Data assimilation (DA) combines model forecasts and observations to estimate the optimal state of the atmosphere with its uncertainty, providing initial conditions for weather prediction and reanalyses for climate research. Yet, existing traditional and machine-learning DA methods struggle to achieve accuracy, efficiency and uncertainty quantification simultaneously. Here, we propose HLOBA (Hybrid-Ensemble Latent Observation-Background Assimilation), a three-dimensional hybrid-ensemble DA method that operates in an atmospheric latent space learned via an autoencoder (AE). HLOBA maps both model forecasts and observations into a shared latent space via the AE encoder and an end-to-end Observation-to-Latent-space mapping network (O2Lnet), respectively, and fuses them through a Bayesian update with weights inferred from time-lagged ensemble forecasts. Both idealized and real-observation experiments demonstrate that HLOBA matches dynamically constrained four-dimensional DA methods in both analysis and forecast skill, while achieving end-to-end inference-level efficiency and theoretical flexibility applies to any forecasting model. Moreover, by exploiting the error decorrelation property of latent variables, HLOBA enables element-wise uncertainty estimates for its latent analysis and propagates them to model space via the decoder. Idealized experiments show that this uncertainty highlights large-error regions and captures their seasonal variability.

翻译：数据同化（DA）通过融合模式预报与观测数据，以估算大气最优状态及其不确定性，为天气预报提供初始条件，并为气候研究提供再分析资料。然而，现有传统及机器学习DA方法难以同时实现精度、效率与不确定性量化。本文提出HLOBA（混合集合潜在观测-背景场同化），这是一种在自编码器（AE）学习得到的大气潜在空间中运行的三维混合集合DA方法。HLOBA分别通过AE编码器和端到端的观测-潜在空间映射网络（O2Lnet）将模式预报与观测数据映射至共享潜在空间，并利用时滞集合预报推断的权重进行贝叶斯更新融合。理想化实验与真实观测实验均表明，HLOBA在分析能力和预报技巧上可与受动力学约束的四维DA方法相媲美，同时实现了端到端的推理级效率，其理论框架适用于任意预报模式。此外，通过利用潜在变量的误差解相关特性，HLOBA能够对其潜在分析结果进行逐元素不确定性估计，并通过解码器将不确定性传播至模式空间。理想化实验表明，这种不确定性估计能有效标识大误差区域并捕捉其季节变化特征。