One of the most important outer-space factors affecting Earth is related to cosmic rays (highly energetic nuclei of extraterrestrial origin), which cause nucleonic–electromagnetic–muon cascade in the terrestrial atmosphere . These cosmic-ray-induced atmospheric cascades form the main source of ionization in the troposphere and stratosphere e.g.,. Nuclear interactions between the nucleonic component of the cascade and nuclei of atmospheric gases such as nitrogen and oxygen can produce radioactive nuclides e.g., including 7Be (half-life 53.22 d) and 10Be (half-life 1.4×106 years). They are called cosmogenic isotopes since galactic and solar cosmic rays form the dominant source of these nuclides in the terrestrial system. Production rates of 7Be and 10Be vary in time following the intensity of galactic cosmic rays (GCRs) modulated by solar magnetic activity (the 11-year solar cycle), geomagnetic field strength, and also sporadic solar energetic particle events (SPEs) see, e.g.,.

The short-living cosmogenic isotope 7Be, which is relatively easy to measure via a proper collection system and γ spectrometry, is routinely measured with daily, weekly, and monthly time resolution in near-ground air and precipitating water at different places around the globe in the framework of atmospheric radiation monitoring. Concentrations of long-living 10Be are measured (via acceleration mass spectrometry, AMS) in natural stratified archives, typically in polar ice cores, with pseudo-annual or longer time resolution e.g.,. In particular, 10Be recorded in polar ice cores serves as a main proxy for long-term solar activity reconstructions in the past (e.g., ).

In addition to the production pattern defined by cosmic-ray fluxes, concentrations of beryllium isotopes at any location are also affected by atmospheric transport and deposition processes, which may essentially distort the production signal. Thanks to the short life of 7Be, high-time-resolution data, and broad distribution of the measuring sites, this isotope has often been used as a tracer for atmospheric dynamics during the recent decades. Its atmospheric transport can be modeled with high accuracy using the known meteorological fields as summarized in Sect. . On the other hand, data on 10Be are mainly measured in polar regions with low temporal resolution and extend far back in the past to times when meteorological data are not available. Accordingly, the atmospheric transport of 10Be is typically modeled using simplified box models based on a parameterization of some specific simulations e.g.,. Thus, there is a need for a realistic model able to simulate atmospheric transport and deposition of beryllium focused in polar regions and (inter)annual timescales that is potentially able to operate in a self-consistent mode without the prescribed meteorology. Such a model needs to be able to reproduce the main pattern of beryllium transport and its deposition in polar regions on the annual timescale.

Since measurements of 10Be are laborious and expensive, their coverage for the last decades is low, making it difficult to compare model results directly with measured data. Moreover, they can be additionally distorted by deposition and post-depositional processes. However, since the two beryllium isotopes are believed to have similar transport and deposition, being different only in production and lifetime, a model applied and verified for 7Be transport can also be generally applied to 10Be . Here we develop such a model, CCM SOCOL-AERv2-BE, to trace isotopes of 7Be and 10Be in the atmosphere with modules for the production, deposition, and transport of 7Be and 10Be.

The main purpose of this work is to present a new combined model of beryllium production and transport and to confront its results with high-resolution (weekly) measurements of 7Be in near-ground air and precipitating water in polar regions. The isotope 7Be was chosen for the analysis because of the following reasons: (i) there are no systematic high-quality 10Be data in air samples since measurements of 10Be are much more difficult (AMS technology) than those of 7Be (γ spectrometry); (ii) 10Be measured in ice cores contains an additional component (deposition), which also affects the measured data and needs to be modeled separately. On the other hand, the model eventually aims at the modeling of the 10Be isotope including its deposition. Since 10Be is typically measured in polar ice cores with pseudo-annual or longer resolution, we are primarily interested in validating the model for high-latitude regions and (inter)annual timescales. The new model version CCM SOCOL-AERv2-BE has been developed here for systematic modeling of 7Be and 10Be production, transport, and deposition in the atmosphere. This model set forms a methodological basis for a detailed study of the atmospheric dynamic and cosmogenic isotope distribution in the terrestrial system. The model computations were performed with full nudging (using ERA5) to the observed meteorological data to verify the capability of the model to trace beryllium isotopes in the atmosphere. The model computations were directly compared with measurements of 7Be isotopes in different high-latitude locations to validate the model.

