GEOS-Chem is a global 3-D chemical transport model (http://www.geos-chem.org, last access: 23 November 2023) that simulates gases and aerosols in both the troposphere and stratosphere (Eastham et al., 2014; Bey et al., 2001). It is driven by archived meteorological data. We use version 14.0.2 (https://wiki.seas.harvard.edu/geos-chem/index.php/GEOS-Chem_14.0.2, last access: 23 November 2023) to simulate the transport and deposition of atmospheric 7Be and 10Be. We drive the model with the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) meteorological reanalysis (http://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/, last access: 23 November 2023; Gelaro et al., 2017b). MERRA-2 has a native resolution of 0.5∘ latitude by 0.667∘ longitude, with 72 vertical levels up to 0.01 hPa (80 km). Here the MERRA-2 data are re-gridded to 4∘ latitude by 5∘ longitude for input to GEOS-Chem for computational efficiency.

GEOS-Chem includes a radionuclide simulation option (222Rn–210Pb–7Be–10Be), which simulates transport (advection, convection, boundary-layer mixing), deposition, and decay of the radionuclide tracers (e.g., Liu et al., 2001, 2004; B. Zhang et al., 2021; Yu et al., 2018). The model uses the TPCORE algorithm of Lin and Rood (1996) for advection, archived convective mass fluxes to calculate convective transport (Wu et al., 2007), and the non-local scheme implemented by Lin and McElroy (2010) for boundary-layer mixing. As mentioned in the Introduction, the standard GEOS-Chem model uses the LP67 7Be and 10Be production rates. After production, 7Be and 10Be attach to ambient submicron aerosols ubiquitously, and their behavior becomes that of aerosols until they are removed by wet-deposition (precipitation scavenging) and dry-deposition processes. Note that neither is the process of attachment explicitly represented, nor is the aerosol size distribution considered in the model. In addition, the decay process is included for the short-lived 7Be with a half-life of 53.2 d. The decay is minor for the long-living 10Be, which has a half-life of 1.39×106 years (e.g., Chmeleff et al., 2010).

Wet deposition includes rainout (in-cloud scavenging) due to stratiform and anvil precipitation (Liu et al., 2001), scavenging in convective updrafts (Mari et al., 2000), and washout (below-cloud scavenging) by precipitation (Wang et al., 2011). Scavenged aerosols from vertical layers above are allowed to be released into the atmosphere during the re-evaporation of precipitation below the cloud. In the case of partial re-evaporation, we assume that half of the corresponding fraction of the scavenged aerosol mass is released at that level because some of the re-evaporation of precipitation are due to partial shrinking of the raindrops, which does not release aerosol (Liu et al., 2001). MERRA-2 fields of precipitation formation and evaporation are used directly by the model wet deposition scheme. Dry deposition is based on the resistance-in-series scheme of Wesely (1989). The process of sedimentation is not included in the model.

To quantify the stratospheric contribution to 7Be and 10Be in the troposphere, we separately transport 7Be and 10Be produced in the model layers above the MERRA-2 thermal tropopause (i.e., stratospheric 7Be and 10Be tracers). This approach was previously used to study cross-tropopause transport of 7Be in GEOS-Chem (Liu et al., 2001; Brattich et al., 2021) and Global Modeling Initiative chemical transport models (Liu et al., 2016; Brattich et al., 2017). The stratospheric fractions of 7Be and 10Be are defined as the ratio of the stratospheric 7Be and 10Be concentrations to the 7Be and 10Be concentrations.

The GEOS-Chem currently uses the LP67 production rates of 7Be and 10Be (Lal and Peters, 1967). These production rates are calculated using an analytically estimated rate of nuclear disintegration (stars) in the atmosphere (stars per gram of air per second), multiplied by the mean production yield of 0.045 atoms per star for 7Be and 0.025 atoms per star for 10Be (Lal and Peters, 1967). These rates are represented as a function of latitude and altitude for the year 1958 and are not time-varying.

