Study on dual-polarization scattering characteristics of millimeter-wave nonspherical ice crystals
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摘要: 传统Mie散射理论基于球形粒子假设，难以精准描述大气非球形冰晶的散射行为，现有研究多局限于94 GHz单频率，缺乏毫米波/亚毫米波宽频段双偏振参数量化，制约偏振雷达气象探测精度。探究六角棱柱、六角平板等六种典型非球形冰晶在35、94、140、220 GHz的双偏振散射特性，量化差分反射率因子（ZDR）、线性退极化比（LDR）对粒子形状与取向的响应。采用离散偶极子近似法（DDA）、时域有限差分法（FDTD），结合XFDTD、HFSS验证。结果显示：除聚合体外，DDA计算后向散射截面与商用软件误差≤1.5 dB；小粒子（等效半径<100 μm）反射率对波长不敏感，大粒子呈形状相关共振且共振位置随波长右移；六角平板ZDR变化最广（9 dB至–9 dB），轴对称粒子LDR集中于–40 dB至–50 dB。双偏振参数可降低对粒子尺寸的依赖，提升宽频段冰晶识别精度，为毫米波/亚毫米波偏振雷达云微物理探测提供理论支撑。Abstract:
Background Traditional Mie theory, assuming spherical particles, is inadequate for characterizing the scattering of atmospheric non-spherical ice crystals. Existing studies are largely limited to single frequency (e.g., 94 GHz), lacking systematic quantification of key dual-polarization parameters across the millimeter/submillimeter wave spectrum, which constrains the accuracy of polarimetric radar for meteorological target detection and classification.Purpose This study aims to systematically investigate the dual-polarization scattering properties of six typical non-spherical ice crystals—hexagonal columns, plates, hollow columns, bullet rosettes, aggregates, and supercooled water droplets—across 35, 94, 140, and 220 GHz bands. It quantifies the responses of differential reflectivity (ZDR) and linear depolarization ratio (LDR) to particle shape and orientation, providing crucial theoretical support for wideband polarimetric radar meteorology.Methods Scattering models were developed using the Discrete Dipole Approximation (DDA) and Finite-Difference Time-Domain (FDTD) methods, cross-validated with commercial software (XFDTD, HFSS). Backscattering cross-sections, ZDR, and LDR were computed for different ice crystals across the frequency bands, analyzing the influence of particle size, geometry, and frequency.Results 1）The reliability of DDA was systematically validated across the 35–220 GHz range. Calculation errors for backscattering cross-sections were ≤1.5 dB for all particles except highly random aggregates. 2) Radar reflectivity factor showed a coupled wavelength dependence: small particles (equivalent radius <100 μm) were wavelength-insensitive (<1 dB difference), while large particles (>100 μm) exhibited significant shape-dependent resonance. The equivalent radius corresponding to resonance extrema increased with wavelength. 3) Characteristic ranges of ZDR and LDR for the six ice crystal types were quantified. Hexagonal plates showed the widest ZDR range (9 dB to –9 dB), while axisymmetric particles exhibited stable LDR values (–40 dB to –50 dB).Conclusions This wideband, multi-particle study addresses prior limitations in frequency coverage and parameter quantification. It demonstrates that the shape-sensitive ZDR and LDR parameters can reduce dependence on particle size distribution and significantly improve ice crystal identification accuracy, providing a key theoretical basis for millimeter/submillimeter wave polarimetric radar applications in cloud microphysics and meteorological target classification. -
图 1 在XFDTD软件中，六种非球形冰晶粒子的示意图
Figure 1. Schematic diagram of six nonspherical ice crystal particles in XFDTD
图 2 四个波长下六角棱柱和六角平板的雷达反射率因子
Figure 2. Radar reflectivity factors for four wavelengths for columns and plates
图 3 四个波长下中空六棱柱和子弹花环的雷达反射率因子
Figure 3. Radar reflectivity factors for four wavelengths for hollows and rosettes
图 4 四个波长下聚合体和过冷水滴的雷达反射率因子
Figure 4. Radar reflectivity factors for four wavelengths for aggregates and droxtals
图 6 六种冰晶粒子
$ {\text{Z}}_{\text{DR}} $ 随粒子旋转的变化Figure 6. Variation in
$ {\text{Z}}_{\text{DR}} $ with particle rotation for six ice crystal particles
图 7 六种冰晶粒子
$ {\text{R}}_{\text{LD}} $ 随粒子旋转的变化Figure 7. Variation in
$ {\text{R}}_{\text{LD}} $ with particle rotation for six ice crystal particles表 1 六种典型冰晶粒子的形状及其参数[17]
Table 1. Tab.1 Six common shapes of ice crystal particles and their parameters
geometric names geometric shapes axle ratio column 
$\begin{cases}a=0.35 L & (L<100 \mu m) \\ a=3.48 L^{0.5} & (L \geqslant 100 \mu m)\end{cases}$ (1) plate 
$\begin{cases}L=2 a & (a \leqslant 2 \mu m) \\ L=2.4883 a^{0.474} & (a \geqslant 5 \mu m) \\ L=2+\left(\left(2.4883 a^{0.474}-2\right) / 4\right) \cdot(a-1) & (2 \mu m<a<5 \mu m)\end{cases}$ (2) hollow 
$\begin{cases}a=0.35 L & (L<100 \mu m) \\ a=3.48 L^{0.5} & (L \geqslant 100 \mu m) \\ h=0.25 L & \end{cases}$ (3) rosette 
$\left\{\begin{array}{l}a=1.552 L^{0.63} \\ t=\dfrac{\sqrt{3} a}{2 \tan \alpha} \quad \alpha=28^{\circ}\end{array}\right.$ (4) aggregate 
$\begin{array}{ll}a_1=0.291 L_1 & a_2=0.323 L_2 \\ a_3=0.359 L_3 & a_4=0.381 L_4 \\ a_5=0.368 L_5 & a_6=0.352 L_6 \\ a_7=0.333 L_7 & a_8=0.312 L_8 \\ D=7.297 L_{\min } & \end{array}$ (5) droxtal 
$\begin{array}{ll}D=2 R & \\ a_1=R \sin \theta_1 & a_2=R \sin \theta_2 \\ L_1=R \cos \theta_1 & L_2=\cos \theta_2 \\ \theta_1=32.35^{\circ} & \theta_2=71.81^{\circ}\end{array}$ (6) 
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表 2 各毫米波频率下复折射率的拟合值
Table 2. The fitted values of the complex refractive index under each millimeter wave frequency
frequency/GHz complex refractive index/m 35 (8.6 mm) 1.7861 +0.0011i94 (3.2 mm) 1.7864 +0.0032i140 (2.1 mm) 1.7866 +0.0043i220 (1.3 mm) 1.7868 +0.0052i
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表 3 对比XFDTD、HFSS和DDA计算六种非球形冰晶粒子在94 GHz下的后向散射截面
Table 3. Comparison of XFDTD, HFSS, and DDA calculations for six types of non-spherical ice crystal particles at 94 GHz for backscattering cross section
particle shapes XFDTD/dBm2 HFSS/dBm2 DDA/ dBm2 column −86.82 −84.85 −86.75 plate −86.01 −85.63 −85.79 hollow −87.93 −85.83 −86.01 rosette −74.19 −75.77 −74.77 aggregate −66.26 −60.58 −62.85 droxtal −72.29 −69.86 −70.23
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