Fractal Dimensions of Biomass Burning Aerosols from TEM Images Using the Box-Grid and Nested Squares Methods

Abstract

The fractal dimension is a key parameter in quantifying the morphology of aerosol aggregates, which is necessary to understand their radiative impact. Here we used Transmission Electron Microscopy (TEM) images to determine 2D fractal dimensions using the nested square and box-grid method and used two different empirical equations to obtain the 3D fractal dimensions. The values ranged from 1.70 ± 0.05 for pine to 1.82 ± 0.07 for Eucalyptus, with both methods giving nearly identical results using one of the empirical equations and the other overestimated the 3D values significantly when compared to other values in the literature. The values we obtained are comparable to the fractal dimensions of fresh aerosols in the literature and were dependent on fuel type and combustion condition. Although these methods accurately calculated the fractal dimension, they have shortcomings if the images are not of the highest quality. While there are many ways of determining the fractal dimension of linear features, we conclude that the application of every method requires careful consideration of a range of methodological concerns.

Keywords

• fractal dimension
• nested square method
• box-grid method
• biomass burning aerosols