Measuring and modeling exposure from environmental radiation on tidal flats

ARTICLE IN PRESS

Nuclear Instruments and Methods in Physics Research A 537 (2005) 658–665 www.elsevier.com/locate/nima

Measuring and modeling exposure from environmental radiation on tidal flats T.J. Gould, C.T. Hess ERL, Department of Physics and Astronomy, University of Maine, 5709 Bennett Hall, Orono, ME 04469-5709, USA Received 16 April 2004; received in revised form 13 July 2004; accepted 21 July 2004 Available online 11 September 2004

Abstract To examine the shielding effects of the tide cycle, a high pressure ion chamber was used to measure the exposure rate from environmental radiation on tidal flats. A theoretical model is derived to predict the behavior of exposure rate as a function of time for a detector placed one meter above ground on a tidal flat. The numerical integration involved in this derivation results in an empirical formula which implies exposure rate / tan1 ðsin tÞ: We propose that calculating the total exposure incurred on a tidal flat requires measurements of only the slope of the tidal flat and the exposure rate when no shielding occurs. Experimental results are consistent with the model. r 2004 Elsevier B.V. All rights reserved. PACS: 29.40.Cs Keywords: High pressure ion chamber; Environmental radiation; Tides; Exposure rate; Gamma-ray flux

1. Introduction Of concern when monitoring environmental radiation is the exposure due to gamma rays from radionuclides found in soil. This work focuses on measuring environmental radiation in the vicinity of tides. A high pressure ion chamber placed on a tidal flat measures exposure rate from environmental radiation. These measurements investigate Corresponding author.

E-mail addresses: [email protected] (T.J. Gould), [email protected] (C.T. Hess).

the dynamic shielding effect of water due to the tide cycle and the effect of changing the solid angle over which the measurements are obtained. By integrating the photon flux over the tidal flat area, we determine the behavior of exposure rate as a function of the distance between the detector and the water. In time, this distance changes according to the tide cycle. Combining these two phenomena gives exposure rate as a function of time. This derivation results in an equation which contains the slope of a tidal flat and the exposure rate when no shielding occurs. With this equation, we calculate the total exposure absorbed by the

0168-9002/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2004.07.288

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detector over an interval of time. We present here the results from a tidal flat in East Sullivan, Maine on 26–27 June, 2003.

659

The exposure rate, DX =Dt; from a gamma emitting radionuclide is given by

the effects of scattering. Such values have been calculated by Beck et al. [2,3] and were used to calculate total exposure rates from soil samples obtained on site. Using d ¼ wðr  h=rÞ and integrating Eq. (2) over a and r yields Z S0 1 1 ema h=w dw: (3) F¼ 2 0 lw þ ms

DX A ¼G 2 (1) Dt R where G is the radionuclide specific gamma factor, A the source activity, and R the distance from the source [1]. Since A=R2 is proportional to the photon flux, F; we first find flux as a function of the distance from the water to determine exposure rate as a function of time in the vicinity of tides. According to Beck [2], the flux from photons of energy E distributed in the soil exponentially with depth is Z 2p Z p=2 Z 1 S0 ðl=rÞr d ms ðr h Þ w F¼ da e e 2 4pr 0 0 h=w

Generally, radionuclides that occur naturally, such as 40K, the uranium series, and the thorium series are distributed uniformly throughout the soil. For this case, l ¼ 0 [2]. In this derivation, we assume that only naturally occurring radionuclides contribute to the total flux. This assumption is justified by gamma spectrum analysis of soil samples. This analysis showed man-made radionuclides (137Cs and 60Co) to contribute o:001 mR=h at one meter above ground while those occurring naturally contribute ð7:56 1:17Þ mR=h:1 Eq. (3) then simplifies to Z S 0 1 ma h=w e dw (4) F¼ 2ms 0

