The parameterizations of aerosol microphysical processes for SOCs such as gas-to-particle partitioning and dry and wet deposition depend on the way the particulate phase is represented in the model. Here, there are two approaches employed in the submodel to represent the particulate-phase SOC: (1) it is assumed as a bulk species or (2) the particle sizes are resolved into n continuous (modal) distributions. The former will be hereinafter referred to as the bulk scheme and the latter referred to as the modal scheme. In the modal scheme, n is equal to the seven log-normal modes of the GMXe submodel, four with hydrophilic coating (ns: nucleation soluble, ks: Aitken soluble, as: accumulation soluble, cs: coarse soluble) and three hydrophobic (ki: Aitken insoluble, ai: accumulation insoluble, ci: coarse insoluble) . Each mode is treated as an individual tracer.

Gas–particle partitioning is assumed to take place when SOC is in equilibrium between the gas and particulate phases. The concentration of the species that is bound to particles (Cparticle) is calculated with 1Cparticle=θ×(Cparticle+Cgas), and the particulate mass fraction (θ) is defined as 2θ=CparticleCparticle+Cgas=Kp×CPM1+Kp×CPM=Kp′1+Kp′, where CPM is the concentration of particulate matter or PM (µgm-3), Kp is the temperature-dependent particle–air partition coefficient (m3µg-1), and Kp′ is the dimensionless Kp.

In a model configuration using size-resolved particles (viz. the modal scheme), each SOC tracer is introduced in the model as eight different species: seven aerosol particles in ns, ks, as, cs, ki, ai, ci modes and one in the gas phase. The particulate fraction of the species in mode i (θi) is calculated using Eq. () with CPMi and Kpi being the PM mass concentration and aerosol–air partition coefficient in the corresponding mode, respectively. The gaseous concentration Cgas is calculated using the sum of Kp values across modes, as well as total Cparticle and CPM: 3Cgas=∑i=17Cparticlei/∑i=17CPMi∑i=17Kpi.

It is noted that this approach may not hold the constraint of mass consistency and is thus subject to further corrections. For the current study, the effects from this problem are expected to be minimal, given the fact that PAHs in the particulate phase are mainly distributed in the accumulation mode and references therein.

For Kp calculation four options of gas–particle partitioning schemes are available in SVOC: (1) a parameterization that is based on adsorption onto aerosol surface , (2) absorption into organic matter , (3) a combination of the two ways of organic matter absorption and black carbon adsorption , and (4) multiple phases of the two-way sorption system . Two schemes used in this study are described below.

Lohmann–Lammel scheme. The Lohmann–Lammel scheme takes into account an adsorption onto black carbon (BC) surface in addition to absorption into organic matter (OM) . This dual-sorption theory empirically calculates Kp according to the following relation, 4Kp=10-12fOMγoctMWoctγOMMWOMρoctKoa+fBCaatm-BCasootρBCKsa, where ρBC is the density of BC (assumed as 1 kg L-1), ρoct is the density of octanol (0.82 kgL-1 at 20 ∘C), Ksa is the partition coefficient between diesel soot and air, aatm-BC is the available surface of atmospheric BC (m2g-1), and asoot is the specific surface area of diesel soot (m2g-1). The adsorptive properties of diesel soot are selected to represent the atmospheric BC because this material is considered the most significant type of BC in polluted air.

The Ksa value is calculated as a function of sub-cooled liquid vapor pressure pL0 using an estimate suggested by , 5log⁡Ksa=-0.85log⁡pL0+8.94-log⁡998asoot, where asoot in the model is set as 18.21 m2g-1.

Soil

For soil volatilization, two parameterization schemes are implemented in the SVOC submodel: the Jury scheme and the Smit scheme . The latter was applied in the study which is based on the volatilization of pesticides from the surface of fallow soils . The volatilization occurs upon partitioning over three soil phases (solid, gas, and liquid). The concentration of the chemical in the soil system (kgm-3) is formulated as 8Csoil=Q×Cvapor, and the capacity factor Q is given by 9Q=ψ+φKwa+ρsoilKwaKsl, where ψ and φ are the volume fractions of air and moisture, respectively; ρsoil is the soil density; Kwa is the water–air partition coefficient where Kwa=1/Kaw; and Ksl is the solid–liquid partition coefficient. Kaw is calculated based on the Henry's law constant: 10Kaw=1/HRTand11H=kH⊖×exp⁡-ΔHsolnR1T-1T0, where H is the temperature-adjusted Henry coefficient (Matm-1), R is the dry air gas constant (8.314 Jmol-1K-1), T is the environment temperature (K), ΔHsoln is the enthalpy of dissolution (Jmol-1).

