Bayesian inference of uncertainty in freshwater quality caused by low-resolution monitoring

Regulatory, low temporal resolution monitoring of freshwater quality does not fully capture the frequency distributions of the requisite parameters, particularly those that are highly skewed and heavy-tailed. Hence the summary statistics ultimately compared to environmental standards are uncertain. Quantifying this uncertainty is crucial for robust water quality assessment and possible remediation, but requires strong assumptions. This paper compares three ways to model the missing data needed to fully characterise a frequency distribution in a Bayesian framework using multi-year/multi-location orthophosphate (arithmetic mean standard), dissolved oxygen (DO; 10th percentile standard) and ammonia (90th percentile standard) data from the Tamar catchment in Southwest England. First, fitting an assumed parametric model of the frequency distribution (lognormal or Weibull), there is appreciable uncertainty around the "best" model fit. Second, Bayesian Model Averaging is more general in accommodating cases where the data are ambiguous with regard to the best model, but does not take into account possibly missing data. Third, a quasi-nonparametric multinomial model of the monitoring process that places some weight on those missing data yields wider and heavier-tailed frequency distributions. One-at-a-time sensitivity analysis suggests that the multinomial model for mean orthophosphate is sensitive to the choice of support range and the prior weights given to the missing data. Sensitivity is lower for 10th percentile DO and 90th percentile ammonia. The resultant probability densities of ecological status under the EU Water Framework Directive span several status classes, meaning ecological status is more uncertain than previously acknowledged. For orthophosphate, the regulatory, empirical determination of ecological status is not only overly precise but also biased.