perform data assimilation

This study addresses the insufficient quantification of uncertainty in numerical weather prediction by introducing, for the first time, multiple conformal prediction (CP) methods—including standard CP, normalized CP, and conformal quantile regression—into a one-dimensional shallow-water model data assimilation framework. These methods are integrated with the ensemble Kalman filter to produce prediction intervals endowed with finite-sample theoretical guarantees. Systematic evaluation using metrics such as average coverage, interval width, upper and lower tail miss rates, and interval score demonstrates that CP effectively characterizes forecast uncertainty and complements traditional ensemble-based approaches within the data assimilation cycle. The work establishes a novel paradigm and empirical foundation for uncertainty quantification that synergistically combines machine learning with physics-driven modeling.

This study addresses the common issue in ensemble forecasting wherein insufficiently rapid growth of ensemble spread leads to inadequate representation of uncertainty. Using the Lorenz '96 system, the work systematically disentangles intrinsic variability, initial condition perturbations, and stochastic model uncertainty to evaluate how various ensemble configurations and parameterization schemes influence spread evolution. It introduces novel Bayesian and streaming stochastic parameterizations featuring temporally coherent structures, revealing that perturbations primarily govern the rate of trajectory decorrelation rather than long-term variance. The analysis further elucidates the interaction mechanisms among distinct uncertainty sources. Experimental results demonstrate that the proposed methods significantly enhance early spread growth and improve consistency between ensemble spread and forecast error, thereby offering theoretical insights and practical guidance for uncertainty modeling in numerical weather prediction systems.

This study systematically investigates the differential sensitivity of ensemble filters to observational network characteristics—namely, observation count, spatial sparsity, and nonlinearity. Using the surface quasigeostrophic (SQG) model, we compare AI-enhanced ensemble filters against the traditional Local Ensemble Transform Kalman Filter (LETKF) in their ability to mitigate multiscale analysis errors. Our key contribution is the first demonstration that AI-based methods exhibit superior robustness under highly nonlinear and spatially sparse observational configurations, achieving significantly better suppression of meso- and submesoscale errors than LETKF; in contrast, LETKF performance is more strongly contingent on observational linearity and density. These findings establish a novel paradigm for evaluating the observational-system adaptability of AI-driven data assimilation algorithms, thereby enabling dynamic reassessment and optimization of Earth observation network design and value.

This work addresses three key challenges in machine learning–based weather surrogate models (e.g., FourCastNet): long-term prediction instability, unphysical behavior, and forecast degradation due to sparse and noisy observational data. To this end, we embed FourCastNet within a 4D-Var variational data assimilation framework, enabling online, real-time correction using partial, noisy ERA5 reanalysis observations. For the first time, both theoretical analysis and numerical experiments demonstrate that the proposed method maintains stable filtering estimation errors—below 0.8 RMSE—at annual timescales, even under severe model instability, extreme observational sparsity, and noise corruption. Moreover, the physically consistent initial conditions generated by the method significantly improve extreme precipitation forecasting: the 72-hour Threat Score increases by 32% over free-running forecasts. The core contribution is a provably convergent ML–DA coupling paradigm that jointly leverages data-driven efficiency and physics-informed robustness.

To address the challenge of effectively assimilating sparse in-situ observations into full-atmosphere states for kilometer-scale weather forecasting initialization, this paper proposes a score-based generative data assimilation framework. First, an unconditional diffusion model is trained to learn the high-resolution atmospheric prior distribution—using HRRR analyses as ground truth. Then, sparse surface observations (e.g., precipitation, wind fields) are implicitly incorporated into the generative process via score matching. This work presents the first end-to-end, retraining-free generative assimilation method at the kilometer scale; it implicitly encodes multivariate physical constraints without explicit numerical physics modeling, thereby ensuring physical consistency and interpretability of generated fields. Experiments demonstrate that, given only 40 observation sites, the method reduces RMSE for surface variables at withheld sites by 10% relative to the HRRR baseline, while faithfully reproducing realistic meteorological structures—including fronts—with high spatial fidelity.

This study addresses the latency and bias in state estimation inherent to conventional filtering methods when applied to rapidly evolving or regime-switching complex systems, which rely solely on past and current observations. To overcome this limitation, the authors propose a continuous-time ensemble Kalman–Bucy smoother (EnKBS) that incorporates future observations to reconstruct the conditional distribution, enabling high-accuracy retrospective state estimation and facilitating causal inference and implicit model structure discovery. The method innovatively establishes, for the first time, a continuous-time smoothing framework that requires neither tangent linear nor adjoint models and converges to the exact solution in the infinite-ensemble limit. By integrating ensemble-based moment estimation with regularization techniques such as covariance localization and inflation, it avoids explicit derivative computations. With only O(10) ensemble members and partial observations, the approach successfully infers causal dynamics in a bivariate trigger-feedback system and recovers structure and parameters in a simplified atmospheric circulation model, substantially outperforming traditional filters.

研究通过数值实验展示了在非气象预测的PDE模型中伪相关性的存在及其对定位方法的需求，并比较了不同EnKF实现的计算效率。

This work addresses the limitations of traditional ensemble filters in handling implicit, non-smooth, or many-to-one observation models, which typically rely on explicit likelihoods or observation derivatives. The authors propose an implicit data assimilation framework that defines the analysis distribution via energy tilting and introduces the Ensemble Control Flow filter (EnCF), which combines stochastic control flows with adjoint matching to learn observation-dependent control policies from terminal energy gradients. For simulator-defined observations, they further develop EnCF-LF to construct a conditional energy surrogate model. This approach uniquely integrates energy tilting with stochastic control flows, enabling filtering updates without requiring explicit likelihoods or derivatives, while theoretically ensuring that local errors do not accumulate. Experiments demonstrate significant performance gains over conventional Kalman-type filters in non-Gaussian, multimodal, and implicit observation settings.

This study addresses the rapid degradation of forecast skill in chaotic systems and the limitations of traditional data assimilation (DA) by exploring the integration of machine learning (ML) with DA. Methodologically, it combines deep learning models, DA algorithms, and numerical weather prediction techniques to optimize system state estimation through the effective fusion of observational data and model forecasts. The core contribution lies in providing a pioneering review of the emerging ML-DA paradigm, delineating its central themes and methodological frameworks. This work offers a novel methodological perspective for state estimation in dynamical systems and establishes a solid foundation for enhancing predictive capabilities in complex systems, such as the atmosphere, while guiding future research directions.

本文提出ADDA框架，通过支持自动微分和并行计算解决数据同化中模拟与同化代码不兼容等问题。