Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Evaluation of the Terrestrial 222Rn Flux from 210Pb Deposition Measurements

Evaluation of the Terrestrial 222Rn Flux from 210Pb Deposition Measurements environments Article 222 210 Evaluation of the Terrestrial Rn Flux from Pb Deposition Measurements Mauro Magnoni *, Luca Bellina, Stefano Bertino, Brunella Bellotto and Enrico Chiaberto ARPA Piemonte, Department of Physical and Technological Risks, 10015 Ivrea, TO, Italy; l.bellina@arpa.piemonte.it (L.B.); s.bertino@arpa.piemonte.it (S.B.); b.bellotto@arpa.piemonte.it (B.B.); e.chiaberto@arpa.piemonte.it (E.C.) * Correspondence: m.magnoni@arpa.piemonte.it 222 2 2 Abstract: The study of the Rn terrestrial flux (Bq/(m s) or Bq/(m h)) is a complex issue involving both radiation-protection and environmental aspects. While the radiation-protection aspects are quite obvious—it has been well known for several decades that soil is the major source of indoor radon—environmental issues such as the correlation with conventional pollutants (PM , PM , 2.5 10 NOX, etc.) and the use of radon for the esmation of the natural component of GHG (CO ) emissions are relatively less discussed in spite of their growing relevance. In this work we present a method for 222 210 the estimation of the average value of Rn flux from HPGe -spectrometry Pb measurements performed on wet and dry deposition samples gathered monthly in the period 2006–2020. The results obtained with this technique give an average radon flux in the period F = 57  27 Bq/(m h), the value of which is comparable with those coming from other methods and direct radon flux measurements as well. The method can thus be used to obtain a worldwide map of the radon flux. Keywords: terrestrial radon flux; environmental radioactivity monitoring network; Pb deposition; HPGe -spectrometry Citation: Magnoni, M.; Bellina, L.; Bertino, S.; Bellotto, B.; Chiaberto, E. Evaluation of the Terrestrial Rn 1. Introduction Flux from Pb Deposition The measurement of the terrestrial radon flux is an important and well known issue Measurements. Environments 2022, 9, for radiation protection: many studies have demonstrated that the radon flux coming from 68. https://doi.org/10.3390/ the ground is by far the most important contribution to the radon levels found in dwellings environments9060068 and workplaces [1–5]. This fact has also been explicitly recognized by many legislations. At Academic Editor: Vernon Hodge the European level, for example, a directive was issued, the 59/2013/Euratom [6], in which each EU member state has a mandate for the individuation and definition of radon priority Received: 24 April 2022 areas, i.e., areas where the radon flux from the ground is significantly greater than the Accepted: 28 May 2022 average. Besides this, many other scientific studies deal with radon flux: many researchers Published: 31 May 2022 have investigated the correlation of radon flux variations with seismic and volcanological Publisher’s Note: MDPI stays neutral phenomena [7–12]. The knowledge of local radon flux values is very important for atmo- with regard to jurisdictional claims in spheric studies as well, aiming to evaluate the motion and the origin of air masses [13–16]. published maps and institutional affil- Radon flux data and measurements are also used for the forecast and estimation of the iations. occurrence of very high concentrations of some conventional pollutants, such as PM , PM , NOX, and benzene, during particular meteorologic conditions, often characterized 2.5 by thermal inversions [17–23]. More recently, a growing interest in radon flux measurements has arisen among Copyright: © 2022 by the authors. researchers trying to evaluate the natural component of greenhouse gases; indeed, the Licensee MDPI, Basel, Switzerland. radon flux can be used as a proxy for the estimation of the terrestrial CO flux [24–28]. In This article is an open access article all these fields of study, the knowledge of the values of the terrestrial radon flux j is crucial. distributed under the terms and Unfortunately, this kind of measurement is far from simple to carry out and currently conditions of the Creative Commons suffers from a great lack of standardization. Very different approaches have been proposed, Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ using many different instruments and detectors. One of the main problems of a direct radon 4.0/). flux measurement is the difficulty in detecting radon coming from the ground without Environments 2022, 9, 68. https://doi.org/10.3390/environments9060068 https://www.mdpi.com/journal/environments Environments 2022, 9, 68 2 of 11 perturbing the exhalation process in a substantial way. Recently, an ongoing European project (traceRadon, [29]) has been trying to tackle these problems by promoting large intercomparison programs of different devices able to follow the time evolution of the radon exhalation rate in different soils. In this work a new and different method is proposed, based on Pb measurements. The evidence of an excess Pb flux of atmospheric origin has been investigated in several works dealing with the sediment accumulation rate and sediment core chronology studies; see, for example [30]. This Pb flux, if properly measured, can also be used to estimate the average value of the terrestrial radon flux indirectly. The method proposed derives the radon flux from an historical series of Pb spectrometry deposition measurements performed in the framework of the RESORAD network, the Italian National Radioactivity Monitoring Network. 2. Materials and Methods After being produced by radioactive decay, radon is separated from its parent Ra and, because of its relatively long half-life (3.82 days), is released into the atmosphere, giving rise to the lower part of the uranium natural radioactive series which substantially contributes to atmospheric radioactivity (see Figure 1). Let us consider in particular the system consisting of six radionuclides, circled in red in Figure 1, having Rn as parent 210 210 214 and ending to Pb. Pb is produced by the decay of Po, the last of the so called 218 214 214 short-lived radon daughters, the others being Po, Pb, Bi, usually named short lived radon daughters because of their very short half lives. Pb is a emitter having a quite long half-life, 22.23 years, emitting a relatively soft radiation (end-point energy 63.5 keV, [31]), followed almost immediately by a low energy line (46.5 keV) coming from the de-excitation of the 0-excited state of Bi. Figure 1. The lower part of the uranium series in atmosphere: the six radionuclides considered in this work are circled in red. It can be observed that, for practical reasons, this system can be simplified and con- sidered substantially equivalent to a five-radionuclide system. Indeed, due to the very short half-life of Po (164 s), which assures an almost immediate achievement of the 214 214 secular equilibrium condition between Bi and Po, the two radionuclides evolve in time together and can thus be considered as a unique radionuclide emitting, almost at the same time, both and radiation. In the following, in order to distinguish the different radionuclides belonging to the system, they will be indicated with the following indexes: Environments 2022, 9, x FOR PEER REVIEW 3 of 11 214 214 the secular equilibrium condition between Bi and Po, the two radionuclides evolve in time together and can thus be considered as a unique radionuclide emitting, almost at the same time, both α and β radiation. In the following, in order to distinguish the Environments 2022, 9, 68 3 of 11 different radionuclides belonging to the system, they will be indicated with the 222 218 214 following indexes: j = 0 for Rn, j = 1 for Po, j = 2 for Pb, j = 3 for the coupled system 214 214 210 Bi/ Po, and j = 4 fo 222 r Pb. 218 214 214 214 j = 0 for Rn, j = 1 for Po, j = 2 for Pb, j = 3 for the coupled system Bi/ Po, and If we assume that the terrestrial radon flux is given by φ, expressed as an atomic j = 4 for Pb. 2 2 flux (atoms/(m ·s) or atoms/(m ·h) while Dj is the corresponding quantities of If we assume that the terrestrial radon flux is given by j, expressed as an atomic flux 2 2 radionuclides that build up in the whole atmosphere (atoms/m ), the following five (atoms/(m s) or atoms/(m h) while D is the corresponding quantities of radionuclides equations may be written: 2 that build up in the whole atmosphere (atoms/m ), the following five equations may be written: 𝑑𝐷 +𝜆 𝐷 d=𝜙 D 𝑑𝑡 + l D = f 0 0 dt dD j+1 𝑑𝐷 + (l + l )D = l D j = 0, 1, 2, 3 j+1 d j+1 i i +(𝜆 +𝜆 )𝐷 =𝜆 𝐷 𝑗 = 0,1,2,3 dt 𝑑𝑡 where λj is the decay constant of the Rn and its progeny and λd is the removal rate of where l is the decay constant of the Rn and its progeny and l is the removal rate of j d the daughters from the atmosphere, due to wet and dry deposition processes, the value the daughters from the atmosphere, due to wet and dry deposition processes, the value of of which is assumed equal for each radionuclide. which is assumed equal for each radionuclide. The solutions of these equations are straightforward, while resulting in quite The solutions of these equations are straightforward, while