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Advances in Space Research 42 (2008) 610–616

Solar activity variations of ionosonde measurementsand modeling results

D. Altadill a,b,*, D. Arrazola b, E. Blanch b, D. Buresova c

a Center for Atmospheric Research, University of Massachusetts Lowell, 600 Suffolk Str. 3rd Floor, Lowell, MA 01854, USAb Observatorio del Ebro, Universitat Ramon Llull, CSIC, Crta. Observatori No. 8, E43520 Roquetes, Spain

c Institute of Atmospheric Physics, ASCR, Bocni II 1401, 141 31 Prague 4, Czech Republic

Received 1 November 2006; received in revised form 19 July 2007; accepted 23 July 2007

Abstract

The time series of hourly electron density profiles N(h) obtained at several mid-latitude stations in Europe have been used to obtainN(h) profiles on a monthly basis and to extract both the expected bottomside parameters and a proxy of the ionospheric variability asfunctions of time and height. With these data we present advances on a ‘‘Local Model’’ technique for the parameters B0 and B1, itsapplicability to other ionospheric stations, to other bottomside ionospheric parameters, and to modeling the time/height variabilityof the profile. The Local Model (LM) is an empirical model based on the experimental results of the solar activity dependence of thedaily and seasonal behavior of the above parameters. The LM improves the IRI-2001 prediction of the B0 and B1 by factor of twoat mid-latitudes. Moreover, the LM can be used to simulate other ionospheric parameters and to build mean N(h) profiles and the devi-ations from them. The modeling of both the average N(h) profiles and their deviations is an useful tool for ionospheric model users whowant to know both the expected patterns and their deviations.� 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Mid-latitude Ionosphere; Bottom side modeling; Ionospheric variability

1. Introduction

As it is widely known in the ionospheric community, theInternational Reference Ionosphere model (IRI) was devel-oped to produce an empirical standard model of the iono-sphere. The IRI predictions are tested against measuredionospheric data and the model is being improved andupdated continuously with the results of the annual work-shops and specific sessions at general meetings. The major-ity of the parameters that define the bottomside electrondensity profile N(h) predicted by IRI are in good agreementwith the measured values during geomagnetically quiet

0273-1177/$34.00 � 2007 COSPAR. Published by Elsevier Ltd. All rights rese

doi:10.1016/j.asr.2007.07.028

* Corresponding author. Present address: Observatorio del Ebro,Universitat Ramon Llull, CSIC, Crta. Observatori No. 8, E43520Roquetes, Spain.

E-mail address: daltadill@obsebre.es (D. Altadill).

periods (e.g., Mosert et al., 2004). However, IRI predic-tions for the two parameters B0 and B1, which determinethe F2 bottomside thickness and shape, respectively (Bili-tza et al., 2000), can show significant disagreement withthe observations (Lei et al., 2004). B0 is equal to the heightdifference between the height of the F2 peak (hmF2) and theheight where the electron density is equal to 0.24 times theF2 layer electron density maximum (NmF2), and B1describes the shape of the profile between the two heightsfrom which the B0 has been obtained (Reinisch andHuang, 1998; Bilitza, 1998). Users of ionospheric modelsrequest specifications of the expected deviations from thepatterns predicted by these models (Ezquer et al., 2004).This requires additional studies of ionospheric variability.Recent investigations into the framework of the IRI modelreport new results that better predict the bottomsideparameters of the IRI profile (Blanch et al., 2007) as wellas the variability of N(h) (Altadill, 2007).

rved.

D. Altadill et al. / Advances in Space Research 42 (2008) 610–616 611

The aim of this short paper is to show the advances ofthe Local Model technique (LM) for the parameters B0and B1 described by Blanch et al. (2007) and to apply thistechnique to model the variability of the electron densityprofile. The new results presented in this paper are com-pared to the results reported in Blanch et al. (2007) andAltadill (2007). The usefulness of this technique for model-ing the behavior of B0 and B1 at four ionospheric stationsover Europe is presented, as well as for modeling other ion-ospheric parameters that are not well represented by IRI.We build a LM for the parameters B0 and B1 for the par-ticular mid- to low-latitude station of El Arenosillo, Spain.Finally, we build a LM of the variability of the profile as afunction of time and altitude for the mid-latitude station ofEbro Observatory, Spain.

