Statistical analysis of bathing water quality in Scotland

QA Mathematics;GE Environmental Sciences

Haggarty, Ruth A. ; Scott, E. M.

University:University of Glasgow

Department:School of Mathematics and Statistics

关键词: bathing water, extreme value, discounting, threshold;   

Others  :  http://theses.gla.ac.uk/553/1/2009haggartymsc.pdf

来源: University of Glasgow

【 摘 要 】

It is of interest, both environmentally and economically, for the water quality at beaches to be maintained and improved wherever possible.In 2006 a new European Community Directive was introduced which set compliance standards in terms of percentile values of different microbial indicators and, provided the public has been informed of the water quality via electronic message signs, permits samples to be discounted from compliance calculations.Consequently, the initial research question posed concerned the definition of a single sample limit (SSL) which could be used to determine the quality of a single sample of bathing water, whether or not it could be discounted and whether or not this could be set generically.The focus of the work later changed to become the definition of discounting limits that could be used to identify the samples which should be removed from the dataset on which compliance with the 2006 Directive is based.Chapter 1 provides an introduction to the general context of the problem, a description of the data and gives details of how compliance is assessed. In Chapter 2 exploratory analysis of the data revealed extensive variation in each of the microbiological indicators considered, both across the bathing water sites and within the same site across different bathing seasons.The distribution of each of two microbial indicators, faecal streptoccoci (FS) and faecal coliforms (FC) was considered and other features of the data including multiple outliers and evidence of bimodality were also apparent at some locations.All of this indicated that the definition of a generic single sample limit would not be achievable.The assumption of log-normality, on which the calculation of percentiles used to assess compliance with the Directive is based, was also investigated.Chapter 3 then used the level of compliance achieved in 2007 (using the data from bathing seasons in 2004 - 2007) as a measure of outcome in order to assess the effectiveness of several different candidate definitions of a single sample limit, including two site independent values and one formulaic approach.Following on from the issues discovered in the initial exploratory analysis of the data and after discussion with SEPA a generic SSL did not seem feasible and hence the stated objective of the work was modified to identifying a discounting limit which could be used to identify samples that could potentially be removed from compliance calculations.Therefore from Chapter 4 onwards only discounting limits are considered and the idea of using extreme value models became the basis of the remaining chapters.Chapter 4 considers the use of extreme value theory, in particular block maxima, k-th largest order statistic and threshold models to identify suitable return levels which could be applied as discounting limits across all sites.The differences between the return level limits obtained from each of the models, their impact on the levels of compliance classification when all counts exceeding the limits were removed and the inclusion of a relevant covariate within the block maxima model were also considered here.Chapter 5 focused on site specific threshold models, in particular, for the locations where electronic message signs are currently in place.The quantity of data removed at each site and the robustness of the discounting limits found using these models was also examined here. Finally, Chapter 6 provides a summary of the findings and discusses limitations of the study and possible future directions.