PPP at low latitudes with ionospheric model exclusively based on single frequency GNSS measurements

1. In oduc ion In sa elli e-based na iga ion and posi ioning, he ionosphe ic delay is conside ed a c ucial e o sou ce. In low la i udes, o ins ance, he p ecise poin posi ioning (PPP) accu acy is se e ely a ec ed by he high ionosphe ic a iabili y (Vee il e al.,2020). Au onomous ecei e s ha ope a e on wo o mo e equencies can elimina e up o 99.9% o he ionosphe ic delay by using he so-called ionosphe ic ee combina ion. Howe e , single equency ecei e s a e no capable o o m he dual equency combina ions and a e he e o e dependen on he ionosphe ic delay de i ed by ionosphe ic models (Ro i a-Ga cia e al.,2020). Global Ionosphe ic Maps (GIMs) a e p oduc s based on Global Na iga ion Sa elli e Sys em (GNSS) da a as ly used o ep esen he ionosphe e and imp o e single equency posi ioning. Since 1998, he GIMs a e compu ed by he Ionosphe e Associa ed Analysis Cen e s (IAACs) and p o ided by he In e na ional GNSS Se ice (IGS) (He nández-Paja es e al.,2009). Cu en ly, he e a e eigh IAACs ha p o ide GIMs: he Cen e o O bi De e mina ion in Eu ope (CODE), Eu opean Space Agency (ESA), Je P opulsion Labo a o y (JPL), Uni e si a Poli ecnica de Ca alunya (UPC), Chinese Academy o Science, Wuhan Uni e si y (WHU), Na u al Resou ces Canada (NRCan), and Ope a ional Tool o Ionosphe ic Mapping And P edic ion/Deu sches Geodä- isches Fo schungsins i u - Technische Uni e si ä München (OPTIMAP/DGFI-TUM) (Fel ens & Schae ,1998; Goss e al.,2019; Roma-Dollase e al.,2018). Di e en es ima ion echniques ha e been de eloped by each cen e . CODE, ESA, NRCan, and WHU gene a e GIMs using sphe ical ha monic (SH) se ies expansion (Goss Abs ac Single equency use s o he Global Na iga ion Sa elli e Sys em (GNSS) should co ec he ionosphe ic delay o ob ain posi ioning solu ions. A aluable sou ce o ionosphe ic delay co ec ions is he global ionosphe ic models (GIMs) o Ve ical To al Elec on Con en . The accu acy o GIMs is he e o e impo an o imp o e he posi ioning accu acy. One o he main issues ha a ec s he GIM pe o mance, especially a low la i ude egions, is he high sensi i i y o he global posi ioning sys em (GPS) L2 equency o ionosphe ic scin illa ion. As an a emp o o e come his issue, in his wo k, we s udy he capabili ies o using only GPS L1 equency o compu e ionosphe ic co ec ions in o m o egional ionosphe ic maps. The pe o mance o he new ionosphe ic model is e alua ed by means o single equency p ecise poin posi ioning, compa ing he posi ioning esul s agains he co ec ion using dual- equency GPS signals, as well as compa ed o he co ec ions p o ided by GIMs p oduced by he in e na ional GNSS se ice. As a esul , he posi ioning pe o mance using single equency model p esen ed simila accu acy o he dual equency models and, a he same ime, p o ided less obse a ions a ec ed by ionosphe ic scin illa ions. These esul s demons a e he easibili y o using single equency GNSS da a o de elop ionosphe ic models and o imp o e he posi ioning o e low la i udes. Plain Language Summa y P ecise Poin Posi ioning (PPP) is a echnique used o de e mine he posi ion o a ecei e on he Ea h’s su ace using signals om Global Na iga ion Sa elli e Sys ems (GNSS), which a e ansmi ed wi h a minimum o wo equencies. The ionosphe e, an ionized laye in he Ea h’s a mosphe e, can cause e o s in GNSS signals and a ec he PPP accu acy. To imp o e accu acy, an ionosphe ic model can be used o co ec hese e o s. In his s udy, we assess an single equency ionosphe ic model. The esul s show ha i is possible o use single equency GNSS da a o de elop ionosphe ic models ha can imp o e posi ioning accu acy o e low la i udes. CHRISTOVAM ETAL. © 2023. The Au ho s. This is an open access a icle unde he e ms o he C ea i e Commons A ibu ion-NonComme cial-NoDe i s License, which pe mi s use and dis ibu ion in any medium, p o ided he o iginal wo k is p ope ly ci ed, he use is non-comme cial and no modi ica ions o adap a ions a e made. PPP a Low La i udes Wi h Ionosphe ic Model Exclusi ely Based on Single F equency GNSS Measu emen s Ana L. Ch is o am1 , Fab icio S. P ol2, Gab iel O. Je ez1, Manuel He nández-Paja es3 , and Paulo