For a particle residing in a column with precipitation, it must first be determined whether it is located within the cloud, above the cloud, or below the cloud, before its wet scavenging can be calculated. Above the cloud, no scavenging occurs; within the cloud, nucleation scavenging is used; and below the cloud, the impaction scavenging scheme is activated. A new option has been implemented in FLEXPART, so that the cloud vertical extent can either be derived from three-dimensional ECMWF fields of specific cloud liquid water content (CLWC) and specific cloud ice water content (CIWC) or from the summed quantity specific cloud total water content (CTWC = CLWC + CIWC). CTWC can be calculated by FLEXPART's ECMWF pre-processor to save storage space required for the FLEXPART input data. Details of how the cloud water is computed by the ECMWF Integrated Forecast System (IFS) model can be found in and the processing of these data is described in . If no cloud water content data are available in the FLEXPART input files, cloud vertical extent can be diagnosed from the vertical distribution of RH as in previous versions of FLEXPART . However, this is considered much less accurate.

Multiple layers of clouds may appear both in the RH based parameterization and in the ECMWF CTWC data. Not all of these cloud layers may be precipitating but, because of lack of detailed information, in FLEXPART we assume that all levels of clouds contribute to surface precipitation. An inspection of the ECMWF cloud fields suggests that this assumption is of minor importance as cloud layers with significant gaps in between account for fewer than 10 % of the large scale precipitation events.

Meteorological information in FLEXPART is available only at the resolution of the ECMWF input data. However, a grid cell with precipitation may, in reality, also contain areas without precipitation, and this can reduce the efficiency of aerosol wet scavenging substantially . The grid surface precipitation intensity (It) is the sum of the advective precipitation intensity Il and convective precipitation intensity Ic from the meteorological input files. To scale this to sub-grid precipitation intensity (I) the empirical relationship for the fraction of a grid cell experiencing precipitation (F) is maintained from previous versions of FLEXPART, described in . If a particle is found to be in or below a cloud with precipitation, the scavenging coefficient Λ is determined by either the in-cloud or below-cloud scheme described in the following two sections.

The nucleation scavenging in FLEXPART is activated only for particles residing in the precipitating fraction of a grid cell F, see , and only at altitudes where cloud water is present. For consistency with I, the column cloud water is also scaled by the precipitating fraction of the clouds, to get the sub-grid precipitating cloud water (PCW): PCW=CTWCFcc Here, cc is the surface cloud cover and so F/cc is the fraction of cloud water in the precipitating part of the cloud. If PCW > 0 in-cloud scavenging is applied.

An important intermediate quantity to determine is the in-cloud removal rate of aerosols due to the removal of cloud water by precipitation, which is given by the cloud water washout ratio I/PCW. To obtain accurate values for I/PCW, it is important that I and PCW are consistent. Both values are derived from ECMWF data, however, I is derived from accumulated precipitation values (i.e., precipitation accumulated during one ECMWF data output interval, typically 1 or 3 h), whereas PCW is an instantaneous quantity, and this can cause small inconsistencies. Furthermore, I/PCW does not take into account the efficacy of turbulent overturning and the replenishment rate of cloud water from condensing water vapor. The aerosol scavenging coefficient Λ (s-1) is now given as Λ=FnucIPCWicr, where Fnuc, the nucleation efficiency, is the fraction of the aerosol within the cloud that is in the cloud water (see Fig. ). While icr represents the cloud water replenishment rate, it cannot be determined from the ECMWF output data. Therefore, the determination of the constant icr was done on the basis of empirical testing in FLEXPART and must be considered a tuning parameter.

Compared to the previous FLEXPART scheme described in , icr/PCW replaces the cloud water representation that was calculated based on an empirical relationship with precipitation rate (cl=2×10-7I0.36). The overall best results were obtained for icr set to a value of 6.1 for the ECMWF cloud water fields, which is used for all simulations in this paper. This resulted in a somewhat slower in-cloud removal rate with the new compared to the old parametrisation. Comparison of the two parametrisations also shows that using icr/PCW gives overall weaker dependence on I, compared to cl in the old removal scheme. For simulations where in-cloud removal constitutes a large fraction of the removal, i.e. especially for soluble accumulation mode aerosols, the empirical value of icr has a large impact on overall removal rates.

In reality, Fnuc depends on many different variables such as aerosol size, chemical composition, surrounding aerosols, temperature and cloud phase and microphysical properties. However, a complete parameterization of Fnuc is not possible in FLEXPART because of a lack of information. What can be constrained within FLEXPART is that most aerosols have very different nucleation efficiency for liquid, mixed-phase and ice clouds. Therefore, we introduced as a new feature that for determining the nucleation efficiency (Fnuc), we now distinguish the efficiency of aerosols to serve as cloud condensation nuclei (CCNeff) and ice nuclei (INeff). By contrast, in the old scheme all aerosols had Fnuc≡0.9. For ice clouds, Fnuc is set equal to INeff, for liquid water clouds, Fnuc is set equal to CCNeff, and for mixed-phase clouds, we use α, the fraction of the cloud water in ice phase shown in Fig.  as a black line see for details on calculations of α, to interpolate between Fnuc and CCNeff: Fnuc=1-αCCNeff+αINeff.

