Introduction
Increasing attention is being paid to atmospheric particulate matter (PM),
which is a major contributor to air pollution issues ranging from adverse
health effects to visibility impairment . Concentrations of PM2.5 and PM10 are
regulated in many countries, especially in North America and Europe. For
example, regulatory concentration thresholds of 12 and 20 µgm-3 have been set for PM2.5 annual mass concentrations in the
United States and Europe, respectively. Furthermore, particles influence the
Earth's energy balance and global climate change .
Three-dimensional chemical-transport models (CTM) are often used to study and
forecast the formation and distribution of PM. The size distribution of
particles is often discretised into sections
e.g. or
approximated by log-normal modes e.g.. Moreover, CTM usually assume that particles are
internally mixed, i.e. each size section or log-normal mode has the same
chemical composition, which may vary in space and time.
The internal-mixing assumption implies that particles of the same diameter
(or in the same size section or log-normal mode) but originating from
different sources have undergone sufficient mixing to achieve a common
chemical composition for a given model grid cell and time. Although this
assumption may be realistic far from emission sources, it may not be valid
close to emission sources where the composition of new emitted particles can
be very different from either background particles or particles from other
sources. Usually, internally and externally mixed particles are not
differentiated in most measurements, which may be size-resolved (e.g. cascade
impactors) but not particle specific . The use of
mass spectrometers for individual particle analysis has shed valuable
information on the chemical composition of individual particles.
Consequently, there is a growing body of observations indicating that
particles are mostly externally mixed e.g..
The mixing state assumption may strongly influence aerosol chemistry and the
hygroscopic characteristics of particles. Particles from different origins
may not be well mixed, and their chemical composition may vary with their
origins, leading to variations in their hygroscopic characteristics. This
chemical identity of particles is gradually lost as the degree of mixing
increases (or completely lost under the internal mixing assumption). By
influencing the hygroscopic characteristics of particles, the mixing state
also influences the formation of secondary organic aerosols (SOA), because
condensation/evaporation differs for species that are hydrophilic and/or
hydrophobic . As the particle wet diameter is
strongly related to the hygroscopic properties of particles, the mixing state
also impacts particle wet diameters and the number of particles that become
cloud condensation nuclei (CCN), because the activation of particles into CCN
is strongly related to the particle wet diameter . By
influencing CCN, the mixing state also affects aerosol wet removal and thus
the aerosol spatial/temporal distribution. Besides, the mixing state
influences the particle optical properties, which depend on both the particle
size distribution (wet diameters) and composition (different chemical species
possess different absorption/scattering properties). found
that the percentage difference in the optical properties between an internal
mixture and external mixture of black carbon and ammonium
sulfate can be over 50 % for wet
aerosols. The mixing state may also influence radiative forcing, as shown by
, who obtained different direct forcing results between
external and internal mixing simulations of black carbon.
Although CTM usually assume that particles are internally mixed, several
models have been developed during the last sesquidecade to represent the
external mixture of particles. A source-oriented model was developed by
and for regional modelling.
In these models, each source is associated with a specific aerosol
population, which may evolve in terms of size distribution and chemical
composition, but does not mix with the other sources (i.e. particle
coagulation is neglected). modelled externally mixed
particles using a stochastic approach. However, such an approach is
computationally expensive when the number of particle species is high. On the
other hand, and simulate
externally mixed particles using modal aerosol models, where aerosol
populations with different mixing states are represented by modes of
different compositions (soluble/mixed or insoluble/not mixed). Although these
models may be computationally efficient, they may not model accurately the
dynamics of mixing. To represent externally mixed particles independently of
their sources and number concentrations, and
considered particles that can be either internally or
externally mixed (i.e. composed of a pure chemical species).
used a threshold mass fraction to define whether the species is of
significant concentration. expanded on
by allowing particles to have different mass
fractions. Similarly, discretised the fraction of
black carbon in the total particle mass into sections of different chemical
compositions. further expanded on these modelling
approaches by discretising the mass fraction of any chemical species into
sections, as well as the size distribution (see
Sect. for details). Based on this discretisation,
derived the equation for coagulation and validated
their model by comparing the results obtained for internal and external
mixing, as well as by comparing both approaches against an exact solution.
However, processes such as condensation/evaporation and nucleation were not
modelled.
This work presents the new Size-Composition Resolved Aerosol Model (SCRAM),
which expands on the model of by including
condensation/evaporation and nucleation processes. Section 2 describes the
model. Equations for the dynamic evolution of particles by
condensation/evaporation are derived. A thermodynamic equilibrium method
may be used in SCRAM to compute the evolution of the particle chemical
composition by condensation/evaporation. Redistribution algorithms, which
allow section bounds not to vary, are also presented for future 3-D
applications. Model validation is presented in Sect. 3 by comparing the
changes in the particle size distribution due to condensational growth for
both externally and internally mixed particles. Section 4 presents an
application of the model with realistic concentrations over Greater Paris.
Model description
This section presents the aerosol general dynamic equations and the structure
of the model. First, the formulation of the dynamic evolution of the aerosol
size distribution and chemical composition by condensation–evaporation is
introduced. Since it is necessary in 3-D CTM to maintain fixed size and
composition section bounds, we present algorithms to redistribute particle
mass and number according to fixed section bounds. For computational
efficiency, a bulk equilibrium method, which assumes an instantaneous
equilibrium between the gas and particle phases, is introduced. Finally, the
overall structure of the model is described. In particular, the treatment of
the different mixing processes to ensure the numerical stability of the model
is discussed.
