a recurrent neural network approach to quantitatively studying … · 2020. 6. 19. · a....

Ann. Geophys., 27, 2111–2125, 2009www.ann-geophys.net/27/2111/2009/© Author(s) 2009. This work is distributed underthe Creative Commons Attribution 3.0 License.

AnnalesGeophysicae

A recurrent neural network approach to quantitatively studyingsolar wind effects on TEC derived from GPS; preliminary results

J. B. Habarulema1,2, L.-A. McKinnell 1,2, and B. D. L. Opperman1

1Hermanus Magnetic Observatory, 7200 Hermanus, South Africa2Department of Physics and Electronics, Rhodes University, 6140, Grahamstown, South Africa

Received: 23 June 2008 – Revised: 16 March 2009 – Accepted: 29 April 2009 – Published: 7 May 2009

Abstract. This paper attempts to describe the search for theparameter(s) to represent solar wind effects in Global Posi-tioning System total electron content (GPS TEC) modellingusing the technique of neural networks (NNs). A study iscarried out by including solar wind velocity (Vsw), protonnumber density (Np) and theBz component of the interplan-etary magnetic field (IMFBz) obtained from the AdvancedComposition Explorer (ACE) satellite as separate inputs tothe NN each along with day number of the year (DN), hour(HR), a 4-month running mean of the daily sunspot number(R4) and the running mean of the previous eight 3-hourlymagnetic A index values (A8). Hourly GPS TEC values de-rived from a dual frequency receiver located at Sutherland(32.38◦ S, 20.81◦ E), South Africa for 8 years (2000–2007)have been used to train the Elman neural network (ENN) andthe result has been used to predict TEC variations for a GPSstation located at Cape Town (33.95◦ S, 18.47◦ E). Quantita-tive results indicate that each of the parameters consideredmay have some degree of influence on GPS TEC at certainperiods although a decrease in prediction accuracy is also ob-served for some parameters for different days and seasons.It is also evident that there is still a difficulty in predictingTEC values during disturbed conditions. The improvementsand degradation in prediction accuracies are both close to thebenchmark values which lends weight to the belief that di-urnal, seasonal, solar and magnetic variabilities may be themajor determinants of TEC variability.

Keywords. Ionosphere (Mid-latitude ionosphere; Modelingand forecasting; Instruments and techniques)

Correspondence to:J. B. Habarulema([email protected])

1 Introduction

The solar wind-magnetosphere-ionosphere (SW-MAG-ION)system is not an easy phenomenon to breakdown in orderto deal with the respective physical mechanisms responsi-ble for the physics and chemistry describing the behaviourof different constituent ions and molecules that contributeto the changes of ionospheric parameters. According toLyon (2000), the SW-MAG-ION form a single system thatowes its existence to the energy and momentum transferfrom the solar wind to the ionosphere through the magne-tosphere. Among the ionospheric parameters influenced bythis transfer of energy is the total electron content (TEC) es-pecially during geomagnetic storms. One of the first exper-imental evidence between the solar wind and variations inelectron content was reported bySethia et al.(1978) wherean inverse relationship between plasmaspheric TEC and so-lar wind velocity was observed during the pre-storm andstorm conditions. A more recent study pointed out that sep-arating agents responsible for ionospheric disturbances es-pecially during magnetically disturbed conditions is com-plicated due to the complexity of the correlation betweenthe solar wind dynamics and ionospheric variations (Biktashet al., 2008). Biktash et al.(2008) showed that the solar windplays an important role in controlling the equatorial iono-sphere during geomagnetic storms by explaining the IMFBz

effects on ionospheric parameters. While most works con-sidered the study of ionospheric behaviour with respect tosolar wind dynamics before, during and after storm condi-tions (e.g.Meza et al., 2005; Fedrizzi et al., 2005; Biktashet al., 2008; Li et al., 2008), this paper attempts to find aquantitative relationship between solar wind and TEC vari-ability through modelling and taking into account both quietand disturbed circumstances over a relatively long period oftime. Like other ionospheric parameters, TEC varies non-linearly and this makes quantifying its fluctuations throughanalytical algorithms a complicated task and therefore it is

Published by Copernicus Publications on behalf of the European Geosciences Union.

