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Evaluation of Monte Carlo-based calibrations of HPGe detectors for in situ gamma-ray spectrometry
Journal of Environmental Radioactivity 100 (2009) 935–940
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Journal of Environmental Radioactivity journal homepage: www.elsevier.com/locate/jenvrad
Evaluation of Monte Carlo-based calibrations of HPGe detectors for in situ gamma-ray spectrometry Jonas Boson a, b, *, Agneta H. Plamboeck a, Henrik Rameba¨ck a, Go¨ran Ågren a, Lennart Johansson b a b
Swedish Defence Research Agency, FOI CBRN Defence and Security, SE-901 82 Umeå, Sweden Department of Radiation Sciences, Umeå University, SE-901 87 Umeå, Sweden
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 August 2008 Received in revised form 25 May 2009 Accepted 4 June 2009 Available online 14 July 2009
The aim of this work was to evaluate the use of Monte Carlo-based calibrations for in situ gamma-ray spectrometry. We have performed in situ measurements at five different sites in Sweden using HPGe detectors to determine ground deposition activity levels of 137Cs from the 1986 Chernobyl accident. Monte Carlo-calculated efficiency calibration factors were compared with corresponding values calculated using a more traditional semi-empirical method. In addition, results for the activity ground deposition were also compared with activity densities found in soil samples. In order to facilitate meaningful comparisons between the different types of results, the combined standard uncertainty of in situ measurements was assessed for both calibration methods. Good agreement, both between the two calibration methods, and between in situ measurements and soil samples, was found at all five sites. Uncertainties in in situ measurements for the given measurement conditions, about 20 years after the fallout occurred, were found to be in the range 15–20% (with a coverage factor k ¼ 1, i.e. with a confidence interval of about 68%). Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Germanium detector HPGe Uncertainty Gamma spectrometry In situ measurements Monte Carlo GUM
1. Introduction High resolution gamma spectrometry is a powerful tool for the identification and quantification of gamma emitting radionuclides, both in the laboratory and in the field. Field measurements using high purity germanium (HPGe) detectors, often referred to as in situ gamma-ray spectrometry, are described in detail by, for example, the ICRU (ICRU, 1994). As suggested by the ICRU, semi-empirical methods are most often used for the necessary efficiency calibrations. More recently, Monte Carlo methods have begun to be employed for calculating in situ measurement calibration factors (e.g. Allyson and Sanderson, 1998; Gering et al., 1998; Likar et al., 2004). Calibration methods based on Monte Carlo calculations facilitate the assessment of calibration factors for a much wider variety of source distributions and measurement conditions, including non-symmetrical geometries, which are difficult to handle analytically. However, before proceeding to use Monte Carlo-based calibrations for more complex measurement geometries one should first confirm that the Monte Carlo model gives
correct results for simpler geometries that are possible to handle experimentally or analytically. As clearly stated by the ISO ‘‘Guide to the Expression of Uncertainty in Measurement’’ (GUM) (ISO, 1995), in order for any comparison between measurement results to be relevant, appropriate estimates of the combined uncertainties of the measurements are essential. The combined standard uncertainty of in situ measurement results will therefore have to be assessed for both the semi-empirical and the Monte Carlo-based calibration methods. As for the semi-empirical calibration method, we previously determined the uncertainty in intrinsic detector efficiency (Boson et al., 2009). However, the uncertainties relating to source matrix parameters such as activity and density depth distributions have yet to be considered. The aim of this work was to evaluate the use of Monte Carlobased calibrations for in situ measurements performed at five different sites. Results were compared both with results from a semi-empirical calibration method and with ground deposition activity densities assessed by soil sample measurements. 2. Materials and methods 2.1. Site descriptions
* Corresponding author. Swedish Defence Research Agency FOI, CBRN Defence and Security, SE-901 82 Umeå, Sweden. Tel.: þ46 90 10 66 95; fax: þ46 90 10 68 00. E-mail address: [email protected] (J. Boson). 0265-931X/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jenvrad.2009.06.006
In situ measurements and soil sampling to determine 137Cs ground deposition levels were performed at five sites in Sweden. Results from site 1 have been
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previously reported by Boson et al. (2006). The sites chosen display a fairly wide range of activity levels and also represent a variety of different soil and vegetation types. Most of the radiocaesium deposition in Sweden derives from the Chernobyl accident in 1986. There is also a minor contribution from atmospheric nuclear weapons tests performed mainly between 1945 and 1963, which resulted in an accumulated activity deposition of about 3 kBq m2 in 1966 (De Geer et al., 1978). Site 1. Ersboda, Umeå, lawn: The Ersboda site is situated within the Umeå city area in northern Sweden (63 510 2300 N, 20 190 1100 E). The measurement point is located in the middle of a large open field or lawn, with at least 20 m to any potentially interfering structure such as trees. Measurement date: 25th October 2004. Site 2. FOI, Umeå, lawn. Site 2 is positioned within the area of the FOI research facility in the city of Umeå in northern Sweden (63 510 100 N, 20 190 5600 E). The site is an open lawn, with at least 8 m to any potentially interfering structure such as trees. Measurement date: 19th September 2006. Site 3. Åheden, Vindeln, Pine forest. The Åheden site is located about 60 km northwest of Umeå in northern Sweden (64 130 5400 N, 19 460 5700 E). The site is a Scots pine forest with an average stand density of 1250 trees ha1 (Plamboeck et al., 2000). Measurement date: 4th August 2006. ¨vle, Spruce forest. Hille is located about 20 km north of the city of Site 4. Hille, Ga Ga¨vle in the central-eastern part of Sweden (60 460 200 N, 17 160 1400 E). The site is a spruce plantation with an average stand density of 3800 trees ha1 and relatively scarce ground vegetation. The diameter of trees at 1.3 m above the ground is 21 cm and the average tree height is approximately 22 m. Measurement date: 16th June 2004. ¨vle, Alder forest. Site 5 is an alder forest wetland close to the Site 5. Hille, Ga Verkmyra stream about 20 km north of the city of Ga¨vle in the centraleastern part of Sweden (60 460 1900 N, 17 160 2800 E). The average stand density of the alder forest is 1650 trees ha1 with a tree height of 26 m and an average diameter at 1.3 m above the ground of 27 cm. Measurement date: 16th June 2004. According to aerial measurements of the fallout after the Chernobyl accident, performed by the Swedish Geological Company SGAB (SGAB, 1986), the region around Umeå (sites 1, 2 and 3) generally received about 10–20 kBq m2 137Cs expressed as a surface equivalent deposition density (i.e. a calibration factor derived for a surface source was used). In order to estimate true ground deposition densities these values should be multiplied by a factor 1.6 (Edvarson, 1991). Sites 4 and 5 are both located in the Ga¨vle region, which received some of the highest levels of Chernobyl fallout in Western Europe, with maximum deposition densities of about 200 kBq m2 (Edvarson, 1991). 2.2. Soil sampling At each of the five sites, 17 soil samples were collected in a cross pattern using soil corers and each core was divided on site into 3 sections with respect to depth. Divisions were made, where possible, according to natural variations in soil density and composition, based on visual inspection (see Table 3). Two different soil corers were used, with radii 2.4 and 2.15 cm, respectively. The sampling and sample preparation procedures were previously described in detail (Boson et al., 2006). At site 4, one of the samples was excluded, as the second and third layers were mistakenly put into the same plastic bag. At sites 2 and 4, where sampling down to about 20 cm depth was difficult due to the frequent occurrence of stones, some of the collected soil cores were significantly shorter than the others. These samples were therefore only divided into two sections. 2.3. Measurements 2.3.1. Laboratory measurements Aliquots of soil samples were analysed for 137Cs content in suitable, pre-calibrated measurement geometries using two lead-shielded HPGe detectors (Ortec Inc., USA, relative efficiencies 50 and 80% at 1333 keV). Depending on sample size, different beakers were used, ranging from 5 to 250 ml. Measurement times were long enough to ensure at least 1000 full-energy peak net counts for most samples. However, no sample was analysed longer than 64 h, in order to reduce total measurement time. As this only concerned samples with low 137Cs content, the effect on overall measurement uncertainty should be marginal. All spectra were evaluated using GammaVision 6.01 (Ortec Inc., USA). All calibrations were done with measurement standards traceable to NIST. Internal laboratory quality assurance includes monitoring of detector response, peak resolution, energy calibration and detector background. 2.3.2. In situ measurements Two different p-type HPGe detectors were used for the in situ measurements (Ortec Inc., USA). Relevant detector specifications are listed in Table 1. Detector 1 was used at sites 1, 2, 4 and 5, and Detector 2 at site 3. The detectors were placed on tripods so that the geometric centre of the germanium crystal was positioned 1.0 m
Table 1 Detector specifications for detectors used for in situ measurements. Characteristic
Detector 1
Detector 2
Efficiencya Crystal length Crystal diameter
36% 65.4 mm 58.3 mm
57% 58.6 mm 69.9 mm
a
Relative a 300 300 NaI(Tl) crystal at 1.33 MeV (60Co).
