Chemistry-climate model SOCOL-AERv2-BEv1 with the cosmogenic Beryllium-7 isotope cycle

. Short-living cosmogenic isotope 7 Be, produced by cosmic rays in the atmosphere, is often used as a probe for atmospheric dynamics. Previously, modelling of the beryllium atmospheric transport was performed using simpliﬁed box-models or air back-tracing codes. While the ability of full atmospheric dynamics models to model beryllium transport was demonstrated earlier, no such ready-to-use model is currently available. Here we present the chemistry-climate model SOCOL-AERv2-BEv1 to trace isotopes of beryllium in the atmosphere. The SOCOL (SOlar Climate Ozone Links) model has been improved by in- 5 cluding modules for the production, deposition, and transport of beryllium. Production was modelled considering both galactic and solar cosmic rays, by applying the CRAC (Cosmic-Ray induced Atmospheric Cascade) model. Radioactive decay of 7 Be was explicitly taken into account. Beryllium transport was modelled without additional gravitational settling due to the small size of the background aerosol particles. An interactive deposition scheme was applied including both wet and dry depositions. The modelling was performed, using a full nudging to the meteorological ﬁelds, for the period of 2003 – 2008 with a spin-up 10 period of 1996 – 2002. The modelled concentrations of 7 Be in near-ground air were compared with the measured, at a weekly cadence, ones in four nearly antipodal high-latitude locations, two in Northern (Finland and Canada) and two in Southern (Chile and Kerguelen Island) hemispheres. The model results agree with the measurements in the absolute level within error bars, implying that the production, decay and lateral deposition are correctly reproduced by the model. The model also correctly reproduces the temporal variability of 7 Be concentrations on the annual and sub-annual scales, including a perfect 15 reproduction of the annual cycle, dominating data in the Northern hemisphere. We also modelled the production and transport of 7 Be for a major solar energetic-particle event of 20-Jan-2005. Concluding, a new full 3D time-dependent model, based on the SOCOL-AERv2, of beryllium atmospheric production, transport and deposition has been developed. Comparison with the real data of 7 Be concentration in the near-ground air fully validates the model and its high accuracy.

1 Introduction Figure 1 shows 7 Be zonal mean production rate as a function of the atmospheric pressure and northern geographical latitude from two sources: GCR (panel A) and SPE (panel B). Since the production of beryllium is nearly symmetric between the global 115 hemispheres, as defined by the geomagnetic shielding, only the Northern hemisphere is shown. Even though the production rate is significantly higher in the polar region, its contribution to the global production is not dominant, because of the small area of the polar regions. For the GCR-related production, the dominant production region is located in the mid-high latitude to the polar (latitude >55 • ) upper stratosphere and mesosphere (above 50-hPa level or ≈35 km). Hardly any beryllium is 120 produced by SEPs in the tropical region. In all cases, the maximum of production lies at mid-/high-latitudes in the stratosphere and the production rate decreases towards the surface, because of the increasing atmospheric depth, and equator due to the 5 https://doi.org/10.5194/gmd-2021-56 Preprint. Discussion started: 7 April 2021 c Author(s) 2021. CC BY 4.0 License. geomagnetic shielding. Due to the much softer energy spectrum, SEPs produce beryllium at shallower atmospheric depths and higher latitudes than GCR do.
2.2 Decay of 7 Be 125 7 Be is a short-living isotope whose decay cannot be neglected because its life-time is shorter than the typical transport/deposition time, in contrast to long-living 10 Be isotope. Accordingly, a standard decay probability of 0.054% per hour (corresponding to the isotope's mean half-life of 53.22 days) was applied during tracing of 7 Be in a way similar to that used by Golubenko et al.
(2020) for 222 Rn. No decay needs to be applied to 10 Be for this kind of modelling. Figure 2 shows the modelled global content of the two beryllium isotopes in the atmosphere after an instant production by the SPE event of 20-Jan-2005 (day zero).

