A methodology to relate black carbon particle number and mass emissions

Black carbon (BC) particle number (PN) emissions from various sources contribute to the deterioration of air quality, adverse health effects, and anthropogenic climate change. This paper critically reviews different fractal aggregate theories to develop a new methodology that relates BC PN and mass concentrations (or emissions factors). The new methodology, named as the fractal aggregate (FA) model is validated with measurements from three different BC emission sources: an internal combustion engine, a soot generator, and two aircraft gas turbine engines at ground and cruise conditions. Validation results of the FA model show that R-2 values range from 0.44 to 0.95, while the Normalised Mean Bias is between -27.7% and +26.6%. The model estimates for aircraft gas turbines represent a significant improvement compared to previous methodologies used to estimate aviation BC PN emissions, which relied on simplified assumptions. Uncertainty and sensitivity analyses show that the FA model estimates have an asymmetrical uncertainty bound (-54%, +103%) at a 95% confidence interval for aircraft gas turbine engines and are most sensitive to uncertainties in the geometric standard deviation of the BC particle size distribution. Given the improved performance in estimating BC PN emissions from various sources, we recommend the implementation of the FA model in future health and climate assessments, where the impacts of PN are significant.