The in-cloud process of nucleation scavenging refers to activation and growth of aerosol particles into cloud droplets . When water vapor reaches supersaturation, a fraction of the aerosol population is activated to cloud droplets. After these cloud droplets have grown to precipitation size, the particles can be removed from the cloud through precipitation . The ability of an aerosol particle to activate to a cloud droplet depends on its size, chemical composition, and the ambient supersaturation .

In aerosol modules of global climate models, the aerosol size distribution can be approximated by, for example, a modal or sectional discretization, which effectively separates the size distribution into different size classes . In each size class the fraction of activated particles can be calculated as the portion of particles that exceed the critical diameter of activation in that size class . However, many models describe the nucleation scavenging by assuming a constant scavenging coefficient for different aerosol size classes .

The current in-cloud nucleation scavenging scheme for liquid clouds introduced here calculates the scavenging coefficients of aerosol based on the fraction of activated particles in each size class, i.e., Fi,nuc,liq in Eq. (). Thus, using the scheme requires that the atmospheric model incorporates a cloud activation parameterization that calculates size segregated cloud activation. Such parameterizations are, e.g., and .

In-cloud impaction scavenging, for liquid clouds, is a process where aerosol particles collide with existing cloud droplets and are thereby removed from the interstitial air of the cloud . This aerosol scavenging by cloud droplets is based on coagulation theory, which quantifies the rate of removal. This is further used to define the scavenging coefficients by impaction . Commonly, these scavenging coefficients, for the full aerosol particle distribution, can be calculated as 2Fi,imp,liq(dp,t)=∫0∞K(dp,Dliq)n(Dliq,t)dDliq, where dp is the wet diameter of the aerosol particle, Dliq is the cloud droplet diameter, K(dp,Dliq) is the collection efficiency between aerosol particles and cloud droplets, and n(Dliq,t) is the cloud droplet number distribution .

In-cloud nucleation scavenging in ice clouds refers to the formation and growth of ice particles . When ice particles are formed, they can quickly grow into precipitation sizes and be removed from the cloud . The formation of ice particles in the atmosphere usually requires an ice nucleus (IN), but they can also be formed without IN if the temperature is very low . Aerosol particles which can act as IN are usually insoluble . In addition, large particles are more efficient in acting as IN than small particles .

The nucleation rate, JT, which is the total number of ice crystals formed in a unit volume of air per unit time, can be expressed as the sum of the nucleation rate in a unit volume of liquid solution, JV, multiplied by the total collective volume of aerosol particles in a unit volume of air, Vt, and the nucleation rate on a unit surface area of liquid solution, JS, multiplied by the total collective surface area of aerosol particles in a unit volume of air, St . However, experimental studies and thermodynamic calculations for the ice–water–air system suggest that the total number of ice crystals formed is dominated by surface-based processes, so that JSSt≫JVVt . With this assumption the total nucleation rate can be simplified to 3JT=ΔICNCΔt=JVVt+JSSt≈JSSt.

Global models usually give the total in-cloud ice nucleation rate, which is here segregated into size-resolved nucleation rates. Since we assume that the number of nucleated ice particles depends only on the aerosol surface area, the scavenging coefficient in ice-containing clouds in size class i is proportional to the ratio between nucleation rate in the size class and the total nucleation rate. Thus, for the scavenging coefficient, for the ice-containing clouds, we get the following in each size class: 4Fi,nuc,ice=Si∑jSjΔICNCni, where Si is the surface area concentration of size class i, ΔICNC is the ice crystal number concentration obtained from the ice cloud activation scheme, and ni is the number concentration in size class i. The total surface area in each size class is derived using the associated number or mass median wet aerosol radius.

