Texture of Stochastic Processes in Physical and Radar Meteorology

正如大多数人每天所经历的那样，天气量，如不可预测的风速和风向变化或降雨量，每时每刻、从一个地方到另一个地方都有很大的变化。大气现象常常涉及这样一些量，它们的变化（波动）分布是未知的，尽管这些波动通常在时间和空间上是相关的。例如，感知到几滴雨通常意味着接下来会有更多的雨。随着公众认为气候变暖更加多变，极端天气更加严重，理解这些广泛变化和相关的现象现在比以往任何时候都更加重要。例如，在这种随机性的海洋中是否存在一种可识别的趋势？本项目将通过开发和应用一种能够检测这种微弱信号的统计分析方法来解决这一问题和相关问题，而无需对潜在分布做出任何假设。也就是说，理想的方法是不可知论而又节俭的。因此，本研究的总体目标是探索云和降水物理、雷达气象学和辐射传输中相关的、因而是间歇性和显著波动的作用。虽然有许多研究致力于研究这种波动的概率分布，但它们的小尺度空间和时间相关性或“结构”受到的关注较少。然而，这种纹理与重要的物理机制交织在一起，例如雨滴的碎片通过碎片的“诞生”或降雨的间歇性和“爆发”而导致更高的雨滴浓度。本研究的主要目的是在最近发现的基于秩和分布无关的纹理缺失方法（相同和独立分布过程或IID）的基础上研究这种小尺度纹理。这是具有科学意义的，因为明显的相关波动导致了一些罕见但重要的事件，如滴聚结。新开发的统计数据分析的秩-时间方法广泛适用，可能有助于识别气候数据的趋势，例如在过去~ 30年的卫星衍生光学深度数据的时间序列中可能出现的全球变暗。这项研究具有社会意义，因为它可能有助于提高气象雷达对降雨的探测范围，从而改善洪水和滑坡的预测。这项研究可能有助于解决一系列问题，从大气污染到仪器噪声诊断。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

As most people experience on a daily basis, weather quantities such as an unpredictably changing wind speed and direction or rainfall rate, vary a great deal from moment to moment and from one location to another. Atmospheric phenomena often involve such quantities whose distribution of variations (fluctuations) is not known although these fluctuations are typically correlated in time and in space. For example, sensing a few raindrops usually implies that more rain is to follow. Understanding such broadly varying and correlated phenomena is now more important than ever as the warming climate is perceived by public as more variable and weather extremes more severe. For example, is there a trend discernible in this sea of randomness? This project will address this and related questions by developing and applying a method of statistical analysis capable of detecting such weak signals, without making any assumptions about the underlying distributions. That is, the desired approach is agnostic yet parsimonious.Thus, the general goal of this research is to explore the role of correlated and, thereby, intermittent and pronounced fluctuations in cloud and precipitation physics, radar meteorology and radiative transfer. While much research has been devoted to studying probability distributions of such fluctuations, their small-scale spatial and temporal correlations or “texture” have received less attention. Yet, this texture is intertwined with important physical mechanisms such as fragmentation of raindrops causing higher drop concentration via the “birth” of fragments or intermittency and “burstiness” of rainfall. The primary objective of this research is to study such small-scale texture on the basis of a recently discovered rank-based and distribution-independent approach to the absence of texture (identical and independently distributed process or IID). This is of scientific significance because pronounced correlated fluctuations are responsible for rare yet important events such as drop coalescence. The newly developed rank-time method of statistical data analysis is broadly applicable and likely to help with discerning trends in climatological data such as a possible global dimming in time series of satellite-derived optical depth data, available for the last ∼ thirty years. This research is of societal relevance because of potential contributions to better detection range of rainfall with weather radar, resulting in improved flood and landslide prediction. The research is likely to contribute to a broad range of problems, from atmospheric pollution to instrumental noise diagnostics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.