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。CMG研究：多尺度非线性区域分解方法模拟气候变化对地下水资源的影响。科罗拉多第十大学地质科学系。Cai，科罗拉多大学计算机科学系。李，科罗拉多大学应用数学系。威廉姆斯，地理系，科罗拉多大学 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。拥有地球上大约30%的淡水，地下水？在调节地表更为剧烈的水文事件时，水的巨大蓄水能力可以成为一种有效的缓冲，因此，在水资源的长期可持续性方面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。高海拔地区的水文过程对气候变化特别敏感，因为存在积雪、冰川和永久冻土。然而，关于地下水如何通过山地补给在源头得到补充、地下水库的规模以及永久冻土如何影响地下水的基本问题仍然存在。由于控制方程的非线性和时空域的多尺度性质，模拟涉及山区补给和多年冻土的地下水流过程面临着数学挑战。研究的目的是开发一个更精确的数学模型和一个新的强大的计算算法和高性能的软件，以研究气候变化对山区流域地下水资源的影响，重点是量化山区补给和冻土水文。研究计划是首先开发一个数学模型，该模型将能够在多尺度空间和时间域中处理复杂地质系统中的耦合流体流动和热传输。其次，将在两个地点进行实地水文地质研究，以收集数据，用于测试数学模型。最后一个阶段是进行数值模拟，以评估地下水储存和流动在山区流域的未来气候变化情景的响应。首先，这项研究将有助于我们在多时空尺度上的水循环过程的科学知识。特别是，这项研究将为加强水循环的地下要素、增加有关山地补给的知识以及将鲜为人知的永久冻土水文学整合到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一个重大的贡献，水文地质科学。非均质地质介质中多尺度流体流动问题的研究一直是一个具有挑战性的课题。一个强大的计算算法的发展，允许有效地模拟水文地质系统在这样一个全面和综合的水平，这将是难以实现的数学家或地球科学家单独。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，并增加一般公众？通过当地媒体和公开讲座，将结果异化，以提高气候和水资源之间联系的知识。新的计算算法由一个强大的和多功能的软件实现，将转移到其他应用领域，并提供给其他研究人员。该项目的跨学科性质将为数学和地球科学的学生提供一个独特的机会，在与他们习惯的不同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培训来实现。最后，将设立一个由所有项目人员参加的数学-地球科学联合研讨会。通过鼓励广泛的参与，这次研讨会将促进数学和地球科学之间更多和持续的未来合作。

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.