3-3-4 using a neural network to make operational forecasts ... · forecasts of ionospheric...

1 Introduction

As of 2010, solar activity passed the turn-ing point of the minimal period and becameactive again toward the next maximal period.In solar maximum, explosive phenomena suchas solar flares often occur on the sun’s surfaceand disturb the earth’s magnetosphere andionosphere. The ionosphere—a vast plasmaregion spreading from an altitude of about 80km to 1000 km—has been utilized by humansas a reflective layer for radio communicationsusing short-wave propagation. In recent years,space shuttles and numerous satellites havebeen orbiting in and above the ionosphere. Assatellite signals reach the ground passingthrough the ionosphere, fluctuations of ionos-pheric electron density resulting from solaractivity significantly influence satellite signalsutilized for such purposes as satellite position-ing systems.

A drastic fluctuation in ionospheric elec-

tron density is called an ionospheric storm,which is classified into two types: a negativephase ionospheric storm (negative storm) hav-ing reduced density, and a positive phaseionospheric storm (positive storm) havingincreased density. The mechanism of negativestorms is considered as follows: Thermalexpansion of the thermospheric neutral atmos-phere is caused by energy flowing into thepolar region, thereby changing the altitude dis-tribution of neutral atmospheric particles, andincreasing nitrogen molecules (N2) to exceedthe mass of oxygen molecules (O) when thetemperature rises at ionospheric altitudes,resulting in a larger ionospheric recombinationcoefficient and thus reduced electron density［1］.On the other hand, the mechanism of positivestorms cannot be explained by the N2/O ratio;ionospheric plasma moves to higher altitudesfor some reason, resulting in reduced N2 den-sity and thus the recombination coefficientbecomes low. While ionization progresses

391NAKAMURA Maho et al.

3-3-4 Using a Neural Network to Make OperationalForecasts of Ionospheric Variations andStorms at Kokubunji, Japan

NAKAMURA Maho, MARUYAMA Takashi, and SHIDAMA Yasunari

An operational model was developed for forecasting ionospheric variations and storms atKokubunji (35° N, 139° E), 24 hours in advance, by using a neural network. The ionospheric crit-ical frequency (foF2) shows periodic variabilities from days to the solar cycle length and alsoshows sporadic changes known as ionospheric storms caused by geomagnetic storms (of solardisturbance origin). The neural network was trained for the target parameter of foF2 at eachlocal time and input parameters of solar flux, sunspot number, day of the year, K-index at Kakio-ka. The training was conducted using the data obtained for the period from 1960 to 1984. Themethod was validated for the period from 1985 to 2003. The trained network can be used fordaily forecasting ionospheric variations including storms using prompt daily reports of K-index,sunspot number, and solar flux values available on-line.

KeywordsIonosphere, Ionospheric storm, Neural network, Geomagnetic index

392 Journal of the National Institute of Information and Communications Technology Vol.56 Nos.1-4 2009

during the daytime, ionospheric plasma is sup-plied to high altitudes from an altitude ofabout 180km, where the production rate ishigh, resulting in an increased F-layer electrondensity[1]. The rises in ionospheric altitude aremainly considered caused by two reasons:upward movement perpendicular to magneticfield lines produced by the E×B drift due toan eastward electric field originating in themagnetosphere［2］, and upward movement par-allel to magnetic field lines produced throughthe collisions of neutral atmospheric particleswith ions due to thermospheric wind withinthe horizontal plane as directed from the polarregion toward the equator［3］. However, theaccurate forecasting of ionospheric stormsincluding negative and positive phases has yetto be realized due to the difficulty of steadyobservations of the upper atmosphere. Ourstudy targeted the development of a practicalsystem for empirically forecasting ionosphericfluctuations including ionospheric storms byusing a neural network with inputs of solaractivity and geomagnetic activity indices.

The artificial neural network (NN) is a cal-culation algorithm that models the cranialnerves of animals and in recent years has beenused in wide-ranging areas as a mechanismsuited for extracting the characteristics of acomplex phenomenon. The NN can learn therelation between inputs (consisting of multipleelements as the reasons for a given phenome-non) and outputs resulting from that phenome-non (functional approximation capability)[4].With many candidate inputs possibly listeddue to the complexity of ionospheric fluctua-tions as natural phenomena, learning by theNN requires data with qualitative stabilityover an extended period. Moreover, some sort-ing out or other ingenious means may be nec-essary to a certain extent for handling largeramounts of data that entail more time neededfor learning. Both sunspot number and solarflux (indicators of periodic fluctuations insolar activity) are used as inputs of the factorsof periodic ionospheric fluctuations caused bysolar activity. Since ionospheric storms havebeen known in most cases to occur by

responding to magnetospheric disturbances,this study also used the K-index—a geomag-netic activity index indicating magnetosphericfluctuations—as part of the inputs.

