Computers & Geosciences 37 (2011) 280–288

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Optimizing the spatial pattern of networks for monitoringradioactive releases

S.J. Melles a,�, G.B.M. Heuvelink a, C.J.W. Twenhofel b, A. van Dijk b, P.H. Hiemstra c,O. Baume a, U. Stohlker d

a Environmental Sciences Group, Wageningen University, P.O. Box 47, 6700 AA, Wageningen, The Netherlandsb National Institute for Public Health and the Environment, The Netherlandsc University of Utrecht, Department of Physical Geography, P.O. Box 80.115, 3508 TC, Utrecht, The Netherlandsd Federal Office for Radiation Protection, Bundesamt fur Strahlenschutz, Germany

a r t i c l e i n f o

Article history:

Received 22 October 2009

Received in revised form

14 April 2010

Accepted 19 April 2010Available online 21 July 2010

Keywords:

Spatial simulated annealing

Radioactive plumes

Radiation

Prediction error variance

Geostatistics

04/$ - see front matter & 2010 Elsevier Ltd. A

016/j.cageo.2010.04.007

esponding author. Ontario Ministry of Natura

st Bank Drive, Peterborough, ON, Canada K9

705 755 1559.

ail addresses: stephajm@gmail.com,

ie.melles@ontario.ca (S.J. Melles).

a b s t r a c t

This study presents a method to optimize the sampling design of environmental monitoring networks

in a multi-objective setting. We optimize the permanent network of radiation monitoring stations in

the Netherlands and parts of Germany as an example. The optimization method proposed combines

minimization of prediction error under routine conditions with maximizing calamity detection

capability in emergency cases. To calculate calamity detection capability, an atmospheric dispersion

model was used to simulate potentially harmful radioactive releases. For each candidate monitoring

network, we determined if the releases were detected within one, two and three hours. Four types of

accidents were simulated: small and large nuclear power plant accidents, deliberate radioactive

releases using explosive devices, and accidents involving the transport of radioactive materials. Spatial

simulated annealing (SSA) was used to search for the optimal monitoring design. SSA was implemented

by iteratively moving stations around and accepting all designs that improved a weighted sum of

average spatial prediction error and calamity detection capability. Designs that worsened the multi-

objective criterion were accepted with a certain probability, which decreased to zero as iterations

proceeded. Results were promising and the method should prove useful for assessing the efficacy of

environmental monitoring networks designed to monitor both routine and emergency conditions in

other applications as well.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Environmental monitoring networks are typically designed todetect variables of interest to human or ecosystem health. Notonly must these networks detect gradual changes in thesevariables, and background patterns, but they must also detectextreme values in case of an emergency. Several types ofmonitoring networks take these dual purposes into account,including air, water, radiation, and climate monitoring networks.The network design problem is clearly of great importance bothfor public health reasons and because costs associated withestablishing and maintaining monitoring stations are typicallyvery high (Chang et al., 2007). Both sampling pattern and dataquality can have an effect on analysis and inference (Muller,1998). It is therefore not surprising that the search for optimal

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sampling patterns has employed several approaches using avariety of pre-defined criteria and solution methodologies(Cressie et al., 1990; Muller, 1998; Loaiciga et al., 1992; deGruijter et al., 2006).

In order to optimize a sampling network, one must first selectan appropriate criterion with which to quantify the suitability of agiven design. Also referred to as the objective function, thecriterion must encompass the sometimes conflicting objectives ofa monitoring network. One of the most common criteria employeduses a geostatistical measure of spatial prediction error to optimizea network for predicting variables at unmeasured locations (Cressieet al., 1990; Loaiciga et al., 1992). In the geostatistical literature,best linear unbiased prediction is found by kriging, and thecriterion to be minimized is referred to as the average predictionerror variance (Zhu and Stein, 2006). Recently, Brus and Heuvelink(2007) showed that, in the context of a linear model with trendcomponents, minimizing the mean kriging variance simulta-neously optimizes estimation of trend parameters.

