EVALUATION OF DETECTION ABILITIES OF MONITORING NETWORKS USING DIFFERENT ASSESSMENT CRITERIA. Radek Hofman, Petr Pecha and Václav Šmídl

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1 EVALUATION OF DETECTION ABILITIES OF MONITORING NETWORKS USING DIFFERENT ASSESSMENT CRITERIA Radek Hofman, Pet Pecha and Václav Šmídl Institute of Infomation Theoy and Automation of the Czech Academy of Sciences, v.v.i., Pod Vodaenskou vezi 4, , Pague 8 (Czech Republic), pecha@utia.cas.cz Abstact: The poblem of evaluation of adiation monitoing netwok quality is consideed. The task is to compae seveal possible configuations of a monitoing netwok fom diffeent points of view. The compaison is pefomed on simulated expeiments whee a twin model is used to simulate obseved data fo all potential configuations of the monitoing netwok. An assimilation pocedue based on the paticle filte appoach is un fo each configuation of the netwok. Specifically, multiple ealizations of segmented Gaussian plume models ae computed, each with diffeent paametes. The simulated measuements fom the netwok sensos ae used to weight likelihood of the paamete ealizations, poviding an empiical posteio distibution of the paametes. The quality of the netwok is then evaluated as an expected value of seveal loss functions with espect to the empiical posteio distibution. The netwok assessment citeia ae established on basis of common suggestions fomulated by administatos the adiation monitoing netwok of the Czech Republic. The aim is to povide a tool that allows the decision makes to compae the poposed configuations fom vaious points of view. The esults fo hypothetical dischage of adioactivity ae pesented. Key wods: Dispesion modelling, dose ates, data assimilation, monitoing netwok. INTRODUCTION Sensos of adiation monitoing netwoks ae nowadays scatteed aound the wold and monito global adiation situation in the case of sevee adiation event. They ae so sensitive that it can be possible to econstuct the significant scenaio paametes initially budened by lage uncetainties by means of optimal blending with coesponding measuements. Howeve, these measuements ae too coase fo small scale events that may occu afte a mino accident in a powe plant. Fo this eason, evey powe plant has its own adiation monitoing netwok that is connected to its contol system. With inceasing demands fo adiation safety the monitoing netwoks ae expanded to impove thei detection capabilities. Testing of the adiation netwoks is done in simulation mode when a hypothetical elease of adioactivity is geneated atificially by means of a twin model. A lot of wok has been invested into the eseach of detectability of a small elease (Uso, L. et al., 2012), and optimal configuation of monitoing netwoks (Zidek, J.V. et al., 2000; Abida, R. et al., 2008; Baume, O.P. et al., 2011; Melles, S.J. et al., 2011). Simulated annealing is the most commonly used tool fo netwok optimization whee a chosen loss function is minimized. Since the optimization is pefomed ove all possible uncetainties in weathe conditions and conditions of the elease, the computation needs to be simplified to achieve tactability. The most commonly simplified step in the optimization is the assimilation pocedue. In the case of detectability, the assimilation pocedue is simple thesholding. It aims at situations, whee only one adiation senso detects the elease. In the simulated annealing optimization, it is usually spatial intepolation o kiging (Heuvelink, G.B.M. et al., 2010), with weathe- and space-independent vaiogam. This simplification appoach is suitable when the netwok is dense enough that the intepolation povides sufficiently accuate esults. In this contibution, we investigate evaluation of a netwok using Bayesian assimilation. The main advantage of Bayesian assimilation is that it is capable to epesent uncetainty of the elease and evaluate pedictions of its evolution. The disadvantage is its computational cost, which is pohibitive in demanding applications of netwok optimization. Theefoe, we do not use the simulation annealing fo optimal positioning of all sensos of a netwok, but povide only tools fo evaluation of selected fixed configuations of a netwok. Thus the esulting algoithm seves as a suppot fo human decision makes who design extensions of the netwok. To achieve computational feasibility we use the combination of a sequential Monte Calo method with an analytical dispesion model (Johannesson, G. et al., 2004; Hiemsta, P.H. et al., 2011). Specifically, we use the segmented Gaussian plume model which was used in Bayesian assimilation in (Pecha, P. et al., 2009). Moeove, we use adaptive stategies to impove convegence popeties of the sequential Monte Calo (Smidl, V. and R. Hofman, 2011). Quality of the netwok is studied via two loss functions: (i) spatial coveage of the affected aea and (ii) misclassification of inhabitants (Heuvelink, G.B.M. et al., 2010). DECISION THEORY FRAMEWORK The pincipal famewok of netwok evaluation is the statistical decision theoy which is commonly used in this context. The main esult of decision theoy unde uncetainty is fomally simple (Bege,J.O., 1985). If we ae to

