Estimation of foF2 from GPS TEC over the South African region

Journal of Atmospheric and Solar-Terrestrial Physics 112 (2014) 20–30

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Estimation of foF2 from GPS TEC over the South African region Nicholas Ssessanga a,b,n, Lee-Anne Mckinnell a,b, John Bosco Habarulema a a b

South African National Space Agency (SANSA) Space Science, P.O. Box 32, Hermanus 7200, South Africa Department of Physics and Electronics, Rhodes University, Grahamstown 6139, South Africa

art ic l e i nf o

a b s t r a c t

Article history: Received 1 October 2013 Received in revised form 10 February 2014 Accepted 12 February 2014 Available online 22 February 2014

This paper describes a statistical method (TEC2F2) of estimating the critical frequency (foF2) values from Global Positioning System (GPS) Vertical Total Electron Content (VTEC). The method has been developed over the South African region using the available ionosonde stations; Grahamstown (33.21S, 26.31E), Hermanus (34.41S, 19.21E), Louisvale (28.51S, 21.21E) and Madimbo (22.41S, 30.91E), and nearby GPS receiver stations. The analysis of the results showed the TEC2F2 method to be more accurate at estimating the foF2 parameter over South Africa than the most commonly used International Reference Ionosphere (IRI-2012) model. On average, the TEC2F2 improves foF2 estimation by 15% (2006-2012) over the IRI-2012 model. The application of this method over the rest of Africa is proposed in order to more accurately estimate the foF2 parameter in regions where ionosondes do not exist. This is a pioneering new method that allows for the utilisation of additional resources to close the gap in ionospheric mapping over Africa. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Total electron content (TEC) Critical frequency of the F2 layer (foF2) IRI-2012

1. Introduction Ionospheric variability is commonly studied using measurements from ground based ionosondes. Although being the most accurate available method for measuring the ionosphere, the use of ionosondes is limited to measurements of the bottomside ionosphere. Ionosondes are also fairly expensive to install and this results in some continents (e.g., Africa) being under-represented in ionospheric databases. Therefore, there is a long recognised need for alternate methods of deriving ionospheric information. One such method is the derivation of Total Electron Content (TEC) from Global Positioning System (GPS) receiver data. Other groups have previously presented efforts related to the estimation of the critical frequency (foF2) from GPS data or TEC. For example Spalla and Cairolo (1994) suggested a simple ((foF2)2 ¼3.51 TEC) model that can provide a coarse estimation of foF2 median values based on the knowledge of TEC. Houminer and Soicher (1996) predicted foF2 from GPS phase delays and in the conclusion of their work, a possibility of using real-time TEC measurements to update the foF2 value determination was suggested. This paper presents new research on a method (here after referred to as TEC2F2) to derive ionospheric foF2 information from GPS Vertical TEC (VTEC) over the South African region by the use of polynomials. The method is based on the high correlation

n Corresponding author at: South African National Space Agency (SANSA) Space Science, P.O. Box 32, Hermanus 7200, South Africa. E-mail address: [email protected] (N. Ssessanga).

http://dx.doi.org/10.1016/j.jastp.2014.02.003 1364-6826 & 2014 Elsevier Ltd. All rights reserved.

(usually greater than 0.80) that exists between VTEC and foF2 (Kouris et al., 2004). The results that are obtained from TEC2F2 are compared to the International Reference Ionosphere (IRI-2012) model and the measured values recorded by the South African ionosondes for validation purposes. The IRI model is an internationally recognized model and the recommended standard model for prediction of plasma parameters in the Earth's ionosphere (Bilitza et al., 2011). This global model is continuously improved with new data by a group of experts spanning the globe (Bilitza and Reinisch, 2008). However, the model still fails to predict accurately during both quiet and disturbed conditions over regions, such as the African sector, where there is a historic paucity of ionospheric data (e.g., McKinnell and Poole, 2004; Adewale et al., 2011; Okoh et al., 2012; Habarulema et al., 2013). The aim of developing the TEC2F2 method is to enable the estimation of the foF2 parameter over Africa in areas without ionosondes. Fig. 1 shows the sparsity of ionosondes as compared to GPS receivers over the African content. The receivers plotted in this map are from the network of African Geodetic Reference Frame (AFREF).

2. foF2 measurement using ionosondes Ionosonde sounders are the most accurate way of measuring ionospheric variations. They operate by using the advantage that the ionospheric plasma is a dispersive medium whose refractive

N. Ssessanga et al. / Journal of Atmospheric and Solar-Terrestrial Physics 112 (2014) 20–30

21

Ionosonde and AFREF GPS receiver network over Africa 40 30

Latitude (deg)

20 10

Ilorin

Addis Ababa

0

−10 −20

AFREF stations Ionosonde stations

Madimbo Louisvale

−30

Grahamstown Hermanus

−40

−40

−30

−20

−10

0

10

20

30

40

50

60

70

Longitude (deg)

Fig. 1. A map showing the paucity of active ionosondes over Africa as compared to the GPS receiver network of the African Reference Frame (AFREF).

index (μ) can be expressed in terms of the density of free electrons (Ne) and the sounding frequency (f) as shown in Eq. (1) (Reinisch, 2009). During operation the sounder transmits radio pulses vertically scanning a large frequency band from about 1 MHz to 30 MHz in order to cover the ionisation structure from the E-region to the F-region (Reinisch, 1986).