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2112 J. B. Habarulema et al.: A quantitative study of solar wind effects on TEC derived from GPS

Inputs INPUT LAYER HIDDEN LAYER OUTPUTLAYER

TEC

COPY LAYER

Fullconnection

Fullconnection

Recurrentlinks

Recurrentlinks (one−one connection)

(consisting of contextunits)

Fig. 1. An Elman neural network structure having one input, one hidden and one output layers.

Identification of physicalparameters that influenceTEC variability

Search for data to represent theidentified parameters

Processing of datain a form that is compatible with NNapplications

Division of the datasetinto training, testing

patterns

Determination of theoptimum architectureusing the training and validating patterns

Predicting TEC values using the testing datasetpattern

accuracy by comparing the predicted and actualmeasured TEC values

Computing the prediction

and validating

Fig. 2. A flow diagram illustrating the procedure followed during the modelling of TEC undertaken in this study.

preferable to resort to empirical modelling. In this regard,given enough historic data describing the variational patternof a certain physical quantity, neural networks (NNs) haveproved to be relatively efficient in estimations or predic-tions involving non-linear approximations particularly TECin terms of physical and geophysical parameters (Hernandez-Pajares et al., 1997; Tulunay et al., 2006; Habarulema et al.,2007, 2009). The understanding of TEC variability, its fore-

casting and now casting is very beneficial for applicationsinvolving long range communications, GPS surveying, nav-igation and other space weather related activities (Stankovet al., 2001; Tulunay et al., 2006). According to the knowl-edge of the authors, no published work is currently availableso far that quantifies the solar wind effects on GPS TEC overthe African region. The attempt undertaken byHabarulema(2007) on a small database over the Square Kilometer Array

Ann. Geophys., 27, 2111–2125, 2009 www.ann-geophys.net/27/2111/2009/

J. B. Habarulema et al.: A quantitative study of solar wind effects on TEC derived from GPS 2113

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Fig. 3. Comparison between hourly GPS TEC and the corresponding predictions for(a) T (Sp), (b) T (Sp, Bz), (c) T (Sp, Np) and(d) T (Sp,Vsw); for day 58 in 2005.

(SKA) Hub location (30.71◦ S, 21.39◦ E), South Africa at10:00 UT showed that a parameter representing solar windcould be an additional input for the NN to learn and gener-alise TEC patterns.Habarulema(2007) consideredVsw andNp (since electron number density was not available at thattime) as separate inputs to the NN and quantification resultsusing the root mean square error (RMSE) method were gen-erally inconclusive. This work is a more comprehensive ex-tension in a sense that it also quantitatively investigates thevariations of IMFBz with TEC fluctuations. Space weatherforecasts and correlation studies between solar wind, mag-netosphere and geomagnetic field measurements have beenperformed with NNs (Wu and Lundstedt, 1997; Weigel et al.,2002, 2003; Vandegriff et al., 2005; Lundestedt, 2006). Van-degriff et al.(2005) used NNs to demonstrate that they werecapable of predicting the arrival of interplanetary shocks onthe Earth.Weigel et al.(2002, 2003) also used NNs to mapsolar wind measurements to the changes in ground magneticfield levels and their predictability with time. These authorsdemonstrated that the solar wind and rate of change of ge-omagnetic field are related and have a strong dependanceon local time and latitude. Enough literature, the underlyingprinciples involved and assumptions made about the deriva-tion of TEC from GPS data are available (e.g.Langley, 2000;

Fedrizzi et al., 2005) and will not be repeated here. It is how-ever worth mentioning that the TEC data used in this studywere derived using the Adjusted Spherical Harmonic Analy-sis (ASHA) algorithm and its details can be found inOpper-man et al.(2007) andOpperman(2007). This paper presentsresults obtained by predicting GPS TEC as a function of sea-sonal variation, diurnal variation, magnetic activity, solar ac-tivity and the parameters representing the solar wind. GPSTEC values predicted using the first four parameters act asa benchmark while determining the solar wind parameter ef-fects on TEC. The seasonal and diurnal variations are rep-resented by day number (DN) and hour (HR), respectively.The 4-month running mean of daily sunspot number (R4)represents solar activity while the magnetic activity is rep-resented by the running mean of the previous eight 3-hourlymagnetic A index values (A8). In this paper, the functionT (Sp) is defined to represent predicted TEC as a function ofDN, HR, A8 and R4 i.e.T (Sp)=T(DN, HR, A8, R4) so thatT (Sp, Bz), T (Sp, Vsw) andT (Sp, Np) represent predictedTEC values after separately addingBz, Vsw, Np respectivelyto Sp. The prediction was undertaken for prestorm, stormand post storm days to assess the performance of the NNmodel during geomagnetic disturbed conditions (6–10 and14–18 May 2005). The overall discussion in this paper tried