Here we update the atmospheric 7Be and 10Be production rates in GEOS-Chem with the latest production model: the CRAC:Be model by P16 (Poluianov et al., 2016) using the solar modulation function record by Herbst et al. (2017). The solar modulation function record is based on the local interstellar spectrum by Herbst et al. (2017), which was also used in the production model. Given spatially and temporally resolved geomagnetic cutoff rigidities, the P16 model allows the calculation of 3-dimensional, temporally variable 7Be and 10Be production rates, which are necessary for input to atmospheric transport models. The P16 production model is regarded as the latest and one of the most accurate production models for 7Be and 10Be and was used in recent general circulation model simulations (e.g., Golubenko et al., 2021; Sukhodolov et al., 2017).

The production rates of 7Be and 10Be are calculated as Eq. (1) by an integral of the yield functions of 7Be and 10Be (Yi, atoms g-1 cm2 sr) and the energy spectrum of cosmic rays (Ji, (sr s cm2)-1) above the cutoff energy Ec: 1QΦ,h,Pc=∑i∫Ec∞YiE,hJiE,ΦdE, where i refers to different types of primary cosmic ray particles (e.g., proton, alpha, and heavier particles). For modeling the contribution of alpha and heavier particles to the total production, their nucleonic ratio in the local interstellar spectrum was set to 0.353 (Koldobskiy et al., 2019). The yield function Yi is a function of height (h) and kinetic energy per incoming primary nucleon (E) and is directly taken from P16. The energy spectrum of cosmic rays Ji is a function of the kinetic energy (E) and depends on the solar modulation function (Φ) (Herbst et al., 2017). Ec is calculated as Eq. (2) as a function of the local geomagnetic rigidity cutoff (Pc): 2Ec=Er(1+ZiPcAiEr2-1), where Zi and Ai are the charge and mass numbers of particles, respectively. Er is the rest mass of a proton (0.938 GeV).

The geomagnetic rigidity cutoff Pc is a quantitative estimation of the Earth's geomagnetic field shielding effect (Smart and Shea, 2005). Cosmic ray particles with rigidity (momentum per unit charge of the particle) higher than the geomagnetic cutoff rigidity value can enter the Earth's atmosphere. In several model simulations of 7Be and 10Be (e.g., Field et al., 2006; Koch et al., 1996; Liu et al., 2001), the production is calculated with a Pc simplified as a function of the geomagnetic latitude and geomagnetic dipole moment, called the vertical Störmer cutoff rigidity equation (see Eqs. 5.8.2–2 in Beer et al., 2012). However, this is different from the real geomagnetic cutoff rigidity inferred from the trajectories of particles with different energies using real geomagnetic field measurements (e.g., Copeland, 2018), which also includes non-dipole moments of the field (Beer et al., 2012) (Fig. S1 in the Supplement). Earlier studies suggested that using the simple centered dipole models (e.g., Störmer cutoff rigidity) for cutoff rigidity approximation is limited as they can significantly distort the cutoff rigidity for some regions (e.g., low-latitude regions) (Pilchowski et al., 2010; Nevalainen et al., 2013).

Here we take the geomagnetic cutoff rigidity from Copeland (2018) that provides the cutoff rigidity at a fine interval (1∘) in both latitude and longitude. This production rate is denoted as P16spa. To investigate the effect of this more realistic representation of cutoff rigidity on 7Be and 10Be simulations, we also perform simulations where the cutoff rigidities are approximated by the Störmer equation (denoted as P16). The influence of the geomagnetic field intensity variations can be considered negligible on annual and decadal timescales and are ignored here (e.g., Muscheler et al., 2007; Zheng et al., 2020). It should be mentioned that the LP67 production is based on an ideal axial dipole cutoff rigidity similar to the P16 production model.

