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Advances in Space Research 60 (2017) 1015–1028

An empirical model of L-band scintillation S4 index constructedby using FORMOSAT-3/COSMIC data

Shih-Ping Chen a, Dieter Bilitza b,c, Jann-Yenq Liu a,⇑, Ronald Caton d, Loren C. Chang a,Wen-Hao Yeh e

a Institute of Space Science, National Central University, TaoYuan 32001, TaiwanbGeorge Mason University, Department of Physics and Astronomy, Fairfax, VA 22030, USA

cNASA, GSFC, Heliospheric Laboratory, Greenbelt, MD 20771, USAdAir Force Research Laboratory, Kirtland Afb, NM 87117, USA

eNational Space Organization, HsinChu 30078, Taiwan

Received 7 June 2016; received in revised form 26 April 2017; accepted 20 May 2017Available online 30 May 2017

Abstract

Modern society relies heavily on the Global Navigation Satellite System (GNSS) technology for applications such as satellite com-munication, navigation, and positioning on the ground and/or aviation in the troposphere/stratosphere. However, ionospheric scintil-lations can severely impact GNSS systems and their related applications. In this study, a global empirical ionospheric scintillationmodel is constructed with S4-index data obtained by the FORMOSAT-3/COSMIC (F3/C) satellites during 2007–2014 (hereafter referredto as the F3CGS4 model). This model describes the S4-index as a function of local time, day of year, dip-latitude, and solar activity usingthe index PF10.7. The model reproduces the F3/C S4-index observations well, and yields good agreement with ground-based reception ofsatellite signals. This confirms that the constructed model can be used to forecast global L-band scintillations on the ground and in thenear surface atmosphere.� 2017 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: S4 scintillation; FORMOSAT-3/COSMIC; Global Navigation Satellite System (GNSS)

1. Introduction

Ionospheric density irregularities can cause radio scintil-lation which may significantly disturb GNSS (Global Nav-igation Satellite System) signals, negatively impactingGNSS-supported communication, navigation, and posi-tioning devices. A number of scintillation models have beendeveloped. The first analytical VHF/UHF scintillationmodel was presented by Fremouw and Rino (1973), whichshowed good agreement with geostationary satellite obser-vations over a station in Ghana near the magnetic equator.

http://dx.doi.org/10.1016/j.asr.2017.05.031

0273-1177/� 2017 COSPAR. Published by Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: tigerjyliu@gmail.com (J.-Y. Liu).

Basu et al. (1976) used in situ measurement of irregularitiesby the OGO-6 satellite’s retarding potential analyzer con-structed a scintillation model for low-latitudes, whileBasu and Hanson (1981) utilized AE-D satellite data tomodel high-latitude scintillations. Aarons (1985) presentedan equatorial scintillation model based on 5 years of scintil-lation indices obtained at Huancayo, Peru by receiving sig-nals from the LES 6 satellite at 254 MHz and the ATS 3satellite at 137 MHz. Franke and Liu (1985) developedan equatorial-latitude multi-frequency scintillation modelusing observations from Ascension Island at VHF, L-,and C-band. Based on the global distribution of electrondensity irregularities measured by a large collection of scin-tillation observations taken during the Wideband, HiLat,

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and Polar Bear satellite experiments and from the US AirForce Research Laboratory’s equatorial scintillation mon-itoring network, Secan et al. (1995) developed theWBMOD (WideBand MODel) ionospheric scintillationmodel to estimate both the S4 scintillation intensity andphase fluctuation (http://spawx.nwra.com/ionoscint/wb-mod.html). Beniguel and Buonomo (1999) developed theGISM (Global Ionospheric Scintillation Model), whichderived both intensity and phase scintillation indices fromthe NeQuick electron density model (Radicella andLeitinger, 2001). Iyer et al. (2006) constructed a model,using geostationary satellite FLEETSAT signals receivedat an Indian magnetic equatorial station during 1987–1989, which took into account seasonal, solar activity,and latitudinal variations in the occurrence rate of scintilla-tions. The model of Abdu et al. (2003) is based on iono-sonde observations of spread-F in the Brazilian sectorand describes the occurrence probability of spread-F interms of local time, day of year, latitude, and solar activity.This model was implemented in the International Refer-ence Ionosphere (IRI) model as described by Bilitza andReinisch (2008). Retterer (2010) developed a theoreticalthree dimensional (3D) ionospheric plasma plume modelto predict the strength of scintillation as a function of timeand geographic location for the low latitudes. An excellentrecent detailed review of ionospheric scintillation modelswas published by Priyadarshi (2015).