Section 2 below describes the configura-tion and learning algorithm of the multi-layerNN used for learning and the inputs/outputs;Section 3 presents the learning and evaluationresults. In addition, Section 4 introduces oper-ation of the newly developed forecasting sys-tem and Section 5 summarizes this study.

2 Constructing a NN model forforecasting ionospheric fluctua-tions

2.1 Multi-layer perceptron and backpropagation method

We used a 3-layer perceptron of the feedforward type in this study. Figure 1 illustratesthe NN configuration. The following explainsthe scheme for learning by the NN. The teachsignals and input elements in the learning willbe discussed in detail in the next section orlater.

The 3-layer perceptron has a so-called hid-den layer between the input and output layers,with all units in one layer being combinedwith all units in the adjacent layer. Each unithas a respective weight, and the learning isperformed by making weight adjustments.

The learning algorithm used is referred toas the back propagation method, where a com-bination of weights is determined throughrepetitive learning so that the square sum oferrors in the target signals and outputs is mini-mized for combination. The adjusted amountof weights is then back-propagated from out-put to input during the learning process inorder to update the NN. The following showsthe algorithm of the back propagation method.Note that there may generally be more thanone output, although the NN configured forthis study only includes one output. The algo-rithm shown below is intended for multiplenumbers (m) of outputs［5］.

Assume that every unit has the weight ofω in the network with n inputs and m out-


δpj＝βopj（1－ opj）（tpj－ opj）,

Unit for the hidden layer:

Σk is given as the sum of errors for allunits k of the next layer to which unit j sendsthe outputs.5. Using corrective amount Δpωji =ηδpj opj of

the weight, weight ωji is corrected for eachlayer from output layer toward input layeras follows:

ωji ←ωji＋Δpωji

6. The learning is deemed completed whensquared error E for all learning patterns isequal to or less than the set value. Other-wise, steps 2 to 5 are repeated for all learn-ing patterns.

2.2 F2 layer critical frequency (foF2)as a target signal

The critical frequency of the F2 layer(foF2), a parameter that expresses the state of

puts. In addition, a unit referred to as thresh-old element is adopted for input as the (n+1)thelement.1. Initialize values of all weights ωji (i = 1, ...,

n +1; j = 1, ..., m) to random small values.Learning rate η (0 < η < = 1) is also set.

2. Target output tp = (tp1, ..., tpm) and corre-sponding input pattern vector ip = (ip1, ...,ipm, 1) are given.

3. Using given weight ωji (i = 1, ..., n +1; j =1, ..., m) and input pattern vector ip, the out-put of each unit from the input layer towardthe output layer is calculated as follows:

Note that f is a logistic function.4. Using determined output Opj and target out-

put tpj (j = 1, ..., m), error δpj of unit j corre-sponding to pattern p is calculated from theoutput layer toward the input layer. Error δpj

is classified as a unit either for output or thehidden layer, and each δpj is determined asfollows:

Unit for the output layer:

Fig.1 Configuration of the neural network


ionospheric fluctuations, is used as the teachsignal of the NN in this study. Note that foF2is also a parameter given by observationsusing a vertical sounder called an ionosonde(Fig. 2), and is one of the parameters readfrom ionograms (Fig. 3) produced fromionosonde observations. The ionogram showsan altitude profile of ionospheric electron den-sity, where the reflective altitudes of radiowaves swept by radar are plotted with the lat-eral and vertical axes denoting frequency andaltitude, respectively. Ionosonde observationhas a history of over 50 years at four locationsin Japan: Wakkanai, Kokubunji, Yamagawaand Okinawa.

Figure 4 shows the general behavior andperiodic fluctuations of foF2. In this figure,plotting is made using the foF2 observationaldata, sunspot numbers, and solar fluxes for the14 years from 1990 to 2004. It is obvious fromthe figure that the sunspot number and solarflux correlate with long-term fluctuations in

foF2. Note that foF2 peaks in spring andautumn, and increases in the maximal periodof solar activity up to several times the level inthe minimal period.

A 15-minute ionosonde observation yields96 foF2 data items per day, and we used anhourly value (of 24 foF2 data items per day),since learning requires data over a span of atleast 20 years. Here, foF2 was extracted fromthe data given by ionograms for the periodfrom 1960 to 2002［6］and values normalizedwith the maximum value in the period wasused for learning.

