B. Ahmad et Gl. Tyler, Systematic errors in atmospheric profiles obtained from Abelian inversion of radio occultation data: Effects of large-scale horizontal gradients, J GEO RES-A, 104(D4), 1999, pp. 3971-3992
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.