Technique for determining midlatitude O+/H+ transition heights from topside ionograms



[1] The midlatitude O+/H+ transition height (where the H+ and O+ number densities are equal) is of importance because it is where the topside altitude distribution of the dominant ions transitions from the ionospheric F region into the plasmasphere, which is considered the inner region of the magnetosphere. This transition height can be determined by fitting ionospheric topside sounder–derived electron density (Ne) profiles to analytical H+ and O+ functions. There are four variables involved in this process, two involving ion number densities and two involving the electron temperature Te. The density variables are the H+ density at the height of the satellite and the O+ density at the base of the profile (taken as 400 km). The temperature variables have been treated using different approaches. In an earlier investigation, diffusive equilibrium ion density profiles, based on an earlier Titheridge height-varying electron temperature function, were used to fit the Ne profiles in which the electron temperature Te and the Te altitude gradient at a base height of 400 km, denoted by T0 and G0, respectively, were free variables. In the present work, T0 and G0 are constrained by using a later Titheridge empirical temperature model. Alternatively, when in situ Langmuir probe Te determinations are available, the problem reduces to one with only one free temperature variable. All three of these approaches, using Titheridge's revised height-varying electron temperature function, are applied to a sequence of midlatitude ISIS 2–derived Ne profiles obtained during a period of prolonged high magnetic activity. The results indicate that in the inner plasmasphere, where the transition height is slowly varying, the approach based on the two free Te parameters (T0 and G0) agrees well with the one using the Langmuir probe input. In the region where the transition height is rapidly increasing, however, the approach based on the empirical temperature model produced the most consistent results for the O+/H+ transition height.

1. Introduction

[2] A major concern in ionospheric modeling is the lack of knowledge of the vertical distribution of electrons in the topside ionosphere as recently discussed by Stankov et al. [2003] and Bilitza [2001] among others. One parameter to characterize this electron density (Ne) distribution is the O+/H+ transition height. This transition altitude of the dominant ions corresponds to the transition of the main ionosphere to the plasmasphere [Bauer, 1973; Lemaire and Gringauz, 1998]. It has been a subject of investigation for several decades using a variety of data sets [see, e.g., Titheridge, 1976; Stankov et al., 2003; Marinov et al., 2004].

[3] One way to study the topside ionosphere is to employ ionospheric topside sounder data. Extensive topside ionospheric observations exist from the swept-frequency sounders carried on the polar-orbiting satellites Alouette 1 and 2 and ISIS 1 and 2 (launched in 1962, 1965, 1969, and 1971, respectively). The two Alouette satellites were each in operation for 10 years; ISIS 1 was in operation for 21 years; and ISIS 2 was in operation for 19 years. They were all designed as analog systems with the data recorded on magnetic tapes at a network of more than 20 globally distributed telemetry stations. Not all of the sounder data recorded on these analog telemetry tapes were converted into 35-mm film format records in the form of ionograms because of cost considerations. In addition, not all of the ionograms recorded onto 35-mm film were processed into Ne profiles because of the cost of the manual effort involved. Approximately 177,000 profiles were produced and are available online from the National Space Sciences Data Center (NSSDC) at Also, more than 400,000 digital ISIS 1 and 2 ionograms from 1969 to the mid-1980s are available from as a result of an analog-to-digital conversion project [Benson, 1996; Bilitza et al., 2003]. An analysis program, based on the profile inversion approach of Jackson [1969], is also available from this Web site. An automatic processing procedure has also been developed for these digital ionograms [Huang et al., 2002; Bilitza et al., 2004]. An illustration of the above analysis program based on the work by Jackson [1969] is presented by Webb et al. [2006]. In this profile inversion, vertical propagation in a horizontally stratified ionosphere is assumed.

[4] The purpose of this paper is to update the work presented by Webb et al. [2006]. The fitting of the Ne profiles to extract the O+/H+ transition heights has been improved by using a new version of the Titheridge temperature model (TM) [Gulyaeva and Titheridge, 2006]. In addition, the deduced O+/H+ transition heights are compared with those derived with the constraint of independent in situ Langmuir probe Te observations.