www.ann-geophys.net/27/2111/2009/ Ann. Geophys., 27, 2111–2125, 2009


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Fig. 4. Similar to Fig. 3, for day 104 in 2005.

to answer the question “If the solar wind has an influenceon TEC fluctuations, should it be taken into account alongwith other standard parameters during TEC predictability ormodelling?”

2 Data sources

The data used for theVsw, Np and the IMFBz parame-ter recorded by the Advanced Composition Explorer (ACE)satellite were downloaded fromhttp://cdaweb.gsfc.nasa.gov/cdaweb/spphys/. GPS TEC data were derived from thedual frequency receivers located at Sutherland (32.38◦ S,20.81◦ E) and Cape Town (33.95◦ S, 18.47◦ E) using theASHA algorithm which makes use of the mapping functionthat assumes the ionosphere to be a single layer of height350 km (Opperman et al., 2007). The availability of GPSTEC data was taken as a reference point for the considerationof solar wind data. The database contained periods with GPSTEC data but without eitherVsw, Np or IMF Bz data. Thisdiscontinuity in the ACE data was catered for, by replacingthese days with the monthly mean values of days for whichdata was available according to the following equation:

Md =1

Nd

Nd∑i=1

Xj=1,2,3 (1)

whereMd represents missing data inVsw (Xj=1), Np (Xj=2)andBz (Xj=3),i=1, 2,...,Nd , with Nd being the total number of days for agiven month.

It should be noted that the most significant amount of miss-ing data was found in theNp parameter followed byVsw andfinally Bz. The ACE satellite is roughly located at the L1point (a point where the gravitational attraction on the satel-lite from the Sun and the Earth cancel out), which is at a dis-tance of more than 200RE (RE is the Earth’s radius in km)from the Earth’s surface, making it relatively more steadywith respect to both the Sun and the Earth. The communica-tion time between the ACE satellite and the Earth is assumedto be small and is hence ignored (Weigel et al., 2002, 2003)during the ENN modelling.

3 Recurrent networks, data processing and NN training

3.1 Recurrent networks

A NN is a powerful tool that can be used to perform thetasks of learning and generalising the variational behavioursand patterns of parameters that exhibit non-linear character-istics through the input-output mapping process. NNs have


http://cdaweb.gsfc.nasa.gov/cdaweb/sp_phys/

http://cdaweb.gsfc.nasa.gov/cdaweb/sp_phys/


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been widely used in many applications that deal with non-linear approximations. A number of textbooks (e.g.Bishop,1995; Haykin, 1994; Fausett, 1994) and published papers(e.g.Weigel et al., 2002; Marra and Marabito, 2005; Tulu-nay et al., 2006; Vandegriff et al., 2005; Habarulema et al.,2007, etc.) elaborate the effectiveness and procedure of us-ing this technique in empirical modelling. There are var-ious ways and algorithms available for implementing NNs(Haykin, 1994; Bishop, 1995). This work uses one form ofrecurrent networks known as Elman networks which handlesfunction learning based on a combination of current inputparameters at any time and a series of previously learned pa-rameters with the corresponding outputs of the entire net-work connection (Elman, 1990). One of the major differ-ences between ordinary feed forward NNs and recurrent El-man neural networks (ENNs) is that the latter has a copylayer of the hidden neurons (Haykin, 1994). The functionalapproach of ENNs enables the correction of time delay be-tween the various input parameters and the output parame-ter during NN training and validating processes. In simpleterms, an ENN is like a modified feed forward NN since ithas an additional layer consisting of context units which al-lows hidden unit patterns to be fed back to themselves (El-man, 1990) and uses a back propagation algorithm. In theENN, each hidden unit has a corresponding context unit and

therefore the number of hidden neurons or nodes is equalto the number of context units in the copy layer (Marra andMarabito, 2005). Figure 1 shows an example of a simplifiedstructure of the ENN having one input, hidden and outputlayers. The mathematical computations are not representedfor clarity and simplicity. The output for single hidden lay-ered ENN, withn input units,m hidden units and one outputunit can be expressed in terms of the activation function andasociated weights along with the corresponding biases at dif-ferent times in an iterative process (Wu and Lundstedt, 1997;Boden, 2002) as follows;

