Here we present a direct comparison of measured and modelled aerosol lifetimes based on an observational constraint provided by radionuclide measurements of the FD-NPP emissions. We investigate the causes of differences between the measurements and models. The measured and modelled aerosol lifetimes are estimated from the ratios of the aerosol (137Cs) to the passive tracer (133Xe) surface concentrations (Sect. 4) at 11 CTBTO measurement sites (Sect. 3) as shown in Fig. 3. Both the measurements and all model simulations show a decrease in these ratios with time due to the removal of aerosols. The aerosol lifetimes are estimated by fitting an exponential decay model (grey lines in Fig. 3) to the daily median ratios over all stations (black triangles; ω in Fig. 3), between 15 and 65 days after the start of the emissions on 11 March. During this time period, measurement data exist from at least five stations each day; i.e. the daily median value ω is calculated from at least five values. The data density before day 15 and after day 65 is quite sparse and there are sampling biases. Before day 15, the measurements are mainly from the closest stations as the plume has not yet reached all sites and mixed through the Northern Hemisphere. After day 65, valid measurement data become sparse because concentrations start to drop below the detection limit and all data below the detection limit were discarded. The remaining valid data after day 65 are mainly from Yellowknife and Spitsbergen with values near the detection limit. If these periods were considered, the lifetimes would be biased high, possibly due to a latitude effect, discussed later.

The measured aerosol (137Cs) to the passive tracer (133Xe) ratios decay with an e-folding lifetime τe (Eq. 1) of 14.3 days (Fig. 3 and Table 2) with a 95 % confidence interval of 13.1–15.7 days (Appendix B and Table B1). The equivalent modelled τe lifetimes vary between 4.8 and 26.7 days with a model mean (±standard deviation) of 10.7 ± 5.5, and a model median (±MAD, Eq. 3) of 9.4 ± 2.3 days (Table 2). Thus, the model mean and median lifetimes are shorter than the lifetime based on the measurements, indicating too quick a removal of the aerosols in the models. However, some individual models have longer lifetimes than measured, and the model mean ±standard deviation encompasses the measured lifetime. Large variations in the modelled lifetimes are expected due to differences in the simulated transport and especially tropospheric removal.

Table 2 shows the lifetime estimates using data only from stations below and above 50∘ N separately. Both measured and mean modelled lifetimes are shorter below 50∘ N than at high latitudes, suggesting less efficient aerosol removal at high latitudes during the time period investigated (March–June). However, a few models (NorESM, ULAQ-CCM, EMAC-1, EMAC-2, and NAME) also have somewhat shorter lifetimes at higher latitudes than at lower latitudes, and two models (CAM5 and FLEXPART) show no change in lifetime with latitude. H. Wang et al. (2013) found that CAM5, with the shortest lifetimes of all models, overestimates aerosol wet removal by super-cooled liquid in mixed-phase clouds, which was improved in CAM5_PNNL. There is a larger spread in model lifetimes and larger deviations from the measurements at high latitudes compared to at lower latitudes, indicating larger uncertainties in the simulation of aerosols at higher latitudes. Similarly, lifetime estimates from the earlier phases (25–45 days after the start of the release, a period when the major emissions were over) are compared to those for later time periods (days 45–65) (Table 2). Both the measurements and the median model give slightly longer lifetimes (by about 0.3–1.0 days) for the earlier phases than for later time periods. This is perhaps unexpected as the radionuclides are initially located in the lower troposphere where they are strongly affected by precipitation scavenging and dry deposition, and later when the radionuclides are mostly located in the relatively dry upper troposphere (or even stratosphere), the removal processes are much less effective which would yield an increase in lifetime. However, since the data used to derive the lifetimes are ground-based and thus biased towards that part of the aerosol population residing in the lower troposphere, neither the measurements nor the models may fully reflect the increase in lifetime due to transport in the upper troposphere. Differences in lifetime between tracers emitted near the surface and those coming from the stratosphere may be substantial, as discussed in Kristiansen et al. (2012). Furthermore, most of the radionuclides were uplifted immediately after the release (Stohl et al., 2012a) and thus quite well mixed in the troposphere already for the earlier time period (days 25–45), as also shown in Fig. 2. In addition, station data from the later time periods (day 45–65) include fewer data points in the calculations than in the earlier phases. Lastly, there are larger variations in the modelled lifetimes for the later phase, and a larger model to measurement deviation, indicating larger uncertainty in the modelled lifetimes for the later phase than for the earlier phase.