Particle dynamics is mostly governed by three processes: coagulation,
condensation/evaporation, and nucleation. Nucleation refers to the
formation of ultra-fine particles from gaseous molecules. SCRAM uses the
parametrisation of for the homogeneous binary
nucleation of sulfate and water. It was adopted from the existing SIREAM code
. It may be replaced by a better parametrisation in future
versions, because it may lead to unrealistic results under some extreme
conditions . For coagulation, SCRAM uses the code
of to simulate the collisions of particles caused by
Brownian motion. Condensation/evaporation describe the mass transfer
process between the gas and particle phases. It is essential to include
condensation/evaporation, because this process not only largely influences
the size distribution of aerosols, but may also change the composition of
particles significantly.
Condensation–evaporation algorithm
The focus of the following subsections is the formulation and implementation
of the condensation/evaporation process. A Lagrangian approach is used to
solve the equations of change for the mass and number concentrations, which
are redistributed onto fixed sections through a redistribution algorithm
(moving diameter, ). Equations are derived to
describe the change with time of the mass concentrations of chemical species
in terms of particle compositions.
Dynamic equation for condensation/evaporation
Let us denote mi the mass concentration of species Xi (1≤i≤c) in a particle and x the vector representing the mass composition of
the particle x=(m1,m2,⋯,mc). Following
, the change with time of the number concentration
n(x,t) (m-3µg-1) of multi-species particles by
condensation/evaporation can be represented by the following equation:
∂n∂t=-∑i=1c∂(Iin)∂mi,
where Ii (µgs-1) is the mass transfer rate between the gas
and particle phases for species Xi. It may be written as follows:
Ii=∂mi∂t=2πDigdpf(Kn,αi)(cig(t)-Ke(dp)cieq(x,t)),
where Dig is the molecular diffusivity of
condensing/evaporating species in the air, and dp and
cig are the particle wet diameter and the gas-phase
concentration of species Xi, respectively. Non-continuous effects are
described by f(Kn,αi) , which depends on the
Knudsen number, Kn=2λdp (with λ the air
mean free path), and on the accommodation coefficient αi=0.5:
f(Kn,αi)=1+Kn1+2Kn(1+Kn)/αi.
Ke(dp) represents the Kelvin effect (for ultra-fine
particles, the curvature tends to inhibit condensation):
Ke(dp)=exp4σvpRTdp,
with R the ideal gas constant, σ the particle surface tension and
vp the particle molar volume. The local equilibrium gas
concentration cieq is computed using the reverse mode of the
ISORROPIA V1.7 thermodynamic model for inorganic
compounds. In the current version of SCRAM, organic compounds are assumed to
be at thermodynamic equilibrium with the gas phase and
condensation/evaporation is computed as described in
Sect. .
Dynamic equation as a function of mass fractions
Following the composition discretisation method of
(detailed in Sect. ), each particle is represented by
a vector p=(f,m), which contains the mass fraction vector
f=(f1,f2,…,f(c-1)) of the first (c-1) species and the
total mass m=∑i=1cmi.
In Eq. (), the chemical composition of particles is described
by the vector x, which contains the mass concentration of each
species. After the change of variable through a [c×c] Jacobian
matrix from n(x,t) to n¯(p,t) (see Appendix
for detail), Eq. () becomes
∂n¯∂t=-∑i=1(c-1)∂(Hin¯)∂fi-∂(I0n¯)∂m,
with I0=∑i=1cIi, Hi=∂fi∂t. As
fi=mim is the mass fraction of species (or group of species)
Xi, we may write
Hi=1m∂mi∂t-mim2∂m∂t=Ii-fiI0m.
The change with time of qi=nmi, the mass concentration of species Xi, can be expressed as
follows:
∂qi∂t=∂n∂tmi+∂mi∂tn.
After the change of variables from qi(x,t) to qi¯(p,t)
(see Appendix ), Eq. () becomes
∂qi¯∂t=-mfi∂n¯∂t+n¯Ii.
Discretisation
As SCRAM is a size-composition resolved model, both particle size and
composition are discretised into sections, while the numbers and bounds of
both size and composition sections can be customised by the user. The
particle mass distribution Q[mmin,mmax] is first divided into
Nb size sections [mk-,mk+] (k=1,…,Nb and
mk-1+=mk-), defined by discretising particle diameters [dmin,dmax] with dmin and dmax, the lower and upper particle
diameters, respectively, and mk=πρdk36. For each of
the first (c-1) species or species groups, the mass fraction is discretised
into Nf fraction ranges. The hth fraction range is represented
by the range Fh-+=[fh-,fh+] where fh-1+=fh-, fmin=0
and fmax=1. Within each size section k, particles are categorised
into Np composition sections, which are defined by the valid
combinations of the fraction ranges of the (c-1) species. The gth
composition section can be represented by
Pg=(Fg1-+,Fg2-+,…,Fgc-1-+). Given the
mass fraction discretisation, those composition sections are automatically
generated by an iteration on all possible combinations
(Nf(c-1)) of the (c-1) species and Nf fraction
ranges. Only the composition sections that satisfy ∑i=1(c-1)Fgi-⩽1 are kept.
The particle mass distribution is discretised into (Nb×Np) sections. Each section j (j=1,…,Nb×Nc)
corresponds to a size section k (k=1,…,Nb) and to a
composition section g=(g1,…,g(c-1)) with g=1,…,Np, gh=1,…,Nf with h=1,…,(c-1). The
total concentration Qij of species i in the jth section can be
calculated as follows:
Qij=∫mk-mk+∫fg1-fg1+…∫fg(c-1)-fg(c-1)+qi¯(m,fg1,…,fg(c-1))dmdfg1…dfg(c-1).
