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Near-real time foF2 predictions using neural networks
ARTICLE IN PRESS
Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1807–1818 www.elsevier.com/locate/jastp
Near-real time foF2 predictions using neural networks Elijah O. Oyeyemia,b,, L.A. McKinnella,b, A.W.V. Poolea a
Department of Physics and Electronics, Rhodes University, Grahamstown 6140, South Africa b Hermanus Magnetic Observatory, Hermanus 7200, South Africa Received 1 March 2006; received in revised form 5 June 2006; accepted 10 July 2006 Available online 6 September 2006
Abstract This paper describes the use of the neural network (NN) technique for the development of a near-real time global foF2 (NRTNN) empirical model. The data used are hourly daily values of foF2 from 26 worldwide ionospheric stations (based on availability) during the period 1976–1986 for training the NN and between 1977 and 1989 for verifying the prediction accuracy. The training data set includes all periods of quiet and disturbed geomagnetic conditions. Two categories of input parameters were used as inputs to the NN. The first category consists of geophysical parameters that are temporally or spatially related to the training stations. The second category, which is related to the foF2 itself, consists of three recent past observations of foF2 (i.e. real-time foF2 (F0), 2 h (F2) and 1 h (F1) prior to F0) from four control stations (i.e. Boulder (40.01N, 254.71E), Grahamstown (33.31S, 26.51E), Dourbes (50.11N, 4.61E) and Port Stanley (51.71S, 302.21E). The performance of the NRTNN was verified under both geomagnetically quiet and disturbed conditions with observed data from a few verification stations. A comparison of the root mean square error (RMSE) differences between measured values and the NRTNN predictions with our earlier standard foF2 NN empirical model is also illustrated. The results reveal that NRTNN will predict foF2 in near-real time with about 1 MHz RMSE difference anywhere on the globe, provided real time data is available at the four control stations. From the results it is also evident that in addition to the geophysical information from any geographical location, recent past observations of foF2 from these control stations could be used as inputs to a NN for near-real time foF2 predictions. Results also reveal that there is a temporal correlation between measured foF2 values at different locations. r 2006 Elsevier Ltd. All rights reserved. Keywords: Ionosphere; Neural networks; Ionospheric prediction
1. Introduction The success of high frequency (HF) communications depends largely on the ability to be able to predict the F2 region peak electron density, foF2. Corresponding author. Department of Physics and Electronics, Rhodes University, Grahamstown 6140, South Africa. Tel.: +27 8481 358884. E-mail addresses: [email protected], [email protected] (E.O. Oyeyemi).
1364-6826/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2006.07.002
This ionospheric parameter, foF2, is one of the most important parameters as far as communication coverage at a specific transmission frequency is concerned (Goodman, 1992). To achieve this task a number of empirical ionospheric models have been developed. Among these models are those of Ching and Chiu (1973), Chiu (1975), Bent et al. (1978), Rush et al. (1983, 1984), Fox and McNamara (1988), Fuller-Rowell et al. (2000) and Bilitza (2001). A comprehensive survey of these models
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has been provided by Bilitza (2002). Many researchers (Bradley, 1993; Williscroft and Poole, 1996; Kouris et al., 1998; Smith and King, 1981; Richards, 2001) have investigated the existence of strong relationships between foF2 and solar and magnetic variations. Kane (1992) and Trı´ skova´ and Chum (1996) have carried out studies on the uniqueness of the connection between foF2 and solar activity during the growth and decay phase of the solar cycle. It was further suggested by Kane (1992), that geomagnetic Ap index could be valuable in improving short-term ionospheric forecasts. An extensive survey of the indices of ionospheric response to solar activity has been provided by Bradley (1993). Studies of day-today variability of the peak F2-layer electron density, NmF2, in relation to solar cycle variation, magnetic activity, latitudinal dependence, and seasonal variations have been extensively discussed by Forbes et al. (2000) and Rishbeth and Mendillo (2001). In recent time, the neural network (NN) technique has been widely employed as an alternative to classical methods for ionospheric prediction problems (Altinay et al., 1997; Wintoft and Cander, 1999; Kumluca et al., 1999; McKinnell and Poole, 2001; Oyeyemi et al., 2005a, b). The use of NNs is generally motivated by their principal ability to deal with non-linear behaviour thereby establishing and modelling the non-linear dynamical processes (both in space and time) associated with the F2 region of
the ionosphere, due to its non-linear dynamic processes arising from solar photon flux, geomagnetic activity and global thermospheric circulation. In a previous paper (Oyeyemi et al., 2005b), we described the application of NNs for the development of a global empirical model for short-term forecasting of the ionospheric F2 region critical frequency (foF2) at any target geographical location up to 5 h in advance. This short-term foF2 forecasting model requires recent past observations of foF2 itself, and therefore, has the limitation that it is not applicable to a geographic location where measured data are not readily available. In view of this, and considering the fact that ionospheric data is not available for vast areas of the globe, especially the ocean areas and where ionosonde stations are not available, we have used recent past observations of foF2 from four selected stations across the globe in this present work to develop a near-real time foF2 global empirical model using the NN technique. These selected stations, called control stations, are Boulder (401N, 254.71E), Grahamstown (33.31S, 26.51E), Dourbes (50.11N, 4.61E) and Port Stanley (51.71S, 302.21E), and their geographic locations are represented as filled squares in Fig. 1. The choice of these control stations is based on the fact that they are reliably known to have data in real time (based on records from the Digital Ionogram Database, DIDBase, University of Massachusetts, Lowell).
80 60
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Fig. 1. Map of global distribution of training, verification and control stations of the near-real time foF2 NN. Where filled circles, open squares and filled squares represent training, verification and control stations, respectively.
