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**Geoscientific Model Development**
An interactive open-access journal of the European Geosciences Union

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GMD | Articles | Volume 12, issue 4

Geosci. Model Dev., 12, 1403–1422, 2019

https://doi.org/10.5194/gmd-12-1403-2019

© Author(s) 2019. This work is distributed under

the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/gmd-12-1403-2019

© Author(s) 2019. This work is distributed under

the Creative Commons Attribution 4.0 License.

Special issue: The PALM model system 6.0 for atmospheric and oceanic boundary-layer...

**Model description paper**
11 Apr 2019

**Model description paper** | 11 Apr 2019

Implementation of the sectional aerosol module SALSA2.0 into the PALM model system 6.0: model development and first evaluation

^{1}Institute for Atmospheric and Earth System Research/Physics, Faculty of Science, University of Helsinki, P.O. Box 68, 00014 Helsinki, Finland^{2}Finnish Meteorological Institute, 00101 Helsinki, Finland^{3}Division of Nuclear Physics, Lund University, 22100 Lund, Sweden^{4}Finnish Meteorological Institute, 70211 Kuopio, Finland^{5}Department of Meteorology, University of Reading, Reading RG6 6BB, UK^{6}Global Centre for Clean Air Research (GCARE), Department of Civil & Environmental Engineering, University of Surrey, Guildford GU2 7XH, UK^{7}Leibniz University Hanover, Institute of Meteorology and Climatology, 30419 Hanover, Germany^{8}Geophysical Institute, University of Bergen, 5020 Bergen, Norway^{9}Helsinki Institute of Sustainability Science, University of Helsinki, 00014 Helsinki, Finland

^{1}Institute for Atmospheric and Earth System Research/Physics, Faculty of Science, University of Helsinki, P.O. Box 68, 00014 Helsinki, Finland^{2}Finnish Meteorological Institute, 00101 Helsinki, Finland^{3}Division of Nuclear Physics, Lund University, 22100 Lund, Sweden^{4}Finnish Meteorological Institute, 70211 Kuopio, Finland^{5}Department of Meteorology, University of Reading, Reading RG6 6BB, UK^{6}Global Centre for Clean Air Research (GCARE), Department of Civil & Environmental Engineering, University of Surrey, Guildford GU2 7XH, UK^{7}Leibniz University Hanover, Institute of Meteorology and Climatology, 30419 Hanover, Germany^{8}Geophysical Institute, University of Bergen, 5020 Bergen, Norway^{9}Helsinki Institute of Sustainability Science, University of Helsinki, 00014 Helsinki, Finland

**Correspondence**: Mona Kurppa (mona.kurppa@helsinki.fi)

**Correspondence**: Mona Kurppa (mona.kurppa@helsinki.fi)

Abstract

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Urban pedestrian-level air quality is a result of an interplay between turbulent dispersion conditions, background concentrations, and heterogeneous local emissions of air pollutants and their transformation processes. Still, the complexity of these interactions cannot be resolved by the commonly used air quality models. By embedding the sectional aerosol module SALSA2.0 into the large-eddy simulation model PALM, a novel, high-resolution, urban aerosol modelling framework has been developed. The first model evaluation study on the vertical variation of aerosol number concentration and size distribution in a simple street canyon without vegetation in Cambridge, UK, shows good agreement with measurements, with simulated values mainly within a factor of 2 of observations. Dispersion conditions and local emissions govern the pedestrian-level aerosol number concentrations. Out of different aerosol processes, dry deposition is shown to decrease the total number concentration by over 20 %, while condensation and dissolutional increase the total mass by over 10 %. Following the model development, the application of PALM can be extended to local- and neighbourhood-scale air pollution and aerosol studies that require a detailed solution of the ambient flow field.

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How to cite.

Kurppa, M., Hellsten, A., Roldin, P., Kokkola, H., Tonttila, J., Auvinen, M., Kent, C., Kumar, P., Maronga, B., and Järvi, L.: Implementation of the sectional aerosol module SALSA2.0 into the PALM model system 6.0: model development and first evaluation, Geosci. Model Dev., 12, 1403–1422, https://doi.org/10.5194/gmd-12-1403-2019, 2019.

1 Introduction

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The coincidence of rising population densities, high air pollutant emissions, and limited ventilation in urban areas leads to an increasing number of air-pollution-related health problems and premature deaths globally every year (Gakidou et al., 2017; WHO, 2016). The local air quality is an outcome of complex interactions between the urban landscape, meteorology, background pollutant concentrations, and local emissions, as well as the chemical and physical processes of air pollutants. Thereby, urban air pollutant concentration fields are highly irregular in both time and space (e.g. Kumar et al., 2011). At the same time, pollutant characteristics, such as the size of aerosol particles and the chemical compositions of both particles and gaseous mixtures, are essential factors in determining health impacts (for review, see, e.g. Kelly and Fussell, 2012). Traditionally used local urban air quality models, such as Gaussian dispersion or semi-empirical street pollution models, cannot resolve these details in concentration fields and interactions due to an inadequate representation of urban complexity and limitations in resolving any fine-scale flow structures (Tominaga and Stathopoulos, 2016).

Detailed information on the variability of urban air pollutant concentrations are, however, highly valuable to urban planning to design healthy living environments (Giles-Corti et al., 2016; Kurppa et al., 2018), to air quality monitoring network design, and to conducting exposure studies. Therefore, a building-resolving tool for simulating and predicting air quality in real complex urban environments in current and future conditions is needed. To determine airflow and dispersion, computational fluid dynamics (CFDs) models, notably large-eddy simulation (LES), are currently the most promising methods. Compared to LES, turbulence models based on Reynolds-averaged Navies–Stokes (RANS) equations can be computationally less demanding, but their ability to resolve instantaneous turbulence structures above a complex urban surface is shown to be clearly weaker (e.g. Antoniou et al., 2017; García-Sánchez et al., 2018, and references within). With either method, the computational costs have been the bottleneck in extending CFD-based air quality modelling from tailpipe emission studies (e.g. Huang et al., 2014; Liu et al., 2011) to neighbourhood-scale studies. Fortunately, constantly increasing computational power has already allowed urban LES modelling for entire neighbourhoods up to 1 day or even more in a supercomputing environment (e.g. Resler et al., 2017). Currently, there are a number of RANS and LES models coupled with some chemical mechanism (Zhong et al., 2016) and a few RANS models with an aerosol module, for instance Mercure_Saturne with MAM (Albriet et al., 2010) and ANSYS-Fluent-based models (Uhrner et al., 2007; Huang et al., 2014) such as CTAG (Wang and Zhang, 2012). There is also at least one LES model including a detailed aerosol module (Liu et al., 2011), which, however, is only applied in a tailpipe emission study. The CTAG model has also been run in an LES mode (Steffens et al., 2013), but to date aerosol simulations have only considered dry deposition (Tong et al., 2016a, b) and chemical composition has been usually ignored.

The fate of aerosol particles in the atmosphere substantially depends on their size distribution. Consequently, detailed aerosol modelling requires size-specific emission and background information as input. Estimates for background aerosol size distributions and concentrations can be attained from larger-scale models, whereas emission data are usually treated as total aerosol mass. Hence, emission size distribution has to be estimated based on the source type and vehicle fleet in the case of traffic emissions. If any important emission source is neglected, aerosol processes are also calculated erroneously. At the same time, as LES outperforms traditionally used urban air quality models in resolving the turbulent wind field and pollutant dispersion, LES-based air quality models produce unique information on pollutant transformation and dispersion processes with accurate emission estimates.

