The focus of nowcasting development is transitioning from physically motivated advection methods to purely data-driven Machine Learning (ML) approaches. Nevertheless, recent work indicates that incorporating advection into the ML value chain has improved skill for radar-based precipitation nowcasts. However, the generality of this approach and the underlying causes remain unexplored. This study investigates the generality by probing the approach on satellite-based thunderstorm nowcasts for the first time. Resorting to a scale argument, we then put forth an explanation when and why skill improvements can be expected. In essence, advection guarantees that thunderstorm patterns relevant for nowcasting are contained in the receptive field at long forecast times. To test our hypotheses, we train ResU-Nets solving segmentation tasks with lightning observations as ground truth. The input of the Baseline Neural Network (BNN) are short time series of multispectral satellite imagery and lightning observations, whereas the Advection-Informed Neural Network (AINN) additionally receives the Lagrangian persistence nowcast of all input channels at the desired forecast time. Overall, we find only a minor skill improvement of the AINN over the BNN when considering fully averaged scores. However, assessing skill conditioned on forecast time and advection speed, we demonstrate that our scale argument correctly predicts the onset of skill improvement of the AINN over the BNN after 2h forecast time. We confirm that, generally, advection becomes gradually more important with longer forecast times and higher advection speeds. Our work accentuates the importance of considering and incorporating the underlying physical scales when designing ML-based forecasting models.

The increasing frequency of extreme weather events due to global climate change urges accurate weather prediction. Recently, great advances have been made by the \textbf{end-to-end methods}, thanks to deep learning techniques, but they face limitations of \textit{representation inconsistency} in multivariable integration and struggle to effectively capture the dependency between variables, which is required in complex weather systems. Treating different variables as distinct modalities and applying a \textbf{two-stage training approach} from multimodal models can partially alleviate this issue, but due to the inconformity in training tasks between the two stages, the results are often suboptimal. To address these challenges, we propose an implicit two-stage training method, configuring separate encoders and decoders for each variable. In detailed, in the first stage, the Translator is frozen while the Encoders and Decoders learn a shared latent space, in the second stage, the Encoders and Decoders are frozen, and the Translator captures inter-variable interactions for prediction. Besides, by introducing a self-attention mechanism for multivariable fusion in the latent space, the performance achieves further improvements. Empirically, extensive experiments show the state-of-the-art performance of our method. Specifically, it reduces the MSE for near-surface air temperature and relative humidity predictions by 28.82\% and 23.39\%, respectively. The source code is available at https://github.com/ShremG/Met2Net.

Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data, machine learning models often deviate from the true system states over time and need to be continually updated as new measurements are taken using data assimilation. Classical data assimilation algorithms typically require knowledge of the measurement noise statistics which may be unknown. In this paper, we introduce a new data assimilation algorithm with a foundation in topological data analysis. By leveraging the differentiability of functions of persistence, gradient descent optimization is used to minimize topological differences between measurements and forecast predictions by tuning data driven model coefficients without using noise information from the measurements. We describe the method and focus on its capabilities performance using the chaotic Lorenz system as an example.

The computationally cheap machine learning architecture of random feature maps can be viewed as a single-layer feedforward network in which the weights of the hidden layer are random but fixed and only the outer weights are learned via linear regression. The internal weights are typically chosen from a prescribed distribution. The choice of the internal weights significantly impacts the accuracy of random feature maps. We address here the task of how to best select the internal weights. In particular, we consider the forecasting problem whereby random feature maps are used to learn a one-step propagator map for a dynamical system. We provide a computationally cheap hit-and-run algorithm to select good internal weights which lead to good forecasting skill. We show that the number of good features is the main factor controlling the forecasting skill of random feature maps and acts as an effective feature dimension. Lastly, we compare random feature maps with single-layer feedforward neural networks in which the internal weights are now learned using gradient descent. We find that random feature maps have superior forecasting capabilities whilst having several orders of magnitude lower computational cost.

In this paper, we present Pangu-Weather, a deep learning based system for fast and accurate global weather forecast. For this purpose, we establish a data-driven environment by downloading $43$ years of hourly global weather data from the 5th generation of ECMWF reanalysis (ERA5) data and train a few deep neural networks with about $256$ million parameters in total. The spatial resolution of forecast is $0.25^\circ\times0.25^\circ$, comparable to the ECMWF Integrated Forecast Systems (IFS). More importantly, for the first time, an AI-based method outperforms state-of-the-art numerical weather prediction (NWP) methods in terms of accuracy (latitude-weighted RMSE and ACC) of all factors (e.g., geopotential, specific humidity, wind speed, temperature, etc.) and in all time ranges (from one hour to one week). There are two key strategies to improve the prediction accuracy: (i) designing a 3D Earth Specific Transformer (3DEST) architecture that formulates the height (pressure level) information into cubic data, and (ii) applying a hierarchical temporal aggregation algorithm to alleviate cumulative forecast errors. In deterministic forecast, Pangu-Weather shows great advantages for short to medium-range forecast (i.e., forecast time ranges from one hour to one week). Pangu-Weather supports a wide range of downstream forecast scenarios, including extreme weather forecast (e.g., tropical cyclone tracking) and large-member ensemble forecast in real-time. Pangu-Weather not only ends the debate on whether AI-based methods can surpass conventional NWP methods, but also reveals novel directions for improving deep learning weather forecast systems.

Data-driven prediction and physics-agnostic machine-learning methods have attracted increased interest in recent years achieving forecast horizons going well beyond those to be expected for chaotic dynamical systems. In a separate strand of research data-assimilation has been successfully used to optimally combine forecast models and their inherent uncertainty with incoming noisy observations. The key idea in our work here is to achieve increased forecast capabilities by judiciously combining machine-learning algorithms and data assimilation. We combine the physics-agnostic data-driven approach of random feature maps as a forecast model within an ensemble Kalman filter data assimilation procedure. The machine-learning model is learned sequentially by incorporating incoming noisy observations. We show that the obtained forecast model has remarkably good forecast skill while being computationally cheap once trained. Going beyond the task of forecasting, we show that our method can be used to generate reliable ensembles for probabilistic forecasting as well as to learn effective model closure in multi-scale systems.

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 for numerical weather prediction. 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 a simple and clear evaluation metric 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. All data is publicly available and the companion code is reproducible with tutorials for getting started. We hope that this dataset will accelerate research in data-driven weather forecasting.