Identifying nonlinear interactions between PM_2.5 and O₃ on small time scales with visibility graph approaches

Identifying nonlinear interactions between PM(2.5 )and O-3 is crucial for fully understanding atmospheric pollution. These interactions between PM(2.5 )and O-3 involve complex chemical processes and boundary layer dynamics under different meteorological drivers. Due to the deficiency of traditional linear statistical methods (e.g. Pearson correlation or Pearson partial correlation analysis), they fail in quantifying nonlinear interactions between PM(2.5 )and O-3 on small time scales and nonlinear features in PM(2.5 )and O-3 series. We adopt two statistical indicators based on visibility graph (VG) algorithm to analyze the PM(2.5 )and O-3 time series: average edge overlap (AEO) as measure for nonlinear interactions and K-np as measure for cross-scale interaction by frequency modulation (FM). Detail studies show that AEO is insensitive to large-scale nonstationary variations but indeed sensitive to nonlinear coupling variations in the tailored models with known prescribed coupling. The AEO can successfully identify true both linear and nonlinear interactions in these tailored models, while Pearson correlation analysis fails. Then AEO is applied to reanalysis data of PM(2.5 )and O-3 to identify events with specific nonlinear interactions between PM(2.5 )and O-3 with significant cross-scale interactions quantified by calculated K-np, which exist in both within and between these pollutant time series. Further analysis shows that the possible mechanisms underlying these nonlinear interactions may be mainly local mixing (or emission) and chemical processes related to meteorological drivers such as surface air temperature, surface solar radiation and surface relative humidity.