To test how the in-cloud wet deposition scheme affects simulated global aerosol concentrations, we used it with the SALSA2.0 in our ECHAM-HAMMOZ global model simulations. In addition, we tested how sensitive the simulated aerosol concentrations are to emission sizes, mixing, and aging when this scheme is used. SALSA is the sectional aerosol module of ECHAM-HAMMOZ global climate model. Details for calculations of aerosol emissions and chemistry in SALSA are presented in . SALSA is a very versatile aerosol microphysics module, which has been implemented in several models of very different spatial resolution . To describe the aerosol population, SALSA uses a hybrid bin sectional approach for calculating the evolution of the size distribution . In SALSA the aerosol population is divided into two subregions depending on their size. The first subregion is from 3 nm to 50 nm and the second is from 50 to 10 µm. These subregions are further divided into size sections defining the minimum and maximum diameter of the particles. In each size section the aerosol particles are assumed to be monodisperse, and chemistry and different microphysical processes are calculated for each size section separately. In addition, the second subregion is divided into externally mixed soluble and insoluble populations. A more detailed description of the newest SALSA version, SALSA2.0, is presented in .

Originally, SALSA used fixed scavenging coefficients, Fi, for different size classes i, in its wet deposition calculations. These coefficients include all the processes for in-cloud and below-cloud scavenging . The fixed coefficients, for stratiform and convective clouds with different phases (liquid, mixed, and ice) and solubilities, are adapted for SALSA from the calculations presented by , and they are presented in detail in . Here we refine the entire scavenging scheme by calculating the scavenging coefficients online.

We used the cloud activation scheme to derive the fraction of activated particles in each size class for our in-cloud nucleation scavenging calculations. However, the original activation scheme considers only the soluble material in particles and therefore neglects any possible insoluble material . For computing the amount of cloud droplets formed, this is a good assumption, as usually most CCN-sized particles contain a large fraction of soluble material. However, when the insoluble fraction is large (> 0.99), the assumption may lead to an underestimation of scavenged particles. This is because for insoluble particles larger than 1 µm with thin soluble coating (for instance mineral dust), the insoluble fraction is ignored in the cloud activation calculation, and for those particles the activation is calculated as it would be calculated for particles with an equivalent dry size derived from of the soluble part of the particles, thus making them less prone to activation. Therefore, we modified the activation calculations to account for the insoluble core in particles. The calculations are otherwise the same, but the critical supersaturation for each size class is calculated using Eq. (17.38) in . The supersaturation calculations, used in the cloud activation, for particles containing an insoluble core are presented in Appendix . As an input for the in-cloud nucleation scavenging coefficients in ice clouds, we used the ice crystal nucleation scheme described in . In our model, only particles which include mineral dust and black carbon are considered as ice nuclei .

As the in-cloud nucleation scavenging was changed into a more functional method, we also needed to alter the calculation of the in-cloud impaction scavenging. We calculate the in-cloud impaction scavenging in SALSA, for liquid clouds, using the same method as described in . This method computes in-cloud impaction as a function of wet aerosol particle size (rp), wet median aerosol particle radius (rpg), and cloud droplet radii (Rliq). Using this same information from our monodisperse size classes for aerosol particles, we can assume that each size class is a log-normal mode, and the in-cloud impaction scavenging coefficients, for liquid clouds, are then obtained as 5Fi,imp,liq=ΛmrpgΔt, where Λmrpg is the mean mass scavenging coefficient, and it is defined as 6Λm(rpg)=∫0∞Λ(rpg)rp3n(rp)drp∫0∞rp3n(rp)drp, and 7Λ(rpg)=∫0∞πRliq2Ut(Rliq)E(Rliq,rpg)n(Rliq)dRliq, which is called the scavenging coefficient in inverse time . In Eqs. () and () n(rp) is the aerosol number, Rliq is the cloud droplet radius, Ut(Rliq) is the terminal velocity of cloud droplets, E(Rliq,rpg) is the collision efficiency between the aerosol particles and cloud droplets, and n(Rliq) is the cloud droplet number .

The in-cloud impaction scavenging, for ice clouds, is calculated following , but as our model assumes that the ice crystals are monodisperse, there is no need to integrate over ice crystal number distribution . Thus, the in-cloud impaction scavenging coefficients are 8Fi,imp,ice=πRice2Ut(Rice)E(Rice,rpg)ICNCΔt, where Rice is the radius of the ice crystal in its maximum extent, Ut(Rice) is the terminal velocity of the ice crystals. and E(Rice,rpg) is the collection efficiency of the collisions between aerosol particles and ice crystals .

For below-cloud scavenging, we used the method, in which we approximated each size class as a log-normal mode. The size-dependent collection efficiency for rain and snow uses an aerosol and collector drop size parameterization described in detail in . Several studies have found that below-cloud scavenging of aerosols does not contribute to the mass deposition budgets as much as in-cloud scavenging does . Thus, we did not analyze below-cloud scavenging separately in our simulations.

