• Українська
  • English
ISSN 2415-3400 (Online)
ISSN 1028-821X (Print)

RETRIEVAL OF RAIN INTENSITY BY SOLUTION OF INTEGRAL EQUATION OF SCATTERING IN THE CASE OF DOUBLE FREQUENCY SENSING

Linkova, AM
Organization: 

O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12, Proskura st., Kharkov, 61085, Ukraine
E-mail: gannalinkova@gmail.com

https://doi.org/10.15407/rej2017.03.023
Language: Russian
Abstract: 

Measurement of precipitation amount is of great inte-rest for solution of many practical problems of national economy
and agriculture. In this case, the inverse problem of recovering the rain intensity using radar methods is an incorrect problem of mathe-matical physics and is described by a nonlinear integral equation. An approach for solving the integral equation of the electromagnetic waves scattering by a polydisperse medium of water drops is considered by means of double frequency remote sensing in the microwave range. Numerical simulation for retrieval of rain intensity in the range of 1…30 mm/h is performed for operating wavelengths 0.82 and 3.2 cm. It is shown that the proposed approach permits to retrieve the rain intensity with an error less than 20 % for intensities > 5 mm/h and with an error up to 60 % for light rains (less than 5 mm/h).

Keywords: double frequency sensing, Fredholm integral equation of the first kind, radar, rain intensity, Tikhonov regularization

Manuscript submitted 22.08.2017
PACS 9260
Radiofiz. elektron. 2017, 22(3): 23-32

Full text (PDF)

References: 
  1. Zabreyko, P. P., Koshelev, A. I., Krasnosel'skiy, M. A., Mikhlin, S. G., Rakovshchik, L. S., Stetsenko, V. Ya., 1968. Integral equations. Мoscow: Nauka Publ. (in Russian).
  2. Rozenberg, V. I., 1972. Scattering and attenuation of electromagnetic radiation by atmospheric particles. Leningrad: Gidrometeoizdat Publ. (in Russian).
  3. Lavrentiev, M. M., Romanov, V. G., Shishatskiy, S. P., 1980. Ill-posed problems of mathematical physics and analysis. Мoscow: Nauka Publ. (in Russian).
  4. Morozov, V. А., 1987. Regular methods for solving the ill-posed problems. Мoscow: Nauka Publ. (in Russian).
  5. Twomey, S., 1996. Introduction to the mathematics of inversion in remote sensing and indirect measurements. New York: Dover Publ.
  6. Tikhonov, A. N., Arsenin, V. Ya., 1979. Methods for solving the ill-posed problems. 2nd ed. Мoscow: Nauka Publ. (in Russian).
  7. Shifrin, K. S., Zolotov, I. G., 1996. Spectral attenuation and aerosol particle size distribution. Appl. Opt., 35(12), pp. 2114–2124. DOI: https://doi.org/10.1364/AO.35.002114
  8. Walters, P. T., 1980. Practical applications of inverting spectral turbidity data to provide aerosol size distribution. Appl. Opt., 19(14), pp. 2353–2365. DOI: https://doi.org/10.1364/AO.19.002353
  9. Westwater, E., Cohen, A., 1973. Application of Backus-Gilbert inversion technique to determination of aerosol size distribution from optical scattering measurements. Appl. Opt., 12(6), pp. 1340–1348. DOI: https://doi.org/10.1364/AO.12.001340
  10. Ben-David, A., Herman, B., Regan, J., 1988. Inverse problem and the pseudoempirical orthogonal function method of solution. 1: Theory. Appl. Opt., 27(7), pp. 1235–1243. DOI: https://doi.org/10.1364/AO.27.001235
  11. Koner, P. K., Battaglia, A., Simmer, C., 2010. A Rain-Rate Retrieval Algorithm for Attenuated Radar Measurements. J. Appl. Meteor. Climatol., 49(3), pp. 381–393. DOI: https://doi.org/10.1175/2009JAMC2279.1
  12. Abshaev, M. T., Dadali, Yu. A., 1966. About the possibilities of microstructural studies of clouds and precipitation by radar methods. Trudy Vysokogornogo geophisicheskogo Instituta, 5, pp. 71–85 (in Russian).
  13. Linkova, A. M., Khlopov, G. I., 2016. Use of the exhaustive search of microstructure parameters of liquid precipitation for solving the inverse problems of recovering their intensity. Naukovi praci Ukrai'ns'kogo gidrometeorologichnogo instytutu, 269, pp. 41–48 (in Russian).
  14. Mardiana, R., Iguchi, T., Takahashi, N., 2004. A dual-frequency rain profiling method without the use of a surface reference technique. IEEE Trans. Geosci. Remote Sens., 42(10), pp. 2214–2225. DOI: https://doi.org/10.1109/TGRS.2004.834647
  15. Stepanenko, V. D., 1973. Radiolocation in meteorology. Lenin-grad: Gidrometeoizdat Publ. (in Russian).
  16. Gunn, R., Kinzer, G. D., 1949. The terminal velocity of fall for water droplets in stagnant air. J. Meteor., 6(4), pp. 243–248. DOI: https://doi.org/10.1175/1520-0469(1949)006<0243:TTVOFF>2.0.CO;2
  17. Van de Hulst, H. C., 1961. Light scattering by small particles. Translated and ed. from English by T. V. Vodop'yanova. Moscow: Inostrannaya literatura Publ. (in Russian).
  18. Aivazyan, G. M., 1991. Propagation of millimeter and submillimeter waves in clouds. Leningrad: Gidrometeoizdat Publ. (in Russian).
  19. Levin, L. M., 1961. A study on the physics of coarsely dispersed aerosols. Мoscow: AN SSSR Publ. (in Russian).
  20. Marshall, J. S., Palmer, W. M., 1948. The distribution of raindrops with size. J. Meteor., 5, pp. 165–166. DOI: https://doi.org/10.1175/1520-0469(1948)005<0165:TDORWS>2.0.CO;2
  21. Zhdanov, A. I., 2006. Introduction to the methods of solving the ill-posed problems: a tutorial. Samara: Izdatelsrvo Samarskogo gosudarstvennogo aerokosmicheskogo universiteta (in Russian).