Available online at www.sciencedirect.com

Advances in Space Research 46 (2010) 974–983
www.elsevier.com/locate/asr

Comparing topside and bottomside-measured characteristicsof the F2 layer peak
Patrick A. Nsumei a, Bodo W. Reinisch a,*, Xueqin Huang a, Dieter Bilitza baCenter for Atmospheric Research, University of Massachusetts Lowell, 600 Suﬀolk Street, Lowell, MA 01854, USAbSpace Weather Laboratory, George Mason University, Fairfax, VA 22030, USA
Received 22 February 2010; received in revised form 11 June 2010; accepted 14 June 2010

Abstract
The ionospheric characteristics of the F2 layer peak have been measured with ionosondes from the ground or with satellites fromspace. The most common characteristics are the F2-peak density NmF2 and peak height hmF2. In addition to these two parameters thispaper studies the F2-peak scale height. Comparing the median values of hmF2 and NmF2 obtained from topside and bottomside sounding shows good agreement in general. The Chapman scale height values for the F2 layer peak derived from topside proﬁles, Hm,top, aregenerally several times larger than Hm,bot derived from bottomside proﬁles.
Ó 2010 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: F2 layer proﬁles; Vary–Chap proﬁle; Scale height; Digisonde; ISIS-2

1. Introduction
In the study of the electron density distribution in theionosphere in connection with radio communication andpositioning applications, information about the F2 layer
peak characteristics is by far the most important input.
The key characteristics of the F2 layer peak, namely thepeak height hmF2, the peak electron density NmF2, andthe Chapman scale height H, play crucial roles in ionospheric dynamics and are routinely measured along withthe electron density (Ne) proﬁles by the Global IonosphericRadio Observatory (GIRO) using the ground-based Digisonde network (Reinisch et al., 2009). It is important tonote that H used here is the scale height for the general
Chapman function that is deduced for a multi-constituentgas (Rishbeth and Garriott, 1969) (see Section 3) andinvolves a scale height that is continuously varying withheight. This is diﬀerent from the simpliﬁed Chapman func*

Corresponding author.
E-mail addresses: Patrick_Nsumei@uml.edu (P.A. Nsumei), Bodo_
Reinisch@uml.edu (B.W. Reinisch), Xueqin_Huang@uml.edu (X.
Huang), dbilitza@gmu.edu (D. Bilitza).

tion which uses a constant scale height for the whole topside F2 layer that is deduced for a single-constituent (O)gas and constant thermospheric temperature.
A large database of bottomside-measured data is available at http://ulcar.uml.edu/GIRO/ (Galkin et al., 2006).
In this paper, we compare the peak characteristics obtained
from bottomside sounding at a few selected stations withthose obtained from topside sounding measurements(e.g., Kutiev et al., 2006; Kutiev and Marinov, 2007;
Depuev and Pulinets, 2004).
Topside Ne proﬁle data are not as abundant as the bottomside data because only a few satellite missions, forexample Alouette, ISIS-1 and ISIS-2 (Benson and Bilitza,2009), have been dedicated to routine Ne proﬁle measurements. These topside measurements were made in the
1970s, while GIRO proﬁle data are routinely available only
for the last three decades. We therefore had to contend ourselves with comparing monthly median values rather thandoing case-by-case comparisons. This process should be
adequate, however, for revealing the presence of any systematic diﬀerences or biases. Because of the limited signal-to-noise ratio in the topside ionograms near the F2
layer critical frequency foF2 there is concern that the0273-1177/$36.00 Ó 2010 COSPAR. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.asr.2010.06.027