There are no unique globally representative values for CCNeff or INeff because they depend not only on the aerosol particle itself, but vary also with aerosol concentrations and cloud properties (e.g., updraft velocities). Some general considerations can however be made. In a review of measurements conducted at the high alpine station Jungfraujoch, showed that Fnuc varies significantly with both aerosol size and cloud phase. found that the fraction of particles with dp>0.1 µm activated in a cloud dropped from 56 % in liquid summer clouds to 0.08 % in winter ice clouds. The lower ice phase values are attributed to the Bergeron–Findeisen process , by which relatively few ice crystals grow at the expense of many more liquid droplets. When the droplets evaporate the non-volatile aerosol content is released back to the atmosphere. This temperature dependent effect is illustrated in Fig. , where the partitioning between cloud water and surrounding air of total aerosol number according to is shown (magenta dots). Also shown in Fig.  are the similar results of (red line) and the BC partitioning (blue line) reported by . Hence it is generally assumed that for most aerosol particles CCNeff>INeff.

found that the average scavenged fractions in clouds during spring in Cumbria, UK, were 0.77 for sulphate and 0.57 for soot in clouds formed in continental air, and 0.62 and 0.44 respectively, for clouds formed in marine air. The time and place for these measurements suggest that these were mainly liquid phase clouds. In other studies , it was found that larger aerosol particles have a higher nucleation efficiency than smaller particles. Such information can be used by FLEXPART users to prescribe appropriate CCNeff and INeff values for different aerosol particle types and sizes.

Raindrops and snow flakes fall at approximately terminal velocity through the air and may scavenge aerosol particles as they collide with them in the ambient air below the cloud base. This below-cloud scavenging process depends both on the probability that the falling hydrometeor collides with an aerosol particle (collision efficiency) and the probability of attachment (coalescence efficiency). Both probabilities together determine the collection efficiency. Collection efficiencies of both snow and rain have a minimum for aerosol particle sizes near 0.1–0.2 µm in what is known as the Greenfield gap . Notice that dry deposition is also least efficient for such particles. For aerosol particles of these sizes, neither Brownian diffusion nor impaction is efficient. Whilst Brownian diffusion is the dominant process of attachment for sub-micron particles, inertial impaction is the dominant process for larger aerosol sizes and becomes dominant above ∼ 1 µm, though there are large discrepancies between theoretical predictions and observations e.g.,. The collection efficiency is strongly dependent on the sizes of both the falling hydrometeors (and their terminal velocity) and the aerosol particles. It also depends on the precipitation type.

The below-cloud scavenging parameterization in FLEXPART differentiates between rain and snow because especially for large aerosol particles a large difference in scavenging efficiency is found between the two, where snow is more efficient than rain . Of many possible parameterizations for liquid precipitation, the one of was chosen, for which all the required information is available in FLEXPART. The parameterization takes into account rain intensity I (used to parameterize droplet size) and the aerosol dry diameter and is based on field measurements over 6 years in Hyytiälä, Finland. The scavenging coefficient λ (s-1) for particles below a cloud is given by log⁡10λλ0=C*a+bdp-4+cdp-3+ddp-2+edp-1+fII00.5, where C* is a scalar, dp=log⁡10DpDp0, λ0=1 s-1, I0=1 mmh-1, and Dp0=1 m. Coefficients for factors a–f are given in Table . While originally intended for particles of size 0.01–0.51 µm, the parameterization by is one of few parameterizations that takes into account data for larger aerosol particles up to 10 µm diameter, and should thus provide reasonable results also for these larger particles. For rain C*=Crain and is a preset scalar variable that makes modifications to the removal scheme possible. The suggested default value for Crain is 1.

For snow scavenging, we use a parameterization reported by , which was also derived from Hyytiälä data, but during snowfall. It is fitted with the same function as given by Eq. () but with coefficients derived for snow and also given in Table . In this study we have used a local temperature threshold of 0 ∘C is to distinguish between rain and snow, but it is also possible to use rain and snow precipitation intensity read directly into the model from ECMWF analysis data. The Kyrö function is independent of precipitation intensity or type of falling snow as is common for snow scavenging parameterizations see e.g.,. The shape of the snow crystals is very important for the scavenging efficiency, but cannot be derived from the ECMWF data. This aspect is thus ignored, and the Kyrö function is averaged over many different types of snow crystal shapes instead.

