RADIO SCIENCE, VOL. 45, RS5007, doi:10.1029/2009RS004332, 2010

Ion density calculator (IDC): A new efficient modelof ionospheric ion densities
P. G. Richards,1 D. Bilitza,2,3 and D. Voglozin1
Received 21 November 2009; revised 15 April 2010; accepted 12 May 2010; published 5 October 2010.

[1] We present a new computationally efficient and accurate model of ion concentrationsin the bottomside ionosphere based on the photochemistry. There has long been a needfor efficient and accurate specification of ionospheric molecular ion concentrations.
Incoherent scatter radars need to specify the relative ion concentrations in order toaccurately determine plasma temperatures. Full physical ionospheric models are available
but too costly and cumbersome for many applications. The international reference
ionosphere (IRI) model is an efficient empirical model that accurately specifies theelectron density but the molecular ion concentrations are based on limited data sets.
Our new ion density calculator (IDC) model uses chemical equilibrium to determine allion concentrations except the O+ density, which cannot be derived from chemical
equilibrium above ∼180 km due to the increasing importance of diffusion. The IDC
model overcomes this problem by using an iterative technique to solve for the O+ density
given the electron density that is provided by the radar or the IRI model and the fact thatthe total ion concentration must sum to the electron density. This quasi‐chemical model
produces very good agreement with satellite measured ion densities and significantly
improves electron and ion temperatures from incoherent scatter radars. It also produces
good agreement with the Field Line Interhemispheric Plasma (FLIP) physical ionospheremodel, which solves the continuity, momentum, and thermal equations. Comparisonswith the IRI model point out the shortcomings of the most recent version, IRI‐2007 inrepresenting molecular ion densities.
Citation: Richards, P. G., D. Bilitza, and D. Voglozin (2010), Ion density calculator (IDC): A new efficient model ofionospheric ion densities, Radio Sci., 45, RS5007, doi:10.1029/2009RS004332.

1. Introduction[2] There has long been a need for improved computationally efficient calculations of ionospheric ion composition. For example, incoherent scatter radars measure
the electron density but need the atomic to molecular ion
concentrations to determine plasma temperatures. Aponte
et al. [2007] and references therein summarize the various techniques to obtain ion densities from radar data.
They investigated a technique to combine the precise

1
Department of Physics and Astronomy, George Mason University,
Fairfax, Virginia, USA.
2
Department of Computational and Data Sciences, George
Mason University, Fairfax, Virginia, USA.
3
Heliospheric Physics Laboratory, NASA Goddard Space Flight
Center, Greenbelt, Maryland, USA.

electron density information in the plasma line with very
accurate ion line spectra to measure the F1 region
molecular ion composition. Full physical ionosphericmodels could be used but they are too costly and cumbersome for many applications. The international reference ionosphere (IRI) empirical model is widely used to
specify the molecular ion concentrations but they arebased on limited data sets. In this paper, we present a
new efficient photochemical model to accurately specify
ionospheric ion densities.
[3] The ion density calculator (IDC) model is basedon the chemistry that forms the basis of the Field LineInterhemispheric Plasma (FLIP) ionosphere model[Richards, 2001, 2002, 2004, and references therein]. The
IDC model closely reproduces the ion densities from theFLIP model, which have recently been used to provide
improved ion and electron temperatures from the Poker
Flat Advanced Modular Incoherent Scatter Radar (PFISR)