2. Flux and exposure rate

h

ema w r2 sin y dr dy

ð2Þ

where S0 is the photon emission rate of soil in g=ðs cm3 Þ; r is the distance from detector in cm to an infinitesimal volume, dV, h the height of detector above ground in cm, y is the polar angle between r and h, w ¼ cos y; a is the azimuthal angle, d is the depth of dV beneath soil in cm, l is the reciprocal of the relaxation length of source activity in cm1 ; r is the soil density in g=cm3 ; and ma ; ms are the attenuation coefficients for photons in air and soil in cm1 : Although Eq. (1) is applicable to point sources while Eq. (2) pertains to the infinite half plane geometry, the multiplicative method of converting flux to exposure rate is still possible with the use of an appropriate constant similar to G: In this derivation we will refer to such constants as GE : However, Eq. (1) is still practical for detector calibration by using lead shielding to correct for scattering. We also note that Eq. (2) accounts for primary radiation only. To ultimately arrive at an exposure rate which accounts also for secondary radiation, we use values of GE designed to include

which requires evaluation by numerical integration. In simplifying Eq. (2), we integrate the angle a over the entire solid angle to include flux contributions from all directions. In certain situations, as when in the vicinity of water, a portion of the solid angle may be shielded from the detector, thus changing the area of integration. As the integrand of Eq. (2) is independent of a; changing the limits of integration of a changes only a multiplicative factor. If F0 is the flux integrated over the entire solid angle, then F ¼ F0 =4;

0papp=2

F ¼ F0 =3;

0pap2p=3

F ¼ F0 =2;

0papp:

For this work, we place a detector on a tidal flat such that at high tide the angle ranges from 0 to 1801, and the detector measures half the radiation as it would if placed in the vicinity of solid ground only (within a small correction to account for 1

Uncertainties for all results are one sigma values.

ARTICLE IN PRESS T.J. Gould, C.T. Hess / Nuclear Instruments and Methods in Physics Research A 537 (2005) 658–665

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photons that penetrate the surface of the water). Throughout the tide cycle, the distance from water to detector changes, requiring modification of the flux integration to describe detector readings as a function of time. We determine this distance from tidal charts that give the water height above mean lower low water (MLLW). From simple geometry, the distance between water and detector, z is

slope. Thus, for Eq. (2) to account for dynamical shielding by water, we modify the limits of integration over y and r. With respect to the lefthand side of Fig. 2, we use the laws of cosines and sines to obtain the equations  z 2 2hzb (6) r20 ¼ h2 þ þ sin a sin a and

H max  HðtÞ z¼ sin b

(5)

where HðtÞ is the water height above MLLW, H max the water height at high tide, and b the angle of slope of the tidal flat. Fig. 1 illustrates these parameters. We note that the angle b is exaggerated for clarity. Eq. (2) applies to an infinite half space geometry provided that source variations only occur with depth [2]. Since we are only concerned with naturally occurring sources uniformly distributed with depth, our premise is that Eq. (2) can be modified to describe the flux on a tidal flat of finite

z r0 ¼ ¼ r0 sin a sin y sinðp=2 þ bÞ

where r0 is the distance from the detector to the ground along r, and we have used small angle approximations for b: Combination of these two equations to solve for r0 gives  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h b sin y þ b2 sin2 y þ cos2 y r0 ¼ cos2 y hðb sin y þ cos yÞ ð8Þ ffi cos2 y while solving for sin y yields  1=2 z z2 2hzb h2 þ 2 þ sin y ¼ sin a sin a sin a

h β

z

Hmax H

MLLW

(10)

α

θ r z

z sin α

π +β 2 z sin α

(9)

which may be expressed in terms of tan y: Thus, the limits of integration are now " #   z 2zb 1=2 1 1þ 0pyptan t h sin a h sin a

Fig. 1. Schematic of water distance parameters.

h

(7)

α

Fig. 2. A side (left) and top (right) view of the HPIC on a tidal flat.

ARTICLE IN PRESS T.J. Gould, C.T. Hess / Nuclear Instruments and Methods in Physics Research A 537 (2005) 658–665

and h ðb tan y þ 1Þ r0 prp1 (11) cos y with b expressed in radians. Again, t and r0 are valid for small values of b ðp10 Þ where it is appropriate to approximate sin b b and cos b 1: On a tidal flat, one half of the detector faces the water, while the other half faces soil only. Thus, we write Eq. (2) as Z p Z p=2 Z 1 S 0 ms ðr h Þ ma h w e w sin y dr dy e F¼ da 4p 0 0 h=w Z 2p Z t Z 1 S0 ms ðrr0 Þ ma r0 þ e da e sin y dr dy 4p p 0 r0 Z 2p Z p=2 Z 1 S 0 ms ðrr0 Þ ma ðr0 lÞ e þ da e p t r0 4p emw l sin y dr dy

