Dynamics of beryllium-7 specific activity in relation to meteorological variables, tropopause height, teleconnection indices and sunspot number
Darko Sarvan, Djordje Stratimirovic, Suzana Blesic, Vladimir Djurdjevic, Vladimir Miljkovic, Jelena Ajtic
aa r X i v : . [ phy s i c s . d a t a - a n ] J u l Dynamics of beryllium-7 specific activity in relation tometeorological variables, tropopause height,teleconnection indices and sunspot number
D. Sarvan a, ∗ , D. Stratimirovi´c b,c , S. Blesi´c d,c , V. Djurdjevic e , V. Miljkovi´c f ,J. Ajti´c a,c, ∗∗ a University of Belgrade, Faculty of Veterinary Medicine, Bulevar oslobod¯enja 18, 11 000Belgrade, Serbia b University of Belgrade, Faculty of Dental Medicine, Dr Suboti´ca 8, 11 000 Belgrade, Serbia c Institute for Research and Advancement in Complex Systems, Zmaja od No´caja 8, 11 000Belgrade, Serbia d Department of Environmental Sciences, Informatics and Statistics, Ca’Foscari Universityof Venice, Mestre, Italy e University of Belgrade, Faculty of Physics, Institute of Meteorology, Studentski trg 12,11 000 Belgrade, Serbia f University of Belgrade, Faculty of Physics, Studentski trg 12, 11 000 Belgrade, Serbia
Abstract
The dynamics of the beryllium-7 specific activity in surface air over 1987–2011 isanalyzed using wavelet transform (WT) analysis and time-dependent detrendedmoving average (tdDMA) method. WT analysis gives four periodicities in theberyllium-7 specific activity: one month, three months, one year, and threeyears. These intervals are further used in tdDMA to calculate local autocor-relation exponents for precipitation, tropopause height and teleconnection in-dices. Our results show that these parameters share common periods with theberyllium-7 surface concentration. tdDMA method indicates that on the char-acteristic intervals of one year and shorter, the beryllium-7 specific activity isstrongly autocorrelated. On the three-year interval, the beryllium-7 specific ac-tivity shows periods of anticorrelation, implying slow changes in its dynamics ∗ Corresponding author ∗∗ Principal corresponding author
Email addresses: [email protected] (D. Sarvan), [email protected] (D. Stratimirovi´c), [email protected] (S. Blesi´c), [email protected] (V. Djurdjevic), [email protected] (V. Miljkovi´c), [email protected] (J. Ajti´c)
Preprint submitted to Journal of L A TEX Templates July 3, 2018 hat become evident only over a prolonged period of time. A comparison of theHurst exponents of all the variables on the one- and three-year intervals suggestsome similarities in their dynamics. Overall, a good agreement in the behaviorof the teleconnection indices and specific activity of beryllium-7 in surface airis noted.
Keywords: beryllium-7, wavelet analysis, periodicities, Hurst exponent,long-range correlations
1. Introduction
Beryllium-7 (half-life 53.22 days) is a naturally occurring radionuclide thatis produced in the upper troposphere (around 30 %) and lower stratosphere(around 70 %) [1]. After formation Be attaches to fine aerosols, and its res-idence time in the atmosphere is long [2, 3, 4, 5]. The ensuing transport ofthe aerosols, and therefore of the radionuclide, is governed by the atmosphericcirculation [6, 7].Concentration of Be in any given location (altitude, latitude, longitude)depends on several factors [8]. First, the source of the radionuclide is its pro-duction in the higher layers of the atmosphere. Therefore, the production rateinfluences the total amount of the radionuclide. Second, transport can increaseor decrease the radionuclide concentration at a particular location, dependingon abundance of Be in the transported air masses. Finally, the rate of theisotope removal influences its concentration in the atmosphere.The above mechanisms have been investigated. Monthly Be specific activ-ities in surface air are inversely correlated with solar activity [6, 9, 10]. Airmasses originating in the upper troposphere and lower stratosphere containhigher concentrations of Be than surface air masses [11]. Beryllium-7 can thusbe used as a stratospheric tracer, and has been investigated as an indicator ofexchange processes between the stratosphere and troposphere [12, 7]. Further,the Be concentration maxima have been correlated with an enhanced verticaltransport and the intrusion of the stratospheric air masses across the tropopause213, 14, 15, 16]. A positive correlation between the tropopause height and the Be specific activity in surface air has been shown [17, 18]. Longitudinal andlatitudinal distribution of Be in the air has been noted [8, 19, 20, 21], and itis in part influenced by horizontal transport within the troposphere. Wet de-position is the most significant mechanism of Be removal from the atmosphere[10, 22, 23], although different studies have shown no correlation or a negativecorrelation of the Be specific activity with precipitation [6, 10, 24, 25, 26, 27].To further explain the behavior of Be in surface air, its relation to lo-cal climate variables, including (but not limited to) temperature, atmosphericpressure, relative humidity, and sunshine hours, has been extensively studied[22, 13, 28, 29, 30, 10, 31, 32, 33, 34]. These studies, however, did not includean analysis of Be relation with large-scale atmospheric circulation.Variability in atmospheric circulation is described by teleconnection pat-terns, such as the North Atlantic Oscillation (NAO), Arctic Oscillation (AO)and Pacific/North American (PNA) [35, 36]. These patterns are a measureof pressure oscillations over different locations, and have been shown to influ-ence large-scale circulation [37, 38, 39], which further reflects on local weatherconditions [40, 41, 42, 43].An influence of NAO on Be has been implied [7, 44], but only relativelyrecent studies have focused on the Be specific activity in the air and large-scale transport. For example, the abundance of Be in Fennoscandia is notonly influenced by NAO [45, 46], but the atmospheric conditions seem to playa more important role than production [47]. Further, AO can modulate thestratosphere-troposphere exchange, and as a consequence, the AO variabilitycan explain a large part of ozone variability in the lower troposphere over NorthAmerica [48]. This finding is also relevant for Be which is, along with ozone,transported from the stratosphere into troposphere.To summarize, there have been a number of studies on the Be specific activ-ity in surface air and its relation with local meteorological conditions, sunspotnumber, and tropopause height, and somewhat fewer studies on the influenceof large-scale atmospheric transport. Most of these studies looked into linear3elationship between the Be specific activity and a set of chosen variables.However, there have been no in-depth statistical analysis encompassing me-teorological variables, tropopause height, sunspot number and teleconnectionindices (which quantify large-scale transport). The goal of our investigation isto look into common periodicities of the mentioned variables, whose existencecould help to understand a relationship between the variables, even if it may notbe linear in its nature. Two statistical analysis methods are used to investigatethe dynamics of the Be surface concentration: wavelet transform analysis andtime-dependant Hurst exponent method.
