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[1] Shortcomings of the representation of the topside electron density profile in the International Reference Ionosphere (IRI) model have been noted in comparison with recently analyzed topside sounder data and also with total electron content (TEC) data. Various studies have proposed corrections of the IRI formulas or have introduced a new formalism. This paper reviews the different approaches, their implications for IRI, and their current status. An important challenge for topside modeling is the truthful representation of profiles in the equatorial anomaly (EA) region over the whole range of the EA fountain. This means that the latitudinal representation has to reproduce the merging of the double-peak signature at F region heights into a single peak at the top of the fountain. In this context, special emphasis is given to the coupling between topside and plasmaspheric models.

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1. Current International Reference Ionosphere Model and Shortcomings

[2] The representation of the topside electron density in the International Reference Ionosphere (IRI) is based on the Bent et al. [1972] model. In this model, the topside is divided into three altitude regimes, and in each regime, the electron density decreases exponentially with a constant segment-specific scale height. Rawer et al. [1978] developed an analytical representation of Bent's scale height using Epstein step and transition functions (see Bilitza [2004] for details). As in the Bent model, the IRI model coefficients are provided as functions of F_{2} peak plasma frequency (f_{o}F_{2}), geomagnetic latitude, and solar activity (F_{10.7}). The analytical representation helped to smooth out some of the unreasonable sharp transitions seen in the original Bent model and resulted in a better agreement with midlatitude total electron content (TEC) measurements [McNamara, 1984].

[3] The Bent et al. [1972] topside model is based primarily on Alouette 1 topside sounder measurements, which cover low and medium solar activities and mostly northern midlatitudes (the satellite had no onboard recording capabilities; the global coverage was therefore determined by the distribution of ground telemetry stations, which were primarily located in northern midlatitudes). As a result, the Bent and IRI topside models show shortcomings at high solar activities and at low and high latitudes. Bilitza [1985] used Jicamarca incoherent scatter data and AE-C and DE-2 satellite in situ measurements to improve the IRI model at low latitudes. But shortcomings persist at high latitudes and high solar activities [e.g., Iwamoto et al., 2002; Coisson et al., 2002]. The IRI working group has given highest priority to the improvement of the electron density topside profile. This is also of great importance for efforts to connect the IRI topside profile to plasmaspheric models [e.g., Gallagher et al., 2000]. In the following sections, topside-modeling efforts will be reviewed with special emphasis on studies that could benefit the IRI model.

2. Functions Used

[4] Simplified aeronomic arguments lead to a Chapman-type profile [e.g., Hargreaves, 1992]

where z = (h − hmF_{2})/H, NmF_{2} and hmF_{2} are the F_{2} peak density and height, H is the topside scale height, and c = 0.5 or 1 for a Chapman α or β function. Other functions often used in topside modeling include parabolic, exponential, and Epstein layer (sech-squared) functions. Bent et al. [1972], for example, combined a parabolic F layer with an exponential representation of the topside. The Epstein layer function is given as

where Z = exp{(h − hmF_{2})/H}and is often also referred to as sech-squared layer function because

which is equal to equation (2) if we substitute Z = exp (2x). Figure 1 is taken from the work of Stankov et al. [2003] showing the topside density distribution provided by these different functions for a scale height of 100 km. The merits of these functions in reproducing measured topside profiles and TEC values have been evaluated in a number of studies using different data sources. Stankov et al. [2003], for example, find that average nighttime profiles obtained from AE-C satellite in situ measurements are best represented by the Epstein formulas, whereas the daytime profiles are better approximated by exponential or α Chapman functions (Figure 2). It is clear from Figure 1 that of the five functions, the α Chapman function will produce the largest TEC values.

[5] IRI improvement efforts involve all of these different model functions. Bent et al. [1972] combined a parabolic F layer with an exponential representation of the topside. Pulinets et al. [2002] and Coisson et al. [2006] use an Epstein layer function, as does the current IRI model in a slightly modified form. Reinisch et al. [2004a, 2004b] and Reinisch [2004] use a Chapman function to merge their ionosonde-based model with their IMAGE/RPI-based plasmasphere model [Huang et al., 2004].

3. IRI Efforts Toward an Improved Topside Model

[6] Like any empirical model, a data-based representation of the topside electron density profile depends critically on the availability of reliable data for a wide range of locations and times. Incoherent scatter radars provide a good long-term record of the topside electron density for a specific location. Satellite topside sounder and in situ instruments, on the other hand, provide global coverage but only during the lifetime of the satellite. Topside modeling activities have relied heavily on measurements from the very first topside sounder satellite, Alouette 1. With the help of NASA's National Space Science Data Center (NSSDC) data from the later Alouette 2 and ISIS 1 and 2 topside sounder satellites and from many satellite in situ instruments have been recently made available online (http://nssdcftp.gsfc.nasa.gov/spacecraft_data) [Bilitza et al., 2003] and are now being used for topside modeling [Gulyaeva, 2003; Bilitza, 2004; Webb et al., 2006]. In addition many not-yet-analyzed ISIS topside soundings have been digitized and processed into electron density profiles as part of a NASA/AISRP-funded data restoration project [Bilitza et al., 2004] and are now also available from the NSSDC ftp site. The combined database established by these efforts will be of great benefit for the IRI modeling effort.