For testing the effect of the current wet-scavenging scheme on global aerosol properties, we used the latest stable version of ECHAM-HAMMOZ (ECHAM6.3-HAM2.3-MOZ1.0), a three-dimensional aerosol–chemistry–climate model. ECHAM6.3 is a general circulation model (GCM) and it solves the equations for divergence, temperature, surface pressure, and vorticity . These large-scale meteorological prognostic variables can be nudged towards data from operational weather forecast models .

ECHAM6.3 is coupled with the Hamburg Aerosol Model (HAM), which calculates all of the aerosol properties within ECHAM-HAMMOZ. These properties include emissions, deposition, radiation, and microphysics . HAM has a comprehensive parameterization for both modal and sectional microphysics representations of aerosol populations. In addition to BC, the aerosol compounds included in this study are organic carbon (OC), organic aerosol (OA) (here assumed to be 1.4 times the modeled OC mass), sulfate (SO4), mineral dust (DU), and sea salt (SS). ECHAM6.3 is further coupled to the chemistry model MOZ (not used here), which contains a detailed stratospheric and tropospheric reactive chemistry representation for 63 chemical species, including nitrogen oxides, tropospheric ozone, and hydrocarbons . The model does not include secondary organic aerosols. In addition, the model assumes the same aerosol emission size distribution per compound and emission sector throughout the whole world. The SALSA global aerosol module is coupled in the ECHAM-HAMMOZ global climate model for all of the simulations presented in this study.

We used a total of six different simulations to investigate the performance of the current wet deposition scheme. The first two simulations were done with the default wet deposition scheme of SALSA (hereafter referred to as “old”) and the wet deposition scheme introduced in this study (hereafter referred to as “current”). The treatment of aerosol aging is identical in baserun_old and baserun_new; i.e., there is no artificial transfer of insoluble particles to soluble size classes. However, aerosol mass can be transferred from the soluble to the insoluble population through coagulation. As will be shown later, in the default model configuration the current scheme resulted in spurious BC vertical profiles. To investigate the reasons for this, we carried out four additional sensitivity simulations where we changed the assumptions of emission size distribution, as well as internal mixing and aging of BC. A schematic of the aerosol emission number size distribution, (N), as a function of diameter Dp, for the different simulations is presented in Fig. . In addition, an overview over the different simulations and their illustrative colors and line styles in the upcoming figures are presented in Table .

In the model simulations, the runs “baserun_new” and “baserun_old” are used to compare the current and old in-cloud scavenging schemes. The simulations “BC_small”, “BC_large”, “BC_soluble”, and “insol2sol” were conducted to evaluate the sensitivity of the current in-cloud scavenging scheme. These sensitivity studies were chosen based on the findings of , who studied how model processes affect the simulated aerosol vertical profiles. Their study indicated that the processes which have the strongest effect on aerosol vertical profiles in the HadGEM model are emission distribution, hygroscopicity, deposition, and microphysical processes .

In the first two sensitivity runs, we altered the BC emission distribution for SALSA. This was done so that all of the BC emissions were directed to either size class of small or large insoluble particles, respectively. In the default configuration the BC emission size distributions are log-normal mass fraction distributions following AEROCOM emission recommendations , which are remapped to the SALSA size classes. The mode radii (rm) and standard deviations σ for the original BC emission size distributions are rm=0.015 µm and σ=1.8, for fossil fuel emissions and rm=0.04 µm and σ=1.8, for wild-fire emissions . In the BC_small simulation, we directed all BC emissions to an insoluble size class where particle diameter spans from 50 to 96.7 nm. In the BC_large simulation, we directed all BC emissions to an insoluble size class where particle diameter spans from 0.7 to 1.7 µm.

To study the sensitivity of the wet deposition scheme to BC hygroscopicity, we conducted a simulation where all BC emissions were directed to soluble size classes. The size distribution for the emissions was the same as for the baserun simulations when they are directed to the insoluble classes. This simulation is referred to as BC_soluble in the model simulations. In the fourth sensitivity study, called insol2sol, insoluble particles are transferred to parallel size classes of soluble particles. This allows for the separation of fresh and aged particles and is a method to simulate aerosol aging used also in other global aerosol models e.g.,. The criterion for transfer is that particles activate at a supersaturation of 0.5 %.

