Validation of a method for ionospheric electron density reconstruction by means of vertical incidence data during quiet and storm periods

A preliminary validation of the technique developed using the NeQuick ionospheric model and the «effective ionization parameter» Az, based on vertical total electron content data ingestion, was carried out in a previous study. The current study was performed to extend the analyzed conditions and confirm the results. The method to validate this technique is based on a comparison between hourly F2 peak values measured with Vertical Incidence (VI) soundings and those calculated with the new technique. Data corresponding to different hours and seasons (equinox, summer solstice, and winter solstice) during the period 2000-2003 (high and medium solar activity conditions) were compared for all available ionosonde stations. The results show a good agreement between foF2 and hmF2 values obtained with the new technique and measurements from vertical incidence soundings during quiet and storms conditions. Mailing address: Dr. Gloria Miró Amarante, The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34014 Trieste (Italy); e-mail: amarante@ictp.it


Introduction
One of the most unpredictable sources of error for single frequency satellite navigation and positioning systems is due to the ionosphere.A good knowledge of the behavior of the ionospheric regions is essential to obtain a better representation of parameters like the Total Electron Content (TEC) which is directly proportional to the time delay of electromagnetic signals.
A technique to reconstruct the spatial and temporal structure of the electron concentration in the ionosphere has been developed using the NeQuick ionospheric electron density model driven by an «effective ionization parameter» called Az (Nava et al., 2003).NeQuick is a quick-run model for ionospheric applications developed at The Abdus Salam ICTP in Trieste (Italy) and the University of Graz (Austria).It has been used by the European Space Agency -ESA satellite navigation and positioning programs and adopted by Recommendation P.531-6 of the ITU-R (International Telecommunication Union, Radiocommunication sector) (now superseded by P. 531-7;ITU, 2001).
Az values are determined minimizing the differences between experimental and modeled vertical TEC global maps.The result is a global grid of Az values for a specific condition which allows us to calculate with the NeQuick model the electron density at any point in the ionosphere including the F2 peak parameters values.
The aim of this paper is to compare these calculated F2 peak values with independent and simultaneous global observations in order to validate the technique.These measurements, the criti-cal frequency in the F2 region (foF2) and the height of the maximum of ionization (hmF2), are obtained experimentally from ground-based vertical ionospheric sounders located around the world.
A preliminary validation was done (Miró Amarante et al., 2003) using data corresponding to four quiet days in the year 2002 (high solar activity conditions).The main results and conclusions of this analysis will be included in this paper.

Ionospheric parameters measured with vertical incidence soundings
The DIDbase software developed by Lowell University lets us extract ionograms from a network of digisondes distributed around the world.This possibility allows manual scaling of the available ionograms to measure the real values of the main ionospheric parameters (critical frequency, height, Ionospheric Total Electron Content -ITEC: Huang and Reinisch, 2001).
The analysis has been done for different conditions summarized in table I.For each period, all the available ionospheric stations were selected (fig.1).The number of locations varies from 13 during the period of March 2000 up to 27 for the 3rd of June 2002.
The manual scaling of the ionograms (almost 8300 ionograms) was done for each considered case and foF2 and hmF2 were extracted to be compared with the reconstructed values.

Ionospheric parameters calculated with the reconstruction technique
Two global grids corresponding to foF2 and hmF2 were obtained from the NeQuick model driven by the «effective ionization parameter» Az.This parameter is calculated by means of the technique described in Nava et al. (2003) in such a way that the differences between experimental and NeQuick model vertical TEC are minimum.The experimental vertical TEC maps used for the minimization are generated with two different techniques.The first is the one developed by CODE (Centre for Orbits DEterminations, http://www.cx.unibe.ch/aiub/ionosphere.html) with two hour intervals and the second one was generated by the University of La Plata, Argentina with one hour intervals (Meza et al., 2002;and Brunini et al., 2004).
The calculated F2 peak values at the available digisonde locations (fig. 1) are extracted

Comparison between measured and calculated peak values
As an example, the critical frequency f oF2 and the maximum height hmF2 for Millstone Hill (middle latitude Northern Hemisphere) and Grahamstown (middle latitude Southern Hemisphere) are shown in fig.2a-d (quiet period) and fig.3a-d (storm period).Calculated F2 peak values using CODE (foF2CODE) and La Plata (foF2LAPLATA) vertical TEC maps are plotted together with the experimental ones (foF2SAO, obtained with Sao-Explorer, http://ulcar.uml.edu/SAO-X/SAO-X.html).
The figures show a good agreement between both foF2 data sets (foF2CODE-foF2SAO and foF2LAPLATA-foF2SAO) during quiet conditions while the differences between calculated and experimental values increase for geomagnetic disturbed conditions.The results are considerably worse in the case of h mF2.However, this is not surprising.NeQuick uses the CCIR (ITU-R) maps for foF2 and M(3000)F2 and an internal map for foE to calculate hmF2 by means of Dudeney's form of the Bradley and Dudeney (1973) formula (see Dudeney, 1983) which works quite well for average (monthly median) conditions but can give larger errors in individual cases.Minimizing differences in electron content also means some minimization for foF2 but hmF2 is not affected.The height error of true height analysis of ionograms can also be quite large.
The left panel of fig. 4 presents the scatter plot of foF2 (F2 peak electron density) reconstructed with the NeQuick model against the corresponding f oF2 ionosonde measurements for quiet periods (2000 and 2002).This example  ) and shows how the agreement between both data sets is also obtained for a very disturbed day.It is important to point out that this storm occurred under middle solar activity conditions (sunspot number = 90) and the analysis was done considering together all the ionospheric effects (positive and negative storms) distributed around the world.
The selected data are classified to create distributions with different conditions of solar activity, vertical TEC mapping technique and quiet or storm periods.The results of the linear regression fitting corresponding to each distribution are summarized in tables II and III for f oF2 and hmF2 respectively.
The correlation coefficients R make clear the difference in accuracy for reconstruction of foF2 and hmF2.In the case of the critical frequency the correlation coefficient is approximately 0.90 which means that the fitting between both data set is excellent.However this value does not exceed 0.70 for the peak height possibly for the reasons indicated above when discussing the results shown in figs.2a-d and 3a-d.The foF2 reconstruction is also good during the studied storm period with values higher than 0.86.It must be noted that regardless of the actual values of the correlation coefficient all the results indicate a very high statistical significance.
The comparison between the two vertical TEC mapping techniques (CODE and La Plata) does not show a clear dependence on the tech-nique of the vertical TEC map used to derive Az values.The number of points corresponding to La Plata technique is higher because these maps are obtained hourly.
The dependence on solar activity is only noticeable for hmF2 where the fitting improves when solar activity decreases.However, further analysis considering low solar activity and storm conditions under very high solar activity should be done in the future.

Conclusions
The comparison of F 2 peak values generated by the new technique of 3D reconstruction of the electron density and the corresponding vertical incidence ionosonde data covering a wide area of different geographical, seasonal and hourly conditions indicates that: -The critical frequency of the F2 layer shows a very good agreement between both data sets during high and middle solar activity quiet periods.
-This agreement is also good for the November 2003 storm considering together all the ionospheric effects (positive and negative storm effects) distributed around the world.
-The hmF2 parameter shows a worse agreement than foF2 values and the worst results have been found for high solar activity.
-The results obtained are not dependent on the technique of the vertical TEC maps used,

Table I .
List of selected periods for the validation of the reconstruction method.