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 atmo sphere. In the case of terrestrial planets the atmosphere in the vicinity o f ray periapsides usually is assumed to be spherically symmetric. This assu mption leads to an integral transform relationship between the profiles of refractivity versus radius and the total bending angle versus the asymptoti c closest approach of rays, where the latter is directly obtainable from oc cultation frequency data and trajectory information. Occultation studies of the giant planets have demonstrated that departures from spherical symmetr y, if not accounted for, can result in serious errors in derived T-p(r) pro files. We analyze errors in atmospheric profiles due to large-scale departu res from spherical symmetry. For analytic convenience we represent departur es from spherical symmetry as locally spherical structures with center of c urvature offset in three dimensions from the center of mass, from which fol low analytic expressions for errors in bending angle and impact parameter a s functions of the offset and trajectory parameters. Since these expression s are not restricted to any specific occultation type, it is easy to identi fy the geometrical configurations and the specific trajectory parameters th at enhance or suppress these errors. Errors in bending angle and impact par ameter carry over into the refractivity and radius profiles, while at the s ame time, new errors are introduced because the bending angle versus impact parameter profile is integrated along a nonvertical path in the presence o f large-scale departures from spherical symmetry, to obtain refractivity an d radius profiles. Similarly, refractivity and radius errors propagate into the temperature and pressure profiles, while a nonvertical path of integra tion in the presence of horizontal gradients provides another opportunity f or new errors to be introduced. We estimate that fractional errors in tempe rature 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, suc h errors are estimated to be less than 1% above 30 km. In the lower parts o f Earth's atmosphere, however, and especially in the lower troposphere, the se errors can be very sensitive to horizontal gradients and hence highly va riable; typically, the error magnitude remains less than 2% for the dry reg ions 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 im precise knowledge of the transmitter and receiver trajectories.