Relative amplitude of the variations of the total electron...

3. Method of Data Processing

[10] The standard GPS technology provides a means for calculation of slant TEC I_s along line of sight (LOS) between GPS satellite and receiver based on phase measurements at each of spaced two-frequency GPS receivers. Data of phase measurements are contained in the RINEX files, available at ftp://sopac.ucsd.edu/pub/.

[11] A method of the TEC calculating was specified and validated in a series of publications [e.g., Afraimovich, 0]. We reproduce here only the final formula for phase measurements:

(1)

where L₁ l₁ and L₂ l₂ are additional paths of the radio signal caused by the phase delay in the ionosphere [m]; L₁ and L₂ represent the number of phase rotations at the frequencies f₁ and f₂; l₁ and l₂ stand for the corresponding wavelengths [m]; const is the unknown initial phase ambiguity [m]; and nL are the errors in determining the phase path [m].

[12] Phase measurements in the GPS can be performed with a high degree of accuracy corresponding to the error of TEC determination of at least 10¹³ m^-2 when averaged on a 30-s time interval, with some uncertainty of the initial value of TEC, however. Filtered out in the range of periods 30-60 min, the standard deviation of TEC series is not worse than 0.2 times 10¹³ m^-2.

[13] To normalize the response amplitude, we have converted "slant'' TEC I_s to an equivalent "vertical'' value I [Klobuchar, 1986]:

(2)

where R_z is the Earth's radius, h_max=300 km is the height of the F2 -layer maximum, and q_s is the elevations of the LOS.

[14] Then we selected continuous TEC series I(t) with a duration of about 2 hours from the obtained TEC data so that we had 22 overlapping time intervals with a 1-hour shift for the day. We used specified threshold of 30^o for elevations q_s to the GPS satellites. I(t) series for all GPS sites in the region under consideration and for all visible satellites were filtered in the timescale of 20-60 min and 2-10 min using running average filtering. Standard deviation s of TEC variations was calculated for each series. The s values were averaged on all series; thus we got for each 2 hours time interval the mean absolute values dI = [S s_i]/m, where i =1, 2, ldots , m; m is a total number of series. The dI represents an absolute value of the amplitude of TEC variations. The distribution of the number of series I_m over days is shown in Table 1. The total number of analyzing series is about 10⁶.

[15] The relative amplitude dI/I₀ is determined by normalization of the dI to the background I₀ value, where I₀ is the absolute vertical TEC obtained with 2-hour time resolution from the global TEC maps in the IONEX format (the so-called global ionospheric maps (GIM) [Mannucci et al., 1998]). The spatial range of GIM is 0-360^o in longitude and 90^oS-90^oN in latitude. The spatial resolution is restricted by the dimensions of an elementary GIM cell ( 5^o and 2.5^o in longitude and latitude, respectively). For the normalization, the I₀ values are used for the GIM cell closest to the GPS station used for determination of the dI value.

[16] The series I_m, dI_m, and dI/I_m were averaged over the chosen area to obtain the mean values of TEC langle I rangle , of the absolute amplitude langle dI rangle and of the relative amplitude langle dI/I rangle of TEC variations in the period ranges of MS and IS ionospheric irregularities.