Available online at www.sciencedirect.com Advances in Space Research 44 (2009) 1309–1313 www.elsevier.com/locate/asr Use of varying shell heights derived from ionosonde data in calculating vertical total electron content (TEC) using GPS – New method Sajan C. Mushini a,*, P.T. Jayachandran a, R.B. Langley b, J.W. MacDougall c b a Department of Physics, University of New Brunswick, Fredericton, NB, Canada E3B5A3 Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, NB, Canada E3B 5A3 c Department of Electrical Engineering, University of Western Ontario, London, Ont., Canada N6A 5B9 Received 3 April 2009; received in revised form 15 July 2009; accepted 20 July 2009 Abstract The dispersive nature of the ionosphere makes it possible to measure its total electron content (TEC). Thus Global Positioning System, which uses dual-frequency radio signals, is an ideal system to measure TEC. When data from an ionosonde situated in polar region was observed, the height of an approximated thin shell of electrons (shell height) used in GPS studies was seen not to be fixed but rather changing with time. Here we introduce a new method in which we included the varying shell heights derived from the ionosonde to map the slant total electron content from GPS to obtain a more precise vertical total electron content of the ionosphere contrary to some previous methods which used fixed shell heights. In this paper we also compared the ionosonde derived TEC with the GPS derived vertical TEC (vTEC) values. These GPS vTEC values were obtained from GPS slant TEC (sTEC) measurements using both fixed shell height and varying shell heights (from ionosonde measurements). For the polar regions, the varying shell height approach produced better results than the fixed shell height and compared to exponential function, Chapman function seems to be a better function to model the topside ionosphere. Ó 2009 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Polar ionosphere; GPS; Ionosonde; Total electron content; Chapman function 1. Introduction The Global Positioning System’s availability both spatially and temporarily and also its usage of dual-frequency signals (F1 = 1.575 GHz and F2 = 1.228 GHz) make it a very suitable system for ionospheric research. The phase advance and the group delay in the GPS signals produced by the ionosphere depend on its total electron content (TEC). Using these advances and delays one can calculate the total electron content along the path the ray has traveled from the satellite to the receiver through the ionosphere (Komjathy, 1997). * Corresponding author. E-mail addresses: m4s86@unb.ca (S.C. Mushini), jaya@unb.ca (P.T. Jayachandran), lang@unb.ca (R.B. Langley), jmacdoug@uwo.ca (J.W. MacDougall). The point at which the ray path intersects the ionosphere is called the ionospheric pierce point (IPP) and the electron content derived from the advances and delays along that ray path is assumed to be present at that point. Some previous studies (Komjathy, 1997) have assumed the ionosphere to be a thin layer around the earth at a height called the shell height. The shell height is defined as the height at which the electrons are distributed equally below and above it, and this height is close to the peak height of the F layer in the ionosphere (Komjathy, 1997; Horvath and Crozier, 2007). In many previous studies (e.g. Komjathy, 1997), the shell height is approximated to be 350 km. However, for the polar regions the fixed shell height assumption may not be valid since the polar ionosphere is very dynamic because of the solar wind–magnetosphere–ionosphere 0273-1177/$36.00 Ó 2009 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2009.07.015 1310 S.C. Mushini et al. / Advances in Space Research 44 (2009) 1309–1313 interaction and presence of ionospheric structures such as polar patches (MacDougall and Jayachandran, 2007). The electron content derived at the Ionospheric Pierce Point (IPP) is called the slant total electron content (sTEC) since the ray path makes an angle with the vertical. This sTEC is then mapped to the vertical using a mapping function to obtain the vertical total electron content (vTEC) at the same height of the IPP (shell height). The ionosonde is another device which is generally used to profile the ionosphere. It is a vertical sounder of the ionosphere which sweeps over a frequency range of 1–20 MHz and works on the principle of reflection (Davies, 1990). From ionosonde vertical sounding profiles, one can obtain the peak frequency and peak heights which correspond to the plasma frequency and height of the maximum electron density at that epoch, respectively. These peak heights obtained from the ionosonde were used as shell heights for mapping the slant TECs to the vertical in our analysis of the GPS data. We used sun-fixed solar geomagnetic coordinates in our calculations since the ionosphere varies much more slowly in these coordinates (Bregstrand and Haas, 2004). We compared the TEC values obtained from ionosonde profiles (bottomside + modeled topside) with the GPS derived vTEC values. The topside profiles from the ionosonde were modeled using a Chapman and exponential functions (Chapman, 1931; Davies, 1990). 