The reliable estimation of ionospheric refraction effects is an important topic in the GNSS (Global Navigation Satellite Systems) positioning and navigation domain, especially in safety-of-life applications. This paper describes a three-dimensional ionosphere reconstruction approach that combines three data sources with an ionospheric background model: space- and ground-based total electron content (TEC) measurements and ionosonde observations. First the background model is adjusted by F2 layer characteristics, obtained from space-based ionospheric radio occultation (IRO) profiles and ionosonde data, and secondly the final electron density distribution is estimated by an algebraic reconstruction technique.

The method described is validated by TEC measurements of independent ground-based GNSS stations, space-based TEC from the Jason 1 and 2 satellites, and ionosonde observations. A significant improvement is achieved by the data assimilation, with a decrease in the residual errors by up to 98 % compared to the initial guess of the background. Furthermore, the results underpin the capability of space-based measurements to overcome data gaps in reconstruction areas where less GNSS ground-station infrastructure exists.

The ionosphere is the upper part of the atmosphere where sufficient free electrons exist to affect the propagation of radio waves. Therefore, the ionospheric parameters, such as three-dimensional electron density distribution, the ionospheric layer peak characteristics, and the total electron content (TEC), are important information for Global Navigation Satellite Systems (GNSS) users. The ingestion of actual ionospheric measurements into a background model, such as NeQuick (see Nava et al., 2008) or International Reference Ionosphere (IRI) (see Bilitza, 2001; Bilitza and Reinisch, 2008), is a commonly applied technique for estimating the ionospheric parameters. Several approaches had been tested for the ionospheric imaging combining actual direct and indirect measurements with either an empirical or a physical model background (see e.g. Angling and Cannon, 2004; Angling, 2008; Schunk et al., 2004; Wang et al., 2004; Scherliess et al., 2009; Brunini et al., 2011; Pezzopane et al., 2011; Galkin et al., 2012; Minkwitz et al., 2015, 2016; Gerzen and Minkwitz, 2016).

Within this work we present a two-step three-dimensional reconstruction approach, which
firstly adjusts the initial background model NeQuick (see Nava et al., 2008)
by the assimilation of F2 layer characteristics, obtained from space-based
ionospheric radio occultation (IRO) profiles and ionosonde data. Secondly,
the final electron density distribution is estimated by the algebraic
reconstruction technique SMART

AATR box plot for the nya2 station. Values for the disturbed period are presented in the top panel, while calm period values are in the bottom panel.

The approach presented is applied in the scope of the project DAIS (Data Assimilation Techniques for Ionospheric Reference Scenarios) to generate synthetic ionospheric reference scenarios (IRSs) for the validation of the European Geostationary Navigation Overlay Service (EGNOS). EGNOS provides value-added services for the estimation of ionospheric refraction effects. The IRSs are introduced by the ESA in order to conduct the EGNOS end-to-end performance simulations and to assure the integrity of the EGNOS system and associated services (see Arbesser-Rastburg, 2004; Schlüter et al., 2013).

The paper is organized as follows. At first the chosen reconstruction area and periods as well as the applied database are described. Section 3 then explains the reconstruction approach. Section 4 presents the validation results, and finally, the results are summarized and discussed.

The reconstruction approach described is tested over the extended EGNOS V3
service region (

The EGNOS APV-1 availability maps for DOYs 010 (left) and 298 (right) in 2011.

The impact of such conditions on the EGNOS system is given in Fig. 2. It
shows the availability of the EGNOS service for aviation approaches with
vertical guidance (APV-1) on DOYs 010 (left) and 298 (right) of the year 2011
(see

We use absolute TEC measurements from ground-based IGS stations as input for
the assimilation and validation. The details of the absolute TEC calculation
are given in Jakowski et al. (2011). For this study, the 1 Hz GPS data of
the IGS receiver network were obtained from

IGS stations that provide independent sTEC measurements for the validation.

The F2 layer characteristics, in particular the critical frequency,

Ionosonde station positions. Black dots are ionosonde stations used only for assimilation, red triangles are ionosonde stations used only for validation, and black triangles inside red triangles are ionosonde stations used for assimilation and validation.

Reconstruction scheme.

In the following, the

For both periods, the data of the low Earth orbit (LEO) satellite mission
COSMIC (see

Dual-frequency altimeter missions, such as Jason 1 and 2, are an excellent
source for vTEC data independent of the GNSS systems. In contrast to the GNSS-derived vTEC, the altimeter measurements are naturally vertical. The
available data of the Jason 1 and Jason 2 missions
(

Ionosonde stations used for validation purposes. Ionosonde stations with italic font are used for assimilation and validation.

Figure 4 outlines a sketch of the developed assimilation process. The single steps are further detailed in the subsections of this section.

