TEC prediction with neural network for equatorial latitude station in Thailand
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2012
Received: 3 June 2010
Accepted: 9 May 2011
Published: 27 July 2012
This paper describes the neural network (NN) application for the prediction of the total electron content (TEC) over Chumphon, an equatorial latitude station in Thailand. The studied period is based on the available data during the low-solar-activity period from 2005 to 2009. The single hidden layer feed-forward network with a back propagation algorithm is applied in this work. The input space of the NN includes the day number, hour number and sunspot number. An analysis was made by comparing the TEC from the neural network prediction (NN TEC), the TEC from an observation (GPS TEC) and the TEC from the IRI-2007 model (IRI-2007 TEC). To obtain the optimum NN for the TEC prediction, the root-mean-square error (RMSE) is taken into account. In order to measure the effectiveness of the NN, the normalized RMSE of the NN TEC computed from the difference between the NN TEC and the GPS TEC is investigated. The RMSE, and normalized RMSE, comparisons for both the NN model and the IRI-2007 model are described. Even with the constraint of a limited amount of available data, the results show that the proposed NN can predict the GPS TEC quite well over the equatorial latitude station.
Key wordsNeural network total electron content low solar activity period IRI-2007 model GPS
The variation of electron density in the ionosphere has significant effects on a radio signal propagating through the Earth’s atmosphere. The total electron content (TEC) is one of the quantities which can describe the ionospheric ionization content. The equatorial region is an anomaly area where the most significant discrepancy of experimental and modeled data has been observed (Yasukevich, 2008). At present, there exist several ionosphere models including IRI-2001 and IRI-2007, which allow calculations of the electron density profile and the TEC. The IRI-2007 is the new release of the IRI model and has many new features. IRI-2007 now offers various options to compute the electron density in the topside ionosphere, the region above the F2 maximum, which is an improvement over the limitations in previous versions of the model (Bilitza, 2004; Coisson et al., 2009).
TEC derived from GPS data has been collected to construct empirical models. Neural network (NN) techniques have been applied to various topics in the study of the upper atmosphere. A number of works employ the NN to predict atmospheric parameters and determine the optimum parameters for modeling, such as the temporal and spatial forecasting of the fOF2 values up to twenty-four hours in advance and near-real time prediction (Tulunay et al., 2000; Oyeyemi et al., 2006), to make operational forecasts of ionospheric variations (Nakamura et al., 2007), the topside ionospheric variability and electron-density modelling (McKinnell and Poole, 2001; Maruyama, 2002), solar proxies pertaining to an empirical model (McKinnell, 2008; Maruyama, 2010), and regional TEC modeling with the NN (Leandro and Santos, 2004; Tulunay et al., 2004b; Maruyama, 2007; Habarulema et al., 2007, 2009b; Watthanasangmechai et al., 2010).
Recently, TEC data have become available in Thailand and some neighboring countries as a result of the SEALION project. This provides the opportunity to study the TEC prediction. Moreover, the availability of historic TEC data is important for the development of the IRI model (Mosert, 2007), as well as the NN model which can learn from prior data (Watthanasangmechai et al., 2010). Better representations of the region above the F peak are of critical importance for many investigations that require TEC predictions (Bilitza, 1997). Thus, we hope that this research will not only lead to a prediction of the TEC over Thailand, but also will contribute to the data pool for this area as well. In this paper, the TEC is measured by the JAVAD-GPS receiver installed at the GPS receiver station, namely; Chumphon (10.72°N, 99.37°E, dip latitude 3°), equatorial latitude station, Thailand. To predict the TEC value, a neural network (NN) was applied in this work. The results of the NN are compared with the observed value (GPS TEC) for NN efficiency testing. In addition, we employ the TEC from the IRI-2007 model, the widely-used ionosphere model for comparison as well.
2. Artificial Neural Network
2.1 Neural Network
2.2 NN inputs and output
The daily SSN, which indicates the solar activity, is collected from the site: ftp.ngdc.noaa.gov. It is considered as one of the input parameters for the first neural network (NN1). Since the amplitude of short-term solar-proxy variations are induced by solar rotation, one solar rotation is equal to 27 days, and the long-term variations follow the 11-year solar activity period (Maruyama, 2010), we choose the 27-day mean SSN as one of the input parameters for the second neural network (NN2) to represent the solar activity. Besides, the sunspot number is more effective for periods longer than 27 days (Maruyama, 2010) for training the neural network, thus we also choose an 81-day mean SSN, three solar rotation periods, as another input parameter for the third neural network (NN3). All of the input parameters are fed into the input space for the TEC prediction. The output of each NN is VTEC. The RMSE values of which are investigated to achieve the optimum NN.
