ELSEVIER Chinese Astronomy and Astrophysics 36 (2012) 169–174

CHINESEASTRONOMYAND ASTROPHYSICS

Short-term Forecast of Solar Proton EventsWith Characteristic Phyiscal Quantities of

Photospheric Magnetic Fields† �

CUI Yan-mei�1 LI Rong 2 LIU Si-qing 1

1Center for Space Science and Applied Research, Chinese Academy of Sciences,Beijing 100190

1Institute of Information, Beijing Materials College, Beijing 101149

Abstract Via the three physical quantities (i.e., the maximal horizontal gra-dient of longitudinal magnetic field |ΔhBz|m, the length of neutral line witha large gradient L, and the number of isolated singular points η), which areused to represent the characteristics of the complexity and non-potentiality ofthe photospheric magnetic fields in solar active regions, a model of the short-term forecast of proton events is built. The effectivity of the short-term forecastof proton events by means of the characteristic physical quantities of magneticfields is verified. In the nowadays commonly used models of short-term forecastof solar proton events, until present the characteristic physical quantituieas ofmagnetic fields are not formally taken to be the factors of forecast. Because thesolar proton events are low probability events, the physical mechanism of theiroccurrence is still not well understood. In the models of their prediction, theproblems of high rates of false alarm or low rates of right alarm often exist. Inthis paper the traditional factors used in the existing models of forecast of protonevents and the characteristic physical quantities of magnetic fields are combinedtogether. By using the method of neural network, a more effective method ofthe short-term prediction of proton events is established. With the 1871 sampledata in 1997-2001, we have set up Model A with the traditional forecast factorsas the input layer, and also Model B with the traditional forecast factors plusthe characteristic physical quantities of magnetic fields as the input layer. Viathe set of 973 sample data of the years 2002 and 2003, we have carried out a

† Supported by National Natural Science Foundation, National Key Basic Research Program and Know-ledge Innovation Engineering of Chinese Academy of Sciences

Received 2010–01–15; revised version 2011–02–19� A translation of Chin. J. Space Sci., Vol.31, No.4, pp.436-440, 2011

� ymcui@cssar.ac.cn

0275-1062/01/$-see front matter c© 2012 Elsevier Science B. V. All rights reserved.PII:

0275-1062/11/$-see front matter © 2012 Elsevier B.V. All rights reserved.doi:10.1016/j.chinastron.2012.04.004

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simulative forecast, and found that under the condition that these two modelspossess the same rate of accuracy in the forecast of proton events, the rate offalse alarm of Model B becomes evidently lower. This has further verified theeffectiveness of the characteristic physical quantities of magnetic fields in short-term prediction. Furthermore, this may improve the actual ability of forecast ofsolar proton events.

Key words: solar proton event, model of forecast of proton event, solarphotospheric magnetic field, BP neural network

1. INTRODUCTION

The solar proton event (SPE) may have large influence on the space environment and astro-nautical enterprise. Therefore its accurate forecast possesses important significance. How-ever, as a low probability event, the physical mechanism of its occurrence is not clear enough.The problem of false alarm rate or low detection rate always exists. Under the prerequisiteof a certain rate of detection, the lowering of the rate of false alarm is a difficult problemfor the prediction of SPE’s.

In Ref.[1], a model of short-term forecast of SPE’s is set up with the BP neural network,and on the basis of the characteristic physical quantities of magnetic fields in active regions(i.e., the maximum horizontal gradient of longitudinal magnetic field |ΔhBz|m, the length ofneutral line of intense gradient L, and the number of isolated singular points η). Herewith, wemay verify the effectiveness of the characteristic physical quantities of photospheric magneticfields in the forecast of proton events. Nowadays, the commonly used factors of prediction ofSPE’s include the position and area of active region, configuration of magnetic field, type inMacIntosh classification, 10.7 cm radio flux, X-ray flux etc. [2−6]. In this paper, these factorsare altogether called as traditional forecast factors. If the traditional forecast factors andthe characteristic physical quantities of photospheric magnetic fields are comprehensivelyconsidered in the choice of prediction elements, then the level of prediction of SPE’s may befurther enhanced.

On the basis of Ref.[1], we comprehensively consider the following forecast factors: theposition, area, magnetic configuration and MacIntosh class of active region, 10.7 cm radioflux, soft X-ray flux, maximum horizontal gradient of longitudinal magnetic field, lengthof neutral line of intense gradient, and number of isolated singular points. Then with themethod of BP neural network, a more effective model of short-term forecast of SPE’s in thecoming 24 hours is established.

