Comments on Total Electron Content

Clearly, the TEC is a significant parameter in the assessment of system effects, and considerable effort has been directed toward the modeling of TEC over the years. In general, the product of two factors controls the TEC: the so-called slab thickness and the peak electron density. Although there are differences, we find that the climatological behavior of TEC is quite consistent with that of the F-region parameter foF2, which has been determined from vertical incidence sounders. In systems work, it is important to recognize that the TEC referred to in reported models is the TEC throughout the full ionosphere for an equivalent zenithal path. In Table 4-8 the electron content (i.e., EC) is reckoned along the ray trajectory, which may be oblique and may even terminate within the ionosphere for low orbit satellites. Provided the full ionosphere is involved in both forms of the electron content, we may transform the modeled (overhead) value to the oblique value through multiplication of the former by the secant of the earth curvature-corrected ray zenith angle at the ionospheric mean height.

Figure 4-17: Electron density and electron collision frequency versus altitude. From Goodman [19911.

In view of the importance of the TEC in the analysis of earth-space propagation effects from VHF through the lower part of the SHF band, a considerable amount of research has been directed toward the development of models for the TEC. From such models, predictions of system effects such as excess group path delay, Faraday rotation, dispersive Doppler, and ionospheric wedge refraction can be made. Two modeling approaches have been generally used, the first based upon integration of selected worldwide electron density profile models, and the second based upon a direct analysis of the TEC data alone. The most successful model in the former category is due to Bent et al. [1975], while Klobuchar et al. [1970; 1977] have developed the most useful models in the latter category. Without going into details about the various available global models, one finds that they generally deliver relative accuracies of the order of 75-80% during the daytime and 65-70% at night. Models perform best at midlatitudes, where most of the contributing data have been obtained. The state-of-the-art global representation of TEC is due to Klobuchar [1975], and a simple version tailored for single-frequency GPS users provides for a 50% reduction in the error introduced by the ionosphere. Greater accuracies may be obtained through use of region-specific modeling approaches and real-time update approaches. For example, new data has been obtained at high latitudes [Klobuchar, 1987] and also at the equator [Anderson and Klobuchar, 1983]. Significant increases in the TEC, which are not predicted by the quiet-day TEC models, have been observed for ray trajectories penetrating the polar cap and, although understood theoretically, are not properly accounted for in existing operational algorithms. A low-latitude TEC model has been developed by Anderson et al. [1985], providing a better representation of the so-called equatorial anomaly region.

Models of TEC for use in estimation of effects such as Faraday rotation or group path delay are critically dependent upon the selection of the underlying sub-model of the ionospheric distribution and how well it describes reality. Considerable activity in the general area of global model improvement has occurred in recent years, and we anticipate a significant improvement in the capability to predict propagation factors that depend upon TEC in the future. Simple models such as the Bent model may be replaced by hybrid versions of more complete models such as the IRI [Rawer, 1981] [Bilitza, 2001], or may be improved by use of update-capable empirical models such as ICED [Tascione, 1988]. Rush et al. [1984] has improved the global model from which the electron concentrations and foF2 may be obtained.

Figure 4-18 gives the diurnal and seasonal variation in TEC for a mid-latitude site. This curve is only representative, but it clearly demonstrates the large day-to-night differences. Although models that attempt to replicate these data trends are more inexact at night (on a percentage basis), the impact of the inaccuracy may not be very profound in practice. This is because system effects depend upon absolute values of TEC and its changes. So far we have been talking mainly about the smoothed ionospheric properties, thereby ignoring structured plasma effects such as those associated with traveling ionospheric disturbances (or TIDs) and other irregularities in TEC which may give rise to focusing and defocusing of radiowaves. On a smaller scale, other effects become important, such as scintillation. Separate methods are appropriate for this class of irregularities, and this will be the logical point of departure for our next section.

Mean TEC Curves July-Dec

Mean TEC Curves July-Dec

Figure 4-18: Representative midlatitude diurnal and seasonal variation of the Total Electron Content (TEC), (a) Monthly means for January-June; (b) Monthly means for July-December

4.4.2 Differential Effects and Ne Distribution

Fluctuations in signal power and phase often accompany radio wave propagation over earth-space paths as a result of inhomogeneities in the ionospheric electron density. In the case of the ionosphere, the fluctuations are due to irregularities in electron density predominantly at F region heights, from 200-600 km. This phenomenon, analogous to the twinkling of stars in the visible part of the electromagnetic spectrum, has been the object of research for roughly half a century, and is referred to as scintillation in the context of radio propagation. It is difficult to do justice to this interesting phenomenon in the space available. Fortunately, there is a plethora of papers dealing with scintillation, and some important ones are cited herein. In any case, scintillation is probably the single most important deleterious factor affecting future systems utilizing the earth-space propagation path in the GHz frequency region. Recall our mention in Chapter 1 regarding the failure of TAC SAT at UHF to fulfill its mission due to scintillation effects. In fact, even at 4 GHz the worst-case scenarios exhibit peak-to-peak fading greater than 9 dB over periods of hour or longer in the equatorial anomaly region. The virulence of equatorial scintillation has been examined by Basu and Basu [1981]. A general discussion of the scintillation phenomenon may be found in previously cited handbooks [Jursa, 1985; Flock, 1987], and reviews of the subject have been prepared by Aarons [1982] and Liu and Franke [1986]. The overall morphology is now fairly well established, although details remain to be clarified. Basu et al. [1985, 1988] have summarized the equatorial and high-latitude data in statistical form for both solar maximum and minimum conditions. The areas of main importance of this effect are given in Fig. 4-19.

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