μ2 ¼ 1  kðN e =f 2 Þ

ð1Þ

When the critical frequency of the radio waves (fc) equals the plasma frequency (fp), the waves are reflected. At this point μ  0, hence Eq. (1) becomes 2

f p ¼ kðN e Þ;

k ¼ ðe2 =4πε0 mÞ  80:5;

ð2Þ

where e is the charge of an electron, εo is permittivity of free space and m is the mass of an electron (Davies, 1990). At the receiver the time delay (τ) that it takes for the radio signal to be reflected back is recorded. Using Eq. (2) and τ, the peak electron density and altitude (cτ=2, c is speed of light) of reflection of the different layers of the ionosphere can be deduced. It is from these two parameters that the electron density profile is generated. In the F layer which is the highest layer in the bottomside ionosphere and most important in this paper, the maximum electron density (NmF2) is measured at a critical frequency known as foF2 with units MHz. The two parameters are related using (Davies, 1990) N m F2 ¼ 1:24  1010 ðfoF2Þ2 ðm  3 Þ:

ð3Þ

provide VTEC. To generalize, Z Rx STEC ¼ Ne dso ; Tx

ð4Þ

where dso is the element of geometric range. In addition to the TEC delay the signal is also influenced by other effects in the system known as biases. To cancel out these effects, an atomic clock which oscillates at 10 MHz is used to generate two L-Band carrier frequencies f1 and f2: f 1 ¼ 1575:42 MHz f 2 ¼ 1227:60 MHz; where the primary signal at f1 is designed to have two modulations and the secondary at f2 is designed to have one modulation (Parkinson and Spilker, 1996; Grewal et al., 2007). On the ground, a dual frequency receiver can be used to eliminate some of the biases on the signal and also determine the phase delay through a Linear Combination (LC) of the observables f1 and f2 (Hofmann-Wellenhof et al., 1994). TEC can then be determined by   1 f 1f 2 ðP 2  P 1 Þ; ð5Þ TEC ¼ 40:3 f 1 þ f 2 where P1 and P2 are pseudo-ranges measured in f1 and f2 respectively (Grewal et al., 2007). The greatest contribution to the TEC parameter is from NmF2. Since NmF2 is directly proportional to ðfoF2Þ2 (Eq. (3)) there exists a high correlation between TEC and foF2. It is from this high correlation as stated in the introduction that the whole TEC2F2 method is based as detailed below.

3. TEC measurement using GPS The ability to measure ionospheric variations using the GPS receiver network depends on the dispersive property of the ionosphere. The ionosphere delays the code signal transmission and advances the phase signal transmission. The amount of phase change from this delay is dependent on ionospheric TEC. TEC is defined as the total number of electrons integrated along the path of the signal from the transmitter (Tx) on the GPS satellite to the receiver (Rx) on ground. TEC is measured in units of 1016 electrons per square meter, where 1016 electrons/m2 ¼1 TEC unit (TECU) (Davies and Hartmann, 1997). TEC is determined at a slant angle from the vertical (STEC) and then mapped to the vertical to

4. Data sources and processing In this study, the process of estimating foF2 from VTEC was first considered for the South African region. This region contains a network of ionosondes that can provide a validation platform for the TEC2F2 method before being expanded to other parts of Africa. Four ionosondes and the corresponding dual frequency (f1, f2) GPS receivers (with a sampling period of 1 s) located in proximity were used to provide foF2 and TEC data respectively. Table 1 gives the ionosondes and the respective GPS receivers used for this study.

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N. Ssessanga et al. / Journal of Atmospheric and Solar-Terrestrial Physics 112 (2014) 20–30

Table 1 Ionosondes and the closest GPS receivers used to provide foF2 and TEC data respectively. Over Hermanus and Grahamstown, the ionosonde and GPS stations are co-located. Ionosonde/ GPS station

Location

Code

Hermanus Grahamstown Louisvale Upington Madimbo Thohoyadou

34.41S, 19.21E 33.31S, 22.41E 28.51S, 21.21E 28.41S, 21.21E 22.41S, 30.91E 23.01S, 30.41E

HE13N (ionosonde), HNUS (GPS) GR13L (ionosonde), GRHM (GPS) LV12P (ionosonde) UPTA (GPS) MU12K (ionosonde) TDOU (GPS)

The ionosonde data are archived at the South African National Space Agency (SANSA) and can also be downloaded from the Space Physics Interactive Data Resource (SPIDR) database (http:// spidr.ngdc.noaa.gov/spidr/) with a sampling period of 15 min. GPS data is available (in RINEX form of either 1 or 30 s interval) from the TrigNet database (http://www.trignet.co.za/) which is a network of permanent continuously operating receiver base stations distributed throughout South Africa at approximately 100 km to 300 km spacing. The data collected from the ionosonde and corresponding GPS receivers covered a period of 7 years starting from 2006 to 2012. This database was selected in-order to cover both the solar minimum and the approach to solar maximum. 4.1. GPS VTEC processing The VTEC values from the GPS observables were extracted using the Rinex GPS-TEC program Version 1.45 developed at Boston College (Seemala and Valladares, 2011). The program uses both f1 and f2 to calculate the relative STEC by removing errors due to clock biases and the tropospheric water vapour effect (Sardón and Zarraoa, 1997). To obtain the absolute TEC values, the differential satellite biases (published by the University of Bern) are included along with the receiver bias values that are calculated by minimizing the TEC variability between 02h00 and 06h00 local time (Doherty et al., 2004). The equivalent vertical TEC at Ionospheric Pierce Point (IPP) altitude of 350 km is calculated assuming the thin shell model (Coco et al., 1991; Wilson and Mannucci, 1993; Ciraolo and Spalla, 1997). The vertical TEC over a particular station is computed by averaging the TEC for individual satellites in view (Habarulema et al., 2013).