Similarly, the number concentration Nj of the jth section may be written
as follows:
Nj=∫mk-mk+∫fg1-fg1+…∫fg(c-1)-fg(c-1)+n¯(m,fg1,…,fg(c-1))dmdfg1…dfg(c-1).
After a series of derivations (see Appendix for details), we
obtain the time derivation of Eq. ():
∂Nj∂t=0,
as well as the time derivation of Eq. ():
∂Qij∂t=NjIgi.
Thus, in each section, the change with time of number and mass concentrations
is given by Eqs. () and ().
Numerical implementation
According to , the condensation/evaporation process may
have characteristic timescales of different magnitudes, because the range of
particle diameters is large. Such a feature induces strong stiffness of the
numerical system. As suggested by , the stiff
condensation/evaporation equations are solved using the second-order
Rosenbrock (ROS2) method .
In addition, potentially unstable oscillations may occur when a dramatic change of
the particle pH occurs. To address this issue, a species flux electro-neutrality
constraint is applied in SCRAM to ensure the
numerical stability of the system.
Size and composition redistribution
By condensation/evaporation, the particles in each size section may grow or
shrink. Because the bounds of size sections should be fixed for 3-D
applications, it is necessary to redistribute number and mass among the fixed
size sections during the simulation after condensation/evaporation.
Similarly, the chemical composition also evolves by
condensation/evaporation, and an algorithm is needed to identify the
particle composition and redistribute it into the correct composition
sections.
Two redistribution methods for size sections may be used in SCRAM: the HEMEN
(Hybrid of Euler-Mass and Euler-Number) scheme of and
the moving diameter scheme of . According to
, both redistribution methods may
accurately redistribute mass and number concentrations.
The HEMEN scheme divides particle size sections into two parts: the number is
redistributed for sections of mean diameter lower than 100 nm and
mass is redistributed for sections of mean diameter greater than
100 nm. The section mean diameters are kept constant and mass
concentrations are diagnosed for sections where number is redistributed,
while number concentrations are diagnosed for sections where mass is
redistributed. The advantage of this scheme is that it is more accurate for
number concentrations over the size range where number concentrations are the
highest and more accurate for mass concentrations where mass concentrations
are the highest. In SCRAM, the algorithm of was
modified to take into account the fact that after
condensation/evaporation, the diameter of a section may become larger
than the upper bound of the next section. In that case, the mean diameter of
the section after condensation/evaporation is used to diagnose in which
fixed-diameter sections the redistribution is performed. This feature allows
us to use larger time steps for condensation/evaporation before
redistribution.
In the moving diameter method, although size section bounds are kept fixed,
the representative diameter of each size section is allowed to vary. If,
after condensation/evaporation, the diameter grows or shrinks outside
section bounds, both the mass and number concentrations of the section are
redistributed entirely into the new size sections bounding that diameter.
For the composition redistribution, a scheme based on the moving diameter
method is applied (i.e. moving mass fraction). First, after
condensation/evaporation, the mass fraction of each species is re-evaluated
within each section. For each section, if the new composition does not match
the section composition (i.e. if the mass fraction of each species does not
fit into the mass fraction bounds of the species for that section), the
section that has a composition that matches the new composition is
identified, and both the number and mass concentrations of each species are
transferred to that section.
The composition redistribution is applied first, followed by the size redistribution for each of the composition sections.
Bulk equilibrium and hybrid approaches
Bulk equilibrium methods assume an instantaneous thermodynamic equilibrium
between the gas and bulk-aerosol phases. For semi-volatile species, the mass
concentrations of both gas and bulk-aerosol phases after
condensation/evaporation are obtained using the forward mode of ISORROPIA
for inorganics and the H2O model for
organics. Because time integration is not necessary, the computational cost
is significantly reduced compared to the dynamic method. Weighting factors
W are designed to distribute the semi-volatile bulk-aerosol mass across the
aerosol distribution . In SCRAM, for each
semi-volatile species i, we redistribute the bulk aerosol evaporating or
condensing mass, δQi=Qiafter bulk eq.-Qibefore bulk eq., between the sections j, using factors that
depend on the ratio of the mass transfer rate in the aerosol distribution
(Eq. ). Because of the bulk equilibrium assumption, the
driving force of (cig-Kecieq) is assumed to
be the same for all size and composition sections, and the weighting factors
are as follows.
Wij=Njdpjf(Kn,αi)∑k=1NsNkdpkf(Kn,αi),
where Nj is the number concentration of section j and dpj
is the particle wet diameter of section j. In case of evaporation, these
weighting factors may not be appropriate, as they may lead to
over-evaporation of some species in some sections, i.e. Qijafter
bulk eq.=Qibefore bulk eq.+δQi×Wij<0. In
the case of over-evaporation, we use a weighting scheme that redistributes
the total bulk aerosol mass rather than the bulk aerosol evaporating or
condensing mass
Wij=Qij∑k=1NsQik
and Qijafter bulk eq.=Qiafter bulk eq.×Wij.
In fact, due to their larger ratios between surface area and particle mass,
small particles may reach thermodynamic equilibrium much faster than large
particles. Particles of diameters larger than 1 µm could require
hours or even days to achieve equilibrium ,
which makes the bulk equilibrium assumption inappropriate for them. In order
to maintain both the computational efficiency of the equilibrium method and
the accuracy of the dynamic one, a hybrid method is adopted in SCRAM based on
the work of and . This method
uses the equilibrium method for small particles (dp<1 µm) and uses the dynamic method to calculate the mass transfer for larger
particles.
Overall time integration and operator splitting in SCRAM
In order to develop a system that offers both computational efficiency and
numerical stability, we perform operator splitting for changes in number and
mass concentrations with time due to emission, coagulation,
condensation/evaporation and nucleation, as explained below.