Xj (t) = f

(n∑

k=1

vjkxk(t) +

m∑h=1

ujhyh(t − 1) + bj

)

Xo(t) =

m∑j=1

Xj (t)woj + bo

whereXj (t) is the output of the hidden unitj at time t ,f =1/(1+e−x) is the activation function,x is the input train-ing vector,j andh are indices for the hidden and contextnodes,k ando are indices for input and output nodes respec-tively, Xo(t) is the output of the output unito at timet , v, u

andw are the connection weights associated with the input,hidden and output layers, respectively andb is the bias. For a



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detailed description about ENN, the reader is referred to thereferences within this section.

3.2 Data processing and NN training

Data for the identified parameters were processed and organ-ised in a form that is compatible with NNs. During the dataorganisation process, the day number (DN) and hour (HR)were each split into sine and cosine components to allow forthe continuous trend of data (Poole and McKinnell, 2000) asfollows;

DNS = sin

(2π × DN

365.25

)DNC = cos

(2π × DN

365.25

)(2)

HRS= sin

(2π × HR

24

)HRC = cos

(2π × HR

24

)(3)

where DNS, DNC, HRS and HRC are the sine and cosinecomponents of DN and HR, respectively.

The procedure for determining magnetic and solar activ-ity representations is clearly presented inHabarulema et al.(2007). Hourly GPS TEC values were extracted using theASHA algorithm from the GPS observations. A total of50 228 data points were used in NN training and validatingprocesses each comprising of DNC, DNS, HRC, HRS, A8,R4 and eitherVsw, Np or Bz. The ENN uses six or seven

input parameters and one output parameter (TEC) throughout the entire study. During the implementation of the NNtechnique, data for 2000–2007 was used in training and val-idating, while the 2005 dataset was used for verifying theaccuracy of the NN model. Figure 2 shows a simplied flowchart of the entire process. This study was conducted in twophases. The first one involved the prediction of TEC as afunction of diurnal variation, seasonal variation, solar activ-ity and magnetic activity, which acted as a benchmark whilequantifying the solar wind effects on GPS TEC. After de-termining the optimum NN architecture and computing theprediction accuracy, each of the solar wind parameters wasincluded as a separate input to the NN along with DN, HR,A8, R4 and the procedure repeated. Details of data analysisare presented in Sect. 5.

4 The solar wind and TEC variations

Solar wind is a stream of energetic particles (in the formof a plasma) that is continuously ejected from the sun andreaches the Earth’s atmosphere at a speed typically in therange 300 km/s to 700 km/s. Its composition is mainly elec-trons and protons (about 95%). The variations of solar winddynamics with TEC are more significantly observed during



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Fig. 7. Variations of the considered solar wind parameters and TEC values (derived and predicted) during 6–10 May 2005.

magnetic storms.Jakowski et al.(1999) studied the relation-ship between the solar wind and TEC before and around solarminimum at different European latitudes usingVsw as one ofthe parameters and found that there exists an anticorrelation.The observed delay betweenVsw and TEC was interpretedas an indication of close coupling of the solar wind with theionosphere-thermosphere dynamics related to the observednegative phases of ionospheric storms a few days after stormonset. Additionally, various studies at all latitudes haveshown that TEC is influenced during geomagnetic storms,a process believed to be driven by injection of the solar windenergy into the magnetosphere and characterised by the southward turning of the IMFBz (Meza et al., 2005; Fedrizzi et al.,2005; Biktash et al., 2008). In this work, the idea was to in-cludeVsw, IMF Bz and the electron number density (Ne) to

the NN. However, data forNe was not available and since thenumber of electrons in the solar wind is roughly equal to thenumber of protons,Np was used instead. The solar wind pa-rameter is considered in this empirical modelling with theprospect of capturing plasmapheric TEC variations duringmagnetic storms especially at high altitudes. However, avery recent study pointed out that separating agents formingionospheric disturbances during storm conditions is too dif-ficult due to the complexity of the correlation between solarwind dynamics and the ionospheric variations (Biktash et al.,2008). A decrease of TEC (from both GPS and ionosonde)has been observed over South Africa during the main phasesof geomagnetic storms. During this period, an increase inVsw andNp is observed.Sethia et al.(1978) showed thatthere is an inverse relationship between plasmaspheric TEC



