Bayesian experimental design of tracer studies to monitor wastewater leakage from sewer networks

Despite more than a decade of research, the magnitude of wastewater leakage from defective sewer systems into groundwater supplies is still largely unknown, partly because reliable measurement methods are lacking. Although recently suggested in-sewer tracer studies present a promising solution, it is unclear how to optimally design such studies in network settings. In this study we present a formal experimental design procedure, which uses Bayesian data analysis to improve the diagnosis of sewer leakage by combining tracer test data with prior knowledge on network topology and condition. From a simulation study, we show that (1) if a single sewer section is expected to have high leakage, that section should be distinguished in measurement layouts through isolated tests or appropriate overlapping of multiple tests; (2) if multiple sections are expected to have high leakage, layouts with tests that cover more than one high-leakage section should be avoided; and (3) if a robust experimental design is desired, a balanced layout of tests that overlap multiple sections of high leakage, yet minimizes stretch length, should be chosen. This design will have the additional benefit of inducing covariance in the posterior distribution of exfiltration estimates, which can be used to advantage in subsequent studies. We apply these guidelines to a case study of a catchment in Zurich, Switzerland, and find that optimal layout design can improve the anticipated gain of information substantially relative to designs based on practical considerations alone. Remaining concerns regarding the procedure include (1) the generally poor understanding of the mechanisms governing sewer leakage, which can hamper reliable prior information on exfiltration; (2) the currently low measurement precision of sewer tracer studies, which might only allow for the detection of large leaks; and (3) the need for numerical implementation of the Bayesian inference procedure, which requires careful tuning and long computation times. In general, we were able to demonstrate that the incorporation of prior information through a Bayesian procedure adds significant value to experimental design, especially in situations with few "hard" data but good site-specific knowledge, which is common in water resources research. Copyright 2010 by the American Geophysical Union.