The simulations were performed with ECHAM-HAMMOZ for the year 2010, with the SALSA aerosol module, using 3-hourly data output, after a 6-month spin-up. The emissions were obtained from the ACCMIP (Emissions for Atmospheric Chemistry and Climate Model Intercomparison Project) emission inventories, which are interpolated, for the period 2000–2100 by using Representative Concentration Pathway 4.5 (RCP4.5) . The model vorticity, divergence, and surface pressure were nudged towards ERA-Interim reanalysis data provided by ECMWF (European Centre for Medium-Range Weather Forecasts) , and the sea surface temperature (SST) and sea ice cover (SIC) were also prescribed. SST and SIC were obtained from monthly mean climatologies from AMIP (Atmospheric Model Intercomparison Project). The analysis is made between the old and the current wet deposition scheme using the ECHAM-HAMMOZ global aerosol–climate model with the SALSA aerosol module. In addition, the sensitivity of the current scheme to emission sizes, aging, and hygroscopicity of BC-containing aerosol is tested using ECHAM-HAMMOZ with SALSA.

To see how the current scheme and the sensitivity studies reproduce the vertical properties of different aerosol compounds, we compared the model simulations against aircraft measurements. The aircraft data were obtained from all NASA's ATom missions (1, 2, 3, and 4), and the dataset was merged data from all instruments which measure atmospheric chemistry, trace gases, and aerosols .

To get the best representative comparison between the ATom aircraft measurements and model data, the model data were sampled to the same time and locations of the aircraft measurements. For the collocation of model vertical profiles with observations, we used the Community Intercomparison Suite (CIS) tool .

BC concentrations were measured with a single-particle soot photometer (NOAA) (SP2) and OA and SO4 concentrations with a CU aircraft high-resolution time-of-flight aerosol mass spectrometer (HR-AMS) . The number concentration of particles with a diameter larger than 100 nm, N100, and total number concentration, Ntot were combined from the data measured with a nucleation-mode aerosol size spectrometer (NMASS), an ultra-high-sensitivity aerosol size spectrometer (UHSAS), and a laser aerosol spectrometer (LAS) .

First, we compared how aerosol properties differ when using the old and the current wet deposition schemes. In order to assess how the two schemes affect aerosol transport and vertical profiles, we compared the modeled aerosol vertical profiles over the tropics (0–30∘ N), the midlatitudes (30–60∘ N), and the Arctic (60–90∘ N). Here we focused on SO4, OC (or OA), and BC as they are readily available from the ATom aircraft campaign measurements.

Figure  shows the vertical profile of BC, OC, and SO4 mass concentration simulated with the old and the current in-cloud wet deposition schemes. The different rows show different latitude bands, as horizontally averaged annual means. The figure illustrates that all three of the compounds show similar differences in the vertical profiles in all three latitude bands, between the two runs. The concentrations for each compound are higher for the current scheme compared to the old scheme for almost the entire vertical domain. The differences between the different wet deposition schemes are greatest at higher altitudes starting from approximately 900 hPa upwards. In the tropics, these differences in the profiles are smaller, compared to the other latitude bands, with a maximum relative difference of approximately 200 % for BC and OC and slightly exceeding 150 % for SO4. These maxima occur at approximately 200 hPa altitude. In the midlatitudes, the differences are slightly higher than in the tropics and the maximum differences in the values are at ∼ 300 hPa altitude. The current method shows ∼ 350 % higher concentrations at maximum for BC and SO4 and ∼ 400 % for OC. The Arctic shows the largest differences in the compound profiles in comparison to the other latitude bands. The difference is largest at ∼ 500 hPa altitude where the concentrations in the current scheme outweigh the concentrations in the old scheme by ∼ 600 % for BC, 650 % for OC, and 800 % for SO4. As emissions of these aerosol particles in the Arctic are low, most aerosol is transported into the Arctic from emission regions outside the Arctic. It is thus evident that the wet removal of these aerosol particles is reduced in the current scheme, which allows for the particles to be transported to higher altitudes and longer distances. In addition, we found that the model accumulates BC at the higher altitudes in simulations spanning several years (not shown), which can be considered spurious behavior.