5. Data analysis The diurnal ionosonde foF2 data (at temporal resolution of 15 min) was interpolated using a cubic spline interpolation method to be of the same sample size as the VTEC data (which was derived at 6 min intervals). The resulting foF2 and VTEC were both smoothed using a running mean method having a span of 3 hours. This was done to reduce the noise in the data which may be due to measurement errors and data reduction processes (Houminer and Soicher, 1996). The smoothed daily ionosonde foF2 values (from each ionosonde station) were correlated with the co-located or nearest GPS receivers daily smoothed VTEC. On average the result was a “hysteresis loop” structure with a correlation coefficient (R) of more than 0.8. Fig. 2 shows an example of a “hysteresis loop” over the Grahamstown station on an arbitrarily chosen day (6 February 2006). The R value was found to be 0.98. This “hysteresis loop” phenomenon is due to the diurnal variation of foF2 and TEC which is a result of strong photo-ionization

during the day and recombination of ions and electrons during the night (Kouris et al., 2004). Based on the value of R the data was filtered with days corresponding to R less than 0.5 exempted from the analysis. This threshold was chosen based on a statistical analysis that on average most days showed an R value above 0.7. Days that had R below 0.5 were found to have Kp greater than 4 (disturbed days) and were not used in this analysis. The filtered data was then grouped according to months and years, due to the relatively large ionospheric seasonal changes from 1 month to the next in a year. The foF2 and VTEC values were correlated on an individual hour–hour basis for each month and the R value corresponding to each hour determined. Fig. 3 shows an example of the monthly variation of R using foF2 values from the Hermanus ionosonde and VTEC values from the Hermanus GPS receiver. The months represented here were chosen with respect to different seasons of the year in the Southern Hemisphere; April (autumn), July (winter), September (spring) and December (summer), in 2011. The result showed that on average foF2 and VTEC had the greatest correlation between 0.7 and 1 during the hours 06h00–15h00 UT, and the least below 0.5 between 20h00 and 23h00 UT. These results were later used during the regression analysis. 5.1. Regression analysis Using the results from the previous procedure, the daily foF2 and VTEC data were divided into four sections; 00h00–05h59 UT, 06h00–14h59 UT, 15h00–19h59 UT and 20h00–23h59 UT, as shown in Fig. 4. For each section the scatter was plotted between the foF2 and TEC values. This was done for each day of the month through out each year in the data set. To each scatter plot, different polynomial functions (f(x)): N

f ðxÞ ¼ ∑ pixN  i ;

ð6Þ

i¼1

of different degrees, N-1, N ¼ 2, 3, 4, 5 were fitted as shown in Fig. 5, where f(x) represents the derived foF2 values in MHz, x the GPS VTEC values in TECU and pi the polynomial coefficients. For each fit the polynomial coefficients, R-squared (R2) and RMSE values were determined within a confidence interval of 95% where R2 ¼ 1 

∑nj ðfoF2j  f ðxÞj Þ2 ∑nj ðfoF2j  foF 2Þ

;

1 n foF 2 ¼ ∑ fo F2j n j sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ∑nj ðfoF2j  f ðxÞj Þ2 ; RMSE ¼ n

ð7Þ

ð8Þ

n is the total number of measured foF2 values and j¼ 1, 2, 3,…,n. The polynomial coefficients corresponding to the fit that provided the best R2 values and the least RMSE value were chosen to be used in building the model for that given month of the year. This process was done for all the four ionosonde stations (listed in Table 1) and the obtained coefficients averaged to be used in the model for that section of the day in a given month of the year over the South African region. Table 2 gives the averaged polynomial coefficients for all 12 months of the year. For each month of the year, the different model coefficients from each time section were put together to form one complete model for the whole day with the exception of the hours between 20h00 and 23h59 UT. Fig. 6 shows different scatter plots of foF2 against VTEC for the time segment 20h00–23h59 UT over the Grahamstown station on an arbitrary chosen period of Days of the

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23

Scatter plot between foF2 and VTEC for Grahamstown station ( 33.3o S, 22.4o E), date: 2006/6/2 6.5 6 5.5

foF2 (MHz)

5

Ionisation

4.5 Recombination

4 3.5 3 2.5 2 2

3

4

5

6

7

8

9

10

11

12

VTEC (TECU)

Fig. 2. Scatter plot of daily foF2 and VTEC for Grahamstown station on an arbitrarily chosen day (6 February 2006). The “Hysteresis Loop” structure is a result of the dominance of ionospheric ionisation during the day and recombination during the night.