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extracted foF2 values may be too small, and that as aconsequence the calculated proﬁles will not reach down
to the actual F2-peak height. To address this concern
about the topside measurements, we compared the F2-peakcharacteristics measured by topside sounding with thosemeasured at a number of ionosonde stations.
In the second part of this study, we discuss the calculation of the Vary–Chap scale height function H(h) and thescale height value Hm at the F2 layer peak (Ram et al.,2009; Zhang et al., 2006; Reinisch et al., 2007), derived
from bottomside and topside Ne proﬁles. For selected locations, the Hm values derived from ground-based measurements, Hm,bot, are then compared with the corresponding
Hm,top, values determined from topside Ne proﬁles. The
diurnal and latitudinal variations of the ratio Hm,top/Hm,bot
are presented for a number of locations. We show in Section 4 that this ratio can vary from 0.5 to 4 with local
time and latitude.
2. Data and observations
This study uses two datasets: (1) ground-based digisonde measured peak characteristics from Ebro Observatory, Spain (MLAT 43°) with data covering the period of
1988–2001, Boulder, USA (MLAT 48°) for the period of
2004–2008, and Millstone Hill, USA (MLAT 53°) for theperiod 1992–2008 data; and (2) ISIS-2 topside Ne measurements covering the period of 1973–1983. The ISIS-2 latitudinal data coverage is such that there are fewer Ne data at
lower latitudes than at higher latitudes, and for the topside/
bottomside comparison of hmF2 and NmF2 we selected thethree locations mentioned above as a compromise
approach. Our analysis includes all available data forwhich F10.7 < 120 and Kp < 3. The data are ﬁrst grouped
according to season, magnetic latitude (MLAT), and magnetic local time (MLT). Data from two additional ionosonde sites, Ramey (MLAT 28.5°) and Jicamarca(MLAT 1.4°), were used for the Hm comparison (Section
3).
2.1. NmF2 and hmF2 at Roquetes (Ebro), Spain
Fig. 1 shows the median values of hmF2 and NmF2 fordiﬀerent seasons, obtained from bottomside and topsidesounding measurements, together with the IRI model values (Bilitza, 2001, 2004; Bilitza et al, 2006). The topside data
displayed in Fig. 1 cover the magnetic latitude range from40° to 46° and include all longitudes. In general, the topsideand bottomside values are in fair agreement showing no signiﬁcant systematic diﬀerences except for the spring evening
period. Here, the topside hmF2 values exceed the bottomside values by up to 110 km (Fig. 1b), while the topside
NmF2 values are up to a factor of 2 smaller than the bottomside values (Fig. 1f). This pattern could be caused bya larger number of topside ionograms during that periodthat are incorrectly scaled. When the TOPIST autoscaling
determines an foF2 value smaller than the actual value,975

the proﬁle calculation will automatically derive a larger
hmF2 value. The reason that this eﬀect is only seen during
spring may be the relative scarcity of topside proﬁles during
this period resulting in a small data sample. A similar
behavior, although to a smaller degree, is seen in winterbetween 18 and 21 MLT. During afternoon hours in winterthe topside NmF2 is also too low and in this case hmF2 is
not aﬀected. This feature is not understood.
For a quantitative analysis we investigated the ratios
Dhm ¼

hmF 2ðtopsideÞ  hmF 2ðbottomsideÞ
hmF 2ðbottomsideÞ

ð1aÞ

NmF 2ðtopsideÞ  NmF 2ðbottomsideÞ
NmF 2ðbottomsideÞ

ð1bÞ

and
DNm ¼

The bar graphs in Fig. 2 represent the percentage deviations for Dhm and DNm showing that 89% of the topsideand bottomside median hmF2 data deviate by less than
15%, and 75% of the topside and bottomside medianNmF2 data deviate by less than 30%. In general, Fig. 2aand b shows that over 70% of the median values of thepeak characteristics from topside measurements are ingood agreement with the bottomside values.
2.2. NmF2 and hmF2 at Boulder, USA
Fig. 3 shows the median hmF2 and NmF2 values andthe IRI model values for Boulder, CO for diﬀerent seasons.
The topside data used in Fig. 3 cover the MLAT range of
46–50° and include all longitudes. Again, we see that thepeak characteristics measured from the topside follow very
similar trends as those measured from the bottomside andthe IRI model.
The bar graph in Fig. 4a shows that for Boulder over
90% of the topside median hmF2 data fall within deviationsof Dhm = ±15%, and Fig. 4b shows that about 70% of thetopside median NmF2 data fall within deviations of
DNm = ±30%. This implies a fairly good agreement
between the median values of the peak characteristics measured from the topside and bottomside. Detailed inspection
revealed that the agreement is best for regions where suﬃcient topside data are available (not shown here).
2.3. NmF2 and hmF2 at Millstone Hill
Fig. 5 shows the medians of measured bottomside andtopside hmF2 and NmF2 values, and the IRI model predictions over Millstone for diﬀerent seasons. The topside data
used in Fig. 5 cover the MLAT range of 50–56° over all
longitudes.
For Millstone Hill, over 80% of the topside medianhmF2 data fall within deviations of Dhm = ±15%(Fig. 6a), however, less than 50% of the topside medianNmF2 data fall within deviations of DNm = ±30%. Thisshows a fairly good agreement between the topside-measured and bottomside-measured hmF2 values, the NmF2

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Fig. 1. F2 layer peak characteristics at Ebro (MLAT 43°) measured from the topside and bottomside, and the IRI model values during periods of low
F107 index (F107 < 120) and low magnetic activity (Kp < 3). Figure panel (a) hmF2–winter, (b) hmF2–spring, (c) hmF2–summer, (d) hmF2–autumn, (e)NmF2–winter, (f) NmF2–spring, (g) NmF2–summer, and (h) NmF2–autumn.

Fig. 2. Bar chart representations of the deviations in F2-peak characteristics over Ebro, Spain, bar graphs of % of median data vs. Dhm (a), andvs. DNm (b).

