A modification to the standard bending-angle correction used in GPS
radio occultation (GPS-RO) is proposed. The modified approach should reduce
systematic residual ionospheric errors in GPS radio occultation
climatologies. A new second-order term is introduced in order to
account for a known source of systematic error, which is generally
neglected. The new term has the form

GPS radio occultation (GPS-RO) measurements are now routinely
assimilated into operational numerical weather prediction (NWP)
systems

Overall, the published results indicate that GPS-RO could have an
increasingly important role in climate monitoring in the coming years,
particularly in the stratosphere. However, one area of potential
concern that could affect climate-monitoring applications is the
impact of “residual ionospheric errors” on the geophysical
retrievals. These arise because the measurement is sensitive to both
the neutral atmosphere and the ionosphere. The first-order
“ionospheric correction” commonly used in the GPS-RO processing

The impact of residual ionospheric errors on GPS-RO retrieval accuracy
has been discussed by a number of authors.

In this study, we present a new, relatively simple approach for
reducing the systematic residual ionospheric error originally
identified and investigated by Vorob'ev and Krasil'nikova (1994). The
method still requires a priori ionospheric information, which is
combined with the observed bending-angle information in order to
estimate a correction term. This work has possible relevance to the
generation of accurate monthly mean geophysical climatologies of the
stratosphere, retrieved from GPS-RO measurements. In particular, it
may be useful when producing GPS-RO climatologies with the new
average-bending-angle method, which has been discussed recently

The theoretical basis of the new method for reducing the systematic
residual ionospheric errors will be outlined, and we will demonstrate
the method in simulations with one-dimensional, spherically symmetric
model ionospheres, where the electron number density is only
a function of the vertical co-ordinate. More detailed simulations
which expand on these results – based on modelling through complex,
three-dimensional ionospheres – will be reported by

In Sect.

It has been demonstrated that GPS-RO measurements provide useful
temperature information in the stratosphere. However, GPS-RO is not
a direct measurement of temperature profile information, and
a retrieval system is required to estimate the geophysical variables
such as pressure, temperature and geopotential height. The basic
components of the GPS-RO geophysical retrieval system are outlined in
Kursinski et al. (1997) and

The GPS satellites transmit signals at two L band frequencies,

As noted earlier, the ionospheric correction is usually performed at
the bending-angle level at most operational processing centres, based
on the approach suggested by Vorobev and Krasilnikova (1994) (VK94,
hereafter). The “corrected” neutral atmosphere bending angle,

One of the strengths of Eq. (

It is interesting to note that VK94 provided an estimate of a systematic residual ionospheric bending-angle error,
although – with the exception of Syndergaard (2000) and Danzer et al. (2013) – this does not seem to have received much attention (see Eq. 22, VK94).
Neglecting the neutral contribution to the refractive index in order to simplify the mathematics (

Applying the standard ionospheric correction (Eq.

The numerator of VK94 (Eq. 22) differs slightly. It has
a factor

Comparing analytically estimated residual ionospheric errors
(Eq.

This error term arises even for the simplest case of a spherically
symmetric ionosphere, with no magnetic field. Integration by parts
shows that the integral in Eq. (

In this study, we propose a modification to the standard ionospheric correction of the form

We have confirmed the accuracy of Eq. (

There is a linear relationship between the residual error value,

The computed

In Appendix A, we provide analytical expressions for

The agreement between the computed

The profiles of the electron number density used to provide
analytical estimates of

The sensitivity of computed

This study has focused on a source of systematic residual ionospheric
error, originally noted in VK94. The results suggest it may be
beneficial to introduce an additional term in the standard
bending-angle ionospheric correction scheme (Eq.

This introduces a new term,

The computed

The impact of the assumed width,

We note that the modified ionospheric correction scheme will be
important in the generation of GPS-RO geophysical climatologies if the
temporal variability of

It must be accepted that

The sensitivity of the computed

One limitation of the new ionospheric correction approach that should
be highlighted is regarding the application to CHAMP (Challenging Minisatellite Payload) data. The
bending angles we receive are not direct measurements but are derived
from a Doppler shift value assuming the refractive index at the low-earth-orbit (LEO)
satellite is unity, meaning the electron density at the LEO is assumed
to be zero. This assumption introduces systematic errors in both the
L1 and L2 bending-angle values which scale as

In summary, we have investigated a systematic residual error in the standard GPS-RO ionospheric correction. A modification to the standard ionospheric correction has been suggested which may be particularly important when generating geophysical climatologies from GPS-RO measurements. The initial results are promising, and they suggest the modified approach should be considered at the GPS-RO processing centres.

Simple 1-D ionosphere models are useful for understanding the
magnitude of

If the electron density is zero at the tangent height,

Equations (

A similar procedure can be followed for a slab ionosphere, where the
electron density is a constant value over a vertical interval of total
width

The asymmetric triangle ionosphere has a peak electron density at

This work was conducted as part of the Radio Occultation Meteorology Satellite Applications Facility (ROM SAF), which is a decentralised operational radio occultation processing centre under EUMETSAT. The authors thank Julia Danzer, Stig Syndergaard and Sergey Sokolovskiy for useful conversations and suggestions during the course of this study. Edited by: U. Foelsche