O. Cama go1 1Depa men o Ca og aphy, São Paulo S a e Uni e si y (UNESP), São Paulo, B azil, 2Depa men o Na iga ion and Posi ioning, Finnish Geospa ial Resea ch Ins i u e, Na ional Land Su ey o Finland, Espoo, Finland, 3Depa men o Ma hema ics, UPC-IonSAT and UPC-IEEC Resea ch G oups, Uni e si a Poli ècnica de Ca alunya (UPC), Ba celona, Spain Key Poin s: • Single equency ionosphe ic models allows o ob ain simila p ecise poin posi ioning accu acy han dual equency ionosphe ic models • Single equency Global Na iga ion Sa elli e Sys em measu emen s p o ide mo e IPPs han dual equency du ing ionosphe ic scin illa ion e en s Co espondence o: A. L. Ch is o am, [email p o ec ed] Ci a ion: Ch is o am, A. L., P ol, F. S., Je ez, G. O., He nández-Paja es, M., & Cama go, P.O. (2023). PPP a low la i udes wi h ionosphe ic model exclusi ely based on single equency GNSS measu emen s. Space Wea he , 21, e2023SW003513. h ps://doi.o g/10.1029/2023SW003513 Recei ed 30 MAR 2023 Accep ed 4 JUL 2023 Au ho Con ibu ions: Concep ualiza ion: Fab icio S. P ol Supe ision: Fab icio S. P ol, Manuel He nández-Paja es, Paulo O. Cama go W i ing – e iew & edi ing: Fab icio S. P ol, Gab iel O. Je ez, Manuel He nández-Paja es 10.1029/2023SW003513 RESEARCH ARTICLE 1 o 13 Space Wea he CHRISTOVAM ETAL. 10.1029/2023SW003513 2 o 13 e al.,2020; Li e al.,2015; Roma-Dollase e al.,2018). The echnique adop ed by JPL is bi-cubic splines whe eas UPC adop ed he omog aphic app oach (He nández-Paja es e al.,1999; Mannucci e al.,1998). The OPTI- MAP use polynomial B-spline o he ionosphe ic modeling (Goss e al.,2020). Common o all p oduc s is he da a dis ibu ion p o ided in IONosphe e map EXchange (IONEX) o ma wi h a spa ial esolu ion 5°×2.5° in longi ude and la i ude, espec i ely, and wi h a empo al esolu ion om 15min o 2h (He nández-Paja es e al.,2017; Schae e al.,1998). The GIMs p o ide To al Elec on Con en (TEC) om hund eds o wo ld- wide pe manen GNSS ecei e s, no mally compu ed om dual equency measu emen s (He nández-Paja es e al.,1999; Mannucci e al.,1998; Schae e al.,1996). Ca ie phase ambigui ies and DCBs a e essen ial pa am- e e s es ima ed by IAACs. The p ocess o es ima ing DCBs and ambigui ies is known as he TEC calib a ion me hod, which can be pe o med ei he ne wo k-wide, such as in he case o GIMs, o wi h indi idual GNSS s a ions (Ci aolo e al.,2007; P ol, Cama go, e al.,2018; Shaikh,2023). The pe o mance o GIMs gene a ed by IGS is consis en wi hin he IAACs (He nández-Paja es e al.,2009), bu usually p o ides lowe pe o mance in low la i ude egions, especially du ing ionosphe ic scin illa ion e en s. P ol, Cama go, e al.(2018), o ins ance, e alua e he pe o mance o TEC calib a ion p ocedu es by analyz- ing he imp o emen in single equency PPP conside ing se e al la i udes. The au ho s ound a wo se PPP pe o mance in low la i udes, mainly due o he ionosphe ic a iabili y associa ed wi h he Equa o ial Ioniza ion Anomaly (EIA) and ionosphe ic scin illa ion. Ro i a-Ga cia e al.(2020) addi ionally assess he quali y o he ionosphe ic models by GNSS posi ioning and showed la ge posi ioning e o s in ecei e s loca ed a la i udes close o he geomagne ic equa o . One o he main challenges in ionosphe ic modeling a low la i udes is he p esence o ionosphe ic i egula i- ies ha can esul in he lack o con inuous GNSS ope a ion, especially in global posi ioning sys em (GPS) L2 equency. The in luence o he ionosphe e is di e en o each equency since he ionosphe e is a dispe si e medium, whe e highe equencies a e less a ec ed when compa ed wi h lowe equencies. Delay e al.(2015) show ha , du ing he p esence o ionosphe ic i egula i ies, he p obabili y o in e up ed acking was la ge on GPS L2 and L5 han on he L1 signal equency. Simila ly, Mo aes e al.(2017) also p esen ha du ing he ionosphe ic i egula i ies' occu ence, he GPS L1 signal is less sensi i e o loss o locks han he L2 equency. Gi en ha GPS L1 pe o ms be e han GPS L2 equency, i is easonable o in es iga e he possibili y o de elop ionosphe ic models exclusi ely based on GPS L1 equencies. In his ega d, Ch is o am e al.