2 choose which netwok,, fom a given set of candidates,, is best, we ae to choose the one that minimizes the expected value of the chosen loss function * n ag min n N E X Ln, X (1) whee models all uncetainty of the elease, is the chosen loss function and is the opeato of expected value. The space of uncetainty contains the following: (i) uncetainty of the elease, given by its paametes, (ii) uncetainty in the weathe conditions, typically modeled by coections of the numeical weathe foecast, and (iii) uncetainty in ealizations of the measuements of the monitoing netwok,. Natually, the numbe of the measuement points and thei position is influence by configuation of the netwok,. We will conside the following loss functions: (i) spatial mean squae eo, and (ii) misclassification of inhabitants. The spatial mean squae eo is defined on the assimilated adiation dose ate in the whole aea, Ln, X D( X ) D( X ) 2 (2) whee is the spatial distibution of the adiation dose ate fo the consideed paametes and is its estimate based on the obseved data. The misclassification of inhabitants is Ln, X I f p I f n (3) whee is the numbe of people incoectly classified as affected by the elease, and analogically is the numbe of people that ae incoectly classified as unaffected. It is computed as a sum ove all inhabited places indexed by, with the numbe of inhabitants being. denotes a theshold fo the gamma dose ate level. Key element of both loss functions is the estimate of the adiation dose ate. This is a esult of assimilation with measuements. The assimilation pocedue thus stongly influences the esults. Due to low infomativeness of measuements, we assume that only few selected paametes of the elease ae assimilated to povide. These paametes will be denoted by. The estimate of the adiation dose ate is povided by a numeical atmospheic dispesion model HARP DISPERSION MODEL The envionmental code HARP with dispesion model based on segmented Gaussian plume model (SGPM) showed to be fast enough fo its deployment in the sequential data assimilation pocedues. Besides that, the model validation benchmaks poved sufficient ageement with simila Euopean codes (e.g. COSYMA, RODOS). This classical Gaussian model is based on Pasquill s stability classification scheme and is consistent with the andom natue of tubulence. Poved semi-empiical fomulas ae available fo appoximation of vaious impotant effects (influence of nea-standing buildings, momentum and buoyant plume ise duing elease, depletion of the plume activity due to emoval pocesses of dy and wet deposition and decay, account fo small changes in suface elevation, altenative dispesion fomulae fo ough o smooth teain etc.). Implemented numeical diffeence scheme enables to appoximate fomation of impotant paent-daughte pais of nuclides. Time dynamics of the eleased mateial is patitioned into a numbe of fictitious one-hou segments with equivalent homogeneous elease souce stength. Each segment of the elease is spead duing the fist hou as a staight-line Gaussian plume. In the following hous of speading accoding to given meteoological conditions, the segment is teated as a polonged puff and its dispesion and depletion duing the movement is simulated numeically by means of a lage numbe of elemental shifts. Moe detailed desciption of the pocedue can be found in (Hofman, R. and P. Pecha, 2011). Fo the pupose of evaluation of the monitoing netwok, we eview only its essential pats. 1. Model paametization. Model paametes that influence the shape of the plume ae: elease souce stength of activity Q [Bq.s -1) ], elease height, categoy of atmospheic stability, height of the mixing laye, teain paametes, etc. Fom these paametes, we conside only to be assimilated fom the measuements. All othe paametes ae given by thei best estimated deteministic values. The weathe conditions ae supposed to be known fom the numeical weathe pediction. Howeve, we calibate the wind speed and wind diection by additive offsets, which ae assumed to be unknown and diffeent at each time step. The composition of nuclides in the elease is assumed to be known. The sensos of the monitoing netwoks measue only the total adiation dose ate, hence thee is not enough infomation to distinguish the nuclides. Howeve, the knowledge of the elease composition is impotant fo wet and dy deposition. 2. Computation of the goundshine and the cloudshine dose ates gound and cloud. The sensos of the monitoing netwoks egiste dose ates fom two souces: cloudshine and deposition. The goundshine is computed as a supeposition of contibution fom all houly segments with index denoting the

