The contribution of plume-scale nucleation to global and regional aerosol and CCN concentrations : evaluation and sensitivity to emissions changes

We implement the Predicting Particles Produced in Power-Plant Plumes (P6) sub-grid sulphate parameterization for the first time into a global chemical-transport model with online aerosol microphysics, the GEOS-Chem-TOMAS model. Compared to simulations using two other previous treatments of sub-grid sulphate, simulations using P6 subgrid sulphate predicted similar or smaller increases (depending on other model assumptions) in globally, annually averaged concentrations of particles larger than 80nm (N80). We test the sensitivity of particle number concentrations in simulations using P6 sub-grid sulphate :: the ::::::::: sensitivity :: of :::::: particle :::::: number :::::::::::: concentrations : to changes in SO2 or NOx emissions to represent recent emissions control changes. For global increases : of ::: 50% in emissions of :::: either : SO2 , :: or NOx, or both SO2 and NOxby 50, we find increases in ::: that:globally, annually averaged N80 of :::::: increase ::: by : 9.00%, 1.47%, or 10.24% , respectively; however, these changes include changes to :::::::::: respectively. :::::::: However, : both sub-grid and gridresolved processes :::::::: contribute :: to ::::: these ::::::: changes. Finally, we compare the model results against observations of particle number concentrations. Compared with previous treatments of sub-grid sulphate, use of the P6 parameterization generally improves correlation with observed particle number concentrations. The P6 parameterization is able to resolve spatial heterogeneity in new-particle formation and growth that cannot be resolved by any constant assumptions about subgrid sulphate. However, the differences in annually averaged aerosol size distributions due to the treatment of sub-grid sulphate at the measurement sites examined here are too small to unambiguously establish P6 as providing better agreement with observations.


Introduction
Anthropogenic aerosol affects human health and the Earth's climate.High aerosol concentrations cause human health problems, including respiratory and cardiovascular diseases, intensification of asthma, a reduction in physical abilities and an increase in mortality rates (Arya, 1999;Dockery et al., 1993;Peng et al., 2005;Stieb et al., 2002).Particles smaller than 100 nm in diameter may have greater health impacts than larger particles (Peters et al., 1997).Aerosols also affect the Earth's climate through direct radiative effects (Charlson et al., 1992) and through indirect radiative effects: changes in cloud reflectivity and lifetime due to changes in the number of aerosol particles acting as Cloud Condensation Nuclei (CCN) (Albrecht, 1989;Twomey, 1974).Both of these aerosol effects are strongly dependent on the size of the aerosol and the magnitude of these effects have large uncertainties (Boucher et al., 2013;Dusek et al., 2006).
One of the largest anthropogenic sources of aerosol mass are sulphur-rich plumes (Dentener et al., 2006).The hydroxyl radical (OH) can oxidize sulphur dioxide (SO 2 ) within these plumes to form sulphuric acid (H 2 SO 4 ), which in turn can condense onto pre-existing particles.If H 2 SO 4 concentrations are high enough, the H 2 SO 4 will cluster with itself and other condensible gases to nucleate new particles (Kulmala and Kerminen, 2008).Anthropogenic sulphur emissions have been shown to have a significant effect on global particle concentrations, particularly in the Northern Hemisphere (Adams and Seinfeld, 2003;Luo and Yu, 2011;Spracklen et al., 2005;Wang and Penner, 2009); however, the magnitude of this impact depends on assumptions made in the modelling studies as will be discussedmomentarily.
There are several factors that determine the rate of particle formation and growth in the plumes of coal-fired power plants.These include the solar radiation and NO x concentrations (through their influence on OH concentrations), and the pre-existing condensation and coagulation sinks.Further complicating the formation and growth rates are that many of these factors vary spatially in the plume.Concentrations of OH in the plume control the SO 2 gas-phase oxidation rate and hence influence H 2 SO 4 concentrations.These OH concentrations depend strongly on NO x (nitric oxide (NO) + nitrogen dioxide (NO 2 )) concentrations and sunlight (Olson et al., 2006).The primary loss mechanism for H 2 SO 4 in the boundary layer is condensation onto existing aerosol particles (Eisele and Tanner, 1993), and so concentrations of H 2 SO 4 also depend strongly on the aerosol condensation sink (approximately proportional to aerosol surface area).The variation in NO x concentrations and the heterogeneity of the condensation sink within a given plume causes H 2 SO 4 concentrations to vary dramatically within the plume (Stevens et al., 2012;Lonsdale et al., 2012).Nucleation and growth rates are strong functions of H 2 SO 4 concentrations, and thus will ::: will :::::::: therefore vary spatially across the plume.Finally, the newly formed particles may be lost by coagulation with larger particles; as the size distribution evolves spatially in the plume, so will these coagulational losses.Currently, global-and regional-scale models typically have resolutions of hundreds and tens of kilometres or more, respectively, and are thus :: the :::::::::: resolutions ::: of :::::::: regional-::: and :::::::::: global-scale :::::: models ::: are ::::::: typically :: at :::: least :::: tens :: or :::::::: hundreds :: of ::::::::: kilometres, ::::::::::: respectively.::::: These :::::: models :::: are ::::::: therefore : unable to accurately resolve the formation and growth of aerosols within these plumes using grid-box averages for chemical concentrations, aerosol concentrations, and meteorological values.