Figure  shows the below-cloud scavenging parameterizations for rain and for snow for different precipitation rates and compares them with the old parameterization used in FLEXPART, which was based on . The aerosol removal rate is increased relative to previous versions of FLEXPART for almost all precipitation rates. Aerosol chemical properties may also influence the below-cloud scavenging coefficient. In FLEXPART, this influence can – to some extent – be accounted for by setting the parameters Crain and Csnow (C* in Eq. ), which are scalars used to scale the collection efficiency for rain and snow, to values different from 1. For example, with Crain=0 (Csnow=0), no below-cloud scavenging for rain (snow) would occur in FLEXPART.

As parameterizations by both and are based on bulk aerosol there may be differentiating factors for certain aerosol types, though very little specific evidence of this exists . Comparisons with other impaction scavenging parameterizations see e.g., for rain show that the scavenging values are on the middle to low side of existing parameterizations and that differences between different parameterizations cover at least one order of magnitude. Choosing values for Crain and Csnow between 0.1 and 10 should cover this uncertainty range.

Mineral dust arguably constitutes the largest mass of aerosols in the atmosphere. Dust particles span a wide range of sizes and can be found far from their source . Small dust particles have been found to mix somewhat with volatile aerosol components but particles larger than 0.5 µm are inert in the atmosphere . Mineral dust is thus well suited to model with FLEXPART. Model experiments were set up to examine the role of impaction and nucleation scavenging as well as dry deposition and gravitational settling for different sizes of mineral dust.

Emission of mineral dust was calculated based on a module presented by . In short, dust emission was initiated from bare land when friction velocity exceeded a threshold value for initiation of saltation, depending on soil properties and soil moisture content. The soil fraction available for erosion was determined from land cover data GLCNMO version 2, based on MODIS images. Vertical fluxes of mineral dust were derived according to . Particles were subsequently released in FLEXPART over a layer of 300 m height, at a 0.5∘ resolution in 6-hourly time steps. We assumed an aerosol particle size distribution in ten particle size bins, varying between 0.2 and 18.2 µm, as suggested by . FLEXPART simulations were run in forward mode for the year 2010.

An evaluation of modeled aerosol lifetimes was recently performed by who made use of measurements of radioactive isotopes released during the Fukushima Dai-Ichi nuclear power plant (FD-NPP) accident in March 2011. The radionuclide cesium-137 (137Cs) was released in large quantities during the accident and measurements suggested that they mainly attached to the ambient accumulation-mode sulphate aerosols . Another radionuclide, the noble gas xenon-133 (133Xe) was also released during the accident and can serve as a passive transport tracer. Both radioactive isotopes were transported and measured across the Northern Hemisphere for more than three months after their release, providing a unique constraint on modeled aerosol lifetimes .

We have used measurements of the aerosol-bound 137Cs and the noble gas isotope 133Xe from March to June 2011 at 11 different measurement stations of the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) network see Fig. 1 of. All measured radionuclide concentrations were corrected for their radioactive decay and converted to activity per cubic meter for comparison with the model data. Detailed descriptions of these measurements and how they can be used to determine aerosol e-folding lifetimes were provided by .

Over the 46 days of measurements (starting 14 days after the initial emission) used to evaluate e-folding times of 137Cs (and, implicitly, of the accumulation mode sulphate aerosol to which it attached), found FLEXPART concentrations to decrease by three orders of magnitude more than the measurements. The decrease started from an initial overestimation of the 137Cs concentrations but later the concentrations were underestimated at all but one CTBTO stations. Consequently, a too short e-folding lifetime of 5.8 days was calculated for FLEXPART as compared to 14.3 days derived from the measurements. In this paper, we repeat the simulations of but with the new removal scheme for aerosols.

FLEXPART has been used in several recent studies to model BC with a focus on the Arctic . All these studies used a FLEXPART version where the in-cloud scavenging efficiency of the reference FLEXPART version had been reduced by one order of magnitude. This has produced realistic concentrations for the Arctic. In this study, we tested the new scheme against measurements at Arctic and mid-latitude stations to assess how well BC concentrations are captured.

For BC, simulations were made both in forward and backward mode, and results were compared to test model consistency. When run in backward mode, FLEXPART output is a gridded emission sensitivity that can be coupled with emission fluxes to obtain the concentrations at the release point. For all simulations, concentrations obtained by forward and backward simulations by FLEXPART differ only due to statistical noise.

Emissions used for BC simulations were ECLIPSE v4.0 available through the website http://eclipse.nilu.no. Added to these are shipping emissions from AEROCOM and GFEDv3.1 emissions for forest and savannah fires , all resolved monthly and on a 0.5∘×0.5∘ grid. European measurements of aerosol absorption were collected from the Database for Atmospheric Composition Research (EBAS) with the aim of using data from stations with similar particle soot absorption photometer (PSAP) instruments. The stations were selected to represent different environments, ranging from locations close to pollution sources in Central Europe to remote locations in the Arctic. We chose the sites Melpitz (MEL, 51.32∘ N 12.56∘ E) in Germany which is surrounded by strong BC sources, Pallas (PAL, 67.80∘ N 27.16∘ E) in Finland and Southern Great Plains (SGP, 36.50∘ N 98∘ W) in the US at intermediate distances from the sources, and Zeppelin (ZEP, 78.93∘ N, 11.92∘ E), Barrow (BRW, 71.30∘ N, 156.76∘ W) and Alert (ALT, 82.50∘ N, 62.34∘ W) as remote sites.

