Computational mathematics of Arctic processes

北极是一个巨大而复杂的环境，它影响着全球范围内的水和能量流动的预算。该项目将为北极的耦合现象开发强有力的计算模型及其数学分析，包括永冻土中的热、水文和机械过程以及选定的生物圈过程。除了与大范围气候有关外，这些过程还对人类和基础设施产生了重大的局部影响。在该项目中开发的模型及其对现实情景的预测性模拟的使用将有助于支持减轻永久冻土融化等影响的计划的知识。研究生和本科生将参与并培训计算数学，以及为项目内外的跨学科努力做出有意义和关键贡献的能力，努力为代表性不足的群体建立有效的指导支助结构。预计将就该项目的主题对本科生和研究生进行培训。该项目将为北极耦合过程模型的近似解开发算法，包括热过程、水文过程、机械过程和生物圈过程。主要的挑战是基本偏微分方程组的非线性和复杂性，以及数据的稀疏性，这在广阔的北极环境中不容易收集。对于许多相关的时间和空间尺度上的耦合系统来说，这些挑战加剧了。研究人员将专注于多个尺度的交叉主题，将永久冻土的X射线图像的微观孔隙尺度与实验的达西尺度联系起来，并将观测中常见的千米风景尺度联系起来。这些努力将支持开发高效的原型和代理模型以及近似质量的新指标，这些工具可用于模拟与北极永久冻土相关的气候事件的现实情景。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。

The Arctic is a vast and complex environment which influences planet-scale budgets of water and energy fluxes. The project will develop robust computational models and their mathematical analyses for coupled phenomena in the Arctic including thermal, hydrological, and mechanical processes in permafrost soils as well as selected biosphere processes. Beside their connections to large scale climate, these processes have significant local impact on humans and infrastructure. The models developed in this project and their use for predictive simulations of realistic scenarios will contribute to the knowledge supporting the plans to mitigate the effects, e.g., of permafrost thaw. Graduate and undergraduate students will be involved and trained in computational mathematics as well as in an ability to contribute meaningfully and critically to the interdisciplinary efforts within and outside the project, with efforts towards an effective mentoring support structure for underrepresented groups. Training both undergraduate and graduate students on the topics of the project is expected.The project will develop algorithms for approximations of solutions to the models of coupled processes in the Arctic including the thermal, hydrological, mechanical, and biosphere processes. The main challenges are the nonlinearity and complexity of the underlying partial differential equations and the sparsity of data which is not easy to collect in the vast Arctic environment. These challenges are exacerbated for coupled systems across the many relevant temporal and spatial scales. The investigators will focus on the cross-cutting theme of multiple scales connecting the microscopic Pore scale of x-ray images of permafrost soil to the Darcy scale of experiments to the Landscape scale of kilometers common in observations. These efforts will support the development of efficient prototype and surrogate models along with new metrics for the quality of the approximations, and these tools can be used for simulations of realistic scenarios of climate events associated with Arctic permafrost.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.