Thus, these models have ::::: These :::::: models :::: have :::::::: therefore typically assumed that some fraction of all anthropogenic SO 2 emissions are oxidized to form sulphate (SO 4 ) at the subgrid scale.This sub-grid sulphate is added to the model via a fixed, pre-assumed size distribution for all anthropogenic sulphate sources.For instance, the study of Makkonen et al. (2009) used the assumption recommended by the AeroCom emissions inventory (Dentener et al., 2006): they emitted the sulphate into a single lognormal mode with a median radius of 500 nm and a standard deviation of 2.0.Many studies (Adams andSeinfeld, 2002, 2003;Pierce andAdams, 2006, 2009;Pierce et al., 2007;Spracklen et al., 2005;Wang and Penner, 2009) have used a bi-modal distribution comprised of a nucleation mode and an Aitken mode with number mean diameters 10 nm and 70 nm, and geometric standard deviations 1.6 and 2.0.Either 5 % or 15 % of the sulphate mass is emitted into the nucleation mode, depending on the study.Several of these studies investigated the sensitivity to the assumptions made about sub-grid sulphate formation.Adams and Seinfeld (2003) and Spracklen et al. (2005) found that if they changed the fraction of SO 2 con-verted to sub-grid sulphate from 0 % to 3 %, CCN at an assumed supersaturation of 0.2 % (CCN(0.2%)) in polluted areas would double.Both models included only sulphate and sea-salt aerosol, so this was believed to be an upper limit for this effect.But the study of Wang and Penner (2009), which included organic matter, black carbon, and dust, varied the fraction of SO 2 converted to sub-grid sulphate over a smaller range ( ::::::: between : 0 % to :: and : 2 %), and also found that CCN(0.2 %) more than doubled over polluted areas.Additionally, they found that CCN(0.2 %) increased by :::: either 23 % to :: or 53 % averaged over ::: the global boundary layer, and that the aerosol indirect effect radiative forcing increased by ::::: either 11 % to :: or 31 % (depending on the grid-resolved nucleation scheme used in the boundary layer).The study of Yu and Luo (2009) used yet another approach for representing sub-grid sulphate, they emitted : : :: of ::: the :::::: emitted SO 2 ::::::: assumed :: to :::: form ::::::: sulphate ::: on ::: the ::::::: sub-grid ::::: scale, : 5 % of sulphur mass : is ::::::: emitted :::::: directly : into the nucleation mode described above and condensed the remaining mass :: is :::::::: condensed : onto the existing accumulation-mode particles.As some of the sulphate formed in the plume must condense onto the pre-existing particles that have been entrained into the plume, this approach is, in this way, more realistic than the other assumptions.Luo and Yu (2011) varied the fraction of sulphate emitted into the nucleation mode from 5 % to 15 %, and found that this increased the CCN(0.2%) ::::::: increased : by up to 18 % over source regions.Furthermore, they found that changing the fraction of emitted SO 2 converted to sub-grid sulphate from 0 % to 5 % changed global boundary-layer CCN(0.2 %) by 11 %.::::: Hence, : CCN concentrations and regional radiative forcings are thus clearly sensitive to the assumptions regarding sulphur partitioning and the size of aerosol formed in sulphur-rich plumes.Lee et al. (2013) recently quantified the uncertainty in CCN concentrations that was due to 28 different uncertain inputs ::::::::: parameters in the GLOMAP global aerosol model.They found that the uncertainties in sub-grid sulphate production contributed just as much to uncertainties in CCN concentrations as the uncertainties in :::: those ::: of SO 2 emissionrates, and had the largest contribution of the 28 inputs to the uncertainty in CCN concentrations over polluted North America and Europe.The global uncertainty in sub-grid sulphate particle size ranked as the twelfth largest contributor to the relative uncertainties in CCN concentrations of the 28 inputs tested, with a global-mean relative uncertainty range (from −2 to +2 standard deviations in CCN concentrations) of about 16.Based on the results of Stevens et al. (2012), the range of possible values used in Lee et al. (2013) for the diameter of sub-grid-sulphate particles ::: used :: in ::::::::::::::: Lee et al. (2013) was reduced to a smaller range than the full range of sub-grid-sulphate assumptions used before :: in ::: the :::::: studies :::: cited ::: in ::: the :::::::: preceding :::::::::: paragraphs.This reduced range would lead to a reduced uncertainty range in CCN concentrations due to uncertainties in sub-grid sulphate compared to the range of estimates :: as : described in the previ-ous paragraph.These large uncertainties in CCN prediction due to sub-grid sulphate formation highlight the need for improved representation of plume-scale particle formation in global and regional models.
In order to more accurately represent this sub-grid sulphate, Stevens and Pierce (2013) introduced a parameterization that predicts the characteristics of aerosol formed in point-source plumes based on variables commonly available in global-and regional-scale models.Specifically, the Predicting Particles Produced in Power-Plant Plumes (P6) parameterization predicts the fraction of SO 2 oxidized to form H 2 SO 4 (f ox ), the fraction of the H 2 SO 4 that forms new particles (f new ), the number of new particles formed per kg SO 2 emitted (N new ), and the median diameter of the newly formed particles (D m ).The P6 parameterization takes as inputs the emissions of SO 2 (E SO2 ) and NO x (E NOx ) from the power-plant, the pre-existing aerosol condensation sink (CS), the downward shortwave radiative flux (DSWRF), the mean boundary-layer wind speed (v g ), the boundarylayer height (BLH), the distance from the source (d), and the background concentrations of SO 2 (bgSO 2 ) and NO x (bgNO x ).In this paper, we implement this parameterization into a global aerosol microphysics model to estimate the contribution of sub-grid-sulphate formation to aerosol size distributions and CCN.
