Atmospheric Sensing Using GNSS RO - GNSS Remote Sensing: Theory, Methods and Applications - page 133

spherically symmetric atmosphere near the tangent point. Same assumption is
embedded in the derivation of the refractivity from bending angel through the Abel
transform.
Departures from the spherical symmetry assumption come from the horizontal
gradients of the refractive index and also the ellipsoidal shape of the earth. The
latter kind of errors becomes significant below 40 km and can be removed through
an oblateness correction (e.g., Kursinski et al. 1997 ; Syndergaard 1998 ). Such
correction is performed by referring the occultation geometry to a local center of
refraction, defined by the origin of a sphere tangential to the ellipsoid at the profile
location (Syndergaard 1998 ).
In the lower troposphere, the water vapor can vary appreciably on horizontal
scales of a few tens of kilometers, which may result in significant horizontal
gradients in refractive index (e.g., Healy et al. 2001). The horizontal gradients in
the atmosphere could lead to systematic representative errors (i.e., difference from
the in-situ local measurements at the tangent points) in bending and refractivity
retrievals (Melbourne et al. 1994 ; Kursinski et al. 1997 ; Ahmad and Tyler 1999 ;
Healy 2001 ; Zou et al. 2002 ; Poli 2004 ; Poli and Joiner 2004 ; Syndergaard et al.
2005 ).
Kursinski et al. ( 1997 ) shows that the along-track refractive index gradients
(i.e., parallel with the ray path) causes refractivity errors of order of 1 % near
the surface, falling linearly with height to 0.2 % at 10 km and then remaining
relatively constant up to 30 km. Healy ( 2001 ) further demonstrated that the cross-
track refractive index gradient (i.e., perpendicular to the ray path, which cause out
of plane bending) can cause larger systematic errors in both the bending angel and
the impact parameter, but the latter is more significant. For example, the impact
parameter error can be off by as large as 100 m near the surface corresponding
to 10 % errors in bending angle in certain cases. Statistic analysis based on the
simulations with various realistic atmospheric field represented by high-resolution
mesoscale model reveals RMS errors of 3 % in bending angel or 1.4 % in
refractivity near the surface caused by the cross-track horizontal gradients.
In the real occultations, the often non-coplanar orbits for occultation transmitter
and receiver result in tangent points drifting horizontally as the ray path descends
deep into the atmosphere. Such horizontal drift leads to refractivity retrieval error
due to Abel transform, because the bending angle at higher altitudes is not the
bending directly above the present tangent point. However, The ray path tangent
point drift is generally of the order of the horizontal averaging interval or less (e.g.
200 km below 10 km), and the resulting errors are therefore relatively small. The
ratio of horizontal drift to vertical descent is greatest near the surface where the
largest error is expected (Kursinski et al. 1997 ). The effects due to tangent point
drift can be accounted for by considering a slanted profile that follows the tangent
point trajectory (e.g., Poli and Joiner 2004 ).
It is worth noting that the magnitude of errors introduced by large-scale
horizontal inhomogeneity in refractivity can vary depending on horizontal gradients,
but, statistically, they should not introduce a significant bias. To fully exploit the
benefit of the RO measurements, it is necessary to take into account the spherical