Copyright 2010 by the American Geophysical Union.
0048‐6604/10/2009RS004332

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that is located at the Poker Flat Research Range near
Fairbanks, Alaska [Richards et al., 2009].
[4] The FLIP model chemical scheme was originallydeveloped from the Atmosphere Explorer mission but
has been updated with more recent laboratory information. The IDC model solves for O+(2P), O+(2D), N+2 , O+2 ,NO+, and N+ using chemical equilibrium. The model also
solves for the NO density because it is important for
converting O+2 into NO+. Solving for the NO density
requires solving for the N(2D) and N2(A) densities,
which are important sources of NO.
[5] It is well known that the O+ ground state [O+(4S)] is
not in chemical equilibrium above approximately 180 km
altitude where diffusion becomes increasingly important.
The key insight of this paper is that, for some important
applications, the electron density is measured or at least
well specified empirically. Given the requirement that the
total ion density must sum to the electron density and that
all of the ions except O+ can be calculated from chemical
equilibrium, we can iteratively solve the equation [e] −[O+] − [NO+] − [O+2 ] − [N+] − [N+2 ] = 0 for the O+
density. In practice, it is difficult to find a solution for O+
when it becomes a minor ion below approximately
150 km because even small errors in measured ion densities or model inputs can lead to significant difficulties infinding a solution for O+. Under some circumstances, thecalculated total molecular ion density can even be larger
than the specified electron density. To avoid this problem,
chemical equilibrium is used for all ions, including O+,
whenever the total calculated molecular ion density isgreater than 85% of the specified electron density. Thisis a reasonable procedure because, under these conditions, O+ is a minor source of NO+ and O+2 and diffusion is not very important. When all ions come fromchemical equilibrium the calculated ion densities arenormalized to the specified electron density to ensuresmooth density profiles.
[6] In standard operating mode, the IDC model uses
the thermospheric O, O2, and N2 densities and neutral
temperature provided by the Mass Spectrometer andIncoherent Scatter radar Extended (NRLMSISE‐00)
model [Picone et al., 2002] together with a user‐supplied
electron density. However, for most of the validation
studies in this paper the IDC model uses the measured
O and N2 densities from the Atmosphere Explore‐C(AE‐C) satellite. For these comparisons, no calculations
are performed if the measured O and N2 densities areunavailable. The NRLMSISE‐00 model always provides
the O2 density because O2 was not measured on AE‐C.
The electron, ion, and neutral temperatures are needed for
calculating the many temperature dependent reaction
rates. The AE‐C satellite measured electron and ion
temperatures but models are used to supply missing
values. The model ion densities are not particularly
sensitive to moderate errors in temperature because most

RS5007of the reaction rates are weak functions of temperature.
The NRLMSISE‐00 model also provides the N(4S)
density, which is important for calculating the NO
density. However, the N(4S) density is halved to agree
better with the FLIP model calculated density and also
produce better agreement between the measured andmodeled NO density.
[7] The photoionization rates are calculated using thesolar irradiances from the EUVAC model [Richards et al.,1994]. The simple photoelectron flux model published by
Richards and Torr [1983] provides the secondary ion
production rates.
[8] The international reference ionosphere (IRI) model
is a widely used empirical model of ionospheric parameters including electron density, electron temperature,
ion composition, ion temperature and ion drift. It is theinternationally recognized standard for the specificationof ionospheric parameters and it was recently adopted by
the International Standardization Organization (ISO) as
Technical Specification TS 16547. IRI development hasrelied on data from all the different techniques used tomeasure ionospheric parameters from the ground and fromspace. Improvement efforts have primarily focused onelectron density and temperature, because these are theparameters most often needed and requested by IRI users.
There are, however, a number of applications that require
accurate specification of ion densities. Examples arecomputations of plasma conductivity requiring electron‐
ion and neutral‐ion collision frequencies [Takeda andAraki, 1985] and theoretical coupling studies that relyon an empirical input for their ionospheric ion composition or use IRI ion composition for starting and boundary
conditions [e.g., Deng and Ridley, 2007]. IRI is also
playing an important role as baseline against which thepredictive skills of physics‐based models are compared[Siscoe et al., 2004] and as resource for educational
purposes, e.g., visualization tools [Watari et al., 2003].
[9] Ion composition modeling for IRI is limited by the
relatively small amount of reliable composition data.
Satellite in situ measurements by Retarding Potential
Analyzer (RPA) or by Ion Mass Spectrometer (IMS)
often do not measure all constituents of the ion gas andtherefore the total ion density and ion composition cannot
be determined. Calibration problems are another cause
for excluding data sets from IRI modeling. Measurements from the ground by incoherent scatter radar arecomplicated by the fact that ion composition and plasma
temperatures are determined simultaneously and therefore are not independent from each other. In fact one ofthe primary reasons for the development of the IDC
model is the improvement of incoherent scatter data
analysis with the help of a more realistic representation of
the ion composition in the bottomside ionosphere.
[10] Currently, IRI provides two options for the ioncomposition (O+, O+2 , NO+) in the bottomside ionosphere.