2. Data and analysis

We used a large database of vertical incidence (VI) ion-ograms from El Arenosillo (37.1�N, 353.3�E) recorded by aDGS 256, covering the time interval from 1993 to 2004.The scaling of the ionogram traces has been manually edi-ted to assure accurate N(h) profiles. The experimentalobservations from this station are used to build a LM sim-ilar to the one obtained for Ebro Observatory (40.8�N,0.5�E) (Blanch et al., 2007). The edited VI ionograms fromPruhonice (50.0�N, 14.6�E) recorded by a DPS-4 for year2004, the automatically scaled ionograms from the DPS-4systems at Athens (38.0�N, 23.5�E) and Juliusruh(54.6�N, 13.4�E), also for year 2004, have been used to testthe possibility of the LM at other latitudes and longitudesover Europe.

In order to build the LM for the bottomside parametersat the latitude of El Arenosillo, we used the methodologydescribed by Blanch et al. (2007). The parameters B0 andB1 are obtained from the Monthly Averaged Representa-tive Profile (MARP) technique (Huang and Reinisch,1996). We computed the MARPs with a percentage ofexclusion of 25%, i.e., for a given month and hour 25%of the individual N(h) profiles having larger deviationscompared to the average N(h) are excluded for computingMARP. The ‘extreme’ N(h) profiles, which are most likelyrelated to disturbed ionospheric conditions, are not used toobtain the MARP. Therefore, for any given month andhour we obtain the expected N(h) profile for quiet iono-spheric conditions (see Huang and Reinisch, 1996 fordetails). We extract from the MARPs of El Arenosillo sta-tion the experimental values of the B0 and B1 parametersto be modeled. The MARPs obtained from other iono-spheric stations over Europe are used for testing the possi-bility of obtaining good LMs of the B0 and B1 parametersat other latitudes.

Moreover, we use the edited Ebro data for the timeinterval from 1995 to 2005 to model the variability ofN(h) at middle latitudes. The MARPs and the individualprofiles from Ebro are used to obtain the ‘standard devia-

tion’ r(h) as a proxy for modeling the variability (seeAltadill, 2007 for details).

We also used the IRI-2001 model to obtain the IRI bot-tomside parameters for the locations of El Arenosillo, Pru-honice, Athens, and Juliusruh in order to compare IRIpredictions with measured parameters. We adopted thestandard option of IRI for computing B0 and B1. Notethat the f0F2 storm model was turned off in IRI-2001because the MARP represents the expected profile for quietionospheric conditions.

We used the same methodology described by Blanchet al. (2007) for data analysis and for building the LM ofthe bottomside parameters. The LM is an empirical modelbased on a general least-square fitting of the measurementsto a harmonic function (Press et al., 1986). According tothe experimental results, the LM simulates the daily andseasonal variations of the modeled parameters as functionsof the solar activity.

3. Experimental and modeling results of N(h) parameters

Fig. 1 depicts the experimental pattern of the daily andannual variations of the B0, B1 parameters for El Areno-sillo and Pruhonice for years of mid- to low-solar activity(the yearly average of F10.7 is lower than 110 s.f.u.). Theplots of Fig. 1 show a clear diurnal variation of the B0with noon values being larger than midnight values, espe-cially in summer. However, a semidiurnal variationappears to be significant in winter. The B1 parameter dis-plays diurnal and semidiurnal variation, but it is not asclear as for B0. The semidiurnal variation of B1 is moreimportant in winter and the diurnal variation in summer.In this case, noon B1 values are lower than midnight val-ues, contrary to the daily behavior of B0, which agreeswith previous results (e.g., Bilitza et al., 2000; Lei et al.,2004). There is also a clear annual variation for bothB0 and B1. The minimum B1 values are observed duringsummer whereas the maximum values occur during winterand the opposite is true for B0 (e.g., Lei et al., 2004).Although Fig. 1 shows the results for El Arenosillo andPruhonice, the same pattern is obtained for the four ion-ospheric stations analyzed in this study. These results con-firm the observational facts at other middle latitudestations (Blanch et al., 2007). In addition, though notshown here, there is significant solar activity dependenceof the yearly averaged values and of the yearly and dailyvariation of the B0 and B1 parameters for El Arenosillosimilar to the results of Blanch et al. (2007) for Ebro.Therefore, we built a LM for El Arenosillo to reproducethe above variations and we assumed that diurnal andsemidiurnal variations of these parameters are modulatedby a seasonal variation, and that the variations of B0 andB1 for El Arenosillo depend on solar activity. Eq. (7) inBlanch et al. (2007) applies also to El Arenosillo, but withdifferent values for the coefficients. This equation isrewritten here

