short-term prediction of solar proton events by neural network method

PERGAMON Chinese Astronomy and Astrophysics 28 (2004) 174-182

CHINESE ASTRONOMY AND ASTROPHYSICS

S h o r t - t e r m P r e d i c t i o n of Solar P r o t o n E v e n t s by N e u r a l N e t w o r k M e t h o d t *

GONG J ian-cun 1 XUE Bing-sen I LIU Si-qing I ZOU Zi-ming 1 MIAO Juan 1 WANG Jia-long 2

1 Center/or Space Science and Applied Research, Chinese Academy o/Sciences, Beijing 100080

2National Astronomical Observatories, Chinese Academy o/ Sciences, Beijing 100012

Abst rac t Based on a large number of statistical results, we study the prediction of solar proton events in depth. By summarizing the relations of the proton events with the area, position, McIntosh structure, magnetic structure of the active region, and the number of solar flare bursts which happened in the active region two days before, a short-term prediction model of solar proton events is built on the lines of artificial neural network. Tests on 12 samples later than 2000 indicate a prediction accuracy of about 83%. Further test predictions are made on the proton events which occurred in Jam-Apr. 2002. It is found that all the 6 events that occurred in this period are correctly predicted. Among them, 3 are predicted 3 days ahead, 2 events - - 2 days ahead, and 1 event - - 1 day ahead.

Key words: Sun: activity--Sun: particle emission--methods: miscellaneous

1. I N T R O D U C T I O N

Short-term prediction of solar proton events has become an important part of space environ- ment forecast, and following the rapid advances in mankind's space activity and development of space science and techniques the effect of solar proton events has received more and more attention from the space science and technology community. As Allen et al.[ 1] pointed out, the effects of solar proton events are too widespread and intensive to be ignored. By short- term prediction we means predictions 1-3 days ahead; by proton events we mean those with energy >10MeV and flux >10pfu measured near the earth (i.e., at 1 AU).

? Supported by National Project of Key Important Basic Science Research Received 2002-11-07; revised version 2003-09-11

* A translation of Chin. J. Space Sci. Vol. 23, No. 6, pp. 443-451, 2003

0275-1062/04/S-see front mat te r © 2004 Elsevier B. V. All r ights reserved. DOI: 10.1016/j.chinastron.2004.04.008

GONG Jian-cun et al. / Chinese Astronomy and Astrophysics 28 (2004) 174-182 175

In the second half of the 50s of the 20th century some solar physicists of Soviet Union studied the short-term prediction of solar proton events with the magnetic field of the solar active region and its variations; in the 1970s the accuracy of the short-term prediction exceeded 70%, but the rate of false report was also rather high [2,3]. Shea et al. [4] and Wang Jialong [5] reviewed the short-term predictions of solar proton events made from the 60s to the 90s, and it was found that the prediction made a rather great development in the 60-70s, but since then the progress was not very good and the prediction accuracy was not much improved until the 90s. Especially, for the years of low solar activity, the prediction accuracy was even worse. For example, almost none of the 5 events which occurred from 1993 to 1995 were accurately predicted.

In 1997, in a discussion on the prediction of terrestrial magnetic bursts, Lundstedt [7] suggested that the application of artificial intelligence may be helpful for improving the prediction accuracy. Hu Xiong et al.[ s] selected the peak flux, rising time and integrated flux of the electromagnetic emission during the solar flare burst among the input parameters in a neural network model for the warning of solar proton events. In a different warning model, Wang Jialong et al.! 9] selected 8 input parameters including the peak flux of the solar electromagnetic emission during the flare burst, the spectral type of the radio burst, the magnetic field type of the sunspot group. As the position of the solar flare on the solar disk is included in the inputs of these two models, both models are quite effective. In 2000, Wang Jialong et al. [l°] proposed a system consisting of two neural network models I and II. Model I predicts either "event" or "no event", and if the former, Model II then predicts specifically the event's intensity class. So it is a composite system different from the available single-model systems. Tests indicate that while maintaining the accuracy of "event" / "no event" prediction, this system has the additional capability of predicting the event's intensity class. Based on these previous works and the practical requirements on the short-term prediction, in this paper we will further study and discuss a short-term prediction system of solar proton events by making use of the formalism of neural network.

