In this study, we explore data assimilation for the Stochastic Camassa-Holm equation through the application of the particle filtering framework. Specifically, our approach integrates adaptive tempering, jittering, and nudging techniques to construct an advanced particle filtering system. All filtering processes are executed utilizing ensemble parallelism. We conduct extensive numerical experiments across various scenarios of the Stochastic Camassa-Holm model with transport noise and viscosity to examine the impact of different filtering procedures on the performance of the data assimilation process. Our analysis focuses on how observational data and the data assimilation step influence the accuracy and uncertainty of the obtained results.

翻译：本研究通过应用粒子滤波框架，探索了随机Camassa-Holm方程的数据同化问题。具体而言，我们的方法整合了自适应退火、抖动和平滑技术，构建了一个先进的粒子滤波系统。所有滤波过程均采用集合并行化方式执行。我们针对具有输运噪声和黏性的随机Camassa-Holm模型，在不同场景下开展了大量数值实验，以考察不同滤波过程对数据同化性能的影响。重点分析了观测数据及数据同化步长对结果精度与不确定性的影响。