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An older model based on the work of Danilov andSemenov [1978] with ion mass spectrometer measurements from 43 rocket flights and a newer model (now thestandard/default) by Danilov and Smirnova [1995] that
expands on the earlier study by adding additional rocket
flights and for the region above 200 km data from the
AE‐C, S3‐1, AEROS‐B, Sputnik‐3 and Cosmos‐274
satellites. Both models describe dependencies on solar
zenith angle, season, and solar activity. For our study weuse the latest version of the model, IRI‐2007, with thestandard ion composition and the magnetic storm model
turned on. The storm model simulates the reduction in
ionospheric electron density that occurs during magnetic
storms. The model is available at the IRI homepage(http://IRI.gsfc.nasa.gov) and at the Community Coordinated Modeling Center (http://ccmc.gsfc.nasa.gov).

2. Atmosphere Explorer Satellite Data
[11] The purpose of the Atmosphere Explorer (AE)mission was to investigate the thermosphere, withemphasis on the energy transfer and processes that govern
its state. The study of photochemical processes accompanying the absorption of solar EUV radiation in theearth’s atmosphere was accomplished by making closely
coordinated measurements of most reacting constituentsand the solar input. This data set is ideally suited to ourstudy, not only because it contains most of the required
measurements, but also because of its extensive verification and accessibility. The data from each instrument wassummarized every 15‐seconds for inclusion in a unified
abstract (UA) database. A detailed description of the data
including calibration techniques is available from the
National Space Science Data Center (NSSDC) web site
ftp://nssdcftp.gsfc.nasa.gov/spacecraft_data/ae/aedoc/.
[12] Numerous studies of the ion and neutral chemistryof the upper atmosphere have benefited from the use of
AE database. The AE program was a major source ofdata for the NRLMSISE‐00 model and has also supported the development of the IRI model. In addition, thethermosphere and ionosphere chemical scheme in generaluse today owes much to the use of the AE data to verify
the applicability of laboratory measured reaction rates tothe space environment.
[13] The AE missions consisted of 3 spacecraft carrying similar instrumentation. This study uses data from the
AE‐C satellite that was launched 16 December 1973 into
an elliptical orbit, which was altered many times in thefirst year of life by means of an onboard propulsion
system employing a 3.5‐lb thruster. The purpose of thesechanges was to alter the perigee height down to 129 km.
After this period, the orbit was circularized and wasraised periodically to about 390 km when it would decay
to 250 km altitude. During the first year, the latitude ofperigee moved from about 10 degrees up to 68 degrees

RS5007north and then down to about 60 degrees south. The
payload on all 3 satellites included instrumentation forthe measurement of solar EUV; the composition of ionsand neutral particles; the density and temperature ofneutral particles, positive ions, and electrons; airglow
emissions; photoelectron energy spectra; and proton andelectron fluxes up to 25 keV.
[14] This study uses neutral densities from the Open
Source Neutral Mass spectrometer (OSS) [Nier et al.,1973], the ion temperature and total ion density fromthe retarding potential analyzer (RPA) [Hanson et al.,1973], and the electron temperature from the cylindricalelectron probe (CEP) [Brace et al., 1973]. The IDC
model ion densities are compared to ion densities fromthe Bennett ion mass spectrometer (BIMS) [Brinton et al.,1973] and the Magnetic Ion Mass Spectrometer (MIMS)[Hoffman et al., 1973]. Comparisons are also made to the
NO densities from the ultraviolet nitric oxide experiment(UVNO) [Barth et al., 1973] because NO is important for
converting O+2 to NO+ below ∼150 km.

3. Results[15] Most of the IDC model validation studies in thispaper compare the model ion densities with ion densities
measured by the AE‐C satellite for magnetically quiet
and disturbed periods in 1974. However, we first showthat the simple IDC model accurately reproduces theFLIP model ion densities both in the daytime andnighttime. These IDC‐FLIP model comparisons aredone for solar maximum conditions to complement the
IDC‐AE‐C comparisons, which are all at solar minimum. We present comparisons for specific AE‐C orbits
followed by statistical comparisons for the January to
November 1974 period when the satellite was in a highly
elliptical orbit.
3.1. The 16–17 March 1990 Solar Maximum
IDC‐FLIP Model Comparisons[16] Figure 1 (top) shows a comparison between the
IDC model (lines) and FLIP model (solid symbols) for
solar maximum conditions at noon 17 March 1990. For
this calculation, the IDC model takes the FLIP model
electron density as input and calculates the ion and NO
densities. The overall agreement between the IDC andFLIP model densities is remarkably good and the FLIP
model electron density agrees well with the Millstone
Hill incoherent scatter radar (open circles). The NO+
density is slightly underestimated at the highest altitudes
due to the neglect of vibrationally excited N2, which
speeds up the O+ + N2 → NO+ + N reaction rate. The
discrepancy would be slightly greater except that the
IDC model uses the reaction rate of Hierl et al. [1997].
This reaction rate is not generally applicable in the