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One can see that the amount of 10 Be decreases exponentially reflecting a slow removal of the isotope through precipitation.
A typical time of the isotope removal is τ 10Be = 550 ± 100 days, implying the residence time of 1 -2 years (cf., e.g., Beer et al., 2012). The decrease of 7 Be isotope concentration is much faster and nearly perfectly exponential with τ 7Be = 72 ± 3 days, which includes both decay and the removal. Since the removal process is assumed to be identical for both isotopes, the concentrations of 10 Be can be used to correct for the system effects. The decay time of 7 Be, estimated in this way, appears 135 1/τ = 1/τ 7Be −1/τ 10Be as τ = 82±4 days which is consistent with the expected e-folding lifetime of 7 Be of 77 days, implying that the decay was accounted correctly in the model. Thus, the 7 Be isotope is fully removed from the atmosphere, mostly due to decay, within one year.
2.3 Transport of cosmogenic isotopes 7 Be and 10 Be After production, beryllium atoms are attached to ambient aerosols for transport and deposition processes. This process is 140 modelled in SOCOL in such a way that beryllium is considered as a gas tracer without additional gravitational settling due to the small size (0.5 -1 µm, see Ioannidou and Paatero, 2014) of the beryllium-carrying background aerosol particles. Different processes such as stratospheric mixing, stratosphere-troposphere exchange (STE), tropospheric transport and deposition, are realistically modelled by the CCM SOCOL (Feinberg et al., 2019). In this study, the advective transport of beryllium isotopes in gas form was performed using Flux-Form Semi-Lagrangian Transport Schemes (Lin and Rood, 1996) embedded in ECHAM5.

Deposition of the beryllium isotopes
Dry deposition is typically modelled using a simplified approach that assumes constant dry deposition velocities over land and ocean, without accounting for seasonal or geographical variability. The tropospheric washout of gases is calculated by using a constant removal rate, irrespective of precipitation occurrence (Hauglustaine et al., 1994). SOCOL-AERv2 employs a more sophisticated scheme based on the surface resistance approach for the estimation of dry deposition velocities (Wesely,150 1989). Deposition of beryllium isotopes is parameterized as a function of surface properties, solubility and reactivity of the considered species (Kerkweg et al., 2006). This scheme considers actual meteorological conditions, different surface types, and trace gas properties like solubility and reactivity. Since beryllium is transported like a gas in the CCM SOCOL, the dry- deposition scheme is similar to other gases in the model (e.g., Revell et al., 2018). Moist convection contributes significantly to transport of energy, momentum, water, and trace gases in global modelling. Since convective clouds are on a scale too 155 small to be resolved in a global model their effects need to be parameterized. The interactive wet deposition scheme used in CCM SOCOL-AERv2 exploits the EAYSY2 version the Scavenging (SCAV) submodule in the ECHAM/MESSy Atmospheric Chemistry (EMAC) model (Tost et al., 2010). This scheme utilize ECHAM5 variables such as liquid and ice water contents, cloud cover, convective and large-scale rain, ice formation, precipitation fluxes, and convective upward mass flux. Scavenging coefficients for gas-phase species are calculated based on Henry's law equilibrium constants. is low in arid regions, e.g., the Sahara and the Middle East. It is also low to the West of the continents, following the low precipitation above the cold ocean currents. The precipitation rate is the highest in the tropical convection zone due to the highest temperature gradients and strong convection in the equatorial area. The deposition, however, is not very high in low latitudes because both the production rate and the downward transport of beryllium are low in the tropics. It is important that 185 gradients of the deposition can be strong even on the regional scale, suggesting that meteorological processes can strongly influence beryllium deposition at any given location (e.g., Usoskin et al., 2009b). This pattern agrees well with a similar previous study (Heikkilä et al., 2008b).

