Meridional transport and deposition of atmospheric 10 Be

. 10 Be concentrations measured in ice cores exhibit larger temporal variability than expected based on theoretical production calculations. To investigate whether this is due to atmospheric transport a general circulation model study is performed with the 10 Be production divided into stratospheric, tropospheric tropical, tropospheric subtropical and tropospheric polar sources. A control run with present day 10 Be production rate is compared with a run during a geomagnetic minimum. The present 10 Be production rate is 4–5 times higher at high latitudes than in the tropics whereas during a period of no geomagnetic dipole ﬁeld it is constant at all latitudes. The 10 Be deposition ﬂuxes, however, show a very similar latitudinal distribution in both the present day and the geomagnetic minimum run indicating that 10 Be is well mixed in the atmosphere before its deposition. This is also con-ﬁrmed by the fact that the contribution of 10 Be produced in the stratosphere is dominant (55%–70%) and relatively constant at all latitudes. The contribution of stratospheric 10 Be is approximately 70% in Greenland and 60% in Antarctica reﬂecting the weaker stratosphere-troposphere air exchange in the Southern Hemisphere.


Introduction
Cosmogenic radionuclides, such as 10 Be, are excellent tools to study past solar activity and past geomagnetic field strength (Beer et al., 1988). They are produced in the atmosphere by nuclear interactions between the high-energetic galactic cosmic ray particles and atmospheric atoms. Because of the modulation of the cosmic ray intensity by the solar wind as well as the geomagnetic field strength the produc-Correspondence to: U. Heikkilä (ulla.heikkilae@eawag.ch) tion of cosmogenic radionuclides has a strong latitude and altitude (atmospheric pressure) dependence (Lal and Peters, 1967;Masarik and Beer, 1999). Recently there have been several studies of the past solar activity (McCracken et al., 2004a;Muscheler et al., 2007;Vonmoos et al., 2006) based on 10 Be records from polar ice cores. However, the interpretation of the 10 Be data is hampered by the uncertainty introduced by the transport of the 10 Be atoms from their origin to the archives and the wet and dry scavenging processes which are responsible for the removal of the 10 Be atoms from the atmosphere.
The relationship between the measured 10 Be fluxes and concentrations in ice cores and the global production rate is not yet fully understood. One open question concerns the source region of 10 Be which is deposited in polar areas. Because of the geomagnetic shielding the solar modulation of 10 Be is strongest at high latitudes (Lal and Peters, 1967;Masarik and Beer, 1999). If the 10 Be deposited in polar ice originated only from latitudes pole-wards of 60 • interpreting the variability of the measured 10 Be concentrations in ice as global production variability would lead to an overestimation of the global production variability. However, there are several reasons to assume that significant mixing takes place in the atmosphere before the 10 Be atoms are deposited. The major part of 10 Be is produced in the stratosphere (50-75% depending on solar activity (Heikkilä et al., 2008a;Masarik and Beer, 1999) and the tropopause height), where 10 Be is mixed within the average residence time of 1-2 years to such an extent that the 10 Be mixing ratio in the air coming from the stratosphere can be assumed to represent the mean stratospheric production within each hemisphere. Therefore we call the 10 Be in the stratosphere "well mixed" although the stratosphere is stably layered and cannot be understood as a mixer. The mixing within each hemisphere is sufficient to mask the latitudinal dependence of the production of 10 Be because it can be considered symmetric in both hemispheres.
