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Relation Between Radon in Schools and in Dwellings: a Case Study in a Rural Region of Southern Serbia – the “Onion Study”

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Relation Between Radon in Schools and in Dwellings: a Case Study in a Rural Region of Southern Serbia – the “Onion Study” Relation between radon in schools and in dwellings: a case study in a rural region of Southern Serbia – 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 Sokobanja 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 Bogdinac -396000 Beli Potok 108 dwellings (living Citluk -398000 Trubarevac Blendija rooms, ground floor). Soko Banja -400000 Rn concentrations, annual Resnik -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.
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