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Fig. 8. Variations of the considered solar wind parameters and TEC values (derived and predicted) during 14–18 May 2005.

and Vsw over an equatorial station, Ootacamund (11.4◦ N,76.6◦ E) as the first experimental evidence during pre-stormand storm conditions. These authors utilised electron con-tent measurements made by Faraday rotation and group de-lay techniques using radio beacon signals from the Appli-cation Technology Satellite (ATS-6) to compute the electroncontent of the plasmasphere. Contrary to studies that dealwith TEC and solar wind variations during storm conditions,this study presents modelling efforts undertaken using datafor both quiet and disturbed conditions to try and quantita-tively determine effects of solar wind on TEC fluctuations.In this work, theVsw magnitude is computed by combiningthe three components of velocity in x-, y- and z-directionsusing the following equation:

Vsw =

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x + V 2y + V 2

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whereVsw is the magnitude of solar wind velocity.

The IMF Bz is one of the indicators usually used to studygeomagnetically disturbed conditions on solar-terrestrial sys-tems. The physical mechanisms guiding the outcomes ofmagnetic storms on TEC variations are different for differentlatitudes and sometimes seasons. It has been observed thatnegative storm effects are the most likely outcomes over mid-latitudes although positive storm effects are also sometimesevident (Buonsanto, 1999). Significant variabilities of theconsidered solar wind parameters and TEC are observed dur-ing the considered magnetic storms of May 2005 as shown inFigs. 7 and 8, Sect. 6.



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5 Data analysis

As mentioned in Sect. 2, hourly GPS TEC data for the twoGPS sites (equiped with Ashtech geodetic grade dual fre-quency receivers) were estimated using the ASHA algorithm.It is known that TEC variability is influenced by seasonal anddiurnal variations, solar and magnetic activities and the ge-ographic position of the GPS receiver (Hofmann-Wellenhofet al., 1992). Only the first four parameters were consideredin this work since we dealt with single station studies. It isclear that a NN would not learn any thing from TEC vari-ability with respect to a constant geographical position. Thedataset under consideration consisting of DN, HR, R4, A8and the solar wind parameters were divided into training andvalidating patterns in the ratio of 7:3, respectively. Hourlydata for 2000–2007 over Sutherland were used for the train-ing and validating processes while hourly data for 2005 overCape Town were used for verifying. It is important to notethat the verification dataset was not included in training, butfell within the training period thus taking into account the so-lar activity level changes. It has been previously shown that aNN model developed at a particular GPS station can be usedto predict TEC variability over another GPS receiver station

that was not involved in NN model development. This hasdemonstrated the temporal and to some extent spatial capa-bility of the NN in dealing with such non-linear approxima-tions within a particular latitudinal range (Habarulema et al.,2009). The ability of the NN model to capture TEC vari-ability at a different station with data not included in trainingmay be attributed to the fact that since the stations have a lat-itudinal difference of∼2◦, the ionospheric pierce point (IPP)which provides an input for the GPS vertical TEC on the re-ceiver used in the NN training (Sutherland) may cover thegeographical location of the receiver located at Cape Town.Keeping DN, HR, A8 and R4 constant, the solar wind pa-rameter representation (Vsw, Np or Bz) was each includedseparately in the ENN training and the respective networksverified. With effect to this, a number of recurrent ENNswere trained in a search for the optimum architecture. Train-ing was monitored until the mean square errors on the test-ing dataset decreased (Habarulema et al., 2007). There isno direct way of determining the number of hidden nodesin the hidden layer. Increasing the number of hidden layerswas found not to have a significant change on the accuracyof results, but makes training easier in terms of time in somecases (Haykin, 1994). An optimum architecture for this work