The approaches described above rely on a known, pre-specifiedmodel for underlying spatial variation (i.e. a known covariancefunction or variogram), which is assumed constant across the

S.J. Melles et al. / Computers & Geosciences 37 (2011) 280–288 281

region of interest (i.e., the stationarity assumption Ben-Jemaaet al., 1995; Brus and de Gruijter, 1997; Van Groeningen et al.,1999). In practice, these conditions may not be satisfied (Zhu andStein, 2006). However, Rouhani and Fiering (1986) showed thatvariance-based approaches to sampling design are generallyrobust to violations of the assumption of stationarity (Loaicigaet al., 1992). For situations where the underlying variogram isunknown, methods have been developed to take uncertainty inthe variogram parameters into account (Zhu and Stein, 2006;Zimmerman, 2006). Alternatively, spatial coverage samplingmethods utilize a measure of the distance between sample pointsas a criterion, and these algorithms can be used in the absence of avariogram or when the relationship between environmentalcovariates is uncertain (Brus et al., 2006).

Methods that use the average prediction error variance canhelp to improve the design of fixed monitoring networks underroutine conditions (Melles et al., 2008), but such an approachneglects to consider one of the prime objectives of thesenetworks: that is, they must be designed to quickly detectaccidental or deliberate releases in emergency situations. Design-ing a network that considers both routine prediction andemergency detection poses special challenges (Chang et al.,2007). This study proposes a combined simulation and variance-based approach to tackle the multi-objective case, and it is thecombination of the two that makes the proposed technique usefuland unique. The approach is demonstrated by optimizingradiation monitoring networks in the Netherlands and part ofGermany. Code developed for its implementation have contrib-uted to an R package for automated spatial interpolation(IntamapInteractive, 2010; Pebesma et al., 2010).

The overall study goal was to optimize the design of a fixedradiation monitoring network for the dual purposes of mappingbackground radiation levels and detecting radiation levels above acritical threshold in emergency settings. To do so, number ofstations was held constant, but the location of stations wasallowed to vary. The specific objectives were to:

�

design a dual purpose or multi-objective criterion thatconsiders routine spatial prediction and emergency detection(i.e. detection capability); � create a function to estimate network detection capability

given simulated releases of radiation plumes tracked throughtime;

� account for monitoring network constraints or risk factors (e.g.

the locations of nuclear power plants and population density).

2. Methods, simulations and algorithms

2.1. Study area and radiation monitoring networks

Radiation monitoring networks are designed to measuregamma dose rates (GDRs) emitted by both natural and human-induced radionuclide releases. The National Institute for PublicHealth and the Environment (RIVM) operates the Dutch NationalRadioactivity Monitoring network (Twenhofel et al., 2005). InGermany, the Federal Office for Radiation Protection (BfS) is theagency responsible for the German network. Monitoring stationsare more or less uniformly spread across the two countries, withincreased densities near nuclear power plants and along countryborders (Fig. 1). However, there is a need to coordinate thesampling design amongst these and other countries becauseradioactive releases can cross political boundaries.

Accidents like the radioactive release at Three Mile Island inPennsylvania (1979) and the Chernobyl nuclear power plant

(NPP) accident in the Ukraine (1986) serve to amplify public fearsrelated to the risks of radiation accidents (Steinhausler, 2003). It istherefore important to take a number of risk factors intoconsideration, such as the locations of nuclear power plants(NPPs, Fig. 1), the road network used in the transport ofradioactive materials, and population density (Fig. 2). Here, weconsider only the position of the radiation sensors and not thenumber of sensors.

2.2. Atmospheric dispersion model simulations

The NPK-PUFF model (Verver et al., 1990) is an atmosphericdispersion model that simulates emissions or puffsfrom a radioactive source over different time intervals (e.g.minutes, hours). This model is part of a GIS-based decisionsupport system used by the RIVM. We used NPK-PUFF (v.4.0.6) tosimulate the release of radioactive plumes in the study area withdifferent magnitudes and varying weather conditions (Fig. 3,Table 1). Four types of accidents were simulated: (1) small and (2)large nuclear power plant accidents selected from a range ofreference nuclear release scenarios; (3) deliberate radiationemissions (RED); (4) and accidents involving the transport ofradioactive materials (SPILL, Table 1). Radioactive releases weresimulated throughout the area of interest, given a modifiableprobability distribution for the release locations based on mapsof: NPP locations (Fig. 1), densely populated urban centers (forRED type accidents), or transportation networks (for SPILLs,Table 2, Fig. 2a and c).