Emissions are first evaluated with an emission time step, which is determined
by the characteristic timescales of emissions obtained from the ratio of
emission rates to aerosol concentrations. The emission time step evolves with
time to prevent adding too much emitted mass to the system within one time
step. Within each emission time step, coagulation and
condensation/evaporation/nucleation are solved, and the splitting time step
between coagulation and condensation/evaporation/nucleation is forced to be
lower than the emission time step. Time steps are obtained from the
characteristic time steps of coagulation (tcoag) and
condensation/evaporation/nucleation (tcond). The larger of the
time steps tcoag and tcond determines the time step of
splitting between coagulation and condensation/evaporation/nucleation. As
coagulation is usually the slower process, the change due to coagulation is
first calculated over its time step. Then,
condensation/evaporation/nucleation are solved simultaneously. The change
due to condensation/evaporation/nucleation is calculated, using time sub
cycles, starting with the sub time step tcond. The next sub time
step for condensation/evaporation/nucleation is estimated based on the
difference between the first- and second-order results provided by the ROS2
solver. Redistribution is computed after each time step of splitting of
coagulation and condensation/evaporation/nucleation.
When the bulk thermodynamic equilibrium approach is used to solve
condensation/evaporation, coagulation and then nucleation are solved after
each emission time step. The resolution is done as previously explained,
except that the dynamic condensation/evaporation solver is disabled: sub
time steps are used to solve coagulation and nucleation during one emission
time step. Condensation/evaporation is then solved using the bulk
equilibrium approach and the redistribution process is applied after the bulk
equilibrium algorithm.
When the hybrid approach is used to solve condensation/evaporation, a
time loop is added with a fixed time step of 600 s outside the emission
time loop to compute bulk equilibrium condensation/evaporation for
equilibrium sections. This additional time loop is designed to ensure that
bulk equilibrium condensation/evaporation of equilibrium sections is
not applied too often, so that the dynamic condensation/evaporation of
dynamic sections has time to evolve. Redistribution is applied after the bulk
equilibrium algorithm. Within this time loop, the aerosol dynamics is solved
as previously explained using the dynamic condensation/evaporation
algorithm for dynamic size sections: emissions are solved followed by
coagulation and condensation/evaporation/nucleation. As in the fully
dynamic approach, redistribution is applied after dynamic
condensation/evaporation.
Model validation
To validate the model, the change with time of internally and externally
mixed aerosol models is compared. The simulations use initial conditions for
number and mass concentrations that are typical of a regional haze scenario,
with constant sulfuric acid vapour source that gives a sulfuric acid
condensation rate of 5.5 µm3cm-3 per 12 h
.
Simulations were conducted for 12 h at a temperature of 298 K and a
pressure of 1 atm. The original reference simulation was first reproduced for internally mixed sulfate particles
(redistribution is not applied). For the sake of comparison between
internally and externally mixed simulations, half of the particles were
assumed to consist of sulfate (species 1) and the other half of another
species of similar physical properties as sulfate (species 2). For internal
mixing, the initial particles are all 50 % species 1 and 50 % species 2;
and for external mixing, half of the initial particles are 100 % species 1
and the other half are 100 % species 2. As both species have the same
physical properties, for any given size section, the sum over all composition
sections of number and mass concentrations of externally mixed particles
should equal the number and mass concentrations of the internally mixed
particles. Particles were discretised into 100 size sections and 10
composition sections for the externally mixed case. Figure
shows the initial and final distributions for the number and volume
concentrations as a function of particle diameters. Both the internally mixed
and externally mixed results are presented in Fig. , along
with the reference results of (500 size sections were used
in the original reference simulation). For the externally mixed simulation,
the results were summed up over composition sections to obtain the
distributions as a function of particle diameter. As expected, an excellent
match is obtained between internal and external mixing distributions, with an
almost 100 % Pearson's correlation coefficient. Furthermore, the accuracy
of the SCRAM algorithm is proved by the excellent match between the results
of these simulations and the reference simulation of . In
order to investigate the influence of the composition resolution on
simulation results, two additional tests are conducted using 2 and
100 composition bins. The mean mass fraction of species 1 is computed for all
particles within each size section, as well as their standard deviations.
Figure shows the size distribution of these statistics. The
mean mass fraction is barely affected by the different composition
resolutions, as the condensation rate of sulfate is independent of the
particle compositions. However, a different composition resolution does lead
to different standard deviation distributions, as only particles with a
larger fraction difference (d>0.2 µm for 2 compositions and
d>0.09 µm for 10 compositions) can be distinguished from each
other under coarser composition resolutions.
Simulation of condensation for hazy conditions: initial distribution
and after 12 h.
Using the same initial conditions and sulfuric acid condensation rate, a
second comparison test was performed, with both coagulation and condensation
occurring for 12 h. As the coagulation algorithm requires size sections to
have fixed bounds , size redistribution was applied for
both the internally and externally mixed cases using the HEMEN method. As in
the first comparison test, Fig. shows that there is an
excellent match between the internally and externally mixed distributions as
a function of particle diameter (no reference simulation was available for
these simulations). This test validates the algorithm of SCRAM to simulate
jointly the coagulation and condensation of externally mixed particles.
Mean and standard deviations of species 1 mass fraction as functions
of particle diameter using 2, 10 and 100 composition sections.
The mixing states of both internally and externally mixed particles at the
end of the simulations of the second test are shown in Fig. .
