Collaborative Research: A Comparison of Local and Nonlocal Transport Theories

这个项目将评估几种关于保守溶质弥散的新兴理论处理方法，涉及它们的数据需求和表示弥散的能力。我们将在北美研究最多、最具代表性的异质场地--密西西比州哥伦布市的Made场地--应用经典的本地和非本地方法。我们将评估传统的对流-弥散方程(ADE)，它被认为需要数千万个节点的局部速度值，以及几种非局部方法，包括时间-非局部多速率质量转移(MRMT)和连续时间随机游走(CTRW)方法，和/或空间分数对流-弥散方程(FADE)。每一种非本地方法在减少准确预测异常迅速和/或顽固的污染迁移所需的信息量方面都显示出很大的希望。然而，对于同一站点，我们必须问这样的问题：每种方法需要多少数据、什么类型的数据才能获得给定的准确度？是不是有些方法捕获了过程的结果行为，因此具有内在的优越性？能否为模型的使用和数据收集制定简单的指导方针？这项拟议的工作将首次对最新和广泛使用的保守溶质运移理论的准确性和数据需求进行系统评估。最终的产品将是一个统一的模型，它包括当前时间和空间非局部控制方程的显著特征，并在控制方程中以局部速度或非局部项放置有关地质复杂性的信息。此外，我们将提供从本地尺度(及其离散化)到非本地术语的信息权衡指南。除了被广泛研究的人造场地外，我们还将对许多类型的合成含水层进行分析。

This project will evaluate several emerging theoretical treatments of the dispersion of a conservative solute, with respect to their data needs and ability to represent dispersion. We will apply classical local, and non-local, methods at perhaps the best-studied and most representative heterogeneous site in North America - the MADE site in Columbus, Mississippi. We will evaluate the traditional advection-dispersion equation (ADE), which is thought to require tens of millions of nodes with local velocity values, and several non-local methods, including the time-non-local multiple-rate mass transfer (MRMT) and continuous time random walk (CTRW) methods, and/or the space-fractional advection-dispersion equation (fADE). Each of the non-local methods show great promise in reducing the amount of information needed to make accurate predictions of anomalously rapid and/or recalcitrant pollution migration. However, given the same site, we must ask the questions: How much data, of what types, are needed to obtain a given level of accuracy for each method? Are some methods capturing the resulting behavior of the process and, thus are inherently superior? Can simple guidelines for model use and data collection be generated? The proposed work would give the first systematic evaluation of the accuracy and data needs of the most recent and widely used theories of conservative solute transport. The final product would be a unifying model that includes the salient features of current time- and space-non-local governing equations, and places information about the geologic complexity in either the local velocities or in non-local terms in the governing equation. Furthermore, we will provide a guide to the tradeoff of information from the local scale (and discretization thereof) to the non-local terms. We will apply the analysis to synthetic aquifers of many types, in addition to the extensively studied MADE site.