NPK-PUFF trajectories can be simulated using meteorologicalforecasts such as those produced by the High Resolution LimitedArea Model for weather prediction (HIRLAM), (Eleveld et al.,2007). In this study, meteorological conditions during simulationswere treated as stochastic and sampled from representativehourly weather data for the area collected from a weather stationat De Bilt, NL, during the year 2005 (Table 3, Fig. 4). Samplingweather conditions from the observed multivariate distribution ofconditions automatically preserves the statistical dependencies(i.e. correlations) between the variables (e.g. wind speed/direction). However, it is hardly realistic to assume that weatherconditions at De Bilt were representative of conditions over theentire spatial domain. This simplification was necessary givendata availability and time constraints. Future developments mayinclude more realistic weather conditions and high resolutionatmospheric dispersion models (see Discussion).

Radioactive plumes were tracked over time, and plumes weredelineated as areas with gamma dose rates (GDR) above criticalthresholds, which were based on the projected amount of air anddepositional radiation at ground level. The threshold was set highenough to trigger emergency response procedures under normalcircumstances (¼ +100 nSv/h). Five thousand accidents of eachtype were simulated and their evolution through time wasmonitored at three time steps. Each of the four accident typesdescribed were combined into a single map with 20,000 plumeaccidents tracked over three time steps.

2.3. Dual purpose optimization criterion

2.3.1. Kriging prediction error variance

The objective function combined two criteria to be optimized:average kriging prediction error variance and network detectioncapability. In this section we detail how interpolation wasperformed by regression kriging and we describe calculation ofthe first criterion.

Kriging variance was calculated by spatial interpolation of(mean) annual GDRs with known predictor variables using

Fig. 1. Current network of gamma dose rate monitoring stations (points, n¼592) in Netherlands (west) and German states of Niedersachsen (northeast) and Nordrhein-

Westfalen (south). See inset map of Europe for point of reference. Locations of two major cities (stars) and nuclear power plants (triangles) are depicted. &EuroGraphics for

administrative boundaries.

Fig. 2. Study area characteristics and environmental predictor variables used in regression kriging.

S.J. Melles et al. / Computers & Geosciences 37 (2011) 280–288282

regression kriging. Regression kriging (RK, Odeh et al., 1995) is ahybrid spatial modelling technique (Zhang et al., 2005a) thatcombines regression with spatial interpolation of regressionresiduals (Hengl et al., 2007). RK has been shown to result inbetter predictions than either approach alone (Zhang et al.,2005a), and the model is mathematically equivalent to universalkriging with external drifts (Hengl et al., 2007).

Spatial correlation in the residuals is modelled by anautocovariance function or variogram that is inferred from theresidual spatial structure in the observed point data. This hybridmodel relies on the geostatistical assumption of stationarity,which implies that spatial correlation depends only on thedistance between points and not on their location (Isaak andSrivastava, 1989). A detailed treatment of the methodology and

Table 3Summary statistics for various weather variables.

Statistic P HM Obukv

Table 2Start location probabilities by accident type.

Land use Probability Accident type

High density urban ð46000 pe=km2Þ 0.70 RED

Medium density urban (3001–6000 pe/km2) 0.28 RED

Low density urban (501–3000 pe/km2) 0.03 RED

Largely unpopulated (1–500 pe/km2) 0.0000001 RED

Highway 0.65 SPILL

Major road 0.15 SPILL

Railway 0.10 SPILL

Airport 0.08 SPILL

Seaway 0.02 SPILL

Land 0.00001 SPILL

Note that all nuclear power plants were modelled with equal probability of an

accident.

S.J. Melles et al. / Computers & Geosciences 37 (2011) 280–288 283

application of regression kriging can be found in Hengl et al.(2007).

The RK interpolation error variance at an unsampled location,s0, is given by the following equation in matrix notation:

s2ðs0Þ ¼ ðC0þC1Þ�cT0 � C

�1� c0þ

þðq0�qT � C�1� c0Þ

T� ðqT � C�1

� qÞ�1� ðq0�qT � C�1

� c0Þ ð1Þ

where C0 and C1 are the nugget and partial sill variation,respectively; c0 is the vector of covariances between the residualsat the observation and prediction locations, here calculated on afine grid (1 km2); T indicates matrix transposition; C is the n�n

variance–covariance matrix of the n residuals; q0 is the vector of k

+ 1 predictors; and qT is the transposed, n� (k+1) matrix ofpredictors at the observation locations. C and c0 are derived fromthe variogram of residual error. It is important to note that thedata values themselves are not used in the calculation of the RKinterpolation error variance. This attractive property allows one toestimate the kriging prediction error variance prior to collectingthe data, and it is this property that is used in the optimizationprocedure after (Brus and Heuvelink, 2007).

