Inges ion o GNSS‐De i ed‐TEC In o NeQuick 2 Model
O e Sou h Ame ica
Taiwo Olusayo Osanyin
1,2
, Claudia Ma ia Nicoli Candido
1,3
, Fabio Becke ‐Guedes
1
,
Yenca Migoya‐O ue
4
, and John Bosco Haba ulema
2,5
1
Na ional Ins i u e o Space Resea ch, São José dos Campos, B azil,
2
Sou h A ican Na ional Space Agency (SANSA),
He manus, Sou h A ica,
3
Uni e si y o Vale do Pa aiba, UNIVAP, São José dos Campos, B azil,
4
STI Uni , The Abdus
Salam In e na ional Cen e o Theo e ical Physics (ICTP), S ada Cos ie a 11, T ies e, I aly,
5
Depa men o Physics and
Elec onics, Rhodes Uni e si y, Makhanda, Sou h A ica
Abs ac This s udy examines he inges ion o o al elec on con en (TEC) da a om a ne wo k o g ound‐
based Global Na iga ion Sa elli e Sys em (GNSS) ecei e s in o he NeQuick 2 model, p o iding a benchma k
o e alua ing he cos ‐e ec i eness o GNSS da a inges ion o nea ‐ eal‐ ime ionosphe ic speci ica ion. A
signi ican educ ion in oo mean squa e e o (RMSE) be ween NeQuick 2 ou pu s and GNSS‐de i ed TEC
was obse ed ac oss a ious es s a ions, including hose loca ed a mid‐la i udes. Du ing geomagne ically
quie pe iods, he pe o mance di e ence be ween using 35 and 166 GNSS s a ions was less han 1%, while a
simila end, less han 2% di e ence was obse ed du ing dis u bed pe iods wi h 34 and 177 s a ions,
espec i ely. These indings highligh he impo ance o he spa ial dis ibu ion o GNSS ecei e s in enhancing
he model's accu acy, pa icula ly o e egions wi h complex ionosphe ic dynamics. Diu nal a ia ions in
e ical TEC ( TEC) o e he es loca ions showed ema kable imp o emen du ing geomagne ic dis u bances,
wi h enhancemen s anging om 37% o 68% in he low‐la i ude egion. Addi ionally, compa isons be ween
NeQuick 2‐de i ed plasma equencies and digisonde obse a ions demons a ed s ong ag eemen in he 100–
200 km al i ude ange, wi h a e age co ela ion coe icien s o 0.97 and 0.95 a São Luís (2.58°S, 44.20°W),
0.93 and 0.55 a Boa Vis a (2.83°N, 60.70°W), and 0.88 o bo h condi ions a Campo G ande (20.40°S,
54.50°W) du ing quie and dis u bed pe iods, espec i ely. The lowe co ela ion obse ed a Boa Vis a du ing
dis u bed condi ions may be a ibu ed o limi ed da a inges ion co e age in he No he n Hemisphe e.
Plain Language Summa y Da a inges ion can be desc ibed as an op imiza ion echnique whe e
ac ual obse a ions and model p edic ions, e e ed o as he backg ound in o ma ion, a e combined o gi e he
bes es ima e o he model s a e. I ends o d i e an empi ical model owa ds one speci ic da a se and compu e
“e ec i e pa ame e s” associa ed wi h he model. O pa icula applica ion is he esponse o he ionosphe e
du ing geomagne ic s o ms. This is impo an o mi iga e he ad e se e ec s o space wea he ‐ ela ed
dis u bances on echnology such as communica ion and na iga ion sa elli e sys ems, as hei signals ansmi
h ough he ionosphe e. The ecen deploymen o he GNSS ecei e ne wo k globally allows o he
homogeneous dis ibu ion o GNSS da a, p o iding an al e na i e o g ound‐based digisonde o applica ions
ela ing o da a inges ion. We de eloped a egional ionosphe ic model ha inco po a es GNSS TEC da a in o he
NeQuick 2 model o e Sou h Ame ica. Speci ically, a spa ial esolu ion indexing me hod was used o he
selec ion o GNSS s a ions, esul ing in an e enly dis ibu ed da a se and subsequen ly minimizing e o s
ela ed o da a inges ion.
1. In oduc ion
The Sou h Ame ican sec o cu s ac oss wo dis inc egions: middle‐ and low‐la i ude egions. The phenomena
d i ing he low‐la i ude ionosphe e con ibu e o c i ical ionosphe ic a iabili y, signi ican ly a ec ing
communica ion and na iga ion sys ems (Co eia e al., 2018; Rama Rao e al., 2006). These phenomena esul
om he complex in e ac ions be ween space wea he and a mosphe ic elemen s (Ha g ea es, 1992; Ma ini‐
Pe ei a e al., 2021). Mo eo e , he ionosphe e o e low la i udes possesses ea u es dis inc om hose o he
mid‐la i udes owing o he low inclina ion o he geomagne ic ield lines and a high ac ion o he inciden sola
adia ion cha ac e izing his egion (Abdu, 2016; Balan e al., 2013; De Ab eu e al., 2017). The mid‐la i udes a e
cha ac e ized by high‐inclina ion magne ic ield lines, which make ambipola di usion and me idional winds he
dominan means o e ical anspo o laye o ma ion and s uc u ing (Abdu, 2016; Mi a, 1946). The o me
RESEARCH ARTICLE
10.1029/2024SW004212
Key Poin s:
•U ilizing spa ial indexing o g ound‐
based GNSS ecei e s' s a ion selec-
ion is use ul o p oducing ewe s a-
ions on he maps
•Inges ion o he TEC map g ea ly
enhances he cha ac e iza ion o he
low‐la i ude ionosphe e unde quie
and dis u bed geomagne ic condi ions
•Bo h s anda d and da a‐d i en
NeQuick ag ee wi h digisonde mea-
su emen s below he F2 laye peak
heigh (hmF2)
Suppo ing In o ma ion:
Suppo ing In o ma ion may be ound in
he online e sion o his a icle.