The correct characterization of the vertical shape of the profiles becomes a difficult task when assimilating only ground-based sTEC because of limited vertical information included in these data (see e.g. McNamara et al., 2008, 2011; Minkwitz et al., 2015; Gerzen and Minkwitz, 2016). The inclusion of space-based sTEC improves the geometry situation. However, the adjustment of the background in terms of the F2 layer characteristics before starting the assimilation procedure seems to be especially advisable (e.g. Bidaine and Warnant, 2010) since the F2 layer dominates the shape of the whole profile.

Reconstructed

Thus, we first estimate global

The adjusted version of the NeQuick model serves as the initial guess for
SMART

To give a special focus on the question of how the inclusion of additional measurements (additional to the ground-based TEC) and the preconditioning of the background influence the assimilation results, we compare two three-dimensional assimilation versions within this work. Version A assimilates only ground-based sTEC and vTEC measurements into the NeQuick model without the preconditioning of Step 1. Version B starts with the adjusted NeQuick (Step 1) and then includes, in addition to the ground-based TEC, space-based sTEC and F2 layer characteristics from ionosondes and IRO profiles within Step 2.

For the assimilation of the F2 layer characteristics, MSCM is used with the
same configurations as detailed in Gerzen et al. (2015). Contrary to the
version used within Gerzen et al. (2015) though, both the ionosonde and IRO
profile data are assimilated by MSCM here. The first estimate of the unknown
parameters

Figure 5 presents as an example

To include the updated F2 layer characteristics, the internal

Figure 6 illustrates the possible improvement of the adjustment described. Electron density profiles are calculated at the position of the independent ionosonde station TO536 (see Table 2) on DOY 295. The NeQuick model profile is depicted in green; the profile calculated after the inclusion of the reconstructed maps, only assimilating ionosonde observations, in blue; the adjustment with ionosonde and IRO observations in red; and the measurement of the ionosonde TO536 as a violet dot.

Electron density profiles: NeQuick model (green) and adjusted NeQuick model (blue is assimilation of ionosondes only, red is assimilation of ionosonde and IRO F2 layer data) compared with the independent ionosonde measurement (violet dot).

The TEC is related to the electron density Ne by TEC

We discretize the ionosphere by a voxelized three-dimensional grid with a horizontal
spatial resolution of 2.5

The SMART

In order to assimilate the F2 layer characteristics using SMART,

The iteration process stops either after a predefined number of iteration steps (we used 26) or if the mean TEC deviation from the assimilated measurements goes below a predefined threshold. Thereafter, an extrapolation from the intersected voxels to those not intersected by any TEC ray path is done using the three-dimensional SCM method, assuming a Gaussian covariance model for the electron densities (see Gerzen and Minkwitz, 2016). Figure 7 presents as an example the reconstructed electron density on DOY 295, 12:30 UT.

Reconstructed three-dimensional electron density.

The IRSs, i.e. vTEC maps, are calculated from the three-dimensional reconstructions by an
integration of the electron density profile values using

IRS calculated from the reconstructed three-dimensional electron density.

Histograms of

For the validation of the adjusted NeQuick (Step 1), the

In Fig. 9, the distribution of the residuals over all reference ionosonde stations is shown, including the mean, standard deviation (SD), and RMS of the residuals. Again, the colour green is used for the results calculated with the NeQuick model, blue for the NeQuick model assimilating solely ionosonde data, and red for the adjusted NeQuick model assimilating ionosonde and IRO data.

The residual statistics indicate the advantage of the preconditioning of the
background using the current F2 layer characteristics. The mean of the

In this subsection we compare the absolute residuals between the Jason 1
and 2 vTEC measurements and the reconstructed vTEC derived from the
reconstruction versions A and B, in detail:

In Fig. 10, the distribution of the absolute residuals is given for the two
investigated periods in five TECU (total electron content unit) bins (the last bin sums up all the higher
values). The

Histogram of the vTEC absolute residuals for Jason 1 (left) and 2 (right) satellites during the quiet (top) and disturbed (bottom) periods.

Table 3 presents the mean, SD, and RMS values of the absolute residuals of Fig. 10. Version B decreases the mean values up to 0.4 TECU compared to version A. However, in most cases the SD of the version B residuals is higher than for version A. We assume that the partial increase in the residual deviation may be caused by inconsistencies in the assimilated ground- and space-based sTEC (see Sect. 4.3). Furthermore, there may be inconsistencies between the GPS and altimeter vTEC (see Azpilicueta and Brunini, 2009).

Mean, RMS, and SD of the absolute Jason residuals.

The histograms and statistics of the

The percentage number of reduced absolute Jason residuals per day of the quiet DAIS period.