2. Data analysis In this study, we have used GPS measurements from Resolute Bay (74°410 5100 N, 94°490 5600 W geog), an International GNSS Service (IGS) site which is in the polar cap. We have used data from three days in 2006 (11th November, 12th November, and 15th November 2006). The IGS provides 30-s dual-frequency RINEX observational files. These observational files contain information about range measured in meters on P1, P2 (P-code pseudo-ranges on L1, L2 frequencies, respectively) and C1 (C/A code pseudo-range on L1). They also have phase information (L1 and L2) measured in cycles on L1 and L2 frequencies. We calculated the slant absolute total electron content (SATEC) from pseudo-ranges and slant relative total electron content (SRTEC) from the carrier phases using Eq. (1) and (2), respectively (Horvath and Crozier, 2007).        P2 P1 ð1Þ   2:852  10þ9 ; SATEC ¼ c c     60 ð2Þ L1  ð2:3247Þ; SRTEC ¼ L2  77 The relative slant total electron content is relative in the sense that there is an ambiguity in the phase which does not give an absolute value but it is very precise. The absolute total electron content from the pseudo-range is absolute but noisy. To obtain a better result we combined them using a method called phase leveling (Komjathy, 1997; Horvath and Crozier, 2007). To minimize the multipath effect, we have used the phase and pseudo-range values which correspond to ±15° from highest elevation angle of the respective satellite pass to obtain the mean difference between the phase and pseudo-range values. This bias was then used to level the whole satellite pass. Since GPS hardware have their inherent delays (satellite bias and receiver bias), they should also be taken into consideration (Komjathy, 1997; Horvath and Crozier, 2007). We obtained these bias values from the University of Bern website (http://www.aiub-download.unibe.ch/ CODE/) and combined them with our slant absolute total electron content values before we did phase leveling (Horvath and Crozier, 2007). This phase leveled slant total electron content is called the slant total electron content. While analyzing the data, cycle slips, where the phase is lost for a certain period of time, were checked for and corrected before phase leveling was done. After obtaining the slant total electron content, we used the mapping function, M(E) (Eq. (3)) (Komjathy, 1997), to obtain the vertical slant total electron content at the ionospheric pierce point at the shell heights obtained from ionosonde measurements. We then mapped the vertical TEC (vTEC) from the pierce point to the point above the receiver using the angle between them. Later, we averaged the vertical total electron content from each satellite to obtain the averaged vertical total electron content. This averaging would smooth out variations caused by horizontal gradients in the ionosphere. These horizontal gradients in the ionosphere are assumed to be small for a particular site and epoch. The elevation angles (E) between the receiver and satellites were obtained from the GPS Toolkit designed by the University of Texas, Austin (Gaussiran et al, 2004). MðEÞ ¼ 1  h i ; e cos arcsin cosðEÞ ReRþh ð3Þ where Re is the radius of earth and h is the shell height (Komjathy, 1997). In our study we also used the Canadian Advanced Digital Ionsonde (CADI) installed at Resolute Bay. For the details of the CADI system please see MacDougall and Jayachandran (2007). Given the dispersive nature of the ionosphere, the heights we obtained from the ionosonde are called the virtual heights. To obtain the real heights from these virtual heights, one has to use numerical methods and we have used a commonly used method called the Polynomial Analysis (POLAN) method (Titheridge, 1985). CADI can provide peak height of F layer/shell height every 1 min. Fig. 1 shows the distribution of shell heights for the three days we have used for this study. One can see that this height varied between 240 km and 380 km during the time period used in this study. So using a fixed shell height will obviously introduce some errors in the vTEC calculations. Instead of using a fixed shell height we have incorporated the peak height obtained from ionosonde as the shell height 1311 S.C. Mushini et al. / Advances in Space Research 44 (2009) 1309–1313 0.3 2000 (a) 0.2 