Radio Science

Diurnal specification of the ionospheric f0F2 parameter using a support vector machine

Authors


Abstract

[1] This paper proposes a method for forecasting the ionospheric critical frequency, f0F2, up to 5 h ahead using the support vector machine (SVM) approach. The inputs to the SVM network are the universal time; day of the year; a 2 month running mean sunspot number (R2); a 3 day running mean of the 3 h planetary magnetic ap index, the solar zenith angle; the present value f0F2(t) and ten previously observed values f0F2(t − i), where i = 1, 2, 3, 4, 19, 20, 21, 22, 23, 24; and the six derivatives of previous 30 day running means of f0F2fmF2(t − j), where j = 19, 20, 21, 22, 23, 24. The output is the predicted f0F2 up to 5 h ahead. The network is trained using the ionospheric sounding data from seven Chinese stations, i.e., Guangzhou, Haikou, Chongqing, Beijing, Lanzhou, Changchun, and Manzhouli stations at solar maximum and minimum. In order to test the predictive ability, the SVM was verified with different data from the training data. The quality of the proposed model prediction is evaluated by comparison with corresponding predictions from the persistence reference, the autocorrelation and the neural network (NN) models. By using data from seven Chinese stations, it is shown that the performance of the SVM model is superior to that of the autocorrelation and persistence models, and that it is comparable to that of the NN model.

1. Introduction

[2] The ionosphere influences short-wave communication and space-terrestrial and intersatellite links and is highly variable due to the influence of solar, geomagnetic, and other sources. The F2 layer critical frequency, f0F2, is one of the most important ionospheric parameters, controlled by local time, geographical latitude, solar and magnetic activity, the background atmospheric wind, and other factors. When intense disturbances occur, the variation of f0F2 can reach or exceed 30% of f0F2, and there is consequently a requirement to be able to forecast f0F2 during these events.

[3] Different methods have been tried for short-term ionospheric forecasting. These include the autocorrelation method [Liu et al., 2005], the multilinear-regression method [Milhailov et al., 1999], the artificial neural network (NN) method [e.g., Cander et al., 1998; Oyeyemi et al., 2005; Chen et al., 2008], the nonlinear radial basis function (RBF) neural network [Francis et al., 2000; Francis et al., 2001], the data-assimilation method [Sojka et al., 2001], and the equivalent sunspot number conjectural method [Secan and Wilkinson, 1997].

[4] Recently, support vector machine theory (SVM) has been used for the prediction of space weather parameters. The foundations of the SVM have been developed by Vapnik [1995], and are gaining popularity due to its many attractive features, and promising performance. SVMs were originally developed to solve classification problems, but they have been extended to the domain of the regression problem [Vapnik et al., 1997]. It is found that this method provides a good compromise between the model complexity and learning ability when there are limited input data.

[5] The SVM method has been successfully applied to a number of fields, including phonetic and literal recognition and time series prediction. In particular we note that Gavrishchaka and Ganguli [2001] used the SVM to model the solar wind-driven geomagnetic substorm activity characterized by the auroral electrojet (AE) index. Qahwaji and Colak [2007] compared several machine learning algorithms for automated short-term solar flare prediction and found that SVMs have better performance than cascade-correlation neural networks and radial basis function networks for predicting whether a McIntosh classified sunspot group is going to flare or not. The SVM was further developed by Li et al. [2008] to combine the K-nearest neighbors (KNN), called the SVM-KNN method, for prediction of solar flares and proton events.

[6] The purpose of this paper is to introduce the SVM as a technique to forecast ionospheric f0F2 up to 5 h ahead. The observed values of f0F2 at middle and low-latitude stations have been used to test this approach. The results have been compared to other prediction techniques.

2. Support Vector Machine

[7] SVMs have recently received significant coverage due to excellent results reported for various applications. A brief description of the SVM [Vapnik, 1995] is given as follows.

[8] In SVM nonlinear regression, the input x is first mapped onto a high-dimensional feature space using some fixed (nonlinear) mapping, and then a linear model is constructed in this feature space. The regression model f(x, w) is given by

equation image

where xi is a multivariate input; wi is a set of weights; i = 1, …, N, where N is the number of input data; b is a bias, and ϕ is a mapping function.

