Previous studies have illustrated that assimilation into numerical weather prediction models of both space-based radio-occultation and advanced-infrared-sounder measurements will add significantly to our knowledge of the atmospheric state. In this study we show the degree to which the information contained in these data are complementary or whether there is significant redundancy between the observations. Initially we examine the retrieval performances based on linear retrieval theory, from which we conclude that the radio-occultation and advanced-infrared-sounder observations contribute their greatest impacts to different parts of the atmospheric temperature and humidity fields. Sequential one-dimensional variational data assimilation (1DVar) simulations using simulated observations ire then used to confirm these conclusions. The results of the 1DVar experiments are in very close agreement with the linear error analyses, and show that the information from the two types of observation are not only important but complementary.