrapolate the recent past using physical models across past, present, and future climates. Current climate models require representations of processes that occur at scales smaller than model grid size, which have been the main source of model projection uncertainty. Recent machine learning (ML) algorithms hold promise to improve such process representations, but tend to extrapolate poorly to climate regimes they were not trained on. To get the best of the physical and statistical worlds, we propose a new framework - termed "climate-invariant" ML - incorporating knowledge of climate processes into ML algorithms, and show that it can maintain high offline accuracy across a wide range of climate conditions and configurations in three distinct atmospheric models. Our results suggest that explicitly incorporating physical knowledge into data-driven models of Earth system processes can improve their consistency, data efficiency, and generalizability across climate regimes., Comment: 26+28 pages, 9+15 figures, 0+3 tables in the main text + supplementary materials. Accepted for publication in Science Advances on Jan 5, 2024

Numerical weather prediction has traditionally been based on physical models of the atmosphere. Recently, however, the rise of deep learning has created increased interest in purely data-driven medium-range weather forecasting with first studies exploring the feasibility of such an approach. To accelerate progress in this area, the WeatherBench benchmark challenge was defined. Here, we train a deep residual convolutional neural network (Resnet) to predict geopotential, temperature and precipitation at 5.625 degree resolution up to 5 days ahead. To avoid overfitting and improve forecast skill, we pretrain the model using historical climate model output before fine-tuning on reanalysis data. The resulting forecasts outperform previous submissions to WeatherBench and are comparable in skill to a physical baseline at similar resolution. We also analyze how the neural network creates its predictions and find that, with some exceptions, it is compatible with physical reasoning. Finally, we perform scaling experiments to estimate the potential skill of data-driven approaches at higher resolutions.

Data-driven algorithms, in particular neural networks, can emulate the effect of sub-grid scale processes in coarse-resolution climate models if trained on high-resolution climate simulations. However, they may violate key physical constraints and lack the ability to generalize outside of their training set. Here, we show that physical constraints can be enforced in neural networks, either approximately by adapting the loss function or to within machine precision by adapting the architecture. As these physical constraints are insufficient to guarantee generalizability, we additionally propose to physically rescale the training and validation data to improve the ability of neural networks to generalize to unseen climates., Comment: Accepted for oral presentation at the 2020 IEEE International Geoscience and Remote Sensing Symposium (IGARSS) 5 pages, 5 figures, 1 table

Data-driven approaches, most prominently deep learning, have become powerful tools for prediction in many domains. A natural question to ask is whether data-driven methods could also be used to predict global weather patterns days in advance. First studies show promise but the lack of a common dataset and evaluation metrics make inter-comparison between studies difficult. Here we present a benchmark dataset for data-driven medium-range weather forecasting, a topic of high scientific interest for atmospheric and computer scientists alike. We provide data derived from the ERA5 archive that has been processed to facilitate the use in machine learning models. We propose simple and clear evaluation metrics which will enable a direct comparison between different methods. Further, we provide baseline scores from simple linear regression techniques, deep learning models, as well as purely physical forecasting models. The dataset is publicly available at https://github.com/pangeo-data/WeatherBench and the companion code is reproducible with tutorials for getting started. We hope that this dataset will accelerate research in data-driven weather forecasting., Comment: Github repository: https://github.com/pangeo-data/WeatherBench; Data download: https://mediatum.ub.tum.de/1524895

Neural networks can emulate nonlinear physical systems with high accuracy, yet they may produce physically-inconsistent results when violating fundamental constraints. Here, we introduce a systematic way of enforcing nonlinear analytic constraints in neural networks via constraints in the architecture or the loss function. Applied to convective processes for climate modeling, architectural constraints enforce conservation laws to within machine precision without degrading performance. Enforcing constraints also reduces errors in the subsets of the outputs most impacted by the constraints., Comment: 21 pages, 11 figures, 9 tables. Submitted to Physical Review Letters

Over the last couple of years, machine learning parameterizations have emerged as a potential way to improve the representation of sub-grid processes in Earth System Models (ESMs). So far, all studies were based on the same three-step approach: first a training dataset was created from a high-resolution simulation, then a machine learning algorithm was fitted to this dataset, before the trained algorithm was implemented in the ESM. The resulting online simulations were frequently plagued by instabilities and biases. Here, coupled online learning is proposed as a way to combat these issues. Coupled learning can be seen as a second training stage in which the pretrained machine learning parameterization, specifically a neural network, is run in parallel with a high-resolution simulation. The high-resolution simulation is kept in sync with the neural network-driven ESM through constant nudging. This enables the neural network to learn from the tendencies that the high-resolution simulation would produce if it experienced the states the neural network creates. The concept is illustrated using the Lorenz 96 model, where coupled learning is able to recover the "true" parameterizations. Further, detailed algorithms for the implementation of coupled learning in 3D cloud-resolving models and the super parameterization framework are presented. Finally, outstanding challenges and issues not resolved by this approach are discussed., Comment: Code and interactive notebook available at https://github.com/raspstephan/Lorenz-Online; see https://doi.org/10.5194/gmd-2019-319 for journal version

