## 1 Introduction
The **B**-matrix is a decisive parameter in the function, and it is a cornerstone of the VarDA framework, influencing information dissemination and smoothing, balancing relationships, and establishing flow-dependent properties [18]. Developing a realistic representation of the **B**-matrix is a primary and ongoing research focus within DA [19]. Graphing with challenges such as the elusive 'true' state, immense dimensionality (\(n\sim 10^{7}\)-\(10^{9}\) elements) [20], and rank deficiency in the DA system, directly and explicitly constructing and operating the **B**-matrix are impractical [19]. In practice, a vast sample of statistical data is used to simulate background errors and then approximately estimate the **B**-matrix, typically consisting of model predictions or observations spanning an extended period, which are underpinned by certain and reasonable assumptions. However, since the **B**-matrix is typically estimated using approximate methods, it may contain substantial errors, particularly in its diagonal elements. These elements represent the variance of state variables, which directly influence the relative weighting of the background state and observations in forming the analysis state, ultimately impacting the overall performance of the DA system [21]. An overestimation of variance biases the analysis state toward observations, neglecting valuable background information, while underestimation may discard useful and crucial observational information [22]. The task of adaptively adjusting background error variances in the **B**-matrix through spatio-temporal scaling based on the current analysis state can be formulated as a decision-making problem. However, traditional methods, which rely on empirical settings, often yield suboptimal assimilation results due to their inability to adapt to the dynamic variability of weather systems [23; 24; 25]. To overcome these limitations, we introduce a new paradigm by leveraging the powerful capabilities of artificial intelligence (AI), specifically deep reinforcement learning (DRL) [26; 27], through algorithms meticulously tailored to the unique demands and structural characteristics of VarDA systems. This approach enhances the flexibility and intelligence of the variance adjustment process. Specifically, we reformulate the variance adjustment task within the framework of a Markov Decision Process (MDP)--a standard model for sequential decision-making [28]--and propose an innovative method, the deep reinforcement learning adaptive spatio-temporal variance adjustment strategy (DRL-AST). In this approach, an intelligent agent--a decision-making module powered by deep neural networks--interacts with the environment, a VarDA-based framework tailored for DRL that formalizes the spatio-temporal variance adjustment process, within the VarDA analysis-prediction cycle. At each step, the agent employs a DRL policy network to map high-dimensional states to variance-scaling actions. Deep learning (DL) facilitates the state-to-action mapping by extracting spatio-temporal feature representations from complex meteorological data, enabling the policy network to generalize across varied weather conditions. The environment updates the **B**-matrix based on this action, performs assimilation and forecasting, and returns the next state alongside a reward reflecting assimilation performance. Ultimately, the DRL-AST iteratively optimizes cumulative rewards to derive an optimal policy network, enhancing the assimilation performance of the VarDA system. Unlike conventional methods, DRL-AST leverages adaptive spatio-temporal adjustments to generate initial states with improved dynamic consistency relative to the numerical model. This approach improves assimilation performance, thereby substantially boosting the predictive accuracy of the numerical model.