The paper is organized as follows: a summary of the previous and existing models is presented in Sect. ; data from 7Be measurements are presented in Sect. ; the model is described in great detail in Sect. ; obtained results are discussed in Sect. ; validation of the model by means of comparisons with measurements is presented in Sect. ; Sect.  summarizes conclusions of the paper.

Studies of the short-living 7Be isotope and its ratio to 10Be provide a precise way to probe large-scale atmospheric dynamical properties and validate the corresponding atmospheric models (e.g., ). For the long-living 10Be isotope, different transport and deposition assumptions as well as models were used (e.g., ). Here we review some key models.

Earlier simulations with the transport model GLOMAC1 by yielded the concentration and deposition of 7Be isotopes in agreement with the data within 20 %. However, the authors conclude that the application of this transport model and scavenging scheme for simulations of deposition and concentration was not well suited for polar regions.

Later, simulations of 7Be and 10Be transport for present and future climatic conditions were performed by with the general circulation model MA-ECHAM4. The model successfully captured the maximum 10Be/7Be ratio in the lower polar stratosphere.

The general ability of a full atmospheric–dynamic model to reproduce the pattern of beryllium transport and deposition even at regional spatial and synoptic temporal scales was demonstrated by , who used the GISS model to simulate 7Be production and transport for the 2 months of January–February 2005 and compared the model's results with daily-resolution near-ground 7Be air concentrations measured at 11 sites worldwide (see Table 1 in ). The results implied that the model captures 7Be transport at synoptic and longer timescales (longer than 4–10 d; see Fig. 5 in ) in both absolute levels and time variability. However, as noted by , the GISS model has a low bias (a factor of two) in the upper troposphere and lower stratosphere, while agreeing well with the surface concentrations. It was proposed that this can be related to model production that is too low and the fact that either the model delivers too much 7Be to the surface or does not scavenge efficiently enough. The GISS model was not further developed in this direction.

Modeling of beryllium isotopes in the Earth's atmosphere was performed earlier using the ECHAM5-HAM atmospheric model and zonal mean production rates. Cosmogenic radionuclides 10Be and 7Be were modeled during the Maunder Minimum and the present-day climate . ECHAM5-HAM simulates beryllium fluxes and concentrations in ice at Greenland sites well, in agreement with the data. In Antarctica, however, the model has some difficulties in reproducing the very low level of precipitation, which leads to an underestimation of the 10Be concentrations in ice. The precipitation rate modeled at the Concordia site was a factor 2–3 too high, leading to 10Be concentrations in ice that are too low, since, after full depletion of 10Be from the atmosphere, further rain or snow dilutes its concentration in the ice. The 7Be surface air concentrations generally agree within a factor of 2 with the observed concentrations. However, modeled concentrations at two Antarctic stations appeared too low. This model was very roughly parameterized , being effectively reduced to a six-box model and not developed further in the application to beryllium transport modeling.

A simplified 2D model of beryllium stratospheric sedimentation was developed by but also not supported further.

Even though a full modeling can be done, transport of 7Be is typically considered, for application purposes, with simple box–reservoir exchange models e.g., or with air-mass tracing codes .

In chemical transport models, wind and temperature values are taken from either (1) general circulation models or from (2) meteorological data. The advantage of the second approach is that chemical transport simulations are linked to real meteorology and the results are inherently compared to observations. Reanalysis extends meteorological data to the past. This allows us to perform long-term simulations which show temporal evolution of the atmosphere's composition. The success of such a task relies on the reanalysis quality, i.e., on the accuracy of the indicator's distributions. This also makes chemical transfer models a powerful tool for evaluating the reanalyses themselves .

The Global Modeling Initiative (GMI) chemistry and transport model (a model with prescribed meteorology) driven by NASA's MERRA assimilated meteorological data was applied to understand the roles of transport and precipitation scavenging processes using the cosmogenic 7Be tracer . The model results agree reasonably well with the 7Be data in general but diverge by a factor of 2 for warm periods. The discrepancy was ascribed to the model's insufficiently detailed spatial sampling.

The approach based on prescribed meteorology is applicable only to recent years when the wind field is known; moreover, it includes neither stratospheric dynamics nor depositional processes and is therefore not suitable for 10Be in polar ice.

Thus, several models of different complexity and accuracy have been developed in the recent past to model transport and deposition of 7Be and 10Be. However, due to the lack of support for radionuclide simulations with the ECHAM-HAM and GISS climate models, a full working model capable of simulating production, transport, and deposition of 7Be and 10Be from all sources is presently missing. The model should be “user-friendly” (i.e., for a user without deep knowledge of climate modeling) and applicable for past or future projections when direct nudging to the meteorological reanalysis data is not possible.

