An improved bottomside for the ionospheric electron density model NeQuick

The ionospheric electron density model NeQuick is a «profiler» which uses the peaks of the E-layer, the F1-layer and the F2-layer as anchor points. In the version prepared for and submitted to the International Telecommunication Union (ITU) the model uses the ITU-R (CCIR) maps for foF2 and M(3000)F2 and adapted maps similar to the ITU-R ones for foE and foF1. Since users found problematic behaviour of NeQuick under conditions of strong differences of foE and foF2 map structures, the profiling was adapted by changing the properties of the Epstein layers used for this purpose. The new formulation avoids both strange horizontal structures of the geographic distribution of electron density in fixed heights and unrealistic peculiarities of the height profile which occasionally occurred with the old version of the model. Since the Epstein layer approach allows for 8 parameters only (3 layer amplitudes and 5 semi-thicknesses) the adaptation was no minor task but needed careful planning of suitable strategies. Mailing address: Dr. Reinhart Leitinger, Institut für Physik, Institutsbereich für Geophysik, Astrophysik und Meteorologie (IGAM), Universität Graz, Universitaetsplatz 5, A8010 Graz, Austria; e-mail: reinhart.leitinger@uni-graz.at F2-layer as anchor points. At any location the anchor points are derived from «maps» for the ionosonde parameters foE, foF1, foF2 and M(3000)F2. The foF2 and M(3000)F2 maps are from ITU-R (CCIR), the foE map is a modified formulation of that due to John Titheridge (see Leitinger et al., 1995, 1996) and foF1 is taken to be 1.4 × foE (Leitinger et al., 1999) during daytime and is set zero during nighttime. The maps are formulated in «modified dip latitude» μ: tan cos I = n { where μ is (Rawer’s) modified dip latitude or «MODIP» (Rawer, 1963); I, the magnetic dip; and φ, the geographic latitude. The peak of the E-layer has a fixed height of 120 km, the F2 peak is constructed from foF2 (symbol fF2), M(3000)F2 (symbol M3) and foE (symbol fE) using Dudeney’s form of the Bradley and Dudeney (1973) formula (see Dudeney, 1983). With M = ( . ) ( . ), M M 0 0196 1 1 2967 1 3 32 32 + n . 0 01 2 . 0 253 t = ( . ) 1 215 E t f / / F2 , f = ∆ 6 @ (if fE= 0 then ∆=−0.012), we get / ( ) h 1490 m= n 6 ) (M km 176 3+ ∆ / A . The height of the F1 anchor point was originally modelled as hmF1= (108.8+ 14× NmF1+ + 0.71× | I | ) km, NmF1 being the F1 peak electron density in electrons per cubic meter and I being the inclination (dip) of the geomagnetic induction vector in degrees. For the bottomside of the F-region, anchor point related profiling is realised by means of a sum of three semi-Epstein layers. With NmF2= = 0.124 fF2 2 , NmF1= 0.124 fF2 2 , NmE= 0.124 fE 2 being the F2, F1 and E-layer peak electron densities, hmF2, hmF1, hmE being the F2, F1 and E-layer peak heights, BF2, BF1, BE the F2, F1 and E-layer thickness parameters, we get for the bottom side