PSAPs measure the particle light absorption coefficient. Conversion of this coefficient to equivalent BC (eBC) mass concentrations is not straightforward and requires certain assumptions , leading to site-specific uncertainties on the order of a factor of two. We have used conversion factors of 6.50 m2g-1 for PAL and 5.50 m2g-1 for ZEP, where site-specific information was available and 10 m2g-1 for MEL, ALT, BRW and SGP. For ALT and BRW a gap with more than a month of missing data for 2007 was filled with climatological values of all available data after year 2000. For PAL only climatological observations were used.

To explore how frequent in-cloud and below-cloud scavenging events are and where they occur, we used a 3-month (December 2006 to February 2007) global ECMWF data set (1∘×1∘ with 92 vertical layers) and classified each grid cell as being either in a cloud-free column or, if clouds exist in the column, in, below or above the cloud. The vertical extent of each layer increases with altitude, which emphasises lower altitudes when a raw count of events is done, so for a more realistic representation the numbers presented here are weighted by the mass of each model layer (using a standard atmosphere). Convective and large scale precipitation events were differentiated using surface precipitation and for each event classified as the larger of the two.

Cloud top heights and the frequency of scavenging events are shown in Fig. , both using the ECMWF cloud water information (blue) and the cloud parameterization based on relative humidity (red). Close to the equator, the precipitating clouds from ECMWF have on average high cloud tops, often extending all the way to the tropopause. For the period examined, more than 96 % of the in-cloud removal events in the tropical band (15∘ S–15∘ N) are convective. For the 15–60∘ latitude range the cloud tops are markedly lower and the frequency of convective removal events drops markedly to 46 % which is a result of both more stratiform clouds and fewer and lower convective clouds. This can be seen in the left panel of Fig.  as an extension of the 25–75 % percentile range, which indicates that there are both low stratiform and high convective cloud tops. The fraction of large scale in-cloud events in this area is 46 %. Poleward of 60∘, stratiform precipitation dominates with 76 % of all events.

Globally, in-cloud scavenging accounts for 85 % (91 % above 1000 m) of the aerosol wet removal events, of which 57 % occur in convective clouds (for ECMWF clouds). The global fraction of in-cloud (solid line), below-cloud (dashed) and total (dotted) removal events as a function of altitude is shown in Fig.  (right). For the ECMWF defined clouds (blue) there are very few below-cloud scavenging events above 1000 m. There is however a slight increase in the frequency of such events around 5000 m, which is due to multiple layers of clouds. In the instances where precipitation was predominantly large scale (21 %), at altitudes above 5000 m, in reality most clouds are likely non-precipitating cirrus clouds, and the ECMWF precipitation is actually originating from lower cloud layers. This could also be related to both convective and large scale clouds residing in the same grid cell, but without information about the three-dimensional distribution of hydrometeors, a correct diagnosis is not possible and many of the high-altitude below-cloud scavenging events are probably not real. However, in total this accounts for only 4 % of all below-cloud scavenging events. Defining clouds on the basis of relative humidity produces an almost 4 times higher occurrence (15 %) of such high altitude (> 1000 m) below-cloud removal events, which is likely unrealistic.

The water phase of clouds influences the removal efficiency for aerosols that are inefficient IN but efficient CCN (or vice versa). The phase partitioning is temperature dependent and varies with season, latitude and altitude. For the 3 months examined, globally 16 % of the in-cloud removal events were liquid only, 7 % were ice only, whereas the remaining 77 % were defined as mixed-phase cloud removal events.

In previous versions of FLEXPART, clouds were parameterized using relative humidity. As can be seen in Fig. , this leads to several differences in the distribution of scavenging events from the ice and liquid water based cloud distribution. For instance, the high frequency of clouds extending all the way to the surface seems unrealistic, and often no clouds could be found in a grid cell with precipitation (not shown). Altogether, in the new scheme the cloud distribution is more consistent with the precipitation data and thus it produces a more realistic distribution of below-cloud and in-cloud scavenging events with 52 % of the events below 1000 m being below-cloud removal events.

