Use o ay acing in models o in es iga e ionosphe ic channel
pe o mance
G. Mi o
´ Ama an e
*
, S.M. Radicella
Ae omony and Radiop opaga ion Labo a o y, Abdus Salam ICTP, S ada Cos ie a 11, 34014 T ies e, I aly
Abs ac
The main pa ame e s ha cha ac e ize an ionosphe ic channel, equency, ele a ion angle, g oup pa h, g ound ange, and apogee
ha e been ob ained by means o 2D ay acing p og am called abc ay03. The analysis has conside ed diffe en hou ly ionosphe ic con-
di ions o ou quie days (25–28 Ma ch 2000) and fi e geog aphic loca ions dis ibu ed in he wo hemisphe es. Elec on densi y p ofiles
define he selec ed ionosphe ic condi ions. Ray acing is un conside ing expe imen al elec on densi y p ofiles om manually scaled
measu emen s ob ained wi h ionosondes. The esul ing adio p opaga ion pa ame e s a e compa ed wi h hose ob ained using he
IRI and NeQuick models d i en by measu ed F2 peak alues.
Keywo ds: Ray acing; Ionosphe e; Elec on densi y p ofiles
1. In oduc ion
The 2-dimensional ay acing echnique used (called
abc ay03) is based on he exp essions in oduced by C o
and Hoogasian (1968) and C o (1969), and has been con-
side ed in p e ious ionosphe ic s udies (Moo head and
Radicella, 1998; Mi o
´, 2000; Mi o
´e al., 2002). The ou -
pu s ob ained wi h his compu ing echnique a e he main
adio p opaga ion pa ame e s o he selec ed equency:
ime delay o he signal a elling om he ansmi e o
he ecei e ( ela ed o g oup pa h), eflec ion heigh o
apogee, g ound ange, and ele a ion angle.
A pa icula ionosphe ic condi ion is inse ed in o he
ay acing p og am using a model o a measu ed elec on
densi y p ofile. The elec on densi y p ofile models used
o his analysis a e he In e na ional Re e ence Ionosphe e
(IRI) (Bili za, 1990, 2001) and NeQuick (Radicella and
Lei inge , 2001; Radicella e al., 2003).
The aim o his pape is o illus a e he effec s o he di -
e ences be ween hese models and he expe imen al elec-
on densi y p ofiles on adio sys em ope a ions. Simila
s udies ound in he bibliog aphy show he impo ance o
hese effec s. Fo example, he impac o he F egion
long- e m end on adio sys ems has been e alua ed by
Cannon Paul e al. (2004). This ecen s udy uses an analy -
ic ay acing echnique – SMART (No man and Cannon,
1997, 1999) – and elec on densi y p ofiles fi ed o CCIR
coefficien s and he esul s show ha a 16 km d op in
hmF2 can in oduce g ound ange changes o 100 km
wi h la ge alues unde ce ain ci cums ances.
The analysis p esen ed in his pape has been di ided
in o wo pa s: (1) s udy o he main adio p opaga ion
pa ame e s o he ou quie days analyzed a fi e iono-
sonde s a ions; (2) s a is ical analysis o he diffe ences in
ele a ion angle, apogee and g oup pa h be ween he wo
models and expe imen al esul s.
2. Me hodology
The expe imen al elec on densi y p ofiles we e p o-
duced di ec ly om he manually scaled ionog ams by
using he NHPC in e sion echnique (Huang and Reinisch,
1997). The model p ofiles ob ained wi h he NeQuick and
*
Co esponding au ho .
E-mail add ess: mi oama an [email protected] (G. Mi o
´Ama an e).
IRI models we e fi ed o oF2 and M3000F2 measu ed
cha ac e is ics.