Numerical approaches to describe the aerosol size distribution and to solve the aerosol general dynamic equations can generally be divided into modal, moment, and sectional approaches. Modal aerosol modules (Ackermann et al., 1998; Liu et al., 2012; Vignati et al., 2004) represent the continuous aerosol size distribution as a superposition of several modes (usually log-normal distributions), whereas moment-based methods track the lower-order radial moments of the aerosol size distribution (McGraw, 1997). Both approaches are computationally efficient due to the small number of prognostic variables. However, the modal approach lacks accuracy in simulating the evolution of the aerosol size distribution, especially if the standard deviations of log-normal modes are not allowed to vary (Whitby and McMurry, 1997; Zhang et al., 1999). Applying the moment approach instead requires resolving a closure problem of the moment evolution equations (Wright et al., 2001). Furthermore, as aerosol properties are tied into moments, which are typically not observed properties except for the first moments, retrieving information on aerosol properties during the simulation increases the computational load. In the sectional approach (Gong et al., 2003; Zaveri et al., 2008; Zhang et al., 2004), the aerosol size distribution is represented as a discrete set of size bins. The sectional approach is flexible and accurate, but it is usually more computationally demanding due to the high number of prognostic variables.

To meet the needs of a high-resolution urban air quality model that can
account for the complex interactions controlling the local air quality at the
neighbourhood to city scale, this article presents the implementation of the
aerosol module SALSA2.0 (Sectional Aerosol Module for Large Scale
Applications; Kokkola et al., 2008, 2018) as a part of the PALM model system
(see Maronga et al., 2015, for a description of PALM 4.0; a description of
version 6.0 is envisaged in this special issue of *Geoscientific Model Development*). The aim is to include aerosol dynamic processes into PALM,
evaluate the model performance under different wind conditions, and study the
relative impact of aerosol processes on the aerosol size distribution and
chemical composition in real urban environment.

The modelling methods and equations of SALSA2.0, implementation into PALM, computational costs, and inevitable numerical issues related to the sectional representation are discussed in Sect. 2. The model evaluation set-up and sensitivity tests are described in Sect. 3 and the results of the model simulations in Sect. 4. Finally, Sect. 5 discusses the applications and limitations of the model.

2 Model description

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The PALM model system (version 6.0) features an LES core for atmospheric and
oceanic boundary layer flows, which solves the non-hydrostatic, filtered,
incompressible Navier–Stokes equations of wind (*u*, *v*, and *w*) and
scalar variables (sub-grid-scale turbulent kinetic energy *e*, potential
temperature *θ*, and specific humidity *q*) in Boussinesq-approximated
form. Note that PALM, originally developed as a pure LES code, now also
offers a RANS-type turbulence parameterization. PALM is especially suitable
for complex urban areas owing to features such as a Cartesian topography
scheme, a plant canopy module, and recent model enhancements like the
so-called PALM-4U (short for PALM for urban applications) components, including an
urban surface scheme (first version described in Resler et al., 2017) and a
land surface scheme (first description in Maronga and Bosveld, 2017). Furthermore,
other PALM-4U components, such as
chemistry and indoor climate modules, have been or are currently being
implemented into the PALM model system to develop a modern and highly
efficient urban climate model (Maronga et al., 2019). Due to its excellent
scalability on massively parallel computer architectures (up to 50 000
processor cores; Maronga et al., 2015), PALM is applicable for carrying out
computationally expensive simulations over large, neighbourhood-scale, and
city-scale domains with a sufficiently high grid resolution for urban LES
(Auvinen et al., 2017; Xie and Castro, 2006). The performance of PALM over urban-like surfaces
has been successfully evaluated against wind tunnel simulations, previous LES
studies, and field measurements
(Kanda et al., 2013; Letzel et al., 2008; Park et al., 2015; Razak et al., 2013). Some fundamental technical
specifications of PALM are represented in
Table 1.

SALSA2.0 (referred to hereafter simply as SALSA) was selected as the basis for representing aerosol dynamics in PALM since one major criterion in its development has been limiting computational expenses without the cost of accuracy. A major share of the expenses stem from having a large number of prognostic variables to describe the aerosol population. SALSA has been optimized for resolving aerosol microphysics in a very large number of grid points, such as in global-scale climate models. Nonetheless, the same aerosol processes and model design choices are relevant at local scale.

In SALSA, the aerosol number size distribution is discretized into
*X*_{B} size bins *i* based on the mean dry particle diameter
${\stackrel{\mathrm{\u203e}}{D}}_{i}$ of each bin. The number *n*_{i} (m^{−3}) and mass
concentration *m*_{c, i} (kg m^{−3}) of each chemical component *c*
are the model prognostic variables. SALSA was originally optimized for
computationally expensive large-scale climate models, and therefore the
number of size bins is kept to a minimum (default *X*_{B}=10) and
only the following chemical components can currently be included: sulfuric
acid (H_{2}SO_{4}), organic carbon (OC), black carbon (BC), nitric acid
(HNO_{3}), ammonium (NH_{3}), sea salt, dust, and water
(H_{2}O). Furthermore, the gaseous concentrations of H_{2}SO_{4},
HNO_{3}, NH_{3}, and semi- and non-volatile organics (SVOCs and
NVOCs) that can condense or dissolve on aerosol particles are also default
prognostic variables. Nitrates and ammonium were not included in the original
SALSA but have later been added (Kudzotsa et al., 2019). The sectional size
distribution can be further divided into subranges 1 (${\stackrel{\mathrm{\u203e}}{D}}_{i}\mathit{\lesssim}\mathrm{50}$ nm) and 2 (${\stackrel{\mathrm{\u203e}}{D}}_{i}\mathit{\gtrsim}\mathrm{50}$ nm). Subrange 1 consists of
the smallest particles assumed to be internally mixed, strongly hygroscopic, and
containing only H_{2}SO_{4}, OC, HNO_{3}, and/or NH_{3}.
Subrange 2 can contain all chemical components and it can be further divided
into strongly hygroscopic (2a) and weakly hygroscopic (2b) subranges to allow for the description of
externally mixed aerosol particle populations (Kokkola et al., 2018). The
evolution of aerosol size distribution is represented using the sectional
hybrid-bin method (Young, 1974; Chen and Lamb, 1994). As a difference to the original
SALSA, ${\stackrel{\mathrm{\u203e}}{D}}_{i}$ is calculated as the geometric mean diameter instead
of the arithmetic mean. Assuming spherical particles, the latter tends to
overestimate the total volume ${\stackrel{\mathrm{\u203e}}{V}}_{i}=\frac{\mathit{\pi}}{\mathrm{6}}{\stackrel{\mathrm{\u203e}}{D}}_{i}^{\mathrm{3}}$, especially for larger aerosol particles when
*X*_{B}∼10.

The original SALSA contains detailed descriptions for the aerosol dynamic processes of nucleation, condensation, dissolutional growth, and coagulation, and here it has been further extended by including dry deposition on solid surfaces and resolved-scale vegetation and gravitational settling. The process of particle resuspension from surfaces is currently neglected. However, the resuspension of road dust, for example, can be included in the model as an additional surface emission (see Sect. 2.2.5).

A detailed description of the aerosol source–sink terms is given below (and in Kokkola et al., 2008 and Tonttila et al., 2017).