Additionally, recent pollution-control technologies installed on power plants reduce SO 2 and NO x emissions.A reduction in SO 2 alone would result in a reduction of particles formed in power-plant plumes.However, concentrations of OH are sensitive to NO x concentrations, which will vary across a given plume (Lonsdale et al., 2012).NO x controls may either increase or decrease OH concentrations in the plume (depending on the environmental conditions).Thus ::::: Hence, in many conditions a reduction in ::::::: reducing NO x may lead to an increase in :::::::::::: concentrations :::: may ::::::: increase : the formation rate of H 2 SO 4 and perhaps an increase in :::::: increase particle formation and growth.The P6 parameterization has been designed to reproduce these effects of changes in SO 2 and NO x emissions on particle formation and growth.Use of some pollution-control technologies, such as selective catalytic reduction and flue gas desulphurisation, may result in formation of sulphur trioxide within the emissions stack, which would quickly form H 2 SO 4 and could result in newparticle formation within the emissions stack (Junkermann et al., 2011;Srivastava et al., 2004).However, these effects are not yet resolved by P6 and so will not be discussed in this work.
In Sect.2, we describe the GEOS-Chem-TOMAS model specifications and we describe the simulations performed for this study.In Sect. 3 we discuss the sensitivities of our results to the treatment of sub-grid sulphate, and how these interact with additional secondary organic aerosol emissions and grid-resolved nucleation scheme.In Sect. 4 we present the results of an adjoint to the P6 parameterization ::::::: Gradient ::::::::: Subroutine, and discuss the sensitivity of our results to the inputs of P6.In Sect. 5 we discuss the sensitivities to SO 2 and NO x emissions.In Sect.6 we compare the results of our simulations with surface-based N10, N40, N80, and N150 measurements.Finally, we present our conclusions in Sect.7.

Model specifications and descriptions of simulations
For this study, we implemented the P6 sub-grid sulphate parameterization into the GEOS-Chem-TOMAS model.GEOS-Chem-TOMAS uses the TwO Moment Aerosol Sectional (TOMAS) microphysics algorithm (Adams and Seinfeld, 2002;Pierce and Adams, 2009) in the GEOS-Chem v9-02 chemical transport model (http://geos-chem.org,Bey et al., 2001).The implementation of TOMAS in GEOS-Chem has been discussed previously (Pierce et al., 2013;Snow-Kropla et al., 2011;Trivitayanurak et al., 2008).The TOMAS module resolves aerosol by both mass and number independently.For this study, the aerosol was simulated using 15 size bins spanning 3 nm to 10 µm (Lee and Adams, 2012).Condensation, coagulation, and nucleation are explicitly resolved in the model.The model was run at 4 • latitude by 5 • longitude resolution with 47 vertical layers from the surface to 0.01 hPa and with meteorological inputs from the GEOS5 re-analysis (http://gmao.gsfc.nasa.gov).
Anthropogenic emissions in GEOS-Chem are provided by the Emissions Database for Global Atmospheric Research (EDGAR) inventory (Olivier et al., 1996), except where it : is : overwritten by the following regional inventories: The Environmental Protection Agency 2005 National Emissions Inventory (NEI05) (http://www.epa.gov/ttn/chief/net/2005inventory.html)over the United States, the Criteria Air Contaminants (CAC) for anthropogenic emissions over Canada (http://www.ec.gc.ca/inrp-npri/), the Big Bend Regional Aerosol and Visibility Study (BRAVO) emissions inventory over Mexico and the southwestern United States (Kuhns et al., 2001), the Streets inventory for Asian emissions (Streets et al., 2003) (Auvray and Bey, 2005).The total annual fossilfuel SO 2 emissions, not including shipping emissions, from these inventories are shown in Fig. 1 for the simulated year, 2005.Biogenic emissions were from the Model of Emissions of Gases and Aerosols from Nature (MEGAN) (Guenther et al., 2006), except for an additional secondary organic aerosol (SOA) source in some simulations that we will describe below.Biomass burning emissions were from the Global Fire Emissions Database version 3 (GFEDv3) (van der Werf et al., 2010).
The P6 parameterization predicts characteristics of subgrid sulphate formed in sulphur-rich plumes based on variables commonly available in global-and regional-scale models.A full description is available in Stevens and Pierce (2013).Specifically, the parameterization predicts the fraction of SO 2 oxidized to form H 2 SO 4 (f ox ), the fraction of the H 2 SO 4 that forms new particles (f new ), the number of new particles formed per kg SO 2 emitted (N new ), and the median diameter of the newly formed particles (D m ).The parameterization takes as inputs the emissions of SO 2 (E SO2 ) and NO x (E NOx ) from the power-plant, the pre-existing aerosol condensation sink (CS), the downward shortwave radiative flux (DSWRF), the mean boundary-layer wind speed (v g ), the boundary-layer height (BLH), the distance from the source (d), and the background concentrations of SO 2 (bgSO 2 ) and NO x (bgNO x ).
