Determination of the mean aerosol residence times in the atmosphere and additional 210Po input on the base of simultaneous determination of 7Be, 22Na, 210Pb, 210Bi and 210Po in urban air

The significant differences in the activities of 210Pb, 210Bi, 210Po and cosmogenic 7Be and 22Na radionuclides in the urban aerosol samples collected in the summers 2010 and 2011 in the Lodz city of Poland were observed. Simultaneous measurement of these radionuclides, after a simple modification of the one compartment model, allows us to calculate both: the corrected aerosol residence times in the troposphere (1 ÷ 25 days) and in the lower stratosphere (103 ÷ 205 days). The relative input of the additional sources (beside of the 222Rn decay in the air) to the total activity concentrations of 210Pb, 210Bi and 210Po radionuclides in the urban air, plays a substantial role (up to 97% of the total activity) only in the case of 210Po.


Introduction
Gaseous 222 Rn escaping from the soil produces in the lower atmosphere a series of longer lived products: 210 Pb (22.3 years), 210 Bi (5 days) and 210 Po (138 days). Since atmospheric aerosols can be transported over long distances, 210 Pb and its progeny concentrations in a particular site may not be connected strictly with the radium activity in adjacent soils but also on meteorological conditions such as: temperature, wet deposition (rainfall) and wind intensity. These radionuclides are readily absorbed on the surface of aerosol particles, and whereas the activity of 210 Pb does not change too much, the activities of 210 Bi and 210 Po grow during the residence time of aerosol particles in the air. Therefore, the activity ratios of 210 Bi/ 210 Pb and 210 Po/ 210 Pb can be useful for tracing the fate of an aerosol and the estimation of its solid particles' lifetimes (residence time) [1].
The simple solution of the 210 Pb, 210 Bi and 210 Po activities relationships assume that the only source of the 210 Bi and 210 Po in the lower atmosphere (troposphere) is decay 210 Pb from the 222 Rn escaping from soil [2]. Commonly used formulas for the aerosol residence time calculation are based on measurement of the isotope ratios of 210 Po/ 210 Pb and 210 Bi/ 210 Pb and application of the steady state equilibrium in one compartment model [3][4][5]. In this model, the decay of 222 Rn nuclide in the air is recognized as an only source of airborne 210 Pb and consequently its daughters: 210 Bi and 210 Po (the air is considered as wellmixed reservoir). This assumption does not take into account the possibility of additional emission of these radionuclides from other sources such as re-suspension of soil in summer, the combustion of coal in the winter, incursions of stratospheric air or emission from anthropogenic sources [6].
However, in general, the residence times determined from the 210 Po/ 210 Pb ratios (2-240 days) are usually much longer of those determined from 210 Bi/ 210 Pb ratios (2-25 days) [7]. It indicates that some additional inputs of 210 Po into troposphere must exist. The evidence of the complementary 210 Po source from the lower stratosphere input (after volcanic eruption) [8] or soil dust [9] as well as from anthropogenic activities (coal combustion) was also recently documented [10][11][12][13]. If these additional 210 Po sources are taken into account, from comparison of two activities ratio: 210 Bi/ 210 Pb and 210 Po/ 210 Pb the so called corrected residence time T RC can be calculated [9].
Very recently [14] published the mathematical solutions for true dependence of 210 Po/ 210 Pb and 210 Bi/ 210 Pb aerosol particles with the additional non-equilibrated 210 Bi and 210 Po radionuclide inputs. The problem 210 Po sources and its ratio to the parent nuclide in the atmosphere is more complex, since after volcanic eruption significant amounts of 210 Po activities also ejected to the stratosphere [8]. The residence time of the solid particles in the stratosphere is usually remarkably longer than those in the lower layers of troposphere where they are finally transported [15]. Moreover, after interactions of the cosmic radiation with nitrogen and oxygen molecules (in the upper troposphere border) two cosmogenic radionuclides: 7 Be and 22 Na, are produced. These radionuclides together with 210 Pb, 210 Bi and 210 Po can be also attached to solid particles moving from stratosphere to troposphere. Therefore, 7 Be and 22 Na can also serve as the additional markers to assess the flow of dust into the lower atmosphere [5].
The instrumental c ray-spectrometry of the collected dust allows beside of 210 Pb on simultaneous determination of 7 Be and 22 Na in the aerosol samples. After radiochemical separation and measurement of 210 Bi and 210 Po in these samples, it would be possible to calculate not only the corrected residence time T RC of aerosol from 210 Pb, 210 Bi and 210 Po ratios in the surface air, but also on the basis of 7 Be to 22 Na ratio, one can calculate the resident times of the aerosol in the lower stratosphere T S [16,17].
Therefore, it seems to be interesting to use modern radionuclide methods (a and c spectrometry as well as liquid scintillation) for simultaneous determination of 7 Be, 22 Na, 210 Pb, 210 Bi, 210 Po in the same aerosol samples in order to trace their fate from the stratosphere to the surface layer of urban air.