Fig. 3. Example radioactive plumes (4100 nSv=h GDR) simulated using an

atmospheric dispersion model (NPK-PUFF) at hour one (bold grey), hour two

(solid), and hour three (dotted) for (a) small NPP type accident, (b) large NPP type

accident, (c) deliberate radioactive release (human-caused), and (d) emission of

radioactivity due to a transport accident. Note that release characteristics of these

example accidents are presented in Table 1, (a) through (d).

Table 1Release characteristics and stochastic samples of meteorological data (hourly values for 2005) used with NPK-PUFF to generate example plumes shown in Fig. 3 for (a)

small NPP accidents, (b) large NPP accidents, (c) deliberate RED radioactive emissions, and (d) transportation spills.

Release Hr Wd10 Ws10 Wd300 Ws300 Wd500 Ws500 P HM Obukv

(a) 1.36 1 13 4.38 37 11.2 39 12.47 0 991 75.15

E+16 Bq 2 10 4.33 35 10.82 38 12.05 0 1171 67.8

Kr-88 3 7 4.29 34 10.45 36 11.63 0 1351 61.28

11-Jul-05 4 0 4.05 32 10.2 35 11.22 0 1531 154.47

(b) 6.78 2 66 7.6 74 12.39 77 13.66 0.01 309 323.61

E+17 Bq 3 63 8 72 12.83 74 14.15 0.02 384 365.14

Kr-88 4 61 8.42 69 13.29 71 14.67 0.02 459 410.56

22-Feb-05 5 59 8.85 66 13.78 69 15.27 0.03 534 459.89

(c) 5.00 16 281 1.71 285 2.86 279 3.42 0 250 �20.39

E+13 Bq 17 298 1.68 297 2.96 289 3.49 0 250 �50.2

Cs-137 18 311 2.37 308 3.18 298 3.65 0 250 24.37

29-Aug-05 19 317 2.11 314 2.91 303 3.32 0 250 6.51

(d) 1.00 20 8 2.26 12 2.91 15 3.35 0.01 150 7.09

E+12 Bq 21 1 2.06 9 2.57 13 2.98 0.01 150 5.88

Cs-137 22 353 1.91 6 2.23 11 2.61 0.02 150 4.95

03-Feb-05 23 344 1.79 2 1.91 7 2.24 0.02 150 4.29

Hr¼hour; Wd10, Wd300, Wd500¼wind direction (degrees) at 10, 300, and 500 m in height; Ws10, Ws300, Ws500¼wind speed (m/s) at 10, 300, and 500 m height;

P¼precipitation (mm); HM¼mixing layer height (m); Obukv¼Monin Obukhov length (a measure of atmospheric stability, m).

Min. 0.0 150.0 �9904.2

Max 3.2 251.0 9951.6

Mean 0.1 391.9 33.5

S.D. 0.2 383.4 1107.8

Acronyms described in Table 1.

N

S

+

N

S

+

N

S

+

10 m 300 m 500 m

Fig. 4. Windrose diagrams for hourly meteorological data collected at De Bilt, NL

in 2005, given atsmoshperic heights as shown. Pedals indicate proportion of time

wind originates from a given direction. Grayscale bands represent wind-speed

increments in 5 m/s.

Sem

ivar

ianc

e

Distance (km) Distance (km)

Fig. 5. Regression residuals calculated from 592 gamma-dose rate observations.

(a) Bubble plot map of residual error ðeÞ. (bc) Semivariograms of e showing two

main directions of anisotropy. (b) Spherical model of e with a nugget variance of

59 nSv/h, a partial sill (sill minus nugget) of 24.5 nSv/h, and a range of 320,000 m.

(c) linear model with a partial sill of 59.5 nSv/h and range of 3,000,000 m.

Table 4Weights to increase detection capability in densely populated areas.

