Precise Ionosphere Modeling Using Regional GPS Network Data

Transcription

1 Journal of Global Positioning Systs () Vol., No. : 8-4 Prcis Ionosphr odling Using Rgional GPS Ntwor Data Y. Gao and Z.Z. Liu Dpartnt of Goatics Enginring Th Univrsity of Calgary Calgary, Albrta, Canada TN N4 -ail: gao@goatics.ucalgary.ca; Tl: ; Fax: Rcivd: July / Accptd: 8 July Abstract. Th ionosphr affcts th lctroagntic wavs that pass through it by inducing an additional transission ti dlay. Th ionosphr influnc has now bco th largst rror sourc in GPS positioning and navigation aftr th turn-off of th Slctiv Availability (SA). In this papr, thods of D gridbasd and 3D toography-basd ionosphric odling ar dvlopd basd on rgional GPS rfrnc ntwors. Prforanc analysis was conductd using data fro two diffrnt rgional GPS rfrnc ntwors. Th odling accuracy of th vrtical TEC (VTEC) is at th lvl of svral TECU for D ionosphric odling and about on TECU for 3D toographic odling aftr a coparison to indpndnt ionosphric ap data or dirctly asurd ionospshric TEC valus. Th data analysis has indicatd that th odling accuracy basd on th 3D toography thod is uch highr than th D grid-basd approach. y words: GPS, Ionosphr, Ionosphr Grid, Toography. Introduction Th ionosphr affcts th lctroagntic wavs that pass through it by inducing an additional transission ti dlay. Th agnitud of this ffct is dtrind by th aount of total lctron contnt (TEC) and th frquncy of lctroagntic wavs. Undr noral solar activity conditions, this influnc on GPS signals is usually in th rang fro a fw trs to tns of trs but it could rach or than trs during svr ionosphr stors. Aftr th turn-off of th Slctiv Availability (SA), th ionosphr ffct has bco th largst rror sourc in GPS positioning and navigation. For high prcision GPS positioning, th ionosphr ffct ust b stiatd so that a corrction can b ad to liinat it fro th GPS obsrvations. Prcis ionosphr ffct stiats ar also iportant for spac wathr rsarch and arth obsrvation applications (ojathy, 997). Th currntly availabl ionosphr corrction odls includ th lobuchar ionosphr paratrs broadcast fro th GPS llits but th lobuchar odl could only corrct about 5% of th total ionosphr ffcts (lobuchar, 987). or prcis ionosphr odl is thrfor rquird. Ionosphr odling thods using GPS data fro ground GPS ntwors hav bn xtnsivly invstigatd in th past svral yars (ojathy, 997; Son, 998; Jaowsi t al., 998; Liao, ; Fdrizzi t al., ). ojathy (997) stablishd a polynoial ionosphric odl basd on data fro rfrnc stations of Intrnational GPS Srvic (IGS) and has copard it to th TOPEX/Posidondrivd (T/P) TEC data. Agrnts at th lvl of 5 TECU wr rportd undr diu and low solar activity conditions (ojathy, 997). Son (998) ployd a two-dinsional grid-basd odl to charactriz th ionosphr activitis ovr th auroral rgion and an accuracy of about 34 c was obtaind. In Gao t al. (), ionosphr paratrs ar stiatd along with llit and rcivr biass using data fro a rgional ara GPS ntwor. To dat, all proposd ionosphric odls could b classifid into two diffrnt catgoris: grid-basd and function-basd. Th arly odling thods ar ostly basd on th function fitting tchniqus such as th broadcast ionosphr odl fro th GPS llits (lobuchar, 987), th polynoial functions (Costr t al., 99; ojathy, 997) and th sphrical haronics (Schar, 999; Walr, 989). On th othr hand, th grid-basd thod, first proposd by th ITRE Corporation and th Air Forc Phillips Laboratory (El-Arini t al., 994 and 995), has donstratd its capability for highr odling accuracy whn copard to th function-basd algoriths. Th grid-basd odling tchniqu has sinc