resulting in quite compli- complicated expressions. However, these expressions can be dramatically simplified cated expressions. However, these expressions can be dramatically simplified considering considering t the he correspon correspondin ding g as asymptotic ymptotic sol solution utions s, , i i.e., .e., the the so solutions lutions ob obtained tained for for t t⟶¥∞. . The asymp- The asympto totic tic so solutions lutions provide ver provide veryy simp simplele and and time time independent independent expr expressions that essions that are much easier are much eato sier handle. to hand Indeed, le. Inde it ed, can i be t can b easilye e demonstrated asily demons that trate the d th exact at the time exact dependent time solutions dependent sdif olu fer tion frs di om ffe ther from asymptotic the as expr ymp essions totic exby pression transient s by factors transien that t fbecame actors tha negligible t very quickly—in a few hours, in accordance with the half-lives of the short lived radon daugh- became negligible very quickly—in a few hours, in accordance with the half-lives of the ters. This does not happen with the last equation, which referred to Pb: in this case the short lived radon daughters. This does not happen with the last equation, which referred transient is a little longer, a few days, being of the order of 1/l . An estimation of the l to Pb: in this case the transient is a little longer, a few days, being of the ord d er of 1/λd. d value will be given in the next sections of this paper. An estimation of the λd value will be given in the next sections of this paper. The asymptotic solutions of the system, expressed in term of activities (inventories), The asymptotic solutions of the system, expressed in term of activities (inventories), being A = 2 l D (Bq/m ), are the following: being 𝐴 =𝜆 𝐷 (Bq/m j ), are the follo j j wing: (1) 𝐴 =𝜙 A = f (1) l f 𝜆 𝜙 A = 𝐴 = 1 l + l 𝜆 +𝜆 1 d l l f 1 2 A = 𝜆 𝜆 𝜙 (l + l ) (l + l ) 𝐴 = 1 d 2 d (𝜆 +𝜆 )×(𝜆 +𝜆 ) l l l f 1 2 3 A = (l + 𝜆 l 𝜆 𝜆) 𝜙 (l + l ) (l + l ) 1 2 3 d d d 𝐴 = (𝜆 +𝜆 )×(𝜆 +𝜆 )×(𝜆 +𝜆 ) l l l l f 1 2 3 4 A = (l + l ) (l + l ) (l + l ) (l + l ) 1 d 2 d 3 d 4 d 𝜆 𝜆 𝜆 𝜆 𝜙 𝐴 = 210 The last equation is the only relevant expression for our purposes, giving the Pb (𝜆 +𝜆 )×(𝜆 +𝜆 )×(𝜆 +𝜆 )× (𝜆 +𝜆 ) atmospheric inventory in the whole atmosphere column (Bq/m ) as a function the radon The last equation is the only relevant expression for our purposes, giving the Pb flux j. Thus, in order to estimate j, the Pb atmospheric inventory A , must be related atmospheric inventory in the whole atmosphere column (Bq/m ) as a function the radon to a measurable quantity, i.e., to the wet and dry deposition, often indicated also as flux φ. Thus, in order to estimate φ, the Pb atmospheric inventory A4, must be related the fallout. The fallout measurements of airborne radionuclides are one of the most to a measurable quantity, i.e., to the wet and dry deposition, often indicated also as the important pillars of any environmental radioactivity network, being one of the most fallout. The fallout measurements of airborne radionuclides are one of the most sensitive measurement techniques, although relatively simple to perform. From decades, important pillars of any environmental radioactivity network, being one of the most routine fallout measurements were performed monthly in our laboratory (Ivrea, northwest sensitive measurement techniques, although relatively simple to perform. From decades, Italy) in the framework of the Italian National Environmental Radioactivity Network routine fallout measurements were performed monthly in our laboratory (Ivrea, (RESORAD). The fallout samples (wet and dry deposition) are collected monthly by means northwest Italy) in the framework of the Italian National Environmental Radioactivity of a stainless steel tank (surface area  4 m ) placed on the roof of the laboratory building Network (RESORAD). The fallout samples (wet and dry deposition) are collected (Figure 2) and always kept wet in order to avoid resuspension [32]. Environments 2022, 9, 68 4 of 11 Figure 2. The stainless steel tank placed on the roof of the building for the collection of the wet and dry deposition samples. Every month, at the end of the sampling period, the deposition is collected and dried. The residue is then weighed, placed in a small jar and measured by means of an hyperpure gamma-X (n-type) germanium detector (40% relative efficiency), able to detect the low energy 46.5 keV gamma emission of Pb (see Figure 3). Figure 3. The little jar containing the 4 g of dry residue placed on to the top of HPGe n-type detector. In order to have a standardized and calibrated counting geometry, a fixed quantity (4 g) of dry residue was put in the jar and uniformly distributed in a thin, cylindrically shaped geometry. As the photopeak efficiency was obtained by tracing with a multi- standard calibration source 4 g of a soil-type material, no self-absorption corrections were needed. In Figure 4, a typical spectrum of a fallout sample is shown: marked in red, a well-shaped Pb peak is clearly visible. Environments 2022, 9, 68 5 of 11 Figure 4. Typical spectrum of a wet and dry deposition sample: the Pb 46.5 keV peak, marked in red, is well shaped and clearly visible. Due to this long-lasting experimental work, a time series of the Pb wet and dry deposition in Ivrea, spanning the years 2005 to 2021, was available for this study. The growth of Pb in the tank, due to the deposition processes, can be modelled by the following differential equation: 210Pb d A 210Pb + l A = F (2) 4 210Pb dt 210Pb 2 210 In which A is the activity (Bq/m ) accumulated in the tank, F is the Pb 210Pb 2 2 210 flux (wet and dry, expressed in term of Bq/m s or Bq/m h) while l is the Pb decay constant. The value of F depends of course on the quantity of Pb present in the 210Pb 210 210 atmosphere, i.e., the Pb atmospheric inventory, A . Being l , the removal rate of Pb 4 d from the atmosphere, by definition the following relationship holds: F = l A (3) 210Pb d 4 Putting the right side of Equation (3) in Equation (2) and solving the differential equation, we obtain: l A 210Pb d l t A =  1 e (4a) where t is the sampling time of the deposition measurements. Considering the typical value of the sampling time (1 month) and the numerical value of the Pb decay constant l , we have l t << 1, and then the expression (4a) can be approximated to: 4 4 210Pb A = l  A  t (4b) from which, taking into account for the last equation of system solution (1), the following 2 2 equation for the radon flux, expressed in term of activity (Bq/m s or Bq/m h) may be written: 210Pb (l + l ) (l + l ) (l + l ) (l + l ) A l 1 2 3 4 0 d d d d F =  (5) l l l l l t 1 2 3 4 d being F = l f, where l is the radon decay constant. 0 0 However, for a robust evaluation of the radon flux, it is more convenient to take 210Pb in Equation (5), instead of the highly variable A monthly values, the corresponding Environments 2022, 9, x FOR PEER REVIEW 3 of 11 214 214 the secular equilibrium condition between Bi and Po, the two radionuclides evolve in time together and can thus be considered as a unique radionuclide emitting, almost at the same time, both α and β radiation. In the following, in order to distinguish the different radionuclides belonging to the system, they will be indicated with the 222 218 214 following indexes: j = 0 for Rn, j = 1 for Po, j = 2 for Pb, j = 3 for the coupled system 214 214 210 Bi/ Po, and j = 4 for Pb. If we assume that the terrestrial radon flux is given by φ, expressed as an atomic 2 2 flux (atoms/(m ·s) or atoms/(m ·h) while Dj is the corresponding quantities of radionuclides that build up in the whole atmosphere (atoms/m ), the following five equations may be written: 𝑑𝐷 +𝜆 𝐷 =𝜙 𝑑𝑡 𝑑𝐷 +(𝜆 +𝜆 )𝐷 =𝜆 𝐷 𝑗 = 0,1,2,3 𝑑𝑡 where λj is the decay constant of the Rn and its progeny and λd is the removal rate of the daughters from the atmosphere, due to wet and dry deposition processes, the value Environments 2022, 9, 68 6 of 11 of which is assumed equal for each radionuclide. The solutions of these equations are straightforward, while resulting in quite complicated expressions. However, these expressions can be dramatically simplified l D 210Pb 4 considering the correspon asymptotic ding asympto valu tic e sol A utions = , i.e., the , obtained solutions ob from tain (4a) ed for as t t⟶¥∞. . Therefore Equation (5) The asymptotic solutions becomes: provide very simple and time independent expressions that are much easier to handle. Indeed, it can be easily demonstrated that the exact time 210Pb (l + l ) (l + l ) (l + l ) (l + l ) A l  l 1 d 2 d 3 d 4 d 4 0 dependent solutions differ from the asymptotic expressions by transient factors that F =  (6) l l l l l 2 3 1 4 d became negligible very quickly—in a few hours, in accordance with the half-lives of the short lived radon daughters. This does not happen with the last equation, which referred 210Pb The A value in Equation (6) it is not a directly measurable quantity and needs to to Pb: in this case the transient is a little longer, a few days, being of the order of 1/λd. 210Pb be evaluated. In principle, the estimation of the A value can be performed