Multiscale Modeling of Cloud Dynamics

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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.