above ground, and a portable multi-channel analyzer (Digidart, Ortec Inc., USA) was used for data acquisition. Spectra were recorded for 1000 or 1800 s, resulting in uncertainties in the 137Cs full-energy peak area due to counting statistics of less than 2% for all sites. All spectra were analysed using GammaVision 6.01 (Ortec inc., USA). 2.4. In situ measurement calibrations Calibration factors for the in situ measurements were calculated using both a previously described semi-empirical method (Boson et al., 2006) and Monte Carlo simulations. For both methods, a three-layer model previously described by Boson et al. (2006), was used for the description of soil density and activity depth distributions. Source matrix data (i.e. thickness, density and fraction of the total 137Cs inventory for each of the three layers) were obtained from soil samples. The Monte Carlo simulations were made using the MCNP5 code, v. 1.40 (Los Alamos National Laboratory, USA). It was previously shown that a Monte Carlo model of Detector 1, based entirely on manufacturer supplied data, overestimates the intrinsic detector efficiency, and suitable efficiency correction factors to compensate for this overestimation have been derived (Boson et al., 2008). Such corrections factors were also calculated for Detector 2, in the same manner as previously described by Boson et al. (2008). For each position (i.e. angle of incidence) and energy, 5 107 particles were simulated. This gave an uncertainty in the fullenergy peak area of the simulated spectrum below 2% in all cases. In this case, since we only intend to measure fallout radiocaesium, the correction factor used was based on an average over all angles for 661.7 keV. Monte Carlo simulations of the entire measurement setup were performed in order to obtain calibration factors for the in situ measurements. A 30 m cut-off radius of the source was used in all in situ simulations, which corresponds to a simulated source area of about 2800 m2. The number of particles in the simulations (2.1–3 109) was large enough to ensure statistical uncertainties below 5% in the full-energy peak count rate. The elemental composition of mineral soil (Table 2) was based on data presented by Finck (1992). The elemental composition of humus was calculated based on data from Site 3 presented by Albrektson and Lundmark (1991). No alterations of the elemental compositions to account for varying water content in soil were made, as the elemental composition of soil is not expected to significantly influence the attenuation of photons with energies exceeding 100 keV (Finck, 1992; D’Alberti and Forte, 2005). The water content does, however, influence photon attenuation in the sense that it affects soil density. This is taken into account as fresh weights are used when calculating soil densities. 2.5. Uncertainty estimations All uncertainty estimations were made in accordance with GUM (ISO, 1995). The temporal variability was ignored in all calculations regarding measurement uncertainties. The main contribution to uncertainty in live time value originates from dead time estimation, but as long as dead time can be kept small it will only have a minor effect on the live time estimate (Gedcke, 2007). As dead times in all measurements were below 10%, neglecting the live time uncertainty was considered to be a valid approximation. 2.5.1. Soil samples Uncertainties in mean values for soil density, soil layer thickness and 137Cs activity were approximated by the standard deviation of the mean. This measure includes uncertainties from the natural variability and random uncertainties from laboratory measurements. It does not, however, include any contribution from Type Table 2 Soil composition used in Monte Carlo simulations (fractions by weight). Element
Humus
Mineral soil
H C O N Al Si Fe
10% 69% 20% 1% – – –
1.1% 1.3% 55.8% – 7.1% 31.5% 3.2%
J. Boson et al. / Journal of Environmental Radioactivity 100 (2009) 935–940 B uncertainties (ISO, 1995), e.g. from calibration standards used in the efficiency calibration. Compared to the natural variability, which is of the order of 10% or more, the addition of a small contribution from uncertainty in the calibration, typically a few percent, will not contribute significantly to the combined uncertainty according to the law of propagation of uncertainties. 2.5.2. In situ measurements The calculation of ground deposition densities according to the semi-empirical calibration method (Boson et al., 2006) is based on the following expression for total in situ measurement efficiency, i.e. full-energy peak count rate, N_ [s1], per activity per unit area, AS [Bq m2]: ZZ n X N_ Ig ai 3ðE; qÞtanðqÞcitot dui dq ¼ As 2d i i
(1)
The expression is a sum over n layers, each having a fraction ai of the total 137Cs inventory and thickness di [m]. Ig is the photon emission probability for a particular energy; 3(E,q) [m2] is the intrinsic detector efficiency as a function of photon energy, i is the total attenuation in air and soil (from all E, and angle of incidence, q; Ctot layers); and ui [m] is depth in layer i. In this work, three layers (n ¼ 3) were used for all sites. Most of the parameters having an impact on total measurement uncertainty lie within the integral, which makes a calculation of combined standard uncertainty according to the law of propagation of uncertainties (ISO, 1995) cumbersome. Instead, we consider the uncertainty in measurement efficiency from a set of 10 discrete angles of incidence and an average depth in each soil layer. The angles chosen correspond to areas contributing to between 5 and 95%, with 10% increments, of the total detector response, which eliminates the need for weighting factors when calculating average uncertainty. The combined standard uncertainties for each site and angle of incidence were calculated using GUM Workbench (Metrodata GmbH, Weil-am-Rhein, Germany). The standard uncertainty of values predicted by the detector efficiency function 3(E,q) is 8.2% for Detector 1 and 5.1% for Detector 2 (Boson et al., 2009). The mass attenuation coefficient for soil, (m/r)soil, is calculated using the empirical formula proposed by Sowa et al. (1989). According to Sowa et al. (1989), the difference between the fitted curve and calculated values is within a 4% range. For 137Cs, the relative uncertainty in the intensity of the 661.7 keV gamma energy is 0.24% (Chu et al., 1999). The standard uncertainty in the linear attenuation coefficient for air is estimated to be about 2% (Boson et al., 2009) and air density is assumed to follow a rectangular distribution between 1.07 and 1.29 kg m3 (corresponding to temperatures and pressures from 15 to 30 C and from 95 to 105 kPa, respectively). Clearly, the description of the source matrix as three discrete homogeneous layers is an approximation that might cause a bias in the final results. In accordance with GUM (ISO, 1995), we therefore introduce a correction factor, k3-layer, to account for this. As the true activity depth distributions are not known, we cannot estimate the value of the correction factor, but we will have to assume that k3-layer ¼ 1. However, by investigating the sensitivity of the final result with respect to changes in activity depth distribution, one can estimate the uncertainty of the correction factor. Hence, two alternative distribution models were tested: one exponential distribution, as suggested by ICRU (1994), and one with the activity concentration linearly decreasing in each layer with the boundary conditions that the activity concentration is continuous at intersections between layers and zero below the third layer. The alternative activity distributions were modelled in MCNP5 and results were compared with a simulation using the three-layer model. Densities were assumed to be the same as in the three-layer model. The tests were based on
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activity distribution data from site 1, because this site displayed the most variable activity depth distribution. With a few exceptions, the uncertainty calculations for the Monte Carlo-based calibrations are, in principle, the same as for the semi-empirical method. The uncertainty in the intrinsic detector efficiency is replaced by the uncertainty in the efficiency correction factor used for the Monte Carlo simulations and the statistical uncertainty in the simulation of the in situ measurement will have to be added. The uncertainty in the attenuation coefficient of air can be assumed to be zero, since the attenuation is calculated by the Monte Carlo code and no interpolations are needed. The uncertainty of the attenuation coefficient in soil, however, is primarily a result of variations in soil composition and can therefore be assumed to be the same for the Monte Carlo simulations as for the semi-empirical method. Uncertainties in Monte Carlo-based calibrations were calculated using GUM Workbench (Metrodata GmbH, Weil-am-Rhein, Germany).