by means An estimation of the λd value will be given in the next sections of this paper. of a purely experimentally method, i.e., simply computing the accumulation of Pb on The asymptotic solutions of the system, expressed in term of activities (inventories), the Earth’s surface by the series: being 𝐴 =𝜆 𝐷 (Bq/m ), are the following: 210Pb 210Pb l tk 𝐴 =𝜙 (1) A = A  e (7) ¥ å k=0 𝜆 𝜙 𝐴 = 210 Pb in which the A is the experimentally measured monthly deposition values. The series 𝜆 +𝜆 should be of course truncated at a sufficiently large k, when the contribution of the last addendum becomes negligible. Unfortunately, because of the quite long half-life of Pb, 𝜆 𝜆 𝜙 𝐴 = the series converges quite slowly and therefore very long historical series of experimental (𝜆 +𝜆 )×(𝜆 +𝜆 ) 210Pb data are likely necessary in order to obtain a reliable estimation of A : for example, after 16 years (the timespan𝜆 of 𝜆 our 𝜆 𝜙 experimental data, 2005–2016), the value of the exponential 𝐴 = factor of Equation (7) is still quite large: 0.61. To overcome this difficulty, a different (𝜆 +𝜆 )×(𝜆 +𝜆 )×(𝜆 +𝜆 ) 210Pb approach can be followed. The individual monthly A values in Equation (7) are 210Pb 𝜆 𝜆 𝜆 𝜆 𝜙 substituted with the average mo nthly value h A i, calculated in the whole time range 𝐴 = (𝜆 +𝜆 )×(𝜆 +𝜆 )×(𝜆 +𝜆 )× (𝜆 +𝜆 ) considered in this study (2005–2021). Equation (7) can thus be rearranged to: The last equation is the only relevant expression for our purposes, giving the Pb 210Pb 210Pb l tk 2 4 A = h A i e (8) atmospheric inventory in the whole atmosphere column (Bq/m ) as a function the radon 210 k=0 flux φ. Thus, in order to estimate φ, the Pb atmospheric inventory A4, must be related to a measurable quantity, i.e., to the wet and dry deposition, often indicated also as the In this expression a geometric series appears, the sum of which can be easily calcu- fallout. The fallout measuremen ¥ts of airborne radionuclides are one of the most l tk 1 lated: e = . Equation (6) of the radon flux can thus be rewritten in its l t k=0 1e ( ) important pillars of any environmental radioactivity network, being one of the most final form: sensitive measurement techniques, although relatively simple to perform. From decades, 210Pb routine fallout measurements were performed monthly in our laboratory (Ivrea, (l + l ) (l + l ) (l + l ) (l + l ) h A i l  l 1 d 2 d 3 d 4 d 4 0 F =  (9) northwest Italy) in the framework of the Italian National Environmental Radioactivity l t l l l l l  1 e 2 3 1 4 d Network (RESORAD). The fallout samples (wet and dry deposition) are collected 3. Results The experimental data considered in this study are gamma spectrometry measure- ments performed with HPGe detectors on the 186 wet and dry deposition samples collected monthly from October 2005 to April 2021. Of these, 46 had to be discarded because the gamma spectra were acquired using p-type 30% germanium detectors, resulting in spec- tra with the Pb emission peaks being very poor in shape and statistics. However, it is still possible to give a good estimation of the average deposition value with the remain- ing 140 available data, as the data are fairly uniformly distributed over the whole period (Figure 5). Environments 2022, 9, 68 7 of 11 Figure 5. Pb wet and dry deposition data from 2005 to 2021, with their uncertainties (2). 2 2 The lowest measured value was 2.0 Bq/m while the maximum was 44.7 Bq/m , the weighted mean value being 19.3  12.8 Bq/m . The high observed variability and the resulting high value of the standard deviation may be easily explained by the very important role of the precipitation events: rain scavenges the atmosphere very effectively, thus substantially increasing the flux of Pb, being the airborne radionuclides attached to the sub-micron atmospheric particulate. In order to investigate more deeply the relationship between the Pb flux and rain, the following simple deposition model can be used: gx y = a + b 1 e (10) where y represents the Pb deposition, the constant a at the right side of Equation (11) is the average contribution of the dry component while the second addendum is the wet component, depending on the amount of rain x (mm) occurring during the sampling time. The interpolation of the experimental data with the function given by Equation (10) is shown in Figure 6: it allows the estimation of the three free parameters of the model (a, b, g) and the related statistical parameters as well (see Table 1). Table 1. Estimated coefficients and statistical parameters of the model. Parameters Estimated Values Model coefficient a 7.80 Bq/m Model coefficient b 56.60 Bq/m Model coefficient g 0.0021 mm Pearson coefficient 0.80 Pearson coefficient CI (95%) 0.71–0.86 210 2 Pb estimated asymptotic value 64.41 Bq/m Environments 2022, 9, 68 8 of 11 Figure 6. Interpolation (red line) of Pb total deposition as a function of the rain cumulated during the sampling time: the grey darker area indicates the interval of confidence of the curve (95%). It is thus possible to evaluate, by means of Equation (10) the Pb average monthly deposition simply evaluating the expression at the corresponding average monthly precipi- tation value x; remembering Equation (4b), the following holds: gx a + b 1 e = l  A  t (11) in which, two unknown quantities appear at the right side of the equation: the removal rate 210 210 l and the Pb inventory A . However A is nothing but the Pb estimated asymptotic d 4 4 value shown in Table 1. Therefore, from (11), the average Pb removal rate l can be 4 1 calculated, giving: l = 3.69  10 h . Putting this number in flux Equation (9) together with all the other physical parameters we get the following value for the average radon flux: F = 57.8 Bq/(m h). It can be observed that Equation (9) can be put in more simplified form: indeed, considering the numerical value just calculated for the removal rate l and the numerical values of the radionuclides decay constants, the following approximations hold: l t (l + l )  l (l + l )  l (l + l )  l (l + l )  l 1 e )  l t 1 1 2 2 3 3 4 4 d d d d d Equation (9) thus becomes: 210Pb h A i l F = (12) l  t 222 210 in which appears only, as physical parameters, the Rn and Pb decay constants, l and l , respectively. It is interesting to notice that average radon flux in the period 2005–2021 estimated using this latter approximate expression (12) gives a result almost identical to that obtained using the “exact” Equation (9): F = 57.1 Bq/(m h). All these estimations are of course affected by a quite large uncertainty whose evalu- ation is not a simple task. For instance, considering the standard deviation of the experi- mental Pb mean monthly deposition value, an apparently sound approach, would lead to a substantial and not realistic overestimation of the real uncertainty. In fact we would Environments 2022, 9, 68 9 of 11 210Pb 2 have: h A i = 19.3  12.8 Bq/m , about 66%. Indeed, the very large standard deviation observed is mainly due to the different precipitation regimes affecting the monthly Pb deposition values rather than to a real variation in the radon flux F from the ground. There- fore, in order to reduce the variability due to precipitations, a new normalized variable is defined for any generic month j: 210Pb 210Pb h A i = w h A i N j j where the normalization coefficients w are given by: w = (13) D x in which D and D(x ) are, respectively, the experimental and the model estimated depo- j j sition data (Equation (11)), evaluated at the corresponding precipitation value x . The resulting average value of this new variable is nearly the same of the original one, while its standard deviation is appreciably reduced: Bq 210Pb h A i = 21.6 10.8 . As a consequence of this, the final best estimation for the radon flux from Pb deposition data is F = 65  32 Bq/(m h). This result is in fairly good agreement with one of the few available radon flux measurements made in the Po Valley, Northern Italy (Facchini et al. [33]): F = 72 Bq/(m h). Other measurements, obtained by means of the exposure of passive nuclear track detectors in soil, were performed by our research group in the same area (Chiaberto E., Magnoni M., Righino F. [34]) and gave a somewhat greater average value, F = 97 Bq/(m h); however, these latter measurements were affected by a substantial overestimation, as no correction for the thoron interference was made at that time. Regardless, the average radon flux value estimated in the present work matches quite well with globally accepted values. For example, Conen (2003 [35]), in a review article, gave a range between 15.1–75.6 Bq/(m h) for the northern hemisphere, with an increasing trend from high (70 N) to low (30 N) latitudes; starting from this figure, a calculation for our latitude (45 N) leads to values very close to our result. 