The ay acing p og am conside s he dis ance be ween
ansmi e and ecei e (D) and he elec on densi y p ofile
as inpu s. The elec on densi y p ofile is loca ed a he ci -
cui midpoin . Fo his s udy, he ansmi e – ecei e links
ha e been selec ed along a me idian. The analyzed dis anc-
es a e calcula ed by inc easing he la i ude in one deg ee
s eps up o 1500 km. The ansmi e – ecei e dis ance
(D) was calcula ed using he exp ession
D¼Reacos½sin kTsin kR
þcos kTcos kRcosðuTuRÞ;ð1Þ
whe e uand ka e longi ude and la i ude o he ansmi e
(T) and he ecei e (R) and Re he adius o he Ea h
(6370 km).
The p og am abc ay03 was un o each dis ance and
ionosphe ic condi ion (expe imen al and model elec on
densi y p ofiles a he ci cui midpoin ). The main adio
p opaga ion pa ame e s ( ime delay, apogee, and g ound
ange) we e calcula ed in he equency ange o 1–
20 MHz (0.1 MHz s ep) and ele a ion angle sweep be ween
6 and 60 deg ees (0.1 deg ee s ep).
The analysis was un o diffe en hou ly ionosphe ic
condi ions (0, 6, 12, and 18 LT) o he ou quie days
(25–28 Ma ch 2000) and o fi e geog aphic loca ions dis-
ibu ed in he wo hemisphe es (Table 1). The selec ed
pe iod co esponds o high sola ac i i y wi h daily sunspo
numbe s g ea e han 155.
2.1. S udy o he main adio p opaga ion pa ame e s o he
ou quie days analyzed a fi e ionosonde s a ions
The fi s s udy ca ied ou using he ay acing esul s
was he compa ison be ween he diffe en analyzed days.
G ound ange, ime delay (o he equi alen g oup pa h),
and apogee o each day (85–88 days o yea 2000) we e
plo ed. The examples shown in Fig. 1 co espond o Mill-
s one Hill and Ascension Island a a ansmission equen-
cy o 12 MHz and 12:00 LT. The le panel shows he
expe imen al elec on densi y p ofiles used as ionosphe ic
condi ions a he midpoin .
I can be seen in he case o Mills one Hill whe e he
p ofiles ha e some a iabili y, he g oup pa h and ange
show he bigges diffe ences in he egion be ween he E
and F1 eflec ions. Howe e , he e a e no significan diffe -
ences a Ascension Island. Fo he es o he ionosonde
s a ions, he esul s show ha Ramey has a simila beha -
io o he o he selec ed No he n Hemisphe e s a ion,
Mills one Hill, and he esul s ob ained a Jicama ca and
G ahams own, in he sou he n Hemisphe e, a e close o
hose ound a Ascension Island.
2.2. S a is ical analysis o he diffe ences in ele a ion angle,
apogee, and g oup pa h be ween model and expe imen al
esul s
A s a is ical analysis has been done compa ing he wo
models (IRI and NeQuick) and he expe imen al esul s in
ele a ion angle, apogee and g oup pa h. Table 2 shows he
s a is ical esul s a Ramey o 00, 06, 12, and 18 LT co -
esponding o NeQuick (NQ) and IRI. The numbe o
cases (numbe ), a e age o absolu e diffe ences (A e age),
s anda d de ia ion (S de ), median o absolu e diffe ences
(Median), cases wi h posi i e diffe ences (>0), and cases
wi h nega i e diffe ences (<0) we e calcula ed o ele a ion
angle, apogee, and g oup pa h. The diffe ences shown o
he g oup pa h a e ela i e (di ided by expe imen al al-
ues) because o he wide ange conside ed. Fo he case
o Ramey, he diffe ences show ha NQ o e es ima es
he h ee pa ame e s o 06, 12, and 18 LT and IRI unde -
es ima es hem o 00 and 12 LT. IRI is wo se han NQ
o 00 LT wi h diffe ences a ound 4 deg ees in ele a ion
angle, 63 km in apogee, and 4% in g oup pa h. NQ is
wo se han IRI o 06, 12, and 18 LT wi h diffe ences
a ound 4–5 deg ees in ele a ion angle, 26–32 km in apo-
gee, and 4–5% in g oup pa h. The shadow panels (Table
2–6)inA e age ow co espond o he compa ison
be ween he IRI and NeQuick models ( he la ges alue)
and he shadow panels in posi i e (>0) and nega i e
(<0) diffe ences ow show he o e es ima ion o unde es i-
ma ion o each model.
