The PartMC-MOSAIC particle-resolved aerosol model was previously developed to predict the aerosol mixing state as it evolves in the atmosphere. However, the modeling framework was limited to a zero-dimensional box model approach without resolving spatial gradients in aerosol concentrations. This paper presents the development of stochastic particle methods to simulate turbulent diffusion and dry deposition of aerosol particles in a vertical column within the planetary boundary layer. The new model, WRF-PartMC-MOSAIC-SCM, resolves the vertical distribution of aerosol mixing state. We verified the new algorithms with analytical solutions for idealized test cases and illustrate the capabilities with results from a 2-day urban scenario that shows the evolution of black carbon mixing state in a vertical column.
Aerosol particles impact the Earth's radiative budget directly by
scattering and absorbing shortwave radiation
Observational evidence shows that aerosol mixing state varies with altitude.
For example,
These experimental findings confirm that the composition of individual
aerosol particles constantly changes during the particles' lifetime as a
result of aging processes such as coagulation
From the application of the different types of aerosol models described above
within spatially resolved three-dimensional
chemical transport
models, we learn that it is important to track the aerosol mixing state in
order to accurately predict particle aging, the associated aerosol optical
properties, and the resulting heating rates
In contrast to the distribution-based models mentioned here,
particle-resolved aerosol models simulate a representative group of particles
distributed in composition space, treating coagulation,
condensation/evaporation, and other important processes on an individual
particle level. Relative particle positions within this computational volume
are not tracked, but processes such as coagulation are instead simulated
stochastically, following the approach pioneered by
For the large number of computational particles needed for atmospheric
simulations, we developed efficient algorithms for coagulation
In previous work PartMC-MOSAIC has been used as a box model
This paper is structured as follows. In Sect.
In this section we describe the model equations that govern the evolution of aerosol particles and trace gases in a vertical column. We include gas-phase chemistry, gas-to-particle conversion, coagulation of aerosol particles, emission of aerosol and gases, and the transport of aerosol particles and trace gases in the vertical column. We ignore horizontal diffusion and advection of trace gases and aerosol particles into and out of the column by assuming horizontal homogeneity.
An aerosol particle contains mass
The concentration of gas-phase species
The evolution of the multidimensional aerosol number distribution is
given by
The evolution of trace gas concentrations is given by
For Eqs. (
Here
For the gas-phase concentrations of Eq. (
We coupled the different model components (WRF, PartMC, and MOSAIC) by
using the operator splitting
The Advanced Research Weather Research and Forecasting (WRF-ARW)
Model (
The Particle-resolved Monte Carlo (PartMC) model (
The Model for Simulating Aerosol Interactions and Chemistry
(MOSAIC) (
This section details the treatment of the turbulent transport term of
Eq. (
Within each grid cell
The aerosol population
Since PartMC-MOSAIC resolves a finite population of particles
We first present the discretization in space and time in terms of
deterministic number concentrations and particle numbers
(Sect.
Schematic of the single-column domain
centered on grid cell
Figure
To account for the variation in
To obtain transported number concentrations and eventually a discrete
number of transported particles, we define the total aerosol number
concentration
Following a finite-volume discretization, we arrange the derivation (see
Appendix
Schematic of
Eq. (
Eventually, we want to perform turbulent transport of discrete particles;
therefore, as the next step we express
Eq. (
Equation (
To determine the discrete particle gain and loss sets, we discretize the
deterministic real-valued particle number gains and losses of
Eq. (
From Eq. (
Schematic of the transport process for
particle number from grid cell
When we sample the sets of gain and loss populations, we wish to
ensure that the gain and loss populations have as many particles in
common as possible. This is done in order to minimize particle
duplications and removals. To accomplish this, it is convenient to define the ratio of loss to gain by
Binomial samples satisfy a conditional property. If
To maintain numerical stability with the explicit finite-volume scheme,
sub-cycle time steps are taken for vertical transport that differ from the
model time step for other processes. Within each sub-cycle time step
To determine an appropriate sub-cycle time step, the transfer rates
are first computed for all grid cells in the column. The sub-cycle
time step must be chosen such that the total particle transition
probabilities are always in
The complete algorithm for stochastic turbulent transport of finite particle
sets is given in Algorithms C1 and C2 (Appendix C1). The
During a given simulation, the number of computational particles changes as
particles are added due to emission, are transferred from one grid cell to
another due to turbulent transport, and are removed by coagulation and dry
deposition. When the number of computational particles falls below half the
initial prescribed number in a given grid cell, in order to maintain an
adequate statistical sample, we duplicate every particle and double the
computational volume. When the number of particles is twice the initially
prescribed number, in order to alleviate the higher computational cost, half
the computational particles are discarded and the computational volume is
halved. This strategy has been previously used for particle populations in
the zero-dimensional PartMC-MOSAIC box model
Particles near the surface are subject to removal by the process of
dry deposition. This is parameterized by evaluating a dry deposition
velocity for each particle in the aerosol population of the lowest
grid cell
In the following section, we will present separate numerical verifications of
the new algorithms for particle transport by turbulent diffusion
(Sect.
For verification of the stochastic transport method of particles presented in
Algorithm C1, the particle transport code was implemented to solve the
one-dimensional diffusion equation given by
The variable grid spacing was determined by
Figure
Variable grid cell edges for the transport test case domain with 10, 20, 40, and 80 vertical layers.
