A study of the ionogram derived effective scale height around the ionospheric hmF 2

The diurnal, seasonal, and solar activity variations of the ionogram derived scale height around the ionospheric F-layer peak ( Hm) are statistically analyzed at Wuhan (114.4 E, 30.6 N) and the yearly variations of Hm are also investigated for Wuhan and 12 other stations where Hm data are available. Hm, as a measure of the slope of the topside electron number density profiles, is calculated from the bottomside electron density profiles derived from vertical sounding ionograms using the UMLCAR SAO-Explorer. Results indicate that the value of median Hm increases with increasing solar flux. Hm is highest in summer and lowest in winter during the daytime, while it exhibits a much smaller seasonal variation at night. A common feature presented at these 13 stations is that Hm undergoes a yearly annual variation with a maximum in summer during the daytime. The annual variation becomes much weaker or disappears from late night to pre-sunrise. In addition, a moderate positive correlation is found between Hm with hmF2 and a strong correlation between the bottomside thickness parameter B0 andHm. The latter provides a new and convenient way for empirical modeling the topside ionospheric shape only from the established B0 parameter set.


Introduction
Knowledge of the spatial distribution of the electron density in the ionosphere, especially the ionospheric profile N e (h), is important for scientific interest, such as ionospheric empirical modelings and ionospheric studies, and for practical applications for time delay correction of the radio wave propagation through the ionosphere, etc.During the past decades, great efforts have been made in the Correspondence to: L. Liu (liul@mail.iggcas.ac.cn) global ionospheric empirical modeling (Bilitza, 2001).Many mathematical functions, such as the Chapman, exponential, parabolic, Epstein functions, have been proposed to describe the ionospheric profiles (e.g.Booker, 1977;Rawer et al., 1985;Rawer, 1988;Di Giovanni and Radicella, 1990;Stankov et al., 2003).Among these functions, the Chapman function is simple and has great potential for analytical modeling of the ionospheric profile (e.g.Huang and Reinisch, 2001).A nice feature of the Chapman profiler is that it only needs information about the electron density and height of the F peak and scale height to give a good representation for the observed topside N e (h).Studies have identified that the Chapman function, even with a constant scale height, fits the topside ionospheric profile well several hundred kilometers above the F2-peak (Reinisch and Huang, 2004;Belehaki et al., 2003).This is enough for most situations because most electrons in the ionosphere are distributed in this region.When the scale height is linearly varied with height, the fit will be greatly improved in the higher region (Lei et al., 2005).
It is evident that the scale height is a key and inherent parameter for ionospheric profiles, especially for the topside profiler (Stankov et al., 2003;Belehaki et al., 2006).However, there are still limited studies on the behavior of the plasma scale height.Recently, Huang and Reinisch (2001) introduced a new technique to extrapolate the topside ionosphere based on information from ground-based ionogram measurements.They approximated the N e (h) both around and above the F2-layer peak (hmF2) by an α-Chapman function with a scale height (H m) determined at hmF2.The parameter H m derived from ionograms is a measure of the electron density profile slope of the topside ionosphere.The H m data is routinely archived at some stations after being derived from the Digisonde ionograms with the UMLCAR SAO-Explorer (http://ulcar.uml.edu/).
In this paper, we conduct a statistical analysis on the variations of the ionogram derived scale height (H m) around the F2-peak during 1999-2004 from routine Published by Copernicus GmbH on behalf of the European Geosciences Union.

Data
The present analysis uses a database of H m observed at Wuhan, College, Narssarssuaq, Chilton, Millstone Hill, Tortosa, Athens, Wallops Is., Ascension Is., Madimbo, Louisvale, Grahamstown and Port Stanley.To investigate the annual variation, H m data at the latter 12 stations were downloaded from the SPIDR web (http://spidr.ngdc.noaa.gov/spidr/).
More than 219 000 ionograms were routinely recorded at Wuhan (China) with a DGS-256 Digisonde during 1999-2004.A huge effort has been made to manually scale those ionograms, and the bottomside profiles are calculated from these hand-scaling ionograms with a standard "true height" inversion program (Reinisch and Huang, 1983;Huang and Reinisch, 1996) inherent in the UMLCAR SAO-Explorer.The critical frequency (foF2) and its height (hmF2) of the Flayer, the IRI bottomside profile thickness parameter B0, etc., are obtained.At the same time, the scale height around the F2-peak (H m) is also derived.The calculation of H m from the bottomside profile can be found in the work of Huang and Reinisch (2001) and Reinisch and Huang (2004).B0 is a bottomside thickness parameter that gives the height difference between hmF2 and the height where the electron density profile has dropped down to 0.24*NmF2.