ð12Þ

where mw is the attenuation coefficient for photons in water, and l is the distance that photons must pass through water to reach the detector. For small values of b; we have   b r0 cos y  h z  l¼ (13) cos y b sin a

For the purpose of numerical integration, we define I as I

The second and third terms, collectively referred to as F2 ; simplify to Z p Z t S0 F2 ¼ da ema r0 sin y dy 4pms 0 0 # Z p=2

ema r0 elðma mw Þ sin y dy :

ð17Þ

Fig. 3 shows numerical integrations of Eq. (17) for photons of energy .1 MeV (ma ¼ 1:95  102 m1 ; mw ¼ 16:7 m1 ) and 2 MeV (ma ¼ 5:75  103 m1 ; mw ¼ 4:9 m1 ) [4]. In these integrations, we set h ¼ 1 m and b ¼ :12 rad (71). The curves fit to these values are of the form I ¼ a tan1 ðbzÞ þ c; where a, b, and c are constants. Table 1 lists the values of these constants. Also listed are values of R1 ms F1 =S 0 ð¼ 0 ema h=w dwÞ obtained by numerical integration. The dynamic geometry involved in this derivation results in an approximate instead of exact solution. The premise of this derivation is that flux

0.25

0.2

ð16Þ

I

0.15

hb  z  tan y  l¼ : (14) cos y h sin a Since the first term, F1 ; is a constant, we integrate it as half of the flat infinite plane and do not include corrections to account for the slope of the flat. Considering the solid angle effect, F1 is simply half the result from Eq. (4), Z S 0 1 ma h=w F1 ¼ e dw: (15) 4ms 0

t

Z t Z 1 p da ema r0 sin y dy 4p 0 0 # Z p=2 ma r0 lðma mw Þ þ e e sin y dy : t

which simplifies to

þ

661

0.1

0.05

0

2 MeV .1 MeV Fit Fit

0

5

10

15

20

25

30

z (m)

Fig. 3. Numerical integration of Eq. (17) for h ¼ 1 m and b ¼ :12 rad (71).

Table 1 Constants obtained from numerical integration of Eq. (17) E (MeV)

a

b ðm1 Þ

c

ms F1 =S0

.1 2

.11 .13

.82 .56

.02 .06

.23 .24

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T.J. Gould, C.T. Hess / Nuclear Instruments and Methods in Physics Research A 537 (2005) 658–665

as a function of time is

  S0 H max  HðtÞ 1 FðtÞ ¼ a tan b þ c þ F1 sin b ms (18) with  HðtÞ ¼ H sin

 2p t þ f þ H 0: T

(19)

The coefficients of Eq. (19) are properties of the tide cycle that are obtainable from tidal charts, where H is the amplitude of the cycle in m, T is the period of the cycle in min, f is the phase of the cycle in rad, and H 0 is an additive constant in m. For simplicity, we consider the constant c negligible in comparison to ms F1 =S 0 : To determine a, we consider the flux for large values of z. From Eq. (18) we have Z S 0 1 ma h=w F ¼ F1 þ F2 ¼ e dw 4ms 0 S0 þa tan1 ðbzÞ: ð20Þ ms For z ! 1; we expect F as given by Eq. (4), Z S 0 1 ma h=w F¼ e dw ¼ 2F1 : (21) 2ms 0 From Eqs. (20) and (21), we see that F2 ¼ F1 for large values of z. Since tan1 ðbzÞ ¼ p=2 for z ! 1; Z S0 p S 0 1 ma h=w ¼ F1 ¼ F2 ¼ a e dw: (22) ms 2 4ms 0 Equation (22) gives the coefficient a as Z 1 1 ma h=w a¼ e dw 2p 0 so that F may now be written as

 Z S 0 1 ma h=w 1 1 þ tan1 ðbzÞ : e dw F¼ 2 p 2ms 0

(23)

(24)

Of note is that direct calculations of a from Eq. (23) for .1 and 2 MeV photons yield .146 and .154, respectively. Discrepancies between these values and those listed in Table 1 arise due to our treatment of F1 as part of the infinite plane, which resurfaces in the right-hand side of Eq. (23). Since

our goal is to replace a with a more meaning full coefficient (the total exposure from soil) that is obtained from experimental data, we consider these discrepancies insignificant. From Eq. (1) the total exposure rate is X DX ¼ 4p GE i Fi (25) Dt i where the sum is over photon energies of significant contribution to the total measurement. Finally, we combine Eqs. (24) and (25), along with a cosmic ray contribution, to get