These models generally suffer from limited data volumebeing based, for example, only on a single satellite and/orground-based observations which are limited to the conti-nental area and lack coverage over ocean and remote areas.Nowadays, the most popular band for satellite communi-cations is the L-band (1–2 GHz, frequency used by GNSSsystems) while the existing scintillation models were pri-marily developed with VHF scintillation observations.Therefore, it is essential to develop an L-band scintillationmodel for global applications.

The FORMOSAT-3/COSMIC (Constellation Observ-ing System for Meteorology, Ionosphere, and Climate orF3/C in short) scintillation data are used to calculate theS4-index (shown in Eq. (1)) by using the signal to noiseratio on the L1 band C/A code (1.575 GHz) of GPSsatellite signals (see Syndergaard (2006) at http://cdaac-www.cosmic.ucar.edu/cdaac/doc/documents/s4_descrip-tion.pdf). This is defined as:

S4 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiI � �Ih ið Þ2

D Er�Ih i ð1Þ

where I ¼ ðL1CASNRÞ2, and < > denotes the averagetaken over one second (50 samples). Uma et al. (2012)and Brahmanandam et al. (2012) reported the global 3Dstructure of the maximum value of each S4 profile recordedby F3/C. For practical use of the F3/C S4-index data onthe Earth’s surface, Liu et al. (2016) developed a methodto convert and integrate the probed radio occultation

(RO) S4-index, to estimate the scintillation on the ground.They report the converted S4-index (hereinafter referred toas the S4-index) distributions globally for various localtimes, seasons, locations, and solar activities. This consti-tutes a significantly larger data base than used in any ofthe earlier scintillation modeling efforts, and provides suffi-cient coverage across the globe and throughout the solarcycle. It provided us with the opportunity to construct auseful and comprehensive ionospheric scintillation model.In this paper, we follow the spirit of the IRI model(Bilitza and Reinisch, 2008) and the approach of Liuet al. (2016) for obtaining S4 data from the F3/C observa-tions of the global S4-index during the 8-year period of2007–2014 (about 12 mega data points), to construct anempirical model (hereafter referred to as the F3CGS4model) for evaluating and predicting the global L-bandscintillation S4-index for ground-based and aviation posi-tioning, navigation, and communication applications.

2. Model development

F3/C is a constellation of six microsatellites, designed tomonitor meteorological and space weather data by per-forming RO observations in both the atmosphere and theionosphere. Due to the large number of samples providedby the six satellites, F3/C obtained up to 2000 scintillationprofiles per day (Anthes et al., 2008). The method devel-oped by Liu et al. (2016) is applied to convert the 3DF3/C S4max, which is the maximum value on each profiles,into a 2D (two dimensional in latitude and longitude) con-verted S4-index map on the ground (hereafter called S4-index). Fig. 1 illustrates diurnal variations of the S4-indexduring the solar minimum year of 2008 (PF10.7mean = 69 s.f.u.) and solar maximum year of 2013(PF10.7 mean = 125 s.f.u.). Here, PF107 = (F10.7+ F10.7A)/2, where F10.7 is the daily value and F10.7Ais the 81-day running mean value of the solar radio fluxat 10.6 cm wavelength. Results show that the equatorial/low-latitude scintillation S4-index initiates at 18:00 LT,exhibits a double-peak in latitude from 18:00 to 20:30LT, and then decays by �03:00 LT in both years. It canbe seen that the intensity in the solar maximum is muchgreater than during solar minimum. The seasonal globalplots in Fig. 2 reveal that the S4-index is prominent inthe low latitudinal region. The pronounced pattern gener-ally follows the magnetic equator for all four seasons. Itis restricted to longitudes from �70� to 0� (SouthAmerican-Atlantic sector) during the D-month (definedas ±45 days around December 22th), from 0� to 40� and140� to 210� (African and Pacific sector) during the J-month (±45 days around June 22th), and around 0� longi-tude (Atlantic sector) during the M- and S-months(±45 days around March 22th and September 22th,respectively).