0

1

2

3

4

5

6

B1

1997 (months)

406080

100120140160180

B0 (k

m)

1997 (months)

J F M A M J J A S O N D

J F M A M J J A S O N D

El Arenosillo

0

1

2

3

4

5

6

B1

2004 (months)

406080

100120140160180

B0 (k

m)

2004 (months)J F M A M J J A S O N D

J F M A M J J A S O N D

Pruhonice

Fig. 1. Daily and annual pattern of the parameters B0 (top) and B1 (bottom) obtained from MARP technique over El Arenosillo (left) and Pruhonice(right) for indicated years.

20 60 100 140 180B0 (MARP)

40

60

80

100

120

140

B0

(L.M

.)

60

80

100

120

B0

(IRI)

20 60 100 140 180B0 (MARP)

0 2 41 3 5 6B1 (MARP)

1

2

3

4

5

B1

(L.M

.)

1

2

3

4

B1

(IRI)

0 2 4 6B1 (MARP)

y = 1.873 + 0.144 x r2 = 0.18

y = 1.553 + 0.415 x r2 = 0.346

y = 25.49 + 0.643 x r2 = 0.594

y = 63.85 + 0.26 x r2 = 0.243

Fig. 2. Scatter plots of experimental parameters B0 (left) and B1 (right)against those obtained by IRI-2001 (top) and by LM technique (bottom)over El Arenosillo station. The plots correspond to year 1997 (low-solaractivity). Solid lines depict the best linear fits for each case, whoseregression equations and correlation coefficients are indicated.

612 D. Altadill et al. / Advances in Space Research 42 (2008) 610–616

P ¼a0 þ b0 cosðX1T � u10Þ þ c0 cosðX2T � u20Þþ ½a1 þ b1 cosðX1T � u11Þ þ c1 cosðX2T � u21Þ�� cosðx1t � fa01 þ b01 cosðX1T � u011Þþ c01 cosðX2T � u021ÞgÞ þ ½a2 þ b2 cosðX1T � u12Þþ c2 cosðX2T � u22Þ� cosðx2t � fa02 þ b02 cosðX1T � u012Þþ c02 cosðX2T � u022ÞgÞ: ð1Þ

Here P is a given parameter (B0 or B1), t means time (0–23 h, expressed in UT), x1 = 2p/24 and x2 = 2p/12 arethe diurnal and semidiurnal angular frequencies, respec-tively. T is the month (1–12 month), and X1 = 2p/12and X2 = 2p/6 are the annual and semiannual angular fre-quencies. The parameters uij and u0ij are phase terms andthe coefficients ai, bi, and ci determine the amplitudes ofthe diurnal, semidiurnal, annual, and semiannualvariations.

After establishing the coefficients of the LM for El Aren-osillo, we can model the B0 and B1 parameters. We com-pare the empirical data (MARP) with the results given byIRI-2001 and by LM in order to assess the goodness ofthe LM. Fig. 2 shows an example of the comparisonsbetween the experimental values and the parametersobtained by LM and by IRI for year 1997. The linear cor-relation coefficient corresponding to the linear fittingbetween time series of the empirical data and of the mod-eled values (r2) is indicated in the plots of Fig. 2. The linearcorrelation coefficient gives ‘a degree’ of linear dependencebetween two series, the larger r2 the better agreement. Themathematical expression of r2 is as follows:

r2 ¼Pðxi � hxiÞðyi � hyiÞ

Nrxry

� �2

; ð2Þ

where xi and yi refer to the time series of the empirical andmodeled data, Æxæ and Æyæ mean their respective average

values, N is the number of data of the time series, and rx

and ry are their respective standard deviations.The agreement of LM with the experimental values is

clearly better than of IRI, r2 for B0 has improved by a fac-tor 2.6, and by a factor 1.7 for B1. Moreover, we comparedthe agreement between the experimental values and thoseobtained by LM and IRI for the other years at El Areno-sillo. Fig. 3 shows the time dependence of r2 of B0 for bothLM and IRI at Ebro (as deduced from Blanch et al., 2007)and at El Arenosillo (obtained in this research). The resultsindicate that the average r2 of B0 computed by LM is about0.65 for Ebro, and 0.62 for El Arenosillo. However, theaverage r2 of B0 computed by IRI is about 0.35 for both

0

0.2

0.4

0.6

0.8

r2(B

0)

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05

Time (year)

0

0.2

0.4

0.6

0.8

r2(B

0)

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05

LMIRI

Ebro

El Arenosillo

40

80

120

160

200

240

F10.