  DX DX 0 1 1 H max  HðtÞ ¼ þ tan1 b Dt sin b Dt 2 p DX c þ ð26Þ Dt where X GE S 0 Z 1 DX 0 i i ¼ 4p emai h=w dw Dt 2msi 0 i

(27)

is the exposure rate as measured when no shielding occurs. Since the detector also measures the exposure from cosmic rays, we add the term, DX c =Dt; to account for that contribution to the total measurement. Casting Eq. (26) in terms of DX 0 =Dt requires that we approximate that the coefficient b is the same for all energies. We make this assumption since we ultimately obtain this coefficient by fitting Eq. (26) to experimental data. Equation (26) gives the total exposure rate as a function of time as measured by a detector on a tidal flat located at the high tide water level.

3. Methods A general electric Reuter–Stokes model RSS111 high pressure ion chamber (HPIC) placed one meter above ground on a tidal flat measures exposure rate in time throughout the cycle of the tide. The analog output of the detector interfaces to a PC laptop via the serial port. A program written in Agilent VEE One Lab V6.01 records the time of day and exposure rate in 1 min intervals. Each recorded exposure rate is the average of 10 successive measurements taken one second apart.

ARTICLE IN PRESS T.J. Gould, C.T. Hess / Nuclear Instruments and Methods in Physics Research A 537 (2005) 658–665 3.5 Ln(Net Exposure Rate, ∆X/∆t (µR/hr))

The standard deviation of these 10 values is recorded as the uncertainty in the measurement. Water heights are obtained from the University of South Carolina’s Tide and Current Predictor2 for a location closest to the actual site of interest. We measure the slope of tidal flats with a laser level and tape measure. Numerical integrations are performed using Mathematica 4.2.3

663

3 2.5 2 1.5 1 0.5 0

4. HPIC calibration -0.5 -0.8

and H max ¼ 3:28 m: We note that this water height data is specific to Sullivan, Maine, and hence, a phase difference may occur between Eq. (28) and the actual tide cycle observed at site. Exposure rate is plotted as a function of the distance between detector and water in Figs. 6 and 7 for incoming and outgoing tides, respectively. The curves fit to 2

http://tbone.biol.sc.edu/tide. Wolfram Research Inc., 100 Trade Center Dr., Champaign, IL 61820, USA. 3

-0.2

0

0.2

Fig. 4. HPIC calibration with

0.4

0.6

0.8

137

Cs source.

14

∆X/∆t H

13

3.5 3

12

2.5

11 2 10 1.5 9 1

8

0.5

7 6 18:00

We present here results from a tidal flat in East Sullivan, Maine on 26–27 June, 2003. Fig. 5 shows exposure rate and water height in time to illustrate the dynamic shielding effect of water. A curve fit to the water height data gives   :008 HðtÞ ¼ ð1:51 mÞ sin t þ :028 þ 1:77 m (28) min

-0.4

20:00

22:00

00:00

02:00

04:00

06:00

0 08:00

Water Height Above Mean Lower Low Water, H (m)

5. Experimental results

-0.6

Ln(Distance, R (m))

Exposure Rate, ∆X/∆t (µR/hr)

The HPIC was calibrated on 9 June, 2003 with a 17:2 mCi 137Cs gamma source. Calibration consisted of measuring exposure rate as a function of the distance between source and detector. Net exposure rates were determined and corrected to account for the 93% spectral sensitivity of the detector for 137Cs [5]. Fig. 4 shows the calibration data. According to Eq. (1) the intercept of the straight line fitted to this data is lnðGAÞ: From the intercept, we calculate GA ¼ ð5:57 :14Þ mR m2 =h: From the known activity of the source, we calculate GA ¼ :33 mR m2 =h mCi  17:2 mCi ¼ 5:68 mR m2 =h:

Time: June 26-27 2003

Fig. 5. Exposure rate and water height.