Coagulation decreases the aerosol number as two aerosol particles collide to
form one larger particle. In SALSA, coagulation is solved using the
non-iterative method by Jacobson (2005). For *n*_{i},

$$\begin{array}{}\text{(1)}& {\displaystyle}{n}_{i,\phantom{\rule{0.125em}{0ex}}t}={\displaystyle \frac{{n}_{i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}}{\mathrm{1}+\mathrm{\Delta}t\sum _{j=i+\mathrm{1}}^{{X}_{\mathrm{B}}}{\mathit{\beta}}_{i,\phantom{\rule{0.125em}{0ex}}j}{n}_{j,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{\Delta}t{\mathit{\beta}}_{i,\phantom{\rule{0.125em}{0ex}}i}{n}_{i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}}}\end{array}$$

and, similarly, for *m*_{c, i},

$$\begin{array}{}\text{(2)}& {\displaystyle}{m}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t}={\displaystyle \frac{{\mathit{\rho}}_{c}\left({\mathit{\upsilon}}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}+\mathrm{\Delta}t\sum _{j=\mathrm{1}}^{i-\mathrm{1}}{\mathit{\beta}}_{j,\phantom{\rule{0.125em}{0ex}}i}{\mathit{\upsilon}}_{c,\phantom{\rule{0.125em}{0ex}}j,\phantom{\rule{0.125em}{0ex}}t}{n}_{i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}\right)}{\mathrm{1}+\mathrm{\Delta}t\sum _{j=i+\mathrm{1}}^{{X}_{\mathrm{B}}}{\mathit{\beta}}_{i,\phantom{\rule{0.125em}{0ex}}j}{n}_{j,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}}}.\end{array}$$

Here, *t* and *t*−Δ*t* are the current and previous time steps,
*β*_{i, j} is the coagulation kernel (m^{3} s^{−1}) of the colliding
aerosol particles in size bins *i* and *j*, *υ*_{c, i} is the aerosol
volume concentration of chemical component *c* in size bin *i*, and *ρ*_{c}
is its density. The coagulation kernel ${\mathit{\beta}}_{i,\phantom{\rule{0.125em}{0ex}}j}={E}_{\mathrm{coal},\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}j}{K}_{i,\phantom{\rule{0.125em}{0ex}}j}$ is the product of a collision kernel
*K*_{i, j} (m^{3} s^{−1}) and a dimensionless coalescence efficiency
${E}_{\mathrm{coal},\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}j}$. For aerosol particles smaller than
2 µm in radius, ${E}_{\mathrm{coal},\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}j}$ can be approximated
as unity (i.e. particles stick together) as the likelihood of bounce-off is
low (Beard and Ochs, 1984). Brownian coagulation is assumed for aerosol particles,
for which *K*_{i, j} in the transition regime is calculated with the
interpolation formula by Fuchs (1964):

$$\begin{array}{}\text{(3)}& {\displaystyle}{K}_{i,\phantom{\rule{0.125em}{0ex}}j}={\displaystyle \frac{\mathrm{4}\mathit{\pi}\left({r}_{i}+{r}_{j}\right)\left({\mathrm{\Gamma}}_{p,\phantom{\rule{0.125em}{0ex}}i}+{\mathrm{\Gamma}}_{p,\phantom{\rule{0.125em}{0ex}}j}\right)}{\frac{{r}_{i}+{r}_{j}}{{r}_{i}+{r}_{j}+\sqrt{{\mathit{\delta}}_{i}^{\mathrm{2}}+{\mathit{\delta}}_{j}^{\mathrm{2}}}}+\frac{\mathrm{4}({\mathrm{\Gamma}}_{p,\phantom{\rule{0.125em}{0ex}}i}+{\mathrm{\Gamma}}_{p,\phantom{\rule{0.125em}{0ex}}j})}{\sqrt{{v}_{p,\phantom{\rule{0.125em}{0ex}}i}^{\mathrm{2}}+{v}_{p,\phantom{\rule{0.125em}{0ex}}j}^{\mathrm{2}}}({r}_{i}+{r}_{j})}}},\end{array}$$

where *r*_{i} (m) is the particle radius, Γ_{p, i} (m^{2} s^{−1}) is
the particle diffusion coefficient, *δ*_{i} (m) is the mean distance from
the centre of the sphere reached by particles leaving the surface of the
sphere and travelling a distance of particle mean free path, and *v*_{p, i}
(m s^{−1}) is the thermal speed of a particle in air.

The condensation of gases on an aerosol particle increases the particle volume
and decreases the gas-phase concentrations. For water vapour, H_{2}SO_{4},
NVOC, and SVOC condensation is calculated by applying the
analytical predictor of a condensation scheme (Jacobson, 2005) in which
the vapour mole concentration *C*_{c,t} at time step *t* after condensation
is first calculated as

$$\begin{array}{}\text{(4)}& {\displaystyle}{C}_{c,t}={\displaystyle \frac{{C}_{c,t-\mathrm{\Delta}t}+\mathrm{\Delta}t\sum _{i=\mathrm{1}}^{{X}_{\mathrm{B}}}\left({k}_{c,i,t-\mathrm{\Delta}t}{S}_{c,i,t-\mathrm{\Delta}t}^{\prime}{C}_{c,s,i,t-\mathrm{\Delta}t}\right)}{\mathrm{1}+\mathrm{\Delta}t\sum _{i=\mathrm{1}}^{J}{k}_{c,i,t-\mathrm{\Delta}t}}},\end{array}$$

where ${k}_{c,i,t-\mathrm{\Delta}t}$ is the particle volume-dependent mass-transfer
coefficient (s^{−1}) in size bin *i* at the previous time step
*t*−Δ*t*, ${S}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}$ is the equilibrium saturation ratio, and
${C}_{c,\phantom{\rule{0.125em}{0ex}}s,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}$ is an uncorrected saturation vapour mole concentration
(mol m^{−3}) of the condensing gas *c*. The change in particle mole
concentration ${c}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t}$ in the aerosol size bin *i* is then given by
the
formula

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{c}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t}={c}_{c,\phantom{\rule{0.125em}{0ex}}s,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}+{k}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}\\ \text{(5)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\left({C}_{c,\phantom{\rule{0.125em}{0ex}}t}-{S}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}{C}_{c,\phantom{\rule{0.125em}{0ex}}s,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}\right),\end{array}$$

which is then translated to aerosol number and mass concentrations. The condensation and evaporation of water vapour on aerosol particles would require a very short time step to avoid non-oscillatory solutions. The applied solution used in SALSA is described in Tonttila et al. (2017).

Furthermore, aerosol particles may grow further due to dissolutional growth
when a gas transfers to a particle surface and dissolves in liquid water on
the surface. This partitioning between the gaseous and particulate phases is
solved for water vapour, nitric acid, and ammonia using the analytical
predictor of dissolution (APD) scheme (Jacobson, 2005) in the following
way. First, the vapour mole concentration *C*_{c, t}
after dissolutional growth at time step *t* is
calculated as

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{C}_{c,\phantom{\rule{0.125em}{0ex}}t}=\\ \text{(6)}& {\displaystyle}& {\displaystyle \frac{{C}_{c,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}+\sum _{i=\mathrm{1}}^{{X}_{\mathrm{B}}}\left\{{c}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}\left[\mathrm{1}-\mathrm{exp}\left(-\frac{\mathrm{\Delta}t{S}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}{k}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}}{{H}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}}\right)\right]\right\}}{\mathrm{1}+\sum _{i=\mathrm{1}}^{{X}_{\mathrm{B}}}\left\{\frac{{H}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}}{{S}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}}\left[\mathrm{1}-\mathrm{exp}\left(-\frac{\mathrm{\Delta}t{S}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}{k}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}}{{H}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}}\right)\right]\right\}}}.\end{array}$$