In summary, both the mean and median modelled aerosol lifetimes are somewhat shorter than the observed aerosol lifetime, although they mostly agree within the standard deviations of the modelled lifetimes. The underestimation of lifetimes by the models is smaller than what was indicated by Kristiansen et al. (2012) based on reported mean modelled lifetimes from the literature, consistent with the findings of Croft et al. (2014). The deviations between observed and modelled aerosol lifetimes are largest for the northernmost stations and at later time periods, indicating higher uncertainties in the simulation of aerosols and aerosol lifetimes at higher latitudes and later times.

The previous section indicated that disagreements between the measurements and the models are largest at higher latitudes and at later time periods. This agrees with several previous studies (e.g. Shindell et al., 2008; Koch et al., 2009), which suggest that models do not capture the Arctic aerosol variations very well. In this study, we have the possibility to evaluate the models' abilities to simulate the aerosol concentrations and transport at different latitudes, by comparing the measured and modelled aerosol (137Cs) and the passive transport tracer (133Xe) data. In this way, we can directly explore how well the models are able to reproduce the observations at the northernmost stations (i.e. above 60∘ N; Yellowknife 62.5∘ N and Spitsbergen 78∘ N) compared to at lower latitudes. We also examine whether there are any temporal variations in the model–observation deviations. The analyses are limited by the low number of Arctic/subarctic stations and the particular season and time period (March–June 2011) of the measurements. Some indications may still be given which might help explain shortcomings with simulated scavenging and/or transport in the models, and if one is the more likely cause for deviations to observations.

We use the ratio of the modelled to measured surface concentrations as means of model score, where a ratio > 1 indicates that the model over-predicts, and a ratio < 1 represents under-predictions (Tables 3 and 4). Figure 4 shows the ratio of modelled to observed aerosol (green circles) and passive transport tracer (blue circles) concentrations as a function of latitude of the measurement stations. Generally, the models reproduce the observed passive tracer (133Xe) values better than the observed aerosol (137Cs) values, indicating that transport is reasonably well represented in the models. Scavenging affects only the aerosols, causing more variability and a larger extent of over- or under-prediction. On average, over all stations and models, the median ratio of modelled to measured passive tracer values is 0.79 (Table 3) and for the aerosols 0.49 (Table 4), suggesting a general under-prediction of both aerosol and passive tracer concentrations. The aerosol underestimation is consistent with the lifetime results from the previous section (Sect. 5.1) which showed that modelled aerosol lifetimes are too short compared to the measurements, and this would yield too much removal and thus under-predictions of the aerosol concentrations.

Furthermore, at the southernmost stations (Wake Island and Oahu) many models over-predict both the aerosol and passive tracer concentrations, whilst under-predicting both at the stations further north (Tables 3 and 4). The exception is Schauinsland (48∘ N) where the models generally over-predict the passive tracer but under-predict the aerosol values. We find the largest under-prediction at the northernmost stations: Yellowknife for the passive tracer and Spitsbergen for the aerosol values. The modelled to measured aerosol ratios have a pronounced latitudinal trend, with ratios decreasing (i.e. larger under-predictions) with increasing latitude (Table 4 and Fig. 4). This indicates that there is too much aerosol removal occurring en route to the Arctic. There is also a slight decrease in modelled to measured passive tracer ratios with latitude (Table 3 and Fig. 4), suggesting that transport to the high latitudes is also not strong enough in the models, and this contributes to the aerosol underestimates at high latitudes. However, the main reason for the aerosol underestimates at high latitudes must be too efficient a simulated removal.

Finally, Fig. 4 illustrates the temporal variations of modelled to measured ratios. The values are medians over 14 day time periods and the size of the circles indicates the time; the larger the circle, the later the time period. Particularly for the aerosol values, some models tend to show a stronger underestimation with time, also evident in the median model.

Our results suggest that modelling of both scavenging and transport are causes for disagreements with observations. Transport to the high latitudes is not strong enough in the models, and this contributes to the model underestimates also of the aerosol tracer at high latitudes. However, the modelled to observed ratios decrease much more strongly with latitude for the aerosol than for the passive tracer, and this indicates that a problem with the aerosol scavenging is the major reason for disagreement between the simulations and the measurements. Scavenging in the models depends strongly on the representation of clouds (temporal and spatial occurrence and dimensions) as well as on the amount of precipitation, which are likely to be the underlying issues. This helps explain the larger deviations between measured and modelled aerosol lifetimes for the northernmost stations and at later time periods as seen in the previous section (Table 2).