(2023) p esen a egional ionosphe ic model de eloped o he low la i ude egion only using single- equency da a. The main disad an age is ha he single equency TEC measu emen s is highly dependen on he code noise. Ne e heless, Ch is o am e al.(2023) ha e shown ha models exclusi ely based on GPS L1 can be used o de ec and analyze equa o ial plasma bubbles, despi e o he code noise and mul ipa h, which can be s ongly mi iga ed o single- equency ionosphe ic moni o ing (He nández-Paja es e al.,2018). Buil on his p e ious wo k, we in end he e o e i y whe he models exclusi ely based on GPS L1 equencies can also be used o imp o e he single- equency PPP pe o mance. The main goal is o e i y i he single equency PPP based on single equency ionosphe ic model can p o ide compa able le el o hose ionosphe ic models ob ained by dual equency GNSS measu emen s. In his in end, he PPP pe o mance ob ained wi h he model de eloped by Ch is o am e al.(2023) is compa ed wi h he single equency PPP esul s aided by o he consolida ed models. Sec ion2 p esen s an o e iew o he me hod de eloped by Ch is o am e al.(2023) based on single equency da a and some modi ica ions o dual equency da a. In addi ion, Sec ion2 also p esen s he con igu a ions used o un he single equency PPP solu ions. Sec ion3 p esen s an ini ial alida ion o TEC alues ob ained by he single and dual equency models. I also includes a b ie discussion abou he impac o ionosphe ic a iabili y on GPS equencies, as well as an assessmen o single equency PPP based on he single equency ionosphe ic model. Sec ion4 p esen s he conclusions. 2. Me hod Sec ion2.1 p esen s an o e iew o he ionosphe ic model p oposed by Ch is o am e al.(2023) exclusi ely based on single equency da a, as well as he adap a ions equi ed o un he same model using dual equency da a. The dual equency model is p esen ed he e o ha e a base o compa ison pu poses. Addi ionally, Sec ion2.2 shows he con igu a ion used o un he single equency PPP solu ions. The PPP algo i hm is used as main indi- ca o o e alua e he p oposed model. 15427390, 2023, 8, Downloaded om h ps://agupubs.onlinelib a y.wiley.com/doi/10.1029/2023SW003513 by Csic O ganización Cen al Om (O icialia Mayo ) (U ici), Wiley Online Lib a y on [27/02/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License Space Wea he CHRISTOVAM ETAL. 10.1029/2023SW003513 3 o 13 2.1. Modeling Ch is o am e al.(2023) de eloped a ionosphe ic egional model o calib a e GNSS single equency measu emen s and de i e ionosphe ic maps showing plasma bubble in one o mos challenging condi ion, he B azilian egion. The au ho s ha e shown, o he i s ime, ha i is possible o de ec ionosphe ic bubbles using single equency GNSS da a. In addi ion, he au ho s also p esen a compa ison o he STEC alues ob ained wi h single and dual equency. The esul s showed ha single equency STEC da a ag ee wi h dual equency da a, wi h di e ences a ying be ween ±2.5 TECU. This di e ence co esponds o he o e all noise le el o code measu emen s, since he single equency STEC alues a e compu ed based on combina ion be ween he obse ables called Code-Minus-Ca ie (CMC). In his sec ion we p esen an o e iew o he ionosphe ic model p oposed by Ch is o am e al.(2023) along wi h he necessa y adap a ions o u ilize dual- equency da a wi h he same model. The ma hema ical o mula ion o ex ac TEC da a using GNSS obse a ions was de eloped in h ee s ages. In he i s s ep, he con e sion o GNSS obse a ions o non-calib a ed TEC da a was pe o med. The second e e s o ambigui y es ima ion by SH modeling. The hi d s ep is ca ied ou o es ima e he absolu e (i.e., calib a ed) TEC alues and ca y ou a egional in e pola ion. The main di e ence be ween he egional modeling using single o dual equency is ela ed o GNSS measu e- men s combina ions. TEC da a es ima ed using dual- equency GNSS measu emen s is pe o med by he geome- y ee combina ion 𝐴𝐴𝐴𝐴 1−𝐴𝐴2 . I elimina es all he e ms independen on he equencies, such as he oposphe ic delay, clocks, and geome ic dis ance. When using single equency, he combina ion be ween he obse ables 𝐴𝐴𝐴𝐴 1−𝐿𝐿1 named CMC is used since i elimina es all geome y-dependen componen s. The combina ions used o compu e TEC using single ( 𝐴𝐴TECSF ) and dual equency ( 𝐴𝐴TECDF ), espec i ely, can be summa ize as ollows: TECSF =𝑘𝑘×(𝑃𝑃1−𝐿𝐿1𝜆𝜆1+𝐵𝐵SF) (1) TECDF =𝐹𝐹×(𝜆𝜆2𝐿𝐿1−𝜆𝜆2𝐿𝐿2+𝐵𝐵DF) (2) whe e 𝐴𝐴𝐴𝐴 𝑖𝑖 and 𝐴𝐴𝐴𝐴 𝑖𝑖 a e he GNSS pseudo ange and ca ie phase, espec i ely; 𝐴𝐴𝐴𝐴 𝑖𝑖 is he wa eleng h in me e s; 𝐴𝐴𝐴𝐴 SF and 𝐴𝐴𝐴𝐴 DF bias e m ha ep esen s he ambigui y e m, and ins umen al delay e m a ec ed by he mul ipa h and he mal noise and he esidual e m o single and dual equency espec i ely. The 𝐴𝐴𝐴𝐴 and 𝐴𝐴𝐴𝐴 e ms con e me e s o delay o he elec ons/m 2 uni s, being 𝐴𝐴𝐴𝐴 = ( 𝑓𝑓𝐿𝐿 12 ∕(2 × 40.3) ) and 𝐴𝐴𝐴𝐴 = ( 𝑓𝑓2 𝐿𝐿1 𝑓𝑓2 𝐿𝐿2 ∕40.3× ( 𝑓𝑓2 𝐿𝐿1 −𝑓𝑓2 𝐿𝐿2)) , wi h 𝐴𝐴𝐴𝐴 𝐿𝐿1 and 𝐴𝐴𝐴𝐴 𝐿𝐿2 ep esen ing he equencies o L1 and L2, espec i ely. The non-calib a ed TEC ep esen s he combina ion be ween he calib a ed TEC, he ambigui y e m, and ins u- men al delay e m a ec ed by he mul ipa h and he mal noise. The ambigui y and ins umen al delay can be sol ed oge he as a unique bias e m ( 𝐴𝐴𝐴𝐴 SF ) o single equency and 𝐴𝐴𝐴𝐴 DF o dual equency. This e m is sol ed in he second s ep using a SH expansion model. The SH model adop ed was he same de eloped by Schae (1999); howe e , 24h o GNSS da a in local ime (LT) is used. The model ob ains enough spa ial in o ma ion o accu- a ely es ima e he coe icien s o sphe ical ha monics wi h a high o de o ha monics. Then, ge s he necessa y co e age o es ima e he SH coe icien s wi h a ypical ha monic o de o 15°. The use o 24h o da a does no in ol e huge p oblems in he es ima ion, since mos o he GNSS s a ions used in he model a e de ined o e he B azilian egion, ha is, he LT and UT a e e y simila among he s a ions, jus implying a sligh smoo hing e ec . I is ele an o men ion ha cycle slips and g oss e o s in he ca ie phase obse a ions mus be elimi- na ed be o e using 𝐴𝐴TECSF o 𝐴𝐴TECDF in he SH model. Fo his pu pose, we used he non-calib a ed TEC alues. The non-calib a ed TEC alues a e compa ed epoch-by-epoch, and he disc epancy be ween he epochs should no be highe han he adop ed h eshold (4 TEC Uni s (TECU), being 1 TECU= 𝐴𝐴1016 el/m 2.) The ambigui y and ins umen al delay e m was compu ed wi h he ollowing equa ion o single and dual equencies, espec i ely: MF × TEC SF = 𝑛𝑛max ∑ 𝑛𝑛=0 𝑛𝑛 ∑ 𝑚𝑚=0  𝑃𝑃𝑛𝑛𝑚𝑚(𝑠𝑠𝑠𝑠𝑛𝑛𝑠𝑠𝑖𝑖𝑖𝑖 𝑚𝑚)[𝐴𝐴𝑛𝑛𝑚𝑚𝑐𝑐𝑐𝑐𝑠𝑠(𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖 𝑠𝑠)+𝐵𝐵𝑛𝑛𝑚𝑚 sin(𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖 𝑠𝑠 )] (3) MF × TEC DF = 𝑛𝑛 max ∑ 𝑛𝑛=0 𝑛𝑛 ∑ 𝑚𝑚=0  𝑃𝑃𝑛𝑛𝑚𝑚(𝑠𝑠𝑠𝑠𝑛𝑛𝑠𝑠𝑖𝑖𝑖𝑖 𝑚𝑚)[𝐴𝐴𝑛𝑛𝑚𝑚𝑐𝑐𝑐𝑐𝑠𝑠(𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖 𝑠𝑠)+𝐵𝐵𝑛𝑛𝑚𝑚𝑠𝑠𝑖𝑖(𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖 𝑠𝑠 )] (4) whe e 𝐴𝐴𝐴𝐴 𝑖𝑖𝑖𝑖 𝑚𝑚 is he la i ude o he ionosphe ic pie ce poin (IPP), 𝐴𝐴𝐴𝐴 𝑖𝑖𝑖𝑖 𝑠𝑠 is he longi ude o IPP in e ms o LT, 𝐴𝐴𝐴𝐴 max is he maximum deg ee o expansion, 𝐴𝐴𝐴𝐴 𝑛𝑛𝑛𝑛 and 𝐴𝐴𝐴𝐴 𝑛𝑛𝑛𝑛 a e he ionosphe e model coe icien s, 𝐴𝐴 𝑃𝑃𝑛𝑛𝑛𝑛 a e he no malized Legend e polynomials o deg ee 𝐴𝐴𝐴𝐴 and o de 𝐴𝐴𝐴𝐴 , and 𝐴𝐴MF is he s anda d mapping unc ion (Schae ,1999). The 15427390, 2023, 8, Downloaded om h ps://agupubs.onlinelib a y.wiley.com/doi/10.1029/2023SW003513 by Csic O ganización Cen al Om (O icialia Mayo ) (U ici), Wiley Online Lib a y on [27/02/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License Space Wea he CHRISTOVAM ETAL. 10.1029/2023SW003513 4 o 13 numbe o pa ame e s is calcula ed by ( 𝐴𝐴𝐴𝐴 max  +1) 2, whe e 𝐴𝐴𝐴𝐴 𝑛𝑛𝑛𝑛 , 𝐴𝐴𝐴𝐴 𝑛𝑛𝑛𝑛 , 𝐴𝐴𝐴𝐴 DF , and 𝐴𝐴𝐴𝐴 SF a e unknown pa ame e s o be es ima ed by he leas squa e me hod. The hi d s ep is ca ied ou o es ima e he absolu e (i.e., calib a ed) TEC alues, which can be di ec ly calcu- la ed a e he ambigui y and ins umen al delay e ms a e calcula ed o all con inuous a cs. The hi d s ep also pe o m a egional in e pola ion in he B azilian egion. The spa ial in e pola ion o he calib a ed Ve ical To al Elec on Con en (VTEC) alues is ca ied ou based on he in e se o he dis ance. I is conside ed a g id o e he B azilian egion wi h a ho izon al esolu ion o 1° in la i ude and 1° in longi ude, wi h an ionosphe ic shell heigh o 450km in al i ude and empo al esolu ion o 6min. The shell heigh adop ed is he same as ha adop ed by he CODG and UQRG models, which can be conside ed app oxima ely he median heigh o elec on densi y o a ypical day ime p o ile (Mannucci e al.,1998). The model is execu ed using da a om app oxima ely 200 g ound-based ecei e s om he