publication . Doctoral thesis . 2015

Elektromagnetische Modellierung von dynamischen statistischen Regenfeldern auf Tropfenskala

Hipp, Susanne;
Open Access English
  • Published: 08 Jun 2015
  • Publisher: Technical University of Munich
  • Country: Germany
Abstract
This work simulates the scattering of electromagnetic waves by a rain field. The calculations are performed for the individual drops and accumulate to a time signal dependent on the dynamic properties of the rain field. The simulations are based on the analytical Mie scattering model for spherical rain drops and the simulation software considers the rain characteristics drop size (including their distribution in rain), motion, and frequency and temperature dependent permittivity. The performed simulations provide results for rain field attenuation and scattering signal Doppler spectra. In dieser Arbeit wird die Streuung von elektromagnetischen Wellen durch Regen...
Subjects
free text keywords: Ingenieurwissenschaften, ddc:620
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Doctoral thesis . 2015
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59 references, page 1 of 4

2 Basic Electromagnetics 13 2.1 Maxwell's Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Gauge Transformations and Wave Equation . . . . . . . . . . . . . . . 15 2.4 The Homogenous Helmholtz Equation and its Solutions . . . . . . . . . 16

3 The Physical Structure of Rain 19 3.1 Rain Drop Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.1.1 Drop Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.1.2 Drop Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.1.3 Drop Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Rain Field Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2.1 Rain Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2.2 Rain Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2.3 Drop Size Distribution . . . . . . . . . . . . . . . . . . . . . . 27

4 Microwave Scattering in Rain Fields 29 4.1 Electromagnetic Scattering . . . . . . . . . . . . . . . . . . . . . . . . 29 4.1.1 Scattering Principles . . . . . . . . . . . . . . . . . . . . . . . 30 4.1.2 Polarisation of the Scattered Field . . . . . . . . . . . . . . . . 34 4.1.3 Scattering by Spheres . . . . . . . . . . . . . . . . . . . . . . . 36 4.1.4 Coherent and Incoherent Signal . . . . . . . . . . . . . . . . . . 39 4.2 Scattering by Statistical Rain Fields . . . . . . . . . . . . . . . . . . . 40 4.2.1 Calculation of Attenuation . . . . . . . . . . . . . . . . . . . . 40 4.2.2 Effective Refractive Index . . . . . . . . . . . . . . . . . . . . . 42 4.2.3 Multiple Scattering . . . . . . . . . . . . . . . . . . . . . . . . 45 4.2.4 Radiative Transfer . . . . . . . . . . . . . . . . . . . . . . . . . 45

5 Numerical Implementation Principles 55 5.1 Random Rain Field Generation . . . . . . . . . . . . . . . . . . . . . . 55 5.2 Calculation of the Scattered Field . . . . . . . . . . . . . . . . . . . . . 57 5.2.1 Mie Coefficients a and b . . . . . . . . . . . . . . . . . . . . . 57 5.2.2 π and τ Functions . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.2.3 Calculation of Field Sample for Step n . . . . . . . . . . . . . . 58 5.3 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.3.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.3.2 Creation of Drops . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.3.3 Volume Population . . . . . . . . . . . . . . . . . . . . . . . . 63 5.3.4 Drop Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6 Simulation Results 65 6.1 Time Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 6.1.1 Co-Polarisation . . . . . . . . . . . . . . . . . . . . . . . . . . 66 6.1.2 Cross-Polarisation . . . . . . . . . . . . . . . . . . . . . . . . . 71 6.2 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.3 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.3.1 Co-Polarised Statistics . . . . . . . . . . . . . . . . . . . . . . 77 6.3.2 Cross Polarised Statistics . . . . . . . . . . . . . . . . . . . . . 81 6.3.3 Statistics for Rain Varying from Drizzle to Monsoon . . . . . . . 84

7 Fokus on Past, Present and Future 89 7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 7.2 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A Scattering 93 A.1 Schematic to Solve the Helmholtz Equation . . . . . . . . . . . . . . . 93 A.2 Solution in Spherical Coordinates . . . . . . . . . . . . . . . . . . . . . 96 A.2.1 Calculations for Spherical Coordinates . . . . . . . . . . . . . . 101 A.2.2 Auxiliary Calculations for Spherical Coordinates . . . . . . . . . 111

E~i N~e1n = E0e−jx cos θ sin θ cos2 ϕn(n + 1) P1n(cos θ) jn(x ) x + cos θ cos2 ϕ d P1n(cos θ) Jn(x ) + sin2 ϕ P1n(cos θ) Jn(x ) ! dθ x sin θ x jn Zπ e−jx cos θjx cos θ d P1n(cos θ)

2n(n + 1) R0π 0 dθ

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Hipp, S., C. Chwala, U. Siart, T. F. Eibert, and H. Kunstmann (2010), “Modelling of Electromagnetic Scattering in Rain Fields for Precipitation Quantification”. Kleinheubacher Tagung. Miltenberg, Germany, Oct. 4-6, 2010.

Hipp, S., U. Siart, C. Chwala, T. F. Eibert, and H. Kunstmann (2011a), “Doppler Noise Modeling for Rain-Rate Obseravtion by Ground-Based Transmission Measurement”. 12th URSI Commission-F Triennial Open Symposium on Radio Wave Propagation and Remote Sensing. Garmisch-Partenkirchen, Germany, Mar. 8-11, 2011.

Hipp, S., U. Siart, C. Chwala, T. F. Eibert, and H. Kunstmann (2011b), “Dynamic Modelling of Atmospheric Microwave Transmission for Precipitation Quantification Using Mie Scattering”. English. 5th European Conference on Antennas and Propagation (EUCAP). Rome, Italy: IEEE, Apr. 11-15, 2011, pp. 3380-3383. ISBN: 978-1-4577- 0250-1.

Hipp, S., U. Siart, C. Chwala, T. F. Eibert, and H. Kunstmann (2011c), “Improved Numerical Efficiency for Modelling of Electromagnetic Attenuation and Noise from Rain Fields with Different Rain Rate”. Kleinheubacher Tagung. Miltenberg, Germany, Sept. 26-28, 2011.

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