2. Method of Atmospheric Parameter Determination

[11]  The specifics of measurements of the signals scattered back by API was described by earlier authors [see, e.g., Belikovich et al., 2002b].

2.1. Method of Measurements

[12]  The experiment was conducted in the following way. The measurements were conducted with a period of 20 s. During the first 3 s the powerful transmitters of the Sura facility were operated, creating artificial periodical irregularities. The effective power of the emission was 150 MW. Then the transmitters were switched to the pulse regime to sound API in the process of their relaxation. During 3-5 s the signals backscattered by API were registered by the partial reflection installation. The pulse duration was 20 or 50  m s, their repetition frequency was 50 Hz, and the bandwidth of the receiver was 40 kHz. The impact on the ionosphere was realized by the extraordinary radio wave at frequencies 5.67 or 5.6 MHz. With the same frequency and polarization the sounding of API and reception of the backscattered signals were conducted. The amplitude and phase of the scattered signals were registered.

[13]  In the observations in the early 1990s, the scattered signals could be registered from six heights at maximum with the vertical resolution of 3-5 km. In the recent experiments the receiving equipment was supplied by a rapidly operated automatic numerical transformer (ADT) and computer for reception and registration of the data. This made it possible to reach in registration a vertical step of 1.4-0.7 km and to improve by an order of magnitude the accuracy of phase and amplitude measurements.

[14]  The control of the general state of the ionosphere was provided by the automatic ionospheric station "Basis." The vertical sounding ionograms were recorded every 5 min.

2.2 Processing Method

[15]  The time dependence of the amplitude of the signal was approximated by the function ln A(t) = ln A₀ - t/t, where t is the time of API relaxation after the switching off the transmitter. At each height the amplitude of the signal was calculated using this formula. The parameters of the approximation were determined by the method of a simple linear regression with the weight function g = exp (-t/t₀), where t₀ is the first approximated value of t. Belikovich [1993] showed that such a procedure makes it possible to minimize the dispersion of the determined values. To determine the atmospheric parameters, the results of the measurements of the vertical profile of the relaxation time t were averaged over 5 or 10 min.

2.3. Determination of the Atmospheric Parameters

[16]  The temperature and density values were calculated using [Benediktov et al., 1993]

(1)

Here H is the scale height (it is derived from the height dependence of t (h ), k is the Boltzmann constant, M_i and M are the mean masses of ions and molecules, and b is the proportionality coefficient: n_im = b r /M, b = 0.38 10^-10 cm ³ s^-1 [see, e.g., Banks and Kockarts, 1973]. K = 2 p n(h)/L is the wave number of the standing wave, where L is its length in the vacuum and n(h) is the refraction coefficient. One can see from equation (1) that the relaxation time of API depends not only on the atmospheric parameters but on the electron concentration via the refraction coefficient of the standing wave. Since the electron concentration profile was not measured in these experiments, the variations in the refraction coefficient with height in the regular E region were taken into account using the electron concentration model [GOST, 1989]. To specify the N(h) profile, a correction was introduced based on the measurements by AIS (automatic ionospheric station) of the critical frequency f_oE: N =N _mod (f₀E/ f₀ E _mod)². Here the index "mod" indicates the model values.

Figure 1

[17]  Figure 1 shows an example of the dependence of the amplitude and relaxation time of the scattered at API signals on the height between 95 and 125 km on 15 June 2001 at 1834 UTC+4 (UTC+4 -- Coordinated Universal Time + 4 hours). The amplitude A is given in dB km^-1, and the relaxation time t is given in seconds. There is also presented the dispersion of the relaxation time (dashed curve). Figure 1 shows that between 100 and 113 km, A 40 dB, the value of t decreases exponentially with height and the dispersion is small. The dispersion rapidly increases above the 113 km level. In this case the altitude interval favorable for determination of atmospheric parameters lies between 101 and 113 km.

2.4. Complicating Factors and Errors of Atmospheric Parameter Determination

[18]  When there is a sporadic E_s layer, besides the atmospheric parameters, also the electron concentration increase in this layer as well as the changes in the ion composition influence the value of t. In particular, Figure 1 shows the increase of t between 95 and 100 km caused by the occurrence of E_s . (For the first time the increase of the relaxation time of API at altitudes where there is a E_s layer was detected while measuring the amplitudes of the signals backscattered by API in summer of 1996 [Belikovich et al., 1998].) The maximum in Figure 1 is caused, first of all, by the increase of ionization in the sporadic layer. Moreover, as one can see from relations (1) the ion composition (in particular, the increase of the portion of metal ions) influences the value of the relaxation time of API at E_s altitudes. Bakhmet'eva et al. (2004) evaluated the masses of metal ions in the observed sporadic E_s layers. As the amplitude of the scattered signals decreases with height, the signal-to-noise ratio also decreases and the error in measurements of the relaxation time grows, respectively.

[19]  In particular, Figure 1 visually shows the increase of the dispersion of the relaxation time above 120 km. This factor leads to a gradual increase in the error of the determination of A and t in the upper part of the studied interval. The measurement error in the lower part of the studied region may increase due to the influence of eddy motions because of a possible rising of the turbopause. To eliminate negative effects of all the above indicated factors on the accuracy of atmospheric parameters determination, a preliminary selection was performed. First, no data with a low signal-to-noise ratio were considered. Second, a criterion of an exponential decrease of the relaxation time t (h) with height was introduced to reduce the influence of the turbulence. Third, the data from the height interval where sporadic layers were observed were rejected.

[20]  The analysis of the errors in the temperature and density determination was performed. In the height interval 102-105 km the error in determination of the temperature and density did not exceed 10% and 15%, respectively, if the corrected model N(h) profile was used. Above ~110 km the error in the temperature and density determination may increase up to 20-25% both due to the decrease in the accuracy of relaxation time measurements and to the dynamics of the electron concentration in the upper part of the ionospheric E layer. Nearly similarly, the accuracy in the lower part of the studied interval may decrease at the presence of turbulence.