TECU(FIX-VARY) TOTAL 1500 1000 0.1 0.0 -0.1 500 -0.2 200 250 0 300 350 400 450 SHELL HEIGHT(Km) 200 220 240 260 280 300 320 340 360 380 400 SHELL HEIGHTS (Km) 0.3 (b) Fig. 1. Distribution of shell heights derived from ionosonde at Resolute Bay on 11th, 12th, 15th November 2006. It was observed that the shell heights varied from 250 km to 400 km. Most shell heights were observed in the range 280–320 km. Bin value of 20 km was used in the figure. TECU(FIX-VARY) in Eq. (3) for the GPS vTEC calculations for all satellites as previously mentioned. Ionosondes can also be used to estimate the TEC in the ionosphere. However, the ionosonde gives only bottomside profiles i.e. profiles only up to the peak of the F layer. So, if one wants to estimate the TEC of the ionosphere, a topside profile of the ionosphere has to be included in the calculation. In this study, the topside profiles were modeled using one of two mathematical functions (exponential and Chapman) (Chapman, 1931; Davies, 1990; Huang and Reinisch, 2001). The combined profiles (bottomside + topside) were then integrated with height to get an estimate of the total TEC of the ionosphere (Huang and Reinisch, 2001). We then compared the TEC values obtained from these profiles with the GPS derived vTEC values. 0.2 0.1 0.0 -0.1 -0.2 0 2 4 6 8 10 PEAK FREQUENCY(MHz) Fig. 2. The difference between the total electron contents derived from GPS using a fixed shell height analysis with shell height at 350 km and using varying shell heights analysis is plotted against (a) shell height and (b) peak frequency. Data were obtained at Resolute Bay on 11th, 12th, 15th November 2006. The varying shell heights were obtained from ionosonde at Resolute Bay. The difference is observed to increase with the electron content in the ionosphere (1 TECU = 1016 electrons/m2). 3. Results Fig. 2(a) and (b) shows the scatter plots where the difference between the vTEC obtained using a fixed shell height at 350 km and varying shell heights obtained from the ionosonde is plotted against the shell height and peak frequency, respectively. In Fig. 2(a), the maximum difference between the vertical electron content obtained using a fixed shell height and by using a varying shell height is around 0.3 TECU. It is also observed that a positive difference is observed when we have shell heights less than 350 km and a negative difference when the shell heights are more than 350 km. It is to be noted in Fig. 2(b) that the difference increases proportionally with the peak frequency which is directly proportional to the total electron content. This indicates that on an active ionosphere day when the ionosphere varies constantly, using a fixed shell height to calculate the TEC values from GPS is not recommended. As mentioned earlier, we modeled the topside ionosphere using two different functions, exponential function and Chapman function. Then we combined the topside with the bottomside profiles and integrated it to obtain the TEC. Fig. 3(a) and (b) shows the scatter plots between the ionosonde derived TEC (Chapman and exponential, respectively) and the GPS vTEC (using ionosonde derived shell heights) for the three days chosen. Agreement between TEC estimates from GPS and Ionosonde (Chapman) is evident in the Fig. 3(a) (0.87 correlation coefficient and 0.89 as slope of the best fit line). As from Fig. 3(b), we saw that the exponential function derived TEC have much 1312 S.C. Mushini et al. / Advances in Space Research 44 (2009) 1309–1313 (a) coefficients were slightly lower than ones obtained using varying shell model. This indicates that the approximation of using the shell height fixed at 350 km is not an accurate but sufficient approximation for the polar region. As we are slowly heading towards the solar maximum, the ionosphere will become much more active and any high precision ionospheric studies should take account of the varying shell height into their analysis. 4. Discussion and conclusions (b) Fig. 3. The correlation between the GPS derived TEC using varying shell heights and the total electron content obtained using ionosonde for (a) bottomside + Chapman topside model, (b) bottomside + exponential topside model. The shift/bias of 0.28 TECU (exponential) and 0.36 TECU (Chapman) that were observed in the plots could be attributed to receiver bias estimation, mapping functions used and also to the topside profile model used. Chapman function (slope of the best fit line for Chapman model derived TEC = 0.89) seems to be a better function to model the polar topside ionosphere compared to exponential function (slope of the best fit line for exponential derived TEC = 1.5). Data were obtained at Resolute Bay on 11th, 12th, 15th November 2006 (1 TECU = 1016 electrons/m2). smaller