A new Bayesian approach for managing bathing water quality at river bathing locations vulnerable to short-term pollution.

Short-term fecal pollution events are a major challenge for managing microbial safety at recreational waters. Long turn-over times of current laboratory methods for analyzing fecal indicator bacteria (FIB) delay water quality assessments. Data-driven models have been shown to be valuable approaches to enable fast water quality assessments. However, a major barrier towards the wider use of such models is the prevalent data scarcity at existing bathing waters, which questions the representativeness and thus usefulness of such datasets for model training. The present study explores the ability of five data-driven modelling approaches to predict short-term fecal pollution episodes at recreational bathing locations under data scarce situations and imbalanced datasets. The study explicitly focuses on the potential benefits of adopting an innovative modeling and risk-based assessment approach, based on state/cluster-based Bayesian updating of FIB distributions in relation to different hydrological states. The models are benchmarked against commonly applied supervised learning approaches, particularly linear regression, and random forests, as well as to a zero-model which closely resembles the current way of classifying bathing water quality in the European Union. For model-based clustering we apply a non-parametric Bayesian approach based on a Dirichlet Process Mixture Model. The study tests and demonstrates the proposed approaches at three river bathing locations in Germany, known to be influenced by short-term pollution events. At each river two modelling experiments ("longest dry period", "sequential model training") are performed to explore how the different modelling approaches react and adapt to scarce and uninformative training data, i.e., datasets that do not include event pollution information in terms of elevated FIB concentrations. We demonstrate that it is especially the proposed Bayesian approaches that are able to raise correct warnings in such situations (> 90 % true positive rate). The zero-model and random forest are shown to be unable to predict contamination episodes if pollution episodes are not present in the training data. Our research shows that the investigated Bayesian approaches reduce the risk of missed pollution events, thereby improving bathing water safety management. Additionally, the approaches provide a transparent solution for setting minimum data quality requirements under various conditions. The proposed approaches open the way for developing data-driven models for bathing water quality prediction against the reality that data scarcity is common problem at existing and prospective bathing waters.

Bayesian estimation of seasonal and between year variability of norovirus infection risks for workers in agricultural water reuse using epidemiological data.

Norovirus infections are among the major causes of acute gastroenteritis worldwide. In Germany, norovirus infections are the most frequently reported cause of gastroenteritis, although only laboratory confirmed cases are officially counted. The high infectivity and environmental persistence of norovirus, makes the virus a relevant pathogen for water related infections. In the 2017 guidelines for potable water reuse, the World Health Organization proposes Norovirus as a reference pathogen for viral pathogens for quantitative microbial risk assessment (QMRA). A challenge for QMRA is, that norovirus data are rarely available over long monitoring periods to assess inter-annual variability of the associated health risk, raising the question about the relevance of this source of variability regarding potential risk management alternatives. Moreover, norovirus infections show high prevalence during winter and early spring and lower incidence during summer. Therefore, our objective is to derive risk scenarios for assessing the potential relevance of the within and between year variability of norovirus concentrations in municipal wastewater for the assessment of health risks of fieldworkers, if treated wastewater is used for irrigation in agriculture. To this end, we use the correlation between norovirus influent concentration and reported epidemiological incidence (R²=0.93), found at a large city in Germany. Risk scenarios are subsequently derived from long-term reported epidemiological data, by applying a Bayesian regression approach. For assessing the practical relevance for wastewater reuse we apply the risk scenarios to different irrigation patterns under various treatment options, namely "status-quo" and "irrigation on demand". While status-quo refers to an almost all-year irrigation, the latter assumes that irrigation only takes place during the vegetation period from May - September. Our results indicate that the log-difference of infection risks between scenarios may vary between 0.8 and 1.7 log given the same level of pre-treatment. They also indicate that under the same exposure scenario the between-year variability of norovirus infection risk may be > 1log, which makes it a relevant factor to consider in future QMRA studies and studies which aim at evaluating safe water reuse applications. The predictive power and wider use of epidemiological data as a suitable predictor variable should be further validated with paired multi-year data.

Addressing and reducing parameter uncertainty in quantitative microbial risk assessment by incorporating external information via Bayesian hierarchical modeling.

Probabilistic quantitative microbial risk assessment (QMRA) studies define model inputs as random variables and use Monte-Carlo simulation to generate distributions of potential risk outcomes. If local information on important QMRA model inputs is missing, it is widely accepted to justify assumptions about these model inputs by using external literature information. A question, which remains unexplored, is the extent to which previously published external information should influence local estimates in cases of nonexistent, scarce, and moderate local data. This question can be addressed by employing Bayesian hierarchical modeling (BHM). Thus, we study the effects and potential benefits of BHM on risk and performance target calculations at three wastewater treatment plants (WWTP) in comparison to alternative statistical modeling approaches (separate modeling, no-pooling, complete pooling). The treated wastewater from the WWTPs is used for restricted irrigation, potable reuse, or influences recreational waters, respectively. We quantify the extent to which external data affects local risk estimations in each case depending on the statistical modeling approach applied. Modeling approaches are compared by calculating the pointwise expected log-predictive density for each model. As reference pathogens and example data, we use locally collected Norovirus genogroup II data with varying sample sizes (n = 4, n = 7, n = 27), and complement local information with external information from 44 other WWTPs (n = 307). Results indicate that BHM shows the highest predictive accuracy and improves estimates by reducing parameter uncertainty when data are scarce. In such situations, it may affect risk and performance target calculations by orders of magnitude in comparison to using local data alone. Furthermore, it allows making generalizable inferences about new WWTPs, while providing the necessary flexibility to adjust for different levels of information contained in the local data. Applying this flexible technique more widely may contribute to improving methods and the evidence base for decision-making in future QMRA studies.

On the implementation of reliable early warning systems at European bathing waters using multivariate Bayesian regression modelling.

For ensuring microbial safety, the current European bathing water directive (BWD) (76/160/EEC 2006) demands the implementation of reliable early warning systems for bathing waters, which are known to be subject to short-term pollution. However, the BWD does not provide clearly defined threshold levels above which an early warning system should start warning or informing the population. Statistical regression modelling is a commonly used method for predicting concentrations of fecal indicator bacteria. The present study proposes a methodology for implementing early warning systems based on multivariate regression modelling, which takes into account the probabilistic character of European bathing water legislation for both alert levels and model validation criteria. Our study derives the methodology, demonstrates its implementation based on information and data collected at a river bathing site in Berlin, Germany, and evaluates health impacts as well as methodological aspects in comparison to the current way of long-term classification as outlined in the BWD.