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2. Data The foF2 values from the worldwide network of ionospheric stations spanning the period 1976–1986 were used for training a NN to develop a near-real time foF2 empirical model. The data was obtained through the Space Physics Interactive Data Resource, SPIDR, a resource of the World Data Centre in Boulder. Although the raw data was not edited or scaled by the authors, the foF2 values were quality controlled in a general trend procedure and all outliers or suspect data removed from the database before training. Table 1 shows the ionospheric stations and their geographical coordinates used for training our NN (NRTNN). Fig. 1 depicts the geographical distribution of the training and verification stations, represented as closed circles and open squares, respectively. The choice of this solar cycle period is based on the fact that one of the four control stations (Grahamstown), where recent past observations of foF2 were obtained, started operation in 1973, and that the availability of foF2 values from these control stations would determine the number of years for which data will be used to Table 1 Ionosonde stations used for training the NN S/N
Station name
Lat. (1N)
Long. (1E)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Lycksele Uppsala Tomsk Moscow Kaliningrad Goose Bay Slough Pointiers Wakkanai Rome Akita Wallops Is Kokubunji Point Arguello Yamagawa Okinawa Vanimo Huancayo Tahiti Brisbane Norfolk Is Mundaring Hobart Campbell Is Argentine Is Scott Base
64.6 59.8 56.5 55.5 54.7 53.3 51.5 46.6 45.4 41.8 39.7 37.9 35.7 34.6 31.2 26.3 2.7 12.0 17.7 27.5 29.0 32.0 42.9 52.5 65.2 77.9
18.7 17.6 84.9 37.3 20.6 299.2 359.4 0.3 141.7 12.5 140.1 284.5 139.5 239.4 130.6 127.8 141.3 284.7 210.7 152.9 169.0 116.3 147.2 169.2 295.7 166.8
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train the NN. Records from the archive (SPIDR) have shown that most stations appear to have sufficient data points within the period 1976–1986 than any other continuous period covering one solar cycle. As a result, we considered this period where we could easily obtain sufficient data points both from these four selected stations and other stations whose geographic coordinates as well as foF2 values are required for training the NN. Data from 11 stations (Table 2) (open squares in Fig. 1) have been used to verify the predictive ability of the near-real time foF2 model both temporally and spatially. 2.1. NN inputs and output The inputs to the near-real time foF2 (NRTNN) model are of two categories. The first category consists of the geophysical parameters that are temporally or spatially related to the training stations (Table 1). This input set consists of: hour number (HR in Universal Time), geographic latitude (y), magnetic inclination (I), magnetic declination (D), solar zenith angle (C), day of the year (DN), A16 index (a 2-day running mean of the 3-h planetary magnetic Ap index), and R2 index (a 2month running mean of sunspot number) and the angle of meridian relative to the subsolar point (M). These parameters are the same as those used for the foF2 global model in Oyeyemi et al. (2005a), since foF2 is still the target output. See Fig. 2 for these input parameters. The second set of inputs, which is related to foF2 itself, consists of recent past observations of foF2 from each of the four control stations (Boulder (40.01N, 254.71E), Grahamstown (33.31S, 26.51E), Dourbes (50.11N, 4.61E) and Port Stanley (51.71S, 302.21E). Poole and McKinnell
Table 2 Selected verification stations S/N
Station name
Lat. (1N)
Long. (1E)
1 2 3 4 5 6 7 8 9 10 11
Yakutsk Magadan Leningrad Churchill Irkutsk Maui Dakar La Reunion Canberra Macquarie Is Halley Bay
62.0 60.0 59.9 58.8 52.5 20.8 14.8 21.1 35.3 54.5 75.5
129.6 151.0 30.7 265.8 104.0 203.5 341.6 55.9 149.0 159.0 333.4
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N
P
DN (Day number) (DNS, DNC) HR (Universal Time) (HRS, HRC) C (Zenith Angle) (CS, CC) θ (Geographic Latitude) D (Mag Declination) (DS, DC) I (Mag Inclination) (IS) A16 (Magnetic Index) R2 (Solar index) M (Angle of Meridian) (MS, MC)
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E.O. Oyeyemi et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1807–1818
S
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F-2g F-1g F0g
F-2p F-1p F0p
F-2b F-1b F0b
F-2d F -1d F0d
Fig. 2. A block diagram of the near-real time foF2 NN architecture.
(2000), Wintoft and Cander (1999), Kumluca et al. (1999) and Oyeyemi et al. (2005b) have demonstrated that foF2 is best predicted by using past observations of foF2 itself. These foF2 related inputs are the three most recent hourly past observations of foF2: F2, F1 and F0, from each of the four control stations, labelled in Fig. 2 as F2p, F1p, F0p, F2g, F1g, F0g, F2b, F1b, F0b, F2d, F1d and F0d. Where F2 and F1 are the hourly values of foF2 recorded 2 and 1 h before the real-time foF2 (i.e. F0) value, respectively, from each of the four control stations. The letters p, g, b and d represent observations from the Port Stanley, Grahamstown, Boulder and Dourbes stations, respectively. For example, F2p represents the foF2 value recorded at Port Stanley 2 h before the hour of interest (HR), and Fop represents the foF2 value recorded at Port Stanley at the HR. The choice of the three recent past observations of foF2 is based on the fact that these values will have the same magnetic effect as the 3-hourly planetary magnetic index, Ap. As a result, one may therefore assume that during large magnetic storms, the foF2 values from certain fixed stations will correlate with foF2 at any other location on the globe. In addition to the first set of inputs, this makes a total of 26 input parameters to the NN. See the block diagram of the NN architecture in
Fig. 2 for a detailed illustration. A comprehensive discussion on the relative importance of these input parameters for the purpose of developing a global foF2 NN empirical model has been provided by Oyeyemi et al. (2005a, b). It should be made clear at this point that apart from the observed values of foF2 from the four chosen stations that were used as inputs to the NN, the NN knows nothing about their geographical information. The NN target output is the observed foF2 value from every other available station used for training the NN corresponding to the most recent foF2 (i.e. F0p, F0g, F0b and F0d) from the four control stations. 2.2. Training the NN The standard fully connected feed-forward NN with backpropagation was employed in this work. A NN is a computer program that is trained to compute the relationship between a given set of inputs and the corresponding output(s). The NN is made up of an input layer, which consists of a set of inputs that feed input patterns to the network. The input layer is followed by at least one hidden (middle) layer, which is later followed by an output layer that produces the output results. The block diagram of the NN architecture in Fig. 2 illustrates
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the inputs and outputs of the NN for our purpose. In Fig. 2 DNS, DNC, HRS, HRC, CS, CC, DS, DC, IS, MS and MC represent sine and cosine components of the day number, hour, solar zenith angle, magnetic inclination, magnetic declination and angle of meridian relative to subsolar point respectively. Details can be found in Oyeyemi et al. (2005a, b). The NN has 26 input nodes with one output node. Several NNs with different architectures were trained to determine the optimal NN that produced the minimum error difference between the observed and predicted values of foF2. The best NN configuration in this case was found to be the one with three hidden layers containing 30, 20 and 15 neurons, respectively. For further information on the NN architecture, the reader is referred to Haykin (1994). Three independent data sets were used for the training (training set), testing (testing set) and verification (verification set) of the NN (Haykin, 1994). Both the training and the testing data sets were randomly selected in the ratio 70% and 30%, respectively, from all data covering the 26 ionospheric stations used in Table 1. The first set of the input parameters in Fig. 2 contains the geophysical information related to each of these 26 stations. The second input set, which is related to foF2 itself, was extracted from the four selected control stations (i.e. Port Stanley, Grahamstown, Boulder and Dourbes). During training the NN is presented with values of the 26 inputs, which produces one output value foF2. As the training is continued, the output is compared with its target value corresponding to these inputs. During this process, a backpropagation algorithm is employed to adjust the weights in such a way as to minimize the error difference between the target and the predicted value of foF2. The testing data set was used during training to determine the optimal NN so that the NN was not over-trained. The training of the NN is terminated when the test error values versus the number of training epochs pass through a predetermined amount (Kumluca et al., 1999; Poole and McKinnell, 2000). At this point the NN is said to have achieved generalization, such that it produces a good performance when presented with a new set of input patterns that were not included in the training of the NN (i.e. the testing set). Finally, the verification data set (from the ionospheric stations in Table 2) was used to verify how well the optimal NN could work for a new set of data to predict foF2 both temporally and spatially.