3. Results and discussion 3.1. Soil samples All measurement results of 137Cs activity concentrations in soil samples were corrected for decay according to the in situ measurement date. Correcting for decay to a common reference date, such as the date for the Chernobyl accident, would be misleading since site 5, because of a substantial redistribution of activity in the area, has accumulated more 137Cs activity since then (Stark et al., 2006). Results for soil sample parameters are shown in Table 3. Note that bulk densities are calculated from fresh weights, i.e. including water content, as these values were used in calculations of the in situ measurement efficiencies. Standard deviations only relate to variability of measured values. Since other contributions, i.e. from calibration standards, are negligible at this level of variability, the standard deviation of the mean is an appropriate estimate of the combined uncertainty. The results in general show a very high inter-sample variation. In particular, the total 137Cs inventories in soil samples from sites 1, 3 and 5 display standard deviations of 50–60%. For site 3, much of this variability stems from one individual soil core containing the equivalent of 47 kBq m2, compared to an average of 19 kBq m2 (standard deviation 9.4 kBq m2) of all 17 samples. In particular, the third layer of this sample has a 137Cs inventory of about 23 kBq m2, whereas the average inventory in the third layer for all 17 samples is 3.7 kBq m2 with a standard deviation of 5.6 kBq m2 (excluding this potential outlier the corresponding values are 2.5 2.7 kBq m2). The high 137Cs inventory in this particular sample is by no means improbable. It could be the effect of water from rain or melting snow containing activity from the initial deposition pouring down a root channel or some other preferential
Table 3 Soil sample results. Uncertainties are presented as one standard deviation. Site 1a
Site 2
Site 3
Site 4
Site 5
Measurement date
25th Oct. 2004
19th Sept. 2006
4th Aug. 2006
16th June 2004
16th June 2004
Vegetation
Lawn
Lawn
Pine heath
Spruce forest
Alder forest
17 17 17 2 5 9.4 3.0 1.21 0.19 1.46 0.24 1.72 0.15 5.1 3.1 1.0 1.1 0.25 0.23 6.4 3.5
17 17 12 1.38 0.80 9.7 1.1 4.4 2.5 0.74 0.23 1.02 0.16 1.39 0.35 1.5 1.6 9.4 4.0 0.78 0.44 11.4 3.9
17 17 17 3.18 0.73 6.82 0.73 13.1 2.8 0.37 0.14 0.97 0.13 1.252 0.080 9.1 4.0 6.0 4.5 3.7 5.6 18.8 9.4
16 16 14 2.50 0.73 5.4 1.2 11.1 2.6 0.32 0.12 1.04 0.11 1.297 0.090 11.3 4.6 74 29 41 19 121 37
17 17 17 3 10 12.2 3.4 0.76 0.15 1.00 0.13 1.05 0.34 93 41 410 280 12 11 520 310
Layer
No. of samples
Thickness (cm)
Density (103 kg m3)
137
Cs activity (kBq m2)
Total activity (kBq m2) a
Boson et al., 2006.
1 2 3 1 2 3 1 2 3 1 2 3
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flow path in the soil. ICRU (2006) also indicates that the spatial variability may increase with depth due to such effects. The sample was re-examined to rule out a handling mistake, and was also split in halves to test if the high 137Cs inventory was caused by a hot particle. This was not the case. Site 5 is located next to the Verkmyra stream, close to its outlet into the Baltic Sea, and is annually flooded during snow melt in spring. Due to this flooding and the resulting deposition of sediments, the alder forest site has accumulated even more radioactivity (Stark et al., 2006), causing a significantly higher average ground deposition compared with site 4, located less than 1 km upstream the Verkmyra stream. Flooding is also the most likely explanation for the high spatial variability encountered in soil samples from site 5. The depth distribution of 137Cs at the studied sites is not consistent between sites. Specifically, the 137Cs distribution at site 1 is drastically different from the other sampling sites (Fig. 1). 3.2. Uncertainties of in situ measurements
Relative activity content (cm-1)
The combined standard uncertainty in the in situ measurement efficiency, estimated by averaging the uncertainty in measurement efficiencies from a set of discrete positions as described in Section 2.5.2, ranges from 12 to 18% for the five sites. These, and all following uncertainties, are presented with a coverage factor k ¼ 1, i.e. for a confidence interval of about 68%. Clearly, the method for the estimation of the combined standard uncertainty used in this work is an approximation when compared with the full sum of integrals in Eq. (1). However, as the uncertainty is fairly constant over all radii contributing significantly to the detector response, it should yield a measure of the uncertainty which is fit-for-purpose. The major contributions to the combined measurement uncertainty come from the intrinsic detector efficiency calibration and the activity depth distributions, particularly the relative activity content in layers 1 and 2. At some sites, there is also a small contribution to uncertainty from soil density, especially at higher angles. Uncertainty contributions from full-energy peak count rate, attenuation coefficients and air density are negligible. The ratios between Monte Carlo calculations of the intrinsic detector efficiencies and empirical measurements yield correction factors of 1.180 for Detector 1, and 1.084 for Detector 2, with about 2.7% standard uncertainty for both detectors. There is no significant angular dependence in the correction factors. Adding this uncertainty and the statistical uncertainty of simulations of in situ measurements to uncertainties of source matrix, air density, photon energy intensity and full-energy peak count rate, the combined standard uncertainty for Monte Carlo-based calibrations
0.4
Site 1
0.3
Site 2 Site 3
0.2
Site 4 Site 5
0.1
0
was found to be between 11 and 17%. This can be considered to be equal to uncertainties of the semi-empirical calibrations. The calibration factor calculated using an exponentially distributed source was found to be about 15% lower than the corresponding calibration factor calculated with the three-layer model. The linearly decreasing model, on the other hand, yielded a calibration factor about 12% higher than the three-layer model. Assuming that these deviations from the results for the three-layer model represent the boundaries of what is realistically possible, we conclude that the potential systematic effect on in situ measurement results arising from the three-layer model has a rectangular distribution with a maximum uncertainty of 15%. This corresponds to a standard uncertainty in the three-layer correction factor of about 8.7%. Propagating uncertainties from the in situ measurement calibration and the three-layer correction factor, combined standard uncertainty of the in situ measurements was found to be between 15 and 20% for the semi-empirical calibration method and 14–19% for the Monte Carlo-calculated value. For future measurements, one can thus assume a 20% uncertainty in in situ measurement results for both calibration methods, given that source matrix data is based on 17 soil samples. If fewer soil samples were to be collected, one can expect the uncertainty to increase. Sowa et al. (1989) also showed that the main contribution to the total in situ measurement uncertainty derives from the uncertainty in activity depth distribution. Sowa et al. (1989) stated total measurement uncertainties between 9 and 32% for caesium. This is similar to the present results, but it should be noted that the calculations of Sowa et al. (1989) were based on shallower activity depth distributions. 3.3. Comparisons between in situ measurements and soil samples Measurement results from all sites are presented in Table 4. Data include total 137Cs inventories in soil samples, as well as results from in situ measurements, calculated both with the semi-empirical calibration method and Monte Carlo simulations. A comparison between mean values of 137Cs in soil samples and 137 Cs ground deposition activity densities determined with in situ measurements is shown in Fig. 2. Results from the three methods where checked for equivalence in accordance with a method described by Kessel et al. (2008). Since all results where found equal within measurement uncertainties, it is reasonable to assume that both in situ calibration methods estimate ground deposition activity densities well, and that the uncertainty of the in situ measurements is neither underestimated, nor overestimated. ICRU (2006) states that the activity contents in a set of soil samples are often found to be log-normally distributed. However, ICRU recommends the use of arithmetic means and standard deviations, simply because this is the most common practice. Because of this, and because not enough samples were collected to determine the true activity distributions with any statistical significance, it was decided to present data as arithmetic mean, standard deviation or Table 4 Results for 137Cs activity ground deposition levels found by the different methods employed. Standard uncertainties are presented with a coverage factor of k ¼ 1. Method
0
5
10
15
20
Depth (cm) Fig. 1. Relative activity distribution in soil samples vs. depth from all five sampling sites.