[7] A particular challenge in modeling the topside electron density profile is the accurate representation of the equatorial anomaly generated by the fountain effect at equatorial latitudes. At F region heights this effect produces the well-known crests at about 18° dip latitude on each side of the magnetic equator and a relative minimum at the magnetic equator (Figure 3). With increasing height, the two latitudinal peaks move closer toward the magnetic equator and merge into a single peak at the magnetic equator at a height of about 1000 km. Almost all topside models are normalized to the F_{2} peak density, NmF_{2}. Models for NmF_{2} are well established and provide the typical camelback signature of the equatorial anomaly. To reach a single equatorial peak at higher altitudes, the topside profile function therefore has to counterbalance the EA signature imprinted by the NmF_{2} model. Rawer et al. [1978] did this through the f_{o}F_{2} dependence of their topside profile shape parameters. Alternatively, a global model for the density at a fixed altitude around 1000 km (with an equatorial peak) could be used to adjust the topside profile parameters automatically (e.g., the approach by Reinisch et al. [2004b], Reinisch [2004], and Triskova et al. [2006]).

[8] An improved representation of the IRI topside electron density profile is also a necessary step toward a successful merging of the ionosphere and plasmasphere models because plasmaspheric models often use the IRI topside density at a certain fixed height as a footprint for their model.

[9] The following sections briefly explain the different IRI topside modeling efforts and their current status.

3.1. Correction Term for IRI Topside Formula

[10]Bilitza [2004] evaluated the current IRI topside model with the Alouette 2, ISIS 1, and ISIS 2 topside sounder data that were mentioned in section 3. In Figure 4a, the noontime ratio between data and model is plotted for different modified dip zones. It shows that at F region altitudes, IRI slightly underestimates the measurements at midlatitudes and overestimates the low-latitude data. But most importantly, IRI significantly overestimates the measurements in the upper topside at all latitudes covered by the Alouette/ISIS topside sounder data (please note that Figures 4a and 4b display the inverse model-to-data ratio). On the basis of these results, Bilitza [2004] deduced a correction term for the IRI topside formula that depends on altitude, local time, and modified dip latitude. With this correction, the IRI topside model provides a good representation of the Alouette/ISIS data as shown by a data-to-model ratio of close to 1 in Figure 4b.

3.2. Combined Ionosonde and IMAGE/RPI Model

[11] Assuming an α Chapman profile with a constant scale height for the topside, Reinisch and Huang [2001] and Reinisch et al. [2004a] have shown how to deduce this scale height from ground ionosonde measurements. Good results are found in comparison with incoherent scatter radar topside data, at least up to the upper transition height where the scale height–determining ion changes from O^{+} to H^{+}. Elaborating on this approach, Reinisch et al. [2004b] and Reinisch [2004] propose to merge the ionosonde model with their IMAGE/RPI plasmaspheric model [Huang et al., 2004]. This is accomplished by letting the scale height vary continuously with altitude. Boundary conditions at the ionosphere-plasmasphere boundary and the F_{2} layer peak (value and first derivative) determine the coefficients used to describe the altitude variation of the scale height. The concept is illustrated in Figures 5 and 6. Candidates for the boundary height are the transition height h_{T}, which marks the transition from a oxygen- to a hydrogen-dominated plasma or a fixed height between 1000 and 3000 km. This very promising new approach to modeling the topside electron density profile is still in an early stage, and a full model description has not yet been developed. Topside sounder and in situ measurements (see section 3.5) will help to fully develop and evaluate this new approach. One of the advantages of this method is the direct merging with a plasmasphere model, a great benefit for the many IRI users that require not only ionospheric but also plasmaspheric density parameters.

with H_{0} = kB_{bot} given as a function of the bottomside thickness B_{bot} and a correction factor k that depends on the F peak density, F peak height, season, and sunspot number. Coisson et al. [2002] have compared the NeQuick model with the ISIS topside sounder data, finding good agreement, especially also at higher altitudes where IRI overestimates the ISIS data (as shown in Figure 4a). A disadvantage of the current NeQuick model is its incomplete representation of the equator anomaly region. Efforts are underway to overcome these shortcomings with the help of ISIS topside sounder data and modifications to the correction factor k. An update of the NeQuick model on the basis of this latest data analysis was presented by Coisson et al. [2006].

