Scattering of a plane electromagnetic wave by axisymmetric rainsdrops /
This paper gives details of the analytical and numerical procedures used to solve the basic problem of the scattering of a plane electromagnetic wave by an axisymmetric raindrop. A nonperturbative solution is obtained by expanding the scattered and transmitted fields in terms of spherical vector wav...
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| author | 257393 Morrison, J. A. Cross, M. J. |
| author_facet | 257393 Morrison, J. A. Cross, M. J. |
| author_sort | 257393 Morrison, J. A. |
| collection | OCEAN |
| description | This paper gives details of the analytical and numerical procedures used to solve the basic problem of the scattering of a plane electromagnetic wave by an axisymmetric raindrop. A nonperturbative solution is obtained by expanding the scattered and transmitted fields in terms of spherical vector wave functions, so that Maxwell's equations are satisfied exactly in the regions exterior and interior to the raindrop, and by combining point matching with least-squares fitting to satisfy the boundary conditions on the surface of theraindrop with sufficient accuracy. Numerical results are presented for scattering by oblate spheroidal raindrops, with eccentricity depending on (and increasing with) drop size, for two orthogonal polarizations of the incident wave. The calculations were made at 4, 11, 18.1 and 30 GHz, in the case in which the direction of propagation of the incident wave is perpendicular to the axis of symmetry of the raindrop, which is of interest for terrestrial microwave relay systems. At 30GHz, the calculations were also made for the casein which the angle between the direction of propagation and the axis of symmetry is 70 degrees and 50 degrees, since different elevation angles are of interest for satellites systems. These basic results were summed earlier overthe drop-size distribution to calculate the differential attenuation and differential phase shift caused by rain, which are of importance in the investigation of cross polarization in radio communication systthe first-order perturbation approximation to the scattering by axisymmetric raindrops that are nearly spherical, which generalizes Oguchi's results for spheroidal raindrops with small eccentricity. Some simplifications that may be made in his formulas are pointed out. The perturbation results serve as a useful check on the least-squares-fitting procedure applied to spheroidal raindrops with small eccentricity. In addition, considerable improvement is obtained in the closeness of the perturbation results to the least-squares-fitting ones, in particular for the larger drop sizes, by perturbing about anequivolumic spherical raindrop, with appropriate perturbation parameter, rather than perturbing about an inscribed spherical raindrop, as did Oguchi. Similar comparisons were also made earlier for the rain-induced differential attenuation and differential phase shift, and these quantities were calculated approximately at frequencies up to 100GHz, using the results correspondingto perturbation about the equivolumic spherical raindrop. Yhe perturbation results are obtained quite inexpensively, whereas the least-squares-fitting procedure is very costly. |
| first_indexed | 2024-03-04T15:10:23Z |
| format | |
| id | KOHA-OAI-TEST:53922 |
| institution | Universiti Teknologi Malaysia - OCEAN |
| last_indexed | 2024-03-04T15:10:23Z |
| record_format | dspace |
| spelling | KOHA-OAI-TEST:539222020-12-19T16:58:50ZScattering of a plane electromagnetic wave by axisymmetric rainsdrops / 257393 Morrison, J. A. Cross, M. J. This paper gives details of the analytical and numerical procedures used to solve the basic problem of the scattering of a plane electromagnetic wave by an axisymmetric raindrop. A nonperturbative solution is obtained by expanding the scattered and transmitted fields in terms of spherical vector wave functions, so that Maxwell's equations are satisfied exactly in the regions exterior and interior to the raindrop, and by combining point matching with least-squares fitting to satisfy the boundary conditions on the surface of theraindrop with sufficient accuracy. Numerical results are presented for scattering by oblate spheroidal raindrops, with eccentricity depending on (and increasing with) drop size, for two orthogonal polarizations of the incident wave. The calculations were made at 4, 11, 18.1 and 30 GHz, in the case in which the direction of propagation of the incident wave is perpendicular to the axis of symmetry of the raindrop, which is of interest for terrestrial microwave relay systems. At 30GHz, the calculations were also made for the casein which the angle between the direction of propagation and the axis of symmetry is 70 degrees and 50 degrees, since different elevation angles are of interest for satellites systems. These basic results were summed earlier overthe drop-size