Atmospheric Dynamics with Phase Changes and Extreme Rainfall Events

大气中的水蒸气在极端天气事件中起着关键作用。世界科学界面临的一个紧迫挑战，也是本奖项的主题，是更好地理解水的动力作用及其对大气能量学的影响。更好的理解将有助于制定未来的社会和经济政策决策。特别是，更准确地预测极端降雨事件有可能挽救人类生命，并更好地减轻数千亿美元的灾害损失。除了促进对科学和数学的理解外，拟议的活动还支持培训具有跨学科专业知识的初级研究人员。为了使这些新的研究人员在未来取得成功，pi将提供指导，以发展将数学与大气科学相结合所需的知识、技能和经验。例如，现代天气预报依赖于将物理洞察力和观测数据结合到数值算法中，以方程形式解决大气动力学的数学描述。此外，除了天气预报本身，还有天气预报的用户，如政府机构、保险业和其他企业。为了评估与天气事件及其影响有关的风险，需要数学和大气科学方面的技术技能。水的相变是水循环的重要组成部分。对天气特别重要的是云层中从水蒸气到液态水的相变，以及随后降水的形成。这些相变释放的热量可以驱动大气环流，反过来，大气环流塑造了云模式和降水的形成。水和大气流体动力学之间的耦合是非线性的，并且仍然是理解的挑战。奖励活动的目的是提高我们对湿润大气动力学的基本理解，包括数学和物理方面的理解，特别是对高降水事件的关注。为了实现这一目标，我们将研究一系列偏微分方程，以阐明这种流动的基本方面，例如：波浪对大规模平衡流动的影响；动能、势能和势能之间的能量传递；以及非饱和流区和饱和流区之间尖锐界面的扩展。所采用的方法包括相变存在下的波动动力学渐近分析、不连续解析解的构造、基于能量原理和平衡关系的观测数据分析以及数值模拟。中纬度地区的极端降雨事件总是与源自热带的大量向极地流动的水汽有关，例如所谓的“大气河流”结构。大气河流及其相关的急流条纹现象是提出的应用研究的中心观测之一。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。

Water vapor in the atmosphere plays a critical role in extreme weather events. A pressing challenge for the world scientific community, and the topic of this award, is to better understand the dynamical role of water and its influence on atmospheric energetics. A better understanding would help shape future social and economic policy decisions. In particular, more accurate prediction of extreme rainfall events has the potential to save human lives, as well as to better mitigate hundreds of billions of dollars in disaster losses. In addition to advancing scientific and mathematical understanding, the proposed activities also support the training of junior researchers with interdisciplinary expertise. To position these new researchers for future success, mentoring will be provided by the PIs to develop the knowledge, skills and experience necessary for integrating mathematics with the atmospheric sciences. For example, modern weather prediction relies on incorporation of physical insight and observational data into numerical algorithms to solve the mathematical description of atmospheric dynamics in terms of equations. Furthermore, beyond weather predictions themselves are the users of weather predictions, such as government agencies, the insurance industry and other businesses. To assess the risks associated with weather events and their impacts, technical skills are needed in both mathematics and atmospheric sciences.Phase changes of water are a key part of the hydrological cycle. Of particular importance for weather is the phase change from water vapor to liquid water within clouds, and the subsequent formation of precipitation. The heat released from these phase changes can drive atmospheric circulations, and, conversely, atmospheric circulations shape the formation of cloud patterns and precipitation. This coupling between water and atmospheric fluid dynamics is nonlinear and remains a challenge to understand. The award activities aim to improve our fundamental understanding--both mathematical and physical--of moist atmospheric dynamics with phase changes, with attention to high precipitation events. To meet this aim, a hierarchy of partial differential equations will be studied in order to elucidate foundation aspects of such flows, such as: the influence of waves on large-scale balanced flows; the transfer of energy between kinetic, potential and latent energies; and the propagation of sharp interfaces between unsaturated and saturated flow regions. The methods to be used include asymptotical analysis of wave dynamics in the presence of phase changes, construction of discontinuous analytical solutions, observational data analysis based on energy principles and balance relations, and numerical modeling. Extreme rainfall events in the mid-latitudes are always associated with large poleward fluxes of moisture originating from the tropics, such as the structures called 'atmospheric rivers.' The phenomena of atmospheric rivers and their associated jet streaks are one of the central observations proposed for application studies.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.