Published by Copernicus Publications on behalf of the European Geosciences Union. 516 U. Heikkilä et al.: Meridional deposition of 10 Be The exchange between stratosphere and troposphere mainly takes place at the subtropical tropopause breaks (Stohl et al., 2003), meaning that 10 Be produced in the stratosphere is mainly deposited in the subtropics. The amount of 10 Be produced in the troposphere at high latitudes is relatively small because the tropopause lies at a higher pressure at high latitudes than in the tropics. Therefore, so far a rather well mixed atmosphere has been assumed for solar activity reconstructions based on 10 Be from polar regions (McCracken et al., 2004a;Muscheler et al., 2007;Vonmoos et al., 2006). However, other studies have questioned this assumption and introduced a so-called polar enhancement coefficient (PEC) which corrects for the higher modulation of the production rate at high latitudes. Mazaud et al. (1994) were the first to estimate the origin of 10 Be measured in the Vostok ice core. By identifying which part of the 10 Be was modulated by the geomagnetic field strength they concluded that 25% of 10 Be was locally produced and 75% originated from lower latitudes. Steig et al. (1996), instead, found that only 35% of 10 Be at Taylor Dome, Antarctica, can be derived from low-latitude sources. On the other hand, they also found a strong correlation between the Taylor Dome data and 10 Be production rates from the whole atmosphere or the whole stratosphere as predicted from the neutron monitor data. Bard et al. (1997) make the assumption that the 10 Be in polar regions is produced pole-wards of 60 • , both in the stratosphere and the troposphere and falls down locally. Using this assumption they calculated a theoretical correction value for the polar enhancement, which was 0.65 when assuming a variability of the 10 Be production of 17% between solar minimum and maximum. McCracken (2004b) introduced 5 different mixing models of the source regions of 10 Be and tested the influence of varying fraction of 10 Be from the lower latitudes. However, the different character of the circulation in the stratosphere and the troposphere was not taken into account.
Recently Field et al. (2006) studied the effect of polar enhancement using a general circulation model (GCM). They found an enhancement of 20% of the 10 Be deposition fluxes near the poles during a solar minimum (drop from =700 MeV to 500 MeV), and a suppression of 20% during a geomagnetic minimum (reduction of 25% of the field strength). In comparison, another recent model study by Heikkilä et al. (2008a), which investigated an even larger solar minimum (the Maunder Minimum, =200 MeV), combined with a climate cooling, found no indication of a polar enhancement. Both model studies agree, however, that the climatic conditions, such as changes in the tropospheric transport or precipitation rate, add some uncertainty to the global production signal in the polar 10 Be deposition fluxes. It is quite difficult to quantify this uncertainty. Heikkilä et al. (2008a) found a meteorological "noise" in the zonal mean deposition fluxes of mostly less than 25% of the total production change between present day and the Maunder Minimum, which can be considered as an extreme climate change for the Holocene. However, this amount depends on the magnitude and type of climate change, as was shown by the different experiments made by Field et al. (2006).
The aim of this study is to improve the interpretation of 10 Be from the ice cores by tracing back the origin of the 10 Be atoms which are deposited in polar regions. The main goals are: 1) to quantify the contribution of different latitudes to the measured 10 Be flux at a given site, 2) to investigate the postulated polar enhancement in the 10 Be deposition and 3) to determine whether the fraction of stratospheric to locally produced atmospheric 10 Be in ice cores depends on the production rate. Therefore we carried out two experiments with extremely different 10 Be production distributions in the atmosphere.
The first experiment was performed with zero geomagnetic field strength. This leads to a 10 Be production rate which is constant at all latitudes, leading to no change polewards of 60 • but to an extreme change of up to a factor of 4-5 at low latitudes. This experiment is called "Laschamp". During the so-called Laschamp event, a geomagnetic excursion which took place approximately 40 kyr before present, the strength of geomagnetic field was close to zero, leading to an enhanced production of 10 Be. This peak can be observed in all ice cores (GRIP, Vostok, Dome C, Byrd and Camp C) covering this period (Baumgartner et al., 1998;Yiou et al., 1985;Raisbeck et al., 1987;Beer et al., 1984Beer et al., , 1987. We use the name "Laschamp" for this experiment for the simplicity throughout the manuscript although this study is conceptual and considers only the 10 Be production change. The ice age climatic conditions during the real Laschamp event were not taken into account. Therefore it is also not possible to compare the results of this study with the measured 10 Be ice core concentrations. The Laschamp experiment was compared with a second experiment representing the present day conditions (this run is referred to as the control run throughout the manuscript). The climatic conditions were the same in both experiments, as well as the solar activity ( =700 MeV). In order to investigate at which latitudes the 10 Be in ice cores was produced, the 10 Be source was divided into seven different components, roughly following the atmospheric circulation structure. The 10 Be produced in the whole stratosphere was considered as one component while the tropospheric 10 Be was divided into 30-degree latitude bands: 10 Be produced in the tropics, subtropics and polar areas, both for the Northern and the Southern Hemisphere. Another interesting issue to investigate is whether there are differences in the stratospheric and local fractions of 10 Be between the hemispheres.