Population density (people/km2) Weight (wp)

1–500 0.25

501–3000 0.33

3001–6000 0.5

46000 1

S.J. Melles et al. / Computers & Geosciences 37 (2011) 280–288284

RK is useful when one has comprehensive information onenvironmental predictor variables that are known to correlatewith the spatial variable of interest. Natural background radiationis known to vary significantly with a few key environmentalpredictors (i.e., elevation and soil type, Melles et al., 2008;Hiemstra et al., 2009). Background radiation is composed ofcosmic, airborne, and terrestrial radiation. The cosmic componentvaries predictably with altitude above sea level (Wissman et al.,2007) and accounts for roughly 50% of the annual dose; theairborne component is primarily related to the amount ofnaturally occuring Radon (222Rn, 220Rn), and their short-livedprogeny, which are exhaled from the soil and transported throughthe air via aerosols. The airborne component accounts for a smallpercentage of the annual radiation dose; but shortly afterprecipitation events, the dose rate can increase by a maximumof up to 100 nSv/h for a few hours, as 222Rn and its progeny arewashed out of the air and deposited onto the ground (Smetsersand Blaauboer, 1997; Hiemstra et al., 2009). Given the short-livednature of this increase in radiation, mean annual precipitationdoes not correlate strongly with mean annual GDRs (Melles et al.,2008). Terrestrial radiation accounts for the other 50% of theannual dose and consists of radiation from the natural decay chainof radionuclides in the soil (i.e. 232Th, 235U, 238U, and 40K), whichcan be modelled as a function of soil type (Smetsers andBlaauboer, 1997; Melles et al., 2008; Hiemstra et al., 2009).

Monitoring network locations and GDR data were acquiredfrom the European Radiological Data Exchange Platform(EURDEP1). Two environmental variables were used to modelthe trend component in RK: elevation and soil type (Fig. 2b and d)as in (Melles et al., 2008). Elevational data were based on theUSGS Global 30 arcsec digital elevation data (U. S. GeologicalSurvey, 1996). Soil effects were modelled using six soil classes as

1 http://eurdep.jrc.it (accessed 22 January, 2008).

categorical predictors after Blaauboer and Smetsers (1996), usingdata from the European Soil Database (European Soil Database,2003). Model parameters were initially estimated by ordinaryleast squares (OLS) and the remaining anisotropic (directional)spatial variation was fit with variogram models. These variogramshave a linear and spherical component in all directions, but thespherical component is more dominant in one direction than theother (Fig. 5). RK was then performed using R (R DevelopmentCore Team, 2008), package gstat (Pebesma, 2004) by GLS. Thesquare root of prediction error variance (Eq. (1)) was used in theobjective function so that GDR prediction errors were in the sameunits and magnitude as the observations themselves.

2.3.2. Detection capability

In this section we describe calculation of the second criterion,calamity detection capability. Detection capability was defined asthe average cost of failing to detect a plume by a minimum of twodetectors within 3 h of a release. The cost of a plume was afunction of its depositional area, the hour at which it wasdetected, and the number of sensors that detected it. Cost wasfurther weighted by population density because it is even morecritical that radioactive plumes be detected if they are situated inhighly populated places. To account for this additional designconstraint, highly populated areas were associated with highercosts if the network failed to detect a release (Table 4). Lastly, if aplume followed a trajectory that carried the radioactivity entirelyoutside the study area, the detection cost was set to zero. Theseweights, probabilities, and time steps can easily be varied andshould be set by expert judgement.

According to the definition above, the cost of failing to detect adeveloping plume satisfies:

C ¼1

3N

XN

i ¼ 1

X3

j ¼ 1

wLUTði,jÞwpði,jÞAi,j

LUT ¼

undetected

single

two

multiple

t1 t2 t3

2 2 2

1 1 1

0 0 0

0 0 0

0BBB@

1CCCA

ð2Þ

where N is the total number of plumes, Ai,j is the deposition areaof plume i at time tj, wLUT(i,j) is the look-up table (LUT) valuecorresponding to the state of plume i at time tj, and wp(i,j) is thepopulation density at the centroid of plume i at time tj. Times t1, t2

and t3 were chosen as 1, 2 and 3 h, respectively. Thus, if anaccident is undetected in hour one, it will be twice as ’costly’ as asimilar accident detected by a single sensor in hour one, accordingto the LUT. Similarly, if an accident is undetected in hour one, butdetected by two sensors in hours two and three, then thecontribution of that accident to the average cost will depend onlyon the conditions of the plume at hour one because plumes thatare detected by two or more sensors are given a weight of zero inthe LUT. Times and weights can easily be changed according touser requirements.