3 time of the segment elease. The goundshine dose is a sum of contibutions fom deposition duing the whole tajectoy of the segment. Just at time, each eleased segment has elative index of its histoy. gound cloud T ) T ) ( ) s1 s st ( ) s1 st T cloud gound s, T ) s, ) exp T 3600 We intoduce the sum D = cloud + gound which denotes the total dose ate [msv.h -1 ] at location coodinates pecisely at hou T since the elease stat. Index uns ove all adionuclides, each nuclide having decay constant [s -1 ]. The eo of measuements is assumed to be elative to the measued dose ates. EVALUATION OF THE EXPECTED LOSS Evaluation of the expected loss (1) is achieved using impotance sampling, whee the uncetainty is epesented by empiical density. The numbe of geneated samples is, with unning index. The weathe conditions ae sampled unifomly fom histoical ecods, foming. The elease conditions ae sampled fom available estimates (Pecha, P. et al., 2009). These samples ae used to geneate the twin model fom which ae geneated the twin dose ates and samples of the obsevations of all competing monitoing netwoks,,. The sampled data ae then teated as tue measuements to obtain the estimate of the assimilated paametes using a Bayesian assimilation pocedue. The paametes ae estimated using impotance sampling by geneating samples,. Each of the samples has associated weight Fo efficient sampling we use the adaptive sequential Monte Calo with the ASIM pocedue (Smidl, V. and R. Hofman, 2013). Specifically, the total numbe of paticles is split into seveal populations, each with adaptively impoved poposal functions. This adaptation significantly speeds up the convegence to accuate estimates. Evaluation of the netwok pefomance citeia (2) is then appoximated by E I K ( k, i, n) ( i) ( n L n X w D D k, i, ) ( ) i1 k 1 asim 2, (5) and equivalently fo the misclassification loss (3). (4) RESULTS As a fist step in moe demanding simulations, we compaed suitability of two designs of a adiation monitoing netwok (RMN). We evaluated two loss functions fo a fixed eleased scenaio (meteoological conditions and a souce tem). Both candidate netwoks contain the ing of detectos aound a powe plant. The fist candidate has detectos located in the inhabited places suounding powe plant (RMN_1) while the second candidate has detectos located in egula concentic cicles aound the powe plant (RMN_2). Simulation setup The expeiment was pefomed as a twin expeiment, i.e. time seies of measuements wee obtained via petubation of values sampled fom HARP model initialized with nominal inputs. To avoid identical twin expeiment, twin model values wee simulated using point-wise meteoological data valid ove the whole computational domain while moe ealistic gidded meteoological data entes the data assimilation pocedue. Spatially and tempoally vaiable diffeences of wind speed and diection between point and gidded data wee estimated duing data assimilation in tandem with the magnitude of elease. Accuacy of the adiation dose sensos poviding cumulative gamma dose ate fom cloudshine and goundshine was 20%. The simulated accident is epesented by one hou continuous elease of adioactivity 5.0E+15 Bq.h -1 of Cs-137. Decay half-life of this adionuclide is appox. 30 yeas. Assimilation was pefomed fo the fist 5 hous of the elease. Spatial integation needed fo evaluation of cloudshine dose ates is appoximated using semifinite cloud model, which is coected on the finite shape at nea distances. Altenative and moe convenient appoach of the finite cloud model based on the n/µ method is successfully tested (Pecha, P. and R. Hofman, 2011) fo configuation when the size of the plume is small compaed to the mean fee path of the gamma ays. Data assimilation is initialized using Monte Calo pocedue fo population of 200 paticles. Five best fit 2-D tajectoies ae then esampled and each of them is subsequently adaptively polifeated to the new populations in the next houly steps. Assimilation esults The assimilated paametes ae asim [ Q, a, b] whee Q is souce stength of adioactive elease [Bq.h-1 ], a is the coection of the pedicted wind diection (in degees), and b is the coection of the wind speed.