4. Conclusions Monthly bulk deposition measurements of Pb performed by means of hyperpure germanium detectors in the framework of the Italian National Environmental Radioactivity Network (RESORAD) allowed the calculation of the average radon flux from soil. The value estimated with this method averaged over the time range considered (2005–2021) is F = 65  32 Bq/(m h)—in quite good agreement with published data, obtained using very different techniques. The proposed method is thus proved to be reliable and useful for radon flux estimation. As Pb deposition measurements are routinely performed all over the world in many environmental radioactivity monitoring networks, this method could be used elsewhere, helping researchers to obtain a worldwide map of the average radon flux, provided that a sufficiently long and reliable historical time series (at least 15–20 years) of Pb data is available. Author Contributions: Conceptualization, M.M.; methodology, M.M., L.B.; software, L.B., S.B.; experimental work, L.B., B.B., S.B.; data curation, M.M., L.B., S.B.; writing—original draft preparation, M.M.; writing—review and editing, M.M., E.C. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Environments 2022, 9, 68 10 of 11 Informed Consent Statement: Not applicable. Data Availability Statement: The experimental data reported in this study can be partially found in the official report of ARPA Piemonte, published in the website: www.arpa.piemonte.it, accessed on 31 March 2022. Conflicts of Interest: The authors declare no conflict of interest. References 1. Tanner, A.B. Radon migration in the ground: A review. In The Natural Radiation Environment; Adams, J.A.S., Lowder, W.M., Eds.; University of Chicago Press: Chicago, IL, USA, 1964; pp. 161–190. 2. Tanner, A.B. Radon migration in the ground: A supplementary review. In The Natural Radiation Environment III; Gesell, T.F., Lowder, W.M., Eds.; CONF-780422; University of Chicago Press: Chicago, IL, USA, 1980; Volume 1, pp. 5–56. 3. Nazaroff, W.W.; Nero, A.V. Radon and Its Decay Products in Indoor Air; Wiley Interscience: New York, NY, USA, 1988. 4. ICPR 65. Protection against 222Rn at Home and at Work; ICRP: Ottawa, ON, Canada, 1993; Volume 23. 5. Venuti, G.C.; Janssen, A.; Olast, M. Indoor Radon Remedial Action: The Scientific Basis and the Practical Implications: Proceedings of the First International Workshop, Rimini, Italy, 27 June–2 July 1993; Nuclear Technology Publishing: Ashford, UK, 1994; Volume 56. 6. Council Directive 2013/59/EURATOM of 5 December 2013 Laying down basic Safety Standards for Protection against the Dangers Arising from Exposure to Ionising Radiation. 2013. Available online: https://ec.europa.eu/energy/sites/ener/files/ documents/CELEX-32013L0059-EN-TXT.pdf (accessed on 31 March 2022). 7. Ulomov, V.I.; Mavashev, B.Z. A precursor of a strong tectonic earthquake. Dokl. Akad. Sci. SSSR 1967, 176, 9–11. 8. Wakita, H.; Nakamura, Y.; Notsu, K.; Noguchi, M.; Asada, T. Radon anomaly: A possible precursor of the 1978 Izo-Oshima-Kinkai earthquake. Science 1980, 207, 882–883. [CrossRef] [PubMed] 9. Shapiro, M.H.; Rice, A.; Mendenhall, M.H.; Melvin, J.D.; Tombrello, T.A. Recognition of environmentally cause variation in radon time series. Pure Appl. Geophys. 1985, 122, 309–326. [CrossRef] 10. Trique, B.; Richon, P.; Perrier, F.; Avouac, J.P.; Sabroux, J. Radon emanation and electric potential variations associated with transient deformation near reservoir lake. Nature 1999, 399, 137–141. [CrossRef] 11. Kawada, Y.; Nagahama, H.; Omori, Y.; Yasuoka, Y.; Ishikawa, T.; Tokonami, S.; Shinogi, M. Time scale invariant changes in atmospheric radon concentration and crustal strain prior to a large earthquake. Nonlinear Processes Geophys. 2007, 14, 123–130. [CrossRef] 12. Cigolini, C.; Laiolo, M.; Ulivieri, G.; Coppola, D.; Ripepe, M. Radon mapping, automatic measurements and extremely high Rn emissions during the 2002–2007 eruptive scenarios at Stromboli volcano. J. Volcanol. Geotherm. Res. 2013, 264, 49–65. [CrossRef] 13. Conen, F.; Robertson, L.B. Latitudinal distribution of Rn flux from continents. Tellus 2002, 54B, 127–133. [CrossRef] 14. Gupta, M.L.; Douglass, A.R.; Kawa, R.; Pawson, S. Use of radon for evaluation of atmospheric transport models: Sensitivity to emissions. Tellus Ser. B Chem. Phys. Meteorol. 2004, 56, 404–412. [CrossRef] 15. Robertson, L.B.; Stevenson, D.S.; Conen, F. Test of a northwards-decreasing Rn source term by comparison of modelled and observed atmospheric Rn concentrations. Tellus Ser. B Chem. Phys. Meteorol. 2005, 57, 116–123. [CrossRef] 16. Vermeulen, A.; Verheggen, B.; Zahorowski, W. Rn Vertical Gradient Measurements and Its Use for Transport Model Calibration; Transcom: Utrecht, The Netherlands, 2008. 17. Zahorowski, W.; Williams, A.G.; Vermeulen, A.; Chambers, S.; Crawford, J.; Sisoutham, O. Diurnal boundary layer mixing patterns characterised by Rn gradient observations at Cabauw. In Proceedings of the 18th AMS Conference on Boundary Layers and Turbulence, Stockholm, Sweden, 9–13 June 2008; Available online: http://ams.confex.com/ams/pdfpapers/139978.pdf (accessed on 31 March 2022). 18. Magnoni, M. Vertical dispersion of radon and conventional pollutants: Some tests on existing and new models, Sources and measurements of radon and radon progeny applied to climate and air quality studies. In Proceedings of the Technical Meeting, Vienna, Austria, 19–22 March 2012. 19. Allegrini, I.; Febo, A.; Pasini, A.; Schirini, S. Monitoring of the nocturnal mixed layer ny means of particulate radon progeny measurements. J. Geophys. Res. 1994, 94, 765–777. 20. Febo, A.; Perrino, C.; Giliberti, C.; Allegrini, I. Use of proper variables to describe some aspects of urban pollution. In NATO ASI Series; Springer: Berlin/Heidelberg, Germany, 1996; pp. 295–315. 21. Sesana, L.; Barbieri, L.; Facchini, U.; Marcazzan, G. Rn as a tracer of atmospheric motions: A study in Milan. Radiat. Prot. Dosim. 1998, 78, 65–71. [CrossRef] 22. Kataoka, T.; Yunoki, E.; Shimizu, M.; Mori, T.; Tsukamoto, O.; Ohashi, Y.; Sahashi, K.; Maitani, T.; Miyashita, K.I.; Iwata, T.; et al. A study of the atmospheric boundary layer using radon and air pollutants as tracers. Bound.-Layer Meteorol. 2001, 101, 131–155. [CrossRef] 23. Garbero, V.; Dellacasa, G.; Bianchi, D.; Magnoni, M.; Erbetta, L. Outdoor radon concentration measurements: Some correlation with major urban pollutants. Radiat. Prot. Dosim. 2009, 137, 332–335. [CrossRef] [PubMed] Environments 2022, 9, 68 11 of 11 24. Steinkopff, T.; Frank, G.; Salvamoser, J. Low Level Measurements of 222Rn in the Atmosphere in the Frame of the GAW-Measuring Programme at the Environmental Research Platform Schneefernerhaus/Zugspitze. In Proceedings of the Technical Meeting on Sources and Measurements of Radon and Radon Progeny Applied to Climate and Air Quality Studies, Vienna, Austria, 22–24 June 2009. 25. Hirsch, A.L. On using Rn and CO to calculate regional-scale CO fluxes. Atmos. Chem. Phys. 2007, 7, 3737–3747. [CrossRef] 2 2 26. Hirsch, A.I.; Fischer, M.L.; Biraud, S.C.; Torn, M.S.; Berry, J.A.; Andrews, A.E.; Peters, W.; Zahorowski, W.; Chambers, S.Z.; Tans, P.P. Combining Eddy Covariance Fluxes, High-Precision Trace Gas Measurements, Chemical Transport Modeling, and Inverse Modeling to Estimate Regional CO2 Fluxes in the Southern Great Plains, USA, Eos Trans. In AGU Fall Meeting Abstracts; American Geophysical Union: San Francisco, CA, USA, 2008; Volume 2008, p. B54A-04. 27. Biraud, S.; Ciais, P.; Ramonet, M.; Simmonds, P.; Kazan, V.; Monfray, P.; O’Doherty, S.; Spain, T.G.; Jennings, S.G. European greenhouse gas emissions estimated from continuous atmospheric measurements and Rn at Mace Head, Ireland. J. Geophys. Res. 2000, 105, 1351–1366. [CrossRef] 28. Schmidt, M. Atmospheric Radon Measurements in the French Greenhouse Gas Monitoring Network (RAMCES). 2009. Available online: https://www-pub.iaea.org/MTCD/Publications/PDF/P1541_web.pdf (accessed on 31 March 2022). 29. TraceRadon, Radon Metrology for Use in Climate Change Observation and Radiation Protection at Environmental Level. 2020. Available online: http://traceradon-empir.eu/ (accessed on 30 March 2022). 30. Abril, J.M.; Brunskill, G.J. Evidence that excess Pb varies with sediment accumulation rate and implication for dating recent sediments. J. Paleolimnol. 2014, 52, 121–137. [CrossRef] 31. Tables of Radionuclides, Monographie BIPM-5, Bureau International des Poids e des Mesures; BIPM: Sèvres, Paris, 2008. 32. Magnoni, M.; Bellina, L.; Bertino, S.; Bellotto, B.; Ghione, M.; Losana, M.C. Measurements of Na in the Atmosphere: Ground Level Activity Concentration Values from Wet and Dry Deposition Samples. Environments 2020, 7, 12. [CrossRef] 33. Facchini, U.; Martini, M.; Morniroli, E.; Procopio, G.; Tamborini, G.; Canuti, A.; Capelli, G. Concentration of radon progeny in the open air and interiors of Milan and other Italian sites. Health Phys. 1981, 41, 23–28. [CrossRef] [PubMed] 34. Chiaberto, E.; Magnoni, M.; Righino, F. Il radon nel suolo: Misure di concentrazione e di flusso. In Proceedings of the Atti del XXXI Congresso AIRP, Ancona, Italy, 20–22 September 2000. 35. Conen, F. Variation of Rn flux and its implications for atmospheric tracer studies. In Proceedings of the 1st International Expert Meeting on Source and Measurements of Natural Radionuclides Applied to Climate and Air Quality Studies, Gif sur Yvette, France, 3–5 June 2003. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Environments Multidisciplinary Digital Publishing Institute

Evaluation of the Terrestrial 222Rn Flux from 210Pb Deposition Measurements

Download PDF
11 pages

Loading next page...