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3. Results and discussion After training, measured data from 11 ionospheric stations (Table 2) (not included in the training of the NN) were used to verify the ability of the near-real time foF2 to predict spatial and temporal variations of foF2 within and outside the training period. We have used different years for each of these stations due to the difficulty in obtaining data from the same year for all 11 stations. Also an effort was made to make use of stations from all latitude regions (i.e. low, mid and high latitudes). Since the model requires three recent past observations of foF2 as inputs during the same period from each of the control stations (Port Stanley, Grahamstown, Boulder and Dourbes stations), we had to find years outside the training period during which data is available from these four stations simultaneously. This period coincided with the years 1987–1989, and so our verification stations were chosen for having data available during this period. Tables 3 and 4 show the error differences between the observed and predicted values of foF2 from the selected verification stations, which were determined by taking the average of the root mean square errors of all foF2 data points present during the period indicated for each station. The errors were evaluated by the application of the root mean square error (RMSE) equation: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X 2 RMSE ¼ t foF2obs foF2pred , N i¼1 where N is the number of data points and foF2obs and foF2pred are the observed and predicted foF2 values, respectively. It can be observed from these tables that the average error difference between the Table 3 RMS prediction errors (MHz) of near-real time foF2 model (foF2 NRTNN model) for seven selected verification stations S/N Station name Latitude (1N)
Longitude RMSE (1E) (MHz)
Period
1 2 3 4 5 6 7
129.6 265.8 104.0 203.5 55.9 159.0 333.4
1978–1979 1978–1979 1978–1979 1977–1978 1982–1983 1984–1985 1978–1979
Yakutsk 62.0 Churchill 58.8 Irkutsk 52.5 Maui 20.8 La Reunion 21.1 Macquarie Is 54.5 Halley Bay 75.5
1.171 1.298 0.931 1.263 0.979 0.667 1.120
Periods of the verification are within training period (1976–1986).
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NRTNN predictions and observed values is about 1.0 MHz RMSE. This suggest that the model will predict foF2 in near-real time with about 1 MHz RMS error anywhere on the globe, provided real time data is available at the four control stations. Fig. 3 shows samples of daily variations of observed and predicted foF2 values for six stations. Also, shown in Fig. 4 are samples of seasonal variations of observed and predicted foF2 values for a few selected stations for years that fall within the training period. Similar samples of comparisons between observed and predicted foF2
Table 4 RMS prediction errors (MHz) of near-real time foF2 model (foF2 NRTNN model) for four selected verification stations S/N Station name Latitude (1N)
Longitude RMSE (1E) (MHz)
Period
1 2 3 4
151.0 30.7 341.6 149.0
1987–1989 1987–1989 1987 1987–1989
Magadan Leningrad Dakar Canberra
60.0 59.9 14.8 35.3
1.028 0.856 1.214 0.940
Period of verification (1987–1989) is beyond the training period (1976–1986).
Maui 1977
Halley Bay 1979
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Fig. 3. Samples of comparisons of daily variations of observed and NRTNN near-real time foF2 model predicted-values (within training period) for two consecutive days starting at 00h00UT on the first of the days indicated for each station.
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Fig. 4. Samples of comparisons of the seasonal variation between measured (observed) and NRTNN near-real time foF2 model predicted values at 00:00UT (right panel) and 12:00UT (left panel) for selected verification stations (during training period) for the year indicated.
ARTICLE IN PRESS E.O. Oyeyemi et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1807–1818
Magadan1989 12
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DAY 101 Dakar 1987
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DAY 80 Leningrad 1989
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values illustrating diurnal and seasonal variations temporally beyond the training period are as shown in Figs. 5 and 6, respectively. As can be seen from Figs. 3–6 the predicted and observed values for these stations have the same type of variation in time. These graphs serve to illustrate that the model successfully predicts the general diurnal and seasonal shape of foF2 behaviour. In order to verify the predictive ability of the NRTNN under both geomagnetically quiet and disturbed conditions, we considered two great storm events that occurred in 17–19 September 1979 and 17–19 November 1989 during and outside the training period, respectively. These periods were considered for this test due to there being sufficient continuous data available from all required stations. Fig. 7a shows the comparison of the NRTNN model predictions with observed values of foF2 during the magnetic storm of 17–19 September 1979. The top panel of Fig. 7a shows the variation of the storm in terms of the magnetic Dst index. A similar comparison during the magnetic storm of 17–19 November 1989 is shown in Fig. 7b for two stations. It can be observed from Figs. 7a and b that the NRTNN model predictions compared well with the observed values in response to the magnetic storm. Of particular interest is the response of model predictions to the sudden drop in foF2 value during magnetic storm of November 1989 (Fig. 7b). These figures illustrate that the NRTNN model can be used to capture storm events on a global scale within the limit of RMSE of about 1 MHz as shown in Tables 3 and 4. A comparison of the NRTNN model predictions was also made with that of our earlier standard foF2 NN global model (Oyeyemi et al., 2005a). A bar graph illustrating the RMSE differences between measured values with the NRTNN and foF2 NN global model predictions for a few selected stations is shown in Fig. 8. The difference in the inputs to the two NNs is that NRTNN has additional recent past observations of foF2 from four control stations. Since in all cases the RMSE obtained by the NRTNN model is smaller than that of the standard foF2 global model, it is evidence that there is a temporal correlation between measured foF2 values at different locations. The results from the error Tables 3 and 4, and graphs of diurnal and seasonal behaviour shown in these Figures indicate that NNs could be employed for near-real time foF2 forecasting within reasonable error limits. We have only compared our results with the observed values because we are
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DAY 266 Predicted
Fig. 5. Samples of comparisons of daily variations of observed and NRTNN near-real time foF2 model predicted-values (outside training period) for two consecutive days starting at 00h00UT on the first of the days indicated for each station.
