Parameter-Independent Reduced Models for Flow and Transport in Groundwater Modeling

地下水建模中与参数无关的流动和传输简化模型

• 批准号: 1314422
• 负责人: William W-G. Yeh
• 金额: $ 25.66万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1314422&HistoricalAwards=false
• 关键词: Parameter; Independent; Reduced; Models; Flow

The overriding objective of this proposal is to develop parameter-independent reduced models for flow and transport equations in groundwater modeling. The reduced model is valid for the entire parameter space in the original full-scale model and is three orders of magnitude smaller than the full-scale model. The proposed methodology combines the data-driven and model-driven methods in that it makes use of input/output data relationships as well as incorporates the physics of the model. Model reduction is based on the Galerkin projection of the high-dimensional model equations onto a subspace, approximated by a small number of optimally chosen basis functions (principal components). Algorithms will be developed to optimize the snapshot selection in the parameter space and time for the construction of the parameter-independent principal components. The reduced model captures the dominating characteristics of the original full-scale model and outputs within a desired degree of accuracy. Additionally, procedures will be developed whereby the reduced model is utilized for optimal experimental design for parameter estimation, Monte Carlo simulation, Bayesian inversion, data assimilation, and groundwater management. Numerical experiments and real case studies will be conducted to show how the proposed parameter-independent reduced models can be used to drastically reduce the computational requirements associated with large-scale groundwater flow and transport models, while satisfying the specified level of error tolerance for meeting the stipulated goal. Groundwater models are used as decision-making tools for the planning and management of water resources systems. In many instances, the groundwater model has to be run a large number of times. A typical model uncertainty analysis requires tens of thousands of model runs to evaluate the uncertainty of the model outputs given the statistical characteristics of the model inputs. It would not be feasible or practical to use a computationally demanding and expensive full-scale model to perform such tasks. The project will develop new algorithms for constructing robust reduced models for groundwater flow and contaminant transport. The new algorithms can be used to perform various critically important hydrological analyses as the reduced models run 1,000 faster than the original full-scale model. The proposed model reduction methodology will be validated and applied to a selected groundwater basin in Southern California. Note that almost 40% of water supply in Southern California is from groundwater pumping. Arrangements have been made with the United States Geological Survey (USGS) office in San Diego for collaborative research participation in order to maximize the immediate applicability of the developed methodology for conjunctive planning of surface water and groundwater in Southern California. However, the proposed methodology is very general and can be applied to other groundwater basins in the country.

这一建议的首要目标是为地下水模拟中的流动和运移方程开发与参数无关的简化模型。简化模型适用于原全尺度模型中的整个参数空间，比全尺度模型小三个数量级。提出的方法结合了数据驱动和模型驱动的方法，因为它利用了输入/输出数据关系，并结合了模型的物理特性。模型降阶是基于高维模型方程对子空间的Galerkin投影，由少量优化选择的基函数(主成分)逼近。为了构造与参数无关的主成分，将开发在参数空间和时间上优化快照选择的算法。简化的模型捕获了原始全尺度模型的主要特征，并在期望的精度范围内输出。此外，还将制定程序，将简化的模型用于参数估计、蒙特卡罗模拟、贝叶斯反演、数据同化和地下水管理的最佳试验设计。数值实验和实际案例研究将展示所提出的独立于参数的简化模型如何在满足规定的误差容限水平的同时，大幅减少与大规模地下水流动和输运模型相关的计算要求。地下水模型被用作水资源系统规划和管理的决策工具。在许多情况下，地下水模型必须运行大量次。典型的模型不确定性分析需要数万次模型运行来评估模型输出的不确定性，给定模型输入的统计特征。使用一个计算量大且昂贵的全尺寸模型来执行这些任务是不可行或不实际的。该项目将开发新的算法，以构建稳健的地下水流动和污染物传输的简化模型。新的算法可以用于执行各种至关重要的水文分析，因为简化的模型比原始的全尺寸模型运行速度快1000。建议的模型简化方法将得到验证，并应用于南加州的一个选定的地下水盆地。请注意，南加州近40%的供水来自地下水抽水。已经与圣地亚哥的美国地质调查局(USGS)办事处作出了合作研究参与的安排，以便最大限度地利用所开发的方法对南加州地表水和地下水进行联合规划。然而，所提出的方法具有很强的通用性，可以应用于我国其他地下水流域。