The standard approach to remove the
effects of the ionosphere from neutral atmosphere GPS radio occultation
measurements is to estimate a corrected bending angle from a combination of
the L1 and L2 bending angles. This approach is known to result in systematic
errors and an extension has been proposed to the standard ionospheric
correction that is dependent on the squared L1

It has been demonstrated that, by using variational data assimilation techniques, GPS radio occultation (GPS-RO) measurements can be assimilated into operational numerical weather prediction (NWP) systems to improve the accuracy of temperatures in the upper troposphere and lower–middle stratosphere (Healy and Thépaut, 2006; Poli et al., 2009; Rennie, 2010). In particular, GPS-RO measurements reduce stratospheric temperature biases in NWP systems and this indicates that such measurements could have an increasingly important role in climate monitoring and climate reanalyses (Poli et al., 2010; Steiner et al., 2013). Notwithstanding the benefits of GPS-RO for the neutral atmosphere, it remains necessary to consider the effect of the ionosphere on the measurements.

Vorob'ev and Krasil'nikova (1994) (hereafter referred to as VK94) proposed a method of combining the GPS-RO bending angles measured at two frequencies (L1 and L2) to provide a first-order correction for the ionosphere. VK94 also showed that the first-order correction leaves a systematic bending angle bias that increases as a function of the electron density squared, integrated over the vertical profile. The relationship between the bias and electron density suggests that the bending angle biases should vary diurnally and as a function of the 11-year solar cycle. This has been demonstrated by various authors, e.g. Kursinski et al. (1997), Mannucci et al. (2011) and Danzer et al. (2013).

Healy and Culverwell (2015) have
proposed a modification to the standard bending angle correction to reduce
the residual systematic ionospheric errors. The modification introduces a
new second-order term that is a function of the square of L1 and L2 bending
angle difference and a weighting term (

Radio occultations, the VK94 ionospheric correction procedure and the
proposed modified correction are described in Sect. 2. Examples of how

Hardy et al. (1994), Kursinski et al. (1997) and Hajj et al. (2002) provide a comprehensive
description of the GPS-RO technique. In summary, the GPS satellites transmit
on two L-band channels (L1, L2) at

Updates to produce the University of Birmingham (UoB) variant of NeQuick.

Radio occultation geometry. Reproduced from Healy (2001).

The standard approach (Abel transform) for inverting GPS-RO measurements requires the assumption of spherical symmetry. Under that assumption, the bending angle of the ray between the GPS satellite and a receiver in LEO is

Horizontal gradients will result in residual errors in the inversion. However, it is expected that these errors are random; therefore, they should not affect monthly or seasonal climatologies.

To a first-order approximation, the refractive index comprises terms
dependent on the neutral atmosphere refractivity (

A monthly median 3-D ionospheric model (in this case NeQuick) and a 1-D
bending angle operator (based on Eq. 1) can be
used to estimate the residual ionospheric error and thereby estimate values
for

Test parameters for height dependence examples

Geographic test parameters.

Electron density profiles for test 1 (

L1 and L2 bending angles for test 1 (

Bending angle residual errors for test 1 (

Estimate of

NeQuick is a monthly median ionospheric electron density model developed at the Aeronomy and Radiopropagation Laboratory (now Telecommunications/ICT for Development Laboratory) of the Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy, and at the Institute for Geophysics, Astrophysics and Meteorology (IGAM) of the University of Graz, Austria (Nava et al., 2008). The model is based on the Di Giovanni–Radicella (DGR) model (Di Giovanni and Radicella, 1990), which was modified for the European Cooperation in Science and Technology (COST) Action 238 to provide electron densities from ground to 1000 km. The model has been designed to have continuously integrable vertical profiles which allows for rapid calculation of the total electron content (TEC) for transionospheric propagation applications. The current version of NeQuick can be run up to a height of 20 000 km and a variant is used in the Galileo Global Navigation Satellite System (GNSS) to calculate ionospheric corrections (Angrisano et al., 2013).