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Fig. 6. Samples of comparisons of the seasonal variation between measured (observed) and NRTNN near-real time foF2 model predicted values at 00:00UT (left panel) and 12:00UT (right panel) for selected verification stations (outside training period) for the year indicated.
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E.O. Oyeyemi et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1807–1818 September 17-19, 1979 storm (Day260-262) 50
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Fig. 7. (a) Samples of comparisons of daily variations of observed and NRTNN near-real time foF2 model predicted-values during magnetic storm of 17–19 September 1979. The top panel shows the variation of the magnetic Dst index during this storm. (b) Samples of comparisons of daily variations of observed and NRTNN near-real time foF2 model predicted-values during magnetic storm of 17–19 November 1989. The variation of the magnetic Dst index during this storm is shown in the top panel.
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Ya
ku
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(1 97 C hu 8rc 79 hi ) ll (1 97 Irk 879 ut sk ) (1 97 8M 79 au ) i (1 La 97 R 7eu 78 ni ) o n M (1 ac 9 qu 82 ar -8 ie 3) Is H ( al 1 98 le y 4Ba 85 y ) (1 M 97 ag 8ad 79 an ) ( Le 19 ni 87 ng -8 ra 9) d (1 98 789 D ) ak C ar an (1 be 98 rra 7) (1 98 789 )
0.000
Fig. 8. Bar graph illustration of the RMSE differences between measured and near-real time foF2 global model (foF2 NRTNN model) and our standard foF2 global model (Oyeyemi et al., 2005a) predictions for all daily hourly values of foF2 for a few selected stations during the period indicated.
unable, at this time, to obtain data from any other near-real time global model.
4. Conclusion In this paper, the application of the NN technique to the development of a global near-real time foF2 empirical model has been illustrated. From the results it is evident that in addition to the geophysical information from any geographic location, recent past observations of foF2 from four control stations (Port Stanley, Grahamstown, Boulder and Dourbes) could be used as inputs to a NN for the purpose of near-real time foF2 predictions. Comparison of the NRTNN predictions with observed values of foF2 during a magnetic storm also provides evidence that there is temporal and spatial correlation between measured foF2 values at different locations. However, it is important to mention here that while the accuracy of this model is impressive considering the amount of data for this work, there could be an improvement if data from more stations were included in the training process. In addition, for the model to be effectively utilized, recent past observations of foF2 from the four control stations must be available in real time. It is the intention of the authors to pursue this research further.
Acknowledgement E.O. Oyeyemi acknowledges the financial support obtained from both the Hartebeesthoek Radio Observatory (HartRAO), a national facility of the National Research Foundation (NRF), and GrinTek Ewation (GEW). References Altinay, O., Tulunay, E., Tulunay, Y., 1997. Forecasting of ionospheric critical frequency using neural networks. Geophysical Research Letters 24, 1467–1470. Bent, R.B., Lepofsky J.R., Llewellyn S.K., Schmid P.G., 1978. Ionospheric range-rate effect in satellite-to-satellite tracking. In: Soicher, H. (Ed.), Operational Modelling of the Aerospace Propagation Environment, Vol. 1. AGARD Conference Proceedings, Vol. 230, pp. 9-1–9-15. Bilitza, D., 2001. International Reference Ionosphere 2000. Radio Science 36, 261–275. Bilitza, D., 2002. Ionospheric models for radio propagation studies. The Review of Radio Science 1999–2002. IEEE Press, Piscataway, NJ, pp. 625–679. Bradley, P.A., 1993. Indices of ionospheric response to solarcycle epoch. Advances in Space Research 13, 25–28. Ching, B.K., Chiu, Y.T., 1973. A phenomenological model of global ionospheric electron density in the E-, F1- and F2regions. Journal of Atmospheric and Terrestrial Physics 35, 1615–1630. Chiu, Y.T., 1975. An improved phenomenological model of ionospheric density. Journal of Atmospheric and Terrestrial Physics 37, 1563–1570.
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Forbes, J.M., Scott, E.P., Xiaoli, Z., 2000. Variability of the ionosphere. Journal of Atmospheric and Solar-Terrestrial Physics 62, 685–693. Fox, M.W., McNamara, L.F., 1988. Improved world-wide maps of monthly median of foF2. Journal of Atmospheric and Terrestrial Physics 50, 1077–1086. Fuller-Rowell, T.J., Araujo-Pradere, E., Codrescu, M.V., 2000. An empirical ionospheric storm-time correction model. Advances in Space Research 25, 139–146. Goodman, J.M., 1992. HF Communications Science and Technology. Van Nostrand Reinhold, New York. Haykin, S., 1994. Neural Networks: A Comprehensive Foundation. Macmillan, Indianapolis, IN. Kane, R.P., 1992. Solar cycle variation of foF2. Journal of Atmospheric and Terrestrial Physics 54, 1201–1205. Kouris, S.S., Bradley, P.A., Dominici, P., 1998. Solar-cycle variation of the daily foF2 and M(3000)F2. Annales de Geophysicae 16, 1039–1042. Kumluca, A., Tulunay, E., Topalli, I., 1999. Temporal and spatial forecasting of ionospheric critical frequency using neural networks. Radio Science 34, 1497–1506. McKinnell, L.A., Poole, A.W.V., 2001. Ionospheric variability and electron density profile studies with neural networks. Advances in Space Research 27, 83–90. Oyeyemi, E.O., Poole, A.W.V., McKinnell, L.A., 2005a. On the global model for fof2 using neural networks. Radio Science 40, RS6011. Oyeyemi, E.O., Poole, A.W.V., McKinnell, L.A., 2005b. On the global short-term forecasting of the ionospheric critical
frequency foF2 up to five hours in advance using neural networks. Radio Science 40, RS6012. Poole, A.W.V., McKinnell, L.A., 2000. On the predictability of foF2 using neural networks. Radio Science 35, 225–234. Richards, P.G., 2001. Seasonal and solar cycle variations of the ionospheric peak electron density: comparison of measurement and models. Journal of Geophysical Research 106 (A12), 12803–12819. Rishbeth, H., Mendillo, M., 2001. Patterns of F2-layer variability. Journal of Atmospheric and Solar-Terrestrial Physics 63, 1661–1680. Rush, C.M., Pokempner, M., Anderson, D.N., Stewart, F.G., Perry, J., 1983. Improving ionospheric maps using theoretically derived values of foF2. Radio Science 28, 95–107. Rush, C.M., Pokempner, M., Anderson, D.N., Stewart, F.G., Perry, J., 1984. Maps of foF2 derived from observations and theoretical data. Radio Science 19, 1083–1097. Smith, P.A., King, J.W., 1981. Long-term relationships between sunspots, solar faculae and the ionosphere. Journal of Atmospheric and Terrestrial Physics 43, 1057–1063. Trı´ skova´, L., Chum, J., 1996. Hysteresis in dependence of foF2 solar indices. Advances in Space Research 18, 145–148. Williscroft, L.A., Poole, A.W.V., 1996. Neural networks, foF2, sunspot number and magnetic activity. Geophysical Research Letters 23, 3659–3662. Wintoft, P., Cander, LjR., 1999. Short-term prediction of foF2 using time delay neural networks. Physics and Chemistry of the Earth (C) 24, 343–347.
Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1807–1818 www.elsevier.com/locate/jastp
Near-real time foF2 predictions using neural networks Elijah O. Oyeyemia,b,, L.A. McKinnella,b, A.W.V. Poolea a
Department of Physics and Electronics, Rhodes University, Grahamstown 6140, South Africa b Hermanus Magnetic Observatory, Hermanus 7200, South Africa Received 1 March 2006; received in revised form 5 June 2006; accepted 10 July 2006 Available online 6 September 2006
Abstract This paper describes the use of the neural network (NN) technique for the development of a near-real time global foF2 (NRTNN) empirical model. The data used are hourly daily values of foF2 from 26 worldwide ionospheric stations (based on availability) during the period 1976–1986 for training the NN and between 1977 and 1989 for verifying the prediction accuracy. The training data set includes all periods of quiet and disturbed geomagnetic conditions. Two categories of input parameters were used as inputs to the NN. The first category consists of geophysical parameters that are temporally or spatially related to the training stations. The second category, which is related to the foF2 itself, consists of three recent past observations of foF2 (i.e. real-time foF2 (F0), 2 h (F2) and 1 h (F1) prior to F0) from four control stations (i.e. Boulder (40.01N, 254.71E), Grahamstown (33.31S, 26.51E), Dourbes (50.11N, 4.61E) and Port Stanley (51.71S, 302.21E). The performance of the NRTNN was verified under both geomagnetically quiet and disturbed conditions with observed data from a few verification stations. A comparison of the root mean square error (RMSE) differences between measured values and the NRTNN predictions with our earlier standard foF2 NN empirical model is also illustrated. The results reveal that NRTNN will predict foF2 in near-real time with about 1 MHz RMSE difference anywhere on the globe, provided real time data is available at the four control stations. From the results it is also evident that in addition to the geophysical information from any geographical location, recent past observations of foF2 from these control stations could be used as inputs to a NN for near-real time foF2 predictions. Results also reveal that there is a temporal correlation between measured foF2 values at different locations. r 2006 Elsevier Ltd. All rights reserved. Keywords: Ionosphere; Neural networks; Ionospheric prediction
1. Introduction The success of high frequency (HF) communications depends largely on the ability to be able to predict the F2 region peak electron density, foF2. Corresponding author. Department of Physics and Electronics, Rhodes University, Grahamstown 6140, South Africa. Tel.: +27 8481 358884. E-mail addresses: [email protected], [email protected] (E.O. Oyeyemi).
1364-6826/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2006.07.002
This ionospheric parameter, foF2, is one of the most important parameters as far as communication coverage at a specific transmission frequency is concerned (Goodman, 1992). To achieve this task a number of empirical ionospheric models have been developed. Among these models are those of Ching and Chiu (1973), Chiu (1975), Bent et al. (1978), Rush et al. (1983, 1984), Fox and McNamara (1988), Fuller-Rowell et al. (2000) and Bilitza (2001). A comprehensive survey of these models
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has been provided by Bilitza (2002). Many researchers (Bradley, 1993; Williscroft and Poole, 1996; Kouris et al., 1998; Smith and King, 1981; Richards, 2001) have investigated the existence of strong relationships between foF2 and solar and magnetic variations. Kane (1992) and Trı´ skova´ and Chum (1996) have carried out studies on the uniqueness of the connection between foF2 and solar activity during the growth and decay phase of the solar cycle. It was further suggested by Kane (1992), that geomagnetic Ap index could be valuable in improving short-term ionospheric forecasts. An extensive survey of the indices of ionospheric response to solar activity has been provided by Bradley (1993). Studies of day-today variability of the peak F2-layer electron density, NmF2, in relation to solar cycle variation, magnetic activity, latitudinal dependence, and seasonal variations have been extensively discussed by Forbes et al. (2000) and Rishbeth and Mendillo (2001). In recent time, the neural network (NN) technique has been widely employed as an alternative to classical methods for ionospheric prediction problems (Altinay et al., 1997; Wintoft and Cander, 1999; Kumluca et al., 1999; McKinnell and Poole, 2001; Oyeyemi et al., 2005a, b). The use of NNs is generally motivated by their principal ability to deal with non-linear behaviour thereby establishing and modelling the non-linear dynamical processes (both in space and time) associated with the F2 region of
the ionosphere, due to its non-linear dynamic processes arising from solar photon flux, geomagnetic activity and global thermospheric circulation. In a previous paper (Oyeyemi et al., 2005b), we described the application of NNs for the development of a global empirical model for short-term forecasting of the ionospheric F2 region critical frequency (foF2) at any target geographical location up to 5 h in advance. This short-term foF2 forecasting model requires recent past observations of foF2 itself, and therefore, has the limitation that it is not applicable to a geographic location where measured data are not readily available. In view of this, and considering the fact that ionospheric data is not available for vast areas of the globe, especially the ocean areas and where ionosonde stations are not available, we have used recent past observations of foF2 from four selected stations across the globe in this present work to develop a near-real time foF2 global empirical model using the NN technique. These selected stations, called control stations, are Boulder (401N, 254.71E), Grahamstown (33.31S, 26.51E), Dourbes (50.11N, 4.61E) and Port Stanley (51.71S, 302.21E), and their geographic locations are represented as filled squares in Fig. 1. The choice of these control stations is based on the fact that they are reliably known to have data in real time (based on records from the Digital Ionogram Database, DIDBase, University of Massachusetts, Lowell).