2. Data
Time series of 11 measured variables were analyzed. The Be specific activityin surface air, five meteorological variables, and the tropopause height were oflocal character – the data were recorded in Helsinki, Finland (60 . ◦ N; 25 . ◦ E;12 m a.s.l). On the other hand, three teleconnection indices and sunspot numberquantify hemispheric circulation, and sun activity, respectively. This set ofvariables was chosen in attempt to include as many as possible factors potentiallyinfluencing the Be specific activity in surface air, but this choice was limitedby the number of meteorological variables available for Helsinki, and by thetemporal resolution of the available teleconnection indices. The length of theinvestigated time series differed, and the start and end date of the analysis werechosen to coincide with the available Be specific activity data – from 1 January1987 to 31 December 2011, thus spanning 25 years.
Beryllium-7 specific activity in surface air.
The analyzed data are a subset ofthe Radioactivity Environmental Monitoring Database (REMdb) supported byREM group from the Institute of Transuranium Elements, of the DG JointResearch Centre (JRC). The Be data prior to 2007 stored in the REMdb ispublic, and an access to the data over the 2007–2011 period can be grantedonly after explicit request. More information on the REMdb can be found on itsweb page (https://rem.jrc.ec.europa.eu/) and in [21, 49, 50]. The measurements4onducted in Helsinki represent the largest set with more than 4 000 data pointsover 1987–2011. The sampling frequency of the measurements varied: prior to1999, the measurements were taken mostly once a week, while the subsequentmeasurements were performed daily or once in two days.
Meteorological variables.
The meteorological data, consisting of mean, mini-mum and maximum temperature, atmospheric pressure, and precipitation, wereobtained from the European Climate Assessment & Dataset (ECA&D) [51]. Theseries consisted of daily data.
Tropopause height.
Tropopause height was calculated following the proceduregiven in [18]. Input data for the calculations were taken form the NCEP/NCARreanalysis [52]. In the procedure, an extrapolation of isobaric heights above andbelow the tropopause to the tropopause pressure was performed using the hy-drostatic approximation. The averaged value of the two extrapolated values wasthen taken as the height of the tropopause. The calculations of the tropopauseheight were performed for each day of the investigated period.
Teleconnection indices.
Sunspot number.
3. Calculations
Two statistical methods were applied in the analysis of the Be specific activ-ity dynamics: wavelet transform analysis and time-dependant Hurst exponentmethod. 5 .1. Wavelet analysis
Wavelet transform (WT) spectral analysis of the Be time series was used tolook into existence of periodic or quasi-periodic cycles in the data [53, 54] andto assess the overall statistical behavior of the Be series [55]. The existenceof cycles was then compared across the chosen datasets to find their commonperiodicities.Wavelet transform analysis is commonly used as a tool to investigate timeseries that contain nonstationarities on a number of different frequencies [56].The WT procedure that we used is described in [55, 57]. In this paper, aset of Derivatives of Gaussian (DOG) wavelets of the tenth order was used tocalculate WT coefficients. The calculated wavelet spectra represent variationsof the analyzed signals on different time scales, and show increased values forthe events occurring at a characteristic time scale. To detect those characteristicscales, a standard peak analysis was performed by searching the maximum andsaddle (for hidden peaks) points in the WT power spectra of the investigatedvariables.
Centered detrended moving average (cDMA) technique operates through anestimate of a generalized variance of the long-range correlated series y ( i ) aroundthe moving average ˜ y n ( i ): ˜ y n ( i ) = 1 n k = n − X k = − n y ( i − k ) , (1)where n is the width of the moving average window. The time series y ( i ) isdetrended by subtracting the local trend ˜ y n ( i ), and for a given window width n ,the characteristic size of fluctuation for detrended time series is calculated by: σ cDMA ( n ) = vuuut N max − n N max − n X i = n [ y ( i ) − ˜ y n ( i )] . (2)6unction σ cDMA ( n ) is calculated for different moving window widths, n ∈ [ n , N max − n ], where N max is the length of the entire series. An increase in thewindow width n increases the function σ cDMA ( n ).When the analyzed time series follows a scaling law, the cDMA function isof a power-law type, i.e. σ cDMA ( n ) ∝ n H , where H is Hurst exponent whichis related to the correlation properties of y ( i ). When 0 . < H <
1, the series y ( i ) has a positive long-range correlation, or persistence; when 0 < H < . H = 0 .
