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G. Bijloos1,2, L. Tubex1, J. Camps1, J. Meyers2

1 SCK•CEN, Belgian Nuclear Research Centre, Boeretang 200, 2400 Mol, Belgium

2 Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300, 3000

Leuven, Belgium

The effect of terrain modeling on simulated dose rates

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Near-range atmospheric dispersion can be modelled on various ways

Ø Different treatments of atmospheric conditions and terrain effects

Do dose rate simulations benefit from improved physical descriptions?

Problem statement

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High

Low

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n Methodologyn Results

n Simulation of Ar-41 routine releasesn Downstream calculations for a 2 km fetch

n Conclusions

Content

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!"!# + % ⋅ '" = ' ⋅ )'" + *+(- − -/), ∀- ∈ 4 ⊂ ℝ

7 (1)with": the concentration field [;7]%: the wind field [>/@]): the eddy diffusivity [>A/@]*: the source strength [;]4: the simulation domain

Step 1: solve " from equation (1) for the near range around the sourcen buildings are omitted

n terrain and atmospheric conditions are incorporated through the choice of % and )

Methodology

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Model ! " methodology

Different choices of ! and " lead to different modelsn Assume a neutral atmospheren Wind field is assumed to be uniform in the horizontal plane

Methodology

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Model ! " methodologyGaussian model constant:

# $ = #&Pasquill-Gifford (PG)Bultynck-Malet (BM)(Tracer experiments)

Analytical solution from 1

(MATLAB)

1 Yi C. 2008. Momentum transfer within canopies. J. Appl. Meteor. Climatol. 47: 262-275.

Model ! " methodologyGaussian model constant:

# $ = #&Pasquill-Gifford (PG)Bultynck-Malet (BM)(Tracer experiments)

Analytical solution from 1

(MATLAB)Particle model power law:

# $ ∝ $&.**Taylor’s statistical turbulence theory

Solve SDE with Euler-Maruyama scheme(MATLAB)

Model ! " methodologyGaussian model constant:

# $ = #&Pasquill-Gifford (PG)Bultynck-Malet (BM)(Tracer experiments)

Analytical solution from 1

(MATLAB)Particle model power law:

# $ ∝ $&.**Taylor’s statistical turbulence theory

Solve SDE with Euler-Maruyama scheme(MATLAB)

Vegetation canopy dispersion model

similarity scaling (>canopy)≈ solve NS eqn1(in canopy)

Standard Gradient Hypothesis

Finite volume method(OpenFOAM)

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Step 2: calculate the ambient gamma dose rates "̇# due to the gamma energy released

per disintegration $# %&' w.r.t. detector location () ∈ ℝ,

̇"# =./012$#

44555

6

7 0 8 (

8 ( 9&:;< ( = ( d( , 8 ( = ( − (′ 9

with

./ = 1.6×10:,GH ⋅ JK ⋅ %&':L a unit conversion factor

012: the absorption coefficient for air [O9/JK]7: the buildup factor0: the linear attenuation coefficient in air [O:L]⋅ 9: the Euclidean norm

Kenis K, Vervecken L, Camps J. 2013. Gamma dose assessment in near-range atmospheric dispersion simulations. SCK•CEN Reports; No. ER-242. 1:26 p.

Methodology

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n Methodologyn Results

n Simulation of Ar-41 routine releasesn Downstream calculations for a 2 km fetch

n Conclusions

Content

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n Dose rate measurements for 7 locations on SCK•CEN site (Mol, Belgium)n Ar-41 releases from the BR1 through the chimney (60 m)

n Data was also distributed in context of the NERIS Atmospheric Dispersion Modelling (ADM) experiment (J. Camps, Dublin 2018 workshop)

SCK•CEN sitecase study

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BR1

chimney

SCK•CEN forest

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Quantile = cut points that divide the range of a probability distribution into intervals with equal probabilities

Simulation of Ar-41 routine releasesQ-Q plot

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Gaussian models are biased + underestimate the observed variance

outliers ?

Particle model seems to perform the best

Canopy model underpredictsoccurrence of dose rates > 120 !"#/ℎ

Gauss (PG) model is biased, but variance is correctly estimated

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Above 100 nSv/h: mainly underestimations

Simulation of Ar-41 routine releasesOutliers?

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Statistical measures [Chang & Hanna (2004)]: let the subscript ! denote the observations and " the predictions, then

VG = exp ln,̇-,/,̇-,0

1

, FAC5 = fraction of data that satisfy15≤,̇-,/,̇-,0

≤ 5

Additionally, also a hypothetical ground release (10 C) was assumed for the same meteorological data as for the stack release.

Findings

n Stack release: 75% < FAC2 < 90 %, FAC10 ≈ 100% (w.r.t. measurements)

Simulation of Ar-41 routine releasesStatistical measures

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Release height [m]

L̇M,N L̇M,O PQ [-] RSTU [-] RSTVW [-]

60 Gauss (PG) Canopy 1.20 0.94 1.0

10 Gauss (PG) Canopy 2.52 0.39 1.0

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n Methodologyn Results

n Simulation of Ar-41 routine releasesn Downstream calculations for a 2 km fetch

n Conclusions

Content

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Concentration discrepancy is much bigger close to the source than for dose rateØ concentration stronger influenced by terrain roughness modeling

Downstream calculations for a 2 km fetchRatio’s at ground level

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Black = concentration ratioRed = dose rate ratio

60 m release (-)10 m release (--)

Ratio = !"#$$ (&!)(")*+, if ≥ 1Ratio = − (")*+,!"#$$ &! if < −1

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n Higher roughness ⇒ concentration maximum closer to sourcen Location of max. dose rate is stronger influenced by the source than by the max.

concentration

Downstream calculations for a 2 km fetchGround profiles

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Low roughness: dose rate doesn’t scale with ground concentration

60 m release

Black = concentrationRed = dose rate

Canopy (-)Gauss PG (--)

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The canopy and the Gaussian model produce quite different concentration

distributions for both release heights

Downstream calculations for a 2 km fetchNon-dimensional ground concentration distributions

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ground release

stack release

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Closer agreement between the models about the location and value of the max. dose rate than about the max. concentration!

Downstream calculations for a 2 km fetchDiscussion about the maximum values

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Max. conc. Location [m] Ratio [-]Release height [m]

Canopy Gauss (PG) !"#$%&'"())

60 238 1369 2.610 1 155 3.1

Max. dose Location [m] Ratio [-]Release height [m]

Canopy Gauss (PG) !"#$%&'"())

60 191 310 1.410 0.3 90 2.1

Max. conc. Location [m] Ratio [-]Release height [m]

Canopy Gauss (PG) !"#$%&'"())

60 238 136910 1 155

Max. dose Location [m] Ratio [-]Release height [m]

Canopy Gauss (PG) !"#$%&'"())

60 191 31010 0.3 90

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n Methodologyn Results

n Simulation of Ar-41 routine releasesn Downstream calculations for a 2 km fetch

n Conclusions

Content

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Despite the different terrain parameterizations, all the three models were capable of

n Predicting more than 75% of the dose rates within a factor twon Predicting the right order of magnitude of the dose rates

⇒ dose rates are robust quantities to estimate⇒ interesting property for source inversion

Conclusions (1)

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An improved physical terrain parametrization can still be beneficial

n It reduces the bias and improves the variance prediction of the dose rates

n More important further downstream (>1 km): dose rates were not found to be

more robust there than concentrations

n Factor 2 – 5 difference between canopy and open field

n Strong influence on the location and value of the max. concentration

n Important for licensing of nuclear installations

Conclusions (2)

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Thank you!

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