4 Figue 1: Compaison of twin model and data assimilation esults. Top left: Twin model: 5.0E+15 Bq.h-1. Bottom left: Simulation based on initial deteministic calculations with nominal inputs 1.0E+15 Bq.h-1. Top and bottom middle: Assimilation esults based on RMN_1 and RMN_2 candidate netwoks. Visualized quantity is cumulative gamma dose ate fom cloudshine and goundshine [msv.h-1]. Top ight: Visualization of population data fom 2003 census used fo constuction of RMN_1. Magnitude of elease is estimated afte the elease goes though the time t=1. Wind speed and wind diection ae estimated independently in each step of the assimilation t=1,,5. Assimilation esults ae compaed with the twin model in Figue 1. We see that both the adiation monitoing netwoks poduced almost equal esults well compaable to the twin model. Estimated values of magnitude of elease wee 5.6E+15 Bq and 6.7E+15 Bq fo monitoing netwok configuations RMN_1 and RMN_2, espectively. The fact that Q was estimated with successful accuacy in both expeiments is justified by the pesence of the teledosimetic system-the fist ing of eceptos aound a powe plant. The slight oveestimation of Q along with undeestimation of wind speed duing time step 4 caused oveall oveestimation of the gamma dose ate in time 5, see Figue 1. Figue 2: Compaison of pefomance of monitoing netwoks RMN_1 and RMN_2 in tems of two loss functions evaluated in time steps t=1,,5. Left: Loss function measuing mean squae eo (MSE) between assimilation esults and twin model. Right: Loss function measuing MSE weighted by population data fo espective gid cells. Loss evaluation The main objective of this pape-the compaison of suitability of diffeent monitoing netwok configuations-is achieved via assessment of capability of Monte Calo data assimilation pocedue to econstuct an accident. The assessment is pefomed by the means of compaison of an assimilation esult with the tue elease epesented by the twin model in tem of a loss function. In Figue 2, data assimilation esults using the two candidate netwoks ae compaed in tem of a loss function measuing mean squae eo (MSE) of the assimilation esult (Left) and MSE weighted by the numbe of people living in gid cells. We obseve that pefomance of data assimilation pocedue fo both candidate netwoks is almost equal in tems of MSE. RMN_2 pefoms slightly bette because it egulaly coves the computational domain. Moe inteesting esults we obtain fo the second loss function measuing the discepancy between the twin model and assimilation esult in tems of misclassified people. We obseve that RMN_1 pefoms much bette since it

5 coves the inhabited locations-the gid points with highest contibutions to the oveall loss. MSE in these gid points is significantly educed in case of RMN_2 due to pesence of eceptos poviding diect infomation of adiation levels. CONCLUSION Pefomance of a adiation monitoing netwok is typically evaluated via Monte Calo study ove the weathe and elease conditions to simulate all potential events. Howeve, the ability of the netwok to help the decision makes stongly depends on the quality of the assimilated esults. This aspect is often ovelooked and netwoks ae optimized using vey simple assimilation pocedues, in ode to keep easonable computational cost. In this pape, we poposed to use the sequential Monte Calo assimilation which fits well into the common Monte Calo appoach. The esulting algoithm is still computationally feasible due to application of the latest adaptive impotance sampling techniques, such as the adaptive multi impotance