Here we present a new version of CCM SOCOL – CCM SOCOL-AERv2-BE – for modeling of production, transport, and deposition of the cosmogenic isotopes of beryllium as well as its validation with the available measurements of 7Be at high-latitude locations. CCM SOCOL is potentially capable of simulating the beryllium transport and deposition and was already used for the estimation of 10Be deposition after major solar energetic particle (SPE) events, but it did not include the state-of-the-art interactive parameterization of the wet and dry deposition introduced recently . A recent model version of CCM SOCOL that simulates aerosols more realistically, however, does not include the treatment of all processes relevant to the beryllium life cycle, and its applicability has not been evaluated. We have further upgraded CCM SOCOL here by adding the production, transport, and deposition of 7Be and 10Be isotopes from both GCRs and SPEs.

For the model verification, we used data on the measured activity (concentration) of the 7Be isotope in near-ground air, with weekly sampling (corrected for the decay) performed in different hemispheres for the period 2002–2008. Higher-time-resolution data are not necessary for several reasons: (i) data availability, since weekly sampling is a standard resolution for most 7Be-measuring stations; (ii) inability of full atmospheric–dynamic models to catch the sub-synoptic timescales because of the rough grid size (see ); and (iii) focus on longer timescales (annual and interannual) for the application to 10Be in ice cores. On the other hand, rougher-resolution data (e.g., monthly or quarterly) are more uncertain because of the decay of short-living 7Be. Thus, we found the weekly-resolution data to be optimal for our purposes.

Traditionally, for short-living isotopes, the measured quantity is not concentration but activity in units of becquerels (number of radioactive decays per second) per cubic meter of air (Bqm-3), as directly measured by a γ spectrometer. Correction for decay between the times of sample collection and measurement is standardly performed (see ). The activity and concentration can be easily translated to each other using the known lifetime of the isotope.

Here we use data from four nearly antipodal high-latitude locations (see Table ). Two locations are in the Northern Hemisphere in Finland (a set of stations) and Canada (Yellowknife), and two are in the Southern Hemisphere: Kerguelen island (French) and Punta Arenas (Chile). The longitudinal separation between the locations in each hemisphere is greater than 140∘. The data series are shown in Fig.  and described below.

Finnish data on the measured 7Be activity were provided for the period 2002–2008 by the Finnish National Radiation and Nuclear Safety Authority (STUK) for four sites (see Table ): Ivalo, Rovaniemi, Kajaani, and Kotka, spanning meridionally 8∘ in latitude. The isotope of 7Be was collected on air filters using a high-volume air sampler on a weekly basis, and then its activity was measured with an HPGe (high-purity germanium) detector inside a 4 in. thick lead shielding in the STUK laboratory. The statistical measurement uncertainty is 3 %–5 % (see a detailed description of the sampling and measurement procedure in ). The data from the four stations were combined as the average of the four locations for each time interval to represent a regional-scale dataset, as shown in Fig. a.

We also used 7Be data from the Yellowknife site (Canada; see Fig. b) kindly provided by the Radiation Protection Bureau of Health Canada. The original data are with daily time resolution but have been combined into weekly samples (correction for decay applied) for consistency with other datasets. The total uncertainty for the measured 7Be activity is defined mostly by statistics and is approximately 7 %–8 %.

For the Southern Hemisphere, we considered weekly 7Be activities measured at Punta Arenas (Chile, CTBTO station code CLP18). During 2002–2006, the data contain many long breaks (about half of weekly data are missing), and hence we considered data since October 2006 only, as shown in Fig. c.

Another Southern Hemisphere station is located at Port-aux-Français, Kerguelen island (CTBT station code FRP30), with data available since 2006 (Fig. d). The data for Punta Arenas and Kerguelen island were obtained via the virtual Data Exploration Centre (vDEC) of the Preparatory Commission for the Comprehensive Nuclear Test-Ban-Treaty Organization (CTBTO). A full description of the sampling and measurement of the CTBTO data is available elsewhere .

