Abstract
Satellite infrared sounders are invaluable tools for making observations of the structure of the atmosphere. They provide much of the observational data used to initialize atmospheric models, especially in regions that do not have extensive surface-based observing systems, such as oceans. However, information is lacking in the presence of cloud, as the cloud layer is opaque to infrared radiation. This means that where information is most desired (such as in a developing storm) it is often in the shortest supply. In order to explore the mathematics of assimilating data from cloudy radiances, a study has been performed using an idealized single-column atmospheric model. The model simulates cloud development in an atmosphere with vertical motion, allowing the characteristics of a 2D-Var data assimilation system using a single simulated infrared satellite observation taken multiple times to be studied. The strongly nonlinear nature of cloud formation poses a challenge for variational methods. The adjoint method produces an accurate gradient for the cost function and minimization is achieved using preconditioned conjugate gradients. The conditioning is poor and varies strongly with the atmospheric variables and the cost function has multiple minima, but acceptable results are achieved. The assimilation system is provided with a prior forecast simulated by adding random correlated Gaussian error to the truth. Assimilating observations comparable to those available from current geostationary satellites allows vertical motion to be retrieved with an error of less than a centimetre per second in most conditions. Moreover, evaluating the second derivative of the cost function at the minimum provides an estimate of the uncertainty in the retrieval. This allows atmospheric states that do not provide sufficient information for retrieval of vertical motion to be detected (such as a cloudless atmosphere or a non-moving opaque cloud layer in the upper troposphere). Retrieval is most accurate with upwards motion.