While Fig.  shows the global distribution of scavenging events, the actual relative probability of in-cloud versus below-cloud scavenging events versus dry removal events for a given particle depends on the distribution of the aerosol. To illustrate this, we released a pulse of 1 million particles representing dust of five different sizes (see Table ) at 10 m a.g.l. over Central Europe on 14 April 2007. Figure  shows the relative frequency of the different removal events for these aerosol particles as a function of time after the release. For the purpose of clearer illustration, we show a polynomial fit through the daily total number of events of each removal type. Initially, below-cloud scavenging and dry removal are the most frequent removal types. Exact numbers at the beginning will vary depending on the location and time of the release. However, as particles are transported to higher altitudes, the relative frequency of in-cloud removal events increases, exceeding that of the other event types from day 4. On day 7 after the emission pulse, the relative frequencies are already similar to the global distribution of scavenging events in the troposphere, where below-cloud scavenging accounts for only 15 % and dry removal for only 3 % of the number of events. Notice that in terms of aerosol mass removed, the importance of below-cloud scavenging and dry removal will decrease even more quickly because the mass of particles remaining in the lower troposphere will also decrease rapidly. This effect has been discussed in . The time dependence of scavenging is an important feature as most primary aerosols are emitted at or near the surface. Figure  also shows that, despite the global dominance of in-cloud scavenging events, below-cloud scavenging or dry removal may be most important, at least for aerosol types for which these removal mechanisms are efficient. The dependence in the efficiency and nature of scavenging also means that aerosol lifetimes are different for fresh and aged aerosols, as discussed in .

Since the below-cloud scavenging scheme has a strong size dependency, an important goal for our mineral dust simulations was to investigate the differences in lifetime for aerosol particles with a large range of different sizes. Also, mineral dust particles are ineffective CCN e.g., and, therefore, below-cloud scavenging is very important for dust. To investigate the sensitivity of dust scavenging to various components of the scavenging scheme, we performed simulations for a range of parameter settings.

The resulting lifetimes (τF) are shown in Table . Lifetimes were calculated as the times when the dust mass has decreased to 1/e of the emitted mass. Values of τF are equivalent to e-folding times if the removal rate is constant. While this is not the case – as shown in the previous section, it allows a simplified lifetime calculation and is sufficient for our purpose of investigating the systematic dependence of lifetime on aerosol particle size and choice of scavenging parameters. It also emphasizes the initial phase of removal when most of the emitted mass is lost.

The accumulation mode particles of mineral dust are in the 0.2 µm size bin, which is locatedclose to the minimum of both impaction efficiency (Fig. ) and dry removal. Consequently, and especially since dust particles are also inefficient CCNs, the 0.2 µm sized particles have very long lifetimes. With the standard parameter settings in FLEXPART for dust (Csnow=Crain=1; CCNeff=0.15; INeff=0.02, highlighted in green in Table ), the lifetime of accumulation mode-sized (0.2 µm) dust is almost 32 days. Even though dust particles are inefficient as CCN, wet removal dominates the total removal for the two smaller reported size bins and nucleation scavenging in liquid water clouds is the dominant removal process. Only if CCNeff is decreased further by one order of magnitude, its importance is diminished and the lifetime increases to > 50 days. Compared to τF obtained from the old scavenging scheme, the 0.2 µm size bins have significantly increased τF. The increase is in part due to fewer clouds extending all the way to the surface (Fig.  left), thus decreasing the low altitude removal most important initially. However, most of the increase is due to the decreased CCNeff and INeff. The version 9 simulation with CCNeff=INeff=0.09 is equivalent to the parameters used for BC v9 simulation in Sect.  (Fig. ).

The loss of particles of size 2.2 µm is more strongly affected by gravitational settling, but still dominated by wet removal. Impaction scavenging is also about four times more efficient for aerosols of this size than for 0.2 µm particles, and thus has a large impact on the atmospheric lifetime. This is important especially close to the sources, when the aerosols are predominantly in the lower troposphere where below-cloud removal occurs most frequently. Consequently, the lifetime τF, 11.6 days, is substantially shorter than for the 0.2 µm particles. There is also a strong sensitivity to the choice of the Csnow value for scavenging due to ice, which is probably related to the strong size dependence of the scheme.

For the even larger particles shown in Table , dry deposition combined with relatively fast gravitational settling take over as the most important removal mechanisms and thus very little effect is seen from altering the wet removal parameters. For the 6.2 µm particles, reducing all wet removal parameters by one order of magnitude, only increases the simulated lifetime by 20 %, compared to the 350 % increase in lifetime for the accumulation mode particles. For the 18.2 µm particles, wet scavenging has virtually no impact on the lifetime, which is entirely controlled by gravitational settling.

A multi-year study of mineral dust, using FLEXPART with the same removal as here

The values stated in , have been changed in Table  to correspond to the settings of icr=6.1 used here.