Ksl can be set equal to the sorption coefficient to soil organic matter Kom times the fraction of organic carbon in soil fOMs. Since Kom data are not available, the coefficient for sorption to soil organic carbon Koc was used to estimate Ksl: 12Ksl=0.56KocfOMs. has suggested a reasonably good regression relationship between Koc and octanol–water partition coefficient Kow for PAHs: 13log⁡(Koc/1000)=0.823log⁡(Kow/1000)-0.727. where the factor of 1000 is needed because Koc and Kow are expressed in cubic meter per kilogram (m3kg-1), whereas in the original regression they used milliliter per gram (mLg-1).

Once Q is computed, the dimensionless fraction of the chemical in the gas phase Fgas is then calculated as 14Fgas=ψQ.

In the Smit scheme, an empirical relation was established between Fgas and cumulative volatilization (CV in percent of substance deposit). CV was determined based on field and greenhouse experiments with numerous pesticides at 21 d after application. For normal to moist field conditions, CV is expressed as 15CV=71.9+11.6log⁡(100Fgas);6.33×10-9<Fgas≤1, and for dry field conditions 16CV=42.3+9.0log⁡(100Fgas);0.2×10-6<Fgas≤1.

Dry deposition is simulated using deposition velocities. For gas-phase SOCs, the velocities are calculated by the DDEP submodel , whereas particulate-bound SOCs are assumed to deposit at similar rates to other aerosols whose velocities are also computed by DDEP. If the modal scheme is selected (see Sect. ), the particle deposition velocity vdSOC at mode i is equal to the aerosol deposition velocity vdaer at the respective mode. On the other hand, for the bulk scheme, vdSOC, is computed as a weighted average of vdaer from the four BC modes (ki, ks, as, and cs) where the weight is the surface area of BC. This approach is most relevant for PAHs as they are assumed to be predominantly transported by sorption to BC. The above relations are formulated as 26amodal scheme: vd,iSOC=vd,iaer;26bbulk scheme: vd,bulkSOC=∑i=14SBCi×vd,iaer∑i=14SBCi; and the BC surface area per unit volume, SBC (cm2cm-3), is given by 27SBCi=4πriexp⁡ln⁡2σgi2Ni×CBCiCaeri, where Ni is the number concentration for mode i (cm-3), ri is the number radius (cm), σgi is the geometric standard deviation, CBCi is the BC concentration (µgm-3) in mode i, and Caeri is the sum of aerosol concentrations in the same mode (µgm-3).

Wet deposition is applied to both gas and particulate SOCs. The gaseous fraction is scavenged into cloud and rain droplets according to diffusion limitation, Henry's law equilibrium, and accommodation coefficient, and this process is parameterized and solved empirically in the SCAV submodel . Particulate-phase SOCs are scavenged in convective updrafts, rainout and washout, and cloud evaporation, with the rate being proportional to BC wet scavenging; hence the change in SOC concentration is described as 28amodal scheme: ΔCSOCiΔt=μSOCiμBCi×ΔCBCiΔt;28bbulk scheme: ΔCSOCΔt=μSOC∑i=14μBCi×∑i=14ΔCBCiΔt; where µ is the particle volume mixing ratio (molSOC/BCmolair-1) and Δt is the model time step (s). Note that Eq. (a) imposes a restrictive prerequisite, namely BC and the particle-bound SOC have similar size distributions. When this condition is not met, there is a high possibility of an artificial mass being produced, usually to the largest aerosol mode. To solve this problem, a correction factor is applied and defined as a function of the ratio of positive fluxes to negative fluxes integrated across levels and modes.

The atmospheric degradation of SOCs in the gas phase as well as within aerosol particles are explicitly treated in SVOC. The gas-phase chemical mechanism is calculated within the MECCA submodel . SOC gaseous degradation is from photochemical reactions with OH, NO3, and O3 radicals, which follow a second-order transformation, with the rate constants k(2) obtained from laboratory studies. The kOH(2) value is typically higher, suggesting that oxidation with OH radical is the dominant loss pathway.