[9] The SVM introduces the loss function to detect the discrepancy between the predicted value and the object value y. The ɛ-insensitive loss function is defined as follows:

equation image

This loss function ignores errors when the difference between the predicted value and the object value is smaller than a threshold ɛ. Data points out of the ɛ-insensitive band are called support vectors, and only support vectors contribute to the optimization solution [Yang et al., 2006].

[10] Regression estimates can be obtained by minimization of the empirical risk on the training data. The empirical risk of the SVM model Remp is described by

equation image

Figure 1 shows a case of fitting a straight line to data using the ɛ-insensitive loss function. By defining (nonnegative) slack variables ξi, ξi*, i = 1… N,

equation image

then equation (3) can be changed to

equation image

where ξi, ξi* represent upper and lower constraints on the outputs of the system.

Figure 1.

Fitting a straight line to data using the ɛ-insensitive loss function.

[11] At the same time, SVM regression performs linear regression in the high-dimension feature space using ɛ-insensitive loss functions and tries to reduce model complexity by minimizing equation imagew2. So the optimization function of the SVM is formulated as minimization of the following function:

equation image

where C is the regularization constant determining the trade-off between the empirical error and the regularized term, under the constrains

equation image

[12] The first step involving equation (6) is to minimize the Vapnik-Chervonenkis (VC) dimension, a parameter representative of the complexity of the model. The second step involves minimizing the errors between the regression and target values, where the target values are the training sample values.

[13] This constrained optimization problem can be set up using Lagrange multipliers, shown in equation (8).

equation image

where αi, αi*, βi, βi* are the Lagrange multipliers. By differentiating these variables w, b, ξi, ξi*, the following conditions can be obtained

equation image
equation image
equation image
equation image

[14] Putting equations (9), (11), and (12) into equation (8), equation (8) is modified to

equation image

subject to constraints

equation image

[15] By using the optimization method, αi, αi* can be solved. So the values of w can be obtained from equation (9) and b is also obtained from

equation image

Hence the regression function (1) can be described as

equation image

[16] The kernel function K (xi, xj) = ϕ(xi)T ϕ(xj) is used here. Typically used are polynomial, Gaussian, and hyperbolic tangent kernels. The Curb kernel function is selected as the kernel function in this paper. This regression function is expressed as

equation image

[17] The major advantage of the kernel-based machine is that it decouples the number of free parameters L (related to the machine capacity) from the previous number of input data, N, which can be very large or even infinite. Once the kernel function is chosen, the kernel representation allows one to learn effectively by choosing the underlying map and dimension N [Gavrishchaka and Ganguli, 2001].

[18] SVM is a combination of a kernel-based architecture and a structural risk minimization (SRM) principle. SRM minimizes an upper bound on the expected risk, which provides solid theoretical grounds for optimizing the generalization ability of SVM. The expected errors (risk) of the trained machine when applied to test data are bounded by the sum of two terms. The first term is the empirical error (risk) given by the mean error on the training set. The second is a function of the VC dimension, which is the measure of the machine capacity (i.e., the ability to learn a relation of a certain complexity). The VC dimension is related to the number of free parameters [Gavrishchaka and Ganguli, 2001]. SVM performs a mapping process from the input to a higher-dimensional feature space by using a kernel function, and finds out the relations between the input and the targets.

[19] Typical NN training algorithms minimize only the first term (empirical-risk minimization) without warranty of optimal generalization and common problems such as local optimization can arise. The optimal NN capacity has to be chosen empirically. SRM, on the other hand, provides an estimation of the second term [Gavrishchaka and Ganguli, 2001].

[20] Typical training algorithms for NNs and other adaptive systems require convergence of the training error to the generalization error for optimal generalization performance. In contrast to this common theoretical principle, SVMs with certain types of kernels have been shown to achieve optimal generalization performance even without convergence of the training and generalization errors [Opper and Urbanczik, 2001]. This feature allows more efficient extraction of useful information from noisy training set.

[21] The ionosphere variations are very complex due to the influence of solar and geomagnetic activities as well as other sources. So the ionosphere is regarded as a nonlinear system, which implies that the SVM method can be used in its predictions. The application of the described SVM (and analogous NN) model to our problem is based on the assumption that a relationship between f0F2 values and the available data can be described as a nonlinear function, which in a dynamic system is modeled as

equation image

where t is time of day in hours; equation imaget+j the is f0F2 value, to be forecast j hour after the present time, where j = 1,2,3,4,5; yt is the f0F2 value, observed at present time; xi is the input variable for the SVM network other than the present value of f0F2, i = 1, 2, ⋯, N, and F is the mapping function.