Materials and methods
The air particulate matter samples were collected in the centre of the Polish city of Lodz, by the ASS-500 station operating as part of the national network for monitoring radiation in the air [18]. Approximately 50,000 m 3 of air was filtered and 2.5-6 g of dust was captured by the quadratic (40 cm 9 40 cm) Petrianov type filters during a typical one-week collection period. For further radioactivity measurements, the filters were divided into two equal parts. From the first part, used for fast radiochemical separation of 210 Bi and 210 Po, three small discs with a diameter of 5 cm were cut off (5.7% of the total dust) for 210 Po determination by a spectrometry after its spontaneous deposition on silver plates by a procedure described by us elsewhere [12].
The 210 Bi was immediately eluted by 100 mL of 2 M HCl solution from the remaining first part of the filter. The elution solution was diluted with water to volume of 200 mL and 210 Bi radionuclide was concentrated by column chromatography with DOWEX 1 9 8 resin. 210 Pb and 210 Po radionuclides were eluted from the column by washing with 50 mL of water followed by passing of 50 mL of 0.1 M HNO 3 . 210 Bi radionuclide was eluted by 100 mL of 1.8 M H 2 SO 4 , and was extracted directly to the liquid scintillation vials, form this solution with two 5 mL portions of 5% (w/v) trioctylphospine oxide in toluene. Finally before the liquid scintillation counting of 210 Bi 10 mL of Ultima Gold F cocktail was added. No additional activities of 210 Pb or 210 Po were observed in the liquid scintillation spectrum.
The average recovery of 210 Bi from the filters by this method was determined by comparison of the 210 Pb and 210 Bi activities for the old filters, with 210 Pb-210 Bi in a radioactive equilibrium state. The average recovery of 210 Bi was equal to 0.8 ± 0.1.
The homogeneity of the 210 Po distribution in the filter sheet was checking by comparison of its activity in the 9 small discs taken from the different parts of the sheet. The 210 Po activity dispersion not exceeded ±3% from the an average value. Therefore, one can assume that activity of 210 Po is uniformly distributed over the whole filter.
The second part of the filter, after overnight drying, was pressed into the standard disc geometry: 0.4 cm thick, with a diameter of 5.2 cm, for instrumental c-spectrometry determinations of 7 Be, 22 Na and 210 Pb. The determination limits (with 10% accuracy) according Curie's formula [19] were for these radionuclides: 3, 0.3 and 1.1 lBq/m 3 , respectively.

Quality assurance
The accuracy of the used analytical procedures and instrumental c-spectrometry measurements was checked using the following standard reference materials: IAEA Soil 327, IAEA Sediment 300, Soil Cu-2006-3. A good compliance of the determined values with those certified has been achieved, as previously reported [12,20].

Result and discussion
In order to evaluate the possible additional input of 210 Pb, 210 Bi and 210 Po activities-DA i from both anthropogenic (coal combustion) as well as from natural sources (stratospheric inflow and soil resuspension), we assumed the existence of radioactive equilibrium between these radionuclides introduced additionally to surface air: The total observed (measured) activities-A ti of these three radionuclides in the air will be the sum of the activities coming from the escaping 222 Rn decay-A Rni and the additional input: However, because of the relatively long half-live of 210 Pb (22.3 years) in comparison to average aerosol residence times (several days), these parts of the total activities-DA i of 210 Pb, 210 Bi and 210 Po, should be constant when solid particles exist in the air. Therefore, the activity relations between these radionuclides, according to the one box model in the steady state, concern A Rni parts only. Because of the above mentioned conditions, the activity of 210 Pb-A RnPb will also be constant, and for the remaining A RnBi and A RnPo activities, according to this model, one can write: where k Bi and k Po denote decay constants of 210 Bi and 210 Po, respectively, and T RC -residence time of aerosols, corrected for addition input of these radionuclides. After introducing relations 2-4 to Eqs. 5 and 6 we obtain a pair of equations: where A mPb , A mBi and A mPo , denote the measured activities of these three radionuclides in the air. The solution of these equations gives following expression for so called ''corrected residence time''-T RC , which is identical to those proposed by Turekian [4] as well as by Poet et al. [3] The results of T RC calculations for the dust samples collected in the summer 2010 and 2011 from the Eq. 9 as well as the calculations of the residence times from the ''classical'' model on the basis of the separate 210 Bi/ 210 Pb-T RBi and 210 Po/ 210 Pb ratios-T RPo are presented in the Table 1.
It is evident that both 210 Bi/ 210 Pb and 210 Po/ 210 Pb methods give overestimated aerosol residence times when they are applied separately. However, the corrected resident times -T RC are close to those calculated on the basis of 210 Bi/ 210 Pb ratios. The 210 Bi concentrations in the surface air during the summer period (*0.3 mBq/m 3 ) are approximately 5-times higher than those for 210 Po (*0.06 mBq/m 3 ). Therefore, the same additional activity input DA does not influence the A Bi /A Pb ratio as much as it does for A Po /A Pb . The discrepancy of residence times between 210 Bi/ 210 Pb and 210 Po/ 210 Pb methods was attributed mainly to the additional sources of 210 Po input to the atmosphere. It is worth mentioning that the 210 Bi/ 210 Pb method can be applied for aerosols with a residence time  [7,21].

