Collaborative Research: A Comparison of Local and Nonlocal Transport Theories

本项目将评估保守溶质弥散的几种新兴理论处理方法，包括它们的数据需求和表示弥散的能力。我们将在北美研究最好、最具代表性的异质遗址——密西西比州哥伦布市的MADE遗址——应用经典的本地和非本地方法。我们将评估传统的平流-色散方程（ADE），该方程被认为需要数千万具有局部速度值的节点，以及几种非局部方法，包括时间-非局部多速率传质（MRMT）和连续时间随机游走（CTRW）方法，以及/或空间分数阶平流-色散方程（fADE）。每一种非局部方法在减少准确预测异常快速和/或顽固污染迁移所需的信息量方面都显示出巨大的希望。然而，给定相同的站点，我们必须提出这样的问题：每种方法需要多少数据、什么类型的数据才能获得给定的精度级别？是否有一些方法捕获了过程的结果行为，从而具有固有的优越性？是否可以生成模型使用和数据收集的简单指南？所提出的工作将首次系统地评估最新和广泛使用的保守溶质输运理论的准确性和数据需求。最终的结果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，并将有关地质复杂性的信息以局部速度或非局部的形式放在控制方程中。此外，我们将提供从局部尺度（及其离散化）到非局部条件的信息权衡的指南。我们将把分析应用于多种类型的合成含水层，除了广泛研究的MADE地点。

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.