Figure  shows the vertical profile of the number concentration of particles with diameters larger than 100 nm, N100, and the total number concentration, Ntot. The N100 profiles show similar differences between the old and the current scheme as for the concentration profiles of different compounds in Fig. . In addition, the relative increase in the concentrations in the current wet deposition scheme is similar. This can be explained by changes in nucleation scavenging in the current scheme, which reduces the wet removal of large particles and thus increases the number concentration of large particles. Particles larger than 100 nm act as a condensation sink for H2SO4 and thus an increase in N100 leads to reduced new particle formation (NPF) and thus to decreased number concentrations of small particles. This can be seen in the Ntot profiles, which show a decrease in the current scheme. This difference is most pronounced in the Arctic, where the relative difference between the current and old schemes in the Ntot concentration reaches its maximum of ∼ 90 % at ∼ 400 hPa. In addition, the changes in rates of NPF and impaction scavenging in our current scheme result in an increased removal of small aerosol particles and thus reduce concentrations even more. These effects become evident when looking at size-resolved wet deposition fluxes.

The annual and global average size distributions of the wet deposition flux of the old and current in-cloud scavenging schemes are presented in Fig. . The wet deposition size distributions confirm what has been observed in the vertical aerosol profiles. There are only modest changes in the mass fluxes between the old and the current schemes. In the soluble population the largest difference is in the size class, which spans diameters between 190–360 nm, where the current scheme exceeds the value of the old scheme by 0.003 µg (m2 s)-1. On the other hand, in the size class 1.7–4.1 µm, the old scheme has a higher value by 0.002 µg (m2 s)-1. In the insoluble population the current scheme exceeds the value of the old scheme by approximately 0.002 µg (m2 s)-1 in the size class 190–360 nm, but in the largest size class the value of the old scheme is higher by 0.005 µg (m2 s)-1. As in steady state the total emissions of a compound must match its total removal, these differences mostly stem from changes in the interplay between dry- and wet deposition processes. However, the number flux in smaller than 50 nm size classes of the soluble population is halved, affecting mainly the removal of SO4 in the smallest size classes. In addition, there is a small increase of approximately 106 (m2 s)-1 in the current scheme in the size class between 190 and 360 nm. For larger than 360 nm size classes the changes are insignificant. These results can be explained by increased concentrations of medium-sized and large particles in the current scheme, which act as a condensation sink for SO4. This leads to fewer small particles as they are mainly formed through NPF from gaseous H2SO4. This effect can also be seen in Fig.  as a slight increase in removed sulfate mass in the accumulation-sized particles of both the soluble and insoluble aerosol populations. As a consequence of the atmospheric concentration of small particles, the wet deposition flux for the smallest size classes is reduced in the current scheme compared to the old.

The lifetime of different aerosol compounds was calculated by dividing the annual mean global mass burden of each compound by the annual mean emissions of the same compound . The lifetimes for different compounds can be found in Table . The global mean lifetime for BC was 9.23 d for the old scheme and 14.62 d for the current scheme. However, experimental studies from different aircraft campaigns indicate that the BC lifetime should be less than 5.5 d . This is a very interesting result: the more physical wet deposition scheme produces more spurious atmospheric lifetimes for BC. Consequently, the ability of the ECHAM-HAMMOZ global climate model, with the SALSA aerosol module, to reliably simulate aerosol vertical profiles and long-range transport of aerosol is also decreased when using the more physical scheme with the default model setup. This may be due to the fact that a more physical treatment of the wet deposition processes makes the model more sensitive to influences outside of the parameterization. We therefore performed further sensitivity simulations and compared their results to observational data.