Model description and setup
The model employed for this study was the ECHAM5-HAM general circulation model.  the Max-Planck Institute for Meteorology, Hamburg, evolving originally from the European Centre of Medium Range Weather Forecasts (ECWMF) spectral weather prediction model. It solves the prognostic equations for vorticity, divergence, surface pressure and temperature, expressed in terms of spherical harmonics with a triangular truncation. Nonlinear processes and physical parametrizations are solved on a Gaussian grid. A complete description of the ECHAM5 GCM is given in Roeckner et al. (2003). The additional aerosol module HAM includes the microphysical processes, the emission and deposition (wet and dry) of aerosols, a sulfur chemistry scheme and aerosol impact radiation (Stier et al., 2005). For this study a middle-atmospheric model version with a horizontal resolution of T42 (2.8×2.8 degrees) with 39 vertical levels up to 0.01 hPa (∼60 km) was used. Each run was allowed to spin up for five years to let 10 Be reach equilibrium and the five following years were used for the analysis. The run was forced with prescribed observational sea surface temperatures and sea ice cover obtained from the international model intercomparison AMIP2 project.
The production rates of the radionuclides were taken from the revised production rate calculations of Masarik and Beer, submitted. The profiles were interpolated as a function of latitude and altitude using the monthly mean solar modulation function reconstructed by Usoskin et al. (2005) for the years 1986-1990 for the control run. For the Laschamp run a constant =700 MeV was used. The deposition of 10 Be is divided into wet and dry deposition and sedimentation. Because the 10 Be atoms are attached to sulfate aerosols the deposition is calculated relative to sulfate deposition. For calculating the dry deposition and sedimentation velocity of 10 Be an area weighted average of the velocity of sulfate aerosols is used. For the wet deposition of 10 Be we assume that 10 Be is scavenged with the same efficiency as the sulfate aerosols. See Heikkilä et al. (2008a) for more details. Globally dry deposition accounts for less than 10% of the total deposition. In Greenland the precipitation rates are relatively high which is why the model suggests a low contribution of dry deposition of less than 10%. Only in the driest areas in Antarctica the dry deposition becomes more important and can be even more than 50% (see Fig. 5.27 and 5.28 of Heikkilä, 2007). For the two experiments of this study the deposition scheme was the same because the climate was kept constant and therefore the sulfate emissions and concentrations were not influenced.
ECHAM5-HAM's ability to reproduce the observed concentrations and deposition fluxes of 10 Be and 7 Be worldwide has been discussed in Heikkilä et al. (2008a). We refer to Figs. 2, 3, 4, 5 and 6. Generally the model was able to reproduce both the observed concentrations and deposition fluxes fairly well. Especially in Greenland the agreement was good when reproducing observed fluxes during a Greenlandic traverse (see Fig. 5 in Heikkilä et al. (2008a)) and also the seasonal changes during a 5-year period at Summit, U. Heikkilä: MERIDIONAL DEPOSITION OF 10 BE he cone same ric and   Greenland (Heikkilä et al., 2008b). Unfortunately not much present day 10 Be data is available from Antarctica. Pedro et al. (2006) measured the snow concentrations of 10 Be in a snow pit from the Law Dome station in the year 2001. Using their average snow accumulation rate we estimate an average deposition flux of 10 Be of ∼100 atoms/m 2 /s, which is comparable with the modeled value of ∼150 atoms/m 2 /s for the average of 1986-1990.

Total deposition and concentration
Global budgets of 10 Be in both runs are listed in Table 1. The production rate of 10 Be in the Laschamp run is approximately twice as high as in the control run. The ratio of stratospheric to tropospheric production is almost unchanged (Laschamp run 1.7, control run 1.9). The stratospheric burden in the Laschamp run has increased relatively more than the production rate because of the very different distribution of 10 Be production. This is also reflected by the longer residence time of 10 Be in the stratosphere (320 days in the Laschamp run, 230 days in the control run). Figure 1 illustrates the zonal mean production rate of 10 Be which has been integrated over all longitudes, integrated over the whole atmospheric depth in the upper part of the figure and below it integrated over the stratospheric and the tropospheric depths separately. It can be seen that the production does not change pole-wards of 60 • . Instead, in the equatorial region the production rate is increased by a factor of 4-5 in the Laschamp run. The decrease of the production flux in the southern high latitudes which is not visible in the northern high latitudes is caused by the high altitude of the Antarctic continent with lower air pressure. Although the production is constant at all latitudes, the separate stratospheric  Units are atoms/m 2 /s. and the tropospheric production fluxes are not because the tropopause pressure is higher in polar latitudes and lower in the tropics. In the control run the tropospheric production of 10 Be has practically no latitudinal dependence because the latitudinal structure of the tropopause height compensates the production structure. The 10 Be produced in the stratosphere can be assumed to be quite well mixed due to its long residence time and therefore changes in the stratospheric production are not expected to have an impact on the latitudinal 10 Be deposition. On the other hand the much larger tropical tropospheric production might increase the deposition fluxes locally.
