Computational mathematics of Arctic processes

北极是一个巨大而复杂的环境，影响着地球尺度上水和能量通量的收支平衡。该项目将开发强大的计算模型，并对北极的耦合现象进行数学分析，包括永久冻土中的热、水文和机械过程，以及选定的生物圈过程。这些过程除了与大尺度气候有关外，还对人类和基础设施产生重大的局部影响。本项目开发的模型及其用于对现实情景进行预测模拟的用途，将有助于为减轻诸如永久冻土融化等影响的计划提供知识支持。研究生和本科生将参与和训练计算数学，以及为项目内外的跨学科努力做出有意义和批判性贡献的能力，努力为代表性不足的群体提供有效的指导支持结构。期望对本科生和研究生进行项目主题的培训。该项目将开发求解北极耦合过程模型的近似算法，包括热、水文、机械和生物圈过程。主要的挑战是潜在的偏微分方程的非线性和复杂性，以及在广阔的北极环境中不易收集的数据的稀疏性。在许多相关的时间和空间尺度上，这些挑战对耦合系统来说更加严重。从冻土x射线图像的微观孔隙尺度到实验的达西尺度，再到观测中常见的千米景观尺度，研究人员将重点关注多尺度的交叉主题。这些努力将支持开发有效的原型和替代模型，以及衡量近似质量的新指标，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。

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.