3. Error Analysis Methods and Reference Model

3.1. Data Sets

[22] Hourly values of f0F2 are used in this paper, depending on the availability, from the seven Chinese stations, i.e., Guangzhou, Haikou, Chongqing, Beijing, Lanzhou, Changchun, and Manzhouli. The training data are made up of the years 1958 and 1964, which were selected to be representative of solar maximum and minimum, respectively. Data from the years 1981 and 1986 are used to test the capability of SVM networks and calculate forecast precision quantitatively. These are also selected to be representative of solar maximum and minimum, respectively. (Because of the significant data gaps at Guangzhou and Chongqing Stations in 1981, the data from these two stations in 1981 was replaced by that from 1982.) The testing set does not contain any data from the training set, so the testing results can be considered to be reasonable. Table 1 shows the names and geographic coordinates of the ionosonde stations used.

Table 1. Names and Geographic Coordinates of the Stations Used
Station/AbbreviationGeographic LatitudeGeographic Longitude
Haikou/HAK20.0°N110.3°E
Guangzhou/GAZ23.1°N113.3°E
Chongqing/CHQ29.4°N106.5°E
Lanzhou/LAZ36.0°N103.9°E
Beijing/BEJ39.9°N116.4°E
Changchun/CHC43.9°N125.4°E
Manzhouli/MAZ49.6°N117.4°E

3.2. Error Analysis Methods

[23] The performance of the SVM is evaluated by the relative error (RE) and the RMS error of the forecasted values to the observed, which are calculated as

equation image
equation image

where f0F2obs and f0F2pred represent the observed values and the forecasted values, respectively.

3.3. Reference Model

[24] First, a successful predictive model must offer a significant increase in performance over the reference technique to prove the value of the method employed. The persistence reference model predicts that the value of an observed parameter at some specified point in the future will be identical to the current measurement of that parameter. This model performs well for quiet time conditions when the terrestrial environment is relatively undisturbed. However, it cannot predict the onset of the short-lived impulsive disturbances that characterize periods of unusually high geomagnetic activity [Francis et al., 2000].

[25] Second, neural networks provide a practical method of modeling ionospheric variations because (1) they are empirical model that can describe nonlinear phenomena strongly involved in the ionospheric variability, (2) they are trained on measured ionosonde data from which they extract the underlying functional relationships, and (3) they are fast enough that they can be used for real-time operation [Wintoft and Cander, 2000].

4. Input and Output to the Model

4.1. Inputs to the Model

[26] The inputs to our model are chosen on the basis of previous experience of parameters known to cause the variations in f0F2, and the inputs and outputs are illustrated in Figure 2.

Figure 2.

A block diagram of the inputs and outputs to the SVM.

4.1.1. Diurnal Variation

[27] We chose the universal time, HR, an integer in the range 0 ≤ HR ≤ 23, as the primary index of the diurnal variation. Using the work of Williscroft and Poole [1996], HR is converted to two quadrature components as follows

equation image
equation image

to avoid unrealistic numerical discontinuity at the midnight boundary.

4.1.2. Seasonal Variation

[28] It has been demonstrated [Williscroft and Poole, 1996; Oyeyemi and Poole, 2004] that not only the hour of the day but also the day of the year has an effect on the variations of f0F2. We use the day number, DN (1 ≤ DN ≤ 365), to describe the seasonal variation, which is converted to two quadrature components.

equation image
equation image

4.1.3. Solar Cycle and Magnetic Variation

[29] Williscroft and Poole [1996] determined the parameter R2 (a 2 month running mean of the daily sunspot number) to be the optimum parameter representing the variation of the solar EUV flux, to produce the minimum root-mean-square error in f0F2. So we choose a 2 month running mean of the preceding daily sunspot number as the input to describe the solar cycle variation. In addition, a 3 d running mean of the preceding 3 h planetary magnetic ap index, MD3(ap) and the solar zenith angle are chosen as inputs to the SVM network.