An overview of the performed simulations is shown in Table S1 in the Supplement. The simulation with the P16spa production rate is considered the standard simulation, while the simulations with the P16 and LP67 production rates are sensitivity tests. The simulation with the P16 production rate is conducted to evaluate the influence of a simplified approximation of cutoff rigidities resulting from a geocentric dipole. In earlier studies, the LP67 production rate was used for global model simulations of 7Be (e.g., Liu et al., 2016; Brattich et al., 2017; Liu et al., 2001; Koch et al., 1996). The purpose of performing the simulation with the LP67 production rate is to evaluate to what extent model simulations are biased when applying the default LP67 production. Since the LP67 production rate applies only for the year 1958 (with a solar modulation function of about 1200 MeV) and does not consider the influences of the solar variations (e.g., 11-year solar cycle), it underestimates the production rate for the period of 2008–2018 that has an average solar modulation function of 500 MeV. To correct for this solar modulation influence, we follow the previous studies (e.g., Liu et al., 2016; Koch et al., 1996) by multiplying the model results by a scale factor of 1.39. It should be noted that this correction is not ideal as the effects of a varying solar modulation on cosmogenic radionuclide production rates depend on altitude and latitude. All simulations are performed from 2002 to 2018, with the first 6 years for spin-up to make sure the 10Be nearly reaches equilibrium in the atmosphere and the 2008–2018 period (11 years) for analysis. The simulations are conducted using a 4∘ latitude × 5∘ longitude resolution for computational efficiency (e.g., Liu et al., 2016, 2004).

To evaluate the model's ability to reproduce the variabilities in the observations, we use the statistical parameters: Spearman correlation coefficients and root mean square error (RMSE) (Chang and Hanna, 2004). Spearman's rank correlation (R) (Myers et al., 2013) is used as it does not make any assumptions about the variables being normally distributed. It is less sensitive to outliers in the data compared to the commonly used Pearson correlation. The fraction of modeled concentrations within a factor of 2 of observations (FA2) is calculated, i.e., for which 0.5<Xmodel/Xobservation<2. Usually, if the scatter plot of the model and measurements is within a factor of 2 of observations, the model is considered to have a reasonably good performance (e.g., Heikkilä et al., 2008b; Brattich et al., 2021). For model comparison with surface air concentrations, the model value from the bottom grid box closest to the corresponding measurement site is selected.

The annual mean 7Be surface air concentration and deposition measurements are taken from a compilation by F. Zhang et al. (2021). The compilation includes a total of 494 annual mean values for surface air 7Be concentrations and 304 for 7Be deposition fluxes. For the deposition measurements, most of them include both wet and dry deposition, while a few are collected only during rainfall events and thus include only wet deposition. It includes the data from the following:

the Environmental Measurements Laboratory (EML; https://www.wipp.energy.gov/namp/emllegacy/index.htm, last access: 23 November 2023) Surface Air Sampling Program (SASP), which began in the 1980s;

The data used for investigating the seasonality of 7Be surface air concentrations are mainly taken from a multiyear compilation dataset of IMS from Terzi and Kalinowski (2017). The seasonal 7Be deposition data are taken from Courtier et al. (2017), Du et al. (2015), Dueñas et al. (2017), Hu et al. (2020), Lee et al. (2015), and Sangiorgi et al. (2019). The vertical profile of 7Be concentrations is taken from the Environmental Measurements Laboratory (EML) High Altitude Sampling Program (HASP), spanning the years of 1962–1983. It should be noted that, different from surface air measurements, the vertical air samples were usually collected during single-day flight campaigns.

There are fewer 10Be measurements compared to 7Be. Here we compiled two datasets of published 10Be surface air measurements (Table S2) (Aldahan et al., 2008; Liu et al., 2022a; Yamagata et al., 2019; Padilla et al., 2019; Rodriguez-Perulero et al., 2019; Huang et al., 2010; Méndez-García et al., 2022; Elsässer et al., 2011; Dibb et al., 1994) and deposition fluxes (Table S3) covering more than 1 year, to validate the model performance. The air samples are continuously collected by filters using a high-flow aerosol sampler. The sampling volume is approximately 700 m3 of air for daily samples (e.g., Liu et al., 2022a) and between 3000 and 5000 m3 for weekly samples (e.g., Yamagata et al., 2019). The deposition data include the precipitation samples (wet deposition) (Graham et al., 2003; Monaghan et al., 1986; Somayajulu et al., 1984; Heikkilä et al., 2008a; Raisbeck et al., 1979; Maejima et al., 2005) and ice core samples (wet and dry deposition) that cover the recent period (Heikkilä et al., 2008a; Zheng et al., 2021a; Pedro et al., 2012; Baroni et al., 2011; Aldahan et al., 1998; Berggren et al., 2009; Auer et al., 2009; Zheng et al., 2023a). The 10Be vertical profile measurements are mainly taken from Dibb et al. (1992, 1994) and Jordan et al. (2003).