Introduction: the NeQuick formulation
The purpose of this paper is to present the reasons for the revision of the bottomside of the three dimensional and time dependent electron density model NeQuick (Radicella and Leitinger, 2001) and to show some of the improvements gained by the revision.
NeQuick was submitted to ITU-R by the European Space Agency and was accepted by the relevant ITU-R authorities in July 2000.Source code, executable and two driver pro-grams are now available on the ITU-R web page <http://www.itu.int/ITU-R/software/studygroups/rsg3/databanks/ionosph>.
NeQuick-ITUR strictly follows relevant ITU-R recommendations and uses the ITU-R relation between average sunspot number (R 12) and 10.7 cm solar radio flux (F10.7) .
The model is formulated in the FORTRAN 77 language, uses a modular design and contains no COMMON blocks.
NeQuick is a «profiler» model which uses the peaks of the E-layer, the F1-layer and the F2-layer as anchor points.At any location the anchor points are derived from «maps» for the ionosonde parameters foE, foF1, foF2 and M(3000)F2.The foF2 and M(3000)F2 maps are from ITU-R (CCIR), the foE map is a modified formulation of that due to John Titheridge (see Leitinger et al., 1995Leitinger et al., , 1996) ) and foF1 is taken to be 1.4 × foE (Leitinger et al., 1999) during daytime and is set zero during nighttime.
The peak of the E-layer has a fixed height of 120 km, the F2 peak is constructed from foF2 (symbol fF2), M(3000)F2 (symbol M3) and foE (symbol f E) using Dudeney's form of the Bradley and Dudeney (1973) formula (see Dudeney, 1983). With . The height of the F1 anchor point was originally modelled as h mF1= (108.8 + 14 × NmF1+ + 0.71× |I| ) km, NmF1 being the F1 peak electron density in electrons per cubic meter and I being the inclination (dip) of the geomagnetic induction vector in degrees.
For the bottomside of the F-region, anchor point related profiling is realised by means of a sum of three semi-Epstein layers.With NmF2= = 0.124 f F2 2 , NmF1= 0.124 f F2 2 , NmE= 0.124 f E 2 being the F2, F1 and E-layer peak electron densities, h mF2, hmF1, hmE being the F2, F1 and E-layer peak heights, BF2, BF1, BE the F2, F1 and E-layer thickness parameters, we get for the bottom side This modification ensures that at the F2 peak the lower layers are «faded out» effectively.Examples: The thickness parameters take different values for the bottomside and for the topside of the layers (B Ebot and BEtop for the E-layer, BF1bot and B F1top for the F1-layer) where HO= Btop/v; v = (0.041163x−0.183981)x+ +1.424472; x = (Btop−150)/100.The profile for the topside, too, is the upper half of an Epstein layer: g is a height gradient for the scale height H O, [rHO+ g(h−hmF2)] restricts the scale height increase, the factor v was introduced to reduce the vertical electron content to observed values.The topside thickness parameter Btop= kBF2, with two different formulations, k= 6.705 − 0.014R12− 0.008 hmF2 (April to September), k=−7.77+0.097(hmF2/Btop) 2 +0.153NmF2 (October to March).In both cases k is restricted to 2≤k≤8.

Reason for the revision
In «mapping» applications of NeQuick (construction of electron density grids in fixed heights below the F2 peak) it became evident that in some cases strong gradients and strange structures appear in E and F1-layer heights (see fig. 1a).An investigation demonstrated that a large fraction of the gradient problem cases was coupled to the following behaviour of the foE and foF2 maps.We found that in the critical regions and time intervals 1a, isoline displays for 100 km and 150 km).Single parameter adaptations could not solve the problem but a more elaborate revision of the original «Di Giovanni-Radicella» (DGR) modelling approach (Di Giovanni and Radicella, 1990;Radicella and Zhang, 1995) was necessary.

The most important revisions
Following an elaborate parameter adaptation strategy and after many tests we adopted the revisions: 1) Replace the formerly complicated formulation for the height of the F1 peak, h mF1, by using hmF1= (hmF2+ hmE)/2.
2) Set foF1 to zero if foE is smaller than 2 MHz and avoid that foF1 gets too close to foF2.The original formulation was f F1 = 1.4 fE under all daytime conditions.Now fF1= 0.85×1.4fE if 1.4 fE> 0.85 fF2.

Comparison of NeQuick-ITUR with the revised NeQuick
The following collection of maps and profiles demonstrates the improvement of the NeQuick properties.
The comparison of fig.2a (revised NeQuick) with fig.1a (NeQuick before revision) clearly shows that strong gradients and strange structures have disappeared.This is especially true for Elayer heights and for the E-F1 transition region.Figure 1b connects the strong gradients and strange structures to the latitude-longitude distribution of E and F1 thickness parameters BEtop, B F1bot and BF1top and to the amplitude of the E-Epstein layer, A(E). Figure 2b shows that after the revision all these parameters are very well behaved.
The profile comparisons of fig.3a-f (January, high solar activity) and fig.4a-f   ties larger than Nm(E) at the presumed E-layer peak of 120 km (top rows of fig.4c,d).
A (upper mid and) high latitude «contamination» of the F2-layer by the F1-layer leading to secondary maxima somewhere between the F1 and the F2 peaks (figs.5 and 6).In some cases the secondary maxima had electron density values 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 under high solar activity conditions (fig.5) and low solar activity conditions (fig.6).
The revised NeQuick has been released on 25 November, 2002 after automatic checking of about 72 000 and systematic visual inspection of hundreds of model profiles gained in all seasons under high, mid and low solar activity conditions and distributed globally in latitude and longitude and distributed over Universal Time (UT) days.

Fig
Fig. 1a,b.NeQuick, original formulation.a) Isolines of electron density in units of 109 m -3 in a geographic latitude versus longitude system.Heights from 100 km (top left) to 450 km (bottom right) in steps of 50 km.Monthly mean conditions for November 1998, 11 h UT. b) Isolines of model parameters in a geographic latitude versus longitude system.Epstein layer amplitudes and thickness parameters.Monthly mean conditions for November 1998, 11 h UT.From top left to bottom right: F2 amplitude, F1 amplitude, E amplitude, BEbot, BEtop, BF1bot, BF1top, BF2bot.