5, the series can be described as an uncorrelated Brownian process.Local complexity in our data sets was investigated using the time-dependentDMA (tdDMA) algorithm [58] in the following manner. First, cDMA algorithmwas applied on the subset of data at the intersection of the time series signaland a sliding window with a width N s , which moved along the series with astep δ s . The scaling exponent H was then calculated for each subset, followingthe cDMA procedure described above, and a sequence of local, time-dependentHurst exponents was obtained. The minimum size of each subset N min wasdefined under a condition that the scaling law σ cDMA ( n ) ∝ n H holds in thesubset, while the accuracy of the technique was achieved with an appropriatechoice of N min and δ min [59].In our tdDMA analysis, window widths of up to N s = 3265 were chosen,with the step δ s = 1. The scaling features of the chosen variables were studiedon four characteristic periods: one month, three months, one year, and threeyears. These periods enclosed the Be specific activity spectral peaks obtainedby the WT analysis.
4. Results and Discussion
The wavelet spectra for the Be data series were calculated in the range of15–1500 points, corresponding to the time span of ten days to four years. Thisrange was chosen having in mind the length of the time series analyzed (dailyrecords in 25 years), so that we can obtain statistically relevant results [60].7ugmented Dickey-Fuller unit-root test was performed on the Be data se-ries. The test showed stationarity of the data series.
Four characteristic periods (corresponding to the time coordinates of thelocal maxima) were detected in the Be spectrum (Fig. 1): the peak around 30days indicating a monthly cycle; the peak around 90 days indicating a seasonalcycle; the peak around 360 days indicating an annual cycle; and the peak around1 000 days implying a longer cycle of around three years (triennial cycle). Aseasonal periodicity has already been observed in the behavior of Be [61, 46].A periodicity of 45–90 days in the Be wavelet spectrum has also been reportedbefore [47], as an intermittent period connected to changes in teleconnectionindices. Similarly, a periodicity of ∼ . Be surface concentrationshas already been noted [6].
100 1000 W a v e l e t po w e r Time (days) Be-728 100091 365
Figure 1: Wavelet spectrum of the Be specific activity in surface air, Helsinki.
Figure 2 shows a comparison of the Be and teleconnection indices WT spec-tra. In general, the teleconnection indices displyed a distinct annual period, andtheir visible peaks were positioned close to the seasonal and triennial Be periods8Fig. 2). The spectral changes of the NAO and PNA indices were particularlyconsistent with the changes in the Be spectrum (with correlation coefficientsof 0.7 and 0.6, respectively).
100 1000 W a v e l e t po w e r Time (days) Be-7 PNA AO NAO
Figure 2: Wavelet transform spectra of the Be specific activity and teleconnection indices: Pa-cific/North American (PNA), Arctic Oscillation (AO), and North Atlantic Oscillation (NAO).
The meteorological data also showed a distinct annual peak, with additionalpeaks not coinciding with the Be periods (Fig. 3). The WT spectra for all tem-perature records, atmospheric pressure and sunspot number correlated well andsignificantly with the Be spectrum (with correlation coefficients larger than0.9). The only time series not following the strong correlation pattern wasprecipitation. These findings could indicate that in general, the atmosphericconditions strongly influence the Be annual cycle, while temperature, atmo-spheric pressure, and sunspot number possibly have a bigger influence on theoverall Be variations. The triennial Be cycle seems to be influenced by acombination of atmospheric conditions and teleconnections, which is in partialagreement with previous studies [6, 46, 62].Finally, the data for tropopause height showed a good overall agreement9
00 1000 W a v e l e t po w e r Time (days) Be-7 TG SS RR PP
Figure 3: Wavelet transform spectra of the Be specific activity and meteorological data:mean daily temperature (TG), sunspot number (SS), precipitation (RR), and atmosphericpressure (PP). with the Be cycles (with correlation coefficient larger than 0.9). As depicted inFig. 4, the tropopause height records displayed a distinct annual peak, togetherwith less evident monthly and seasonal peaks. The tropopause height gavea multiannual peak indicating a period somewhat shorter than the triennial Be peak. This tropopause height periodicity of ∼ Be specific activity in surface air was observed by [17, 18, 50]. Be surface concentration The Be periods found in WT analysis were further used in tdDMA to in-vestigate features of long-range dependence in the datasets. Specifically, thevalues of the Hurst exponents calculated on these intervals describe autocorre-lation behavior of each investigated variable. In addition, a comparison of thelocal Hurst exponents of different variables on a given characteristic scale couldunveil similarities in their dynamics. 10
00 1000 W a v e l e t po w e r Time (days) Be-7 TH
Figure 4: Wavelet transform spectra of the Be specific activity and tropopause hight (TH).
Figure 5 shows the local Hurst exponents for the Be specific activity on itscharacteristic periods. On the shortest characteristic interval of one month, theexponents implied a strong autocorrelation, with the mean Hurst exponent of0.72. With an increase in the characteristic period to three months, the meanHurst exponent increased to 0.90, and this same pattern was repeated on theinterval of one year – the mean Hurst exponent was 0.87, with no anticorrelationbouts. A significant change in the behavior of the local Hurst exponents occurredon the interval of three years, where we found a multiyear period with theexponents close to 0.5, followed by an anticorrelated regime. The mean Hurstexponent for this three-year period decreased to 0.58 (Fig. 5).The local Hurst exponents on different characteristic intervals suggest thatthe temporal changes in the Be specific activity are most likely slow. Namely,the high values of the exponents on shorter time-scales of one and three months,and even one year, imply almost identical behavior in the Be records. Forexample, with the mean Hurst exponent of 0.90, within every trimester, thetype of changes (i.e., an increase or decrease in the measured values) were almostthe same as the type of changes within the preceding and subsequent trimester.11 .00.51.0 1990 2000 20100.51.00.51.0 1990 2000 20100.51.0
Year H u r s t e x ponen t Figure 5: Local Hurst exponents and their mean values for the Be specific activity on itscharacteristic periods.
