Theory of GNSS Radio Occultation - GNSS Remote Sensing: Theory, Methods and Applications - page 112

5.3.2 Bending Angle Retrieval

After the phase delays are calibrated to remove special and general relativistic
effects and to remove the GPS and LEO clock errors, a time series of excess phase
delay at both GNSS frequencies (e.g., L1 and L2 for GPS) are derived. Then the
atmospheric bending in the ionosphere and neutral atmosphere can be inferred.
In the ionosphere and upper part of the neutral atmosphere, the radio signals
can be assumed to be monochromatic (e.g., single-tone or single-ray), i.e., only
one ray connects the transmitter and receiver at one instant. The geometric optics
(or ray optics) concept can be applied to describe the radio signal propagation, as
the diffraction effect can be neglected. The computation of bending angles is thus
straightforward as they are unambiguously related to the instantaneous frequency of
the received signal.
In the lower troposphere, however, radio signals become non-monochromatic
(e.g., multiple-tone) and may have a very complex structure due to multipath effects
caused mainly by water vapor structures (Gorbunov and Gurvich 1998 ; Sokolovskiy
2001 ). The atmospheric multipath occurs when sharp vertical variations in atmo-
spheric refractivity structure create multiple, simultaneous signal paths connecting
the transmitter and receiver through the atmosphere. In the multipath regions, the
bending angles cannot be derived directly from the instantaneous frequency of the
measured signal because the instantaneous frequency will be related, not to a single
ray, but to two or more rays.
Generally, it is practical to split the bending angle retrieval into two altitude
ranges. Above the lower troposphere where atmospheric multipath is not significant,
the bending angles at both frequencies are derived based on geometric optics from
the differential form of the excess phase (or excess Doppler) after appropriate noise
filtering (Vorob'ev and Krasil'nikova 1994 ; Kursinski et al. 1997 ;Hajjetal. 2002 ).
In the lower troposphere, where atmospheric multipath cannot be neglected, the
radio-holographic (wave optics) techniques are needed to accurately reconstruct the
bending angle from the phase and amplitude measurements (e.g., Gorbunov 2002 ;
Jensen et al. 2003 ).

5.3.2.1 Geometric Optics Method

The sum of the extra phase delay due to the ionosphere and neutral atmosphere
is determined after the calibration process. The differential form of the excess
phase delay, also called extra Doppler shift can be derived. Based on geometric
optics assumption, the accumulation of atmospheric bending along a ray path can
be measured as an extra Doppler shift relative to that expected for a straight-line
(in vacuum) signal path (Vorob'ev and Krasil'nikova 1994 ; Kursinski et al. 1997 ;
Hajj et al. 2002 ). By using the geometry and notation in Fig. 5.4 , the extra Doppler