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

本建议的首要目标是开发参数无关的简化模型的流动和输运方程在地下水模拟。简化模型对原始全尺寸模型中的整个参数空间都有效，并且比全尺寸模型小三个数量级。所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，并结合了物理模型。模型降阶是基于高维模型方程到子空间上的Galerkin投影，由少量最佳选择的基函数（主成分）近似。 将开发算法来优化参数空间和时间中的快照选择，以构建与参数无关的主成分。简化模型捕获了原始全尺寸模型的主要特征，并在所需的准确度内输出。 此外，程序将被开发，从而减少模型用于参数估计，蒙特卡罗模拟，贝叶斯反演，数据同化和地下水管理的最佳实验设计。 数值实验和真实的案例研究将显示如何建议的参数无关的简化模型可以用来大大减少与大规模地下水流和输运模型相关的计算要求，同时满足指定的误差容限水平，以满足规定的目标。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多次。考虑到模型输入的统计特征，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。使用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，用于构建地下水流和污染物迁移的稳健简化模型。新算法可用于执行各种至关重要的水文分析，因为简化模型的运行速度比原始全尺寸模型快1,000倍。建议的模型简化方法将进行验证，并应用于选定的地下水盆地在南加州。请注意，南加州近40%的供水来自地下水抽取。 已与美国地质调查局（USGS）圣地亚哥办事处作出安排，以便合作参与研究，以便最大限度地立即适用于所制定的方法，对南加州的地表水和地下水进行联合规划。然而，拟议的方法是非常普遍的，可以适用于其他地下水流域在该国。

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.