Similarly, the differences in the type of changes from one year to another alsoseemed negligible. Only over a prolonged period of time, which was three yearsin the case of the Be specific activity, we observed a variation in the Bedynamics: the highly correlated regime apparently shifted to slightly correlated,even anticorrelated behavior. This would suggest an existence of a crossover inthe radionuclide’s behavior on large (multiyear) scales that is maybe masked bythe presence of a one-year peak in the Be wavelet spectrum.
To further analyze the observed behavior and possibly find a source ofcrossover in the Be dynamics, we compared its local Hurst exponents on theone- and three-year intervals with the exponents of the other investigated vari-ables (Figs. 6 and 7). Similarities in the temporal evolution of these Hurstexponents are described by the correlation functions also shown in Figs. 6 and7, with some characteristic values given in Table 1.12 .51.0 1990 2000 20100.51.00.51.00.51.00.51.0 1990 2000 20100.51.0 -10 -8 -6 -4 -2 0 2 4 6 8 10-0.50.00.5-0.50.00.5-0.50.00.5-0.50.00.5-10 -8 -6 -4 -2 0 2 4 6 8 10-0.50.00.5 C o rr e l a t i on c oe ff i c i en t H u r s t e x ponen t Be-7THRRPNANAO AO Year
Lag (years)
Figure 6: Left – local Hurst exponents on the one-year interval for (top to bottom): the Be specific activity, Arctic Oscillation, North Atlantic Oscillation, Pacific/North American,precipitation, and tropopause height, over 1987–2011. Right – correlation function betweenthe local Hurst exponents of the Be specific activity and the corresponding variables.
On the one-year interval, the variables were autocorrelated, apart from NAOand precipitation over short periods (Fig. 6). The minima of the correlationfunctions occurred when the Be specific activity was correlated with the corre-sponding variable’s values recorded later in time (Table 1). On the other hand,the maximum correlations showed a moderate to strong correlation (except pre-cipitation) which occurred when the Be specific activity was correlated withthe corresponding variable’s values recorded earlier in time. The strength of an-ticorrelation was less than the strength of correlation (i.e., the absolute value ofthe minimum was less than the absolute value of the maximum). These correla-13 able 1: The correlation value for time lag equal 0, maximum and minimum of the correlationfunctions given in Figs. 6 and 7. The time lags for which the minimum and maximum arereached are given in years. When time lag is positive, the Be specific activity is correlatedwith the corresponding variable’s values recorded earlier in time (” Be is in the future”), andvice versa.
Period One year Three yearscorr. coeff. maximum minimum corr. coeff. maximum minimumVariable lag=0 (lag in years) (lag in years) lag=0 (lag in years) (lag in years)0.54 -0.37 0.19 -0.72AO 0.42 (-0.9) (2.7) -0.02 (4.3) (-3.6)0.68 -0.60 0.30 -0.71NAO 0.61 (-0.7) (3.6) -0.29 (10) (9.3)0.59 -0.26 0.56 -0.51PNA -0.14 (-4.1) (1.5) 0.56 (0) (-4.8)0.27 -0.14 0.45 -0.86RR -0.04 (-10) (6.2) -0.52 (10) (3.4)0.64 -0.49 0.42 -0.65TH -0.47 (-5.1) (0.1) 0.09 (-10) (6.1) tion coefficients could imply that changes in the teleconnection indices reflectedon the changes in the Be specific activity with a varying time lag: from lessthan a year for AO and NAO, to ∼ The long-range autocorrelations (on the three-year interval) give insight intothe complexity of the variables’ behavior (Fig. 7). While on the one-year inter-val, there were no significant variations in the type of changes in the Be specificactivity from one year to the next, the temporal evolution was different on thethree-year interval. Although the radionuclide’s concentration showed strongautocorrelation prior to 1990 and after 2010, there were significant differences14uring the period in-between. The transition in the correlation mode, from cor-related to anticorrelated, occurred in all of the variables, except the tropopauseheight which was anticorrelated throughout the 1987–2011 period (Fig. 7). C o rr e l a t i on c oe ff i c i en t H u r s t e x ponen t Be-7THRRPNANAO AO Year
Lag (years)
Figure 7: Same as Fig. 6 on the three-year interval.
