Atmospheric Sensing Using GNSS RO - GNSS Remote Sensing: Theory, Methods and Applications - page 128

6.2.1 Spatial Resolution (Vertical and Horizontal Resolution)

The vertical resolution of RO sounding retrieved through the geometric optic
method is constrained by the diffraction limit (i.e., the diameter of the first Fresnel
zone) as well as the vertical refractivity gradient (Kursinski et al. 1997 ). The first
Fresnel zone is defined as the region within which the path lengths differences are
within a half wavelength of the path of minimum phase delay. The diameter of first
Fresnel zone decreases as refractivity increases, such that the vertical resolution
improves from 1.4 km in the upper troposphere and stratosphere to 0.2 km
near the moist boundary layer top where large refractive gradient is generally found
(Kursinski et al. 2000a ). For a GNSS RO limb sounding geometry, the bending
angle retrieval at a tangent point is not a local point measurement but an integration
of bending along the ray path. The bending generally increases exponentially at
lower altitude due to the denser atmosphere. Therefore, most of the bending occurs
near the tangent point (e.g., over 50 % (Kursinski et al. 1997 )), where the ray
path is closest to the Earth's surface. For simplicity, the horizontal resolution ( l )
can be defined by the distance traversed by a ray path as it enters and exits a
spherically symmetric atmospheric layer with thickness represented by the vertical
resolution ( z ) (Kursinski et al. 2000a ). The relation between the horizontal and
vertical resolution can be expressed as

2 p 2R z ;

l (6.10)

where R is the radius of the atmosphere at the tangent height. Given the improving
vertical resolution from 1.4 km in the upper troposphere and stratosphere to
0.2 km near the boundary layer, the horizontal resolution also improves from
270 to 100 km.
The more sophisticated radio-holographic retrieval methods (e.g., Canonical-
Transform or Full-Spectrum-Inversion) eliminate the Fresnel diffraction limit of
vertical resolution imposed by the geometric optics assumption. Gorbunov et al.
( 2004 ) demonstrates the theoretical estimation of vertical resolution to be 60 m in
their simulation studies. Such high vertical resolution measurement is not achievable
by the passive nadir-viewing satellite sounders. In such case, much finer horizontal
resolution ( 60 km) can be achieved.

6.2.2 Accuracy and Precision Analysis

The theoretical estimation of RO measurement accuracy was first discussed in
Yunck et al. ( 1988 ) and later updated by Kursinski ( 1994 ). A much more compre-
hensive analysis of the RO theoretical accuracy was carried out through analytical
and simulation studies in Kursinski et al. ( 1997 ). Based on these studies, under
certain mean conditions, the refractivity retrieval error is generally large in the lower