Calculation of the additional inflow of 210 Pb, 210 Bi and 210 Po activities
After calculating T RC values the additional activities X = DA Pb = DA Bi = DA Po coming from other than 222 Rn sources, can be evaluated from the Eqs. 8 or 9, by the following formula: where A mPb, Bi is the measured activity of 210 Pb and 210 Bi, k Po is decay constant of 210 Po. The relative contribution [%] of this additional activity DA i /A mi = D i to the measured activities of 210 Pb, 210 Bi, and 210 Po can be calculated from the following formulas: and for 210 Po Such calculated values of X as well as its relative contribution to the total activities of these three radionuclides in the surface air are presented in Table 2.
As was expected, because of the low concentrations of 210 Po in the lower troposphere, only in the case of this radionuclide does its additional inflow both from natural and anthropogenic sources play a substantial role (up to 97% of the total activity).
For continental surface air Moore et al. [9] estimated that the suspended soil particles could account for about the half of the additional sources of 210 Po, whereas stratospheric injection and anthropogenic sources give together only *10% contribution.
However, the relative importance of each of these sources (including plant decomposition) may be different for urban air. Apart from soil resuspension, the sources of the additional 210 Po and 210 Bi activities-X, in the case of Lodz can be emissions from the three coal fired power stations located within the city, as well as stratospheric injections. The stratospheric contribution can be appraised by checking the possible correlations between X = DA Po and the surface air activity of the cosmogenic radionuclides 7 Be or 22 Na produced in the stratosphere-troposphere border. As is evident from Fig. 1, such a correlation does not exist.
On the other hand, the simultaneous comparative determinations of 7 Be and 22 Na in the surface aerosol samples can be used to trace the transport of the suspended solid particles from the stratosphere to the surface air. The number of the generated isotopes 7 Be and 22 Na depends on the intensity of cosmic radiation and also on the latitude, but their activity concentrations in the troposphere are strongly influenced by the intensity of precipitation. The seasonal changes in the activity ratio of 7 Be/ 22 Na in samples of aerosols allow us to calculate the retention time of these isotopes in the stratosphere-T S , if the residence times in the troposphere-T RC are known. The ratio of their activity R a in the surface air is given by the following formula [16,17].
R a ¼ P Be ð1 À expðÀk Be T S ÞÞ expðÀk Be T RC Þ P Na ð1 À expðÀk Na T S ÞÞ expðÀk Na T RC Þ ð14Þ where P theoretical nuclide production rate in the stratosphere, 7 Be and 22 Na respectively. The theoretical value of the P Be /P Na is equal to 1.1 9 10 3 , k is decay constants of  Fig. 1 Values of the additional DA Po activities are plotted against 7 Be activities in Lodz aerosol samples 7 Be and 22 Na, respectively, T RC is residence time in the atmosphere, T S is residence time in the stratosphere.
The measured air activities of 7 Be and 22 Na as well as calculated values of T S and total atmospheric residence times T A = T S ? T RC are summarized in the Table 3. The determined stratospheric residence times-T S in the range 102-205 days are quite comparable with the scarce data for aerosol residence time in the stratosphere [15,22].
The possible volcanic emissions of 210 Po can be considered as point sources with irregular eruptive activity and supply to the stratosphere. The relatively long residence time of stratospheric aerosols enables its transport to nonseismic regions. However, during this time the activity of unsupported 210 Po should decrease remarkably, and such influence on the total 210 Po activity was observed only temporarily in regions adjacent to an active volcano [23,24] and input of stratospheric 210 Po to the lower tropospheric air in Central Poland is likely negligible. Therefore, the observed additional activities of 210 Po in the urban air are likely caused by resuspension of surface soil and anthropogenic emissions mainly from coal-fired power plants. However, in order to quantify the relative contributions of these sources, additional measurements of so called ''index trace elements'' (specific for soil dust and coal combustion emissions) in aerosol samples should be done.

Conclusions
The significant differences in the aerosol residence times calculated by 210 Bi/ 210 Pb and 210 Po/ 210 Pb methods can be explained by additional sources of 210 Po in urban air to the 222 Rn flux from soil. A simple modification of the one compartment model allows both the corrected troposphere aerosol residence times as well as the relative input of these sources to the total activity concentrations of 210 Pb, 210 Bi and 210 Po radionuclides in the urban air to be calculated. Simultaneous measurement of two cosmogenic radionuclides, 7 Be and 22 Na, in aerosol samples also allows the stratospheric aerosol residence time to be also determined.
The latter values can serve as a measure of the rate of exchange of air masses at the border of stratosphere-troposphere areas, which is important in the observation of long-term effects of particulate impurities on climate change.
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