During 1993–2005, the local Be Hurst exponent decreased, which may sug-gest that over this period there was a weakened effect of some global parameters,which have an impact on the dynamics of the Be specific activity. Over thisperiod, AO, PNA and precipitation changed the mode, i.e. from correlated toanticorrelated, and vice versa. The transition of the AO and PNA teleconnec-tion indices into the anticorrelated regime, which happened in ∼ Be specific activity shift into an anticorrelated regime. The correla-tion in the Be series was first reduced between 1995 and 2000, and the actualtransition in the correlation mode (from correlated to anticorrelated) occurred15n 2000. Further evolution of the Hurst exponents showed that AO reversedback into the correlated regime in 2000, but the PNA reversal took another fiveyears. The transition back into the correlated mode of the Be specific activityoccurred later still, in 2008.The maximum and minimum values of the correlation functions (Fig. 7 andTable 1) show that in contrast to the one-year interval, anticorrelation betweenthe Hurst exponents of the investigated variables and the Be specific activitywas stronger than their correlation. Further, the minima for the AO and PNAcorrelation functions occurred for a time lag of 4–5 years, which agrees with theaforementioned delay with which the mode reversals of the Be Hurst exponentsfollowed the shifts in the teleconnections’ autocorrelations (Fig. 7).The slow changes in the dynamics of the Be specific activity could be in-terconnected with the changes in the teleconnections. In one scenario of theinterconnection, a direct influence of the indices on the Be specific activitycould be assumed. This scenario would then suggest a relatively long responsetime (4–5 years) in which the correlation changes in large-scale atmospheric cir-culation were mirrored by the correlation changes in the radionuclide activity.On the other hand, if the teleconnection indices and Be specific activity had acommon driving mechanism, then the changes would first occur in the behav-ior of AO, then PNA and Be specific activity (Fig. 7). The correlation modeshifts for AO and PNA were not only earlier, but also faster (note a prolongedperiod in the second half of the 1990s during which the Be Hurst exponenthovered close to 0.5). This slow reaction of the Be specific activity to a drivingmechanism would result from additional forces that dampen the influence andthus prolong the response time. Another potential interconnection between thevariables is a combination of the two scenarios, encompassing a common driv-ing mechanism and an influence that teleconnections exert on the Be specificactivity in surface air.A possible explanation for the observed change in the correlation of thevariables (Fig. 7) could lie in the solar activity during 1993–2005. This periodencompassed the end of solar cycle 22 (1986–1996) and most of solar cycle 23161996–2008). In contrast to solar cycle 22 with high solar activity, solar cycle 23was noticeably smaller [63], and the changes in correlation modes could reflectthose changes in solar activity. It is worth noting here that over 1993–2005, thedecrease in the correlation of the Be series was not associated with a decreasein the measured Be specific activity. A major influence of solar forcing on the Be surface concentration for timescales longer than one year has been noticedby [64].It is also interesting to note that the precipitation Hurst exponents on thethree-year period (Fig. 7) showed a decrease in anticorrelation from 1987 to1994, and an increase in anticorrelation from 2006 to 2011, just as the Hurstexponents of the Be specific activity exhibited the opposite behavior. Overthe period in-between, 1994–2006, precipitation was autocorrelated while the Be Hurst exponent hovered around 0.5 and then shifted into anticorrelation(Fig. 7). Further, very strong anticorrelation between the precipitation and BeHurst exponents of -0.86 was noted with a time lag of approximately three years(Table 1).Finally, some caveats in our analysis should be mentioned. The availabilityof the Be data limited the analysis to time periods from ten days to four years,not allowing investigation of periodicities on shorter time scales, such as thecycles found in a wavelet analysis of daily Be concentrations [54]. It also lim-ited our insight into longer, multiannual or interdecadal, periodicities reportedin [45]. Moreover, WT spectral analysis is a linear method which detects linearcombinations of characteristic frequencies unless their magnitude is very small[53]. Further studies should aim at improvements that look into recognitionof these linear combinations, and their separation from true characteristic fre-quencies inherent to the data. The future modelling efforts could possibly profitfrom the results of the comparison of the WT spectra of the Be specific activity,meteorological parameters, and teleconnection indices, and use our findings forre-calibration of modelling strategies.Further, in our analysis an emphasis was given to an interrelationship be-tween the Be specific activity and other parameters. A mutual linkage between17he parameters was not discussed, although our results offered some ready con-clusions. For example, on the short characteristic intervals of one and threemonths, all teleconnection indices were autocorrelated (not shown), while pe-riods of anticorrelation first occurred in NAO on the one-year interval (Fig. 6)and then in AO and PNA on the three-year interval (Fig. 7). These results im-ply a very similar behavior between the AO and PNA teleconnections and the Be specific activity, including slow changes which become evident only on thethree-year interval.
5. Conclusions
Wavelet transform spectral analysis revealed the existence of four character-istic periods in the Be specific activity: a one-month cycle, a three-month cycle,an annual cycle, and a triennial cycle. Our results implied that the tropopauseheight, atmospheric conditions (especially temperature), atmospheric pressure,and the sunspot number, significantly influence the overall Be spectral behav-ior. The seasonal period also seems to be influenced by large-scale atmosphericcirculation, particularly by the NAO and PNA indices, and by the tropopauseheight, which seems to also influence the monthly Be period. The triennial Becycle is likely to be influenced by a combination of atmospheric conditions andteleconnections. In our data, the characteristic time periods of the NAO andPNA patterns seemed to match the periods of the radionuclide’s activity betterthan AO.Local Hurst exponent analysis offered further insight into the complex dy-namic of the Be specific activity in surface air and its relationship to dynamicsof meteorological parameters and teleconnection indices. Comparisons weremade on the Be specific activity characteristic periods of one year and threeyears. On the time period of one year and shorter, the Be specific activity wasstrongly autocorrelated. The longest, three-year interval, showed some periodsof anticorrelation implying that changes in the dynamics of this radionuclideare slow and evident only on the scale of three years. Similarities in the overall18attern of the Hurst exponents on the four characteristic intervals suggest agood agreement in the AO, PNA and Be specific activity behavior.
Acknowledgements
This paper was realized within the following projects: ”Advanced analyti-cal, numerical and methods of analysis of fluid mechanics and complex systems”(No. OI174014), ”Phase transitions and characterization of inorganic and or-ganic systems” (No. OI171015), and ”Climate changes and their influence onthe environment: impacts, adaptation and mitigation” (No. III43007), financedby the Ministry of Education, Science and Technological Development of theRepublic of Serbia (2011-2016). Suzana Blesi´c has received funding from theEuropean Unions Horizon 2020 research and innovation programme under theMarie Sklodowska-Curie grant agreement No. 701785. The authors would liketo thank the REM group for provision of the beryllium-7 specific activity mea-surements from the REM data base (REMdb at the Institute of TransuraniumElements, REM group, DJ JRC Ispra site, European Commission).