Site 1a
Site 2
Site 3
Site 4
Site 5
6.37 0.85 11.39 0.95 18.8 2.3 121.3 8.9 519 76 Soil samples (kBq m2) In Situ – Semi emp. 5.76 0.97 11.1 1.7 14.4 2.4 109 22 420 80 Cal. (kBq m2) In Situ – Monte Carlo 6.05 0.95 11.8 1.7 16.6 2.8 112 21 464 85 Cal. (kBq m2) a
Boson et al., 2006.
J. Boson et al. / Journal of Environmental Radioactivity 100 (2009) 935–940
Normalized ground deposition
1.4 1.2 1
Soil samples
0.8
In Situ (semi empirical)
0.6
In Situ (Monte Carlo)
0.4 0.2 0
1
2
3
4
5
Site # Fig. 2. 137Cs ground deposition levels as determined by soil samples and in situ measurements, using either semi-empirical or Monte Carlo-based calibration methods. All values are normalized to the arithmetic mean of soil samples from each site. Uncertainties for soil samples represent the standard deviation of the mean (n ¼ 17; n ¼ 16 for site 4), and for in situ measurements the combined standard uncertainty of the measurement (k ¼ 1).
standard deviation of the mean. However, this may be the cause of the small, non-significant systematic difference between the mean 137 Cs activity of soil samples and in situ measurements of 137Cs ground deposition activity levels seen in Fig. 2. Better agreement is found between the soil samples and in situ measurement results, if the geometric mean of soil samples is used. Due to the high spatial variability of the 137Cs activity ground deposition, it is important that the area from which samples are collected matches the field of view of the in situ measurement (Tyler et al., 1996). If this is not the case, comparisons between in situ measurements and soil samples may not yield correct results. In the present work, the 8 m radius area, within which soil samples were collected, was found to contribute to between 72 and 82% of the total detector response. This is consistent with data by Tyler et al. (1996), which indicate a fraction of the infinite yield at an 8 m radius of about 70–85% for mass depths b between 1 and 14 g cm2. Most notably, the standard uncertainty of the mean 137Cs activity content in soil samples is less than the uncertainty of the corresponding in situ measurements. In effect, if a sufficiently large number of soil samples were to be collected, in situ measurements would be made redundant. However, it should be stressed that the relatively large number of soil samples collected in the present work were needed to gain information about the inter-sample variability for the uncertainty assessment. For future measurements, a much smaller number of soil samples may suffice to provide reasonable precision in source matrix data used for in situ measurement calibrations. The uncertainty of in situ measurements as a function of the number of soil samples collected for the calibration is a question that remains to be addressed. Furthermore, in situ measurements will probably be more favourable in the case of fresh fallout. When the activity is located near the surface of the ground, uncertainties in soil sample parameters will not influence the combined uncertainty of in situ measurements to the same extent. This will most likely lead to reduced uncertainties in in situ measurements. 4. Conclusions Both semi-empirical and Monte Carlo-based calibration methods yielded comparable results, i.e. within measurement uncertainties, as compared to soil sampling and laboratory measurements. We
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therefore conclude that it is safe to apply Monte Carlo-based calibrations to investigate more complex geometries that cannot be handled by the semi-empirical calibration method. The overall in situ measurement uncertainty was found to be 15–20% for both the semi-empirical and the Monte Carlo-based detector efficiency calibrations. The largest contributions to the in situ measurement uncertainty came from the intrinsic detector efficiency calibration and the activity depth distribution. The correction factor to compensate for the inherent approximation in the model that describes the 137Cs activity depth distribution also contributes, but to a lesser extent. Both of these uncertainties, however, are possible to reduce, should it be considered necessary. The uncertainty in the intrinsic detector efficiency can be reduced to less than 4% by changing the expression for the detector efficiency function (Boson et al., 2009). The uncertainties introduced by the three-layer model could certainly be investigated and reduced. Acknowledgement This work was supported by the Swedish Radiation Protection Agency and the Swedish Emergency Management Agency. The authors would like to thank Dr. Bjo¨rn Sandstro¨m for valuable comments on the manuscript, and Dr. Torbjo¨rn Nyle´n for helpful discussions about statistical methods. References Albrektson, A., Lundmark, T., 1991. (In Swedish) vegetationens storlek och omsa¨ttning inom en barrskog i norra Sverige, samt na¨ring i vegetation och mark och dess omsa¨ttning i samband med va¨xandet. Institutionen fo¨r skogssko¨tsel arbetsrapporter nr 52. Swedish University of Agricultural Sciences, Umeå, Sweden. Allyson, J.D., Sanderson, D.C.W., 1998. Monte Carlo simulation of environmental airborne gamma-spectrometry. Journal of Environmental Radioactivity 38, 259–282. Boson, J., Lidstro¨m, K., Nyle´n, T., Ågren, G., Johansson, L., 2006. In situ gamma-ray spectrometry for environmental monitoring: a semi empirical calibration method. Radiation Protection Dosimetry 121, 310–316. Boson, J., Ågren, G., Johansson, L., 2008. A detailed investigation of HPGe detector response for improved Monte Carlo efficiency calculations. Nuclear Instruments and Methods in Physics Research A 587, 304–314. Boson, J., Rameba¨ck, H., Ågren, G., Johansson, L., 2009. Uncertainty in HPGe detector calibrations for in situ gamma-ray spectrometry. Radiation Protection Dosimetry 134, 122–129. Chu, S.Y.F., Ekstro¨m, L.P., Firestone, R.B., 2/28/1999. WWW table of radioactive isotopes, database version. from URL. http://nucleardata.nuclear.lu.se/ nucleardata/toi/. D’Alberti, F., Forte, M., 2005. Calibration of a HPGe detector for in-situ gamma spectrometry: a comparison between a Monte Carlo based code and an experimental method. Radioactivity in the Environment 7, 199–206. De Geer, L.-E., Arntsing, R., Vintersved, I., Sisefsky, J., Jakobsson, S., Engstro¨m, J-Å, 1978. Particulate radioactivity, mainly from nuclear explosions, in air and precipitation in Sweden mid-year 1975 to mid-year 1977. National Defence Research Institute, Stockholm. FOA C 40089-T2(A1). Edvarson, K., 1991. Fallout over Sweden from the Chernobyl accident. In: Moberg, L. (Ed.), The Chernobyl Fallout in Sweden: Results from a Research Programme on Environmental Radiology. Swedish Radiation Protection Institute, Stockholm, pp. 47–65. Finck, R.R., 1992. High Resolution Field Gamma Spectrometry and its Application to Problems in Environmental Radiology. Thesis, University of Lund, Department of Radiation Physics, SE-214 01, Malmo¨, Sweden. Gedcke, D., 2007. Simply managing dead time errors in gamma-ray spectrometry. Ortec, application note AN63. http://www.ortec-online.com/application-notes/ AN63.pdf. Gering, F., Hillmann, U., Jacob, P., Fehrenbacher, G., 1998. In situ gamma-spectrometry several years after deposition of radiocaesium, II. Peak-to-valley method. Radiation Environmental Biophysics 37, 283–291. ICRU, 1994. International Commission on Radiation Units and Measurements, Gamma-Ray Spectrometry in the Environment. ICRU Report 53, Bethesda, MD, USA. ICRU, 2006. International Commission on Radiation Units and Measurements, Sampling for Radionuclides in the Environment. ICRU Report 75, Oxford University Press. ISBN 0199211418. International Organisation for Standardisation, ISO, 1995. Guide to the Expression of Uncertainty in Measurement. Geneva, Switzerland. ISBN 92-67-10188-9.
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Kessel, R., Berglund, M., Wellum, R., 2008. Application of consistency checking to evaluation of uncertainty in multiple replicate measurements, accreditation and quality assurance. Journal for Quality, Comparability and Reliability in Chemical Measurement 13, 293–298. Likar, A., Vidmar, T., Lipoglavsˇek, M., Omahen, G., 2004. Monte Carlo calculation of entire in situ gamma-ray spectra. Journal of Environmental Radioactivity 72, 163–168. Plamboeck, A.H., Nyle´n, T., Grip, H., 2000. Uptake of cations under two different water regimes in a boreal Scots pine forest. The Science of the Total Environment 256, 175–183.