4.1.4. Inputs Related to f0F2

[30] Since the f0F2 values themselves should be meaningful in forecasting the f0F2, the present value of f0F2 is fed to the model and several derivatives of the f0F2 are considered. The value f0F2(t) is the value of the ionosphere f0F2 at the starting time t. Recent observed values of f0F2, f0F2(t − i), where i = 1, 2, 3, 4, 19, 20, 21, 22, 23, 24 from each of the geographic locations are included as the inputs to the SVM network. The values f0F2(t − 1), f0F2(t − 2), …, are calculated on 1 and 2 h preceding f0F2 values, respectively.

[31] In the case of the derivatives, the 30 d running mean of fmF2 (t − j), (where j = 19, 20, 21, 22, 23, 24) were used, which were based on experiments. By choosing these derivatives, we guide the model with data for 24 h earlier and benefit from the natural (quiet time) reproducibility of the ionosphere.

4.2. Output to the Model

[32] The primary objective of this work is to develop a SVM model to forecast f0F2 values up to 5 h ahead for a single station. Therefore, the outputs from our model are values of f0F2 (t + k), where k = 1, 2, 3, 4, 5, respectively.

5. Results and Discussion

[33] The networks were trained according to the method described above, using data from 1958 and 1964. To test the applicability of the SVM method of f0F2 forecasting in China, we select the observed data of 2 years (1981 and 1986) at each station (solar maximum and minimum, respectively), and used the above method to calculate the prediction errors up to 5 h ahead. Data not included in the training sets from seven stations are used to verify the performance of the SVM networks. Selection of these years is based on the data availability. The performance of the SVM model has been quantified in terms of the RMS error and has been compared with the autocorrelation, NN, and the persistence model. So the standard feed-forward neural network with back propagation learning built and used in this paper has the same inputs and outputs as the model, which has one hidden layer with 15 hidden nodes. Data spanning the period 1958–1968, which include all periods of calm and disturbed magnetic activity, were used for training the NN.

[34] In Tables 2 and 3, errors between the observed and forecasted values are calculated by taking the RMS errors of all f0F2 data points available during the period indicated for each station, which could verify the predictive ability of the SVM model up to 5 h ahead beyond the training period at solar maximum and minimum, respectively. Although not shown here we note that the forecasted error of the autocorrelation model is constant during the day except for the first hour. The time constant of the autocorrelation model is usually less than 2 h, which means that for prediction of 2 or more hours ahead, the highest autocorrelation coefficients that determine the prediction error are not the values at the neighboring hours but those at the same local time on the neighboring days [Muhtarov and Kutiev, 1999].

Table 2. Prediction Errors of f0F2 for Seven Stations at Solar Maximum
Station1 h Forecast2 h Forecast3 h Forecast4 h Forecast5 h ForecastYear
RMS of the SVM MODEl (MHz)
HAK0.871.161.221.251.271982
GAZ0.941.191.231.351.411982
CHQ1.121.241.341.361.401982
LAZ0.630.690.750.820.941981
BEJ0.570.670.750.860.971981
CHC0.650.730.780.860.901981
MAZ0.660.730.770.820.851981
 
RMS of the NN Model (MHz)
HAK1.001.171.201.221.241982
GAZ1.071.291.411.411.441982
CHQ1.081.231.271.321.371982
LAZ0.610.750.730.770.921981
BEJ0.610.700.730.820.901981
CHC0.630.740.790.840.921981
MAZ0.660.740.780.790.831981
 
RMS of the Autocorrelation Model (MHz)
HAK1.381.421.421.421.421982
GAZ1.691.751.751.751.751982
CHQ1.531.571.571.571.571982
LAZ0.930.970.970.970.971981
BEJ0.930.970.970.970.971981
CHC0.950.990.990.990.991981
MAZ0.971.001.001.001.001981
 
RMS of the Persistence Model (MHz)
HAK1.602.583.374.004.501982
GAZ1.672.643.434.084.651982
CHQ1.552.343.023.634.161982
LAZ1.101.812.412.943.401981
BEJ1.051.782.422.973.451981
CHC1.031.682.242.723.151981
MAZ1.041.672.232.713.131981
 
RE of the SVM Model (%)
HAK7.208.408.778.949.231982
GAZ7.899.4610.0010.3010.481982
CHQ9.4110.9711.7211.9312.141982
LAZ6.237.097.468.5610.281981
BEJ5.236.617.478.7310.471981
CHC6.157.437.898.408.691981
MAZ6.347.157.618.379.551981
Table 3. Prediction Errors of f0F2 for Seven Stations at Solar Minimum
Station1 h Forecast2 h Forecast3 h Forecast4 h Forecast5 h ForecastYear
RMS of the SVM Model (MHz)
HAK0.881.041.071.081.101986
GAZ0.851.021.071.101.111986
CHQ0.770.910.960.970.981986
LAZ0.530.590.600.600.611986
BEJ0.460.500.520.520.531986
CHC0.460.490.490.540.571986
MAZ0.410.450.460.470.481986
 