Most models do not consider oxidation rate of particulate-phase SOCs as experimental aerosols studied in laboratory cover only a small part of relevant atmospheric aerosols. For PAHs, such as benzo(a)pyrene, which stays mostly in the particulate phase, the degradation is more efficient by surface reactions with O3 and references therein with the rate depending on the substrate. The SVOC submodel includes the degradation process of PAHs on aerosol particles from the O3 reaction with one assumption; that is, the heterogeneous reaction does not lead to a change in the oxidant concentration. Due to a limited number of kinetic studies of heterogeneous reactions of PAHs, only two species are considered (phenanthrene and benzo(a)pyrene). Nevertheless, the submodel structure provides a relatively straightforward approach to allow more species in the future.

The reaction rate coefficient for particulate-phase phenanthrene with O3 at aerosol surfaces was derived from laboratory experiments using chemically unspecific model aerosol (silica) with PAH surface coverage of less than a monolayer . To this end, the second-order rate coefficient, k(2), in cm4molec-1s-1 was derived from the reported phenanthrene (PHE) decay kinetics, kO3,het(2) (cm3molec-1s-1), as k(2)=kO3,het(2)/SV=6.2±4.8×10-17 cm4molec-1s-1, with SV (cm-1) being the experimental aerosol surface concentration (0.56±0.43 cm-1 in ). In the submodel, kO3,het(2) (cm3molec-1s-1) is calculated using the ambient aerosol surface concentration. As for benzo(a)pyrene, the pseudo-first-order rate coefficient, kO3,het(1) in reciprocal seconds (s-1), was derived from surface-adsorbed benzo(a)pyrene reaction with O3 on solid organic and salt aerosols following the Langmuir–Hinshelwood mechanism .

Biotic and abiotic processes in surface compartments contribute to the degradation of chemicals and are strongly dependent on local environmental conditions, e.g., nutrient contents, water, temperature, PH, and light. In SVOC, these factors are not explicitly quantified. The degradation is alternatively described as following a first-order decay law (Eq. ). The 10 K temperature warming is assumed to double the rate of degradation (Eq. ), following recommendations in chemical risk assessment and consistent with findings, such as a two-time increase in the growth of hydrocarbon-degrading microbes found in soils . 29∂CSOCs∂t=-ksfc×CSOCs,30ksfc(T)=ksfc(Tref)×2T-Tref10, where CSOCs is the substance concentration (kgm-3) in surface compartments (i.e., soil, vegetation, or ocean) and ksfc is the first-order decay rate (s-1). Tref is the reference temperature, i.e., 298 K for soil and 273 K for ocean. Note that the degradation in vegetation is calculated assuming the same ksfc for the soil compartment.

The model simulations were performed for four PAH species: phenanthrene (PHE), pyrene (PYR), fluoranthene (FLT), and benzo(a)pyrene (BaP). To simulate the fate and environmental distribution of these species, the model requires some physicochemical properties as summarized in Table S5 of the Supplement. These include equilibrium partition coefficients and their related energies of phase transfer. The characteristics from PHE to BaP are indicated by decreasing volatility (as molar mass increases), increasing Koa and Kow, and decreasing water solubility (as Cws and Henry's coefficients decrease). The properties also include the second-order rate coefficients for homogeneous oxidation with OH, O3, and NO3 except for BaP where the gaseous reaction is switched off. Heterogeneous oxidation by O3 is simulated only for PHE and BaP. Furthermore, the model also requires compound solute parameters for simulations using the ppLFER gas–particle partitioning scheme (Table S6).

As model input, several emission datasets were employed in the study. Emission estimates for PAHs were obtained from the annual mean inventory of for the year 2008. They applied regression and technology split methods to construct country-level emissions for six categories (coal, petroleum, natural gas, solid wastes, biomass, and an industrial process category) or six sectors (energy production, industry, transportation, commercial/residential sources, agriculture, and deforestation/wildfire) before further regridding the emissions to a 0.1∘×0.1∘ grid.