SGAB, 1986. Cs-137 ground deposition map over Sweden. Map 1, 2000000. Sowa, W., Martini, E., Gehrcke, K., Marschner, P., Naziry, M.J., 1989. Uncertainties of in situ gamma spectrometry for environmental monitoring. Radiation Protection Dosimetry 27, 93–101. Stark, K., Wallberg, P., Nyle´n, T., 2006. Post-depositional redistribution and gradual accumulation of 137Cs in a riparian wetland ecosystem in Sweden. Journal of Environmental Radioactivity 87, 175–187. Tyler, A.N., Sanderson, D.C.W., Scott, E.M., Allyson, J.D., 1996. Accounting for spatial variability and fields of view in environmental gamma ray spectrometry. Journal of Environmental Radioactivity 33, 213–235.
Contents lists available at ScienceDirect
Journal of Environmental Radioactivity journal homepage: www.elsevier.com/locate/jenvrad
Evaluation of Monte Carlo-based calibrations of HPGe detectors for in situ gamma-ray spectrometry Jonas Boson a, b, *, Agneta H. Plamboeck a, Henrik Rameba¨ck a, Go¨ran Ågren a, Lennart Johansson b a b
Swedish Defence Research Agency, FOI CBRN Defence and Security, SE-901 82 Umeå, Sweden Department of Radiation Sciences, Umeå University, SE-901 87 Umeå, Sweden
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 August 2008 Received in revised form 25 May 2009 Accepted 4 June 2009 Available online 14 July 2009
The aim of this work was to evaluate the use of Monte Carlo-based calibrations for in situ gamma-ray spectrometry. We have performed in situ measurements at five different sites in Sweden using HPGe detectors to determine ground deposition activity levels of 137Cs from the 1986 Chernobyl accident. Monte Carlo-calculated efficiency calibration factors were compared with corresponding values calculated using a more traditional semi-empirical method. In addition, results for the activity ground deposition were also compared with activity densities found in soil samples. In order to facilitate meaningful comparisons between the different types of results, the combined standard uncertainty of in situ measurements was assessed for both calibration methods. Good agreement, both between the two calibration methods, and between in situ measurements and soil samples, was found at all five sites. Uncertainties in in situ measurements for the given measurement conditions, about 20 years after the fallout occurred, were found to be in the range 15–20% (with a coverage factor k ¼ 1, i.e. with a confidence interval of about 68%). Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Germanium detector HPGe Uncertainty Gamma spectrometry In situ measurements Monte Carlo GUM
1. Introduction High resolution gamma spectrometry is a powerful tool for the identification and quantification of gamma emitting radionuclides, both in the laboratory and in the field. Field measurements using high purity germanium (HPGe) detectors, often referred to as in situ gamma-ray spectrometry, are described in detail by, for example, the ICRU (ICRU, 1994). As suggested by the ICRU, semi-empirical methods are most often used for the necessary efficiency calibrations. More recently, Monte Carlo methods have begun to be employed for calculating in situ measurement calibration factors (e.g. Allyson and Sanderson, 1998; Gering et al., 1998; Likar et al., 2004). Calibration methods based on Monte Carlo calculations facilitate the assessment of calibration factors for a much wider variety of source distributions and measurement conditions, including non-symmetrical geometries, which are difficult to handle analytically. However, before proceeding to use Monte Carlo-based calibrations for more complex measurement geometries one should first confirm that the Monte Carlo model gives
correct results for simpler geometries that are possible to handle experimentally or analytically. As clearly stated by the ISO ‘‘Guide to the Expression of Uncertainty in Measurement’’ (GUM) (ISO, 1995), in order for any comparison between measurement results to be relevant, appropriate estimates of the combined uncertainties of the measurements are essential. The combined standard uncertainty of in situ measurement results will therefore have to be assessed for both the semi-empirical and the Monte Carlo-based calibration methods. As for the semi-empirical calibration method, we previously determined the uncertainty in intrinsic detector efficiency (Boson et al., 2009). However, the uncertainties relating to source matrix parameters such as activity and density depth distributions have yet to be considered. The aim of this work was to evaluate the use of Monte Carlobased calibrations for in situ measurements performed at five different sites. Results were compared both with results from a semi-empirical calibration method and with ground deposition activity densities assessed by soil sample measurements. 2. Materials and methods 2.1. Site descriptions
* Corresponding author. Swedish Defence Research Agency FOI, CBRN Defence and Security, SE-901 82 Umeå, Sweden. Tel.: þ46 90 10 66 95; fax: þ46 90 10 68 00. E-mail address: [email protected] (J. Boson). 0265-931X/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jenvrad.2009.06.006
In situ measurements and soil sampling to determine 137Cs ground deposition levels were performed at five sites in Sweden. Results from site 1 have been
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previously reported by Boson et al. (2006). The sites chosen display a fairly wide range of activity levels and also represent a variety of different soil and vegetation types. Most of the radiocaesium deposition in Sweden derives from the Chernobyl accident in 1986. There is also a minor contribution from atmospheric nuclear weapons tests performed mainly between 1945 and 1963, which resulted in an accumulated activity deposition of about 3 kBq m2 in 1966 (De Geer et al., 1978). Site 1. Ersboda, Umeå, lawn: The Ersboda site is situated within the Umeå city area in northern Sweden (63 510 2300 N, 20 190 1100 E). The measurement point is located in the middle of a large open field or lawn, with at least 20 m to any potentially interfering structure such as trees. Measurement date: 25th October 2004. Site 2. FOI, Umeå, lawn. Site 2 is positioned within the area of the FOI research facility in the city of Umeå in northern Sweden (63 510 100 N, 20 190 5600 E). The site is an open lawn, with at least 8 m to any potentially interfering structure such as trees. Measurement date: 19th September 2006. Site 3. Åheden, Vindeln, Pine forest. The Åheden site is located about 60 km northwest of Umeå in northern Sweden (64 130 5400 N, 19 460 5700 E). The site is a Scots pine forest with an average stand density of 1250 trees ha1 (Plamboeck et al., 2000). Measurement date: 4th August 2006. ¨vle, Spruce forest. Hille is located about 20 km north of the city of Site 4. Hille, Ga Ga¨vle in the central-eastern part of Sweden (60 460 200 N, 17 160 1400 E). The site is a spruce plantation with an average stand density of 3800 trees ha1 and relatively scarce ground vegetation. The diameter of trees at 1.3 m above the ground is 21 cm and the average tree height is approximately 22 m. Measurement date: 16th June 2004. ¨vle, Alder forest. Site 5 is an alder forest wetland close to the Site 5. Hille, Ga Verkmyra stream about 20 km north of the city of Ga¨vle in the centraleastern part of Sweden (60 460 1900 N, 17 160 2800 E). The average stand density of the alder forest is 1650 trees ha1 with a tree height of 26 m and an average diameter at 1.3 m above the ground of 27 cm. Measurement date: 16th June 2004. According to aerial measurements of the fallout after the Chernobyl accident, performed by the Swedish Geological Company SGAB (SGAB, 1986), the region around Umeå (sites 1, 2 and 3) generally received about 10–20 kBq m2 137Cs expressed as a surface equivalent deposition density (i.e. a calibration factor derived for a surface source was used). In order to estimate true ground deposition densities these values should be multiplied by a factor 1.6 (Edvarson, 1991). Sites 4 and 5 are both located in the Ga¨vle region, which received some of the highest levels of Chernobyl fallout in Western Europe, with maximum deposition densities of about 200 kBq m2 (Edvarson, 1991). 2.2. Soil sampling At each of the five sites, 17 soil samples were collected in a cross pattern using soil corers and each core was divided on site into 3 sections with respect to depth. Divisions were made, where possible, according to natural variations in soil density and composition, based on visual inspection (see Table 3). Two different soil corers were used, with radii 2.4 and 2.15 cm, respectively. The sampling and sample preparation procedures were previously described in detail (Boson et al., 2006). At site 4, one of the samples was excluded, as the second and third layers were mistakenly put into the same plastic bag. At sites 2 and 4, where sampling down to about 20 cm depth was difficult due to the frequent occurrence of stones, some of the collected soil cores were significantly shorter than the others. These samples were therefore only divided into two sections. 2.3. Measurements 2.3.1. Laboratory measurements Aliquots of soil samples were analysed for 137Cs content in suitable, pre-calibrated measurement geometries using two lead-shielded HPGe detectors (Ortec Inc., USA, relative efficiencies 50 and 80% at 1333 keV). Depending on sample size, different beakers were used, ranging from 5 to 250 ml. Measurement times were long enough to ensure at least 1000 full-energy peak net counts for most samples. However, no sample was analysed longer than 64 h, in order to reduce total measurement time. As this only concerned samples with low 137Cs content, the effect on overall measurement uncertainty should be marginal. All spectra were evaluated using GammaVision 6.01 (Ortec Inc., USA). All calibrations were done with measurement standards traceable to NIST. Internal laboratory quality assurance includes monitoring of detector response, peak resolution, energy calibration and detector background. 2.3.2. In situ measurements Two different p-type HPGe detectors were used for the in situ measurements (Ortec Inc., USA). Relevant detector specifications are listed in Table 1. Detector 1 was used at sites 1, 2, 4 and 5, and Detector 2 at site 3. The detectors were placed on tripods so that the geometric centre of the germanium crystal was positioned 1.0 m
Table 1 Detector specifications for detectors used for in situ measurements. Characteristic
Detector 1
Detector 2
Efficiencya Crystal length Crystal diameter
36% 65.4 mm 58.3 mm
57% 58.6 mm 69.9 mm
a
Relative a 300 300 NaI(Tl) crystal at 1.33 MeV (60Co).