2. T H E P R E D I C T I O N M E T H O D A N D P A R A M E T E R S

The solar proton event is a strong solar burst activity. It needs quite a long process of energy storage, so it must have been accompanied by the evolution of the region of energy storage (the active region) and some other features of solar activity, such as the variation of the radio emission background. Gathering the information together will help us to understand the precursor features of the solar proton event. But the various parameters and their evolutionary features are very complicated, and it is very difficult to give a simple description with a normal statistical law. The experiences of our previous studies tell us that it will be better to analyze the data of solar activity and to build a prediction model by an algorithm along the lines of neural network.

2.1 Pred ic t ion P a r a m e t e r s We select the prediction parameters according to the following three principles. The

first is to select those quantities that are related in theory to the generation or propagation of solar proton events; the second is to select those quantities that are statistically related to the generation or propagation; and the third is to select those observational quantities

176 GONG Jian-cun et al. / Chinese Astronomy and Astrophysics 28 (2004) 174-182

that are easily obtained, so facilitating the practical execution of the prediction. According to these three principles, the following seven parameters were selected: area of the sunspot group in the active region X1, the McIntosh type of the sunspot group X2, magnetic type of the sunspot group X3, number of medium and small bursts (class M and class C) generated in the active region X4, flux density of the 10cm wavelength radio emission on the whole solar disk X~, intensity of the soft X-ray background emission on the whole disk X6, and heliographic longitude of the active region XT.

In fact, for the prediction of solar proton event we have to predict separately for each of the important active regions on the solar disk if any proton event will happen in a short time and of what class the event will be. The method is: for the given active region we take all the 7 parameters X 1 - X 7 on the day 1, and the first 6 parameters on the day 2, now labelled Xs-X13. Thus, a total of 13 parameters X1- X13 constitute the input of the model, and the output is the prediction of the "event" / "no event" status for the days 3, 4, 5. We use as input the parameters on two successive days because we consider any variation in two days may have an important effect on the prediction, and we use only the first six rather than all seven parameters on the second day because of the motion of the active region in longitude in the mean time. In addition, as the connection function in the neural network model is nonlinear, linear gradation and valuation of the input parameters are not necessary, and some subjective element is allowed to facilitate the digitization of the input parameters. An explanatory description of the seven parameters X 1 - X 7 now follows. 2.1.1 Area of the Sunspot Group in the Active Region

The greater the area of the sunspot group, the stronger the magnetic field, and the larger the energy of the background magnetic field of the whole active region, thus a relatively small increase in the area will be enough to produce a rather large burst [11]. Some available statistics have provided the production rate of flares of class > M for different grades of sunspot group area [12], so we can take it as a rough measure of the relative production rate of the proton flare. Considering the way the production rate of proton flare increases with increasing area, we took a denser gradation for areas above 1000 and divided the area S into 6 grades: S _< 200, 200 < S _< 500, 500 _> S < 1000, 1000 > S < 2000, 2000 < S < 3000, and S > 3000. The unit of sunspot area is 10 -6 the area of solar hemisphere. 2.1.2 The McIntosh Type of Sunspot Group

The McIntosh classification is an improved Ziirich classification. It not 0nly reflects the structure of the large spots in the group, but also takes into consideration any smaller spots within the dipole group, as well as their structures. Moreover, if we lack observational data on the magnetic field, then the McIntosh classification will play a very good supplementary role.

Meanwhile, as a short-term prediction parameter of different classes of soft X-ray bursts, the McIntosh type of spot group can provide a rough approximation of the production rate of proton events through Table 1, which gives the statistical relationship between the soft X-ray bursts and the solar proton events.