Co espondence o:
T. O. Osanyin,
[email p o ec ed]
Ci a ion:
Osanyin, T. O., Ma ia Nicoli Candido, C.,
Becke ‐Guedes, F., Migoya‐O ue, Y., &
Haba ulema, J. B. (2025). Inges ion o
GNSS‐de i ed‐TEC in o NeQuick 2 model
o e Sou h Ame ica. Space Wea he ,23,
e2024SW004212. h ps://doi.o g/10.1029/
2024SW004212
Recei ed 8 OCT 2024
Accep ed 31 JUL 2025
Au ho Con ibu ions:
Concep ualiza ion: Taiwo
Olusayo Osanyin, Claudia Ma ia Nicoli
Candido, Fabio Becke ‐Guedes,
Yenca Migoya‐O ue, John
Bosco Haba ulema
Da a cu a ion: Taiwo Olusayo Osanyin
Fo mal analysis: Taiwo Olusayo Osanyin
In es iga ion: Taiwo Olusayo Osanyin,
Claudia Ma ia Nicoli Candido,
Fabio Becke ‐Guedes, Yenca Migoya‐
O ue, John Bosco Haba ulema
Me hodology: Taiwo Olusayo Osanyin,
Claudia Ma ia Nicoli Candido,
Fabio Becke ‐Guedes, Yenca Migoya‐
O ue, John Bosco Haba ulema
© 2025. 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.
OSANYIN ET AL. 1 o 19
e ec esul s in he edis ibu ion o he elec on densi y, o ming a ough a he magne ic equa o and c es s a
±15–20° o he magne ic equa o (Hanson & Mo e , 1966; Kelley, 2009; Nigussie e al., 2022). Howe e , he
posi ions o he EIA c es s a e s ongly dependen on geog aphical longi ude and sola ac i i y. This plasma
anomaly is known as he Equa o ial Ioniza ion Anomaly (EIA) (Apple on, 1946; Rome o‐He nandez e al., 2020).
The p incipal d i e s de ining he cha ac e is ics o he EIA a e he zonal elec ic ield and me idional neu al
winds. The eas wa d elec ic ield d i es a e ical plasma oun ain a he magne ic equa o du ing he day ime,
c ea ing an EIA. The neu al wind e ec esul s in he in e hemisphe ic asymme y o he EIA by modula ing he
plasma oun ain and mo ing he ionosphe e a he conjuga e hemisphe es o di e en al i udes (Balan &
Bailey, 1995). Howe e , he compe ing e ec s o he chemical p ocess,
E X
Bd i , and neu al winds du ing
s o ms a e qui e dynamic. The e o e, p edic ing he e olu ion o he ionosphe ic EIA du ing s o ms emains a
c ucial challenge in sophis ica ed models o he uppe a mosphe e (S ole e al., 2008; Zhang & Pax on, 2021).
Because o he dange ous e ec s o space wea he e en s on bo h g ound‐ and space‐based echnological sys ems,
con inuous ionosphe e moni o ing is impo an o eliable o ecas s and speci ica ions o he nea ‐Ea h space
en i onmen . Fo his pu pose, he e has been a high demand o highly accu a e and e icien ionosphe ic
co ec ion me hods o e he pas ew decades (e.g., Blanch e al., 2013). Di e en app oaches ha e been adop ed
o assess and minimize ionosphe ic e ec s, including ionosphe ic empi ical and heo e ical models such as he
NeQuick 2 model (Aa e al., 2018; Na a e al., 2006; Radicella & Na a, 2020), he In e na ional Re e ence
Ionosphe e (Bili za e al., 2022; Bili za & Reinisch, 2008; Galkin e al., 2012), and heo e ical models (Huba
e al., 2008; Ridley e al., 2006). Rela i e o he in insic limi a ions ollowing he de elopmen o empi ical
models, hey canno p edic u u e beha io o p o ide accu a e desc ip ions o ionosphe ic dynamics in a eas
wi h limi ed da abases (e.g., Haba ulema e al., 2010; Migoya‐O ué e al., 2017; Radicella & Na a, 2020).
NeQuick 2 is a h ee‐dimensional ionosphe ic elec on densi y empi ical model ha calcula es he o al elec on
con en along any line‐o ‐sigh (LOS) using nume ical in eg a ion (Na a e al., 2008). I uses ei he he smoo hed
sunspo numbe (R12) o an equi alen o he sola adio lux index (F10.7) o desc ibe he a e age s a e and
egula a ia ions in he ionosphe e. Owing o he s ong co ela ion be ween he wo indices, one can be con-
e ed in o he o he using a simple o mula (Zhao & Han, 2008). O en, di icul ies can occu when using sola ‐
based indices because hey a e a om he ideal p oxies equi ed o sola ac i i y in he EUV pa o he sola
adia ion spec um (Na a e al., 2006). This has led o he de elopmen o se e al “e ec i e” indices (Az) in a
p ocess known as da a inges ion. Gene ally, da a inges ion is a me hod o combining obse a ions wi h a model o
e ec i ely exp ess ionosphe ic mo phology, acili a ing a be e unde s anding o space wea he and co ec ing
ionosphe ic e o s in GNSS na iga ion and posi ioning. When he sola adio lux is adjus ed in NeQuick, i is
called he E ec i e Ioniza ion Le el; o he wise, i is e e ed o as he E ec i e Sunspo Numbe (Nigussie
e al., 2012).
