Radio Science

Statistical validation of a technique for estimating total electron content from bottomside ionospheric profiles



[1] Digisonde sounders provide routine estimates of an ionosonde total electron content (ITEC) parameter that is taken to represent the vertical electron content of the ionosphere. The procedure involves integration under a profile, extrapolated to the topside from the measured bottomside by assuming an alpha Chapman layer with a constant scale height appropriate to that found just below the layer peak. The validity of the resultant ITEC parameter has been investigated here using measured height profiles of electron density from an incoherent scatter radar operated at a middle latitude site in the United Kingdom for several years around 1970. The data set of some 4000 profiles of electron density up to 700 km was used to determine statistically the relationship between the ITEC estimate and the measured total electron content calculated from the electron density observations. The results confirm that the ITEC method yields a generally reliable measure of the total content below 700 km, especially during nighttime, while in the daytime hours there is an overall tendency toward a small underestimate. An investigation of the differences between the modeled and measured densities with height in the topside, which are probably linked to the transition from O+ to H+ plasma, shows that during the day, excesses immediately above the peak may be compensated for at greater heights in the integration of the ITEC content.

1. Introduction

[2] The ionosphere affects Earth-space communication systems, especially during extreme space weather events. Radio wave propagation is modified in a number of ways by the effects of the integrated electron density along the ionospheric ray path between the satellite and the receiver, the so-called total electron content (TEC). In consequence, TEC is a key parameter in the description of the impact of the ionized atmosphere on the propagation of radio signals, understanding of which is crucial for the operation of many applications, including navigation satellite systems like GPS, Global Navigation Satellite System (GLONASS), and the future Galileo system. TEC can be measured by a number of essentially standard techniques, including Faraday rotation, group delay, and dispersive carrier phase. In general, these techniques measure the electron content along a slant signal path between a satellite and the ground, from which the equivalent vertical TEC is found by simple geometric conversion. However, Huang and Reinisch [2001] proposed a new technique to estimate the total electron content of the ionosphere using ground-based ionosondes. While the proposed method had the advantage of giving a direct measurement of the vertical TEC, it must be noted that, in reality, the ionograms only contain direct information about the vertical electron density profile of the bottomside ionosphere up to the peak of the F2 layer, and normally, some two thirds of the electrons comprising the TEC are in the topside.

[3] In the method, the profile above the peak was approximated by an α Chapman function with constant scale height (HT), derived from the bottomside profile shape at the F2 peak. The ionosonde total electron content (ITEC) was then calculated from the height integral over the entire profile according to the equation

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The upper limit of the integration (hmax) was chosen to be 1000 km in the original study, a height retained for the estimation of the ITEC parameter provided by Digisonde software. The formulation of the Chapman function outlined above depends on only three parameters, the peak density (NmF2), the peak height (hmF2), and the scale height (HT). The solar zenith angle dependence is contained in NmF2, which is estimated from the ionogram, while the peak height can be obtained from the true height inversion of the ionogram. It is assumed that the bottomside electron density profile (NB) also gives an indication of the profile shape above hmF2. Once NB(h) is calculated from the measured h′(f) trace in the ionogram, the shape of the profile at the F2 peak is used to derive an estimate of the topside scale height (HT). Scale height can be introduced by describing the bottomside profile by an α Chapman layer with variable scale height H(h) [Rishbeth and Garriot, 1969]:

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Here Hm is the scale height at the F2 peak, that is, Hm = H(hmF2). The ITEC method assumes that the determination of Hm from equation (3) will be a reasonable estimate for the scale height of the topside profile in equation (2), that is, HT = Hm.

[4] Several attempts have been made to try to validate ITEC, essentially on the basis of case studies. These have compared ITEC estimates with TEC values derived from incoherent scatter radar and satellite observations, the latter involving Faraday rotation at middle latitudes, TOPEX at the equator, and use of GPS. They showed that ITEC is generally within about 10% of the satellite TEC [Huang and Reinisch, 2001; Reinisch and Huang, 2001; Reinisch et al., 2001; Belehaki and Tsagouri, 2002]. Recently, a systematic comparison between ITEC and GPS-derived TEC values, estimated for the same geographic location using 12 consecutive months of measurements, found that the ITEC parameter can provide a qualitatively representation of the ionospheric electron content up to 1000 km [Belehaki et al., 2003]. Indeed, it was suggested that the residual differences between GPSTEC and ITEC may provide information about the plasmaspheric contribution to the former, as deduced from the diurnal and seasonal behavior and the variation during geomagnetic storms.

[5] As a next stage, before ITEC can be considered as an operational parameter, the current study involves a statistical investigation of the relationship between ITEC and the vertical total electron content, both calculated from the same set of electron density profiles that had been obtained from incoherent scatter radar (ISR) observations. For this purpose, the electron density profile has been reconstructed using the bottomside profile from the ISR observations and a topside profile extrapolated according to the Huang and Reinisch [2001] method. A statistical comparison between the reconstructed and the observed ISR profiles should provide conclusive evidence on the validity of the ITEC parameter as an alternative method of measuring the total electron content from ionosonde observations.