Artificial neural-networks have the potential to emulate cloud processes with higher accuracy than the semi-empirical emulators currently used in climate models. However, neural-network models do not intrinsically conserve energy and mass, which is an obstacle to using them for long-term climate predictions. Here, we propose two methods to enforce linear conservation laws in neural-network emulators of physical models: Constraining (1) the loss function or (2) the architecture of the network itself. Applied to the emulation of explicitly-resolved cloud processes in a prototype multi-scale climate model, we show that architecture constraints can enforce conservation laws to satisfactory numerical precision, while all constraints help the neural-network better generalize to conditions outside of its training set, such as global warming., Comment: ICML 2019 Workshop. Climate Change: How Can AI Help? 3 pages, 3 figures, 1 table

Humans excel at detecting interesting patterns in images, for example those taken from satellites. This kind of anecdotal evidence can lead to the discovery of new phenomena. However, it is often difficult to gather enough data of subjective features for significant analysis. This paper presents an example of how two tools that have recently become accessible to a wide range of researchers, crowd-sourcing and deep learning, can be combined to explore satellite imagery at scale. In particular, the focus is on the organization of shallow cumulus convection in the trade wind regions. Shallow clouds play a large role in the Earth's radiation balance yet are poorly represented in climate models. For this project four subjective patterns of organization were defined: Sugar, Flower, Fish and Gravel. On cloud labeling days at two institutes, 67 scientists screened 10,000 satellite images on a crowd-sourcing platform and classified almost 50,000 mesoscale cloud clusters. This dataset is then used as a training dataset for deep learning algorithms that make it possible to automate the pattern detection and create global climatologies of the four patterns. Analysis of the geographical distribution and large-scale environmental conditions indicates that the four patterns have some overlap with established modes of organization, such as open and closed cellular convection, but also differ in important ways. The results and dataset from this project suggests promising research questions. Further, this study illustrates that crowd-sourcing and deep learning complement each other well for the exploration of image datasets.

The representation of nonlinear sub-grid processes, especially clouds, has been a major source of uncertainty in climate models for decades. Cloud-resolving models better represent many of these processes and can now be run globally but only for short-term simulations of at most a few years because of computational limitations. Here we demonstrate that deep learning can be used to capture many advantages of cloud-resolving modeling at a fraction of the computational cost. We train a deep neural network to represent all atmospheric sub-grid processes in a climate model by learning from a multi-scale model in which convection is treated explicitly. The trained neural network then replaces the traditional sub-grid parameterizations in a global general circulation model in which it freely interacts with the resolved dynamics and the surface-flux scheme. The prognostic multi-year simulations are stable and closely reproduce not only the mean climate of the cloud-resolving simulation but also key aspects of variability, including precipitation extremes and the equatorial wave spectrum. Furthermore, the neural network approximately conserves energy despite not being explicitly instructed to. Finally, we show that the neural network parameterization generalizes to new surface forcing patterns but struggles to cope with temperatures far outside its training manifold. Our results show the feasibility of using deep learning for climate model parameterization. In a broader context, we anticipate that data-driven Earth System Model development could play a key role in reducing climate prediction uncertainty in the coming decade., Comment: View official PNAS version at https://doi.org/10.1073/pnas.1810286115

Ensemble weather predictions require statistical post-processing of systematic errors to obtain reliable and accurate probabilistic forecasts. Traditionally, this is accomplished with distributional regression models in which the parameters of a predictive distribution are estimated from a training period. We propose a flexible alternative based on neural networks that can incorporate nonlinear relationships between arbitrary predictor variables and forecast distribution parameters that are automatically learned in a data-driven way rather than requiring pre-specified link functions. In a case study of 2-meter temperature forecasts at surface stations in Germany, the neural network approach significantly outperforms benchmark post-processing methods while being computationally more affordable. Key components to this improvement are the use of auxiliary predictor variables and station-specific information with the help of embeddings. Furthermore, the trained neural network can be used to gain insight into the importance of meteorological variables thereby challenging the notion of neural networks as uninterpretable black boxes. Our approach can easily be extended to other statistical post-processing and forecasting problems. We anticipate that recent advances in deep learning combined with the ever-increasing amounts of model and observation data will transform the post-processing of numerical weather forecasts in the coming decade.