525

ANNALS OF GEOPHYSICS, VOL. 48, N. 3, June 2005

Key words ionosphere – electron density models –profilers

1. Introduction: the NeQuick formulation

The purpose of this paper is to present the rea-sons for the revision of the bottomside of thethree dimensional and time dependent electrondensity model NeQuick (Radicella and Leitinger,2001) and to show some of the improvementsgained by the revision.

NeQuick was submitted to ITU-R by theEuropean Space Agency and was accepted bythe relevant ITU-R authorities in July 2000.Source code, executable and two driver pro-

grams are now available on the ITU-R webpage <http://www.itu.int/ITU-R/software/study-groups/rsg3/databanks/ionosph>.

NeQuick-ITUR strictly follows relevantITU-R recommendations and uses the ITU-Rrelation between average sunspot number (R12)and 10.7 cm solar radio flux (F10.7)

. ( . . )F R R63 7 0 728 0 00089.10 7 12 12= + +

or

( ) ..

R F167273 1123 6408 99

. .

.

12 10 7 63 7

0 5

= + +-

-6 @

with saturation of the F2 layer critical frequen-cy foF2 and the transfer parameter M(3000)F2at R12=150 (Recommendation ITU-R P.1239,ITU-R, 1997).

The model is formulated in the FORTRAN 77language, uses a modular design and containsno COMMON blocks.

NeQuick is a «profiler» model which usesthe peaks of the E-layer, the F1-layer and the

An improved bottomside for the ionosphericelectron density model NeQuick

Reinhart Leitinger (1), Man-Lian Zhang (2) and Sandro M. Radicella (3)(1) Institut für Physik, Institutsbereich für Geophysik, Astrophysik und Meteorologie (IGAM),

Universität Graz, Austria(2) Laboratory for Space Weather, Center for Space Science and Applied Research,

Chinese Academy of Sciences, Beijing, People’s Republic of China(3) The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy

AbstractThe ionospheric electron density model NeQuick is a «profiler» which uses the peaks of the E-layer, the F1-lay-er and the F2-layer as anchor points. In the version prepared for and submitted to the International Telecommu-nication Union (ITU) the model uses the ITU-R (CCIR) maps for foF2 and M(3000)F2 and adapted maps sim-ilar to the ITU-R ones for foE and foF1. Since users found problematic behaviour of NeQuick under conditionsof strong differences of foE and foF2 map structures, the profiling was adapted by changing the properties of theEpstein layers used for this purpose. The new formulation avoids both strange horizontal structures of the geo-graphic distribution of electron density in fixed heights and unrealistic peculiarities of the height profile whichoccasionally occurred with the old version of the model. Since the Epstein layer approach allows for 8 parame-ters only (3 layer amplitudes and 5 semi-thicknesses) the adaptation was no minor task but needed careful plan-ning of suitable strategies.

Mailing address: Dr. Reinhart Leitinger, Institut für Phy-sik, Institutsbereich für Geophysik, Astrophysik und Meteo-rologie (IGAM), Universität Graz, Universitaetsplatz 5, A-8010 Graz, Austria; e-mail: reinhart.leitinger@uni-graz.at

F2-layer as anchor points. At any location theanchor points are derived from «maps» for theionosonde parameters foE, foF1, foF2 andM(3000)F2. The foF2 and M(3000)F2 maps arefrom ITU-R (CCIR), the foE map is a modifiedformulation of that due to John Titheridge (seeLeitinger et al., 1995, 1996) and foF1 is takento be 1.4 × foE (Leitinger et al., 1999) duringdaytime and is set zero during nighttime.

The maps are formulated in «modified diplatitude» µ: tan cosI=n { where µ is(Rawer’s) modified dip latitude or «MODIP»(Rawer, 1963); I, the magnetic dip; and ϕ, thegeographic latitude.

The peak of the E-layer has a fixed height of120 km, the F2 peak is constructed from foF2(symbol fF2), M(3000)F2 (symbol M3) and foE(symbol fE) using Dudeney’s form of theBradley and Dudeney (1973) formula (see Du-deney, 1983).

With M= ( . ) ( . ),M M0 0196 1 1 2967 13 3

2

3

2+ -n.0 01- 2.0 253t = ( . )1 215

E-tf //F2

,f =∆ 6 @ (iffE= 0 then ∆=−0.012), we get /( )h 1490m= n6

)(M km1763+ -∆/ A .The height of the F1 anchor point was origi-

nally modelled as hmF1= (108.8+ 14× NmF1++ 0.71× | I | ) km, NmF1 being the F1 peak elec-tron density in electrons per cubic meter and Ibeing the inclination (dip) of the geomagneticinduction vector in degrees.