 
/lp/multidisciplinary-digital-publishing-institute/evaluation-of-the-terrestrial-222rn-flux-from-210pb-deposition-suRfKX8J9k

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
Multidisciplinary Digital Publishing Institute
Copyright
© 1996-2022 MDPI (Basel, Switzerland) unless otherwise stated Disclaimer The statements, opinions and data contained in the journals are solely those of the individual authors and contributors and not of the publisher and the editor(s). MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Terms and Conditions Privacy Policy
ISSN
2076-3298
DOI
10.3390/environments9060068
Publisher site
See Article on Publisher Site

Abstract

environments Article 222 210 Evaluation of the Terrestrial Rn Flux from Pb Deposition Measurements Mauro Magnoni *, Luca Bellina, Stefano Bertino, Brunella Bellotto and Enrico Chiaberto ARPA Piemonte, Department of Physical and Technological Risks, 10015 Ivrea, TO, Italy; l.bellina@arpa.piemonte.it (L.B.); s.bertino@arpa.piemonte.it (S.B.); b.bellotto@arpa.piemonte.it (B.B.); e.chiaberto@arpa.piemonte.it (E.C.) * Correspondence: m.magnoni@arpa.piemonte.it 222 2 2 Abstract: The study of the Rn terrestrial flux (Bq/(m s) or Bq/(m h)) is a complex issue involving both radiation-protection and environmental aspects. While the radiation-protection aspects are quite obvious—it has been well known for several decades that soil is the major source of indoor radon—environmental issues such as the correlation with conventional pollutants (PM , PM , 2.5 10 NOX, etc.) and the use of radon for the esmation of the natural component of GHG (CO ) emissions are relatively less discussed in spite of their growing relevance. In this work we present a method for 222 210 the estimation of the average value of Rn flux from HPGe -spectrometry Pb measurements performed on wet and dry deposition samples gathered monthly in the period 2006–2020. The results obtained with this technique give an average radon flux in the period F = 57  27 Bq/(m h), the value of which is comparable with those coming from other methods and direct radon flux measurements as well. The method can thus be used to obtain a worldwide map of the radon flux. Keywords: terrestrial radon flux; environmental radioactivity monitoring network; Pb deposition; HPGe -spectrometry Citation: Magnoni, M.; Bellina, L.; Bertino, S.; Bellotto, B.; Chiaberto, E. Evaluation of the Terrestrial Rn 1. Introduction Flux from Pb Deposition The measurement of the terrestrial radon flux is an important and well known issue Measurements. Environments 2022, 9, for radiation protection: many studies have demonstrated that the radon flux coming from 68. https://doi.org/10.3390/ the ground is by far the most important contribution to the radon levels found in dwellings environments9060068 and workplaces [1–5]. This fact has also been explicitly recognized by many legislations. At Academic Editor: Vernon Hodge the European level, for example, a directive was issued, the 59/2013/Euratom [6], in which each EU member state has a mandate for the individuation and definition of radon priority Received: 24 April 2022 areas, i.e., areas where the radon flux from the ground is significantly greater than the Accepted: 28 May 2022 average. Besides this, many other scientific studies deal with radon flux: many researchers Published: 31 May 2022 have investigated the correlation of radon flux variations with seismic and volcanological Publisher’s Note: MDPI stays neutral phenomena [7–12]. The knowledge of local radon flux values is very important for atmo- with regard to jurisdictional claims in spheric studies as well, aiming to evaluate the motion and the origin of air masses [13–16]. published maps and institutional affil- Radon flux data and measurements are also used for the forecast and estimation of the iations. occurrence of very high concentrations of some conventional pollutants, such as PM , PM , NOX, and benzene, during particular meteorologic conditions, often characterized 2.5 by thermal inversions [17–23]. More recently, a growing interest in radon flux measurements has arisen among Copyright: © 2022 by the authors. researchers trying to evaluate the natural component of greenhouse gases; indeed, the Licensee MDPI, Basel, Switzerland. radon flux can be used as a proxy for the estimation of the terrestrial CO flux [24–28]. In This article is an open access article all these fields of study, the knowledge of the values of the terrestrial radon flux j is crucial. distributed under the terms and Unfortunately, this kind of measurement is far from simple to carry out and currently conditions of the Creative Commons suffers from a great lack of standardization. Very different approaches have been proposed, Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ using many different instruments and detectors. One of the main problems of a direct radon 4.0/). flux measurement is the difficulty in detecting radon coming from the ground without Environments 2022, 9, 68. https://doi.org/10.3390/environments9060068 https://www.mdpi.com/journal/environments Environments 2022, 9, 68 2 of 11 perturbing the exhalation process in a substantial way. Recently, an ongoing European project (traceRadon, [29]) has been trying to tackle these problems by promoting large intercomparison programs of different devices able to follow the time evolution of the radon exhalation rate in different soils. In this work a new and different method is proposed, based on Pb measurements. The evidence of an excess Pb flux of atmospheric origin has been investigated in several works dealing with the sediment accumulation rate and sediment core chronology studies; see, for example [30]. This Pb flux, if properly measured, can also be used to estimate the average value of the terrestrial radon flux indirectly. The method proposed derives the radon flux from an historical series of Pb spectrometry deposition measurements performed in the framework of the RESORAD network, the Italian National Radioactivity Monitoring Network. 2. Materials and Methods After being produced by radioactive decay, radon is separated from its parent Ra and, because of its relatively long half-life (3.82 days), is released into the atmosphere, giving rise to the lower part of the uranium natural radioactive series which substantially contributes to atmospheric radioactivity (see Figure 1). Let us consider in particular the system consisting of six radionuclides, circled in red in Figure 1, having Rn as parent 210 210 214 and ending to Pb. Pb is produced by the decay of Po, the last of the so called 218 214 214 short-lived radon daughters, the others being Po, Pb, Bi, usually named short lived radon daughters because of their very short half lives. Pb is a emitter having a quite long half-life, 22.23 years, emitting a relatively soft radiation (end-point energy 63.5 keV, [31]), followed almost immediately by a low energy line (46.5 keV) coming from the de-excitation of the 0-excited state of Bi. Figure 1. The lower part of the uranium series in atmosphere: the six radionuclides considered in this work are circled in red. It can be observed that, for practical reasons, this system can be simplified and con- sidered substantially equivalent to a five-radionuclide system. Indeed, due to the very short half-life of Po (164 s), which assures an almost immediate achievement of the 214 214 secular equilibrium condition between Bi and Po, the two radionuclides evolve in time together and can thus be considered as a unique radionuclide emitting, almost at the same time, both and radiation. In the following, in order to distinguish the different radionuclides belonging to the system, they will be indicated with the following indexes: Environments 2022, 9, x FOR PEER REVIEW 3 of 11 214 214 the secular equilibrium condition between Bi and Po, the two radionuclides evolve in time together and can thus be considered as a unique radionuclide emitting, almost at the same time, both α and β radiation. In the following, in order to distinguish the Environments 2022, 9, 68 3 of 11 different radionuclides belonging to the system, they will be indicated with the 222 218 214 following indexes: j = 0 for Rn, j = 1 for Po, j = 2 for Pb, j = 3 for the coupled system 214 214 210 Bi/ Po, and j = 4 fo 222 r Pb. 218 214 214 214 j = 0 for Rn, j = 1 for Po, j = 2 for Pb, j = 3 for the coupled system Bi/ Po, and If we assume that the terrestrial radon flux is given by φ, expressed as an atomic j = 4 for Pb. 2 2 flux (atoms/(m ·s) or atoms/(m ·h) while Dj is the corresponding quantities of If we assume that the terrestrial radon flux is given by j, expressed as an atomic flux 2 2 radionuclides that build up in the whole atmosphere (atoms/m ), the following five (atoms/(m s) or atoms/(m h) while D is the corresponding quantities of radionuclides equations may be written: 2 that build up in the whole atmosphere (atoms/m ), the following five equations may be written: 𝑑𝐷 +𝜆 𝐷 d=𝜙 D 𝑑𝑡 + l D = f 0 0 dt dD j+1 𝑑𝐷 + (l + l )D = l D j = 0, 1, 2, 3 j+1 d j+1 i i +(𝜆 +𝜆 )𝐷 =𝜆 𝐷 𝑗 = 0,1,2,3 dt 𝑑𝑡 where λj is the decay constant of the Rn and its progeny and λd is the removal rate of where l is the decay constant of the Rn and its progeny and l is the removal rate of j d the daughters from the atmosphere, due to wet and dry deposition