Because the emissions inventories used by GEOS-Chem do not provide source-specific emissions, but instead emissions summed across a 1 • × 1 • grid, the distance downwind from the source is not calculable.We therefore use a length scale equal to half of the square root of the grid cell horizontal area, as suggested in Stevens and Pierce (2013), for the distance from the source (d) required for P6.In GEOS-Chem-TOMAS, the value of the boundary-layer height (BLH) used as input to P6 is based on BLH values from the GEOS-5 reanalysis.We note that the BLH values from the GEOS-5 reanalysis were found to be unrealistically low under night-time conditions, and thus ::::::: therefore : the boundary-layer heights within GEOS-Chem-TOMAS used as input to P6 have been adjusted from the original GEOS-5 reanalysis values by limiting them to a minimum of the mechanical mixing depth, which is calculated based on the local friction velocity (Heald et al., 2012;Walker et al., 2012).We also note that the BLH values were defined within the GEOS-5 dataset as the height where the diffusivity falls below a critical value (Rienecker, 2006).The BLH values used to create the P6 parameterization came from the North American Regional Reanalysis dataset, where they were defined as the height where the turbulent kinetic energy falls below a critical value (Mesinger et al., 2006), and these values may differ due to the different definitions.However, of the nine inputs to the P6 parameterization, the BLH is the input to which all outputs of P6 have the weakest sensitivity :::::::::::::::::::::: (Stevens and Pierce, 2013) .We therefore do not expect that uncertainties in BLH values will have a large impact on our results.We also make the following assumption about the sizes of individual sources, as recommended in Stevens and Pierce (2013): We assume that within each model grid cell, the SO 2 emissions are split between an equal number of low emitters, medium emitters, and high emitters.We define high emitters, medium emitters, and low emitters based on the emissions data for power-plants in the United States compiled from the Clean Air Markets (CAM) data (United States Environmental Protection Agency, 2012) as follows: For medium emitters, we use the log-space mean emission rates for a power plant in the USA during 2010.For low and high emitters, we use an emission rate that is one standard deviation below or above the mean in log space, respectively.The low, medium, and high emission rates of SO 2 are 0.0606 kg s −1 , 0.202 kg s −1 , and 1.00 kg s −1 , respectively.We further assume that the low, medium, and high emitters emit 0.0300 kg N s −1 , 0.0840 kg N s −1 , and 0.290 kg N s −1 of NO x , derived in the same way from the 2010 EPA CAM NO x emissions data.
We performed 19 simulations with GEOS-Chem-TOMAS, summarized in Table 1 ::: and ::::::::: described :::::: below.All simulations were performed with meteorology and emissions for the year 2005.Simulations labelled NoSGS did not include any sub-grid sulphate emissions.Simulations labelled AS3 emitted 3 % of anthropogenic SO 2 as sub-grid sulphate, using the bi-modal size distribution described in Adams and Seinfeld (2003) comprised of a nucleation mode containing 15 % of the emitted sulphate mass with a 10 nm number mean diameter and a geometric standard deviation of 1.6; and an Aitken mode containing the rest of the sulphate mass with a 70 nm number mean diameter and a geometric standard deviation of 2.0.Simulations labelled LY5 emitted 5 % of anthropogenic SO 2 as sub-grid sulphate, emitting 5 % of the sulphate into the same nucleation mode as AS3, but the remaining sulphate was condensed onto pre-existing aerosol, as was done for one of the simulations described in Luo and Yu (2011).Simulations labelled P6 used the P6 parameterization to predict the fraction of anthropogenic SO 2 to emit as sub-grid sulphate, as well as the fraction of the emitted sulphate to emit as particles or condense onto pre-existing particles, and the size of the emitted particles.The amount of sub-grid sulphate emitted and the size of the particles emitted therefore varied with each time step and with each model grid cell in simulations labelled P6.
Secondary organic aerosol (SOA) production in TOMAS is calculated as 10 % of global monoterpene emissions (based on MEGAN, (Guenther et al., 2006)), resulting in approximately 19 Tg yr −1 of SOA.However, the study of Spracklen et al. (2011) suggested that including emissions of an additional 100 Tg yr −1 of SOA co-located with anthropogenic pollution yields much better agreement of organic aerosol mass with Aerosol-Mass-Spectrometer-based observations.This additional source of "anthropogenically controlled" SOA has been implemented into GEOS-Chem-TOMAS previously (D'Andrea et al., 2013), where it was also found to provide much better agreement with size distribution observations.This SOA is condensed irreversibly to the Fuchs-corrected aerosol surface area as this was shown to give the best agreement with size distributions in D' Andrea et al. (2013).Simulations labelled "yXSOA" therefore contain additional emissions of 100 Tg yr −1 of SOA correlated :::::::: co-located : with anthropogenic CO emissions.Simulations labelled "nXSOA" do not contain these additional emissions.One limitation of our yXSOA simulations is that the extra SOA does not aid in the sub-grid nucleation and growth as the P6 scheme does not handle sub-grid growth from SOA.The implications of this will be discussed in the results section.
In Fig. 2 we show the annually averaged changes in :::::: changes ::: in ::::::: annually :::::::: averaged : boundary-layer N80 between the four AS3 simulations and the corresponding simulations with no sub-grid sulphate.Regardless of SOA amount and grid-resolved nucleation scheme, the inclusion of AS3 sub-grid sulphate increases N80 over industrialized regions.However, the two simulations that include anthropogenically controlled SOA (yXSOA, panels a and c) show a greater increase in N80, especially over the Northern Hemisphere.In these simulations, the newly formed sub-grid sulphate particles grow more quickly due to the condensation of the additional SOA mass, and a greater fraction grow larger than 80 nm.This is consistent with the findings of D'Andrea et al. ( 2013), where including an additional 100 Tg yr −1 of SOA was found to increase globally and annually averaged boundary-layer N80 by 29.9 %.The increased survivability of the sub-grid sulphate particles can also be seen in the N3, N10 and N40 changes (Table 2).The two AS3 simulations with anthropogenically controlled SOA show smaller decreases in N3 and larger increases in N10 and N40 from the corresponding no sub-grid sulphate cases than the AS3 simulations without this extra source of SOA.
The two AS3 simulations with ternary nucleation (Napa) show a much greater increase in N80 over north-western South America and the Malay Archipelago.In these regions, little ammonia is present, so less nucleation is predicted by the ternary nucleation scheme than the activation nucleation scheme.Thus :::::::: Therefore, when no sub-grid sulphate is included, the simulations with activation-type nucleation (Act) have higher N80 in these regions than the simulations with ternary nucleation, and so the addition of a fixed amount of sub-grid sulphate causes a smaller relative change in N80 for the activation-type nucleation simulations than the ternary nucleation simulations in these regions.
