Application of Density Plots and Time Series Modelling to the Analysis of Nitrogen Dioxides Measured by Low-Cost and Reference Sensors in Urban Areas

Abstract

Temporal variability of NO2 concentrations measured by 28 Envirowatch E-MOTEs, 13 AQMesh pods, and eight reference sensors (five run by Sheffield City Council and three run by the Department for Environment, Food and Rural Affairs (DEFRA)) was analysed at different time scales (e.g., annual, weekly and diurnal cycles). Density plots and time variation plots were used to compare the distributions and temporal variability of NO2 concentrations. Long-term trends, both adjusted and non-adjusted, showed significant reductions in NO2 concentrations. At the Tinsley site, the non-adjusted trend was −0.94 (−1.12, −0.78) µgm−3/year, whereas the adjusted trend was −0.95 (−1.04, −0.86) µgm−3/year. At Devonshire Green, the non-adjusted trend was −1.21 (−1.91, −0.41) µgm−3/year and the adjusted trend was −1.26 (−1.57, −0.83) µgm−3/year. Furthermore, NO2 concentrations were analysed employing univariate linear and nonlinear time series models and their performance was compared with a more advanced time series model using two exogenous variables (NO and O3). For this purpose, time series data of NO, O3 and NO2 were obtained from a reference site in Sheffield, which were more accurate than the measurements from low-cost sensors and, therefore, more suitable for training and testing the model. In this article, the three main steps used for model development are discussed: (i) model specification for choosing appropriate values for p, d and q, (ii) model fitting (parameters estimation), and (iii) model diagnostic (testing the goodness of fit). The linear auto-regressive integrated moving average (ARIMA) performed better than the nonlinear counterpart; however, its performance in predicting NO2 concentration was inferior to ARIMA with exogenous variables (ARIMAX). Using cross-validation ARIMAX demonstrated strong association with the measured concentrations, with a correlation coefficient of 0.84 and RMSE of 9.90. ARIMAX can be used as an early warning tool for predicting potential pollution episodes in order to be proactive in adopting precautionary measures.