Daily variation and geomagnetic dependence of Wuhan H m
There are appreciable diurnal and day-to-day variations in the ionogram derived scale height around the F2-peak, H m, derived from Digisonde measurements.Figure 1  H m for those three quiet days (27-29 October 2004) in general follows the average behavior.In contrast, for three geomagnetically disturbed days (29-31 October 2003), the variability of H m is enhanced and it significantly deviated from the median behavior.This indicates the redistribution of the ionospheric ionization during geomagnetic disturbances due to the storm impact.Thus, for constructing a complete ionospheric image during storms, H m may present complementary characteristics of the ionosphere.
The effects of geomagnetic storms on the ionosphere are well-known to be complicated and stochastic.The geomagnetic dependence of H m at Wuhan has been statistically investigated with the planetary geomagnetic indices, 3-hour K p and A p , and the daily K p and A p .Although H m may greatly deviate from the average pattern under individual disturbed situations, the correlations of H m with these indices are poor, as depicted in Fig. 2. It implies a complicated dependence of H m on geomagnetic activity.Furthermore, it also suggests insignificant differences in the averaged values of H m at specified times for those 6 years if we separate the data into two groups, low (A p <15) and moderate to high (A p >15) magnetic activity levels.

Seasonal and solar activity variations of Wuhan H m
Several atmospheric and ionospheric parameters display regular seasonal and solar activity variations (e.g.Richards, 2001;Lei et al., 2005).At low and middle latitudes, the primary source of ionization in the F-region is the EUV solar irradiances.The solar activity dependence of ionospheric characteristics has been studied in the early various ionospheric observations.Richards et al. (1994) have shown that the solar cycle variation of most solar EUV flux lines can be scaled accurately enough for aeronomic applications by using F107p = (F107 + F107A)/2, where F107A is the 81-day running mean of daily F107 index.Now we use F107p as an indicator of the solar activity level in this analysis.
Figure 3 presents the mothly diurnal variation of H m at Wuhan in 2002.The average and day-to-day variability of the monthly H m is described by the corresponding median and upper and lower quartiles, which are represented in lines with vertical bars, respectively.It can be observed from the figure that the values of median H m vary from 30-80 km.As seen from Fig. 3, H m are roughly of a similar behavior in the months from November to February.It is true for H m grouped in March and April, May to August, and September and October, respectively.Thus, to look for their seasonal variation, the parameters in months from November to February are classified as winter, March and April as spring, May to August as summer, and September and October as autumn, respectively.
Diurnal variations of the median H m for four seasons under high (F107p>180) and moderate-to-low (F107p<140) solar activity levels are plotted in Fig. 4. In Fig. 4, data are grouped according to their solar activity levels.The possible influence of geomagnetic activities is not excluded.
Under moderate-to-low and high solar activities, a morning increase in H m is followed by an afternoon decrease.There is no significant change in H m during the nighttime compared with the daytime, except for a small peak in the winter under high solar activity.In notable diurnal variation with a maximum around 10:00 LT and a minimum around midnight.Both under high and moderate-to-low solar activity, H m is at its minimum during nighttime.The winter peak of H m shifts to local midday under high solar activity and even later under moderate-tolow solar activity.The diurnal variation of seasonal median H m is not so appreciable in other seasons as that in summer.An evident feature found in Figs. 3 and 4 is that the mean daytime values of H m are highest in summer and lowest in winter, while insignificant seasonal differences are seen in the nighttime H m. During the daytime, the observed H m values in summer are about 20 km larger than those in other seasons.
According to Huang and Reinisch (2001), there is a good correlation between H m and the slab thickness of the ionosphere, which is defined by the ratio of ionospheric total  electron content to the peak density.The seasonal feature of Wuhan H m is also similar to the general trend for the slab thickness to decrease from summer to equinox to winter as reported by Goodwin et al. (1995), Jayachandran et al. (2004) and Wu et al. (1998).
It is evident that the solar activity level should have an influence on H m. Figure 5 gives a scatterplot of Wuhan H m versus F107p at 04:00 UT in winter.Although the data set has not covered a full solar cycle, the solar activity index F107 during the observations extends from the minimum of 80 to the maximum of 285.5 (on 28 September 2001), with a mean value of 157.In order to study the solar activity variations of H m, we investigate the relationship between H m and F107p at each specified time for the four seasons.It dindicates that the overall trend of the H m change is a linear increase with respect to F107p, namely the values of H m tend to be higher for higher solar activities.Thus, the solar dependence of H m may be represented with the rate of increase with solar flux, dH m/dF107p.Figure 6 demonstrates dH m/dF107p against universal time for the four seasons.The value of dH m/dF107p averages at 0.13 km per solar flux unit by day and night.
If the scale height in an α-Chapman function represents the scale height of the neutral atmosphere, the plasma scale height should be roughly twice as large as the Reinisch and Huang (2004) method.The neutral temperature Tn at Wuhan, provided by the MSIS model (Picone et al., 2002), is shown in the fifth panel of Fig. 8.It is obvious that H m is not strongly connected with T n.It is also true for electron or ion temperatures, because there is a significant morning rise in electron and ion temperatures in the F-layer (Oyama et al., 1996;Sharma et al., 2005), while it does not occur in H m.
It should be mentioned that the classical scale height is defined as kT /mg (here k is the Boltzmann constant, T is the temperature, m is the mass and g the gravitation acceleration), while the scale height H m, derived from ionograms, is actually a measure of the slope of the topside electron number density profile with a Chapman function, thus it does have not the classical physical meanings.This point has been made by Huang and Reinisch (2001).But H m derived from the ionograms has some physical meanings.First, the ionogram derived H m is a measure of the N e (h) profile, thus it may be thought of as an index for the slope of the topside ionosphere.It has values in topside N e (h) modeling applications.Second, this H m is also a measure of slab thickness, although their values may be different from each other, according to the statistical study of Huang and Reinisch (2001) on NmF2, TEC and H m. In addition, although the Chapman theory can only be applied in the E-and F1-layer, the distribution of the electron density of the topside ionosphere Ann.Geophys., 24, 851-860, 2006 www not far away from the F-layer peak can be well described by the Chapman function.Thus, the ionogram derived H m should contain information on the ionospheric chemical and dynamic processes.This point deserves further investigation.