The changes in N80 between simulations with LY5 subgrid sulphate and the corresponding simulations with no subgrid sulphate (not shown) are similarly distributed spatially to those from the AS3 simulations, but greater in magnitude (see Table 2).The effects of changing SOA amount and grid-resolved nucleation scheme are also similar for the LY5 simulations.The increase in the magnitude of the changes in N80 for the LY5 simulations relative to the AS3 simulaitons ::::::::: simulations : is in part due to the increased ::::: greater : fraction of SO 2 that is assumed to be oxidized on the sub-grid scale (5 % for LY5, compared to 3 % for AS3).In addition, while both AS3 and LY5 sub-grid sulphate use the same size distribution for nucleation mode particles, the remaining sulphate mass is emitted as Aitken-mode particles in AS3, whereas the remaining mass is condensed onto pre-existing particles in LY5.In the LY5 simulations, particles emitted into the nucleation mode in one model time step will be grow by sub-grid condensation during following time steps, and this will speed their growth to CCN sizes.In contrast, the Aitken-mode particles emitted in simulations using the AS3 sub-grid sulphate scheme will remove nucleation-mode particles in subsequent time steps through coagulation.Because of these effects, the LY5 scheme more efficiently produces CCN-sized particles.
We note that the LY5 simulations with anthropogenically controlled SOA are the only simulations that show an increase in N3 compared to the simulations without sub-grid sulphate (Table 2).As the nucleation-mode sub-grid sulphate is still being emitted with median diameter 10 nm, as in the AS3 simulations, one would expect a decrease in the number of sub-10 nm particles, as was seen for the AS3 simulations.Through inspection of globally averaged size distributions (not shown), we have determined that the number of sub-10 nm particles decreases in these simulations as well, but the increases in N10 are sufficiently large to more than compensate for these decreases, resulting in a net increase in N3.
4 The P6 adjoint :::::::: Gradient :::::::::: Subroutine, and sensitivities to P6 inputs In order to better understand the results of P6 simulations, including differences between P6 simulations due to SOA amount and emissions, and differences in the P6 simulations from AS3 and LY5 simulations, we have created an adjoint to the P6 parameterization.This adjoint ::::::: Gradient ::::::::: Subroutine. :::: This :::::::: subroutine : allows us to quickly test the sensitivity of the P6 outputs (fraction of emitted SO 2 oxidized to form H 2 SO 4 (f ox ), fraction of that H 2 SO 4 that forms new particles (f new ), median diameter of newly formed particles (D m ), and number of newly formed particles per kg SO 2 emitted (N new )) to changes in each of the P6 inputs (emissions of SO 2 (E SO2 ) and NO x (E NOx ) from the source, background condensation sink of pre-existing particles (CS), downward shortwave radiative flux (DSWRF), mean boundary-layer wind speed (v g ), boundary-layer height (BLH), distance from the source (d), and mean background concentrations of SO 2 (bgSO 2 ) and NO x (bg :::::: bgNO x )).We can use the adjoint :::::::: subroutine : to calculate the derivative of each of the outputs of P6 with respect to each of the inputs of P6 for a given set of inputs.We have run the P6 adjoint ::::::: Gradient ::::::::: Subroutine offline using the monthly-mean values of each of the P6 inputs as output by GEOS-Chem-TOMAS.(While the values from the P6 adjoint ::::::: Gradient ::::::::: Subroutine calculated based on monthly means of the P6 inputs will not be equal to monthly-means of values calculated based on the instantaneous values of the P6 inputs due to non-linearities in the equations, we do not expect that the differences due to these non-linearities would qualitatively alter any of our analysis below.)We discuss below the results of the adjoint of :::::::: subroutine ::::::: applied :: to : simulation P6 nXSOA Napa.We choose P6 nXSOA Napa for this discussion because, as noted above, the P6 parameterization does not currently include the effects of anthropogenically controlled SOA on sub-grid new-particle formation and growth, and because the scaled Napari ternary nucleation scheme has been shown to yield results that compare more favourably with observations (Westervelt et al., 2013).
We show in Fig. 4 the annually averaged values of each of the P6 outputs, as calculated offline by the adjoint :: P6 ::::::: Gradient :::::::::: Subroutine for simulation P6 nXSOA Napa.(We note that because emissions rates are assumed (e.g.high emitters, medium emitters and low emitters, see Sect. 2) for the purposes of calculating the P6 outputs, we can calculate these outputs even where there are no emissions, such as over oceans.However, since the amount of sub-grid sulphate to be emitted is expressed as a fraction of SO 2 emissions (f ox ), no sub-grid sulphate will be emitted in the absence of SO 2 emissions.)In Fig. 5 we show the annually averaged sensitivity of N new to each of the P6 inputs for simulation P6 nXSOA Napa, as the percentage change in N new for a percentage change in the input.For each latitude and longitude point, we exclude months where no nucleation would be predicted based on the monthly mean of the P6 inputs, as the sensitivity of N new to a change in the P6 inputs is ill-defined for no-nucleation cases.