The FLEXPART model set-up for simulating the aerosol-bound cesium transport after the Fukushima accident was the same as in , except for the updates in the cloud and wet scavenging schemes described in this paper. Furthermore, used only one aerosol size mode, with d=0.4 µm. Here, a more realistic aerosol size distribution was used, and compared to the measurements of 137Cs surface activity by . For these simulations, the mass was emitted in six different size bins (Table ) ranging from d=0.4 to 6.2 µm. The size bins with logarithmic mean diameters of [0.4, 0.65, 1, 2.2, 4, and 6.2] µm received 1, 2, 10, 40, 32, and 15 % of the emitted mass. The resulting relative aerosol surface size distribution is shown in Fig. b at the time of the release (green) and for an aged distribution after 40 days (cyan) together with the measured 137Cs aerosol surface activity size distribution (red) of . It is worth noting that started their measurements 47 days after the largest emission but probably sampled mainly 137Cs from small later releases. The measured size distribution of 137Cs is bimodal with peaks around d=1 and 0.02 µm. The larger peak at 1 µm fits well the released size distribution in FLEXPART. The peak of the aged size distribution is dominated by particles of 0.6 µm. While the initial release included a significant fraction of particles with diameter larger than 1 µm (52 % by mass and 7 % by aerosol number), their fraction is reduced considerably by day 40 (3 % by mass and < 0.1 % by number). The smaller mode around 0.02 µm is not represented in the model but it accounts for only 5–6 % of the total mass.

For evaluating the modeled aerosol lifetimes in the same way as , we calculate the ratio of the aerosol (137Cs) to the passive tracer (133Xe) at each measurement station shown in Fig. a. The ratios decrease with time due to removal of aerosols. We further calculate the daily median ratios (median concentration for each day over all stations), and fit an exponential decay model (grey lines in Fig. c) to these daily ratios. The fit is done over days 15–65 after the start of emissions, for which sufficient measurement data exist seefor details. This excludes the initial phase of removal (as shown in Fig. ) and thus emphasizes the role of in-cloud scavenging. We therefore use the e-folding time of the exponential decay model as an estimate for the aerosol lifetime (τe).

The e-folding lifetime estimate obtained by for the previous version of FLEXPART was 5.8 days, indicating a too quick removal of the aerosols compared to the measurement-derived τe value of 14.3 days. However, there was only a slight underestimation of the atmospheric concentrations, partly explained by an initial overestimation. The new scavenging scheme produces a longer e-folding lifetime of 10.0 days (Fig. c). The longer lifetime is mainly due to slower in-cloud scavenging and a broader range of aerosol particle sizes emitted, which have different removal efficiencies. Both the below-cloud scavenging as well as the dry removal are size-dependent. This also explains the shift towards smaller particle sizes from the initial distribution to the aged distribution in Fig. b.

The e-folding times calculated individually for the different size bins are reported in Table . Simulation #1 in the top row (green) show the results with scavenging parameters set to values believed to be valid for sulfate, which are also used in the simulation shown in Fig. . The e-folding lifetimes range from 11.7 days for the 0.4 µm size bin, to 5.4 days for the 4 µm bin. Even the smallest two aerosol size bins have a shorter e-folding lifetime than what is derived from the CTBTO measurements. For the largest size bin, concentrations after 15 days were too low for a robust estimate of lifetime.

The second column in Table  for each aerosol size bin reports the ratio of modeled to observed concentrations averaged over the whole period, assuming that all 137Cs was attached to aerosols of that size bin. Assuming that 137Cs attached exclusively to particles smaller than 1 µm (first two size bins), which have the most realistic lifetimes compared to the observation-derived lifetime, leads to a large overestimate of the observed concentrations (ratios of 18.7 and 11). This might to some extent be due to an overestimate of the emissions used here, by . Indeed, other authors e.g. have found smaller emissions, but the source term uncertainty of about a factor of two cannot alone explain the overestimates by the smaller modes. Assuming that all 137Cs attached to particles larger than 2.2 µm, on the other hand, leads to underestimates of both the concentrations and the lifetimes compared to the observations.

From the differences between the simulations for different aerosol sizes, it is also possible to investigate the relative importance of different removal mechanisms for the different aerosol sizes. Furthermore, several different in-cloud parameters INeff and CCNeff were tested. In simulations #2 and #3 in Table , INeff and CCNeff were reduced to values of 0.4 and 0.15, respectively. In simulations #4 and #5, in-cloud and below-cloud scavenging were separately turned off completely. For these simulations, only one aerosol size was used. Comparison of the lifetimes and ratio of these simulations with the original 137Cs simulation #1 (Table ) shows that for submicron particles the governing removal process is in-cloud scavenging. For particles in the range ∼ 0.05–0.8 µm, dry deposition is slow and also the below cloud removal in FLEXPART is not very efficient, which leaves in-cloud scavenging to control the lifetime. This is apparent from how changes in removal efficiency influence the model values and lifetimes differently for different aerosol sizes. When CCNeff and INeff are reduced by 60 % to 0.4 in simulation #2, the atmospheric burden is increased by a factor of 5 for 0.4 µm particles. The lifetime however, only changes from 11.7 to 17.9 days, i.e. by a factor of ∼ 1.6. For the four larger aerosol size bins much smaller changes are found between #1 and #2 in concentration, lifetime and ratio, due to the less dominant role of in-cloud scavenging for these particles.