In addition to 7Be activity measured in near-ground air, we also exploited data on the quarterly total-deposition 7Be measurements (without separating dry and wet depositions) measured in collected precipitation water at Rovaniemi and Ivalo stations, as provided by STUK. The fallout sample collection period was 1 month, but the three samples were combined together to form a quarterly sample. Hence, the four measured samples for each year cover the period of January to March, April to June, July to September, and October to December. The reference date was set to the middle of the sampling period (since the decay time of 7Be is shorter than the sampling interval) and the activities were decay-corrected to this date see. The 7Be deposition averaged over the two locations is shown in Fig. .

We used an extended version of CCM SOCOL with the aerosol module – AERv2 . This version consists of the general circulation model MA-ECHAM5 and the atmospheric chemistry module MEZON combined with an aerosol module AER , interacting with each other every 2 h of modeling. In this study, MA-ECHAM5 is nudged with fifth-generation ECMWF atmospheric reanalysis data from the global climate ERA5 (eraiaT42L39) reanalyses. The chemical part of the MEZON core includes 56 chemical species of oxygen, hydrogen, nitrogen, carbon, chlorine, bromine, and sulfur groups, 295 gas-phase reactions, 64 photolysis reactions, and 16 heterogeneous reactions on stratospheric aqueous sulfuric acid aerosols as well as three types of polar stratospheric clouds. CCM SOCOL-AERv2-BE uses the horizontal resolution T42, where T refers to triangular truncation and the number denotes the series of spherical harmonics. The horizontal resolution is about 2.8∘×2.8∘ (≈300×300 km in the equatorial region). The vertical grid is defined using a sigma-hybrid coordinate system, which is calculated by a linear combination of surface pressure and constant coefficients that define the vertical coordinate. The model has 39 vertical levels between the Earth's surface and the 0.01 hPa level (≈80 km). The real orography is smoothed over the model grid cells. The aerosol module exploits a sectional microphysical scheme whereby the aerosol particle size distribution is represented by 40 discrete size bins. The model simulates the advective transport of stratospheric aerosol by the Brewer–Dobson large-scale circulation and gravitational sedimentation. We have made some adaptations of the main model to focus on beryllium transport, as described below.

In this section, we validate the model by comparing the simulation results with actual measurements of the near-ground-air 7Be concentration in air filters performed in boreal and austral high-latitude regions (Sect. ), as shown in Fig. .

First, we compared the modeled 7Be activity with the measured one for the all-Finland record, which was compiled from four stations (see Sect. ) as shown in Fig. a. The linear Pearson correlation between the modeled and measured weekly series is highly significant at r=0.68±0.02 (p value <10-6). The standard correlation analysis does not distinguish between different frequencies and/or timescales. Therefore, we show in Fig.  the global wavelet coherence, which is an analog of the correlation coefficient but extending it into the frequency domain between the modeled and measured 7Be activities.

Figure  depicts the coherence for the Finnish stations. The coherence is highly significant (confidence level above 95 %) at all timescales between 1 month and 2 years. Although there are discrepancies on the very short timescales related to synoptic noise, the model correctly reproduces some strong spikes in the beryllium activity, such as earlier in 2003, which are often related to sudden stratospheric warming (SSW) events . It is important that the long-term variability (at an annual timescale) is correctly reproduced by the model.

However, neither correlation coefficient nor coherence analyses provide information on the absolute level match between the series. In order to assess possible model biases we considered the difference between the modeled and measured weekly 7Be concentrations as shown in Fig. a. The difference is insignificant at 0.16±0.7 mBqm-3, implying the absence of a systematic bias in the model. The mean (averaged over seven yearly values) level of the modeled activity (2.05 mBqm-3) is close to the measured one (1.86 mBqm-3), within 10 % (the difference is 0.19±0.19 mBqm-3). The z test suggests that this difference is insignificant. On the other hand, there is an essential difference between the model and the measurements regarding the magnitude of summer peaks in 2007 and 2008. It could potentially be related to the local atmospheric aerosol properties, but the AERONET (AErosol RObotic NETwork) station in Sodankylä (northern Finland) did not show any anomalies for that time. The discrepancies appear during warm periods, in agreement with other direct models .

For the Canadian station, the agreement between the modeled and measured activities (Fig. b) is nearly perfect, including a correct reproduction of the very strong seasonal cycle and sudden short spikes, e.g., in late 2003. The Pearson correlation coefficient is r=0.78±0.02 (p value <10-6). The coherence between the simulated and measured datasets (Fig. b) is highly significant at all timescales between 1 month and 1.5 years. The difference between the modeled and measured concentrations is -0.25±1.05 mBqm-3 (Fig. b). The overall mean level of modeled activity (2.15 mBqm-3) is close to the measured one (2.4 mBqm-3), within 10 % (the difference is 0.24±0.22 mBqm-3). The z test suggests that the difference is insignificant, implying the absence of the model bias. The most pronounced difference between the model and the measurements was observed in 2008.

