Quantifying aerosol mixing state with entropy and diversity measures

Abstract

Abstract. This paper presents the first quantitative metric for aerosol population mixing state, defined as the distribution of per-particle chemical species composition. This new metric, the mixing state index χ, is an affine ratio of the average per-particle species diversity D α and the bulk population species diversity D γ , both of which are based on information-theoretic entropy measures. The mixing state index χ enables the first rigorous definition of the spectrum of mixing states from so-called external mixture to internal mixture, which is significant for aerosol climate impacts, including aerosol optical properties and cloud condensation nuclei activity. We illustrate the usefulness of this new mixing state framework with model results from the stochastic particle-resolved model PartMC-MOSAIC. These results demonstrate how the mixing state metrics evolve with time for several archetypal cases, each of which isolates a specific process such as coagulation, emission, or condensation. Further, we present an analysis of the mixing state evolution for a complex urban plume case, for which these processes occur simultaneously. We additionally derive theoretical properties of the mixing state index and present a family of generalized mixing state indexes that vary in the importance assigned to low-mass-fraction species.

Elemental Mixing State of Aerosol Particles Collected in Central Amazonia during GoAmazon2014/15

“…The Shannon entropy of a probability distribution quantifies how uniform the distribution is. Shannon entropy is maximized if every element in the distribution is equally probable, and the entropy decreases the more likely any individual element becomes [20]. With this information entropy, diversity values are defined with the following equations: The diversity values contain the same type of information, but represent it in another way.…”

“…From Riemer and West [20], f a is a ratio of the total mass of the ath component and the total mass of the sample, however this is equivalent to the ratio of the mean mass of the ath component and the mean mass of particles within the sample:…”

“…The method of parameterizing mixing state used here is based on calculating mass fractions for different groupings of the individual components defined and is reproduced from Riemer and West [20]. The absolute mass of a given component a, within a given particle i, is labeled as m a i where a = 1, ..., A (and A is the total number of components) and i = 1, ..., N (the total number of particles).…”

“…Recently, more nuanced metrics were developed to quantify the mixing state of a population of aerosols [20]. Here, Riemer and West utilize an information theoretic approach to determine specific mixing states in populations of aerosols.…”

A single-column particle-resolved model for simulating the vertical distribution of aerosol mixing state: WRF-PartMC-MOSAIC-SCM v1.0

“…The magnitude of these impacts on climate depends not only on the bulk amount of aerosol material in the atmospheric column, but also on its vertical distribution within the column (Haywood and Shine, 1997;Schulz et al, 2006;Zarzycki and Bond, 2010;Samset and Myhre, 2011;Ban-Weiss et al, 2012), and on the microphysical characteristics of the aerosol population, such as the size distribution of the particles and the aerosol composition on a per-particle level (McFiggans et al, 2006;Moffet and Prather, 2009;Zelenyuk and Imre, 2009;Zelenyuk et al, 2010). For the purposes of this paper we use the term "aerosol mixing state" to refer to the distribution of chemical species across the aerosol population (Riemer and West, 2013;Winkler, 1973). This is distinct from the use of the term "mixing state" for the arrangement of components within a particle (e.g., homogeneous mixture or core-shell arrangements).…”