3. Creation of an Alternate Model

[5]  The problem of revealing and description of the dependence of the modeled parameter on input conditions may be solved using different approaches. Currently three methods of solution of this problem are available. The first includes a statistical treatment of the experimental data and drawing of the electron concentration dependence on various input parameters in the table form or creating typical n_e vertical profile for the chosen characteristic conditions. This approach has its defects: low flexibility of the model, large averaging over the input parameters, and too approximate splitting of these parameters (for example, a simple separation of solar activity to "high" and "low"). The second method is based on description of the entire n_e(h) vertical profile which is some continuous function including as arguments such parameters as j, c, S, F_10.7 (or W ), and others. Any change in the arguments leads to a change in the entire profile.

[6]  The third method is based on representation of n_e values at some fixed height by a functional depending on different physical input parameters. Usually the functional is linear relative the input parameters and gives values of n_e at a fixed height as a sum of model functions each depending on one (more seldom, on several) input parameters. To obtain the general model, several such functionals (key points) with a fixed step (e.g., 5 km) are formed in such a way that the n_e behavior at these heights would most adequate represent the behavior of the entire n_e(h) profile. Some characteristic points (maximum, minimum, inflection point) may be also chosen as key point. Thus, for the same given input parameters, there are several different by height key points. Approximating these points by some polynomial one can obtain a continuous n_e(h) profile. In this paper we used the latter method of model creation. For each chosen height an expression was written, its coefficients being found by the multiple regression method.

[7]  The database of experimental data used in this paper consists of the measurements of n_e in middle and lower latitudes at undisturbed solar and geophysical conditions compiled by Nesterova and Ginzburg [1985] and Belikovich et al. [1983]. For the profiles for which in the databases there was no information on c, Kp, or F_10.7 the corresponding parameters were calculated on the basis of the geographical coordinates ( j, l ) and local time (LT). Obviously, erroneous profiles and profiles strongly different from the statistical series (the causes of the latter were, as a rule, disturbed conditions not indicated in the catalogs) were rejected. On the whole the database contained: 236 profiles obtained by rocket methods, 450 profiles obtained by the partial reflection method, and 59 profiles derived from the data on LF and VLF radio wave reflection (the A3 method) for the period 1948-1984. Because of the presence of considerable seasonal variations in n_e the data were split into three subsets corresponding to winter (November, December, January, and February), equinox (March, April, September, and October), and summer (May, June, July, and August). Assuming the existence of considerable longitudinal effects we split the data on n_e into three groups corresponding to the following longitudes: l = 340^o -100^o (Eurasia), l = 100^o -220^o (Oceania), and l = 220^o -340^o (America).

Figure 1

[8]  Since the main part of the database consists of the measurements conducted by two methods (rocket and PR) with different accuracy characteristics, a comparative analysis of these two groups was performed. Table 1 shows the values of log n_e and their standard deviations s for winter and summer. Figure 1 shows the values of D = log (n_e) _r - log(n_e) _pr for winter, summer, and equinox (in this case to increase the statistical reliability of the analysis results no separation on longitudes was done). One can see that below 67.5 km the values of D are comparable to and even higher than the standard deviations s. As far as we have no ground to prefer any of the considered methods, the further analysis was performed for h 70 km. (Thus the C layer is out of the further consideration). Moreover, the data of both groups above 67.5 km may be considered as coinciding only in equinoxes. In summer and winter the PR method gives, respectively, overestimated and underestimated values of n_e as compared to the data of rocket measurements. Nevertheless the discrepancies lie within the measurement errors. Therefore, analyzing the n_e dependencies on various solar and geophysical conditions, the data of rocket measurements and measurements by the PR method may be considered jointly as one database. One should note, however, that above 85 km in winter and equinoxes the discrepancy between the two methods begins to increase again. So to minimize the errors related to nonhomogeneity of the used data the range of the considered height was taken to be 70-85 km.