Beryllium isotope from a strong SPE
While GCR always bombard the Earth's atmosphere with slightly variable intensity, major SPEs make a different impact, 190 producing sporadic short (typically several hours) but very intense fluxes of energetic particles entering the atmosphere mostly in polar regions. Potentially, extreme SPEs, orders of magnitude stronger than those observed during the recent decades, can be recorded in cosmogenic isotope data (Usoskin et al., 2006;Usoskin et al., 2020a), and a proper model is needed to study them (Sukhodolov et al., 2017). Here, we modelled transport of such SPE-produced beryllium which was traced separately  from the GCR-produced one to perform a detailed study, based on the SPE of 20-Jan-2005. In order to distinguish between 195 different sources, we traced five beryllium tracers for the isotope: one for GCR-produced beryllium and four tracers for the SEP-scenarios as described above.
Production of the 7 Be isotope during this SPE ( Figure 1B) appears mostly in the polar stratosphere and lower mesosphere.
After production, the isotope starts decaying and being caught by the air dynamics. Figure 5 shows an example of the SPEproduced isotope concentration on the 30-th day after the event (19-Feb-2005). One can see that the production pattern has 200 been already smeared by the transport, leading, in particular to an essential hemispheric difference. It is interesting that tropospheric concentrations are higher at mid/low latitudes around 30 • than in polar regions, because of the atmospheric circulation (i.e. increased stratosphere-troposphere coupling and large-scale downward motion in the troposphere). As an example, the modelled activity of 7 Be in near-ground air is shown in Figure 6 as averaged over Finland. The locally (polar troposphere) produced beryllium dominates during the first 20 days after the event, but then the transport starts playing a role, leading to 205 the very low concentrations during the subsequent period. The level of activity for this event in the near-air in Finland is very low, a factor 100 lower than the typical level (around 900-1500 uBq/m3) of activity due to GCR during the winter season (see Figure 8A).
Although the SPE of 20-Jan-2005 was a very strong one, the second strongest directly observed, its imprint in cosmogenic isotopes is not detectable on the background of air-transport dynamic and GCR variability. An SPE must be stronger by a 210 factor of ten or more than this one to become detectable in isotope records even on the daily scale (cf. Sukhodolov et al., 2017;Usoskin et al., 2020a).    The data series are shown in Figure 8 and described below.  Figure 8B. The total uncertainty for the measured 7 Be activity is defined mostly by statistics and is approximately 7 -8%.  Figure 8D).
The data for Punta Arenas and Kerguelen Island were obtained via the virtual Data Exploration Centre (vDEC) of the 255 Preparatory Commission for the Complete Nuclear Test-Ban-Treaty Organisation (CTBTO). A full description of the sampling and measurement of the CTBT data is available elsewhere (Miley et al., 1998;Medici, 2001).
In addition to 7 Be activity measured in near-ground air, we also exploited data on the quarterly total-deposition 7 Be measurements (without separating dry and wet depositions) measured in collected precipitation water at Rovaniemi and Ivalo stations, as provided by STUK and previously published in Leppänen (2019). The fallout sample collection period was one month, but the three samples were combined together to form a quarterly sample. Hence, the four measured samples for each year cover period of January to March, April to June, July to September and October to December, respectively. The reference date was set to the middle of the sampling period (since the decay time of 7 Be is shorter than the sampling interval) and the activities were decay-corrected to this date (see Leppänen, 2019). The 7 Be deposition averaged over the two locations is shown in Figure 9.