con inuous ope a - ing GNSS s a ions h oughou Ame ica, especially o e he B azilian egion. The da a om RBMC (B azilian Ne wo k o Con inuous GNSS Moni o ing), IGS, GNSS Na Ae (De Paula e al.,2022), LISN (Low la i ude Ionosphe ic Senso Ne wo k), and RAMSAC (Red A gen ina de Moni o eo Sa eli al Con inuo) a e used. The loca ion o he GNSS s a ions used in egional model a e p esen ed in Figu e1a. 2.2. Posi ioning Se ings The GNSS PPP wi h single equency da a is an impo an s a egy o e alua e he ionosphe ic models (Ro i a-Ga cia e al.,2020), complemen ing he di ec assessmen in he ionosphe ic domain (He nández-Paja es e al.,2017). The main poin is o e alua e he quali y o he ionosphe ic delay based on di ec co ec ions o e ca ie phase and pseu- do ange measu emen s. In his wo k, he e alua ion is pe o med o assess he quali y o he de eloped egional iono- sphe ic model when using single equency TEC da a and compa e i wi h he esul s ob ained by he same model, when using dual equency GNSS da a. The mos usual ionosphe ic p oduc s o GNSS applica ions, ha is, GIMs p o ided by IGS, UQRG, and CODG, a e also included in he posi ioning analysis. The UQRG and CODG p oduc s a e selec ed because hey ha e shown some o he bes esul s in e ms o GNSS posi ioning (Je ez e al.,2023). Once he single and dual equency TEC alues a e ob ained by he p oposed me hod, VTEC g ids a e expo ed in IONEX o ma wi h he p e iously men ioned esolu ion (1°×1° in la i ude and longi ude, upda ed e e y 6min). To analyze he pe o mance o he ionosphe ic models, as applied o he GNSS posi ioning, he RTKLib is used (Takasu & Yasuda,2009). Single equency PPP in kinema ic posi ioning me hod is chosen o e alua e he ionosphe ic models, as he kinema ic mode di ec ly applies he ionosphe ic delay o co ec he GNSS obse - a ions epoch by epoch. Table1 summa ized he PPP se ings. Fo he analysis, 37 s a ions om RBMC a e used (Figu e1b). I is impo an o men ion ha he s a ions used o he alida ion we e chosen o co e se e al la i udes in he B azilian egion. The days chosen a e DOYs 3–9, as well as 21–31 o 2014. These days a e selec ed because hey ha e clea e idence o plasma bubbles occu ence Figu e 1. Loca ion o GNSS s a ions (a) o egional model (b) o he posi ioning assessmen . The dashed line ep esen s he Magne ic Equa o . 15427390, 2023, 8, Downloaded om h ps://agupubs.onlinelib a y.wiley.com/doi/10.1029/2023SW003513 by Csic O ganización Cen al Om (O icialia Mayo ) (U ici), Wiley Online Lib a y on [27/02/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License Space Wea he CHRISTOVAM ETAL. 10.1029/2023SW003513 5 o 13 o e he B azilian egion. The main analysis is pe o med o e alua e he imp o emen ha he TEC ob ained om he p oposed model o e s o PPP du ing he p esence o plasma bubbles. In he ollowing sec ion, we show he PPP esul s when applying he p oposed me hod. Th ee pa ame e s we e used o e alua e he h ee-dimensional (3-D) PPP e o : mean e o , s anda d de ia ion (STD), and he oo mean-squa e e o (RMS) o he es i- ma ions. The main 3-D e o is compu ed by aking he di e ences be ween he coo dina es ob ained in he PPP p ocessing and he e e ence coo dina es. The e e ence coo dina es we e ob ained om inal solu ion o he SIs ema de Re e encia Géocen ico pa a las Ame - icas (SIRGAS) a epoch 2014. 3. Resul s Sec ion3.1 p esen s an ini ial alida ion o TEC alues ob ained by he single and dual equency models. Sec ion3.2 p esen s b ie discussion abou ionosphe ic a iabili y impac on GPS equencies. Sec ion3.3 shows he single equency PPP assessmen based on single equency ionosphe ic model. 