The time variations in aerosol lifetimes can be examined further by considering the instantaneous lifetimes, τinst (defined in Sect. 4). In this section we use global modelled data as opposed to the previous sections that focused on modelled concentrations at the measurement stations. The estimate of instantaneous lifetimes uses the global aerosol (137Cs) and passive tracer (133Xe) burdens as simulated by the models. Kristiansen et al. (2012) also provide an estimate for the burdens using the station measurements and a 1-D box model. This estimate is however limited by the assumption of a well-mixed state in the atmosphere and only valid approximately after about 3 weeks after the release until about 9 weeks (Appendix C). Therefore, global burdens estimated from the measurement data are only available for a limited time period. The global burdens are shown in Appendix C and Fig. C1. The modelled global aerosol (137Cs) burdens increase initially due to continuous cesium emissions but decrease as the aerosols are removed from the atmosphere, while the passive tracer (133Xe) global burdens stay approximately constant in the models after the xenon emissions cease. In the following, we analyse the instantaneous lifetimes obtained from the global burdens.

We use the ratios of the aerosol (137Cs) to the passive tracer (133Xe) global burdens, and calculate the instantaneous lifetimes (Eq. 2) from these ratios, as shown in Table 5 and Fig. 5. In the first week after the start of the release, the modelled instantaneous lifetimes are about 2 days (Table 5), much shorter than the e-folding lifetimes presented in Sect. 5.1 for later time periods. This illustrates that the initial removal was quicker, as previously suggested by Kristiansen et al. (2012) and illustrated in Croft et al. (2014). This is due to the emissions occurring at low altitudes and co-location of the plume with strong precipitation. After about 3 weeks, estimates for the instantaneous lifetimes from the measurement data are also possible and give a lifetime of 9.3–10.9 days, which is mostly longer than the median model lifetime of about 6.0–10.4 days (Table 5). After about 7 weeks (day 45–50), the instantaneous lifetimes reach some quasi-steady state with less variability (Fig. 5). The occurrence of this less variable steady state is related to the emissions. Between day 10 and 40 there are low-level emissions of 137Cs, about 1 order of magnitude less than during the highest emissions around day 5. Because the emission was a point source (and not global) and its geographical distribution is rather local, one continues to see the impact of single deposition events, making the instantaneous lifetime fluctuate considerably. On day 40 all emissions of 137Cs end in the model simulations. The planetary boundary layer (PBL) is soon emptied of most 137Cs, and the remaining 137Cs (mainly in the free troposphere) is more widely spread and gives rise to a more stable instantaneous lifetime, and thus a quasi-steady state with less variability. The modelled instantaneous lifetimes over days 49 to 63 (weeks 8–9; shaded area in Fig. 5) vary between 2.8 and 19.0 days with a model median of 10.4 ± 2.5 days. The median instantaneous lifetime for the same time period based on the measurements is 9.6 ± 0.7 days. In this period, the median modelled lifetimes are closer to, but slightly longer than those based on measurement data, in contrast to earlier phases. This could be due to more prominent modelled than real mixing into the stratosphere where lifetimes are longer. This stratospheric mixing is not evident in the surface measurement data.

The further steady increase in the instantaneous lifetimes in the later phases after about day 65 (Fig. 5) is attributed to transport and mixing into regions where the lifetimes are longer, such as the upper troposphere and the stratosphere. After some time, the troposphere is mainly cleaned by wet scavenging while aerosols that have been transported into the stratosphere remain, as the removal there is inefficient, especially for AM aerosols for which also gravitational settling is very slow. The total aerosol mass and the lifetimes are then dominated by the stratospheric loading, giving a continuous increase in lifetime (Cassiani et al., 2013). The large variations in the steady increase of instantaneous lifetime between models might be related to how the models simulate transport into the upper troposphere and stratosphere. The longest lifetimes at later stages are probably given by models that inject a fraction of the aerosols quickly into the stratosphere (probably even by a single event) and have an efficient removal in the troposphere, which would give a large (and increasing) fraction of the aerosols residing in the upper troposphere and stratosphere. Furthermore, models with diffusive advection schemes may excessively “leak” aerosols into the stratosphere. Thus, the instantaneous lifetimes at later stages are probably more indicative of the upper tropospheric/stratospheric aerosol fraction and are less useful to constrain tropospheric removal. In addition, the well-mixed assumption required for the measurement-derived lifetimes breaks down once a substantial fraction of the material is in the stratosphere. This means that measurement-derived and model-derived instantaneous lifetimes for the later phases are not entirely comparable, as they are not derived in a consistent way. It is expected that the measurement-derived instantaneous lifetimes are systematically lower, since they are based on surface measurements with the assumption of a constant scale height. Calculating the global burdens based on the modelled station data and the box model reveals that for some models, the box-model estimates indeed underestimate the full global burdens (see Appendix C and Fig. C1).

