Effects of measurement and quantization conditions on informative parameters of raindrop echo signal

V. V. Zavolokin ; V. I. Tambovtsev

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 12 (2020) no. 1, pp. 63-72

Résumé

The physical and mathematical model of the echo signal reflected from cloud-rain systems was presented and substantiated. The algorithms for obtaining unbiased, efficient and consistent estimates of the first and second initial moments of raindrop echo signal were proposed. The estimation schemes of physical parameters of raindrop were proposed based on the reflected signal power estimation, such as induced dipole moment of a raindrop, attenuation during signal propagation along the spherical coordinate of the distance back and forth, and the parameters of the cloud-rain system, such as rain intensity, water content of the cloud-rain system. The correlation between the estimation of dielectric permittivity and conductivity of raindrops was shown. The relationship between the induced dipole moment of raindrops and the estimates of the dielectric permittivity and conductivity of raindrops is shown. This relationship is expressed through the relationship between the optical and electrical characteristics of raindrops. These relations make it possible to create and solve systems of algebraic equations for statistical estimates of the dielectric permittivity and conductivity of raindrops, based on previously performed estimates of the induced dipole moment of raindrops, which are obtained on the basis of statistical algorithms for generating consistent and unbiased estimates of the first and second moments of the rain echo. The relationship of estimation formation with measurement conditions that depend on the time of year and day is shown. The proposed statistical algorithms allow us to eliminate the bias of these estimates of physical parameters caused by three components: thermal noise of the receiver, echo signals received on the side lobes of the antenna and quantization noise. This makes these estimates not only unbiased, but also physically realizable. The formation of estimates based on the proposed algorithms assumes a truly coherent measurement system.

Détail

Keywords: signal power estimation of meteorological echo, numerical solution of meteorological goal equation, conductivity and dielectric permittivity of a raindrop, radiophysical and electrochemical problems.
Mots-clés : dipole moment of a raindrop, quantization noise

Bibliographie

[1] Zavolokin V.V., Zubkov V.A., Chepel' E.V., “Mathematical Model Construction of Meteorological Signals for Coherent Pulse Radar”, Voprosy radioelektroniki. Seriya: Radiolokatsionnaya tekhnika (RLT), 2008, no. 2, 129–136 (in Russ.)

[2] Doviak R.J., Zrnic D.S., Doppler Radar and Weather Observations, Academic Press Inc., Orlando–San Diego–San Francisco–New York–London–Toronto–Montreal–Sydney–Tokyo–São Paulo, 458 pp.

[3] Stepanenko V.D., Radiolocation in Meteorology (Radiometeorology), Gidrometeoizdat Publ., L., 1966, 351 pp. (in Russ.)

[4] Landsberg G.S., Elementary Textbook of Physics, v. 2, Electricity and Magnetism, Nauka Publ., M., 1985, 479 pp. (in Russ.)

[5] Sadovskiy I.N., Kuz'min A.V., Sharkov E.A., Sazonov D.S., Pashinov E.V., Asheko A.A., Batulin S.A., Analysis of Dielectric Permittivity Models of Aquatic Environment Used in Water Areas Sounding, Preprint Pr-2172, IKI RAN Publ., M., 2013, 60 pp. (in Russ.)

[6] Penskoy A.S., Waves in Waveguides in Terms of Polar Dielectric Films, Cand. phys. and math. sci. diss., Volgograd, 2016, 111 pp. (in Russ.)

[7] J.S. Marshall, W. Palmer, “The distribution of raindrops with size”, J. Meteorol., 5 (1948), 165–166

[8] Shishkin N.S., Pershina T.A., “Research on Mist Droplets Charging in Terms of Corona Discharges among Charged Large Droplets”, Tr. GGO, 1973, no. 302, 55–61 (in Russ.)

[9] Stalevich D.D., Uchevatkina T.S., “Change in Number of Raindrops Convergence during Precipitation”, Cloud Physics and Active Impacts, Proceedings of the order of the red banner of the main geophysical Observatory. A.I. Voeikov (GGO), 420, Gidrometeoizdat Publ., L., 1979, 3–14 (in Russ.)

[10] Gradshteyn I.S., Ryzhik I.M., Tables of Integrals, Sums, Series and Products, Fizmatgiz Publ., M., 1962, 1100 pp. (in Russ.)

[11] Tikhonov V.I., Statistical Radio Engineering, Radio i svyaz' Publ., M., 1982, 624 pp. (in Russ.)

[12] Pugachev V.S., Theory of Random Process and Its Application to Automatic Control Problems, Fizmatgiz Publ., M., 1960, 883 pp. (in Russ.)

[13] Venttsel' E.S., Probability Theory, Nauka Publ., M., 1969, 576 pp. (in Russ.)

[14] Balyasnikov B.M., Vorona M.S., Zavolokin V.V., Korshunov A.Yu., Maksimenko M.D., Odinochenko N.M., “A Mathematical model of the quantization of the signals reflected from expended spatial interference”, Proceedings of the Mozhaisky Military Space Academy, 633:2 (2011), 131–138 (in Russ.)

[15] Muchnik V.M., Physics of Thunderstorm, Gidrometeoizdat Publ., L., 1974, 351 pp. (in Russ.)

[16] Bondarenko T.G., “Some Data on Electrical Conductivity of Precipitation”, Trudy GGO, 1962, no. 134, 33–37 (in Russ.)

[17] Shirman Ya.D., Manzhos V.N., Theory and Processing Technology of Radar Data in Terms of Background Noise, Radio i svyaz' Publ., M., 1981, 416 pp. (in Russ.)

[18] Bean B.R., Dutton E.J., Radio Meteorology, Govt. Print. Office, Washington, U.S., 1966, 435 pp.