The extended SALSA module
The Sectional Aerosol module for Large-Scale Applications (SALSA;
) is used as the basis for developing a unified
sectional microphysical model for aerosols, clouds and precipitation. The
SALSA module, previously employed in the ECHAM climate
model family, discretises the aerosol size distribution into 10 size bins
according to the dry particle diameter as shown in
Fig. . The predicted variables for each bin are the
aerosol number and compound masses as well as the mass of condensed water,
which can be used to determine the bin mean wet particle size. The total
diameter range covered by the bins (from 3 nm to 10 µm by
default) is divided into subranges, 1a and 2a. This division into subranges
aims at minimising the number of tracer variables. This is achieved by
including only those chemical compounds that are significantly abundant in
each subrange. Subrange 1a covers the three smallest bins (up to 50 nm)
and the particles are assumed to be internally mixed, being composed of
sulfate and organic carbon, which contribute to the growth of newly formed
particles. Subrange 2a includes particles larger than 50 nm, whose
composition may comprise all the chemical compounds in the model. The module
can be configured to include seven additional bins (designated 2b) parallel to
the bin regime 2a (i.e. same bin diameters), which allow for the description of
externally mixed particle populations. In a typical example, soluble
compounds would be emitted to 2a and insoluble compounds to 2b. The spacing
of the size bins is set logarithmically equidistant within each of the
subranges. Further details about the bin discretisation can also be found in
. With these settings, the spectral resolution is quite
coarse, but does provide a good compromise between computational cost and
model performance. Note, however, that the numbers given here represent the
default settings – the number of bins can be set to be larger, if necessary.
The SALSA module includes detailed methods for solving the key microphysical
processes, which are called sequentially. Coagulation is modelled based on the
equations in . For a particle number this is given as
ni,t=ni,t-11+Δt∑j=i+1JKi,jnj,t-1+12ΔtKi,ini,t-1
and, similarly, for a volume concentration
vi,t=vi,t-1+Δt∑j=1i-1Kj,ivj,tni,t-h1+Δt∑j=i+1JKi,jnj,t-1.
In the above equations, Ki,j is the total coagulation kernel for the
colliding particles in bins i and j, ni,t is the particle number
concentration in bin i at time step t (t-1 refers to the previous
time step), vi,t is the volume concentration, Δt the length of
the time step and J is the total number of particle bins. Please note that
the bin indices 1…J should be interpreted to cover all the bins of
all particle categories in the model (aerosol, clouds, precipitation) sorted
by increasing particle size.
For coagulation kernels with aerosol particles, we assume Brownian
coagulation, whose kernel in the continuum regime is given as
Ki,jB=2π(di+dj)(Dp,i+Dp,j),
where di and dj are the diameters of the colliding particles and
Dp,i and Dp,j their corresponding diffusion
coefficients. For the transition regime, the formula by is
used. For larger particles, i.e. cloud droplets and precipitation, the
convective enhancement of Brownian coagulation and gravitational collection
are also included, and given as
Ki,jBC=Ki,jB0.45Rej1/3Sci1/3Rej≤1,dj≥diKi,jB0.45Rej1/2Sci1/3Rej>1,dj≥di
and
Ki,jGC=Ei,jcπdi+dj22|Vf,i-Vf,j|,
respectively . In the above equations, Sci is the
particle Schmidt number, Rej is the Reynolds number, Ei,jc is
the collection efficiency and Vf,i is the particle fall speed.
The latter is parameterised as
Vf,i=di2(ρp-ρa)gβ18γdi<40µm2×103diρa,refρa2di≥40µm,
where ρp is the particle/droplet density and ρa is
the air density. ρa,ref is a reference air density (given at the
standard conditions for temperature and pressure, 273.15 K and 1000 hPa), g is the gravitational
acceleration, γ is the dynamic viscosity of air and β is the
Cunningham slip correction factor. The total coagulation kernels in
Eqs. () and () are obtained as the sum Ki,j=Ki,jB+Ki,jBC+Ki,jGC. All the
coagulation kernels are currently updated each time step. However, this is
computationally inefficient and the use of lookup tables with
bilinear
interpolation in particle size is planned.
Condensation of water vapour and aerosol precursors gases (currently sulfuric
acid and organics) is based on the analytical predictor of condensation (APC)
scheme by . The scheme first calculates the new vapour
mole concentration as
Ct=Ct-1+Δt∑i=1Jki,t-1Si,t-1Cs,i,t-11+Δt∑i=1Jki,t-1,
where ki,t-1 is the mass transfer coefficient in size bin i based on
the current time step, J is the total number of bins (including all particle
categories), Si,t-1 is the equilibrium supersaturation and
Cs,i,t-1 is the saturation mole concentration over a flat
surface. The new particle mole concentrations for each condensing vapour are
then given in a semi-implicit form.
