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是更好地理解水的动力作用及其对大气能量学的影响，这也是本次奖项的主题。更好的理解将有助于塑造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拯救人类生命，并更好地减轻数千亿美元的灾害损失。除了增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长的初级研究人员。为了使这些新的研究人员在未来取得成功，私人投资机构将提供指导，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和观测数据结合到数值算法中，以方程的形式解决大气动力学的数学描述。此外，除了天气预报本身，天气预报的用户还包括政府机构、保险业和其他企业。要评估与天气事件相关的风险及其影响，需要掌握数学和大气科学方面的技术技能。水的相变是水文循环的关键部分。对天气特别重要的是云内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，大气环流塑造了云型和降水的形成。水和大气流体动力学之间的这种耦合是非线性的，仍然是一个难以理解的挑战。颁奖活动旨在增进我们对湿润大气动力学与相变的数学和物理方面的基本理解，同时关注高降水事件。为了达到这一目的，我们将研究一系列偏微分方程组，以阐明这种流动的基本方面，例如：波浪对大尺度平衡流动的影响；动能、势能和势能之间的能量传递；以及非饱和和饱和流动区域之间的尖锐界面的传播。所使用的方法包括存在相变的波动动力学的渐近分析、构造不连续的解析解、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总是伴随着大量来自热带地区的水汽流向极地，比如被称为“大气河流”的结构。大气河流现象及其相关的喷流条纹是建议进行应用研究的中心观测之一。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.