The measurement data during the first 15 days after the start of the emissions are insufficient to derive an aerosol lifetime. However, for the model simulation #1, the intermittent e-folding time for the full size distribution of 137Cs during the first 15 days is 6.1 days, compared to the 10 days found over the 45-day period in Table . This is due to the reduction of below-cloud scavenging and dry removal events (shown in Fig. ) combined with a reduction of in-cloud scavenging as well, as after 15 days a large and increasing fraction of the left-over aerosol particles reside above the cloud tops. As particles with more efficient removal are lost, the lifetime is more and more influenced by the longer-lived particles over time and thus the model e-folding lifetime estimate increase with time. This last effect applies in FLEXPART only when the aerosol size distribution consists of more than one specific aerosol kind (i.e. modal size or different removal parameters).

In Fig. d the mean model/observed concentration ratios at the different stations are plotted against latitude. A prominent feature of FLEXPART and indeed most models used by is a tendency to overpredict concentrations at low latitudes and underpredict concentrations at high latitudes. This tendency is also present with the new removal scheme, where model / observation ratios decrease with latitude. The green line shows a logarithmic fit to the station median data. The same fit was done to the mean from a simulation using FLEXPART version 9 (pink). This shows that the new model, while still having a systematic latitudinal dependence, represents a clear improvement over the old version. One possible explanation of the decreasing model / observation ratios with latitude might be that in-cloud scavenging in ice clouds is too effective. However, sensitivity simulations where only INeff was reduced (not shown) revealed that this change had only a small effect in further reducing the latitudinal bias. One of the possible causes of this is the high proportion of mixed phase clouds (77 %) which reduces the impact of the latitudinal dependence of the frequency of ice-phase clouds after that much time for an emission pulse. Another possibility is that cloud phase is not well captured by the ECMWF model, as in many other models . It may also be relevant that the clouds have on average higher cloud tops near the equator, so that temperature and thus the mixing state of clouds does not have a strong enough latitudinal dependence in the Northern Hemisphere at the time of this simulation (March–May).

It has been notoriously difficult to model BC accurately. For example, Arctic seasonal variations and Arctic haze periods are not captured well in most models . Some of this can be accredited to BC aerosol undergoing stages of transformation after its release to the atmosphere from a hydrophobic to a hydrophilic state e.g.,. The aerosol ageing processes that would influence in-cloud scavenging are not readily included in FLEXPART and the constant removal parameters cannot account for this transformation. Therefore, several aerosol parameter combinations were tested with FLEXPART both in backward and forward mode. There are observations that urban BC is transformed very quickly into particles with aged, hydrophylic characteristics . Therefore, a representation resembling physical properties of aged BC (BC #1 in Table ) was selected as our reference set-up for BC. Our assumptions regarding the values of CCNeff and INeff were based on the findings of that BC is much more efficiently removed in liquid water clouds than in ice clouds. showed that aerosol composed of mainly elemental carbon had the highest fraction of non activated particles. A size distribution with a modal mean diameter of 0.15 µm was assumed.

In addition to our simulations for our reference BC species, seven other simulations were performed to test the sensitivity of model results at different latitudes, altitudes and times of the year to changes in the parameters describing the different removal mechanisms. For this, parameter settings were varied within ranges thought to be suitable for BC. Table  summarizes the parameter choices for these simulations.

Column burdens and vertical distribution of the eight simulations are shown in Fig. . The concentrations are FLEXPART output from five vertical layers with upper borders of 100, 1000, 5000, 10 000 and 50 000 m. The BC column burdens (shown with white lines in Fig.  on the right hand side y axis) are overall somewhat high when compared to other studies e.g.,, with the exception of simulation #4, which has strongly enhanced in-cloud removal. The dashed black line shown in all the panels is the column burden of the reference simulation (#1).

All simulations produce a quite similar latitudinal distribution. The strongest sources of BC are at mid latitudes and most of BC at high altitudes is also found in this region for all simulations. Thus, the highest column burdens are found near 35∘ N in all simulations. The two simulations with reduced in-cloud scavenging (#2 and #8), have the highest column burdens. While increasing Crain by a factor of 10 (simulation #5) reduces the burden significantly, a similar, but an even stronger effect can be achieved with a reduced aerosol size (simulation #3), as smaller particles have higher dry deposition velocities. This shows that in the absence of efficient wet removal, dry removal can be important as well. Though it generally accounts for less than 10 % of total removal in our simulations for particles with d<1 µm, in simulation #3 it accounts for 48 % of the removal. Only simulations #5–#8, which have phase dependent changes to removal parameters, produce burdens with a noticeable different dependence on latitude when compared to simulation #1.

