Model Structure Reduction and Robust Experimental Design for Constructing Reliable and Cost-Effective Groundwater Models

0336952叶数学模型已成为流域水资源规划、水质管理、污染源检测和修复设计不可或缺的工具。 然而，经过30多年的研究，模型的标定问题仍然没有完全解决。 水文地质学家可能没有足够的信心将其校准模型用于预测和决策目的。 地下水模型的建立主要有两个难点：（1）真实的含水层的地质结构通常是非常复杂和未知的;（2）可用于模型校正的数据在数量和质量上都非常有限。 这两个困难在模型校准过程中密切相关。 一个简单的模型结构可能无法既拟合观测数据又产生可靠的预测。 另一方面，当数据有限时，复杂的模型结构可能导致过度参数化，从而呈现包含大量不确定性的模型。 很好地理解，能够很好地拟合现有数据的模型在其包含显著的模型误差时不一定是用于预测的良好模型。 因此，提出了以下具有挑战性的问题：可以确定一个模型，满足指定的模型应用程序的精度要求（例如，用作决策工具）时，数据是有限的，模型误差是显着的？ 此外，当模型结构高度复杂和未知时，是否可以找到一种稳健的数据收集设计，可以为识别可靠的模型提供足够的信息？ 本研究试图解决这些问题。该建议的首要目标是进行理论分析，以找到模型结构的简化、模型参数的可识别性、模型应用的可靠性和实验设计的鲁棒性之间的定量关系。 基于这些理论结果，我们将提出一种计算模型降阶结构误差的新算法。 当含水层系统的真实的结构高度复杂且未知时，我们也将提出一种新的稳健设计算法。 影响声明：该研究试图解决地下水模拟中的模型结构识别和实验设计这一长期存在的问题。 预期成果包括制定一个具有成本效益和可行的办法，以确定一个对预测和决策有用的最简单的模型。 所开发的方法可以应用于各种模拟模型，包括地下水流，污染物传输，海水入侵和生物降解。为了最大限度地提高研究结果的即时适用性，我们与美国地质勘探局圣地亚哥办事处进行了合作安排。

0336952YehMathematical models have become indispensable tools for basin water resources planning, water quality management, pollution source detection and remediation design. After more than 30 years of study, however, the model calibration problem still is not resolved completely. Hydrogeologists may not have sufficient confidence in using their calibrated models for prediction and decision-making purposes. There are two major difficulties in groundwater modeling: (1) the geological structure of a real aquifer usually is very complex and unknown, and (2) the data that can be used for model calibration usually are very limited, in both quantity and quality. These two difficulties are closely interconnected during the model calibration process. A simple model structure may not be able to both fit the observed data and produce reliable predictions. On the other hand, a complex model structure may cause over-parameterization when data are limited, thus rendering a model that contains a large amount of uncertainties. It is well understood that a model that can fit the existing data well may not necessarily be a good model for prediction when it contains significant model error. The following challenging problems thus are presented: can a model be identified that satisfies the accuracy requirement of specified model applications (for example, for use as a decision-making tool) when the data are limited and the model error is significant? Furthermore, can a robust data collection design be found that can provide sufficient information for identifying a reliable model when model structure is highly complex and unknown? This study attempts to address these problems. The overriding objective of this proposal is to perform theoretical analyses to find the quantitative relationships among the reducibility of a model structure, identifiability of a model parameter, reliability of a model application and the robustness of an experimental design. Based on these theoretical results, we will present a new algorithm for calculating the structure error of model reduction. We also will present a new algorithm for robust design when the real structure of the aquifer system is highly complex and unknown. Impact statement: The proposed research attempts to resolve a long-standing problem of model structure identification and experimental design in groundwater modeling. The expected results include the development of a cost-effective and feasible approach for identifying a least complex model that is useful for prediction and decision-making. The developed methodologies can be applied to a variety of simulation models, including groundwater flow, contaminant transport, seawater intrusion and biodegradation. To maximize the immediate applicability of the research results, we have made arrangements with the USGS office in San Diego for collaboration.