Multiscale Modeling of Cloud Dynamics

该项目从应用和计算数学的角度研究湍流在云的发展和演变中的作用。从云滴和湍流（微米到米）到湍流上升气流（米到公里），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。例如，这两种尺度在确定云层反射了多少太阳辐射以及形成了多少降水（如果有的话）方面都至关重要。为了研究这些复杂的相互作用，首席研究员将采用多尺度渐近模型和随机模型，建立在他以前使用这些方法的工作基础上。利用多尺度渐近模式，该项目的一个问题是由云脉冲和热气流引起的大尺度上升气流与中尺度波动对从低空到高海拔的水输送的影响。其次，利用随机建模技术，研究气溶胶和液滴大小分布（细尺度）与云量和寿命（粗尺度）之间的关系。为了模拟从微米到公里的尺度上的这些过程，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精细尺度相互作用，然后这些精细尺度的过程将与湍流云上升气流的粗尺度确定性演化相结合。该项目将开发云中水和能量传输模型的数学方法，这在天气预报、气候科学和空气污染方面具有重要意义。目前，云是气候变化预估中不确定性的主要来源，因为目前尚不清楚增加的云量是使地球变冷（由于对入射阳光的反射增加）还是使地球变热（由于云储存和重新分配热能的能力）。此外，云以各种方式与气溶胶和空气污染相互作用，影响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特性（如云量和云的寿命）和较小尺度特性（如液滴大小分布和气溶胶颗粒）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，这些活动的目标是高中中有很大比例的学生来自代表性不足的群体。

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.