How many particles do we need to measure aerosol mixing state?

Atmospheric aerosols are evolving mixtures of different chemical species.  The term “aerosol mixing state” is commonly used to describe how different chemical species are distributed throughout a particle population.  A population is “fully internally mixed” if each individual particle consists of same species mixtures, whereas it is fully externally mixed if each particle only contains one species. Mixing state matters for aerosol health impacts and for climate-relevant aerosol properties, such as the particles’ propensity to form cloud droplets or the aerosol optical properties.

The mixing state metric χ quantifies the degree of internal or external mixing and can be calculated based on the particles’ species mass fractions. Several field studies have used this metric to quantify mixing states for different ambient environments using sophisticated single-particle measurement techniques. Inherent to these methods is a finite number of particles, ranging from a few hundred to several thousand particles, used to estimate the mixing state metric. 

This study evaluates the error that is introduced in calculating χ due to a limited particle sample size.  We used the particle-resolved model PartMC-MOSAIC to generate a scenario library that encompasses a large number of reference particle populations and that represents a wide range of mixing states. We stochastically sub-sampled these particle populations using sample sizes of 10 to 10,000 particles and recalculated χ based on the sub-samples. This procedure mimics the impact of only having a limited sample size as it is common in real-world applications. The finite sample size leads to a consistent overestimation of χ, meaning that the populations appear more internally mixed than they are in reality. These findings are experimentally confirmed using single-particle SP-AMS measurement data from the Pittsburgh area. We also determined confidence intervals of χ for our sub-sampled populations. To determine χ within a range of  +/- 10 percentage points requires a sample size of at least 1000 particles.