Fig.2 10C type ionosonde transceiver

Fig.3 Scheme of ionospheric observation

Fig.4 Long-term ionospheric fluctuations


2.3 Input parametersPeriodic fluctuations in the ionosphere can

roughly be considered a superposition of threecomponents of cyclic fluctuations: 11-yearfluctuations due to the 11-year solar cycle,seasonal fluctuations, and daily fluctuationsdue to solar irradiation. Geomagnetic fluctua-tions causing ionospheric storms must also beinput for the NN in addition to these threecyclic fluctuations. The following describesthe input parameters and numerical processingperformed for learning in detail.2.3.1 Sunspot number

Solar activity fluctuates in a cycle of about11 years and entails fluctuations of extremeultraviolet (EUV) solar radiation, which con-tributes to the production of F-layer ionos-pheric electron density. Thus, the ionosphereis significantly influenced by solar activity.There is also the sunspot number as an indexfor indicating solar activity. Such phenomenalactivity as a solar flare or coronal mass ejec-tion (CME) is known to occur at places sub-ject to the sun's intense magnetic field (knownas sunspots). Multiple sunspots often appear ina state of gathering (referred to as sunspotgroup). Sunspot relative number R is definedby using f to denote the total number ofsunspots existing in all sunspot groups visibleon the entire surface of the sun, g the numberof sunspot groups, and k the coefficient forcompensating for variances caused byobservers and/or telescopes as follows:

R＝k（10g＋ f）（1）

In the solar activity cycle of about 11years, a period with maximum R is referred toas the solar maximum, and that with minimumR as the solar minimum. R fluctuates not onlyin the 11-year solar cycle but also in a 27-daycycle due to the sun’s rotation. The observedsunspot number is quantitative data consistent-ly accumulated according to evaluation equa-tion (1) since more than 300 years ago, andhigh accuracy regarding the cyclic nature ofsunspot number fluctuations is statisticallyguaranteed［7］. Thus, the NN uses the sunspot

number as one item of input data. To prepareinput data for this study, one data item per daysince 1960 was taken［8］with its normalizationmade with the maximum value in the periodfrom 1960 to 2002. Since the learning did notsatisfactorily converge with the daily data,smoothing was done using the numerical val-ues of 3 and 27 days before each subject day,in order to use the two resultant sunspot num-bers for input. 2.3.2 Solar flux

Another index for indicating solar activityis solar flux (F10.7), which is defined as theintensity of solar radio waves having a wave-length of 10.7 cm (2800 MHz) showering theearth as measured at Ottawa, and indicated inunits of 10－22 (W/m2Hz). One observationaldata item per day of solar flux (F10.7) can betaken. To prepare inputs, we also employedthe F10.7 data since 1960［9］and normalizedthat data with the maximum value. Similarlyto the case of sunspot numbers, large fluctua-tions only appeared when using the daily dataand learning did not satisfactorily converge. Agood convergence resulted from taking 3- and27-day averages to smooth the data and usingthe results for input. 2.3.3 Seasonal fluctuations

The second most significant factor ofionospheric fluctuations following solar activ-ity is seasonal fluctuations. Changes in theamount of incoming solar irradiation due tothe positional relation of latitude/longitudewith the sun significantly affect generation ofthe ionosphere. The Day of Year (DOY) isused for inputting seasonal fluctuations. Therepetitive use of DOY—consisting of 1 to 365days (or 366 days)—results in a drastic drop atthe return from 365 to 1. To avoid such dis-continuity of data, two input data items (DOY1 and DOY 2) were prepared as shown below,along with respective sin and cos calculations.In addition, each input was normalized to fallwithin the range of 0 to 1 in order for the NNto learn.


2.3.4 Daily fluctuationsTo incorporate daily fluctuations due to

solar irradiation into inputs, learning was per-formed with each local one-hour value, asclassified into 24 values. The learning periodswere independent of each other. The outputdata were arranged in order of time for execu-tion, and normalized with the maximum valuein the learning period at each one-hour valuefor learning. 2.3.5 Geomagnetic activity K-index

Cyclic fluctuations due to solar activityand seasonal fluctuations are consideredreproducible by using solar observational dataand DOY input. However, for accidental fluc-tuations such as ionospheric storms, geomag-netic fluctuations causing such storms must beadded to the inputs. There is a delay of aboutone to two days for an accidental solar fluctu-ation to reach and influence the earth’s ionos-phere by passing through the magnetosphere.By using this delay, learning informationabout one day before in the NN enables fore-casting.

