A global climate model represents the physical processes of the ocean, sea ice, atmosphere, and land, as well as their interactions by coupling different components in one system. Within a climate model, the ocean and the atmosphere are the two main compartments, which are highly linked to each other. They give/receive their feedback to/from each other in one system thus influencing each other consistently. In contrast to stand-alone models of the ocean or atmosphere, which rely on forcings, a coupled model essentially evolves freely with little influence of forcings. Therefore, the simulation from a coupled model system may be far away from the real state (e.g., Mulholland et al., 2015). Data assimilation (DA) allows constraining the model state by incorporating observations to correct the model evolution in state space (e.g., Zhang & Moore, 2015). With decent initialization, a coupled system is equipped with the potential for real-world prediction.There are two main approaches to DA in a coupled system: weakly coupled DA (WCDA) and strongly coupled DA (SCDA) (Penny & Hamill, 2017). WCDA analyses the state of one or more compartments within a coupled system separately by assimilating their own observations and other components in the system are then influenced indirectly via the coupled model dynamics. WCDA is the most commonly used DA approach for a coupled system (Zhang et al., 2020). One example is our previous study (Tang et al., 2020), who assimilated satellite sea surface temperature (SST) and temperature and salinity profiles into the ocean component for a coupled ocean-atmosphere model. The study found improvements of not only the ocean variables, which were directly updated by the DA, but also the atmosphere variables like the air temperature and wind speed. Most of the previous WCDA experiments assimilated observations of both the ocean and the atmosphere (e.g.,