However, the zonal mean total deposition fluxes (including wet and dry deposition and sedimentation) of 10 Be, shown in Fig. 2, in absolute as well as in normalised units show no such difference in the latitudinal distribution. The absolute fluxes are about a factor of 2 higher due to higher production rate (twice as high globally) in the Laschamp run, but the normalised fluxes are practically identical. Especially in the polar regions there is no enhancement. Figure 2 also depicts the deposition change in percent between the Laschamp run and the control run. For comparison we also show the change between the Maunder Minimum experiment (Heikkilä et al., 2008a), which included a climate cooling, and the control run. This change in the Maunder Minimum experiment is mostly below 8% while the global production change is 32%. The change is slightly larger in the Laschamp experiment, mostly below 10% and at some points below 20% of the global mean production raise of 100%. At some points in the high polar latitudes the change is larger than that, both in  the Maunder Minimum and the Laschamp experiment. However, if we look at the differences of the normalised deposition fluxes at these latitudes we see that the fluctuations can be considered as negligible. Because the fluxes in the polar regions are extremely low, even small fluctuations account for a larger relative change. This cannot be connected to a polar enhancement which refers to a clear latitudinal change reflecting the latitudinal production change because the fluctuations seen in Fig. 2 can be positive or negative and show no latitudinal pattern similar to the production change. Such small changes could also be caused by different realizations of actual weather between the two runs. Generally these results suggest that independent of the latitudinal distribution of the 10 Be production or the climate conditions the distribution of the 10 Be deposition fluxes remains the same and reflects clearly the production raise.
The reason for the unchanged normalised 10 Be flux is the constant climate between both experiments. The scavenging of 10 Be in the model study is connected with sulfate scavenging because we assume that 10 Be atoms are attached to sulfate aerosols (Heikkilä et al., 2008a). A scavenging efficiency which depends on the sulfate scavenging efficiency is calculated for 10 Be. Because the meteorology in both runs was unchanged the sulfate scavenging efficiency remains constant between the control and the Laschamp run and also the relative amount of scavenged 10 Be remains unchanged. The 10 Be atoms produced in the tropics above the cloud level in the Laschamp run are not scavenged and hence reside longer in the troposphere, as is reflected by the longer tropospheric residence times (discussed in Chapter 3.2), or rise to the stratosphere. Figure 3 illustrates the change in the zonal mean concentrations of 10 Be in air. The change has been calculated in percent from the concentrations in the Laschamp run, compared with the control run. The change is almost always positive because of the approximately doubled production rate in the Laschamp run compared with the control run. We see that the change is largest in the tropics as expected due to the larger production raise there. At high altitudes the concentration change is very large because the high concentrations of 10 Be in the upper troposphere which are not scavenged are raised to the stratosphere by the Brewer-Dobson circulation and therefore increase the stratospheric concentrations more. At high latitudes in the troposphere the change is quite small (<100%) because there the production rate did not change and also reflects the fact that only a small amount of 10 Be atoms reach the high latitudes. This will be further discussed in the following paragraphs.
To further investigate the transport paths of 10 Be we show the different components of the 10 Be deposition fluxes in Fig. 4. The components are 10 Be produced in the stratosphere, in the tropical (0-30 • ), subtropical (30 • -60 • ) and polar (60 • -90 • ) troposphere, Northern and Southern Hemisphere separately. The sum of all these components is the total deposition flux shown in Fig. 2. It is clear that the dominant component is the stratospheric 10 Be. The tropospheric components somewhat increase the deposition fluxes locally, but their contribution is not large. Especially the contribution of polar tropospheric (60 • -90 • ) production is very low, a result which is not consistent with earlier assumption that 10 Be measured in polar regions mostly originates from high latitudes, i.e. Bard et al. (1997).
