CMG COLLABORATIVE RESEARCH: Mathematics and Electromagnetics for Monitoring Transport Processes in Sea Ice

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)资助的。阿拉斯加大学费尔班克斯分校提供资金，用于开发电磁监测海冰内部状态、其微结构的热演变及其控制的运输过程的方法。PIS将在北极和南极进行基础数学研究和实地实验，旨在恢复微结构剖面及其在冰盖季节循环关键阶段的演变。他们将开发原位层析成像方法来获得低频下海冰的复杂介电常数分布，并开发数学技术来使用这些数据来重建复合微结构的光谱测量的演变，其中包含关于卤水几何形状和连通性的详细信息。他们将研究这一措施在渗流阈值附近的临界行为，渗流阈值是流体流动开启或关闭的地方。我们的工作将产生新的流体和热输运系数的光谱表示，并将光谱测量描述为自由能最小化，就像在统计力学中一样。他们将分析光谱测量的特征值间距分布的热演化，以此作为描述海冰卤水微结构中有序/无序转变的有力方法，这是受随机矩阵理论的启发。他们还将从微观结构的随机图形表示中开发复介电常数和其他传输特性的多尺度数值模型，以帮助重建计算。他们的结果将提供关于冰雪形成、融化过程和洪水冻结循环的有价值的信息，并为在气候和生物地球化学模型中对这些过程进行参数化提供见解。拟议工作的主要特点包括：？井间层析成像和岩心直接测量技术的发展在实验室和巴罗附近的北极进行初步测试、验证和改进，并进行南极测量。通过光谱测量连接电磁、热力和流体传输的交叉性质关系的发展，以及海冰传输过程的电磁成像的相关方法。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).Eicken 0934683University of Alaska FairbanksFunds are provided to develop methods of electromagnetically monitoring the internal state of sea ice, the thermal evolution of its microstructure, and the transport processes it controls. The PIs will conduct fundamental mathematical studies, as well as field experiments in the Arctic and Antarctic, directed at recovering microstructual profiles and their evolution at critical phases in the seasonal cycle of the ice pack. They will develop in situ tomographic methods to obtain the complex permittivity profile o sea ice at low frequency, and mathematical techniques to use this data to reconstruct the evolution of the spectral measure of the composite microstructure, which contains detailed information about brine geometry and connectedness. They will investigate the critical behavior of this measure near the percolation threshold, where fluid flow turns on or off. Our work will yield novel spectral representations for fluid and thermal transport coefficients, and characterizations of the spectral measure as a free energy minimizer, as in statistical mechanics. They will analyze the thermal evolution of the distribution of eigenvalue spacings for the spectral measure as a powerful way of characterizing the order/disorder transition in the brine microstructure of sea ice, as motivated by the theory of random matrices. They will also develop multiscale numerical models of the complex permittivity and other transport properties from random graph representations of the microstructure to aid reconstruction calculations. Their results will yield valuable information on snow-ice formation, melt processes, and flood-freeze cycling, and provide insights on parameterizing these processes in climate and biogeochemical models. Key features of the proposed work include:? Development of cross-borehole tomography and direct measurement techniques on cores. Initial testing, validation and refinement in the lab and the Arctic near Barrow, with Antarctic measurements.? Development of cross-property relations connecting EM, thermal, and fluid transport via the spectral measure, and related methods for EM imaging of transport processes in sea ice.