集合雪花的雷达散射
Radar scattering by aggregate snowflakes
摘要：
利用瑞利-甘斯理论计算了真实聚集雪花的雷达散射特性。我们发现，雪花的几何形状对散射的影响可以描述在一个单一的通用功能，这只取决于聚集体的整体形状，而不是组成薄片的原始冰晶的几何形状或大小。这个函数在小尺寸时可以用一个简单的解析表达式很好地近似;对于较大的雪花，我们用一条曲线拟合我们的数值数据。然后，我们演示了如何允许一个特性的雪花半径来自双波长雷达测量的原始晶体的大小或习惯的知识，而在同一时间显示，这个细节是至关重要的使用这些数据来估计冰水含量。我们还表明，“有效半径”，表征颗粒体积投影面积的比例，不能推断出从双波长雷达数据的聚合物。最后，我们考虑的误差近似雪花的“空气-冰球体”，并表明，对于足够小的聚集预测的双波长比通常同意在几个百分点之内，提供一些照顾，在选择球的半径和空气-冰混合物的介电常数;在更大的尺寸下，雷达变得对颗粒形状更敏感，并且发现与球体模型相关联的误差相应地增加。
英文摘要：
The radar scattering properties of realistic aggregate snowflakes have been calculated using the Rayleigh-Gans theory. We find that the effect of the snowflake geometry on the scattering may be described in terms of a single universal function, which depends only on the overall shape of the aggregate and not the geometry or size of the pristine ice crystals which compose the flake. This function is well approximated by a simple analytic expression at small sizes; for larger snowflakes we fit a curve to our numerical data. We then demonstrate how this allows a characteristic snowflake radius to be derived from dual-wavelength radar measurements without knowledge of the pristine crystal size or habit, while at the same time showing that this detail is crucial to using such data to estimate ice water content. We also show that the `effective radius', characterising the ratio of particle volume to projected area, cannot be inferred from dual-wavelength radar data for aggregates. Finally, we consider the errors involved in approximating snowflakes by `air-ice spheres', and show that for small enough aggregates the predicted dual wavelength ratio typically agrees to within a few percent, provided some care is taken in choosing the radius of the sphere and the dielectric constant of the air-ice mixture; at larger sizes the radar becomes more sensitive to particle shape, and the errors associated with the sphere model are found to increase accordingly.
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