Relation between radon in schools and in dwellings: a case study in a rural region of Southern – the “Onion Study”

P. Bossew 1, Z.S. Žuni ć 2, C. Carpentieri 3, N. Veselinovi ć 2, G. Venoso 3, T. Tollefsen 5, S. Antignani 3, P. Kolarž 4, V. Udovi čić4, R. Banjanac 4, F. Bochicchio 3

1 German Federal Office for Radiation Protection, Köpenicker Allee 120-130, 10318 Berlin, Germany; [email protected] 2 Institute of Nuclear Sciences “Vinca”, University of Belgrade, P.O. Box 522, 11000, Belgrade, Serbia 3 Italian National Institute of Health, Viale Regina Elena 299, 00161 Rome, Italy 4 Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia 5 Institute for Transuranium Elements, European Commission - DG Joint Research Centre, Via E. Fermi 2749, 21027 Ispra (VA), Italy Rationale & background - 1

• question 1: is there a statistical relationship between indoor Rn concentrations in dwellings (C) and schools (S) at nearby locations? (it can be expected for physical reasons)

• question 2: if so, how can it be quantified? Can C and S be predicted from each other?

Onion1-SEERAS-pb140525 2 of 16 Rationale & background - 2

-380000 • Background 1: Kriging school surveys are easier -400000 Bq/m³ than surveys of dwellings; -420000 600 identification of Rn prone Serbia 550 -440000 500 Vlasotince areas and estimates of Rn in 450 -460000 Bojnik dwellings from Rn in schools Crna Trava 400 350 -480000 would be practical. Lebane Surdulica Vladicin Han 300 Vranje BG • Background 2: -500000 250 For S Serbia a “school Rn” Medveda 200 -520000 150 XK Bujanovac map has been created. Can 100 Borsilegrad it be used for assessing -540000 50 Trgoviste

indoor Rn risk in dwellings? -560000 Presevo MK • Background 3: 980000 1000000 1020000 1040000 1060000 1080000 1100000 1120000 980000 EU-BSS treats dwellings Bossew P. et al (2014): Geographical distribution of the annual mean and workplaces equally. radon concentrations in primary schools of Southern Serbia e application of geostatistical methods. J. Environmental Radioactivity 127, 141-148

Onion1-SEERAS-pb140525 3 of 16 problem & strategy

• main problem: schools and dwellings not at same location ⇒ how to compare them? Previous investigations of several authors: no or little relationship. • strategy: small project designed such that a relationship can likely be noticed ... if it exists.

Onion1-SEERAS-pb140525 4 of 16 The “onion project”

-390000 • Sokobanja municipality: Jošanica -392000 Vrmdza Mužinac 12 villages / towns, in -394000

each one primary school; Žuckovac -396000 Beli Potok 108 dwellings (living Citluk -398000 rooms, ground floor). Soko Banja -400000 Rn concentrations, annual -402000 20 to 50 50 to 100 mean, 2012-2013. TE 100 to 200 -404000 Rn, Bq/m³ 200 to 300 detectors, CR-39, Italian -406000 National Institute of Jezero -408000 Health. 1022000 1026000 1030000 1034000 1038000 1042000

• Houses selected in spatial 1 0.9 1000 relation to school in 0.8 ⇒ 0.7 “distance shells” 0.6 500 realized “onion” design, to 0.5 planned 0.4 facilitate recognition of 0.3 0 0.2 cumulativehouses of fraction relation schools ~ dwelling 0.1 0 -500 as function of distance. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 area of circle around school (km²)

-1000

towns projected on each other; centre=school -1000 -500 0 500 1000 Onion1-SEERAS-pb140525 5 of 16 Examples

Josanica

Blendija

Onion1-SEERAS-pb140525 6 of 16 methods

• @ question 1 (qualitative): - collocation C(x) to locations of S(x’) - aggregation of C(x i) into towns - cross-variography (~ correlation C(x)~S(x’) in dependence of distance (x,x’)) - reduction to univariate : R:= ratio C(x)/S(x’) in dependence of distance (x,x’) • @ question 2 (quantitative): - evaluation of ratio R seems easiest; - bivariate association / correlation measures, joint distribution (C,S), conditional distributions, statistics on these. - cokriging etc. does not seem appropriate for this case.

In any case: quite a bit of statistics necessary.... Will not be presented here see article (in preparation)

Onion1-SEERAS-pb140525 7 of 16 results 1 - qualitative

collocation, home estim. 5.5aggregation into towns: 2.3 at school location: 5.3 2.2 5.1

2.1 4.9

2 4.7

1.9 4.5 4.3 1.8 4.1 ln(school,Bq/m³) 1.7 3.9 log10(homesBq/m³) estim., 1.6 3.7

1.5 3.5 1.5 1.7 1.9 2.1 2.3 2.5 3.5 3.7 3.9 4.1 4.3 4.5 4.7 log10(school, Bq/m³) ln(GM(home), Bq/m³)

0.45

0.4 All methods show:

0.35 1 there is a relation between 0.3 2 3 0.25 4 dwellings and schools! 0.2 5 7

Gamma ((Bq/m³)²) Gamma 0.15 8 9 0.1 Clark-type pseudo-crossvariogram, 10 γ (α) α 0.05 model *12 (h):=(1/2) E[(Z 1(x)-Z2(x+h)) ]; α 0 Z1=dwelling, Z 2=school, here =2 0 100 200 300 400 500 600 700 800 900 1000 9 estimates with different estimation parameters lag (m)