above ground, and a portable multi-channel analyzer (Digidart, Ortec Inc., USA) was used for data acquisition. Spectra were recorded for 1000 or 1800 s, resulting in uncertainties in the 137Cs full-energy peak area due to counting statistics of less than 2% for all sites. All spectra were analysed using GammaVision 6.01 (Ortec inc., USA). 2.4. In situ measurement calibrations Calibration factors for the in situ measurements were calculated using both a previously described semi-empirical method (Boson et al., 2006) and Monte Carlo simulations. For both methods, a three-layer model previously described by Boson et al. (2006), was used for the description of soil density and activity depth distributions. Source matrix data (i.e. thickness, density and fraction of the total 137Cs inventory for each of the three layers) were obtained from soil samples. The Monte Carlo simulations were made using the MCNP5 code, v. 1.40 (Los Alamos National Laboratory, USA). It was previously shown that a Monte Carlo model of Detector 1, based entirely on manufacturer supplied data, overestimates the intrinsic detector efficiency, and suitable efficiency correction factors to compensate for this overestimation have been derived (Boson et al., 2008). Such corrections factors were also calculated for Detector 2, in the same manner as previously described by Boson et al. (2008). For each position (i.e. angle of incidence) and energy, 5 107 particles were simulated. This gave an uncertainty in the fullenergy peak area of the simulated spectrum below 2% in all cases. In this case, since we only intend to measure fallout radiocaesium, the correction factor used was based on an average over all angles for 661.7 keV. Monte Carlo simulations of the entire measurement setup were performed in order to obtain calibration factors for the in situ measurements. A 30 m cut-off radius of the source was used in all in situ simulations, which corresponds to a simulated source area of about 2800 m2. The number of particles in the simulations (2.1–3 109) was large enough to ensure statistical uncertainties below 5% in the full-energy peak count rate. The elemental composition of mineral soil (Table 2) was based on data presented by Finck (1992). The elemental composition of humus was calculated based on data from Site 3 presented by Albrektson and Lundmark (1991). No alterations of the elemental compositions to account for varying water content in soil were made, as the elemental composition of soil is not expected to significantly influence the attenuation of photons with energies exceeding 100 keV (Finck, 1992; D’Alberti and Forte, 2005). The water content does, however, influence photon attenuation in the sense that it affects soil density. This is taken into account as fresh weights are used when calculating soil densities. 2.5. Uncertainty estimations All uncertainty estimations were made in accordance with GUM (ISO, 1995). The temporal variability was ignored in all calculations regarding measurement uncertainties. The main contribution to uncertainty in live time value originates from dead time estimation, but as long as dead time can be kept small it will only have a minor effect on the live time estimate (Gedcke, 2007). As dead times in all measurements were below 10%, neglecting the live time uncertainty was considered to be a valid approximation. 2.5.1. Soil samples Uncertainties in mean values for soil density, soil layer thickness and 137Cs activity were approximated by the standard deviation of the mean. This measure includes uncertainties from the natural variability and random uncertainties from laboratory measurements. It does not, however, include any contribution from Type Table 2 Soil composition used in Monte Carlo simulations (fractions by weight). Element
Humus
Mineral soil
H C O N Al Si Fe
10% 69% 20% 1% – – –
1.1% 1.3% 55.8% – 7.1% 31.5% 3.2%
J. Boson et al. / Journal of Environmental Radioactivity 100 (2009) 935–940 B uncertainties (ISO, 1995), e.g. from calibration standards used in the efficiency calibration. Compared to the natural variability, which is of the order of 10% or more, the addition of a small contribution from uncertainty in the calibration, typically a few percent, will not contribute significantly to the combined uncertainty according to the law of propagation of uncertainties. 2.5.2. In situ measurements The calculation of ground deposition densities according to the semi-empirical calibration method (Boson et al., 2006) is based on the following expression for total in situ measurement efficiency, i.e. full-energy peak count rate, N_ [s1], per activity per unit area, AS [Bq m2]: ZZ n X N_ Ig ai 3ðE; qÞtanðqÞcitot dui dq ¼ As 2d i i
(1)
The expression is a sum over n layers, each having a fraction ai of the total 137Cs inventory and thickness di [m]. Ig is the photon emission probability for a particular energy; 3(E,q) [m2] is the intrinsic detector efficiency as a function of photon energy, i is the total attenuation in air and soil (from all E, and angle of incidence, q; Ctot layers); and ui [m] is depth in layer i. In this work, three layers (n ¼ 3) were used for all sites. Most of the parameters having an impact on total measurement uncertainty lie within the integral, which makes a calculation of combined standard uncertainty according to the law of propagation of uncertainties (ISO, 1995) cumbersome. Instead, we consider the uncertainty in measurement efficiency from a set of 10 discrete angles of incidence and an average depth in each soil layer. The angles chosen correspond to areas contributing to between 5 and 95%, with 10% increments, of the total detector response, which eliminates the need for weighting factors when calculating average uncertainty. The combined standard uncertainties for each site and angle of incidence were calculated using GUM Workbench (Metrodata GmbH, Weil-am-Rhein, Germany). The standard uncertainty of values predicted by the detector efficiency function 3(E,q) is 8.2% for Detector 1 and 5.1% for Detector 2 (Boson et al., 2009). The mass attenuation coefficient for soil, (m/r)soil, is calculated using the empirical formula proposed by Sowa et al. (1989). According to Sowa et al. (1989), the difference between the fitted curve and calculated values is within a 4% range. For 137Cs, the relative uncertainty in the intensity of the 661.7 keV gamma energy is 0.24% (Chu et al., 1999). The standard uncertainty in the linear attenuation coefficient for air is estimated to be about 2% (Boson et al., 2009) and air density is assumed to follow a rectangular distribution between 1.07 and 1.29 kg m3 (corresponding to temperatures and pressures from 15 to 30 C and from 95 to 105 kPa, respectively). Clearly, the description of the source matrix as three discrete homogeneous layers is an approximation that might cause a bias in the final results. In accordance with GUM (ISO, 1995), we therefore introduce a correction factor, k3-layer, to account for this. As the true activity depth distributions are not known, we cannot estimate the value of the correction factor, but we will have to assume that k3-layer ¼ 1. However, by investigating the sensitivity of the final result with respect to changes in activity depth distribution, one can estimate the uncertainty of the correction factor. Hence, two alternative distribution models were tested: one exponential distribution, as suggested by ICRU (1994), and one with the activity concentration linearly decreasing in each layer with the boundary conditions that the activity concentration is continuous at intersections between layers and zero below the third layer. The alternative activity distributions were modelled in MCNP5 and results were compared with a simulation using the three-layer model. Densities were assumed to be the same as in the three-layer model. The tests were based on
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activity distribution data from site 1, because this site displayed the most variable activity depth distribution. With a few exceptions, the uncertainty calculations for the Monte Carlo-based calibrations are, in principle, the same as for the semi-empirical method. The uncertainty in the intrinsic detector efficiency is replaced by the uncertainty in the efficiency correction factor used for the Monte Carlo simulations and the statistical uncertainty in the simulation of the in situ measurement will have to be added. The uncertainty in the attenuation coefficient of air can be assumed to be zero, since the attenuation is calculated by the Monte Carlo code and no interpolations are needed. The uncertainty of the attenuation coefficient in soil, however, is primarily a result of variations in soil composition and can therefore be assumed to be the same for the Monte Carlo simulations as for the semi-empirical method. Uncertainties in Monte Carlo-based calibrations were calculated using GUM Workbench (Metrodata GmbH, Weil-am-Rhein, Germany).
