Uncertainty methods for groundwater flow and transport modelling

地下水系统的不确定性分析通常用于导出系统因变量的矩作为系统参数不确定性的函数；通常只估计前两个矩。然而，对于许多问题来说，重要的不是第一个和第二个时刻，而是PDF尾部的估计才是关键。污染物首次到达生物圈点或受体的经典问题就是这样一个例子。虽然分析人士可能会估计出浓度的全部分布，但公众、监管机构和法院往往只关心污染物最早可能到达地下水井的情况。经济决策往往是根据这些低概率事件做出的。分析人员的困难是浓度PDF尾的稳健性。分布尾部概率估计的重要因素包括参数不确定性、相关性和确定不确定性的方法。提出的研究计划的目标是开发和实施可应用于详细复杂地下水模型的不确定性方法。这些方法将应用于核废料深地质处置库的风险和安全评价。这些方法也将适用于评价地下水保护区和在裂缝或多孔介质中污染物到达生物圈点的法医模拟。对于法医模型，将探讨的案例研究包括：分析污染物到达市政井场，该井场向具有统计意义的儿童癌症集群的社区供水；破产信托分配给有各种健康影响（癌症）的个人作为污染物暴露浓度和持续时间的函数。

Uncertainty analyses of groundwater systems are commonly used to derive the moments of the system dependent variables as a function of the uncertainty in the system parameters; usually only the first two moments are estimated.  For many problems however, it is not the first and second moment that are important but rather it is estimates at the tails of the PDF that are critical.  The classical problem of the first arrival of a contaminant at a biosphere point or receptor is one such example.  While analysts may estimate the full distribution of the concentration, the public, regulators and courts are often only concerned with the earliest possible arrival of a contaminant to a groundwater well.  Economic decisions often are made on these low-probability occurrences.  The difficulty for the analyst then is the robustness of the concentration PDF tails.  Important factors in the estimation of the probability at the tail of the distribution include parameter uncertainty, correlation, and the method used to determine the uncertainty.    The objective of the proposed research program is to develop and implement uncertainty methods that can be applied to detailed complex groundwater models.  The methods will be applied in the risk and safety assessment of deep geologic repositories for nuclear waste.  The methods will also be applicable for the assessment of groundwater protection zones and the forensic simulation of contaminant arrival at a biosphere point in either fractured or porous media.  For the forensic modeling, the case studies that will be explored include: the analysis of the arrival of a contaminant at a municipal well field that supplies water to a community with a statistically significant childhood cancer cluster; and the allocation of a bankruptcy trust to individuals with various health impacts (cancers) as a function of contaminant exposure concentration and duration.