7(s

.f.u.

)

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05

Fig. 3. Long-term solar activity dependence of the linear coefficient ofcorrelation (r2) obtained between IRI-2001 and MARP (grey bars), andbetween LM and MARP (black bars) for B0 over Ebro (middle) and overEl Arenosillo (bottom). The coefficients r2 are obtained from best linearfits as indicated in Fig. 2. The top plot shows the yearly averages of theadjusted solar radio flux at 2800 MHz (1 s.f.u. = 10�22 W m�2 Hz�1).

40

60

80

100

120

140

160

180

40

60

80

100

120

140

160

180

B0 (k

m)

B0 (k

m)

B0 (k

m)

2004 (months)

40

60

80

100

120

140

160

180

Experimental

IRI

LM technique

J F M A M J J A S O N D

J F M A M J J A S O N D

Pruhonice

J F M A M J J A S O N D

Athens

Juliusruh

Fig. 4. Comparison of the daily and yearly experimental course of B0(grey dots) with that obtained by IRI-2001 (grey line), and the LMtechnique (black line) for year 2004 at indicated ionospheric stations.

D. Altadill et al. / Advances in Space Research 42 (2008) 610–616 613

Ebro and El Arenosillo. The latter means an improvementof the LM by about a factor of 1.8 compared with IRI pre-dictions. Although not shown here, we obtained a similarimprovement for the B1 parameter. In this case, the aver-age r2 of B1 computed by LM is of about 0.38 and 0.33for Ebro and El Arenosillo, respectively, and the averager2 of B1 computed by IRI is about 0.20 for both Ebroand El Arenosillo. Therefore, the improvement we get forB1 is about 0.35/0.2 on average. The lower values of r2

for B1 compared with B0 are indicative of the rather‘‘noisy’’ temporal behavior of B1 (Fig. 1). Therefore, theformulation in terms of Fourier harmonics does not cap-ture the temporal variation of B1 as well as it does forB0. Moreover, we confirmed a significant bias in the IRIprediction for parameters B0 and B1 with solar activity;IRI behaves better for high sunspot activity years. Thiseffect has already been reported by Sethi and Mahajan(2002), Lei et al. (2004), and Blanch et al. (2007). Fig. 3shows that r2 of B0 computed by IRI follows the trendof the solar activity, especially at Ebro station. However,the results of the r2 of B0 computed by LM do not show

the above bias with sunspot activity. In summary, theresults obtained with LM always behave significantly betterthan those predicted by IRI.

Based on this analysis, it can be expected that applyingthe LM technique to the calculation of IRI parameters atother mid-latitude stations can significantly improve theIRI prediction. Although we were not able to build similarLM for other stations because of the lack of data availabil-ity, the results we get by the least-squares fitting techniquefor these stations show similar patterns of variability andsimilar improvements compared to IRI predictions.Fig. 4 shows the results of the comparison of the experi-mental B0 parameter with those generated by the fittingtechnique and IRI at other European stations.

We applied the least-squares fitting technique for otherionospheric measurements and the preliminary resultsshow that this technique can reasonably well simulate thedaily and seasonal variations of theses parameters. Fig. 5shows comparisons between the experimental parametersand the LM technique for the peak height of the E andF2 layers, hmE and hmF2, and the equivalent neutral scaleheight Hm at hmF2. These results show that this techniquecan be useful for modeling other ionospheric characteris-tics, especially those not reproduced well by IRI such ashmE, for which IRI always gives a constant value.

2005 (months)

20

40

60

80

100

Hm

(km

)

200

240

280

320

360

hm

F2(k

m)

2005 (months)

100

105

110

115

hm

E (k

m)

2005 (months)

J F M A M J J A S O N D

J F M A M J J A S O N D

20 40 60 80 10 0Hm (MARP)

30

50

70

90

Hm

(L.M

.)

200

240

280

320

360

h mF 2

(L.M

.)

200 240 28 0 320 36 0h m F2 (MARP)

100

105

110

115

hm

E (L

.M)

100 105 110 115h m E (MARP)

y = 13.27 + 0.953 x r2 = 0.953

y = 8.82 + 0.815 x r2 = 0.815

y = -13.5 + 1.33 x r2 = 0.72

Fig. 5. Examples of comparison of the daily and yearly course (left panel) of some experimental parameters over Ebro station (grey dots) with thatobtained by the LM technique (black line) for year 2005. The right panel shows the scatter plots of experimental parameters against those obtained by theLM technique. Solid lines depict the best linear fits of each case, whose equations and correlation coefficients are indicated.

