Supplementary materials

1.1. Monte Carlo simulations

Monte Carlo simulations (Harrison, 2009; Likar et al., 2004; Malins et al., 2015; Narayan et

al., 2012) are sometimes the only feasible way to resolve real-world radiation transport

problems as many geometries are often too complex to model within a calibration facility or

problems are encountered in the complete removal of background contributions (Kirk, 2010).

Furthermore, results derived from physical calibration tend to only describe one specific

geometry due to cost restrictions and controls on radioactive source dispersal (Maučec et al.,

2009). In this application, Monte Carlo codes were the only feasible means to optimise the

lead shielding design and correct the count rate with respect to variables such as tree diameter,

wood density and radial distribution of 137Cs throughout the tree. The software package Monte

Carlo N-particle (MCNP5) code released by Los Alamos Laboratories in the United States

was used (Briesmeister, 1993). It was chosen for its flexibility and the fact it provides a

relatively high-level interface whereby the user can define fairly complex geometries, source

descriptions and collect specified response data in the form of tallies. The program operates

by providing input cards, coded in its own custom language, that describe the system’s

geometry and the materials contained within it. The number of source starting particles is

also described alongside their energy and spatial distribution and finally tally specifications

are used to collect relevant information about certain components of the system. Only the 662

keV photon, emitted from its daughter 137Ba with a probability of 0.85 per decay, was used in

simulations. Background contributions from natural radionuclides were not considered as the

number of counts within the 137Cs dwarfed other contributions in that spectral area.

1.2. Detector and shield

Arguably the most sensitive component of the entire model was the detector and its shield

given that small deviations in geometry, materials or density from the actual detector could

lead to significant systematic errors in estimated count rates (Maučec et al., 2004). Hence,

considerable time was taken to recreate the manufacturer’s detector specifications (released

by Bicron) within the MCNP5 environment. A cross-sectional diagram can be found in the

supplementary materials. The active volume was modelled as a 76 76 mm cylinder of

NaI:Tl (density of 3.65 g cm-3), which was surrounded by 2 mm of aluminium (density of 2.70

g cm-3) outer. The complex geometry of the photomultiplier tube was simplified to the

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protective aluminium outer canning (2 mm) with an empty vacuum contained inside. The

multichannel analyser was described as 5 mm of aluminium. The dimensions of the lead

shield and steel clasps (used to hold the detector in place) were measured precisely using

callipers and a tape measure. Recorded measurements alongside its relative position

surrounding the detector were carefully encoded into MCNP5 geometry. A density of 11.34

and 8.05 g cm-3 was used for lead and steel, respectively. A detailed diagram can be found in

the supplementary materials.

To simulate the response of a gamma-ray detector the F8 tally within MCNP5 was

implemented to produce a pulse height distribution. Gaussian Energy Broadening was applied

to this tally to recreate the statistical spread of photon across the spectrum brought about by

imperfect conversion of photons to electrical signal by the detector (de Groot et al., 2009). To

ensure that simulated spectral responses were comparable to ones obtained by the actual

detector a simple benchmark experiment was undertaken where a 0.3 MBq 137Cs point source

was placed 0.3 m in front of the detector. The number of counts in the peak at 662 keV

recorded in lab experiments were found to be within 1% of Monte Carlo simulation.

1.3. Tree model

It was determined that full energy photons where likely to be out of the detector’s field of

view beyond 2 m, above and below the detector, given the angle of the detector and amount of

shielding presented by the lead shield on its sides of the detector. Consequently, the tree

model was 4 m long with the detector situated in the middle. For each geometry, the diameter

of the tree was varied between 10 and 140 cm, which spanned the diameter range that was

present at the sampling sites in the PSRER. Unlike the circumference of the tree that could be

easily measured in the field, parameters such as wet wood density and bark thickness could

not be measured without causing damage to the tree. Subsequently, to account for natural

variation that was likely to be encountered in the field, these parameters were assumed to

follow normal distributions (Auty et al., 2014). A mean and standard deviation of 0.8 g cm-3

and 0.13 g cm-3, respectively, was used for green wood density for the models. Values were

estimated from historical records maintained by the PSRER. Another factor that was likely to

change between trees depending on the age of the tree was the bark thickness. Bark thickness

variation data was not available within the PSRER, therefore a simplified model based upon

Strandgard and Walsh’s (2011) data was used to estimate bark thickness for a given tree

diameter. Wet wood density and bark thickness were randomly sampled for individual

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diameters based upon these distribution models providing natural variance likely to be found

in the field.

To allow for the distribution of contamination within the tree to be changed at the final and

accounted for a specified diameter of tree, the tree was split into 1 cm layers and separate

simulations were run for individual layers. This was performed for each set of sampled of

bark thickness, wet wood density and diameter. Weighting of individual layers could then be

performed to enable a projected distribution to be modelled (Figure 1).