Based on Figs. 1 and 2, the scintillation model can besubdivided into low latitude and high latitude parts, whichare connected/overlapped between ±45� and ±65� dip

Fig. 1. The global S4-index diurnal variation during (a) solar minimum year of 2008, and (b) solar maximum year of 2013.

Fig. 2. The diurnal mean S4-index geographic distribution in equinoxes (±45 days to March 22th and September 22th) and solstices (±45 days to June22th and December 22th) during the 8-year period.

Fig. 3. The weighting that combines the low latitude model weight (red line), and the high latitude model weight (blue line) of the model. Dashed linesdepict the boundary of the low latitudinal part of ±45� dip latitude, the high latitudinal part of ±65� dip latitude, and the intersection points at ±55� diplatitude with 50% weighting for each part. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version ofthis article.)

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latitude as illustrated in Fig. 3. In developing the S4-indexmodel, we assume that the diurnal variations (in local time,LT), annual variations (in day of year, DOY), dip-latitudinal variations, and solar activity variations (in solarflux index, PF10.7) are mutually independent andorthogonal:

S4 ¼ SDiurnalðLTÞ � SAnnualðDOY;LongitudeÞ� SDipðDipÞ � SPF10:7ðYear;DOY;PF10:7Þ � k ð2Þ

where k is the calibration constant, which is the ratio of theS4-index derived from F3/C to that observed by a co-located GNSS receiver on the ground.

We first model the diurnal term SDiurnal. Fig. 4 displaysthe overall median in the diurnal variation of the S4-indexin the equatorial region (±5� in dip-latitude) during the 8-year period. It is below S4 = 0.1 until about 18:00 LT,increases steeply, reaching a peak value at about 20:30LT, and then decreases drops below S4 = 0.1 at about03:00 LT. Note that the S4-index is the strongest during19:00–02:00 LT. This variation of the S4-index can be rep-resented by two normal distribution curves as:

SDiurnalðLTÞ ¼ a

rffiffiffiffiffiffi2p

p � exp �ðLT� 20:5Þ22r

!þ 0:075 ð3Þ

a = 0.5, and r = 1.3 for 12 < LT/decimal hours 5 20.5,a = 1.3, and r = 3.5 for 20.5 < LT/decimal hours 5 36

(= 24 + 12).The parameters are chosen so that there is a smooth

transition between the two segments with only a minimaljump at LT = 20.5. Fig. 4 shows that the diurnal variationof the S4-index is fitted well by Eq. (3). Note that the inter-cept of the 0.075 in Eq. (3) will be removed in the final inte-grated modeling.

On the other hand, the annual variation of the S4-indexis rather complex. We have tested a polynomial approach(1st to 10th order) for the ±5� dip-latitude region during19:00–02:00 LT have been tested by fitting to 1st to 10th

Fig. 4. The diurnal variation of the F3/C S4-index at dip-equator during 2007standard deviation. (For interpretation of the references to colour in this figu

order polynomials. Fig. 5 reveals that the RMSE (root-mean-square error) is greatly reduced after the 5th-orderpolynomial. Therefore, a 6th-order polynomial is beingadopted to represent annual variations. We further subdi-vide the globe into 36 longitudinal sectors, and determinethe annual polynomial for each sector. Hence the S4-index annual variation can be written as

SAnnualðDOY; longitudeÞ ¼X7j¼1

aj �DOYðj�1Þ !

i

; ð4Þ

where aj denotes the jth-order polynomial coefficients ofthe ith longitude sector (i = 1–36). To obtain the S4value for a specific longitude, a linear interpolation isapplied between the two adjacent longitude sector mid-points. Fig. 6 shows the annual variations of the S4-index at the magnetic equator for the 12 longitudesand illustrates the favorable agreement between observa-tions and model.

