Infiltration drives a Heavy–Tailed Distribution of Combined Sewer Overflow Spill Durations

Alex Lipp , Barnaby Dobson 

Combined sewer overflows (CSOs) discharge untreated wastewater into natural water bodies during periods of excess sewer flow, posing environmental risks. Using ~ 4 million CSO spill events recorded by Event Duration Monitors across England (2020–2024), we characterize the statistical distribution of spill durations. We find that while spills exceeding four hours represent only 6.4 % of events, they account for 78.2 % of total spill time, suggesting a disproportionate environmental impact. Formal likelihood ratio tests indicate that this heavy-tailed distribution is well described by a stretched exponential model with a shape parameter of 0.18, a result that is consistent for data from different Water & Sewerage Companies. The fitted model shows periodic residuals correlated with diurnal fluctuations in domestic water use. Hydraulic modelling reproduces the observed heavy tail only when groundwater infiltration is included, suggesting that long-duration spills are primarily driven by infiltration rather than exceptional precipitation events. We further show that the observed scaling can be approximated by the first passage times of a sewer head time-series modelled as fractional Brownian motion. Given the outsized influence of long-duration spills, we recommend explicitly incorporating tail behavior into hydraulic model calibration. We propose the use of the parameters of the stretched exponential distribution as metrics for this calibration and for assessing CSO performance more widely.