processes, the value the daughters from the atmosphere, due to wet and dry deposition processes, the value of of which is assumed equal for each radionuclide. which is assumed equal for each radionuclide. The solutions of these equations are straightforward, while resulting in quite The solutions of these equations are straightforward, while resulting in quite compli- complicated expressions. However, these expressions can be dramatically simplified cated expressions. However, these expressions can be dramatically simplified considering considering t the he correspon correspondin ding g as asymptotic ymptotic sol solution utions s, , i i.e., .e., the the so solutions lutions ob obtained tained for for t t⟶¥∞. . The asymp- The asympto totic tic so solutions lutions provide ver provide veryy simp simplele and and time time independent independent expr expressions that essions that are much easier are much eato sier handle. to hand Indeed, le. Inde it ed, can i be t can b easilye e demonstrated asily demons that trate the d th exact at the time exact dependent time solutions dependent sdif olu fer tion frs di om ffe ther from asymptotic the as expr ymp essions totic exby pression transient s by factors transien that t fbecame actors tha negligible t very quickly—in a few hours, in accordance with the half-lives of the short lived radon daugh- became negligible very quickly—in a few hours, in accordance with the half-lives of the ters. This does not happen with the last equation, which referred to Pb: in this case the short lived radon daughters. This does not happen with the last equation, which referred transient is a little longer, a few days, being of the order of 1/l . An estimation of the l to Pb: in this case the transient is a little longer, a few days, being of the ord d er of 1/λd. d value will be given in the next sections of this paper. An estimation of the λd value will be given in the next sections of this paper. The asymptotic solutions of the system, expressed in term of activities (inventories), The asymptotic solutions of the system, expressed in term of activities (inventories), being A = 2 l D (Bq/m ), are the following: being 𝐴 =𝜆 𝐷 (Bq/m j ), are the follo j j wing: (1) 𝐴 =𝜙 A = f (1) l f 𝜆 𝜙 A = 𝐴 = 1 l + l 𝜆 +𝜆 1 d l l f 1 2 A = 𝜆 𝜆 𝜙 (l + l ) (l + l ) 𝐴 = 1 d 2 d (𝜆 +𝜆 )×(𝜆 +𝜆 ) l l l f 1 2 3 A = (l + 𝜆 l 𝜆 𝜆) 𝜙 (l + l ) (l + l ) 1 2 3 d d d 𝐴 = (𝜆 +𝜆 )×(𝜆 +𝜆 )×(𝜆 +𝜆 ) l l l l f 1 2 3 4 A = (l + l ) (l + l ) (l + l ) (l + l ) 1 d 2 d 3 d 4 d 𝜆 𝜆 𝜆 𝜆 𝜙 𝐴 = 210 The last equation is the only relevant expression for our purposes, giving the Pb (𝜆 +𝜆 )×(𝜆 +𝜆 )×(𝜆 +𝜆 )× (𝜆 +𝜆 ) atmospheric inventory in the whole atmosphere column (Bq/m ) as a function the radon The last equation is the only relevant expression for our purposes, giving the Pb flux j. Thus, in order to estimate j, the Pb atmospheric inventory A , must be related atmospheric inventory in the whole atmosphere column (Bq/m ) as a function the radon to a measurable quantity, i.e., to the wet and dry deposition, often indicated also as flux φ. Thus, in order to estimate φ, the Pb atmospheric inventory A4, must be related the fallout. The fallout measurements of airborne radionuclides are one of the most to a measurable quantity, i.e., to the wet and dry deposition, often indicated also as the important pillars of any environmental radioactivity network, being one of the most fallout. The fallout measurements of airborne radionuclides are one of the most sensitive measurement techniques, although relatively simple to perform. From decades, important pillars of any environmental radioactivity network, being one of the most routine fallout measurements were performed monthly in our laboratory (Ivrea, northwest sensitive measurement techniques, although relatively simple to perform. From decades, Italy) in the framework of the Italian National Environmental Radioactivity Network routine fallout measurements were performed monthly in our laboratory (Ivrea, (RESORAD). The fallout samples (wet and dry deposition) are collected monthly by means northwest Italy) in the framework of the Italian National Environmental Radioactivity of a stainless steel tank (surface area  4 m ) placed on the roof of the laboratory building Network (RESORAD). The fallout samples (wet and dry deposition) are collected (Figure 2) and always kept wet in order to avoid resuspension [32]. Environments 2022, 9, 68 4 of 11 Figure 2. The stainless steel tank placed on the roof of the building for the collection of the wet and dry deposition samples. Every month, at the end of the sampling period, the deposition is collected and dried. The residue is then weighed, placed in a small jar and measured by means of an hyperpure gamma-X (n-type) germanium detector (40% relative efficiency), able to detect the low energy 46.5 keV gamma emission of Pb (see Figure 3). Figure 3. The little jar containing the 4 g of dry residue placed on to the top of HPGe n-type detector. In order to have a standardized and calibrated counting geometry, a fixed quantity (4 g) of dry residue was put in the jar and uniformly distributed in a thin, cylindrically shaped geometry. As the photopeak efficiency was obtained by tracing with a multi- standard calibration source 4 g of a soil-type material, no self-absorption corrections were needed. In Figure 4, a typical spectrum of a fallout sample is shown: marked in red, a well-shaped Pb peak is clearly visible. Environments 2022, 9, 68 5 of 11 Figure 4. Typical spectrum of a wet and dry deposition sample: the Pb 46.5 keV peak, marked in red, is well shaped and clearly visible. Due to this long-lasting experimental work, a time series of the Pb wet and dry deposition in Ivrea, spanning the years 2005 to 2021, was available for this study. The growth of Pb in the tank, due to the deposition processes, can be modelled by the following differential equation: 210Pb d A 210Pb + l A = F (2) 4 210Pb dt 210Pb 2 210 In which A is the activity (Bq/m ) accumulated in the tank, F is the Pb 210Pb 2 2 210 flux (wet and dry, expressed in term of Bq/m s or Bq/m h) while l is the Pb decay constant. The value of F depends of course on the quantity of Pb present in the 210Pb 210 210 atmosphere, i.e., the Pb atmospheric inventory, A . Being l , the removal rate of Pb 4 d from the atmosphere, by definition the following relationship holds: F = l A (3) 210Pb d 4 Putting the right side of Equation (3) in Equation (2) and solving the differential equation, we obtain: l A 210Pb d l t A =  1 e (4a) where t is the sampling time of the deposition measurements. Considering the typical value of the sampling time (1 month) and the numerical value of the Pb decay constant l , we have l t << 1, and then the expression (4a) can be approximated to: 4 4 210Pb A = l  A  t (4b) from which, taking into account for the last equation of system solution (1), the following 2 2 equation for the radon flux, expressed in term of activity (Bq/m s or Bq/m h) may be written: 210Pb (l + l ) (l + l ) (l + l ) (l + l ) A l 1 2 3 4 0 d d d d F =  (5) l l l l l t 1 2 3 4 d being F = l f, where l is the radon decay constant. 0 0 However, for a robust evaluation of the radon flux, it is more convenient to take 210Pb in Equation (5), instead of the highly variable A monthly values, the corresponding Environments 2022, 9, x FOR PEER REVIEW 3 of 11 214 214 the secular equilibrium condition between Bi and Po, the two radionuclides evolve in time together and can thus be considered as a unique radionuclide emitting, almost at the same time, both α and β radiation. In the following, in order to distinguish the different radionuclides belonging to the system, they will be indicated with the 222 218 214 following indexes: j = 0 for Rn, j = 1 for Po, j = 2 for Pb, j = 3 for the coupled system 214 214 210 Bi/ Po, and j = 4 for Pb. If we assume that the terrestrial radon flux is given by φ, expressed as an atomic 2 2 flux (atoms/(m ·s) or atoms/(m ·h) while Dj is the corresponding quantities of radionuclides that build up in the whole atmosphere (atoms/m ), the following five equations may be written: 𝑑𝐷 +𝜆 𝐷 =𝜙 𝑑𝑡 𝑑𝐷 +(𝜆 +𝜆 )𝐷 =𝜆 𝐷 𝑗 = 0,1,2,3 𝑑𝑡 where λj is the decay constant of the Rn and its progeny and λd is the removal rate of the daughters from the atmosphere, due to wet and dry deposition processes, the value Environments 2022, 9, 68 6 of 11 of which is assumed equal for each radionuclide. The solutions of these equations are straightforward, while resulting in quite complicated expressions. However, these expressions can be dramatically simplified l D 210Pb 4 considering the correspon asymptotic ding asympto valu tic e sol A utions = , i.e., the , obtained solutions ob from tain (4a) ed for as t t⟶¥∞. . Therefore Equation (5) The asymptotic solutions becomes: provide very simple and time independent expressions that are much easier to handle. Indeed, it can be easily demonstrated that the exact time 210Pb (l + l ) (l + l ) (l + l ) (l + l ) A l  l 1 d 2 d 3 d 4 d 4 0 dependent solutions differ from the asymptotic expressions by transient factors that F =  (6) l l l l l 2 3 1 4 d became negligible very quickly—in a few hours, in accordance with the half-lives of the short lived radon daughters. This does not happen with the last equation, which referred 210Pb The A value in Equation (6) it is not a