RMS of the NN Model (MHz)
HAK0.891.051.061.071.141986
GAZ0.891.021.121.141.141986
CHQ0.770.900.940.980.991986
LAZ0.540.550.640.670.691986
BEJ0.490.530.540.550.561986
CHC0.480.520.550.550.601986
MAZ0.430.470.470.480.481986
 
RMS of the Autocorrelation Model (MHz)
HAK1.231.351.351.351.351986
GAZ1.221.331.331.331.331986
CHQ1.111.141.141.141.141986
LAZ0.710.740.740.740.741986
BEJ0.610.630.630.630.631986
CHC0.580.610.610.610.611986
MAZ0.540.560.560.560.561986
 
RMS of the Persistence Model (MHz)
HAK1.382.202.873.433.961986
GAZ1.312.032.623.133.601986
CHQ1.081.692.152.542.891986
LAZ0.801.191.501.762.011986
BEJ0.701.041.311.541.761986
CHC0.690.971.201.401.581986
MAZ0.600.881.121.331.511986
 
RE of the SVM MODEl (%)
HAK10.5812.2612.7912.8712.921986
GAZ10.8212.3012.6912.8412.941986
CHQ10.0611.7011.9712.2212.321986
LAZ8.158.929.139.339.461986
BEJ6.847.377.597.737.831986
CHC7.167.637.647.657.751986
MAZ6.897.457.617.918.031986

[35] As expected the SVM errors increase from 1 to 5 h. However, despite the fact that the errors are relatively large at some stations, the RMS errors of the forecasted f0F2 values are small compared with the values of f0F2. In addition, it is shown that SVM performs better than the autocorrelation and the persistence model, and that it is comparable to the NN method at solar maximum and minimum. Taking Beijing station as an example, the RMS errors of the SVM model for prediction of 1 h ahead are 0.57 MHz in 1981 (solar maximum) and 0.46 MHz in 1986 (solar minimum), while those of the autocorrelation, NN, and persistence models are 0.93, 0.61 and 1.05 MHz in 1981 and 0.61, 0.49, and 0.70 MHz in 1986, respectively.

[36] The forecasting errors at solar maximum are usually larger than that at solar minimum for the same station. For example, the RMS error is 0.65 MHz in 1981 at Changchun, but only 0.46 MHz in 1986. This is clearly due to the fact that the ionosphere is denser for higher sunspot numbers. As more sunspots mean more solar flares and more impact on the ionosphere statistically.

[37] Similarly, the RMS error is higher at low latitudes than at middle latitudes. These larger errors may be a result of the equatorial anomaly and the increased ionospheric variability in the low-latitude region, due to complex electrodynamic interactions involving the neutral wind, the Earth’s magnetic field, and electric field in the F region. Alternately the larger errors may be due to the denser ionosphere in the low-latitudinal region, which makes Δf0F2 and RMS larger at low latitudes than at middle latitudes [e.g. Abdu, 1997; Fejer, 2002].

[38] In Figure 3 the forecasted f0F2 values are shown for Haikou in 1981. Figure 3a depicts a comparison between the observed f0F2 values and the forecasted values 1 h ahead and shows that the SVM model provides an accurate prediction. The predictions present comparatively smooth diurnal variations, which are close to the observations during both the ascent and descent phases and reproduce the general behavior of ionospheric variations. However, the remarkable differences between predicted and observed values are found during the daytime on days 97,105,110,111, and 105. Figure 3b shows the absolute deviations. The dots show absolute deviations between the observed and forecasted values of the SVM model at each hour, the solid line represents the forecasted errors of the persistence model. The RMS error of the SVM model for prediction of 1 h ahead is 0.77 MHz, while that of the persistence models is 1.25 MHz.

Figure 3.

(a) Comparison between the observed (dots) and forecasted values (solid line) 1 h ahead at Haikou in 1981. (b) The absolute deviations between the observed and forecasted values of the SVM model (dots) and that of the persistence model (solid line) at Haikou in 1981.