As reported in the previous section, ECHAM-HAMMOZ, using the SALSA aerosol module, with the current, more physical scheme, in its default setup, produced spuriously long lifetimes of all aerosol compounds, especially BC. With the sensitivity simulations we aimed to explore different possibilities to improve the BC vertical profiles and long-range transport in the model. In order to increase nucleation scavenging of BC, we considered three different possibilities to make BC-containing particles more susceptible to cloud droplet activation. One way to achieve this is to emit BC into larger particles, which require less aging to be activated at a given supersaturation. This was tested in simulation BC_large. Another way is to mix BC with soluble compounds in order to enhance hygroscopicity of BC-containing particles and thus their cloud activation susceptibility. This can be done in two ways: either by emitting BC directly to soluble size classes (simulation BC_soluble) or by emitting BC to insoluble size classes and transferring particles to soluble classes after aging (simulation insol2sol). A third way is to emit BC into smaller size classes in order to facilitate the transfer of BC into larger, more easily activated particles by coagulation (simulation BC_small).

Figure shows vertical profiles of BC, OA, and SO4 simulated with the current wet deposition scheme for the different sensitivity simulations and with the old scavenging scheme, together with the average values from ATom aircraft measurements. The gray shaded area shows the standard deviation for the aircraft measurements. For BC, the simulations baserun_old, BC_large, BC_soluble, and insol2sol show a better match with observed vertical profiles than the other simulations in every latitude band. These simulations fall between the standard deviation limits of the ATom aircraft simulations almost everywhere, with the exception of the tropics, where they underestimate the concentrations starting from ∼ 600 hPa downwards. In addition, in the tropics, BC_soluble and insol2sol represent the BC concentrations slightly better than BC_large and baserun_old between 500 and 300 hPa. BC_small and baserun_new overestimate the BC concentrations at all latitudes, except in the tropics at lower altitudes starting from ∼ 700 hPa downwards, where they represent the BC concentrations slightly better than the other sensitivity simulations. As we saw in the previous chapter, the reduced efficiency in the wet deposition increases BC concentrations at higher altitudes, which causes baserun_new to overestimate the BC concentrations. This is because the default emission sizes of BC particles are not very susceptible to cloud activation. In addition, although BC_small aimed at increasing BC wet removal by emitting BC to small particle sizes and thus enhancing their collection by coagulation to large particles, it is apparent that coagulation is not very efficient in doing so.

Compared to baserun_new, most of the sensitivity studies show better agreement of the modeled BC profiles with the measurements. However, it needs to also be checked how they affect OA and SO4 concentrations. At all latitude regions OA concentrations in all of the simulations show similar results as the measurements. Exceptions exist for insol2sol and baserun_old simulations, which underestimate OA concentrations in the midlatitudes as well as at higher altitudes in the tropics and the Arctic. In the tropics the insol2sol simulation underestimates OA concentrations starting from approximately 700 hPa upwards and baserun_old from approximately 400 hPa upwards. In addition, the old scheme underestimates the OA concentrations at higher altitudes in the midlatitudes and the Arctic. The shape of the curve of the old scheme is different compared to observations and the rest of the simulations, especially in the Arctic. The old scheme exhibits a concentration minimum between 400 and 500 hPa, while observations are near the maximum values at those altitudes. At most, insol2sol underestimates the measurements at the highest altitudes, in all of the latitude bands, where the concentrations are over 1 order of magnitude less than the measurements. As the aging of aerosol particles in insol2sol is simulated by moving all insoluble particles that can activate to cloud droplets at 0.5 % supersaturation, almost all OA that is originally emitted to insoluble size classes is moved to soluble size classes. Thus, this enhances the activation and consequently the wet deposition of OA. Faster wet removal reduces the amount of OA transported to higher altitudes and thus reduces the OA concentrations. OA concentrations from all other simulations fall between the standard deviation limits of the ATom aircraft measurements everywhere, with only a slight overestimation between approximately 900 and 800 hPa in the tropics.