2. Data and Analysis

[6] A prototype incoherent scatter radar was operated at the midlatitude site of Malvern (52.1°N, 2.3°W) in the United Kingdom between 1968 and 1971. The resultant data set of some 4000 profiles of ionospheric electron density up to a height of 700 km was originally compiled into a graphical atlas and was subsequently digitized. These values have been used to form the database for the present study. Each ISR bottomside electron density profile was extrapolated to the topside using the Huang and Reinisch [2001] method. The ITEC parameter was then estimated from the integral of the reconstructed electron density with height up to 700 km. The upper limit of 700 km was chosen to correspond to the maximum height of the profiles measured by the radar. The actual total electron content (TEC700) was then also estimated from the integral of the observed electron density up to the same height. A representative example is presented in Figure 1, for a profile taken at 1457 LT on 18 February 1970. The scale height at the peak of the F2 layer for this specific case was found from equation (3) to be 50.7 km. Following the assumption of the Huang and Reinisch [2001] method, this value was used for the scale height in the topside ionosphere. The topside electron density was then calculated by means of equation (2), using hmax equal to 700 km, with the resultant value of the ITEC parameter then being determined using equation (1). The difference between ITEC and TEC700 for this specific case was found to be only about 1%, though it can be seen that differences in shape below and above a height of about 470 km act to cancel each other in the integration.

Figure 1.

Comparison of the ISR profile (marked with crosses) taken on 18 February 1970 at 1457 UT in Malvern, with the extrapolated profile (marked with dots) according to the Reinisch and Huang [2001] method.

[7] To investigate the relation between the calculated ITEC and the measured TEC700, the 4000 profiles were divided into daytime and nighttime cases. Profiles taken from 1 hour after local sunrise to 1 hour before local sunset were considered as daytime cases, while profiles taken from 1 hour after local sunset to 1 hour before local sunrise were assigned to the nighttime group. In total there were 1682 profiles classified as daytime, with a further 1211 profiles in the nighttime category. The profiles around dawn and dusk were eliminated from the present study. It was considered that changes in the shape of the ionospheric profile at these times, particularly around sunrise, might possibly add an additional complication to the investigation.

3. Results

[8] The scatterplots of the actual TEC700 against the corresponding estimated ITEC are presented in Figure 2a for the daytime profiles and in Figure 2b for the nighttime profiles. Both plots show a high degree of correlation between the observed and modeled total electron content up to 700 km. The line drawn corresponds to the best fit line. The intercept of the line shows that the TEC700 values exceed those from ITEC by about 2.5 TECU (1 TECU = 1016 el m−2) for daytime cases, which is about 10% of the overall average content, while at night, the intercept is negative and less than 0.4 TECU. The gradient of the fit is almost exactly unity for the nighttime data but is reduced to 0.86 in the daytime plot.

Figure 2.

Comparison between the ITEC and TEC700 parameters calculated using the electron density versus height profiles observed with Malvern ISR during (a) daytime and (b) nighttime.

[9] An investigation of the seasonal relationship between the ITEC and the TEC700 was performed to examine further the discrepancies during daytime. It can be noted that no seasonal dependence of significance could be seen in the analysis of the nighttime observations. The best fit line gradients were very close to unity, and the intercepts were small at all seasons, so the corresponding nighttime plots are not presented here. Figure 3 shows that the agreement between the modeled and the observed daytime values is better in winter than in summer. The best fit line intercept for winter months has the TEC700 values exceeding those from ITEC by only about 2 TECU, which is similar in magnitude to the systematic error of the TEC calculated by GPS [Jakowski and Sardon, 1996]. However, it can also be seen from Figure 3 that this difference increases to more than 4 TECU during the summer months. A similar seasonal effect was found in an earlier comparison between the ionogram-derived ITEC and GPS-measured TEC (GPSTEC) over Athens (38°N) based on measurements over a 12-month period [Belehaki et al., 2003].

Figure 3.

Seasonal dependence of the relation between TEC and ITEC.