Emissions of aerosol species such as organic carbon (OC), black carbon (BC), mineral dust (DU), and sea salt (SS) were included. For BC and OC, the Representative Concentration Pathway (RCP) 6.0 emission scenario of the IPCC (Intergovernmental Panel on Climate Change) was used and accessible via ftp://ftp-ipcc.fz-juelich.de/pub/emissions/gridded_netcdf (last access: 15 February 2018). Emissions are calculated for anthropogenic, biomass burning, ship, and aircraft. The RCP database provides a seasonality only for the biomass burning and ship emissions. In this study, seasonal-scale factors were applied to the anthropogenic emission whereby the seasonality was based upon the monthly variation of the Hemispheric Transport of Air Pollutants (HTAP) v2.2 anthropogenic emission inventory . BC emissions from all sectors were assumed to be hydrophobic. For OC, it was assumed to be 65 % hydrophilic and 35 % hydrophobic upon biomass burning emissions and to be 100 % hydrophobic upon anthropogenic and ship emissions. Both OC and BC were emitted at Aitken mode, which spans the size range from about 5 to 50 nm in diameter. A factor of 1.724 was used to scale the OC emissions to primary organic matter (OM). It is noteworthy that the formation of secondary organic aerosols (SOAs) from atmospheric oxidation and condensation of volatile organic compounds (VOCs) were not treated in the simulations. In the model, particulate organic matter is emitted and transported as a bulk aerosol species (OM).

DU and SS emissions were computed online by the ONEMIS submodel . DU emission flux is calculated based on wind speed at 10 m altitude and soil parameters . The emission of SS particles by bubble bursting is described as wind-speed-dependent particle mass and number fluxes at accumulation (50–500 nm) and coarse (>500 nm) modes. In ONEMIS, the fluxes are determined from precalculated lookup tables following the parameterization. SVOC submodel accounts for OM fraction in the SS mass fluxes (JSS), and the fraction is estimated using a 10 m wind (v10)-dependent empirical relationship derived from Fig. 2a in . Equation () below is used to calculate the OM mass fluxes, JOM, in kgm-2s-1. 31JOM=JSS×120.781+0.03exp⁡0.48v10+0.241+0.05exp⁡0.38v10.

Emissions of other gases including volatile organic species (SO2, CO, NH3, NO, CH4, and non-methane hydrocarbon (NMHC)) were prescribed using the IPCC RCP6.0 dataset . Global estimates for the soil properties dry bulk density and organic matter fraction were obtained from and , respectively.

The model was run on a spectral T42 grid in the horizontal (approximately 2.8∘ in a lat–long grid) and 19 unevenly distributed layers in the vertical with the top level at 10 hPa. The vertical layers are discretized using a hybrid coordinate (the lowest level follows the terrain and become a surface of constant pressure in the stratosphere). All simulations were run for a 3-year period (i.e., 2007–2009), with a 1-year spinup (i.e., 2006), and nudged toward the European Centre for Medium-range Weather Forecasts (ECMWF) reanalysis data . Note that the simulation period was selected based on the representative year of PAH emissions (i.e., 2008) and the availability of reliable observation data (see the Supplement Sect. SIII).

Factor separation analysis was used to quantitatively evaluate the contributions to changes in a particular output variable that result from changing components of model input and physics parameterizations. The model sensitivity to four model components (hereinafter, “factors”) was tested. The four factors were the following:

Temporal resolution of emissions (hereinafter, fac1). The PAH emission inventory of was based on 2008 annual emission totals from all sectors (see Sect. ). The emissions were divided over the year using monthly factors derived from BC anthropogenic emissions. Two sets of simulations were carried out to test the sensitivity of model output to the seasonal profile of emission. The first set used constant emissions throughout the simulations, whereas the second set used a monthly emission interval.

The factor separation technique is described in the Supplement Sect. SIV including the equations used to compute the model sensitivity to four factors. A total of 16 (or 2n) experiments summarized in Fig.  are necessary to supply the complete solution for the factor analysis. The ABLN (annual + bulk + Lohmann–Lammel + no volatilization) experiment is designed to be the base simulation (f0), in which annual emission (A), the bulk scheme (B), the Lohmann–Lammel scheme (L), and no re-volatilization (N) were applied. SMPW (i.e., Seasonal emission + Modal scheme + PpLFER scheme + With re-volatilization) is referred to as the target simulation (f1234) in which the more sophisticated choice of the four features (factors) was tested. The total (gas + particle) concentration at the lowest model level was selected for its higher relevance with all the factors (compared to, for example, atmospheric burden) and to facilitate direct comparison with observations.