3. Results and Discussions
The proposed NN (NN3) is the feed-forward network with a back propagation algorithm. It consists of five nodes or neurons in the input layer, nine nodes in the hidden layer, and one output node in the output layer, as shown in Fig. 1. The input layer is fed with the sine and cosine components of the day number and the hour number, and the 81-day mean SSN. The initial weight and biases for the training process are set to be random values. The Levenberg-Marquardt algorithm is applied as the training function. The output of the proposed NN is compared with GPS TEC and IRI-2007 TEC. We take the normalized RMSE into account for the result comparison. The normalized RMSE is the RMSE value divided by the background TEC to avoid the effect from the TEC background.
3.1 Hourly comparison
To evaluate the performance of NN, the hourly model is constructed. The data set for the learning process comprises TEC in 2005, 2006, 2008 and 2009. Following the learning process, NN output is compared with GPS TEC and IRI-2007 TEC on equinox and solstice days in 2007. In 2007, equinox days occur on March 20 and September 23, while solstice days occur on June 21 and December 22 (U.S. Naval Observatory; http://www.erh.noaa.gov/box/equinox.html), respectively. However, we compare the results on December 25 for the solstice day due to a loss of data on December 22.
Background TEC, RMSE and normalized RMSE values of GPS TEC and predicted values (NN TEC and IRI-2007 TEC) for different days (equinox and solstice days) in 2007 over Chumphon station.
Background TEC (TECU)
RMSE (TECU) between
Normalized RMSE between
All year 2007
Among various methods to predict TEC, the results prove that the hourly model yields one of the appropriate tools for TEC prediction purposes. Even though there is a considerable difficulty for NN to learn during the TEC prediction process on equinox days during this period due to the occurrence of an equatorial plasma bubble, which includes various ionospheric irregularity scales, causing a large day-tonight variation and a drastically-fluctuating component of the TEC, the hourly model is still able to predict TEC quite well. If we consider in terms of the normalized RMSE as shown in Table 1, the normalized RMSE from the hourly model is smaller than that from the IRI-2007 model for the entire year over Chumphon. We do not mean to imply that the IRI-2007 model is not appropriate to use for TEC prediction, however, we presume that the IRI-2007 database may not cover Southeast Asia data and, in particular, over Chumphon equatorial latitude station, for example. However, our NN TEC performs well during the period studied since the NN model learns from the local TEC value. This is a reason why the hourly model can well predict TEC values as mentioned above.
3.2 Seasonal comparison
Since seasonal variation plays an important role in TEC variation, we also carry out a seasonal TEC comparison to investigate the possibility of NN to predict the seasonal TEC. In this paper, there are four distinct seasons, which are the March equinox, the June solstice, the September equinox and the December solstice. Each season is represented by a monthly median value. Meaning, we take the median to each hourly data of 31-day TEC data in March, predicted from the method described in Fig. 1, in order to obtain the 24-hour seasonal TEC for the March equinox, for example. Thus the 24-hour monthly median TEC values are cited as the seasonal TEC. For the seasonal comparison, hereafter, we refer to the NN as the seasonal model.
Background TEC, RMSE and normalized RMSE values of GPS TEC and predicted values (NN TEC and IRI-2007 TEC) for different seasons which are March (representing the March equinox), June (representing the June solstice), September (representing the September equinox) and December (representing the December solstice), respectively, in 2007 over Chumphon station.
Background TEC (TECU)
3.3 0030 LT comparison
3.4 0630 LT comparison
3.5 1230 LT comparison
Average TEC, RMSE and normalized RMSE values of GPS TEC and predicted values (NN TEC and IRI-2007 TEC) for different times in 2007 which are 0030 LT, 0630 LT, 1230 LT and 1830 LT, respectively, over Chumphon station.
Average TEC (TECU)
3.6 1830 LT comparison
The normalized RMSE values of the GPS TEC and the predicted values (NN TEC and IRI-2007 TEC) for each of the four comparisons of Subsections 3.3 to 3.6, over Chumphon station, are compared and shown in Table 3. We found that our NN model can be used to predict TEC values at different times of the year 2007 over Chumphon, the equatorial latitude station. The minimum normalized RMSE value is 0.114 from the 1230 LT comparison, while the maximum over is 0.334 from the 0030 LT comparison. We can infer that the proposed NN model can give the best TEC approximation at local midday due to the smallest normalized RMSE value it gives. However, the NN TEC from the 0030 LT model needs to be leveled up to decrease the normalized RMSE value.