S.J. Melles et al. / Computers & Geosciences 37 (2011) 280–288 285

The two criteria were combined into a single objectivefunction as follows:

min½w1Cr1þw2Cr2� ð3Þ

where Cr1 is the average kriging error criterion, Cr2 is the calamitydetection capability criterion and w1 and w2 are the relativeweights assigned to each criterion. The relative weights assigneddepend on the objectives of the institute in charge of the network.For the purposes of this research, weights were assigned such thatboth criteria contributed more or less equally to the combinedcriterion.

2.4. Spatial simulated annealing

Spatial simulated annealing (Van Groeningen and Stein, 1998) isthe spatial counterpart to simulated annealing (SSA, Kirkpatricket al., 1983), and as such the algorithm uses slight perturbations ofprevious designs and a random search technique to solve spatialoptimization problems. For the present study, the procedure beganwith the current monitoring network design. Optimization pro-ceeded iteratively by randomly moving monitoring stations one byone, calculating the objective function, and accepting improveddesigns over a set number of SSA iterations. With SSA, worseningdesigns are accepted with a decreasing probability (generally set topr20%) to avoid selection of local minima, and the ‘coolingschedule’ of SSA dictates the rate at which p decreases to zero. Weused the simplest and most commonly used cooling schedule,whereby p was set to exponentially decrease as a function ofnumber of iterations to ensure convergence (Heuvelink et al., 2006;Brus and Heuvelink, 2007).

In addition to the cooling schedule and the initial p, anotherimportant parameter in SSA is the stopping criterion. Here wechose to perform a fixed number of iterations, but it is also possibleto stop SSA when there is no improvement in the criterion over aset number of iterations. Alternatively, one may choose to stopwhen p declines to a final value set by the user (Heuvelink et al.,2006; Brus and Heuvelink, 2007). SSA is useful for problems thatcannot be solved either analytically or by an exhaustive search, butthe method is essentially heuristic because it is not possible toguarantee that the final sample pattern is a true optimum(Kirkpatrick et al., 1983). By repeating the annealing algorithmmultiple times and checking if we arrive at a similar solution, wecan be more confident that a near optimal solution has beenattained (Brus and Heuvelink, 2007). We optimized the monitoringnetwork over a total of k¼4000 iterations, and we repeated theannealing algorithm three times to ensure solutions were similar.

Fig. 6. Optimized sampling pattern given simulated accident scenarios and start locatio

of accidents of each type. (b) Final sampling pattern optimized for combined objective

One of these solutions was optimized over a total of k¼8000iterations because it was apparent that the objective function wasstill decreasing after k¼ 4000 iterations.

Analyses and simulations were performed using a set offunctions written in the R language for statistical computing(R Development Core Team, 2008).

3. Results

The size and development of each accident was the result ofweather conditions sampled at the start of each simulation—inaddition to the parameterization of NPK-PUFF. Figs. 1 and 2a and cdepict maps of power plant locations, urban centers, andtransportation routes, respectively: each of these locations hadan associated accident probability (Table 2). As there were alimited number of NPPs and high density urban areas in theregion ðpopulation46000=km2

Þ, the combined accident map(Fig. 6a) was dominated by radioactive releases originating inthese areas and developing in all directions. Winds in theNetherlands typically come from the southwesterly directionand their magnitudes increase with atmospheric height (Fig. 4). Itis difficult to detect an increase in the number of plumesoriginating from the predominant wind direction in Fig. 6a, butgiven that weather conditions were treated as stochastic, plumesfrom a southwesterly direction were more likely to occur. Thegoal here was to optimize the fixed monitoring network for allpossible conditions throughout the year, so we aimed to simulateenough releases to cover all possible weather conditions.

Small and large NPP accidents covered a much larger area thanmodelled RED type accidents (Fig. 6a) due to the magnitude ofnuclides released (Table 1). Transport spills are barely recogniz-able on Fig. 6a as a series of small dark speckles. Indeed,transportation type accidents had plumes above the criticalthreshold in only approximately 10% of NPK-PUFF simulations.The majority of RED type accidents originated in the denselypopulated cities of Amsterdam, Rotterdam, Den Haag, Koln,Dusseldorf, and Essen.

