ELECTRON DENSITY PROFILE RECOVERY ACCURACY AND APPLICATION OF POLYNOMIAL APPROXIMATIONS IN THE FREQUENCY-AND-ANGULAR SOUNDING OF THE IONOSPHERE

• Дата: 2019
• Автор: Galushko, V. G.
• Формат: Стаття
• Мова: rus
• Опубліковано: Видавничий дім «Академперіодика» 2019
• Теми: ionosphere; electron density profile; oblique sounding; probe signal angles of arrival; polynomial approximation; ионосфера; профиль электронной концентрации; наклонное зондирование; углы прихода пробных сигналов; полиномиальная аппроксимация; іоносфера; профіль електронної концентрації; похиле зондування; кути приходу пробних сигналів; поліноміальна апроксимація
• Онлайн доступ: http://rpra-journal.org.ua/index.php/ra/article/view/1316
• Назва журналу: Radio physics and radio astronomy

PACS numbers: 94.20.Bb,94.20.TtPurpose: Analysis of the error in recovering the height profile of the electron density of the ionosphere by the frequency-andangular  sounding technique in  dependence  on the accuracy of measuring vertical plane angles of arrival of the probe signals and inexactness of  specifying the  propagation  path length. Development of algorithms for ionospheric diagnostics in the case of a limited number of the sounding frequencies on the basis of polynomial approximations of the sought for electron density profile or measured frequency-and-angular characteristic of the probe signals.Design/methodology/approach: To treat the inverse problem of recovering the ionospheric electron density profile, the standard method is applied for solving an Abel integral equation relating the sought for profile to frequency dependences of arrival angles of the probe signals propagating along oblique radio paths. The accuracy of the developed algorithm is analyzed with the use of the statistical theory of measurement error estimation.Findings: The error of recovering the electron density profile of the ionosphere by the frequency-and-angular sounding technique has been estimated in dependence on the accuracy of measuring the arrival angles of the probe signals and inexactness of specifying the propagation path length. Algorithms have been developed for ionospheric diagnostics in the case of a limited number of sounding frequencies, based on polynomial approximations of either the sought for electron density profile or the frequency dependence of the arrival angles of the probe signals.Conclusions: The ray optics technique is used within the isotropic plasma approximation to solve the inverse problem of oblique sounding of a plane stratified ionosphere in the integral formulation. The measured parameters are frequency dependences of the vertical plane angles of arrival of HF signals propagating along single-hop radio paths of moderate lengths (up to 1000 km). It is shown that to provide the accuracy of electron density profile recovering, comparable to the characteristics of modern ionosondes, the error in measuring the frequencyand-angular characteristics of the probe signals should not exceed 0.5 degree for path lengths 300 to 1000 km.The error of the method associated with inaccurate knowledge of the propagation path length is determined by the relative error of its specification. This fact makes it possible to use non-dedicated signals for frequency-and-angular sounding of the ionosphere, for example, emissions of modern HF broadcasting stations which, as a rule, are equipped by several transmitters (some of them by dozens) being located on areas of units of kilometers in size and radiate simultaneously at several carrier frequencies. For diagnostic links of several hundreds of kilometers in length it can be supposed that all transmitters of a given broadcast center are located at a single place. The error of recovering the electron density profile in this case will make a few tenths of a percent.For ionospheric diagnostics in the case of a limited number of sounding frequencies, algorithms for recovering the electron density height distribution  have  been  developed on the basis of polynomial approximations of either the sought for profile or the measured function.Key words: ionosphere, electron density profile, oblique sounding, probe signal angles of arrival, polynomial approximationManuscript submitted 19.06.2019Radio phys. radio astron. 2019, 24(3): 184-194REFERENCES1. REINISCH, B. W., HAINES, D. M., BIBL, K., GALKIN, I., HUANG, X., KITROSSER, D. F., SALES, G. S. and SCALI, J. L., 1997.  