T a b l e 1 The statistical relationship between soft X-ray bursts and solar proton events in the three years 1989, 1990, 1991

1989 1990 1991 Total Number of burstS of classes M3-M9 148 62 126 331 Number of proton events 8 6 8 22 Probability of burst accompanying proton event (%) 5.4 9.7 6.3 6.7

Number of all class-M bursts 584 284 551 1419 Number of proton events 8 6 8 22 Probability of burst accompanying proton event (%) 1.4 2.1 1.5 1.6

Number of all class X bursts 51 16 49 116 Number of proton events 15 6 9 30 Probability of burst accompanying proton event (%) 29.4 37.5 18.4 25.9

From Table 1 we can see tha t the probabilities are different for the different years. So such a digitization is quite approximate and average . When the McIntosh types of spot groups are taken as the input element of the prediction model, we will divide them into 5 classes as shown in Table 2.

Table 2 The classes of spot group McIntosh types input to the neural network model

Class 1 2 3 4 5 Types FKC, FKI, FHC, FKO, FAI, EHI, FAO, EHO, EAO,

EKC EKI FHI, EHC, EKO, DKI, EAI, DKO, HKX, DKC DKC DAO, DAC, DAI,

DHI, CAO, CKO, CHO

2.1.3 The Magnetic Type of Sunspot Groups The magnetic type of a sunspot group reflects qualitatively the distribution of the

magnetic field of the whole spot group, as well as the structure of the magnet ic field in the local area. A magnetic field with a complex structure such as the (f-type structure means a rather large deviation from the potential field, and rapid energy release is easily

triggered off. Combining the magnetic type and the area of the spot group, differences in the magnetic energy content and the stability of magnetic structure can be clearly discriminated. Following Zhang Guiqing et al. [12], the magnetic field type is given the values shown in Table 3.

Table 3 The valuation for the magnetic field types of spot groups

Magnetic field type ~ /3 /37,')' ~,/35,/3"Y~ V5 Value 0.05 0.25 0.35 0.65 0.98

2.1.4 Number of Class C and Class M Bursts in the Active Region The number of small (class C) and medium (class M) bursts occurred one and two days

before in the active region is a measure of small and medium activities in the active region, and it is one of the impor tant markers of recent activity in the active region. From the statistics of the numbers of small and medium bursts which occurred one and two days before the known proton events, we can obtain the classification and valuation of this input element shown in Tables 4 and 5.

178 GONG Jian-cun et al. / Chinese Astronomy and Astrophysics ~8 (2004) 174-182

Table 4 The classification and valuation of the numbers of C-class and M-class bursts generated one day before (used for X4)

Number of C-class burs ts /d 0 1 2 ->3 Value 0.02 0.13 0.17 0.25

Number of M-class bursts /d 0 1-2 3-4 ->5 Value 0 0.17 0.30 0.50

Table 5 The classification and valuation of the numbers of C-class and M-class bursts generated two days before (used for Xn)

Number of C-class bursts/d 0 1-2 3-4 ->5 Value 0.02 0.22 0.25 0.30

Number of M-class bursts/d 0 1-2 3-4 ->5 Value 0 0.33 0.50 0.67

2.1.5 Flux Density of 10.7 cm Radio Emission and Whole-disk Flux of Soft X-ray Emission Here, the flux density (in sfu) of the radio emission at 10.7 cm wavelength and the flux (in

W / m 2) of the soft X-ray emission (1-8 ~) refer to the background emissions of the quiet sun. These two kinds of emission are par t of the solar thermal radiation. An enhancement in the background emission is in fact an enhancement in the slowly-varying component of the thermal radiation. Physically, such enhancement should be understood as being caused by an increase either in the mass density or volume of the coronal condensation regarded as the source of the slowly-varying emission, i.e., by there being more electrons t rapped in the magnetic field of the active region. Based on some simple statistics, we can make the classification and valuation for these two input elements as shown in Tables 6 and 7.