April (autumn) 2011

July (winter) 2011 1 Correlation coefficient (R)

Correlation coefficient (R)

1 0.75 0.5 0.25 0

− 0.25 − 0.5 0

2.5

5

7.5

10

12.5

15

17.5

20

22.5

25

0.75 0.5 0.25 0

− 0.25 − 0.5 0

2.5

5

7.5

Hours (UT)

Correlation coefficient (R)

Correlation coefficient (R)

0.75 0.5 0.25 0

2.5

5

7.5

10

12.5

15

15

17.5

20

22.5

25

20

22.5

25

December (summer) 2011

September (spring) 2011

0

12.5

Hours (UT)

1

−0.25 − 0.5

10

17.5

20

22.5

25

1 0.75 0.5 0.25 0 − 0.25

− 0.5 −0.75

1

0

2.5

5

Hours (UT)

7.5

10

12.5

15

17.5

Hours (UT)

Fig. 3. An example of the monthly variation of the correlation coefficient (R) between foF2 and VTEC values at Hermanus for the different months in 2011. The months shown here are chosen based on the different seasons (autumn, winter, spring and summer). A high R value above 0.7 is seen to occur during 06h00–15h00 UT and the least R below 0.5 during 20h00–23h00 UT.

Year (DOY, 101-110), 2006. The plots show that VTEC and foF2 do not have a consistent relationship. Because of this inconsistency, this segment (20h00–23h59 UT) was not modeled, hence not represented in the TEC2F2 model.

6. Results and discussion To test the performance of the TEC2F2 model, VTEC data from all four GPS receiver stations listed in Table 1 was used to estimate the foF2 values. The results were then compared to the ionosonde data and the IRI-2012 model (represented as IRI further on in the text). This was done for the daily, seasonal and solar cycle

variations. Most of the results presented here are from the year 2010 which had the most continuous data throughout the data set. 6.1. Daily variation Fig. 7 shows the daily comparison of ionosonde, TEC2F2 model and IRI model foF2 values over Grahamstown where the ionosonde and GPS receivers are co-located. The days chosen are around the equinox in March and solstice in June 2010. It can be observed that the TEC2F2 model performs better than the IRI model when estimating the peak daily foF2 values both during the equinox (Fig. 7a) and solstice (Fig. 7b). The IRI model underestimates and overestimates the peak foF2 values during equinox and solstice periods respectively. These inaccuracies by the IRI

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VTEC from Hermanus GPS (34.4o S, 19.2o E ), 2011/08/26

VTEC (TECU)

20 Smoothed data Original data

15 10 5 0

0

5

10

15

20

25

20

25

Hour (UT) o

o

foF2 from Hermanus ionosonde (34.4 S, 19.2 E), 2011/08/26 8

foF2 (MHz)

7 6 5 4 3 2

0

5

10

15 Hour (UT)

Fig. 4. An example of the division of daily foF2 and VTEC from the Hermanus ionosonde and GPS receiver respectively. The data is divide into four sections; 00h00–05h59 UT, 06h00–14h59 UT, 15h00–19h59 UT and 20h00–23h59 UT based on the monthly variation of R with time as shown in Fig. 3.

00h00 − 05h59 UT

foF2 (MHz)

5

9.2 9 foF2 (MHz)

5.5

06h00 − 14h59 UT

foF2 vs VTEC f(x) Prediction bounds (fit)

4.5 4

3.5

R−squared: 0.992 RMSE: 0.092

3

8.8 8.6 8.4 8.2

R−sqaured: 0.968 RMSE: 0.070

8

2

f(x)= p1*x + p2*x + p3

2.5 5

6

7

f(x) = p1*x +p2

7.8 8

9

20

10

20.5

21

21.5

22

22.5

23

23.5

24

24.5

VTEC (TECU)

VTEC (TECU) 15h00 −19h59 UT 9

foF2 (MHz)

8 7 6 5

R−sqaured: 0.997 RMSE: 0.097

2

4

f(x)= p1*x + p2*x + p3

6

8

10

12

14

16

18

20

22

24

VTEC (TECU)

Fig. 5. Polynomial fit to different parts of the “Hysteresis loop”. The loop split was based on the daily variation of R as shown in Fig. 3.

model over the South African region have been pointed out before by other groups. For example, McKinnell (2003) and Okoh et al. (2010) have developed models; the South African bottomside Ionospheric Model (SABIM) model and South African Ionospheric Map (SAIM) respectively, to better predict the foF2 parameter based on the availability of the ionosonde data. A correlation between the daily measured foF2 values from the four ionosonde stations and the two models, TEC2F2 and IRI, was performed over the 7 year period and the R2 and RMSE values determined. Table 3 provides the summary of the results. TEC2F2 gave an average R2 value of 0.69 and RMSE of 0.73 MHz as compared to the IRI which gave an average value of R2 ¼0.54 and RMSE ¼0.86 MHz. This result shows that on average, the

TEC2F2 improves foF2 estimation by 15% over the IRI model. The same improvement was obtained from the work done by Okoh et al. (2010). However, it should be pointed out that the aim of developing the TEC2F2 model was not to improve the SABIM or SAIM but to complement the two models using the GPS data, with the intention of extending this method to the rest of Africa where there are no ionosonde measurements.