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977

Fig. 3. Diurnal variations of F2-peak characteristics at Boulder (MLAT 48°) measured from the topside and bottomside, and IRI model values during
periods of low F107 index (F107 < 120) and low magnetic activity (Kp < 3). Figure panel (a) hmF2/winter, (b) hmF2/spring, (c) hmF2/summer, (d) hmF2/
autumn, (e) NmF2/winter, (f) NmF2/spring, (g) NmF2/summer, and (h) NmF2/autumn.

Fig. 4. Bar chart of deviations in peak characteristics over Boulder, Colorado: bar graphs of % of median data vs. Dhm (a), and vs. DNm (b).

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Fig. 5. Diurnal variations of F2-peak characteristics at Millstone Hill (MLAT 53°) measured from the topside and bottomside, and IRI model peakcharacteristics during periods of low F107 index (F107 < 120) and low geomagnetic activity (Kp < 3). Figure panel (a) hmF2/winter, (b) hmF2/spring, (c)hmF2/summer, (d) hmF2/autumn, (e) NmF2/winter, (f) NmF2/spring, (g) NmF/summer, and (h) NmF2/autumn.

Fig. 6. Bar chart representations of the deviations in peak characteristics over Millstone Hill: bar graph of % of median data vs. Dhm (a), and vs. DNm (b).

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Fig. 7. Left: ISIS-2 Ne proﬁle (black dots), right: calculated scale height H(h)/Hm proﬁle from the N(h) proﬁle shown on the left. The Vary–Chap proﬁle(red line) calculated with H(h) shown on the right is superimposed on the measured proﬁle on the left. (For interpretation of color mentioned in this ﬁgure
the reader is referred to the web version of the article.)

Fig. 8. Seasonal plot of topside Hm vs. MLT for MLAT = 67 ± 3°. Top left (winter), top right (spring), bottom left (summer) and bottom right (autumn).
The red line represents the median values. (For interpretation of color mentioned in this ﬁgure the reader is referred to the web version of the article.)agreement, however, is marginal. The larger ionosphericvariability at high magnetic latitudes (MLAT at Millstone
Hill is 53°) is most likely the reason for the lower agreementof the topside and bottom values at Millstone compared tothe stations at lower latitude, Ebro and Boulder.
3. Vary–Chap representation of Ne proﬁles and calculationof the Vary–Chap scale height function H(h)The general a-Chapman proﬁle given by Rishbeth andGarriott (1969) has a neutral scale height H(h) that varies
with height, and we therefore call it the Vary–Chap function (Reinisch et al. 2007):



1=2
Hm
1
Ne ¼ Nmð2aÞ
exp ð1  y  expðyÞÞ
2
H ðhÞ

with

y¼

Z h

dh
H
ðhÞ
hm

ð2bÞ

Representation of a measured N(h) proﬁle as a Vary–Chapfunction requires knowledge of H(h). Huang and Reinisch(2001) have shown that Eq. (1a) can be solved for H(h) as
function of N(h):

2
N ðhÞ
X ðhÞ½1  ln X ðhÞ
Nm
2
Z h
1
N ðhÞ
dh
X ðhÞ ¼ 1 þH m hm N m

H ðhÞ ¼ H m

ð3aÞ

with

ð3bÞ

Physically reasonable H(h) functions are obtained for any
value Hm that satisﬁes the condition

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Fig. 9. Median Hm,top vs. MLT for (a) MLAT = 0 ± 5°, (b) MLAT = 08 ± 3°, (c) MLAT = 48 ± 3°, (d) MLAT = 53 ± 3°, (e) MLAT = 67 ± 3°, and (f)MLAT = 87 ± 3°.

Fig. 10. Diurnal and seasonal variations of Hm,bot for Millstone Hill (MLAT = 53°). The red line represents the median values. (For interpretation ofcolor mentioned in this ﬁgure the reader is referred to the web version of the article.)

2
Z hs 
N ðhÞ
H m > 0:6
dh
Nm
hm

ð3cÞ

for the topside proﬁle, where hs is the height of the satellite,andZ hm 
Hm P
h0

N ðhÞ
Nm

2
dh

ð3dÞ

for the bottomside proﬁle (Reinisch and Huang, 2004)
where h0 is the bottom height of the F2 layer. Fig. 7

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Fig. 11. Diurnal and seasonal variations of Hm,bot at four locations (a) Jicamarca, (b) Ebro, (c) Boulder, and (d) Millstone.

