Atmospheric Sensing Using GNSS RO - GNSS Remote Sensing: Theory, Methods and Applications - page 132

6.2.5 Retrieval Errors

To derive the neutral atmospheric bending angle profile, the ionospheric induced
bending can be removed via the simple linear combination approach (Sect. 5.4.4.1 ) ,
by assuming spherically symmetric atmosphere and that the two frequency (e.g.,
L1 and L2) signals travel in straight line and are along the same path (Vorobev and
Krasilnikova 1994 ).
This ionospheric calibration process effectively removes the first order iono-
spheric term (1/ f 2 ). Higher order term contributions constitute the major source
of error during day-time solar maximum at high altitudes (e.g., Kursinski et al.
1997 ) and require further calibration (e.g., Bassiri and Hajj 1993 ). In addition, the
spherically symmetric atmosphere assumption could become less accurate due to
the long signal travel distance within the ionosphere. The presence of horizontal
gradient of electron density, small-scale variation (e.g., over E -region) and the
ionospheric scintillations (e.g., over low latitudes due to magnetic storms) could
produce residual ionospheric residual errors that can't be removed by the simple
linear combination calibration process.
The ionospheric residual errors decrease rapidly at lower altitude in the neutral
atmosphere, but could be the dominant error source in the upper stratosphere.
Explicit consideration for the ionosphere yields more accurate neutral atmospheric
bending angles, especially for high altitudes where the ionospheric bending is
significant (e.g., Wee et al. 2010 ). The magnitude and long-term drift of such errors
are not well understood and could be very important for climate monitoring and
warrant additional study.

6.2.5.1 Upper Boundary Condition

Derivation of refractivity requires the Abelian integration of the bending angle
extended to the top of the atmosphere (e.g., Eq. 5.15 ) . Similarly, the temperature
retrieval requires the hydrostatic integration of refractivity up to the top of the
atmosphere (e.g., Eq. 6.4 ) and practically uses a-priori temperature at a high altitude
(e.g., upper stratosphere).
Therefore, the errors in the high-altitude bending angle or density used in the
Abelian integrals, or the a-priori temperature error will result in errors in the
refractivity, pressure and temperature retrievals. Such upper boundary condition
induced errors decrease rapidly at lower altitudes, but will limit the accuracy of
the refractivity and temperature retrievals near the altitudes where upper boundary
condition is applied.

6.2.5.2 Spherically Symmetric Atmosphere Assumption

The bending angle derivation from excess Doppler (e.g., geometric optics method)
or excess phase and amplitude (e.g., radio-holographic method), assumes local