6.2. Annual and seasonal variation Fig. 8 shows ionosonde, TEC2F2 model and IRI model foF2 over the four ionosonde stations at local Sunrise (02h00 UT), noon

N. Ssessanga et al. / Journal of Atmospheric and Solar-Terrestrial Physics 112 (2014) 20–30

25

Table 2 Averaged polynomial coefficients for every month of the year used in TEC2F2. Month

00h00–05h59 UT

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

06h00–14h59 UT

15h00–19h59 UT

p1

p2

p3

p4

p1

p2

p1

p2

 9.016e  006  1.492e  003 1.881e  005 3.915e  004 2.832e  003  2.017e  002 5.025e  001 5.343e  003  8.958e  003 4.339e 004  8.569e  004 2.471e  004

 1.894e  003 3.336e 002  1.169e  002  1.737e  002  8.869e  002 0.318 1.373  0.173 0.227  2.291e  02 2.381e  02  1.081e  02

0.332 2.476e  02 0.508 0.524 1.291  1.016

1.206 2.890 0.912 1.442  1.31 3.149

1.953  1.530 0.656 2.416e  02 0.358

 2.250 6.580 0.170 2.540 1.869

0.238 0.238 0.303 0.265 0.195 0.194 0.166 0.224 0.277 0.263 0.227 0.347

2.497 2.497 1.441 2.643 3.772 3.572 4.209 3.096 2.140 2.321 1.626  0.432

0.299 0.216 0.281 0.297 0.442 0.489 0.492 0.367 0.335 0.230 0.205 0.201

1.699 2.878 2.001 2.180 0.731 0.897 1.358 1.603 1.682 2.505 2.757 3.410

Grahamstown (33.3o S, 22.4o E) scatter plot between foF2 and VTEC; Time (20h00 23h59 UT) 2006/4/11, DOY 101 2006/4/12, DOY 102 2006/4/13, DOY 103 2006/4/15, DOY 105 3.5 5 3 3.8 3

1.5

foF2 (MHz)

foF2 (MHz)

3.4 3.2

3

4 VTEC (TECU)

3

5

3

2006/4/17, DOY 107

2.8 2.75

5

2.4

2

4 VTEC (TECU)

2 2.8

6

2006/4/19, DOY 109 3.5

3.2

3

3.4

3.1

2.5

1.5

3.3 3.2

3

4 VTEC (TECU)

5

3.1

3 3.2 VTEC (TECU)

2006/4/20, DOY 110

3.5

2

2.7

4 VTEC (TECU)

0

5

foF2 (MHz)

foF2 (MHz)

2.85 foF2 (MHz)

4 VTEC (TECU)

2.6

2.2

2006/4/18, DOY 108

2.9

3

2 1

1 0.5

3

foF2 (MHz)

foF2 (MHz)

2

2.8 foF2 (MHz)

4

3.6 2.5

3 2.9

3

4 VTEC (TECU)

5

2.8

4

5 VTEC (TECU)

6

Fig. 6. 20h00–23h00 UT scatter plots between Grahamstown ionosonde foF2 values and VTEC from the co-located GPS receiver on an arbitrarily chosen continuous 8 days of the year 2006. The results show no consistent pattern between foF2 and VTEC during this time of the night which makes this segment difficult to model.

(10h00 UT) and after Sunset (18h00 UT) in 2010. South African Standard Time, SAST¼UT þ 2. It is observed that the IRI model underestimates the foF2 values at all stations as compared to the TEC2F2 model especially before Sunrise (Fig. 8a) and after Sunset (Fig. 8c). At local mid-day (Fig. 8b), the annual variations cause seasonal changes to be well defined. A comparison between TEC2F2 model and the IRI shows that TEC2F2 better estimates the foF2 parameter during all seasons (autumn, winter, spring and summer). This is well pronounced especially at the Grahamstown and Hermanus stations. To confirm this result a further analysis of the 10h00 UT results was done. In Fig. 9 the difference between the IRI, TEC2F2 and the measured foF2 values was determined and the RMSE calculated at all four ionosonde locations. Noticeable from the residues at all

four stations is that the TEC2F2 model estimates the 10h00 UT foF2 values better than the IRI model annually. On average, TEC2F2 had a RMSE value of 0.51 MHz as compared to the IRI RMSE of 0.70 MHz. Between the different ionosonde stations, TEC2F2 performed better at Grahamstown and Hermanus with RMSE values below 0.4 MHz as compared to Madimbo and Louisvale with RMSE values above 0.6 MHz. Fig. 10 shows scatter plots between the measured foF2 values and the two models; IRI and TEC2F2, using data from all four stations, with a line of best fit (y) inserted. The results in Fig. 10 show that TEC2F2 provides a better correlation with the measured values as compared to the IRI model. High R2 values above 0.8 from the TEC2F2 model are observed at both Grahamstown and Hermanus as compared to Louisvale (R2 ¼ 0.59) and Madimbo (R2 ¼0.48).

N. Ssessanga et al. / Journal of Atmospheric and Solar-Terrestrial Physics 112 (2014) 20–30

This inaccuracy is seen to be more pronounced at Madimbo than the other stations and was attributed to the distance between the ionosonde and the closest GPS receiver (Thohoyandou) used. The distance between the two is approximately 130 Km. From this result, note should be taken that the accuracy of using the TEC2F2 model to estimate foF2 values from GPS VTEC at particular location decreases with increasing distance between the point of interest and the closest GPS station chosen. Nevertheless the results still show that TEC2F2 is more accurate than the IRI model.

