We compare strongly coupled data assimilation (SCDA) and weakly coupled data assimilation (WCDA) by analyzing the assimilation effect on the estimation of the ocean and the atmosphere variables. The AWI climate model (AWI‐CM‐1.1) is coupled with the parallel data assimilation framework (PDAF). Only satellite sea surface temperature data are assimilated. For WCDA, only the ocean variables are directly updated by the assimilation. For SCDA, both the ocean and the atmosphere variables are directly updated by the assimilation. Both WCDA and SCDA improve ocean state and yield similar errors. In the atmosphere, WCDA gives slightly smaller errors for the near‐surface temperature and wind velocity than SCDA. In the free atmosphere, SCDA yields smaller errors for the temperature, wind velocity, and specific humidity than WCDA in the Arctic region, while in the tropical region, the errors are generally larger. Plain Language Summary Satellite sea surface temperature observations are combined with a coupled ocean‐atmosphere model to improve the estimation of the ocean as well as the atmosphere variables. This is done by the so‐called strongly coupled data assimilation, which updates not only the ocean state but uses the cross‐covariance to update the atmosphere variables directly through the assimilation algorithm. The results are compared with the weakly coupled data assimilation, which only updates the ocean state directly. Both of the two assimilation algorithms improve the estimation of the ocean temperature. In the atmosphere, the strongly coupled data assimilation outperforms the weakly coupled data assimilation only in the Arctic region while in the low latitudes the strongly coupled data assimilation deteriorates the results. Key Points Strongly coupled data assimilation is implemented for a coupled ocean atmosphere model Satellite sea surface temperatures are the only observations for assimilation Strongly coupled data assimilation performs better in the Arctic region than the weakly coupled data assimilation