2. DATA SIFTING

The selected materials of solar magnetic fields are the SOHO/MDI longitudinal magne-tograms of full solar disk[7]. The principles of selection of active region magnetogramsand the methods of calculations of the characteristic physical quantities of magnetic fields(|ΔhBz|m, L, η) are the same as in Ref.[1]. The data of solar soft X-ray flux come from the

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GOES observations∗. All the material of solar active regions (including the areas of activeregions, positions and MacIntosh classes), and the solar 10.7 cm radio fluxes, as well as theproton event data come from the SWPC network station∗∗. The selected period of all thesedata is from Jan.1, 1997 to Dec.31, 2003. Besides, the proton events which occurred duringthe observations of the forecast factors are not taken into consideration [1]. Finally, therehave been selected altogether 1501 MDI magnetograms of 794 active regions, and there are20 corresponding proton events (see Table 1).

3. MODEL BUILDING AND EXAMINATION

In this work the 3-layer BP neural network is adopted. The details and performance of theBP algorithm can be found in Ref.[8]. The input layer corresponds to the forecast factors ofthis paper, which may be used to predict the appearance of proton events in the coming 24hours. In order for the model built by us can yield better results, first of all we have to makethe preprocessing of data. In the following the method of data preprocessing is described.

Via the Boltzmann function

x′ = D2 +D1 − D2

1 + exp[(x − x0)/W ],

the three physical quantities of the magnetic field in active region, i.e., |ΔhBz|′m, L, andη, are transformed to be |ΔhBz|′m, L′, and η′ [1,7]. For the solar soft X-ray flux (Fx), thetransformation is made according to the relation between the probability of occurrence offlares in the coming 24 hours and the Boltzmann function, which is represented by theexpression F

′X . The parameters in this function are listed in Table 2. The details of the

concrete calculation and transformation can be found in Ref.[9].

Table 1 Parameters related to the occurrence of proton events

proton events related flare & active regiontime of time of peak related time of flare active

beginning peak value flux CME flare max. class regionyear- day UT day UT peak flux posi- day UT day UT posi- serialmonth (pfu) tion tion number1997-11 04 08:30 04 11:20 72 W 04 06:10 04 05:58 X2/2B S14W33 81001998-05 02 14:20 02 16:50 150 Halo 02 14:06 02 13:42 X1/3B S15W15 82101999-05 05 18:20 05 19:55 14 Halo 03 06:06 03 06:02 M4/2N N15E32 85252000-02 18 11:30 18 12:15 13 W 18 09:54 17 20:35 M1/2N S29E07 88722000-06 07 13:35 08 09:40 84 Halo 06 15:54 06 15:25 X2/3B N20E18 90262000-06 10 18:05 10 20:45 46 Halo 10 17:08 10 17:02 M5/3B N22W38 90262000-07 14 10:45 15 12:30 24000 Halo 14 10:54 14 10:24 X5/3B N22W07 90772000-11 24 15:20 26 20:30 940 Halo 24 05:30 24 05:02 X2/3B N20W05 92362001-03 29 16:35 30 06:10 35 Halo 29 10:26 29 10:15 X1/1N N14W12 93932001-04 10 08:50 11 20:55 355 Halo 10 05:30 10 05:26 X2/3B S23W09 94152001-10 19 22:25 19 22:35 11 Halo 19 16:50 19 16:30 X1/2B N15W29 96612001-11 04 17:05 06 02:15 31,700 Halo 04 16:35 04 16:20 X1/3B N06W18 96842001-11 22 23:20 24 05:55 18,900 Halo 22 23:30 22 23:30 M9/2N S15W34 97042002-03 17 08:20 17 08:50 13 Halo 15 23:06 15 23:10 M2/1F S08W03 98662002-04 17 15:30 17 15:40 24 Halo 17 08:26 17 08:24 M2/2N S14W34 99062002-07 16 17:50 17 16:00 234 Halo 15 20:30 15 20:08 X3/3B N19W01 302002-11 09 19:20 10 05:40 404 SW 09 13:31 09 13:23 M4/2B S12W29 1802003-05 28 23:35 29 15:30 121 Halo 28 00:50 28 00:27 X3/2B S07W17 3652003-10 26 18:25 26 22:35 466 Halo 26 17:54 26 18:19 X1/1N N02W38 4842003-10 28 12:15 29 06:15 29,500 Halo 28 10:54 28 11:10 X17/4B S16E08 486

∗http://www.ngdc.noaa.gov/stp/SOLAR/ftpsolarflares.html#xray∗∗http://www.swpc.noaa.gov/ftpdir/indices/SPE.txt

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Table 2 Parameters in Boltzmann functions for transforming magnetic field

characteristic quantities (|∇hBz|m, L, η) and solar soft X-ray flux

x D1 D2 x0 W|∇hBz |m 0.164 0.738 521.72 95.472

L 0.062 0.848 763.08 382.97η −0.196 0.730 9.344 22.663

FX −15.57 0.98 −0.46 0.16

Table 3 Classification and transformation of sunspot group areas, magnetic types,

MacIntosh types, and solar 10.7cm radio flux

area (A) > 1000 500∼1000 200∼500 < 200 no sunspotsarea after transformation (A′) 0.38 0.20 0.09 0.03 0

magnetic type (MT) δ βγ, γ β α No sunspotsmagnetic type after transformation (MT′) 0.47 0.34 0.20 0.05 0.0

MacIntosh type (Mac) (a) (b) (c) (d) (e)MacIntosh type after transformation (Mac′) 0.81 0.68 0.31 0.08 0.0

F10.7 fast peak med lowF ′

10.7 0.77 0.69 0.45 0.34

The areas, magnetic types and MacIntosh classes of sunspot groups as well as the10.7 cm solar radio fluxes are also transformed according to their relations with the rate ofoccurrence of flares (see Table 3). The results can be found in Ref.[10].