A variety of geomagnetic activity indiceshave been proposed and used by geomagneticobservatories covering the entire world toquantitatively capture various magnetosphericdisturbances. There are wide-ranging indicessuch as the AE index for monitoring aurorabehavior in the polar region, Dst index forindicating ring currents developed duringmagnetic storms, ap index for indicating thelevel of geomagnetic activity in the mid-lati-tude region, and Kp index linearly convertedfrom the ap index［10］. The Kp index averagesthe K-index, a local geomagnetic activityindex for various regions, and has been widely

used as an index for indicating geomagneticactivity of the entire earth. In addition, the Kpindex is considered suitable as input for learn-ing, since this index can monitor the occur-rence of geomagnetic disturbances that pro-duce ionospheric fluctuations. In fact, manystudies on ionospheric fluctuations conductedin Europe have actually used the ap or Kpindex［12］–［14］. However, these indices lackpromptness and require much time for fixingvalues. In contrast, among the K-indices usedfor determining the Kp index, the Kakioka K-index［15］observed at the Kakioka Geomag-netic Observatory in Japan shows promptnesswhere its preliminary figures for each day areannounced the next morning to enable earlyuse as inputs for forecasting. Targeting theconstruction of a more practical forecastingsystem, we decided to use the K-indices asinputs of geomagnetic activity indices. Inaddition, as the AE index reflects energy flow-ing in from the magnetosphere more sensitive-ly than the K or Kp index, it should essentiallybe included in the inputs. However, there is aninsufficient period for the database to accumu-late the AE index as provisional values. Thus,we did not use the AE index since the learningrequired for the NN may be degraded. Once asufficient amount of data is accumulated overseveral years, the AE indices may be used asinputs.

The K-indices indicate the degree of geo-magnetic disturbance in integers from 0 to 9,with eight points of the daily indices beingcalculated every three hours in universal time.Note that the component of daily fluctuationsremains included in the Kakioka indices［16］(but removed from the Kp indices due to aver-aging), and 20 K-indices equivalent to 2.5days were used as inputs for learning by theneural network. Numerical values normalizedwith the maximum number of 9 were used forlearning. In addition, ΣK or the sum of eightK-indices for a given day has been used toindicate disturbances during a given day.Table 1 shows the relation of ΣK with thedegree of geomagnetic disturbance proposedby the Kakioka Geomagnetic Observatory［17］.


ΣK well expresses the degree of geomagneticdisturbance. However, it is known that theinfluences of geomagnetic fluctuations on theionosphere vary depending on local time［1］;therefore, in order to effectively incorporatethe local time dependence into inputs of thisstudy, we extracted 10 examples of largeionospheric storms that occurred in the pastand conducted superposition analyses for pat-terns of geomagnetic fluctuations known tohave caused ionospheric storms. Figure 5shows the results. The horizontal axis repre-sents local time and a superposition is madefor fluctuation patterns of K-indices for 3.5days prior to the occurrence of ionosphericstorms. The vertical axis represents the sum of

totalized K-indices and error bars are used toindicate standard deviation for the number ofevents. The results of analyses indicate thatthe fourth to seventh K-indices (indicated byarrows) from the previous day to the day whenan ionospheric storm occurred exceed the nor-mal level. Based on these results, we decidedto split the eight K-indices at eight points in aday into two for use as inputs: the sum ofindices corresponding to four points (4th to7th) in a day and the sum of indices corre-sponding to the 8th point in said day, includ-ing the 1st to 3rd points the next day. The K-index resulting from this summing process isdefined as Σ’K, which is equivalent to the twodays added to the inputs for learning. Notethat Σ’K was also normalized with the possiblemaximum value of 36.

2.4 Configuration of the networks andlearning parameters

The network was structured in three layerswith a total of 30 inputs and one output, andone-hour value of foF2 was used for a targetsignal. A total of 24 NNs were configured foreach time division for learning, and outputsfrom each NN were arranged in order of timefor execution. Note that small initial values ofweight were set in the range from – 0.5 to 0.5by using random numbers.

Once inputs and outputs were determined,a network could be configured. For actuallearning in the NN, however, learning parame-ters must be properly set in order for the learn-ing to converge. Some parameters were avail-able regarding the learning momentum todetermine learning speed, number of data pat-terns used for learning, and number of hiddenlayers in the network. These parameters weredetermined based on learning being executeda number of times with a review made aftereach execution on a trial-and-error basis.Table 2 summarizes the learning parametersused in this study.

The termination of learning may be deter-mined when the learning error drops below theset value［5］. However, in actual learning,reviewing only the error does not provide a

Table 1 Degree of geomagnetic distur-bance and ∑K

Fig.5 Superposition analyses of geomag-netic K-index fluctuation patternsprior to a large ionospheric storm


basis for judging whether learning is proceed-ing in good condition. As such, we set a targetlearning error to a very small value and ranmany cycles of learning while monitoring theprocesses of square and generalization errorsduring the learning process. The generaliza-tion error is defined as a square error for datanot used for learning, thereby functioning asan index of generalization capability of thelearning process. As learning proceeded, thesquare error was gradually and steadilyreduced to converge with a certain value,while the generalization error relative to anobservational value generally increased from acertain point. The latter phenomenon is knownas over-learning, where the capability of gen-eralizing unlearned data is considered deterio-rated. For execution, we used the weight at thepoint where the generalization error beganincreasing during learning in each local time(LT) and recorded the number of learningcycles at that point as the cycle providing thebest learning results. There were about 7,000cycles of learning based on such a manner forthe entire time zone.