80 60
Latitude [deg]
40 20 0 -20 -40 -60 -80 -150
-100
-50
0 Longitude [deg]
50
100
150
Fig. 1. Map of global distribution of training, verification and control stations of the near-real time foF2 NN. Where filled circles, open squares and filled squares represent training, verification and control stations, respectively.
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2. Data The foF2 values from the worldwide network of ionospheric stations spanning the period 1976–1986 were used for training a NN to develop a near-real time foF2 empirical model. The data was obtained through the Space Physics Interactive Data Resource, SPIDR, a resource of the World Data Centre in Boulder. Although the raw data was not edited or scaled by the authors, the foF2 values were quality controlled in a general trend procedure and all outliers or suspect data removed from the database before training. Table 1 shows the ionospheric stations and their geographical coordinates used for training our NN (NRTNN). Fig. 1 depicts the geographical distribution of the training and verification stations, represented as closed circles and open squares, respectively. The choice of this solar cycle period is based on the fact that one of the four control stations (Grahamstown), where recent past observations of foF2 were obtained, started operation in 1973, and that the availability of foF2 values from these control stations would determine the number of years for which data will be used to Table 1 Ionosonde stations used for training the NN S/N
Station name
Lat. (1N)
Long. (1E)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Lycksele Uppsala Tomsk Moscow Kaliningrad Goose Bay Slough Pointiers Wakkanai Rome Akita Wallops Is Kokubunji Point Arguello Yamagawa Okinawa Vanimo Huancayo Tahiti Brisbane Norfolk Is Mundaring Hobart Campbell Is Argentine Is Scott Base
64.6 59.8 56.5 55.5 54.7 53.3 51.5 46.6 45.4 41.8 39.7 37.9 35.7 34.6 31.2 26.3 2.7 12.0 17.7 27.5 29.0 32.0 42.9 52.5 65.2 77.9
18.7 17.6 84.9 37.3 20.6 299.2 359.4 0.3 141.7 12.5 140.1 284.5 139.5 239.4 130.6 127.8 141.3 284.7 210.7 152.9 169.0 116.3 147.2 169.2 295.7 166.8
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train the NN. Records from the archive (SPIDR) have shown that most stations appear to have sufficient data points within the period 1976–1986 than any other continuous period covering one solar cycle. As a result, we considered this period where we could easily obtain sufficient data points both from these four selected stations and other stations whose geographic coordinates as well as foF2 values are required for training the NN. Data from 11 stations (Table 2) (open squares in Fig. 1) have been used to verify the predictive ability of the near-real time foF2 model both temporally and spatially. 2.1. NN inputs and output The inputs to the near-real time foF2 (NRTNN) model are of two categories. The first category consists of the geophysical parameters that are temporally or spatially related to the training stations (Table 1). This input set consists of: hour number (HR in Universal Time), geographic latitude (y), magnetic inclination (I), magnetic declination (D), solar zenith angle (C), day of the year (DN), A16 index (a 2-day running mean of the 3-h planetary magnetic Ap index), and R2 index (a 2month running mean of sunspot number) and the angle of meridian relative to the subsolar point (M). These parameters are the same as those used for the foF2 global model in Oyeyemi et al. (2005a), since foF2 is still the target output. See Fig. 2 for these input parameters. The second set of inputs, which is related to foF2 itself, consists of recent past observations of foF2 from each of the four control stations (Boulder (40.01N, 254.71E), Grahamstown (33.31S, 26.51E), Dourbes (50.11N, 4.61E) and Port Stanley (51.71S, 302.21E). Poole and McKinnell
Table 2 Selected verification stations S/N
Station name
Lat. (1N)
Long. (1E)
1 2 3 4 5 6 7 8 9 10 11
Yakutsk Magadan Leningrad Churchill Irkutsk Maui Dakar La Reunion Canberra Macquarie Is Halley Bay
62.0 60.0 59.9 58.8 52.5 20.8 14.8 21.1 35.3 54.5 75.5
129.6 151.0 30.7 265.8 104.0 203.5 341.6 55.9 149.0 159.0 333.4
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T U
OUTPUT foF2
I
N
P
DN (Day number) (DNS, DNC) HR (Universal Time) (HRS, HRC) C (Zenith Angle) (CS, CC) θ (Geographic Latitude) D (Mag Declination) (DS, DC) I (Mag Inclination) (IS) A16 (Magnetic Index) R2 (Solar index) M (Angle of Meridian) (MS, MC)
NEAR-REAL TIME foF2 NN
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S
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F-2g F-1g F0g
F-2p F-1p F0p
F-2b F-1b F0b
F-2d F -1d F0d
Fig. 2. A block diagram of the near-real time foF2 NN architecture.