[10] It must also be noted that the gradients of the best fit lines consistently fall below unity, indicating a slight tendency for the ITEC method to overestimate the content at the greater magnitudes. The consistent, though small, positive intercepts found in the daytime plots are difficult to explain, but they demonstrate that the detailed actuality of the situation is more complex than that represented by very simple assumptions underlying the ITEC method. The rotation of the lines perhaps accentuates the overall underestimates of ITEC when compared to the observed values indicated by the positive daytime intercepts. To account for this discrepancy in daytime it must be recalled that there is a composition change in the ionospheric plasma at some height in the topside, where the O+ dominance lower down gives way to the essentially H+ plasma of the protonosphere. While the transition height between the plasma regimes is often taken to be about 700 km, it is known to have wide variations. The O+/H+ transition height varies but seldom drops below 500 km at night or 800 km in the daytime, though it may be found as high as 1100 km, depending on the geophysical conditions and in particular on solar activity. Increased solar activity can cause thermal expansion of the atmosphere, resulting in an increase in the transition height [Denton et al., 1999]. Indeed, the differences seen between the measured topside profile and that based on the constant scale height assumption may be a reflection of this composition change. To check this hypothesis, the differences between the measured and the reconstructed electron densities were examined at different heights through the ionosphere. The average difference between the electron density modeled using the constant scale height assumption (NeRHM) and that actually measured by the radar (NeISR) is plotted as a function height in Figure 4, for profiles taken at three different hours of the day classified according to the season of the year. The averages have been estimated for differences binned into 50 km height groups. The corresponding plots for two nighttime hours are shown in Figure 5. The difference is by definition zero up to the height of the layer peak, which is of course considerably higher for the nighttime examples. At noon, the constant scale height assumption appears to result in an overestimate of the topside electron density immediately above the layer peak, with a difference that maximizes by about 400 km and subsequently decreases with height to become a small underestimate above 600 km. In the morning and afternoon, the positive differences immediately above the layer peak are smaller in general than at noon, with the transition to negative values setting in by 450 km in some of the plots. The height at which the measured and modeled profiles cross is clearly dependent on both local time and season. Indeed, it can be seen that at 0900 LT in summer, the constant scale height assumption results in an underestimate of the electron densities at all heights above about 350 km. Figure 5 shows that the difference between the observed and the modeled electron density is smaller at night than during the day by almost an order of magnitude, commensurate with the lower nighttime electron densities in the topside ionosphere. For both of the nighttime hours included here, the difference maximizes at around 500 km but remains positive up to the highest height. However, in general, the small magnitude of the difference contributes less than 0.5 TECU to the integrated content, in accord with the better correlation found at night in the plots of Figure 2.

Figure 4.

Height dependence of the average difference between the modeled electron density (NeRHM) and that measured by the radar (NeISR) for three daytime hours and four seasons, with electron densities in m−3 and height in km.

Figure 5.

Height dependence of the average difference between the modeled electron density (NeRHM) and that measured by the radar (NeISR) for two nighttime hours and four seasons, with electron densities in m−3 and height in km.

4. Discussion and Conclusions

[11] The aim of this work was to investigate the validity of the ITEC parameter, calculated routinely by all ground-based Digisondes, as a reasonable estimate of the total electron content through the ionosphere. The database used for this purpose consisted of a set of some 4000 electron density height profiles measured by an incoherent scatter radar at a site in the United Kingdom. Each electron density profile was then reconstructed using the bottomside profile from the ISR observation and a topside profile extrapolated using the Reinisch and Huang [2001] method. The comparison between the measured and reconstructed profiles has demonstrated that the agreement in the integrated content is very good for the nighttime cases, with the intercept of the best fit line for the correlation between the measured TEC700 and the modeled ITEC being found to be less than 0.4 TECU. For the daytime examples, the discrepancy is larger, with the statistical results giving an overall intercept of 2.5 TECU or about 10% of the average content, but with that for summer reaching 4.4 TECU.

[12] The plots of the difference between the modeled and measured electron densities showed that at night (Figure 5), the use of a constant scale height resulted in an overestimate throughout the topside at all seasons, though the magnitudes were so small that the integrated effect on the content was not particularly significant, as indicated by the small negative intercept in Figure 2. By day, the situation was more complex (Figure 4), though there was some evidence to suggest that a positive difference immediately above the peak could be giving way to negative values higher up, thus providing a fortuitous aid to the agreement between the ITEC parameter and the measured TEC. The alpha Chapman constant scale height assumption underlying the ITEC method appears to yield topside electron densities that are marginally too large at night, while by day more significant excesses immediately above the peak give way to underestimates at the highest heights in most of the categories investigated in the study. Clearly, these differences must reflect the changes in the composition of the actual plasma that do not follow the simplistic nature of the model assumption underlying the ITEC parameter. In practice, the transition to an H+ plasma at the greatest heights will be reflected in the scale height and hence the profile shape, with consequences for the integrated content. However, the known simple variations in the transition height alone are unable to explain the details of differences found here. Nevertheless, while a physical explanation may be beyond the purposes of the current study, it is encouraging to report the apparent success of the ITEC parameter in yielding a first-order estimate of the vertical ionospheric total electron content. The investigation has shown that, notwithstanding the fact that under typical conditions two thirds of the electrons are likely to reside in the topside, an ionosonde probing below the peak may be able to provide a reasonable estimate of the total electron content in a vertical section through the whole ionosphere. It should be noted that the ITEC parameter routinely estimated by Digisondes relates to an integration up to 1000 km, as opposed to the 700 km height limit of the present observations. While the content difference between the two altitudes is likely to be small, the current study has shown that in some circumstances, the additional height integration in the calculation of the content may serve to provide further compensation for excess densities closer to the layer peak, thus improving the vertical content estimate given by the ITEC parameter that is output by Digisonde software.


[13] This work was initiated within the collaborative framework of European Action COST 271. A.B. was supported in part by NATO grant ESTCLG979784.