ReferencesReferences [1] D. Lal, B. Peters, Cosmic ray produced radioactivity on the Earth, in:K. Sitte (Ed.), Kosmische Strahlung II / Cosmic Rays II, Vol. 9 / 46 / 2 ofHandbuch der Physik / Encyclopedia of Physics, Springer Berlin Heidel-berg, 1967, pp. 551–612. doi:10.1007/978-3-642-46079-1_7 .[2] D. M. Koch, D. J. Jacob, W. C. Graustein, Vertical transport of tropo-spheric aerosols as indicated by Be and
Pb in a chemical tracer model,J. Geophys. Res. 101 (D13) (1996) 18651–18666. doi:10.1029/96JD01176 .[3] T. Tokieda, K. Yamanaka, K. Harada, S. Tsunogai, Seasonal varia-tions of residence time and upper atmospheric contribution of aerosols19tudied with Pb-210, Bi-210, Po-210 and Be-7, Tellus B 48 (5). doi:10.1034/j.1600-0889.1996.t01-4-00006.x .[4] C. Due˜nas, M. Fern´andez, J. Carretero, E. Liger, S. Ca˜nete, Long-termvariation of the concentrations of long-lived Rn descendants and cosmogenic Be and determination of the MRT of aerosols, Atmos. Environ. 38 (9)(2004) 1291–1301.[5] U. Heikkil¨a, J. Beer, V. Alfimov, Beryllium-10 and beryllium-7 in precip-itation in D¨ubendorf (440 m) and at Jungfraujoch (3580 m), Switzerland(1998-2005), J. Geophys. Res. 113 (D11). doi:10.1029/2007JD009160 .[6] E. Gerasopoulos, C. Zerefos, C. Papastefanou, P. Zanis, K. O’Brien, Low-frequency variability of beryllium-7 surface concentrations over the EasternMediterranean, Atmos. Environ. 37 (13) (2003) 1745–1756.[7] P. Cristofanelli, P. Bonasoni, L. Tositti, U. Bonaf`e, F. Calzolari, F. Evan-gelisti, S. Sandrini, A. Stohl, A 6-year analysis of stratospheric intrusionsand their influence on ozone at Mt. Cimone (2165 m above sea level), J.Geophys. Res. 111 (D3) (2006), d03306. doi:10.1029/2005JD006553 .[8] H. W. Feely, R. J. Larsen, C. G. Sanderson, Factors that cause seasonal vari-ations in Beryllium-7 concentrations in surface air, J. Environ. Radioact.9 (3) (1989) 223–249.[9] F. Cannizzaro, G. Greco, M. Raneli, M. Spitale, E. Tomarchio, Concentra-tion measurements of Be at ground level air at Palermo, Italy–comparisonwith solar activity over a period of 21 years, J. Environ. Radioact. 72 (3)(2004) 259–271.[10] M. K. Pham, M. Betti, H. Nies, P. P. Povinec, Temporal changes of Be,
Cs and
Pb activity concentrations in surface air at Monaco and theircorrelation with meteorological parameters, J. Environ. Radioact. 102 (11)(2011) 1045–1054. 2011] L. Bourcier, O. Masson, P. Laj, J. Pichon, P. Paulat, E. Freney, K. Sellegri,Comparative trends and seasonal variation of Be,
Pb and
Cs at twoaltitude sites in the central part of France, J. Environ. Radioact. 102 (3)(2011) 294–301.[12] P. Zanis, E. Gerasopoulos, A. Priller, C. Schnabel, A. Stohl, C. Zerefos,H. G¨aggeler, L. Tobler, P. Kubik, H. Kanter, H. Scheel, J. Luterbacher,M. Berger, An estimate of the impact of stratosphere-to-troposphere trans-port (STT) on the lower free tropospheric ozone over the Alps using Be and Be measurements, J. Geophys. Res. 108 (D12) (2003), 8520. doi:10.1029/2002JD002604 .[13] D. Todorovic, D. Popovic, G. Djuric, Concentration measurements of Beand
Cs in ground level air in the Belgrade City area, Environ. Internat.25 (1) (1999) 59–66.[14] S. Daish, A. Dale, C. Dale, R. May, J. Rowe, The temporal variations of Be,
Pb and
Po in air in England, J. Environ. Radioact. 84 (3) (2005)457–467.[15] M. Yoshimori, Production and behavior of beryllium 7 radionuclide in theupper atmosphere, Adv. Space Res. 36 (5) (2005) 922–926.[16] C. Papastefanou, Beryllium-7 aerosols in ambient air, Aerosol Air Qual.Res. 9 (2) (2009) 187–197.[17] E. Gerasopoulos, P. Zanis, A. Stohl, C. Zerefos, C. Papastefanou,W. Ringer, L. Tobler, S. H¨ubener, H. G¨aggeler, H. Kanter, L. Tositti,S. Sandrini, A climatology of Be at four high-altitude stations at the Alpsand the Northern Apennines, Atmos. Environ. 35 (36) (2001) 6347–6360.[18] A. Ioannidou, A. Vasileiadis, D. Melas, Time lag between the tropopauseheight and Be activity concentrations on surface air, J. Environ. Radioact.129 (2014) 80–85. 2119] A. Kulan, A. Aldahan, G. Possnert, I. Vintersved, Distribution of Be insurface air of Europe, Atmos. Environ. 40 (21) (2006) 3855–3868.[20] B. R. Persson, E. Holm, Be,
Pb, and