This result also suggests that changes in the location of the geomagnetic pole, the so-called polar wander, brought up by McCracken (2004b), would not be of importance. The largest contribution to the deposition fluxes is the stratospheric fraction, which is mixed to such an extent that changes in the location of the geomagnetic pole can be neglected.
These results are somewhat different from the findings of Field et al. (2006), who detected an additional 20% reduction of the deposition fluxes pole-wards of 30 • -40 • and an increase of up to 60% in the equatorial region in their reduced geomagnetic field strength experiment although the geomagnetic reduction was only 25% from the present day strength. We found no latitudinal pattern in the deposition change and generally the fluctuations from the global mean change was much smaller than theirs (Fig. 2), although we reduced the geomagnetic field strength to zero. Their strong latitudinal dependence of the change seems to reflect quite directly the production changes in the tropics, being higher at low latitudes where the production due to geomagnetic reduction is enhanced. At high latitudes they find an increase of only 8% while the global mean production increase is 10%, which does not reflect the production change because the production rate did not change pole-wards of 60 • .
It is not possible to explain the differences between the two models without having more information of the transport paths and the distribution of the 10 Be production between the stratosphere and the troposphere in the GISS model used by Field et al. (2006). A known difference between the models is that for the runs of the present work we used the middle atmosphere version with 39 vertical layers, reaching up to 0.01 hPa including the whole stratosphere. The model runs by  layers. This may lead to differences in the atmospheric distribution and residence times of 10 Be. The too rapid downward transport from the stratosphere to the troposphere is a known weakness of ECHAM5-HAM (Timmreck et al., 1999) and is reflected by the relatively short (less than one year) stratospheric residence times of 10 Be in Table 1. It is caused by the too coarse vertical resolution in the tropopause region (Timmreck et al., 1999). The average atmospheric residence time of 10 Be has been determined to be 1-2 years (Raisbeck et al., 1987). Earlier studies made by ECHAM5-HAM's standard version with 31 vertical levels revealed that this residence time was largely underestimated, being in the order of 8 months. Using the middle atmospheric version of ECHAM5-HAM with 39 vertical levels increases the stratospheric residence time slightly but, what is more important, the stratospheric transport is better described. This has an    important impact on the 10 Be concentrations in the tropospheric air, and therefore it probably also influences the distribution of the 10 Be deposition. Another difference between the models is the horizontal resolution used (4 • -5 • in the GISS model, 2 • -3 • in ECHAM5-HAM). A coarser horizontal resolution is known to cause numerical diffusion which leads to a larger transport of species towards high latitudes. Both models differ very largely in this sense. 16 different models were compared in the AeroCom model comparison experiment (Textor et al., 2006). The fraction of sulfate aerosol transported to polar latitudes (pole-ward of 80 • ) was investigated. The fraction of sulfate transported to polar latitudes in the GISS model was among the largest (10-11%) of all models whereas in the ECHAM5 model the fraction was among the smallest (2%), see Figs. 10 and 12 of Textor et al. (2006). This difference however does not explain the modeled polar enhancement by the GISS model because their deposition flux reflects very directly the local production change. Figure 5 illustrates the stratospheric and tropospheric burdens of 10 Be and the respective residence times. The residence time for 10 Be in the troposphere is defined as the tropospheric burden divided by total deposition.

Burdens and residence times
The latitudinal distribution of the burdens of 10 Be in both the stratosphere and the troposphere shows no large changes. The stratospheric burden in the Laschamp run reflects the tropopause height because the production rate is constant at all latitudes. In the control run the larger stratospheric burden at high latitudes is connected to the higher production rate there which is reflected by the symmetry between the Northern and Southern Hemisphere unlike in the Laschamp run.
In the tropospheric low latitudes the burden is clearly increased in the Laschamp run due to the much higher production rate of 10 Be there. The residence time in the troposphere is higher by ∼5 days equator-ward of 40 • in the Laschamp run which causes the tropospheric tropical burden of 10 Be to increase. Pole-ward of 40 • the residence time is slightly shorter. At high latitudes pole-ward of 70 • the residence time becomes much longer reflecting the lower precipitation rates in the polar regions and therefore the increased residence of the 10 Be atoms in the troposphere.