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RS5007[17] Figure 1 (bottom) shows a comparison between
the IDC model (lines) and the FLIP model (solid
symbols) for solar maximum conditions at midnight
16 March 1990. For this calculation, the IDC model takes
the FLIP model electron density as input and calculates
the ion and NO densities. The overall agreement between
the IDC and FLIP model densities is remarkably good for
O+, O+2 , and NO+. The IDC model underestimates the N+
density above 350 km at night due to the neglect ofdiffusion. The FLIP model underestimates the electron
density from the Millstone Hill incoherent scatter radar(open circles) by almost a factor of 2. The nighttime
ionosphere is difficult for any ionosphere model to model
accurately because small errors in input parameters(winds, neutral densities, plasmaspheric fluxes) can
produce large deviations in electron density as the ionosphere decays. This is not a problem in the daytime
ionosphere because it is a driven system that is close to
local equilibrium.

Figure 1. Comparison of ion and electron densities
from IDC model (lines) with those from the FLIP model(solid symbols) for (top) noon 17 March 1990 and (bottom) midnight 16 March 1990. The open circles are from
the Millstone Hill incoherent scatter radar. The IDC
model uses the FLIP model electron densities and the
NRLMSISE‐00 neutral densities.

ionosphere because the rate is affected by vibrational
excitation in the laboratory above 1000 K. Although N2
is vibrationally excited in the thermosphere it is notnecessarily the same as in the laboratory. The FLIP
model solves diffusion equations for the N2 vibrational
distribution in the thermosphere but this is too cumbersome and time consuming for the IDC model. Using
the reaction rate of Hierl et al. [1997] is a reasonable
compromise.

3.2. The 12 September 1974 Daytime Low Kp AE‐C
Comparisons[18] The September 1974 period has previously beenstudied using the FLIP model [Richards, 2002, 2004].
September 1974 was also a period of low to moderate
solar activity with the daily F10.7 index ranging from 78
on 1 September and steadily rising to a peak of 106 on
13 September and then steadily declining. The 3‐monthaverage F10.7 index (F10.7A) was 91. Magnetic activity
was low until a major storm occurred on 15 September.
[19] The detailed model‐data single‐orbit comparisonspresented in this paper are for the MIMS measured ion
densities, but statistical comparisons with BIMS ion
densities are also shown. The RPA instrument provides athird measurement of the total ion density but does notprovide individual ion densities. The three methods givedifferent total ion density values but they generally agree
within the stated instrumental errors.
[20] Figures 2a and 2b show the ion density model‐
data comparisons for the down leg portion of orbit 3156
on 12 September 1974 when the satellite was descending
from the South Polar Region to perigee over northern
Australia. The day 12 September 1974 was a magnetically quiet day following an extended period of low
magnetic activity.
[21] Figure 2a shows the case when the IDC model(lines) uses the measured total ion density from the
MIMS instrument (symbols) for the electron density as
well as the OSS measured O and N2 density. Note thatthe model always uses the NRLMSISE‐00 O2 density
because the satellite did not measure the O2 density. The
IDC model used the CEP measured electron temperatureand the RPA measured ion temperature, which was also
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Figure 2. Comparison of ion and electron densities for the down leg and up leg portions of AE‐C
Orbit 3156 on 12 September 1974. (a) The IDC model (lines) and AE‐C MIMS data (symbols)for the down leg with the IDC model using the MIMS measured electron densities and the OSS
measured neutral densities. (b) The IDC and IRI model densities for the down leg with IDC using
the IRI electron densities and the NRLMSISE‐00 model neutral densities. (c and d) The same
comparisons as Figures 2a and 2b for the up leg. The large diamond shows the NmF2 measured
by the Canberra ionosonde.
viously, the electron, ion, and neutral temperatures areneeded for calculating the many temperature dependent
reaction rates. There is excellent agreement between the
MIMS total ion density and the peak electron densityfrom the Canberra (35S, 149E) ionosonde (large diamond)for this orbit. The agreement between the measurements(symbols) and the IDC model (lines) in Figure 2a is very
good for O+ and N+ at all altitudes and very good formolecular ions below 250 km. Above 250 km, the IDC
model increasingly underestimates the MIMS molecularion densities. However, the model agrees well with the
BIMS ion densities (not shown) above 250 km on thisorbit. Because there were no UVNO measurements onorbit 3156, the NO density is from orbit 3168 on thesame day, which had similar altitude, latitude, and local

