Clearance capacity of the atmosphere: the reason that the number of haze days reaches a ceiling

China has experienced rapid development in the past 30 years but, alongside and associated with this growth, increased levels of pollution too. However, despite the continued increase in emissions of haze-forming aerosols in the twenty-first century, the annual number of haze days in some megacities has not risen in tandem. Various mechanisms have been proposed for “city dimming”, but the cause of the hiatus remains unclear. We found that the number of haze days in Taiyuan experienced a sharp increase during 1980–1998, with a growth rate 51.6 days/10a, and then exhibited fluctuating variation around a stable high level from 1998 to 2014, while at the same time the average visibility during haze days started to decrease. We present a novel method to explain the long-term variation in the number of haze days via a temporal-piecewise function of human activities and atmospheric cleaning processes: the number of haze days increases with the level of human activity before reaching the upper limit and then remains at a high level due to the restriction of a relatively stable number of strong cleaning days.