Stratospheric fractions
We have noted that the most important contribution of 10 Be to the deposition fluxes is from the stratosphere. Figure 6 shows the 2-D field of the stratospheric fraction of the 10 Be deposition fluxes in the control run (above) and in the Laschamp run (below). It seems that the stratospheric fraction is relatively constant zonally. The largest fractions occur in the mid-latitudes. In the Laschamp run the area of largest fraction is shifted towards the poles. The stratospheric fraction in the tropics is lower in the Laschamp run than in the control run due to the larger tropical tropospheric production. Figure 7 shows the zonal means of the same stratospheric fractions as the Fig. 6, as well as the fractions of the tropospheric production bands. These fractions show partly significant changes. As mentioned earlier, the stratospheric fraction in the Laschamp run is lower in the tropics due to higher tropical production. Because the fraction of stratospheric production of the total production is globally 65% the stratospheric fraction has to be higher at high latitudes, pole-wards of 40 • -50 • , to compensate for the lower fractions in the tropics. The production changes in the troposphere cause the fractions to change only locally. The higher tropical production in the Laschamp run increases the tropical fractions slightly (less than 5%) at all latitudes, but mostly in the tropics. The subtropical fraction and the polar fraction are reduced in the Laschamp run because of the increased stratospheric fraction at those latitudes. The changes are very similar in both hemispheres. The stratospheric fraction is slightly larger in the Northern Hemisphere due to the stronger stratosphere-troposphere exchange there (Holton et al., 1995;Stohl et al., 2003).
The exact fractions of the components of the 10 Be deposition fluxes at some of the most important ice core sites in Greenland and Antarctica are listed in Table 2. First, the total deposition fluxes are listed in the control run and the Laschamp run showing that the increase in the 10 Be deposition is approximately 100% at all sites consistently with the production raise in the Laschamp run. These fluxes cannot be compared with present day observations from the ice core sites due to lack of data. We refer to Heikkilä et al. (2008a) for a comparison with the 10 Be ice core concentrations during the Maunder Minimum. Generally the modelled concentrations agreed well with the measured ones in Greenland but were too low by a factor of 2 in Antarctica due to somewhat high modelled precipitation rates at the driest Antarctic sites.
An encouraging result for the use of 10 Be in ice cores is the fact that the relative contributions of 10 Be from the different  24% 24% 23% % of total production 2.5% 6.5% 8.5% 8.5% 6.5% 2.5% 65% Fig. 8. This figure shows at which latitudes the 10 Be, produced at a given part of the atmosphere (x-axis), is deposited (y-axis). For example: 10 Be produced in the troposphere between 60-90 • S is deposited to 16% between 60-90 • S, to 65% between 30-60 • S and to 15% between 0-30 • S (see the leftmost stack). This figure illustrates the division in the control run. The Laschamp run is not shown because the division is quite similar, please refer to Table 3 for the exact figure.   Fig. 8. This figure shows at which latitudes the 10 Be, produced at a given part of the atmosphere (x-axis), is deposited (y-axis). For example: 10 Be produced in the troposphere between 60-90 • S is deposited to 16% between 60-90 • S, to 65% between 30-60 • S and to 15% between 0-30 • S (see the leftmost stack). This figure illustrates the division in the control run. The Laschamp run is not shown because the division is quite similar, please refer to Table 3 for the exact figure. source regions are quite constant between both experiments. In Greenland, in the control run the stratospheric fraction in the deposition fluxes is approximately 70%, and half of the rest originates from the tropospheric subtropics and the other half from polar latitudes. The contribution of 10 Be produced in the tropics or the other hemisphere are almost negligible. In Antarctica the fraction of stratospheric source of 10 Be is slightly lower than in the Northern Hemisphere, probably due to the weaker stratosphere-troposphere exchange in the Southern Hemisphere. Also the fraction of the local tropospheric production is larger (20-24%) than in Greenland (∼14%). This result agrees very well with Mazaud et al. (1994), who estimated that at Vostok drilling site 75% of the 10 Be is transported from lower latitudes (or the stratosphere) and only 25% is locally produced. The situation is slightly changed in the Laschamp run. The fraction of the stratospheric source is increased in the polar regions, as shown in the earlier section. This reduces slightly the fraction of tropospheric subtropical and polar fraction and increases the tropical fraction by a few percent but the stratospheric component still remains the dominant one. Also the contributions of the tropospheric fractions are unchanged, i.e. the tropical production fraction is very low and the subtropical and polar production contribute approximately equal amounts to the total deposition.  Table 2 also shows the stratospheric mixing, i.e. the stratospheric source divided into 30 • latitude bands. This division exists only for the Laschamp run. The fractions of the different production regions can probably roughly be generalised to the control run because the latitudinal distribution of the stratospheric burden of 10 Be is very similar in both runs (see Fig. 5). This division shows that 10 Be is equally mixed in the stratosphere in both hemispheres. Approximately 30% of the total 10 Be deposition comes from the stratospheric midlatitudes whereas the tropical and polar latitude production contribute 16-19% each. Approximately 10% of the total 10 Be deposition originates from the stratosphere of the opposite hemisphere but the tropospheric contribution of the opposite hemisphere is negligible.
