  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.