3. Results and discussion 3.1. Soil samples All measurement results of 137Cs activity concentrations in soil samples were corrected for decay according to the in situ measurement date. Correcting for decay to a common reference date, such as the date for the Chernobyl accident, would be misleading since site 5, because of a substantial redistribution of activity in the area, has accumulated more 137Cs activity since then (Stark et al., 2006). Results for soil sample parameters are shown in Table 3. Note that bulk densities are calculated from fresh weights, i.e. including water content, as these values were used in calculations of the in situ measurement efficiencies. Standard deviations only relate to variability of measured values. Since other contributions, i.e. from calibration standards, are negligible at this level of variability, the standard deviation of the mean is an appropriate estimate of the combined uncertainty. The results in general show a very high inter-sample variation. In particular, the total 137Cs inventories in soil samples from sites 1, 3 and 5 display standard deviations of 50–60%. For site 3, much of this variability stems from one individual soil core containing the equivalent of 47 kBq m2, compared to an average of 19 kBq m2 (standard deviation 9.4 kBq m2) of all 17 samples. In particular, the third layer of this sample has a 137Cs inventory of about 23 kBq m2, whereas the average inventory in the third layer for all 17 samples is 3.7 kBq m2 with a standard deviation of 5.6 kBq m2 (excluding this potential outlier the corresponding values are 2.5 2.7 kBq m2). The high 137Cs inventory in this particular sample is by no means improbable. It could be the effect of water from rain or melting snow containing activity from the initial deposition pouring down a root channel or some other preferential
Table 3 Soil sample results. Uncertainties are presented as one standard deviation. Site 1a
Site 2
Site 3
Site 4
Site 5
Measurement date
25th Oct. 2004
19th Sept. 2006
4th Aug. 2006
16th June 2004
16th June 2004
Vegetation
Lawn
Lawn
Pine heath
Spruce forest
Alder forest
17 17 17 2 5 9.4 3.0 1.21 0.19 1.46 0.24 1.72 0.15 5.1 3.1 1.0 1.1 0.25 0.23 6.4 3.5
17 17 12 1.38 0.80 9.7 1.1 4.4 2.5 0.74 0.23 1.02 0.16 1.39 0.35 1.5 1.6 9.4 4.0 0.78 0.44 11.4 3.9
17 17 17 3.18 0.73 6.82 0.73 13.1 2.8 0.37 0.14 0.97 0.13 1.252 0.080 9.1 4.0 6.0 4.5 3.7 5.6 18.8 9.4
16 16 14 2.50 0.73 5.4 1.2 11.1 2.6 0.32 0.12 1.04 0.11 1.297 0.090 11.3 4.6 74 29 41 19 121 37
17 17 17 3 10 12.2 3.4 0.76 0.15 1.00 0.13 1.05 0.34 93 41 410 280 12 11 520 310
Layer
No. of samples
Thickness (cm)
Density (103 kg m3)
137
Cs activity (kBq m2)
Total activity (kBq m2) a
Boson et al., 2006.
1 2 3 1 2 3 1 2 3 1 2 3
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flow path in the soil. ICRU (2006) also indicates that the spatial variability may increase with depth due to such effects. The sample was re-examined to rule out a handling mistake, and was also split in halves to test if the high 137Cs inventory was caused by a hot particle. This was not the case. Site 5 is located next to the Verkmyra stream, close to its outlet into the Baltic Sea, and is annually flooded during snow melt in spring. Due to this flooding and the resulting deposition of sediments, the alder forest site has accumulated even more radioactivity (Stark et al., 2006), causing a significantly higher average ground deposition compared with site 4, located less than 1 km upstream the Verkmyra stream. Flooding is also the most likely explanation for the high spatial variability encountered in soil samples from site 5. The depth distribution of 137Cs at the studied sites is not consistent between sites. Specifically, the 137Cs distribution at site 1 is drastically different from the other sampling sites (Fig. 1). 3.2. Uncertainties of in situ measurements
Relative activity content (cm-1)
The combined standard uncertainty in the in situ measurement efficiency, estimated by averaging the uncertainty in measurement efficiencies from a set of discrete positions as described in Section 2.5.2, ranges from 12 to 18% for the five sites. These, and all following uncertainties, are presented with a coverage factor k ¼ 1, i.e. for a confidence interval of about 68%. Clearly, the method for the estimation of the combined standard uncertainty used in this work is an approximation when compared with the full sum of integrals in Eq. (1). However, as the uncertainty is fairly constant over all radii contributing significantly to the detector response, it should yield a measure of the uncertainty which is fit-for-purpose. The major contributions to the combined measurement uncertainty come from the intrinsic detector efficiency calibration and the activity depth distributions, particularly the relative activity content in layers 1 and 2. At some sites, there is also a small contribution to uncertainty from soil density, especially at higher angles. Uncertainty contributions from full-energy peak count rate, attenuation coefficients and air density are negligible. The ratios between Monte Carlo calculations of the intrinsic detector efficiencies and empirical measurements yield correction factors of 1.180 for Detector 1, and 1.084 for Detector 2, with about 2.7% standard uncertainty for both detectors. There is no significant angular dependence in the correction factors. Adding this uncertainty and the statistical uncertainty of simulations of in situ measurements to uncertainties of source matrix, air density, photon energy intensity and full-energy peak count rate, the combined standard uncertainty for Monte Carlo-based calibrations
0.4
Site 1
0.3
Site 2 Site 3
0.2
Site 4 Site 5
0.1
0
was found to be between 11 and 17%. This can be considered to be equal to uncertainties of the semi-empirical calibrations. The calibration factor calculated using an exponentially distributed source was found to be about 15% lower than the corresponding calibration factor calculated with the three-layer model. The linearly decreasing model, on the other hand, yielded a calibration factor about 12% higher than the three-layer model. Assuming that these deviations from the results for the three-layer model represent the boundaries of what is realistically possible, we conclude that the potential systematic effect on in situ measurement results arising from the three-layer model has a rectangular distribution with a maximum uncertainty of 15%. This corresponds to a standard uncertainty in the three-layer correction factor of about 8.7%. Propagating uncertainties from the in situ measurement calibration and the three-layer correction factor, combined standard uncertainty of the in situ measurements was found to be between 15 and 20% for the semi-empirical calibration method and 14–19% for the Monte Carlo-calculated value. For future measurements, one can thus assume a 20% uncertainty in in situ measurement results for both calibration methods, given that source matrix data is based on 17 soil samples. If fewer soil samples were to be collected, one can expect the uncertainty to increase. Sowa et al. (1989) also showed that the main contribution to the total in situ measurement uncertainty derives from the uncertainty in activity depth distribution. Sowa et al. (1989) stated total measurement uncertainties between 9 and 32% for caesium. This is similar to the present results, but it should be noted that the calculations of Sowa et al. (1989) were based on shallower activity depth distributions. 3.3. Comparisons between in situ measurements and soil samples Measurement results from all sites are presented in Table 4. Data include total 137Cs inventories in soil samples, as well as results from in situ measurements, calculated both with the semi-empirical calibration method and Monte Carlo simulations. A comparison between mean values of 137Cs in soil samples and 137 Cs ground deposition activity densities determined with in situ measurements is shown in Fig. 2. Results from the three methods where checked for equivalence in accordance with a method described by Kessel et al. (2008). Since all results where found equal within measurement uncertainties, it is reasonable to assume that both in situ calibration methods estimate ground deposition activity densities well, and that the uncertainty of the in situ measurements is neither underestimated, nor overestimated. ICRU (2006) states that the activity contents in a set of soil samples are often found to be log-normally distributed. However, ICRU recommends the use of arithmetic means and standard deviations, simply because this is the most common practice. Because of this, and because not enough samples were collected to determine the true activity distributions with any statistical significance, it was decided to present data as arithmetic mean, standard deviation or Table 4 Results for 137Cs activity ground deposition levels found by the different methods employed. Standard uncertainties are presented with a coverage factor of k ¼ 1. Method
0
5
10
15
20
Depth (cm) Fig. 1. Relative activity distribution in soil samples vs. depth from all five sampling sites.