Ionospheric sounding in support of over-the-horizon radar. Radio Sci. vol. 32, no. 4, pp. 1681–1694. DOI: https://doi.org/10.1029/97RS008412. BRYUNELLI, B. E., 1988. Physics of the ionosphere. Moscow, Russia: Nauka Publ. (in Russian).3. GROZOV, V. P., NOSOV, V. E., KOTOVICH, G. V., KIM, A. G., MATYUSHONOK, S. M. and RATOVSKI, K. G., 2004. Comparison of basic parameters of  the ionosphere at a slightly oblique path with vertical sounding data. Geomagnetism i aeronomiya. vol. 44, no. 3, pp. 372–377. (in Russian).4. DAVIES, K., 1989. Ionospheric radio. London, United Kingdom: Peter Peregrinus Ltd. 5. REINISCH, B. W., 1996. Modern Ionosondes. In: H. KOHL, R. RÜSTER, and K. SCHLEGEL, eds. Modern Ionosphere Science. Katlenburg-Lindau, FRG: European Geophysical Society Publ., pp. 440–458.6. AFRAIMOVICH, E. L., 1982. Interference methods of ionospheric radio sounding. Moscow, Russia: Nauka Publ. (in Russian).7. GERSHMAN, B. N., ERUKHIMOV, L. M. and YASHIN, Y. Y., 1984. Wave phenomena in the ionosphere and space plasma. Moscow, Russia: Nauka Publ. (in Russian).8. REINISCH, B. W. and GALKIN, I. A., 2008. A new digisonde for research and monitoring applications. In: XXIX URSI GA Abstracts. Chicago, Illinois, USA, p. 131.9. GALUSHKO, V. G., 1991. On the possibility of frequencyangle sounding of the atmosphere. Radiophys. Quantum Electron. vol. 34, no. 7, pp. 689–691. DOI: https://doi.org/10.1007/BF0103960510. GALUSHKO, V. G., 1993. Restoration of the Ionosphere Electron Density Profile from the Data of Frequency-andAngular Sounding. In: XXIV URSI GA Abstracts. Kyoto, Japan, p. 323.11. GALUSHKO, V. G., YAMPOLSKI, Y. M. and REINISCH, B. W., 2000. Frequency-and-Angular Sounding of the Ionosphere with the Use of a DPS Receive System. In: Proceedings of the Progress in Electromagnetics Research Symposium (PIERS-2000). Cambridge, MA, USA, p. 603.12. GALUSHKO, V. G., 1997. Frequency-and-angular sounding of the ionosphere. Telecommun. Radio Eng. vol. 51, no. 6-7, pp. 1–6. DOI: https://doi.org/10.1615/TelecomRadEng.v51.i6-7.1013. GALUSHKO, V. G. and LITVINENKO, G. V., 2001. Recovering the three-dimensional structure of ionospheric electron density distribution by angular-and-frequency sounding. Radio Phys. Radio Astron. vol. 6, no. 3, pp. 222–229.  (in Russian).14. BELEY, V. S., GALUSHKO, V. G. and YAMPOLSKI, Y. M., 1995. Traveling ionospheric disturbance diagnostics using HF  signal  trajectory  parameter  variations. Radio Sci. vol. 30, no. 6, pp. 1739–1752. DOI: https://doi.org/10.1029/95RS0199215. GALUSHKO, V. G., BELEY, V.  S., KOLOSKOV, A. V., YAMPOLSKI, Y. M., REINISCH, B. W. and PAZNUKHOV, V. V., 2003. Frequency-and-angular HF sounding and  ISR  diagnostics of TIDs. Radio Sci. vol. 38, is. 6, id. 1102. DOI: https://doi.org/10.1029/2002RS00286116. GALUSHKO, V. G., KASCHEEV, A. S., PAZNUKHOV, V. V., YAMPOLSKI, Y. M. and REINISCH, B. W., 2008. Frequency-and-angular sounding of traveling ionospheric disturbances in the model of three-dimensional density  waves.  Radio Sci. vol. 43, is. 4, id. RS4013. DOI: https://doi.org/10.1029/2007RS00373517. PAZNUKHOV, V. V., GALUSHKO, V. G. and REINISCH, B. W., 2012. Digisonde observations of TIDs with frequency and angular sounding technique. Adv. Space Res. vol. 49, no. 4, pp. 700–710. DOI: https://doi.org/10.1016/j.asr.2011.11.01218. GALUSHKO, V. G., KASHCHEYEV, A. S., KASHCHEYEV, S. B., KOLOSKOV, A. V., PIKULIK, I. I., YAMPOLSKI, Y. M., LITVINOV, V. A., MILINEVSKY, G. P. and RAKUSA-SUSZCZEWSKI, S., 2007. Bistatic HF diagnostics of TIDs over the Antarctic Peninsula. J. Atmos. Solar-Terr. Phys. vol. 69, is. 4-5, pp. 403–410.  DOI: https://doi.org/10.1016/j.jastp.2006.05.01019. KRAVTSOV, Y. A. and ORLOV, Y. I., 1980. Geometrical optics of inhomogeneous media. Moscow, Russia: Nauka Publ.  (in Russian).20. TRICOMI, F., 1960. Integral equations. Moscow, Russia: Inostrannaya Literatura Publ. (in Russian).21. KRASNOV, M. L., KISELYOV, A. I. and MAKARENKO, G. I., 1976. Integral equations. Moscow, Russia: Nauka Publ. (in Russian).22. GORODETSKI, S. E., 1980. Radio transmitter devices for backbone radio communication. Moscow, Russia: Svyaz’ Publ. (in Russian).23. LIST OF HF TRANSMITTERS FOR RADIO BROADCAST [online]. [viewed  18.06.2019]. Available from: http://guzei.com/radio/sw_list.html24. MACDOUGALL, J. W. and LI, X., 2001. Meteor observations with a modern digital ionosonde. J. Atmos. Solar-Terr. Phys. vol. 63., is. 2-3, pp. 135–141.  DOI: https://doi.org/10.1016/S1364-6826(00)00143-725. RIETVELD, M. T., WRIGHT, J. W., ZABOTIN, N. and PITTEWAY, M. L. V., 2008. The EISCAT Tromsø Dynasonde. XXIX URSI GA Abstracts. Chicago, Illinois, USA, p. 132. DOI: https://doi.org/10.1016/j.polar.2008.02.00126. REILLY, M. H., 1985. Ionospheric true height profiles from oblique ionograms. Radio Sci. vol. 20, no. 3, pp. 69–72. DOI: https://doi.org/10.1029/RS020i003p0028027. ALPERT, Y. L., 1972. Electromagnetic wave propagation and ionosphere. Moscow, Russia: Nauka Publ. (in Russian).28. MAX, J., 1983. Methods and techniques of signal processing in physical measurements. Vol. 1: Basic principles and classical methods. Moscow, Russia: Mir Publ. (in Russian).29. TIKHONOV, A. N. and ARSENIN, V. Y., 1986. Methods of solving ill-posed  problems. Moscow, Russia: Nauka Publ. (in Russian).30. LAWSON, C. and HANSON, R., 1986. Solving least squares problems. Moscow, Russia: Nauka Publ. (in Russian).31. PRUDNIKOV, A. P., BYCHKOV, Y. A. and  MARICHEV, O. I., 1981. Integrals and series. Moscow, Russia: Nauka Publ. (in Russian).