Globally, Migoya‐O ué e al. (2015) inges ed TEC da a om he Global Ionosphe ic Maps (GIM) in o IRI
(In e na ional Re e ence Ionosphe e) model o ep oduce he c i ical equency o he F2 laye du ing bo h high
and low sola ac i i y. Recen ly, he econs uc ion o elec on densi y dis ibu ion using da a‐d i en empi ical
models has been mo e di ec ed owa d local/ egional conce ns (Haj a e al., 2016; Rao, 2007). This is because
local models a e supe io o global models. The la e may smoo h ou he unique ea u es o a pa icula loca ion.
Hence, de eloping local/ egional models is necessa y o sa elli e communica ion and na iga ion sys ems ap-
plica ions. Haba ulema and Ssessanga (2017) adop ed a simila concep in A ica and pe o med egional GNSS
da a inges ion using he IRI 2012 model. They alida ed hei indings wi h neighbo ing TEC om GNSS,
digisondes, and elec on densi y p o iles ob ained om COSMIC Radio Occul a ion da a. Likewise, Migoya‐
O ué e al. (2017) conduc ed a cha ac e iza ion s udy by inco po a ing egional GNSS TEC da a om he ne wo k
o Global Ionosphe ic Maps (GIM) in o he NeQuick 2 model o ep oduce a se ies o c i ical equency maps
o e A ica's EIA egion. The inges ion me hod conside s all he a ailable GIM/GNSS‐de i ed da a o e a
de ined g id. Recen ly, he i s applica ion o da a inges ion in he NeQuick 2 model o e B azil was conduc ed
by Osanyin e al. (2023). They in es iga ed he pe o mance o he NeQuick 2 model using a single‐s a ion
inges ion echnique du ing ou geomagne ic s o ms anging om weak o mode a e s o ms in 2014. Thei
indings showed a iabili y in he imp o emen o he model du ing he s o m pe iods, wi h he highes
imp o emen (∼83%) epo ed du ing he June e en . Howe e , he s udy sugges ed a u he in es iga ion o he
da a inges ion echnique employing mul iple GNSS s a ions o be e unde s and ionosphe ic a iabili y o e his
complex egion, especially du ing hou s o de elopmen o ionosphe ic i egula i ies such as sp ead F and plasma
bubbles.
P ojec adminis a ion: Taiwo
Olusayo Osanyin
Resou ces: Taiwo Olusayo Osanyin,
Yenca Migoya‐O ue, John
Bosco Haba ulema
So wa e: Taiwo Olusayo Osanyin,
Yenca Migoya‐O ue, John
Bosco Haba ulema
Supe ision: Claudia Ma ia Nicoli
Candido, Fabio Becke ‐Guedes,
Yenca Migoya‐O ue, John
Bosco Haba ulema
Valida ion: Taiwo Olusayo Osanyin,
Claudia Ma ia Nicoli Candido,
Fabio Becke ‐Guedes, Yenca Migoya‐
O ue, John Bosco Haba ulema
Visualiza ion: Taiwo Olusayo Osanyin
W i ing – o iginal d a : Taiwo
Olusayo Osanyin
W i ing – e iew & edi ing: Taiwo
Olusayo Osanyin, Claudia Ma ia Nicoli
Candido, Fabio Becke ‐Guedes,
Yenca Migoya‐O ue, John
Bosco Haba ulema
Space Wea he
10.1029/2024SW004212
OSANYIN ET AL. 2 o 19
Al hough ema kable imp o emen s in clima ological models by he inges ion o g ound‐based GNSS TEC da a
ha e been p esen ed in he li e a u e men ioned abo e, ou s udy ocuses on he alida ion o op imal GNSS
ecei e s a ions whose TEC da a would be su icien o imp o e he NeQuick 2 model o e Sou h Ame ica using
he echnique o spa ial esolu ion indexing o da a selec ion and mul iple s a ion echnique o da a inges ion. In
his con ex , he objec i es o his s udy aim o add ess he ollowing scien i ic ques ions: (a) How he dis ibu ion
o g ound‐based GNSS ecei e s a ions a ec he pe o mance o da a inges ion in NeQuick model? (b) Wha is
he minimal GNSS ecei e numbe o s a ions equi ed o an inges ion scheme? (c) To wha ex en do he
op imal d i e s de e mined by da a inges ion imp o e he model p edic ions? and (d) How e ec i e is he
NeQuick inges ion mode in desc ibing he de elopmen o he EIA o ionosphe ic a iabili y du ing geomag-
ne ically quie and dis u bed condi ions o e Sou h Ame ica? Conce ning he abo e ques ions, his pape p esen s
an algo i hm o adap ing g ound‐based GNSS da a in o NeQuick 2 o s udy he de elopmen o EIA o e Sou h
Ame ica and econs uc ionosphe ic pa ame e s such as TEC and c i ical equency maps. The algo i hm applies
o egional GNSS ne wo ks wi hin se e al hund ed kilome e s. The e o e, he signi icance o he s udy lies in
in es iga ing he minimal g ound‐based measu emen s able o modi y he NeQuick 2 model o e a complex
egion o imp o e egional ionosphe ic s udies.
2. Desc ip ion o he Da a Se and he Backg ound Model's Imp o emen
This s udy encloses obse a ions om he GNSS‐de i ed TEC and digisonde da a. The digisonde and GNSS da a
pa ame e s we e wi hin 100–500 km and 0–20000 km. Howe e , a comp ehensi e alida ion es was u he
limi ed o he F2 laye peak heigh (hmF2) because he opside p o ile o he digisonde measu emen is modeled
and no sui able o alida ion pu poses.