Figure S2 shows the comparison between 7BeP16 and 7BeLP67 production rates for the year 1958. Generally, the 7BeP16 production rate shows a similar production distribution to the 7BeLP67 production rate, with a maximum 7Be production over the polar stratosphere (∼100 hPa). The 7BeLP67 production rate shows, on average, about a 72 % higher production rate compared to 7BeP16 in the stratosphere and about 38 % in the troposphere (Fig. S2c; Table S4). On a global average, the 7BeLP67 production rate is about 60 % higher than that of 7BeP16, as shown in previous studies (Poluianov et al., 2016). The stratospheric production contributes about 67 % to the total production for the 7BeLP67 production rate, while it is about 62 % for the 7BeP16 production rate for the year 1958.

The 10BeLP67 production rate in the GEOS-Chem model uses the identical source distribution as 7Be with a scaling factor based on the estimates from surface air measurements (Koch and Rind, 1998). This leads to a constant 10BeLP67/7BeLP67 production ratio (0.55) throughout the entire atmosphere. However, as shown in many 7Be and 10Be production models (e.g., Poluianov et al., 2016; Masarik and Beer, 2009), 7Be and 10Be have different altitudinal production distributions. The P16 production shows an increasing 10Be/7Be production ratio from higher altitudes (0.35) to lower altitudes (0.6) (Fig. S3). Using a constant 10Be/7Be production ratio may thus result in large errors in the modeled 10Be concentrations as well as 10Be/7Be ratios. The stratospheric production contributes about 67 % of the total production with 10BeLP67, while it is about 58 % with the 10BeP16 production for the year 1958 (Table S4).

Figure 1 shows the comparison between 7BeP16 and 7BeP16spa production rates for the period 2008–2018. The global production is similar for P16spa and P16 (Table S4). However, considering non-dipole moment influence on geomagnetic cutoff rigidity, 7BeP16spa and 10BeP16spa production rates in the Southern Hemisphere show production rates that are ∼11 % higher compared to the Northern Hemisphere (Table S4). This difference is not present when an axial dipole is assumed. Compared to the P16 production rate, the 7BeP16spa production rate is 30 %–40 % lower over eastern Asia and southeastern Pacific but 40 %–50 % higher over North America and from subtropical South Atlantic to Australia (Fig. 1). 10BeP16spa shows similar results to 7BeP16spa. These differences are not constant throughout the atmospheric column but generally increase with altitude (Fig. 1d).

Figure 2 compares the simulated 7BeP16spa averaged over 2008–2018 with the measurements. Due to the data availability, the measurements do not necessarily cover the same period as model simulations. The model deposition fluxes here include both dry and wet deposition. About 93.7 % of modeled air 7BeP16spa concentrations agree within a factor of 2 with the observed values. The model also shows reasonable agreement with the measured deposition fluxes (60.9 % within a factor of 2), although the discrepancy between the modeled and observed deposition fluxes is larger than that for surface air concentrations. The deposition fluxes are usually less well monitored compared to the air 7Be samples and cover only shorter periods (e.g., 1 or 2 years). Further, the limited model resolution applied here may not be able to capture meteorological conditions on local scales (e.g., precipitation, convection, and tropopause folding) in some sites (e.g., Yu et al., 2018; Spiegl et al., 2022), especially for coastal regions when the sub-grid-scale orographic precipitation is important.