Fo he case o Mills one Hill (Table 3), he diffe ences
show ha NQ o e es ima es he h ee pa ame e s and
IRI unde es ima es hem o 00, 06, and 18 LT. NQ is
wo se han IRI wi h diffe ences a ound 3–6 deg ees in
ele a ion angle, 25–38 km in apogee, and 3–5% in g oup
pa h.
A Jicama ca (Table 4), he diffe ences show ha NQ
o e es ima es he h ee pa ame e s and IRI unde es ima es
hem o 00 and 06. IRI is wo se han NQ o 06 and 12 LT
wi h diffe ences a ound 5–10 deg ees in ele a ion angle, 46–
80 km in apogee and 5–10% in g oup pa h. NQ is wo se
han IRI o 00 and 18 LT wi h diffe ences a ound 3–6
deg ees in ele a ion angle, 20–51 km in apogee, and 2–6%
in g oup pa h.
The diffe ences ob ained o G ahams own (Table 5)
show ha NQ o e es ima es he h ee pa ame e s o
06, 12, and 18 LT and IRI unde es ima es he h ee
pa ame e s o 00, 06, and 18 LT. IRI is wo se han
NQ o 00 LT wi h diffe ences a ound 5 deg ees in ele a-
ion angle, 47 km in apogee, and 5% in g oup pa h. NQ
Table 1
Geog aphic coo dina es, geomagne ic la i udes and modified dip la i udes
o he selec ed ionosonde s a ions
S a ion La . Long. La . Geomag. Modip
Ascension Is 7.9 345.6 1.40 23.24
G ahams own 33.3 26.5 33.80 50.97
Jicama ca 12.0 283.2 0.68 0.65
Mills one H. 42.6 288.5 53.99 55.90
Ramey 18.5 292.9 29.89 42.48
is wo se han IRI o 12 LT wi h diffe ences a ound 6
deg ees in ele a ion angle, 41 km in apogee, and 5% in
g oup pa h.
Fo he case o Ascension Island (Table 6), he diffe -
ences show ha NQ o e es ima es he ele a ion angle
and g oup pa h o 06 and 18 LT and IRI unde es ima es
he h ee pa ame e s. IRI is wo se han NQ o 12 LT
wi h diffe ences a ound 4 deg ees in ele a ion angle,
25 km in apogee and 4% in g oup pa h. NQ is wo se han
IRI o 06 and 18 LT wi h diffe ences a ound 3–5 deg ees
in ele a ion angle, 28–30 km in apogee, and 3–6% in
g oup pa h.
Fig. 1. Range, g oup pa h, and apogee e sus ele a ion angle o each selec ed day ( igh panel) and he co esponding expe imen al elec on densi y
p ofiles (le panel) o Mills one Hill and Ascension Island.
Table 2
S a is ical esul s a Ramey o ele a ion angle, apogee and g oup pa h diffe ences co esponding o NeQuick (NQ) and IRI
Table 3
S a is ical esul s a Mills one Hill o ele a ion angle, apogee and g oup pa h diffe ences co esponding o NeQuick (NQ) and IRI
Table 4
S a is ical esul s a Jicama ca o ele a ion angle, apogee and g oup pa h diffe ences co esponding o NeQuick (NQ) and IRI
Table 5
S a is ical esul s a G ahams own o ele a ion angle, apogee and g oup pa h diffe ences co esponding o NeQuick (NQ) and IRI
3. Conclusions
The diffe ences in g oup pa h and ange ound in he
compa ison be ween he ou quie days when eflec ion
occu s in he F1 egion confi m p e ious esul s by he
au ho s (Mi o e al., 2005). The F1 egion is c i ical o
de e mine he main adio p opaga ion pa ame e s using
ay acing h ough ionog am-de i ed elec on densi y
p ofiles.
