5. Reconstruction of n_e(h) Profiles

[17]  The condition n_e/(2p f) 1 is fulfilled for the sounding signals in the E and F ionospheric regions It makes it possible to simplify considerably calculations of radio wave propagation. It was shown first numerously [Beynon and Jones, 1965; Titheridge, 1967] and later analytically [Vodolazkin et al., 1989a, 1989b] that the use of the linearized in terms of n_e absorption coefficient k in formula (5) makes it possible to obtain values which almost do not differ from the results of the full-wave theory. Therefore for the E and F regions expression (5) may be presented in the form

(13)

where K is the kernel which does not depend on the collision frequency.

5.1. E Layer

[18]  The determination of the effective collision frequency in this layer was performed to check the agreement between the gas-kinetic evaluations and the "point" (that is, related to a narrow height interval) empirical estimates [Danilkin et al., 1978]. To do this, the absorption measurements of "o" waves at two frequencies f₁=2 MHz and f₂=2.25 MHz were used. The absorption at the f₁ frequency and virtual heights of the "o" trace in the ionogram from the frequency interval including f₂ were the initial data for the determination of the h₀ and H parameters of the model (8). After restoration of the N(h) profile which was assumed to be applicable up to the reflection level h_r(f₂) of the second frequency, for this frequency the input into the absorption of the region h h_r(f₁) and the absorption D L(f₂) for the interval from h_r(f₁) to h_r(f₂) were calculated. Taking into account the linearized formula (13) the absorption was presented in the form [Danilkin et al., 1978]

where n_e is some mean value of the collision frequency over the height interval from h_r(f₁) to h_r(f₂) and G is the value depending for each observation point only on the working frequencies f₁ and f₂. The value of was easily estimated from the above formula. Because of regular diurnal variations of the electron concentration and also variations in solar activity the position of the interval D h = h_r(f₂) - h_r(f₁) also varied and that made it possible to study the vertical profile of the collision frequency.

Figure 3

Figure 4

[19]  The results of the determination at Rostov on Don for three seasons (spring, summer, and winter) of 1973 are presented in Figure 3. For the sake of comparison the results of the gas-kinetic calculations are also shown in Figure 4. One can see that a satisfactory agreement exists between the theory and experiment. Similar conclusions follow from the experimental estimates of n_e by Beynon and Jones [1965], Ganguly [1974], and Ganguly and Jain [1975]. The analysis of the specifics of the Appleton method showed [Vodolazkin et al., 1989a] that the results obtained on its basis are not reliable in the E layer. The error due to the errors in measurements of virtual heights reaches 100%. At the same time, similar estimates for the maximum of the F region should be taken into account because their errors are only a few tens of percents and do not cover the discrepancies between the theory and experiments.

5.2. Valley and F Region

[20]  The experimental n_e(h) profiles were determined in several stages. At the first stage simplified calculation schemes [Danilkin et al., 1975, 1976] of radio wave absorption measurements only of the ordinary polarization and only in the daytime were used. In all intervals between the adjacent levels of radio wave absorption h_i and h_i-1 the same approximation was accepted

(14)

For the height interval including the valley it gave at the bottom of the F region the collision frequencies below the gas-kinetic ones. Later on when it was found that empirical estimates of n_e cannot be less than the gas-kinetic ones, this model for the interlayer region was substituted by

(15)

with p>1 [Vodolazkin et al., 1983]. Therefore at the second stage the calculation of n_e(h) profiles was performed using the approximations (14) and (15). Using this method the [Vodolazkin et al., 1983] empirical model was created. It uses the data on the absorption of " o " waves obtained at 10 frequencies from the 2.00-6.25 MHz range during 1973 ( F_10.7=100). It manifests only the seasonal variations of n_e(h) below 200 km in the daytime. The model was obtained by an averaging of 51, 17, and 20, and 20 individual n_e(h) profiles for spring, summer, fall, and winter, respectively. The results are presented in Figure 4.

[21]  Restoration of individual n_e(h) profiles and their averaging showed that the discrepancy between the experiment and theory exists only in the F region, the empirical dependencies showing smaller vertical gradient. So a special method of calculations of n_e(h) profiles only in the F region was developed [Vodolazkin et al., 1979] for the model

(16)

The averaged results of the n_e determination for winter and summer of 1979 obtained on the basis of the measurements of the " o " waves absorption in the after dusk period are also presented in Figure 4. One can see that in the F region the empirical estimates of n_e exceed the gas-kinetic ones by a factor of 2-6 and more than by a factor of 10 in the daytime and at night, respectively. In the gas-kinetic calculations of n_e(h) for the given geophysical conditions one has to use model values of T_e and concentrations of the multicomponent atmosphere. They correspond to some average situation and for each particular case may have considerable differences, the latter fact leading to a large uncertainty in n_e(h). So rocket-ground-based experiments have been conducted. They had two goals. The main one was to obtain the data (concentration of electrons and neutral particles, and electron temperature) for the gas-kinetic calculations of the collision frequency. The second goal was to exclude the errors appearing at calculating of nonmonotonous N(h) profiles from the data of the ground-based vertical sounding (VS) and to check the accuracy of their reconstruction in the entire inner ionosphere.

Figure 5

Figure 6

[22]  It was shown in the rocket-ground-based experiments that the use of direct measurements of the needed parameters for gas-kinetic estimates in the F region does not eliminate the discrepancy between the theory and experiments. The discrepancy still takes place reaching an order of magnitude and more [Danilkin et al., 1989]. An example of the comparison of such results for one of rocket flights is presented in Figure 5 [Biryukov et al., 1980]. Thus, in the F region all experimental estimates of the collision frequency based on the VS by "o" waves exceed the gas-kinetic evaluations. The comparison of the rocket N(h) profiles to the profiles based on the VS data showed their satisfactory agreement [Danilkin et al., 1989] (see Figure 6). This means that reconstruction of n_e(h) profiles on the basis of only VS data does not introduce rough errors.