Parametric study of E. coli incidence with reference to the New Zealand freshwater standards and the Manawat\=u-Whanganui region

The New Zealand National Policy Statement for Freshwater Management 2020 sets several targets for freshwater quality, six of which are measurements of rivers; others relate to lakes. Each regional council is required to monitor freshwater quality and to respond as prescribed in order to meet the targets. One target of particular public interest is based on four criteria determined from recent E. coli readings, and concerns the health risk of swimming in a river. However, the inherent variability of the data makes it difficult to determine the water quality state and trend reliably, particularly using traditional methods based on percentiles. Therefore, in this study we return to the parametric lognormal model of E. coli distribution, from which the official criteria were developed. We interpret the classification system in terms of the parametric model and show that the parametric model can reduce uncertainty and can incorporate more useful information, especially from very high E. coli readings, and is suitable for censored data. We apply the parametric model for state and trend to 135 sites in the Manawat\=u-Whanganui region.