Effects of pollution controls
As described in Sect.2, we performed additional simulations in order to test the effects of pollution controls upon our results.The simulations P6 hiSO2, P6 hiNOx, and P6 hiboth differ from P6 nXSOA Napa only in that the emissions of SO 2 , NO x , or both SO 2 and NO x have been increased by 50 %.Emissions of sub-grid sulphate in the P6 sub-grid sulphate scheme (and both other sub-grid sulphate schemes used in this study) are normalized by the modelled emissions of SO 2 .Thus ::::::::::: Consequently, the emissions of sub-grid sulphate would be increased by 50 % in the P6 hiSO2 and P6 hiboth simulations if the P6 outputs remained constant.The differences in globally, annually averaged N3, N10, N40, and N80 between the P6 hiSO2, P6 hiNOx, and P6 hiboth simulations and the P6 nXSOA Napa simulation are shown in Table 3, and the annually averaged differences ::::::::: differences :: in ::::::: annually ::::::: averaged :::: N80 : are shown in Fig. 7.The globally, annually averaged N80 in simulations P6 hiSO2, P6 hiNOx, and P6 hiboth increase from the P6 nXSOA Napa simulation by 9.00 %, 1.47 %, and 10.24 %, respectively.The increase in :::::: Greater SO 2 emissions provides an increase in ::::::: increase new-particle formation and growth through the additional source of sulphate, at both the grid-resolved and subgrid scales.The increased :::::: Greater NO x concentrations in the P6 hiNOx and P6 hiboth simulations allow for greater OH production and faster oxidation of SO 2 , at both the gridresolved and sub-grid scales, except in the most polluted regions.
The increases in the assumed emissions of SO 2 (E SO2 ) and NO x (E NOx ::::: E NOx ) used as input to P6 will alter the values of the P6 outputs, and thus :::: hence : the number and size of sub-grid sulphate formed in the emissions sensitivity simulations.As :::::::: Increases :: in : the background concentrations of SO 2 (bgSO 2 ) and NO x (bgNO x ) will be increased in the P6 hiSO2 and P6 hiNOx simulations, respectively, there will also be ::: will :::: lead :: to : differences in the P6 outputsdue to differences in bgSO 2 and bgNO x .Additionally, .:::: The changes in sulphate formation and growth (at both the gridresolved and sub-grid scales) ::: due :: to :::::::: increased ::::::: bgSO 2 ::: and :::::: bgNO x : will result in changes to the grid-resolved aerosol condensation sink (CS ::: CS), which will also influence the P6 outputs.We have used the adjoint ::: P6 ::::::: Gradient ::::::::: Subroutine : to estimate the differences in the annually averaged P6 outputs between the P6 hiSO2, P6 hiNOx, and P6 hiboth simulations, and the P6 nXSOA Napa simulation (Fig. 8).The fraction of SO 2 oxidized (f ox ) in the P6 hiSO2 simulation does not significantly differ from that of the P6 nXSOA Napa simulation (Fig. 8a), as f ox is not sensitive to E SO2 , bgSO 2 , or CS.The number of new particles formed per kg SO 2 emitted (N new ) in P6 hiSO2 generally decreases by 20-30 % over polluted regions (Fig. 8b) due to an increase in the condensation sink.However, since N new is normalized by SO 2 emissions, which are increased by 50 % in this simulation, there would still be a net increase in the :::::: absolute number of sub-grid sulphate particles formed :: on ::: the ::::::: sub-grid :::: scale.In order to demonstrate the net change in the :::::: absolute number of sub-grid particles formed, including the increases due to increased :: 50 % :::::: increase :::: due ::: to ::: the ::: 50 % :::::: increase :: in SO 2 emissions, we plot the relative difference between N new • 1.5 from the P6 hiSO2 and P6 hiboth simulations and the value of N new in the P6 nXSOA Napa simulation in Fig. 9.In simulation P6 hiSO2 (Fig. 9a), it is only over eastern China that there is a net decrease in the :::::: absolute number of sub-grid sulphate particles formed, ::::: even :::: after ::::::::: accounting ::: for ::: the :: 50 % ::::::: increase :: in ::: the ::::::: number :: of ::::::: sub-grid ::::::: sulphate ::::::: particles ::::::: emitted : due to the additional SO 2 emissions.This decrease in the ::::::: absolute number of sub-grid particles formed is due to the increase in ::::::: increased : SO 2 emissions greatly increasing the condensation sink in eastern China (not shown).The median diameter of newly formed particles (D m ) in simulation P6 hiSO2 increases by 13-16 % over most of the globe (Fig. 8c).Thus :::::::: Therefore, both the emitted number and :::::: number :::: and ::: the size of sub-grid sulphate particles are increased :::: larger : in the P6 hiSO2 simulation, and :: the :::::::: increased :::::: particle ::::::: number :::::::::::: concentrations ::: in ::: this ::::::::: simulation :: are :::: due :: in ::: part :: to ::::::: changes :: in : sub-grid processes contribute to the increase in the particle concentrations from the increase in :::::::: processes.The value of f ox in the P6 hiNOx simulations decreases over very polluted regions and increases over remote regions (Fig. 8d), but these relative changes are less than 20 % (or an absolute change in f ox of 1 %) in either direction.Whether f ox decreases or increases depends on the NO x concentrations in the region.In high-NO x regimes, in-plume OH concentrations (and hence SO 2 oxidation) will decrease with increasing NO x , and oxidation will increase with increasing NO x in low-NO x regimes.The value of N new in P6 hiNOx decreases by 10-20 % over most of the globe, with greater decreases over Europe and China (Fig. 8e).The value of D m decreases by 11-14 % over most of the globe (Fig. 8f).These increases in f ox and decreases in N new and D m will result in more sub-grid oxidation of SO 2 , but fewer and smaller new particles emitted at the sub-grid scale.Thus ::::: Hence, the only change in sub-grid sulphate that may contribute to the modelled increase in N80 (Fig. 7b) is an increase in condensation of sub-grid-oxidized SO 2 onto pre-existing particles less than 80 nm in diameter.It is therefore likely that the increases in N80 in this simulation are primarily due to gridresolved processes.