3 Results of learning and its evalu-ation

To review the reproducibility of periodicfluctuations due to solar activity, the results oflearning about fluctuations are described interms of several tens of years, seasons, anddays (as described in Section 3.1), and theirerrors are compared with those given by theresults from the IRI empirical model for the

ionosphere (described in Section 3.2). Inaddition, reproduced examples and forecastingscores including the negative/positive phasesof ionospheric storms are described (in Sec-tion 3.3).

3.1 Reproducibility of periodic fluctua-tions

3.1.1 Reproducing long periodic fluc-tuations (11-year solar cycle)

First, Fig. 6 shows a reproduced long-termfluctuation. This figure also compares one-hour observational value of foF2 (shown inthe middle) with outputs of one-hour valuefrom the NN (shown at the bottom) for theperiod of 1985 to 1996, from which no datawas picked for learning. Moreover, the aver-age fluctuation over three days is also shownat the top in terms of sunspot number (solidline) and solar flux (dotted line). The outputsfrom the NN well reproduced the fluctuationsof the observational foF2 in synchronism withthe approximative 11-year cycle of solar activ-ity. In addition to this 11-year cycle, it is alsoobvious that annual and seasonal fluctuationsare reproduced. Note that outputs from the NNshow less scattering of values compared toobservational values. This implies that the NNcannot necessarily follow extreme increases ordecreases in values, which may occur at suchabnormal events as ionospheric storms.3.1.2 Reproducing seasonal and daily

fluctuationsFigure 7 is presented to review the repro-

ducibility of seasonal and daily fluctuationswith data plotted for seven days. In this figure,the data of a relatively quiet seven days interms of geomagnetic activity were selectedand extracted from 1992 (right column) as thesolar maximum period, and from 1985 (leftcolumn) as the minimum period for March(top), August (middle) and October (bottom),thereby allowing a comparison to be made byfocusing on observational values (dotted line)and outputs from the NN (blue solid line). It isobvious from the figure that normal values inboth maximum and minimum periods are wellreproduced with the NN for each season.

Table 2 Learning parameters


3.2 Comparison with an empiricalmodel (IRI)

A comparison was made relative to a com-monly used empirical model known as inter-national reference ionosphere (IRI)［18］. IRI

uses a geomagnetic index referred to as the apindex instead of the K-index for indicatingmagnetospheric influences. By using IRI, weprepared outputs with an identical one-hourvalue for the same period as for the NN (1985

Fig.6 Reproducing long cyclic fluctuations

Fig.7 Reproducing seasonal and daily fluctuations


to 1996). By using both methods, we com-pared square errors of outputs from the NNand IRI in the same period to actual observa-tional values. First, correlation coefficientswith respect to the observational values werecalculated and compared for each year duringthe period (Fig. 8). The correlation coefficientfor outputs from IRI dropped to 0.76 due tolarge errors in the solar maximum period,while the coefficient for those from the NNconstantly remained above 0.92 through bothmaximum and minimum periods.

Next, the square errors for each LT werecompared in the maximum and minimum peri-ods (Fig. 9).

According to Fig. 9, reproduction by the

NN is considered better in terms of accuracythan that by IRI in most time periods in springand autumn during both maximum (left col-umn) and minimum (right column) periods.The electron density is highest in spring andautumn during the year. There are large errorsin outputs from IRI (upper level) in time peri-ods around evening during both maximum andminimum periods. In contrast, no significantbias on errors due to local time is observedwith outputs from the NN. The reasoningbehind the error bias on IRI is considered alack of observational data in Asia (includingJapan).

3.3 Reproducing ionospheric storms3.3.1 Example of forecasting ionos-

pheric stormsThe following describes three successful

examples of forecasting negative and positivestorms. Figures 10 to 15 indicate forecastedstorms for three days including the day onwhich an ionospheric storm occurred. The toplevels in the figures indicate a transition in theK-index; the middle levels indicate observedfoF2 (red dot), forecasted foF2 (blue dottedline), and the median value for 27 days beforethe observational day (black solid line). Inaddition, the bottom levels indicate the vari-ance between values forecasted by the NNusing actual K-indices and those forecastedunder the assumption that geomagnetic activi-ty quietly underwent a transition (where all

Fig.9 Comparison of square errors in spring and autumn during maximal and minimal periods atlocal time for the NN and IRI model

Fig.8 Comparison of correlation coeffi-cient between NN outputs andobservational values with thatbetween the IRI model and obser-vational values for 12 years (onesolar cycle)


inputs for K-indices become 1) during NNexecution. Ionospheric storms forecasted asbeing reduced in number from a quiet periodare indicated with blue bars, while stormsforecasted as being increased in number areindicated with red bars.

