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 and a land surface scheme first description in. 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 . Due to its excellent scalability on massively parallel computer architectures up to 50 000 processor cores;, 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 . The performance of PALM over urban-like surfaces has been successfully evaluated against wind tunnel simulations, previous LES studies, and field measurements . Some fundamental technical specifications of PALM are represented in Table .

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 XB size bins i based on the mean dry particle diameter D‾i of each bin. The number ni (m-3) and mass concentration mc,i (kgm-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 XB=10) and only the following chemical components can currently be included: sulfuric acid (H2SO4), organic carbon (OC), black carbon (BC), nitric acid (HNO3), ammonium (NH3), sea salt, dust, and water (H2O). Furthermore, the gaseous concentrations of H2SO4, HNO3, NH3, 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 . The sectional size distribution can be further divided into subranges 1 (D‾i≲50 nm) and 2 (D‾i≳50 nm). Subrange 1 consists of the smallest particles assumed to be internally mixed, strongly hygroscopic, and containing only H2SO4, OC, HNO3, and/or NH3. 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 . The evolution of aerosol size distribution is represented using the sectional hybrid-bin method . As a difference to the original SALSA, 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 V‾i=π6D‾i3, especially for larger aerosol particles when XB∼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. ).

A detailed description of the aerosol source–sink terms is given below (and in and ).

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 fSALSA, 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 ΔtLES 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 mH2O,i per size bin i can be represented either as a prognostic variable or as a diagnostic variable and calculated at each ΔtSALSA based on the equilibrium solution using the Zdanovskii–Stokes–Robinson (ZSR) method . 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 ni, mc,i, and gaseous compound introduces a new prognostic variable that is transported by the flow in PALM. Increasing the number of prognostic variables XPV from the default value of XPV=6 (wind components u, v, w and scalars e, θ, and q) to 12XPV=6+ΔXPV=6+XB(XCC+1)+XG, where XB is the number of size bins, XCC the total number of chemical components (aerosol phase), and XG=5 the total number of gaseous compounds, increases the computational load tremendously. To estimate the increase in computational costs caused by significantly increasing XPV, and also resolving the aerosol dynamics, simulations over a simple test domain of 20m×20m×20m (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 . Adding XB=10 size bins composed of XCC=2 chemical components (water always present) introduces ΔXPV=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 ΔtSALSA 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 ΔtSALSA (runs 12–13). Considering the longer timescales of aerosol dynamic processes compared to dispersion e.g., ΔtSALSA=10Δt is considered to be reasonable in urban simulations with a grid resolution of ∼1 m and Δt∼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 ni of which the volume υc,i and mass concentrations mc,i are calculated based on the geometric mean diameter D‾i. Aerosol emissions are defined similarly. In other words, the total number concentration is preserved in the initialization, whereas uncertainties arise when estimating mc,i or vc,i.

Limiting XB 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 XB, four different configurations are tested (Fig. ). All configurations cover particles from 3 nm to 2.5 µm, and subrange 1 includes particles up to 10 nm. The default configuration contains XB=10 with two bins in subrange 1. The second configuration contains XB=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 XB=50 was tested.

The total aerosol particle volume concentration V is highly sensitive to XB, and the rate of overestimation increases with decreasing XB (Fig. ). 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. c) improves with higher XB. To compromise between computational costs and modelling accuracy, XB=10 is used in this evaluation study.

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 . 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. ).

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 .

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 512×512×128 grid box with the measurement site approximately at the centre of the domain (Fig. ). A uniform grid spacing of Δx,y,z=1.0 m is applied within the lowest 96 m, and above the vertical grid Δz is stretched by a factor of 1.04, resulting in a total domain height of around 164 m and a maximum Δz,max≈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 . 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 zv,min=4.0 m were included in the simulations. They were modelled as springtime deciduous broadleaf trees with a constant LAD =0.6 m2 m-3 from zv,min to the tree top. This LAD value was estimated as a lower limit for urban street trees in northern Europe in spring . 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. ) 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 EFn=1.33×1014 km-1 vehicle-1 is used (Table ), which is an estimate specific to the measurement site . EFn 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 H2SO4 (4 % of the total mass) . 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; 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 EFH2SO4 or EFSVOC is given by NAEI, the following estimates were applied: EFH2SO4=0.1EFSO2 and EFSVOC=0.01EFNMOG , where NMOG stands for non-methane organic gases. The latter is rather conservative compared to emission rates applied by 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;. Similar to , ADCHEM was operated as a one-dimensional column trajectory model along HYSPLIT 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 . 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 ) 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 ; 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 .

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 z0=0.05 m and the drag coefficient applied for the trees is CD=0.5 seeand 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 XB=2+8 (see Sect. ). All aerosol processes, except nucleation, are switched on, and the following chemical components are included: H2SO4, OC, BC, HNO3, and NH3. 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 XB was examined for the morning simulation. Firstly, the following four simulations with XB=2+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 XB is tested by replicating the baseline morning simulation with less XB=1+7 (LB) and more bins XB=2+10 (MB).

The advection of both momentum variables and scalars was based on the fifth-order advection scheme by together with a third-order Runge–Kutta time-stepping scheme . The pressure term in the prognostic equations for momentum was calculated using the iterative multigrid scheme . 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, ΔtSALSA=1.0 s in all simulations, which is a safe choice since the turbulence timescale is smaller than any aerosol process timescale .

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.

To give a general picture of aerosol particle concentrations and dispersion in this study, Fig.  illustrates the modelled total aerosol number concentrations Ntot and wind speed U at z=3.5 m a.g.l. for all baseline simulations. The horizontal distribution of Ntot is shown to follow that of emissions (see Fig. ) and, for instance, courtyards remain relatively clean. Nevertheless, wind controls the dispersion, which is seen as up to 70 % higher Ntot 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 Ntot compare well against the measured values (Fig. ), 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 Ntot in the vertical is correctly modelled except for a measured increase in concentrations within the lowest 2 m. Despite the modelled Ntot being 50 %–100 % higher than measured in the evening (Fig. b), 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 . Comparing the mean values of all seven modelled profiles, their variation is shown to be larger than that between the measured and modelled Ntot at the exact measurement location.

Naturally, the coarse sectional representation of the aerosol size distribution with XB=10 means some details, such as a drop in concentrations at D≈60 nm (Fig. ), 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. b 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. , 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.