The size and composition of particles containing black carbon (BC) are
modified soon after emission by condensation of semivolatile substances and
coagulation with other particles, known collectively as “aging” processes.
Although this change in particle properties is widely recognized, the
timescale for transformation is not well constrained. In this work, we
simulated aerosol aging with the particle-resolved model PartMC-MOSAIC (Particle Monte Carlo – Model for Simulating Aerosol Interactions and Chemistry) and
extracted aging timescales based on changes in particle cloud condensation
nuclei (CCN). We simulated nearly 300 scenarios and, through a regression
analysis, identified the key parameters driving the value of the aging
timescale. We show that BC's aging timescale spans from hours to weeks,
depending on the local environmental conditions and the characteristics of
the fresh BC-containing particles. Although the simulations presented in this
study included many processes and particle interactions, we show that 80 % of
the variance in the aging timescale is explained by only a few key
parameters. The condensation aging timescale decreased with the flux of
condensing aerosol and was shortest for the largest fresh particles, while
the coagulation aging timescale decreased with the total number concentration
of large (

Particles containing black carbon (BC) alter Earth's energy
balance by scattering and absorbing solar radiation

These changes in particle characteristics, termed “aging”, often increase
the particles' susceptibility to cloud droplet nucleation and wet removal

To improve upon using one constant value for the aging timescale, several
studies have developed parameterizations of BC's aging timescale that vary
with environmental conditions.

This study builds on the work of

In a first-order model of aging, particles transition from fresh to aged
according to an aging timescale,

Before discussing the full set of sensitivity simulations in Sect.

The Particle Monte Carlo model

We simulated 288 plume scenarios, varying meteorological conditions,
emissions of gases and particles, and the background number concentration,
with further description given in Sect.

We determined aging timescales from the particle-resolved results by tracking
changes in CCN activity over two consecutive time steps. A particle's
ability to activate cloud formation depends on its dry diameter

Figure

The number distributions corresponding to fresh emissions, prior to any
aging, are shown in Fig.

Aerosol emissions and initial conditions for baseline simulation.

Gas-phase initial conditions and emissions for baseline simulation.

Two-dimensional probability density distribution
shows changes in particle properties. As particles increase in size
(horizontal axis) and hygroscopicity (vertical axis), they are able to
activate at lower critical supersaturation thresholds (superimposed lines).

For the entire particle population, this change in the particle properties
is quantified using the first-order aging timescale defined in Eq. (

The temporal evolution of the timescale is shown for the baseline scenario in Fig.

Any particle that transitions from fresh at

For a single scenario, overall aging timescale for

Hygroscopicity parameter assigned to aerosol species

The contribution of condensation and coagulation to the overall aging
timescale is shown by separate timescales for aging by condensation
(

Probability density function of aerosol mass species in simulations (black line in each graph) show that model cases represent variation in atmospheric conditions from ambient observations (vertical colored lines). Probability density functions include all output time steps in the full ensemble of sensitivity simulations. References for observations corresponding to each line: (a) Sun et al. (2010), (b) Takegawa et al. (2005, 2006), (c) Aiken et al. (2009), (d) DeCarlo et al. (2008); Docherty et al. (2008); Cubison et al. (2006), (e) Drewnick et al. (2004a, b), (f) Weimer et al. (2006), (g) Allan et al. (2003a, b), (h) Lanz et al. (2007), (i) Zhang et al. (2004, 2005a, b, c, 2007), (j) Dusek et al. (2006); Hings et al. (2007), (k) Topping et al. (2004), (l) Bae et al. (2006).

Input parameters varied in the ensemble of sensitivity simulations. Scenarios corresponding to the baseline conditions are indicated in bold. All combinations of scenarios were included in the full ensemble of 288 simulations.

The aging timescales shown in Fig.

The input parameters that were varied between the scenarios are shown in
Table

Figure

Variance in the aging timescale is shown by the probability density
distribution in Fig.

Black carbon's aging timescale ranges from minutes to weeks (Fig.

The procedure in applying a nonparametric regression is as follows: (1) select
a set of candidate independent variables to test; (2) use most (90 % of
simulations) of the data as the training set to find the expected value of
the aging timescale as a function of the independent variables, as will be
explained below; and (3) evaluate this expected aging timescale using the rest of
the data (10 % of simulations), called the testing set. The timescale from
the regression is assessed by how well it predicts the values of the aging
timescale in the testing set, represented by

Figure

Probability density function of

Alternatively, the expected probability that a fresh particle will age,
given its characteristics or the aging conditions that it experiences, can be
estimated from a nonparametric regression. We applied the kernel density
regression introduced by

Candidate variables included in the regression analysis.