Figure 3 shows the spatial distribution and zonal mean of measurements in comparison with the model-simulated 7BeP16spa surface air concentrations and deposition fluxes. Generally, the model captures the spatial distribution of 7Be air concentrations and deposition fluxes. The “latitudinal pattern” of surface air 7Be concentrations differs from that of the 7Be production rate, reflecting the effects of atmospheric transport and deposition processes. The model suggests high 7Be air concentrations, mainly over the dry regions (Fig. 3a), due to low wet deposition rates (e.g., desert regions over northern Africa, Arabian Peninsula, central Australia, and central Antarctica), and over high-altitude regions (e.g., Tibetan Plateau). The model captures the observed latitudinal peaks in surface air concentrations over the subtropics and mid-latitudes (Fig. 3c around 30–40∘ N and 30–40∘ S). These peaks are consistent with the high stratospheric contribution (25 %–30 %) at mid-latitudes (Fig. S4). The model overestimates 7Be air concentrations over the Arctic (70–90∘ N; Fig. 3c) by about 30 %–40 %. By contrast, high 7Be deposition fluxes are observed at mid-latitudes due to the influence of the high precipitation (wet deposition) and strong stratosphere–troposphere exchange (Fig. 3d). In the Northern Hemisphere, the model-simulated deposition fluxes peak at a lower latitude (∼30∘ N) relative to the observations (∼45∘ N). These modeled spatial distributions of the air concentrations and deposition rates of 7Be also agree generally well with previous model simulations (e.g., Heikkilä and Smith, 2012).

The modeled 7BeP16spa air concentrations show better agreements (smaller RMSE and higher FA2 values) with the measurements in comparison to 7BeLP67 (Fig. S5). 7BeLP67 tends to overestimate the absolute values of 7Be concentrations. This is caused by (i) the overestimation of the 7Be production rate by LP67 for a given solar modulation function and (ii) the use of a simple scale factor to account for the solar modulation influence on the LP67 7Be production rate.

We also examine whether using the dipole approximation of the cutoff rigidity or real cutoff rigidity (P16 and P16spa, respectively) in the production model leads to significantly different results (Fig. 4). Although large regional differences (up to 40 %–50 %, Fig. 1) in the production model are observed between P16spa and P16 production rates, such differences are reduced in surface air concentrations and deposition fluxes due to transport and deposition processes, as expected. The 7BeP16sap air concentrations show higher values (∼7 %) over 10–40∘ S and lower values (∼12 %) over the East Asian region (Fig. 4a) compared to 7BeP16. These differences are higher for the deposition fluxes, up to 10 % higher over the 10–40∘ S and up to 18 % lower over the east Asian region (Fig. 4b). Since the total deposition flux reflects precipitation scavenging through the tropospheric column, it tends to be more sensitive to 7Be air concentrations at higher altitudes and downward transport of 7Be from the stratosphere. Indeed, model results suggest that deposition fluxes have a higher stratospheric fraction compared to surface air concentrations (Fig. S4), as previously shown by Liu et al. (2016). The 7BeP16spa deposition fluxes show better agreement with measurements than those of 7BeP16 (Fig. S5). The comparison for 10Be shows similar results to 7Be except with less than 10 % difference. For 10Be deposition fluxes in Antarctica and Greenland, this influence is less than 3 %. This is because the dominant contribution of 10Be is from the stratosphere where the hemispheric production differences are diminished by the long stratospheric residence time of 10Be. However, it does not suggest that the cutoff rigidity including the non-dipole influence could be ignored for 10Be deposition in polar regions, as the spatial pattern of cutoff rigidities was very different in the past, e.g., during the Laschamps geomagnetic field minimum around 41 000 years before the present (Gao et al., 2022). Further studies are warranted to investigate this spatial cutoff rigidity influence on 10Be in more detail.

Figure 5 shows the comparison between modeled annual mean 10BeP16spa surface air concentrations (or deposition fluxes) averaged over 2008–2018 and measurements. The 10BeP16spa shows similar spatial distributions as 7BeP16spa because both radionuclides share the same transport and deposition processes. The model underestimates the measured 10Be surface air concentrations and deposition fluxes at some sites (Fig. 5b, d). This may be attributed to the influence of resuspended dust with 10Be attached, which could typically contribute 10 %–35 % to the air 10Be concentrations (Monaghan et al., 1986). It should be mentioned that 7Be decays in the dust because of its short half-life and therefore does not contribute to the surface air 7Be concentrations. Indeed, data for which a careful examination of the recycled dust 10Be in samples was conducted (e.g., Monaghan et al., 1986) or from locations that are less influenced by recycled dust 10Be (e.g., polar regions; dots in Fig. 5b–d) show better agreement with the model simulations. This suggests the importance of considering the dust contribution when measuring the air 10Be samples. The model also shows relatively good agreement with most 10Be deposition data from polar ice cores (marked as dots in Fig. 5d) within a factor of 2.