Figure 1. Cross-sectional diagram of detector setup and tree

1.4. Ground model

The ground model aimed to develop the ground calibration coefficient (Gcal), which was

derived from the ratio of unshielded (Gu) and shielded (Gs) counts coming from the ground as

a function of changing tree diameter (eq. 3). Estimating ground activity was not the primary

focus of this study, consequently only a simplified model of the ground was used, and no

attempt was made to distinguish activities in field results using the final model. The reason for

this was that the vertical burial depth distribution was likely to change significantly on a

different spatial scale making estimation difficult without the peak-to-valley method. The

model consisted of a uniform disc of 137Cs source extending 10 m horizontal to the tree and to

a depth of 10 cm. The soil was modelled on the standard soil composition outlined by Beck et

al. (1972) and had a density of 1.3 g cm-3.

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Figure 2. Example exponential radial distribution

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1.5. Sample sites

Table 1. Soil sample locations and dose rate measurements at the three field sites. Soil 137Cs

activities given in Bq/kg and dose rates in µSv/hr at 1 m.Tulgovichskoe Vorotetskoe Krukovskoe

Coords. Soil activity

(Bq kg-1)

Dose rate

(µSv hr-1)

Coords. Soil

activity

(Bq kg-1)

Dose rate

(µSv hr-1)

Coords. Soil activity

(Bq kg-1)

Dose

rate

(µSv

hr-1)

51°52,731'

29°38,112'

996 ± 199 0.35 51°45,528'

30°00,808'

4450 ±

890

1.24 51°33,371'

30°13,194'

50500 ± 11000 10.1

51°52,744'

29°38,130'

997 ± 199 0.29 51°45,521'

30°00,836'

4340 ±

868

1.25 51°33,365'

30°13,218'

70600 ± 14100 12.5

51°52,732'

29°38,144'

1030 ± 205 0.31 51°45,507'

30°00,827'

6060 ±

1212

1.25 51°33,356'

30°13,213'

34100 ± 6810 9.8

51°52,723'

29°38,132'

1240 ± 248 0.29 51°45,512'

30°00,800'

4940 ±

987

1.04 51°33,355'

30°13,187'

58200 ± 11600 10.5

51°52,734'

29°38,129'

1030 ± 205 0.33 51°45,516'

30°00,817'

4810 ±

960

1.15 51°33,360'

30°13,198'

35400 ± 7070 8.8

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Figure 3. In situ detector in position.

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1.6. Transfer factors

Table 2. Cs-137 concentration ratios from IAEA (2014). AM – arithmetic mean, AMSD –

standard deviation of the arithmetic mean, GM – geometric mean, GMSD – standard

deviation of the geometric mean.

Wildlife

group

Concentration ratio (CR) Bq/kg,fresh weight whole

organism:Bq/kg, dry weight soil

AM AMSD GM GMSD Min. Max N

Trees 0.14 0.24 0.075 3.1 0.0012 1.8 487

Trees-

broadleaf0.14 0.22 0.075 3.1 0.0012 1.3 252

Trees

coniferous0.15 0.25 0.075 3.2 0.0012 1.8 235

Table 3. Values of 137Cs activity in trees at the three sites based on the soil data available for

each site and application of the appropriate concentration ratio. Soil and tree activities in

Bq/kg

Tulgovichskoe Vorotetskoe Krukovskoe

Soil

activity

Birch and

Pine activity

Soil activity Birch and Pine

activity

Soil activity Birch and Pine

activity

996 ± 199 60 - 90 4450 ± 890 267 - 400 50480 ± 11000 2960 – 4610

997 ± 199 60 - 90 4340 ± 868 260 - 390 70550 ± 14100 4230 – 6350

1030 ± 205 62 - 93 6060 ± 1212 364 - 545 34070 ± 6810 2040 – 3070

1240 ± 248 74 - 112 4940 ± 987 296 - 445 58200 ± 11600 3500 – 5240

1030 ± 205 62 - 93 4810 ± 960 289 - 434 35400 ± 7070 2130 - 3190

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Table 4. Cs-137 wood and bark activity in trees sampled

Site ID Tree

Circ.