2.1. Geomagne ic Da a
Figu e 1a shows he a ia ion in bo h he dis u bance s o m ime (Ds ) and plane a y index (Kp) o he quie (10
Ma ch 2015) and dis u bed (17 Ma ch 2015) pe iods analyzed in his s udy. The in e als o in e es we e
iden i ied om he Wo ld Da a Cen e o Geomagne ism, Kyo o. In e ms o he Kp index, geomagne ic ac i i y
can be classi ied as quie (Kp <4), ac i e (Kp =4), mino s o m (Kp =5), o majo o se e e s o m (Kp >5) (Tan
e al., 2018). The geomagne ic s o m on 17 Ma ch 2015, was he s onges du ing sola cycle 24, wi h a minimum
Figu e 1. (a) Va ia ion o Dis u bance S o m Time (Ds ) and plane a y index (Kp) o geomagne ic quie on Ma ch 10 (black) and s o m ime on Ma ch 17 ( ed),
(b) Loca ions o GNSS s a ions collec ed o e Sou h Ame ica on 10 Ma ch 2015, and (c) Tes s a ions used o alida ion, whe e s a ions in blue ma ke s a e
ep esen a i es o GNSS ecei e s om he No h o he Sou h and hose in blue ma ke s a e o s a ions o digisonde measu emen . The ed lines in (b) and (c) ep esen
he geomagne ic equa o .
Space Wea he
10.1029/2024SW004212
OSANYIN ET AL. 3 o 19
Ds o −223 nT a 23 UT and a maximum Kp o 8 a 12, 15, and 21 UT (s o m main phase), co esponding o
s ong dis u bance geomagne ic condi ions.
2.2. G ound‐Based GNSS Da a
GNSS TEC da a o e Sou h Ame ica we e collec ed du ing he s udy pe iod om a wide da abase ne wo k o he
In e na ional GNSS Se ice (IGS), Low‐La i ude Ionosphe ic Senso Ne wo k (LISN), UNAVCO ne wo k,
A gen inian (RAMSAC), Chilean ne wo k, B azilian ne wo k (RBMC), and U uguayan ne wo k (REGNA). This
enables u he in es iga ion o he ionosphe ic a iabili y in a wide spa ial dis ibu ion. The da a co e 10°N–
60°S la i ude and 30°–80°W longi ude, wi h app oxima ely 312 ecei e s on 17 Ma ch 2015, and 274 ecei e s on
10 Ma ch 2015. The la i udinal and longi udinal dis ibu ions o he GNSS s a ions on 10 Ma ch 2015, a e shown
in Figu e 1b, and he loca ions o he ins umen s used in he alida ion s age a e displayed in Figu e 1c. The
geog aphic and geomagne ic coo dina es o he ins umen s used o he alida ion a e lis ed in Table 1. Ba ch
p ocessing o he GNSS TEC da a was pe o med using he TEC calib a ion so wa e de eloped a Bos on
College (Seemala & Vallada es, 2011). The so wa e uses a dual‐ equency echnique o co ec GPS obse a-
ions wi h an es ima ion o he ionosphe ic delay ob ained by a linea combina ion o dual‐ equency pseudo ange
measu es. Owing o possible e o sou ces associa ed wi h he hin‐shell app oxima ion o he ionosphe e and
geome y du ing he con e sion o slan o e ical TEC (Da ies & Ha mann, 1997; Mannucci e al., 1998), a
quali y con ol check was pe o med on he p ocessed GNSS da a by emo ing ou lie s using he median and
median a e age de ia ion (MAD) echnique. This me hod has been widely employed in he li e a u e (Duba-
zane & Haba ulema, 2018; Hube & Ronche i, 2009; Pignabe i e al., 2019) and is ega ded as he mos e icien
and obus me hod. Fu he , only TEC co esponding o sa elli e links wi h an ele a ion g ea e han 30° was
conside ed o emo e e o s due o mul ipa h (Takahashi e al., 2014) a e which da a was selec ed a a 1‐h
in e al. The local ime (LT) a each s a ion was calcula ed by ans o ming he uni e sal ime (UT) using he
exp ession LT =UT ±LONG/15°, whe e LONG is he longi ude o each da a poin (Liu e al., 2020).
Fu he mo e, TEC maps o e Sou h Ame ica we e gene a ed using he EMBRACE echnique, and he de ails o
he me hodology can be ound in Takahashi e al. (2016).
2.3. Obse a ions F om Digisonde Da a
The s udy includes analyses o ionosphe ic pa ame e s, such as he F laye heigh s and plasma equencies, aken
om digisonde obse a ions in B azil. The da a we e ob ained om he open‐access eposi o y o he EMBRACE
(B azilian S udy and Moni o ing o Space Wea he ). Using he Sao Explo e so wa e (Reinisch e al., 2005), he
10‐min cadence ionog ams we e manually scaled o ou ep esen a i e ionosphe ic loca ions, as shown by he
blue ci cles in Figu e 1c. Digisonde measu emen s we e aken om s a ions a he no he n c es o he EIA (Boa
Vis a), nea he magne ic equa o (SALU), and a he sou he n c es and bo de o he sou he n EIA c es (MSCG
and CHPI), espec i ely.
Table 1
Geog aphic and Geomagne ic Coo dina es o GNSS Recei e s and Digisonde S a ions Used o Valida ion
Recei e s a ion S a ion code Obse a ion
Geog aphic Geomagne ic
Local imeLa . (
o
) Lon. (
o
) La . (
o
) Lon. (
o
)
Boa Vis a BOAV GPS/Digisonde 02.83 −60.70 11.03 14.15 UT‐3
Belem BELE GPS −01.40 −48.45 01.68 25.78 UT‐3
Sao Luis SALU Digisonde −02.58 −44.20 −1.19 29.46 UT‐3
Riobamba RIOP GPS −01.65 −78.66 10.34 −6.74 UT‐3
Colide MTCO GPS −10.80 −55.45 −03.19 15.82 UT‐3
Rio Pa anaíba MGRP GPS −19.20 −46.17 −14.42 21.88 UT‐3
Campo G ande MSCG Digisonde −20.40 −54.50 −11.98 14.19 UT‐3
Cachoei a Paulis a CHPI Digisonde −22.68 −44.98 −17.86 21.88 UT‐3
San a Rosa SRLP GPS −36.62 −64.29 −23.98 05.19 UT‐5
San Juan SUAN GPS −43.29 −65.11 −29.95 5.03 UT‐5
Space Wea he
10.1029/2024SW004212
OSANYIN ET AL. 4 o 19
The F2 laye equency,
oF2is well known o be p opo ional o he ionosphe ic ioniza ion peak alue (NmF2)
h ough he ela ion:
NmF2=1.24 ×104( oF2)2(1)
whe e NmF2is exp essed in cm
−3
and oF2in MHz.