Figure 6 shows the simulated annual zonal mean vertical profiles of 7BeP16spa and 10BeP16spa concentrations compared with those from aircraft measurements in the troposphere and stratosphere from the EML/HASP. The measurements cover different regions and specific meteorological conditions; hence they should only provide a range in which the model results should lie. Following previous modeling studies (Heikkilä et al., 2008b; Koch et al., 1996), we compare model zonal mean values in each 15∘ latitude band with the corresponding observations.

The simulated 7BeP16spa profiles agree well with the measurements, especially capturing the peaks at ∼20–22 km at mid-latitudes and low latitudes (e.g., Fig. 6c, e, h). The feature that 7Be increases with altitude without a peak at 22 km at northern high latitudes (60–75∘ N) is also captured by the model (Fig. 6a). The 7BeP16spa shows high concentrations in the polar stratosphere and low values over the equatorial stratosphere (Fig. S6), mainly reflecting the latitudinal distribution of the production. This “latitudinal structure” is modulated for 10BeP16spa in the stratosphere as 10Be is better mixed than 7Be due to its slow decay, together with a relatively long residence time in the stratosphere (Waugh and Hall, 2002). Both 7Be and 10Be show very low concentrations in the tropical upper troposphere, reflecting the frequent injection of air from the lower troposphere in wet convective updrafts, where aerosols are efficiently scavenged (Fig. S6).

The model also reasonably simulated 10Be vertical profiles compared with observations, with a tendency to underestimate observations in the stratosphere (Fig. 6j–l). A previous general circulation model study by Heikkilä et al. (2008b) also showed model stratospheric 10Be that is too low compared to measurements. They attributed this underestimation to too short a stratospheric air residence time in the model, which prevents 10Be concentrations from sufficiently accumulating in the stratosphere. However, this may not be the case in our study, as the stratospheric air residence time in the MERRA-2 reanalysis agrees reasonably with the observations (Chabrillat et al., 2018). Another explanation is that the 10Be production rate may be underestimated in the stratosphere. 7Be is less affected by this process than 10Be because of its short half-life compared to its stratospheric residence time (Delaygue et al., 2015).

Table 1 shows the global budgets for 7BeP16spa and 10BeP16spa over the period of 2008–2018. About 22.1 % of tropospheric 7BeP16spa is lost by radioactive decay, 75.8 % by convective and large-scale precipitation, and 2.1 % by dry deposition. The wet deposition contributes to about 97 % of total deposition for 7BeP16spa and 10BeP16spa (Table 1; Fig. S7), which is slightly higher than the ∼93 % contribution in previous model studies (Heikkilä et al., 2008b; Koch et al., 1996; Spiegl et al., 2022). The global mean tropospheric residence time of 7BeP16spa is about 21 d, which is comparable to that reported by previous model studies: 18 d by Heikkilä et al. (2008b) and 21 d by Koch et al. (1996) and Liu et al. (2001). This also agrees with the residence time of about 22–35 d estimated from the observed deposition fluxes and air concentrations at 30–75∘ N (Bleichrodt, 1978). The averaged tropospheric residence time of 10BeP16spa is about 24 d, which is consistent with the 20 d suggested by Heikkilä et al. (2008b).

The seasonality of 7Be is influenced by (a) the amount of precipitation, (b) the stratosphere–troposphere exchange processes, and (c) the vertical transport of 7Be in the troposphere. The roles of these factors may vary depending on location. We compare the seasonal variations of modeled 7BeP16spa and 7BeLP67 concentrations with measurements from a dataset compiled by Terzi and Kalinowski (2017), with the data covering more than 6 years (Fig. 7). It should be noted that the model 7Be results and MERRA-2 precipitation rates are averaged over the years of 2008–2018, while the measurements are based on the data availability over the period 2001–2015.

