Markov Chain Modeling of Combined Sewer Tank Overflow

Abstract

Increasing urbanization and climate change frequently overwhelm the capacity of combined sewer overflow (CSO) tanks, posing significant risks to the environment, public health, and the economy. This study applied a discrete-time Markov chain (DTMC) model to analyze the stochastic behavior of monthly CSO tank overflow volumes, incorporating uncertainties such as rainfall variability and operational conditions. We used a decade of data (2013–2022) from two CSO tanks (HCS01 and HCS04) in Hamilton, Canada, and categorized the monthly overflow data into five states—no overflow, minor overflow, moderate overflow, major overflow, and severe overflow—using the elbow method and silhouette score. Our results show distinct overflow dynamics between the tanks: HCS04 demonstrated robust resilience, with an 84% probability of no overflow following months of no or minor overflow, and only a 4% chance of severe overflow, suggesting that it was more stable. In contrast, HCS01 exhibited greater instability with a 65% probability of no overflow and a higher probability of severe overflow, particularly after major overflow events. These findings emphasize the need for tailored management strategies for each tank. This study’s novel application of the DTMC model, combined with data uncertainty incorporation, provides valuable probabilistic insights into CSO dynamics, informing better infrastructure planning and overflow risk mitigation.