Here, ${H}_{c,\phantom{\rule{0.125em}{0ex}}i}^{\prime}$ is the dimensionless Henry's constant for chemical compound *c* in size bin
*i*:

$$\begin{array}{}\text{(7)}& {\displaystyle}{H}_{c,\phantom{\rule{0.125em}{0ex}}i}^{\prime}={m}_{v}{c}_{\mathrm{w},\phantom{\rule{0.125em}{0ex}}i}{R}^{*}T{H}_{c},\end{array}$$

where *m*_{v} (mol m^{−3}) is the molecular weight of water,
*c*_{w, i} (mol m^{−3}) is the mole concentration of liquid water in
aerosol size bin *i*, ${R}^{*}=\mathrm{8.206}$ m^{3} atm K^{−1} mol^{−1} is the
universal gas constant, *T* (K) is the ambient temperature, and
*H*_{c} (mol kg^{−1} atm^{−1}) is the Henry's law constant estimated by
the thermodynamic model PD-FiTE (Topping et al., 2009). Finally, the new
particle mole concentration ${c}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t}$ is given by

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{c}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t}={\displaystyle \frac{{H}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}{C}_{c,\phantom{\rule{0.125em}{0ex}}t}}{{S}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}}}+\left({c}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t}-{\displaystyle \frac{{H}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}{C}_{c,\phantom{\rule{0.125em}{0ex}}t}}{{S}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}}}\right)\\ \text{(8)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\mathrm{exp}\left(-{\displaystyle \frac{\mathrm{\Delta}t{S}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}{k}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}}{{H}_{c,\phantom{\rule{0.125em}{0ex}}i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}^{\prime}}}\right),\end{array}$$

which is then translated to number and mass concentrations. The evaporation of gases from aerosol particle surfaces, with water being an exception, is not considered.

Dry deposition removes aerosol particles from air when they collide with a
surface and stick to it. Here, the original scheme in SALSA allowing dry
deposition on horizontal surfaces was extended by also including deposition
on vertical solid surfaces (e.g. building walls) and resolved-scale
vegetation. Deposition on sub-grid vegetation (e.g. grass surface) is not yet
implemented. By default, dry deposition velocity *v*_{d} (m s^{−1}) is
calculated by applying the size-segregated scheme by Zhang et al. (2001)
(hereafter Z01), which is the most applied dry deposition scheme in numerical
studies. For size bin *i*,

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{v}_{\mathrm{d},\phantom{\rule{0.125em}{0ex}}i}=\underset{\mathrm{settling}\phantom{\rule{0.25em}{0ex}}\mathrm{velocity},{v}_{c,\phantom{\rule{0.125em}{0ex}}i}}{\underbrace{{\displaystyle \frac{({\mathit{\rho}}_{\mathrm{p}}-{\mathit{\rho}}_{\mathrm{a}}){\stackrel{\mathrm{\u203e}}{D}}_{i}^{\mathrm{2}}g{G}_{i}}{\mathrm{18}{\mathit{\eta}}_{\mathrm{a}}}}}}+{\mathit{\u03f5}}_{\mathrm{0}}{u}_{*}\mathrm{exp}(-{\mathit{\text{St}}}_{i}^{\mathrm{1}/\mathrm{2}})\\ \text{(9)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\left[\underset{\mathrm{Brownian}\phantom{\rule{0.25em}{0ex}}\mathrm{diffusion}}{\underbrace{{\mathit{\text{Sc}}}_{i}^{-\mathit{\gamma}}}}+\underset{\mathrm{impaction}}{\underbrace{{\left({\displaystyle \frac{{\mathit{\text{St}}}_{i}}{\mathit{\alpha}+{\mathit{\text{St}}}_{i}}}\right)}^{\mathit{\beta}}}}+\underset{\mathrm{interception}}{\underbrace{{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\left({\displaystyle \frac{{\stackrel{\mathrm{\u203e}}{D}}_{i}}{A}}\right)}^{\mathrm{2}}}}\right],\end{array}$$

where *ρ*_{p} and *ρ*_{a} are the particle and air
densities (kg m^{−3}), *g* (m s^{−2}) is the gravitational
acceleration, *G*_{i} is the Cunningham slip-correction factor,
*η*_{a} (kg m^{−1} s^{−1}) is the dynamic viscosity of air,
*ϵ*_{0}=3 and *β*=2 are empirical constants, *u*_{*} (m s^{−1}) is
the friction velocity of above a surface, *St*_{i} is the Stokes
number, *Sc*_{i} is the particle Schmidt number, *γ* and *α*
are empirical constants that depend on the surface type, and *A* is the
characteristic radius of the different surface types and seasonal categories.
Note that the aerodynamic resistance in the original Z01 formulation is not
considered here as LES resolves the aerodynamic effect explicitly. For solid
surfaces, *u*_{*} is solved within PALM by applying a stability-adjusted
logarithmic wind profile, whereas for the resolved-scale vegetation an
estimation ${u}_{*}=\sqrt{{C}_{\mathrm{D}}}U$ (Prandtl, 1925), where
*C*_{D} is the canopy drag coefficient and $U=\sqrt{{u}^{\mathrm{2}}+{v}^{\mathrm{2}}+{w}^{\mathrm{2}}}$ is
the three-dimensional wind speed, is applied. Z01 has been suggested to
overestimate *v*_{d} for submicron particles
(Petroff and Zhang, 2010; Mingxuan et al., 2018), and therefore as an alternative to Z01, the
formulation by Petroff and Zhang (2010) (hereafter P10) for the deposition
velocity can be used (see Sect. S1 in the Supplement). The different
parameterizations Z01 and P10 for *v*_{d} over built surfaces and
deciduous broadleaf trees during leaf-on period are visualized in
Fig. 1.

Dry deposition on vegetation creates a local sink term,

$$\begin{array}{}\text{(10)}& {\displaystyle \frac{\partial {n}_{i}}{\partial t}}=-\text{LAD}{v}_{\mathrm{d},\phantom{\rule{0.125em}{0ex}}i}{n}_{i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t},\end{array}$$

which depends on the local leaf area density (LAD), whereas dry deposition on horizontal surfaces and building walls is implemented by means of surfaces fluxes:

$$\begin{array}{}\text{(11)}& {\displaystyle}{F}_{{n}_{i}}=-{v}_{\mathrm{d},\phantom{\rule{0.125em}{0ex}}i}{n}_{i,\phantom{\rule{0.125em}{0ex}}t-\mathrm{\Delta}t}.\end{array}$$

The same equations apply for *m*_{c, i}. When not in contact with a surface,
only gravitational settling contributes to dry deposition and generates a
downward flux of particles, which is mainly important for large
particles (*D*>1.0 µm) (Zhang et al., 2001; Petroff and Zhang, 2010). Dry
deposition and gravitational settling are currently calculated only for
aerosol particles and not for gaseous components.

In the model evaluation represented here, nucleation is assumed to have already occurred (Rönkkö et al., 2007; Uhrner et al., 2007), and the nucleation-mode aerosol particles are given to the model as an input. That notwithstanding, new particle formation by sulfuric acid can be taken into account by calculating the apparent rate of formation of 3 nm sized aerosol particles according to the parameterization by Kerminen and Kulmala (2002), Lehtinen et al. (2007), or Anttila et al. (2010). To calculate the “real” nucleation rate, users can choose between the binary (Vehkamäki et al., 2002), ternary (Napari et al., 2002a, b), kinetic (Sihto et al., 2006; Riipinen et al., 2007), or activation-type (Riipinen et al., 2007) nucleation.

