First‐order based cumulative distribution function for solute concentration in heterogeneous aquifers: Theoretical analysis and implications for human health risk assessment
First‐order based cumulative distribution function for solute concentration in heterogeneous aquifers: Theoretical analysis and implications for human health risk assessment
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DOI：
10.1002/2013wr015024
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发表时间：
2014-05
影响因子：
5.4
通讯作者：
F. P. Barros;A. Fiori
中科院分区：
文献类型：
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作者：
F. P. Barros;A. Fiori
量化异质含水层中溶质浓度的不确定性是人类健康和生态风险分析的重要一步。由于地下特征的不完整，证明需要对传输进行概率表示。我们推导了单点浓度累积分布函数（CDF），同时考虑了水力传导率的空间统计结构、空间维数、注入源尺寸、佩克莱特数和监测位置的采样体积。 CDF 是面向应用的，并以对数电导率方差的一阶形式导出。我们说明了几个关键参数如何控制浓度 CDF 的形状。 CDF 形状很重要，因为它反映了羽流的不确定性和稀释状态。检查从双峰到单峰 CDF 的转变，并通过分析浓度变异系数进一步支持结果。结果表明统计各向异性比（即水力传导率相关尺度之间的比率）在确定 CDF 形状中的重要性。还显示了浓度 CDF 尾部采样体积的重要性以及所提出的模型与 β-CDF 方法（即 beta 分布）之间的比较。最后，我们通过评估人类健康风险 CDF 来说明如何在应用中使用该框架。我们的结果对于低到中度异质含水层和与水力传导率相关长度相比较小的源尺寸正式有效。所提出的方法可以作为其他方法的基准工具。
Quantifying the uncertainty of solute concentration in heterogeneous aquifers is an important step in both human health and ecological risk analysis. The need for a probabilistic representation of transport is justified by the incomplete characterization of the subsurface. We derive the one‐point concentration cumulative distribution function (CDF) while taking into account the spatial statistical structure of the hydraulic conductivity, space dimensionality, the injection source size, the Péclet number, and the sampling volume at the monitoring location. The CDF is application oriented and derived at first order in the log‐conductivity variance. We illustrate how several key parameters control the shape of the concentration CDF. The CDF shape is important since it reflects both uncertainty and the dilution state of the plume. The transition from a bimodal to a unimodal CDF is examined and results are further supported by analyzing the concentration coefficient of variation. Results indicate the significance of the statistical anisotropy ratio (i.e., the ratio between the hydraulic conductivity correlation scales) in determining the CDF shape. The importance of the sampling volume in the tails of the concentration CDF and a comparison between the proposed model with the β‐CDF approach (i.e., beta distribution) are also shown. Finally, we illustrate how the framework could be used in applications by evaluating the human health risk CDF. Our results are formally valid for low to moderate heterogeneous aquifers and source sizes small as compared to the hydraulic conductivity correlation length. The proposed approach can serve as a benchmark tool for other methods.