Annual variation of H m at 13 stations
The Earth's ionosphere is known to undergo a yearly variation (e.g.Kawamura et al., 2002;Yu et al., 2004).It is well known that in some parts of the world the predominant variation of foF2 is semiannual, but elsewhere it is significantly annual, usually with a winter maximum (e.g.Torr and Torr, 1973;Yu et al., 2004).To investigate the yearly variation of H m, besides Wuhan, data at College, Narssarssuaq, Chilton, Millstone Hill, Tortosa, Athens, Wallops Is., Ascension Is., Madimbo, Louisvale, Grahamstown and Port Stanley were also collected.H m data at these 12 ionosonde stations can be available on the SPIDR web.The latitude of these stations varies from 64.9 • N to 51.7 • S.An interesting feature of daytime H m, which occurs at all latitudes, is its significant annual variation with a summer maximum.Figure 7 shows the time sequence of the day-by-day H m at a specific time during the daytime over these global 12 stations.During the daytime, the annual component is dominant in the yearly variation of H m.
We choose the Wuhan station as an example to show the yearly variation of H m and hmF2, foF2 and the IRI bottomside profile thickness parameter B0. Figure 8 shows the dayby-day values of these parameters over Wuhan around local noon and midnight, respectively.The yearly variation of H m at Wuhan also shows the common feature at the other 12 stations.In addition, H m has a similar phase with that of hmF2 and B0 and an opposite one with foF2.At midnight, the yearly variation of hmF2 and B0 becomes much weaker and tends to disappear.In contrast, the annual variation of foF2 is predominant with a peak in summer.
Figure 9 illustrates the amplitudes of the annual and semiannual components of H m, hmF2, foF2 and B0 at Wuhan at different times, while Figure 10 represents the annual phase of these parameters at Wuhan.The yearly variation of Wuhan foF2 has notable annual and semiannual components, although its daytime annual phase is in winter, while at night, its annual variation is predominant with a peak in summer.In contrast, the behaviors of H m, hmF2 and B0 are somewhat   different from that of foF2.Their annual phases are in summer (Fig. 10).As shown in Fig. 9, daytime H m and hmF2 at Wuhan undergo a strong yearly variation with a predominant annual component, while at night the yearly variations become much weaker and tend to disappear.Both the annual and semiannual components of H m and B0 become insignificant at night.