In summary, we find that the modelled instantaneous lifetimes were initially short (about 1–2 days) and the initial removal quicker than for later time periods. At later times (weeks 4–7) the instantaneous lifetimes obtained by measurements were generally longer than obtained from the models, as also seen in Sect. 5.1 from station locations. After that, the modelled instantaneous lifetimes are influenced by mixing into the stratosphere and not representative anymore of scavenging processes in the troposphere.

To interpret our estimates of aerosol lifetime, we first discuss an exemplified evolution of the aerosol burden after a unit pulse emission (Fig. 6). In our example, the decay of the burden is not perfectly exponential but consists of different characteristic timescales. There is a fast initial removal with a short time decay τ1, which represents the time period when the aerosols are mostly residing in the PBL and are very susceptible to dry and wet deposition. The second period has slower removal with a timescale τ2, and represents the period when most of the aerosols are residing in the free troposphere. The last time period, with the slowest decay timescale τ3, is the period when most of the aerosols are removed from the troposphere and only the fraction that was transported into the stratosphere remains.

The exemplified curve would depend on where on the globe the emissions take place, during which season, and it might differ from year to year. Thus, the timescales will vary greatly for different cases, and also for different models simulating the meteorology for the given case differently. τ1 would be very different for all cases, probably depending on a few precipitation events, while different cases and models would have a smaller spread for τ2 and τ3 which are affected by processes on a more global scale. Global mean lifetimes (e.g. Croft et al., 2014) would be mainly determined by the initial behaviour (τ1) and it could be argued that knowing the initial lifetime is important for estimating the aerosol burden, the radiative forcing, and climate sensitivity.

In this study we focus mainly on the intermediate timescale τ2 because sufficient measurement data were only available from about 2 weeks after the start of the release, until about day 65 (Sect. 5.1). We do not have sufficient measurements to constrain τ1, but it is likely that some of the same processes contribute to the determination of both τ1 and τ2. While τ1 is probably mainly impacted by processes within the PBL, τ2 is additionally influenced by how the aerosols are mixed out of the PBL, transported in the free troposphere, and finally brought back into the PBL. That way it is possible that models that capture τ2 well also perform well for τ1. In our case, another difference between τ1 and τ2 is that the former was mostly determined by a few individual precipitation events near Fukushima, while the latter is determined by removal occurring worldwide.

The evolution of the burden in Fig. 6 can be approximated by the sum of three exponential functions, i.e. ft=f1exp-tτ1+f2exp-tτ2+f3exp-tτ3, where f1+f2+f3=1.

A mean lifetime can be calculated as τm=f1τ1+f2τ2+f3τ3, which corresponds to the area under the curve f(t).

Using an optimizing convolution approach we can find the coefficients in Eq. (4) which give the best agreement between the aerosol burdens obtained from the model simulations (Appendix C) and the expression in Eq. (4). Table 6 shows the characteristic timescales τ1, τ2, and τ3 obtained from the convolution approach, calculated for the different models from their aerosol (137Cs) burdens, as well as the mean lifetime τm (Eq. 5). The initial timescale τ1 is fastest and around 2 days, which is related to the low-altitude emissions of hydrophilic aerosols. The intermediate timescale τ2 is around 12 days, and the longest timescale τ3 about 150–200 days. The estimated τ3 is very uncertain for most models as it is very close to the a priori estimate of 200 days. The exceptions are the NorESM and GISS-ModelE models which had longer time series available. The model mean and median for τ3 are therefore calculated based on these two models only. The mean lifetime τm is rather short, on the order of 2–3 days, and is strongly affected by τ1, which was also demonstrated by Croft et al. (2014). The estimate for τ2 shows good agreement with the instantaneous lifetime τinst over weeks 8–9 from Fig. 5 and Table 5, and for most models the e-folding lifetime τe from Fig. 3 and Table 2 also fits well with τ2. This clearly demonstrates that in this study the focus is on the intermediate timescale τ2.

Our results show that there are significant deviations between aerosol lifetimes obtained from models and those obtained from observations. The modelled lifetimes have a large spread but are generally shorter than the observed lifetime. In addition, large biases in model to observed surface concentrations were found, with an overall under-prediction of both the aerosol (137Cs) and passive tracer (133Xe) concentrations. The model–observation deviations can be due to inaccuracies in the source emissions, errors in scavenging and convective transport, and incorrect diffusivity of the models. These issues are discussed more in the following.