3.1. VTEC Plasma Bubbles Maps Wi h Analyzed Models In o de o pe o m an ini ial alida ion, a isual compa ison o he ionosphe ic models is p esen ed in Figu e2. This example shows snapsho VTEC maps ob ained om ionosphe ic models o he B azilian egion in DOY 003 o 2014 a 02h UT. (a) and (b) panels shows he maps a ailable om he IGS (CODG and UQRG) whe eas (c) and (d) panel p esen he maps ob ained by he p oposed me hods. Due o he di e en spa ial esolu ion, he maps p o ided by he p oposed me hod a e qui e di e en om he maps a ailable om IGS In he maps a ailable om IGS, he p esence o he no he n and sou he n c es o he EIA a e clea ly obse ed, whe e hese wo egions a e cha ac e ized by highe elec on densi y alues. Fo he maps ob ained wi h he p oposed me hods, i is also possible o see he c es s o EIA, howe e wi h se e al i egula i ies in he egion. In addi ion, wo well-de ined VTEC deple ion (plasma bubbles) can be seen aligned wi h he geomagne ic equa o . No ice ha he main di e ence be ween he ionosphe ic maps is he abili y o de ec plasma bubbles. This di e ence can be explained by he spa ial and empo al esolu ion di e ences. CODG and UQRG p oduce iono- sphe ic maps wi h a spa ial esolu ion o 2.5° in la i ude and 5° in longi ude and a empo al esolu ion o 2h and 15min, espec i ely. The g id size used by he IGS models a e la ge han he scale size o he plasma bubbles de ec ed by g ound-based obse a ions. Indeed, he scale size o he plasma bubbles a e in le el o 100m o a ew kms (Bha acha yya,2022). 3.2. Ionosphe ic Va iabili y on GPS F equencies Du ing s ong ionosphe ic e en s, he GPS L1 signal is less sensi i e o loss o lock han using dual equency da a (GPS L1 and L2). The e o e, in egions suscep ible o s ong ionosphe ic e en s, mo e TEC da a a e expec ed o be obse ed wi h single equency da a. In such case, single equency da a can he e o e imp o e he imaging o ionosphe ic bubbles due o he p o ided be e da a co e age. One way o analyze his poin is coun ing he numbe o IPPs obse ed by dual and single equency da a. To pe o m his compa ison, he B azilian egion is di ided in o 4 sub- egions (quad an s). Figu e3 shows a compa a i e example o VTEC maps and spa ial dis ibu ion o IPPs be ween single and dual equency da a. In his expe imen al analysis, he o al numbe o IPPs coun ed o single equency da a was 27,970, whe eas 27,008 IPPs we e obse ed o dual equency da a. I may be no iced ha he e a e di e en IPPs densi ies o each quad an . A summa y o he numbe o IPPs o each quad an (Q) wi h single and dual equency da a is lis ed in Table2. Fo he pe iod conside ed, excep o a ew ins ances a e he plasma bubble passage (a ound 02h UT), he numbe o IPPs o single equency is conside ably highe han hose o dual equency, hese alues a e highligh ed (bold) in Table2. The lowe numbe o IPPs occu s because, as p e iously men ioned, he L2 equency is mo e suscep ible o ionosphe ic e ec s, which p oduces GNSS loss o lock and eini ializa ions o he TEC es ima ion. The main di e ence o he IPP numbe s be ween he I em PPP se ings Fil e ype Combined solu ions ob ained by o wa d and backwa d il e s Ele a ion mask Cu o angle 10° Ea h ides co ec ion Ea h ides co ec ions T oposphe e co ec ion Es ima ion o oposphe ic delays du ing PPP Sa elli e epheme is/clock P ecise epheme ides (sp3) and sa elli e clock co ec ions (clk_5s) acqui ed om IGS p oduc s Na iga ion sys em Global Posi ioning Sys em (GPS) cons ella ion Recei e /sa elli e an enna Co ec ion o he phase cen e a ia ion o bo h ansmi e and ecei e an ennas PhWindup Phase wind up co ec ions Ambigui y No s a egy o ambigui y solu ion, because me ic accu acy is expec ed Ou age o ese ambigui y/slip h eshould 5/0.05m DCB da a Co ec ions o di e en ial ins umen al bias be ween he ci il and p ecise codes (CI-P1) Table 1 PPP Se ings 15427390, 2023, 8, Downloaded om h ps://agupubs.onlinelib a y.wiley.com/doi/10.1029/2023SW003513 by Csic O ganización Cen al Om (O icialia Mayo ) (U ici), Wiley Online Lib a y on [27/02/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License Space Wea he CHRISTOVAM ETAL. 10.1029/2023SW003513 6 o 13 L1 and L1L2 is, he e o e, he loss o lock o he L2 measu emen s. As expec ed, be e co e age o IPPs is ob ained wi h single equency TEC da a when compa ed wi h dual equency. 