Table 3 Root mean square error (RMSE) and R-squared (R2) values for TEC2F2 model and IRI-2012 model for years 2006–2012. Year

2006 2007 2008 2009 2010 2011 2012 Average

6.3. Solar cycle variation Due to the limited GPS data-set as compared to ionosonde data-set, the validation of the TEC2F2 model over the solar cycle

8

6

2 0

2 0

25

IRI R2: 0.496 TEC2F2 R2: 0.976 5 10 15 20

0

8 foF2 (MHz)

8

6

4

25

2 25

0

0

IRI R2: 0.326 TEC2F2 R2: 0.886 5 10 15 20

2010/3/26 DOY 85

8

6

TEC2F2

6 4 2

2 25

25

10

0

IRI R2: 0.435 TEC2F2 R2: 0.925 5 10 15 20

Hour (UT) IRI

IRI R2: 0.595 TEC2F2 R2: 0.918 5 10 15 20 Hour (UT)

4

Hour (UT)

6

2010/3/25 DOY 84

8

0

2010/3/22, DOY 81 10

Hour (UT)

2010/3/24, DOY 83

2

0.646 0.472 0.466 0.527 0.604 0.453 0.594 0.537

IRI R2: 0.477 TEC2F2 R2: 0.870 5 10 15 20

2 25

10

2

0.789 0.596 0.647 0.637 0.770 0.713 0.713 0.695

4

10

foF2 (MHz)

foF2 (MHz)

2010/3/23, DOY 82

IRI R2: 0.657 TEC2F2 R2: 0.920 5 10 15 20

0.701 0.651 0.801 0.725 0.846 1.324 0.983 0.861

6

10

4

0.548 0.683 0.691 0.699 0.631 1.000 0.909 0.732

8

Hour (UT)

Hour (UT)

6

IRI

4

4 IRI R2: 0.658 TEC2F2 R2: 0.974 5 10 15 20

TEC2F2

8

6

4

IRI

foF2 (MHz)

8

foF2 (MHz)

10

foF2 (MHz)

foF2 (MHz)

10

TEC2F2

Grahamstown (33.3o S, 22.4o E) daily variation of foF2 2010/3/20, DOY 79 2010/3/21, DOY 80 10

2010/3/19, DOY 78

R2

RMSE (MHz)

foF2 (MHz)

26

0

25

0

IRI R2: 0.491 TEC2F2 R2: 0.912 5 10 15 20

Hour (UT) Smoothed measured foF2

25

Hour (UT)

Measured foF2

Grahamstown (33.3o S, 22.4o E) daily variation of foF2 2010/6/22, DOY 173

2010/6/25, DOY 176

6

6

6

6

4

4 2

IRI R2: 0.519 TEC2F2 R2: 0.880 0

5

10

15

20

25

4 2

IRI R2: 0.828 TEC2F2 R2: 0.864

0

0

foF2 (MHz)

8

foF2 (MHz)

8

2

5

10

15

20

0

25

5

15

20

IRI R2: 0.907 TEC2F2 R2: 0.936

0

25

0

2010/6/29, DOY 180

6

6

6

0 0

0

25

4

2

2 IRI R2: 0.961 TEC2F2 R2: 0.960 5 10 15 20

foF2 (MHz)

6

foF2 (MHz)

8

foF2 (MHz)

8

4

0

IRI R2: 0.871 TEC2F2 R2: 0.847 5 10 15 20

0 0

5

Hour (UT)

Hour (UT) IRI

TEC2F2

10

15

20

25

Hour (UT) Smoothed measured foF2

20

25

4

2

IRI R2: 0.709 TEC2F2 R2: 0.887

0 25

15

2010/7/1, DOY 182

2010/6/30, DOY 181

8

2

10

Hour (UT)

8

4

5

Hour (UT)

Hour (UT)

2010/6/26, DOY 177

10

4

2

IRI R2: 0.855 TEC2F2 R2: 0.932

0 0

Hour (UT)

foF2 (MHz)

2010/6/23, DOY 174

8

foF2 (MHz)

foF2 (MHz)

2010/6/21, DOY 172 8

IRI R2: 0.649 TEC2F2 R2: 0.916 0

5

10

15

20

25

Hour (UT)

Measured foF2

Fig. 7. A comparison of daily variation of foF2 values from TEC2F2, IRI and the measured data from the Grahamstown ionosonde station during equinox in March (a) and solstice in June (b), year 2010. The TEC2F2 model shows a better estimation of the peak foF2 values than the IRI model both during equinox and solstice.

N. Ssessanga et al. / Journal of Atmospheric and Solar-Terrestrial Physics 112 (2014) 20–30

Before Sunrise 02h00 UT (04h00, SAST), year 2010 o o o o Louisvale (28.5 S, 21.2 E) Grahamstown (33.3 S, 22.4 E) 10

10

8 foF2 (MHz)

foF2 (MHz)

8 6 4

6 4 2

2 0

0

50

100

150

200

250

300

350

0

400

0

50

100

150

Day number o

o

8 foF2 (MHz)

foF2 (MHz)

8 6 4

50

100

150

200

250

300

350

350

400

350

400

350

400

350

400

350

400

o

6 4

0

400

Measured foF2

TEC2F2

50

100

IRI model

150

200

250

300

Day number

Local noon, 10h00 UT (12h00, SAST), year 2010 o o o o Grahamstown (33.3 S, 22.4 E) Louisvale (28.5 S, 21.2 E) 14 12 foF2 (MHz)

12 foF2 (MHz)