time but was shifted 30 degrees in longitude to the east.
The ion density calculations were not done for orbit 3168
because there were no measured O or N2 densities. Thereis good agreement between the measured and modeled
NO density.
[22] If the measured electron and neutral densities
were not available, the IRI‐2007 and NRLMSISE‐00
densities could be used to estimate the ion composition on
12 September 1974. Figure 2b shows the ion density
comparisons between the IDC model (lines) and theIRI‐2007 model (symbols) when the IRI‐2007 electron
density and the NRLMSISE‐00 model neutral densities
are used for the IDC model calculations. The IRI‐2007
model also supplies the electron, ion, and neutral temperatures. This would be the default model calculation in

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become more important. Note that below approximately
180 km, all model densities including O+ are generally
obtained from chemical equilibrium because the total
molecular ion density exceeds 85% of the electron density.
[24] Figures 2c and 2d show similar ion density comparisons to Figures 2a and 2b but for the up leg portion oforbit 3156 on 12 September 1974 when the satellite wasascending from perigee over northern Australia acrossthe equator into the Northern Hemisphere. The agreement between the IDC model and the AE‐C data is
excellent for all ions including N+2 and N+. However, theIRI model problems indicated in Figure 2b are also evident in Figure 2d.

Figure 3a. Comparison of ion and electron densities
from the IDC model (lines) and AE‐C Orbit 3209
down‐leg (symbols) 15 September 1974. The large diamond shows the NmF2 measured by the Hobart ionosonde during the satellite over‐flight. The IDC model
uses the MIMS measured electron densities and the
OSS measured neutral densities.

the absence of measured electron densities. The IRI‐2007
model was evaluated at the same points along the orbit as
the measurements. The IRI‐2007 model electron density
is a little lower than the measured total ion density but
it is still a good representation. The IRI‐2007 model
underestimates the measured molecular ion densities below
200 km and overestimates them above 200 km. However,
the main problem with the IRI‐2007 model NO+ and O+2
densities is the shape of altitude profiles. The MIMS
profiles are Chapman like with a single peak below
150 km while the IRI‐2007 profiles have a peak above
200 km. Similar problems with the IRI nighttime molecular ion densities have been reported by Vlasov et al.
[2005] and Nicolls et al. [2006] who combined radarelectron density measurements and airglow emissions
and found that the IRI model overestimates the nighttime
O+2 density above ∼230 km.
[23] Above ∼200 km, the NO+ and O+2 IDC model
profiles approximately follow the scale heights of N2 andO2 respectively. This can be readily understood from thechemistry. Taking O+ as the dominant O+2 source above
200 km, O+2 production ≈ k1[O+][O2] and loss = k2[O+2 ][e],where k1 and k2 are reaction rate coefficients. Given that[e] ≈ [O+] above ∼200 km, then [O+2 ] ≈ (k1/k2)[O2]. A
similar analysis applies to NO+ but it is more complicatedbecause there are other sources. Below 200 km, the scaleheights change because other sources of O+2 and NO+

3.3. The 15 September 1974 Daytime High Kp AE‐C
Comparisons[25] Figures 3a, 3b, and 3c show ion density comparisons for the down leg portion of AE‐C orbit 3209 on
15 September 1974. This was a magnetically disturbed
day following an extended period of low magnetic
activity. The measured peak electron density decreased bya factor of 2 from 12 September to 15 September.
[26] Figure 3a shows the comparison between themeasured and modeled ion densities when the IDC model
uses the measured total ion densities from the MIMS
instrument for the electron density as well as the measured O and N2 densities and electron and ion temperatures. Even under these disturbed conditions, theFigure 3b. Comparison of ion and electron densities
from the IDC model (lines) and AE‐C Orbit 3209
down‐leg (symbols) 15 September 1974. The IDC model
uses the IRI electron densities and the NRLMSISE‐00
model neutral densities.