An optimized network design is shown in Fig. 6b. The majorityof network stations were highly clustered around nuclear powerplants and densely populated urban centers in the optimizeddesign pattern. In comparison with the current monitoringnetwork (Fig. 1), more sensors were moved into the Netherlands;there were less stations concentrated at the border between theNetherlands and Germany; and there were fewer evenly dis-persed stations in the optimized network pattern.

ns. (a) Map of simulated radioactive emissions (plumes) showing only a 10% subset

function.

14

16

18

20

0 2000 4000 6000 8000)k( snoitaretI

Com

bine

d ob

ject

ive

func

tion

4

6

8

10

12

8.21 8.23 8.25 8.27 8.29)h/vSn( rorre noitciderP

Det

ectio

n ca

pabi

lity

(C)

Fig. 7. (a) Decrease and leveling off of objective function with increasing iterations for three repeats of SSA algorithm. (b) Trade-off between two optimization criteria for

curves shown in (a). Asterisks represent simulation end-points (best designs).

S.J. Melles et al. / Computers & Geosciences 37 (2011) 280–288286

As expected, the objective function improved during the threerepeats of the simulated annealing algorithm (Fig. 7a). Althoughthe objective function had begun to level off when SSA wasterminated at 4000 iterations, it is apparent that more iterationswere necessary to reach the minimum as evidenced by the lowervalue obtained with 8000 iterations. Fig. 7b shows how meanprediction error variance and detection capability changed as SSAprogressed. Generally as detection capability improved, meanprediction error worsened. Given the costs associated with failingto detect a radioactive release in densely populated areas,network detection cost dominated the change in the objectivefunction at the expense of mean prediction error. That is to saypredictive accuracy for mapping annual background GDR levelsdecreased overall as stations became more clustered aroundNPPs and urban areas. However, this decrease was very slight(e.g., criterion 1 ranged between 8.21 and 8.29).

Overall, optimization was slow in terms of computationalefficiency (12+ days for k¼4000 iterations on a windowsoperating system with a 3.01 GHz processor and 4.0 GB of RAM).

4. Discussion and conclusions

Radiation monitoring networks in the Netherlands and twoneighboring German states were optimized using a combinedvariance-based and simulation approach. The objective functionwas a combination of two equally weighted criteria: regressionkriging prediction error variance, which emphasized theimportance of monitoring background levels of radiationunder routine conditions, and detection capability, whichemphasized the networks ability to detect an accident in theevent of a nuclear emergency. An obvious advantage of thecombined method we have presented in this paper is that fixedmonitoring networks can be optimized for both routine predictionerror and emergency cases.

We found few examples in the literature with strongsimilarities to the proposed method. Although simulation basedapproaches are well known and often used to generate multiplecontaminant fields with a range of uncertainties (Loaiciga et al.,1992), the focus has generally been on optimizing designs todetect a single contaminant source (Meyer and Brill, 1988;Marryott et al., 1993; Reed and Minkster, 2004; Zhang et al.,2005). For example, Meyer et al. (1994) used Monte Carlosimulation of groundwater transport to characterize uncertaintyin the source location of a single contaminant plume from alandfill site. These authors also used a multi-objective formulation

of their objective function, and analogous to our study, simulatedannealing was used to optimize the design of the groundwatermonitoring network. Their objective function included: number ofmonitoring wells; probability of detecting a contaminant plume;and the area of contamination at the time of detection.Alternatively, variance-based approaches have focused on opti-mization under conditions of nonstationarity (Atkinson and Lloyd,2007) or unknown variogram/covariance function (Zhu and Stein,2006; Zimmerman, 2006). Our method uses an atmosphericdispersion model to generate multiple contaminant fields withnumerous release locations and links simulation model resultswith multi-criteria optimization of a monitoring network.

The focus here was not on predicting unmeasured values ifextremes were detected. Rather our approach emphasizes detec-tion of emergency releases and associated costs if a network failsto detect spreading contaminant plumes originating from prob-abilistic start locations. Spatial prediction error was included inthe objective function to account for routine GDR conditions,which are the prevailing monitored state. Once detected, othermore advanced methods can be used to model the field ofextremes and delineate the contaminant surface (e.g., Chang et al.,2007; Kazianka and Pilz, 2009). Zhu and Stein (2006) suggest thatunless the nature of nonstationarity is known ahead of time,adaptive design schemes may be necessary to refine a monitoringnetwork as more information becomes available (e.g., Datta et al.,2009). In the context of radiation monitoring, mobile monitoringdevices are available to increase network density during anemergency. Heuvelink et al. (2009) show how these mobilemonitoring devices can be optimized to better delineate thespreading contaminant as part of an emergency response strategy.