ci,t=ci,t-1+Δtki,t-1(Ct-Si,t-1Cs,i,t-1)
While the APC scheme is mass preserving and numerically stable, condensation
and evaporation of water vapour on small droplets and especially small
aerosol particles requires a very short time step (≪ 1 s) to
avoid non-oscillatory solutions. Since this goes beyond the practical range
for the applications in this paper, where in general we aim towards a
time step around 1 s, two sets of measures are taken. First, for small aerosol
particles with ambient relative humidity (RH) below 98 %, the wet
size of aerosol particles is determined as an equilibrium solution based on
the molalities of different particle species ,
and the APC equations are solved only above 98 % RH. Second, a
simple substepping method is applied with Eqs. ()
and (), where the substep length for cloud droplets is user
defined and currently set as Δtc=0.1 s. For
non-activated aerosol above the 98 % threshold for RH, even further
time splitting was found necessary and the timescale is Δta=tc/10. The equilibrium saturation ratio is updated for each
substepping cycle due to changing droplet/particle size (temperature is kept
constant).
Although not used in the context of this paper, new particle formation by
sulfuric acid is included in the model. There, the activation-type nucleation
is formulated according to and the formation rate of
3 nm particles is calculated according to .
Cloud droplets
In the new extended SALSA, cloud droplets are treated with a sectional
description as well (Fig. ). Strictly speaking, to
reproduce the evolution of the aerosol size distribution through cloud
processing and wet scavenging accurately, which is the goal of this work, a
two-dimensional dry–wet diameter bin system would be required. This is
because cloud activation depends essentially on the dry aerosol size
distribution, while collision processes and deposition rates depend strongly
on the wet particle size. Although such two-dimensional frameworks have been
developed e.g., the approach is computationally highly
demanding for large-eddy modelling applications spanning timescales of days
while covering relatively large domains with high spatial resolution, all of
which are pursued here. As a compromise between accuracy and computational
cost, a unique strategy is proposed, where cloud droplets are described based
on the dry size of the activated aerosol (i.e. cloud condensation nuclei,
CCN) with the same prognostic bin quantities as for the aerosol bins. The
particle diameters at the bin edges for the cloud droplet and non-activated
aerosol regimes are set identical within their common size range
(specifically, the 2a,b bins as a default setting) as shown in
Fig. . Therefore, each cloud droplet bin is accompanied by
a parallel aerosol bin. This way, the shape of the aerosol size distribution
and the number concentration are preserved upon cloud droplet activation as
well as upon droplet evaporation though subject to the typical uncertainties
inherent to the sectional approach . While the CCN dry
diameter is known accurately (to the extent allowed by the spectral
resolution of the size sections), the wet size of the cloud droplets,
determined by Eqs. ()–(), represents a mean over
each CCN size class.
Two methods are available for simulating the formation of cloud droplets in
the extended SALSA. One is the parameterisation by ,
which takes as an input the aerosol properties and updraft velocity (along
with atmospheric thermodynamic properties) to determine the maximum
supersaturation in a parcel of air and thus the critical particle diameter
for activation. Another is based on resolving the wet aerosol particle
diameter; once the wet diameter of a particle exceeds the critical diameter corresponding to the resolved
supersaturation from the host model, the particle is activated. Since the condensation of water vapour is
solved dynamically for high RH, it is preferable to use the latter approach instead of the parameterised one for consistency
in terms of the peak supersaturation and it is the approach used in the
experiments of this work. This allows for droplet activation also in other
parts of the cloud apart from the cloud base, e.g. due to radiative cooling
effects at the cloud top or supersaturation caused by mixing of air masses.
However, if the vertical resolution of the host model is coarse (several tens
of metres and above) it becomes necessary to use the parameterised method.
With coarse resolutions the supersaturation peak at the cloud base may be
underestimated due to averaging effects, which yields underestimated cloud
droplet number concentrations.
The relatively coarse spectral resolution of the aerosol bins may induce
unwanted discontinuities in the activation spectrum with increasing
saturation ratio due to the particle size discretisation. To mitigate these
effects, the extended SALSA accounts for the distribution of particle number
and mass within the critical aerosol size bin using linearly fitted slopes
between the bin centres with both of the available
methods for cloud activation.
Evaporation and deactivation of cloud droplets is accounted for through the
resolved condensation, upon which activated aerosol particles are released
back to the aerosol bin regime as illustrated in Fig. .
For this to take place, a very simple diagnostic is used, where subsaturation
with respect to water vapour is required and the cloud droplet diameter
should be smaller than 50 % of the critical diameter dictated by the
properties of the CCN (or 2 µm at maximum). Together with the
representation of collision–coalescence processes by Eqs. ()
and (), this enables the model to account for aerosol aging
inside the clouds. However, please note that chemical processing of aerosol
is not presently included in the extended SALSA.
Precipitation
Due to our strategy of describing the cloud droplet distribution based on the
dry CCN size, the wet droplet diameter in each bin represents a mean over all
activated CCN of the corresponding size. Although the wet droplet size can be
expected to be somewhat correlated with the dry CCN size, neglecting the
variability in the dry–wet size relationship is an oversimplification when
predicting the mass and number of particles converted to drizzle droplets.