Inaccuracies in the source emissions will affect the absolute model-simulated values and therefore the biases in the model to observed concentrations (Tables 3–4 and Fig. 4). It cannot be ruled out that our 137Cs emissions are too low, or there were errors in the injection heights. However, the 137Cs source term used is rather on the high side compared to others (e.g. Chino et al., 2011). Also, the 133Xe source term has been confirmed independently (Stohl et al., 2012b) and has rather low uncertainty. Overall, uncertainties in the assumed source term and its implementation are likely not the main reasons for the general underestimation of the aerosol (137Cs) and passive tracer (133Xe) concentrations. The lifetime estimates (Fig. 3 and Table 2) are not affected by the absolute values of the source term used. However, these lifetime estimates would be affected by possible late emissions of radionuclides long after the start of the release. Such late additional releases could be either direct late emissions from FD-NPP or indirect releases by resuspension of deposited radionuclides. Kristiansen et al. (2012) discussed this uncertainty and found no evidence for such late emissions, neither in the measurement data nor in the existing literature on the FD-NPP accident.

Most models have treated cesium solely as sulfate aerosols, while it is possible that some of the cesium attached to other aerosol components with different deposition properties. Initially, many non-soluble aerosols could have been present around the power plant, which might be removed less efficiently from the atmosphere in the first days after emission before mixing internally with soluble aerosol components. The assumption that cesium attached solely to sulfate could result in scavenging that is too strong during the first few days after the release, and can therefore contribute to the overall underestimations of the aerosol (137Cs) concentrations (Table 4). The e-folding lifetimes (Table 2) should not be affected by errors in the modelled scavenging efficiency in the initial phase (τ1 in Fig. 6), as the e-folding lifetimes have been derived only for later periods (after 15 days, i.e. τ2 in Fig. 6) when the aerosols are likely internally mixed and aerosol components undergo similar removal.

More importantly, the models' treatment of aerosol scavenging is essential for both the modelled lifetime and absolute concentrations. The modelled representation and distribution of clouds, as well as rain patterns and rain intensity, are important factors since they determine where and how much aerosol is removed. Further, the horizontal resolution of the model and meteorological input data might have a large impact in terms of clouds and precipitation (intensity and spatial extent). Higher horizontal resolution can in general lead to more resolved large-scale and less sub-grid convective clouds (Hagemann et al., 2006). The scavenging parameterizations, including cloud and rain definitions and occurrences, differ greatly between the models (Table A1), and are likely the major cause of model differences and deviations between models and observations. This issue is further discussed in Sect. 6.6.

Additionally, the coupling between aerosol scavenging and the convection scheme in the models may represent a large source of uncertainty and thus contributes to both model–observation deviations and differences between models. Different aerosol amounts may reach the dry upper troposphere depending on how aerosols are scavenged in convective updrafts and whether updrafts are allowed in the convection scheme to overshoot the level of neutral buoyancy. This has an immediate impact on lifetime via the convective scavenging and also longer term effects, depending on how much aerosol can reach the upper troposphere. Finally, the diffusivity of the models, i.e. either pure numerical diffusivity or apparent diffusivity caused by less representative winds, may be an important cause of the deviations between the models and observations, and the differences between models. If the models are too diffusive, they may unphysically transport aerosols to higher altitudes where they are preserved. Once too much aerosol mass reaches high altitudes, e-folding lifetimes would be very long. At the same time vertical diffusion that is too excessive would mean that the aerosols are not confined sufficiently to the lowest model levels (Koch et al., 2009) and thus the models will probably underestimate mass near the surface. These topics of coupling convection with scavenging, and diffusivity should be investigated further.

Comparing the lifetime estimates in Table 2 and the aerosol concentration bias values in Table 4, it seems that some models have a large bias to the measured aerosol concentrations, yet still have a realistic lifetime. For example, OsloCTM3 has a relatively small bias (ratio 0.76, i.e. -24 % relative bias) and a lifetime of 8.8 days, while OsloCTM2 highly underestimates the aerosol concentrations (ratio 0.02, i.e. -98 % relative bias) and has a lifetime estimate of 11.2 days, closer to the lifetime estimate from the observations (14.3 days). This is probably because the concentrations are strongly influenced by the treatment of the quick removal in the first few days when the plume was at low altitude and co-located with areas of strong precipitation, whereas the lifetimes derived for later time periods are insensitive to this initial removal. Depending on how the models simulate this initial episode (e.g. how the aerosol plume and precipitation areas align), different amounts of aerosols can survive the first few days. This is clearly seen in Fig. 7, which shows how the total atmospheric aerosol (137Cs) burdens for the different models vary over the first 3 weeks after the initial release. As an example, OsloCTM2 has stronger aerosol removal than OsloCTM3 during the first 3 weeks. Further, even relatively small differences in lifetimes can lead to large concentration differences after several multiples of the lifetime. For instance, assume tracers with 6 and 10 days' e-folding lifetimes. After 60 days, total atmospheric burdens of these two tracers will differ by a factor of 50 (reduced to 1/403 and 1/22 026, respectively, of the initial burden). This might also explain why aerosol models differ so widely from each other at later times (e.g. in remote regions like the Arctic), whereas they agree much more closely in earlier time periods and closer to the source regions (e.g. Table 4).