3.3. Assessmen by Single F equency PPP In a p elimina y e alua ion, i is analyzed he esul s o a single day o show de ails o he PPP accu acy when applying he TEC p o ided by di e en models o accoun o he ionosphe ic delay. Figu e4 shows a compa - ison be ween he 3-D posi ioning e o s h oughou he day oge he wi h a co esponden keog am o Cachoe- i a Paulis a (CHPI) s a ion (22.7°S, 45.0°W), and he ionosphe ic scin illa ion S4 index a he same la i udinal sec o , loca ed in he sou he n c es o he EIA. In o de o apply he keog am echnique, i is equi ed o ix he la i ude, and hen s ack he wes -eas slices o he econs uc ed VTEC maps da a o o m one image (P ol, He nández-Paja es, e al.,2018; Sil a e al.,2019). In his case, hey we e gene a ed wi h he de eloped single equency ionosphe ic model. Acco ding o he daily beha io , he ini ial (00–04h UT) and inal (22–24h TU) hou s showed he highes 3D e o alues, which a e caused by deple ions in he ionosphe ic plasma densi y, as seen in he keog ams. This beha io occu s due o ionosphe ic plasma ins abili y (Rayleigh-Taylo ins abili y), which igge s plasma deple ions (bubbles) a e he sunse (Takahashi e al.,2015). In he keog ams, we can see he gene al plasma bubble mo ion p og essing om wes o eas , ep esen ed by a il ed da k blue egion ela i e o he empo al axis o he igu e, well connec ed wi h he highes PPP e o s in he ini ial and inal hou s o he day. A he same ime, i can be seen he highe alues o ionosphe ic scin illa ion index (S4). This esul con i ms he close ela ionship be ween he ionosphe ic plasma bubbles occu ences and he ionosphe ic scin illa ion, causing high e o s in posi ioning. Unde s ong ionosphe ic scin illa ions caused by he ionosphe ic plasma bubbles, he GNSS ecei e acking loop pe o mance is deg aded, causing low posi ioning accu acy. I is impo an o poin ou ha he inc eased posi ioning e o s du ing he 00–04h UT a e no associa ed wi h he con e gence o he single equency kinema ic PPP since we used combined solu ions ob ained by o wa d and backwa d il e ing. Figu e 2. Example o ionosphe ic models o he B azilian egion, o DOY 003 o 2014 a 02h UT. (a) and (b) panels co esponds o CODG and UQRG (c) and (d) co esponds o models ob ained wi h L1 and L1L2. 15427390, 2023, 8, Downloaded om h ps://agupubs.onlinelib a y.wiley.com/doi/10.1029/2023SW003513 by Csic O ganización Cen al Om (O icialia Mayo ) (U ici), Wiley Online Lib a y on [27/02/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License Space Wea he CHRISTOVAM ETAL. 10.1029/2023SW003513 7 o 13 A e unde s anding he co espondence be ween he plasma bubble keog ams and PPP pe o mance o one s a ion, six ep esen a i e s a ions we e chosen o e alua e di e en la i udinal egions o he ionosphe e. The selec ed s a ions we e BRAZ (15.9°S, 47.9°W); CHPI (22.7°S, 45.0°W); BOAV (2.8°N, 60.7°W); PBJP (07.1°S, 34.9°W); POAL (30.1°S, 51.1°W) and SMAR (29.7°S, 53.7°W). Figu e5 p esen s he 3D e o calcula ed o each epoch, and o each model, in he ep esen a i e s a ions. Again, la ge posi ioning e o s a e no iced in he ini ial and inal hou s o he day, when he ionosphe ic i egula i ies associa ed o equa o ial plasma bubbles impac ed he GNSS obse a ions mo e e ec i ely. I is impo an o highligh ha he magni udes o 3D e o s a e conside ed high o PPP, eaching up o 3m. Conside ing he en i e day o da a (24h ), he mean e o , STD, and RMS o each model a e summa ized in Table3. Acco ding o he s a is ics, he UQRG p esen ed a be e pe o mance compa ed o he o he s model in e ms o mean and RMS, whe eas he p oposed model using dual equency p esen ed a be e pe o mance in e ms o STD. When we compa e he s a is ics esul s be ween he models, he di e ence is in he decime e le el, while he e o is in he me e le el. The e o e, i is possible o conclude ha he p oposed models showed esul s compa ible wi h he models a ailable om he IGS, including he single equency model. As he main goal o he p oposed model is o p o ide a easible da a sou ce o map he plasma bubbles, he nex e alua ion is ca ied ou only in pe iods o ionosphe ic plasma bubbles occu ence. In his ega d, Figu e6 shows he 3D e o ob ained in PPP and calcula ed du ing he pe iods wi h plasma bubble occu ences (00–06h UT). As a esul , s a ions BRAZ, PBJP, CHPI, and BOAV, Figu e 3. Compa a i e example he Ve ical To al Elec on Con en maps and spa ial dis ibu ion o IPPS o e he B azilian egion in DOY 003 o 2014 a 1.2h UT be ween single and dual equency. The dashed line indica es he geomagne ic equa o . The con inuous line ep esen s he di ision o he map in o quad an s. (a) and (b) panels p esen maps wi h single equency (L1); (c) and (d) panels p esen s maps wi h dual equency (L1 and L2). Time (UT) F equencies 1°Q2°Q3°Q4°Q 1.0h L1 6,715 6,746 8,583 4,388 