Sulfuric acid condenses to form particulate sulfate (species 1). During the
simulation, pure species 2 particles mix with pure sulfate particles by
coagulation and condensation of sulfuric acid. Figure shows
that, at the end of the simulation, the sulfate mass fraction is greater for
particles of lower diameters, because the condensation rate is greater for
those particles. Particles with diameters greater than 10 µm
remain unmixed. However, the external mixing state provides a more detailed
mixing map, from which it is possible to distinguish mixed particles from
unmixed ones and to trace the origin of each particle. In this test case
where the effect of condensation dominates that of coagulation, most mixed
particles are originally pure species 2 particles coated with newly condensed
sulfuric acid (Fig. ).
Simulation with realistic concentrations
To test the impact of external mixing on aerosol concentrations, simulations
of coagulation, condensation/evaporation and nucleation were performed
with SCRAM using realistic ambient concentrations and emissions extracted
from a simulation performed over Greater Paris for July 2009 during the
MEGAPOLI (Megacities: Emissions, urban, regional and Global Atmospheric
POLution and climate effects, and Integrated tools for assessment and
mitigation) campaign .
Simulation set-up
Simulation of both coagulation and condensation for hazy conditions:
initial distribution and after 12 h.
Data were extracted from one grid cell of the 3-D simulation performed by
over Greater Paris. This surface grid cell was chosen
because black carbon (BC) emissions are high in that location, due to high
traffic emissions. Figure shows the BC emission map at
02:00 UT, on 1 July 2009. The highest emission rate is located at the grid
cell centre of longitude and latitude (2.28∘ E,
48.88∘ N), which was selected here to extract the SCRAM simulation
input data for emissions, background gas and aerosol concentrations, and
initial meteorological conditions (temperature and pressure). In the absence
of specific information on individual particle composition, all initial
aerosol concentrations extracted from the database were assumed to be 100 %
mixed (i.e. aged background aerosols).
Distribution after 12 h: particle mass concentration
as a function of diameter and mass fraction of species 1.
BC emissions over Greater Paris at 02:00 UT, 1 July 2009.
Simulations start at 02:00 UT (1 July 2009), i.e. just before the morning
peak of traffic emissions, and last 12 h. As our simulations are 0D, the
transport of gases and particles and the deposition processes are not taken
into account. Therefore, emissions accumulate, potentially leading to
unrealistically high concentrations. To avoid this artifact, the duration of
the emissions was limited to the first 40 min of simulation. This time
duration is calculated using the average BC emission rate between 02:00 and
03:00 UT, so that BC emissions lead to an increase in BC concentrations
equal to the difference between BC concentrations after and before the
morning traffic peak, i.e. between 06:00 and 02:00 UT
(Fig. ). Besides, gas-phase chemistry (such as SOA formation)
is not included in SCRAM, and is expected to be solved separately using a
gas-phase chemistry scheme. In the simulations of this work, SOA originate
either from initial conditions or they are emitted as semi-volatile organic
compounds during the simulation. They partition between the gas and the
aerosol phases by condensation/evaporation.
The size distribution ranging from 0.001 to 10 µm was discretised
into seven sections with bounds at 0.001, 0.005, 0.01, 0.0398, 0.1585,
0.6310, 2.5119 and 10 µm. As in , 31
particulate species were included in our simulations. In order to reduce the
computational cost of the externally mixed simulations, these species were
grouped into five groups based on their chemical nature, which influences the
formation of particles and their optical properties. Black carbon, organic
species, inorganic species and dust are separated. Although sulfate could be
separated from nitrate and ammonium for optical properties or for comparisons
to observations of mixing state , and although
chloride and sodium could be grouped together in a marine environment, all
inorganic species are grouped together here for the sake of simplicity.
However, because the hydrophylic properties of the particles strongly
influence their formation and cloud condensation nuclei, hydrophylic and
hydrophobic organic species are separated. In summary, the hydrophilic
inorganic group (HLI) contains five inorganic species (sodium, sulfate,
nitrate, ammonium and chloride); the hydrophilic organic group (HLO) contains
9 hydrophilic surrogate organic species (BiA2D, BiA1D, BiA0D, GLYOXAL, MGLY,
BiMT, BiPER, BiDER and BiMGA); the hydrophobic organic group (HBO) contains
14 hydrophobic surrogate organic species (AnBlP, AnBmP, BiBlP, BiBmP, BiNGA,
NIT3, BiNIT, AnCLP, SOAlP, SOAmP, SOAhP, POAlP, POAmP and POAhP); the black
carbon group (BC) contains only black carbon; and the dust group (DU)
contains all the neutral particles made up of soil, dust and fine sand. Refer
to for detailed nomenclature of the organic
species. For each of the first four groups, the mass fraction of the group
over the total mass is discretised into 3 mass fraction sections
([0.0,0.2),(0.2,0.8],(0.8,1.0]), leading to 20 possible particle
composition sections, as shown in Table . Among them,
there are 5 unmixed particles and 15 mixed particles. Here “unmixed” is
used in an approximate sense: it means that the mass fraction of one chemical
component group is high (between 0.8 and 1), while the mass fractions of the
other chemical component groups are low (between 0 and 0.2). The dust mass
fraction is not discretised, as it is obtained by mass conservation. Note
that although as an example we chose dust to be the group for which mass
fraction is not treated explicitly, another group could be chosen as the
group for which mass fraction is not treated explicitly. If all groups need
to have their mass fraction treated explicitly, additional composition
sections for the last group could be added to the current composition list
without any modification to the main structure of the SCRAM code. The mass
fraction of the last group would still be obtained by mass conservation, and
the composition section of the particles would be chosen depending on this
mass fraction.
20 externally mixed particle compositions.