Aerosol particle emissions can be given to the model as an input by applying
three levels of detail (LOD): parameterized (LOD1, units kg m^{−2} s^{−1}) or detailed (LOD2, units m^{−2} s^{−1})
two-dimensional surface fluxes or three-dimensional sources (LOD3, units m^{−3} s^{−1}). Using LOD1, aerosol emissions are given as particulate
mass (PM) emissions, from which the size-segregated number emissions
${E}_{{n}_{i}}$ are calculated within the model implementing default aerosol size
distributions and mass compositions for each emission category EC
(e.g. traffic, domestic heating, etc.). LOD2 and LOD3 emission data include
${E}_{{n}_{i}}$ and the mass composition per each EC, based on which the
mass emission per size bin *i* and chemical component *c* are then calculated
within the model. Gaseous emissions can be specified using any LOD. The time
dependency of the aerosol emissions has not been implemented yet.

SALSA is integrated into PALM as an optional PALM-4U module, which directly
utilizes the momentum and scalar concentration fields of the parent model as
input. The aerosol source–sink terms are resolved sequentially at a
user-specified frequency *f*_{SALSA}, while the prognostic equations
and thus the transport of aerosol number and mass as well as gas concentrations
are resolved at every LES time step Δ*t*_{LES} in PALM.
Molecular diffusion is assumed negligible compared with turbulent
diffusion and is thus ignored.

Since water is a default chemical component in SALSA, PALM needs to be run in
the humid mode (i.e. calculate the prognostic equation for specific humidity
*q*). The particle water content ${m}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O},\phantom{\rule{0.125em}{0ex}}i}$ per size bin *i* can
be represented either as a prognostic variable or as a diagnostic variable
and calculated at each Δ*t*_{SALSA} based on the equilibrium
solution using the Zdanovskii–Stokes–Robinson (ZSR)
method (Stokes and Robinson, 1966). The feedback on temperature and humidity due to
the condensation of water vapour on particles can be switched off. Moreover,
SALSA can be run together with the available PALM-4U chemistry module to
transfer the gas concentrations, while the impact of aerosol particles on
radiative transfer has not been implemented yet.

Each *n*_{i}, *m*_{c,i}, and gaseous compound introduces a new prognostic
variable that is transported by the flow in PALM. Increasing the number of
prognostic variables *X*_{PV} from the default value of
*X*_{PV}=6 (wind components *u*, *v*, *w* and scalars *e*, *θ*, and
*q*) to

$$\begin{array}{}\text{(12)}& {\displaystyle}{X}_{\mathrm{PV}}=\mathrm{6}+\mathrm{\Delta}{X}_{\mathrm{PV}}=\mathrm{6}+{X}_{\mathrm{B}}({X}_{\mathrm{CC}}+\mathrm{1})+{X}_{\mathrm{G}},\end{array}$$

where *X*_{B} is the number of size bins, *X*_{CC} the total
number of chemical components (aerosol phase), and *X*_{G}=5 the total
number of gaseous compounds, increases the computational load tremendously.
To estimate the increase in computational costs caused by significantly
increasing *X*_{PV}, and also resolving the aerosol dynamics,
simulations over a simple test domain of
$\mathrm{20}\phantom{\rule{0.125em}{0ex}}\mathrm{m}\phantom{\rule{0.125em}{0ex}}\times \phantom{\rule{0.125em}{0ex}}\mathrm{20}\phantom{\rule{0.125em}{0ex}}\mathrm{m}\phantom{\rule{0.125em}{0ex}}\times \phantom{\rule{0.125em}{0ex}}\mathrm{20}\phantom{\rule{0.125em}{0ex}}\mathrm{m}$ (see Fig. S1 in
the Supplement) were conducted with varying set-ups for SALSA.

The relative changes in computational load per simulation are given in Table
2. Adding *X*_{B}=10 size bins composed of
*X*_{CC}=2 chemical components (water always present) introduces
Δ*X*_{PV}=35 new prognostic variables and increases the original
computational time by nearly a factor of 4 (run 1). Calculating the
aerosol water content at each Δ*t*_{SALSA} instead of treating
it as a prognostic variable is even more demanding (run 2). Of all aerosol
dynamic processes, coagulation is the most expensive (run 3). Including more
chemical components further increases the computational time (runs 8–13),
which can be notably decreased by lengthening Δ*t*_{SALSA} (runs 12–13). Considering the longer timescales of aerosol
dynamic processes compared to dispersion
(e.g. Pryor and Binkowski, 2004; Kumar et al., 2008), Δ*t*_{SALSA}=10Δ*t*
is considered to be reasonable in urban simulations with a grid resolution of
∼1 m and Δ*t*∼0.1. In any case, the computational expenses
are multiplied when SALSA is included, which limits the size of LES model
domains to be considered.

The initial aerosol size distribution is defined by setting the number
concentration of particles in each bin *n*_{i} of which the volume
*υ*_{c, i} and mass concentrations *m*_{c, i} are calculated based
on the geometric mean diameter ${\stackrel{\mathrm{\u203e}}{D}}_{i}$. Aerosol emissions are
defined similarly. In other words, the total number concentration is
preserved in the initialization, whereas uncertainties arise when estimating
*m*_{c, i} or *v*_{c, i}.

Limiting *X*_{B} in a sectional aerosol module is a simple method to
reduce computational costs and memory demand. However, this results in an
inevitable loss of accuracy as the aerosol size range covers many orders of
magnitude from a few nanometres to several micrometres. To test the sensitivity
of the representation of the aerosol number and mass size distribution to
*X*_{B}, four different configurations are tested
(Fig. 2). All configurations cover particles
from 3 nm to 2.5 µm, and subrange 1 includes particles up to
10 nm. The default configuration contains *X*_{B}=10 with two bins in
subrange 1. The second configuration contains *X*_{B}=8 and only
one bin in subrange 1, whereas the third configuration contains two
additional bins in subrange 2 compared to the default configuration.
Additionally, an ideal configuration with *X*_{B}=50 was tested.

The total aerosol particle volume concentration *V* is highly sensitive to
*X*_{B}, and the rate of overestimation increases with decreasing
*X*_{B} (Fig. 2). Overestimating
particle volume causes errors in, for instance, calculating the coagulation
kernel, gas-to-particle mass transfer, and deposition velocity. Furthermore,
the ability of a sectional module to capture narrow features in a size
distribution (e.g. in Fig. 2c) improves with
higher *X*_{B}. To compromise between computational costs and
modelling accuracy, *X*_{B}=10 is used in this evaluation study.

3 Model evaluation set-up

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The performance of the SALSA module in PALM is evaluated against measurements of the vertical variation of the aerosol number size distribution and concentrations in a street canyon (Pembroke Street) in central Cambridge, United Kingdom, over consecutive 24 h on 20–21 March 2007 (Kumar et al., 2008, 2009). During the measurement campaign, the predominant wind direction (WD) was from the northwest and perpendicular to the street canyon. Furthermore, there is a large pedestrian area upwind of the site with no traffic emissions, and hence emissions from adjacent streets were unlikely to affect the measurements. The building height is around 14–18 m on the upwind and 11–15 m on the downwind side of the street canyon (Fig. 3).

Aerosol size distributions in the size range *D*=5–2738 nm were
measured pseudo-simultaneously at four heights (*z*=1.00, 2.25, 4.62, and
7.37 m above ground level, a.g.l.) using a fast-response differential
mobility spectrometer (DMS500). The measurement location was on the
northwestern side of Pembroke Street around 66 m from the closest
intersection in the southwest. Traffic volumes along the street were
simultaneously measured. Moreover, 30 min averaged meteorological data,
including wind speed (*U*) and direction, ambient air temperature (*T*), and
relative humidity (RH), were measured 40 m a.g.l. at some 500 m from the
sampling site. For more information on the measurements, refer to
Kumar et al. (2008).

