A PM2.5 persistence index (PPI) to quantify the magnitude and duration of pollution

Fine particulate matter (PM₂.₅) is routinely monitored worldwide to support environmental regulation and public health policy. Commonly reported metrics, including annual mean concentrations and short-term regulatory exceedance counts, provide essential summaries of long-term exposure and episodic events but do not fully capture the temporal structure of daily pollution patterns and remain dependent on policy-specific thresholds. To jointly characterize the magnitude and persistence of PM₂.₅ exposure, we introduce the PM₂.₅ persistence index (PPI), a simple, threshold-free scalar defined as the largest integer k such that at least k days in a year exhibit daily mean PM₂.₅ concentrations ≥ k µg m⁻³. Geometrically, PPI corresponds to the intersection of the ranked daily concentration curve with the identity line. For example, a PPI value of 23 indicates at least 23 days in the year at or above 23 µg/m³. Application to daily regulatory data from four major U.S. metropolitan areas showed that PPI is strongly associated with annual means yet reveals additional variation reflecting differences in persistence of elevated concentrations, with consistent city-specific patterns and reasonable temporal stability. By formalizing the magnitude–frequency relationship in an intuitive, threshold-free form, PPI offers a transparent complement to conventional metrics for characterizing particulate pollution.