Figure a shows that using monthly emissions increases PAH concentrations in DJF and decreases the concentrations in JJA over the areas from the middle to high latitudes of the Northern Hemisphere (NH). This result is expected and is attributed to emissions during the northern winter (summer) being higher (lower) than annual means and photochemistry being less (more) active. Over the Arctic, the relative changes (f^1/f0) in DJF show a median increase of approx. 30 % for PHE, PYR, and FLT, and 7 % for BaP, whereas f^1/f0 in JJA is weaker in magnitude for PHE and PYR (-16 %) but comparable for FLT (-28 %) and BaP (-5 %). Accounting for seasonality leads to generally lower bias for PHE, and this effect is more pronounced in the middle latitudes rather than in high latitudes (Supplement Sect. SVII, Fig. S22).

In general, f^1/f0 becomes smaller over the northern midlatitudes by around half. The upper (lower) quartile of f^1/f0 in DJF (JJA) indicates that about one-quarter of the areas of the temperate and polar regions experience an at least 40 % increase (decrease), most were located in northeastern Eurasia (see the left panels of Figs. S6 and S7). Note f^1/f0 over the tropics are small to negligible (±1 %) mainly due to little variation in emissions from anthropogenic sectors. PAH concentrations may be higher in dry season due to increased amounts of biomass burning, but they are poorly represented in the current inventory. In southern middle and high latitudes, the direct effects of emission change are substantially opposite in sign to the effects seen in the northern latitudes, being negative in DJF (median ranges from -4 % to -32 %) and positive in JJA (7 %–25 %).

The total interactions between fac1 and other factors generally produce opposite signals to f^1 over middle and high latitudes in the two seasons. This result indicates that the changes in other factors tend to buffer the influence of monthly emission on increasing or decreasing f0 concentrations. Some exceptions are seen over parts of East Asia in DJF for all species (Fig. S6, right panels) and over the Southern Ocean in JJA for BaP (Fig. S7, right panels) where the interactions work to reinforce the direct effects. In DJF, the degree of interactions is smaller or comparable to the size of f^1 for the Arctic and northern midlatitudes but becomes stronger by at least double for Antarctica. The opposite tendency is seen in JJA but only applies to PYR and FLT. In agreement to f^1, the interaction effects are less apparent over the tropics. Note that the positive effects in f^14 during local summer tend to be more dominant than the effects in other combinations for PHE, PYR, and FLT (Figs. S18–S20). In the simulation, the presence of re-volatilization in summer tends to suppress f^1 by promoting more gases available for long-range transport, and thus implies a negative feedback.

The direct effects of the modal scheme (f^2) vary among species (Fig. c). f^2 is almost absent for PHE as the species resides almost completely in the gas phase. For PYR and FLT, f^2 is negative during DJF over northern midlatitudes (f^2/f0 quartiles range from -5 % to -30 %) and the Arctic (-50 % to -75 %), whereas it is hardly visible in JJA or over other regions. Further analysis reveals stronger particle deposition results when the aerosol phase is discretized into different modes (not shown). In long-range transport under modal aerosol representation, the aerosols are more associated with larger particles, hence particle deposition becomes more effective. The choice of size discretization has only minor effects for atmospheric levels, except for BaP, especially during DJF, for which overestimates are significantly compensated for (Fig. S25). Actually, for BaP, the modal scheme generally decreases the concentrations in the Arctic (as median, -35 % in DJF and -15 % during JJA) and increases (approx. 5 %) those over the mid- and low-latitude landmass (Figs. S8d and S9d, left panels).