(cm)

Specie

s

Bark activity Wood activity

Krukovskoe 1 141 Pine 22390 ± 4640 3410 ± 705

Krukovskoe 2 122 Pine 17370 ± 3600 3200 ± 680

Krukovskoe 4 96 Pine 44800 ± 9240 4010 ± 840

Krukovskoe 5 82 Pine 28600 ± 5900 3600 ± 750

Vorotetskoe 12 114 Pine 2320 ± 492 578 ± 123

Vorotetskoe 13 169 Pine 1280 ± 275 575 ± 125

Vorotetskoe 15 178 Pine 3310 ± 693 1010 ± 209

Tulgovichskoe 21 110 Birch 268 ± 57 54 ± 12

Tulgovichskoe 22 152 Pine 274 ± 61 48 ± 11

Tulgovichskoe 24 213 Pine 312 ± 66 67 ± 16

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Table 5. Activity of 137Cs in trees at field sites derived from sampling and in situ measurement. Activity estimates derived from concentration

ratios provided for comparison. Activities provided in Bq/kgCore samples In situ gamma-ray spectrometry Mobile gamma-ray spectrometry Transfer factor

Site ID Tree Circ.

(cm)

Species Wood activity Wood activity Ground activity Ground activity Depth (cm) Wood activity

Krukovskoe 1 141 Pine 3414 ± 705 3310 ± 1050 7180 ± 2230 5302 ± 636 6 ± 3 2044 – 6349

Krukovskoe 2 122 Pine 3202 ± 680 3930 ± 1270 6560 ± 2160 5302 ± 636 6 ± 3 2044 – 6349

Krukovskoe 3 122 Pine 3202 ± 680 4900 ± 1610 5770 ± 1900 5302 ± 636 6 ± 3 2044 – 6349

Krukovskoe 4 96 Pine 4014 ± 840 4490 ± 1550 7240 ± 2620 5302 ± 636 6 ± 3 2044 – 6349

Krukovskoe 5 82 Pine 3600 ± 750 4280 ± 1450 7110 ± 2730 5302 ± 636 6 ± 3 2044 – 6349

Krukovskoe 6 117 Pine - 4160 ± 1400 5730 ± 1920 5302 ± 636 6 ± 3 2044 – 6349

Krukovskoe 7 118 Pine - 3270 ± 1100 5880 ± 1970 5302 ± 636 6 ± 3 2044 – 6349

Krukovskoe 8 138 Pine - 3200 ± 1010 6770 ± 2120 5302 ± 636 6 ± 3 2044 – 6349

Krukovskoe 9 119 Pine - 4110 ± 1370 7180 ± 2390 5302 ± 636 6 ± 3 2044 – 6349

Krukovskoe 10 87 Pine - 5330 ± 2010 8240 ± 3100 5302 ± 636 6 ± 3 2044 – 6349

Krukovskoe 11 120 Pine - 3670 ± 1220 6180 ± 2050 5302 ± 636 6 ± 3 2044 – 6349

Vorotetskoe 12 114 Pine 578 ± 123 521 ± 177 794 ± 270 509 ± 91 9 ± 10 260 - 545

Vorotetskoe 13 169 Pine 575 ± 125 463 ± 162 742 ± 215 509 ± 91 9 ± 10 260 - 545

Vorotetskoe 14 169 Pine 575 ± 125 445 ± 156 773 ± 224 509 ± 91 9 ± 10 260 - 545

Vorotetskoe 15 178 Pine 1010 ± 209 435 ± 158 615 ± 174 509 ± 91 9 ± 10 260 - 545

Vorotetskoe 16 114 Pine - 593 ± 201 778 ± 264 509 ± 91 9 ± 10 260 - 545

Vorotetskoe 17 111 Pine - 417 ± 143 681 ± 234 509 ± 91 9 ± 10 260 - 545

Vorotetskoe 18 112 Pine - 382 ± 131 716 ± 245 509 ± 91 9 ± 10 260 - 545

Vorotetskoe 19 89 Pine - 518 ± 194 896 ± 336 509 ± 91 9 ± 10 260 - 545

Vorotetskoe 20 99 Pine - 529 ± 190 758 ± 272 509 ± 91 9 ± 10 260 - 545

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Tulgovichskoe 21 110 Birch 54 ± 12 125 ± 44 172 ± 60 121 ± 62 BDL 60 - 112

Tulgovichskoe 22 152 Pine 48 ± 11 96 ± 29 138 ± 42 121 ± 62 BDL 60 - 112

Tulgovichskoe 23 152 Pine 48 ± 11 94 ± 29 141 ± 43 121 ± 62 BDL 60 - 112

Tulgovichskoe 24 213 Pine 67 ± 16 70 ± 19 143 ± 38 121 ± 62 BDL 60 - 112

Tulgovichskoe 25 211 Oak - 87 ± 23 178 ± 47 121 ± 62 BDL 60 - 112

Tulgovichskoe 26 185 Pine - 65 ± 18 163 ± 45 121 ± 62 BDL 60 - 112

Tulgovichskoe 27 169 Pine - 76 ± 23 137 ± 41 121 ± 62 BDL 60 - 112

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