NeQuick is a “profiler” which makes use of three profile anchor points at the E layer peak, the F1 peak and the F2 peak. To specify the anchor points it uses the layer critical frequencies (foE, foF1, foF2) and the F2 maximum usable frequency factor (M3000(F2)) (Davies, 1965). foE is determined using a solar zenith angle model, foF1 is assumed to be proportional to foE during daytime and zero during nighttime, and foF2 and M3000(F2) are derived from the ITU-R (CCIR) coefficients in the same way as the International Reference Ionosphere (IRI) (Bilitza and Reinisch 2008).

Between 100 km and the peak of the F2 layer, NeQuick uses an electron density profile based on the superposition of five semi-Epstein layers (Epstein, 1930; Rawer, 1983); i.e. the Epstein layers have different thickness parameters for their top and bottom sides. The top side of NeQuick is a simplified approximation to a diffusive equilibrium. A semi-Epstein layer represents the model top side with a height-dependent thickness parameter that has been empirically determined.

The model used in this work is the University of Birmingham's translation of the NeQuick v2.0.2 from FORTRAN into Python. Very minor (negligible) differences in results are observed due to the use of different interpolation routines. The Python code has been largely vectorised to increase the speed of operation. Some additional modifications have been made and are described in Table 1.

In each of the examples shown in the following sections the same basic
procedure has been followed to estimate the value of

Use NeQuick to estimate a vertical profile of electron density.

Convert the electron density (

Estimate bending angle using the 1-D observation operator for L1 and L2.

Form the VK94 corrected bending angle (

Since no neutral atmosphere is included in the estimate of the refractive
index,

Vertical TEC from NeQuick for 12:00 UT, F10.7

Estimated residual bending angle error for 12:00 UT,
F10.7

Estimated

Since the bending angles are known, this can be rearranged to provide an
estimate of

In real data the corrected bending angles increase rapidly towards the
surface. This means that the impact of any residual error becomes less
insignificant below approximately 40 km. Furthermore, the VK94 correction
assumes that the ray impact parameter/tangent height is below the ionosphere
(i.e. the electron density is zero). Consequently, the main area of interest
for

The Figs. 2 to 5
show two examples of the vertical electron density profile, the L1

Solar cycle dependence of

The geographic dependence of bending angle correction can be demonstrated by
plotting maps of the TEC (Fig. 6), residual
bending angle (Fig. 7) and

The solar cycle dependence of

Solar cycle test parameters.

Section 3 has presented examples of how

Parameter ranges for random

The random

Estimated model parameters and associated variances

Scatter plot of

Global, daytime and nighttime bending angle errors for three models

Histograms of globally distributed bending angle errors for zero

The aim of this model is to produce a very simple polynomial function that
mimics some of the form of

The Python code curve_fit from the scipy.optimize package has
been used to fit the model. The parameter results and the associated
variances are shown in Table 6. A plot of the
NeQuick estimated

The second set of 25 000 randomly distributed points has been used to assess
the reduction in residual bending angle for each of the

Both the scal-

Histograms of daytime bending angle errors for zero

Histograms of nighttime bending angle errors for zero

Figures 17 and 18 show histograms for residual bending angle for day and night respectively.
In the daytime, the scal-

Many studies of ionospheric refraction of transionospheric radio waves have
shown that, in addition to the level of ionisation, the shape of the
vertical electron density profile plays a significant role, e.g.
Jakowski et al. (1994) and
Hoque and Jakowski (2008, 2010). It is important to remember that the functional model of

Using the random selection of vertical profiles from the NeQuick the median

This limitation can be overcome using the simple

The NeQuick variant used to produce the results in this paper can be requested from the Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Observing Atmosphere and Climate with Occultation Techniques – Results from the OPAC-IROWG 2016 Workshop”. It is a result of the International Workshop on Occultations for Probing Atmosphere and Climate, Leibnitz, Austria, 8–14 September 2016.

This work was undertaken as part of a visiting scientist study funded by the Radio Occultation Meteorology Satellite Application Facility (ROM SAF), which is a decentralised processing centre under the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT). The original NeQuick Fortran code was provided by ITCP. Edited by: Anthony Mannucci Reviewed by: Norbert Jakowski and one anonymous referee