2.4. Adap a ion o he NeQuick 2 Model o G ound‐Based GNSS TEC Da a
The inges ion p ocess in ol es calcula ing an e ec i e ioniza ion le el based on e ical To al Elec on Con en
( TEC) measu emen s om GNSS ecei e s. The modi ied NeQuick 2 hen inco po a es his e ec i e ioniza ion
le el o be e ma ch ou pu s o in e es , such as neighbo ing TEC, he plasma equency, and F2 laye c i ical
equency. The subsequen s eps a e duly ollowed.
S ep 1: G id‐Based Spa ial Resolu ion Indexing o S a ions densi y selec ion
The s udy employs a g id‐based app oach o selec GNSS s a ions in Sou h Ame ica. The me hod in ol es he
ollowing sub‐s eps:
1. Load and s uc u e GNSS s a ion me ada a (s a ion ID, longi ude, la i ude, and ellipsoidal heigh . This da a
con ains he o e all s a ions o e he egion o s udy o a speci ic DOY.
2. Di ide he egion in o g id cells: The s udy a ea is di ided in o ixed g id cells, s a ing wi h 2° in la i ude ×2°
in longi ude spa ial esolu ion.
3. Compu e he median ellipsoidal heigh in each g id cell in 2) abo e
4. Selec closes ‐ o‐median heigh in each g id cell.
5. Repea he p ocess o di e en spa ial esolu ions: S eps 2 and 3 a e epea ed using di e en spa ial eso-
lu ions (e.g., 2 ×4, 4 ×4, e c) o assess he impac o esolu ion on GNSS s a ion selec ion.
6. Plo he esul ing s a ions om (5) on a map (see Figu e 2).
Figu e 2. Sequence o GNSS ecei e s a ions gene a ed a di e en esolu ions wi h he co esponding numbe o s a ions o e Sou h Ame ica on 10 Ma ch 2015. The
uppe panel ep esen s maps in e ed om uni o m esolu ion (n ×n), and he lowe panels a e hose om non‐uni o m esolu ion (n ×m). The legend in each plo
indica es he spa ial g id index sizes.
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The me hod desc ibed in s ep 1 was implemen ed using GNSS s a ions on 10 and 17 Ma ch 2015 conside ing
uni o m (n x n) and non‐uni o m (n x m) g id esolu ions. In he uni o m g id, la i ude and longi ude bin sizes
emain cons an , whe eas in he non‐uni o m g id, la i ude sepa a ion (n) is ixed due o he spa se ecei e
dis ibu ion. As shown in Figu e 2, spa ial indexing echnique esul s in e enly dis ibu ed and good spa ial
co e age o GNSS s a ions geog aphically. In he case o uni o m g id, he numbe o GNSS s a ions dec eases as
he g id size inc eases. Fo ins ance, a coa se g id size o 6° ×6° esul s in 57 selec ed GNSS s a ions compa ed
o ine g id sizes.
S ep 2: Collec ion o GNSS TEC da a om each map ob ained in S ep 1
The indi idual maps shown in Figu e 2a e p oduc s o s a ion maps based on spa ial g id selec ion. The basic idea
is o e alua e he map whose TEC da a p oduces he leas oo mean squa e e o in he NeQuick 2 model a e
da a inges ion. The TEC da a om each map we e loaded as a single ile, il e ed o a speci ic epoch, and g idded
wi h a esolu ion o 1° ×1° o achie e a ine TEC esolu ion be o e inges ing in o he model.
S ep 3: Model's op imiza ion
NeQuick 2 is op imized as a unc ion o he daily e ec i e ioniza ion le el (Az) o be adap ed o he measu ed
TEC alues. Following he single s a ion echnique desc ibed in (Na a e al., 2006; Nigussie e al., 2012;
Osanyin e al., 2023), a simila me hodology has been employed o he mul iple s a ion echnique ha is,
inges ion o TEC maps (Na a e al., 2011). This echnique sea ches o a ange o alues o ioniza ion pa ame e
(F
10.7index) o minimize he de ia ion o he model om measu ed alues. We p esen a da a inges ion model o
he egional ionosphe e based on a bina y sea ch algo i hm op imiza ion echnique.
The algo i hm in ol es a FORTRAN i e a ion p ocess (see Figu e 3) ha op imally upda es he model's es ima e
by s a is ically minimizing he di e ences be ween he measu ed alue and he model's p edic ion as gi en in
Equa ion 2.
∆ TEC ( )= TECm i − TECo i (2)
whe e TECm and TECo a e he model's p edic ed TEC and GNSS obse ed TEC a ime and g id poin i. A
he s a , he NeQuick 2 calcula es TEC a each epoch and co esponding g ids (g id la i ude and g id longi ude)
ob ained in S ep 2 using he inpu o he daily sola adio lux (F10.7index) as he sola ac i i y p oxy. A each g id
poin , he del a TEC (∆ TEC) is es ima ed. The i e a ion p ocess, implemen ed in he lowcha op imizes he
F10.7 index based on whe he he modeled TEC is g ea e o less han he GNSS TEC, using a 0.1 ×F10.7
inc emen /dec emen . A ela i e e o h eshold ypically 5% (Adol s e al., 2022; Ma e al., 2022; Mengis u
Tsidu & Melaku Zegeye, 2020; Osanyin e al., 2023) ensu es model accu acy, pa icula ly in low‐la i ude.