distribution to calculate the differential attenuation and differential phase shift caused by rain, which are of importance in the investigation of cross polarization in radio communication systthe first-order perturbation approximation to the scattering by axisymmetric raindrops that are nearly spherical, which generalizes Oguchi's results for spheroidal raindrops with small eccentricity. Some simplifications that may be made in his formulas are pointed out. The perturbation results serve as a useful check on the least-squares-fitting procedure applied to spheroidal raindrops with small eccentricity. In addition, considerable improvement is obtained in the closeness of the perturbation results to the least-squares-fitting ones, in particular for the larger drop sizes, by perturbing about anequivolumic spherical raindrop, with appropriate perturbation parameter, rather than perturbing about an inscribed spherical raindrop, as did Oguchi. Similar comparisons were also made earlier for the rain-induced differential attenuation and differential phase shift, and these quantities were calculated approximately at frequencies up to 100GHz, using the results correspondingto perturbation about the equivolumic spherical raindrop. Yhe perturbation results are obtained quite inexpensively, whereas the least-squares-fitting procedure is very costly.This paper gives details of the analytical and numerical procedures used to solve the basic problem of the scattering of a plane electromagnetic wave by an axisymmetric raindrop. A nonperturbative solution is obtained by expanding the scattered and transmitted fields in terms of spherical vector wave functions, so that Maxwell's equations are satisfied exactly in the regions exterior and interior to the raindrop, and by combining point matching with least-squares fitting to satisfy the boundary conditions on the surface of theraindrop with sufficient accuracy. Numerical results are presented for scattering by oblate spheroidal raindrops, with eccentricity depending on (and increasing with) drop size, for two orthogonal polarizations of the incident wave. The calculations were made at 4, 11, 18.1 and 30 GHz, in the case in which the direction of propagation of the incident wave is perpendicular to the axis of symmetry of the raindrop, which is of interest for terrestrial microwave relay systems. At 30GHz, the calculations were also made for the casein which the angle between the direction of propagation and the axis of symmetry is 70 degrees and 50 degrees, since different elevation angles are of interest for satellites systems. These basic results were summed earlier overthe drop-size distribution to calculate the differential attenuation and differential phase shift caused by rain, which are of importance in the investigation of cross polarization in radio communication systthe first-order perturbation approximation to the scattering by axisymmetric raindrops that are nearly spherical, which generalizes Oguchi's results for spheroidal raindrops with small eccentricity. Some simplifications that may be made in his formulas are pointed out. The perturbation results serve as a useful check on the least-squares-fitting procedure applied to spheroidal raindrops with small eccentricity. In addition, considerable improvement is obtained in the closeness of the perturbation results to the least-squares-fitting ones, in particular for the larger drop sizes, by perturbing about anequivolumic spherical raindrop, with appropriate perturbation parameter, rather than perturbing about an inscribed spherical raindrop, as did Oguchi. Similar comparisons were also made earlier for the rain-induced differential attenuation and differential phase shift, and these quantities were calculated approximately at frequencies up to 100GHz, using the results correspondingto perturbation about the equivolumic spherical raindrop. Yhe perturbation results are obtained quite inexpensively, whereas the least-squares-fitting procedure is very costly.12PSZJBLElectromagnetic waves |
| spellingShingle | Electromagnetic waves 257393 Morrison, J. A. Cross, M. J. Scattering of a plane electromagnetic wave by axisymmetric rainsdrops / |
| title | Scattering of a plane electromagnetic wave by axisymmetric rainsdrops / |
| title_full | Scattering of a plane electromagnetic wave by axisymmetric rainsdrops / |
| title_fullStr | Scattering of a plane electromagnetic wave by axisymmetric rainsdrops / |
| title_full_unstemmed | Scattering of a plane electromagnetic wave by axisymmetric rainsdrops / |
| title_short | Scattering of a plane electromagnetic wave by axisymmetric rainsdrops / |
| title_sort | scattering of a plane electromagnetic wave by axisymmetric rainsdrops |
| topic | Electromagnetic waves |
| work_keys_str_mv | AT 257393morrisonja scatteringofaplaneelectromagneticwavebyaxisymmetricrainsdrops AT crossmj scatteringofaplaneelectromagneticwavebyaxisymmetricrainsdrops |