The evaluation is done for three different periods (LT is for local time): 08:30–09:30 LT (morning), 21:00–22:00 LT (evening), and 03:00–04:00 LT (night-time). No daytime evaluation is presented here in order to minimize the role of thermal and vehicle-induced turbulence (VIT) on pollutant transport. The evening and night-time periods represent time after sunset, while the morning measurements were conducted under partly cloudy conditions.

Simulations are conducted over a domain of a $\mathrm{512}\times \mathrm{512}\times \mathrm{128}$ grid box
with the measurement site approximately at the centre of the domain
(Fig. 3). A uniform grid spacing of
${\mathrm{\Delta}}_{x,y,z}=\mathrm{1.0}$ m is applied within the lowest 96 m, and above
the vertical grid Δ_{z} is stretched by a factor of 1.04, resulting in
a total domain height of around 164 m and a maximum
${\mathrm{\Delta}}_{z,\phantom{\rule{0.125em}{0ex}}\text{max}}\approx \mathrm{3.5}$ m.

The building-height and vegetation maps for the study area were constructed
from 1 m horizontal resolution digital surface models (DSMs) and digital terrain
models (DTMs) (Environment Agency UK data archive) following Kent et al. (2018).
First, the DTM was subtracted from the DSM to set the terrain height to zero.
Next, buildings were separated from other surface elements using a building
footprint dataset from the OS MasterMap^{®}
Topography Layer (Ordnance Survey 2014). The vegetation map was formed from the
remaining pixels by first removing the residue pixels around buildings and
then performing dilation of the raster map to remove holes and unify
vegetated areas. Only vegetation elements higher than ${z}_{\mathrm{v},\phantom{\rule{0.125em}{0ex}}\mathrm{min}}=\mathrm{4.0}$ m were included in the simulations.
They were modelled as
springtime deciduous broadleaf trees with a constant LAD =0.6 m^{2} m^{−3} from *z*_{v, min} to the tree top.
This LAD value was estimated as a lower limit for urban street trees
in northern Europe in spring (Gillner et al., 2015). Excluding the details of
local vegetation is acceptable since there are no trees close to the
measurement site and overall the amount of vegetation is low.

Only road traffic lanes are defined as source areas for aerosol particles and
gaseous compounds. The emission map (Fig. 3) was
created by first extracting the roads, tracks, and paths from the OS
MasterMap^{®} Topography Layer and then
manually removing pedestrian areas and small streets. Finally, raster erosion
was applied to the remaining map to result in a lane width of 6–7 m on
Pembroke Street.

In the simulations, a total aerosol number emission factor EF${}_{n}=\mathrm{1.33}\times {\mathrm{10}}^{\mathrm{14}}$ km^{−1} vehicle^{−1} is
used (Table 3), which is an estimate specific to
the measurement site (Kumar et al., 2009). EF_{n} was distributed to
a representative aerosol number size distribution with the shape estimated from the measured size distribution at the lowest level *z*=1.0 m during each
simulation time (see Sect. S3). Aerosol emissions are assumed to be composed
of mainly black (48 %) and organic carbon (48 %) and some
H_{2}SO_{4} (4 % of the total mass) (Maricq, 2007; Dallmann et al., 2014).
Emission factors of gaseous compounds are instead calculated using the
fleet-weighted road transport emission factors for 2008 by the National
Atmospheric Emissions Inventory (NAEI; Walker, 2011) and the following
fleet composition: 75 % petrol and 19 % diesel passenger cars,
1 % buses, 3 % light and 1 % heavy-duty diesel vehicles, and
1 % motorcycles. Since no EF${}_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}}$ or EF_{SVOC} is given by NAEI, the following estimates were
applied: EF${}_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}}=\mathrm{0.1}{\text{EF}}_{{\mathrm{SO}}_{\mathrm{2}}}$
(Arnold et al., 2006, 2012; Miyakawa et al., 2007) and EF_{SVOC}=0.01EF_{NMOG} (Zhao et al., 2017),
where NMOG stands for non-methane organic gases. The latter is
rather conservative compared to emission rates applied by Albriet et al. (2010)
for a light-duty diesel truck. Both aerosol and gaseous emissions are
introduced as constant fluxes per unit area.

The background aerosol particle number and trace gas concentrations are produced with the trajectory model for Aerosol Dynamics, gas and particle phase CHEMistry and radiative transfer (ADCHEM; Roldin et al., 2011). Similar to Öström et al. (2017), ADCHEM was operated as a one-dimensional column trajectory model along HYSPLIT (Stein et al., 2015) air mass trajectories. In total, the gas and aerosol particle compositions were simulated along 48 trajectories arriving at central Cambridge between 20 March at 00:00 and 21 March at 23:00 (one every hour). All air mass trajectories started 5 days upwind of Cambridge over the Arctic Ocean (see Fig. S5). The anthropogenic trace gas emissions along the trajectories were taken from the European Monitoring and Evaluation Programme (EMEP) emission inventory for 2007 and the size-resolved primary particle emissions from the global emission inventory from Paasonen et al. (2016). These vertical profiles of the background concentrations (Sect. S5) are introduced to the simulation domain by a decycling method, in which constant background concentrations are fixed at the lateral boundaries.

In all simulations, a neutral atmospheric stratification is assumed for
simplicity as no information on the atmospheric stratification or boundary
layer height was available. Thus, a constant *θ*=*T* (*z*=40 m)
(Table 4) is applied throughout the domain. The flow is
driven by an external pressure gradient force above *z*=120 m. The gradient
was set so that the horizontal mean *U* (*z*=40 m) over the whole simulation
domain equals (±0.1 m s^{−1}) the measured *U*
(Table 4; see Fig. S7 for vertical profiles).
Furthermore, the domain height was 164 m for all simulations.
This is >13 h, where *h*=12.08 m is the mean building height over the domain, which should be enough
to correctly resolve the small-scale turbulent structures within the urban
canopy (Coceal et al., 2006).

Cyclic lateral boundary conditions are applied for the flow, *q*, and *e*,
which is reasonable since the surroundings do not notably differ from the
simulation domain. A Neumann (free-slip) boundary condition is applied at the
top boundary and also at the bottom and top for all scalars. The roughness
height is *z*_{0}=0.05 m (Letzel et al., 2012) and the drag coefficient applied
for the trees is *C*_{D}=0.5 (see Kent et al., 2017, and references within).

Baseline simulations used to evaluate the performance of the model in the
morning, evening, and at night are conducted with the default number of
aerosol size bins ${X}_{\mathrm{B}}=\mathrm{2}+\mathrm{8}$ (see
Sect. 2.5). All aerosol processes, except
nucleation, are switched on, and the following chemical components are
included: H_{2}SO_{4}, OC, BC, HNO_{3}, and NH_{3}.
All aerosol particle are assumed to be internally mixed and hygroscopic, and
thereby no subrange 2b was applied.

In addition to the base run, the sensitivity to different aerosol processes
and the number of size bins *X*_{B} was examined for the morning
simulation. Firstly, the following four simulations with ${X}_{\mathrm{B}}=\mathrm{2}+\mathrm{8}$
are conducted: no aerosol processes (NOAP), only coagulation (COAG), only dry
deposition (scheme Z01) on solid surfaces and vegetation (DEPO), and only
condensation (COND). In the first three, particles are assumed to constitute
only OC in order to limit computational costs, given that
coagulation and dry deposition do not depend on aerosol composition.
COND is instead performed with an identical set-up to the baseline
simulation, except that other processes were switched off. Secondly, the
sensitivity to *X*_{B} is tested by replicating the baseline morning
simulation with less ${X}_{\mathrm{B}}=\mathrm{1}+\mathrm{7}$ (LB) and more bins
${X}_{\mathrm{B}}=\mathrm{2}+\mathrm{10}$ (MB).

