The lower-order moments of the drop size distribution (DSD) have generally been considered difficult to retrieve accurately from polarimetric radar data because these data are related to higher-order moments. For example, the 4.6th moment is associated with a specific differential phase and the 6th moment with reflectivity and ratio of high-order moments with differential reflectivity. Thus, conventionally, the emphasis has been to estimate rain rate (3.67th moment) or parameters of the exponential or gamma distribution for the DSD. Many double-moment “bulk” microphysical schemes predict the total number concentration (the 0th moment of the DSD, or M₀) and the mixing ratio (or equivalently, the 3rd moment M₃). Thus, it is difficult to compare the model outputs directly with polarimetric radar observations or, given the model outputs, forward model the radar observables. This article describes the use of double-moment normalization of DSDs and the resulting stable intrinsic shape that can be fitted by the generalized gamma (G-G) distribution. The two reference moments are M₃ and M₆, which are shown to be retrievable using the X-band radar reflectivity, differential reflectivity, and specific attenuation (from the iterative correction of measured reflectivity Z_h using the total Φ_dp constraint, i.e., the iterative ZPHI method). Along with the climatological shape parameters of the G-G fit to the scaled/normalized DSDs, the lower-order moments are then retrieved more accurately than possible hitherto. The importance of measuring the complete DSD from 0.1 mm onwards is emphasized using, in our case, an optical array probe with 50 µm resolution collocated with a two-dimensional video disdrometer with about 170 µm resolution. This avoids small drop truncation and hence the accurate calculation of lower-order moments. A case study of a complex multi-cell storm which traversed an instrumented site near the CSU-CHILL radar is described for which the moments were retrieved from radar and compared with directly computed moments from the complete spectrum measurements using the aforementioned two disdrometers. Our detailed validation analysis of the radar-retrieved moments showed relative bias of the moments M₀ through M₂ was <15 % in magnitude, with Pearson’s correlation coefficient >0.9. Both radar measurement and parameterization errors were estimated rigorously. We show that the temporal variation of the radar-retrieved mass-weighted mean diameter with M₀ resulted in coherent “time tracks” that can potentially lead to studies of precipitation evolution that have not been possible so far.

中文翻译：

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使用CSU-CHILL X波段极化雷达检索液滴尺寸分布的低阶矩：一个案例研究

通常认为，液滴尺寸分布（DSD）的低阶矩很难从极化雷达数据中准确获取，因为这些数据与高阶矩有关。例如，第4.6矩与特定的微分相位相关，第6矩与反射率相关，而高阶矩的比率与微分反射率相关。因此，常规上，重点是估计DSD的降雨率（第3.67矩）或指数或伽马分布的参数。许多双重矩的“整体”微物理方案可以预测总数浓度（DSD的第0时刻，即M ₀）和混合比（或等效地，3次时刻中号₃）。因此，很难直接将模型输出与极化雷达观测值进行比较，或者很难将给定的模型输出与雷达观测值进行正向模型比较。本文介绍了如何使用DSD的双矩归一化以及由此产生的稳定内在形状，该形状可以通过广义伽玛（GG）分布进行拟合。两个基准时刻是中号₃和中号₆，其被示出为检索使用X波段雷达反射率，反射率差，以及特定衰减（从所测量的反射率的迭代校正Ž _ħ使用总Φ _{d p}约束，即迭代ZPHI方法）。GG的气候形状参数与按比例缩放/归一化的DSD拟合，然后可以比迄今更准确地检索低阶矩。 在我们的案例中，强调了从0.1毫米开始测量完整DSD的重要性，它使用分辨率为50  µm的光学阵列探头与约170  µm的二维视频测速仪搭配使用米的分辨率。这避免了小滴的截断，从而避免了低阶矩的精确计算。描述了一个复杂的多小区风暴的案例研究，该风暴穿越了CSU-CHILL雷达附近的仪器站点，为此从雷达中提取了力矩，并与使用上述两个测距仪从完整频谱测量中直接计算出的力矩进行了比较。雷达检索到的时刻的我们的详细验证分析显示时刻的相对偏差中号₀通过中号₂是<15 在幅度％，与Pearson相关系数> 0.9。雷达测量和参数化误差均经过严格估算。我们表明，雷达取回的质量加权平均直径随M ₀的时间变化会导致连贯的“时间轨迹”，这有可能导致迄今尚无降水研究。