3.7 TEC comparison on an individual day
For Figs. 9 to 12, each of which includes (from top to bottom) the comparison between the GPS TEC, the NN TEC and the IRI-2007 TEC, the difference between the GPS TEC and the NN TEC (ΔTEC, the error of the NN model), the difference between the daily SSN and 81-day mean SSN (ΔSSN), and the daily geomagnetic-activity index, Ap, all in 2007. Positive errors, which are related to the solar proxy variation represented by ΔSSN, are noticed on the 35th day of the 0030 LT comparison in Fig. 9, and on the 195th day of the 1230 LT comparison in Fig. 11. For the 35th day in Fig. 9, the ΔSSN is about 10, while the ΔTEC is about 3 TECU (the background TEC is equal to 5.971 TECU). The background TEC is an average GPS TEC value for the whole year 2007 at any represented time. The ΔSSN is about 16, while the ΔTEC is about 5 TECU (the background TEC is equal to 23.791 TECU), on the 195th day in Fig. 11. The trend of the ΔTEC variation and the ΔSSN variation resemble each other during about 10 days before, and after, the 195th day of the 1230 LT comparison in Fig. 11, as well. The TEC error corresponding to the largest ΔSSN at around the 160th day is not prominent. Generally, daily errors caused by using an 81-day mean SSN as a solar input are not very significant.
An error, unrelated to both the solar proxy index and the geomagnetic-activity index, can be seen on the 270th day of the 0030 LT comparison in Fig. 9. We presume that such an error is attributed to other origins, such as forcing below the ionosphere including coupling with planetary wave activities (Lastovicka, 2006; Borries et al., 2007; Maruyama, 2010). The remaining errors are caused by the large day-to-day variation of the TEC in the equatorial latitude region itself.
This work investigates an NN model which has 9 neurons in the single hidden layer for TEC prediction at Chumphon station, Thailand. The parameters which impact the TEC data were taken as the NN inputs. In this study, we have considered six comparisons to show the NN TEC. To investigate the effectiveness for using the NN as a TEC prediction tool, the RMSE and normalized RMSE of the NN TEC were computed and compared with those of the IRI-2007 TEC, as described. The result is that the proposed NN model, in the case of all of the comparisons described above, can well predict the TEC compared with the IRI-2007 TEC. For some periods, even though there is a considerable difficulty for the NN to learn during the TEC prediction process due to large variations of TEC, not only on equinox days, but also on solstice days, our model is still able to predict TEC quite well. This difficulty may be attributed to the occurrence of an equatorial plasma bubble and to day-to-day TEC variations in the equatorial region. Besides the TEC variation effect, three possible mechanisms, including the geomagnetic-activity index, the solar proxy and another effect which originated below the Earth’s ionosphere, which contribute to the TEC prediction error are introduced as error sources for the equatorial latitude region. Moreover, this work adopts the method of Otsuka (Otsuka et al., 2002) for deriving the GPS TEC. In this method, the hourly average of the VTEC is assumed to be uniform within the receiver surrounding area of approximately 1000 km. Since this assumption may be invalid at an equatorial region where a steep latitudinal variation of the TEC, caused by an equatorial anomaly, exists, it may be one of the possible reasons for the difference between the NN TEC and the IRI-2007 TEC. In the case of all comparisons, the NN model underestimates the GPS TEC, which needs to be leveled up in a newer version; however, the NN TEC agrees overall with the GPS TEC. The IRI-2007 model underestimates the GPS TEC as shown in all the comparisons, except the estimation at 1830 LT which the IRI-2007 model overestimates. In this research, we show that the NN is a potentially effective method for TEC prediction in an equatorial region.
5. Future Works
Future works include expanding the input space in order to include most of the impact factors of the TEC, developing the GPS TEC database for at least one solar cycle (~11 years), and adding TEC data from other stations within Thailand. In addition, the study in Maruyama (2010) shows that other solar proxies besides the sunspot number may be more optimal, hence, we will experiment with various options in future works.
We would like to thank the National Institute of Information and Communications Technology (NICT) and King Mongkut’s Institute of Technology Ladkrabang (KMITL), for technical and funding support through the SEALION project. The IRI-2007 model available on the NASA website is extensively used and appreciated. In addition, we are grateful to Prof. LeeAnne McKinnell, Rhodes University, South Africa, for kind advice and useful suggestions about NN input parameters. We are grateful to Asst. Prof. Prasert Kenpankho and Mr. Noraset Wichaipanich, KMITL, Thailand for technical discussions. Finally, we thank anonymous reviewers who greatly improved this manuscript.
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