Onion1-SEERAS-pb140525 8 of 16 lagged ratio

γ (1) lagged ratio q(h) := E[Z 1(x)/Z 2(x+h)] = 2 *12 (h) of log Z, h = distance between locations of observations z 1 and z 2 cumulative version: Q(h):= E[Z 1(x)/Z 2(x‘): |x-x‘| ≤h] probabilistic: P(a,h) := prob(Z 1(x)/Z 2(x‘))>a: |x-x‘| ≤h → P(a,h)=prob(dwelling ≥ a · school | distance ≤h) → prob(dwelling ≥ threshold | school) = P(threshold/school, h) if Q(h) ~ LN: prob(dwelling ≥ threshold | school) = 1 - Φ((ln(thresh/school)-µ)/ σ) Φ= standard normal, µ=ln(GM), σ=ln(GSD) µ, σ are functiuons of h ! In particular important for h=0: dwelling on hypothetically same location as school

Onion1-SEERAS-pb140525 9 of 16 lagged ratio - 2

AM and GM of the ratio (dwelling/school) in dependence of maximal distance between them.

curves = Kernel regression, median and quantiles over the ensemble of many estimates of Q(h)

For h=0: GM ≈ 0.5 (0.45 … 0.55), GSD ≈ 1.62 AM ≈ 0.55

under LN hypothesis: probability that dwelling > reference value c, given value of school, at (hypothetically) same location (h=0)

from estimates GM, GSD as above.

Ex.: school=200: prob(dwelling>100) = 0.50 (0.41 … 0.58) prob(dwelling>300) = 0.011 (0.006 … 0.019)

Onion1-SEERAS-pb140525 10 of 16 lagged ratio - 3

predictions based on modelled ratio

 prob(dwelling > threshold | school)

Expectation E[dwelling | school] not reliable !

prob(dwelling > threshold | school) > p 0

Onion1-SEERAS-pb140525 11 of 16 bivariate -1

Alternative: estimate a model of the bivariate (joint) distribution F 12 of dwellings and schools Ψ Ψ at lag h, by F12 (z 1, z 2)(h)= ϑ(h)(F 1(z 1),F 2(z 2))=: (z 1,z 2) (Sklar theorem) ∂Ψ ∂ From this, prob(Z 1>t | Z 2=z 2) = 1- (t,z 2)/ F2(z 2)

Problems: estimate model (copula) Ψϑ and parameters ϑ; good estimates of

Fi(z i) required.

Possibilities: ρ γ 1) Bi-Gaussian via Spearman (h=0) = 1 – 12 *12 (0); γ *12 = cross-variogram for ranks of z 1 and z 2. 2) Gumbel via ϑ = 1/(1-τ) ( τ=Kendall correlation) here we try option 2; lagged τ(0) ≈ 0.48; problems: - estimation of parameters ϑ not easy!

- estimation of true distributions F 1 and F 2 uncertain!

Onion1-SEERAS-pb140525 12 of 16 bivariate - 2

predictions based on modelled bivariate distributions (schools, dwellings)

prob(dwelling > threshold | school)

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 prob[dwelling>100] 0.2 0.1 450 0 400 y = 0.62x + 10.98 2 100 R = 0.98 0 100 200 300 400 500 600 700 350 90 E[school] 300 80 probability prob(dwelling>100) 250 70 200 60 as function of Rn in school 150 50 E[dwelling; model] E[dwelling; 100 40 50 30 prob(C>100)>p 0 20 0 100 200 300 400 500 600 700 10 E[school] which in domain of fraction 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 fraction of domain affected slope = mean ratio dwelling/school p ≈ 0.62 (compare for ratio model: 0.55) Onion1-SEERAS-pb140525 13 of 16 validation ? how to validate? Problem: data not sufficient for dividing into calibration and validation set. 1

0.9 comparison of empirical empir 0.8 bivar and modelled probability, 0.7 ratio prob(dwelling>100 | school) 0.6 uncert. for empirical: (q05,q95) 0.5 under Poisson hypothesis 0.4

0.3 prob(dwelling>100) 0.2

0.1 1 0 0.9 30 40 50 60 70 80 90 100 110

0.8 AM(dwelling) per town

0.7

0.6

0.5 comparison of probabilities estimated 0.4 with the two models (ratio; bivariate)

prob(C>100; ratio) prob(C>100; 0.3

0.2

0.1 not really consistent! – further work 0 required for clarification! 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 prob(C>100; bivar) Onion1-SEERAS-pb140525 14 of 16 conclusions

1. We could show that there is a relationship between Rn (annual mean concentrations) in schools and in dwelllings. (To be expected for physical reasons.) 2. We could quantify ratios between dwellings and schools; but the uncertainty is relatively high… probably a consequence of

(a) the small data set; (b) the variability of physical characteristics of schools and houses, which acts as „noise“ which obscures the relationship in tendency; (c) parametrization of models is difficult.

Therefore the tentative maps shown here have to be taken with caution .

Roughly, a dwelling hypothetically at the same location as a school has Rn level ca. 60% of the one of the school.

Onion1-SEERAS-pb140525 15 of 16 To do

1. Validation: must be left until more data are available. 2. Try different models 3. Improve parameterization of models 4. Uncertainty budget of bivariate estimates? 5. Compare with different datasets (SI, MK, Rep. Srpska, XK, IT, AT)

Onion1-SEERAS-pb140525 16 of 16