Model Structure Identification in Three Dimensions and Observation Design in Groundwater Modeling

0001082是的，建立一个可靠的流域水资源管理模型是一个具有挑战性的问题，因为实际的含水层结构非常复杂，而且大部分是未知的，而我们只有非常有限的数据来校准模型。三个主要困难是：(1)如何确定适当的模型复杂性水平；(2)如何对未知分布参数值进行参数化和识别；(3)如何判断所选模型的现有数据的充分性。在我们最近的研究中，我们开发了一种新的方法来确定模型复杂性和估计模型结构及其相应的参数值在一个二维分布参数系统的地下水模拟。我们定义了一个广义逆问题，其中模型的复杂程度由可用数据和模型应用的精度要求决定。我们进一步发展了一种求解二维广义逆问题的逐步回归方法，以及一种构建地下水模型的新方法。新方法在南加州地下水流域水资源管理问题中的应用证明了其实用性。我们发现，通过一个简单的模型结构和几个确定的参数来表示各种水力和质量输运特性，可以满足管理要求。我们还发现，现有的数据不足以以所需的精度识别某些边界条件。这项工作探索了地下水模拟的新领域。主要目标是：(1)使我们的模型结构识别方法更加通用。我们将考虑分区和其他参数化方法，如有限元插值和克里格。我们将把这个方法扩展到三维空间。要确定的参数结构不仅包括水力传导性，还包括初始条件和边界条件以及源项。(2)建立广义逆逆问题的理论基础。我们将定义模型结构的可辨识性，并找出其充分条件。我们还将考虑如何将地质构造信息纳入三维模型结构识别过程。(3)发展观察设计的方法论。在找到最不复杂的模型结构后，我们可以将观测设计问题转化为从所有充分可行的设计中找出最具成本效益的设计的优化问题。我们的最终目标是定量地将观测设计与模型结构复杂性、模型参数可辨识性和模型应用可靠性联系起来。结果将与蒙特卡罗模拟进行比较。我们将把我们的研究成果应用于南加州的一家水资源机构。

0001082YehThe development of a reliable model for basin water resources management is a challenging problem because real aquifer structure is highly complex and mostly unknown and that we only have very limited data to calibrate the model. The three major difficulties are: (1) How to determine an appropriate level for model complexity; (2) How to parameterize and identify the unknown distributed parameter values; and (3) How to judge the sufficiency of existing data for the chosen model. In our recent studies, we have developed a new approach to fix model complexity and to estimate a model structure and its corresponding parameter values for groundwater modeling in a 2-dimensional distributed parameter system. We have defined a generalized inverse problem, in which the model complexity level is set by available data and the accuracy requirements of model applications. We have further developed a stepwise regression method to solve the generalized inverse problem in two dimensions as well as a new methodology for constructing groundwater models. The utility of the new methodology was demonstrated by an application to a water resources management problem of a groundwater basin in Southern California. We have found that management requirements were satisfied by a simple model structure with a few identified parameters to represent various hydraulic and mass transport properties. We also found that existing data are insufficient to identify certain boundary conditions with the required accuracy.This work explores new frontiers in groundwater modeling. The key objectives are: (1) To make our methodology for model structure identification more general. We will consider zonation and such other parameterization methods as finite element interpolation and kriging. We will extend the methodology to three dimensions. Parameter structures to be identified will include not only hydraulic conductivity but also initial and boundary conditions and source terms. (2) To build the theoretical basis of the generalized inverse inverse problem. We will define model structure identifiability and find its sufficient conditions. We will also consider how information on geological structure can be incorporated into model structure identification procedure in three dimensions. (3) To develop methodology for observation design. After the least complex model structure is found, we can formulate the observation design problem into an optimization to find the most cost-effective design from all sufficient and feasible designs. Our ultimate goal is to quantitatively link observation design to model structure complexity, model parameter identifiability, and model application reliability. Results will be compared to Monte Carlo simulations. We will apply our research results with a water resources agency in Southern California.