3.4
The correlation between H m and hmF2, B0 Scatterplots of the scale height H m versus hmF2, foF2 and B0 at Wuhan at local noon (04:00 UT) and midnight (16:00 UT) during 1999-2004 are given in the left and right panels of Fig. 11, respectively.In general, H m (also B0) shows a moderate positive correlation with hmF2 and a very weak negative or poor correlation with foF2.
A striking feature shown in Fig. 11 is the strong correlation between H m and the IRI bottomside thickness parameter B0 at all local times over Wuhan (with a correlation coefficient as high as 0.92-0.99).Both parameters B0 and H m are dependent on the shape of the electron density profile in the F region.This dependence justifies the strong correlation between both parameters.Reinisch et al. (2004) discussed the possibility to calculate H m from the IRI parameters B0, B1 and D1.Their ultimate purpose is searching for an alternate path to an estimate of the topside profile based on the bottomside one.Our result suggests that the strong correlation between H m and B0 provides a new and convenient way for future modeling of the topside ionospheric shape only from the established B0 parameter set.This point may be helpful for improving the IRI profile prediction in the future.The positive correlation of H m with hmF2 suggests that the physical processes involved in controlling the variation of hmF2 may also be responsible for that of H m. That hmF2 greatly depends on the direct effect of horizontal neutral wind is well known from the past and well explained by the theory of the thermospheric winds.Neutral winds and electric fields act to shift the F peak from the balance height to a new level.It is the physical basis of deriving the meridional neutral wind from ionospheric observations (e.g.Rishbeth et al., 1978;Buonsanto et al., 1997;Liu et al., 2003Liu et al., , 2004)).The annual variation arises from the summer to winter thermospheric circulation wind.The meridional neutral wind (Wn) for Wuhan around hmF2 obtained by the HWM93 model (Hedin et al., 1996) is illustrated in the bottom panel of Fig. 8.As expected, during daytime, the model Wn shows a similar annual pattern as that of hmF2 and H m. It indicates that Wn not only contributes to the ionospheric height but also to the shape of the ionospheric profile.At night, the model Wn still has a significant annual variation, which is far from that of H m. This point deserves further study, although the current version of the HWM93 model has its limitations.

Summary
This paper investigates the diurnal, seasonal, and solar activity variations of the ionogram derived scale height around hmF2 observed at Wuhan and the yearly variations of H m at Wuhan and 12 other stations.The main results are summarized as follows: (1) It shows that H m observed at Wuhan has appreciable diurnal and day-to-day variations.Significant disturbances in H m are presented during geomagnetic active periods.However, the dependence of H m on magnetic activity is complicated.
(2) The diurnal behaviors of seasonal median H m under both solar activities are found to be similar.Median values of H m are highest in summer and lowest in winter during the daytime.At nighttime, H m exhibits a much weaker seasonal variation.H m tends to a higher value with increasing solar flux.
(3) A distinct annual variation of H m is observed at Wuhan and 12 other stations, i.e.H m has a higher value in summer and a lower value in winter during the daytime.This annual variation becomes much weaker or disappears at the time interval from late night to pre-sunrise.
(4) A strong correlation is found between H m and the bottomside thickness parameter B0 at all local times.It provides a new and convenient way for modeling the topside ionospheric shape only from the established B0 parameter set.In general, H m shows a moderate positive correlation with hmF2 and negative and little correlation with foF2 depending on the local time.

Fig. 1 .
Fig. 1.Diurnal variations of the scale height (H m) derived from Digisonde measurements recorded at Wuhan during 29-31 October 2003 and 27-29 October 2004.The median values of H m in the nearest 31 days are plotted in dashed lines for a reference.The 3-hour K p index is illustrated in the histograms.The corresponding daily sum K p and solar index F107 indices are also labeled.Local Time, LT, is UT plus 7.6 h at Wuhan.

Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .
Fig. 3. Diurnal variations of H m at Wuhan in 2002.Lines with bars, respectively, represent the monthly median values of H m and the corresponding upper and lower quartiles.The local noon and local night are also indicated with open and solid circles near the abscissa, respectively.

Fig. 7 .
Fig. 7. Time sequences of values of scale height (H m) at hmF2 over 12 stations at specified day times during 2000-2004.The names and their locations of the stations are labeled.

Fig. 8 .
Fig. 8. Time sequences of values of scale height H m, foF2, hmF2, B0, thermospheric temperature T n (at the height of hmF2 from MSIS model), and southward neutral wind W n (at the height of hmF2 from HWM model) over Wuhan at 04:00 UT (left) and 16:00 UT(right) during 1999-2004.

Fig. 10 .
Fig. 10.Phase of the annual component of H m, foF2, hmF2 and B0 at Wuhan in 2000-2001.The phases are in months.