Following the approach used in IRI for F-region param-eters, we construct the latitudinal variation of the modelbased on a magnetic inclination (dip) based coordinate.Fig. 7a depicts the global distribution of the overall meanS4-index in a dip latitude longitude coordinate system dur-ing the entire 8-year period. It reveals four intense (peak)scintillation zones appearing at low latitudes of ±20� andhigh latitudes of ±70�. It can be seen that in low latitudes,the intensity of the northern peak is greater/wider than thatof the southern one. Fig. 7c shows the variation of the peaklocations with solar activity. It can also be seen that the lowlatitude northern and southern peaks vary between 15� and25� dip latitude and increase toward higher latitudes withincreasing solar activity. Here, we apply a 20-order polyno-mial function to describe the location of the northern peak(PNL), and give a symmetric location for the southern peak(PSL). Five functions, which are obtained by inserting thefive parameter sets in Eq. (5) using different sets of param-eters for the four major latitudinal peaks: the Northern

–2014 (blue curve) and the model fitting (red curve). Error bars denote ±1re legend, the reader is referred to the web version of this article.)

Fig. 5. The RMSE between the F3/C S4-index monthly variation at the dip-equator during 2007–2014 and the nth-order polynomial retrieval. Note thatthe RMSE becomes stable after the 6th-order polynomial retrieval (red circle). (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)

Fig. 6. The monthly variation of the F3/C S4-index at the dip-equator at selected longitudinal sectors during 2007–2014 (blue curves) and corresponding6th-order polynomial retrievals (red curves). Error bars denote ±1 standard deviation. (For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)

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Fig. 7. (a) The total mean of F3/C S4-index during 2007–2014, note that the red solid/dot-line curve indicates the dip-latitudes of the Northern/SouthernHigh-Latitude S4 peaks along longitudinal direction, the black solid/dashed line is the Northern Low-Latitude peaks and its mirror projection to the dip-equator as the Southern Low-Latitude peaks. (b) The F3/C S4-index dip-latitudinal variation (blue curve) and the model simulation (red curve), which isthe summation of the Equatorial part (gray curve), the Low-latitudinal part (green curve), and the High-latitudinal part (black curve). (c) The dip-latitudesof the four major peaks under increasing PF10.7. The blue lines indicate F3/C observation, and the red lines are model fitting. Error bars denote ±1standard deviation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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high latitudinal peak (NH), Northern low latitudinal peak(NL), Southern low latitudinal peak (SL), and Southernhigh latitudinal peak (SH) as well as the intensity at thedip equator (SEq) (Fig. 7b). Fig. 7c reveals that with

increasing solar activity at low latitudes tend to move pole-ward. At the high latitudes, the two observed northern andsouthern peaks (PNH, PSH) move southward. It can be seenthat the southward movement of the PSH appears

Fig. 8. The dip-latitudinal distribution of the F3/C S4-index at selected longitudes during 2007–2014 (blue curves), and the model fitting (red curves).Error bars denote ±1 standard deviation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version ofthis article.)

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insignificant. Nevertheless, four linear fits are adopted todescribe the positional (PNH, PNL, PSL, PSH) of the fourpeaks response to solar activity individually. Furthermore,SF is inserted into a of SNL to describe the peak intensity ofthe northern low latitudinal peak. Note that a for the restof the peaks are constants. Thus, the latitudinal (dip) vari-ation can be expressed as,

SDipðDipÞ ¼ SNH þ SNL þ SEq þ SSL þ SSH ð5Þ

where

SNH;NL;Eq;SL;SH Dipð Þ ¼ a

rffiffiffiffiffiffi2p

p � exp �ðDip�Dip0Þ2ð2rÞ2

!