For the bottomside of the F-region, anchorpoint related profiling is realised by means of asum of three semi-Epstein layers. With NmF2== 0.124 fF2

2 , NmF1= 0.124 fF22 , NmE= 0.124 fE

2 be-ing the F2, F1 and E-layer peak electron densi-ties, hmF2, hmF1, hmE being the F2, F1 and E-layerpeak heights, BF2, BF1, BE the F2, F1 and E-layerthickness parameters, we get for the bottom side

( ) expN h =

( ) expN h =

( ) ( ) ( ) ( )

exp

exp

exp

N h N h N h N h

Bh h

NB

h h

N

N

1

4

1

4

1

4

F F E

F

F

mF

mF

F

mF

F

F

mFF

E

E

mEE

2 1

2

2

2

2

2

2

1

1

11

= + +

+-

-

+

+

gg

gg

( ) expN h =

d

d

^^

^^

n

n

hh

hh

<

7

7

F

A

A

Bh h

d1LL

mL

2

1-+ ff

exp=g c m

with ( )d h h BmF L2= - , ε1=10, ε 2=2, index L:or F1, or E.

This modification ensures that at the F2peak the lower layers are «faded out» effective-ly. Examples: if d = 99 the argument of the «fad-ing out» exponential is 0.1, if d = 4.5 it is 2, ifd = 0.5 it is 5, if d = 0 it is 10.

The thickness parameters take different val-ues for the bottomside and for the topside of thelayers (BEbot and BEtop for the E-layer, BF1bot andBF1top for the F1-layer)

( )( )

( )exp

expN hz

Nz

1

4 mFtop 2

2=+6 @

with

( )( )

z

HrH g h h

rg h hh h

1OO mF

mF

mF

2

2

2=

++ -

--

< F

where HO= Btop/v; v = (0.041163x−0.183981)x++1.424472; x = (Btop−150)/100.

The profile for the topside, too, is the upperhalf of an Epstein layer: g is a height gradient forthe scale height HO, [rHO+ g(h−hmF2)] restrictsthe scale height increase, the factor v was intro-duced to reduce the vertical electron content toobserved values. The topside thickness parameterBtop= kBF2, with two different formulations,k= 6.705−0.014R12−0.008 hmF2 (April to Sep-tember), k=−7.77+0.097 (hmF2/Btop)2+0.153 NmF2

(October to March). In both cases k is restrictedto 2≤k≤8.

2. Revision of the NeQuick bottomside

2.1. Reason for the revision

In «mapping» applications of NeQuick (con-struction of electron density grids in fixed heightsbelow the F2 peak) it became evident that in somecases strong gradients and strange structures ap-pear in E and F1-layer heights (see fig. 1a). An in-vestigation demonstrated that a large fraction ofthe gradient problem cases was coupled to the fol-lowing behaviour of the foE and foF2 maps. Wefound that in the critical regions and time intervals

526

Reinhart Leitinger, Man-Lian Zhang and Sandro M. Radicella

527

An improved bottomside for the ionospheric electron density model NeQuick

Fig

.1a

,b.

NeQ

uick

, ori

gina

l for

mul

atio

n. a

) Is

olin

es o

f el

ectr

on d

ensi

ty in

uni

ts o

f 10

9 m

-3in

a g

eogr

aphi

c la

titud

e ve

rsus

long

itude

sys

tem

. Hei

ghts

from

100

km

(to

p le

ft)

to 4

50 k

m (

bott

om r

ight

) in

ste

ps o

f 50

km

. Mon

thly

mea

n co

nditi

ons

for

Nov

embe

r 19

98, 1

1 h

UT.

b)

Isol

ines

of

mod

el p

a-ra

met

ers

in a

geo

grap

hic

latit

ude

vers

uslo

ngitu

de s

yste

m. E

pste

in la

yer

ampl

itude

s an

d th

ickn

ess

para

met

ers.

Mon

thly

mea

n co

nditi

ons

for

Nov

em-

ber

1998

, 11

h U

T. F

rom

top

left

to b

otto

m r

ight

: F2

ampl

itude

, F1

ampl

itude

, Eam

plitu

de, B

Ebo

t, B

Eto

p, B

F1b

ot, B

F1t

op, B

F2b

ot.

ab

528

Reinhart Leitinger, Man-Lian Zhang and Sandro M. Radicella

Fig

.2a

,b.