The advection of both momentum variables and scalars was based on the
fifth-order advection scheme by Wicker and Skamarock (2002) together with a third-order
Runge–Kutta time-stepping scheme (Williamson, 1980). The pressure term in
the prognostic equations for momentum was calculated using the iterative
multigrid scheme (Hackbusch, 1985). In order to enable similar flow
conditions for all simulations, feedback to PALM was switched off; i.e.
changes in specific humidity due to the condensation of water on aerosol
particles were not allowed. Therefore *q* also remained constant. Here,
Δ*t*_{SALSA}=1.0 s in all simulations, which is a safe
choice since the turbulence timescale is smaller than any aerosol process
timescale (Kumar et al., 2008).

Simulations were conducted with the PALM model revision 3125. This was a model version prior to the 6.0 release, but reproducibility with version 6.0 was ensured by repeating the NOAP simulation. All simulations were first run for 2 h to create a quasi-stationary state of the flow, after which SALSA was switched on and run for 70 min. Data output was collected within the last 60 min with a 0.5–1 Hz frequency. Simulations were performed on the Centre for Scientific Computing (CSC) Taito supercluster. Using 64×64 Intel Haswell processor cores, one 70 min long simulation with SALSA required between 17 h (NOAP) and 52 h (MB) of computing time.

4 Results

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Modelled aerosol number concentrations were compared against measurements at the measurement location and six additional horizontal points on the northern side of the street canyon within the evaluation domain of 30 m×30 m (Fig. 3). The additional six profiles were analysed to include possible error in defining the measurement location and also to illustrate the variation in concentrations at different adjacent points in a street canyon. In the evaluation, the modelled values were linearly interpolated to the measurement heights and the measured size distributions to the modelled size bins. All modelled and measured values are hourly averaged.

To give a general picture of aerosol particle concentrations and dispersion
in this study, Fig. 4 illustrates the modelled
total aerosol number concentrations *N*_{tot} and wind speed *U* at
*z*=3.5 m a.g.l. for all baseline simulations. The horizontal distribution of
*N*_{tot} is shown to follow that of emissions (see
Fig. 3) and, for instance, courtyards remain
relatively clean. Nevertheless, wind controls the dispersion, which is seen
as up to 70 % higher *N*_{tot} inside the street canyons for the
calmer night-time compared to the more windy evening simulation (see Fig. S8)
despite the lower emission rates at night. Interestingly, pollutant
accumulation occurs close to the measurement site within the evaluation
domain.

The modelled mean vertical profiles of *N*_{tot} compare well against
the measured values (Fig. 5), especially in
the morning. Indeed, the additional six profiles are also generally within
a factor of 2of observations (see Fig. S9). The rate of change in
*N*_{tot} in the vertical is correctly modelled except for a measured
increase in concentrations within the lowest 2 m. Despite the modelled
*N*_{tot} being 50 %–100 % higher than measured in the evening
(Fig. 5b), concentrations are of the same
order of magnitude. This deviation from measurements is comparable to typical
differences in measured aerosol number concentrations with different
instruments (Ankilov et al., 2002; Hornsby and Pryor, 2014). Comparing the mean values of all
seven modelled profiles, their variation is shown to be larger than that
between the measured and modelled *N*_{tot} at the exact measurement
location.

Naturally, the coarse sectional representation of the aerosol size distribution with *X*_{B}=10 means some details, such as a drop in concentrations at *D*≈60 nm (Fig. 6),
cannot always be captured by the model. Furthermore, omitting any emission
sources can produce error. For instance, an underestimation of the number of
particles larger than 20 nm at *z*=2.25 m and *z*=4.62 m in the
night-time (Fig. 6b and c) could stem from excluding
some elevated sources, such as tailpipe emissions of trucks. Nonetheless,
the model predictions are mainly within a factor of 2 of the measurements
(see Fig. S10). The size distributions display very similar shapes to that of
emissions, showing that the result is very sensitive to the quality of the
input emission data.

At the same time, a mismatch with the measurements near the surface is to be expected, as the LES technique lacks reliability close to walls. Maronga et al. (2015), for instance, showed that the turbulent flow over a homogeneous surface is not well-resolved for the lowest six grid points, which corresponds to the lowest 5 m in these simulations. In that context, the modelled concentration fields agree exceptionally well with the measurements.

At the temporal and spatial scales applied in the simulations, dry deposition
changes the total aerosol number concentrations most, with a relative
difference Δ*N*_{tot}< −20 %, especially in areas with
vegetation but also in the wake of buildings
(Fig. 7). Coagulation (COAG) changes
*N*_{tot} only by less than 1 %. The impact of condensation and
dissolutional growth (COND) on *N*_{tot} is negligible, as expected,
since condensation only grows particles (Kumar et al., 2011).

Neglecting all aerosol processes overestimates *N*_{tot} (see
Fig. S11), and therefore including dry deposition is essential for modelling
realistic *N*_{tot}. Above the roof level (*z**≳*15 m), the role
of dry deposition starts to weaken
(Fig. 8), which is also attributable to
lower aerosol concentrations. The smallest aerosol particles are most strongly
affected by aerosol processes independently of modelling height
(Fig. 9): this is because more efficient Brownian
diffusion leads to higher deposition velocities *v*_{d} (see
Fig. 1) and coagulation rates. Furthermore,
the smallest particles grow through condensation and dissolutional growth, which
instead leads to less efficient removal by dry deposition. The impact of dry
deposition and, to a lesser extent, coagulation decreases with height, and above
the roof level the observed Δ*N*_{tot} is likely due to aerosol
processes acting upwind of the measurement site.

While condensation and dissolutional growth do not directly affect the number
concentrations, the total mass and chemical composition of aerosol particles
are shown to change. Over the whole evaluation domain, condensation and
dissolutional growth increase PM_{tot} by over 10 % below
the roof height (Fig. 10). Comparing the initial chemical
composition of the background aerosol concentrations and emissions
(Table 5) with the modelled composition shows
that the mass fraction of nitrates has especially increased, from 0 % to
8 %. This increased particulate mass of nitrates originates solely from
the condensation of background gaseous HNO_{3} as there are no traffic-related emissions of gaseous HNO_{3}. The simulated mass fraction of BC is very close to that of the aerosol emissions, while other mass
fractions that also change due to condensation and dissolutional growth vary
more. Deposition decreases PM_{tot}, but the relative change is
clearly lower than for *N*_{tot}, as the smallest particles, which are most
affected by dry deposition, represent only a tiny share of the total mass.

Further decreasing the number of aerosol size bins *X*_{B} is a
tempting method in order to reduce the computational load. Indeed, the total
CPU time is reduced by −24 % when ${X}_{\mathrm{B}}=\mathrm{1}+\mathrm{7}$ (LB), while setting
${X}_{\mathrm{B}}=\mathrm{2}+\mathrm{10}$ (MB) increases the CPU time by +18 % compared to the
baseline simulation in the morning. However, as shown in
Sect. 2.5 and Fig. S12, the capability to
describe the details of aerosol size distribution drops rapidly when
decreasing *X*_{B}.

Despite the background *N*_{tot} and total aerosol number emissions
EF_{n} being equal for the baseline, LB, and MB simulations, modelled
*N*_{tot} values are not equal (Fig. 11). The
difference is entirely attributable to the dissimilar effectiveness of
aerosol processes with a lower (LB) and higher (MB) level of detail in
representing the aerosol size distribution. Interestingly, using fewer size
bins (LB) has a very minor impact on the horizontal field of
*N*_{tot},
while more bins (MB) result in $\left|\mathrm{\Delta}{N}_{\mathrm{tot}}\right|>\mathrm{5}$ %. This is
still smaller than Δ*N*_{tot} due to deposition.