The mass fractions of the 10 Be production in different regions are shown in the rightmost column.

Atmospheric mixing
So far we have investigated from which part of the atmosphere the 10 Be in ice cores originates. Another interesting question is the destiny of 10 Be, i.e. at which latitudes the 10 Be, produced at a given region of the atmosphere, is finally deposited. We calculated the percentages of different latitudes of the deposition with respect to the source re-gions stratosphere and the 30-degree tropospheric production bands (Table 3). An illustration of these percentages in the case of the control run is shown in Fig. 8. Table 3 reads so that below the "Production" the different atmospheric regions (stratosphere or the tropospheric 30-degree bands) are shown and next to them the percentages of 10 Be which is deposited at latitudes shown above them. The sum of these percentages is 100%. The numbers in parenthesis show the results of the Laschamp run, the other ones the control run.
These percentages show that the 10 Be which is produced both in the polar and the subtropical latitudes is mostly (∼60-65%) deposited in the subtropics. A similar fraction of the rest (∼15%) of the polar 10 Be is deposited in the polar and tropical latitudes whereas the rest (∼30%) of the subtropical 10 Be is deposited in the tropics and only very little (∼5%) of it in the polar latitudes. Very little (2-5%) of the polar or subtropical 10 Be is transported to the opposite hemisphere. The tropical 10 Be is mostly (∼60%) deposited in the tropics. Half of the rest (∼20%) reaches the tropics of the opposite hemisphere and the other half is deposited in the subtropics. The 10 Be which is produced in the stratosphere is quite well mixed within each hemisphere and equally deposited in the tropics and the subtropics (∼25%). It hardly reaches the polar latitudes (2-3%) reflecting the strongest stratosphere-troposphere exchange in Table 3. This table shows at which latitudes (in the title of the table) 10 Be, produced at a given region of the atmosphere (below "Production" in the table), is deposited in the control run. Laschamp run is in parenthesis. The largest differences are printed in bold. See Fig. 8  the subtropical latitudes. Although only a negligible part of the stratospheric 10 Be is deposited in the polar regions, the stratospheric 10 Be contributes the most (∼65%, see Table 2) to the total deposition in polar regions, because the absolute deposition in polar regions is low. These distributions in both hemispheres are symmetric. The destiny of 10 Be produced in a given region in the atmosphere does not largely change although the production distribution changes between the control run and the Laschamp run. Some differences between the control and the Laschamp run are introduced by the fact that the tropospheric tropical burden of 10 Be is enhanced in the Laschamp run due to the much larger tropospheric tropical production rate. In the control run a very large fraction of the 10 Be, produced in the tropics, is deposited at these latitudes (Northern Hemisphere: 62%, Southern Hemisphere: 58%). In the Laschamp run these fractions are up to 10% lower because the tropical production is larger but relatively the same amount of 10 Be is scavenged and therefore the tropospheric concentrations are enhanced. The 10 Be which stays in the atmosphere is transported towards the mid-latitudes (30 • -60 • ), either directly or over the stratosphere, and deposited there. This is reflected by the slightly enhanced fractions of the deposition of the tropically produced 10 Be in the latitudes between 30 • -60 • (Northern Hemisphere: raise from 17% to 21%, Southern Hemisphere: raise from 17% to 20%, Table 3).