Additionally, by comparing the instantaneous lifetimes in Table 5 with the aerosol concentration bias values in Table 4, the models with positive biases (greater than 1, i.e. overestimation of the aerosol concentrations) tend to show longer instantaneous lifetime in the first few weeks (Fig. 8a). The models that strongly underestimate the aerosol concentrations have a shorter instantaneous lifetime in the first weeks. This confirms that the initial quick removal is modelled differently by the various models, which affects the absolute concentrations and bias calculations. Furthermore, there seems to be a positive correlation of lifetimes for different time periods (Fig. 8b). Most models that have short instantaneous lifetimes in the first 3 weeks also have short instantaneous lifetimes for later time periods.

Our results show that there is a large spread in the model results. This is due to the different ways the models simulate transport and scavenging. We note that the range of models in our analysis is quite wide. Many are developed for climate applications and may have been adapted for longer lifetime aspects, while others are more focused on dispersion and transport on a shorter timescale. In addition, some models are related to each other, which will affect the model ensemble. However, as some models are related by driving meteorology, others are related by aerosol module, which makes it difficult to categorize this appropriately.

Sensitivity simulations of the NorESM model (not shown) indicate that between five ensemble members, all simulating their own meteorological conditions, there were no large differences in lifetime. This suggests that the lifetime estimates are independent of the meteorological situation, although the difference between the different models might be greater than a perturbed ensemble of one model, and resolution effects might also play a role. Croft et al. (2014) showed that the e-folding lifetimes do not depend very much on the exact model set-up (emission altitude, location, and time). Therefore, the model's scavenging parameterizations are likely to be the main cause of inter-model differences in e-folding times in this study, especially at time periods around 15–65 days after the release start.

The vertical distribution of the modelled aerosols will likely differ substantially between the various model simulations. At later time periods, the troposphere would be mainly cleaned by wet scavenging while aerosols that have been transported into the stratosphere (or upper troposphere) remain, as the removal there is inefficient. The total aerosol mass and the lifetimes are then dominated by the upper tropospheric and stratospheric loading, giving an increase in lifetime (Cassiani et al., 2013). The different stratospheric loadings might therefore be a cause of large model differences. For example, in the OsloCTM2 and OsloCTM3 simulations, about 70–80 % of the burden is stratospheric at the end of the simulation. OsloCTM2 has a higher stratospheric loading than OsloCTM3, which might be related to its coarser resolution and thus stronger diffusion, which partly explains why OsloCTM2 generally has a longer lifetime (Table 2). By calculating tropospheric burdens and the associated lifetimes (burden relative to wet deposition, not shown), this yields the lifetime with respect to scavenging without the effect of stratospheric mixing; then the lifetime for OsloCTM3 is longer than for OsloCTM2, highlighting the impact of the different stratospheric aerosol loadings at later times.

The vertical distribution of the aerosols is explored further for four different models which span the range in modelled lifetimes, FLEXPART with a short lifetime (∼ 6 days), EEMEP with the longest (∼ 27 days), and OsloCTM3 and NorESM with lifetimes closer to, but still lower than the measurements (8.8 and 10.5 days, respectively). Figure 9 shows the total aerosol (137Cs) mass as a function of latitude for these four models, in four different height layers (surface, 0–5, 5–10, and above 10 km) at three different time steps (14, 28, and 41 days after the first emissions). The aerosol concentrations in the surface layer (lowest model level) peak around the latitude of the emission pulse for all models. FLEXPART and NorESM generally have more aerosols at the surface than OsloCTM3 and EEMEP and this is particularly evident at the northernmost latitudes. The same trend can be seen in the lower troposphere (0–5 km) except OsloCTM3 is closer to or above FLEXPART while NorESM has consistently more mass at these heights. At higher altitudes (5–10 and above 10 km), OsloCTM3 and NorESM have the most aerosol mass. This indicates that models with lifetimes closer to the measurements have more mass at higher altitudes. The FLEXPART and EEMEP models with lifetimes that deviate more from the observations show lower fractions of the aerosol mass at higher altitudes.

