In this study, a new model was explored which corrects for higher
order ionospheric residuals in Global Positioning System (GPS) radio
occultation (RO) data. Recently, the theoretical basis of this new
“residual ionospheric error model” has been outlined

The proposed new model for computing the residual ionospheric error is
the product of two factors, one of which expresses its variation from
profile to profile and from time to time in terms of measurable
quantities (the L1 and L2 bending angles), while the other
describes the weak variation with altitude. A simple integral
expression for the residual error

In this follow-up study the overall objective was to explore the validity of the new residual ionospheric error model for more detailed simulations, based on modeling through a complex three-dimensional ionosphere.

The simulation study was set up, simulating day and night GPS RO
profiles for the period of a solar cycle with and without an
ionosphere. The residual ionospheric error was studied, the new error
model was tested, and temporal and spatial variations of the model
were investigated. The model performed well in the simulation study,
capturing the temporal variability of the ionospheric
residual. Although it was not possible, due to high noise of the
simulated bending-angle profiles at mid- to high latitudes, to perform
a thorough latitudinal investigation of the performance of the model,
first positive and encouraging results were found at low
latitudes. Furthermore, first application tests of the model on the
data showed a reduction in temperature level of the ionospheric
residual at 40 km from about

The radio occultation (RO) technique gains
information about the
physical properties of a planetary atmosphere by detecting a change in
a radio signal when it passes through this atmosphere. With the
instalment of the Global Positioning System (GPS) constellation this
principle could be applied to scan the Earth's atmosphere. Using the
GPS frequencies

The measured observables during an RO event are the phase delays of the
transmitted electromagnetic signals L1 and L2, which are
detected from a low Earth orbit (LEO) satellite. From the primary
quantity of phase delay, bending angles and, after further processing,
geophysical information such as temperature and pressure can be
obtained. However, the total phase delay of the signals consists of
neutral atmospheric phase delays as well as ionospheric phase
delays. In order to be able to study the characteristics of the
neutral atmosphere, the use of an ionospheric correction procedure is
necessary. To first order it is possible to remove the ionospheric
contribution (see, e.g.,

The remaining residual ionospheric error is a function which varies
with the 11-year solar cycle, being higher at daytime compared to
nighttime

Radio Occultation Meteorology
Satellite Applications Facility (ROM SAF) level-3 products describe the monthly mean
state of the atmosphere in the form of zonal averages, i.e., averages
over all longitudes in 5

Residual ionospheric errors are often described as the omission of
higher-order magnetic terms in the ionospheric refractive index. It
has been noted by

Healy and Culverwell made calculations based on this expression which
showed that it produces residual errors comparable to those produced
in more complex simulations. They also noticed that in this model
there is a simple relationship between the residual error and the
L1 and L2 bending angles

The proposed new residual ionospheric error model is mainly suited for
performing a bending-angle correction on bending-angle climatologies –
i.e., it is understood as a climatological correction – instead of
applying it on single bending-angle profiles. Recently, it has been
proposed for climatological studies with GPS RO data to perform the
averaging of the atmospheric parameters already in bending-angle space

The model does not correct for the residual ionospheric error that arises
from horizontal gradients of the ionosphere, or those errors that are caused
by the Earth's magnetic field (see companion paper

Although

In this specific follow-up study the work of Healy and Culverwell is
extended, by testing the new residual ionospheric error model for
a more complex situation, using simulated GPS RO data (see description
of data, Sect.

The study should help us to say whether the residual ionospheric error model is applicable to the more complex situation of a three-dimensional non-spherically symmetric ionosphere.

To first order the ionosphere-corrected bending angle

It is known that the magnitude of the residual ionospheric errors
corresponds to the ionospheric electron density values; i.e., larger
electron densities produce larger residual
errors.

The numerator of VK94 Eq. (22) differs slightly, which has however no significant impact on the error estimate.

:The last two equations suggest a relationship between the residual and
the actual bending angle. Healy and Culverwell calculated the residual
ionospheric error for the case of a Chapman layer ionosphere and
found, as expected from the above, that the residual error

We suggest that the new model term (Eq.

We perform a simulation study, since this has the decisive advantage
that the residual error

The advantage of the RESIC model is that the rapidly varying component
of the residual error can be directly calculated from the GPS RO
data. Hence the solar cycle dependency can be captured quite
easily. However, the coefficient

With the EGOPS software (End-to-End Generic Occultation Performance
and Processing System) version

The non-spherical three-dimensional ionosphere was simulated with the
NeUoG model from the University of Graz

Monthly mean solar flux.

