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

该奖项由2009年《美国复苏和再投资法案》(公法111-5)资助。CMG研究：气候变化对地下水资源影响建模的多尺度非线性区域分解方法S。美国科罗拉多大学地质科学系，美国科罗拉多大学计算机科学系。科罗拉多姆大学应用数学系。科罗拉多大学地理系的威廉姆斯说，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。地下水蕴藏着地球上约30%的淡水？S巨大的蓄水量可以有效地缓冲地表更剧烈的水文事件，因此，在水资源的长期可持续发展中，它扮演着一个重要但往往被忽视的角色。高海拔山区是重要的水源地。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地补给从源头补充、地下水库的规模以及永久冻土对地下水的影响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特性，涉及山地补给和多年冻土的地下水流动过程的建模面临着数学挑战。研究的目的是开发一种更精确的数学模型、一种新的稳健的计算算法和高性能的软件来研究气候变化对山区流域地下水资源的影响，重点是对山区补给和冻土水文进行量化。该研究计划首先开发一个数学模型，该模型将能够在多尺度的空间和时间域中处理复杂地质系统中的流体流动和热传输耦合。其次，将在两个地点进行现场水文地质研究，为检验数学模型收集数据。最后一个阶段是进行数值模拟，以评估未来气候变化情景对山区流域地下水蓄流的响应。首先，本研究将有助于我们在多空间和时间尺度上对水循环过程的科学认识。特别是，这项研究将对加强水循环的地下因素、增加关于山脉补给的知识以及将鲜为人知的永久冻土水文学纳入水资源研究作出独特的贡献。其次，将为描述水循环过程的耦合多物理系统开发高度并行和健壮的数值算法和软件。第三，提出的数学模型开发将是对水文地质科学的重大贡献。处理非均匀地质介质中的多尺度渗流问题一直是一个具有挑战性的问题。开发一种强大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单独难以实现的。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。这项研究将有助于水资源的长期规划，并通过当地媒体和公开讲座将结果异化，从而增加公众S对气候与水资源关系的认识。新的计算算法由一个强大而通用的软件实现，将可转移到其他应用领域，并可供其他研究人员使用。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本国部门以外的地方上课，要求数学学生参与实地工作，要求地球科学学生接受计算数学培训来实现。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，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.