Estimating wastewater dilution using chemical markers and incomplete flow measurements: Application to normalisation of SARS-CoV-2 measurements

Abstract

Combined sewers, which collect both wastewater and surface water, are found across the globe, especially in older urban centres. These systems pose a challenge when taking chemical and biological measurements, be that chemical contaminants, illicit drugs or — in the case of wastewater-based epidemiology — disease markers, as signals are compromised by dilution caused by inflow of and infiltration of surface and ground water respectively. Therefore an estimate of dilution is required to normalise sample measurements. We construct a Bayesian estimator for the dilution of wastewater samples, and use it to estimate the prevalence of SARS-CoV-2 in Wales using data from the Welsh Government Wastewater Monitoring Programme. We consider the situation where flow measurements are available at respective wastewater treatment works, but are regularly unreliable because of combined sewer outflows (CSOs) and wastewater storage tanks, which divert wastewater out of the system when capacity has been exceeded. However, we also have proxies for the flow from various chemical markers (e.g. phosphate, ammonium, electrical conductivity), whose level per unit of population should remain consistent. The new flow estimator has multiple advantages compared to existing procedures, which include: credible intervals for the estimates; optimal weighting of the chemical markers; systematic handling of missing and censored values; and model-based smoothing without lags. Implementation of these advances can better control for variation in a noisy system, making insights from wastewater monitoring programmes more resilient to exogenous influences, ultimately benefiting the monitoring and management of human and environmental health.