Stieltjes Functions and Spectral Analysis in Sea Ice Physics

海冰物理中的 Stieltjes 函数和光谱分析

• 批准号: 2206171
• 负责人: Kenneth Golden
• 金额: $ 53.81万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2206171&HistoricalAwards=false
• 关键词: Stieltjes; Functions; Spectral; Analysis; Sea

Polar sea ice is a critical component of Earth's climate system. Precipitous losses of Arctic sea ice affect not only the polar marine environment, but can impact, for example, weather patterns, ocean currents, storm tracks, and precipitation amounts in the Northern Hemisphere. As a material, sea ice is a multiscale composite of pure ice with millimeter-scale brine inclusions and centimeter-scale polycrystalline microstructure. Even the ice pack itself is a granular composite of ice floes in a sea water host. A principal challenge in modeling sea ice and its role in climate is how to use information on small scale structure to find the effective or homogenized properties on larger scales relevant to process studies and coarse-grained climate models. Also of interest is the inverse problem of recovering parameters controlling small scale processes from large scale observations, such as in remote sensing. These central issues are addressed in this project by exploiting special mathematical properties of effective parameters that are common to several important problem areas in sea ice modeling. They include fluid and electromagnetic transport through sea ice, diffusion processes like heat flux enhanced by brine convection, and ocean surface waves in the ice pack. Sea ice shares close similarities with other naturally occurring and engineered composites. Our mathematical results on sea ice will give new insights and findings about other composite materials, and vice versa. This research will help to advance how sea ice is represented in climate models and improve projections of the fate of Earth's sea ice packs and the ecosystems they support. This project will also provide support, training, and research opportunities for undergraduate and graduate students. A powerful approach in the mathematical theory of homogenization is the analytic continuation method, which provides integral representations for the effective parameters of composite materials, treated as Stieltjes functions of their parameters. The complexities of composite microgeometries are distilled into the spectral properties of self-adjoint operators, like the Hamiltonian in quantum physics, which become random matrices when the system is discretized. Early applications of the method to sea ice focused on remote sensing and electromagnetic properties, with sea ice treated as a two-phase composite. Extensions of the method to polycrystalline media, advection diffusion processes, and surface waves through the ice pack have yielded only elementary bounds on the effective parameters, based on the coarsest information like the mass of a spectral measure in the integral, which is the brine volume fraction for sea ice as a two-phase composite, or the area fraction of ocean covered by ice floes for surface waves. However, exploiting deep parallels with random matrix theory descriptions of quantum physics brings Anderson transition concepts like field localization, mobility edges, eigenvalue repulsion, and band gaps into homogenization for classical transport in two-phase composites. In the funded work we will explore new insights that this approach can give us in the above problem areas, where the effective parameters are Stieltjes functions. For example, how do sea ice effective properties depend on crystal size and structure, can some ocean waves be localized by the ice pack geometry, and how does the fractal nature of composite geometry influence effective transport and spectral properties. This approach opens many questions of mathematical interest, while at the same time provides novel tools to address questions of critical importance in understanding sea ice processes in the rapidly changing polar marine environment.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.

极地海冰是地球气候系统的重要组成部分。北极海冰的大量减少不仅影响极地海洋环境，而且可能影响北方半球的天气模式、洋流、风暴路径和降水量等。海冰作为一种物质，是纯冰与毫米级盐水包裹体和厘米级多晶显微结构的多尺度复合体。甚至连冰层本身也是由海水中的浮冰颗粒状复合物组成的。模拟海冰及其在气候中的作用的一个主要挑战是如何使用小尺度结构的信息来找到与过程研究和粗粒度气候模型相关的大尺度上的有效或均匀属性。也感兴趣的是恢复参数控制小尺度过程从大尺度观测，如遥感的逆问题。这些核心问题在这个项目中，利用特殊的数学特性的有效参数，是常见的几个重要问题领域的海冰建模。它们包括通过海冰的流体和电磁传输，盐水对流增强的热通量等扩散过程，以及冰层中的海洋表面波。 海冰与其他天然存在的和工程合成物有着密切的相似之处。我们在海冰上的数学结果将为其他复合材料提供新的见解和发现，反之亦然。这项研究将有助于推进海冰在气候模型中的表现方式，并改善对地球海冰及其所支持的生态系统命运的预测。该项目还将为本科生和研究生提供支持，培训和研究机会。 均匀化数学理论中的一种强有力的方法是解析延拓法，它提供了复合材料有效参数的积分表示，将其视为参数的Stieltjes函数。复合微几何的复杂性被提炼成自伴算子的谱性质，就像量子物理学中的哈密顿算子，当系统离散化时，它们变成随机矩阵。该方法在海冰上的早期应用主要集中在遥感和电磁特性上，海冰被视为两相复合物。该方法的扩展到多晶介质，平流扩散过程，并通过浮冰表面波只产生了基本的边界上的有效参数，基于粗糙的信息，如质量的光谱测量的积分，这是盐水的体积分数海冰作为一个两相的复合材料，或面积分数的海洋覆盖的浮冰表面波。然而，利用量子物理学的随机矩阵理论描述的深刻相似之处带来了安德森过渡概念，如场局部化，迁移率边缘，本征值排斥，带隙到均匀化的经典运输两相复合材料。在资助的工作中，我们将探索新的见解，这种方法可以给我们在上述问题领域，其中有效的参数是Stieltjes函数。例如，海冰的有效性质如何取决于晶体的大小和结构，一些海浪可以通过浮冰的几何形状来定位，以及复合几何形状的分形性质如何影响有效的传输和光谱特性。这种方法打开了许多数学的兴趣问题，而在同一时间提供了新的工具，以解决至关重要的问题，在了解海冰过程中迅速变化的极地海洋environment.This奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

项目成果

Global Sea Ice Concentration Climate Data Records, Algorithm Theoretical Basis Document (OSI-450-a, OSI-430-a, OSI-458)

全球海冰浓度气候数据记录、算法理论基础文件（OSI-450-a、OSI-430-a、OSI-458）

• 发表时间: 2022
• 期刊: European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT
• 作者: Lavergne T., Sorensen A.

Order to disorder in quasiperiodic composites

• DOI: 10.1038/s42005-022-00898-z
• 发表时间: 2022-06
• 期刊: Communications Physics
• 影响因子: 5.5
• 作者: D. Morison;N. B. Murphy;E. Cherkaev;K. Golden

Physics of the cryosphere

冰冻圈物理学

• DOI: 10.1038/s42254-023-00610-2
• 发表时间: 2023
• 期刊: Nature Reviews Physics
• 影响因子: 38.5
• 作者: Banwell, Alison F.;Burton, Justin C.;Cenedese, Claudia;Golden, Kenneth;Åström, Jan
• 通讯作者: Åström, Jan