For

SNH(Northern high latitudinal peak), Dip0 = PNH, a = 5.1, andr = 8,SNL(Northern low latitudinal peak), Dip0 = PNL, a = SF, andr = 11,SEq(Equatorial), Dip0 = 0, a = 78, and r = 20,SSL(Southern low latitudinal peak), Dip0 = PSL, a = 36, andr = 11,SSH(Southern high latitudinal peak), Dip0 = PSH, a = 7.8, andr = 11,

where

SFðLongitudeÞ ¼ 3360

25ffiffiffiffiffiffi2p

p � exp �ðLongitude � 90Þ2ð50Þ2

!þ 1

Fig. 9. The F3/C S4-index within ±5� dip correlation with PF10.7 during 2007–2014 (blue curve), and the model fitting (red line). Error bars denote ±1standard deviation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 10. The (a) diurnal variation (b) longitudinal variation (c) annual variation (d) solar activity variation of F3/C S4-index in high latitude region (60–85� dip) of northern/southern hemisphere (left/right panel) during 2007–2014 (blue curve), and corresponding model fit (red line). Error bars denote ±1standard deviation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 11. (a) An illustration of the RO technique. The segment length of the shell at h0 altitude along an occultation sounding path with the tangent heightat h is 2L2. (b) The ratio of segment length at a greater altitude h0 to that at tangent height for various sounding paths with tangent height at h = 100, 200,300, 400, 500, 600, and 700 km.

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Fig. 8 depicts the latitudinal distribution of the S4-indexalong the six longitude sectors �180�, �120�, �60�, 0�, 60�,and 120� during the 8-year period. The model fitted curvesfor PF10.7 = 90 s.f.u. and observations are in good agree-ment, except for the high latitude ionosphere beyond±75� dip latitude.

It is well known that the S4-index is very sensitive tosolar activity. Based on the daily average of the S4-indexover the equatorial ionosphere of ±5� dip latitude duringthe 8-year period (Fig. 9), we construct the S4-index

response to solar activity in the equatorial ionosphere,which can be expressed in linear form as,

SPF10:7ðPF10:7Þ ¼ 0:0016 � PF10:7þ 0:023 ð6ÞThe northern and southern high latitude ionosphere

(±60� to ±85� dip) response to the solar activity are some-what different, which will be constructed as follows.

To construct the high latitude model, six sine and twolinear functions are applied to describe the diurnal, longitu-dinal, annual, and PF10.7 variations of both the northern

Fig. 12. The model simulated S4-index diurnal variation of 30�W to 90�W longitude comparing with Fig. 1 during (a) solar minimum year 2008 (meanPF10.7 = 69 s.f.u.), and (b) solar maximum year 2013 (mean PF10.7 = 125 s.f.u.).

Fig. 13. The model simulated S4-index geographic distribution in equinoxes and solstices comparing with Fig. 2 with input PF10.7 = 90 s.f.u. (the meanPF10.7 value during 2007–2014).

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and southern high latitude regions from ±60� to ±85� diplatitudes. Fig. 10 reveals that the diurnal peak appears ataround midnight 00:00 LT in the northern hemisphere,and at about 14:00 LT in the southern hemisphere. Forthe longitudinal variation, the most prominent S4-indexoccurs at both �120� and 60� longitude in the northernhemisphere, but only at 120� longitude in the southern

hemisphere. The annual S4-index peak in the northernhemisphere occurs during February-April, while in thesouthern hemisphere the peak occurs during June–August.Similar to the low latitudes, the high latitude S4-index alsoincreases linearly with the PF10.7 index. Hence, the highlatitude S4-index can be modeled with a combination ofthese four orthogonal sine functions. Finally, by combining

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the low and high latitudinal models, for any given time,location, and solar activity, based on Eq. (2), the S4-index accordingly can be computed.

3. Discussion and conclusion

Dymond (2012) suggested that the angle between theline-of-sight of F3/C and the geomagnetic field-lines couldresult in a maximum in the S4-index at about 45�. How-ever, good agreements between the current model resultand ground based data of SCINDA shown in Fig. 15 (alsothose of Sun et al. (2015)) indicate that the angle effect ofDymond (2012) might be insignificant to our model.