2. Analysis of Topside Ne Profiles Without Te Input

[5] Webb et al. [2006] used the electron temperature (Te) function of Titheridge [1998] in a diffusive equilibrium model consisting of O+ and H+ to fit the Ne profiles derived from topside sounder profiles with Ne = n(O+) + n(H+), where n(O+) is the O+ number density and n(H+) is the H+ number density. The approach derives from equations originally presented by Titheridge [1972] that included multiple ion species, ambipolar electric field effects, and different Te and Ti values. Webb and Essex [2001] extended this approach to include the entire plasmasphere, with the n(O+) calculated iteratively upward from the topside ionosphere along a magnetic field line to the equator and n(H+) calculated iteratively downward from the magnetic field line apex. Here this later approach is modified with n(H+) calculated downward from the location of the sounding satellite. The assumption of diffusive equilibrium is reasonable in midlatitude regions [see, e.g., Webb and Essex, 2001] where the field lines are nearly vertical (e.g., at an altitude of 1800 km the L = 3 dipole field line deviates from the vertical by only ∼5°). For the purposes of this study, only H+ and O+ were considered, and other ion species, such as He+, were ignored. During periods of high solar activity, n(He+) can be greater than n(H+) but probably only above the 1400-km altitude of ISIS 2 (used in this study) and thus will not greatly effect the present results. The Te expression has two free parameters, namely, the electron temperature and the electron temperature gradient at a base height of 400 km, designated by T0 and G0, respectively. The ion temperature is determined from Te using the neutral temperature determined from the Mass Spectrometer Incoherent Scatter (MSIS) model [Picone et al., 2002] and an expression given by Titheridge [1998]. T0 and G0, along with n(O+) at 400 km and n(H+) at the satellite altitude, are adjusted to best fit the Ne profile in a least squares sense. This fit with four free parameters will be referred to as the free parameter fit (FPF).

3. Analysis of Topside Ne Profiles With Te Input

[6] Sometimes the FPF technique does not return realistic temperature parameters for T0 and G0, and so the computed O+/H+ transition heights become suspect. These unrealistic values are, in part, due to the insensitive nature of diffusive equilibrium to small changes in temperature which, consequently, requires large T0 and/or G0 variations to modify the fitted Ne profile by an appreciable amount that are sometimes required in the fitting process [Webb et al., 2006]. Two possible solutions to this problem are presented here: the first is to use in situ Te satellite measurements as a restraint for the possible Te solutions and the second is to obtain the T0 and G0 values from the global TM.

[7] If in situ Te satellite measurements are available, the fitting technique can be improved by setting the model at the satellite altitude to the measured value. In the case of Alouette 2 and ISIS 1 and 2, Langmuir probe instruments provide Te and Ne data [Florida, 1969; Brace and Theis, 1981]. By fixing Te at the satellite location to the Langmuir probe–determined value, the fitted free temperature parameters are reduced from two to one since G0 is a function of T0 and Te at another point along the Ne profile; that is, G0 is no longer an independent variable. We will refer to the fits done in this manner as the Langmuir probe fit (LPF). The Langmuir probe Ne and Te values are available from the NSSDC (e.g., for ISIS 2 at To avoid using uncertain measurements, the Te results from the Langmuir probe are only used when the “confidence value (Te)” provided in the data files was greater than five, which agrees with results presented by Murphree [1980].

[8] The second Te input approach is to use the TM empirical relationships for T0 and G0, which vary as a function of local time and geomagnetic latitude as well as with solar and geomagnetic activity. Here we will refer to this approach as the Titheridge model fit (TMF). The advantage of the TMF approach is that the TM T0 and G0 values have global coverage and so are not dependent on the availability of Langmuir probe observations. Furthermore, using the fixed T0 and G0 values in the fit reduces the number of free variables to the two ion density parameters discussed earlier. As was previously mentioned, unrealistic results can occur in the values of T0 and G0 when an FPF is undertaken. The TMF avoids this problem by fixing the T0 and G0 values but at the expense of only producing average values for these parameters at the location of interest and, as such, may not reflect local conditions prevailing at the time of the observations.