The passive tracer also shows large differences between models (e.g. Table 3). Even models from the same “family” (e.g. GISS, CAM, and ECHAM) give quite different results for the passive tracer. In addition, the four models based on ECHAM5 seem to simulate the passive tracer transport quite differently. This could be due to differences in the driving meteorological fields or advection schemes used in the models. The tracer transport is affected by four processes: (1) large-scale transport, (2) convective transport, (3) turbulent transport, and (4) artificial numerical diffusion. All four processes are sensitive to horizontal and vertical resolution, even if the models are all nudged towards the same reanalysis. Another possibility is that the implementation of the point source was treated differently in the models; e.g. the flux was added at slightly different times (before or after certain physical processes) in the model (see Fig. 7). To identify the exact reasons why there are such large differences warrants a further study.

In this study we have used modelled surface concentrations at the times when observation data exist, amounting to 433 data points over all 11 stations and measurement times (March to June 2011) considered. Croft et al. (2014) did a similar lifetime estimate but derived from modelled surface concentrations of 137Cs from continuous time series at the 11 stations during March to June 2011 using about 19 000 hourly values. They found a lifetime for GEOS-Chem of about 16.7 days, while in this study the lifetime estimate for GEOS-Chem is longer (20.2 days). For five other models (GISS-modelE, FLEXPART, BCC SGCM CAM, EMAC-1, and EMAC-2) we calculated the difference in the estimated lifetime using continuous (1-hourly or 3-hourly) time series at the stations, compared to using only the 433 data points at the times of the measurements. For all five models, the lifetime is slightly shorter (by 0.2 to 0.9 days) when using the continuous data than when using only data at the measurement times, but the difference is much smaller than for GEOS-Chem (3.5 days). GEOS-Chem is sensitive to the initial scavenging and transport as apparent in Fig. 3 by the anomalous values at Wake Island in the early time period. Insufficient scavenging at mid–high latitudes may also play a role, as seen in the overestimation of aerosol concentrations in Table 4, and this seems to contribute to the longer lifetime for the selection of points used in this study. Further discussion on the scavenging parameterization in GEOS-Chem is given in Sect. 6.6.

Another issue with the measurement sampling is how to deal with measurement values below the detection limit (BDL). In our analysis we have discarded all data BDL, however, this might bias the measurements high. To address this, we did a sensitivity test where all measurement values BDL were set to 1% of the detection limit, and were included in the analysis. This increased the number of station values from 433 to 495. The stations with the most data BDL are Ulan Bator, Ashland, and St. Johns, and the BDL values occur mostly between days 40 and 70. During days 15 to 65, the time period of the lifetime estimate in Fig. 3, there are 38 BDL values mostly at Ulan Bator and Ashland. Using also BDL values in the analysis, the e-folding lifetime over days 15–65 decreased by 0.7 days (from 14.3 to 13.6 days) compared to when discarding BDL values. This illustrates that a small bias might be present when removing values BDL, but the difference is not significant, indicating that the measurement numbers are robust to BDL values. Besides, since exactly the same stations' data points are used for the derivation of the e-folding lifetimes from the measurement data and the modelled data, it is likely that the same bias is present in both the modelled and measurement data sets, and therefore the comparison of modelled and measured lifetimes remains valid.

A sensitivity test with the NAMEIII model was done (not shown) where the model's scavenging coefficients were decreased by a factor of 10. It is not suggested that the initial scavenging coefficients were a factor of 10 too high, but it was done to demonstrate the results of running the model with different scavenging coefficients. Decreasing the scavenging coefficients by a factor of 10 increased the e-folding lifetime from 5.5 to 13.1 days (not shown), illustrating the dependency of estimated lifetimes on scavenging treatment.