(2000), Wintoft and Cander (1999), Kumluca et al. (1999) and Oyeyemi et al. (2005b) have demonstrated that foF2 is best predicted by using past observations of foF2 itself. These foF2 related inputs are the three most recent hourly past observations of foF2: F2, F1 and F0, from each of the four control stations, labelled in Fig. 2 as F2p, F1p, F0p, F2g, F1g, F0g, F2b, F1b, F0b, F2d, F1d and F0d. Where F2 and F1 are the hourly values of foF2 recorded 2 and 1 h before the real-time foF2 (i.e. F0) value, respectively, from each of the four control stations. The letters p, g, b and d represent observations from the Port Stanley, Grahamstown, Boulder and Dourbes stations, respectively. For example, F2p represents the foF2 value recorded at Port Stanley 2 h before the hour of interest (HR), and Fop represents the foF2 value recorded at Port Stanley at the HR. The choice of the three recent past observations of foF2 is based on the fact that these values will have the same magnetic effect as the 3-hourly planetary magnetic index, Ap. As a result, one may therefore assume that during large magnetic storms, the foF2 values from certain fixed stations will correlate with foF2 at any other location on the globe. In addition to the first set of inputs, this makes a total of 26 input parameters to the NN. See the block diagram of the NN architecture in
Fig. 2 for a detailed illustration. A comprehensive discussion on the relative importance of these input parameters for the purpose of developing a global foF2 NN empirical model has been provided by Oyeyemi et al. (2005a, b). It should be made clear at this point that apart from the observed values of foF2 from the four chosen stations that were used as inputs to the NN, the NN knows nothing about their geographical information. The NN target output is the observed foF2 value from every other available station used for training the NN corresponding to the most recent foF2 (i.e. F0p, F0g, F0b and F0d) from the four control stations. 2.2. Training the NN The standard fully connected feed-forward NN with backpropagation was employed in this work. A NN is a computer program that is trained to compute the relationship between a given set of inputs and the corresponding output(s). The NN is made up of an input layer, which consists of a set of inputs that feed input patterns to the network. The input layer is followed by at least one hidden (middle) layer, which is later followed by an output layer that produces the output results. The block diagram of the NN architecture in Fig. 2 illustrates
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the inputs and outputs of the NN for our purpose. In Fig. 2 DNS, DNC, HRS, HRC, CS, CC, DS, DC, IS, MS and MC represent sine and cosine components of the day number, hour, solar zenith angle, magnetic inclination, magnetic declination and angle of meridian relative to subsolar point respectively. Details can be found in Oyeyemi et al. (2005a, b). The NN has 26 input nodes with one output node. Several NNs with different architectures were trained to determine the optimal NN that produced the minimum error difference between the observed and predicted values of foF2. The best NN configuration in this case was found to be the one with three hidden layers containing 30, 20 and 15 neurons, respectively. For further information on the NN architecture, the reader is referred to Haykin (1994). Three independent data sets were used for the training (training set), testing (testing set) and verification (verification set) of the NN (Haykin, 1994). Both the training and the testing data sets were randomly selected in the ratio 70% and 30%, respectively, from all data covering the 26 ionospheric stations used in Table 1. The first set of the input parameters in Fig. 2 contains the geophysical information related to each of these 26 stations. The second input set, which is related to foF2 itself, was extracted from the four selected control stations (i.e. Port Stanley, Grahamstown, Boulder and Dourbes). During training the NN is presented with values of the 26 inputs, which produces one output value foF2. As the training is continued, the output is compared with its target value corresponding to these inputs. During this process, a backpropagation algorithm is employed to adjust the weights in such a way as to minimize the error difference between the target and the predicted value of foF2. The testing data set was used during training to determine the optimal NN so that the NN was not over-trained. The training of the NN is terminated when the test error values versus the number of training epochs pass through a predetermined amount (Kumluca et al., 1999; Poole and McKinnell, 2000). At this point the NN is said to have achieved generalization, such that it produces a good performance when presented with a new set of input patterns that were not included in the training of the NN (i.e. the testing set). Finally, the verification data set (from the ionospheric stations in Table 2) was used to verify how well the optimal NN could work for a new set of data to predict foF2 both temporally and spatially.
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3. Results and discussion After training, measured data from 11 ionospheric stations (Table 2) (not included in the training of the NN) were used to verify the ability of the near-real time foF2 to predict spatial and temporal variations of foF2 within and outside the training period. We have used different years for each of these stations due to the difficulty in obtaining data from the same year for all 11 stations. Also an effort was made to make use of stations from all latitude regions (i.e. low, mid and high latitudes). Since the model requires three recent past observations of foF2 as inputs during the same period from each of the control stations (Port Stanley, Grahamstown, Boulder and Dourbes stations), we had to find years outside the training period during which data is available from these four stations simultaneously. This period coincided with the years 1987–1989, and so our verification stations were chosen for having data available during this period. Tables 3 and 4 show the error differences between the observed and predicted values of foF2 from the selected verification stations, which were determined by taking the average of the root mean square errors of all foF2 data points present during the period indicated for each station. The errors were evaluated by the application of the root mean square error (RMSE) equation: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X 2 RMSE ¼ t foF2obs foF2pred , N i¼1 where N is the number of data points and foF2obs and foF2pred are the observed and predicted foF2 values, respectively. It can be observed from these tables that the average error difference between the Table 3 RMS prediction errors (MHz) of near-real time foF2 model (foF2 NRTNN model) for seven selected verification stations S/N Station name Latitude (1N)
Longitude RMSE (1E) (MHz)
Period
1 2 3 4 5 6 7
129.6 265.8 104.0 203.5 55.9 159.0 333.4
1978–1979 1978–1979 1978–1979 1977–1978 1982–1983 1984–1985 1978–1979
Yakutsk 62.0 Churchill 58.8 Irkutsk 52.5 Maui 20.8 La Reunion 21.1 Macquarie Is 54.5 Halley Bay 75.5
1.171 1.298 0.931 1.263 0.979 0.667 1.120
Periods of the verification are within training period (1976–1986).
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NRTNN predictions and observed values is about 1.0 MHz RMSE. This suggest that the model will predict foF2 in near-real time with about 1 MHz RMS error anywhere on the globe, provided real time data is available at the four control stations. Fig. 3 shows samples of daily variations of observed and predicted foF2 values for six stations. Also, shown in Fig. 4 are samples of seasonal variations of observed and predicted foF2 values for a few selected stations for years that fall within the training period. Similar samples of comparisons between observed and predicted foF2
Table 4 RMS prediction errors (MHz) of near-real time foF2 model (foF2 NRTNN model) for four selected verification stations S/N Station name Latitude (1N)
Longitude RMSE (1E) (MHz)
Period
1 2 3 4
151.0 30.7 341.6 149.0
1987–1989 1987–1989 1987 1987–1989
Magadan Leningrad Dakar Canberra
60.0 59.9 14.8 35.3
1.028 0.856 1.214 0.940
Period of verification (1987–1989) is beyond the training period (1976–1986).
Maui 1977
Halley Bay 1979
14
12
10
foF2 (MHz)
foF2 (MHz)
12 8 6 4
10 8 6
2 0 DAY86
4
DAY87
DAY346
La Reunion 1982
Irkutsk 1979
16
16
14
14 12
10
foF2 (MHz)
foF2 (MHz)
12 8 6 4
10 8 6 4
2
2
0 DAY75
0
DAY76
DAY81
Macquarie 1984
DAY82 Yakutsk 1979
7
14
6
12
5
foF2 (MHz)
foF2 (MHz)
DAY347
4 3
10 8 6 4 2
2 DAY14 Observed
DAY15 Predicted
0 DAY82 Observed
DAY83 Predicted
Fig. 3. Samples of comparisons of daily variations of observed and NRTNN near-real time foF2 model predicted-values (within training period) for two consecutive days starting at 00h00UT on the first of the days indicated for each station.