Table 6 The classification and valuation of the 10.7 cm wavelength background emission on the

whole solar disk (X~ and X12)

10.7cm flux density <150 150-199 200-249 250-299 >300 Value 0.28 0.57 0.71 0.86 0.98

Table 7 The classification and valuation of the soft X-ray background emission on the whole solar disk (X6 and X13)

X-ray emission class <B5 B5-B6 B7-B8 B9-C1.7 C1.8-C2.4 C2.5-C2.9 >C3.0 Value 0.17 0.20 0.25 0.50 0.70 0.90 0.98

Note: C and B mean multiplying by 10 -6 W/m 2 and 10 -7 W/m 2, respectively.

2.1.6 Heliographic Longitude of the Active Region The distribution of solar proton flares on the solar disk has a east-west a symmet ry , i.e.,

the distribution is a function of the heliographic longitude. Wang Jialong et al. [13] made a statistical s tudy of the longitude distribution of proton flares observed in the period 1977-- 1982. The result shows tha t the number of proton flares tends to increase from the eastern rim of the solar disk, through the central part , to the western rim, and tha t the number on the western rim can be two or even more times the number on the eastern rim.


It is generally believed that the east-west asymmetry is caused by the propagation condition of the proton streams in the interplanetary space, and is strongly correlated with the state of interplanetary magnetic field or the shape of its magnetic lines. This parameter is classified and valuated as shown in Table 8.

Table 8 Classification and valuation of the heliographic longitude of the active region

Longitude 90°E-56°E 55°E-26°E 25°E-15°W 16°W-50°W 51°W-90°W Value 0.13 0.38 0.88 0.98 0.88

2.2 P r e d i c t i o n M o d e l B a s e d o n N e u r a l N e t w o r k In the last section we have selected a number of factors that are well correlated with

proton events and analyzed their correlative characteristics. But the prediction of proton events is a process of synthetic judgement, while the behaviour of those measures of solar activity is of a different kind. Proton events are preceded by complicated precursor features in various combinations, and we have to make some judgement on them.

It is no doubt very difficult to manually pick out the correct precursors from among so many clues, while differences in different people's experience may lead to errors. Increased speed of the computer and advances in computational methods have made it relatively easy to carry out complicated computations and derivations. What we have to do is to construct a suitable computational method to train the computer, by means of great many past case histories, to correctly grasp the characteristics of the precursors of proton events and so to make automatic judgement as to whether there is going to be a proton event, when a fresh set of input parameters are presented.

The selection criteria of our computational method are the abilities to learn and to self-improve, and neural network meets exactly these criteria.

Neural network is an artificial network composed of great many interconnected simple processing elements called neural elements. It was originally constructed for simulating the structure and function of the brain's neural system. The neural elements are nonlinear elements generally possessing of multiple inputs and one output. Usually, the totali ty of the input signals received by the neural elements is not enough to determine the various proper relations between its inputs and output, and a characteristic function is needed to describe such relations and to produce a new output.

The dynamic characteristics of a neural network are mainly exhibited by the order by which the various neural elements alter their states, by how often the elements make their calculations, by the number of iterations that relates to the total time, and so on.

When the dynamic characteristics of the network are related to the amplitudes of the inputs, i.e., when the various neural elements are computed according to a definite probability model defined by the amplitudes of inputs, and when the computing frequency of the element's output and the process of state alteration are determined by probability, then such dynamic characteristics will play a special role in solving the optimization problem.

Using the total connection network with reverse propagation shown in Fig. 1, training is performed with a supervised learning algorithm. Here Xi( t ) denotes the input parameters, Y~(t), the output parameters, and the elements in the middle from m + 1 to N belong to a hidden layer. The weights Wij correlate Xi( t ) to Y~(t); the weights are adjusted so as to make the calculated output Yi(t) approach the actual output Y/(t) to within the expected error


o . . . x i ( t ) . . . o o . . . z d t ) . . . o o . . . ~ ( t ) . . . o

1 m m + l N N+I N + n

l Input layer ] [ Implicit layer [ [ output layer [

m neural elements N neural elements n neural elements

Fig. 1 The scheme Of artificial neural network

range: this is the learning process. Applying the learned weights Wij (t) to the presented inputs, we obtain the predicted set of output parameters.