In combination with the east-west effect in the source regions of proton events, thelongitudinal position Loc of an active region on the solar surface is treated as follows:

L′oc =

⎧⎪⎨⎪⎩

Loc

90× 5.0 (for active regions on the western side of solar surface)

−Loc

90× 5.0 (for active regions on the eastern side of solar surface)

,

The state of occurrence of proton events in the 24h after the time of observation offorecast factors is denoted with the symbol [1,0]. If a proton appears, the symbol becomes1. On the contrary, it is 0. Table 4 lists two examples of the model’s input and outputparameters after the data processing.

Table 4 Examples of model input and output

input layer (forecasting parameter) output layer

A′ MT ′ M ′ac F ′

10.7 L′oc F ′

X |∇hBz |′m L′ η′ with or without SPE0.11 0.34 0.68 0.69 0.44 0.096175 0.25634 0.19847 0.19557 00.24 0.47 0.81 0.77 0 0.096175 0.43358 0.85854 0.34491 1

In the establishment of the model, all the sample data are divided into two parts. Forthe period 1997–2001, there are altogether 1871 sample data which are used as the trainingdata set to build the model of forecast. In 2002–2003, the corresponding number is 973.There are two types of models. In Model A, the input layer contains the traditional forecastfactors, while the characteristic physical quantities of magnetic fields are not included. InModel B both the traditional forecast factors and the characteristic physical quantities ofmagnetic fields are contained. Besides, the BP neural network method requires that thenumbers of sample data which correspond to the cases with and without proton events arethe same. So in the process of training, the number of sample data with the occurrence of

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proton events is increased so that it is equal to the number of sample data without protonevents.

Tables 5 and 6 list the results of measurements and forecasts for the years 2002 & 2003with, respectively, Model A and Model B. Via the comparison of the results and forecasts, itis found that these two models have the same probability of prediction, i.e., 5/8 =62.5%, butthe difference between the rates of false alarms is very large. Model A gives rise to 98 falsealarm, while Model B – 58 false alarms, which is evidently much smaller. This evidentlyimplies that the comprehensive consideration of various factors of forecast can enhancethe ability of prediction of proton events. At the same time, this again demonstrates theeffectiveness of the characteristic physical quantities of magnetic fields in the forecast ofproton events.

Table 5 Results of examination of Model A for the data of 2002 & 2003 years

number of forecast enents0 1

0 867 98number of 89.8% 10.2% 965

observed envents 1 3 537.5% 62.5% 8

total number 870 103 973

Table 6 Results of examination of Model B for the data of 2002 & 2003 years

number of forecast enents0 1 total number

0 907 58number of 94.0% 6.0% 965

observed events 1 3 537.5% 62.5% 8

total number 910 63 973

4. CONCLUSIONS

In Ref.[1] the BP neural network is used to set up the model of short-term forecast ofSPE’s on the basis of the characteristic physical quantities of magnetic field (the maximalhorizontal gradient of longitudinal magnetic field |ΔhBz|m, the length of neutral line withstrong gradient L, and the number of isolated singular points η). This model is adoptedto verify the effectiveness of the characteristic physical quantities of photospheric magneticfields in the prediction of proton events. In order to build a more effective model of short-term forecast of SPE’s, we combine the traditional factors (i.e., the position, area, type ofmagnetic configuration, MacIntosh type , solar 10.7 cm radio flux, soft x-ray flux, etc.) withthe characteristic physical quantities of solar photospheric magnetic fields, and establish amodel of short-term prediction of SPE’s in the coming 24 hours. The model may be dividedinto types A and B. The input layer of Model A contains only traditional forecaster factors,while that of Model B contains both the traditional forecast factors and the characteristicphysical quantities of magnetic fields. By using these two models, the forecasts are madewith the observational data in the years 2002 & 2003. The results reveal that on thecondition of one and the same rate of accurate predictions, the Model B’s rate of false

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alarm is much lower. This affirms that the comprehensive consideration of various factors ofprediction may enhance the ability of forecast of proton events. Besides, this again justifiesthe effectiveness of the characteristic physical quantities of magnetic fields in the short-termforecast of proton events.

It is necessary to mention that the model of short-term forecast of proton events builtin this work is applicable only to the proton events produced by the active regions within the30◦ area around the solar disk center. In our future work and via the effect of projection, weshall successively introduce the characteristic physical quantities of magnetic fields outsidethe 30◦ region, so that a more extensive model of short-term forecast of SPE’s may beestablished.

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