In the Southern Hemisphere from 25–40∘ S, the 7Be concentration peak is observed in austral summer (December–February), resulting from the combined influence of stratospheric intrusions and strong vertical transport during this season (Villarreal et al., 2022; Zheng et al., 2021b; Koch et al., 1996). The summer peak is also observed at northern mid-latitudes. This “summer peak” feature is well simulated by the model at some sites (e.g., KWP40 (29.3∘ N, 47.9∘ E), AUP04 (37.7∘ S, 145.1∘ E) and AUP10 (31.9∘ S, 116∘ E) shown in Fig. 7) but not at others (e.g., GBP68 (37.1∘ S, 12.3∘ W) and PTP53 (37.7∘ N, 25.7∘ W) in Fig. 7). This may not be related to stratospheric intrusion in the model as the simulated stratospheric contributions (Fig. S4) agree fairly well with estimates inferred from measurements, i.e., ∼25 % on annual average at northern mid-latitude surface (Dutkiewicz and Husain, 1985; Liu et al., 2016). Hence this could be due to the errors in vertical transport (e.g., convection) during the summer season.

The sites at northern high latitudes (>50∘ N) show spring peaks that are well simulated by the model (e.g., ISP3 (64.1∘ N, 21.9∘ W)). This spring peak coincides with high stratospheric contributions, reflecting the influence of stratospheric intrusions. The influence of precipitation changes is also seen at several sites, especially in locations with high precipitation rates (e.g., monsoon regions). For example, two sites from Japan (JPP38 (36.3∘ N, 139.1∘ E) and JPP37 (26.5∘ N, 127.9∘ E) in Fig. 7) show summer minima coinciding with the high precipitation, even with relatively high stratospheric contributions in the same month.

The seasonal variation of stratospheric contribution is quite similar for the sites located in the Northern Hemisphere, with a high contribution in spring and a low contribution in fall. This is consistent with the estimates based on air samples that indicate stratospheric contributions varying from ∼40 % in spring to ∼15 % in fall at latitudes 38–51∘ N (Dutkiewicz and Husain, 1985).

Generally, the model simulates the annual cycle of surface air 7Be concentrations well for most sites in terms of amplitude and seasonality (Fig. 7). For a few sites (e.g., DEP33 (47.9∘ N, 7.9∘ E)), the model captures the observed seasonality but not the correct absolute values. This could be partly due to the coarse resolution of the model. The 7BeLP67 is normalized to 7BeP16spa as we focus on the comparison of seasonal variability between these simulations. The very similar features (differences within 1 %) between all simulations using different production rates indicate a dominant influence of the meteorological conditions on the seasonal variations of the air 7Be concentrations.

Figure 8 compares model results with the seasonal 7Be deposition flux observations over the overlapping periods. Usually, high precipitation leads to high 7Be deposition fluxes (e.g., Du et al., 2015). Interestingly, low deposition fluxes are observed during the summer season in Taipei (Lee et al., 2015; Huh et al., 2006) coinciding with high precipitation. This feature is well captured in the model. Taipei has a typhoon season in summer when strong precipitation can occur in a very short period. The atmospheric 7Be could be removed quickly at the early stage of the precipitation event, while at the later stage there is little 7Be left in the air that can be removed (Ioannidou and Papastefanou, 2006).

To examine the ability of model to simulate 10Be in polar regions, we compare model results with two sub-annual ice core records (Fig. 9): the GRIP record from Greenland (1986–1990) (Heikkilä et al., 2008c) and the DSS record from Antarctica (2000–2009) (Pedro et al., 2011b). It should be noted that the direct measurements from ice cores are concentrations in the ice (atoms g-1). To calculate deposition fluxes, the ice concentrations are multiplied by ice accumulation rates. However, for sub-annual accumulations, this bears large uncertainties. Therefore, we calculate the modeled 10Be concentrations for the selected sites using the model deposition fluxes at the selected sites, timed by ice density and then divided by the corresponding model precipitation rates.

