Abstract. This paper presents the results of the Ensemble Riemannian Data Assimilation for relatively high-dimensional nonlinear dynamical systems, focusing on the chaotic Lorenz-96 model and a two-layer quasi-geostrophic (QG) model of atmospheric circulation. The analysis state in this approach is inferred from a joint distribution that optimally couples the background probability distribution and the likelihood function, enabling formal treatment of systematic biases without any Gaussian assumptions. Despite the risk of the curse of dimensionality in the computation of the coupling distribution, comparisons with the classic implementation of the particle filter and the stochastic ensemble Kalman filter demonstrate that with the same ensemble size, the presented methodology could improve the predictability of dynamical systems. In particular, under systematic errors, the root mean squared error of the analysis state can be reduced by 20 % (30 %) in Lorenz-96 (QG) model.

中文翻译：

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集成黎曼数据同化：走向高维实现

摘要。本文介绍了相对高维非线性动力系统的集合黎曼数据同化的结果，重点是混沌 Lorenz-96 模型和大气环流的两层准地转 (QG) 模型。这种方法中的分析状态是从联合分布推断出来的，该分布将背景概率分布和似然函数最佳耦合，从而能够在没有任何高斯假设的情况下对系统偏差进行正式处理。尽管在计算耦合分布时存在维数灾难的风险，但与粒子滤波器和随机集合卡尔曼滤波器的经典实现的比较表明，在相同的集合大小下，所提出的方法可以提高动力系统的可预测性。特别是，