Atmospheric Sensing Using GNSS RO - GNSS Remote Sensing: Theory, Methods and Applications - page 150

atmosphere, for every negative elevation angle ray with bending angle ˛ N , there is
a corresponding positive elevation angle ray, with bending angle ˛ P with the same
impact parameter, and is in fact equal to the second term in Eq. ( 6.14 ). These two
bending angles can be differenced to derive the so-called “partial bending angle”.
The partial bending angle corresponds to the accumulated bending from a segment
of the ray path below the altitude of the receiver.

Z r R

1
n

dn
dr

dr
p .nr/ 2 ˛ 0 .a/ ˛ N .a/ ˛ P .a/ D 2a

a 2 r t :

(6.15)

r t

The refractive index below the receiver can then be retrieved through the slightly
modified Abel transform (Healy et al. 2002 ), which is similar to the spaceborne
GPS occultation case, but the refractive index at the receiver, n R can no longer be
neglected:

n.a/ D n R exp 1

Z n R r R :

˛ 0 .x/dx
p x 2

(6.16)

a 2 x D a

The refractive index profile is transformed to a function of altitude rather than
impact parameter using the relation a D nr at the tangent point. In practice, ˛ N and
˛ P , as functions of a , are derived from the measured excess Doppler shifts in a
similar way to that used for the spaceborne RO case. Consequently, the atmospheric
thermodynamic parameters such as density temperature, pressure and humidity
can be inferred based on the airborne RO refractivity measurement following the
approach used in spaceborne RO retrieval as described in Sect. 6.1 .
The geometric optics retrieval technique has been adapted from the spaceborne
RO to the airborne measurements, and simulation studies have been carried out by
several authors (Healy et al. 2002 ; Lesne et al. 2002 ; Mousa and Tsuda 2004 ;Xie
et al. 2008 ). A number of field campaigns have also been conducted, and preliminary
comparisons of measurements with radiosonde observations and numerical weather
prediction (NWP) model analyses have been reported (Aoyama et al. 2004 ; Xie et al.
2008 ; Muradyan et al. 2010 ). Due to the multipath effect in the lower troposphere,
the geometric optics retrieval technique encounter challenges, the more advanced
radio-holographic retrieval method is thus needed to derive more accurate and
higher vertical resolution RO soundings (e.g., Xie et al. 2012b ).
Contrary to the spaceborne RO observation, with a GNSS receiver inside the
atmosphere, the receiver is either still (e.g., on mountain-top) or moving (e.g., air-
borne, in the order of 0.25 km/s) much slower than the GNSS occultation satellite
( 3.87 km/s) and the LEO satellites ( 7.8 km/s). A typical airborne/mountain-
top radio occultation generally takes 20-30 min to sample the atmosphere from
the altitude ( 5-10 km) of the receiver down to the surface. The sampling rate
requirement for the airborne/mountain-top RO measurements is thus lower than that
for the spaceborne RO, such that it can be satisfied by an off-the-shelf commercial
GPS receiver (Xie et al. 2008 ).