400

0 0

14

10 8 6

10 8 6 4 2

4 0

50

100

150

200

250

300

350

0

400

0

50

100

o

150

200

250

300

Day number

Day number o

o

Madimbo (22.4 S, 30.9 E)

o

Hermanus (34.4 S, 19.2 E)

14

14

12

12

10

foF2 (MHz)

foF2 (MHz)

350

2

Day number

8 6 4

10 8 6 4

2

2

0 0

50

100

150

200

250

300

Day number

350

0

400

Measured foF2

TEC2F2

50

100

IRI model

150

200

250

300

Day number

After Sunset 18h00 UT (20h00, SAST), year 2010 o o o o Grahamstown (33.3 S, 22.4 E) Louisvale (28.5 S, 21.2 E) 10

10 8

8 foF2 (MHz)

foF2 (MHz)

300

Hermanus (34.4 S, 19.2 E) 10

2

6 4 2

6 4 2

0 0

50

100

150

200

250

300

350

0

400

0

50

100

Day number o

150

200

250

300

Day number o

o

Madimbo (22.4 S, 30.9 E)

o

Hermanus (34.4 S, 19.2 E)

10

10

foF2 (MHz)

8 foF2 (MHz)

250 o

Madimbo ( 22.4 S, 30.9 E)

6 4 2 0

200

Day number

10

0

27

8 6 4 2

0

50

100

150

200

250

300

350

400

Day number Measured foF2

0 TEC2F2

50

100

150

200

250

300

Day number IRI model

Fig. 8. Variation of foF2 values from TEC2F2, IRI and measured data from the four ionosonde stations; Grahamstown, Louisvale, Madimbo and Hermanus. The plots are chosen for the time: (a) before Sunrise (02h00 UT), (b) local noon (10h00 UT) and (c) after Sunset (18h00 UT), for the year 2010.

28

N. Ssessanga et al. / Journal of Atmospheric and Solar-Terrestrial Physics 112 (2014) 20–30

Difference between measured foF2 values and the models (IRI and TEC2F2), 10h00 UT year 2010 Grahamstown (33.3o S, 22.4o E)

Louisvale (28.5o S, 21.2o E) 5

2

Δ foF2 (MHz)

Δ foF2 (MHz)

4

0 −2

IRI RSME: 0.708 MHz TEC2F2 RSME: 0.387 MHz

−4

0

50

100

150 200 250 Day number o

0

−5

300

350

400

0

IRI RSME: 0.653 MHz TEC2F2 RSME: 0.653 MHz 100 150 200 250 300

50

o

o

Madimbo (22.4 S, 30.9 E)

400

350

400

o

Hermanus (34.4 S, 19.2 E)

5

5

Δ foF2 (MHz)

Δ foF2 (MHz)

350

Day number

0

IRI RSME: 0.761 MHz TEC2F2 RSME: 0.626 MHz

−5

0

50

100

150 200 250 Day number

0

IRI RSME: 0.672 MHz TEC2F2 RSME: 0.374 MHz

−5

300

350

400

0 IRI

50

100

150 200 250 Day number

300

TEC2F2

Fig. 9. Residues between 10h00 UT measured foF2 from ionosonde stations; Grahamstown, Louisvale, Madimbo and Hermanus, and models (IRI and TEC2F2).

Scatter plots between the models (IRI and TEC2F2) and measured foF2 from four ionosonde stations, time 10h00 UT year 2010 10 o o Grahamstown (33.3 S, 22.4 E) 8

10 8 6

6 y = 0.3705*x + 4.1409; R2 = 0.481

y = 0.8018*x + 1.296; R2 = 0.813 4

4 2

4

6

8

10

12

14

2

4

6

2

4

6

2

4

6

2

4

6

8

10

12

14

10 o

o

Louisvale (28.5 S, 21.2 E)

10 TEC2F2 foF2 (MHz)

IRI foF2 (MHz)

8 6 y = 0.2486*x + 4.9267; R2 = 0.326

4 2 10

4

6

8

10

12

14

Madimbo (22.4o S, 30.9o E)

5 y = 0.4741*x + 3.1072; R2 = 0.593 0 8

10

12

14

10

8

8

6

6 y = 0.2769*x + 4.6205; R2 = 0.293

4 2

4

10

6

o

8

10

12

y = 0.3705*x + 4.1409; R2 = 0.481

4 14

8

10

12

14

10

o

Hermanus (34.4 S, 19.2 E) 8

5

6

y = 0.8058*x + 1.2949; R2 = 0.777

4 2

3

4

y = 0.3558*x + 4.0875; R2 = 0.448 5 6 7 8 9

0 10

8

10

12

14

Measured foF2 (MHz)

Measured foF2 (MHz) Model vs measured foF2

Line of best fit (y)

Fig. 10. Scatter plots between 10h00 UT measured foF2 values from the four ionosonde stations and the two models: IRI (left) and TEC2F2 (right), for the year 2010.

variation was constrained to a few years when both data-sets existed. Two stations Grahamstown and Louisvale, with the longest ionosonde serving database and nearest GPS receivers located at Grahamstown and Upington respectively were chosen for this validation. The years 2006 and 2012 were selected to represent solar minimum and approach to solar maximum respectively.