It is important to recognize that the final sample patternshown in Fig. 6b is not unique. Given the same starting conditions,resulting spatial configurations can be fairly different, even if thefinal objective function values are equivalent (Zhu and Stein,2006). In practice, network designers could experiment using ourapproach and arrive at an ensemble of sampling patterns thathave the same or similar performance. Or, given that mostnetwork planners have other constraints to consider(i.e., economic costs, station placement restrictions, accessibilityand space requirements), they could select a specific design thataddresses objectives other than or additional to the onesconsidered here.

We are aware that the proposed approach also has limitations.The combined simulation and variance-based approach is verycomputationally intensive. In addition to the time involved in theSSA iterations, one needs to run the NPK-PUFF model (Verver

S.J. Melles et al. / Computers & Geosciences 37 (2011) 280–288 287

et al., 1990) to simulate 1000’s of radiation releases. Interpolationof 592 points took almost 1.5 min of CPU time on our system, butcalculating network detection capability required relatively littletime to compute, depending on the number of accidentsconsidered. Calculation of network detection capability usedbetween 22 s and 3 min of CPU time to check for the detectionof 15,000 and 60,000 plumes using 170 and 592 points,respectively. If a subset of stations was reserved to minimizeprediction error alone, this could reduce computational timesubstantially because interpolation would not need to beperformed at each SSA iteration. Computational time could thenbe reduced by more than 60%. Alternatively, interpolation can besped up by encoding knowledge that at each iteration, only asingle sample location is changed. So, only a single row andcolumn in the n�n kriging matrix need change. Heuvelink et al.(2009) suggest that this can be implemented using a blockGaussian elimination algorithm (Golub and Van Loan, 1996),which is also easily amenable to parallel computing. Thuscomputation time could be significantly reduced.

The NPK-PUFF model is perhaps one of the largest sources ofuncertainty in the simulation-based approach. This modelincludes meteorological variables that have limited predictiveabilities due to their inherent uncertainties. Atmospheric disper-sion models must also account for numerous processes such as:relative diffusion given wind shear and turbulence; advection as afunction of space and time; diurnal cycles of boundary layerheight and stability; wet and dry deposition; and linear chemicaltransformations of radioactive decay (Verver et al., 1990).Virtually any simulation model could be employed, however,and linked to the optimization approach we have described in asimilar manner.

Another limitation to our approach is that several other sourcesof uncertainty were unaccounted for. Uncertainty in variogramestimation was not taken into account and therefore routine spatialprediction error may be underestimated. Only a single nuclide wasmodelled using the NPK-PUFF model, which means that GDRs werealso underestimated. We partially compensated for this under-estimate by lowering the GDR critical threshold to 100 nSv/h from amore typical 200 nSv/h emergency alert threshold. The lower alertthreshold was recently recommended in the framework of theCouncil of Baltic Sea States, but higher levels (i.e., up to 200 nSv/h ormore) are typically used by GDR networks in most Europeancountries. Lastly, as mentioned previously, it is a large over-simplification to assume that weather conditions at De Bilt arerepresentative of all GDR release locations across the study area. Afuture improvement to the methodology could involve using morerealistic weather conditions either sampled from weather stations inthe vicinity of release locations or simulated using high resolutionclimate models.

Despite the drawbacks, our combined simulation and var-iance-based approach to fixed network design is appealing in itssimplicity and flexibility. The method can be used to examinehow an environmental monitoring network responds to a hugevariety of release conditions. Other design constraints than theones considered here can also be easily implemented. Withcareful interpretation of results, design constraints and trade-offsbetween criteria can be explicitly examined.

Acknowledgements

The authors are grateful for financial support from theEuropean Commission under the Sixth Framework Programme,INTAMAP project Contract No. 033811 with the DG INFSO actionLine IST-200502.5.12 ICT for Environmental Risk. This researchwas also partially funded by the Dutch Research Programme

Space for Geo-Information (RGI), project RGI-302. The viewsexpressed herein are those of the authors and do not necessarilyreflect the views of RGI or the European Commission. We thankSebastiano Trevisani and Dick Brus for constructive and helpfulcomments.

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