On the Measurement and Potential Applications of Non-Rayleigh Signal Statistics to Studies of Clouds and Rain

雷达气象学的一个基本假设是，由云或雨等分布目标散射的波幅值的信号统计量可以用瑞利统计量准确地描述。这一假设在20世纪70年代首次在理论基础上受到挑战，随后在80年代出现了一些观测证据。在20世纪90年代，Jameson和他的合作者Kostinski发展了另一种理论基础来量化非瑞利统计对雷达测量的影响，并质疑非瑞利信号统计的早期观测证据，认为它建立在一个错误的物理模型的假设上。这项由两部分组成的拨款将把首席研究员的工作扩展到：1)从观测中量化非瑞利信号统计对雷达测量的影响程度和幅度；2)研究利用这种偏差的方法，以提高我们对所观察到的物理系统的理解。使用正常扫描程序，将收集来自不同雷达的时间序列数据，以记录与瑞利信号统计的偏差。在各种气象条件和扫描程序下的观测将使研究者能够探索雷达测量的幅度和潜在影响，以及表征和/或减轻这种影响的方法。在第二部分，PI将发展理论和测量方法，利用相关脉冲样本和非瑞利信号统计对雨中的聚类进行有用的观测，并探索在降水空间结构研究中的潜在应用，以期改进雨和/或雪演变的数值模型。更广泛的影响：这项工作的首要贡献将是提高我们对降水雷达测量不确定性的理解，其解释依赖于瑞利统计理论。测量中不确定度的表达对于定量应用（如降雨估计）至关重要。在大部分降水系统中，确实存在与瑞利统计理论偏差的条件，但它们对测量的影响尚未量化。

One of the basic assumptions in radar meteorology is that the signal statistics for the amplitudes of waves scattered by distributed targets such as clouds or rain are described accurately by Rayleigh statistics. This assumption was first challenged in the 1970's on a theoretical basis, with some observational evidence following in the 1980's. In the 1990's, Jameson and his collaborator Kostinski developed an alternative theoretical basis to quantify the impact of non-Rayleigh statistics on radar measurements, and questioned the earlier observational evidence for non-Rayleigh signal statistics, arguing that it rested on an assumption of an erroneous physical model. Work under this two-component grant will extend the principal investigator's work to 1) quantify, from observations, the extent and magnitude to which non-Rayleigh signal statistics impact radar measurements, and 2) investigate means to exploit such deviations to improve our understanding of the physical systems observed. Time-series data from different radars, using normal scanning procedures, will be collected to document deviations from Rayleigh signal statistics. Observations under a variety of meteorological conditions and scanning procedures will allow the investigator to explore the magnitude and potential effects on radar measurements as well as ways to characterize and/or mitigate the same. In the second component the PI will develop the theory and measurement approach for useful observations of clustering in rain using correlated pulse samples and non-Rayleigh signal statistics, and explore potential applications to the study of spatial structures in precipitation, with a view towards improving numerical models of rain and/or snow evolution. Broader Impacts: The foremost contribution of this work will be to improve our understanding of uncertainties in precipitation radar measurements, the interpretation of which rest on Rayleigh statistical theory. The expression of the uncertainty in the measurement is critical for quantitative applications such as rainfall estimation. Conditions under which deviations from Rayleigh statistical theory may be expected do exist in large parts of precipitation systems, yet their impact on the measurements have not been quantified.