Many ensemble-based data assimilation (DA) methods use observation space localization to mitigate the sampling errors due to the insufficient ensemble members. Observation space localization is simpler and more timesaving than model space localization in implementation, but more difficult to directly assimilate satellite radiance observations, a kind of non-local observations. The vertical locations of radiance observations are undetermined and the transmission of observational information is thereby obstructed. To determine the vertical coordinates of radiance observations, a weighted average hypsometry is proposed. Using this hypsometry, AMSU-A radiance observations are directly assimilated with an ensemble four-dimensional variational (En4DVar) DA system. It consists of a four-dimensional ensemble-variational (4DEnVar) system providing ensemble covariance and a 4DVar system. Observing system simulation experiments show that the hypsometry alleviates the degradations in the late period of medium-range forecast in the Northern Extratropics that occur in the traditional peak-based hypsometry. It obviously improves the analysis qualities and forecast skills of the En4DVar system and its two components, especially in the Southern Extratropics, when incorporating AMSU-A radiance observations. The improvement in the En4DVar-initialized forecast is comparable to that in the 4DVar-initialized forecast in the Southern Extratropics and Tropics. It indicates that a proper hypsometry enables efficient extraction of useful information from AMSU-A radiance observations by 4DEnVar with observation space localization. Therefore, the 4DEnVar provides high-quality ensemble covariances for En4DVar.

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