As is the case for the direct effects, the interaction contributions are peculiar to individual species (Fig. d). For PHE, the interaction effects in DJF are reflected in negative concentration responses over the Arctic (18 %) and positive over Antarctica (7 %), in contrast to relatively mild influences over other regions or in JJA. For PYR and FLT, the effects are negative over the Arctic both in DJF (quartiles vary from -20 % to -75 %) and in JJA (-6 % to -120 %). It is interesting to note that the interaction between the modal and ppLFER schemes has a major influence on the negative signal (Figs. S15, S16, S19, S20), suggesting that the decrease in simulated concentration associated with the change from bulk to modal could be intensified when the ppLFER scheme is used. In the remaining areas, the interaction effects vary in sign spatially as illustrated in the right panels of Figs. S8b and c to S9b and c. Nevertheless, it shows for both species that maximum influences occur over the Southern Ocean in DJF (where the effects may reach 2 orders of magnitude) and midlatitude landmass in JJA (more than a factor of 5). As for BaP, the median effects are negative (-7 % to -30 %) in both seasons, although some positive signals are apparent in parts of high latitudes while the tropical oceans bear small synergistic effects. Similar to other species, the degree of interactions is stronger than f^2 by more than a factor of 3 for the majority of grid cells (Figs. S8d–S9d, right panels). The large fractions of the effects are dominated by 2-factor and 3-factor combinations related to the interaction with the ppLFER scheme and/or re-volatilization (Figs. S17, S21).

Figure e shows that the direct effects of the ppLFER scheme (f^3) show little spatial heterogeneities in both seasons and for all species. The effects are barely important for PHE due to a low gas–aerosol partition constant (Kp); f^3 is positive for PYR and FLT over polar regions and northern midlatitudes especially in winter when low temperature favors partitioning to aerosols (higher Kp). The median of f^3/f0 varies from 1 % to 25 % with some parts of Antarctica showing an increase larger than 50 %. For BaP, the effects are overall negative (by at least -5 %) with f^3/f0 reflecting a positive north–south gradient (increasing from the Arctic to Antarctica), associated in part with stronger signals over oceans (Figs. S10d and S11d, left panels). In particular under the modal size discretization, the choice of gas–particle partitioning scheme has only minor effects for atmospheric levels, except for BaP for which model overestimates are compensated by the choice of the ppLFER scheme (Fig. S25). Under the bulk size discretization, the ppLFER scheme tends to enhance some of the overestimates in the Arctic summer (FLT, PYR; Figs. S23–S24). The application of ppLFER increases Kp as this module is calculated from not only interaction with BC and OM (as in Lohmann–Lammel scheme) but also with some other aerosol matrices. Higher Kp indicates higher particle mass fraction. For PYR and FLT, this leads to an increase in total atmospheric lifetime as the aerosol phase is not degraded, and can therefore be transported over a larger distance. For BaP, the additional particles are subject to depositions and heterogeneous oxidation by ozone, particularly in regions away from sources. The factor influence is notably too small for PHE as oxidations occur in both phases.

The effects from fac3 interactions vary by region and are relatively stronger than f^3 (Fig. f). This finding is common to all species and seasons. The degree of effects is weaker for PHE compared to that for other species. However, the interactions increase polar concentrations in local summer by 20 % to a factor of 5, mainly associated with the coupled effect of ppLFER and volatilization (f^34, Figs. S14 and S18). For PYR and FLT, there is a high spatial variability over extratropical regions in local summer, as indicated by the interquartile range (distance between the third and first quartiles). With regard to synergistic terms, ppLFER interactions with the modal scheme and re-volatilization, in 2- or 3-factor combinations, are more important than other contributions (Figs. S15–S16 and S19–S20). For BaP, the interaction effects show negative signals similar to f^3, suggesting a positive feedback. The interactions exert a stronger influence on the concentrations of the oceans than on that of land, except in the tropics (Figs. S10d and S11d, right panels). The median of relative effects ranges from -1 % to a factor of -10, minimum (maximum) in the northern (southern) extratropics. Two second-order interactions likely make major contributions, i.e., f^34 which dominates the response over oceans and f^23 which dominates over land (Figs. S17 and S21).

The direct effects of re-volatilization (f^4) are illustrated in Fig. g. f^4 is positive in the tropics in both seasons, with the median f^4/f0 ranging from 5 % to 50 %. Intensive re-volatilization in this region would increase net surface fluxes, thereby increasing concentrations. For PHE, positive f^4 values are more localized over the tropical landmass, whereas negative f^4 values are predicted over the tropical ocean (Figs. S12a and S13a; left panels). The positive (negative) effects over land (ocean) areas are also apparent at higher latitudes during most of the year. This reflects the fact that the negative effects on concentrations over ocean act contrary to the positive effects on net surface fluxes, mainly caused by the nonlinear relationships of air–sea gas exchange (deposition and volatilization), air and surface burden, atmospheric oxidation, and emissions. Accounting for re-volatilization compensates for a significant part of underestimates of PHE in the Arctic during summer, but adds to overestimates in midlatitudes (Fig. S22).