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consisted of the configuration 6:8:1 for the standard param-eters (Sp=DN, HR, A8 and R4) and changed to 7:9:1 whenthe solar wind parameter was included in the study. The ar-chitecture consisted of one input layer, one hidden layer andone output layer having one neuron. In the determinationof the optimum NN architecture, the root mean square error(RMSE) method has been used. The followed procedure wasthe addition of one hidden node at a time, training the NN,testing it with data and finally computing the RMSE betweenthe GPS TEC and the NN predicted TEC values (Habarulemaet al., 2009). The NN architecture that gave the least RMSEwas adopted as the one suitable for TEC prediction. Thecomputation of correlation coefficients has been used as acomplementary option during the NN architecture determi-nation. The RMSE and correlation coefficient,µ are defined

as

RMSE=

√√√√ 1

N

N∑i=1

(T m − T p)2 (5)

µ =1

δmδp

(N∑

i=1

(T mi − T

m)(T

pi − T

p)

)(6)

whereδm andδp are the respective standard deviations formeasured and predicted TEC defined by

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√√√√ 1

N

N∑i=1

(T mi − T

m)2,



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3

3.5

4

RM

SE

(T

EC

U)

T(Sp)

T(Sp, B

z)

T(Sp, N

p)

T(Sp, V

sw)

Fig. 11. Computed RMSE values between GPS TEC and predicted TEC for the available months in 2005.

δp =

√√√√ 1

N

N∑i=1

(Tpi − T

p)2, (7)

andT m andT p are the measured and predicted TEC,Tm

andT

pare their respective means over a length interval of the to-

tal number of observations,N under consideration. Table 1shows the RMSE values obtained for different network archi-tectures on different days. The number of hidden nodes thatprovided the optimum architecture was found to be∼n+2where n is the number of inputs to the ENN. The final dis-cussed results in the following section are obtained by pre-dicting hourly and daily TEC as a function of either six orseven parameters and may be mathematically expressed as

Tp ≡

f (Sp), for standard parameters

f (Sp, Vsw), Vsw included

f (Sp, Np), Np included

f (Sp, Bz), IMF Bz included

(8)

whereSp≡{DN, HR, R4, A8} represent the standard param-eters that influence TEC variability, DN≡{DNC, DNS} andHR≡{HRC, HRS}. An important point to note is thatwe have used results from the ENN trained at Sutherland(32.38◦ S, 20.81◦ E) to predict TEC changes at a receiver sitelocated at Cape Town (33.95◦ S, 18.47◦ E). Its basis is the re-cent study byHabarulema et al.(2009) which showed that it

Table 1. RMSE (between predicted and measured GPS TEC) forsome days in 2005 for different architectures when DN, HR, R4and A8 are included in the ENN as inputs.

Network Architecture RMSE (TECU)denotation configuration day 60 day 100 day 250 day 291

A 6:6:1 13.3247 8.3594 5.8260 6.7112B 6:7:1 2.0740 2.3914 2.0723 2.4126C 6:8:1 2.1627 1.7717 1.3522 1.9618D 6:9:1 2.6417 3.2795 1.8668 1.9108E 6:10:1 2.8451 2.3629 1.8298 1.9035

is possible to predict TEC variations at GPS receiver stationswhere data was not included in training, within a latitudinalrange of∼1–3 degrees.

6 Results and discussion

6.1 Diurnal TEC predictions

Figures 3, 4, 5 and 6 show the comparison of hourly GPSTEC and the predicted values as a function of the standardparameters (seasonal and diurnal variations, solar and mag-netic activities) and after separate inclusion of each solarwind parameter for days 58, 104, 185 and 285 in 2005 overCape Town (33.95◦ S, 18.47◦ E). Table 2 shows the com-puted RMSE values between GPS TEC and the correspond-ing predicted values. This table indicates that all solar wind



0 4 8 12 16 20 245

10

15

20

25

Time, UT (hrs)

TE

C (

TE

CU

)

(a)

0 4 8 12 16 20 242

4

6

8

10

12

14

16

Time, UT (hrs)

TE

C (

TE

CU

)

(b)

0 4 8 12 16 20 245

10

15

20

25

30

Time, UT (hrs)

TE

C (

TE

CU

)

(c)

0 4 8 12 16 20 244

6

8

10

12

14

16

18

20

22

Time, UT (hrs)

TE

C (

TE

CU

)

(d)

GPS TEC T(Sp) T(S

p, B

z) T(S

p, N

p) T(S

p, V

sw)

Fig. 12. A plot of monthly average GPS TEC for each hour and the corresponding predictions with all parameters used for the monthsrepresenting(a) summer (January),(b) winter (June),(c) autumn (March) and(d) spring (September) in 2005.

