TY - JOUR

T1 - Generalized Schumann and variation moment methods used for the determination of the equatorward boundary of the ultra-energetic relativistic electron precipitations into the auroral middle atmosphere

AU - Remenets, George F.

AU - Astafiev, Aleksandr M.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this paper, we present (i) the comparison of a solution accuracy of an inverse VLF problem for very low frequency (VLF) wave propagation (10–16 kHz) in the “Earth – sporadic Ds layer of atmosphere ionization” as estimated by three different methods of eiganvalue calculation and (ii) an estimation of latitude uncertainty for the equatorward (southern) boundary of Ultra-energetic Relativistic Electron (URE) precipitations into the middle polar atmosphere. The uncertainty for 1982–1987 years was caused by the different years, seasons, months, hours of daytime and electric conductivities of ground surface. Sporadic Ds layer was caused by the URE precipitations with the electron energies about 100 MeV into the polar region of atmosphere with a geographical latitude range 63–67 N degrees. The results of application of new accurate generalized Schumann (GS) method and of the approximate variation moment (VM) method used for an eigenvalue problem were compared with the results of another accurate method in which the Ricatti nonlinear equation (RNLE) was used. Comparison has been performed for the values of one (main) eigenvalue of a transversal operator for the corresponding model waveguide and for the determined positions of the URE precipitation equatorward boundary, the eigenvalue was being a function of the disturbance time. This comparison provides an estimation which method is preferable during simultaneous observations and analysis of a geophysical disturbance. In the second part of the study, the influence of the electrical conductivity in the waveguide model on the accuracy of equatorward boundary determination for the 16 kHz radio path “England – Kola peninsula” was analyzed, based on the data from the fixed location of two sources (in North Norway and in England) and a receiver (on Kola Peninsula) of the radio signal. It was shown that the uncertainty introduced by different values of the ground conductivity was 2–3 times less than the differences in the boundary position between different events under study.

AB - In this paper, we present (i) the comparison of a solution accuracy of an inverse VLF problem for very low frequency (VLF) wave propagation (10–16 kHz) in the “Earth – sporadic Ds layer of atmosphere ionization” as estimated by three different methods of eiganvalue calculation and (ii) an estimation of latitude uncertainty for the equatorward (southern) boundary of Ultra-energetic Relativistic Electron (URE) precipitations into the middle polar atmosphere. The uncertainty for 1982–1987 years was caused by the different years, seasons, months, hours of daytime and electric conductivities of ground surface. Sporadic Ds layer was caused by the URE precipitations with the electron energies about 100 MeV into the polar region of atmosphere with a geographical latitude range 63–67 N degrees. The results of application of new accurate generalized Schumann (GS) method and of the approximate variation moment (VM) method used for an eigenvalue problem were compared with the results of another accurate method in which the Ricatti nonlinear equation (RNLE) was used. Comparison has been performed for the values of one (main) eigenvalue of a transversal operator for the corresponding model waveguide and for the determined positions of the URE precipitation equatorward boundary, the eigenvalue was being a function of the disturbance time. This comparison provides an estimation which method is preferable during simultaneous observations and analysis of a geophysical disturbance. In the second part of the study, the influence of the electrical conductivity in the waveguide model on the accuracy of equatorward boundary determination for the 16 kHz radio path “England – Kola peninsula” was analyzed, based on the data from the fixed location of two sources (in North Norway and in England) and a receiver (on Kola Peninsula) of the radio signal. It was shown that the uncertainty introduced by different values of the ground conductivity was 2–3 times less than the differences in the boundary position between different events under study.

KW - 100 MeV electron precipitation

KW - Eigenvalue problem

KW - Electric conductivity

KW - Equatorward (southern) boundary of precipitation

KW - Generalized Schumann method

KW - Ground surface

KW - Polar middle atmosphere

KW - Sporadic ionospheric layer

KW - Variation moment method

KW - Very low frequencies

UR - http://www.scopus.com/inward/record.url?scp=85057832659&partnerID=8YFLogxK

U2 - 10.1016/j.jastp.2018.11.019

DO - 10.1016/j.jastp.2018.11.019

M3 - Article

AN - SCOPUS:85057832659

VL - 182

SP - 186

EP - 193

JO - Journal of Atmospheric and Solar-Terrestrial Physics

JF - Journal of Atmospheric and Solar-Terrestrial Physics

SN - 1364-6826

ER -