Therefore, a type of autoconversion parameterisation is formulated. Here, a
log-normal distribution (selected because of mathematical simplicity) is
assumed to describe the variation of the droplet wet size within each cloud
droplet bin. The mode diameter is given by the known bin mean wet cloud
droplet diameter and the geometric standard deviation is set as
σgac=1.2, which results in a relatively narrow
distribution and is similar to the values used for the cloud droplet size
distribution in the UCLA Large-Eddy Simulation Code (UCLALES) with bulk
microphysics. Setting a commonly used threshold diameter for drizzle
droplets, d0=50 µm, the number and mass concentrations of
newly formed drizzle from the cloud droplet bins are obtained as an integral
over the log-normal distribution from d0 upwards.
The evolution of precipitation is described with an additional set of size
bins (Fig. ). However, since the growth of the drizzle
droplets through collection processes is critical to reach rain drop size and
produce realistic surface precipitation rates, the precipitation bins are
defined according to the wet drop diameter, different from the cloud and
aerosol size bins. While the predicted bin properties are again similar to
aerosol and cloud droplets, now the aerosol mass (instead of the mass of
water) represents a mean for each precipitation size class. This is in
contrast with our emphasis of tracking the aerosol size distribution
properties but is an acceptable compromise, since the number concentration
of rain drops is always much smaller than the concentration of cloud droplets
or aerosols. Thus, their influence on the shape and chemical composition of
the ambient aerosol size distribution upon drop evaporation is not
considerably obscured by the averaging effects acting on the properties of
the aerosol particles embedded inside the rain drops. The precipitation bins
cover the size range from 50 µm to 2 mm. This range is divided
into seven (currently fixed) sections with strongly non-uniform spectral
resolution; up to the diameter of 100 µm (first 3 bins) the bin
resolution gradually decreased from 5 to 35 µm and above the
100 µm range the resolution decreases from 100 µm to
1 mm.
Collection and scavenging of cloud droplets and aerosol particles by
precipitation are treated by the coagulation (Eqs.
and ) as well. Aerosol particles collected by precipitation
accumulates the aerosol mass inside the size bins. Upon evaporation of a
drizzle or rain drop, it is assumed that a single particle is released
and it is placed in an aerosol bin with the mean diameter
closest to the released dry particle size. The size of the released particle
is obtained simply based on the mass and the bulk density of the aerosol.
This adds the contribution of drizzle formation on the aerosol processing in
the model, albeit, again omitting the chemical processing.
Coupled UCLALES–SALSA
UCLALES is a large-eddy model based on the
Smagorinsky–Lilly subgrid model. In the doubly periodic domain, advection of
momentum variables is based on a fourth-order difference equation with
time-stepping by the leap-frog method. For scalars, simple forward
time stepping is used. Prognostic variables in the UCLALES are the three wind
components u, v and w (with the standard meteorological notation),
liquid water potential temperature θl and total water mixing
ratio qt, plus some additional prognostic scalars depending on the
selected thermodynamic level (e.g. rain water). UCLALES contains three
thermodynamic levels, which comprise dry, moist and precipitating
thermodynamical models, the latter two of which are based on the saturation
adjustment method. UCLALES does not include a description for aerosol.
Rather, the microphysical processes are driven by a prescribed cloud
condensation nuclei (CCN) concentration, taken to represent the cloud droplet
number. The drizzle formation is given by as
∂qr∂t=kcqc2xc2,
where qr is the precipitation mixing ratio, qc is the
cloud condensate mixing ratio xc=qc/Nc, where
Nc is the CCN concentration and kc is a coefficient
taking into account the droplet size distribution width and non-equilibrium
effects . Sedimentation of the drizzle and rain drops is
determined by sedimentation velocity, which depends on the diagnosed droplet
size according to Eq. ().
Coupling the extended SALSA module into UCLALES yields extensive changes in
the thermodynamic core of the model as compared to the version based on bulk
microphysics, thus adding a new thermodynamic level (Level 4). With the
coupled UCLALES–SALSA, condensation and evaporation of water vapour on cloud
droplets, rain drops and aerosols is explicitly computed (Eq. ).
Therefore, instead of qt in case of the saturation adjustment
method, level 4 treats qc, qr and the water-vapour mixing
ratio (qv) as separate prognostic variables. This allows
non-equilibrium conditions with respect to water vapour in UCLALES–SALSA, in
contrast to the standard UCLALES. θl is retained as a
prognostic variable, which allows for simple treatment of the latent heat
transfer during moist adiabatic transitions.
UCLALES has an option to calculate cloud interaction with radiation using a
four-stream radiative transfer solver . The radiation
calculation accounts for the diurnal cycle and takes as an input the total
number concentration of cloud droplets and the cloud water content. With
UCLALES–SALSA, the total number of droplets and condensate mass are obtained
as the sum over the cloud droplet size bins and used to calculate radiative
transfer the same way as in UCLALES (the aerosol fields are not coupled with
radiation in the current model version).