Fig. 12. Seasonal plot of RHm (ratio of topside to bottomside-measured Hm) vs. MLT for (a) MLAT = 0 ± 5° (topside) and 1.4° (bottomside), (b)MLAT = 08 ± 3° (topside) and 08° (bottomside), (c) MLAT = 43 ± 3° (topside) and 43° (bottomside), (d) MLAT = 48 ± 3° (topside) and 48°(bottomside), (e) MLAT = 53 ± 3° (topside) and 53° (bottomside) and (f) MLAT = 67 ± 3° (topside) and 67° (bottomside).

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illustrates the duality relation of N(h) and H(h). The left
panel shows a measured topside proﬁle (black dots), andthe right panel the derived H(h) function. Of course, byinserting the derived H(h) function into Eq. (3a), the measured N(h) function is reproduced (red curve in left panel).
For our analysis
R we have arbitrarily set Hm,bot and Hm,top
equal to Hm = (Ne/Nm)2dh at the bottomside or topside,
respectively, satisfying Eqs. (3c) and (3d). One would therefore expect Hm,top > Hm,bot since the topside electron content
is generally larger than the bottomside content, and this wasindeed reported by Kutiev et al. (2009).
3.1. Deriving Hm from topside and bottomside proﬁlesFig. 8 shows the diurnal variations of Hm,top for diﬀerent
seasons calculated from ISIS-2 Ne proﬁles using Eq. (3c).
This example is for the latitude range of 67 ± 3° where sufﬁcient data were available for most parts of the day. The
median values of Hm,top, connected by a red line, show little
diurnal variations at this latitude, and only a small seasonalvariations with slightly larger values in spring and summer.
The latitudinal variation, illustrated by the six panels in
Fig. 9, is also small, and seems to be largest in the equatorial region with a minimum at local noon.
For the Hm,bot values more signiﬁcant diurnal and latitudinal variations have previously been reported (e.g., Nambala et al., 2008; Reinisch et al., 2007). Fig. 10 shows forthe mid latitude station Boulder, CO (MLAT = 48°) a clear
maximum for Hm,bot at local noon during spring and summer. A very large noon maximum is observed at Jicamarca,
Peru (MLAT = 1.4°) as shown in panel (a) of Fig. 11.
For spring and summer, a noon maximum is also observedat the other three latitudes shown in Fig. 11, Ebro (43°),
Boulder (48°), and Millstone (53°).
3.2. Comparison of topside and bottomside-measured Hm
The discussion in Section 3.1 revealed diﬀerent diurnal
and latitudinal variations of Hm,top and Hm,bot. To asses
these diﬀerences, we deﬁne the ratio RHm = Hm,top/Hm,bot
as the ratio of topside-measured Hm to bottomside Hm.
Fig. 12a–f shows RHm vs. MLT for diﬀerent seasons andlatitudes. As expected the topside values of Hm are generally larger than the bottomside values, an exception is seen
over the magnetic equator at noon. The RHm values range
from 0.5 to 4; the lowest values of RHm occur around noon.
4. Summary
We have presented data of the F2-peak characteristics
hmF2, NmF2, and Hm measured by ionosondes from above
or below the F2 layer peak. We used ISIS-2 topside proﬁlesfrom the 1970s and bottomside proﬁles measured at ﬁve digisonde stations during more recent times, limiting the analysis to comparing monthly median values. Our study showsthat in regions where suﬃcient topside-measured peak data
were available, the peak heights show good agreement withthose measured at three ground stations, and both are well
represented by the IRI-2001 model. For NmF2, good agreement between topside-measured and bottomside-measured
values is found at two stations, Ebro and Boulder, while signiﬁcant discrepancies seem to exist for Millstone Hill. This
station is at fairly high magnetic latitude (53° MLAT) compared to Ebro and Boulder, and the increased ionosphericvariability is very likely the cause for the discrepancies. Furthermore, the data we compared were not based on simultaneous measurements and some of the diﬀerences could be
due to the longitudinal and/or solar cycle biases of either
one of the two data sets (more likely the satellite data set).
It is also important to remember that the topside data usedin this study covered a certain range of magnetic latitudes
and included all longitudes. Therefore, some of the observed
discrepancies may be the result of the type of binning used. In
summary, we conclude that topside sounding data provide
valid measurements of hmF2 and NmF2.
The Hm values derived from topside and bottomside
sounding are diﬀerent physical quantities representing the
integral of the squared normalized electron density of thetopside and bottomside proﬁle. Since the topside electron
content is usually larger than the bottomside content, Hm,top
is mostly larger than Hm,bot.. Our analysis indicates that
Hm,top Rshows little diurnal and latitudinal variation. Since
Hm = (Ne/Nm)2dh , this result means that the normalized
topside content stays constant with time and latitude. This
is not the case for the normalized bottomside content,
however.
Acknowledgment
This research was supported by NASA Grant
NNX09AJ74G and by the AF Research Laboratory undercontract FA8718-06-C-0072.
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