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

本提案的首要目标是为地下水模拟中的流动和输送方程开发参数无关的简化模型。简化模型对原全尺寸模型的整个参数空间有效，比原全尺寸模型小3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，并结合了模型的物理特性。模型约简是基于高维模型方程在子空间上的伽辽金投影，由少量最优选择的基函数（主成分）近似。将开发算法来优化在参数空间和时间上的快照选择，以构建与参数无关的主成分。简化模型捕获原始全尺寸模型的主要特征，并在所需的精度范围内输出。此外，将开发程序，利用简化模型进行参数估计、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。将进行数值实验和实际案例研究，以显示所提出的参数无关简化模型如何用于大幅减少与大规模地下水流动和输送模型相关的计算需求，同时满足满足规定目标的指定容错水平。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给定模型输入的统计特征的模型输出的不确定性。使用计算要求高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，用于构建地下水流动和污染物输送的鲁棒简化模型。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1000。提出的模型减少方法将被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%的供水来自抽取地下水。已与圣地亚哥的美国地质调查局（美国地质调查局）办事处作出安排，以便参与合作研究，以便最大限度地立即适用于南加州地表水和地下水联合规划所制订的方法。但是，所提议的方法非常笼统，可以适用于该国的其他地下水盆地。

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.