[39] Figures 4–7 show some samples of daily variations of the observed and forecasted f0F2 values up to 5 h ahead for 4 consecutive days for Guangzhou, Haikou, Lanzhou, and Changchun stations. Figures 47 show that curves for the observed and forecasted f0F2 values have almost the same type of variation in time, but the SVM model provides more accurate predictions 1 h ahead than 2–5 h ahead again.

Figure 4.

Examples of comparisons between the observed and SVM forecasted values of f0F2 for 4 consecutive days for Guangzhou in (a) 1981 and (b) 1986.

Figure 5.

Examples of comparisons between the observed and SVM forecasted values of f0F2 for 4 consecutive days for Haikou in (a) 1981 and (b) 1986.

Figure 6.

Examples of comparisons between the observed and SVM forecasted values of f0F2 for 4 consecutive days for Lanzhou in (a) 1981 and (b) 1986.

Figure 7.

Examples of comparisons between the observed and SVM forecasted values of f0F2 for 4 consecutive days for Beijing in (a) 1981 and (b) 1986.

[40] Sudden variations are not well-modeled by the SVM model, which means this technique still fails to predict sharp peaks in daytime f0F2. Two factors could account for the relatively poor behavior of the model. First, periods of elevated ionospheric activity are rare in comparison with quiet time conditions. Therefore the training process is biased against the prediction of these infrequently occurring events. Second, the time scales associated with the sharp peaks are much smaller than the resolution of the input time series. Therefore the input time series does not contain sufficient information about the dynamics of these events to model their rapid changes accurately [Francis et al., 2000]. For example, most obviously the penetration of solar wind effects to midlatitudes is missing, which occurs on time scales of a few hours and thus are lost in the smoothing of solar cycle and magnetic activity inputs to the SVM analysis. The strength of the model may be the solar wind can be included in future work to improve the predictions further.

[41] Also evident in Figure 4b is the response of the SVM model to the sudden magnetic storms on days 38 and 41 in 1986. Figure 4 shows a clear storm, and a possibly weak storm is shown in Figures 6b and 7b (same event, different station). Not only is the forecasted 1 h error of the SVM model higher under “disturbed” ionospheric conditions, but the 2–5 h predictions almost miss the storm and approximately follow the average daily variation. This happens because the forecasting technique does not include an appropriate knowledge of the solar phenomena and magnetospheric influences. In addition, events occurring infrequently in the data set will be modeled poorly for any data driven model. In the future we will need to develop storm time forecasting models in which storm parameters should be added to the inputs and storm f0F2 data should be selected from the observed values f0F2.

[42] The results presented in this section demonstrate the potential usage of the SVM model to predict f0F2 up to 5 h ahead in quiet and disturbed conditions, although the predicted f0F2 is in better agreement during quiet condition. An improvement over this model can be achieved if ionospheric forecasting in storm time is considered.

6. Conclusion

[43] The SVM method has been used for ionospheric short-term forecasting up to 5 h ahead. On the basis of f0F2 observations at Guangzhou, Haikou, Chongqing, Beijing, Lanzhou, Changchun, and Manzhouli stations at solar maximum and minimum, the prediction quality has been quantitatively estimated at different stations and times. The error analysis shows that the forecasting can perform well within the reasonable error limit. According to the present study, it is evident that the SVM technique can be used successfully in short-term forecasting of f0F2. The performance of the SVM was compared with the autocorrelation, NN, and persistence models. This indicates that its performance is superior to that of the autocorrelation and persistence models, and that it is comparable to that of the NN model. As expected the SVM method is more accurate at forecasting 1 h than 5 h ahead.

[44] Sharp peaks in the observations are not well-modeled by the SVM model, because the input time series does not contain sufficient information about the dynamics of these events to model their rapid changes accurately. For example, the penetration of solar wind effects to midlatitudes is missing. These occur on time scales of a few hours and are lost in the smoothing of solar cycle and magnetic activity inputs to the SVM analysis.

[45] The SVM forecasting method proposed can be applied not only to the short-term forecasting of f0F2, but also to that of other ionospheric parameters, such as M(3000)F2, total electron content (TEC), and the profile of electron density N(h).

Acknowledgments

[46] This work was supported by the National Key Laboratory of Electromagnetic Environment, and the National Natural Science Foundation of China (grants 61032009, 60771050, 60871076, 40974092, and 40904040).