  An optimal estimation inverse method is presented which can be used to
retrieve simultaneously vertical profiles of temperature and specific humidity,
in addition to surface pressure, from satellite-to-satellite radio occultation
observations of the Earth's atmosphere. The method is a non-linear, maximum
{\it a posteriori} technique which can accommodate most aspects of the real
radio occultation problem and is found to be stable and to converge rapidly in
most cases. The optimal estimation inverse method has two distinct advantages
over the analytic inverse method in that it accounts for some of the effects of
horizontal gradients and is able to retrieve optimally temperature and humidity
simultaneously from the observations. It is also able to account for
observation noise and other sources of error. Combined, these advantages ensure
a realistic retrieval of atmospheric quantities.
  A complete error analysis emerges naturally from the optimal estimation
theory, allowing a full characterisation of the solution. Using this analysis a
quality control scheme is implemented which allows anomalous retrieval
conditions to be recognised and removed, thus preventing gross retrieval
errors.
  The inverse method presented in this paper has been implemented for bending
angle measurements derived from GPS/MET radio occultation observations of the
Earth. Preliminary results from simulated data suggest that these observations
have the potential to improve NWP model analyses significantly throughout their
vertical range.

Atmospheric and Oceanic Physics