The data set used in this paper is unique due to a verylong slant segment at the tangent height of the satellite-to-satellite RO measurement. This ensures that the RO willcorrectly probe S4 at a certain altitude. Fig. 11a displaysthe slant segment length per unit altitudinal interval (i.e.shell thickness of 5 km) versus height. It can be seen thatalong an individual RO link that the segment length ofthe shell at the tangent height (h) is much longer than thatat any greater altitude (h0). Fig. 11b illustrates the segmentlength as well as the ratio of the segment length at altitudesabove the tangent height to that at the tangent height (i.e.the tangent length) for various sounding paths (i.e. ROlinks). Owing to the tangent length being the longest one,the ratio at greater altitudes is less than 1. Taking an E-region sounding path with the tangent height at 100 kmaltitude as an example, the segment length at F-region300 km and E-region 100 km altitude are 40 km and510 km, respectively. This means that the ratio of thesounding geometry of the F-region to that of the E-region is about 0.08 (=40/510). The segment length at thetangent height dominates the RO sounding ray path. Inother words, unless the S4 intensity in the F-region is12.8 (=510/40) times greater than that in the E-region,the E-region scintillation can be correctly probed by theF3/C RO sounding without being contaminated by theF-region scintillation.

Fig. 14. The model simulated S4-index at northern (left panel) and souther

Analysis of RO soundings are typically based on theassumption of spherical symmetry, while the E- and F-region irregularities often extend over thousands of kilome-ters in width (Davies, 1990). For a typical F3/C RO sound-ing, the sounding length ranges from hundreds tothousands of kilometers (shorter than 3000 km). Becausethis is on the same order of the scale as the horizontalextension of the E- or F-region irregularities, the assump-tion of spherical symmetry may be applicable. Based onthe above explanations, for the vertical conversion, theionospheric, especially F-region, scintillation can representthe scintillation observed on the ground well (Liu et al.,2016). Here, we further compare the model simulationswith previous observation results.

Fig. 12 presents the diurnal variations in the solar max-imum and minimum, which are computed by our model forthe longitudinal section (30�W to 90�W). The model fea-tures in dip latitude are noticeably narrower than the data(Fig. 1). Both data and model show that the northern peakis stronger than the southern, but the difference of the twopeaks in the model result is more obvious. Nevertheless, themodel results are similar to the observational results shownin Fig. 1, and the results on global S4 distribution pre-sented by Liu et al. (2016) and Basu et al. (1988).

Su et al. (2006) reported pronounced irregularity occur-rence along the dip equator by using ROCSAT-1 in-situion density measurements at 600 km orbital altitude. Theoccurrence rate of the irregularities was found to be higherin the Atlantic sector during both equinox months, in theBrazilian sector in December, and in both the Africanand Pacific sectors in June. Sun et al. (2015) found thatthe distributions of the ROCSAT-1 irregularity occurrenceand the low latitudinal ground-based GNSS phase fluctua-tions are nearly identical, which indicates that low latitudi-nal scintillation is mainly caused by F-region irregularities.Due to the limited distribution of ground-based GNSSreceivers, Sun et al. (2015) display rather coarse distribu-tions making direct comparisons to our model results diffi-cult. During the equinox months, the greatest intensities

n (right panel) polar latitude in 00:00 LT with input PF10.7 = 90 s.f.u.

Fig. 15. (a) The locations of the 9 SCINDA ground based scintillation observation sites, which are Addis Ababa (ADD, 9.03�N, 38.77�E), Bangkok(BKK, 14.08�N, 100.61�E), Calcutta (CAL, 22.58�N, 88.37�E), Cuiaba (CBA, 15.56�S, 61.07�W), Dakar (DKR, 14.68�N, 22.46�W), Honolulu (HNL,21.52�N, 162.99�W), Kwajalein Atoll (KWA, 9.4�N, 167.47�E), Tirunelveli (TIR, 8.68�N, 77.81�E), and Chung-Li (TPE, 24.97�N, 121.19�E). (b) The S4-index of the SCINDA network (blue lines) sites ADD, BKK CAL, CBA, DKR, and (c) HNL, KWA, TIR, TPE comparing with the model simulated S4-index (red lines) in 2013. Error bars denote ±1 standard deviation. (For interpretation of the references to colour in this figure legend, the reader is referredto the web version of this article.)

