Accurate estimation of the background error covariance matrix denoted as B remains a critical challenge in numerical weather prediction (NWP), directly influencing data assimilation (DA) performance and forecast accuracy. Although hybrid ensemble-variational (EnVar) methods combine static and flow-dependent matrices to improve assimilation, their effectiveness is constrained by empirically fixed weights. To address this limitation, we propose DRL-EnVar, an adaptive hybrid EnVar DA method enhanced with deep reinforcement learning. DRL-EnVar integrates deep learning (DL) components, including a novel cyclic convolution module to extract abstract features from data, and employs reinforcement learning (RL) to dynamically optimize hybrid weighting strategies. The system adaptively combines multiple ensemble-based flow-dependent matrices with one or more static matrices to construct a time-varying hybrid matrix B that better reflects real-time background errors. Experimental results demonstrate that DRL-EnVar performs better than the traditional ensemble Kalman filter (EnKF) and hybrid covariance DA (HCDA) methods, especially under sparse observations or transitional changes in state variables. It achieves competitive or superior assimilation accuracy with lower computational cost, and can be flexibly integrated into both three-dimensional variational assimilation (3DVar) and four-dimensional variational assimilation (4DVar) frameworks. Overall, DRL-EnVar offers a novel and efficient approach to adaptive DA, particularly valuable for improving forecast skill during transitional weather regimes.

The C-band Advanced Scatterometer (ASCAT) has the advantages of good spatial-temporal coverage and low sensitivity to nonextreme rainfall. While the perceived wind speed underestimation issues of ASCAT sea surface wind (SSW) retrievals can be mitigated using appropriate high wind speed scalings, the low spatial resolution in ASCAT remains a challenge, which implicitly leads to the blurring effect in tropical cyclone (TC) inner-core regions. To overcome this issue, the 2-D variational (2DVAR) analysis method is modified from 12.5 to 1.8 km grid size, where the latter allows super-resolution (SR) spatial structure functions, empirically trained on synthetic aperture radar (SAR) data, to enhance TC structure retrievals of ASCAT. The method first employs triple collocation analysis to estimate observation and background errors under different TC categories. After that, the relevant spatial parameters during the data assimilation process are determined and linked to TC features. These analyses contribute to constructing SAR-learned structure functions, complementing ASCAT-observed TC characteristics, and then achieving TC vortex reconstruction and wind field SR. Validation studies demonstrate that the SR products possess the correct small-scale properties of TC inner-core structures, such as radius of maximum wind (RMW), TC asymmetry, and wind variability. Notably, the proposed SR approach can achieve a significant reduction in error standard deviations (SDs) of ($l,t$) wind components (by 37% and 33%, respectively) when compared to spatial interpolated results. The encouraging results suggest the feasibility of the method in enhancing the abundant but lower resolution scatterometer winds, potentially contributing to future advancements in TC advisories.

Time series forecasting is crucial, yet the challenge of escalating errors in chaotic data and natural phenomena prediction endures. Existing methods for recursive strategies face difficulties in Multi-Input Multi-Output scenarios. A unified learning framework addressing error growth alongside these models is lacking, despite advanced neural networks. While dynamical system theory has inspired research in time series forecasting, these approaches struggle to estimate and mitigate error growth adequately. To address these gaps, we introduce Phase-Space-Guided Forecasting (PSGF), rooted in dynamical system theory. PSGF transforms data into high-dimensional phase space, quantifies error growth rates, and incorporates them into the neural network via Error Growth Awareness Loss (EGAL). PSGF enhances the utilization of dynamical constraints, reducing the need for additional feature engineering or hyperparameter tuning. Experimental results on chaotic systems and real-world climate data demonstrate PSGF’s significant accuracy improvements on diverse deep learning models.