Site 1a
Site 2
Site 3
Site 4
Site 5
6.37 0.85 11.39 0.95 18.8 2.3 121.3 8.9 519 76 Soil samples (kBq m2) In Situ – Semi emp. 5.76 0.97 11.1 1.7 14.4 2.4 109 22 420 80 Cal. (kBq m2) In Situ – Monte Carlo 6.05 0.95 11.8 1.7 16.6 2.8 112 21 464 85 Cal. (kBq m2) a
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Normalized ground deposition
1.4 1.2 1
Soil samples
0.8
In Situ (semi empirical)
0.6
In Situ (Monte Carlo)
0.4 0.2 0
1
2
3
4
5
Site # Fig. 2. 137Cs ground deposition levels as determined by soil samples and in situ measurements, using either semi-empirical or Monte Carlo-based calibration methods. All values are normalized to the arithmetic mean of soil samples from each site. Uncertainties for soil samples represent the standard deviation of the mean (n ¼ 17; n ¼ 16 for site 4), and for in situ measurements the combined standard uncertainty of the measurement (k ¼ 1).
standard deviation of the mean. However, this may be the cause of the small, non-significant systematic difference between the mean 137 Cs activity of soil samples and in situ measurements of 137Cs ground deposition activity levels seen in Fig. 2. Better agreement is found between the soil samples and in situ measurement results, if the geometric mean of soil samples is used. Due to the high spatial variability of the 137Cs activity ground deposition, it is important that the area from which samples are collected matches the field of view of the in situ measurement (Tyler et al., 1996). If this is not the case, comparisons between in situ measurements and soil samples may not yield correct results. In the present work, the 8 m radius area, within which soil samples were collected, was found to contribute to between 72 and 82% of the total detector response. This is consistent with data by Tyler et al. (1996), which indicate a fraction of the infinite yield at an 8 m radius of about 70–85% for mass depths b between 1 and 14 g cm2. Most notably, the standard uncertainty of the mean 137Cs activity content in soil samples is less than the uncertainty of the corresponding in situ measurements. In effect, if a sufficiently large number of soil samples were to be collected, in situ measurements would be made redundant. However, it should be stressed that the relatively large number of soil samples collected in the present work were needed to gain information about the inter-sample variability for the uncertainty assessment. For future measurements, a much smaller number of soil samples may suffice to provide reasonable precision in source matrix data used for in situ measurement calibrations. The uncertainty of in situ measurements as a function of the number of soil samples collected for the calibration is a question that remains to be addressed. Furthermore, in situ measurements will probably be more favourable in the case of fresh fallout. When the activity is located near the surface of the ground, uncertainties in soil sample parameters will not influence the combined uncertainty of in situ measurements to the same extent. This will most likely lead to reduced uncertainties in in situ measurements. 4. Conclusions Both semi-empirical and Monte Carlo-based calibration methods yielded comparable results, i.e. within measurement uncertainties, as compared to soil sampling and laboratory measurements. We
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therefore conclude that it is safe to apply Monte Carlo-based calibrations to investigate more complex geometries that cannot be handled by the semi-empirical calibration method. The overall in situ measurement uncertainty was found to be 15–20% for both the semi-empirical and the Monte Carlo-based detector efficiency calibrations. The largest contributions to the in situ measurement uncertainty came from the intrinsic detector efficiency calibration and the activity depth distribution. The correction factor to compensate for the inherent approximation in the model that describes the 137Cs activity depth distribution also contributes, but to a lesser extent. Both of these uncertainties, however, are possible to reduce, should it be considered necessary. The uncertainty in the intrinsic detector efficiency can be reduced to less than 4% by changing the expression for the detector efficiency function (Boson et al., 2009). The uncertainties introduced by the three-layer model could certainly be investigated and reduced. Acknowledgement This work was supported by the Swedish Radiation Protection Agency and the Swedish Emergency Management Agency. The authors would like to thank Dr. Bjo¨rn Sandstro¨m for valuable comments on the manuscript, and Dr. Torbjo¨rn Nyle´n for helpful discussions about statistical methods. References Albrektson, A., Lundmark, T., 1991. (In Swedish) vegetationens storlek och omsa¨ttning inom en barrskog i norra Sverige, samt na¨ring i vegetation och mark och dess omsa¨ttning i samband med va¨xandet. Institutionen fo¨r skogssko¨tsel arbetsrapporter nr 52. Swedish University of Agricultural Sciences, Umeå, Sweden. Allyson, J.D., Sanderson, D.C.W., 1998. Monte Carlo simulation of environmental airborne gamma-spectrometry. Journal of Environmental Radioactivity 38, 259–282. Boson, J., Lidstro¨m, K., Nyle´n, T., Ågren, G., Johansson, L., 2006. In situ gamma-ray spectrometry for environmental monitoring: a semi empirical calibration method. Radiation Protection Dosimetry 121, 310–316. Boson, J., Ågren, G., Johansson, L., 2008. A detailed investigation of HPGe detector response for improved Monte Carlo efficiency calculations. Nuclear Instruments and Methods in Physics Research A 587, 304–314. Boson, J., Rameba¨ck, H., Ågren, G., Johansson, L., 2009. Uncertainty in HPGe detector calibrations for in situ gamma-ray spectrometry. Radiation Protection Dosimetry 134, 122–129. Chu, S.Y.F., Ekstro¨m, L.P., Firestone, R.B., 2/28/1999. WWW table of radioactive isotopes, database version. from URL. http://nucleardata.nuclear.lu.se/ nucleardata/toi/. D’Alberti, F., Forte, M., 2005. Calibration of a HPGe detector for in-situ gamma spectrometry: a comparison between a Monte Carlo based code and an experimental method. Radioactivity in the Environment 7, 199–206. De Geer, L.-E., Arntsing, R., Vintersved, I., Sisefsky, J., Jakobsson, S., Engstro¨m, J-Å, 1978. Particulate radioactivity, mainly from nuclear explosions, in air and precipitation in Sweden mid-year 1975 to mid-year 1977. National Defence Research Institute, Stockholm. FOA C 40089-T2(A1). Edvarson, K., 1991. Fallout over Sweden from the Chernobyl accident. In: Moberg, L. (Ed.), The Chernobyl Fallout in Sweden: Results from a Research Programme on Environmental Radiology. Swedish Radiation Protection Institute, Stockholm, pp. 47–65. Finck, R.R., 1992. High Resolution Field Gamma Spectrometry and its Application to Problems in Environmental Radiology. Thesis, University of Lund, Department of Radiation Physics, SE-214 01, Malmo¨, Sweden. Gedcke, D., 2007. Simply managing dead time errors in gamma-ray spectrometry. Ortec, application note AN63. http://www.ortec-online.com/application-notes/ AN63.pdf. Gering, F., Hillmann, U., Jacob, P., Fehrenbacher, G., 1998. In situ gamma-spectrometry several years after deposition of radiocaesium, II. Peak-to-valley method. Radiation Environmental Biophysics 37, 283–291. ICRU, 1994. International Commission on Radiation Units and Measurements, Gamma-Ray Spectrometry in the Environment. ICRU Report 53, Bethesda, MD, USA. ICRU, 2006. International Commission on Radiation Units and Measurements, Sampling for Radionuclides in the Environment. ICRU Report 75, Oxford University Press. ISBN 0199211418. International Organisation for Standardisation, ISO, 1995. Guide to the Expression of Uncertainty in Measurement. Geneva, Switzerland. ISBN 92-67-10188-9.
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SGAB, 1986. Cs-137 ground deposition map over Sweden. Map 1, 2000000. Sowa, W., Martini, E., Gehrcke, K., Marschner, P., Naziry, M.J., 1989. Uncertainties of in situ gamma spectrometry for environmental monitoring. Radiation Protection Dosimetry 27, 93–101. Stark, K., Wallberg, P., Nyle´n, T., 2006. Post-depositional redistribution and gradual accumulation of 137Cs in a riparian wetland ecosystem in Sweden. Journal of Environmental Radioactivity 87, 175–187. Tyler, A.N., Sanderson, D.C.W., Scott, E.M., Allyson, J.D., 1996. Accounting for spatial variability and fields of view in environmental gamma ray spectrometry. Journal of Environmental Radioactivity 33, 213–235.