Az ( )=F10.7( )±0.1×F10.7( )(3)
whe e Az is he op imized lux a ime .
The i e a ion p ocess con inues un il he desi ed h eshold is achie ed, and he inal ou pu o he algo i hm is he
e ec i e ioniza ion pa ame e , ega ded as he op imum lux (Az). The abo e‐desc ibed op imiza ion echnique is
applied o all he GNSS g idded maps in S ep 2. The Az alues om each map a e he egional Az o e he de ined
g id, which is subsequen ly used in he model as he new sola ac i i y p oxy o econs uc desi ed ionosphe ic
pa ame e s o in e es . The abo e is summa ized in Figu e 3, simila o he concep adop ed by A iq e al. (2021).
The model's accu acy is e alua ed using he Roo Mean Squa e E o (RMSE)
RMSE =
(∑N
i=1(TECGNSS −TECNeQuick(Az))2)
N
√
√
√
√(4)
whe e N ep esen s he numbe o indi idual obse a ions du ing he cu en in e al and TECGNSS and
TECNeQuick a e TEC alues om GNSS measu emen and NeQuick 2 model, espec i ely.
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3. Resul s and Discussions
3.1. S a is ical Analysis o Da a Inges ion Using Di e en Spa ial Resolu ions o S a ion Selec ion
Figu e 4shows he s a is ical esul s o NeQuick's pe o mance be o e and a e da a inges ion o geomagne -
ically quie (DOY 069) and dis u bed (DOY 076) condi ions, using he RMSE and pe cen age imp o emen as
me ics. Six GNSS ecei e s, Boa Vis a (BOAV), Belem (BELE), Riobambe (RIOP), Colide (MTCO), Rio
Pa anaiba (MGRP), San a Rosa (SRLP), and Sua Juan (SUAR) we e used o in e nal alida ion. Figu e 4A) and
(b) ep esen he RMSE and pe cen age imp o emen ob ained o he 0.5 TECu h eshold, and he esul is shown
o uni o m (n ×n, le panel) and non‐uni o m (n ×m, igh panel) esolu ion. A he op o each plo is he
legend, which indica es he esolu ion and he co esponding numbe o GNSS s a ions whose TEC da a we e
e ie ed and used o imp o e he model.
Among he a ious colo s used in Figu e 4, g ay ep esen s he s anda d NeQuick 2 model d i en by he daily
F10.7 index. The o he colo s co espond o esul s based on a e age Az alues de i ed om he maps shown in
Figu e 2. As expec ed, he s anda d NeQuick p edic ion exhibi s he highes RMSE compa ed o he adap ed
e sion o he model. Al hough one would an icipa e g ea e imp o emen wi h an inc easing numbe o inges ed
GNSS s a ions, his end does no hold consis en ly, pa icula ly o non‐uni o m esolu ions, whe e p edic ion
accu acy luc ua es. While he esul s o non‐uni o m g ids a e gene ally compa able o hose o uni o m g ids,
hey a e no discussed u he he e due o he signi ican ly highe numbe o GNSS s a ions in ol ed. Uni o m
esolu ion o e s mo e consis en pe o mance ac oss la i udes wi h ewe s a ions. In panels (a) and (b), RMSE
Figu e 3. The lowcha o adap ing he NeQuick 2 model o g ound‐based GNSS TEC measu emen .
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Figu e 4. Roo ‐mean‐squa e e o (RMSE) and pe cen age imp o emen alues o di e en spa ial esolu ions using
h eshold o (a) 0.5 TECu (b) 3 TECu and (c) h eshold o 0.5 TECu and 3 TECu o 6 ×6 esolu ion only conside ing he
equa o ial, low‐la i ude and mid‐la i ude s a ions om he No h o he Sou h.
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OSANYIN ET AL. 8 o 19
alues depic ed in (a) and (e) end o dec ease ac oss he s a ions, wi h ela i ely lowe imp o emen shown in (c)
and (g), especially in he mid‐la i ude egion (SRLP) du ing quie geomagne ic condi ions.
On a e age, he RMSE ac oss la i udes shows nea ly he same le el o imp o emen o bo h he (8 ×8) and
(2 ×2) g id esolu ions. This e lec s he co e idea o he me hodology in e alua ing he op imal quan i y o
g ound‐based GNSS da a needed o enhance he NeQuick model. Fo DOY 067, 35 and 166 GNSS s a ions we e
used o he (8 ×8) and (2 ×2) g ids, esul ing in imp o emen s o 25.11% and 25.78%, espec i ely. Howe e , on
he dis u bed day (DOY 076), he (8 ×8) g id achie ed a sligh ly highe imp o emen o 1.14% mo e han he
(2 ×2) g id despi e using ewe s a ions (34 compa ed o 177). The main inding he e is ha ewe s a ions may
achie e simila desi ed accu acy in TEC and oF2 es ima ion as opposed o using all he a ailable da a, which
slows down he compu a ion p ocess. This is use ul in minimizing compu a ional cos s o eal‐ ime applica ions
such as nowcas ing and o ecas ing based on his me hodology. The esul s may be di e en o moni o ing small‐
scale s uc u es such as medium‐scale (T a elling Ionosphe ic Dis u bances) TIDs. In simila s udies conduc ed
by Migoya‐O ué e al. (2017) and Haba ulema and Ssessanga (2017), he au ho s used all a ailable GNSS s a ions
du ing he s udy pe iod o ep oduce he c i ical equency maps o e A ica. While he app oach in his s udy
s ongly depends on da a a ailabili y o e a de ined g id (e.g., Sou h Ame ica), i may no be sui able o e A ica,
whe e he e is da a pauci y.
