Truncation in the scaling of urban pollution control

Urban scaling models assume homogeneous stochastic processes across a city system exhibiting power-law behavior. Strong persistent systematic factors may, however, cause deviations from scaling curves and reflect local heterogeneities in processes that govern individual cities' conformity to system mean trends. We conduct a scaling analysis across several quantitative properties of municipal pollution performance in Chinese cities and verify the findings using data from Japan, South Africa, India, and European cities. A generalized truncated power-law model is proposed to capture the region where performance metrics for small cities fall below the linear-fitted curve. We hypothesise that the truncation arises from limited capability of smaller cities in performing pollution abatement activities requiring high process complexity. Pollution control strategies that facilitate the transition from a fragmented response of each small city to a collaborative mode can provide a solution to even-out lags and inequalities across the national urban system.