López Martínez Iago, Alvarez Díaz César, Gil Díaz José Luis, Revilla Cortezón José A, Juanes José A
Submarine Outfall and Environmental Hydraulics Group (GESHA), Environmental Hydraulics Institute (IH Cantabria), Universidad de Cantabria, Avda. de los Castros, s/n., 39005, Santander, Spain.
J Environ Monit. 2010 Jan;12(1):369-76. doi: 10.1039/b903563j. Epub 2009 Aug 11.
The calculation of percentiles proposed in the Directive 2006/7/EC (parametric approach) to evaluate bathing water quality uses two parameters: mean (micro) and standard deviation (sigma). These two parameters are good descriptors of data populations only when data are log normally distributed. Several previous studies have shown that a log transformation is sufficient to achieve normality, while other studies suggest that log normality in bathing water quality datasets is seldom attained. In our study, log normality was achieved in 59.6% of the cases. In order to try to obtain a transformation parameter for Box-Cox (lambda) that provides the best fit and perhaps normality in bathing water datasets, the maximum likelihood estimation (MLE) method was applied to 40.4% of the remaining (non log normal) datasets. Results show that there is no transformation parameter that ensures normality for all datasets. In fact, normality is only reached in 10.3% of these datasets but, in these cases, the parametric approach seems to be a good one to evaluate bathing water quality. In cases where normality was not fulfilled even by application of the MLE method, a non-parametric approach to calculate percentiles is considered the most appropriate one. When percentile values obtained through the parametric and non-parametric Hazen approaches are compared, it is shown that the percentage of bathing waters changing their classification is low (12.3%). In these cases, the Hazen approach provides the worst classification in a vast majority of cases (90.6%), being this change important in some cases, in which classification is downgraded from having "Excellent" to "Sufficient" quality. Therefore, the Hazen approach is more appropriate for calculating percentiles, since it provides better estimators of percentile values. Furthermore, this method involves a more conservative approach for the classification of bathing water quality, providing an additional security for bathers' health. The fact that normality is not fulfilled and that classification of bathing waters could change must be considered by policymakers in order to adopt an alternative method for evaluating bathing waters quality.
2006/7/EC号指令中提出的用于评估沐浴水质量的百分位数计算方法（参数法）使用两个参数：均值（μ）和标准差（σ）。只有当数据呈对数正态分布时，这两个参数才是数据总体的良好描述指标。此前的多项研究表明，进行对数变换足以实现正态性，而其他研究则表明，沐浴水质量数据集中很少能达到对数正态性。在我们的研究中，59.6%的案例实现了对数正态性。为了尝试获得能在沐浴水数据集中提供最佳拟合甚至正态性的Box-Cox变换参数（λ），最大似然估计（MLE）方法被应用于其余40.4%的（非对数正态）数据集。结果表明，不存在能确保所有数据集都呈正态性的变换参数。实际上，这些数据集中只有10.3%达到了正态性，但在这些情况下，参数法似乎是评估沐浴水质量的一种好方法。在即使应用MLE方法也未实现正态性的情况下，采用非参数法计算百分位数被认为是最合适的。当比较通过参数法和非参数法（黑曾法）获得的百分位数时，结果表明沐浴水分类发生变化的百分比很低（12.3%）。在这些情况下，黑曾法在绝大多数案例（90.6%）中给出的分类最差，不过在某些情况下这种变化很重要，例如分类从“优秀”降至“良好”。因此，黑曾法更适合计算百分位数，因为它能提供更好的百分位数值估计。此外，该方法在沐浴水质量分类方面采用了更保守的方法，为沐浴者的健康提供了额外保障。政策制定者必须考虑到未实现正态性以及沐浴水分类可能发生变化这一事实，以便采用替代方法来评估沐浴水质量。