The Chilean data (Fig. c) depict reasonable agreement between the model and the measurements. Since the data contain no seasonal pattern, as correctly reproduced by the model, the formal correlation is insignificant at r=0.06. However, it is dominated by the short-term variability, while the wavelet coherence analysis (Fig. c) suggests that the two datasets are significantly coherent at timescales longer than 3 months. The difference between the modeled and measured concentrations is 0.06±0.68 mBqm-3 (Fig. c). The mean levels of the modeled and measured series agree nearly perfectly, within 2 %: 1.74 vs. 1.71 mBqm-3 for the modeled and measured activities, respectively, implying the absence of bias.

Data from Kerguelen island (Fig. d) also depict reasonable agreement, including correctly reproduced spikes and the lack of an annual cycle. Similar to the Chilean data, the formal correlation is insignificant at r=0.06, but the coherence (Fig. d) is highly significant at monthly and annual timescales. The difference between the modeled and measured concentrations is 0.33±0.6 mBqm-3 (Fig. d). The mean levels of the modeled and measured series are reasonably matched, with a difference of 18 %: 2.02 vs. 1.65 mBqm-3 for the modeled and measured activities, respectively, also indicating no significant bias. The observed small systematic discrepancy 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) may be too rough to catch the actual 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 and contains no biases, at least for the locations where the orographic scale is comparable to the model's grid size, but it may have larger uncertainties for unresolvable spatial scales. It is important that the model correctly reproduces the 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 7Be in the near-surface air (expressed in measured activity), we also compared the 7Be deposition modeled by CCM SOCOL-AERv2-BE with that measured in northern Finland, as shown in Fig. . The agreement is very good: the average levels (183 and 188 Bqm-2 for the modeled and measured data, respectively) agree within 2.5 %, and the correlation is highly significant (r=0.86-0.06+0.04, p<10-6). However, while the overall agreement is very good, the discrepancy can be significant for individual years. Thus, we conclude that the model also reproduces the depositional flux of 7Be reasonably well on the yearly timescale.

A full 3D transient model of production, transport, and deposition of cosmogenic 7Be and 10Be isotopes in the atmosphere has been developed. The model, named CCM SOCOL-AERv2-BE, is based on CCM SOCOL, specifically tuned for the best performance in tracing beryllium, and the CRAC production model. Realistic modeling of the 7Be isotope was performed for the years 2002–2008, with a 5-year model spin-up during 1996–2001. The measured weekly concentrations of 7Be in near-ground air have been compared with the model prediction for four nearly antipodal high-latitude locations: two in the Northern (Finland and Canada) and two in the Southern (Chile and Kerguelen island) Hemisphere. The model results generally agree well with the measurements in the absolute level within error bars, implying that the production, decay, and lateral deposition are correctly reproduced by the model. However, a larger discrepancy (up to 20 %) was observed at Kerguelen island where the orographic scale is much smaller than the model grid size. The model correctly reproduces the temporal variability of 7Be concentrations on the annual and sub-annual scales, including a good reproduction of the annual cycle, which dominates data in the Northern Hemisphere, and the absence of such a cycle in the Southern Hemisphere. In addition, occasional anomalous events such as SSWs are well reproduced by the model. This validates the newly developed model to be able to correctly simulate the production, transport, and deposition of the 7Be (and hence, 10Be) isotope on local or regional spatial (in high-latitude regions) and monthly or annual temporal scales. The modeled 7Be distribution is also in general agreement with earlier computations based on a similar approach (e.g., ).

We have also modeled the production and transport of 7Be for a major solar energetic particle event on 20 January 2005, which was one of the largest directly observed events. It was shown that, at minimum, an order-of-magnitude stronger event is needed to become observable in the beryllium data.

Concluding, the new full 3D time-dependent CCM SOCOL-AERv2-BE model of 7Be and 10Be atmospheric production, transport, and deposition has been developed and validated using directly measured data. The model is recommended to be used in studies related to, e.g., atmospheric dynamical patterns, extreme solar particle storms, long-term solar activity reconstruction from cosmogenic proxy data, and solar–terrestrial relations.