614 D. Altadill et al. / Advances in Space Research 42 (2008) 610–616

4. Experimental and modeling results of variability

parameters

As already mentioned above, there is increased interestin the framework of International Reference Ionospheremodel to specify the ionospheric variability. This is ofinterest for model users who, in addition to knowing theclimatology of the ionosphere (ionospheric models) alsoneed the expected deviations from it (variability models).Our preliminary results on ionospheric variability werebased using the continuous database of vertical incidencesoundings at Ebro Observatory from 1995 to 2005. Weused as the variability proxy the deviation of the individualprofiles from the MARP profile, which is representative forquiet ionospheric conditions for a given month and hour(see Altadill, 2007 for details) in terms of percentage valuesrp(h). The results indicate that the main temporal varia-tions of rp(h) (daily, seasonal, and long-term) depend onheight and local time, and the main systematic behaviorof the F-region variability above this mid-latitude stationare as follows. The rp(h) decreases with height from thebottom of the F-region up to hmF2 during nighttime, andincreases with height during daytime. The rp(h) aroundhmF2, rp(hmF2) is larger at night (15% on average) than

during daytime (11.5%), as expected. The larger variabilityoccurs at the base of the F-region, rp(hB), during night-time, with typical values of 30–40%. The daytime valuesof rp(hB) are very low, about 5%, i.e., they are practicallyconstant. Note that the height of the base of the F-region(hB) is about 250 km at night and 150 km during theday. The rp(hB) is larger from dusk to midnight,rp(hB, DM) � 34%, than from midnight to dawn,rp(hB, MD) � 27%. There is no significant long-termdependence of the rp(hmF2) with neither the sunspot activ-ity nor the geomagnetic activity. However, the long-termbehavior of rp(hB) does depends on local time. Therp(hB, MD) increases with increasing sunspot activity from�18% at solar minimum to �32% at solar maximum andthe rp(hB, DM) has no significant solar cycle dependence.The yearly pattern of rp(hmF2) has a clear annual variation,which depends on local time. Whereas the nighttime pat-tern of rp(hmF2) maximizes during winter (�15%) andreaches a minimum during summer (�13%), the daytimepattern of rp(hmF2) minimizes during winter (�10%) andmaximizes during summer (�12%). The yearly pattern ofrp(hB) depends on both local time and solar activity. Bothrp(hB, DM) and rp(hB, MD) display a semiannual varia-tion and they maximize during equinoxes (�38%) and min-

10

20

30

40

50

σ p(hB

) (%

)

10

20

30

40

50

σ p(hB

) (%

)

10

20

30

40

50σ

p(h

B) (%

)

10

20

30

40

50

σp(

hB)

(%)

1995 199 6 1 997 1998 1999 2000 2001 200 2 2 003 2004 2005

Time (year)

40

80

120

160

200

240

F10.

7 (s

.f.u.

)

MD

MD

DM

DM

Fig. 6. Comparison of the experimental seasonal and long-term depen-dence of rp(h) (black shaded plots) from 1995 to 2005 for Ebro with thatobtained by the LM technique (grey shaded plots). The middle plotsindicate the above comparison for Midnight–Dawn local time sector(MD) and the lower ones for the Dusk–Midnight local time sector (DM).The top plot shows the monthly averages of the adjusted solar radio flux at2800 MHz for the same time period.

D. Altadill et al. / Advances in Space Research 42 (2008) 610–616 615

imize during solstices (�30%) for years of high-solar activ-ity. However, rp(hB,DM) displays an annual variation foryears of mid- to low-solar activity, where it maximizes dur-ing summer (�37%) and minimizes during winter (�30%),while there is no clear yearly pattern for rp(hB,MD).