Table 2. RMSE between GPS TEC and predicted TEC values fordays 58, 104, 185 and 285 in 2005.

Day RMSE (TECU) between GPS TEC and(in 2005) T (Sp) T(Sp, Bz) T (Sp, Np) T (Sp, Vsw)

58 1.6171 1.5873 1.3105 1.3112104 2.3562 2.7691 2.7958 3.1242185 0.9472 0.9689 1.2377 1.2506285 1.2015 1.0100 0.9443 1.2727

parameters considered slightly improved the prediction ac-curacy for day 58 while no improvement is observed on days104 and 185. The inclusion ofBz andNp gives improve-ments of∼15.94% and∼21.41% for day 285 whileVsw

slightly degrades the prediction accuracy by∼5.93% with

respect to Sp. Once again, these results are obtained by veri-fying the ENN at a GPS receiver site whose data was not in-volved in model development and this confirms the previousstudy byHabarulema et al.(2009). Prediction accuracies interms of both degradation and improvement are close to thevalues of reference when solar wind parameters are includedfor these quiet days. In all cases, the TEC diurnal shape iscorrect at almost all times of the day.

Figures 7 and 8 show the variations of the solar wind pa-rameters and GPS TEC along with the predicted values for 6–10 and 14–18 May 2005. These particular dates were chosenbecause they contained days when magnetic storms occured.These two figures are meant to specifically show the perfor-mance of the ENN model during prestorm, storm and poststorm conditions. The prediction accuracies for these dateswhen different parameters are included in ENN modellingare shown in Fig. 9. There was a magnetic storm on 8 May



Jan March June Sept0

0.5

1

1.5

2

2.5

3R

MS

E (

TE

CU

)

Jan March June Sept0.95

0.96

0.97

0.98

0.99

1

Coe

ffici

ent o

f det

erm

inat

ion

( μ2 )

T(Sp)

T(Sp, B

z)

T(Sp, N

p)

T(Sp, V

sw)

Fig. 13. Comparison of RMSE and coefficient of determination (µ2) values for the months representing autumn, winter, spring and summerin 2005.

which appears to have led to positive storm effects when theTEC values are compared to relatively quiet days before andafter the storm. There was a stronger magnetic storm on 15May 2005 that led to the significant fluctuation of IMFBz

and sudden jump in bothVsw andNp. As a result signifi-cant TEC fluctuations are observed. For both of these stormdays a statistical improvement is observed in Fig. 9 after theinclusion ofBz andNp. While the ENN correctly identifiesthe TEC variational pattern on 8 May, the result is differenton 15 May for all parameters considered. In addition, allcombinations of different parameters strongly underpredictthe magnitude of TEC values on 8 May. In both cases, theinclusion ofVsw degrades the prediction accuracy, an indi-cation that solar wind velocity may not be an efficient rep-resentation of solar wind in TEC modelling during magneticstorms. This should be investigated further for more stormconditions. However, these results clearly demonstrate that itis still difficult to accurately predict diurnal TEC behaviourduring magnetically disturbed conditions.

6.2 Seasonal TEC predictions

Figure 10 shows the comparison of average daily GPS TECand the predicted values for January to October 2005 overCape Town (33.95◦ S, 18.47◦ E). Due to a lack of data,November and December are not represented. Figure 11shows the computed RMSE values between GPS TEC andT (Sp), T (Sp, Bz), T (Sp, Np), T (Sp, Vsw). The three so-lar wind parameters included led to average improvementsin TEC prediction for January and February. BothBz andNp improve the prediction accuracy for March and Augustwhile results are more or less constant for June and Septem-ber for these solar wind parameters. No change is observedfor October whenVsw is included, whileBz andNp degradethe prediction accuracy with respect toSp. Figure 12 showsthe average diurnal TEC variations for January, March, Juneand September representing summer, autumn, winter andspring, respectively. The distinct observation from thisfigure is that all parameters underpredicted GPS TEC foralmost the whole month of January as seen in Fig. 12a



