Scattering by Hail and Sleet Particles at Microwave and Millimeter Wave Frequencies

Abstract

Scattering by hail and sleet particles, prolate and oblate spheroids with axial ratios up to 1.8, is considered using the point matching technique. For computing, the truncated modal index and the recurrence relations are discussed. Numerical results, at 30 and 100 GHz, show that the extinction cross sections of the hail particles oscillate around twice the geometrical cross sections of the particles in the resonance region. It is found that the bistatic scattering and the back scattering depend strongly on the material components of the particles. The effects of the particle shape on the extinction cross section, the bistatic scattering cross section and the radar back scattering cross section are shown. INTRODUCTIONThe precipitation effects, scattering and attenuation, often cause problems [1][2][3][4][5] in the satellite-earth links. The effects of rain, especially rain scattering [6] in the forward and backward directions [7], have been investigating by several researchers. The Nordic countries, however, are suffering from other types of precipitation beside the rain. References [4,5,8] discuss the effects of the melting layer of precipitation. Some general discussions have also been presented on hail and sleet, but it is still necessary to develop a theoretical model. The Olympus beacons provide now a possibility to measure the attenuation and depolarization caused by hail and sleet. Now, the first stage of developing the theoretical model has been made.. The shape of hail and sleet particles is approximated to a spheroid. Because of the truncated modal index and the recurrence relations working likely, the fine computing of the extinction cross section, the bistatic scattering cross section and the radar back scattering cross section can be performed at 1-100 GHz by using the point matching technique [1]. The salient points of the computing, together with numerical results at 30 and 100 GHz are presented here. SCATTERING CROSS SECTIONS Consider, a hail or sleet particle is illuminated by a plane wave as shown in Fig 1. The scattered field can be expanded into a double series in terms of the spherical vector wave functions with the expansion coefficients found by the point matching technique [1]. The vector scattering amplitude, resulted from the scattered far field approximation, is also a double series in terms of the spherical harmonics [9] which are functions of the angles (9, 4) on the surface of a sphere. Based upon the vector scattering amplitude, the extinction cross section oe,, the bistatic scattering cross section 0rji (j refers to the received polarization while i refers to the incident one), and the radar back scattering cross section crb can be obtained. Symmetrical semiaxis a and the incident wave direction ki define the incident plane, while the scattering plane is determined by the incident wave direction k, and the scattering direction k,. The scattering angle, vertical incidence and side incidence are also shown in Fig 1. Vertical polarization, v, and horizontal polarization, h, are connec...

Bistatic scattering of microwave and millimeter wave by a melting layer of precipitation

“…cross section of a single melting snow particle [4]1, Q is a function of z [3], i and j represent the incident and received polarizations, respectively, ana (=0.325 cm) is the maximum equivolumetric radius of raindrop, aso and ks are two parameters connected to the density of the dry snow particle [3] and [4,9]. In a special case of 01 = 02 and O = 00, the effective radar reflectivity factor can be derived from equation (4).…”

Research and New Developments in Microwave Communications in Finland

“…Helsinki University of Technology and Finnish Meteorological Institute have made a very comprehensive study of attenuation effects of oxygen, watervapour, clouds, rain, melting layer and scintillation at frequencies from 10 to 57 GHz for ESA [7,8,9,10,11,12].…”