The percentage number of reduced absolute Jason residuals per day of the disturbed DAIS period.

Histograms of sTEC residuals for Kiruna station: DOYs 009–021 (left) and DOYs 286–303 (right) in 2011.

To assess the capability for estimating sTEC, the following parameters are
compared:

Figure 13 exemplarily depicts the histograms of the sTEC residuals at the station Kiruna. On the left-hand side, the distribution of the residuals for the quiet period is shown and on the right-hand side the disturbed period is shown. An overestimation by the NeQuick model (green) is visible for both periods in accordance with the results presented in Nigussie at al. (2012) and Gerzen and Minkwitz (2016). The distributions of the version A (violet) and B (red) residuals are similar. Both versions crucially decrease the mean, RMS, and SD values of the residuals in comparison to the corresponding NeQuick statistics.

Table 4 (quiet) and Table 5 (storm) summarize the median, RMS, and SD of the
absolute residuals

The statistics of the absolute sTEC residuals in TECU for DOYs 009–021.

sTEC

The validation of the reconstructed electron density profiles with the
reference

The statistics of the absolute sTEC residuals in TECU for DOYs 286–303.

Coverage of the reconstructed array by space-based data (right) and by ground-based data (left) exemplarily on DOY 011 in 2011, 09:30 UT. A pixel is coloured blue if at least one voxel above this pixel is intersected by at least one sTEC ray path.

Both versions A (assimilation of ground-based data only) and B (assimilation of ground-, space-based, and ionosonde data) are validated with the Jason 1 and 2 vTEC measurements. During the storm period, this comparison indicates a slightly lower mean value of the absolute residuals of version B compared to version A.

The assimilation of ground-based sTEC clearly improves the initial guess of the NeQuick model. The median of the TEC residuals is decreased by up to 65 % during the quiet period and by up to 62 % during the storm period. However, no or only a very small advance (up to 16 %) is observed after the additional inclusion of the space-based and ionosonde data in the assimilation procedure. This is probably due to inconsistencies between the assimilated space-based data and the reference ground-based sTEC as detailed in the validation section.

Within this work, time series of three-dimensional electron density and IRSs, representing quiet and disturbed ionospheric conditions, are generated and cross-validated. These electron density values are deduced from the three-dimensional assimilation of ground- and space-based TEC and F2 layer characteristics into the NeQuick model.

The validation results show that a crucial improvement is achieved by the
adjustment of the whole background to the measured F2 layer characteristics
within a preconditioning step. A decrease in the

Through the subsequently assimilation of the ground- and space-based TEC into the preconditioned background a decrease of the sTEC residual statistics up to 62 % (Kiruna station) is gained. The space-based sTEC measurements cover wide regions where ground-based data are sparse (see Fig. 15). Hence, the use of additional LEO satellites (like SWARM and GRACE) looks very promising to fill the remaining data gaps. A further advantage of the space-based data is their measurement geometry, which is complementary to the angle-limited geometry of the ground-based TEC data.

Summarizing the results, on the one hand, the validation clearly shows the potential of data assimilation especially when combining the data from different data sources,. On the other hand, several results of this study indicate inconsistencies in the data obtained from different measurement instruments. This reflects a serious problem for all data-driven approaches and dealing with such inconsistencies is still a challenging task. Advanced filter methods, allowing the simultaneous filtering of all used data types, may contribute significantly to the solution for this problem.

Moreover, the inverse problem behind the ionosphere reconstruction remains ill-posed and highly underdetermined with angle-limited measurement geometry, even if all currently available measurements are used. Due to the sparseness of the available data and the limited geometry, potential artefacts in the final electron density reconstructions cannot be ruled out and have to be treated carefully. This underlines that the appropriate estimation of the correlation, between the electron density at a measurement location and a location where no measurements are available, is a necessity for an improved reconstruction of the ionosphere. We are currently working on methods that estimate the correlation lengths and variance components of parametric covariance models of the electron densities (see Minkwitz et al., 2015, 2016). However, a systematic study that investigates the spatial and temporal electron density correlations is highly recommended.

The ionosonde data, i.e. SAO files, were acquired from the following FTP
server:

The authors declare that they have no conflict of interest.

We would like to express our gratitude to the Aeronomy and Radio Propagation
Laboratory of the Abdus Salam International Centre for Theoretical Physics
Trieste, Italy, providing NeQuick version 2.0.2 for scientific purposes. The
authors thank the CDAAC
(

The research presented here is partly carried out under a contract to ESA in the framework of the European GNSS Evolution Programme (EGEP). The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. The topical editor, K. Hosokawa, thanks L. R. Cander and the one anonymous referee for help in evaluating this paper.