Systematic errors in atmospheric profiles obtained from Abelian inversion of radio occultation data: Effects of large-scale horizontal gradients

Reduction of radio occultation data to retrieve atmospheric profiles (T-p(r)) requires knowledge or assumption of the horizontal structure of the atmosphere. In the case of terrestrial planets the atmosphere in the vicinity of ray periapsides usually is assumed to be spherically symmetric. This assumption leads to an integral transform relationship between the profiles of refractivity versus radius and the total bending angle versus the asymptotic closest approach of rays, where the latter is directly obtainable from occultation frequency data and trajectory information. Occultation studies of the giant planets have demonstrated that departures from spherical symmetry, if not accounted for, can result in serious errors in derived T-p(r) profiles. We analyze errors in atmospheric profiles due to large-scale departures from spherical symmetry. For analytic convenience we represent departures from spherical symmetry as locally spherical structures with center of curvature offset in three dimensions from the center of mass, from which follow analytic expressions for errors in bending angle and impact parameter as functions of the offset and trajectory parameters. Since these expressions are not restricted to any specific occultation type, it is easy to identify the geometrical configurations and the specific trajectory parameters that enhance or suppress these errors. Errors in bending angle and impact parameter carry over into the refractivity and radius profiles, while at the same time, new errors are introduced because the bending angle versus impact parameter profile is integrated along a nonvertical path in the presence of large-scale departures from spherical symmetry, to obtain refractivity and radius profiles. Similarly, refractivity and radius errors propagate into the temperature and pressure profiles, while a nonvertical path of integration in the presence of horizontal gradients provides another opportunity for new errors to be introduced. We estimate that fractional errors in temperature profiles can be as large as a few percent for the Martian atmosphere above 20 km, decreasing in magnitude closer to the surface. For Earth, such errors are estimated to be less than 1% above 30 km. In the lower parts of Earth's atmosphere, however, and especially in the lower troposphere, these errors can be very sensitive to horizontal gradients and hence highly variable; typically, the error magnitude remains less than 2% for the dry regions of Earth's troposphere. We have not addressed the effect on errors of water vapor gradients, or of more extreme structures such as sharp weather fronts. A small variation on this approach can incorporate errors due to imprecise knowledge of the transmitter and receiver trajectories.