2 Gao t al:: Prcis Ionosphr odling Using Rgional GPS Ntwor Data 9 bn xtnsivly usd for both global and rgional ntwor-basd ionosphr rcovry (Gao t al., 994; FAA, 997; Son, 998; Liao, ). No attr whthr it is function or grid-basd, currnt ionosphr odling is two-dinsional in natur, which assus that th ionosphr is condnsd on a singl shll at a fixd altitud abov th arth surfac. This assuption, howvr, is only an approxiation to th rality and it is not physically tru. In ordr to furthr iprov th ionosphr odling accuracy and th odl s snsitivity to tporal ionosphr variations, ionosphric toography odling thod has startd to rciv or attntions in th rcnt yars (Rayund t al., 99 and 994; Rayund, 995; How, 997; Liu t al., a and b). An ionosphr toographic odl can dscrib th ionosphr fild in a thr-dinsional fra instad of a two-dinsional fra as usd by prvious thods. As a rsult, th ionosphr toography thod would allow for or prcis xploration of th ionosphric charactristics and subsquntly for or prcis odling accuracy. This papr dscribs th rcnt rsarch rsults in th ara of high prcision ionosphr odling using rgional GPS rfrnc ntwor data and focuss on D gridbasd and 3D toography-basd ionosphric odling. Th papr is organizd as follows. In Sction, ionosphric dlays ar drivd fro GPS dual-frquncy obsrvations including an algorith for carrir phas lvling on cod-drivd ionosphric dlay asurnts. Sction 3 discusss a D ionosphr odling thod whil a 3D ionosphr toographic odl is prsntd in Sctions 4. Nurical rsults and prforanc analysis ar providd in Sction 5. Conclusions ar givn in Sction 6. GPS IONOSPHERE EASUREENTS A dual-frquncy GPS rcivr usd at a rfrnc station consists of both cod and carrir phas obsrvations on L (575.4 H and L (7.6 H frquncis, dnotd as Pi and i (i, ) in th following. athatically th corrsponding obsrvations can b dscribd as L Frquncy: P + c( dt dt) + dorb + dtrop + I + bp B P ρ c dt + d + ε ( P ) () ult / P ρ + ( ) + λ + orb + trop + L Frquncy: dt N d d B + + ε ( ) () d ult / I b P ρ + c( dt dt) + dorb + dtrop + I + bp B P whr + d + ε( P ) (3) ult / P ρ + c( dt dt) + λ N + d orb + dtrop I + b i fi /(f f ), i ρ B + + ε( ) (4), ; d ult / is th tru gotric rang btwn rcivr and llit (); is th spd of light (/s); c dt is th llit cloc rror with rspct to GPS ti (s); dt is th rcivr cloc rror with rspct to GPS ti (s); L i λ i is th wavlngth of GPS signal on (); N i is th carrir phas intgr abiguity (cycl); d trop I d orb d ult is th troposphric dlay (); is th ionosphric dlay paratr (); is th llit orbit rror (); is th ultipath ffct (); b is th llit hardwar dlay (); B is th rcivr hardwar dlay (); and ε( ) is th asurnt nois (). Diffrncing th cod obsrvations fro L and L rsults in th following ionosphr asurnts: P P I + b B + ε ( P ) (5) P whr b b P b, B B P B. b and B rprsnt P P th diffrntial hardwar dlays btwn th L and L frquncis and thy ar oftn rfrrd to as llit and rcivr L/L intr-frquncy biass. Although ths biass ar actually ti dpndnt, in practic thy ar vry stabl ovr ti on a scal of days to onths so that thy can b tratd as constants during ionosphr odling (Gao, t al, 994; Schar, 999). As to th bias agnitud, th llit intr-frquncy bias is usually in th rang of svral nanosconds whil th rcivr intrfrquncy bias could b as larg as or than nanosconds (Gao t al., 994). Considring th uch highr nois lvl of th ionosphr asurnts drivd fro th cod asurnts, th carrir phas obsrvations fro L and L dscribd in quations () and (4) can b usd to sooth th cod obsrvation for a or prcis vrtical TEC stiat. Such carrir phas soothing tchniqu is also oftn rfrrd as carrir phas lvling. Givn blow is a soothing function that has bn dscribd in Gao t al. ().