The learning process of the neural network is very similar to the way humans acquire skills through training. By a definite process (algorithm) of (gradually) adjusting the weights the network is trained to produce increasingly bet ter sets of output parameters. The training can be divided into two kinds: supervised and un-supervised. The sample in supervised training demands that each input parameter is matched with the target parameter repre- senting the required output. The training requires many such paired samples. In the course of training, the output parameters of the network are calculated from the input parameters of the training sample, then they are compared with the sample's target parameters, and the weights of the network are adjusted to decrease the residuals until these are within the acceptable range.

In this way, we trained our neural network with observed data of solar activity, which include situations both with and without proton events. After repeated training the neural network will gather up some "prediction experience". We then re-tested the data used in the training and found that the network has a prediction accuracy of bet ter than 90%. A number of datasets were tested and the results proved that the model was stable.

After completing the tests of the prediction model, we have verified again the accuracy of the model wi th untrained historical and new observational data, and good results were obtained in all the cases.

3. M O D E L V E R I F I C A T I O N A N D T E S T P R E D I C T I O N S

3.1 The Result of Sampling Tests In the process of constructing the model, proton events which occurred before 2000

were taken as the training sample, and 12 events observed after 2000 were taken as the test sample. Table 9 is the comparison between the predictions and the actual observations.

Under the heading "observation", 0.9 means a proton event; 0.1 means no proton events. Under the heading "prediction", >0.5 means that there is going to be a proton event, <0.5 means there is not going to be one. This table shows that 2 out of the 12 predictions are wrong, or the rate of correct prediction is about 83%. The overall rate of correct prediction,


R, is the ratio between the total number of correct predictions t (of both "proton event" and "no proton event") and the total number of actual observations T (of both "proton event days" and "no proton event days"), R = t / T .

Table 9 Test results of the neural network model

Prediction 0.51 1.00 0.80 0.38 1.00 1.00 Observation 0.90 0.90 0.90 0.90 0.90 0.90 Prediction 1.00 0.92 0.76 0.06 0.42 0.41

Observation 0.90 0.90 0.10 0.10 0.10 0.10

3.2 Event Predictions Next, we made a comparison between the predictions of proton events in Jam-Apr.

2001 and the real situation. There is a total of 6 proton events in the period. All the 6 events were correctly predicted by our model: 3 events are predicted 3 days ahead, two events are predicted two days ahead, and 1 event is predicted one day ahead.

3.3 Test Predictions for April 2001 In addition, for each day in the period 2001 April 1-23, we made a prediction of a proton

event occurring in the next three days. Comparing our predictions with real happenings, we find: of the 23 predictions, 13 are correct (R -- 56.5%); of the 10 wrong predictions, 7 are false alarms, 3 are failures (predicted no events when actually an event occurred in the next three days).

4. C O N C L U S I O N S A N D D I S C U S S I O N

From the results of model verification mentioned above, we can make the following conclu- sions and discussion:

(1) The model has a strong capability of predicting proton events, but it is not very good for periods when no proton events occur, i.e., the rate of false alarms is relatively high. The main cause of this result is tha t the number ratio between "event days" and "no event days" is very different in the training sample and the target sample. One of the prerequisites for the training sample selection is the occurrence of a flare burst or proton event stronger than Class M. Of course, the model parameters trained on this basis will be biased towards positive predictions. To improve the prediction accuracy in the quiet sun period with few proton events, the training sample should include days of the quiet sun with no proton events or flare bursts.

(2) There are two mechanisms of accelerating protons: besides acceleration in the flares and CMEs, protons can also be accelerated by shock waves. It is possible tha t the proton events generated by shock wave acceleration are not counterparted by large flare events. Then for proton events caused by this second mechanism, the prediction capability of our model is likely to be small.

(3) The selection of prediction parameters is limited by the observational measures. The current study indicates that the generation of solar proton events is closely related to the magnetic features of the active region. So, for the selection of prediction parameters, if the fine structure features of the active region is included, the prediction accuracy of proton events will be further improved.


R e f e r e n c e s

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short-term prediction of solar proton events by neural network method

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