CMG Research: Multiscale nonlinear domain decomposition method for modeling the impact of climate change on groundwater resources

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。气候变化对地下水资源影响的多尺度非线性区域分解模拟。蔡欣，美国科罗拉多大学计算机科学系李，科罗拉多大学应用数学系。持续的气候变化给未来的水资源带来了不确定性。水循环包括将气候和水资源的各种要素联系起来的基本过程。拥有大约30%的地球淡水，地下水？中国巨大的蓄水能力可以成为调节地表更剧烈水文事件的有效缓冲，因此，在水资源的长期可持续性中发挥着重要但往往被忽视的作用。高海拔山区是重要的水源地区。由于积雪、冰川和永久冻土的存在，高海拔地区的水文过程对气候变化特别敏感。然而，关于地下水如何通过山区补给在源头得到补充、地下水水库的大小以及永久冻土如何影响地下水等基本问题仍然存在。由于控制方程的非线性和时空域的多尺度性质，涉及山地补给和永久冻土的地下水流动过程建模面临着数学上的挑战。研究的目标是建立更精确的数学模型、新的鲁棒计算算法和高性能软件来研究气候变化对山地流域地下水资源的影响，重点是山地补给和永久冻土水文的量化。研究计划是首先建立一个能够处理多尺度时空复杂地质系统中流体流动和热输运耦合的数学模型。其次，将在两个地点进行实地水文地质研究，为数学模型的测试收集数据。最后进行数值模拟，评估山地流域地下水储流量对未来气候变化情景的响应。首先，该研究将有助于我们在多时空尺度上对水循环过程的科学认识。特别是，本研究将对加强水循环的地下元素、增加对山地补给的认识以及将鲜为人知的永久冻土水文纳入水资源研究中做出独特的贡献。其次，将为描述水循环过程的耦合多物理场系统开发高度并行和鲁棒的数值算法和软件。第三，提出的数学模型的发展将是对水文地质科学的重大贡献。处理非均质地质介质中的多尺度流体流动问题是一个长期存在的挑战。开发一种健壮的计算算法，可以在如此全面和综合的水平上有效地对水文地质系统进行建模，这是数学家或地球科学家难以单独实现的。水资源可持续性和气候变化是全球和地方关注的紧迫问题。这项研究将有利于水资源的长期规划和提高公众对水资源的认识。通过当地媒体和公开讲座，传播美国关于气候和水资源之间联系的知识。新的计算算法实现了一个强大的和通用的软件将转移到其他领域的应用，并提供给其他研究人员。这个项目的跨学科性质将为数学和地球科学专业的学生提供一个独特的机会，让他们在不同于他们习惯的智力和物理环境中相互交流。这将通过要求学生在他们的家庭部门之外上课，数学学生参加实地工作，地球科学学生接受计算数学训练来实现。最后，将设立一个数学-地球科学联合研讨会，让所有项目人员参加。通过鼓励广泛参与，本次研讨会将促进数学和地球科学之间未来更多和持续的合作。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).CMG Research: Multiscale Nonlinear Domain Decomposition Method for Modeling the Impact of Climate Change on Groundwater ResourcesS. Ge, Department of Geological Sciences, University of Colorado X. Cai, Department of Computer Science, University of ColoradoC. Li, Department of Applied Mathematics, University of ColoradoM. Williams, Department of Geography, University of Colorado Continuing climate change poses uncertainties on future water resources. The water cycle encompasses fundamental processes that link various elements of climate and water resources. Holding approximately 30% of Earth's fresh water, groundwater?s enormous storing capacity can be an effective buffer in regulating more drastic hydrologic events on the surface, therefore, plays an important but often overlooked role in long-term sustainability of water resources. High altitude mountainous regions are vital source areas for water. Hydrologic processes in high-altitude regions are particularly sensitive to climate change because of the presence of snow, glaciers, and permafrost. Yet, basic questions remain regarding how groundwater is replenished at its source by mountain recharge, the size of groundwater reservoirs, as well as how permafrost influences groundwater. Modeling the groundwater flow processes involving mountain recharge and permafrost faces mathematical challenges due to nonlinearity of the governing equations and multiscale nature of the spatial and temporal domains. The objective of the research is to develop a more accurate mathematical model and a new robust computational algorithm and high performance software to study the impact of climate change on groundwater resources in mountain watersheds, with a focus on quantifying mountain recharge and permafrost hydrology. The research plan is to first develop a mathematical model that will be capable of handling coupled fluid flow and heat transport in complex geologic systems in multiscale spatial and temporal domains. Second, field hydrogeologic study at two sites will be conducted to gather data for testing the mathematical model. The final stage is to conduct numerical simulations to assess the response of groundwater storage and flow in mountain watersheds to future climate change scenarios.First, this study will contribute to our scientific knowledge on water cycle processes at multi spatial and temporal scales. In particular, this study will make a unique contribution to strengthening the subsurface element of the water cycle, increasing knowledge on mountain recharge, and integrating little known permafrost hydrology into a water resource study. Second, highly parallel and robust numerical algorithms and software will be developed for the coupled multi-physics system describing the water cycle processes. Third, the proposed mathematical model development will be a substantial contribution to hydrogeologic sciences. Dealing with multiscale fluid flow problems in heterogeneous geologic media has been a long standing challenging. Development of a robust computational algorithm allows efficiently modeling of hydrogeologic systems at such a comprehensive and integrated level that would be difficult to achieve by either mathematicians or geoscientists alone. Water resource sustainability and climate change are pressing issues of global and local concern. This study will benefit long term planning of water resources and increase general public?s knowledge on the linkage between climate and water resources, by dissimilating results through local media and public lectures. The new computational algorithm implemented by a robust and versatile software will be transferable to other areas of application and available to other researchers. The cross-discipline nature of this project will afford students in mathematics and geosciences a unique opportunity to interact with each other in intellectual and physical settings that differ from those they are used to. This will be achieved by requiring students to take classes outside their home departments, math students to participate in field work, geoscience students to be trained in computational mathematics. Finally a joint math-geosciences seminar will be established to involve all project personnel. By encouraging broad participation, this seminar will foster more and sustained future collaborations between mathematics and geosciences.