Comparison with observations
In order to assess the sub-grid sulphate schemes simulated in our study, we used data from the 21 surfacebased aerosol size distribution measurements compiled by D'Andrea et al. ( 2013) from the following sources: the BEA-CHON campaign (Levin et al., 2012), the European Supersites for Atmospheric Aerosol Research (www.eusaar.net,Asmi et al., 2011;Reddington et al., 2011), the RoMANS 2 campaign (instrumentation and site descriptions are same as RoMANS 1 campaign as per Levin et al., 2009), Environment Canada (Leaitch et al., 2013;Pierce et al., 2012;Riipinen et al., 2011), and Kent State University (Erupe et al., 2010;Kanawade et al., 2012).The measurement sites span many terrain types, including forests, mountains, rural sites, arctic sites and coastal sites.However, urban sites were excluded because the 4 • × 5 • resolution used for this study cannot resolve urban features.All size distribution measurements were obtained using either a Differential Mobility Particle Sizer (DMPS) (Aalto et al., 2001) or a Scanning Mobility Particle Sizer (SMPS) (Wang and Flagan, 1990).For a map of the locations as well as figures showing the sizedistribution comparisons for similar simulations, please see D' Andrea et al. (2013).
For brevity, we do not show the full comparisons at the sites in figures, but we list in Table 4 the log-mean bias (LMB), slope of a linear regression of the logarithms of the values (m), and coefficient of determination (R 2 ) between the annually averaged N10, N40, N80, and number concentrations of particles larger than 150 nm (N150) for each simulation (excluding the emissions sensitivity tests) and those measured at the 21 surface sites.These statistics evaluate how well the model captures the magnitude and variability across the measurement sites.We do not compare simulated N3 against observations because measurements of particles smaller than 10 nm were not available at most of the surface sites, and we include N150 to show more information about the larger end of the size distribution.Compared to the choice of SOA amount or grid-resolved nucleation scheme, the choice of sub-grid sulphate scheme has a small effect on the goodness-of-fit metrics shown here.The maximum changes in LMB, m, and R 2 between simulations that differ only in sub-grid sulphate scheme are 0.087, 0.109, and 0.030, respectively.Many other uncertain model parameters and processes can also change aerosol number concentrations, such as emissions and deposition rates, and a change in these parameters or processes within the model may affect our goodness-of-fit metrics.
The simulations without sub-grid sulphate and without anthropogenically controlled SOA (NoSGS nXSOA) are both biased high for N10, and biased low for N40, N80, and N150.For these cases, the inclusion of any of the three subgrid sulphate schemes considered here increases N40, N80, and N150 at the expense of N10, and therefore decreases the absolute LMB.However, when anthropogenically controlled SOA is included, the simulations without sub-grid sulphate (NoSGS yXSOA) tend to have small positive biases for each size range (except for the NoSGS yXSOA Act N40, which has a small negative bias).The AS3 and LY5 sub-grid sulphate schemes increase aerosol concentrations at all sizes for the cases with anthropogenically controlled SOA, (since the extra SOA enhances survivability of the small particles, as shown by D' Andrea et al., 2013) and so increase this positive bias.The P6 parameterization predicts that a larger fraction of sub-grid sulphate will condense onto pre-existing particles for the cases with this extra SOA due to the increased coagulation ::::::::::: condensation sink, and so only N150 increases from the NoSGS yXSOA cases, and N10, N40, and N80 decrease due to enhanced coagulation from the larger aerosol.These decreases lead to a decrease ::::::: reduction in the absolute LMB from the NoSGS yXSOA Napa case to the P6 yXSOA Napa case for all size ranges except for N150, and only a small increase in the absolute LMB for all size ranges from the NoSGS yXSOA Act case to the P6 nXSOA Act case.
Log-linear regressions for all cases and all size ranges yield slopes less than 1.This is generally due to an overprediction of aerosol number concentrations at the cleaner sites, and an underprediction of aerosol number concentrations at the more polluted sites.To a certain extent, this behaviour is expected due to model resolution effects alone.The cleanest sites will be influenced by pollution within the same grid cell, and local pollution sources that may influence the measurements at the most polluted sites will be diluted to the model resolution.For nearly all combinations of size range, SOA amount and grid-resolved nucleation scheme, the LY5 sub-grid sulphate scheme yields the slope closest to one.The differences in aerosol number concentrations between sim-ulations, while small everywhere, are greatest for polluted sites, which would be expected if anthropogenic sulphate is a strong contributor to particle number concentrations at these sites.The LY5 scheme typically predicts more particles at all sites than any other sub-grid sulphate scheme, as evidenced by the more positive LMB, but these differences are most pronounced at the most polluted sites.Where the LMB is negative, this increase in aerosol number concentrations yields better agreement with measurements at the more polluted sites.Where the LMB is positive, this increase yields a worse agreement with the measurements at the more polluted sites, but a more consistent bias against the measurements across all of the sites.
Regardless of the SOA amount or grid-resolved nucleation scheme used, simulations using P6 sub-grid sulphate had higher R 2 values for N80 and N150 than any other sub-grid sulphate scheme included in this study.For those cases using activation nucleation, the simulations using the P6 scheme had the highest R 2 values for N10 and N40 as well.While this difference is small, we believe that this improved correlation is due to the fact that the P6 parameterization predicts different amounts and sizes of sub-grid sulphate under different conditions, and thus can ::: can :::::::: therefore represent more spatial heterogeneity that ::: than : the other sub-grid sulphate schemes tested in this study.