BOAV and MGRP a e loca ed in he no he n and sou he n equa o ial ioniza ion anomaly (EIA) c es egions,
espec i ely, while MTCO lies in he o ‐equa o ial zone. Despi e i s p oximi y o he equa o alongside RIOP,
BELE shows g ea e imp o emen o DOY 069, likely in luenced by longi udinal di e ences. MGRP eco ds he
leas imp o emen , highligh ing he need o u he e inemen o clima ological models o e he Sou he n EIA
c es . This egion, loca ed wi hin he co e o he Sou h Ame ican Magne ic Anomaly (SAMA), expe iences
p onounced ionosphe ic a iabili y (Abdu e al., 2005). In con as o he quie pe iod, DOY 076 shows he highes
imp o emen a he sou he n c es (MGRP), sugges ing ha da a inges ion is highly sensi i e o bo h la i ude and
geomagne ic ac i i y (Osanyin e al., 2023). No ably, o DOY 076, he (10 ×10) g id esolu ion achie es
compa able imp o emen o o he esolu ions, despi e using only 27 s a ions. This unde sco es he c i ical ole o
GNSS s a ion dis ibu ion in model pe o mance. The e o e, a well‐dis ibu ed GNSS ne wo k wi h b oad spa ial
co e age can signi ican ly enhance clima ological models.
Based on he esul s in Figu e 4, a minimum o 35 GNSS s a ions, co esponding o he 8 ×8 g id esolu ion, is
ecommended o inges ion, as i deli e s supe io pe o mance ac oss la i udes unde geomagne ically dis u bed
condi ions, which a e o pa icula conce n o he space wea he communi y. Consequen ly, he NeQuick 2 esul s
p esen ed in he ollowing sec ions o alida ion a e based on he imp o emen s achie ed using he 8 ×8 g id
esolu ion.
3.2. EIA De elopmen and Va iabili y O e Sou h Ame ica
The s udy o EIA de elopmen o e Sou h Ame ica has been in es iga ed unde bo h quie (10 Ma ch 2015) and
dis u bed (17 Ma ch 2015) geomagne ic condi ions using a TEC mapping echnique. The GNSS maps we e
p oduced using (1° ×1°) spa ial and 1‐h empo al esolu ion, and he esul s we e compa ed o he NeQuick 2
model. Bo h day ime and pos ‐sunse EIA (PS‐EIA) we e obse ed. Diu nal a ia ion a speci ic loca ions dis-
plays TEC a ia ion du ing he hou s o he day wi h TEC enhancemen s be ween (13:00‐15:00 LT) and nea
local midnigh a (20:00‐21:00 LT) in he low‐la i ude s a ions du ing he dis u bed pe iod.
3.2.1. Quie Time; 10 Ma ch 2015
A sequence o 2‐D TEC maps cons uc ed om GNSS measu emen s o e Sou h Ame ica on 10 Ma ch 2015, is
shown in Figu e 5a a 2‐h in e als om 11:00‐01:00 UT. The magne ic condi ions du ing hese obse a ions
we e quie (Kp =2, Ds = − 8 nT), and he F
10.7was app oxima ely 120.9 ×10
−22
Wm
−2
Hz
−1
. Fo accu acy and
be e compa ison wi h NeQuick, 239 s a ions we e used o gene a e he maps a e excluding hose u ilized (35
s a ions) o he model's imp o emen . Deple ion and enhancemen o TEC alues can be seen in he colo ba
wi h maxima a ound ed. I can be obse ed ha he EIA s a s o de elop a 11:00 UT (∼8:00 LT a 30°W) on he
eas e n coas o B azil du ing he day and expands wes wa d wi h maximum enhancemen be ween 17:00 and
19:00 UT (14:00 and 16:00 LT). In e hemisphe ic asymme y can be obse ed, wi h a mo e p onounced no he n
c es a 19:00 UT. The EIA asymme y has been explained by plasma ecombina ion esul ing om he e ec s o
me idional winds (De Siquei a e al., 2011; Khadka e al., 2018; Lou i e al., 2022), whe eas he deg ee depends
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OSANYIN ET AL. 9 o 19
As such, he model is bes sui ed o long‐ e m, a e age ionosphe ic condi ions a he han eal‐ ime o e en ‐
speci ic applica ions.
In his s udy, we in es iga ed he minimum numbe o g ound‐based GNSS ecei e s needed o signi ican ly
imp o e he pe o mance o NeQuick 2 o e a de ined spa ial g id ac oss Sou h Ame ica. This app oach p o ides
a benchma k o cos ‐e ec i e da a inges ion in clima ological models. Ou esul s indica e ha employing a
uni o m g id esolu ion (n ×n) no only educes he numbe o equi ed GNSS s a ions bu also yields mo e
consis en pe o mance ac oss la i udes. No ably, he RMSE be ween GNSS obse a ions and NeQuick 2 p e-
dic ions dec eased subs an ially, pa icula ly du ing geomagne ically dis u bed condi ions. Imp o emen s anged
om 4% o 45% on quie days and 33%–68% du ing dis u bed pe iods, unde sco ing he sensi i i y o he
inges ion scheme o bo h geog aphic la i ude and geomagne ic ac i i y. In e es ingly, using da a om jus 35 and
166 GNSS s a ions du ing quie condi ions esul ed in less han 1% di e ence in pe o mance, sugges ing ha a
smalle , well‐dis ibu ed ne wo k can be su icien o model enhancemen , a he han elying on a la ge numbe
o s a ions.