Summary and conclusions
In this study we assessed the question of how well the observed 10 Be concentrations in ice cores reflect the global production changes. Another issue was to investigate whether we find the so called "polar enhancement", i.e. an enhanced amplitude of the polar deposition of 10 Be compared with the global production, which has been widely discussed in the literature. We modelled two periods with a very different latitudinal 10 Be production distribution, a present day situation and a geomagnetic minimum (field strength zero, as for example during the Laschamp geomagnetic minimum 40 kyr before present). Because of the total lack of the geomagnetic field the 10 Be production has no latitudinal dependence, a strong contrast to the present day situation where the production rate pole-wards of 60 • is up to a factor of 5 larger than in the equatorial area. The global average 10 Be production was twice as large in the Laschamp run than in the control run.
A comparison of the zonally averaged deposition fluxes of 10 Be gave no indication of a polar enhancement. The latitudinal distribution of the deposition fluxes is very similar in the control run and the Laschamp run, except that in the Laschamp run the fluxes are twice as large than in the control run due to the enhanced global mean production rate. The normalised fluxes show hardly any difference. The relative change of the normalised zonal mean 10 Be deposition fluxes has no latitudinal dependence and fluctuates between ±10-20%. Statistically a polar enhancement smaller than this noise level could exist but in that case it should be largest in the tropics where the production rate changes the most. This however is not the case. When comparing the simulated deposition flux change from another 10 Be run during a solar minimum, the Maunder Minimum, which also included a climate cooling (Heikkilä et al., 2008a), the change from the control run is very similar and mostly below 10% in both experiments. These results suggest that the deposition fluxes of 10 Be reflect well the changes in the global average 10 Be production rate. However, it must be kept in mind that the climatic conditions add to the variability so that the observed 10 Be deposition fluxes reflect a larger production variability than the global average production. The cooling during the Maunder Minimum was estimated to cause climatic fluctuations of less than 25% of the production change (Heikkilä et al., 2008a). Another study, which compared 10 Be and 14 C records using a statistical method to identify a common component in both data sets, estimated the climatic fluctuations to be less than 10% on time scales of 100 years .
We divided the 10 Be production into different atmospheric source regions to be able to trace back the origin of the 10 Be in polar regions. The most important source region is the stratosphere, where we can assume 10 Be to be quite well mixed within each hemisphere during the residence time of 10 Be of 1-2 years. The fraction of stratospheric 10 Be in the zonal mean deposition fluxes did not vary significantly, between 0.5 (equator) and 0.7 (30 • -60 • ). At the main ice core drilling sites in Greenland the fraction is approximately 70% and slightly lower at approximately 60% in Antarctica reflecting the less efficient stratosphere-troposphere exchange in the Southern Hemisphere. In the Laschamp run these fractions were slightly enhanced. The 10 Be produced in the tropics practically does not reach the polar regions (fraction 2-5%). The fractions of the subtropical and polar tropospheric production of 10 Be are equally large (∼15%) in the Arctic deposition fluxes. In Antarctica the fraction of locally (polar tropospheric) produced 10 Be is slightly larger (15-20%) than the subtropical fraction (10%).
We also investigated at which latitudes the 10 Be, produced at a given atmospheric region, is finally deposited. The stratospheric 10 Be is equally deposited in the subtropics and tropics but only a very small fraction of it (2%) is deposited at polar latitudes. The polar tropospheric 10 Be is mostly deposited in the subtropics as well as the subtropical 10 Be. The tropical 10 Be is mostly deposited in the tropics. However, because the absolute stratospheric production rate is much larger than the polar tropospheric production rate, the absolute amount of stratospheric 10 Be in polar regions is still the dominant component in the deposition flux. The differences in this atmospheric mixing between the control run with present day 10 Be production and the geomagnetic minimum, the "Laschamp" run, are not very large pointing that the atmospheric mixing of 10 Be is independent of production in a constant climate.
The fact that the 10 Be in the stratosphere is mixed in each hemisphere independent of its original distribution also applies to other long-lived nuclides, such as 36 Cl or 26 Al, to the volcanic debris and the bomb-test produced peaks of 90 Sr and 137 Cs. The very different latitudinal production distribution in the Laschamp run changed mainly the concentrations of tropospheric tropical 10 Be, which is rapidly scavenged from the air before it is transported to higher latitudes. The fact that the stratospheric hemispherically well mixed fraction of 10 Be is the dominant component in the 10 Be deposition fluxes world-wide gives confidence to the earlier assumption that 10 Be in the deposition fluxes reflects the global production rate (Muscheler et al., 2007;Vonmoos et al., 2006).