Conclusions
In this study, we implemented the P6 parameterization for sub-grid sulphate into the GEOS-Chem-TOMAS global chemical-transport model.This is the first implementation of P6 into a global model.We have shown that the P6 parameterization predicts smaller or similar increases in globally, annually averaged N80 attributable to sub-grid sulphate than two other previously used assumptions for subgrid sulphate, depending on model assumptions regarding SOA and nucleation.When we included emissions of :::: using ::::::: previous ::::::::: treatments :: of ::::::: sub-grid :::::::: sulphate, :::::::: including : an additional 100 Tg yr −1 of SOA while using previous treatments of sub-grid sulphate, the increases in ::: led :: to ::: an ::::::: increase :: in :: the : N80 attributable to sub-grid sulphate increased ::::::: particles.This increase was due to increases :: an ::::::::::: enhancement : in condensational growth of the sub-grid sulphate particles.The proportion of global N80 attributable to sub-grid sulphate depends not only on the choice of sub-grid sulphate scheme, but also on other model parameters and processes that affect preexisting N80 and the grid-resolved condensational growth of sub-grid sulphate.
However, the number of new sub-grid sulphate particles predicted by the P6 parameterization depends strongly on the pre-existing aerosol condensation sink.The increase in :::::::: additional ::::: SOA ::::::::: increased ::: the :: pre-existing condensation sinkdue to the additional SOA drastically decreased , :::::::: drastically :::::::::: decreasing : the sub-grid new-particle formation predicted by the P6 parameterization, thus ::: and : decreasing the influence of sub-grid sulphate on N80.For sufficiently large pre-existing condensation sink, the P6 sub-grid sulphate scheme predicted that nearly all sub-grid sulphate would condense onto pre-existing particles, and the growth of these particles resulted in enhanced coagulational losses and more efficient removal by deposition, producing little change in aerosol number concentrations.
Finally, we have compared the simulated annually averaged N10, N40, N80, and N150 against those measured at 21 surface-based measurement sites.Differences in sub-grid sulphate scheme were not found to strongly affect the number concentrations in these size ranges at these sites.For cases without anthropogenically controlled SOA, a reduction in the absolute log-mean bias between simulated and observed number concentrations was obtained :::::: reduced : by including any sub-grid sulphate scheme.When anthropogenically controlled SOA was included, the AS3 and LY5 schemes tended to increase the absolute log-mean bias.The P6 sub-grid sulphate scheme only slightly increased the absolute log-mean bias or reduced ::::: altered : the absolute log-mean bias from the case with no sub-grid sulphate.This was due to the reduction in new-particle formation predicted under higher condensation sink conditions.The R 2 values for N80 and N150 were highest when using the P6 sub-grid sulphate scheme, regardless of SOA amount or grid-resolved nucleation scheme.For the Activation-type grid-resolved nucleation cases, the P6 sub-grid sulphate scheme also yielded the highest R 2 values for the N10 and N40, as well.We believe that the P6 scheme yields better correlation with observations because the differences in sub-grid scale new-particle formation and growth under different conditions predicted by the P6 sub-grid sulphate scheme allows it to better represent spatial heterogeneity in these processes than constant assumptions about the number and size of sulphate formed at the sub-grid scale.
The additional anthropogenically controlled SOA included in many of our simulations would be expected to condense onto the newly formed particles at the sub-grid scale, a process that is not currently resolved by P6.Anthropogenically controlled SOA may preferentially form in coalfired power-plant plumes, and so this additional SOA may condense preferentially onto particles formed within these plumes compared to pre-existing particles.The P6 parameterization thus ::::::: therefore : likely underestimates the number and size of newly formed particles in simulations where anthropogenically controlled SOA is included.However, we note that when the anthropogenically controlled SOA was included, the simulations with P6 sub-grid sulphate had smaller absolute log-mean biases from observed aerosol number concentrations than the simulations with AS3 or LY5 sub-grid sulphate, and similar absolute log-mean biases to the simulations with no sub-grid sulphate.This would suggest that the number of newly formed particles predicted by P6 when anthropogenically controlled SOA is included may be more realistic than the number of newly formed particles predicted by the AS3 or LY5 sub-grid sulphate assumptions.Other uncertain model processes also influence aerosol number concentrations, so it is also possible that the P6 parameterization benefits from a cancelling of errors in this case.We intend to include sub-grid condensation of SOA in a future version of P6 to better resolve these uncertainties.
Due to the physical basis of the P6 parameterization, we believe it to yield more representative predictions for the number and size of aerosol formed than previous assumptions about sub-grid sulphate.Moreover, no constant assumption about the number and size of sub-grid sulphate formed can resolve differences in new-particle formation and growth due to changes in background chemical or meteorological conditions.However, the differences between simulated size distributions at the surface-based measurement sites considered in this work were too small to establish P6 as unambiguously providing better agreement with observations.Continuing evaluation of the P6 parameterization against observations is therefore planned as future work.Table 2. Globally :::::: Changes :: in ::::::: globally, annually averaged changes in N3, N10, N40 and N80 attributable to sub-grid sulphate emissions.Each simulation is compared to the NoSGS case with the same SOA emissions and the same grid-resolved nucleation scheme.
over Asia, and the Cooperative Programme for Monitoring and Evaluation of the Long-

Table 1 .
Summary of GEOS-Chem-TOMAS simulations performed.The different sub-grid sulphate schemes and nucleation schemes are ::::: further : described in Sect. 2. Extra SOA refers to emissions of 100 Tg yr −1 of SOA, co-located with emissions of CO.

Table 4 .
Log-mean bias (LMB), slope of the log-linear regression (m), and coefficient of determination (R 2 ) between the simulated annually averaged N10, N40, N80, and N150 and those measured at 21 surface sites.For each group of simulations with the same SOA amount and grid-resolved nucleation scheme, the best statistical result in each column is bolded.For each group of simulations with the same sub-grid sulphate scheme, the best statistical result in each column is italicized.