Probability density function of aging
timescales for the full ensemble of sensitivity simulations, computed at
three environmental supersaturation levels:

Procedure for applying kernel
regression to predict black carbon's aging timescale and quantifying the
portion of variance explained by that prediction, shown for a hypothetic
input variable

At each time step in each simulation of the testing set, the expected value
of

Analogous to Eq. (

In Sect.

In this study we used a Gaussian kernel function with standard deviation

If the timescale depends only on the candidate variable

To illustrate our approach
for including particle-level variables, we demonstrate the regression
procedure using the wet diameter as the independent variable

It is therefore useful to introduce a size-resolved aging timescale that
accounts for differences in aging rates between particles of different
sizes. Size-resolved aging timescales were computed at each time

For a particle-resolved population of fresh particles

The temporal evolution of the size-resolved aging timescale is shown for the
baseline scenario in the middle column of Fig.

A comparison between Fig.

For baseline scenario,

In this study, we performed a series of multivariate kernel regressions to
identify the combination of independent variables that best explain variance
in black carbon's aging timescale. In many cases, we extracted aging
timescales that depend both on characteristics of individual particles, such
as

Coefficient of determination

Coagulation aging timescale as a
function of wet diameter and number of large, CCN-active particles

We found that most variance in the aging timescale is explained by only a
few independent variables. Explained variance

Figure

Bulk aging timescale for two fresh
particle size distributions under different aging regimes. Condensation,
coagulation, and overall aging timescales are given for

Rate at which particles of specific
size transition from fresh to aged

While the expected aging timescale computed in terms of

The regression surfaces

In this section we apply the regression surfaces shown in Fig.

For these two size distributions (Fig.

The sensitivity of the bulk aging timescales to

While

Global models that employ first-order aging models assume a fixed timescale
of 1–3 days, but observations show that aging timescales can be as short as
a few hours in polluted areas

Sensitivity of aging timescale to

As in all relationships for BC's aging timescale, the value of the aging
timescale depends strongly on the criterion used to distinguish fresh and
aged particles. Particle activation at a specific environmental
supersaturation is the aging criterion applied in this study, representing
changes in particle characteristics that most affect their susceptibility to
wet deposition. Table

This study identifies the minimal set of independent variables needed to explain variance in black carbon's aging timescale. We simulated the evolution of gases and aerosols in a series of urban scenarios with the particle-resolved model PartMC-MOSAIC and extracted time-dependent aging timescales based on the rate at which individual particles transition from CCN-inactive to CCN-active at a specified environmental supersaturation. The value of the aging timescale spanned orders of magnitude, depending on local environmental conditions and the supersaturation threshold at which CCN activity was evaluated. Aging timescales were shorter than an hour under conditions of rapid secondary aerosol formation, but on the order of days in the absence of secondary aerosol precursors. Condensation aging timescales exhibited more variation than coagulation aging timescales, and the relative importance of each aging mechanism depended on the size range of particles to be aged. We performed a nonparametric regression analysis on model data from 288 scenarios in order to identify the independent variables with which aging timescales are best correlated and quantified the portion of variance explained by regressions in terms of these variables. This paper is the groundwork for the development of aging parameterizations suitable for use in global models.

To our knowledge, this is the first study to apply a regression analysis to
identify the minimal set of parameters needed to explain variance in black
carbon aging rates. After evaluating a number of independent variables, we
found that the flux of secondary aerosol, the hygroscopicity of secondary
aerosol, and the size distribution of CCN-inactive (fresh) BC-containing
particles were the minimal set of parameters needed to explain 80 % of
variance in the condensation aging timescale. On the other hand, 90 % of
variance in the coagulation aging timescale was explained by only two
variables: the size distribution of fresh BC-containing particles and the
number concentration of particles that are both large (

This project is funded by NASA. N. Riemer also acknowledges US EPA grant 835042. Its contents are solely the responsibility of the grantee and do not necessarily represent the official views of the US EPA. Furthermore, US EPA does not endorse the purchase of any commercial products or services mentioned in the publication. The authors are grateful to Matthew West and Peter Maginnis for their suggestions in the early stages of this work. We also thank the two anonymous reviewers for their helpful comments. Edited by: H. Su