Prediction of illness risk near ocean outfalls using frequency distributions of bacterial concentrations

Water quality managers traditionally assess the illness risk associated with indicator bacteria in bathing waters by comparing an average concentration to a concentration standard, where the average may be determined from a frequency distribution of concentrations. The United States EPA concentration standards are determined as the concentration which gives an acceptable illness rate according to a mathematical relation between the concentration and illness rate (concentration–response relation). However, further use can be made of the frequency distribution and concentration–response relation. This paper presents a method for combining the temporal concentration frequency distribution with a concentration–response relation to obtain the averaged illness rate (that is, the expected illness rate). First the method is developed for the concentration frequency distribution at a single location. The method is also extended for the case where the temporal concentration frequency distribution is known at a number of points throughout the area in the vicinity of the outfall, in which case spatial contours of averaged illness rate can be determined. The methods are demonstrated for a site at the North Shore, New Zealand.