values than the GPS derived TEC (0.87 correlation coefficient and 1.5 as slope of the best fit line). So Chapman function (slope of the best fit line for Chapman model derived TEC = 0.89) seems to be a better function to model the polar topside ionosphere compared to exponential function (slope of the best fit line for exponential derived TEC = 1.5).We are in the process of doing a more elaborate study on the validity of different topside models for the polar region. We have also correlated (figures not shown) ionosonde TEC (Chapman and exponential) and GPS vTEC using fixed shell height and the correlation The ionosphere is a very dynamic system which changes both spatially and temporarily. Most past studies assumed that electron density of the ionosphere peaks at a constant height (350 km) and some studies took varying shell heights in to consideration but these shell heights were obtained from ionosphere models (Komjathy and Langley, 1996). Our ionosonde data analysis show shell heights which vary from 250 km to 400 km (Fig. 1). This we think is a significant change in the ionosphere which should be taken into account. It is seen in Fig. 2(a) that the difference between the electron contents derived from using varying shell heights derived from ionosonde data and a fixed shell height at 350 km, increases as the electron content in the ionosphere increases. This shows that if there is an increase in electron content due to solar activities, the fixed shell method is not accurate enough. From the scatter plots (Fig. 3(a) and (b)) between the total electron content derived from GPS and total electron content from the ionosonde for all 3 days, we observed that the electron content derived from the ionosonde using a Chapman function modeled topside profiles had a shift/ bias of 0.36 TECU with the GPS derived electron content while the electron content derived from the ionosonde using exponential function modeled topside profiles had a shift/bias of 0.28 TECU with the GPS derived electron content. At midlatitudes (McKinnell et al., 2007) such a shift or bias in the scatter plot is usually attributed to plasmasphere electron content in ionospheric studies. But since our station is in the polar region, the plasmasphere’s contribution is negligible. As less than 5% is the error that can be attributed to ionosonde derived bottomside TEC (Huang and Reinisch, 2001), we think that most of this shift or bias observed in our results is mainly due to the following reasons. The first reason we think is the receiver bias. It has to be noted that receiver biases which were used were monthly averages. Recent studies also show that for higher latitudes above 60°N, there is no proven method which would give us an accurate receiver bias (Rideout and Coster, 2006). The second reason we think that may affect the results is the mapping function. The general mapping function we used is designed best for mid and low latitudes where the highest elevation angle of the GPS satellites can be 90° (Komjathy, 1997). For higher latitudes this is not true since the satellite elevation angle is never 90°. This shows that more studies are required to design a mapping function for higher polar S.C. Mushini et al. / Advances in Space Research 44 (2009) 1309–1313 latitudes and as well as for receiver bias calculations for GPS receivers at high latitudes given the activity in the higher latitude ionosphere. Precise ionospheric studies should also include varying shell heights since the ionosphere is not constant in time. The third reason we think is due to the topside model used for ionosonde analysis. Chapman function seems to be a better function compared to exponential function to model the topside ionosphere for polar latitudes. One still has to study different topside models to find out a model which would give a better result for polar ionosphere given its variability. Acknowledgments We thank the Natural Sciences and Engineering Research Council (NSERC). Operation of CADIs is done in collaboration with the Canadian Space Agency (CSA). We also thank IGS for providing us with GPS data. References Bregstrand, S., Haas, R. Comparison of ionospheric activity derived from GPS and different VLBI networks. In: IVS General Meeting Proceedings, pp. 447–451, 2004. Chapman, S. The absorption and dissociative or ionizing effect on monochromatic radiation in an atmosphere on a rotating earth. Proc. Phys. Soc. 43 (1), 26–45, 1931. 1313 Davies, K. Ionospheric Radio IEE Electromagnetic Waves Series 31. Peter Peregrinus Ltd., 1990. Gaussiran, T., Munton, D., Harris, B. et al. An open source toolkit for GPS processing, total electron content effects, measurements and modeling. 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