Neupauer Roseanna M, Wilson John L
Department of Earth and Environmental Science, New Mexico Institute of Mining and Technology, Socorro, NM, USA.
J Contam Hydrol. 2003 Oct;66(1-2):39-58. doi: 10.1016/S0169-7722(03)00024-X.
Backward location and travel time probabilities can be used to determine the prior position of contamination in an aquifer. These probabilities, which are related to adjoint states of concentration, can be used to improve characterization of known sources of groundwater contamination, to identify previously unknown contamination sources, and to delineate capture zones. The first contribution of this paper is to extend the adjoint model to the case of a decaying solute (first-order decay), and to describe two different interpretations of backward probabilities. The conventional interpretation accounts for the probability that a contaminant particle could decay before reaching the detection location. The other interpretation is conditioned on the fact that the detected contaminant particle actually reached the detection location, despite this possibility of decay. In either case, travel time probabilities are skewed toward earlier travel times, relative to a conservative solute. The second contribution of this paper is to verify the load term for a monitoring well observation. We provide examples using one-dimensional models and hypothetical aquifers. We employ an infinite domain in order to verify the monitoring well load. This new but simple one-dimensional adjoint solution can also be used to verify higher-dimensional numerical models of backward location and travel time probabilities. We employ a semi-infinite domain to illustrate the effect of decay on backward models of pumping well probabilistic capture zones. Decay causes the capture zones to fall closer to the well.
反向位置和运移时间概率可用于确定含水层中污染物的先前位置。这些与浓度伴随状态相关的概率，可用于改进对已知地下水污染源的特征描述、识别先前未知的污染源以及划定捕获区。本文的第一个贡献是将伴随模型扩展到溶质衰减（一级衰减）的情况，并描述反向概率的两种不同解释。传统解释考虑了污染物粒子在到达检测位置之前可能衰减的概率。另一种解释则基于这样一个事实：尽管存在衰减的可能性，但检测到的污染物粒子实际上到达了检测位置。在任何一种情况下，相对于保守溶质，运移时间概率都偏向于更早的运移时间。本文的第二个贡献是验证监测井观测的负荷项。我们提供了使用一维模型和假设含水层的示例。为了验证监测井负荷，我们采用了无限域。这个新的但简单的一维伴随解也可用于验证更高维的反向位置和运移时间概率数值模型。我们采用半无限域来说明衰减对抽水井概率捕获区反向模型的影响。衰减会使捕获区更靠近水井。
