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

6. Correspondence Between the Amplitude Characteristics of TEC Variations and Parameters of Local Irregularities of Electron Density

[35] The estimate of the relative amplitude dN/N of a local disturbance of the electron density is very important for physics of ionospheric irregularities (and also for calculation of statistical characteristics of transionospheric signals). The transition from the amplitude characteristics of TEC variations to values of dN/N is far from being simple.

[36] First, the amplitude of TEC disturbance dI demonstrates a strong aspect dependence because of the integral character of transionospheric sounding. The maximum amplitude dI corresponds to wave disturbances with the wave vector K perpendicular to the direction r of the LOS [Afraimovich et al., 1992], i.e., when the condition is fulfilled,

(3)

where a and q are the azimuth and the elevation angle of the wave vector K of TID, and a_s and q_s are the azimuth and the elevation angle of LOS.

[37] Aspect dependence of the amplitude of TEC disturbance is important in studying wave disturbances. Condition (3) limits the number of LOS for which reliable detecting of ionospheric irregularities on the background of noises is possible.

[38] Afraimovich et al., [1992] have shown that for the Gaussian distribution of the electron density, the amplitude of TEC disturbance M(g ) is determined by the aspect angle g between the K and r vectors and also by the ratio of the disturbance wavelength l to the half thickness of the ionization maximum D:

(4)

For the phase velocity od about 200 m s ^-1 and the period of about 1000 s, the wavelength l is comparable to the value of the half thickness D of the ionization maximum. At the values of the elevation angle q_s equal to 30^o, 45^o, and 60^o, the width of "the directivity diagram'' M(g) at the level of 0.5 is equal to 25^o, 22^o, and 15^o, respectively. If D exceeds the wavelength l by a factor of 2, the directivity diagram becomes narrower in width by 14^o, 10^o, and 8^o, respectively.

[39] The presence of magnetic field alters the picture of the motion transfer from the neutral gas to the electron component of the ionosphere. Since the magnetic field is not pulled by the neutral gas, the field lines may be considered as still. In this case, the approximation in which the motion of the electron component occurs only along the field lines with the velocity u cos y, where y is the angle between the vector of the magnetic field and the vector u of the neutral gas velocity, may be acceptable. Thus the amplitude of a disturbance of the electron density dN/N depends on the angular relations g and y between three vectors.

[40] However, in our case, because of averaging of the results over directions to different satellites and also because of large number of GPS stations over a vast territory where the values of g and y angles vary within a wide range, aspect effects are pronounced not so strongly as for some variations in TEC.

[41] Thus the relation between dN/N and dI/I may be presented in the form

(5)

where k_max is the maximum value of the transitional coefficient from dN/N to dI/I under optimum aspect conditions.

[42] We performed a modelling to evaluate the value of k_max. The model of TEC measurements developed by Afraimovich and Perevalova [2004] makes it possible to calculate spatial and time distribution of the local electron density N in the ionosphere along the LOS and then using the coordinates of the receiver and satellites to perform integrating N along the LOS with the given time step. As a result, time series of TEC similar to the input experimental data are obtained.

[43] The model of N takes into account vertical profile, diurnal and seasonal variations of the electron density governed by the solar zenith angle, and also irregular disturbance of N of smaller amplitude and spatial scales in the form of a superposition of propagating wave or isolated irregularities. The GPS satellite motion can be modelled by a few ways. A detailed description of the model was given by Afraimovich and Perevalova [2004].

[44] In this paper, diurnal and seasonal variations of N were neglected in the model calculations. A stationary isolated irregularity in the form of a sphere with radius R_d was chosen as a disturbance. The electron density within the irregularity smoothly decreases from the center to the periphery:

(6)

where A_d is the amplitude of the disturbance in the percent of the value N_max within the maximum of the F2 layer (i.e., A_d= dN/N ); x, y, z are the coordinates of the current point in the topocentrical coordinates system (TCS) connected to the GPS receiver; x_max, y_max, z_max are the TCS coordinates of the irregularity center (point M). It was taken that the irregularity is located at a height of the F2 layer maximum ( z_max=300 km). The position of the irregularity relative to the GPS receiver (i.e., the coordinate center of TCS) was governed by the elevation angle q and azimuth a of the radius vector of point M. Two cases were considered: q=45^o and q=60^o. In both cases, a=45^o. The radius R_d of the irregularity consequently was chosen to be equal 30, 100, and 300 km. That corresponded to the irregularities scales considered in the paper. The relative amplitude of the disturbance dN/N in all cases was assumed to be equal to 10%.

[45] The visual motion of the GPS satellite within the interval from 1200 to 1300 UT was given by the change in the azimuth a_S(t) of LOS from 0 to 90^o. The elevation angle q_S(t) remained constant. The calculations were performed for two trajectories: q_S=45^o and q_S=60^o. The trajectories were chosen in such a way that at one of them the LOS during the studied interval crossed the center of the electron density irregularity.

Figure 12

[46] The modelling results are shown in Figure 12. Figures 12a and 12e show the behavior of a_S(t). Figures 12b-12d and 12f-12h show the results of the calculations of TEC at q_S=45^o and q_S=60^o, respectively. The I₄₅ and I₆₀ TEC dependencies for the trajectories with q_S=45^o and q_S=60^o are shown by thick and thin curves. LOS corresponding to I₄₅ intersects the N irregularity center at the moment when a_S=45^o (on the left). LOS corresponding to I₆₀ intersects the irregularity center at the moment a_S=45^o (on the right).

[47] In the cases when LOS does not cross the irregularity N (thin line in Figure 12b and thick line in Figure 12f), TEC remains constant during the entire observational time. It should have been expected at the constant elevation angle q_S and the absence of the diurnal variations of N. A well-pronounced disturbance in the form of a single pulse in the TEC variations is well seen for the trajectories where LOS passes through the irregularity N. The width of the pulse is proportional to the irregularity radius R_d. The TEC maximum in the pulse is observed in the moment when the angle between LOS and radius vector of the center of the irregularity is minimal. It corresponds to a_S= a =45^o. This moment is shown in the Figure 12 by the dashed line.

[48] The absolute amplitude of a TEC disturbance dI depends on several factors. First, it is proportional to R_d, because the length of LOS interval laying within disturbed values of N at other equal conditions increases with an increase of the irregularity scale. Moreover, dI depends on the mutual position of the irregularity N and LOS. One can clearly see in Figures 12c, 12d, 12g, and 12h that the highest values of dI are reached when LOS passes through the irregularity center. Both the disturbance amplitude dI and TEC value I are also determined by the elevation angle of LOS and the amplitude of the disturbance N in the irregularity.

[49] The calculated values of the relative amplitude dI/I of TEC disturbance and of the coefficient k_max are shown in Table 2. Both parameters, as well as the values of dI and I, demonstrate considerable variability depending on the disturbance parameters, electron density, and measurements conditions.

[50] In the majority of cases, the value of k_max varies within 0-0.3. In the most favorable conditions of the registration, when LOS crosses the center of the N spherical irregularity, k_max = 0.5-0.6 (results 2 and 11 in Table 2). In this case the radius of the irregularity R_d=100 km is comparable to the half thickness of the F2 layer. The latter means that the TEC disturbance with the relative amplitude dI/I=5% can be caused by an electron density irregularity localized in the maximum of the F2 layer and having the relative amplitude dN/N not less than 10% and characteristic scale comparable to the half thickness of the F2 layer.