Comparison between modelled and measured data 265
First, we compared the modelled 7 Be activity with measured for the all-Finland record, compiled from four stations (see Section 4.1) as shown in Figure 8A. The linear Pearson correlation between the modelled and measured weekly series is highly significant r=0.68±0.02 (p-value <10 −6 ). Figure 10A shows the global wavelet coherence, which is an analogue of the correlation coefficient but extending it into the frequency domain, between the modelled and measured 7 Be activities for the Finnish stations. The coherence is highly significant (confidence level above 95%) at all time scales between one The Chilean data ( Figure 8C) depicts a reasonable agreement between the model and the measurements. Since the data contains no seasonal pattern, as correctly reproduced by the model, the formal correlation is insignificant r =0.06. However, it is dominated by the short-term variability, while the wavelet coherence analysis ( Figure 10C) suggests that the two datasets are significantly coherent at time scales longer than 3 months. The mean levels of the modelled and measured series agree nearly 290 perfectly, within 2%, viz. 1.74 vs. 1.71 mBq/m 3 for the modelled and measured activities, respectively.
Data from the Kerguelen island ( Figure 8D) also depicts a reasonable agreement, including correctly reproduced spikes.
Similar to the Chilean data, the formal correlation is insignificant r =0.06, but the coherence ( Figure 10D) is highly significant at monthly and annual time scales. The mean levels of the modelled and measured series are not well-matched, with the difference of 18%, viz. 2.02 vs. 1.65 mBq/m 3 for the modelled and measured activities, respectively. This may be related to the peculiarity of this site which is located on a small island (about 100 km across) in the middle of the ocean, while the model grid (about 300×300 km) is too rough to catch the orography.
Therefore, we conclude that the model correctly (within 10%) calculates the mean levels of beryllium concentration for both northern and southern high-latitude locations, at least for the locations where the orographic scale is comparable to the grid size but may have larger uncertainties for unresolvable spatial scales. It is important that the model correctly reproduces the 300 seasonal variability or its absence as well as some sudden spikes, particularly during the late winter and spring seasons likely related to SSW events.
In addition to the concentration of 7 Be in near-surface air (expressed in measured activity), we also compared the beryllium deposition modelled by SOCOL with that measured in the Northern Finland, as shown in Figure 9. The agreement is very good: the average levels (183 and 188 Bq/m 2 for the modelled and measured data, respectively) agree within 2.5%, the correlation 305 is highly significant (r=0.86 +0.04 −0.06 , p < 10 −6 ). However, the discrepancy can be significant for individual years. Thus, we conclude that the model reasonably well reproduces also the depositional flux of 7 Be on the yearly time scale.

Conclusions
A full 3D model of production, transport and deposition of cosmogenic beryllium isotopes in the atmosphere has been developed. The model named as SOCOL-AERv2-BEv1 is based on the chemistry-climate model SOCOL, specifically tuned for the 310 best performance in tracing beryllium, and the CRAC production model. Realistic modelling of 7 Be isotope was performed for the years 2002 -2008, with a 5-year model spin-up during 1996 -2001. The measured weekly concentrations of 7 Be in near-ground air have been compared with the model results for four nearly antipodal mid/high-latitude locations, two in the Northern (Finland and Canada) and two in the Southern (Chile and Kerguelen Island) hemispheres. The model results generally agree well with the measurements at the absolute level within error bars, implying that the production, decay and lateral 315 deposition are correctly reproduced by the model. However, a larger discrepancy was observed at the Kerguelen Island where the orographic scale is much smaller than the model grid size. The model correctly reproduces the temporal variability of 7 Be concentrations on the annual and sub-annual scales, including a perfect reproduction of the annual cycle, which dominates data in the Northern hemisphere, and the absence of this cycle in the Southern hemisphere. This fully validates the newly developed model to be able to correctly simulate the production, transport and deposition of 7 Be on the local/regional spatial and 320 monthly/annual temporal scales. The modelled beryllium distribution is also in general agreement with earlier computations based on a similar approach.
We have also modelled the production and transport of 7 Be for a major solar energetic-particle event of 20-Jan-2005, which was one of the largest directly observed events. It is shown that an order of magnitude stronger event is needed to become observable in the beryllium data.

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Concluding, a new full 3D time-dependent model, based on SOCOL-AERv2, of beryllium atmospheric production, transport and deposition has been developed and validated using directly measured data. The model is recommended to be used in studies operating staff for producing and providing the corresponding data under a vDEC agreement (https://www.ctbto.org/specials/vdec/). KG thanks E. Rozanov for Fortran lessons, S. Poluyanov for ORAVA cluster setting, and M.V. Vokhmyanin for assistance in big data analysis. here. The red dashed line denotes the 95% confidence level against the AR(1) red noise.