Annual average calculated BC concentrations in the surface layer (0–100 m) in the northern hemisphere are shown in Fig.  for the reference simulation (top left) and as differences from this reference for the other seven simulations. Overall, there are only small differences between the various model runs in the major BC source regions, where the concentrations are strongly influenced by local emissions. Further away from the source regions, differences in removal have a stronger effect. Simulation #4, with enhanced in-cloud scavenging in both liquid and ice clouds, stands out with very low concentrations in the Arctic and other remote regions. The remaining simulations have concentrations within ±50 %. It is worth noting that there are a few distinct geographical features in Fig. . For example, turning off the below-cloud removal by snow (simulation #6) only has a small effect that can be seen north of 60∘ N. In simulation #8, where liquid in-cloud removal is reduced, modeled surface concentrations are increased in remote tropical areas. Simulation #7, where the overall removal efficiency is maintained, but no differentiation of cloud phase is made, illustrates the relative effect of the cloud phase dependency of in-cloud removal.

The monthly measured (black) and modeled (blue; simulation #1 in Table ) BC concentrations at six measurement stations are shown in Fig. . The station locations are marked in Fig.  and are at different distances from major source areas. The aerosols measured at the different stations thus have very different ages. For simulation #1, at Melpitz the mean mass weighted FLEXPART aerosol age is 1.3 days, at Pallas it is 3.8 days and at Zeppelin it is 7.7 days. The age is defined as the time it takes for the aerosol to reach the station after its emission. The aerosol age depends not only on the transport, but also on the removal between emission and observation.

Increased removal efficiency would, on average, reduce aged BC more than fresh BC, resulting in a less aged aerosol population. Systematic differences in model bias for stations close to and stations far away from source regions can thus allow to separate errors in emissions versus errors in simulated aerosol lifetimes. In Table  the median modeled concentrations at the six stations are reported for all the sensitivity simulations. Seven of the eight simulations overestimate the concentrations at Melpitz by a factor of almost 2, especially in summer (Fig. ). This suggests that local emissions around Melpitz are too high, as changes in the removal parametrisation have little effect on the concentrations (Table ).

Moving away from the source regions, stations Southern Great Plains and Pallas have model concentrations close to the observed average for all the simulations except for simulation #4 which underpredicts the concentration at these two stations by a factor of 2.1 and 8, respectively. Annual mean BC concentrations at the three Arctic stations Alert, Barrow and Zeppelin are underpredicted by the model (mainly due to very low simulated summertime concentrations, see Fig. ). This alone would indicate a too fast removal and thus a too short BC lifetime. However, indicative of total global removal rates, the column burden is, also for the Arctic, on the high side of most current model estimates and therefore also burden/emission estimates of the BC lifetime of 9.0 days is higher than in many other models .

Observations at all stations except Southern Great Plains have a seasonal cycle, with lowest concentrations during summer and higher concentrations during winter. The Southern Great Plains station has a somewhat different seasonality than the other stations, with a peak in autumn, and this is quite well captured by the model. The four higher-latitude stations all show a pronounced winter/spring peak, which is well reproduced by the model. .

In Fig.  (bottom panel) a comparison between the observations and model simulation #1 and a simulation using FLEXPART v9 is shown as a 48 h moving average. With a Pearson's squared correlation coefficient of r2=0.44, simulation #1 captures nearly half of the variability of the observations with generally higher concentrations during December–May, and large peaks in the observations in January and December. There are noticeable differences between the two simulations, but not all of them are due to wet removal as FLEXPART v10 includes also other changes than the removal. Also, the concentration simulated using v9 is a point estimate from a backward simulation and simulation #1 a (1∘×1∘) grid average from a forward simulation, so they are not directly comparable. Of most significance however is the higher concentrations in the spring months April–May, where simulation #1 capture the observed high levels of BC and the v9 does not. On average for the year, v10 concentrations are about twice as high as the v9 data with annual median (9.5 and 6.8 µg), median (9.5 and 6.8 µg) and mean (47.6 and 21.1 µg) values for the two respectively.

FLEXPART aerosol age at Zeppelin was also used to examine the role of the removal processes in the variability. showed observed concentrations of aerosol submicron mass had a strong dependence on trajectory accumulated precipitation. Shown in the top panel in Fig.  is the mean model age corresponding to 6-hourly observations. Also a smoothed 48 h fit is shown in red. Depending on the season, the youngest BC aerosols are found in combination with either the highest observed concentrations (winter) or very low concentrations (summer) and have two different explanations. The high aerosol episodes with low age in winter (e.g., peak on 15 January) are related to fast transport from the Yamal Peninsula and the Kara Sea. In this area there are large emissions from the gas and oil industry , and if these emissions are transported quickly and nearly without removal to Zeppelin, concentrations there increase strongly. In summer, there is a persistent background of relatively low aerosol concentrations. Occasionally, this background is reduced further by scavenging events occurring close to the station. This removal only leaves BC from the small local sources of BC on Svalbard, leading to both a low age and low concentrations of the simulated BC.