For the studied species of mid semivolatility, PYR and FLT, a positive signal is apparent over the high and middle latitudes during local summer in contrast to a negative signal during local winter (Fig. g). Similar to PHE, the negative signal is confined over oceans (Figs. S12b–c and S13b–c; left panels). The summer increases are stronger (20 % to a factor of 10) than the winter decreases (-10 % to -60 %) and the magnitudes are higher in FLT than in PYR. The near-ground concentrations of PYR and FLT are estimated to be ≈30 %–80 % in midlatitudes of which ≈30 % are attributable to re-volatilization. In the Arctic, re-volatilization compensates for ≈60 % of PYR underestimation (Fig. S23) and explains most of, ≈60 %–80 %, the FLT overestimation (Fig. S24). For BaP, f^4 is positive consistently across regions and seasons (f^4/f0 ranges from 20 % to a factor of 10), with substantial effects occurring over oceans (Figs. S12d–S13d; left panels). Accounting for re-volatilization creates some overestimates in the Arctic during summer (Fig. S25). It should be noted that the parameterization adopted here to describe volatilization from soils (the Smit scheme) is derived from an experimental study on mid-polar-to-polar pesticides and there is a need to validate and eventually sophisticate the parameterization to apolar substances.

The interactions generally point toward positive effects for the high-to-medium volatility species (Fig. h), despite some negative effects present over parts of the southern (northern) oceans in DJF (JJA) (Figs. S12–S13; right panels). As for BaP, the effects are uniformly negative, inferring the interactions work in opposition to f^4. The negative response is almost entirely caused by the negative f^34, i.e., the 2-factor interaction between re-volatilization and the ppLFER scheme (Figs. S17, S21). Compared to f^4, the degree of interactions is weaker for PHE, except in polar regions during local summer where the interactions could amplify f^4. The above implies that f^4 may point in the right direction regardless of the influences from other factor changes. In contrast, the degree of interactions is overall comparable to f^4 for the other species.

Firstly, the comparison to land monitoring stations is as follows.

Central tendency. Table  shows statistical indices for near-surface concentrations of atmospheric PAHs from observations and simulations and their comparisons, averaged across stations in the Arctic, northern midlatitudes, and the tropics. We can see that observed mean concentrations are higher for PHE and smaller for BaP over all regions. Furthermore, the Arctic concentrations are lower than those in the northern midlatitudes by a factor of around 20 and those in the tropics by approx. 2 orders of magnitude. The model captures well these species and regional variations, but the magnitudes are both underestimated and overestimated. In the Arctic, it underestimates PHE (MB =-0.060 ngm-3) and BaP (MB =-0.006 ngm-3) concentrations but slightly overestimates PYR (MB =0.001 ngm-3) and FLT (MB =0.04 ngm-3). In the NH midlatitudes, the model overestimates the three species predominantly occurring in the gas phase (MB =0.077–0.867 ngm-3) but underestimates BaP (MB =-0.58 ngm-3). Negative bias is seen in the tropics for three PAHs (MB =-3.443 to -6.851 ngm-3). Nevertheless, the comparison of model and observations at individual monitoring stations can be different from the regional mean statistics, as described in the Supplement Sect. SVIII. Comparing all four PAHs, a larger degree of bias is found for BaP, which increases from the northern midlatitudes (NMB =-0.58, NMBF =-1.40, FAC2 =0.31, FAC10 =0.79) to the Arctic (NMB =-0.92, NMBF =-12.17, FAC2 =0.17, FAC10 =0.33).

Secondly, the comparison to ship cruise measurements is as follows. Measurements of PHE, PYR, and FLT concentrations over the Atlantic Ocean were taken during a cruise in July 2009 . Figure  shows the ship sample concentrations overlaying the simulated PAH concentrations. Sample arithmetic (geometric) means during the whole cruise transect are 322 (209), 95 (88), and 128 (111) pgm-3 for PHE, PYR, and FLT, respectively. The model poorly reproduces the remote marine environments and overall underestimates the observations, except at 3 locations along the North American coast. The simulated means across sampling positions are 23 (7), 20 (3), and 39 (2) pgm-3, respectively, and the underestimation ranges from a factor of 2 to 1000. The degree of bias is most apparent over the tropical South Atlantic at latitude band 5–15∘S.

