Polarimetric Emission of Rain Events: Simulation and Experimental Results at X-Band
<p>Shape of a raindrop for equivalent radii: 0.25, 0.50 … 3.25 mm.</p> "> Figure 1 Cont.
<p>Laws and Parsons equivalent radii distribution vs. rain rate (0.25 … 150 mm/h).</p> "> Figure 2
<p>Geometry of the scattering problem.</p> "> Figure 2 Cont.
<p>Scattering by a raindrop: Electric incident field propagates along <math display="inline"> <semantics> <mover accent="true"> <mi>z</mi> <mo>^</mo> </mover> </semantics> </math>, drop axis along <math display="inline"> <semantics> <mrow> <msub> <mover accent="true"> <mi>z</mi> <mo>^</mo> </mover> <mi>p</mi> </msub> </mrow> </semantics> </math>, α: drop canting angle (nutation), and β: angle between the azimuth of the direction of observation and the wind direction (precession).</p> "> Figure 3
<p>Scattering power patterns in the XZ plane for incidence from Z-direction (indicated by the arrow) at X-polarization, and different equivolumetric drop radii from 0.5 (inner curves) to 3.0 mm (outer curves) and frequencies: a) 1.4 GHz, b) 2.56 GHz, c) 10.68 GHz, d) 19.0 GHz, e) 22.0 GHz, f) 37.0 GHz, and g) 94.0 GHz. Plots normalized and in decibels, maximum value shown in each figure.</p> "> Figure 4
<p>Bistatic scattering power patterns in the XY plane of a Pruppacher-Pitter raindrop: Equivolumetric radius 3.0 mm, frequency 34.8 GHz. Polarizations of the incident and scattered waves are (a) vertical-vertical, (b) horizontal-horizontal, (c) vertical-horizontal, (d) horizontal-vertical.</p> "> Figure 5
<p>Real and imaginary parts of the amplitude scattering functions vs. raindrop radii at 13 GHz. Direction of propagation of the incident wave: <math display="inline"> <semantics> <mover accent="true"> <mi>x</mi> <mo>^</mo> </mover> </semantics> </math>, horizontal (<math display="inline"> <semantics> <mover accent="true"> <mi>y</mi> <mo>^</mo> </mover> </semantics> </math>) and vertical polarizations (<math display="inline"> <semantics> <mover accent="true"> <mi>z</mi> <mo>^</mo> </mover> </semantics> </math>). BEM solution (solid line) agrees well with Oguchi [<a href="#B15-remotesensing-01-00107" class="html-bibr">15</a>] (dotted line) for raindrops up to 3.25 mm radius. Rayleigh solution (dashed line) agrees with BEM solution up to 1 mm.</p> "> Figure 6
<p>Real and imaginary parts of the amplitude scattering functions vs. raindrop radii at 13 and 34.8 GHz. Direction of propagation of the incident wave: <math display="inline"> <semantics> <mover accent="true"> <mi>x</mi> <mo>^</mo> </mover> </semantics> </math>, vertical polarization (<math display="inline"> <semantics> <mover accent="true"> <mi>z</mi> <mo>^</mo> </mover> </semantics> </math>). BEM solution (solid line) shows an excellent agreement with Oguchi 1977 [<a href="#B17-remotesensing-01-00107" class="html-bibr">17</a>] (not shown), while Mie solution (dashed line) agrees only up to 1 to 1.5 mm radii.</p> "> Figure 7
<p>Meteorological data of a rain event date August 18, 1998, 0-12 h.</p> "> Figure 8
<p>Simulation results (left) and radiometric measurements (right). Date: August 18, 1998, 0-12 h.</p> "> Figure 8 Cont.
<p>Simulation results (left) and radiometric measurements (right). Date: August 18, 1998, 0-12 h.</p> ">
Abstract
:1. Introduction: Theoretical Formulation of the Polarimetric Emission by Rain
- Tv and Th are brightness temperatures at vertical and horizontal polarizations, respectively (Instead of Tv and Th, the first and second Stokes parameters are sometimes defined as I = Tv + Th, and Q = Tv-Th),
- TU and TV are the third and fourth Stokes elements, respectively,
- λ is the electromagnetic wavelength, η is the wave impedance, kB is the Boltzmann’s constant, and B is the radiometer’s bandwidth.
2. Computation of the Scattering by Raindrops Using the Boundary Element Method
- the Rayleigh approximation for small spheres in comparison with wavelength,
- the Mie expression for spheres whose size is comparable to wavelength, or
- optical approximation for spheres much larger than the wavelength.
2.1. Formulation of the Boundary Element Method (BEM)
2.2. BEM Applied to Raindrop Scatterers
2.3. Inter-Comparison between Scattering Methods
3. Polarimetric Emission of Rain Events
4. Conclusions
Acknowledgements
References and Notes
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Duffo, N.; Vall llossera, M.; Camps, A.; Corbella, I.; Torres, F. Polarimetric Emission of Rain Events: Simulation and Experimental Results at X-Band. Remote Sens. 2009, 1, 107-121. https://doi.org/10.3390/rs1020107
Duffo N, Vall llossera M, Camps A, Corbella I, Torres F. Polarimetric Emission of Rain Events: Simulation and Experimental Results at X-Band. Remote Sensing. 2009; 1(2):107-121. https://doi.org/10.3390/rs1020107
Chicago/Turabian StyleDuffo, Nuria, Mercedes Vall llossera, Adriano Camps, Ignasi Corbella, and Francesc Torres. 2009. "Polarimetric Emission of Rain Events: Simulation and Experimental Results at X-Band" Remote Sensing 1, no. 2: 107-121. https://doi.org/10.3390/rs1020107