A robust regression analysis method to determine the significance of trends in concentrations of heavy metals in UK ambient air and improve network design and emission inventories

A novel application of the Theil-Sen robust regression method for determining the temporal trends in the concentration of heavy metals in UK ambient air over the period 2005–2020 is presented and compared to other regression methods. We have demonstrated improvements over non-robust methods of regression, proving the ability to tease out trends that are small with respect to the variability of the concentration measurement. The method is used to identify, in general, large and significant trends in the concentrations of Ni, As, Pb and V over the period 2005–2020, either across the UK as a whole or at groupings of site classifications in the UK. These trends have been compared to trends in emission data determined in the same manner. Although the results for most metals provide confidence that the UK metal network of monitoring sites is successful in appropriately capturing changes in emissions, a key finding of this work is the disagreement between trends in measured concentrations and emissions for Cu, Mn and Ni, for which we suggest improvements in future network design. The results also indicate that UK emission data for V should be reviewed, as we propose that the rate of reduction of V emissions is likely to have been overestimated.