3 Journal of Global Positioning Systs ( P P ) ( w ) ( w ) + ( w ) ( P P ) ( w ) + ( w ) + ( w ) [, ( P P ) + δ ( ) ] (6) whr is th ti poch indx; ( P P soothd ionosphr asurnt and ( w ) ( w ) ( P P ) ) is th (7) σ σ ( P P ) + σ δ ( ) ( ), ( ) ( ) (8) δ (9) Not that th soothd ionosphr asurnts in quation (6) ar still corruptd by th intr-frquncy biass bp and BP which thrfor nd to b stiatd along with th ionosphric dlay paratrs. 3 D IONOSPHERE ODELING Th ionosphr is a rgion of ionizd plasa that xtnds fro roughly 5 to abov th surfac of th arth. Gnrally, th ionosphr can b dividd into svral layrs in altitud according to lctron dnsity, which rachs its pa valu at about 35 in altitud. For D ionosphric odling, th ionosphr is assud to b concntratd on a sphrical shll of infinitsial thicnss locatd at th altitud of about 35 abov th arth s surfac (Gao t al., 994). Th iplntation of th singl-layr grid odl rquirs coputation of th intrsction of th lin-of-sight btwn th GPS rcivr and th obsrvd llit on th ionosphr shll as illustratd in Figur. Th intrsction point of th GPS signal with th ionosphric shll is dfind as pirc point at which th slant ionosphric dlay has an lvation angl of E. Ionosphr shll Ionosphr Pirc point E GPS llit j An ionosphric grid odl consists of grids distributd on th ionosphric shll in prst spacing usually 3 o x 3 o. Any pirc point thrfor will fall within a spcific grid dfind by its surrounding four grid points. Th slant ionosphric dlay at a pirc point, which has lvation angl of E, can b lind to th vrtical ionosphric dlay at th sa location by a apping function sf(e). anwhil th vrtical ionosphric dlay at th pirc point can b dscribd by th vrtical ionosphric dlays at its surrounding grid points. Th rlationship btwn th slant ionosphric dlay at th pirc point and th vrtical ionosphric dlays of its surrounding four grid points can b xprssd by th following quation: 4 ) ( P P ) sf ( E) ( I v p () sf ( E) / [cos( E) /( + h / R)] () whr E is th llit lvation angl; R is th arth radius; h is th hight of th ionosphr shll abov th arth s surfac; ( I v ) is th vrtical ionosphric dlay paratr at th grid point ; p is a wighting function which is usd to projct th vrtical ionosphric dlay at grid point to th pirc point. Taing into account th xistnc of L/L intrfrquncy biass b and B, w can stablish th following ionosphr obsrvation quation for a llit (j) and rcivr (i) pair: 4 ij ij ij v ) ( P P ) sf ( E ) ( I p + b B () Equation () is th fundantal quation for th grid point vrtical ionosphric dlay stiation in grid-basd D ionosphric odling using carrir soothd coddrivd ionosphr asurnts. As to paratr stiation, th standard last squars or alan filtring thod can b usd to facilitat th optial stiation of th vrtical ionosphric dlay paratrs and th llit/rcivr intr-frquncy biass. ij ij Rcivr i 4 3D Toographic odling Earth surfac h 35+R R Earth cntr O Fig. Ionosphr Shll A two-dinsional (D) ionosphric odl as dscribd in th last sction has difficulty to charactriz th ionosphric fild in th full spatial dinsions bcaus it is unabl to provid th vrtical ionosphric profil. A thr-dinsional (3D) ionosphric odl thrfor is xpctd. A 3D ionosphric odling thod using

4 Gao t al:: Prcis Ionosphr odling Using Rgional GPS Ntwor Data toography tchniqu will b dscribd in th following which is abl to charactriz not only th ionosphric horizontal profil but also th vrtical on. Toography-basd odling consists of two fundantal stps. First, intgral asurnts ar ad of th diu of intrst, idally along any paths fro any diffrnt viwing angls. Scond, ths intgral asurnts ar invrtd to obtain an stiat of th fild (How, 997). In ionosphric toography, th intgral asurnts ar th lins of sight btwn th GPS rcivrs and llits, which pass through th ntir ionosphr. A 3D ionosphric odl can b constructd using th toography tchniqu, horizontally by sphrical haronics functions (SHFs) and vrtically by th pirical orthogonal functions (EOFs). Th haronics functions ar priarily ford by th first svral ordrs of haronics. Th high-ordr haronics howvr iprov th sharpnss of th fronts. EOFs ar drivd fro xisting data st (obsrvation data or odl data) of th diu of our intrst. Th obsrvation quation of ionosphric toography can b givn as follows (Liu t al., a and b): TEC λ δn( λ, z ds (3) (, ds [ N + N )] whr TEC is th total lctron contnts along th lin of sight fro a GPS llit to a ground GPS rcivr and is th ionosphric lctron dnsity at th N gospatial position of z ). is th a priori valu of N which could b an output fro an pirical odl that rflcts th dtrinistic portion of our a priori inforation. δn is th corrction to th a priori valu. λ, z ar longitud, latitud and altitud, rspctivly, rfrncd to a solar-goagntic coordinat syst. For th convninc purpos, w could lt N b approxiatly qual to zro, naly N TEC N. Thus w hav, δ N ds (4) Th corrction for th lctron dnsity function δn can b odld by a sris of spac-location rlatd functions. or spcifically w can ploy sphrical haronic xpansions horizontally and pirical orthogonal functions (EOFs) vrtically to odl th ionosphric lctron corrction tr. Th intgration of ths two sts of functions nabls us to dpict th ionosphr fild in a 3D od as follows: δn n [ a n cos( λ) + b n sin( λ)] Pn (cosφ) Z ( (5) P n whr (cosφ) is th associatd Lgndr polynoial of ordr and dgr n ; ( is th pirical orthogonal function (EOF); a n and b n ar th cofficints to b stiatd. Cobining Equations (4) and (5), th obsrvation quation for ionosphric 3D odling can thn b stablishd by th following quation: TEC n n n Z n [ a cos( λ) + b sin( λ)] P n ) (cosφ Z an cos( λ) Pn (cosφ) Z ( ds n n ) (ds + b sin( λ) P (cosφ) Z ( z ds (6) n Equation (6) is th fundantal obsrvation quation for 3D ionosphric odling using toography invrsion tchniqu, through which th GPS drivd total lctron contnt (TEC) and th cofficints dscribing th ionosphr fild ar lind. Th rst tas of ionosphric toography is to optially stiat th odl cofficints in quation (6) in which th nubr of th unnown odl paratrs is dtrind by th truncation liits of SHFs and EOFs. A so-calld wightd, dapd last squars tchniqu has bn dvlopd via a cobination of wighting and daping procdurs dscribd in Liu t al. (a and b). 5 Rsults AND ANALYSIS Th data fro two rgional GPS rfrnc ntwors, SWEPOS and SCIGN, wr procssd to gnrat rgional ionosphric odl using th dvlopd D gridbasd and 3D toography tchniqus. 5. Rsults of D Grid-Basd odling Th data fro th Swdish GPS rfrnc ntwor (SWEPOS) has bn usd to valuat th prforanc of th D grid-basd ionosphr odling thod. Th SWEPOS ntwor (Figur ) consists of continuously oprating GPS stations xtnding fro latitud 55 to 69 dgrs north with an avrag station sparation of around (Liao, ). Data usd in th nurical analysis includs a total of fiv days of conscutivly tracd GPS data collctd during ay 7-, 999. For th purpos of this rsarch, only tn stations in th southrn portion of th SWEPOS (th two stations in th bloc fra ar not includd du to an accidnt loss of

5 Journal of Global Positioning Systs data) wr usd in th nurical coputation. Th tn stations ar locatd within a rang of approxiatly 55 o N to 6 o N in gographic latitud and o E to 8 o E in gographic longitud. btwn UofC and CODE stiats as wll as th RS valu ovr th conscutiv fiv days. Th TEC stiats in th cntral rgion of th ground SWEPOS ntwor (56 o N and 59 o N) ar vry consistnt to th stiats drivd fro th CODE global TEC aps. Th ovrall agrnt was at th lvl.4~3. TECU. On th othr hand, th consistncy has bn dgradd for grids off th cntral latitud rgion (53 o N and 6 o N) to a lvl of up to 4.6 TECU. This is du to th fact that th ionosphr asurnt dnsity in th cntral rgion is highr than othr boundary rgions ovr a rgional ntwor. Fig. Rfrnc Stations in SWEPOS Shown in Figur 3 and 4 ar th vrtical TEC stiats at latituds of 59 o N and 56 o N rspctivly with a grid siz of 3 o 3 o basd on th fiv-day