Further, recent revisions to GEOS-Chem that introduce an explicit dependence of wet removal efficiency on (1) cloud liquid and ice water content, (2) cloud temperature, and (3) cloud fraction from the assimilated meteorological fields have yielded about 40 % lower mean lifetimes in the Arctic spring and summer (Croft et al., 2015; Q. Wang et al., 2014). Two revised simulations based on these changes, GEOS-Chem_T258 and GEOS-Chem_allT, are included here (Fig. 10 and Table 7) for comparison to the default scavenging in GEOS-Chem (GEOS-Chem_Orig, same simulation as labelled GEOS-Chem in all previous tables and figures). Simulation GEOS-Chem_T258 updates the scavenging scheme relative to GEOS-Chem_Orig through processes (1)–(3), but preserves the restriction for large-scale in-cloud scavenging of aerosols to temperatures above 258 K. Simulation GEOS-Chem_T258 produces a significantly lower aerosol concentration bias (1.69 vs. 5.53) relative to observations (Fig. 10). In addition, the e-folding lifetimes for the station data are shorter by up to 6 days (Table 7). These improvements imply that using an explicit dependence of wet removal rates on cloud properties may be necessary to properly capture aerosol lifetimes. Simulation GEOS-Chem_T258 yields the greatest change in the lifetimes for earlier periods (about 30 % for days 25–45, Table 7), indicating that these scavenging revisions influence removal efficiency in or near the boundary layer more than in the free troposphere. The simulated station e-folding lifetimes for days 45–65 are insensitive to these scavenging revisions at temperatures warmer than 258 K, suggesting that the day 46–65 e-folding lifetimes characterize scavenging efficiency at colder temperatures in the free troposphere. Implementing these large-scale scavenging revisions at all temperatures (simulation GEOS-Chem_allT) yields the closest agreement with the observed day 45–65 e-folding lifetimes (13.2 days vs. 14.7 days), although the aerosol concentration bias relative to observations becomes negative (ratio 48, i.e. -0.52 relative bias). This illustrates the important control of scavenging efficiency in the free troposphere and at temperatures colder than 258 K on these e-folding lifetimes.

The present study suggests that models generally have too short a sulfate lifetime, while in a recent study Samset et al. (2014) found that models seem to have too long a black carbon (BC) lifetime, in line with other recent studies (Bauer et al., 2013; Q. Wang et al., 2014). These and other studies (e.g. H. Wang et al., 2013) using vertical profiles of BC from aircraft measurements have shown that the models tend to underestimate the concentrations close to ground, while overestimating at higher altitudes, particularly in the upper troposphere. The overall tendency for the atmospheric column is an overestimation and hence a conclusion that models require a shorter lifetime and more wet removal to reproduce the measurements. However, a uniform reduction of the modelled BC lifetime would lead to an even larger underestimation at the surface in the Arctic (Eckhardt et al., 2015). This points to considerable regional and vertical differences in lifetimes, which was clearly illustrated by Croft et al. (2014) using the GEOS-Chem model. They showed that modelled lifetimes were lowest and less than 5 days in the boundary layer below 2 km, and increased by several orders of magnitude with altitude as wet removal mechanisms became increasingly less efficient with altitude. Lastly, transport issues may cause the apparent misfit between surface and higher altitudes. In our study, we have shown that some models underestimate transport particularly to the northernmost stations.

Eckhardt et al. (2015) compared both surface and aircraft measurements of sulfate and black carbon (BC) in the Arctic to model output from 11 different models. They found that the models generally underestimate the surface concentrations of BC and sulfate in winter/spring, whereas concentrations in summer were overestimated. For sulfate, they found very large differences in the model ensemble, with an apparent anti-correlation between modelled surface concentrations and total atmospheric columns. They also found a strong correlation between surface-measured sulfate and BC concentrations, which indicated that the sources contributing to sulfate and BC are similar throughout the Arctic, and that the aerosols are internally mixed and undergo similar removal. Neither Eckhardt et al. (2015) nor Samset et al. (2014) found an obvious factor (model type or aerosol treatment) that could explain why some models performed better than others.

Our findings suggest that the models tend to underestimate aerosol lifetimes compared to radionuclide observations, in contrast to what is found for BC from some of the other studies mentioned above. Of course, the differences may arise from the different properties of sulfate and BC. The removal time of BC depends strongly on its mixing state and emitted size distribution (Reddington et al., 2013). Specifically, in models, the BC removal timescale is also dependent on the aging parameterizations, which are often very simple and might be a confounding factor. This could mean that our results are not representative of BC and are certainly not representative of freshly emitted BC. However, the high correlation and similar behaviour of sulfate and BC found by Eckhardt et al. (2015) suggests that their fate in the remote atmosphere is similar. The disagreement between models and observations is particularly evident for the Arctic regions, and there seems to be a mismatch between the surface and at higher altitudes. Therefore, we recommend that radionuclides, in particular 133Xe and 137Cs, be measured in the free troposphere in the days and weeks following any detection coming from abnormal atmospheric releases. Such measurement will allow us to understand if the models can reproduce the atmospheric burden and vertical profiles of the aerosols, and better constrain modelled aerosol lifetimes.