NeQ

uick

, rev

ised

. a)

Isol

ines

of

elec

tron

den

sity

in u

nits

of

109

m-3

in

a ge

ogra

phic

latit

ude

vers

uslo

ngitu

de s

yste

m. H

eigh

ts f

rom

100

km (

top

left

) to

450

km

(bo

ttom

rig

ht)

in s

teps

of

50 k

m. M

onth

ly m

ean

cond

ition

s fo

r N

ovem

ber

1998

, 11

h U

T. b

) Is

olin

es o

f m

odel

par

amet

ers

ina

geog

raph

ic la

titud

e ve

rsus

long

itude

sys

tem

. Eps

tein

laye

r am

plitu

des

and

thic

knes

s pa

ram

eter

s. M

onth

ly m

ean

cond

ition

s fo

r N

ovem

ber

1998

, 11

h U

T. F

rom

top

left

to b

otto

m r

ight

: F2

ampl

itude

, F1

ampl

itude

, Eam

plitu

de, B

Ebo

t, B

Eto

p, B

F1b

ot, B

F1t

op, B

F2b

ot.

ab

529

An improved bottomside for the ionospheric electron density model NeQuick

the isolines of foF2 and foE are nearly orthogonalto each other leading to difficult profile transi-tions. Isoline displays of electron density for con-stant height clearly show that the foE structure(isolines nearly parallel to the abscissa) is correct-ly forced at the E-layer peak (at a height of 120km) but not above and below where the reason-able and expected structure is interrupted bystrange features in the diagonal of the display (fig.1a, isoline displays for 100 km and 150 km). Sin-gle parameter adaptations could not solve theproblem but a more elaborate revision of the orig-inal «Di Giovanni-Radicella» (DGR) modellingapproach (Di Giovanni and Radicella, 1990;Radicella and Zhang, 1995) was necessary.

2.2 The most important revisions

Following an elaborate parameter adapta-tion strategy and after many tests we adoptedthe revisions:

1) Replace the formerly complicated formu-lation for the height of the F1 peak, hmF1, by us-ing hmF1= (hmF2+ hmE)/2.

2) Set foF1 to zero if foE is smaller than 2MHz and avoid that foF1 gets too close to foF2.The original formulation was fF1= 1.4 fE underall daytime conditions. Now fF1= 0.85×1.4 fE if1.4 fE> 0.85 fF2.

3) Introduce simplified formulations for thethickness parameters BF1top, BF1bot and BEtop.

Fig. 3a,b. Height profiles of electron density: January; R12=150; 0 h UT; geografic longitude 0°E (a), 60°E (b);0 h LT (a), 4 h LT (b); geografic latitudes 0°N (top left) to 75°N (bottom right), latitude spacing 15°. Solidcurves: revised NeQuick, dotted curves: NeQuick, old formulation.

a b

530

Reinhart Leitinger, Man-Lian Zhang and Sandro M. Radicella

Fig. 3c-f. Height profiles of electron density: January; R12=150; 0 h UT; geografic longitude 120°E (c), 180°E(d), 240°E (e), 300°E (f); 8 h LT (c), 12 h LT (d), 16 h LT (e), 20 h LT (f); geografic latitudes 0°N (top left) to 75°N(bottom right), latitude spacing 15°. Solid curves: revised NeQuick, dotted curves: NeQuick, old formulation.

c d

e f

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An improved bottomside for the ionospheric electron density model NeQuick

The complete set of thickness parameters nowis BF2=38.5NmF2/d with d=exp[(−3.467+0.857..ln(fF2

2) + 2.02ln(M3)]; BF1top= 0.3(hmF2− hmF1);BF1bot= 0.5(hmF1− hmE); BEtop= 0.5(hmF1− hmE) orBEtop= 7 whatever is larger; BEbot= 5.

3. Comparison of NeQuick-ITUR with the revised NeQuick

The following collection of maps and pro-files demonstrates the improvement of theNeQuick properties.

The comparison of fig. 2a (revised NeQuick)with fig. 1a (NeQuick before revision) clearly

shows that strong gradients and strange structureshave disappeared. This is especially true for E-layer heights and for the E-F1 transition region.Figure 1b connects the strong gradients andstrange structures to the latitude-longitude distri-bution of E and F1 thickness parameters BEtop,BF1bot and BF1top and to the amplitude of the E-Ep-stein layer, A(E). Figure 2b shows that after the re-vision all these parameters are very well behaved.