data. Th rsults show clarly th diurnal bhavior of th ionosphr and th variations fro day to day. Ths vrtical TEC stiats ar consistnt with diurnal ionosphr bhavior considring th ovrall chang pattrn. For xtrnal coparison purpos, th vrtical TEC stiats drivd fro th global ionosphr aps (GI) providd by th Cntr of Orbit Dtrination in Europ (CODE) ar also shown in Figur 3 and 4. CODE is on of th fiv Intrnational GPS Srvic (IGS) ionosphr analysis cntrs that hav supplid global TEC aps sinc Jun, 998 on a rgular basis to th Crustal Dynaics Data Inforation Systs (CDDIS), a global data cntr of IGS. Th ovrall consistncy in trs of RS valus btwn th global TEC aps drivd fro diffrnt analysis cntrs is rportd to b at th lvl of 3~5 TECU although th inconsistncy could rach up to 7~ TECU btwn so cntrs. Providd in Tabl ar th daily RS valus of th TEC stiat diffrncs Vrtical TEC (TECU) Vrtical TEC (TECU) Tab. RS Valus of TEC Estiat Diffrncs (TECU) Goagntical Local Ti (Day) Fig. 3 VTEC at Goagntic Latitud 59 o N Goagntical Local Ti (Day) Fig. 4 VTEC at Goagntic Latitud 56 o N UofC CODE UofC CODE Grid Latitud Day Day Day 3 Day 4 Day 5 Day ~5 53 o N o N o N o N

6 Gao t al:: Prcis Ionosphr odling Using Rgional GPS Ntwor Data 3 5. Rsults of 3D Toographic odling Th prforanc analysis of 3D toographic odling was conductd using GPS data obsrvd fro six GPS rfrnc stations within th Southrn California Intgratd GPS Ntwor (SCIGN) on ay 5,. Th SCIGN consists of 5 GPS stations and is priarily dsignd to onitor th crustal dforation and arthqua activitis in southrn California rgion (SCIGN, ). Th gographical distribution of th slctd six stations is shown in Figur 5. A total of 6 pochs of dual frquncy GPS asurnts fro six stations at a data rat of 3 sconds wr usd for th construction of an ionosphric toography odl for th rgion. To assss th odling accuracy, th 3 asurnts, collctd idiatly aftr th 6 pochs, wr usd as prdiction data points for coparison purpos. Error (TECU) Nubr of Ionosphric Dlays (an.56 TECU, RS.7 TECU) Fig. 6 Vrtical Ionosphric Toography odling Errors TECdirct TECodl RE % (7) TEC dirct Th rsults indicatd that th odl-drivd slant ionosphric dlays hav a an rror of.4% with rspct to th dirctly asurd ionospshric dlay valus. ost rlativ rrors varid btwn 4.% and +4.%. Th 3D toographic odling thrfor has producd uch lowr ionosphric odling rrors or bttr odling accuracy than th D grid-basd odling thod. It is also worth to ntion that a carrir phas lvling procdur was not iplntd during th 3D toography ionosphric odling coputation. So it is xpctd that a furthr accuracy iprovnt can b obtaind if th nois lvl of th cod-drivd ionosphric dlay asurnts is rducd via carrir phas soothing. Fig. 5 Distribution of Six SCIGN Rfrnc Stations Onc th toography odl cofficints wr obtaind, th obtaind odl paratrs ar usd to calculat th ionosphric dlay for any lin of sight btwn a GPS rcivr and llit. If th odl drivd ionosphric dlays can b copard to its dirctly asurd valu fro th dual frquncy GPS obsrvations, th 3D toography ionosphric odling accuracy can thn b assssd. Th coparison rsults ar providd in Figur 6 whr th diffrncs indicatd an agrnt for th vrtical ionosphric dlays btwn th odl-drivd stiats and th dirct asurnts at th lvl of. TECU. Shown in Figur 7 ar th rror stiats in prcntag calculatd using th following quation: Prcnt (%) Nubr of Ionosphric Dlays (an Error.4%) Fig. 7 Slant Ionosphric Toography odling Error in Prcntag 6 Conclusions Both two and thr-dinsional ionosphric odling thods hav bn dscribd in this papr and thir prforanc hav bn assssd basd on data fro two diffrnt rgional GPS rfrnc ntwors. Th agrnt for D grid-basd odling is at th lvl of svral TECU whn copard to an indpndnt sourc whil th agrnt for 3D toographic odling is at th lvl of about on TECU copard to th dirctly asurd ionosphr valus fro dual-frquncy GPS