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computed by our model are found on the eastward side ofthose reported by Sun et al. (2015), while in the solsticemonths, the two yield good agreements. On the otherhand, during the J- and S-month, the greatest intensitiesfrom the model are located westward of those observedby Su et al. (2006), while the two are in agreement duringthe M- and D-months. In general, we find that our modelresults shown in Fig. 13 agrees with both in-situROCSAT-1 satellite measurement by Su et al. (2006)and the ground-based GPS phase fluctuations presentedby Sun et al. (2015). The apparent similarity betweenthe latitude-longitude distribution of the S4-index derivedby our model and that found in the ground-based phaseobservations suggest that our model could very well rea-sonably represent the low latitudinal S4-index measuredfrom the ground.

It has been suggested that the highly fluctuating electrondensity in the auroral oval produces intense scintillation inthe VHF/UHF band. (Basu et al., 1990). Fig. 14 revealsthat our model predicts a zone with enhanced S4-index atabout 75� dip latitude, and encompasses the North Polein agreement with the northern auroral oval of Feldstein(1986). On the other hand, the southern high-latitude S4scintillations mainly appear around the South Pole ataround 80�S which is more in the polar cap than in theauroral oval. This suggests that our model can be used tocompute the high latitude scintillation in the northernhemisphere but should be treated cautiously in the south-ern hemisphere.

To validate the model performance at a given time andlocation, we hereby once again compare with data from aground-based GPS L1-band S4-index observation net-work: The Scintillation Network Decision Aid (SCINDA)(http://fas.org/spp/military/program/nssrm/initiatives/scinda.htm) in 2013 (Fig. 15). Since the S4max is used toestimate the S4 scintillation on the ground, the S4-indexderived from Eq. (2) is been calibrated by dividing by a fac-tor of 2.8, i.e. the calibration constant k = 1/2.8 (for detail,see Fig. 10 of Liu et al. (2016)), and a daytime backgroundS4 = 0.07, derived from the SCINDA observation, shouldbe added. The comparisons in Fig. 15b and c shows thatthe model does well in predicting the SCINDA observa-tions. The model somewhat overestimates observations atDKR and underestimates diurnal peak S4 values duringthe M-, J-, and S-months at KWA. Overall the model resultexhibits good agreement with the SCINDA data, whichonce again reveals that our model reproduces L-band scin-tillation observed on the ground well.

In summary, the scintillation distributions generatedfrom our new model are in good agreement with those ofthe F-region irregularities observed by satellites and asobserved on ground-based GPS receivers. This confirmsthat the F-region irregularity dominates the scintillationobserved on the Earth’s surface. Therefore, our model willprovide an estimate of L-band scintillation with inputsincluding the date, location, time, and PF10.7 for use in

a variety of applications for positioning, navigation, andcommunication systems. With the aid of scintillation datafrom the upcoming FORMOSAT-7/COSMIC-2 (Leeet al., 2013; Liu et al., 2015) RO scintillation data, themodel will be further modified and improved in the future.

Acknowledgments

This study has been partially supported by the project,MOST 103-2628-M-008-001, granted by Ministry ofScience and Technology (MOST) of Taiwan, and I-Dream project of NARLabs to National Central Univer-sity. The work is related to 2016 International Team: 375Ionospheric Space Weather Studied by RO and Ground-based GPS TEC Observations, (team leader: Liu J.Y.(TW)) granted by International Space Science Institute,ISSI-Bern. The authors thank Professor Lung-Chih Tsaiat National Central University for suggesting the use ofS4-index data from SCINDA.

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