Fig. 11 shows the variation of 10h00 UT foF2 values from IRI, TEC2F2 and the two ionosonde stations. The upper and lower panels represent solar minimum (2006) and approach to solar maximum (2012) periods. Residues between the two models and the measured foF2 are shown in Fig. 12. The TEC2F2 model shows a better estimation of the foF2 values during solar minimum than

N. Ssessanga et al. / Journal of Atmospheric and Solar-Terrestrial Physics 112 (2014) 20–30

Louisvale (28.5o S, 21.2o E) 10h00 UT, year 2006

16

16

14

14

12

12 foF2 (MHz)

foF2 (MHz)

Grahamstown (33.3o S, 22.4o E) 10h00 UT, year 2006

10 8 6

10 8 6

4

4

2

2 0

0

0

50

100

150 200 Day number

250

300

350

50

100

150 200 Day number

250

300

Louisvale (28.5o S, 21.2o E) 10h00 UT, year 2012

Grahamstown (33.3o S, 22.4o E) 10h00 UT, year 2012 16 15

16 15

13

13

foF2 (MHz)

foF2 (MHz)

29

11 9

11 9

7

7

5

5 0

20

40

60

80

100

120

140

0

10

20

Day number

30

40

50

60

Day number Measured foF2

TEC2F2

IRI

Fig. 11. Variation of 10h00 UT foF2 values corresponding to solar minimum (2006) and approach to solar maximum (2012) at two ionosonde location; Louisvale and Grahamstown. The TEC2F2 shows a better estimation of foF2 values during solar minimum than during solar maximum.

Louisvale (28.5o S, 21.2o E) 10h00 UT, year 2006

4

4

2

2

Δ foF2 (MHz)

Δ foF2 (MHz)

Grahamstown (33.3o S, 22.4o E) 10h00 UT, year 2006

0 −2

−4 −6

0

50

100

150

0

−2 −4

IRI RSME = 0.529 MHz TEC2F2 RSME = 0.367 MHz 200 250 300 350

−6

50

100

150

Day number o

Day number o

o

4

2

2

Δ foF2 (MHz)

Δ foF2 (MHz)

4

0

−2

0

−2 −4

−4

80

100

120

o

Louisvale (28.5 S, 21.2 E) 10h00 UT, year 2012

Grahamstown (33.3 S, 22.4 E) 10h00 UT, year 2012

IRI RSME = 1.515 MHz TEC2F2 RSME = 1.314 MHz −6 0 20 40 60

IRI RSME = 0.448 MHz TEC2F2 RSME = 0.512 MHz 200 250 300

140

−6

0

10

20

IRI RSME = 0.795 MHz TEC2F2 RSME = 0.935 MHz 30 40 50

60

Day number

Day number IRI

TEC2F2

Fig. 12. Residues between the 10h00 UT model results (IRI and TEC2F2) and the measured foF2 during solar minimum (2006) and approach to solar maximum (2012). The measured values are from Grahamstown and Louisvale ionosonde stations. The TEC2F2 shows a low RMSE during solar minimum than during the approach to solar maximum.

during solar maximum. During solar maximum, the TEC2F2 model overestimates the foF2 values on average by a magnitude of 1 MHz. A comparison between the two models shows that the TEC2F2 model performs better than the IRI model during solar minimum as compared to the approach to solar maximum. However, it should be noted that these conclusions have been reached using a limited amount of data corresponding to solar maximum. A comprehensive validation of the TEC2F2 is proposed

as the GPS database over South Africa expands to include more data from the solar maximum period.

7. Conclusion In this work we have shown that the foF2 parameter can be estimated from GPS VTEC provided the Kp is less than 4.

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N. Ssessanga et al. / Journal of Atmospheric and Solar-Terrestrial Physics 112 (2014) 20–30

The results have also shown that the TEC2F2 model is more accurate at estimating foF2 values than the IRI model over the South African region (mid-latitude). On average, the TEC2F2 improved foF2 estimation by 15% over the IRI model. Therefore, it is the aim of the authors to provide the IRI community with an option to improve the future versions of real time IRI estimation of foF2 by including the TEC2F2 model. However, the model had some probable areas for improvement:

 The accuracy of using TEC2F2 at a particular location depends



on the spatial distance between the GPS receiver chosen to provide the VTEC data and the point of interest. This was observed when the foF2 values from Madimbo ionosonde station were compared to foF2 values from TEC2F2 using VTEC from Thohoyandou GPS receiver that is 130 km away. The model estimates foF2 values more accurately during solar minimum than during solar maximum. This was due to the limited GPS data set (2006–2012) which did not include enough data from the solar maximum period. A better adaptation of the model to solar maximum variations has to be made as GPS database over South Africa expands to include more data.

The spatial distribution of GPS receivers over the African region as compared to ionosondes (Fig. 1) indicates that this method would be suitable to be applied over the rest of Africa where the distribution of ionosondes is significantly lacking. Since the model coefficients are dependent on latitude and longitude, a set of new coefficients would be required to adapt the model from midlatitudes to low-latitudes. References Adewale, A., Oyeyemi, E., Adeniyi, J., Adeloye, A., Oladipo, O., 2011. Comparison of total electron content predicted using the IRI-2007 model with GPS observations over Lagos, Nigeria. Indian J. Radio Space Phys. 40, 21–25. Bilitza, D., McKinnell, L.-A., Reinisch, B., Fuller-Rowell, T., 2011. The international reference ionosphere today and in the future. J. Geod. 85, 909–920. Bilitza, D., Reinisch, B., 2008. International reference ionosphere 2007: improvements and new parameters. Adv. Space Res. 42, 599–609.

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