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Figure 3c. Comparison of ion and electron densities
from the IRI‐2007 model (lines) and AE‐C Orbit 3209
down‐leg (symbols) 15 September 1974.

agreement between the measurements (symbols) and the
IDC model (lines) is excellent for all ions except for
O+2 above 200 km. The O+2 problem most likely indicatesa problem with the NRLMSISE‐00 model O2 density
under these disturbed conditions. Indeed, the
NRLMSISE‐00 model O and N2 densities are considerably lower than the OSS measurements on this day[Richards, 2002]. The NO+ density is particularly wellmodeled at all altitudes and there is excellent agreement
between the satellite total ion density and the peak electron density from the Hobart (43S, 147E) ionosonde(large diamond).
[27] There is also generally good agreement between
the measured and modeled NO density, which has
greatly increased compared to 12 September. The irregular NO behavior below ∼180 km is caused by irregularities in the measured ion temperatures, which wereused for the neutral temperatures. The NO density isvery sensitive to neutral temperature through the reaction
O2 + N → NO + O.
[28] The main limitations on the accuracy of the IDC
model ion densities during ionospheric storms are theaccuracies of the IRI‐2007 electron density and the
NRLMSISE‐00 model neutral densities. This is illustrated in Figure 3b, which shows the ion density comparisons between the IDC model (lines) and the AE‐C
MIMS (symbols) for 15 September 1974 when the IRI‐
2007 electron density and the NRLMSISE‐00 model
neutral densities are used for the IDC model calculations. The IRI‐2007 storm model gives a factor of 1.5
reduction in peak electron density from the magnetically

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quiet 12 September. The measurements show a factor of
2 reduction in peak electron density. The IDC model
reproduces the NO+, O+2 and N+2 measured densities
reasonably well below 200 km but greatly over estimates
the O+ densities between 170 and 260 km. The NO
densities are also not as well modeled primarily because
the NRLMSISE‐00 model neutral temperature is lower
than the measured ion temperature.
[29] Despite the IDC model problems under disturbed
conditions illustrated in Figure 3b, it is still far superior to
the IRI‐2007 model ion densities. Figure 3c shows thecomparison between the AE‐C measured (symbols) andIRI‐2007 model (lines) ion densities for 15 September.
There is poor agreement between the IRI‐2007 modeland the data for all ions on this magnetically disturbed
day. Comparing Figure 3c with Figure 3b shows that the
IDC model gives superior results although the O+ density
is not satisfactory in either case because the NRLMSISE‐
00 model underestimates the molecular neutral densities.
N+2 and NO densities are not shown in Figure 3c because
they are not available from the IRI‐2007 model.
[30] Figure 4 shows the comparison of the IDC modeland satellite data for the upleg portion of orbit 3209 when
the satellite was ascending over the equator to theNorthern Hemisphere from perigee over northern Australia. The IDC model uses the measured total ion densityfrom the MIMS instrument for the electron density as
well as the measured neutral density and electron and ion
temperatures. The upleg portion of the orbit shows little
evidence of magnetic disturbance, which is as expected

Figure 4. Comparison of ion and electron densities
from IDC (lines) and AE‐C Orbit up‐leg 3209 (symbols)for 15 September 1974. The IDC model uses the MIMS
measured electron densities and the OSS measured
neutral densities.