Accurate knowledge of Tropical Cyclone (TC) inner-core structures contributes to a better understanding of TC thermodynamics. The Advanced Scatterometer (ASCAT) can measure ocean surface winds at a good spatial-temporal coverage, but the TC inner structures are largely blurred by its 20-km footprint. In this study, the Two-Dimensional Variational (2DVAR) scheme is considered to enhance the TC inner-core structure, by "learning" background spatial error covariances from high-resolution Synthetic Aperture Radar (SAR) winds. We find that the length scales of the stream function are close to the radii of maximum wind speeds and length scales of the velocity potential are dependent on TC asymmetry scales. All these parameters can be provided by ASCAT data. Experimental results prove that the proposed method can enhance TC inner-core structures and thus achieve super-resolution. The promising results contribute to our long-term goal of developing a general method for providing TC inner-core structures from all scatterometer winds available for nowcasting, allowing temporal monitoring of TC winds.

In the field of numerical weather prediction, fine-grained precipitation fields play a crucial role in forecasting and analyzing the spatial distribution and intensity of the precipitation. Historically, it is customary to employ the interpolation technique to downscale the low-resolution initial field output by assimilation systems, aligning with the requirements of a high-resolution forecasting model. Currently, data-driven deep learning methods offer novel solutions to address this challenge. In this letter, we propose a spatial downscaling algorithm for precipitation data generated from the North American Land Data Assimilation System (NLDAS), called Gaussian-perceptual-based generative adversarial network (GP-GAN). Specifically, the GP-GAN introduces a Siamese Gaussian-perceptual module (SGPM) which maps the data reconstructed from the generator and ground-truth to Gaussian latent space to learn the distribution of precipitation. Moreover, the adaptive weighted loss function (AWLF) is proposed to strengthen the emphasis and understanding of extreme precipitation events. Experimental results on the RainNet dataset comprising hourly precipitation over the USA demonstrate that GP-GAN provides better performance than other generative adversarial networks (GANs) and diffusion models in improving spatial resolution.

Accurate retrieval of ocean surface wind speed (OSWS) has a vital impact on maritime transportation planning and extreme weather forecast. Current models leveraging deep-learning (DL) techniques have demonstrated considerable potential for satellite remote-sensing wind retrieval. However, these models tend to focus on synchronizing the retrieved wind speeds with the label, neglecting the inherent absolute error (AE) embedded within the label and thus resulting in retrieval errors. To mitigate the disruptive impact of AE on retrieval accuracy, we introduce a novel network called TCNet, which retrieves observations of cyclone global navigation satellite system (CYGNSS) as OSWS. The network constructs an AE module (AEM), guided by triple collocation (TC) method for improved accuracy in real-time wind retrieval by calculating the AE as loss value. These calculations guide the network training process, thereby enhancing retrieval accuracy. Meanwhile, the wind speed dataset imbalance and inherent averaging characteristics of networks frequently result in wind speed uncertaintines in extremes. Notably, this occurs as a gross underestimation of high-speed winds. Therefore, TCNet incorporates an adaptive penalty module (APM) to solve this problem. By assigning higher penalty factors to high-speed winds, the sensitivity of network to its retrieval is improved. Experimentally, the APM in TCNet exhibited a remarkable reduction of AE in high-speed wind retrieval and mitigates the understating of high-speed scenarios while maintaining an overall error that is not significantly increased. Importantly, TCNet demonstrated notable resistance to noise and portrayed excellent generalizability, providing fresh insights into weather forecasting, climate research, and other marine applications.

Sea Surface Temperature (SST) prediction has attracted increasing attention due to its critical role in climate change. Traditional SST prediction methods can be mainly divided into two types, the physics-based numerical methods and the data-driven methods. However, the above methods have certain limitations, the former type can not perform well when the physical prior information is incomplete, while latter type can not perform well when the training data is insufficient. This paper uses a deep neural network to extract some valuable information from the data, and then introduces the space-time partial differential equation (PDE) to model the prior physical information referring to SST. By incorporating them together, a new Space-Time PDE-guided Neural Network (STPDE-NET), which can better deal with the prior physical information incompleteness and data insufficiency problems mentioned above is proposed. In the experiments, we compare our STPDE-NET with several famous or state-of-the-art SST prediction methods. The experimental results show that STPDE-NET outperforms the compared methods in most SST prediction circumstances, especially when the training data is insufficient.