Po in the surface air from theArctic to Antarctica, J. Environ. Radioact. 138 (2014) 364–374.[21] M. Hern´andez-Ceballos, G. Cinelli, M. M. Ferrer, T. Tollefsen, L. D. Felice,E. Nweke, P. Tognoli, S. Vanzo, M. D. Cort, A climatology of Be in surfaceair in European Union, J. Environ. Radioact. 141 (2015) 62–70.[22] C. Papastefanou, A. Ioannidou, Depositional fluxes and other physical char-acteristics of atmospheric beryllium-7 in the temperate zones (40 ◦ N) with adry (precipitation-free) climate, Atmos. Environ. 25 (10) (1991) 2335–2343.[23] A. Ioannidou, C. Papastefanou, Precipitation scavenging of 7be and 137csradionuclides in air, J. Environ. Radioact. 85 (1) (2006) 121–136.[24] F. Cannizzaro, G. Greco, M. Raneli, M. C. Spitale, E. Tomarchio, Be-haviour of Be air concentration observed during a period of 13 yearsand comparison with sun activity, Nucl. Geophys. 9 (1995) 597–607. doi:10.1016/0969-8086(95)00043-7 .[25] N. Ali, E. Khan, P. Akhter, N. Khattak, F. Khan, M. Rana, The effect of airmass origin on the ambient concentrations of Be and
Pb in Islamabad,Pakistan, J. Environ. Radioact. 102 (1) (2011) 35–42.[26] J. Chao, Y. Chiu, H. Lee, M. Lee, Deposition of beryllium-7 in Hsinchu,Taiwan, Appl. Radiat. Isot. 70 (2) (2012) 415–422.[27] F. Pi˜nero Garc´ıa, M. Ferro Garc´ıa, M. Azahra, Be behaviour in the at-mosphere of the city of Granada January 2005 to December 2009, Atmos.Environ. 47 (2012) 84–91.[28] D. Todorovic, D. Popovic, J. Nikolic, J. Ajtic, Radioactivity monitoringin ground level air in Belgrade urban area, Radiat. Prot. Dosim. 142 (2-4)(2010) 308–313. doi:10.1093/rpd/ncq211 .2229] J. Ajti´c, D. Todorovi´c, A. Filipovi´c, J. Nikoli´c, Ground level air beryllium-7 and ozone in Belgrade, Nucl. Technol. Radiat. 23 (2) (2008) 65–71. doi:10.2298/NTRP0802065A .[30] J. V. Ajti´c, D. J. Todorovi´c, J. D. Nikoli´c, V. S. Durd¯evi´c, Ground level airberyllium-7 and ozone in Belgrade, Nucl. Technol. Radiat. 28 (4) (2013)381–388. doi:10.2298/NTRP1304381A .[31] S. M. Papandreou, M. I. Savva, K. L. Karfopoulos, D. J. Karangelos, M. J.Anagnostakis, S. E. Simopoulos, Monitoring of Be atmospheric activityconcentration using short term measurements, Nucl. Technol. Radiat. 26 (2)(2011) 101–109. doi:10.2298/NTRP1102101P .[32] A. C. Carvalho, M. Reis, L. Silva, M. J. Madruga, A decade of Be and
Pb activity in surface aerosols measured over the Western Iberian Penin-sula, Atmos. Environ. 67 (0) (2013) 193–202.[33] R. Lozano, M. Hern´andez-Ceballos, J. Rodrigo, E. S. Miguel, M. Casas-Ruiz, R. Garc´ıa-Tenorio, J. Bol´ıvar, Mesoscale behavior of Be and
Pbin superficial air along the Gulf of Cadiz (south of Iberian Peninsula),Atmos. Environ. 80 (2013) 75–84.[34] L. Tositti, E. Brattich, G. Cinelli, D. Baldacci, 12 years of Be and
Pb inMt. Cimone, and their correlation with meteorological parameters, Atmos.Environ. 87 (2014) 108–122.[35] J. M. Wallace, D. S. Gutzler, Teleconnections in the Geopotential HeightField during the Northern Hemisphere Winter, Mon. Wea. Rev. 109 (4)(1981) 784–812.[36] A. G. Barnston, R. E. Livezey, Classification, seasonality and persistenceof low-frequency atmospheric circulation patterns, Mon. Wea. Rev. 115 (6)(1987) 1083–1126. 2337] J. W. Hurrell, Decadal trends in the north atlantic oscillation: Re-gional temperatures and precipitation, Science 269 (5224) (1995) 676–679. doi:10.1126/science.269.5224.676 .[38] M. H. P. Ambaum, B. J. Hoskins, D. B. Stephenson, Arctic Oscillation orNorth Atlantic Oscillation?, J. Clim. 14 (16) (2001) 3495–3507.[39] J. M. Wallace, North atlantic oscillatiodannular mode: Two paradigms–one phenomenon , Q. J. R. Meteorol. Soc. 126 (564) (2000) 791–805. doi:10.1002/qj.49712656402 .[40] D. J. Leathers, B. Yarnal, M. A. Palecki, The Pacific/North American tele-connection pattern and United States climate. Part I: Regional temperatureand precipitation associations, J. Clim. 4 (5) (1991) 517–528.[41] D. J. Leathers, M. A. Palecki, The Pacific/North American teleconnectionpattern and United States climate. Part II: Temporal characteristics andindex specification, J. Clim. 5 (7) (1992) 707–716.[42] D. W. J. Thompson, J. M. Wallace, The Arctic Oscillation signature in thewintertime geopotential height and temperature fields, Geophys. Res. Lett.25 (9) (1998) 1297–1300. doi:10.1029/98GL00950 .[43] R. W. Higgins, A. Leetmaa, V. E. Kousky, Relationships between climatevariability and winter temperature extremes in the United States, J. Clim.15 (13) (2002) 1555–1572.[44] J. Hedfors, A. Aldahan, A. Kulan, G. Possnert, K.-G. Karlsson, I. Vin-tersved, Clouds and Be: Perusing connections between cosmic rays andclimate, J. Geophys. Res. 111 (D2), d02208. doi:10.1029/2005JD005903 .