4. Examples of Fitting Ne Profiles

[9] To demonstrate the different fitting techniques used on topside Ne profiles, ISIS 2 sounder-derived Ne contours from 24 February 1973 (also used by Murphree [1980]) shown in Figure 1 will be used. The contours were produced from manually derived Ne sounder profiles available from the NSSDC ( Vertical dashed lines on this contour plot show the locations and times of two topside Ne profiles that will be analyzed in detail. The profiles were derived from the free-space extraordinary (X) mode traces on the ionograms in Figure 2. The free-space ordinary (O) mode traces on these ionograms are used as an independent test of the inversion process. The days preceding 24 February was a period of high geomagnetic activity. A Kp = 7 storm occurred approximately 3 days before 24 February, and Kp had been at a heightened level of 4 to 6 since the storm. Using the simple expression for the nightside plasmapause location of Carpenter and Anderson [1992], this corresponds to L ∼ 3, which is noted in Figure 1. It can be seen that this location corresponds to a rapid drop in the plasmaspheric Ne indicating the location of the plasmapause [see, e.g., Grebowsky et al., 1978]. Using the selection criteria discussed in section 3, Langmuir probe Te observations are only available between 0744 and 0750 UT, and thus the LPF technique cannot be applied to the Ne after this interval.

Figure 1.

Sounder-derived contour plot (log10Ne m−3) for 24 February 1973. The vertical lines denoted by P1 and P2 denote the locations of the Ne topside profiles presented in Figures 3 and 4. Also shown is the approximate location of the plasmapause (denoted by PP) obtained from the expression given by Carpenter and Anderson [1992] for Kp ≈ 5.

Figure 2.

Portions of ISIS 2 ionograms (from 35-mm film) recorded at (a) 0744:11 UT and (b) 0751:19 UT on 24 February 1973 corresponding to P1 and P2 in Figure 1, respectively. The white trace near the bottom of each ionogram indicates the receiver's automatic gain control voltage.

[10] An example of the results obtained by using each of the fitting techniques is presented in Figure 3, which corresponds to P1 in Figure 1. This Ne profile is well within the plasmasphere. Here very good fits were obtained between the ISIS 2–derived Ne profile and the sum of the modeled n(O+) and n(H+) profiles (which, assuming charge conservation, equals the Ne profile) for all three of the fitting techniques. Once the n(O+) and n(H+) profiles have been obtained, it is a simple task to determine the O+/H+ transition height, which in this case was around 480 km.

Figure 3.

O+/H+ transition heights determined from least squares fits to the ISIS 2 Ne profile denoted by P1 in Figure 1 assuming a diffusive equilibrium H+ and O+ plasma. The data correspond to 0143 LMT and L = 1.8. T0 and G0 are the electron temperature and the electron temperature gradient at the 400-km base height, respectively. The left plot shows the results from using the free parameter fit (FPF), the middle plot using Titheridge model fit (TMF), and the right plot using Langmuir probe fit (LPF). All three give similar results for the O+/H+ transition height (TH).

[11] Under certain conditions, the O+/H+ transition height will occur above the satellite altitude as would occur for a high-speed H+ flow in the trough or polar wind [see, e.g., Grebowsky et al., 1978]. The fitting procedure will then either return a very small positive value for n(H+) at the top of the profile or, possibly, a physically unreal negative value. In the latter case the fit is repeated under the assumption that the Ne profile reflects only O+ in diffusive equilibrium. Figure 4 illustrates the results of applying this analysis to a profile obtained in the midlatitude trough region. It was obtained when ISIS 2 was at the location indicated by P2 in Figure 1. As was noted above, the LPF approach cannot be used at this time. In this case the Ne and n(O+) fits overlap, confirming that little or no H+ is present below the satellite and that, presumably, the O+/H+ transition height is located near or above the satellite. Thus the fitting procedures can handle the two main possibilities, i.e., when the O+/H+ transition height occurs below or above the satellite.