Figures 10 to 12 show three examples ofsuccessfully forecasted negative storms. Fig-ures 10 and 11 each show an example of fore-casting an event, where a negative stormoccurred two days after the occurrence ofmagnetic storms. In both examples, the K-indices underwent a transition with a value of3 or more from the afternoon to evening of thesecond day. In Fig. 11, the fourth K-index(18:00 to 20:00 LT) increased to 6 and thefifth K-index (21:00 to 23:00 LT) to 7 on May22, 2002. This coincides with the trend ofmagnetic fluctuation patterns on the daybefore and two days before as given by super-position analyses shown in Fig. 5. Figure 12shows an example of relatively quiet negative

storms that occurred from December 29 to 31,2002. The sum of daily K-indices (ΣK) under-went a transition of 20, 16, 11 and 11 duringthe four days from December 28 through 31.The four-day ΣK implies relatively quiet dis-turbances according to Table 1, which showsthe degree of geomagnetic disturbance pro-posed by the Kakioka Geomagnetic Observa-tory. Consequently, the forecasting is under-stood as being made for cyclic geomagneticdisturbances due to coronal holes occurringduring an approximate 27-day cycle of solaractivity.

Next, Figs. 13 to 15 show three examplesof successfully forecasted positive storms. Inthe example for the period of November 20 to22, 2002 (in Fig. 13), the K-index increased to5 on November 20, with about the same levelof geomagnetic disturbance being retained

Fig.10 Example 1 with negative stormsforecasted on May 12, 2002

Fig.11 Example 2 with negative stormsforecasted on May 24, 2002

Fig.12 Example 3 with negative stormsforecasted on December 31, 2002

The top level indicates the K-index; the mid-dle level indicates the observational foF2 val-ues (red dot), outputs (blue dotted line)obtained by the NN, and monthly medianvalues of observational values (solid line);the bottom level indicates forecasted fluctua-tion by using variances relative to outputswhen setting K to a constant value (K = 1) inthe NN, where red indicates an increasingtrend of fluctuation from a quiet period, andblue indicates a decreasing trend. The sameapplies to other related figures.


over the next two days. Following these mag-netic disturbances, positive storms occurred inthe ionosphere for several days. Based on acomparison of median values (solid line) andobservational values (red dot) shown in themiddle of the figure, ionospheric electron den-sity is understood as having only increasedduring the daytime and not at nighttime. Suchlocal time dependence was also reproduced

well in the NN. Figures 14 and 15 show exam-ples indicating magnetospheric and ionospher-ic disturbances that continued for three daysafter intense solar flares occurred on October28, 2003. In this event, the intensity of solarflares reached abnormally high X17.2 onOctober 28, 2003 11:51 UT; and was laterreferred to as the “Halloween Event” due tothese almost unprecedented magnetic stormsin history. The magnetic disturbances thenlasted until 6:11 UT (15:11 JST) on October29［19］. Although the ionosphere was drasti-cally disturbed in responding to these geomag-netic disturbances, the NN could forecastthese disturbances very accurately over a widerange. Satellite positioning systems and simi-lar systems were forecast as being influencedby such a drastic event due to the drastic dis-turbances or changes in ionospheric electrondensity. The NN is considered significant forconstructing an ionospheric storm forecastingsystem, since it at least forecasted the occur-rence of such drastic disturbances.3.3.2 Score of forecasting ionospheric

stormsTo comprehensively discuss forecast accu-

racy, we newly introduced ionospheric distur-bance index δobs, the basis of which lies inobservational values. Index δobs is defined asthe variance between the average and monthlymean values of foF2 taken from 6 a.m. until 6p.m. on a given day. The days on which posi-tive and negative storms occurred are definedas those with δobs of 1 MHz or more and –1

Fig.15 Example 3 with positive stormsforecasted on October 31, 2003

Fig.14 Example 2 with positive stormsforecasted on October 28, 2003

Fig.13 Example 1 with positive stormsforecasted on November 22, 2002The top level indicates the K-index; the mid-dle level indicates the observational foF2values (red dot), outputs (blue dotted line)obtained by the NN, and monthly mean val-ues of observational values (solid line); thebottom level indicates forecasted fluctuationby using variances relative to outputs whensetting K to a constant value (K = 1) in theNN, where red indicates an increasing trendof fluctuation from a quiet period, and blueindicates a decreasing trend. The sameapplies to other related figures.