except at 03:00 UT whereT (Sp), T (Sp, Np) andT (Sp, Bz)are greater than GPS TEC by∼0.870 TECU, 0.779 TECUand 0.629 TECU, respectively, and 04:00 UT whereT (Sp,Np)'T (Sp, Bz)'GPS TEC. An underprediction is also ob-served for March between∼08:00 UT and 16:00 UT. Fig-ure 13 is a representation of RMSE between derived GPSTEC and its predicted values as a function of all consid-ered parameters. Represented in Fig. 13 are also the coef-ficients of determination (square of correlation coefficients)between GPS TEC and TEC values as predicted by differentparameter combinations. With regard toSp as a benchmark,Bz, Np andVsw improve the TEC predictions by∼15.16%,∼25.07% and∼27.38%, respecively for January (summer).For March,Bz andNp gave improvements of∼24.27% and∼25.50%, respectively. In June (winter), the inclusion ofVsw doesn’t change results whileNp improves the predic-tion by an average of∼21.86%. For September, bothBz

and Np led to an overprediction between∼05:00 UT and13:00 UT, whileSp underpredicts TEC between 09:00 UTand 11:00 UT. Difficulties in generating accurate predictionsin spring have been observed before (Habarulema et al.,2007) and may be due to the strong variations exhibited byTEC during the equinoxes (Kouris et al., 1999) and thereforeall parameters that influence TEC probably have high vari-ation levels (Habarulema et al., 2009) including solar wind.In the Northern Hemisphere,Girish et al.(1997) obtained asignificant correllation between the variations of solar windparameters and TEC during the sunspot maximum in winterand spring. We have obtained a statistical correllation be-tween TEC variations and atleast one of solar wind parame-ters investigated in all seasons through ENN modelling. Ourresults indicate a relative agreement forNp andVsw duringthe declining phase of the solar cycle 23 (year 2005) in theSouthern Hemisphere which may be a confirmation that thesolar wind dynamics influence TEC variations at both solaractivity levels and in both hemispheres. Based on statisticalanalysis, it can be deduced that both daily and monthly aver-age TEC predictions were improved by includingVsw in thedatabase for spring. Confirmation of this result requires moreanalysis since only one station’s data has been analysed.

7 Conclusions and future work

This paper has attempted to explain the study of quantifyingsolar wind effects on GPS TEC using ENN modelling. GPSTEC has been predicted as a function of DN, HR, R4 and A8,and the results used as a benchmark to try and quantify so-lar wind influence on GPS TEC. Statistical analysis revealedboth improvements and degradation in TEC prediction accu-racies for different parameter combinations and for differentdays and seasons. An analysis was performed for both quietand storm conditions. Although the inclusion ofBz andNp

improved the prediction accuracy for both stormy days (8 and15 May), an underprediction was observed for 8 May while

the variational trend pattern was incorrect for 15 May. Theseresults show that it is still difficult to predict TEC variabilityduring magnetic storms. We have investigated only three so-lar wind parameters in this study and although a degradationin TEC prediction has been observed in some cases, resultsindicate that the solar wind parameter may be a potential ad-ditional input to the ENN during TEC predictions. This claimshould be investigaed further by; (1) examining more solarwind parameters, (2) looking for a method of combining thethree investigated parameters to obtain one single quantitycontainingBz, Np andVsw information since they all pro-vide varying magnitudes in the prediction accuracy improve-ment during different days and seasons and (3) including thesolar wind parameters in a multi-station model where the ge-ographical location of the GPS receivers will be taken intoaccount.

Acknowledgements.Thanks to Chief Directorate Surveys and Map-pings (CDSM) and IGS community for making GPS data available.The authors acknowledge the ACE project teams (D. J. McComasof Southwest Research Institute and N. Ness of Bartol Research In-stitute) for making the solar wind data available. J. B. Habarulemagreatly thanks the South African National Astrophysics and SpaceScience Programme, University of Cape Town, South Africa for thefinancial support.

Topical Editor M. Pinnock thanks two anonymous referees fortheir help in evaluating this paper.

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