We try to model the above systematic time/height pat-tern of variability using a simple formulation, like theone described above. In order to do that, we select threereference heights (hmF2, hB (day time), and hB (night time))and three local time sectors (daytime, dusk to midnight,and midnight to dawn). These reference heights wereselected because of the smooth dependence of rp(h) withaltitude. As a reference and according to the results ofAltadill (2007) we consider hB (day time) to be 150 km,and hB (night time) to be 250 km (see Figs. 2 and 3 ofAltadill (2007)). The local time sectors we selected becausethey contain systematic seasonal and long-term patterns.We apply the model technique by fitting the experimentalresults to annual and semiannual variations depending onsolar activity, using as a proxy for the solar activity theannual smoothed sunspot number (Rz12). Therefore, rp

for a given local time sector and height level may beexpressed as:

rp ¼ a0 þ b0 cosðX1T � u1Þ þ c0 cosðX2T � u2Þ: ð3Þ

Here T is month (1–12 month), X1 = 2p/12 and X2 = 2p/6are the angular frequencies corresponding to the annualand semiannual variation, respectively, and u1 and u2 aretheir respective phases. The coefficient a0 is the yearly aver-age of rp, and b0 and c0 are the annual and semiannualamplitudes, respectively.

Because the coefficients and phases in Eq. (3) dependonly on solar activity, this makes a simple formulationfor rp possible. The results of using this Local Model forthe variability (LMV) are depicted in Fig. 6. From this fig-ure we observe that the experimental long-term and sea-sonal patterns of rp(hB, DM) are quite well reproduced(qualitatively and quantitatively), though the model pro-duces smooth patterns. However, the experimental long-term and seasonal patterns of rp(hB, MD) are not repro-duced in detail by the LMV, but the model does followthe main patterns qualitatively.

We combined both Local Models for the Ebro station(i.e., the LM for bottomside parameters and the LM forvariability proxy) to investigate how well the LM modelsreproduce the expected N(h) profiles and the expected devi-ations from that N(h) for given local time, season, andsolar activity. Fig. 7 shows two examples of that fitting pro-cess. Although the agreement between the experimentaland modeled results is not perfect, the modeled resultsmatch both the average profile and the expected deviationsvery well as shown in Fig. 7.

5. Summary and discussion

We have presented some advances to the Local Modeltechnique for the parameters B0 and B1 described by

Blanch et al. (2007), its applicability to other ionosphericstations and to other bottomside ionospheric parameters.The Local Model technique developed here has also beenused for modeling the time/height variability of the elec-tron density profile for middle latitude station. The LocalModel (LM) is an empirical model based on a generalleast-square fitting of measurements to a harmonic func-tion and it is based on the experimental results of the solaractivity dependence of the daily and seasonal behavior ofthe above parameters. The LM technique also providesan improved description of the variations of the analyzedbottomside parameters at middle latitudes under quiet ion-

100

150

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250

300

350

400

450

Plasma Frequency (MHz)

150

200

250

300

350

400

450

'Tru

e' h

eigt

h (k

m)

3 4 5 6 7

3 4 5 6 7

100

150

200

250

300

350

400

450

1 2 3 4 5 6

1 2 3 4 5 6

150

200

250

300

350

400

450

'Tru

e' h

eigt

h (k

m)

December 2004(00:00 LT)

June 2005 (12:00 LT)

Fig. 7. Two examples (local time and season are indicated on legend) ofthe comparison between the experimental average N(h) profile andexpected deviations (top panel) and those obtained by the LM technique(bottom panel) over Ebro station. The thick black lines are the averageprofiles (experimental at top and simulated at bottom). The individualprofiles at the indicated local times are depicted as thin grey lines. Errorbars indicate the ‘standard deviation’ r(h).

616 D. Altadill et al. / Advances in Space Research 42 (2008) 610–616

ospheric conditions. Moreover, this LM technique can alsobe used to simulate the expected variability of the electrondensity profiles at middle latitude. The results from the var-iability model indicate that the experimental long-term andseasonal patterns of variability are quite well reproduced,however, the variability patterns are smoothed. Althoughthe simulated results do not exactly reproduce the experi-mental profiles and their variations, they are very reason-able. Therefore, we believe that the combined modelingof N(h) parameters and deviation will be a useful tool forionospheric model users who want to know both the pre-dicted patterns and deviations.

Further work is needed to assess the usefulness of thistechnique for other longitudes and latitudes and for con-struction of a global model.

Acknowledgements

This research has been supported by Spanish projectsREN2003-08376-C02-02 of MCYT, international coopera-tion project 2004CZ0002 of CSIC, and 2006BE00112 ofAGAUR, and also by Grant No. 1QS300120506 of theGrant Agency of the Academy of Sciences of the CzechRepublic, and by USAF Grant FA8718-L-0072 of theAF Research Laboratory.

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