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Figure 5. Medians of the ratios of the measured to modeled densities for all data from January to
November 1974. (a) The case for the MIMS measured ion densities. (b) The case for the BIMS
measured ion densities. The lines with solid circles show the ratio of the MIMS (BIMS) to RPA
total densities. (c and d) The cases when the MIMS and BIMS measured ion densities are normalized to the RPA total ion density. The IDC calculations use the OSS measured O and N2 densities.

for the equatorial region. Once again, the agreement
between the ion measurements (symbols) and the IDC
model (lines) is excellent. The NO density is overestimated in the model.
3.4. All 1974 Daytime Statistical AE‐C Comparisons[31] Figure 5 shows the ratios of the measured to themodeled densities for all daytime orbits from January
through November 1974 when the orbit was highly
elliptical. The orbit became nearly circular during
December. Ratios outside the range 0.01 to 100 were
eliminated from the analysis as most likely indicating aproblem with either the measured ion density or themeasured neutral densities and temperatures that are used
as model inputs. Both medians and averages were calculated but only medians are plotted to minimize theeffect of outliers. The IDC calculations use the OSS
measured O and N2 densities and the NRLMSISE‐00 O2
densities. The Brace and Theis [1978] empirical model
provides Te whenever the CEP measurements are notavailable. This model is based on the CEP Te measurements from AE‐C and provides an accurate representation of the data. The NRLMSISE‐00 model is used forthe ion temperature whenever the RPA data are notavailable. This data selection produces approximately
60,000 data points for the ratio analysis. The data weredivided into 10 km altitude bins for the analysis and bins
with fewer than 100 data points were excluded from theplots.
[32] Figure 5a shows the altitude variation of thedensity ratios when the IDC model uses the measured
total ion density from the MIMS instrument for theelectron density. Figure 5b shows the same thing whenthe BIMS ion density is used for the electron density. Thelines with solid circles in Figures 5a and 5b also show theratio medians of the MIMS and BIMS to the RPA total
ion densities. The MIMS ion densities are generally
about 10% larger than the RPA ion densities while the
BIMS ion densities are generally about 20% smaller thanthe RPA ion densities. Figures 5a and 5b show model‐

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Figure 6. Ratio of measured to modeled MIMS NO+
densities. The crosses show the medians and the diamonds with error bars show the averages and standard
deviations. The numbers adjacent to the error bars show
the number of points at each altitude.

data agreement to be typically within 25% between 150
and 300 km except for the BIMS NO+ density. The O+
density ratio increases below ∼200 km where it becomesa minor ion and the model is most likely to use chemical
equilibrium for all species.
[33] The RPA instrument provides a third measurementof the total ion density, which can be used for the electron density in the IDC model. Since the RPA does notprovide individual ion densities, we obtained individual
ion densities by normalizing the MIMS and BIMS ion
densities using the RPA total ion density. The implicit
assumption is that the MIMS and BIMS relative ion
concentrations are correct but that the overall magnitude
needs to be adjusted. This normalization has a double
effect on the measured to modeled molecular ion density
ratios. For example, the normalization increases the
BIMS ratios by increasing the measured ion densities. It
also decreases the IDC model molecular ion densities by
increasing the electron recombination rate. The opposite
is true for the MIMS molecular ion densities. Figures 5c
and 5d show the same results as Figures 5a and 5b exceptthat the IDC model used for the RPA electron density
and the MIMS and BIMS densities have been normalized
to the RPA density.
[34] It is not clear which of the three ion measurements
is the most accurate. However, it may be significant that
the RPA normalization brings the MIMS and BIMS ion
density ratios into better agreement.
[35] The statistical results in Figure 5 show that the
IDC model produces a satisfactory representation of the