3.4. Intercosmos-19 Model

[13]Pulinets et al. [2002] have used Intercosmos-19 topside sounder data to develop a global model for the topside electron density during high solar activity conditions. Similar to the NeQuick model, they use an Epstein layer function (equation (2)) with varying scale height but using the much simpler height dependence

with a constant H_{0}. The latest version of this model was presented by Depuev and Pulinets [2004] on the basis of about 10,000 Intercosmos-19 profiles. The model parameters are given in tabulated form with 10° steps in latitude and 30° steps in longitude for different local times and seasons. The advantage of this model is the simple access it provides to the fundamental variation patterns seen in the IK-19 data including systematic longitudinal features. A disadvantage is the nonanalytical form and its limited coverage in local time and solar activity.

3.5. Fixed Height Model

[14]Triskova et al. [2006] have produced global models of electron density at specific heights on the basis of in situ satellite measurements from AE-C, -D, and -E, and Intercosmos-24 and -25:

Their height selection reflects the increase of the upper transition height with solar activity and the special orbit characteristics of the AE and IK satellites. A spherical harmonics representation in terms of magnetic local time (MLT) and invdip is used to approximate the data. Coefficients are provided for different seasons and different levels of solar activity. The invdip latitudinal variable as introduced by Truhlik et al. [2001] is defined such that it is close to the dip latitude near the equator and closer to the invariant latitude at higher latitudes. Comparisons of the new model with ISIS 2 Langmuir probe measurements show good agreement, whereas IRI overestimates the data (Figure 7). Detailed validation of the model using five satellite data sets are shown by Triskova et al. [2006].

[15] Vertical profiles can be obtained by linear interpolation between the model heights on the basis of Booker's [1977] technique of assuming piecewise sections of constant gradient. Booker's formalism is satisfactory as a first approximation. However, it sometimes leads to nonphysical profiles. Therefore a more convenient representation mechanism using a Chapman function with variable scale height is now being investigated in collaboration with Reinisch et al. [2004b], combining the fixed-height approach with the method described in section 3.2.

3.6. Topside Half-Width Model

[16]Gulyaeva's [2003] modeling efforts have focused on the topside half-density point, h0.5_{top}. This is the height where the topside electron density has dropped down to half the F_{2} peak density, a point that can be easily scaled from topside profiles. For a α Chapman function this height is related to the Chapman scale height H by

[17]Gulyaeva [2003] used ISIS1-2 and IK19 topside sounder profiles to develop a model for h0.5_{top} in terms of sunspot number, local time, and geomagnetic latitude. Figure 8 illustrates the improvement obtained when using Gulyaeva's [2003]h0.5_{top} model to adjust the IRI topside model. Here a correction factor is introduced into the IRI topside formula such that IRI reaches half the F_{2} peak density at h0.5_{top} from the Gulyaeva [2003] model. More validations of this approach are required before its usage can be recommended for IRI.

4. Summary

[18] The IRI working group has given very high priority to improving the electron density profile in the topside ionosphere and specifically in the upper topside where comparisons with topside sounder data have established a systematic overestimation by the model. On the preceding pages we have briefly described the major modeling efforts that are currently underway focused on this specific IRI goal. This includes efforts that (1) try to correct the original IRI formalism (section 3.1), (2) are quite promising but still in a very early stage of development (section 3.2), (3) have been continuously improved and refined over more than a decade and reached a stage of maturity that warrants inclusion in IRI (3.3 NeQuick model), (4) are an excellent representation of a specific limited data source (section 3.4), (5) are based on global satellite-specific models at selected fixed heights (section 3.5), or (6) introduce a new characteristic parameter for the topside (section 3.6).

[19] The IRI goal is to integrate all of these modeling approaches and results into one new IRI topside model of highest reliability and accuracy. Approaches 2, 5, and 6 are on their way toward such a unification using the common buildup of a Chapman function. Similarly, approaches 3 and 4 have as their common backbone the Epstein function formalism. A partial integration of these two efforts (3 and 4) has already led to improvements of the NeQuick model, and this work is continuing with a special focus now on an accurate representation of the equator anomaly region. Approach 1 is a temporary fix for a clearly defined problem of the current IRI electron density profile in the upper topside and as such will be included in the next version of IRI. In addition to this standard IRI topside representation, the new IRI will offer a second option, allowing users to access the predictions of the NeQuick model. The NeQuick model was selected because it has reached the highest degree of maturity of the six modeling approaches and has been tested also by researchers other than the model developers themselves. By providing these two new options, the IRI model will also facilitate comparisons between the different approaches and will provide an estimate of the uncertainty that still exists in climatological representations of the electron density in the topside ionosphere. Naturally, it is also an important goal of this article to instigate comparisons of these different models with ground and space data and thus help to determine the most accurate model for a future version of the IRI model.

Acknowledgments

[20] We thankfully acknowledge the information, graphs and figures provided by the different modeling teams. D.B. was supported by NSF grants 0245457 and 0417666. B.W.R. was supported by NASA under subcontract 83822 from Southwest Research Institute and by Air Force grant F19628-C-0092.