The profile comparisons of fig. 3a-f (Janu-ary, high solar activity) and fig. 4a-f (April, lowsolar activity) show that two profile peculiari-ties have disappeared with the revision:

a) A low latitude «contamination» of the E-layer by the F1-layer leading to electron densi-

Fig. 4a,b. Height profiles of electron density: April; R12=20; 0 h UT; geografic longitude 0°E (a), 60°E (b); 0h LT (a), 4 h LT (b); geografic latitudes 0°N (top left) to 75°N (bottom right); latitude spacing 15°. Solid curves:revised NeQuick, dotted curves: NeQuick, old formulation.

a b

532

Reinhart Leitinger, Man-Lian Zhang and Sandro M. Radicella

Fig. 4c-f. Height profiles of electron density: April; R12=20; 0 h UT; geografic longitude 120°E (c), 180°E (d),240°E (e), 300°E (f); 8 h LT (c), 12 h LT (d), 16 h LT (e), 20 h LT (f); geografic latitudes 0°N (top left) to 75°N(bottom right); latitude spacing 15°. Solid curves: revised NeQuick, dotted curves: NeQuick, old formulation.

c d

e f

533

An improved bottomside for the ionospheric electron density model NeQuick

ties larger than Nm(E) at the presumed E-layerpeak of 120 km (top rows of fig. 4c,d).

b) A (upper mid and) high latitude «contam-ination» of the F2-layer by the F1-layer leadingto secondary maxima somewhere between theF1 and the F2 peaks (figs. 5 and 6). In some cas-es the secondary maxima had electron densityvalues larger than Nm(F2) (e.g., bottom of fig.5). These artifacts tended to appear in the «old»NeQuick around 10 h Local Time (LT) both un-der high solar activity conditions (fig. 5) and lowsolar activity conditions (fig. 6).

The revised NeQuick has been released on 25 November, 2002 after automatic checking of

about 72000 and systematic visual inspection ofhundreds of model profiles gained in all seasonsunder high, mid and low solar activity conditionsand distributed globally in latitude and longitudeand distributed over Universal Time (UT) days.

REFERENCES

BRADLEY, P.A. and J.R. DUDENEY (1973): A simple modelof the vertical distribution of electron concentration inthe ionosphere, J. Atmos. Terr. Phys., 35, 2131-2146.

DI GIOVANNI, G. and S.M. RADICELLA (1990): An analyticalmodel of the electron density profile in the ionosphere,Adv. Space Res., 10, 27-30.

Fig. 5. Height profiles of electron density: July;R12=150; 16 h UT; geografic longitude 270°E; 10 hLT; geografic latitudes 0°N (top left) to 75°N (bot-tom right); latitude spacing 15°. Solid curves: re-vised NeQuick, dotted curves: NeQuick, old formu-lation.

Fig. 6. Height profiles of electron density: April;R12=20; 20 h UT; geografic longitude 210°E; 10 hLT; geografic latitudes 0°N (top left) to 75°N (bot-tom right); latitude spacing 15°. Solid curves: re-vised NeQuick, dotted curves: NeQuick, old formu-lation.

534

Reinhart Leitinger, Man-Lian Zhang and Sandro M. Radicella

DUDENEY, J.R. (1983): The accuracy of simple methods fordetermining the height of the maximum electron con-centration of the F2-layer from scaled ionosphericcharacteristics, J. Atmos. Terr. Phys., 45, 629-640.

ITU-R (1997): Reference ionosphere characteristics, Rec-ommendation P.1239 (approved in 1997-05, managedby ITU-R Study Group SG3).

LEITINGER, R., J.E. TITHERIDGE, G. KIRCHENGAST and W.ROTHLEITNER (1995): A «simple» global empiricalmodel for the F-layer of the ionosphere, Wiss. Bericht1/1995, IMG Universität Graz.

LEITINGER, R., J.E. TITHERIDGE, G. KIRCHENGAST and W.ROTHLEITNER (1996): Ein «einfaches» globales em-pirisches Modell für die F-Schicht der Ionosphäre,Kleinheubacher Berichte, 39, 697-704.

LEITINGER, R., S.M. RADICELLA, B. NAVA, G. HOCHEGGER

and J. HAFNER (1999): NeQuick – COSTprof – NeUoG-plas, a family of 3D electron density models, in Pro-ceedings of the COST251 Madeira Workshop, 75-89.

RADICELLA, S.M. and R. LEITINGEr (2001): The evolution ofthe DGR approach to model electron density profiles,Adv. Space Res., 27, 35-40.

RADICELLA, S.M. and M.L. ZHANg (1995): The improvedDGR analytical model of electron density height pro-file and total electron content in the ionosphere, Ann.Geofis., XXXVIII (1), 35-41.

RAWER, K. (1963): Propagation of decameter waves (HFband), in Meteorological and Astronomical Influenceson Radio Wave Propagation, edited by B. LANDMARK

(New York Academic Press), 221-250.