Firstly, there is no consistent seasonal cycle in the GRIP 10Be measurement, indicating a strong role of local meteorology. The model does not reproduce the mean seasonal cycle, partly because the model was not run for the exact same period. However, we note that the measurements for the year 1988 show an annual cycle similar to that in the model, suggesting that the model 10Be seasonality falls within the range of the observations. For the DSS site, the model simulates the austral winter minima but not the austral fall maxima (February–April). These model biases could be due to the limited model resolution and local effects (e.g., ice redistribution due to wind blow) that are not resolved by the model. Such discrepancies were also reported by previous model studies using the ECHAM5-HAM general circulation model (2.8∘ × 2.8∘) over the overlap period (Heikkilä et al., 2008c; Pedro et al., 2011a). Global model simulations at higher resolutions or using a regional model could help improve the agreements between model results and measurements in Greenland and Antarctica. However, it should be kept in mind that local surface processes can cause a high degree of spatial variability in the impurity concentrations in ice cores, even for short distances (Gfeller et al., 2014), which cannot be resolved in climate models.

Figure 10 shows the modeled zonal mean 10BeP16spa/7BeP16spa ratios during boreal spring (March–May) and austral spring (September–November), respectively, when the stratosphere–troposphere exchange is strong in either of the two hemispheres. Also shown is the comparison of the altitudinal profile of the 10BeP16spa/7BeP16spa ratio with measurements from three aircraft missions (Jordan et al., 2003). The model 10BeP16spa/7BeP16spa ratio generally lies within the ranges of measurements (Fig. 10c). Due to the decay of 7Be and long residence time in the stratosphere, the 10Be/7Be ratio is higher (>1.5) in the stratosphere and increases with altitude, with a maximum (>10) in the tropical stratosphere. During the period without strong stratospheric intrusion (e.g., the autumn season in Northern Hemisphere, Fig. 10b), the monthly 10Be/7Be ratio near the surface is around 0.9–1. This surface 10Be/7Be ratio could be up to 1.4 when the strong stratosphere–troposphere exchange happens (e.g., the spring season in Northern Hemisphere; Fig. 10a).

Figure 11 compares model surface air 7BeP16spa and 10BeP16spa concentrations and 10BeP16spa/7BeP16spa ratios with monthly mean observations in Tokyo (Yamagata et al., 2019) during the period of 2008–2014. Here we mainly focus on the relative variations, and 7Be and 10Be data are normalized. The model captures the observed variability in Tokyo well. 7Be and 10Be show a peak in early spring (March–May), while the 10Be/7Be ratio shows a wider peak over March–July. The summer minima of 7Be and 10Be are due to strong scavenging associated with the monsoon/typhoon season precipitation. While the 10Be/7Be ratio is independent of precipitation scavenging, the peaks of 10Be/7Be coincide well with the enhancements of stratospheric contribution in the model. This indicates that the 10Be/7Be ratio is a better indicator of the vertical transport and stratospheric intrusion influences than either tracer alone.

Here we examine the ability of the model to simulate the inter-annual variability of 7Be surface air concentrations, especially whether the model can simulate the solar modulation influence using the updated production model. Figure 12 shows the comparison of model-simulated annual mean surface air 7Be concentrations with measurements during 2008–2018 from four sites: Kiruna, Ljungbyhed, Vienna, and Hong Kong SAR (Kong et al., 2022; Zheng et al., 2021b). The tropospheric 7Be production rate from each site is also plotted for comparison as measured annual mean surface air 7Be concentrations are predominantly influenced by the local tropospheric 7Be production signal (Zheng et al., 2021b).

The model 7BeP16spa surface air concentrations show a better agreement with annual 7Be measurements (higher R value) compared to 7BeLP67 concentrations at all surface sites (Fig. 12). The variability in the measurements (Kiruna, Ljungbyhed, and Vienna) agrees well with the trend in production, suggesting a dominant influence of solar modulations during this period. This is further supported by strong deviations between 7BeP16spa and 7BeLP67 as no solar influence is considered in 7BeLP67. This also emphasizes the importance of including solar modulation of the 7Be and 10Be production in modeling studies, especially for high-latitude regions. The mismatch of measurements and production at Kiruna from 2012 to 2015, together with the similar year-to-year variability between 7BeP16spa and 7BeLP67, suggests the meteorological influence is dominant at Kiruna for this period. This also suggests that meteorological influences can suppress the solar signal in the 7Be and 10Be observations.