L1L2 6,495 6,548 8,841 4,381 1.2h L1 7,517 7,123 8,745 4,585 L1L2 6,824 6,992 8,608 4,584 1.4h L1 7,830 7,441 8,855 4,850 L1L2 7,129 7,035 8,843 4,789 1.6h L1 7,673 7,649 8,727 5,206 L1L2 7,178 7,357 8,651 5,201 1.8h L1 7,456 7,812 8,672 5,789 L1L2 7,499 7,383 8,258 5,595 2.0h L1 7,735 7,935 8,750 5,560 L1L2 7,747 7,825 8,788 5,923 Table 2 Numbe o IPPs Pe Quad an Du ing 1 h Pe iod O e B azilian Region o DOY 004 o 2014 15427390, 2023, 8, Downloaded om h ps://agupubs.onlinelib a y.wiley.com/doi/10.1029/2023SW003513 by Csic O ganización Cen al Om (O icialia Mayo ) (U ici), Wiley Online Lib a y on [27/02/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License Space Wea he CHRISTOVAM ETAL. 10.1029/2023SW003513 8 o 13 Figu e 4. (a) Keog am o he Ve ical To al Elec on Con en alues o he la i udinal sec ion o 22.7°S (CHPI s a ion) in e ms o longi ude and hou s; (b) 3D e o o he same GNSS s a ion and (c) S4.index a la i udinal sec ion o (23.2°S) o DOY003 o 2014. Figu e 5. 3D e o in me e s o DOY 003 o 2014. 15427390, 2023, 8, Downloaded om h ps://agupubs.onlinelib a y.wiley.com/doi/10.1029/2023SW003513 by Csic O ganización Cen al Om (O icialia Mayo ) (U ici), Wiley Online Lib a y on [27/02/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License Space Wea he CHRISTOVAM ETAL. 10.1029/2023SW003513 9 o 13 loca ed in egions wi h high ionosphe ic ac i i y, p esen ed he 3D e o a ound 15m whe eas he e o is a ound 5 and 10m in POAL and SMAR s a ions, espec i ely. This di e ence among he s a ions occu s because BRAZ, PBJP, CHPI, and BRAZ a e in he c es s o he EIA, whe e ionosphe ic scin illa ions a e mo e e ec i e, while POAL and SMAR a e close o he mid-la i ude egion. The co esponding mean, STD, and RMS o he 3D e o s in each model a e summa ized in Table4. Analyzing he s a is ics, he model p oposed wi h single equency p esen ed he bes pe o mance, ollowed by he p oposed model wi h dual equency and UQRG. In his case, CODG p esen ed he wo s pe o mance. In addi ion, he p oposed model was also e alua ed du ing a day cha ac e - ized by low ionosphe ic ac i i y DOY 171. Figu e7 p esen s he 3D e o ob ained in PPP o 24h o da a o non-dis u bed day. I can be seen ha o all ep esen a i e s a ions, he 3D e o did no exceed 5m. Addi ionally, a simila beha io be ween he models can be obse ed. Table5 summa- ize he co esponding mean, STD and RSM alues o 3D e o s o each model. Acco ding o he s a is ics, he p oposed models using single and dual equency p esen ed a simila mean, STD and RMS alues. The CODG p esen ed a be e pe o mance in e ms o mean and RMS, whe eas, in his case, he URQG p esen ed he wo s pe o mance. I is impo an o poin ou ha he di e ence is negligible. The e o e, i can be in e ed ha he p oposed models demons a ed esul s consis en wi h he models p o ided by IGS. To p o ide an o e iew o he model pe o mance conside ing se e al days and s a ions, we also es ima ed he s a is ics using he 37 s a ions selec ed du ing he dis u bed days. The esul s a e shown in Figu e8. Compa - ing he s a is ical esul s be ween he esul s ob ained wi h 24h o da a and only he pe iod o plasma bubble occu ences, i is no ed ha , in he pe iod ha bubbles a e occu ing, he esul s a e mo e dispe se, especially in e ms o RMS since he la ges e o s occu in his pe iod. The esul s using 24h o da a a e smoo hed ou by he pe iod when no ionosphe ic i egula i ies a e p esen . In addi ion, conside ing he la i udinal dis ibu- ion, we can no e a pa e n. Fo he s a ions nea he la i ude o 15°S, close o he Sou he n EIA c es , he e o s among he s a ions end o con e ge o a common alue. This beha io e eals ha he models p esen ed a Model Mean (m) STD (m) RMS (m) CODG 1.56 1.91 2.47 UQRG 1.55 1.87 2.44 L1 1.76 2.06 2.72 L1L2 1.70 1.82 2.49 Table 3 Mean, S anda d De ia ion and Roo Mean Squa e 3D E o Du ing 24h o Da a, Conside ing Each Model o DOY003, 2014 Figu e 6. 3D e o in me e s du ing plasma bubble occu ence (00–06h UT) o DOY 003 o 2014. 15427390, 2023, 8, Downloaded om h ps://agupubs.onlinelib a y.wiley.com/doi/10.1029/2023SW003513 by Csic O ganización Cen al Om (O icialia Mayo ) (U ici), Wiley Online Lib a y on [27/02/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License