MHz or less, respectively. In addition, a daywith 0.6 MHz ≤ |δobs | ≤ 1 MHz is specified asa semi-disturbance day and that within 0.6MHz downwardly or upwardly beyond therange as a quiet day. Similarly, disturbanceindex δNN is defined for outputs from the NN.Table 3 lists the relations between δobs and δNN.During the 11 years (4,383 days) used for theevaluation, negative storms were observed on225 days, including 93 days forecasted by theNN as days of negative storms and semi-dis-turbance (negative), 13 days of positive stormsand semi-disturbance (positive), and 119 daysof no particular disturbance (quiet range).Conversely, positive storms were observed on275 days, including 97 days forecasted by theNN as days of positive storms (includingsemi-disturbance), 20 days of negative storms,and 158 days of no disturbance. The resultsindicate a total of 3,179 quiet days, including2,262 days forecasted within the range of 0.6MHz. Thick characters in the table indicatethe number of days correctly forecasted, or2,488 days out of the total of 4,383 days(56.8%). The shaded cells indicate the daysforecasted significantly incorrectly, or 661days out of the 4,383 days (15.1%), and cellswith thin characters on a white backgroundindicate the days forecasted incorrectly but notsignificantly.

4 Disclosing the forecasting sys-tem using the neural network

The following lists the functions requiredfor practically forecasting ionospheric fluctua-tions.

- Providing latest (semi-real-time) infor-mation

- Automatically updating and disclosingdata on websites

- Showing data of about three days tocheck the transition of ionospheric fluc-tuations

- Showing the observational and monthlymedian values, in order to check changesin values for normality and abnormality

To fulfill this requirement, we prepared asystem that automatically acquired informa-tion on sunspot numbers［8］, solar fluxes［9］,and geomagnetic K-indices［15］from a websiteupdated daily, and then added this information toa database as inputs for the neural network［20］.The neural network automatically accesses thedatabases once a day, executes forecasting andupdating, and then updates the plots of fore-casted values externally disclosed on the serv-er. The system is currently disclosed on thewebsite of the National Institute of Informa-tion and Communications Technology, RadioPropagation Project at http://wdc.nict.go.jp/(as shown in Fig. 16).

Table 3 Accuracy of forecasting ionos-pheric storms

Fig.16 Website disclosure of ionosphericfluctuation forecasting


5 Conclusion

In this study, we constructed a system forforecasting ionospheric fluctuations about 24hours ahead in the skies over Tokyo by using aneural network. We targeted constructing asystem capable of practical use in the fields ofshort-wave and satellite communications byforecasting fluctuations 24 hours ahead, aswell as accommodating normal cyclic fluctua-tions in the ionosphere and also accidentalfluctuations in the negative/positive phases ofionospheric storms.

The ionospheric electron density is knownto be determined by the balance between thegeneration of plasma due to extreme ultravio-let radiation and its elimination due to atmos-pheric chemical reactions involving signifi-cant solar activity. In addition, accidental dis-turbances such as chromospheric eruptionsdisturb the geomagnetosphere and triggeraccidental fluctuations in the ionosphere.Based on these facts, ionospheric fluctuationsequivalent to two cycles of solar activity (from1960 to 1984) were learned by using a neuralnetwork provided with inputs of sunspot num-bers and solar fluxes that represent solar fluc-tuations, and K-indices that represent geomag-netic activity. The neural network used theback propagation method of a 3-layer percep-tron, where many trials were made on combi-nations of inputs and learning parameters, inorder to determine the best suited learning.During the course of parameter adjustments, itbecame empirically apparent that many countsof learning were essential for stable learningby a large neural network, and that the finalresults of learning were largely affected by thesorting-out of input parameter combinations.

We were able to improve the accuracy of fore-casting ionospheric storms by newly definingand adding Σ’K to the inputs used in thisstudy. The learning was evaluated for a period(from 1985 to 1996) not used for learning.Consequently, learning was well executedwith long-term fluctuations over a period ofabout 11 years due to solar activity, along withannual, seasonal and daily fluctuations, and amodel was established with better accuracythan the commonly used IRI model. Ionos-pheric storms could also be forecasted, includ-ing increases or decreases in the electron den-sity for many events. However, forecastingionospheric storms also failed on many occa-sions, thereby requiring further improvementsin forecasting probability. In the future, a sys-tem offering better accuracy in forecastingionospheric storms should be constructed byusing solar wind and time variations of geo-magnetic storms as input data. A similar sys-tem should also be developed for the skies notonly over Tokyo but also over the area stretch-ing from Hokkaido to Kagoshima and Oki-nawa, where ionospheric observations are pro-vided. Once realized, both systems are expect-ed to be useful for modeling the ionosphericdelay, and forecasting and establishing mea-sures for disturbances in the growing field ofsatellite communications.

