**Progress in Understanding Horizontal Resolution of Radio Occultation Measurements**

**B. Ahmad, G. L. Tyler (Stanford University)**

The meaning of high vertical resolution and the ``horizontal'' resolution
of radio occultation measurements has been subject to interpretation of
the Abel transform relationships between the occultation ray paths and
an assumed spherically symmetric atmospheric refractivity field. For
the spherically symmetric case the refractivity field is recovered
exactly, within the limitations of ray optics. Only brute force methods
have been available for analysis of non-spherically symmetric cases.
For example, ray tracing is employed to calculate the ray asymptotes
for perturbed, approximately symmetric models, followed by application
of the Abel inversion to retrieve the apparent refractivity, which then
can be compared with the model results. In instances where the bending
angle is small a straight ray model leads to the inversion kernel for
the Abel transform (Ahmad & Tyler, ``The 2-D Resolution Kernel
associated with Retrieval of Ionospheric and Atmospheric Refractivity
Profiles by Abelian Inversion of Radio Occultation Phase Data,''
submitted to RADIO SCIENCE, April, 1997). Weighted integrals of the
2-D refractivity field employing the inversion kernel then give the
corresponding Abel inversion directly. This approach permits rapid
computation of the effects of departures from spherical symmetry.
Inspection of the inversion kernel provides insight into the Abel
transform inversion procedure. An interesting and useful result is
understanding of the artifacts created by atmospheric structures of
limited horizontal extent. Transformation of the curved ray case
appropriate for thick atmospheres to an equivalent straight ray case
yields the kernel function for the curved rays in a spherically
symmetric atmosphere. A remaining problem
is to estimate the effects of ray path deviation from the background
path on the analysis; for realistic cases this effect is believed to
be small, however.