Composition
Mixing
Mass fraction of each groups
index
state
(%)
HLI
HLO
HBO
BC
DU
1
Unmixed (DU)
0–20
0–20
0–20
0–20
0–100
2
Mixed
0–20
0–20
0–20
20–80
0–80
3
Unmixed (BC)
0–20
0–20
0–20
80–100
0–20
4
Mixed
0–20
0–20
20–80
0–20
0–80
5
Mixed
0–20
0–20
20–80
20–80
0–60
6
Unmixed HBO)
0–20
0–20
80–100
0–20
0–20
7
Mixed
0–20
20–80
0–20
0–20
0–80
8
Mixed
0–20
20–80
0–20
20–80
0–60
9
Mixed
0–20
20–80
20–80
0–20
0–60
10
Mixed
0–20
20–80
20–80
20–80
0–40
11
Unmixed (HLO)
0–20
80–100
0–20
0–20
0–20
12
Mixed
20–80
0–20
0–20
0–20
0–80
13
Mixed
20–80
0–20
0–20
20–80
0–60
14
Mixed
20–80
0–20
20–80
0–20
0–60
15
Mixed
20–80
0–20
20–80
20–80
0–40
16
Mixed
20–80
20–80
0–20
0–20
0–60
17
Mixed
20–80
20–80
0–20
20–80
0–40
18
Mixed
20–80
20–80
20–80
0–20
0–40
19
Mixed
20–80
20–80
20–80
20–80
0–20
20
Unmixed (HLI)
80–100
0–20
0–20
0–20
0–20
In each group, water may also be present, although it is not
considered when computing the mass fractions (it is calculated separately with the thermodynamic
equilibrium models).
The model memorises the relationship between each species index and group
index, and it stores the mass concentrations separately for each species
within each size-composition section. The total mass concentration of each
group is computed from the mass concentration of each species based on the
species-group relations, allowing the computation of the mass fraction of
each group.
Aerosol dynamics and mixing state
To understand how initial concentrations mix with emissions, four scenarios
were simulated. In scenario (A), only emissions are taken into account in the
simulation. Only coagulation is added to emissions in scenario (B), while
only condensation/evaporation (C/E) is added to emissions in scenario
(C). In scenario (D), emissions and all the aerosol dynamic processes are
taken into account, including nucleation (however, no nucleation occurred
during the simulation due to low sulfuric acid gas concentrations).
Transport BC concentration profile of 1 July 2009.
Result mass distributions of externally mixed particles as a
function of particle diameter for the different chemical compositions for six
different simulation scenarios: (a) emission only; (b)
emission + coagulation; (c) emission+C/E; (d)
emission + coagulation + C/E + nucleation; (e) initial
condition; and (f) internal mixing result.
Result number distributions of externally mixed particles as a
function of particle diameter for the different chemical compositions for six
different simulation scenarios: (a) emission only; (b)
emission + coagulation; (c) emission + C/E; (d)
emission + coagulation + C/E + nucleation; (e) initial
condition; (f) internal mixing result.
The mass and number distributions of each chemical composition after 12 h of
simulation are shown in Figs. and as a
function of particle diameter, as well as their initial distributions in
sub-figure (e). Bars with greyscale represent unmixed particles, while bars
with colours are mixed particles. Each bar corresponds to a chemical
composition index (CI). However, any CI with a small number or mass
concentrations are not really visible from the plot, so they are regrouped
into mixed-other (for mixed CI) and unmixed-other (for unmixed CI) in the
plot. The chemical compositions and the CI value associated with colour bars
are listed in Table . All emitted particles are unmixed:
CI 1 (100 % DU) into size section (4–6), CI 3 (100 % BC) into size
section (3–6). So any mixed particles represented in sub-figure (a) of
Figs. and are due to initial condition
instead of emissions. Besides, emissions also involve gas-phase POA and
H2SO4, which can not be observed in sub-figure (a) of
Figs. and as they has no interaction
with particle phase under scenario (A). Organic vapours which may lead to the
production of SOA are not included in the emissions, while a certain
concentration of such vapours is defined within the initial condition.
Mixing state after 12 h simulation.
Process
No Dynamic
Coagulation
C/E
C/E+Coag+Nucl
scenario (A)
scenario (B)
scenario (C)
scenario (D)
Mixed particle number (%)
42
79
48
51
Mixed particle mass (%)
83
85
64
76
As shown by the simulation of scenario (A), emissions lead to high number
concentrations of BC in the sections of low diameters (mostly below
0.631 µm) and to high mass concentrations of dust and BC in the
sections of high diameters (mostly above 0.631 µm).
The comparison of scenarios (A) and (B) shows that coagulation does not
affect much mass concentrations, but significantly reduces the number
concentrations of particles in the sections of diameters lower than
0.631 µm. Also, due to coagulation, small particles migrated to
higher sections. For example, Fig. shows the mixed CI 15
particles that originate from the third size section migrated to the fourth
size section, and this could result from coagulation between CI 14 size
section 4 particles with CI 3 size section 3 particles, or between two CI 15
size section 3 particles.
As shown by the simulation of scenario (C), C/E leads to high mass and
number concentrations of unmixed HBO (CI 6 – mass fraction of HBO (81.2 %)
above 80 % (exact mass fraction of the dominant group will be specified
within the parentheses right after the group name here after)), increasing
the amount of unmixed particles. Organic matter of low and medium
volatilities is emitted in the gas phase following . This
organic matter condenses subsequently on well-mixed particles (CI 14 with
mixed HLI (31 %) and HBO (41 %)), in sufficient amount to increase the
mass fraction of HBO (81 %) to over 80 % and, therefore, transfer
particles to the unmixed category CI 6 (these particles are not exactly
unmixed since up to 20 % may correspond to HLI (10 %), but a finer
composition resolution would be required to analyse their mixed
characteristics). The condensation of organic matter on freshly emitted BC
particles (CI 3) also occurs, as shown by the mixed BC (26 %) and HBO
(68 %) particles (CI 5) which appear in the third and fourth size sections.