Figure 4.

Same as Figure 3 except for the ISIS 2 Ne profile denoted by P2 in Figure 1 at 0200 LMT and L = 3.7. No LPF is given because reliable Langmuir probe Te was not available. In this case the O+/H+ transition height occurs near or above the satellite altitude, and the diffusive equilibrium is based almost solely on O+.

[12] Figure 5 shows the O+/H+ transition heights obtained from the three fitting techniques for 26 Ne profiles between 0744 and 0752 UT on 24 February 1973. The results indicate that in the inner plasmasphere, where the transition height is slowly varying, the FPF and LPF techniques agree well, while the TMF values are slightly higher. The latter's higher values are probably due to the global averaged T0 and G0 values used in the fits. In the region where the transition height is rapidly increasing around 0749 UT; however, the approach based on the empirical temperature model produced the most consistent results for the O+/H+ transition height. In the same region, the FPF retuned no O+/H+ transition height. This result appears to be due to unrealistically high T0 and G0 values obtained in this region, which forced the transition height far above the satellite altitude. Furthermore, any O+/H+ transition height within a few hundred kilometers of the satellite altitude should be considered suspect since they correspond to only a few data points in the sounder profile. The best way to accurately determine the O+/H+ transition heights near or above the 1400 km region would be to use Ne sounder-derived profiles from higher topside sounder satellites, such as Alouette 2 or ISIS 1.

Figure 5.

O+/H+ transition heights, obtained from the FPT, TMF, and LPF fitting techniques, for the 26 Ne profiles from Figure 1 between 0744 and 0752 UT on 24 February 1973. Values near the satellite altitude are potentially artifacts of the fitting procedure.

5. Discussion

[13] In the previous sections our technique for determining the O+/H+ transition height from topside Ne profiles was demonstrated. The Ne fitting approach assumes that both the n(O+) and n(H+) profiles can be approximated by diffusive equilibrium. This assumption will be best for n(O+), which is controlled primarily by diffusion and the photochemistry of the underlying ionosphere, under most circumstances in the altitude region where it is dominant. At altitudes where H+ becomes the dominant ion, the exact nature of the n(O+) profile is less important, as it will not be the primary contributor to the Ne profile.

[14] The assumption of diffusive equilibrium for n(H+), under certain circumstances, e.g., in light ion outflow regions, can be questionable and the resulting fitted variables suspect. Of prime concern in our goal to determine the O+/H+ transition height are the cases where H+ becomes the dominant ion within the range of the topside sounding under consideration. When O+ dominates up to the satellite altitude, we cannot determine any information on H+ (beyond determining that the O+/H+ transition height is above the satellite).

[15] Three different fitting techniques were considered: one previously presented by Webb et al. [2006] and two new techniques that provide Te input in one form or another to restrict the Ne fit. All three of these approaches used a revised height-varying electron temperature function [Gulyaeva and Titheridge, 2006]. They were applied to a sequence of midlatitude ISIS 2–derived Ne profiles obtained during a magnetic storm. The results indicate that in the inner plasmasphere, where the transition height is slowly varying, the FPF approach (based on the two free Te parameters T0 and G0) agrees well with the LPF approach (using a Langmuir probe input). In the region where the transition height is rapidly increasing, however, the TMF approach (based on the Titheridge empirical temperature model) produced the most consistent results for the O+/H+ transition height.

[16] Future work will include the analysis of Ne profiles derived from topside sounders on the Alouette 2 and ISIS 1 satellites which were in polar elliptical orbits with apogees of 3000 and 3500 km, respectively. Data from these satellites will complement the uniform global coverage provided by ISIS 2 (polar circular 1400-km altitude orbit) and will allow much higher O+/H+ transition heights to be determined. These higher transition heights can occur during the day or in solar maximum conditions. At these higher altitudes under solar maximum conditions, n(He+) may become larger than n(H+), and some consideration will need to be given to including He+ in the fitting of the Ne profiles.


[17] This work was supported by NASA's Living With a Star (LWS) Targeted Research and Technology (TR&T) program.