1 these data sets are of the form DX Dt / tan ðzÞ; in agreement with the results of the numerical integration of Eq. (17). The water distance z was calculated using Eq. (5). The value of b was measured to be 6.761. In Fig. 8, we fit two curves to the experimental data using Eq. (26). Table 2 lists the coefficients obtained from these fits. For Fit 1, we use Eq. (28). In Fit 2, we modify the phase angle in Eq. (28) so that high tide occurs when the exposure rate is a minimum. The total exposure, X ; is obtained by integrating these equations over the duration of the measurements ð724 min 12 hÞ: A direct calculation using the exposure rate data points gives the total exposure

ARTICLE IN PRESS T.J. Gould, C.T. Hess / Nuclear Instruments and Methods in Physics Research A 537 (2005) 658–665

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Table 2 Exposure rate curve-fit coefficients

12

DX 0 Dt

9:09 :13 9:28 :10

Fit 1 Fit 2

8

b ðm1 Þ

DX c Dt

:32 :02 :36 :01

2:50 :12 2:27 :09

ðmR=hÞ

X ðmRÞ 122:1 4:6 122:3 3:3

6 4 12 ∆X/∆t Fit

2 0 0

5

10

15

20

25

z (m)

Fig. 6. Exposure rate for incoming tide.

14

Exposure Rate, ∆X/∆t (µR/hr)

ðmR=hÞ

10

Exposure Rate, ∆X/∆t (µR/hr)

Exposure Rate, ∆X/∆t (µR/hr)

14

11

10

9

0m 0.5 m 1m 2m 5m

8

12 7

10

0

200

400

600

800

1000

1200

Elapsed Time, t (min) 8

Fig. 9. Exposure rate as a function of time for varying distance between detector and water level at high tide.

6 4 ∆X/∆t Fit

2 0 0

5

10

15

20

25

z (m)

for the duration of the measurements as ð122:2 3:5Þ mR: One can see that the calculation is robust with respect to small changes in the three coefficients.

Fig. 7. Exposure rate for outgoing tide.

6. Discussion

Exposure Rate, ∆X/∆t (µR/hr)

13 12 11 10 9 8 7

Data Fit 1 Fit 2

6 0

100

200

300

400

500

600

700

800

Elapsed Time, t (min)

Fig. 8. Exposure rate as a function of time with fitted curves.

Fig. 5 reveals the necessity for special treatment of radiation measurements obtained in the vicinity of ocean tides. A single exposure rate measurement obtained at high tide of 6 mR=h leads to a calculation of 72 mR total exposure over 12 h. Similarly, a single measurement at low tide of 12 mR=h implies 144 mR over the same time period. Obviously, calculations which do not account for the shielding effect of water lead to spurious results. This work proposes that the total exposure on a tidal flat may be calculated using Eq. (26), requiring only measurements of the slope of the tidal flat and exposure rate when no shielding occurs. Water height data is obtained from tidal

ARTICLE IN PRESS T.J. Gould, C.T. Hess / Nuclear Instruments and Methods in Physics Research A 537 (2005) 658–665 Table 3 Total exposure over 12 h

665

Acknowledgements

z0 ðmÞ

X ðmRÞ

0.0 0.5 1.0 2.0 5.0

122:1 4:6 123:6 4:7 125:0 4:8 127:2 4:8 131:2 4:8

We especially thank V.E. Guiseppe for assistance in instrumentation and fieldwork. Thanks to D.J. Breton, Dr. G.F. Bernhardt, and Dr. C.W. Smith for insightful discussions.

References charts and the exposure rate caused by cosmic rays is taken as constant. So far, this analysis is specific to a detector placed at the high tide water level. We generalize to any location by adding a constant term, z0 ; to Eq. (5) where, z0 is the distance between the detector and high tide water level. Fig. 9 generalizes Fit 1 for different values of z0 ; while Table 3 gives the corresponding total exposure over 12 h as obtained by integration of the functions.

[1] K.S. Krane, Introductory Nuclear Physics, 6th ed., Wiley, New York, 1986. [2] H.L. Beck, et al., In Situ Ge(Li) and Na(Tl) gamma-ray spectrometry, Technical report, HASL-258, New York, September 1972. [3] H.L. Beck, Exposure rate conversion factors for radionuclides deposited on the ground, Technical report, EML378, New York, July 1980. [4] H. Cember, Introduction to Health Physics, 2nd ed., McGraw-Hill, New York, 1983. [5] RSS-111 Environmental Monitoring Station Operation Manual, GE Reuter-Stokes, Twinsburg, OH.