As shown by comparing scenarios (A) and (B) and scenarios (C) and
(D), coagulation significantly reduces number
concentrations. The mass concentrations of fine particles (diameters lower
than 0.631 µm) are also reduced. Furthermore, the composition
diversity increases. For example, as demonstrated by the difference between
scenarios (C) and
(D), newly mixed particles of CI 4
(between 20 and 80 % of HBO (78 % for size 4 and 73 % for size 5)) are
formed by the coagulation of unmixed particles from CI 6 with others within
the fourth and fifth size sections.
Result mass distributions of externally mixed particles as a
function of particle diameter for the different chemical compositions for
four different C/E simulation scenarios: (a) external bulk
equilibrium; (b) internal bulk equilibrium; (c) external
hybrid method; and (d) internal dynamic.
Table shows the percentage of mixed particles for each
scenario based on both particle number and mass concentrations. It seems that
large particles are better mixed than small particles as the mixing
percentages of mass are always higher than those of number. However, this
phenomenon is specific to this case study; it is caused by the assumption of
all initial particles being internally mixed and the initial conditions
dominating for large particles due to their low emissions and the short
duration of the simulations.
The number/mass mixing percentages after emission only (scenario A) provide a
baseline for the analysis of the three other scenarios. In scenario (A),
42 % (resp. 83 %) of the particle number (resp. mass) originates from
initial conditions and is mixed, while the remaining particles are due to
emissions and are unmixed. The comparison of scenarios (A) and (B) shows that
coagulation increases the mixing percentages, especially for small particles
of high number concentrations. The mass mixing percentages decrease in
scenario (C) because the condensation of freshly emitted organic matter on
large mixed particles leads to particles with a mass fraction of organic
matter (HBO) higher than 80 %, i.e. unmixed. When all aerosol dynamic
processes are taken into account (scenario D), only 51 % of particle number
concentration and 76 % of particle mass concentration are mixed. The mixing
percentages are greater than those of scenario (C), as mixing increases by
coagulation, but the mass mixing percentage is lower than in scenario (A)
(emissions only) because of the strong condensation of HBO emitted in the gas
phase.
External versus internal mixing
To investigate the consequence of the internal mixing hypothesis, a
simulation of scenario (D) (all aerosol dynamic processes are taken into
account) is conducted by assuming all particles to be internally mixed.
Externally and internally mixed 12 h simulations lead to a similar total
aerosol mass concentration after 12 h (33.09 µgm-3 for
internal mixing and 33.35 µgm-3 for external mixing) as well
as to similar total number concentrations (1.16×1010 #m-3 for internal mixing and 1.07×1010 #m-3 for external mixing). The bulk mass
concentrations of individual species are also similar, although external
mixing leads to slightly lower ammonium concentrations (2.68 #m-3 versus 2.70 #m-3), slightly higher nitrate
concentrations (3.19 #m-3 versus 3.03 #m-3) and
higher chloride concentrations (0.36 #m-3 versus
0.25 #m-3). The size distributions for number and for
individual species masses are also very similar in the internal and external
mixing simulations.
Figure d and f compare the mass distributions and
compositions within each size section after 12 h of the internal and
external mixing simulations. External mixing provides more detail about the
particle mixing state, as within each size section particles have different
compositions. For example, in the case of internal mixing, particles in size
section 4 (diameter between 0.0398 and 0.1585 µm) are all mostly
hydrophobic organics (CI 4: HBO (76 %) between 20 and 80 %). The particle
compositions are more detailed in the external mixing simulation: while less
than half of the particles are mostly hydrophobic organics (HBO 78 %) (CI
4) as in internal mixing, a large amount are unmixed particles (CI 6: HBO
(82 %) between 80 and 100 %), and some are equally mixed with BC and
hydrophobic organics (CI 5). In size section 5, as in the internal mixing
simulation, mixed particles dominate (CI 14 – HLI 46 %, HBO 36 %), but
many have a different composition (CI 4 and 5) and some are unmixed HBO
83 % (CI 6), BC 91 % (CI 3) and dust 90 % (CI 1). For particles in size
section 6, particles are mixed particles of CI 12 (HLI 54 %,DU 29 %),
while external mixing also shows that some particles are unmixed (BC 99 %
(CI 3) and dust 98 % (CI 1)) and there are CI 14 (HLI 46 %, HBO 35 %)
particles that originated from size section 5 through coagulation.
Bulk equilibrium and hybrid approaches
Result number distributions of externally mixed particles as a
function of particle diameter for the different chemical compositions for
four different C/E simulation scenarios: (a) external bulk
equilibrium; (b) internal bulk equilibrium; (c) external
hybrid method; and (d) internal dynamic.
Additional external mixing tests were conducted using the bulk equilibrium
and hybrid approaches for C/E to evaluate both their accuracy and
computational efficiency. In the hybrid approach, the lowest four sections
are assumed to be at equilibrium (up to diameters of 0.1585 µm),
whereas the other sections undergo dynamic mass transfer between the gas and
particle phases.
The accuracy of these approaches is evaluated by comparing the mass and
number distributions after 12 h simulations with the bulk equilibrium or the
hybrid approaches to the mass and number distributions computed dynamically
(see Figs. and ).
For externally mixed particles, the dynamic mass distribution is shown in
Fig. c; the bulk equilibrium and hybrid mass distributions
are shown in Fig. a and c, respectively. The dynamic
number distribution is shown in Fig. c; the bulk equilibrium
and hybrid mass distributions are shown in Fig. a and c,
respectively. For internally mixed particles, the dynamic mass/number
distributions are shown in Figs. d and
d and the bulk equilibrium mass/number distributions in
Figs. b and
b, respectively.