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data below approximately 250 km given the uncertainties
in the data. The high altitude problems do not affect theusefulness of the model for applications to empiricalmodels or radar analysis because the molecular ions areminor constituents at these altitudes. The results in
Figures 5a and 5b were obtained without restriction onmagnetic activity. We repeated the analysis for several
different levels of Ap and there was little effect on the
results.
[36] It is not clear why all the MIMS molecular ion
ratios increase so much above 250 km while the BIMS
NO+ and N+2 ratios do not. The increase of the ratios withaltitude could be due to the fact that low densities may be
below the measurement threshold. This would skew theratio distributions to higher values. In fact, the scatter inthe ratios increases substantially with altitude. This canbe seen in Figure 6, which shows the basic statistics forthe ratio of measured to modeled MIMS NO+ densities.
The crosses show the medians while the diamonds witherror bars show the averages and standard deviations. The
numbers adjacent to the error bars show the number ofpoints for each altitude. To avoid cluttering the figures,
20 km altitude bins have been used in Figure 6 rather
than 10 km bins. This coarser resolution reduces thestandard deviations slightly but does not significantly
change the medians and averages. Figure 6 shows that
below approximately 300 km, the medians and averages
are very close and the standard deviations are relatively
small.
3.5. The 29 January 1971 Daytime Rocket Densities[37] There are few ion density measurements below
130 km at mid latitudes because these require rocket
flights. Figure 7 shows a comparison of ion densities
from IDC and FLIP models (lines without symbols) withthose from a rocket flight at Keweenaw, Michigan on
29 January 1971 [Aikin et al., 1977]. The rocket data aredisplayed with lines and symbols. The local time was
14.17 and the solar zenith angle was 67 degrees. The
IDC model (Figure 7, top) used the measured total ion
density as the electron density and the NRLMSISE‐00
model neutral densities. There is good agreement for theatomic ions but only fair agreement for the molecularions. The instrument was unable to distinguish between
N+2 and Si+ ions so the bulge around 105 km may comefrom an Si+ layer. However, the rocket did measurenumerous metallic ions and none of these shows a bulge
near 105 km. On the other hand, the good N+2 agreement
above 115 km is evidence that there could be an
Si+ layer.
[38] The FLIP model (Figure 7, bottom) produces
better agreement with the measured NO+ and O+2 densities. The better agreement with the data comes from thelarger NO densities due to the inclusion of diffusion in

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RS5007at these altitudes, it could have been produced earlier atthis location or even transported from higher latitudes.

4. Conclusions

Figure 7. Comparison of IDC and FLIP model ion andelectron densities with densities from a rocket flight at
Keweenaw, Michigan on 29 January 1971 at 14.167
LT. The symbols show the data while the lines without
symbols show the model values. (top) The IDC model
used the rocket measured electron density and the
NRLMSISE‐00 model neutral densities. (bottom) The
standard FLIP model calculation.

the FLIP model. Indeed, there is very good agreement
above 105 km when the IDC model uses the FLIP model
NO density, which is a factor of 2 larger than the IDC
model density on this day. The FLIP model NO density islarger because the two previous days had very high levelsof magnetic activity. The magnetic activity enhances the
production of NO above 130 km and then it diffuses
downward where the NO lifetime is of the order of a day.
The rapid fall off of the O+2 density below 105 km may
indicate that the actual NO density is even larger than the
FLIP model NO density in this region. Keweenaw is at ahigh enough latitude (L = 3.9) to be affected by aurorally
produced NO. There is no evidence of auroral activity at
the time of the rocket flight but, as NO has a long lifetime[39] This work has demonstrated an accurate andefficient model for specifying ionospheric ion densities
that is based on the photochemistry. The model accurately reproduces the ion densities from the comprehensive FLIP physical model that solves the full continuity
and momentum equations. It also produces satisfactory
agreement with satellite data.
[40] The accuracy of the IDC ion densities will becompromised if there is rapid convection or soft auroral
particle precipitation. Moderate convection of plasma to
the radar site would not affect the utility of the IDC
model because the basic chemistry is unchanged. On theother hand, rapid convection is a major problem for any
model because it increases the ion temperature andchanges reaction rates. Auroral precipitation is not as
problematic as rapid convection for the IDC model
because the additional production is implicit in themeasured electron density. We tested the IDC model by
inputting the electron density from a FLIP model run that
had auroral precipitation. The IDC model does not haveauroral precipitation. There was good agreement between
the FLIP and IDC models for the atomic to total
molecular ion density ratio, which is the main need forthe radar analysis. However, the O+2 was relatively moreabundant than NO+ in the FLIP model calculation.
[41] This model will be useful for obtaining moreaccurate electron and ion temperatures from incoherent
scatter radars. It could be incorporated directly into theinternational reference ionosphere model or could be
used to build a better analytical specification of the ion
densities.

[42] Acknowledgments. This research was supported by NASA
grants NNX07AN03G and NNX08AF43G to George Mason University.

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D. Bilitza, Department of Computational and Data Sciences,
George Mason University, Fairfax, VA 22030, USA.
P. G. Richards and D. Voglozin, Department of Physics andAstronomy, George Mason University, Fairfax, VA 22030,
USA. (prichar1@gmu.edu)

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