directly measurable quantity and needs to to Pb: in this case the transient is a little longer, a few days, being of the order of 1/λd. 210Pb be evaluated. In principle, the estimation of the A value can be performed by means An estimation of the λd value will be given in the next sections of this paper. of a purely experimentally method, i.e., simply computing the accumulation of Pb on The asymptotic solutions of the system, expressed in term of activities (inventories), the Earth’s surface by the series: being 𝐴 =𝜆 𝐷 (Bq/m ), are the following: 210Pb 210Pb l tk 𝐴 =𝜙 (1) A = A  e (7) ¥ å k=0 𝜆 𝜙 𝐴 = 210 Pb in which the A is the experimentally measured monthly deposition values. The series 𝜆 +𝜆 should be of course truncated at a sufficiently large k, when the contribution of the last addendum becomes negligible. Unfortunately, because of the quite long half-life of Pb, 𝜆 𝜆 𝜙 𝐴 = the series converges quite slowly and therefore very long historical series of experimental (𝜆 +𝜆 )×(𝜆 +𝜆 ) 210Pb data are likely necessary in order to obtain a reliable estimation of A : for example, after 16 years (the timespan𝜆 of 𝜆 our 𝜆 𝜙 experimental data, 2005–2016), the value of the exponential 𝐴 = factor of Equation (7) is still quite large: 0.61. To overcome this difficulty, a different (𝜆 +𝜆 )×(𝜆 +𝜆 )×(𝜆 +𝜆 ) 210Pb approach can be followed. The individual monthly A values in Equation (7) are 210Pb 𝜆 𝜆 𝜆 𝜆 𝜙 substituted with the average mo nthly value h A i, calculated in the whole time range 𝐴 = (𝜆 +𝜆 )×(𝜆 +𝜆 )×(𝜆 +𝜆 )× (𝜆 +𝜆 ) considered in this study (2005–2021). Equation (7) can thus be rearranged to: The last equation is the only relevant expression for our purposes, giving the Pb 210Pb 210Pb l tk 2 4 A = h A i e (8) atmospheric inventory in the whole atmosphere column (Bq/m ) as a function the radon 210 k=0 flux φ. Thus, in order to estimate φ, the Pb atmospheric inventory A4, must be related to a measurable quantity, i.e., to the wet and dry deposition, often indicated also as the In this expression a geometric series appears, the sum of which can be easily calcu- fallout. The fallout measuremen ¥ts of airborne radionuclides are one of the most l tk 1 lated: e = . Equation (6) of the radon flux can thus be rewritten in its l t k=0 1e ( ) important pillars of any environmental radioactivity network, being one of the most final form: sensitive measurement techniques, although relatively simple to perform. From decades, 210Pb routine fallout measurements were performed monthly in our laboratory (Ivrea, (l + l ) (l + l ) (l + l ) (l + l ) h A i l  l 1 d 2 d 3 d 4 d 4 0 F =  (9) northwest Italy) in the framework of the Italian National Environmental Radioactivity l t l l l l l  1 e 2 3 1 4 d Network (RESORAD). The fallout samples (wet and dry deposition) are collected 3. Results The experimental data considered in this study are gamma spectrometry measure- ments performed with HPGe detectors on the 186 wet and dry deposition samples collected monthly from October 2005 to April 2021. Of these, 46 had to be discarded because the gamma spectra were acquired using p-type 30% germanium detectors, resulting in spec- tra with the Pb emission peaks being very poor in shape and statistics. However, it is still possible to give a good estimation of the average deposition value with the remain- ing 140 available data, as the data are fairly uniformly distributed over the whole period (Figure 5). Environments 2022, 9, 68 7 of 11 Figure 5. Pb wet and dry deposition data from 2005 to 2021, with their uncertainties (2). 2 2 The lowest measured value was 2.0 Bq/m while the maximum was 44.7 Bq/m , the weighted mean value being 19.3  12.8 Bq/m . The high observed variability and the resulting high value of the standard deviation may be easily explained by the very important role of the precipitation events: rain scavenges the atmosphere very effectively, thus substantially increasing the flux of Pb, being the airborne radionuclides attached to the sub-micron atmospheric particulate. In order to investigate more deeply the relationship between the Pb flux and rain, the following simple deposition model can be used: gx y = a + b 1 e (10) where y represents the Pb deposition, the constant a at the right side of Equation (11) is the average contribution of the dry component while the second addendum is the wet component, depending on the amount of rain x (mm) occurring during the sampling time. The interpolation of the experimental data with the function given by Equation (10) is shown in Figure 6: it allows the estimation of the three free parameters of the model (a, b, g) and the related statistical parameters as well (see Table 1). Table 1. Estimated coefficients and statistical parameters of the model. Parameters Estimated Values Model coefficient a 7.80 Bq/m Model coefficient b 56.60 Bq/m Model coefficient g 0.0021 mm Pearson coefficient 0.80 Pearson coefficient CI (95%) 0.71–0.86 210 2 Pb estimated asymptotic value 64.41 Bq/m Environments 2022, 9, 68 8 of 11 Figure 6. Interpolation (red line) of Pb total deposition as a function of the rain cumulated during the sampling time: the grey darker area indicates the interval of confidence of the curve (95%). It is thus possible to evaluate, by means of Equation (10) the Pb average monthly deposition simply evaluating the expression at the corresponding average monthly precipi- tation value x; remembering Equation (4b), the following holds: gx a + b 1 e = l  A  t (11) in which, two unknown quantities appear at the right side of the equation: the removal rate 210 210 l and the Pb inventory A . However A is nothing but the Pb estimated asymptotic d 4 4 value shown in Table 1. Therefore, from (11), the average Pb removal rate l can be 4 1 calculated, giving: l = 3.69  10 h . Putting this number in flux Equation (9) together with all the other physical parameters we get the following value for the average radon flux: F = 57.8 Bq/(m h). It can be observed that Equation (9) can be put in more simplified form: indeed, considering the numerical value just calculated for the removal rate l and the numerical values of the radionuclides decay constants, the following approximations hold: l t (l + l )  l (l + l )  l (l + l )  l (l + l )  l 1 e )  l t 1 1 2 2 3 3 4 4 d d d d d Equation (9) thus becomes: 210Pb h A i l F = (12) l  t 222 210 in which appears only, as physical parameters, the Rn and Pb decay constants, l and l , respectively. It is interesting to notice that average radon flux in the period 2005–2021 estimated using this latter approximate expression (12) gives a result almost identical to that obtained using the “exact” Equation (9): F = 57.1 Bq/(m h). All these estimations are of course affected by a quite large uncertainty whose evalu- ation is not a simple task. For instance, considering the standard deviation of the experi- mental Pb mean monthly deposition value, an apparently sound approach, would lead to a substantial and not realistic overestimation of the real uncertainty. In fact we would Environments 2022, 9, 68 9 of 11 210Pb 2 have: h A i = 19.3  12.8 Bq/m , about 66%. Indeed, the very large standard deviation observed is mainly due to the different precipitation regimes affecting the monthly Pb deposition values rather than to a real variation in the radon flux F from the ground. There- fore, in order to reduce the variability due to precipitations, a new normalized variable is defined for any generic month j: 210Pb 210Pb h A i = w h A i N j j where the normalization coefficients w are given by: w = (13) D x in which D and D(x ) are, respectively, the experimental and the model estimated depo- j j sition data (Equation (11)), evaluated at the corresponding precipitation value x . The resulting average value of this new variable is nearly the same of the original one, while its standard deviation is appreciably reduced: Bq 210Pb h A i = 21.6 10.8 . As a consequence of this, the final best estimation for the radon flux from Pb deposition data is F = 65  32 Bq/(m h). This result is in fairly good agreement with one of the few available radon flux measurements made in the Po Valley, Northern Italy (Facchini et al. [33]): F = 72 Bq/(m h). Other measurements, obtained by means of the exposure of passive nuclear track detectors in soil, were performed by our research group in the same area (Chiaberto E., Magnoni M., Righino F. [34]) and gave a somewhat greater average value, F = 97 Bq/(m h); however, these latter measurements were affected by a substantial overestimation, as no correction for the thoron interference was made at that time. Regardless, the average radon flux value estimated in the present work matches quite well with globally accepted values. For example, Conen (2003 [35]), in a review article, gave a range between 15.1–75.6 Bq/(m h) for the northern hemisphere, with an increasing trend from high (70 N) to low (30 N) latitudes; starting from this figure, a calculation for our latitude (45 N) leads to values very close to our result. 