Signal Frequency Dependence of Ionospheric Scintillations: An Indicator of Irregularity Spectrum Characteristics

Abstract

Multifrequency scintillation observations show that strong amplitude scintillations on very high frequency (VHF) signals are accompanied by weak L‐band scintillations near the dip equator and strong L‐band scintillations in equatorial ionization anomaly (EIA) region. For several decades this has been attributed to higher ambient plasma density in the EIA region. Recent work suggests that occurrence of stronger L‐band scintillations in the EIA region requires that the intermediate‐scale (~100 m to few km) ionospheric irregularity spectrum in this region be significantly shallower than that in the equatorial region. However, this has not been established so far. Signal frequency dependence of amplitude scintillations is characterized by the frequency exponent that determines the dependence on signal frequency of the S4 index: the standard deviation of normalized intensity fluctuations. In this paper, theoretical calculations of the frequency exponent for VHF and L‐band signals are carried out using different irregularity spectra and compared with observations in order to characterize power‐law irregularity spectra in different latitude zones. Intermediate‐scale irregularities in the equatorial and low‐latitude region, which are aligned with the geomagnetic field, are described by a two‐dimensional model. Model simulations show that the frequency exponent derived from S4 indices for VHF and L‐band signals is determined only by the characteristics of the irregularity spectrum and hence can be utilized to identify the nature of the power‐law irregularity spectrum. Frequency exponents computed using VHF and L‐band observations near the dip equator and EIA regions show distinct patterns, which clearly indicate steep and shallow irregularity spectra, respectively, in these regions.

Space Diversity Mitigation Effects on Ionospheric Amplitude Scintillation With Basis on the Analysis of C/NOFS Planar Langmuir Probe Data

“…It is well known that S 4 tends to saturate with increasing δNi and that the relationship between the two parameters begins to depart from linearity for S 4 ≈ 0.6, as observed in Figure 5a of Bhattacharyya et al (2017) and Figure 1a of Bhattacharyya et al (2019). The correct relationship between the two parameters for all scattering conditions is obtained by a computationally involved numerical solution of a parabolic equation satisfied by the fourth moment of the complex amplitude, as the signal propagates through the irregularity layer (Bhattacharyya et al, 2017(Bhattacharyya et al, , 2019. For the present purposes, a simple and approximate working model, guided by the results from the above references, has been alternatively implemented and used: (i) Equation 1 is accepted for S 4 ≤ 0.6; (ii) Equation 1 is used to determine δNi 0.6 and δNi 1.0 , at which S 4 = 0.6 and S 4 = 1.0, respectively; (iii) it is assumed that…”

“…Equation , resulting from the weak‐scatter theory, clearly indicates a linear dependence between S 4 and δNi , which is only valid for weak to moderate scintillation. It is well known that S 4 tends to saturate with increasing δNi and that the relationship between the two parameters begins to depart from linearity for S 4 ≈ 0.6 , as observed in Figure 5a of Bhattacharyya et al (2017) and Figure 1a of Bhattacharyya et al (2019). The correct relationship between the two parameters for all scattering conditions is obtained by a computationally involved numerical solution of a parabolic equation satisfied by the fourth moment of the complex amplitude, as the signal propagates through the irregularity layer (Bhattacharyya et al, 2017, 2019; Carrano & Rino, 2016).…”

“…It is well known that S 4 tends to saturate with increasing δNi and that the relationship between the two parameters begins to depart from linearity for S 4 ≈ 0.6 , as observed in Figure 5a of Bhattacharyya et al (2017) and Figure 1a of Bhattacharyya et al (2019). The correct relationship between the two parameters for all scattering conditions is obtained by a computationally involved numerical solution of a parabolic equation satisfied by the fourth moment of the complex amplitude, as the signal propagates through the irregularity layer (Bhattacharyya et al, 2017, 2019; Carrano & Rino, 2016). For the present purposes, a simple and approximate working model, guided by the results from the above references, has been alternatively implemented and used: (i) Equation is accepted for S 4 ≤ 0.6; (ii) Equation is used to determine δNi 0.6 and δNi 1.0 , at which S 4 = 0.6 and S 4 = 1.0, respectively; (iii) it is assumed that S 4 = 1.0 at [ δNi 1.0 + ( δNi 1.0 − δNi 0.6 )] = ( 2δNi 1.0 − δNi 0.6 ); (iv) the derivatives d S 4 / d (δNi) at δNi 0.6 and ( 2δNi 1.0 − δNi 0.6 ) are respectively equal to 0.6/ δNi 0.6 and 0; (v) a third‐degree polynomial is adjusted to the two points [ δNi 0.6 , S 4 = 0.6] and [(2 δNi 1.0 − δNi 0.6 ), S 4 = 1.0], considering the respective derivatives; and (vi) S 4 = 1.0 for δNi ≥ (2 δNi 1.0 − δNi 0.6 ).…”

“…For the present purposes, a simple and approximate working model, guided by the results from the above references, has been alternatively implemented and used: (i) Equation is accepted for S 4 ≤ 0.6; (ii) Equation is used to determine δNi 0.6 and δNi 1.0 , at which S 4 = 0.6 and S 4 = 1.0, respectively; (iii) it is assumed that S 4 = 1.0 at [ δNi 1.0 + ( δNi 1.0 − δNi 0.6 )] = ( 2δNi 1.0 − δNi 0.6 ); (iv) the derivatives d S 4 / d (δNi) at δNi 0.6 and ( 2δNi 1.0 − δNi 0.6 ) are respectively equal to 0.6/ δNi 0.6 and 0; (v) a third‐degree polynomial is adjusted to the two points [ δNi 0.6 , S 4 = 0.6] and [(2 δNi 1.0 − δNi 0.6 ), S 4 = 1.0], considering the respective derivatives; and (vi) S 4 = 1.0 for δNi ≥ (2 δNi 1.0 − δNi 0.6 ). As an initial test, the approximate working model has been applied to the input data adopted by Bhattacharyya et al (2017) and Bhattacharyya et al (2019) (namely, L = 50 km, L o = 10 km , ν = 2.0, z S = 35,786 km , z = 350 km, and f = 251 MHz) and the corresponding results displayed a reasonable agreement, for small zenith angles. The next section will display the curves S 4 (δNi) for the parameters, frequencies, and zenith angles used in the present contribution, which exhibit smooth transitions from the weak to the strong scattering and saturation regimes similar to those observed in Figures 7a, 7c, and 7e of the paper by Carrano and Rino (2016), for spectral indices less than 2.5.…”

“…As an initial test, the approximate working model has been applied to the input data adopted by Bhattacharyya et al (2017) and Bhattacharyya et al (2019) (namely, L = 50 km, L o = 10 km, ν = 2.0, z S = 35,786 km, z = 350 km, and f = 251 MHz) and the corresponding results displayed a reasonable agreement, for small zenith angles. The next section will display the curves S 4 (δNi) for the parameters, frequencies, and zenith angles used in the present contribution, which exhibit smooth transitions from the weak to the strong scattering and saturation regimes similar to those observed in Figures 7a, 7c, and 7e of the paper by Carrano and Rino (2016), for spectral indices less than 2.5.…”