Multiscale Modeling of Cloud Dynamics

该项目从应用数学和计算数学的角度研究了湍流在云的发展和演变中的作用。理解云中细尺度和粗尺度之间的多尺度相互作用是一个根本性的挑战，从云滴和湍流(微米到米)到湍流上升气流(米到公里)。例如，这两个尺度在确定云反射了多少太阳辐射以及形成了多少降水(如果有的话)方面都是至关重要的。为了研究这些复杂的相互作用，首席研究员将使用多尺度渐近模型和随机模型，建立在他之前对这些方法的工作基础上。利用多尺度渐近模式，该项目的问题之一是粗尺度上升气流与来自云脉冲和热力的中尺度波动对水从低海拔向高海拔输送的影响。其次，利用随机模拟技术，目标是研究气溶胶和液滴尺寸分布(细尺度)与云量和寿命(粗尺度)之间的关系。为了模拟这些从微米到公里的尺度上的过程，首席研究员将使用随机模型来表示湍流和液滴演化之间的细尺度相互作用，然后将这些细尺度过程与湍流云上升气流的粗尺度确定性演化相结合。该项目将开发用于模拟云中水和能量传输的数学方法，这在天气预报、气候科学和空气污染中具有重要意义。目前，云层是气候变化预测中不确定性的主要来源，因为目前仍不清楚云层增加是会使地球降温(由于入射阳光的反射增加)，还是会使地球变热(由于云层储存和重新分配热能的能力)。此外，云与气溶胶和空气污染以各种方式相互作用，影响着当地的日常大气现象。对于这两个问题，云的不确定作用是由云尺度属性(如云量和云的寿命)和小尺度属性(如液滴尺寸分布和气溶胶粒子)的复杂相互作用决定的。该项目将使用现代数学技术来阐明这些问题。该项目支持的教育活动将把数学、云物理和气候科学联系起来，它们针对的是学生比例较高的高中，这些学生来自代表不足的群体。

The project investigates the role of turbulence in cloud development and evolution, from an applied and computational mathematics perspective. There is a fundamental challenge to understand multiscale interactions between fine scales and coarse scales in clouds, from cloud droplets and turbulence (micrometers to meters) to turbulent updrafts (meters to kilometers). Both scales are of key importance in determining, for instance, how much solar radiation is reflected by clouds and how much (if any) precipitation is formed. To study these complex interactions, the principal investigator will employ multiscale asymptotic models and stochastic models, building on his previous work with these methodologies. Using multiscale asymptotic models, one of the questions of the project is the effect of the coarse-scale updrafts versus the intermediate-scale fluctuations from cloud pulses and thermals on water transport from low altitudes to higher altitudes. Secondly, using stochastic modeling techniques in addition, the goal is to investigate relationships between aerosol and droplet-size distributions (fine scales) and cloud amount and lifetime (coarse scales). To model these processes across scales from micrometers to kilometers, the principal investigator will use stochastic models to represent the fine-scale interactions between turbulence and droplet evolution, and these fine-scale processes will then be coupled with the coarse-scale deterministic evolution of turbulent cloud updrafts.This project will develop mathematical methods for the modeling of water and energy transport in clouds, which is of fundamental importance in weather prediction, climate science, and air pollution. At present, clouds are a primary source of uncertainty in projections of climate change, since it is still unclear whether increased cloud cover will cool the planet (due to increased reflection of incoming sunlight) or heat it (due to the capacity of clouds to store and redistribute thermal energy). In addition, clouds interact with aerosols and air pollution in various ways, influencing day to day local atmospheric phenomena. For both of these issues, the uncertain role of clouds is determined by the complex interplay of both cloud-scale properties (such as cloud amount and lifetime of a cloud) and smaller-scale properties (such as droplet size distribution and aerosol particles). The project will use modern mathematical techniques to shed light on these questions. Educational activities supported by this project will connect mathematics, cloud physics, and climate science, and they are aimed at high schools with a large percentage of students from underrepresented groups.