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foF2 (MHz)
foF2 (MHz)
Halley Bay 1979 12:00UT 14 12 10 8 6 4 2 0 0
Halley Bay 1979 00:00UT
12 10 8 6 4 2 0
50 100 150 200 250 300 350 400 DAY NUMBER
0
6 4 2 0
foF2 (MHz)
foF2 (MHz)
8
50 100 150 200 250 300 350 400 DAY NUMBER Irkutsk 1979 12:00UT
14 12 10 8 6 4 2 0 0
0
4 2
50 100 150 200 250 300 350 400 DAY NUMBER Macquarie Is 1994 00:00UT
10 foF2 (MHz)
6
50 100 150 200 250 300 350 400 DAY NUMBER Irkutsk 1979 00:00UT
14 12 10 8 6 4 2 0
50 100 150 200 250 300 350 400 DAY NUMBER Macquarie Is 198412:00UT
8 foF2 (MHz)
La Reunion 1982 00:00UT
0 0
8 6 4 2 0
0 0
0
50 100 150 200 250 300 350 400 DAY NUMBER
foF2 (MHz)
8 6 4 2 0 0
50 100 150 200 250 300 350 400 DAY NUMBER Observed
Predicted
50 100 150 200 250 300 350 400 DAY NUMBER Churchill 1979 00:00UT
Churchill 1979 12:00UT 10 foF2 (MHz)
50 100 150 200 250 300 350 400 DAY NUMBER
10 foF2 (MHz)
foF2 (MHz)
La Reunion 1982 12:00UT 16 14 12 10 8 6 4 2 0
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14 12 10 8 6 4 2 0 0
50 100 150 200 250 300 350 400 DAY NUMBER Observed
Predicted
Fig. 4. Samples of comparisons of the seasonal variation between measured (observed) and NRTNN near-real time foF2 model predicted values at 00:00UT (right panel) and 12:00UT (left panel) for selected verification stations (during training period) for the year indicated.
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Magadan1989 12
foF2 (MHz)
10 8 6 4 2 DAY 100
DAY 101 Dakar 1987
14
foF2 (MHz)
12 10 8 6 4 2 0 DAY 79
DAY 80 Leningrad 1989
14 12 foF2 (MHz)
values illustrating diurnal and seasonal variations temporally beyond the training period are as shown in Figs. 5 and 6, respectively. As can be seen from Figs. 3–6 the predicted and observed values for these stations have the same type of variation in time. These graphs serve to illustrate that the model successfully predicts the general diurnal and seasonal shape of foF2 behaviour. In order to verify the predictive ability of the NRTNN under both geomagnetically quiet and disturbed conditions, we considered two great storm events that occurred in 17–19 September 1979 and 17–19 November 1989 during and outside the training period, respectively. These periods were considered for this test due to there being sufficient continuous data available from all required stations. Fig. 7a shows the comparison of the NRTNN model predictions with observed values of foF2 during the magnetic storm of 17–19 September 1979. The top panel of Fig. 7a shows the variation of the storm in terms of the magnetic Dst index. A similar comparison during the magnetic storm of 17–19 November 1989 is shown in Fig. 7b for two stations. It can be observed from Figs. 7a and b that the NRTNN model predictions compared well with the observed values in response to the magnetic storm. Of particular interest is the response of model predictions to the sudden drop in foF2 value during magnetic storm of November 1989 (Fig. 7b). These figures illustrate that the NRTNN model can be used to capture storm events on a global scale within the limit of RMSE of about 1 MHz as shown in Tables 3 and 4. A comparison of the NRTNN model predictions was also made with that of our earlier standard foF2 NN global model (Oyeyemi et al., 2005a). A bar graph illustrating the RMSE differences between measured values with the NRTNN and foF2 NN global model predictions for a few selected stations is shown in Fig. 8. The difference in the inputs to the two NNs is that NRTNN has additional recent past observations of foF2 from four control stations. Since in all cases the RMSE obtained by the NRTNN model is smaller than that of the standard foF2 global model, it is evidence that there is a temporal correlation between measured foF2 values at different locations. The results from the error Tables 3 and 4, and graphs of diurnal and seasonal behaviour shown in these Figures indicate that NNs could be employed for near-real time foF2 forecasting within reasonable error limits. We have only compared our results with the observed values because we are
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Fig. 5. Samples of comparisons of daily variations of observed and NRTNN near-real time foF2 model predicted-values (outside training period) for two consecutive days starting at 00h00UT on the first of the days indicated for each station.
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Fig. 6. Samples of comparisons of the seasonal variation between measured (observed) and NRTNN near-real time foF2 model predicted values at 00:00UT (left panel) and 12:00UT (right panel) for selected verification stations (outside training period) for the year indicated.
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Fig. 7. (a) Samples of comparisons of daily variations of observed and NRTNN near-real time foF2 model predicted-values during magnetic storm of 17–19 September 1979. The top panel shows the variation of the magnetic Dst index during this storm. (b) Samples of comparisons of daily variations of observed and NRTNN near-real time foF2 model predicted-values during magnetic storm of 17–19 November 1989. The variation of the magnetic Dst index during this storm is shown in the top panel.
ARTICLE IN PRESS E.O. Oyeyemi et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1807–1818
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Fig. 8. Bar graph illustration of the RMSE differences between measured and near-real time foF2 global model (foF2 NRTNN model) and our standard foF2 global model (Oyeyemi et al., 2005a) predictions for all daily hourly values of foF2 for a few selected stations during the period indicated.
unable, at this time, to obtain data from any other near-real time global model.
4. Conclusion In this paper, the application of the NN technique to the development of a global near-real time foF2 empirical model has been illustrated. From the results it is evident that in addition to the geophysical information from any geographic location, recent past observations of foF2 from four control stations (Port Stanley, Grahamstown, Boulder and Dourbes) could be used as inputs to a NN for the purpose of near-real time foF2 predictions. Comparison of the NRTNN predictions with observed values of foF2 during a magnetic storm also provides evidence that there is temporal and spatial correlation between measured foF2 values at different locations. However, it is important to mention here that while the accuracy of this model is impressive considering the amount of data for this work, there could be an improvement if data from more stations were included in the training process. In addition, for the model to be effectively utilized, recent past observations of foF2 from the four control stations must be available in real time. It is the intention of the authors to pursue this research further.
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