sampling (AMIS), and evaluates pefomance of the selected candidates of a adiation monitoing netwok. The algoithm will seve as a suppoting tool fo consideations of potential netwok extension by human decision makes. Demo of the tool is available online at Finally, we should point out futhe significant featue of the poposed technique. It epesents efficient advanced tool fo online Bayesian tacking of the adioactive plume popagation. It povides moe accuate pognosis of evolution of adiological situation and bette identification of the most contaminated aeas (e.g. see top left and bottom left pictues in Figue 1). It can suppot decision making unde nuclea emegency elated to the intoduction of ugent countemeasues on population potection. It esticts theat of possible fatal health and social consequences in case of eoneously classified aeas. Nevetheless, a lot of wok should be done, mainly in the field of multi-segment and multi-nuclide analysis of an accidental scenaio. ACKNOWLEDGEMENT This wok was suppoted by gant VG of the Ministy of Inteio of the Czech Republic. REFERENCES Abida, R., M. Bocquet, N. Vecauteen and O. Isnad, 2008: Design of a monitoing netwok ove Fance in case of a adiological accidental elease. Atmospheic Envionment, 42, Baume, O. P., A. Gebhadt, C. Gebhadt, G. B. M. Heuvelink and J. Pilz, 2011: Netwok optimization algoithms and scenaios in the context of automatic mapping. Computes & Geosciences, 37, Bege, J. O., 1985: Statistical Decision Theoy and Bayesian Analysis, Spinge, New Yok. Heuvelink, G. B. M., Z. Jiang, S. De Buin and C. J. W. Twenhöfel, 2010: Optimization of mobile adioactivity monitoing netwoks. Intenational Jounal of Geogaphical Infomation Science, 24, Hiemsta, P. H., D. Kassenbeg and A. van Dijk, 2011: Assimilation of obsevations of adiation level into an atmospheic tanspot model: A case study with the paticle filte and the ETEX tace dataset. Atmospheic Envionment, 45, Johannesson, G., B. Hanley and J. Nitao, 2004: Dynamic Bayesian models via Monte Calo an intoduction with examples. Technical epot, Lawence Livemoe National Laboatoy. Melles, S. J., G. B. M. Heuvelink, C. J. W. Twenhöfel, A. van Dijk, P. H. Hiemsta, O. Baume and U. Stöhlke, 2011: Optimizing the spatial patten of netwoks fo monitoing adioactive eleases. Computes & Geosciences, 37, Pecha, P. and R. Hofman, 2011: Constuction of obsevational opeato fo cloudshine dose fom adioactive cloud difting ove the teain. Poc. of 14th Intenational Confeence on Hamonisation within Atmospheic Dispesion Modelling fo Regulatoy Puposes. Pecha, P., R. Hofman and V. Šmídl, 2009: Bayesian tacking of the toxic plume speading in the ealy stage of adiation accident. Poc. of Euopean Simul. and Modelling Confeence ESM. Smidl, V. and R. Hofman, 2011: Efficient sequential Monte Calo assimilation fo ealy phase of adiation accident. Technometics, accepted. Thompson, I. M. G., C. E. Andesen, L. Bøtte-Jensen, E. Funck, S. Neumaie and J. C. Sáez-Vegaa, 2000: An intenational intecompaison of national netwok systems used to povide ealy waning of a nuclea accident having tansbounday implications. Radiation potection dosimety, 92, Uso, L, P. Astup, K.B. Helle, W. Raskob, C. Rojas-Palma and J. C. Kaise, 2012: Impoving evaluation citeia fo monitoing netwoks of weak adioactive plumes afte nuclea emegencies. Envionmental Modelling & Softwae, 38 (2012). Zidek, J. V., W. Sun and N. D. Le, 2000: Designing and integating composite netwoks fo monitoing multivaiate Gaussian pollution fields. Jounal of the Royal Statistical Society: Seies C, 49,