In summa y, compa ing he ay acing h ough mea-
su ed and modeled p ofiles leads o he ollowing conclu-
sions (Table 7): (1) NQ o e es ima es he h ee
pa ame e s, (2) IRI unde es ima es he h ee pa ame e s,
and (3) NQ and IRI pe o mances o he h ee pa ame e s
a e simila wi h diffe ences a ound 4 deg ees in ele a ion
angle, 33 km in apogee, and 4% in g oup pa h.
Acknowledgemen s
The au ho s a e g a e ul o D . Moo head o Nep une
Rada L d., Glousces e , U.K., o his help in unde s and-
ing he ay- acing echnique, o he Cen e o A mosphe -
ic Resea ch a Uni e si y o Massachuse s Lowell, USA,
o da a and so wa e suppo and o he IRI and NeQuick
g oups.
Re e ences
Bili za, D. In e na ional Re e ence Ionosphe e 1990. NSSDC 90-22,
G eenbel , Ma yland, 1990.
Bili za, D. In e na ional Re e ence Ionosphe e 2000. Radio Science 36 (2),
261–275, 2001.
Cannon Paul, S., Roge s Neil, C., Hall Ch is, M. T ends in c i ical
equencies and laye heigh s o e T omso and hei consequen ial
impac o adio sys em modeling. Ad ances in Space Resea ch 34,
2085–2091, 2004.
C o , T.A. Me hods and applica ions o compu e ay acing. S an o d
Elec onics Labs ech. Repo . SU-SEL- 69-007, 1969.
C o , T.A., Hoogasian, H. Exac ay calcula ions in a quasi-
pa abolic ionosphe e wi h no magne ic field. Radio Science 3, 69–
74, 1968.
Huang, X., Reinisch, B.W. Ve ical elec on densi y p ofiles om
digisonde ionog ams. The a e age ep esen a i e p ofile. Annali di
Geofisica 39 (4), 751–756, 1997.
Mi o
´, G. Ca ac e izacio
´n del canal ionos e
´ ico pa a un enlace HF pun o a
pun o median e e
´cnicas de azado de ayos, Ph.D. Thesis, Uni e s-
idad Complu ense de Mad id, 2000. (In Spanish).
Mi o
´, G., De la Mo ena, B.A., Radicella, S.M., He aiz, M. Wo s cases
o a one-hop High F equency Link. Annals o Geophysics 45 (1),
201–205, 2002.
Table 7
S a is ical esul s (numbe o cases (numbe ), a e age o absolu e diffe ences (A e age), cases wi h posi i e diffe ences (>0) and cases wi h nega i e
diffe ences (<0)) o ele a ion angle, apogee and g oup pa h co esponding o NeQuick (NQ) and IRI
The shadow panels show he o e es ima ion o unde es ima ion o each model. (All s a ions).
Table 6
S a is ical esul s a Ascension Island o ele a ion angle, apogee and g oup pa h diffe ences co esponding o NeQuick (NQ) and IRI

Mi o Ama an e, G., Zhang, M.L., Radicella, S.M. Ionog am in e sion F1
laye ea men effec in ay acing. Annals o Geophysics 48 (3), 483–
489, 2005.
Moo head, M.D., Radicella, S.M. Using 2D ay acing o model he
effec s o e ical p ofile a iabili y on oblique pa h p opaga ion a
HF equencies. P oceedings o he Side Wo kshop o COST 251,
1998.
No man, R.J., Cannon, P.S. A wo-dimensional analy ic ay acing
echnique accommoda ing ho izon al g adien s. Radio Science 32 (2),
387–396, 1997.
No man, R.J., Cannon, P.S. An e alua ion o a new 2-D analy ic
ionosphe ic ay acing echnique – SMART. Radio Science 34 (2),
489–499, 1999.
Radicella, S.M., Lei inge , R. e olu ion o he DGR app oach o model
elec on densi y p ofiles. Ad ances in Space Resea ch 27 (1), 35–40,
2001.
Radicella, S.M., Lei inge , R., Na a, B., Coisson, P. A flexible 3D
ionosphe ic model o sa elli e na iga ion applica ions. In e na ional
Symposium on GPS/GNSS P oceedings, Tokyo, Japan, 305–310,
2003.