Fo he i s ime, we examined he e olu ion o he Equa o ial Ioniza ion Anomaly (EIA) o e Sou h Ame ica
using he NeQuick 2 model. The da a‐inges ed e sion o he model demons a ed imp o ed capabili y in
cap u ing he spa ial and empo al de elopmen o he EIA. Addi ionally, we e alua ed he model's accu acy in
p edic ing plasma equencies by compa ing i s ou pu s wi h digisonde obse a ions. The esul s show s ong
ag eemen a lowe al i udes (100–200 km), wi h dec easing co ela ion a he F‐ egion peak (∼250–350 km),
likely due o limi a ions in e ical esolu ion and dynamic ionosphe ic p ocesses.
O e all, ou indings highligh he impo ance o s a egically dis ibu ed GNSS s a ions o enhancing iono-
sphe ic models h ough da a inges ion. These insigh s a e pa icula ly ele an o ongoing e o s o deploy low‐
Table 2
Co ela ion Coe icien Be ween Digisonde Measu emen s and Inges ed NeQuick 2 o he Plasma F equency a Di e en
Heigh s Du ing Quie (DOY 069) and Dis u bed (DOY 076) Geomagne ic Condi ions Be o e and A e Da a Inges ion
SALU BOAV MSCG
Al i ude (km) Quie Dis u bed Quie Dis u bed Quie Dis u bed
100 0.97/0.97 0.97/0.96 0.93/0.95 0.57/0.55 0.89/0.91 0.91/0.87
150 0.99/0.99 0.99/0.99 0.96/0.98 0.67/0.65 0.95/0.96 0.96/0.95
200 0.94/0.96 0.90/0.91 0.80/0.87 0.30/0.40 0.72/0.77 0.75/0.82
250 0.81/0.77 0.68/0.71 0.71/0.58 0.16/0.54 0.42/0.27 0.18/0.27
300 0.64/0.49 0.50/0.57 0.65/0.58 0.21/0.21 0.82/0.92 0.50/0.84
350 0.64/0.77 0.70/0.77 0.82/0.86 0.64/0.62 0.94/0.93 0.80/0.53
400 0.68/0.85 0.82/0.81 0.93/0.97 0.87/0.84 0.85/0.91 0.74/0.91
Table 3
Roo Mean Squa e E o (RMSE) Be ween Digisonde Measu emen and Inges ed NeQuick 2 o he Plasma F equency a
Di e en Heigh s Du ing Quie (DOY 069) and Dis u bed (DOY 076) Geomagne ic Condi ions Be o e and A e Da a
Inges ion
SALU BOAV MSCG
Al i ude (km) Quie (TECu) Dis u bed (TECu) Quie (TECu) Dis u bed (TECu) Quie (TECu) Dis u bed (TECu)
100 0.94/0.73 0.92/0.80 0.81/0.55 1.09/1.06 0.82/0.76 0.83/0.74
150 0.71/0.58 0.69/0.62 0.92/0.60 1.40/1.41 1.03/0.91 0.96/0.87
200 1.33/1.16 1.54/1.39 1.54/1.07 2.30/2.34 1.79/1.61 1.56/1.32
250 1.72/1.90 2.23/2.12 2.21/2.80 3.57/3.45 2.24/2.60 3.90/3.84
300 2.19/2.45 2.45/2.37 2.72/3.34 4.02/3.95 2.33/2.87 3.45/3.39
350 2.49/1.89 2.04/1.80 2.32/2.31 2.55/3.24 1.82/1.57 2.52/2.37
400 1.68/1.66 1.84/2.06 2.03/2.10 1.72/2.21 2.35/1.66 3.53/2.15
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OSANYIN ET AL. 16 o 19
cos GNSS ecei e ne wo ks in unde ‐obse ed egions. Fu he mo e, his s udy ep esen s he i s compa ison
o NeQuick 2 plasma equency es ima es wi h digisonde da a o e Sou h Ame ica, con ibu ing o a be e
unde s anding o ionosphe ic beha io du ing space wea he dis u bances and suppo ing he de elopmen o
egion‐speci ic ionosphe ic models.
Da a A ailabili y S a emen
We acknowledge he STI Uni o he ICTP, T ies e, I aly, o p o iding he NeQuick 2 sou ce code (h ps:// -
ic 4d.ic p.i /nequick2/sou ce-code). We hank Emb ace/INPE o p o iding he digisonde da a (h ps://www2.
inpe.b /climaespacial/). The Ds index da a (h ps://wdc.kugi.kyo o-u.ac.jp/wdc/) was ob ained om he Wo ld
Da a Cen e o Geomagne ism, Kyo o. Kp index and sola adio lux da a can be accessed om he NOAA
(Na ional Oceanic and A mosphe ic Adminis a ion) websi e (h ps://spd .gs c.nasa.go /pub/da a/omni/). The
GNSS g ound‐based ecei e da a we e collec ed om di e en GNSS ne wo ks in Sou h Ame ica: RBMC
om IBGE (h ps://www.ibge.go .b ), RAMSAC o A gen ina (h ps://www.ign.gob.a /Nues asAc i idades/
Geodesia/Ramsac/Desca gaRinex), IGS (h ps://cddis.nasa.go /a chi e/gnss/da a/hou ly); and UNAVCO
(h ps://www.una co.o g/da a/gps-gnss/gps-gnss.h ml). The Py hon code o selec ing GNSS da a used in he
NeQuick 2 model and samples o GNSS da a du ing he s udy pe iod a e a ailable in he Zenodo eposi o y a
T. Osanyin, (2025).
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Figu e 9. Va ia ion o F2 laye c i ical equency ( oF2) du ing (a) quie (10 Ma ch 2015) and (b) dis u bed (17 Ma ch 2015)
geomagne ic condi ions. The ed solid lines depic digisonde measu emen , blue solid and g een do ed lines a e NeQuick 2
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Acknowledgmen s
Taiwo Osanyin since ely hanks he Sou h
A ican Na ional Space Agency (SANSA),
He manus, Sou h A ica, o hei inancial
suppo and hospi ali y h ough he
Scien i ic Commi ee on Sola ‐Te es ial
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