6. Conclusions

[28]  Concluding, we emphasize once more that the estimation of the accuracy of numerical simulation of the N distribution in LREI is a rather complicated problem. It may seem that the simplest way to determine the error D N is a comparison of the N simulation results to its values measured by rockets. However, the errors in measurements of local values of N during the first tens of seconds after an explosion may reach unacceptably large values (up to an order of magnitude) due to the increase in the radiation level (if probe methods of measurements are used) and the medium nonstationarity along the radio wave propagation path (if the dispersion interferometer is used).

[29]  In these conditions a special attention should be drawn to the measurement methods based on radiolocation of the ionospheric plasma and analysis of the parameters of radio wave propagating in the ionosphere [see, e.g., Al'pert, 1972; Galkin et al., 1971]. It is worth noting that many very popular methods (the methods of pulse radiosounding, partial reflection, incoherent scatter and others) are not acceptable for studying LREI at t 100 s after the explosion due to the high level of the radio wave absorption. In the short-wave range (used for radiophysical measurements of the medium parameters) at the first seconds after the explosion according to equation (1) the condition e' e'' is fulfilled in LREI. In this case it is impossible to find if the exponential depletion of the field is due to the absorption or to the exit into the caustic shadow. Irregularity of the absorption in such medium initiates the emission diffusion into the regions with the stronger absorption [Kravtsov, 1967]. One can show that the trajectory of the electromagnetic energy of the SW range waves in LREI is influenced by the distribution in it of not only real but imaginary part of the plasma permeability as well.

[30]  It follows from the performed studies that the conditions of radio wave propagation though LREI are mainly determined by the attenuation. Therefore evaluating the accuracy of the N numerical simulation in the lower ionosphere one should concentrate attention on methods of absorption measurements. Such methods are [Galkin et al., 1971] the method of the vertical sounding of the ionosphere (A1), method of registration of the extraterrestrial sources (A2), method of registration of the field strength of the signal from a remote radio station operating in permanent regime (A3), and others. We note that the A1 method is not acceptable for measurements of the radio wave attenuation in LREI because of a high level of the attenuation and the most suitable and often used is the A2 method (see, for example, the review by Belikovich and Benediktov [1969]).

[31]  The remote measurements of the N(h) vertical profile within LREI on the basis of the absorption d w measured by the A2 method are based on the solution relative to N(h) of integral equation (25). Belikovich et al. [1964] reduced equation (25) to the Fredholm equation of the first type with the residual kernel and obtained a general formula for calculation of N(h) from the d (w) curve. It follows from this solution that to find N at some height h_i, it is enough to know n _eff, dn _eff/dh and the attenuation function d (w) with its frequency derivatives w = n _eff(h_i). To obtain the N(h) profile within the height interval h=40-80 km one has to have measurements of these values in the frequency range from a few megahertz to hundreds of megahertz. Unfortunately, there are no experimental values of the radio wave absorption in the needed amount and with acceptable accuracy [Belikovich and Benediktov, 1973; Zhulin, 1964].

[32]  At the same time, the available measurements of attenuation at various frequencies make it possible not only to estimate the errors of the simulation results of the absorption in LREI but to check the errors in simulation of N. Actually, the errors in measurements of radio wave attenuation D d/ d are of a few percent [see, e.g., Belikovich and Benediktov, 1973, Figure 1], so we principally are able to control the errors in the attenuation calculations with very high accuracy. Using the algorithm developed above (the methodical error of which does not exceed a few percent), we may the entire discrepancy between the calculated and measured values of the attenuation explain by the error in N simulation in the conditions of SNE. At the same time, asymptotic estimates (27) show that at correct enough approximation of the values of n _eff(h) (see curve 2 in Figure 4) the relative error D N/N D d/ d . Thus the method of attenuation measurements used during the experimental SNE makes it possible to check the error in simulation of N with the accuracy of a few percent. However, as far as the radio wave absorption within LREI is determined by integral (25), to provide such error in simulation of the N(h) profile one needs the corresponding accuracy of agreement between the simulation results and the measured values of attenuation within the entire frequency range (from a few megahertz to a thousand and more megahertz). For the frequencies from a few megahertz to hundreds of megahertz one has to take into account fairly correctly the level of the synchrotron radioemission of the high-energy electrons of the artificial radiation belt formed during SNE [Peterson, 1967; Zhulin, 1964].

[33]  It has been mentioned above that the results of the numerical simulation of N in the frequency range from 100 to 1000 MHz [Kozlov, 1967, 1971; Kozlov and Kudimov, 1969; Kozlov and Raizer, 1966] have an error of tens of percent. For the lower boundary of this range the calculated values of the attenuation by 50-90% exceed the experimental values. For the upper boundary the simulation results are by about the same value lower than the experimental data. Therefore the N(h,t) profile from Kozlov [1967, 1971], Kozlov and Kudimov [1969], and Kozlov and Raizer [1966] strictly speaking is not able to explain the frequency dependence of d (w) in the frequency range from a few megahertz to 1000 MHz obtained experimentally.

[34]  For the sake of objectivity, one has to note that during the recent years a series of papers has appeared [Kozlov, 1987a, 1987b; Kozlov et al., 1982, 1988, 1990; Smirnova et al., 1984; Vlaskov et al., 1983]. These papers in our opinion make it possible to improve considerably the method of numerical simulation of the spatial-time distribution of N in LREI of SNE and achieve an agreement between the simulation results and experimental data in the entire frequency range. The decrease of the considered interval down to a few megahertz provides a need to study the electron-ion balance kinetics of the ionosphere disturbed by the explosion up to F region heights [see, e.g., Dyadichev and Kozlov, 1976]. Development of a specified mode on the basis of these publications requires more attentive choice of the reaction rate constants currently determined within a rather broad interval, specification of the initial data on the explosives, atmospheric state etc. Specifying this model in the regions located at the periphery of the direct visibility from the explosion point, one should consider in more detail the problem of propagation of penetrating radiation in the inhomogeneous atmosphere [Lobolev, 1997a, 1997b; Kukhtevich and Mashkovich, 1979]) and provide taking into account the voluminous character of this radiation source and its motion in space.