For internally mixed particles, the comparisons between
Fig. b and d and between Fig. b and d
indicate that the bulk equilibrium approach leads to significantly different
distributions and compositions than the dynamic approach. This result also
holds for externally mixed particles, as shown by the comparisons between
Figs. c and a and between
Figs. c and a. For example, more
inorganic species condense on particles in the fourth size section (between
0.0398 and 0.1585 µm) in the case of bulk equilibrium compared to
the fully dynamic case. This section is dominated by CI 14 (HLI 33 %, HBO
61 %) (equal mixture of inorganic and hydrophobic organics) for bulk
equilibrium, instead of CI 6 (HBO 81 %) (unmixed hydrophobic organics) for
dynamic. Internal and external distributions are similar with the dynamic
approach, as well as with the bulk equilibrium approach. Although internal
and external compositions are different with the dynamic approach, they are
quite similar with the bulk equilibrium approach. However, with the bulk
equilibrium approach, similarly to the dynamic approach, unmixed particles of
CI 3 (unmixed BC) remain present in most size sections for externally mixed
particles.
The mass and number distributions and compositions obtained with the hybrid
approach are similar to the fully dynamic approach. For example, the
over-condensation of inorganic species in the fourth size section (leading to
particles of CI 14 (HLI 33 %, HBO 61 %) with bulk equilibrium) is
restrained with the hybrid approach, as the fourth size section is computed
dynamically, and particles consist of CI 6 (HBO 81 %), as with the dynamic
approach.
Computational times.
Process
C/E
C/E bulk
C/E hybrid
Coag
C/E + Coag
C/E + Coag bulk
C/E + Coag hybrid
Internal mixing(s)
7.1
0.11
0.4
0.06
7.3
0.14
0.5
External mixing(s)
63.2
0.3
54.2
48.4
122.8
31.5
113
Table shows the computational times (CPU) required for each
simulation on a DELL Precision T3500 workstation (the lowest integration time
step: 1). External mixing requires more CPU, especially for computing
coagulation and dynamic C/E. The largest difference between internal
and external mixing occurs for computing coagulation, which is almost 800
times slower with external mixing. Bulk equilibrium C/E provides a huge
economy in CPU time for all simulations compared to dynamic C/E, while
the computational advantage of hybrid C/E is more obvious for internal
mixing (17 times faster than dynamic C/E) than external mixing (15 %
faster than dynamic C/E). This significant speed degradation of the
hybrid C/E scheme in the external mixing case is probably a consequence
of small time steps used in the ROS2 solver because of the redistribution
among the different composition sections performed after each time step. In
other words, it takes CPU time to compute the dynamic distribution among the
different composition sections.
Conclusions
The new Size-Composition Resolved Aerosol Model (SCRAM) has been developed to
simulate the dynamic evolution of externally mixed particles due to
coagulation, condensation/evaporation, and nucleation. The general dynamic
equation is discretised for both size and composition. Particle compositions
are represented by the combinations of mass fractions, which may be chosen to
correspond either to the mass fraction of the different species or to the
mass fraction of groups of species (e.g. inorganic, hydrophobic organics,
etc.). The total numbers and bounds of the size and composition sections are
defined by the user. An automatic classification method is designed within
the system to determine all the possible particle compositions based on the
combinations of user-defined chemical species or groups and their
mass-fraction sections.
The model was first validated by comparison to internally mixed simulations
of condensation/evaporation of sulfuric acid and of
condensation/evaporation of sulfuric acid with coagulation. It was also
validated for condensation against a reference solution.
The model was applied using realistic concentrations and typical emissions of
air pollution over Greater Paris, where traffic emissions are high. Initial
concentrations were assumed to be internally mixed. Simulations lasted 12 h.
Although internally and externally mixed simulations lead to similar particle
size distributions, the particle compositions are different. The externally
mixed simulations provide details about particle mixing states within each
size section when compared to internally mixed simulations. After 12 h,
49 % of number concentrations and 24 % of mass concentrations are not
mixed. These percentages may be higher in 3-D simulations, because initial
aerosol concentrations should not be assumed as entirely internally mixed
over an urban area. Coagulation is quite efficient at mixing particles, as
52 % of number concentrations and 36 % of mass concentrations are not
mixed if coagulation is not taken into account in the simulation. On the
opposite end, condensation may decrease the percentage of mixed particles
when low-volatility gaseous emissions are high.
Assuming bulk equilibrium when solving condensation/evaporation leads to
different size and composition distributions than the dynamic approach under
both the internally and externally mixed assumptions. With the bulk
equilibrium approach, internally and externally mixed assumptions lead to
similar average compositions as a function of size, and unmixed particles
remain under the externally mixed assumption, which were also observed with
the dynamic C/E approach.
Although the simulation of externally mixed particles increases the
computational cost, SCRAM offers the possibility to investigate particle
mixing state in a comprehensive manner. Besides, its mixing state
representation is flexible enough to be modified by users. Better
computational performance could be reached with fewer, yet appropriately
specified species groups and more optimised composition discretisations. For
example, about half of the 20 compositions designed in this work have really
low mass concentrations (e.g. see Figs. ,
, and ). Those
compositions might be dynamically deactivated in the future version of SCRAM
to lower computational cost by using an algorithm to skip empty sections
during coagulation and C/E processing.
Future work will focus on the optimisation and incorporation of SCRAM into
the Polyphemus air quality modelling platform for 3-D simulations. In order
to investigate its performance in modelling air quality over Greater Paris,
model simulation results will be compared to observations
.