For SO4, all of the sensitivity simulations show similar trends as the measurements but overestimate concentrations almost everywhere. In the tropics, the shape of the vertical profile in baserun_old is similar to the observations and the rest of the simulations. In the midlatitudes, the vertical profile in baserun_old shows stronger variation than observations and the rest of the simulations, overestimating the values below 800 hPa and overestimating them above 600 hPa. Over the Arctic, baserun_old underestimates concentrations throughout the whole column, the maximum difference to observed values being almost 1 order of magnitude. The effect that insol2sol has on OA concentrations is also visible in the SO4 profiles, but here the effect is much weaker. In the tropics, insol2sol and baserun_old show better agreement with the measurements from 700 hPa upwards than the other simulations, with only a slight overestimation. Between approximately 900 and 700 hPa, all of the simulations overestimate the measurements. This may be due to simplified sulfate chemistry in the model as SO4 is mainly formed through chemical transformation . In the midlatitudes, all simulations overestimate the SO4 concentrations, with the exception of insol2sol and baserun_old. The insol2sol reproduces the SO4 profile slightly better than the other simulations from approximately 600 hPa upwards. However, near the surface, all simulations overestimate the SO4 concentrations by approximately half an order of magnitude. In the Arctic, all of the simulations have similar SO4 profiles with a slight overestimation between approximately 700 and 300 hPa altitude, with the exception of baserun_old. In addition, at the highest altitudes all of the simulations underestimate the SO4 concentrations. The different sensitivity tests do not alter the SO4 concentrations much compared to baserun_new because most of it condenses onto soluble particles. In addition, the new particles formed through nucleation are added to the soluble aerosol population. Thus, the SO4 vertical profiles are similar in all of the sensitivity simulations, with the exception of insol2sol where some of the SO4, which repartitions from the insoluble to the soluble population, is activated more efficiently.

Figure shows the vertical profiles of N100 and Ntot, simulated with different studies, together with ATom aircraft measurements. From the figure we can see that N100 profiles between different sensitivity simulations are similar in the midlatitudes and the Arctic. In these latitude bands, the sensitivity simulations slightly underestimate the N100 concentrations when compared to the measurements, but the trend is similar throughout the entire vertical column. However, insol2sol underestimates the N100 profiles slightly more in the midlatitudes and the Arctic. In addition, baserun_old underestimates N100 profiles even more than the other simulations, especially in the Arctic, where the maximum difference occurs at approximately 500 hPa altitude and is more than 90 cm-3 less than observed values. In the tropics, the simulations show a good correlation with the measurements as almost all of the profiles follow the shape of the profile of the ATom aircraft measurements, except for the surface concentrations, which are underestimated by a factor of approximately 2.5 compared to the measurements. In addition, in the tropics, insol2sol and baserun_old underestimate N100 more than the other simulations from 800 hPa upwards. For insol2sol, this is also due to more efficient activation compared to baserun_new for medium-sized particles which reduces the transport to higher altitudes.

The Ntot profiles are similar in shape in all sensitivity simulations, with only a modest difference (600 cm-3 at maximum), mostly at higher altitudes. In the tropics the trend of the profiles varies between simulations and measurements. All of the simulations tend to overestimate the Ntot concentrations at the surface and at the highest altitudes by over 50 %. However, they underestimate the Ntot concentrations at approximately 400–700 hPa, with the exception of baserun_old, which overestimates these concentrations. In the midlatitudes, all of the simulations represent Ntot concentrations fairly well (approximately 500 cm-3 underestimation and 4000 cm-3 overestimation at most) when compared to the measurements, with the exception of baserun_old, which overestimates these concentrations at all altitudes with almost 1 order of magnitude at maximum. However, in the Arctic, all of the sensitivity simulations underestimate the Ntot profiles. At higher altitudes, starting from approximately 600 hPa upwards, insol2sol underestimates Ntot least, showing quite good agreement with the measurements with only around 300 cm-3 difference at most. The baserun_old simulation, on the other hand, shows good agreement with the measurements at highest altitudes and below 600 hPa but overestimates the Ntot profile between 600 and 200 hPa by over 5000 cm-3 at most.

One of the reasons for the differences in the Ntot and N100 surface concentrations may be due to a misrepresentation of the emitted particle size distribution. In ECHAM-HAMMOZ the same aerosol emission size distribution per compound and emission sector is assumed throughout the whole world, which is not very realistic for every aerosol particle source . At higher altitudes, the aerosol microphysical processes correct the aerosol size distribution towards more realistic profiles.

To investigate the effects of the different sensitivity studies further, we computed the size and mass distribution of the wet deposition flux (Fig. ). The mass fluxes in the soluble population do not change much between baserun_new and the different sensitivity studies, except for the insol2sol simulation, which allows for sufficiently hygroscopic particles of the insoluble population to be repartitioned to the soluble population. This leads to an increase in DU mass in the soluble population and a decrease in the insoluble population. In addition to more efficient wet removal of DU due to this process, this also increases dry deposition and sedimentation (not shown) of DU in insol2sol. For the mass fluxes in the insoluble population, BC_large and BC_soluble show an increase in the largest size class for DU. This effect is due to more efficient removal of BC-containing particles, which allows for more SO4 to condense on larger, DU-containing particles, which enhances the activation of these particles.