[45] A.-P. Lepp¨anen, A. Pacini, I. Usoskin, A. Aldahan, E. Echer, H. Evange-lista, S. Klemola, G. Kovaltsov, K. Mursula, G. Possnert, Cosmogenic Bein air: A complex mixture of production and transport, J. Atmos. Sol-Terr.Phy. 72 (13) (2010) 1036–1043. 2446] A.-P. Lepp¨anen, I. Usoskin, G. Kovaltsov, J. Paatero, Cosmogenic Be and Na in Finland: Production, observed periodicities and the connection toclimatic phenomena, J. Atmos. Sol-Terr. Phy. 74 (2012) 164–180.[47] A.-P. Lepp¨anen, J. Paatero, Be in Finland during the 1999-2001 Solarmaximum and 2007-2009 Solar minimum, J. Atmos. Sol-Terr. Phy. 97(2013) 1–10.[48] J.-F. Lamarque, P. G. Hess, Arctic oscillation modulation of the northernhemisphere spring tropospheric ozone, Geophys. Res. Lett. 31 (6) (2004),l06127. doi:10.1029/2003GL019116 .[49] M. Hern´andez-Ceballos, G. Cinelli, T. Tollefsen, M. Mar´ın-Ferrer, Identifi-cation of airborne radioactive spatial patterns in Europe – Feasibility studyusing Beryllium-7, J. Environ. Radioact. 155–156 (2016) 55–62.[50] M. Hern´andez-Ceballos, E. Brattich, G. Cinelli, J. Ajti´c, V. Djurdjevi´c,Seasonality of Be concentrations in europe and influence of tropopauseheight, Tellus B 2016, 68, 29534. doi:10.3402/tellusb.v68.29534 .[51] A. K. Tank, J. Wijngaard, G. K¨onnen, R. B¨ohm, G. Demar´ee, A. Gocheva,M. Mileta, S. Pashiardis, L. Hejkrlik, C. Kern-Hansen, R. Heino, P. Besse-moulin, G. M¨uller-Westermeier, M. Tzanakou, S. Szalai, T. P´alsd´ottir,D. Fitzgerald, S. Rubin, M. Capaldo, M. Maugeri, A. Leitass, A. Bukantis,R. Aberfeld, A. van Engelen, E. Forland, M. Mietus, F. Coelho, C. Mares,V. Razuvaev, E. Nieplova, T. Cegnar, J. Antonio L´opez, B. Dahlstr¨om,A. Moberg, W. Kirchhofer, A. Ceylan, O. Pachaliuk, L. Alexander,P. Petrovic, Daily dataset of 20th-century surface air temperature and pre-cipitation series for the European Climate Assessment, Int. J. Climatol.22 (12) (2002) 1441–1453. doi:10.1002/joc.773 .[52] E. Kalnay, M. Kanamitsu, R. Kistler, W. Collins, D. Deaven, L. Gandin,M. Iredell, S. Saha, G. White, J. Woollen, Y. Zhu, M. Chelliah,W. Ebisuzaki, W. Higgins, J. Janowiak, K. C. Mo, C. Ropelewski, J. Wang,25. Leetmaa, R. Reynolds, roy Jenne, D. Joseph, The NCEP/NCAR 40-yearreanalysis project, Bull. Am. Meteorol. Soc. 77 (3) (1996) 437–471.[53] M. Braˇciˇc, A. Stefanovska, Wavelet-based analysis of humanblood-flow dynamics, Bull. Math. Biol. 60 (5) (1998) 919–935. doi:10.1006/bulm.1998.0047 .[54] S. Kikuchi, H. Sakurai, S. Gunji, F. Tokanai, Temporal variation of Beconcentrations in atmosphere for 8 y from 2000 at Yamagata, Japan: solarinfluence on the Be time series, J. Environ. Radioact. 100 (2009) 515–521. doi:10.1016/j.jenvrad.2009.03.017 .[55] C. Torrence, G. P. Compo, A practical guide to wavelet analysis, Bull. Am.Meteorol. Soc. 79 (1) (1998) 61–78.[56] J. Lewalle, M. Farge, K. Schneider, Wavelet transforms, in: C. Tropea,A. Yarin, J. Foss (Eds.), Handbook of Experimental Fluid Mechanics,Springer-Verlag, Berlin Heidelberg, 2007, pp. 1378–1398.[57] D. Stratimirovi´c, S. Miloˇsevi´c, S. Blesi´c, M. Ljubisavljevi´c, Wavelet analysisof discharge dynamics of fusimotor neurons, Phys. A 291 (1-4) (2001) 13–23.[58] A. Carbone, G. Castelli, H. Stanley, Time-dependent Hurst exponent infinancial time series, Phys. A 344 (1-2) (2004) 267–271.[59] G. Consolini, R. De Marco, P. De Michelis, Intermittency and multifrac-tional Brownian character of geomagnetic time series, Nonlinear Proc.Geoph. 20 (4) (2013) 455–466. doi:10.5194/npg-20-455-2013 .[60] C.-K. Peng, J. Mietus, J. Hausdorff, S. Havlin, H. Stanley,A. Goldberger, Long-range anticorrelations and non-gaussian behav-ior of the heartbeat, Phys. Rev. Lett. 70 (9) (1993) 1343–1346. doi:10.1103/PhysRevLett.70.1343 .2661] M. Yamamoto, A. Sakaguchi, K. Sasaki, K. Hirose, Y. Igarashi, C. K. Kim,Seasonal and spatial variation of atmospheric
Pb and Be deposition:features of the Japan Sea side of Japan, J. Environ. Radioact. 86 (1) (2006)110–131.[62] J. Angell, J. Korshover, Quasi-biennial variations in temperature, totalozone, and tropopause height, J. Atmos. Sci. 21 (5) (1964) 479–492.[63] NASA (National Aeronautics and Space Administration), Marshall SpaceFlight Center, http://solarscience.msfc.nasa.gov/predict.shtml visited on28 June 2015.[64] S. Talpos, N. Rimbu, D. Borsan, Solar forcing on the7