7 4 Journal of Global Positioning Systs obsrvations. Basd on th dvlopd 3D toographic ionosphric odl, th slant ionosphric dlays could b wll rcovrd with a an rror of.4%, indicating a significant iprovnt of accuracy ovr th D gridbasd odling. or nurical analysis, howvr, is rquird to furthr invstigat th prforancs of th D and 3D ionosphric odls prsntd in this papr. Acnowldgnts This rsarch was supportd by a stratgic grant fro th Natural Scincs and Enginring Rsarch Council of Canada (NSERC). Th Southrn California Intgratd GPS Ntwor and its sponsors, th W.. c Foundation, NASA, NSF, USGS, SCEC, ar thand for providing data usd in this study. Rfrncs Costr, A.J., E.. Gaposchin and L.E. Thornton (99). Ral- Ti Ionosphric onitoring Syst Using GPS. Navigation, Journal of Institut of Navigation, Vol.39, No., pp.9-4. El-Arini,.B., C.J. Hgarty, J.P. Frnow and J.A. lobuchar (994). Dvlopnt of an Error Budgt for a GPS Wid- Ara Augntation Syst (WAAS), Procdings of Th Institut of Navigation National Tchnical ting, San Digo, CA, January, 994. El-Arini,.B., R.S. Conr, T.W. Albrtson, J.. Ragan, J.A. lobuchar and P.H. Dohrty (995). Coparison of Ral- Ti Ionosphric Algoriths for a GPS Wid-Ara Augntation Syst (WAAS). Navigation, Journal of Th Institut of Navigation, Vol.4, No.4, pp FAA (997). Spcification for th Wid Ara Augntation Syst, FAA-E-89C (draft), 997. Fdrizzi,., R.B. Langly, A. ojathy,.c. Santos, E.R. d Paula and I.J. antor (). Th Low-Latitud Ionosphr: onitoring its Bhavior with GPS, Procdings of ION GPS, 4 th Intrnational Tchnical ting of th Satllit Division of th Institut of Navigation, Salt La City, UT, Sptbr -4,. Gao, Y., P. Hroux and J. ouba (994). Estiation of GPS Rcivr and Satllit L/L Signal Dlay Biass Using Data fro CACS, Procdings of IS-94, Banff, Canada, August 3 - Sptbr, 994. Gao, Y., X. Liao and Z.Z. Liu (). Ionosphr odling Using Carrir Soothd Ionosphr Obsrvations fro a Rgional GPS Ntwor, Goatica, Vol. 56, No., pp How, B.. (997). 4-D Siulations of Ionosphric Toography, Procdings of ION National Tchnical ting, Santa onica, California January 4-6, 997. Jaowsi, N., E.Sardon and S. Schlütr (998). GPS basd TEC Obsrvations in Coparison with IRI95 and th Europan TEC odl NTC, Advancs in Spac Rsarch, Vol., pp lobuchar, J.A. (987). Ionosphric Ti-Dlay Algorith for Singl-Frquncy GPS Usrs, IEEE Transactions on Arospac and Elctronic Systs, Vol. AES-3, No.3, pp ojathy, A. (997). Global Ionosphric Total Elctron Contnt apping Using th Global Positioning Syst, Ph.D. dissrtation, Dpartnt of Godsy and Goatics Enginring Tchnical Rport NO. 88, Univrsity of Nw Brunswic, Frdricton, Nw Brunswic, Canada, 48pp. Liao, X. (). Carrir Phas Basd Ionosphr Rcovry Ovr A Rgional Ara GPS Ntwor, UCGE Rports, Nubr 43, Univrsity of Calgary, Calgary, Albrta, Canada, pp. Liu, Z.Z. and Y. Gao (a). Optiization of Paratrization in Ionosphric Toography, Procdings of ION GPS, Salt La City, Utah, USA, Sptbr -4,. Liu, Z.Z. and Y. Gao (b). Ionosphric Toography Using GPS asurnts, Procdings of IS-, Banff, Albrta, Canada, Jun 5-8,. Rayund, T.D. (995). Coparisons of Svral Ionosphric Toography Algoriths, Ann. Gophys., 3, pp Rayund, T.D., J.R. Austn, S.J. Fran, C.H. Liu, J.A. lobuchar and J. Stalr (99). Application of Coputrizd Toography to th Invstigation of Ionosphric Structurs, Radio Scinc, 5, pp Rayund, T.D., Y. Brslr, D.N. Andrson and R.E. Danill (994). odl-assistd Ionosphric Toography: A Nw Algorith, Radio Scinc, 9, pp SCIGN (). Southrn California Intgratd GPS Ntwor, accssd on April st,. Schar, S. (999). apping and Prdicting th Earth s Ionosphr Using th Global Positioning Syst, Ph.D dissrtation, Astronoical Institut, Univrsity of Brn, Switzrland, pp5. Son, S. (998). Wid Ara Ionosphr Grid odling in th Auroral Rgion. UCGE Rports Nubr 3, Ph.D thsis, Th Univrsity of Calgary, Calgary, Albrta, Canada. Walr, J.. (989). Sphrical Cap Haronic odling of High Latitud agntic Activity and Equivalnt Sourcs with Spars Obsrvations, Journal of Atosphric and Trrstrial Physics, Vol.5, No., pp.67-8.