Comparing the modelled particulate masses is not that straightforward and is thus not represented here. The background concentrations and emissions of particulate mass differ between the simulations because the mass size distribution is calculated from the sectional number size distribution, which is different for all simulations.

5 Discussion and conclusions

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This article represents a novel, high-resolution, LES-based urban aerosol model that resolves aerosol particle concentrations, size distributions, and chemical compositions at spatial and temporal scales of 1.0 m and 1.0 s for entire neighbourhoods.

An evaluation study of the vertical variation of the aerosol number size distribution and total number concentration in a simple street canyon in central Cambridge, UK, shows good agreement against measurements. The model can predict the dilution of concentrations in the vertical as well as the number of aerosol particles in different size bins generally within a factor of 2 of observations. The spatial distribution of aerosol concentrations is mostly determined by the flow and emissions. As regards the individual impact of aerosol dynamic processes, dry deposition is shown to decrease local number concentrations by over 20 %, which is nonetheless at the lower end of $\mathrm{\Delta}{N}_{\mathrm{tot}}=[-\mathrm{35},-\mathrm{15}]$ % estimated by Huang et al. (2014) for an open space with traffic. Coagulation has a very minor impact, which agrees with previous timescale analyses (Kumar et al., 2009; Zhang et al., 2004) and CFD modelling studies (Albriet et al., 2010; Huang et al., 2014; Wang and Zhang, 2012). Condensation and dissolutional growth increase particulate mass by over 10 %. The role of aerosol dynamic processes is shown as important for both number and mass, especially in areas with low wind speeds, such as in courtyards and the shelter of trees. Furthermore, comparing six additional modelling profiles to the measured one shows the limited representativeness of point measurements and supports performing air quality modelling which also gives the spatial variability of concentrations.

With increasing modelling complexity, the number of potential sources of modelling uncertainty is augmented. One of the largest sources of uncertainty is related to the quality of the emission data. A major reason to evaluate the aerosol model against the dataset by Kumar et al. (2008) was that the measured concentrations were mainly affected by traffic emissions along Pembroke Street, which simplified the emission estimations.

Aerosol modelling uncertainties caused by simplifying assumptions and model design are discussed in detail in Kokkola et al. (2008). One of the main challenges in simulating both the aerosol number and mass also in this study is the limited number of aerosol size bins, whereas the aerosol dynamic processes have less impact. Another inevitable error in sectional aerosol modelling is made when assuming a spherical particle shape and defining the aerosol volume from the bin mean diameter. Despite these limitations, the model simulated the observed number concentrations correctly.

Further arguments for applying the selected dataset were the availability of measurements of the vertical variability of aerosol number size distribution at high temporal resolution, but also the simplicity of the urban morphology at the measurement location. The influence of aerosol dynamic processes on aerosol concentration is determined by their size distribution, and thus measurements only of the total number concentration or particulate mass (e.g. Weber et al., 2006) were considered insufficient for this model evaluation. To our knowledge, there are only a few datasets on the vertical variation of the aerosol size distribution in an urban environment (Kumar et al., 2008; Li et al., 2007; Marini et al., 2015; Quang et al., 2012; Sajani et al., 2018). Of these datasets, the measurement location of Kumar et al. (2008) in a street canyon with no urban vegetation was simple enough for the first evaluation study. Modelling individual street trees and their aerodynamic impact without exact information on the distribution of leaf area introduces another source of uncertainty for resolving the flow. Furthermore, dry deposition is strongly tree species dependent (e.g. Popek et al., 2013; Sæbø et al., 2012) and therefore sensitive to the correct modelling of different species. Finally, high-resolution topography and land use information were freely available for this specific site.

At the same time, no high-resolution evaluation data for the flow were
available, and therefore the modelling set-up was kept as simple as possible.
Hence, the thermal and vehicle-induced turbulence was excluded from the
simulations. The increase in *N*_{tot} for *z*=1.0–2.25 m
observed in the measurements could be explained by either of the two sources of
turbulence. Kumar et al. (2008) argued that the increase is likely due to
more efficient dry deposition near the surface or the complex dispersion pattern
within the canyon caused by both topography and vehicle-induced turbulence.

Keeping in mind the aforementioned uncertainties and required computational resources, the presented model provides a novel and flexible tool to study, for example, how the shape, size, and location of urban obstacles affect air pollutant transport and transformation at a neighbourhood scale. For instance, the potential of urban vegetation to improve air quality by acting as a biological aerosol filter (Beckett et al., 1998) depends on the size-dependent deposition velocity of aerosol particles, which is explicitly calculated within the model. The model can also provide information at high enough resolution to perform air pollutant exposure studies or to design a representative air pollution monitoring network. The aerosol module SALSA can be further coupled with an online chemistry module, which are both embedded in the PALM model system as so-called PALM-4U components. This will extend the applicability of the model from aerosol processes to more complex chemical processes and will allow researchers to examine different urban processes simultaneously such as radiation or thermal comfort. Moreover, ongoing model development aims at extending the application of the model from supercomputing environments to personal PCs in future (Maronga et al., 2019).

Code and data availability

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Code and data availability.

The PALM code, including the sectional aerosol model SALSA, can be freely downloaded from http://palm.muk.uni-hannover.de (last access: 29 March 2019). The distribution is under the GNU General Public License v3. More about the code management, versioning, and revision control of PALM can be found in Maronga et al. (2015). The exact version of the source code used in this study is additionally freely available at https://doi.org/10.5281/zenodo.2575325. The stand-alone version of the SALSA model is freely available at https://github.com/UCLALES-SALSA/SALSA-standalone/ (last access: 29 March 2019) and the input datasets at https://doi.org/10.5281/zenodo.1565752 (Kurppa, 2018).

Supplement

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Supplement.

The supplement related to this article is available online at: https://doi.org/10.5194/gmd-12-1403-2019-supplement.

Author contributions

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Author contributions.

MK developed the model code with support from HK, JT, and BM. MK and CK prepared the morphological data and PK the evaluation data. MK, AH, MA, and LJ designed the simulations and MK carried them out. MK prepared the paper with contributions from all co-authors.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

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Acknowledgements.

MK acknowledges Sasu Karttunen for technical support and Basit Khan, Farah Kanani-Sühring, Renate Forkel, and Sabine Banzhaf for cooperation, valuable discussions, and model testing. This study was financially supported by the doctoral programme in Atmospheric Sciences (ATM-DP, University of Helsinki), the Helsinki Metropolitan Region Urban Research Program and the Academy of Finland (181255, 277664), the trans-national project SMURBS (http://www.smurbs.eu/, last access: 29 March 2019; grant agreement no. 689443), and the Helsinki metropolitan Air Quality Testbed (HAQT).

Review statement

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Review statement.

This paper was edited by Samuel Remy and reviewed by Bo Yang and one anonymous referee.

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Short summary

This paper describes the implementation of a sectional aerosol module, SALSA, into the PALM model system 6.0. The first evaluation study shows excellent agreements with measurements. Furthermore, we show that ignoring the dry deposition of aerosol particles can overestimate aerosol number concentrations by 20 %, whereas condensation and dissolutional growth increase the total aerosol mass by over 10 % in this specific urban environment.

This paper describes the implementation of a sectional aerosol module, SALSA, into the PALM...

Geoscientific Model Development

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