As reported in , the measured concentrations of BaP over the Asian marginal seas, the Indian Ocean, the South Pacific Ocean, and North Pacific Ocean are 131 (45), 14 (3), 9 (2), and 8 (3) pgm-3, respectively, for the arithmetic (geometric) means of all samples. Similar to other species, the model also underestimates the BaP concentrations with mean values being 75 (15), 4 (0.05), 0.09 (0.03), and 0.2 (0.06) pgm-3, respectively. The discrepancy appears relatively smaller over the Asian marginal seas as compared to other locations (Fig. ). A substantial degree of bias is seen over the Indian Ocean covering approximately the area bounded by 70–90∘E and 10–30∘S, with simulated values being more than 2 orders of magnitude smaller than the observed.

The model tendency to underestimate the marine air concentrations may likely be due to several factors. (a) The grid resolution is not sufficient to reproduce fine-scale processes at the grid points close to shipping tracks; (b) high uncertainties associated with the air–sea gas exchange parameterizations still exist, most notably in the estimation of gas transfer velocity; (c) the global inventory may significantly underestimate emissions from ocean shipping and does not well characterize the spatial and temporal variability of biomass burning plumes as another potential point of origin of pollutants in the marine air ; and (d) PAH concentration over remote oceans is controlled by atmospheric components (e.g., temperature, wind speed, boundary layer height, photochemical degradation) and the dynamical and biogeochemical components of the ocean. However, the ocean components have not been covered in the simulation; (e) the particulate-bound PAHs may undergo too fast heterogeneous oxidation (most relevant for BaP), leading to short atmospheric lifetimes and weaker long-range transport. BaP, mostly stays in the particulate phase, presumably also in seawater, and therefore may be somewhat underestimated due to the neglect of sea-spray-driven aerosol suspension.

Measurements of particulate mass fraction (θ) were available only from the E3 station in Europe and IADN stations (I1–I7) in North America (see Table S11). Table  presents summary statistics on monthly mean θ from observations and simulations including some performance metrics. The observed mean θ is smaller for PHE (0.051±0.035) and higher for BaP (0.949±0.067). This result is expected as volatility decreases (hence θ increases) from (lighter) PHE to (heavier) BaP. The θ values for PYR and FLT are larger by over 5 times than those for PHE and lower by around one-third than those for BaP. The model reproduces well the distinct differences among species but underestimates the observed θ for PHE, PYR, and FLT. The degree of negative bias is relatively large in PHE (NMB =-0.910 and NMBF =-10.145), whereas for the isomer pair of PYR and FLT, the model exhibits a similar performance with a slight improvement in PYR (NMB =-0.410 and NMBF =-0.694). With regard to BaP, there is a satisfactorily small bias (MB =0.015, RMSE =0.074, NMB =0.016, and NMBF =0.016) although the observed and simulated values have a very weak correlation (r=0.03).

Figure  shows the seasonal mean θ averaged over 3 years for all PAHs. Observations show that θ for BaP varies less than those for 3–4-ring PAHs. Although the model adequately reproduces this feature as well as seasonal variation of individual species, the simulated θ of PHE, PYR, and FLT is generally lower than the observations (except for PYR in winter). For BaP, differences between model and observations are less than 10 % in all months. The SVOC submodel describes the gas–particle partitioning of atmospheric SOCs as a function of temperature and aerosol phase composition. The underestimation might be related to the fact that the submodel assumes the particle to be fully in equilibrium with the gas phase at all times. It neglects kinetic limitations of molecular diffusivity that could lead to the trapping of particles inside viscous (or semisolid) organic aerosol coatings. This shielding effect increases equilibration times of the particles, thereby reducing part of θ from the mass available for gas–particle partitioning. Deviations from measurements can also be partly attributed to the locations of some stations that are within, or close to, residential and industrial area (namely I4, I6, and I7) where the scale and gradient in anthropogenic emissions are not resolved by the model grid resolution nor represented by the emission inventory.