4. Conclusions Monthly bulk deposition measurements of Pb performed by means of hyperpure germanium detectors in the framework of the Italian National Environmental Radioactivity Network (RESORAD) allowed the calculation of the average radon flux from soil. The value estimated with this method averaged over the time range considered (2005–2021) is F = 65  32 Bq/(m h)—in quite good agreement with published data, obtained using very different techniques. The proposed method is thus proved to be reliable and useful for radon flux estimation. As Pb deposition measurements are routinely performed all over the world in many environmental radioactivity monitoring networks, this method could be used elsewhere, helping researchers to obtain a worldwide map of the average radon flux, provided that a sufficiently long and reliable historical time series (at least 15–20 years) of Pb data is available. Author Contributions: Conceptualization, M.M.; methodology, M.M., L.B.; software, L.B., S.B.; experimental work, L.B., B.B., S.B.; data curation, M.M., L.B., S.B.; writing—original draft preparation, M.M.; writing—review and editing, M.M., E.C. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Environments 2022, 9, 68 10 of 11 Informed Consent Statement: Not applicable. Data Availability Statement: The experimental data reported in this study can be partially found in the official report of ARPA Piemonte, published in the website: www.arpa.piemonte.it, accessed on 31 March 2022. Conflicts of Interest: The authors declare no conflict of interest. References 1. Tanner, A.B. Radon migration in the ground: A review. In The Natural Radiation Environment; Adams, J.A.S., Lowder, W.M., Eds.; University of Chicago Press: Chicago, IL, USA, 1964; pp. 161–190. 2. Tanner, A.B. Radon migration in the ground: A supplementary review. In The Natural Radiation Environment III; Gesell, T.F., Lowder, W.M., Eds.; CONF-780422; University of Chicago Press: Chicago, IL, USA, 1980; Volume 1, pp. 5–56. 3. Nazaroff, W.W.; Nero, A.V. Radon and Its Decay Products in Indoor Air; Wiley Interscience: New York, NY, USA, 1988. 4. ICPR 65. Protection against 222Rn at Home and at Work; ICRP: Ottawa, ON, Canada, 1993; Volume 23. 5. Venuti, G.C.; Janssen, A.; Olast, M. Indoor Radon Remedial Action: The Scientific Basis and the Practical Implications: Proceedings of the First International Workshop, Rimini, Italy, 27 June–2 July 1993; Nuclear Technology Publishing: Ashford, UK, 1994; Volume 56. 6. Council Directive 2013/59/EURATOM of 5 December 2013 Laying down basic Safety Standards for Protection against the Dangers Arising from Exposure to Ionising Radiation. 2013. Available online: https://ec.europa.eu/energy/sites/ener/files/ documents/CELEX-32013L0059-EN-TXT.pdf (accessed on 31 March 2022). 7. Ulomov, V.I.; Mavashev, B.Z. A precursor of a strong tectonic earthquake. Dokl. Akad. Sci. SSSR 1967, 176, 9–11. 8. Wakita, H.; Nakamura, Y.; Notsu, K.; Noguchi, M.; Asada, T. Radon anomaly: A possible precursor of the 1978 Izo-Oshima-Kinkai earthquake. Science 1980, 207, 882–883. [CrossRef] [PubMed] 9. Shapiro, M.H.; Rice, A.; Mendenhall, M.H.; Melvin, J.D.; Tombrello, T.A. Recognition of environmentally cause variation in radon time series. Pure Appl. Geophys. 1985, 122, 309–326. [CrossRef] 10. Trique, B.; Richon, P.; Perrier, F.; Avouac, J.P.; Sabroux, J. Radon emanation and electric potential variations associated with transient deformation near reservoir lake. Nature 1999, 399, 137–141. [CrossRef] 11. Kawada, Y.; Nagahama, H.; Omori, Y.; Yasuoka, Y.; Ishikawa, T.; Tokonami, S.; Shinogi, M. Time scale invariant changes in atmospheric radon concentration and crustal strain prior to a large earthquake. Nonlinear Processes Geophys. 2007, 14, 123–130. [CrossRef] 12. Cigolini, C.; Laiolo, M.; Ulivieri, G.; Coppola, D.; Ripepe, M. Radon mapping, automatic measurements and extremely high Rn emissions during the 2002–2007 eruptive scenarios at Stromboli volcano. J. Volcanol. Geotherm. Res. 2013, 264, 49–65. [CrossRef] 13. Conen, F.; Robertson, L.B. Latitudinal distribution of Rn flux from continents. Tellus 2002, 54B, 127–133. [CrossRef] 14. Gupta, M.L.; Douglass, A.R.; Kawa, R.; Pawson, S. Use of radon for evaluation of atmospheric transport models: Sensitivity to emissions. Tellus Ser. B Chem. Phys. Meteorol. 2004, 56, 404–412. [CrossRef] 15. Robertson, L.B.; Stevenson, D.S.; Conen, F. Test of a northwards-decreasing Rn source term by comparison of modelled and observed atmospheric Rn concentrations. Tellus Ser. B Chem. Phys. Meteorol. 2005, 57, 116–123. [CrossRef] 16. Vermeulen, A.; Verheggen, B.; Zahorowski, W. Rn Vertical Gradient Measurements and Its Use for Transport Model Calibration; Transcom: Utrecht, The Netherlands, 2008. 17. Zahorowski, W.; Williams, A.G.; Vermeulen, A.; Chambers, S.; Crawford, J.; Sisoutham, O. Diurnal boundary layer mixing patterns characterised by Rn gradient observations at Cabauw. In Proceedings of the 18th AMS Conference on Boundary Layers and Turbulence, Stockholm, Sweden, 9–13 June 2008; Available online: http://ams.confex.com/ams/pdfpapers/139978.pdf (accessed on 31 March 2022). 18. Magnoni, M. Vertical dispersion of radon and conventional pollutants: Some tests on existing and new models, Sources and measurements of radon and radon progeny applied to climate and air quality studies. In Proceedings of the Technical Meeting, Vienna, Austria, 19–22 March 2012. 19. Allegrini, I.; Febo, A.; Pasini, A.; Schirini, S. Monitoring of the nocturnal mixed layer ny means of particulate radon progeny measurements. J. Geophys. Res. 1994, 94, 765–777. 20. Febo, A.; Perrino, C.; Giliberti, C.; Allegrini, I. Use of proper variables to describe some aspects of urban pollution. In NATO ASI Series; Springer: Berlin/Heidelberg, Germany, 1996; pp. 295–315. 21. Sesana, L.; Barbieri, L.; Facchini, U.; Marcazzan, G. Rn as a tracer of atmospheric motions: A study in Milan. Radiat. Prot. Dosim. 1998, 78, 65–71. [CrossRef] 22. Kataoka, T.; Yunoki, E.; Shimizu, M.; Mori, T.; Tsukamoto, O.; Ohashi, Y.; Sahashi, K.; Maitani, T.; Miyashita, K.I.; Iwata, T.; et al. A study of the atmospheric boundary layer using radon and air pollutants as tracers. Bound.-Layer Meteorol. 2001, 101, 131–155. [CrossRef] 23. Garbero, V.; Dellacasa, G.; Bianchi, D.; Magnoni, M.; Erbetta, L. Outdoor radon concentration measurements: Some correlation with major urban pollutants. Radiat. Prot. Dosim. 2009, 137, 332–335. [CrossRef] [PubMed] Environments 2022, 9, 68 11 of 11 24. Steinkopff, T.; Frank, G.; Salvamoser, J. Low Level Measurements of 222Rn in the Atmosphere in the Frame of the GAW-Measuring Programme at the Environmental Research Platform Schneefernerhaus/Zugspitze. In Proceedings of the Technical Meeting on Sources and Measurements of Radon and Radon Progeny Applied to Climate and Air Quality Studies, Vienna, Austria, 22–24 June 2009. 25. Hirsch, A.L. On using Rn and CO to calculate regional-scale CO fluxes. Atmos. Chem. Phys. 2007, 7, 3737–3747. [CrossRef] 2 2 26. Hirsch, A.I.; Fischer, M.L.; Biraud, S.C.; Torn, M.S.; Berry, J.A.; Andrews, A.E.; Peters, W.; Zahorowski, W.; Chambers, S.Z.; Tans, P.P. Combining Eddy Covariance Fluxes, High-Precision Trace Gas Measurements, Chemical Transport Modeling, and Inverse Modeling to Estimate Regional CO2 Fluxes in the Southern Great Plains, USA, Eos Trans. In AGU Fall Meeting Abstracts; American Geophysical Union: San Francisco, CA, USA, 2008; Volume 2008, p. B54A-04. 27. Biraud, S.; Ciais, P.; Ramonet, M.; Simmonds, P.; Kazan, V.; Monfray, P.; O’Doherty, S.; Spain, T.G.; Jennings, S.G. European greenhouse gas emissions estimated from continuous atmospheric measurements and Rn at Mace Head, Ireland. J. Geophys. Res. 2000, 105, 1351–1366. [CrossRef] 28. Schmidt, M. Atmospheric Radon Measurements in the French Greenhouse Gas Monitoring Network (RAMCES). 2009. Available online: https://www-pub.iaea.org/MTCD/Publications/PDF/P1541_web.pdf (accessed on 31 March 2022). 29. TraceRadon, Radon Metrology for Use in Climate Change Observation and Radiation Protection at Environmental Level. 2020. Available online: http://traceradon-empir.eu/ (accessed on 30 March 2022). 30. Abril, J.M.; Brunskill, G.J. Evidence that excess Pb varies with sediment accumulation rate and implication for dating recent sediments. J. Paleolimnol. 2014, 52, 121–137. [CrossRef] 31. Tables of Radionuclides, Monographie BIPM-5, Bureau International des Poids e des Mesures; BIPM: Sèvres, Paris, 2008. 32. Magnoni, M.; Bellina, L.; Bertino, S.; Bellotto, B.; Ghione, M.; Losana, M.C. Measurements of Na in the Atmosphere: Ground Level Activity Concentration Values from Wet and Dry Deposition Samples. Environments 2020, 7, 12. [CrossRef] 33. Facchini, U.; Martini, M.; Morniroli, E.; Procopio, G.; Tamborini, G.; Canuti, A.; Capelli, G. Concentration of radon progeny in the open air and interiors of Milan and other Italian sites. Health Phys. 1981, 41, 23–28. [CrossRef] [PubMed] 34. Chiaberto, E.; Magnoni, M.; Righino, F. Il radon nel suolo: Misure di concentrazione e di flusso. In Proceedings of the Atti del XXXI Congresso AIRP, Ancona, Italy, 20–22 September 2000. 35. Conen, F. Variation of Rn flux and its implications for atmospheric tracer studies. In Proceedings of the 1st International Expert Meeting on Source and Measurements of Natural Radionuclides Applied to Climate and Air Quality Studies, Gif sur Yvette, France, 3–5 June 2003.

Journal

Environments – Multidisciplinary Digital Publishing Institute

Published: May 31, 2022

Keywords: terrestrial radon flux; environmental radioactivity monitoring network; 210Pb deposition; HPGe γ-spectrometry

There are no references for this article.