Furthermore, we simulated neutral atmospheric events, employing the
same ECMWF analysis field from 1 January

In this study the ionosphere-corrected bending angle

Finally, the bending-angle profiles were studied as mean profiles
averaged over all longitudes within a latitude band, studied
separately for day and night. Additionally the following zonal
climatologies were tested: 5

Residual nighttime (blue) and daytime (orange) bending angle
dependent on time (left hand side), and night- and daytime L1 and L2 bending-angle
difference squared dependent on time (right hand side), studied on three impact altitudes
and for latitude band 0

The key quantities of interest in the simulation study are the
residual ionospheric error

As an initial analysis we investigated for the latitude band
0

Since the residual error is a very small number, we could observe that
noise has a significant impact in the residual error analysis. The
noise in the simulated data was about on the same order of magnitude
as the residual error itself, which led to occasionally large
fluctuations in the quantity

To partially overcome the problem of the noise, we decided to perform a vertical
smoothing step, as described in the Sect.

As a next step, we studied in Fig.

Note that the values for the coefficient

Finally

In order to perform a latitudinal investigation of the coefficient

Scatterplot and linear fit with fitting coefficient

Nevertheless, the results shown in this section support the hypothesis
that the model term

In this section the proposed model for correcting the residual
ionospheric error in GPS RO data is tested. As an initial
investigation the correction was applied on all simulated daytime
bending-angle profiles in the latitude band 0

From the one-dimensional simulation study performed by

The coefficient

Comparison of the residual ionospheric
correction to the monthly mean daytime residual error at latitude band
0

Testing the effect of the residual ionospheric
correction on temperature profiles, studied for latitude band 0

As a next step, in Fig.

Figure

Residual ionospheric errors are a topic of major concern in GPS RO
data. Sensitivity tests have shown that, at bending-angle level and
30 km altitude, residual errors of the order of about
0.05

Recently, a new model for correcting the residual ionospheric error,
suitable for bending-angle climatologies, was introduced and tested
for simulations with a one-dimensional Chapman layer ionosphere

This study was a follow-up investigation which explored the proposed model for a more complex simulation with a three-dimensional ionosphere. The simulation study enabled the investigation of the residual ionospheric error directly as the difference between bending angle climatologies simulated with ionosphere and their colocated neutral atmospheric bending-angle climatologies. Furthermore, the residual error was computed from the new residual ionospheric error model. One of the main goals was to check the hypothesis that the rapidly varying factor of the model, which depends only on measurable quantities, captures the temporal behavior of the residual ionospheric error.

It was possible to show at low latitudes correlation between the
residual ionospheric error and the model term which depends on the
solar activity. However, at mid- to high latitudes a decreasing signal-to-noise ratio
in the simulated data prohibited us from studying correlations. From the correlation
study, the model coefficient could
be calculated at low latitudes, showing to be between about

As a next step, a first attempt of correcting bending-angle data with
the proposed error model was conducted. Tested for the latitude band
0

For a thorough study of the latitudinal dependance of the coefficient

Furthermore, we also propose studying the RESIC method in simulations
using different models for the complex ionosphere than the NeUoG
model, in order to obtain a good estimate for the coefficient

In summary, this simulation study presented some encouraging first results which support the recently proposed residual ionospheric error model. The RESIC model showed clear correlation with the simulated residual error. Furthermore we could determine the model coefficient at low latitudes, showing it to be in line with results from spherically symmetric Chapman layer ionosphere simulations. We suggest that further investigation of the proposed model for residual ionospheric correction, especially at higher latitudes, is worth undertaking.

This work was conducted as part of the Radio Occultation Meteorology Satellite Applications Facility (ROM SAF), which is a decentralized operational radio occultation processing center under EUMETSAT. J. Danzer was a ROM SAF visiting scientist for this project, and S. Healy and I. Culverwell are members of the ROM SAF. Furthermore, we thank the Wegener Center, which provided the processing and simulation software, and especially Gottfried Kirchengast, for his support and the discussions about the ionosphere model. Finally, we acknowledge the BENCHCLIM project (P22293-N21), which provided the basis for this cooperation. Edited by: J. Y. Liu