The number fluxes in the soluble population for the different sensitivity simulations show most change in the two smallest size classes, which increase by a factor of approx 1.3 in the insol2sol simulation and approximately 1.1 for BC_large and BC_soluble when compared to baserun_new (shown in Fig. ). These differences stem from changes in medium-sized and large particle concentrations, which act as a condensation sink for SO4 and thereby regulate the amount of SO4 available for new particle formation. In addition, there is a slight increase in OC in the insol2sol-simulated number distribution, which is being transferred from the insoluble population. Otherwise, there is no notable change in other compounds as the SO4 dominates the number distribution in the soluble population. The relative BC mass contribution to the wet deposition number flux of the insoluble aerosol population reflects the assumptions made in the different sensitivity studies very well. While for BC_large and BC_soluble the BC mass fraction in the medium-sized insoluble particles disappears, in BC_small the BC fraction in the 50 to 100 nm insoluble particles is about 3 times larger than in baserun_new (shown in Fig. ). This shows that coagulation is not effective in moving BC from these small insoluble particles to large soluble particles. In insol2sol, most of the BC is transferred from the insoluble to the soluble aerosol population before removal, which can be seen in a strong decrease in removed insoluble aerosol number for that simulation.

In addition to the evaluation of the simulated vertical aerosol profiles, we used the modeled atmospheric lifetimes of all aerosol compounds as an indicator of the model skill in the different simulations. Here we estimated the atmospheric lifetime of a compound as the yearly and global mean mass burden of the compound divided by its total yearly mean emission. The compiled mean lifetimes for the different simulations and compounds as well as the mean and spread of lifetimes from several AEROCOM models (CAM5-ATRAS, EC-Earth, TM5, ECHAM-HAM, ECHAM-SALSA, ECMWF-IFS, EMEP, GEOS, GFDL-AM4, GISS-OMA, INCA, NorESM2, OsloCTM3, and SPRINTARS) are presented in Table  . The spread is calculated as half the difference between the first and third quantiles .

With the assumption that the AEROCOM mean atmospheric lifetimes are the current best guess, we can use Table  to select a simulation that best reproduces these mean lifetimes and therefore could be regarded as the best solution to address the overestimated BC lifetimes in baserun_new. However, we must keep in mind that AEROCOM means are global-climate-model-based results, and thus it is not completely certain that these lifetimes of different compounds reflect the actual lifetimes in the real atmosphere. While baserun_old, baserun_new, and BC_small overestimate the BC lifetime by factors of 1.6, 2.5, and 2.8, respectively, BC_large, insol2sol, and BC_soluble all produce BC lifetimes within 1 d of the AEROCOM mean. In addition, the BC lifetimes should be less than 5.5 d according to . However, the different sensitivity studies also affect the atmospheric lifetimes of the other species, and some of them considerably. For instance, the lifetime of DU in insol2sol is almost 4.5 times shorter than the AEROCOM mean, while both BC_large and BC_soluble overestimate this mean only slightly by half a day. On the other hand, the atmospheric lifetime of OC in insol2sol is closest to the AEROCOM mean compared to all other simulations using the current wet deposition scheme. However, in this setup of ECHAM-HAMMOZ all OC is emitted as primary particles, while in reality a large fraction of the organic aerosol is formed as secondary organic aerosol (SOA) in the atmosphere. Modeling the processes leading to SOA formation more realistically would most likely affect the modeled OC lifetimes quite substantially. The atmospheric lifetime of SO4 in insol2sol is also closest to the AEROCOM mean, but BC_large and BC_soluble also model the SO4 lifetime fairly well. For SS, the atmospheric lifetime does not change when changing the wet removal algorithm or during any of the sensitivity tests as SS is only emitted to the soluble population. The lifetimes for all simulations are more than 0.7 d higher than the AEROCOM mean (about a factor of 2). This has already been discussed by and .