Figure
Number concentration as predicted by the model at
To verify the convergence of the transport algorithm to the
analytical solution, we quantified the error in the total number concentration for ensemble member
The total relative error for ensemble member
Figure
We expect that the stochastic particle solution
Here we see that the total error is bounded by the stochastic and
finite-volume errors. The stochastic error is
Figure
To verify Algorithm C3 for dry deposition we developed a test case that only
considered the removal of particles by dry deposition. The simulation was
initialized with two monodisperse particle populations with different
diameters, 1 and 10
Figure
Evolution of mass concentration due to dry deposition for particles of
diameter 1
We constructed an idealized scenario to illustrate the model
capabilities of WRF-PartMC-MOSAIC-SCM. The scenario is similar to the
box model study presented in
We simulated a 48 h episode, starting at 06:00 local standard time (LST).
Initial gas mixing ratios were based on initial conditions given by
The model allows for the inclusion of aerosol emissions within any grid cell
in the column and has flexibility in the choice of the parameters of the size
distribution as well as the particle composition of the emitted particles.
Carbonaceous aerosols were emitted at the surface from three different
sources: diesel vehicles, gasoline vehicles, and meat cooking. Due to the
importance of the timing of atmospheric turbulent mixing and emissions, we
applied a diurnal cycle to the particle emission rates. This is in contrast
to
WRF-PartMC-MOSAIC-SCM was initialized with 59 vertical levels,
logarithmically spaced with 16 levels in the lowest 1
Initial and emitted aerosol distribution parameters.
Time series of diesel and gasoline area source surface emissions for the 48 h simulated period.
Given the complexities of the multidimensional aerosol distribution,
we must project the distribution for purposes of displaying results.
We take
The one-dimensional cumulative number distribution
We can also construct two-dimensional number distributions with
respect to dry diameter,
In this section we present an illustration of model output and will focus on
the evolution of the mixing state of black-carbon-containing particles within
the boundary layer. However, before we discuss the results of the aerosol
mixing state in detail, we will provide a brief description of the bulk
quantities of the scenario. For this 48 h scenario, the temperature and
relative humidity varied over time, as simulated by the WRF model and shown
in Fig.
Time–height sections of
Time–height sections showing
mixing ratios of
Figure
Time–height sections of aerosol mass
concentrations of
Figure
Figure
Figure
Figure
Two-dimensional number distributions
To understand how the mixing state of black-carbon-containing particles
evolves in time and with respect to height, Fig.
At 06:00 LST on the second day, the horizontal lines representing fresh
emissions were most pronounced at the surface. As a result of the stable
boundary layer limiting the vertical extent of turbulent mixing, the fresh
emissions were contained to levels near the surface. By 12:00 LST, the
height of the boundary layer had grown to
While Fig.
The WRF-PartMC-MOSAIC-SCM model has computational cost for evaporation/condensation proportional to the number of computational particles, computational cost for coagulation proportional to the number of coagulation events, and computational cost for transport proportional to the number of sampled particles. As a result, the evaporation/condensation of secondary species is the dominant cost of the model, comprising more than 97 % of the computational cost for the simulation presented here. By contrast, the particle transport is computationally inexpensive, typically representing less than 2 % of the cost.
The WRF-PartMC-MOSAIC-SCM model is both computationally and memory intensive and therefore benefits greatly from parallelization. While the host WRF model utilizes a horizontal decomposition that is not applicable to the single-column model, the WRF-PartMC-MOSAIC-SCM model features a vertical domain decomposition where the gas and aerosol domain is distributed across multiple cores. Since the dominant cost is evaporation/condensation, which is a per-particle process and requires no communication with neighboring grid cells, the model scales efficiently even when the domain is decomposed to a single grid cell per core.
In this paper we presented the development and application of the WRF-PartMC-MOSAIC-SCM model. This model, for the first time, resolves the aerosol composition on a per-particle level in an Eulerian single-column domain and couples the aerosol- and gas-phase chemistry with the meteorology.
We developed and implemented two new algorithms, a stochastic aerosol transport algorithm to treat vertical turbulent diffusion, and a stochastic aerosol dry deposition algorithm. Both model processes were verified with test cases and performed as expected when compared to analytical solutions. A stochastic sampling strategy, which does not track particle position, was used to reduce the computational burden of particle transport. This method relies on an explicit discretization of the diffusion equation and the use of nearest-neighbor diffusion. Potential future model development includes the implementation of other numerical methods for turbulent diffusion, such as higher-order and/or semi-implicit schemes, and non-local boundary layer schemes such as ACM2.
To illustrate the newly coupled model capabilities, an idealized urban scenario was developed. This 48 h simulation showed the evolution of the black carbon mixing state due to coagulation, secondary aerosol formation, particle emission, dry deposition, and turbulent transport. In the presented scenario, freshly emitted diesel and gasoline particles existed in the highest concentrations near the surface where they were emitted. As particles were vertically mixed due to turbulent transport, emitted particles experienced changes in composition due to coagulation with aged particles as well as due to condensation of secondary aerosol species. While we focused on the composition of black-carbon-containing particles to demonstrate the model capabilities, we do store the full composition for each computational particle, so a similar analysis can be made for other aerosol species.
Future applications of the model include quantifying the impact of aerosol
mixing state on secondary aerosol formation and on climate-relevant aerosol
properties, such as aerosol absorption and CCN concentration, and comparing
these findings to existing studies
The box model version of PartMC is available from
See Table
Symbols used in this paper.
This appendix contains the derivation steps between
Eqs. (
We consider a finite-volume discretization of
Eq. (
See Algorithm C1 for the sub-cycling method used to simulate stochastic
particle transport over a single model time step
The authors declare that they have no conflict of interest.
The authors acknowledge funding from the Office of Science (BER), U.S. Department of Energy, under grants DE-SC0003921 and DE-SC0011771. Jeffrey H. Curtis acknowledges support from a Computational Science and Engineering Fellowship from the University of Illinois at Urbana-Champaign. Matthew West acknowledges NSF grant CMMI-1150490.Edited by: Alex B. Guenther Reviewed by: two anonymous referees