Acknowledgments

We wish to thank our colleagues in theSpace Environment Group and the staff at theWorld Data Center (WDC) for Ionosphere forproviding the ionogram data, and the staff atthe Kakioka Geomagnetic Observatory forproviding the Kakioka K-indices.

References01 G. W. Prölss, "Ionospheric F-region storms," Vol. 2 of Handbook of Atmospheric Electrodynamics, CRC

Press, 1995.

02 N. Matuura, "Theoretical models of ionospheric storms," Space Sci. Rev., Vol. 13, pp. 124–189, 1972.

03 T. Maruyama, "4.4 Ionospheric storm," Wave Summit Course, Science of Space Weather, edited by K.

Marubashi and T. Ondoh, Ohm-sya, 2000. (in Japanese)

04 K. Funahashi, "On the approximate realization of continuous mappings by neural networks," Neural Net-


works, Vol. 2, pp. 183–192, 1989.

05 S. Haykin, Neural Networks: A Comprehensive Foundation, Prentice Hall PTR, Upper Saddle River, NJ,

1994

06 World Data Center for Ionosphere, 2000. http://wdc-c2.nict.go.jp/

07 Memcalc, Questions and Answers. http://www.gms-jp.com/MemCalcHP/4-1.htm

08 Pierre Cugnon, "SIDC RWC Belgium World Data Center for the Sunspot Index," 4 2002.

http://sidc.oma.be/index.php3/

09 Solar radio monitoring programme. http://www.nrc-cnrc.gc.ca/eng/services/hia/radiomonitoring.html

10 World Data Center for Geomagnetism, Kyoto. http://swdcwww.kugi.kyoto-u.ac.jp/wdc/Sec3.html

11 O. Altinay, E. Tulunay, and Y. Tulunay, "Forecasting of ionospheric critical frequency using neural net-

works," Geophys. Res. Lett., Vol. 24, pp. 1467–1470, 1997.

12 P. Wintoft and Lj. R. Cander, "Ionospheric foF2 storm forecasting using neural networks," Phys. Chem.

Earth, Vol. 25, No. 4, pp. 267–273, 2000.

13 L. A. Williscroft and A. W. V. poole, "Neural networks, foF2, sunspot number and magnetic activity," Geo-

phys. Res. Lett., Vol. 23, No. 24, pp. 3659–3662, December 1996.

14 E. O. Oyeyemi, A. W. V. Poole, and L. A. McKinnel, "On the global short-term forecasting of the ionos-

pheric critical frequency foF2 up to 5 hours in advance using neural networks," Radio Sci., Vol. 40, No.

RS6012, 2005, doi: 10.1029/2004RS003239.

15 Kakioka Magnetic Observatory. http://www.kakioka-jma.go.jp/

16 T. Yumura, "On the "three-hour-range indices" K at Kakioka," Memoirs of the Kakioka Magnetic Observa-

tory, Vol. 6, pp. 1–17, 1951.

17 K. Koike, "Statistics of the k-index," Kakioka Magnetic Observatory, Gijutsu Hokoku, Vol. 31, pp. 32–46,

1991.

18 D. Bilitza, K. Rawer, L. Bossy, and T. Gulyaeva, "International reference ionosphere-past, present,

future," Adv. Space Res., Vol. 13, No. 3, pp. 3–23, 1993.

19 M. A. Abdu, T. Maruyama, I. S. Batista, S. Saito, and M. Nakamura, "Ionospheric responses to the Octo-

ber 2003 superstorm: Longitude/local time effects over equatorial low and middle latitudes," J. Geo-

phys. Res., Vol. 112, No. A10306, 2007, doi: 10.1029/2006JA012228.

20 M. I. Nakamura, T. Maruyama, and Y. Shidama, "Using a neural network to make operational forecasts

of ionospheric variations and storms at Kokubunji, Japan," Earth Planets Space, Vol. 59, pp. 1231–1239,

2007.


NAKAMURA Maho, Ph.D.

Expert Researcher, Space-Time Standards Group, New Generation Network Research Center

Ionosphere, Information Engineering

MARUYAMA Takashi, Ph.D. (Eng.) Executive Researcher

Upper Atmospheric Physics

SHIDAMA Yasunari, Ph.D.

Professor, Faculty of Engineering,Department of Computer Science &Engineering, Shinshu University

Mathematical and ComputationalAnalysis of Nonlinear Systems

3-3-4 using a neural network to make operational forecasts ... · forecasts of ionospheric...

Documents